<?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>nsmr_to_aa1.out</source>

<heading><![CDATA[
Prover9 (64) version 2026-3T, March 2026.
Process 718280 was started by veroff on b146-03,
Wed Apr  8 20:19:29 2026
The command was "prover9 -f nsmr_to_aa1.in".
]]></heading>

<proof number="1" length="28457" max_count="73">

<comments><![CDATA[
% Proof 1 at 9754.29 (+ 0.42) seconds: "aa1".
% Length of proof: 28457 (0 new hints)
% Level of proof: 1330
% Maximum clause weight: 1015.000 (73 w/o degradation)
% Given clauses in run: 29902
% Given clauses in proof: 28440 (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 * (y * y)) * z = x * ((y * y) * z)
    ]]></literal>
    <attribute><![CDATA[
      label("NucSq_m")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="33" 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="34" 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="35" 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="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[
      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="41" 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="42" 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="43" 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="44" 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="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[
      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="50" 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="51" 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="52" 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="53" 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="54" 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="55" 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="56" 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="57" 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="58" 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="59" 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="60" 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="61" 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="62" 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="63" 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="64" 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="65">
    <literal><![CDATA[
      x * (1 * 1) = x
    ]]></literal>
    <justification jstring="[para(7(a,2),8(a,1,2))].">
      <j1 rule="para" parents="7 8"/>
    </justification>
  </clause>

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

  <clause id="67">
    <literal><![CDATA[
      x \ (1 * (x * y)) = y
    ]]></literal>
    <justification jstring="[para(7(a,2),9(a,1,2))].">
      <j1 rule="para" parents="7 9"/>
    </justification>
  </clause>

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

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

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

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

  <clause id="72">
    <literal><![CDATA[
      x * (1 * (x \ y)) = y
    ]]></literal>
    <justification jstring="[para(7(a,2),10(a,1,2))].">
      <j1 rule="para" parents="7 10"/>
    </justification>
  </clause>

  <clause id="73">
    <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="74">
    <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="75">
    <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="76">
    <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="77">
    <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="78">
    <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="79">
    <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="80">
    <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="81">
    <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="82">
    <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="83">
    <literal><![CDATA[
      (x / y) \ x = y
    ]]></literal>
    <justification jstring="[para(12(a,1),9(a,1,2))].">
      <j1 rule="para" parents="12 9"/>
    </justification>
  </clause>

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

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

  <clause id="86">
    <literal><![CDATA[
      (x * (y * z)) * 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="87">
    <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="88">
    <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="89">
    <literal><![CDATA[
      (x * y) \ ((x * (y / z)) * z) = a(x,y / z,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="90">
    <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="91">
    <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="92">
    <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="93">
    <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="94">
    <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="95">
    <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="96">
    <literal><![CDATA[
      x \ (1 * (x * y)) = L(y,x,1)
    ]]></literal>
    <justification jstring="[para(7(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="97">
    <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="98">
    <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="99">
    <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="100">
    <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="101">
    <literal><![CDATA[
      L(x,y,z / (y * x)) = ((z / (y * x)) * y) \ z
    ]]></literal>
    <justification jstring="[para(12(a,1),18(a,2,2))].">
      <j1 rule="para" parents="12 18"/>
    </justification>
  </clause>

  <clause id="102">
    <literal><![CDATA[
      (x * y) / (x * y) = R(1,x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="103">
    <literal><![CDATA[
      (x * y) / (y * 1) = R(x,y,1)
    ]]></literal>
    <justification jstring="[para(8(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="104">
    <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="105">
    <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="106">
    <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="107">
    <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="108">
    <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="109">
    <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="110">
    <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="111">
    <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="112">
    <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="113">
    <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="114">
    <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="115">
    <literal><![CDATA[
      T(T(T(x,y),z),u) = T(T(T(x,u),y),z)
    ]]></literal>
    <justification jstring="[para(23(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="116">
    <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="117">
    <literal><![CDATA[
      (x * (y * y)) \ (x * ((y * y) * z)) = z
    ]]></literal>
    <justification jstring="[para(32(a,1),9(a,1,2))].">
      <j1 rule="para" parents="32 9"/>
    </justification>
  </clause>

  <clause id="118">
    <literal><![CDATA[
      (x * (y * ((z * z) * u))) \ ((x * (y * (z * z))) * u) = a(x,y * (z * z),u)
    ]]></literal>
    <justification jstring="[para(32(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="32 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="119">
    <literal><![CDATA[
      (x * ((y * y) * (z * u))) \ (((x * (y * y)) * z) * u) = a(x * (y * y),z,u)
    ]]></literal>
    <justification jstring="[para(32(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="32 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="120">
    <literal><![CDATA[
      (x * ((y * y) * z)) \ (x * ((y * y) * z)) = a(x,y * y,z)
    ]]></literal>
    <justification jstring="[para(32(a,1),14(a,2,2)),flip(a)].">
      <j1 rule="para" parents="32 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="121">
    <literal><![CDATA[
      (x * ((y * y) * z)) \ ((x * (y * y)) * (z * u)) = L(u,z,x * (y * y))
    ]]></literal>
    <justification jstring="[para(32(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="32 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="122">
    <literal><![CDATA[
      ((x * (y * (z * z))) * u) / (y * ((z * z) * u)) = R(x,y * (z * z),u)
    ]]></literal>
    <justification jstring="[para(32(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="32 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="123">
    <literal><![CDATA[
      x \ (y * ((z * z) * x)) = T(y * (z * z),x)
    ]]></literal>
    <justification jstring="[para(32(a,1),22(a,2,2)),flip(a)].">
      <j1 rule="para" parents="32 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="124">
    <literal><![CDATA[
      x * ((x \ y) * (z * z)) = y * (z * 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="125">
    <literal><![CDATA[
      (x * (y * (z * z))) * u = (x * y) * ((z * z) * u)
    ]]></literal>
    <justification jstring="[para(33(a,1),32(a,1,1))].">
      <j1 rule="para" parents="33 32"/>
    </justification>
  </clause>

  <clause id="126">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(7(a,1),34(b,1))].">
      <j1 rule="para" parents="7 34"/>
    </justification>
  </clause>

  <clause id="127">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x * z != y
    ]]></literal>
    <literal><![CDATA[
      1 = z
    ]]></literal>
    <justification jstring="[para(8(a,1),34(a,1))].">
      <j1 rule="para" parents="8 34"/>
    </justification>
  </clause>

  <clause id="128">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(10(a,1),34(a,1))].">
      <j1 rule="para" parents="10 34"/>
    </justification>
  </clause>

  <clause id="129">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * x != y
    ]]></literal>
    <literal><![CDATA[
      1 = z
    ]]></literal>
    <justification jstring="[para(7(a,1),35(a,1))].">
      <j1 rule="para" parents="7 35"/>
    </justification>
  </clause>

  <clause id="130">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(8(a,1),35(b,1))].">
      <j1 rule="para" parents="8 35"/>
    </justification>
  </clause>

  <clause id="131">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(12(a,1),35(a,1))].">
      <j1 rule="para" parents="12 35"/>
    </justification>
  </clause>

  <clause id="132">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      (x * z) / u != y
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(11(a,1),36(a,1))].">
      <j1 rule="para" parents="11 36"/>
    </justification>
  </clause>

  <clause id="133">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z / u != y
    ]]></literal>
    <literal><![CDATA[
      x * u = z
    ]]></literal>
    <justification jstring="[para(11(a,1),37(a,1))].">
      <j1 rule="para" parents="11 37"/>
    </justification>
  </clause>

  <clause id="134">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ u != y
    ]]></literal>
    <literal><![CDATA[
      z * x = u
    ]]></literal>
    <justification jstring="[para(9(a,1),38(a,1))].">
      <j1 rule="para" parents="9 38"/>
    </justification>
  </clause>

  <clause id="135">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(7(a,1),43(a,2))].">
      <j1 rule="para" parents="7 43"/>
    </justification>
  </clause>

  <clause id="137">
    <literal><![CDATA[
      x * y != x
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(8(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="8 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="138">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      x \ z = y
    ]]></literal>
    <justification jstring="[para(10(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="10 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="139">
    <literal><![CDATA[
      x * (x \ (y * z)) != y * u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(10(a,2),43(a,1))].">
      <j1 rule="para" parents="10 43"/>
    </justification>
  </clause>

  <clause id="140">
    <literal><![CDATA[
      (x / y) * z != x
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(12(a,1),43(a,2))].">
      <j1 rule="para" parents="12 43"/>
    </justification>
  </clause>

  <clause id="141">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(8(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="8 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="142">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(8(a,1),44(a,2))].">
      <j1 rule="para" parents="8 44"/>
    </justification>
  </clause>

  <clause id="143">
    <literal><![CDATA[
      x * (y \ z) != z
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(10(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="10 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="145">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      z / y = x
    ]]></literal>
    <justification jstring="[para(12(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="12 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="146">
    <literal><![CDATA[
      x * (y * (z * z)) != u * (z * z)
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(33(a,1),44(a,1))].">
      <j1 rule="para" parents="33 44"/>
    </justification>
  </clause>

  <clause id="148">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(11(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="11 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="150">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(9(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="9 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="151">
    <literal><![CDATA[
      L(x,y,z) != (z * y) \ u
    ]]></literal>
    <literal><![CDATA[
      z * (y * x) = u
    ]]></literal>
    <justification jstring="[para(18(a,2),47(a,1))].">
      <j1 rule="para" parents="18 47"/>
    </justification>
  </clause>

  <clause id="152">
    <literal><![CDATA[
      T(x,y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(22(a,2),47(a,1))].">
      <j1 rule="para" parents="22 47"/>
    </justification>
  </clause>

  <clause id="153">
    <literal><![CDATA[
      x \ (y * z) != z
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(9(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="9 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="154">
    <literal><![CDATA[
      x \ ((y * z) * u) != a(y,z,u)
    ]]></literal>
    <literal><![CDATA[
      y * (z * u) = x
    ]]></literal>
    <justification jstring="[para(14(a,2),48(a,1)),flip(a)].">
      <j1 rule="para" parents="14 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="155">
    <literal><![CDATA[
      T(x,y) != y \ (z * y)
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(22(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="22 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="156">
    <literal><![CDATA[
      T(T(x,y),z) != T(u,y)
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),49(a,1))].">
      <j1 rule="para" parents="23 49"/>
    </justification>
  </clause>

  <clause id="157">
    <literal><![CDATA[
      T(x,y) != L(T(z,y),u,w)
    ]]></literal>
    <literal><![CDATA[
      L(z,u,w) = x
    ]]></literal>
    <justification jstring="[para(25(a,2),49(a,1)),flip(a)].">
      <j1 rule="para" parents="25 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="158">
    <literal><![CDATA[
      L(x,y,z) != u \ (u * L(w,y,z))
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(9(a,2),50(a,1)),flip(a)].">
      <j1 rule="para" parents="9 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="159">
    <literal><![CDATA[
      T(L(x,y,z),u) != L(w,y,z)
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(25(a,1),50(a,1))].">
      <j1 rule="para" parents="25 50"/>
    </justification>
  </clause>

  <clause id="160">
    <literal><![CDATA[
      R(L(x,y,z),u,w) != L(v5,y,z)
    ]]></literal>
    <literal><![CDATA[
      R(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(29(a,2),50(a,1))].">
      <j1 rule="para" parents="29 50"/>
    </justification>
  </clause>

  <clause id="161">
    <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),50(a,1))].">
      <j1 rule="para" parents="30 50"/>
    </justification>
  </clause>

  <clause id="162">
    <literal><![CDATA[
      T(R(x,y,z),u) != R(w,y,z)
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(27(a,1),51(a,1))].">
      <j1 rule="para" parents="27 51"/>
    </justification>
  </clause>

  <clause id="163">
    <literal><![CDATA[
      R(R(x,y,z),u,w) != R(v5,y,z)
    ]]></literal>
    <literal><![CDATA[
      R(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(31(a,1),51(a,1))].">
      <j1 rule="para" parents="31 51"/>
    </justification>
  </clause>

  <clause id="164">
    <literal><![CDATA[
      ((x / y) * y) * z = x * z
    ]]></literal>
    <justification jstring="[hyper(57,a,12,a)].">
      <j1 rule="hyper" parents="57 12"/>
    </justification>
  </clause>

  <clause id="165">
    <literal><![CDATA[
      (x * (x \ y)) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(57,a,10,a)].">
      <j1 rule="hyper" parents="57 10"/>
    </justification>
  </clause>

  <clause id="166">
    <literal><![CDATA[
      x * L(L(y,z,u),w,v5) = x * L(L(y,w,v5),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,30,a)].">
      <j1 rule="hyper" parents="58 30"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      x * (y \ (z * y)) = x * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,22,a),flip(a)].">
      <j1 rule="hyper" parents="58 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="168">
    <literal><![CDATA[
      x * ((y / z) * z) = x * y
    ]]></literal>
    <justification jstring="[hyper(58,a,12,a)].">
      <j1 rule="hyper" parents="58 12"/>
    </justification>
  </clause>

  <clause id="169">
    <literal><![CDATA[
      x * (y * (y \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(58,a,10,a)].">
      <j1 rule="hyper" parents="58 10"/>
    </justification>
  </clause>

  <clause id="170">
    <literal><![CDATA[
      x * (y \ (y * z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(58,a,9,a)].">
      <j1 rule="hyper" parents="58 9"/>
    </justification>
  </clause>

  <clause id="171">
    <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="172">
    <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="173">
    <literal><![CDATA[
      T(T(x,y),z) \ u = T(T(x,z),y) \ u
    ]]></literal>
    <justification jstring="[hyper(61,a,23,a)].">
      <j1 rule="hyper" parents="61 23"/>
    </justification>
  </clause>

  <clause id="174">
    <literal><![CDATA[
      (x * (x \ y)) \ z = y \ z
    ]]></literal>
    <justification jstring="[hyper(61,a,10,a)].">
      <j1 rule="hyper" parents="61 10"/>
    </justification>
  </clause>

  <clause id="175">
    <literal><![CDATA[
      x \ (y * 1) = x \ y
    ]]></literal>
    <justification jstring="[hyper(62,a,8,a)].">
      <j1 rule="hyper" parents="62 8"/>
    </justification>
  </clause>

  <clause id="176">
    <literal><![CDATA[
      (x * y) / y = (x / z) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,12,a,b,11,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="63 12 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="177">
    <literal><![CDATA[
      (x / y) * y = 1 * x
    ]]></literal>
    <justification jstring="[hyper(63,a,12,a,b,7,a(flip))].">
      <j1 rule="hyper" parents="63 12 7"/>
    </justification>
  </clause>

  <clause id="178">
    <literal><![CDATA[
      (x * y) / y = x * 1
    ]]></literal>
    <justification jstring="[hyper(63,a,11,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="63 11 8"/>
    </justification>
  </clause>

  <clause id="179">
    <literal><![CDATA[
      x \ (x * y) = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10,a,b,9,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="63 10 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="180">
    <literal><![CDATA[
      x * (x \ y) = y * 1
    ]]></literal>
    <justification jstring="[hyper(63,a,10,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="63 10 8"/>
    </justification>
  </clause>

  <clause id="181">
    <literal><![CDATA[
      x * (x \ y) = 1 * y
    ]]></literal>
    <justification jstring="[hyper(63,a,10,a,b,7,a(flip))].">
      <j1 rule="hyper" parents="63 10 7"/>
    </justification>
  </clause>

  <clause id="182">
    <literal><![CDATA[
      1 \ (x * 1) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,66,a,b,8,a)].">
      <j1 rule="hyper" parents="63 66 8"/>
    </justification>
  </clause>

  <clause id="183">
    <literal><![CDATA[
      (x * (x \ 1)) \ y = y
    ]]></literal>
    <justification jstring="[para(10(a,2),66(a,1,1))].">
      <j1 rule="para" parents="10 66"/>
    </justification>
  </clause>

  <clause id="184">
    <literal><![CDATA[
      ((1 / x) * x) \ y = y
    ]]></literal>
    <justification jstring="[para(12(a,2),66(a,1,1))].">
      <j1 rule="para" parents="12 66"/>
    </justification>
  </clause>

  <clause id="185">
    <literal><![CDATA[
      1 \ x != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(66(a,1),47(a,2))].">
      <j1 rule="para" parents="66 47"/>
    </justification>
  </clause>

  <clause id="186">
    <literal><![CDATA[
      K(x,x) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,16,a,b,68,a)].">
      <j1 rule="hyper" parents="63 16 68"/>
    </justification>
  </clause>

  <clause id="187">
    <literal><![CDATA[
      (x \ x) * y = y
    ]]></literal>
    <justification jstring="[para(68(a,2),7(a,1,1))].">
      <j1 rule="para" parents="68 7"/>
    </justification>
  </clause>

  <clause id="188">
    <literal><![CDATA[
      x * (y \ y) = x
    ]]></literal>
    <justification jstring="[para(68(a,2),8(a,1,2))].">
      <j1 rule="para" parents="68 8"/>
    </justification>
  </clause>

  <clause id="189">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      1 != z
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(68(a,1),38(b,1))].">
      <j1 rule="para" parents="68 38"/>
    </justification>
  </clause>

  <clause id="190">
    <literal><![CDATA[
      (x \ x) \ y = y
    ]]></literal>
    <justification jstring="[para(68(a,2),66(a,1,1))].">
      <j1 rule="para" parents="68 66"/>
    </justification>
  </clause>

  <clause id="191">
    <literal><![CDATA[
      (x / x) * y = y
    ]]></literal>
    <justification jstring="[para(77(a,2),7(a,1,1))].">
      <j1 rule="para" parents="77 7"/>
    </justification>
  </clause>

  <clause id="192">
    <literal><![CDATA[
      x * (y / y) = x
    ]]></literal>
    <justification jstring="[para(77(a,2),8(a,1,2))].">
      <j1 rule="para" parents="77 8"/>
    </justification>
  </clause>

  <clause id="193">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      1 != z
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(77(a,1),36(b,1))].">
      <j1 rule="para" parents="77 36"/>
    </justification>
  </clause>

  <clause id="194">
    <literal><![CDATA[
      x / ((1 / y) * y) = x
    ]]></literal>
    <justification jstring="[para(12(a,2),78(a,1,2))].">
      <j1 rule="para" parents="12 78"/>
    </justification>
  </clause>

  <clause id="195">
    <literal><![CDATA[
      x / 1 != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(78(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="78 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="196">
    <literal><![CDATA[
      T(x,R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,27,a,b,110,a(flip))].">
      <j1 rule="hyper" parents="42 27 110"/>
    </justification>
  </clause>

  <clause id="197">
    <literal><![CDATA[
      T(x,L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,25,a,b,110,a(flip))].">
      <j1 rule="hyper" parents="41 25 110"/>
    </justification>
  </clause>

  <clause id="198">
    <literal><![CDATA[
      T(x,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,23,a,b,110,a(flip))].">
      <j1 rule="hyper" parents="40 23 110"/>
    </justification>
  </clause>

  <clause id="199">
    <literal><![CDATA[
      T(L(x,y,z),x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(110(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="110 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      T(R(x,y,z),x) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(110(a,1),27(a,1,1)),flip(a)].">
      <j1 rule="para" parents="110 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="201">
    <literal><![CDATA[
      T(x,y) != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(110(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="110 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="202">
    <literal><![CDATA[
      K(x,x) * y = y
    ]]></literal>
    <justification jstring="[para(186(a,2),7(a,1,1))].">
      <j1 rule="para" parents="186 7"/>
    </justification>
  </clause>

  <clause id="203">
    <literal><![CDATA[
      x * K(y,y) = x
    ]]></literal>
    <justification jstring="[para(186(a,2),8(a,1,2))].">
      <j1 rule="para" parents="186 8"/>
    </justification>
  </clause>

  <clause id="204">
    <literal><![CDATA[
      (x * y) / y = z / (x \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,80,a,b,11,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="63 80 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="205">
    <literal><![CDATA[
      x / (y \ x) = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,80,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="63 80 10"/>
    </justification>
  </clause>

  <clause id="206">
    <literal><![CDATA[
      x / (y / (z \ y)) = x / z
    ]]></literal>
    <justification jstring="[hyper(60,a,80,a)].">
      <j1 rule="hyper" parents="60 80"/>
    </justification>
  </clause>

  <clause id="207">
    <literal><![CDATA[
      x * (y / (z \ y)) = x * z
    ]]></literal>
    <justification jstring="[hyper(58,a,80,a)].">
      <j1 rule="hyper" parents="58 80"/>
    </justification>
  </clause>

  <clause id="208">
    <literal><![CDATA[
      (x / (y \ x)) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(57,a,80,a)].">
      <j1 rule="hyper" parents="57 80"/>
    </justification>
  </clause>

  <clause id="209">
    <literal><![CDATA[
      R(x,y,z) \ ((x * y) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(36,a,20,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="36 20 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="210">
    <literal><![CDATA[
      ((x * y) * z) / a(x,y,z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(14(a,2),80(a,1,2))].">
      <j1 rule="para" parents="14 80"/>
    </justification>
  </clause>

  <clause id="211">
    <literal><![CDATA[
      (x * y) / K(x,y) = y * x
    ]]></literal>
    <justification jstring="[para(16(a,2),80(a,1,2))].">
      <j1 rule="para" parents="16 80"/>
    </justification>
  </clause>

  <clause id="212">
    <literal><![CDATA[
      (x * (y * z)) / L(z,y,x) = x * y
    ]]></literal>
    <justification jstring="[para(18(a,2),80(a,1,2))].">
      <j1 rule="para" parents="18 80"/>
    </justification>
  </clause>

  <clause id="213">
    <literal><![CDATA[
      (x * y) / T(x,y) = y
    ]]></literal>
    <justification jstring="[para(22(a,2),80(a,1,2))].">
      <j1 rule="para" parents="22 80"/>
    </justification>
  </clause>

  <clause id="214">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      z \ x = y
    ]]></literal>
    <justification jstring="[para(80(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="80 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="215">
    <literal><![CDATA[
      x / (y / ((z \ x) \ y)) = z
    ]]></literal>
    <justification jstring="[para(80(a,2),80(a,1,2))].">
      <j1 rule="para" parents="80 80"/>
    </justification>
  </clause>

  <clause id="216">
    <literal><![CDATA[
      (x / y) \ x = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,83,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="63 83 10"/>
    </justification>
  </clause>

  <clause id="217">
    <literal><![CDATA[
      x * ((y / z) \ y) = x * z
    ]]></literal>
    <justification jstring="[hyper(58,a,83,a)].">
      <j1 rule="hyper" parents="58 83"/>
    </justification>
  </clause>

  <clause id="218">
    <literal><![CDATA[
      ((x / y) \ x) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(57,a,83,a)].">
      <j1 rule="hyper" parents="57 83"/>
    </justification>
  </clause>

  <clause id="219">
    <literal><![CDATA[
      ((x / (y / z)) \ x) \ y = z
    ]]></literal>
    <justification jstring="[hyper(36,a,80,a,b,83,a(flip))].">
      <j1 rule="hyper" parents="36 80 83"/>
    </justification>
  </clause>

  <clause id="220">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ u != y
    ]]></literal>
    <literal><![CDATA[
      u / x = z
    ]]></literal>
    <justification jstring="[para(83(a,1),39(a,1))].">
      <j1 rule="para" parents="83 39"/>
    </justification>
  </clause>

  <clause id="221">
    <literal><![CDATA[
      (x / y) \ z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(83(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="83 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="222">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      y / z = x
    ]]></literal>
    <justification jstring="[para(83(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="83 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="223">
    <literal><![CDATA[
      T(x,1) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,22,a,b,182,a)].">
      <j1 rule="hyper" parents="63 22 182"/>
    </justification>
  </clause>

  <clause id="224">
    <literal><![CDATA[
      T(T(x,1),1) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,223,a,b,223,a)].">
      <j1 rule="hyper" parents="63 223 223"/>
    </justification>
  </clause>

  <clause id="225">
    <literal><![CDATA[
      K(x,1) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,223,a)].">
      <j1 rule="hyper" parents="55 223"/>
    </justification>
  </clause>

  <clause id="226">
    <literal><![CDATA[
      T(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,223,a)].">
      <j1 rule="hyper" parents="54 223"/>
    </justification>
  </clause>

  <clause id="227">
    <literal><![CDATA[
      K(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,226,a)].">
      <j1 rule="hyper" parents="55 226"/>
    </justification>
  </clause>

  <clause id="228">
    <literal><![CDATA[
      L(x,y,z) != (u \ u) * L(w,y,z)
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(187(a,2),50(a,1)),flip(a)].">
      <j1 rule="para" parents="187 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="229">
    <literal><![CDATA[
      R(x,y,z) != (u \ u) * R(w,y,z)
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(187(a,2),51(a,1)),flip(a)].">
      <j1 rule="para" parents="187 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="230">
    <literal><![CDATA[
      x * (y \ y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(188(a,1),44(a,2))].">
      <j1 rule="para" parents="188 44"/>
    </justification>
  </clause>

  <clause id="231">
    <literal><![CDATA[
      T(x,T(T(x,y),z)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,23,a,b,198,a(flip))].">
      <j1 rule="hyper" parents="40 23 198"/>
    </justification>
  </clause>

  <clause id="232">
    <literal><![CDATA[
      (x * (x \ 1)) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(10(a,2),135(a,1,1))].">
      <j1 rule="para" parents="10 135"/>
    </justification>
  </clause>

  <clause id="233">
    <literal><![CDATA[
      ((1 / x) * x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(12(a,2),135(a,1,1))].">
      <j1 rule="para" parents="12 135"/>
    </justification>
  </clause>

  <clause id="234">
    <literal><![CDATA[
      K(x,1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(225(a,2),135(a,1,1))].">
      <j1 rule="para" parents="225 135"/>
    </justification>
  </clause>

  <clause id="235">
    <literal><![CDATA[
      (x \ x) \ (1 * y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(190(a,2),135(a,1))].">
      <j1 rule="para" parents="190 135"/>
    </justification>
  </clause>

  <clause id="236">
    <literal><![CDATA[
      x \ x != y
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(187(a,1),137(a,1)),flip(a)].">
      <j1 rule="para" parents="187 137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="237">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      1 * x = y
    ]]></literal>
    <justification jstring="[para(9(a,1),185(a,1))].">
      <j1 rule="para" parents="9 185"/>
    </justification>
  </clause>

  <clause id="238">
    <literal><![CDATA[
      T(x,R(T(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,23,a,b,196,a(flip))].">
      <j1 rule="hyper" parents="40 23 196"/>
    </justification>
  </clause>

  <clause id="239">
    <literal><![CDATA[
      T(T(x,y),L(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(197(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="197 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="240">
    <literal><![CDATA[
      (x \ 1) * (x * x) = x
    ]]></literal>
    <justification jstring="[hyper(34,a,33,a(flip),b,71,a(flip))].">
      <j1 rule="hyper" parents="34 33 71"/>
    </justification>
  </clause>

  <clause id="241">
    <literal><![CDATA[
      R(x,x \ 1,y) = y / ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(71(a,1),20(a,2,1))].">
      <j1 rule="para" parents="71 20"/>
    </justification>
  </clause>

  <clause id="243">
    <literal><![CDATA[
      x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(73(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="73 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      L(x \ 1,x,y) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(73(a,1),18(a,2,2))].">
      <j1 rule="para" parents="73 18"/>
    </justification>
  </clause>

  <clause id="245">
    <literal><![CDATA[
      x * ((1 / x) * (1 / x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(34,a,33,a(flip),b,81,a(flip))].">
      <j1 rule="hyper" parents="34 33 81"/>
    </justification>
  </clause>

  <clause id="246">
    <literal><![CDATA[
      ((1 / x) * (x * y)) \ y = a(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(81(a,1),14(a,2,2)),flip(a)].">
      <j1 rule="para" parents="81 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="247">
    <literal><![CDATA[
      R(1 / x,x,y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(81(a,1),20(a,2,1))].">
      <j1 rule="para" parents="81 20"/>
    </justification>
  </clause>

  <clause id="249">
    <literal><![CDATA[
      (x \ y) * T(x,x \ y) = y
    ]]></literal>
    <justification jstring="[hyper(63,a,111,a,b,10,a)].">
      <j1 rule="hyper" parents="63 111 10"/>
    </justification>
  </clause>

  <clause id="250">
    <literal><![CDATA[
      x \ (y * T(z,y)) = x \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(62,a,111,a)].">
      <j1 rule="hyper" parents="62 111"/>
    </justification>
  </clause>

  <clause id="251">
    <literal><![CDATA[
      x * (y * T(z,y)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,111,a)].">
      <j1 rule="hyper" parents="58 111"/>
    </justification>
  </clause>

  <clause id="252">
    <literal><![CDATA[
      (x * T(y,x)) * z = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(57,a,111,a)].">
      <j1 rule="hyper" parents="57 111"/>
    </justification>
  </clause>

  <clause id="253">
    <literal><![CDATA[
      T(x * (y * y),x) = (y * y) * x
    ]]></literal>
    <justification jstring="[hyper(34,a,32,a(flip),b,111,a),flip(a)].">
      <j1 rule="hyper" parents="34 32 111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="254">
    <literal><![CDATA[
      T((x * y) / x,x) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,12,a(flip),b,111,a),flip(a)].">
      <j1 rule="hyper" parents="34 12 111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="255">
    <literal><![CDATA[
      (x * T(y,x)) / x = y
    ]]></literal>
    <justification jstring="[hyper(35,a,12,a,b,111,a(flip))].">
      <j1 rule="hyper" parents="35 12 111"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      x \ (y * T(x,y)) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,10,a,b,111,a(flip))].">
      <j1 rule="hyper" parents="34 10 111"/>
    </justification>
  </clause>

  <clause id="257">
    <literal><![CDATA[
      x * (y * (y \ T(z,x))) = z * x
    ]]></literal>
    <justification jstring="[para(10(a,2),111(a,1,2))].">
      <j1 rule="para" parents="10 111"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z,T(y,z))
    ]]></literal>
    <justification jstring="[para(111(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="111 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="259">
    <literal><![CDATA[
      (x * (T(y,x) * z)) \ ((y * x) * z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(111(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="111 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="260">
    <literal><![CDATA[
      (x * (y * T(z,x * y))) \ (z * (x * y)) = a(x,y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(111(a,1),14(a,2,2)),flip(a)].">
      <j1 rule="para" parents="111 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="261">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * y) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(111(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="111 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      (x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(111(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="111 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="263">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[para(111(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="111 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="264">
    <literal><![CDATA[
      ((x * y) * z) / (T(x,y) * z) = R(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[para(111(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="111 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="265">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / (z * y) = R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[para(111(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="111 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="266">
    <literal><![CDATA[
      x * T(T(y,x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),111(a,1,2))].">
      <j1 rule="para" parents="23 111"/>
    </justification>
  </clause>

  <clause id="267">
    <literal><![CDATA[
      x * L(T(y,x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(25(a,2),111(a,1,2))].">
      <j1 rule="para" parents="25 111"/>
    </justification>
  </clause>

  <clause id="268">
    <literal><![CDATA[
      x * R(T(y,x),z,u) = R(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(27(a,2),111(a,1,2))].">
      <j1 rule="para" parents="27 111"/>
    </justification>
  </clause>

  <clause id="269">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      y * u != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(111(a,1),34(a,1))].">
      <j1 rule="para" parents="111 34"/>
    </justification>
  </clause>

  <clause id="270">
    <literal><![CDATA[
      x * y != z * x
    ]]></literal>
    <literal><![CDATA[
      T(z,x) = y
    ]]></literal>
    <justification jstring="[para(111(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="111 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="271">
    <literal><![CDATA[
      x * T(y,x) != z * x
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(111(a,2),44(a,2)),flip(a)].">
      <j1 rule="para" parents="111 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="272">
    <literal><![CDATA[
      T(x,y) * x = x * T(x,y)
    ]]></literal>
    <justification jstring="[para(198(a,1),111(a,1,2))].">
      <j1 rule="para" parents="198 111"/>
    </justification>
  </clause>

  <clause id="273">
    <literal><![CDATA[
      R(x,y,z) * x = x * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(196(a,1),111(a,1,2))].">
      <j1 rule="para" parents="196 111"/>
    </justification>
  </clause>

  <clause id="274">
    <literal><![CDATA[
      L(x,y,z) * x = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(197(a,1),111(a,1,2))].">
      <j1 rule="para" parents="197 111"/>
    </justification>
  </clause>

  <clause id="275">
    <literal><![CDATA[
      T(x / (x / y),x / y) = y
    ]]></literal>
    <justification jstring="[hyper(63,a,113,a,b,83,a)].">
      <j1 rule="hyper" parents="63 113 83"/>
    </justification>
  </clause>

  <clause id="276">
    <literal><![CDATA[
      T(x / y,y) = (y \ x) * 1
    ]]></literal>
    <justification jstring="[hyper(63,a,113,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="63 113 8"/>
    </justification>
  </clause>

  <clause id="277">
    <literal><![CDATA[
      T(T(x / y,z),y) = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(113(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="278">
    <literal><![CDATA[
      T(L(x / y,z,u),y) = L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(113(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="279">
    <literal><![CDATA[
      T(x,y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      z / y = x
    ]]></literal>
    <justification jstring="[para(113(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="113 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="280">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(177(a,2),135(a,1))].">
      <j1 rule="para" parents="177 135"/>
    </justification>
  </clause>

  <clause id="281">
    <literal><![CDATA[
      x / y != z * 1
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(178(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="178 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="282">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(178(a,2),141(a,1))].">
      <j1 rule="para" parents="178 141"/>
    </justification>
  </clause>

  <clause id="283">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(178(a,2),142(a,1))].">
      <j1 rule="para" parents="178 142"/>
    </justification>
  </clause>

  <clause id="284">
    <literal><![CDATA[
      x \ (y * (y \ x)) = 1
    ]]></literal>
    <justification jstring="[hyper(34,a,10,a,b,180,a(flip))].">
      <j1 rule="hyper" parents="34 10 180"/>
    </justification>
  </clause>

  <clause id="285">
    <literal><![CDATA[
      x * 1 != y * z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(180(a,1),43(a,1))].">
      <j1 rule="para" parents="180 43"/>
    </justification>
  </clause>

  <clause id="286">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(180(a,2),141(a,1))].">
      <j1 rule="para" parents="180 141"/>
    </justification>
  </clause>

  <clause id="287">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(180(a,2),142(a,1))].">
      <j1 rule="para" parents="180 142"/>
    </justification>
  </clause>

  <clause id="288">
    <literal><![CDATA[
      1 * x != y * z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(181(a,1),43(a,1))].">
      <j1 rule="para" parents="181 43"/>
    </justification>
  </clause>

  <clause id="289">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,18,a,b,183,a),flip(a)].">
      <j1 rule="hyper" parents="63 18 183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="290">
    <literal><![CDATA[
      K(x \ 1,x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,16,a,b,183,a)].">
      <j1 rule="hyper" parents="63 16 183"/>
    </justification>
  </clause>

  <clause id="291">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,18,a,b,184,a),flip(a)].">
      <j1 rule="hyper" parents="63 18 184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="292">
    <literal><![CDATA[
      K(x,1 / x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,16,a,b,184,a)].">
      <j1 rule="hyper" parents="63 16 184"/>
    </justification>
  </clause>

  <clause id="293">
    <literal><![CDATA[
      ((1 / (x * y)) * x) * y = a(1 / (x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14,a,b,184,a),flip(a)].">
      <j1 rule="hyper" parents="63 14 184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="294">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,20,a,b,194,a),flip(a)].">
      <j1 rule="hyper" parents="63 20 194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="295">
    <literal><![CDATA[
      (x * L(L(y,z,u),w,v5)) / T(x,L(L(y,z,u),w,v5)) = L(L(y,w,v5),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,213,a,b,30,a)].">
      <j1 rule="hyper" parents="63 213 30"/>
    </justification>
  </clause>

  <clause id="296">
    <literal><![CDATA[
      x / T(y,y \ x) = y \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),213(a,1,1))].">
      <j1 rule="para" parents="10 213"/>
    </justification>
  </clause>

  <clause id="297">
    <literal><![CDATA[
      (T(x,y) * z) / T(T(x,z),y) = z
    ]]></literal>
    <justification jstring="[para(23(a,1),213(a,1,2))].">
      <j1 rule="para" parents="23 213"/>
    </justification>
  </clause>

  <clause id="298">
    <literal><![CDATA[
      (x * y) / z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(213(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="213 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="299">
    <literal><![CDATA[
      (x * L(x,y,z)) / x = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(197(a,1),213(a,1,2))].">
      <j1 rule="para" parents="197 213"/>
    </justification>
  </clause>

  <clause id="300">
    <literal><![CDATA[
      x / (x * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,12,a,b,240,a)].">
      <j1 rule="hyper" parents="35 12 240"/>
    </justification>
  </clause>

  <clause id="301">
    <literal><![CDATA[
      (x \ 1) \ x = x * x
    ]]></literal>
    <justification jstring="[hyper(34,a,10,a,b,240,a)].">
      <j1 rule="hyper" parents="34 10 240"/>
    </justification>
  </clause>

  <clause id="302">
    <literal><![CDATA[
      (x \ 1) * ((x * x) * y) = x * y
    ]]></literal>
    <justification jstring="[para(240(a,1),32(a,1,1)),flip(a)].">
      <j1 rule="para" parents="240 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="303">
    <literal><![CDATA[
      (x * T(T(y,x),z)) / x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,23,a,b,254,a),flip(a)].">
      <j1 rule="hyper" parents="40 23 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="304">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(254(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="254 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="305">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * z) / y = x
    ]]></literal>
    <justification jstring="[para(254(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="254 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="306">
    <literal><![CDATA[
      T((x * y) / x,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(254(a,1),198(a,1,2))].">
      <j1 rule="para" parents="254 198"/>
    </justification>
  </clause>

  <clause id="307">
    <literal><![CDATA[
      (1 / x) * (1 / x) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[para(83(a,1),301(a,1,1)),flip(a)].">
      <j1 rule="para" parents="83 301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="309">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = y \ z
    ]]></literal>
    <justification jstring="[para(111(a,1),138(a,1)),flip(b)].">
      <j1 rule="para" parents="111 138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="313">
    <literal><![CDATA[
      x \ y != z \ y
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(10(a,1),153(a,1,2))].">
      <j1 rule="para" parents="10 153"/>
    </justification>
  </clause>

  <clause id="314">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(20(a,2),280(a,1,1))].">
      <j1 rule="para" parents="20 280"/>
    </justification>
  </clause>

  <clause id="315">
    <literal><![CDATA[
      x * T(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(213(a,1),280(a,1,1))].">
      <j1 rule="para" parents="213 280"/>
    </justification>
  </clause>

  <clause id="316">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      y * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(255(a,1),280(a,1,1))].">
      <j1 rule="para" parents="255 280"/>
    </justification>
  </clause>

  <clause id="317">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(10(a,1),282(a,1,1))].">
      <j1 rule="para" parents="10 282"/>
    </justification>
  </clause>

  <clause id="318">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(111(a,2),282(a,1,1))].">
      <j1 rule="para" parents="111 282"/>
    </justification>
  </clause>

  <clause id="319">
    <literal><![CDATA[
      (1 * x) / y != z
    ]]></literal>
    <literal><![CDATA[
      x / y = z
    ]]></literal>
    <justification jstring="[para(177(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="177 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="320">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(10(a,1),283(a,1,1))].">
      <j1 rule="para" parents="10 283"/>
    </justification>
  </clause>

  <clause id="321">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(111(a,2),283(a,1,1))].">
      <j1 rule="para" parents="111 283"/>
    </justification>
  </clause>

  <clause id="322">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(18(a,2),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="18 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="323">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(83(a,1),286(a,1,2))].">
      <j1 rule="para" parents="83 286"/>
    </justification>
  </clause>

  <clause id="324">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(9(a,2),287(a,1,2))].">
      <j1 rule="para" parents="9 287"/>
    </justification>
  </clause>

  <clause id="325">
    <literal><![CDATA[
      ((x * y) * z) / a(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(14(a,2),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="326">
    <literal><![CDATA[
      (x / y) \ (z * (z \ x)) = y
    ]]></literal>
    <justification jstring="[para(12(a,1),74(a,1,2,2,2))].">
      <j1 rule="para" parents="12 74"/>
    </justification>
  </clause>

  <clause id="327">
    <literal><![CDATA[
      x \ ((x * y) * L(z,y,x)) = y * z
    ]]></literal>
    <justification jstring="[para(18(a,2),74(a,1,2,2))].">
      <j1 rule="para" parents="18 74"/>
    </justification>
  </clause>

  <clause id="328">
    <literal><![CDATA[
      x \ ((y * z) * (z \ (y \ x))) = a(y,z,z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(76(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="76 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="329">
    <literal><![CDATA[
      L(x \ (y \ z),x,y) = (y * x) \ z
    ]]></literal>
    <justification jstring="[para(76(a,1),18(a,2,2))].">
      <j1 rule="para" parents="76 18"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      x * K(y \ x,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(10(a,1),91(a,1,1))].">
      <j1 rule="para" parents="10 91"/>
    </justification>
  </clause>

  <clause id="331">
    <literal><![CDATA[
      x * K(y,x / y) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),91(a,1,1))].">
      <j1 rule="para" parents="12 91"/>
    </justification>
  </clause>

  <clause id="332">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x)
    ]]></literal>
    <justification jstring="[para(91(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="91 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="333">
    <literal><![CDATA[
      (x * y) * z != y * x
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(91(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="91 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="334">
    <literal><![CDATA[
      R(T(x,R(x,y,z) \ u),y,z) = (R(x,y,z) \ u) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,27,a,b,112,a)].">
      <j1 rule="hyper" parents="63 27 112"/>
    </justification>
  </clause>

  <clause id="335">
    <literal><![CDATA[
      x \ T(y,y \ z) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(62,a,112,a)].">
      <j1 rule="hyper" parents="62 112"/>
    </justification>
  </clause>

  <clause id="336">
    <literal><![CDATA[
      T(x,x \ y) \ z = ((x \ y) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(61,a,112,a)].">
      <j1 rule="hyper" parents="61 112"/>
    </justification>
  </clause>

  <clause id="337">
    <literal><![CDATA[
      T(x,x \ y) / z = ((x \ y) \ y) / z
    ]]></literal>
    <justification jstring="[hyper(59,a,112,a)].">
      <j1 rule="hyper" parents="59 112"/>
    </justification>
  </clause>

  <clause id="338">
    <literal><![CDATA[
      x * T(y,y \ z) = x * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,112,a)].">
      <j1 rule="hyper" parents="58 112"/>
    </justification>
  </clause>

  <clause id="339">
    <literal><![CDATA[
      T(x,x \ y) * z = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(57,a,112,a)].">
      <j1 rule="hyper" parents="57 112"/>
    </justification>
  </clause>

  <clause id="340">
    <literal><![CDATA[
      T(x,y) = (x \ (x * y)) \ (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),112(a,1,2))].">
      <j1 rule="para" parents="9 112"/>
    </justification>
  </clause>

  <clause id="341">
    <literal><![CDATA[
      T(T(x,y),x \ z) = T((x \ z) \ z,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="342">
    <literal><![CDATA[
      T(L(x,y,z),x \ u) = L((x \ u) \ u,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="343">
    <literal><![CDATA[
      T(R(x,y,z),x \ u) = R((x \ u) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(112(a,1),27(a,1,1)),flip(a)].">
      <j1 rule="para" parents="112 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="344">
    <literal><![CDATA[
      T(x,(x \ y) \ y) = x
    ]]></literal>
    <justification jstring="[para(112(a,1),198(a,1,2))].">
      <j1 rule="para" parents="112 198"/>
    </justification>
  </clause>

  <clause id="345">
    <literal><![CDATA[
      x / T(y,y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(112(a,2),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="112 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="346">
    <literal><![CDATA[
      ((x \ y) \ y) * x = x * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(344(a,1),111(a,1,2))].">
      <j1 rule="para" parents="344 111"/>
    </justification>
  </clause>

  <clause id="347">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(7(a,1),126(a,1))].">
      <j1 rule="para" parents="7 126"/>
    </justification>
  </clause>

  <clause id="348">
    <literal><![CDATA[
      (x * (x \ y)) * z != y * u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(165(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="165 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="349">
    <literal><![CDATA[
      (x * (x \ y)) * z != y * u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(165(a,1),43(a,2))].">
      <j1 rule="para" parents="165 43"/>
    </justification>
  </clause>

  <clause id="350">
    <literal><![CDATA[
      (x / (y * (y \ z))) * z = x
    ]]></literal>
    <justification jstring="[hyper(323,a,169,a)].">
      <j1 rule="hyper" parents="323 169"/>
    </justification>
  </clause>

  <clause id="351">
    <literal><![CDATA[
      x / (y \ ((x / z) * z)) = y
    ]]></literal>
    <justification jstring="[hyper(320,a,171,a),flip(a)].">
      <j1 rule="hyper" parents="320 171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="352">
    <literal><![CDATA[
      x / y != (z / u) * u
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(176(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="176 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="353">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(176(a,1),280(a,1,1))].">
      <j1 rule="para" parents="176 280"/>
    </justification>
  </clause>

  <clause id="354">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(179(a,2),43(a,1))].">
      <j1 rule="para" parents="179 43"/>
    </justification>
  </clause>

  <clause id="355">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(179(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="179 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="356">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(179(a,2),230(a,1))].">
      <j1 rule="para" parents="179 230"/>
    </justification>
  </clause>

  <clause id="357">
    <literal><![CDATA[
      x * (y * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(179(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="179 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="358">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(179(a,2),286(a,1))].">
      <j1 rule="para" parents="179 286"/>
    </justification>
  </clause>

  <clause id="359">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(12(a,1),356(a,1,2))].">
      <j1 rule="para" parents="12 356"/>
    </justification>
  </clause>

  <clause id="360">
    <literal><![CDATA[
      x \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(111(a,1),356(a,1,2))].">
      <j1 rule="para" parents="111 356"/>
    </justification>
  </clause>

  <clause id="361">
    <literal><![CDATA[
      x \ (y * T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(111(a,2),356(a,1,2))].">
      <j1 rule="para" parents="111 356"/>
    </justification>
  </clause>

  <clause id="362">
    <literal><![CDATA[
      T((x * y) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(113(a,2),356(a,1))].">
      <j1 rule="para" parents="113 356"/>
    </justification>
  </clause>

  <clause id="363">
    <literal><![CDATA[
      x \ (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(180(a,1),356(a,1,2))].">
      <j1 rule="para" parents="180 356"/>
    </justification>
  </clause>

  <clause id="364">
    <literal><![CDATA[
      x \ (1 * y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(181(a,1),356(a,1,2))].">
      <j1 rule="para" parents="181 356"/>
    </justification>
  </clause>

  <clause id="365">
    <literal><![CDATA[
      (x * y) \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(91(a,1),356(a,1,2))].">
      <j1 rule="para" parents="91 356"/>
    </justification>
  </clause>

  <clause id="366">
    <literal><![CDATA[
      x \ (x * (y \ (y * z))) != u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(9(a,2),358(a,1))].">
      <j1 rule="para" parents="9 358"/>
    </justification>
  </clause>

  <clause id="367">
    <literal><![CDATA[
      T(x,x) != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(22(a,2),358(a,1))].">
      <j1 rule="para" parents="22 358"/>
    </justification>
  </clause>

  <clause id="368">
    <literal><![CDATA[
      x \ (y * T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(111(a,2),358(a,1,2))].">
      <j1 rule="para" parents="111 358"/>
    </justification>
  </clause>

  <clause id="370">
    <literal><![CDATA[
      (x / (y \ x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(204(a,1),280(a,1,1))].">
      <j1 rule="para" parents="204 280"/>
    </justification>
  </clause>

  <clause id="371">
    <literal><![CDATA[
      ((x * y) / y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      x \ z = u
    ]]></literal>
    <justification jstring="[para(204(a,2),359(a,1,1))].">
      <j1 rule="para" parents="204 359"/>
    </justification>
  </clause>

  <clause id="372">
    <literal><![CDATA[
      x / (y \ x) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(205(a,2),43(a,1))].">
      <j1 rule="para" parents="205 43"/>
    </justification>
  </clause>

  <clause id="373">
    <literal><![CDATA[
      x / y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      u \ x = y
    ]]></literal>
    <justification jstring="[para(205(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="205 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="374">
    <literal><![CDATA[
      (x * (x \ y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ z = u
    ]]></literal>
    <justification jstring="[para(205(a,1),359(a,1,1))].">
      <j1 rule="para" parents="205 359"/>
    </justification>
  </clause>

  <clause id="375">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      y / u = x
    ]]></literal>
    <justification jstring="[para(216(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="216 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="376">
    <literal><![CDATA[
      (x / y) * ((z / y) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,12,a(flip),b,217,a),flip(a)].">
      <j1 rule="hyper" parents="347 12 217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="377">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      u / z = x
    ]]></literal>
    <justification jstring="[para(217(a,2),145(a,1))].">
      <j1 rule="para" parents="217 145"/>
    </justification>
  </clause>

  <clause id="378">
    <literal><![CDATA[
      ((x / y) \ x) * (y \ z) = z
    ]]></literal>
    <justification jstring="[hyper(347,a,10,a(flip),b,218,a),flip(a)].">
      <j1 rule="hyper" parents="347 10 218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="379">
    <literal><![CDATA[
      x * (((y / x) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(287,a,218,a),flip(a)].">
      <j1 rule="hyper" parents="287 218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="380">
    <literal><![CDATA[
      ((x / y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y \ u = z
    ]]></literal>
    <justification jstring="[para(218(a,2),138(a,1))].">
      <j1 rule="para" parents="218 138"/>
    </justification>
  </clause>

  <clause id="381">
    <literal><![CDATA[
      T(x / (x / y),y) = x / (x / y)
    ]]></literal>
    <justification jstring="[para(219(a,1),344(a,1,2))].">
      <j1 rule="para" parents="219 344"/>
    </justification>
  </clause>

  <clause id="382">
    <literal><![CDATA[
      L(T(x,x \ y),x \ y,z) = (z * (x \ y)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(249(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="249 18"/>
    </justification>
  </clause>

  <clause id="383">
    <literal><![CDATA[
      (x \ y) * z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(249(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="249 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="384">
    <literal><![CDATA[
      (x \ y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(249(a,1),356(a,1,2))].">
      <j1 rule="para" parents="249 356"/>
    </justification>
  </clause>

  <clause id="385">
    <literal><![CDATA[
      T(x / (x / y),(z / (x / y)) \ z) = y
    ]]></literal>
    <justification jstring="[para(83(a,2),275(a,1,2))].">
      <j1 rule="para" parents="83 275"/>
    </justification>
  </clause>

  <clause id="386">
    <literal><![CDATA[
      T(x / y,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(276(a,2),141(a,1)),flip(b)].">
      <j1 rule="para" parents="276 141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="387">
    <literal><![CDATA[
      x * T(x \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,111,a,b,290,a)].">
      <j1 rule="hyper" parents="347 111 290"/>
    </justification>
  </clause>

  <clause id="388">
    <literal><![CDATA[
      (x \ 1) \ K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(138,a,290,a(flip))].">
      <j1 rule="hyper" parents="138 290"/>
    </justification>
  </clause>

  <clause id="389">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ ((x * (y \ 1)) * y) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(290(a,2),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="290 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="390">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(326(a,1),143(a,1,2)),flip(a)].">
      <j1 rule="para" parents="326 143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="391">
    <literal><![CDATA[
      (x * (x \ y)) / z != u
    ]]></literal>
    <literal><![CDATA[
      y / z = u
    ]]></literal>
    <justification jstring="[para(326(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="326 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="392">
    <literal><![CDATA[
      R(x,y,y \ z) * z = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(20(a,2),350(a,1,1))].">
      <j1 rule="para" parents="20 350"/>
    </justification>
  </clause>

  <clause id="393">
    <literal><![CDATA[
      (x / y) \ x != z \ u
    ]]></literal>
    <literal><![CDATA[
      u / y = z
    ]]></literal>
    <justification jstring="[para(376(a,1),153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="376 153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="394">
    <literal><![CDATA[
      (x / T(y,y \ z)) * ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[para(296(a,1),376(a,1,2,1))].">
      <j1 rule="para" parents="296 376"/>
    </justification>
  </clause>

  <clause id="395">
    <literal><![CDATA[
      ((x / y) \ x) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ z = u
    ]]></literal>
    <justification jstring="[para(378(a,1),356(a,1,2))].">
      <j1 rule="para" parents="378 356"/>
    </justification>
  </clause>

  <clause id="396">
    <literal><![CDATA[
      T(x,x \ y) * (((x \ y) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[para(296(a,1),379(a,1,2,1,1))].">
      <j1 rule="para" parents="296 379"/>
    </justification>
  </clause>

  <clause id="397">
    <literal><![CDATA[
      (x \ 1) * x != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(388(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="388 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="398">
    <literal><![CDATA[
      L(x,y,1) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,67,a(flip),b,96,a),flip(a)].">
      <j1 rule="hyper" parents="63 67 96"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="400">
    <literal><![CDATA[
      a(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,398,a)].">
      <j1 rule="hyper" parents="53 398"/>
    </justification>
  </clause>

  <clause id="401">
    <literal><![CDATA[
      L(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(398(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="398 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="402">
    <literal><![CDATA[
      L(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(398(a,1),50(a,2))].">
      <j1 rule="para" parents="398 50"/>
    </justification>
  </clause>

  <clause id="403">
    <literal><![CDATA[
      R(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,102,a,b,192,a),flip(a)].">
      <j1 rule="hyper" parents="129 102 192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="405">
    <literal><![CDATA[
      (x * y) / y = R(x,y,1)
    ]]></literal>
    <justification jstring="[para(8(a,1),103(a,1,2))].">
      <j1 rule="para" parents="8 103"/>
    </justification>
  </clause>

  <clause id="406">
    <literal><![CDATA[
      R(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(405(a,1),282(a,1))].">
      <j1 rule="para" parents="405 282"/>
    </justification>
  </clause>

  <clause id="407">
    <literal><![CDATA[
      L(x \ 1,x,1 / x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(347,a,184,a(flip),b,244,a),flip(a)].">
      <j1 rule="hyper" parents="347 184 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="408">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(347,a,174,a(flip),b,244,a),flip(a)].">
      <j1 rule="hyper" parents="347 174 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="409">
    <literal><![CDATA[
      L(x \ 1,x,y) \ z = ((y * x) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(61,a,244,a)].">
      <j1 rule="hyper" parents="61 244"/>
    </justification>
  </clause>

  <clause id="410">
    <literal><![CDATA[
      x * L(y \ 1,y,z) = x * ((z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,244,a)].">
      <j1 rule="hyper" parents="58 244"/>
    </justification>
  </clause>

  <clause id="411">
    <literal><![CDATA[
      L(x \ 1,x,y) * z = ((y * x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(57,a,244,a)].">
      <j1 rule="hyper" parents="57 244"/>
    </justification>
  </clause>

  <clause id="412">
    <literal><![CDATA[
      x / L(y \ 1,y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(222,a,244,a(flip))].">
      <j1 rule="hyper" parents="222 244"/>
    </justification>
  </clause>

  <clause id="413">
    <literal><![CDATA[
      (x * y) * L(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(150,a,244,a(flip))].">
      <j1 rule="hyper" parents="150 244"/>
    </justification>
  </clause>

  <clause id="414">
    <literal><![CDATA[
      L(x \ 1,x,y / x) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),244(a,2,1))].">
      <j1 rule="para" parents="12 244"/>
    </justification>
  </clause>

  <clause id="415">
    <literal><![CDATA[
      T((x * y) \ x,z) = L(T(y \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(244(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="244 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="416">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(244(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="244 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="417">
    <literal><![CDATA[
      L(T(x,x \ 1),x \ 1,y) = (y * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(112(a,2),244(a,1,1))].">
      <j1 rule="para" parents="112 244"/>
    </justification>
  </clause>

  <clause id="418">
    <literal><![CDATA[
      x * R(1 / y,y,z) = x * (z / (y * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,247,a)].">
      <j1 rule="hyper" parents="58 247"/>
    </justification>
  </clause>

  <clause id="419">
    <literal><![CDATA[
      R(1 / x,x,y) * z = (y / (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(57,a,247,a)].">
      <j1 rule="hyper" parents="57 247"/>
    </justification>
  </clause>

  <clause id="420">
    <literal><![CDATA[
      R(1 / x,x,y) \ y = x * y
    ]]></literal>
    <justification jstring="[hyper(214,a,247,a(flip))].">
      <j1 rule="hyper" parents="214 247"/>
    </justification>
  </clause>

  <clause id="421">
    <literal><![CDATA[
      R(1 / x,x,x \ y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[para(10(a,1),247(a,2,2))].">
      <j1 rule="para" parents="10 247"/>
    </justification>
  </clause>

  <clause id="422">
    <literal><![CDATA[
      R(1 / (x / y),x / y,y) = y / x
    ]]></literal>
    <justification jstring="[para(12(a,1),247(a,2,2))].">
      <j1 rule="para" parents="12 247"/>
    </justification>
  </clause>

  <clause id="423">
    <literal><![CDATA[
      T(x / (y * x),z) = R(T(1 / y,z),y,x)
    ]]></literal>
    <justification jstring="[para(247(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="247 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="425">
    <literal><![CDATA[
      x * T(T(y,x),z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),271(a,1,2)),flip(b)].">
      <j1 rule="para" parents="23 271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="426">
    <literal><![CDATA[
      x / y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      u * y = x
    ]]></literal>
    <justification jstring="[para(180(a,2),281(a,2))].">
      <j1 rule="para" parents="180 281"/>
    </justification>
  </clause>

  <clause id="427">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(10(a,2),285(a,1,2))].">
      <j1 rule="para" parents="10 285"/>
    </justification>
  </clause>

  <clause id="428">
    <literal><![CDATA[
      x * (y \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(68(a,2),285(a,1,2))].">
      <j1 rule="para" parents="68 285"/>
    </justification>
  </clause>

  <clause id="429">
    <literal><![CDATA[
      (x * y) / y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(178(a,2),285(a,1))].">
      <j1 rule="para" parents="178 285"/>
    </justification>
  </clause>

  <clause id="430">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(180(a,2),285(a,1))].">
      <j1 rule="para" parents="180 285"/>
    </justification>
  </clause>

  <clause id="431">
    <literal><![CDATA[
      (x * (x \ 1)) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(10(a,2),288(a,1,1))].">
      <j1 rule="para" parents="10 288"/>
    </justification>
  </clause>

  <clause id="432">
    <literal><![CDATA[
      ((1 / x) * x) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(12(a,2),288(a,1,1))].">
      <j1 rule="para" parents="12 288"/>
    </justification>
  </clause>

  <clause id="433">
    <literal><![CDATA[
      (x / x) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(77(a,2),288(a,1,1))].">
      <j1 rule="para" parents="77 288"/>
    </justification>
  </clause>

  <clause id="434">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(177(a,2),288(a,1))].">
      <j1 rule="para" parents="177 288"/>
    </justification>
  </clause>

  <clause id="435">
    <literal><![CDATA[
      x * T(T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(23(a,1),315(a,1,2))].">
      <j1 rule="para" parents="23 315"/>
    </justification>
  </clause>

  <clause id="436">
    <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),315(a,1,2))].">
      <j1 rule="para" parents="25 315"/>
    </justification>
  </clause>

  <clause id="437">
    <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),315(a,1,2))].">
      <j1 rule="para" parents="27 315"/>
    </justification>
  </clause>

  <clause id="438">
    <literal><![CDATA[
      ((x / y) * y) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / z = u
    ]]></literal>
    <justification jstring="[para(177(a,2),319(a,1,1))].">
      <j1 rule="para" parents="177 319"/>
    </justification>
  </clause>

  <clause id="439">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ (x * y) = z
    ]]></literal>
    <justification jstring="[para(11(a,1),386(a,1,1))].">
      <j1 rule="para" parents="11 386"/>
    </justification>
  </clause>

  <clause id="440">
    <literal><![CDATA[
      T(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(80(a,1),386(a,1,1))].">
      <j1 rule="para" parents="80 386"/>
    </justification>
  </clause>

  <clause id="441">
    <literal><![CDATA[
      T(x * y,K(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ (y * x) = z
    ]]></literal>
    <justification jstring="[para(211(a,1),386(a,1,1))].">
      <j1 rule="para" parents="211 386"/>
    </justification>
  </clause>

  <clause id="442">
    <literal><![CDATA[
      x / y != x * z
    ]]></literal>
    <literal><![CDATA[
      L(z \ 1,z,x) = y
    ]]></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="443">
    <literal><![CDATA[
      (x * y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(412(a,1),359(a,1,1))].">
      <j1 rule="para" parents="412 359"/>
    </justification>
  </clause>

  <clause id="444">
    <literal><![CDATA[
      ((x * y) \ x) * (L(y \ 1,y,x) \ z) = z
    ]]></literal>
    <justification jstring="[para(412(a,1),378(a,1,1,1))].">
      <j1 rule="para" parents="412 378"/>
    </justification>
  </clause>

  <clause id="445">
    <literal><![CDATA[
      L(x \ 1,x,y) * (((y * x) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[para(412(a,1),379(a,1,2,1,1))].">
      <j1 rule="para" parents="412 379"/>
    </justification>
  </clause>

  <clause id="446">
    <literal><![CDATA[
      L(L(x \ 1,x,y),y * x,z) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(413(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="413 18"/>
    </justification>
  </clause>

  <clause id="447">
    <literal><![CDATA[
      x \ y != z * y
    ]]></literal>
    <literal><![CDATA[
      R(1 / z,z,y) = x
    ]]></literal>
    <justification jstring="[para(420(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="420 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="448">
    <literal><![CDATA[
      R(x,x \ 1,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(80(a,1),420(a,1,1,1))].">
      <j1 rule="para" parents="80 420"/>
    </justification>
  </clause>

  <clause id="449">
    <literal><![CDATA[
      x / (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,x) = z
    ]]></literal>
    <justification jstring="[para(420(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="420 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="450">
    <literal><![CDATA[
      K(x,y) = (y * x) \ ((y \ (y * x)) * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),92(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="451">
    <literal><![CDATA[
      K(x \ 1,x) \ 1 = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(290(a,2),93(a,1,1))].">
      <j1 rule="para" parents="290 93"/>
    </justification>
  </clause>

  <clause id="452">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(94(a,1),185(a,1))].">
      <j1 rule="para" parents="94 185"/>
    </justification>
  </clause>

  <clause id="453">
    <literal><![CDATA[
      T(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(114(a,1),360(a,1))].">
      <j1 rule="para" parents="114 360"/>
    </justification>
  </clause>

  <clause id="454">
    <literal><![CDATA[
      (1 / x) \ L(y,x,1 / x) = x * y
    ]]></literal>
    <justification jstring="[hyper(128,a,18,a,b,184,a(flip))].">
      <j1 rule="hyper" parents="128 18 184"/>
    </justification>
  </clause>

  <clause id="455">
    <literal><![CDATA[
      x \ L(y,x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(128,a,18,a,b,183,a(flip))].">
      <j1 rule="hyper" parents="128 18 183"/>
    </justification>
  </clause>

  <clause id="456">
    <literal><![CDATA[
      x \ (y * (z * z)) = (x \ y) * (z * z)
    ]]></literal>
    <justification jstring="[hyper(128,a,165,a(flip),b,33,a(flip))].">
      <j1 rule="hyper" parents="128 165 33"/>
    </justification>
  </clause>

  <clause id="457">
    <literal><![CDATA[
      (T(x,x \ y) / z) \ ((x \ y) \ y) = z
    ]]></literal>
    <justification jstring="[hyper(128,a,112,a(flip),b,12,a)].">
      <j1 rule="hyper" parents="128 112 12"/>
    </justification>
  </clause>

  <clause id="458">
    <literal><![CDATA[
      (1 / x) \ (y * y) = x * (y * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,81,a(flip),b,33,a(flip))].">
      <j1 rule="hyper" parents="128 81 33"/>
    </justification>
  </clause>

  <clause id="459">
    <literal><![CDATA[
      (x * (y * y)) \ z = (y * y) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(128,a,76,a(flip),b,32,a)].">
      <j1 rule="hyper" parents="128 76 32"/>
    </justification>
  </clause>

  <clause id="460">
    <literal><![CDATA[
      (x \ 1) * (y * y) = x \ (y * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,71,a(flip),b,33,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 71 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="461">
    <literal><![CDATA[
      (x * x) * ((y * (x * x)) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(128,a,10,a(flip),b,32,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 10 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="462">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      T(z,u) = u \ x
    ]]></literal>
    <justification jstring="[para(111(a,1),128(b,1)),flip(c)].">
      <j1 rule="para" parents="111 128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="463">
    <literal><![CDATA[
      L(x,y \ 1,y) / ((y \ 1) * x) = y
    ]]></literal>
    <justification jstring="[hyper(131,a,18,a,b,183,a(flip))].">
      <j1 rule="hyper" parents="131 18 183"/>
    </justification>
  </clause>

  <clause id="464">
    <literal><![CDATA[
      (x * y) / (z * z) = x * (y / (z * z))
    ]]></literal>
    <justification jstring="[hyper(131,a,168,a(flip),b,33,a)].">
      <j1 rule="hyper" parents="131 168 33"/>
    </justification>
  </clause>

  <clause id="465">
    <literal><![CDATA[
      (x * y) / ((z * z) * y) = x / (z * z)
    ]]></literal>
    <justification jstring="[hyper(131,a,164,a(flip),b,32,a(flip))].">
      <j1 rule="hyper" parents="131 164 32"/>
    </justification>
  </clause>

  <clause id="466">
    <literal><![CDATA[
      ((x \ y) \ y) \ (T(x,x \ y) * z) = z
    ]]></literal>
    <justification jstring="[hyper(132,a,112,a,b,80,a),flip(a)].">
      <j1 rule="hyper" parents="132 112 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="467">
    <literal><![CDATA[
      T(x,x \ y) \ (((x \ y) \ y) * z) = z
    ]]></literal>
    <justification jstring="[hyper(132,a,112,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="132 112 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="468">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = z
    ]]></literal>
    <justification jstring="[para(213(a,1),132(b,1)),flip(c)].">
      <j1 rule="para" parents="213 132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="469">
    <literal><![CDATA[
      R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,31,a,b,20,a(flip))].">
      <j1 rule="hyper" parents="133 31 20"/>
    </justification>
  </clause>

  <clause id="470">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * (L(L(x,u,w),y,z) \ v5) = v5
    ]]></literal>
    <justification jstring="[hyper(133,a,30,a,b,80,a)].">
      <j1 rule="hyper" parents="133 30 80"/>
    </justification>
  </clause>

  <clause id="471">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,29,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="133 29 20"/>
    </justification>
  </clause>

  <clause id="472">
    <literal><![CDATA[
      T(R(x,y,z),u) * (y * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,27,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="133 27 20"/>
    </justification>
  </clause>

  <clause id="473">
    <literal><![CDATA[
      (x / ((y \ z) \ z)) * T(y,y \ z) = x
    ]]></literal>
    <justification jstring="[hyper(134,a,112,a,b,83,a)].">
      <j1 rule="hyper" parents="134 112 83"/>
    </justification>
  </clause>

  <clause id="474">
    <literal><![CDATA[
      (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(134,a,30,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="134 30 18"/>
    </justification>
  </clause>

  <clause id="475">
    <literal><![CDATA[
      (x * y) * R(L(z,y,x),u,w) = x * (y * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(134,a,29,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="134 29 18"/>
    </justification>
  </clause>

  <clause id="476">
    <literal><![CDATA[
      x * L(y,z \ x,z) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,18,a,b,174,a(flip))].">
      <j1 rule="hyper" parents="134 18 174"/>
    </justification>
  </clause>

  <clause id="477">
    <literal><![CDATA[
      (x * y) * T(L(z,y,x),u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,25,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 25 18"/>
    </justification>
  </clause>

  <clause id="478">
    <literal><![CDATA[
      (x * T(y,y \ z)) / ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(220,a,112,a(flip),b,9,a)].">
      <j1 rule="hyper" parents="220 112 9"/>
    </justification>
  </clause>

  <clause id="479">
    <literal><![CDATA[
      (x * y) * ((1 / y) * (1 / y)) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(245(a,1),33(a,2,2))].">
      <j1 rule="para" parents="245 33"/>
    </justification>
  </clause>

  <clause id="480">
    <literal><![CDATA[
      L(x \ T(y,z),x,z) = (z * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(257(a,1),18(a,2,2))].">
      <j1 rule="para" parents="257 18"/>
    </justification>
  </clause>

  <clause id="481">
    <literal><![CDATA[
      x * T(x \ (y * x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(22(a,1),266(a,1,2,1))].">
      <j1 rule="para" parents="22 266"/>
    </justification>
  </clause>

  <clause id="482">
    <literal><![CDATA[
      x * T(T(T(y,x),z),u) = T(T(y,z),u) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),266(a,1,2,1))].">
      <j1 rule="para" parents="23 266"/>
    </justification>
  </clause>

  <clause id="483">
    <literal><![CDATA[
      T(x,y) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(266(a,1),43(a,1))].">
      <j1 rule="para" parents="266 43"/>
    </justification>
  </clause>

  <clause id="484">
    <literal><![CDATA[
      T(x / y,z) * y = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(113(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="485">
    <literal><![CDATA[
      T((x * y) / x,z) * x = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(254(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="254 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="486">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(112(a,1),266(a,1,2,1))].">
      <j1 rule="para" parents="112 266"/>
    </justification>
  </clause>

  <clause id="487">
    <literal><![CDATA[
      T(x / (x / y),z) * (x / y) = (x / y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(275(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="275 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="488">
    <literal><![CDATA[
      (L(x,y,z) * (x * u)) \ ((x * L(x,y,z)) * u) = a(L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(274(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="274 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="489">
    <literal><![CDATA[
      ((x * L(y,z,u)) * y) / (y * L(y,z,u)) = R(x,L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(274(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="274 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="490">
    <literal><![CDATA[
      (x * T(x \ y,z)) / x = T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(305,a,277,a)].">
      <j1 rule="hyper" parents="305 277"/>
    </justification>
  </clause>

  <clause id="491">
    <literal><![CDATA[
      x * T(x \ y,z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(277(a,1),271(a,1,2)),flip(b)].">
      <j1 rule="para" parents="277 271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="493">
    <literal><![CDATA[
      (x * T(x \ y,z)) / x != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(277(a,1),318(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="277 318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="494">
    <literal><![CDATA[
      (x \ 1) \ (x * y) = (x * x) * y
    ]]></literal>
    <justification jstring="[hyper(138,a,302,a)].">
      <j1 rule="hyper" parents="138 302"/>
    </justification>
  </clause>

  <clause id="495">
    <literal><![CDATA[
      (x * x) * (x \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(128,a,10,a(flip),b,302,a),flip(a)].">
      <j1 rule="hyper" parents="128 10 302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="496">
    <literal><![CDATA[
      (x \ 1) * (y * (x * x)) = x * T(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,251,a(flip),b,302,a)].">
      <j1 rule="hyper" parents="63 251 302"/>
    </justification>
  </clause>

  <clause id="497">
    <literal><![CDATA[
      x * ((x * x) \ y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,169,a(flip),b,302,a),flip(a)].">
      <j1 rule="hyper" parents="63 169 302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="498">
    <literal><![CDATA[
      (x * x) \ T(y,x \ 1) = x \ (y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(128,a,257,a(flip),b,302,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 257 302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="499">
    <literal><![CDATA[
      x \ ((x \ 1) * y) = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(128,a,169,a(flip),b,302,a(flip))].">
      <j1 rule="hyper" parents="128 169 302"/>
    </justification>
  </clause>

  <clause id="500">
    <literal><![CDATA[
      (x * x) \ ((x \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(128,a,76,a(flip),b,302,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 76 302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="501">
    <literal><![CDATA[
      (x * x) \ 1 = x \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,73,a(flip),b,302,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 73 302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="502">
    <literal><![CDATA[
      (x \ 1) \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      (x * x) * y = z
    ]]></literal>
    <justification jstring="[para(302(a,1),356(a,1,2))].">
      <j1 rule="para" parents="302 356"/>
    </justification>
  </clause>

  <clause id="503">
    <literal><![CDATA[
      x * ((x * x) \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      x \ 1 = y
    ]]></literal>
    <justification jstring="[para(501(a,2),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="501 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="504">
    <literal><![CDATA[
      (x * T(y,z)) / x = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[para(254(a,1),303(a,1,1,2,1))].">
      <j1 rule="para" parents="254 303"/>
    </justification>
  </clause>

  <clause id="505">
    <literal><![CDATA[
      ((x / y) * T(y,z)) / (x / y) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[para(275(a,1),303(a,1,1,2,1))].">
      <j1 rule="para" parents="275 303"/>
    </justification>
  </clause>

  <clause id="506">
    <literal><![CDATA[
      (x * T(y,z)) / x != u
    ]]></literal>
    <literal><![CDATA[
      T((x * y) / x,z) = u
    ]]></literal>
    <justification jstring="[para(304(a,1),318(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="304 318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="507">
    <literal><![CDATA[
      T(x,(y * x) / y) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,306,a)].">
      <j1 rule="hyper" parents="54 306"/>
    </justification>
  </clause>

  <clause id="508">
    <literal><![CDATA[
      T(x \ y,y / x) = x \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),507(a,1,2,1))].">
      <j1 rule="para" parents="10 507"/>
    </justification>
  </clause>

  <clause id="509">
    <literal><![CDATA[
      (x / y) * (y \ x) = (y \ x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(134,a,508,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 508 22"/>
    </justification>
  </clause>

  <clause id="510">
    <literal><![CDATA[
      (x * y) \ (x * ((z \ y) * z)) = L(K(z \ y,z),y,x)
    ]]></literal>
    <justification jstring="[para(330(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="330 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="511">
    <literal><![CDATA[
      (x \ y) * x != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) = z
    ]]></literal>
    <justification jstring="[para(330(a,1),43(a,1))].">
      <j1 rule="para" parents="330 43"/>
    </justification>
  </clause>

  <clause id="512">
    <literal><![CDATA[
      x \ ((y \ x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(330(a,1),356(a,1,2))].">
      <j1 rule="para" parents="330 356"/>
    </justification>
  </clause>

  <clause id="513">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x / y) = z
    ]]></literal>
    <justification jstring="[para(331(a,1),356(a,1,2))].">
      <j1 rule="para" parents="331 356"/>
    </justification>
  </clause>

  <clause id="514">
    <literal><![CDATA[
      (x / (x / y)) * y = y * (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(134,a,381,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 381 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="515">
    <literal><![CDATA[
      ((x * x) / y) \ 1 = y / (x * x)
    ]]></literal>
    <justification jstring="[hyper(131,a,83,a(flip),b,460,a),flip(a)].">
      <j1 rule="hyper" parents="131 83 460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="516">
    <literal><![CDATA[
      (x \ 1) * ((y * y) * z) = (x \ (y * y)) * z
    ]]></literal>
    <justification jstring="[para(460(a,1),32(a,1,1)),flip(a)].">
      <j1 rule="para" parents="460 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="517">
    <literal><![CDATA[
      L((x * x) \ 1,x * x,y \ 1) = (y \ (x * x)) \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(460(a,1),244(a,2,1))].">
      <j1 rule="para" parents="460 244"/>
    </justification>
  </clause>

  <clause id="518">
    <literal><![CDATA[
      T(x \ 1,x) = (x * x) \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,256,a(flip),b,494,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 256 494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="519">
    <literal><![CDATA[
      L(x \ 1,x,x) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,244,a,b,518,a)].">
      <j1 rule="hyper" parents="347 244 518"/>
    </justification>
  </clause>

  <clause id="521">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) * ((1 / x) \ y) = x \ y
    ]]></literal>
    <justification jstring="[para(83(a,1),495(a,2,1))].">
      <j1 rule="para" parents="83 495"/>
    </justification>
  </clause>

  <clause id="522">
    <literal><![CDATA[
      (x * ((y \ 1) * z)) \ ((x * y) * ((y * y) \ z)) = a(x,y,(y * y) \ z)
    ]]></literal>
    <justification jstring="[para(497(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="497 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="523">
    <literal><![CDATA[
      (x \ 1) * (x * (x * y)) = x * L(y,x,x)
    ]]></literal>
    <justification jstring="[para(18(a,2),497(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="524">
    <literal><![CDATA[
      x \ ((x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      (x * x) \ y = z
    ]]></literal>
    <justification jstring="[para(497(a,1),356(a,1,2))].">
      <j1 rule="para" parents="497 356"/>
    </justification>
  </clause>

  <clause id="525">
    <literal><![CDATA[
      x * ((x * x) \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(499(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="499 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="526">
    <literal><![CDATA[
      (x * x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) \ y = z
    ]]></literal>
    <justification jstring="[para(500(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="500 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="528">
    <literal><![CDATA[
      (x * (y * z)) / L(T(y,z),z,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(131,a,251,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="131 251 97"/>
    </justification>
  </clause>

  <clause id="529">
    <literal><![CDATA[
      (x * y) / L(z \ y,z,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(131,a,169,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="131 169 97"/>
    </justification>
  </clause>

  <clause id="530">
    <literal><![CDATA[
      (x * y) / L(z,y / z,x) = x * (y / z)
    ]]></literal>
    <justification jstring="[hyper(131,a,168,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="131 168 97"/>
    </justification>
  </clause>

  <clause id="532">
    <literal><![CDATA[
      x * L(y,z,x / z) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,164,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="63 164 97"/>
    </justification>
  </clause>

  <clause id="533">
    <literal><![CDATA[
      L(x * x,y,z) = x * x
    ]]></literal>
    <justification jstring="[hyper(34,a,33,a,b,97,a),flip(a)].">
      <j1 rule="hyper" parents="34 33 97"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="534">
    <literal><![CDATA[
      L(x,y * y,z) = x
    ]]></literal>
    <justification jstring="[hyper(34,a,32,a,b,97,a),flip(a)].">
      <j1 rule="hyper" parents="34 32 97"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="535">
    <literal><![CDATA[
      L(x \ T(y * x,y),x,y) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,257,a(flip),b,97,a),flip(a)].">
      <j1 rule="hyper" parents="34 257 97"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="536">
    <literal><![CDATA[
      L(x \ (y \ ((y * x) * z)),x,y) = z
    ]]></literal>
    <justification jstring="[hyper(34,a,76,a(flip),b,97,a),flip(a)].">
      <j1 rule="hyper" parents="34 76 97"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="537">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),x * y) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,97,a(flip),b,211,a)].">
      <j1 rule="hyper" parents="133 97 211"/>
    </justification>
  </clause>

  <clause id="538">
    <literal><![CDATA[
      x \ (y * L(z,x \ y,x)) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(128,a,165,a(flip),b,97,a(flip))].">
      <j1 rule="hyper" parents="128 165 97"/>
    </justification>
  </clause>

  <clause id="539">
    <literal><![CDATA[
      (x * (y * (z * u))) \ ((x * (y * z)) * L(u,z,y)) = a(x,y * z,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(97(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="97 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="540">
    <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(97(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="97 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="541">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * (L(z,y,x) * u)) = L(u,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(97(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="97 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="542">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x)
    ]]></literal>
    <justification jstring="[para(97(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="97 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="543">
    <literal><![CDATA[
      ((x * (y * z)) * u) / (L(z,y,x) * u) = R(x * y,L(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(97(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="97 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="544">
    <literal><![CDATA[
      (x * y) * z != x * (y * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(97(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="97 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="545">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(97(a,1),356(a,1,2))].">
      <j1 rule="para" parents="97 356"/>
    </justification>
  </clause>

  <clause id="546">
    <literal><![CDATA[
      x \ ((x * y) * L(z,y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(97(a,2),356(a,1,2))].">
      <j1 rule="para" parents="97 356"/>
    </justification>
  </clause>

  <clause id="547">
    <literal><![CDATA[
      K(x \ 1,x) * L(y,x,x \ 1) = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(290(a,2),97(a,1,1))].">
      <j1 rule="para" parents="290 97"/>
    </justification>
  </clause>

  <clause id="548">
    <literal><![CDATA[
      x * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,L(z,y,x)) = L(z,y,x) \ u
    ]]></literal>
    <justification jstring="[para(97(a,1),309(a,1))].">
      <j1 rule="para" parents="97 309"/>
    </justification>
  </clause>

  <clause id="549">
    <literal><![CDATA[
      L(x,1,y) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),534(a,1,2))].">
      <j1 rule="para" parents="7 534"/>
    </justification>
  </clause>

  <clause id="550">
    <literal><![CDATA[
      L(x,y * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(534(a,1),50(a,2))].">
      <j1 rule="para" parents="534 50"/>
    </justification>
  </clause>

  <clause id="551">
    <literal><![CDATA[
      L(x,y \ (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(307(a,1),534(a,1,2))].">
      <j1 rule="para" parents="307 534"/>
    </justification>
  </clause>

  <clause id="552">
    <literal><![CDATA[
      L(x,1,y) = z \ (z * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,9,a,b,549,a),flip(a)].">
      <j1 rule="hyper" parents="347 9 549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="553">
    <literal><![CDATA[
      a(x,y,z * z) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,533,a)].">
      <j1 rule="hyper" parents="53 533"/>
    </justification>
  </clause>

  <clause id="554">
    <literal><![CDATA[
      L(T(x * x,y),z,u) = T(x * x,y)
    ]]></literal>
    <justification jstring="[para(533(a,1),25(a,2,1))].">
      <j1 rule="para" parents="533 25"/>
    </justification>
  </clause>

  <clause id="555">
    <literal><![CDATA[
      a(x,y,1) = 1
    ]]></literal>
    <justification jstring="[para(7(a,1),553(a,1,3))].">
      <j1 rule="para" parents="7 553"/>
    </justification>
  </clause>

  <clause id="556">
    <literal><![CDATA[
      L(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(52,a,555,a)].">
      <j1 rule="hyper" parents="52 555"/>
    </justification>
  </clause>

  <clause id="557">
    <literal><![CDATA[
      a(x,y,K(1,z)) = 1
    ]]></literal>
    <justification jstring="[para(227(a,2),555(a,1,3))].">
      <j1 rule="para" parents="227 555"/>
    </justification>
  </clause>

  <clause id="558">
    <literal><![CDATA[
      (x * (y \ (1 / y))) * z = x * ((y \ (1 / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(134,a,551,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 551 18"/>
    </justification>
  </clause>

  <clause id="559">
    <literal><![CDATA[
      L(x \ y,x,1 / x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(347,a,184,a(flip),b,99,a),flip(a)].">
      <j1 rule="hyper" parents="347 184 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="560">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(347,a,183,a(flip),b,99,a),flip(a)].">
      <j1 rule="hyper" parents="347 183 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="561">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,174,a(flip),b,99,a),flip(a)].">
      <j1 rule="hyper" parents="347 174 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="563">
    <literal><![CDATA[
      L(x \ y,x,z) * u = ((z * x) \ (z * y)) * u
    ]]></literal>
    <justification jstring="[hyper(133,a,99,a,b,11,a)].">
      <j1 rule="hyper" parents="133 99 11"/>
    </justification>
  </clause>

  <clause id="564">
    <literal><![CDATA[
      L(x \ y,x,z) \ u = ((z * x) \ (z * y)) \ u
    ]]></literal>
    <justification jstring="[hyper(61,a,99,a)].">
      <j1 rule="hyper" parents="61 99"/>
    </justification>
  </clause>

  <clause id="565">
    <literal><![CDATA[
      L(x \ y,x,z / x) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),99(a,2,1))].">
      <j1 rule="para" parents="12 99"/>
    </justification>
  </clause>

  <clause id="566">
    <literal><![CDATA[
      L(x \ y,x,z / y) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[para(12(a,1),99(a,2,2))].">
      <j1 rule="para" parents="12 99"/>
    </justification>
  </clause>

  <clause id="567">
    <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),99(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="568">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,w) = L((w * x) \ (w * y),z,u)
    ]]></literal>
    <justification jstring="[para(99(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="99 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="569">
    <literal><![CDATA[
      L(x,y,z) != (z * y) \ (z * u)
    ]]></literal>
    <literal><![CDATA[
      y \ u = x
    ]]></literal>
    <justification jstring="[para(99(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="99 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="570">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[para(111(a,1),99(a,2,1))].">
      <j1 rule="para" parents="111 99"/>
    </justification>
  </clause>

  <clause id="571">
    <literal><![CDATA[
      L(x \ (1 / y),x,y) = (y * x) \ K(y,1 / y)
    ]]></literal>
    <justification jstring="[para(292(a,2),99(a,2,2))].">
      <j1 rule="para" parents="292 99"/>
    </justification>
  </clause>

  <clause id="572">
    <literal><![CDATA[
      L(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ y = z
    ]]></literal>
    <justification jstring="[para(99(a,2),363(a,1))].">
      <j1 rule="para" parents="99 363"/>
    </justification>
  </clause>

  <clause id="573">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),z * y) = (z * (y * x)) \ ((z * y) * u)
    ]]></literal>
    <justification jstring="[para(97(a,1),99(a,2,1))].">
      <j1 rule="para" parents="97 99"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      L(x \ L(y,z,u),x,u * z) = ((u * z) * x) \ (u * (z * y))
    ]]></literal>
    <justification jstring="[para(97(a,1),99(a,2,2))].">
      <j1 rule="para" parents="97 99"/>
    </justification>
  </clause>

  <clause id="575">
    <literal><![CDATA[
      L(L(x \ y,x,z),z * x,u) = (u * (z * x)) \ (u * (z * y))
    ]]></literal>
    <justification jstring="[para(99(a,2),99(a,1,1))].">
      <j1 rule="para" parents="99 99"/>
    </justification>
  </clause>

  <clause id="576">
    <literal><![CDATA[
      (R(x,y,z) * (y * z)) / z = x * y
    ]]></literal>
    <justification jstring="[hyper(131,a,107,a,b,xx)].">
      <j1 rule="hyper" parents="131 107"/>
    </justification>
  </clause>

  <clause id="577">
    <literal><![CDATA[
      R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(128,a,252,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="128 252 107"/>
    </justification>
  </clause>

  <clause id="578">
    <literal><![CDATA[
      R(x,x \ y,z) \ (y * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(128,a,165,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="128 165 107"/>
    </justification>
  </clause>

  <clause id="579">
    <literal><![CDATA[
      R(x / y,y,z) \ (x * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(128,a,164,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="128 164 107"/>
    </justification>
  </clause>

  <clause id="580">
    <literal><![CDATA[
      R(x,y,L(z,y,x)) \ (x * (y * z)) = y * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,97,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="128 97 107"/>
    </justification>
  </clause>

  <clause id="581">
    <literal><![CDATA[
      R(x,y,(x * y) \ z) \ z = y * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(128,a,10,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="128 10 107"/>
    </justification>
  </clause>

  <clause id="582">
    <literal><![CDATA[
      (x * y) * R(x * y,x,y) = ((x * y) * x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,273,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="63 273 107"/>
    </justification>
  </clause>

  <clause id="583">
    <literal><![CDATA[
      R(x,y,T(z,y)) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,251,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="63 251 107"/>
    </justification>
  </clause>

  <clause id="584">
    <literal><![CDATA[
      R(x,y / z,z) * y = (x * (y / z)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,168,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="63 168 107"/>
    </justification>
  </clause>

  <clause id="585">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,73,a(flip),b,107,a),flip(a)].">
      <j1 rule="hyper" parents="63 73 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="586">
    <literal><![CDATA[
      R(x,y,z * z) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,33,a(flip),b,107,a),flip(a)].">
      <j1 rule="hyper" parents="35 33 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="587">
    <literal><![CDATA[
      R(x,y * y,z) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,32,a(flip),b,107,a),flip(a)].">
      <j1 rule="hyper" parents="35 32 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="588">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(131,a,73,a(flip),b,107,a(flip))].">
      <j1 rule="hyper" parents="131 73 107"/>
    </justification>
  </clause>

  <clause id="589">
    <literal><![CDATA[
      (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,107,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="128 107 97"/>
    </justification>
  </clause>

  <clause id="590">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * z) * R(x,y,z)) = K(y * z,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(107(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="107 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="591">
    <literal><![CDATA[
      (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u)
    ]]></literal>
    <justification jstring="[para(107(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="107 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="592">
    <literal><![CDATA[
      ((x * R(y,z,u)) * (z * u)) / ((y * z) * u) = R(x,R(y,z,u),z * u)
    ]]></literal>
    <justification jstring="[para(107(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="107 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="593">
    <literal><![CDATA[
      R(x,y,y) * ((y * y) * z) = ((x * y) * y) * z
    ]]></literal>
    <justification jstring="[para(107(a,1),32(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="594">
    <literal><![CDATA[
      (x * y) * z != u * (y * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),44(a,1))].">
      <j1 rule="para" parents="107 44"/>
    </justification>
  </clause>

  <clause id="595">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="107 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="596">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) * (z * y) = (x * (y * z)) * K(z,y)
    ]]></literal>
    <justification jstring="[para(91(a,1),107(a,1,2))].">
      <j1 rule="para" parents="91 107"/>
    </justification>
  </clause>

  <clause id="597">
    <literal><![CDATA[
      R(x,y \ 1,y) * K(y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(290(a,2),107(a,1,2))].">
      <j1 rule="para" parents="290 107"/>
    </justification>
  </clause>

  <clause id="598">
    <literal><![CDATA[
      R(x,y,z * z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(586(a,1),51(a,2))].">
      <j1 rule="para" parents="586 51"/>
    </justification>
  </clause>

  <clause id="599">
    <literal><![CDATA[
      R(x,y,z \ (1 / z)) = x
    ]]></literal>
    <justification jstring="[para(307(a,1),586(a,1,3))].">
      <j1 rule="para" parents="307 586"/>
    </justification>
  </clause>

  <clause id="600">
    <literal><![CDATA[
      R(x,1,y) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),587(a,1,2))].">
      <j1 rule="para" parents="7 587"/>
    </justification>
  </clause>

  <clause id="601">
    <literal><![CDATA[
      R(x,y * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(587(a,1),51(a,2))].">
      <j1 rule="para" parents="587 51"/>
    </justification>
  </clause>

  <clause id="602">
    <literal><![CDATA[
      (x * y) * (z \ (1 / z)) = x * (y * (z \ (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(133,a,599,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 599 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="603">
    <literal><![CDATA[
      R(x / (1 / y),1 / y,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(347,a,194,a(flip),b,108,a),flip(a)].">
      <j1 rule="hyper" parents="347 194 108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="604">
    <literal><![CDATA[
      R(x / y,y,x \ z) = z / (y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,172,a(flip),b,108,a),flip(a)].">
      <j1 rule="hyper" parents="347 172 108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="605">
    <literal><![CDATA[
      R((x / y) / z,z,y) = x / (z * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,171,a(flip),b,108,a),flip(a)].">
      <j1 rule="hyper" parents="347 171 108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="606">
    <literal><![CDATA[
      R(x / y,y,y \ z) = (x * (y \ z)) / z
    ]]></literal>
    <justification jstring="[para(10(a,1),108(a,2,2))].">
      <j1 rule="para" parents="10 108"/>
    </justification>
  </clause>

  <clause id="607">
    <literal><![CDATA[
      R(x / (y / z),y / z,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),108(a,2,2))].">
      <j1 rule="para" parents="12 108"/>
    </justification>
  </clause>

  <clause id="608">
    <literal><![CDATA[
      T((x * y) / (z * y),u) = R(T(x / z,u),z,y)
    ]]></literal>
    <justification jstring="[para(108(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="108 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="609">
    <literal><![CDATA[
      R(x / T(y,z),T(y,z),y) = (x * y) / (y * T(y,z))
    ]]></literal>
    <justification jstring="[para(272(a,1),108(a,2,2))].">
      <j1 rule="para" parents="272 108"/>
    </justification>
  </clause>

  <clause id="610">
    <literal><![CDATA[
      R(R(x,y,z) / u,u,y * z) = ((x * y) * z) / (u * (y * z))
    ]]></literal>
    <justification jstring="[para(107(a,1),108(a,2,1))].">
      <j1 rule="para" parents="107 108"/>
    </justification>
  </clause>

  <clause id="611">
    <literal><![CDATA[
      R(x / R(y,z,u),R(y,z,u),z * u) = (x * (z * u)) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(107(a,1),108(a,2,2))].">
      <j1 rule="para" parents="107 108"/>
    </justification>
  </clause>

  <clause id="612">
    <literal><![CDATA[
      R(R(x / y,y,z),y * z,u) = ((x * z) * u) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(108(a,2),108(a,1,1))].">
      <j1 rule="para" parents="108 108"/>
    </justification>
  </clause>

  <clause id="613">
    <literal><![CDATA[
      x * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ (x * y) = u
    ]]></literal>
    <justification jstring="[para(74(a,1),139(a,1,2))].">
      <j1 rule="para" parents="74 139"/>
    </justification>
  </clause>

  <clause id="614">
    <literal><![CDATA[
      R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(91(a,1),209(a,1,2,1))].">
      <j1 rule="para" parents="91 209"/>
    </justification>
  </clause>

  <clause id="615">
    <literal><![CDATA[
      R(x,K(y \ x,y),z) \ (((y \ x) * y) * z) = K(y \ x,y) * z
    ]]></literal>
    <justification jstring="[para(330(a,1),209(a,1,2,1))].">
      <j1 rule="para" parents="330 209"/>
    </justification>
  </clause>

  <clause id="616">
    <literal><![CDATA[
      R(x * y,L(z,y,x),u) \ ((x * (y * z)) * u) = L(z,y,x) * u
    ]]></literal>
    <justification jstring="[para(97(a,1),209(a,1,2,1))].">
      <j1 rule="para" parents="97 209"/>
    </justification>
  </clause>

  <clause id="617">
    <literal><![CDATA[
      (1 / x) \ L(L(y,x,1 / x),z,u) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(128,a,30,a,b,291,a)].">
      <j1 rule="hyper" parents="128 30 291"/>
    </justification>
  </clause>

  <clause id="618">
    <literal><![CDATA[
      R(R(x,1 / y,y),z,u) / y = R(x,z,u) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(131,a,31,a,b,294,a)].">
      <j1 rule="hyper" parents="131 31 294"/>
    </justification>
  </clause>

  <clause id="619">
    <literal><![CDATA[
      K(x,1 / x) * x = R(x,1 / x,x)
    ]]></literal>
    <justification jstring="[para(292(a,2),294(a,1,1))].">
      <j1 rule="para" parents="292 294"/>
    </justification>
  </clause>

  <clause id="620">
    <literal><![CDATA[
      x * (y \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(9(a,1),324(a,1,2,2,2))].">
      <j1 rule="para" parents="9 324"/>
    </justification>
  </clause>

  <clause id="621">
    <literal><![CDATA[
      L(T(x \ (y \ z),u),x,y) = T((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(329(a,1),25(a,2,1))].">
      <j1 rule="para" parents="329 25"/>
    </justification>
  </clause>

  <clause id="622">
    <literal><![CDATA[
      L(L(x \ (y \ z),u,w),x,y) = L((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(329(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="329 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="623">
    <literal><![CDATA[
      L(x,y,z) != (z * y) \ u
    ]]></literal>
    <literal><![CDATA[
      y \ (z \ u) = x
    ]]></literal>
    <justification jstring="[para(329(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="329 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="624">
    <literal><![CDATA[
      L(x,(y \ z) / x,y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[para(83(a,1),329(a,1,1))].">
      <j1 rule="para" parents="83 329"/>
    </justification>
  </clause>

  <clause id="625">
    <literal><![CDATA[
      (x * (y * y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      (y * y) \ (x \ z) = u
    ]]></literal>
    <justification jstring="[para(329(a,1),550(a,1))].">
      <j1 rule="para" parents="329 550"/>
    </justification>
  </clause>

  <clause id="626">
    <literal><![CDATA[
      x * y != x * z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(10(a,1),348(a,1,1))].">
      <j1 rule="para" parents="10 348"/>
    </justification>
  </clause>

  <clause id="628">
    <literal><![CDATA[
      (x * (x \ y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(80(a,1),353(a,1,1,1))].">
      <j1 rule="para" parents="80 353"/>
    </justification>
  </clause>

  <clause id="629">
    <literal><![CDATA[
      (x * T(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) * z = u
    ]]></literal>
    <justification jstring="[para(213(a,1),353(a,1,1,1))].">
      <j1 rule="para" parents="213 353"/>
    </justification>
  </clause>

  <clause id="630">
    <literal><![CDATA[
      x \ y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ (x \ y) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),354(a,1,2))].">
      <j1 rule="para" parents="10 354"/>
    </justification>
  </clause>

  <clause id="632">
    <literal><![CDATA[
      x \ (y * x) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(y,x) = u
    ]]></literal>
    <justification jstring="[para(111(a,1),354(a,1,2))].">
      <j1 rule="para" parents="111 354"/>
    </justification>
  </clause>

  <clause id="634">
    <literal><![CDATA[
      x \ y != z * (u \ (u * (z \ w)))
    ]]></literal>
    <literal><![CDATA[
      x * w = y
    ]]></literal>
    <justification jstring="[para(9(a,2),355(a,2,2))].">
      <j1 rule="para" parents="9 355"/>
    </justification>
  </clause>

  <clause id="635">
    <literal><![CDATA[
      x \ y != z * T(u,z)
    ]]></literal>
    <literal><![CDATA[
      x * (u * z) = y
    ]]></literal>
    <justification jstring="[para(22(a,2),355(a,2,2))].">
      <j1 rule="para" parents="22 355"/>
    </justification>
  </clause>

  <clause id="636">
    <literal><![CDATA[
      x \ y != (z / u) * u
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(83(a,1),355(a,2,2))].">
      <j1 rule="para" parents="83 355"/>
    </justification>
  </clause>

  <clause id="637">
    <literal><![CDATA[
      x \ (x * y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * y = u
    ]]></literal>
    <justification jstring="[para(179(a,2),355(a,2)),flip(a)].">
      <j1 rule="para" parents="179 355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="638">
    <literal><![CDATA[
      (x / y) \ x != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * y = u
    ]]></literal>
    <justification jstring="[para(216(a,2),355(a,2)),flip(a)].">
      <j1 rule="para" parents="216 355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="639">
    <literal><![CDATA[
      x * (y * T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),357(a,1,2,2))].">
      <j1 rule="para" parents="22 357"/>
    </justification>
  </clause>

  <clause id="640">
    <literal><![CDATA[
      x * (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(68(a,1),357(a,1,2,2))].">
      <j1 rule="para" parents="68 357"/>
    </justification>
  </clause>

  <clause id="641">
    <literal><![CDATA[
      x * ((y / z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(83(a,1),357(a,1,2,2))].">
      <j1 rule="para" parents="83 357"/>
    </justification>
  </clause>

  <clause id="643">
    <literal><![CDATA[
      x * (y / (z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(205(a,2),357(a,1,2))].">
      <j1 rule="para" parents="205 357"/>
    </justification>
  </clause>

  <clause id="644">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(216(a,2),357(a,1,2))].">
      <j1 rule="para" parents="216 357"/>
    </justification>
  </clause>

  <clause id="645">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(289(a,1),357(a,1))].">
      <j1 rule="para" parents="289 357"/>
    </justification>
  </clause>

  <clause id="646">
    <literal><![CDATA[
      (x / (y \ x)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ z = u
    ]]></literal>
    <justification jstring="[para(10(a,1),371(a,1,1,1))].">
      <j1 rule="para" parents="10 371"/>
    </justification>
  </clause>

  <clause id="648">
    <literal><![CDATA[
      (x * y) / T(x,y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(22(a,2),372(a,1,2))].">
      <j1 rule="para" parents="22 372"/>
    </justification>
  </clause>

  <clause id="649">
    <literal><![CDATA[
      (x * (x \ y)) / z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y / z) = w
    ]]></literal>
    <justification jstring="[para(326(a,1),372(a,1,2))].">
      <j1 rule="para" parents="326 372"/>
    </justification>
  </clause>

  <clause id="650">
    <literal><![CDATA[
      (x * T(y,x)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ z = u
    ]]></literal>
    <justification jstring="[para(22(a,2),374(a,1,1,2))].">
      <j1 rule="para" parents="22 374"/>
    </justification>
  </clause>

  <clause id="651">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) != u
    ]]></literal>
    <literal><![CDATA[
      y \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(99(a,2),374(a,1))].">
      <j1 rule="para" parents="99 374"/>
    </justification>
  </clause>

  <clause id="652">
    <literal><![CDATA[
      x * y != z * u
    ]]></literal>
    <literal><![CDATA[
      (x * y) / u = z
    ]]></literal>
    <justification jstring="[para(9(a,1),390(a,1,2))].">
      <j1 rule="para" parents="9 390"/>
    </justification>
  </clause>

  <clause id="653">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      z / w = u
    ]]></literal>
    <justification jstring="[para(9(a,2),390(a,1,2))].">
      <j1 rule="para" parents="9 390"/>
    </justification>
  </clause>

  <clause id="654">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(83(a,1),390(a,1,2))].">
      <j1 rule="para" parents="83 390"/>
    </justification>
  </clause>

  <clause id="655">
    <literal><![CDATA[
      ((1 / x) * x) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(184(a,1),390(a,1,2))].">
      <j1 rule="para" parents="184 390"/>
    </justification>
  </clause>

  <clause id="656">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(179(a,1),390(a,1,2))].">
      <j1 rule="para" parents="179 390"/>
    </justification>
  </clause>

  <clause id="657">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(179(a,2),390(a,1))].">
      <j1 rule="para" parents="179 390"/>
    </justification>
  </clause>

  <clause id="658">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      y / T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(213(a,1),391(a,1))].">
      <j1 rule="para" parents="213 391"/>
    </justification>
  </clause>

  <clause id="659">
    <literal><![CDATA[
      R(x / y,y,x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      z / (y * (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(108(a,2),391(a,1))].">
      <j1 rule="para" parents="108 391"/>
    </justification>
  </clause>

  <clause id="660">
    <literal><![CDATA[
      (x * (x \ y)) \ z != u \ w
    ]]></literal>
    <literal><![CDATA[
      w / (y \ z) = u
    ]]></literal>
    <justification jstring="[para(205(a,1),393(a,1,1))].">
      <j1 rule="para" parents="205 393"/>
    </justification>
  </clause>

  <clause id="661">
    <literal><![CDATA[
      T(x / y,(x / y) \ x) != z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(112(a,2),395(a,1))].">
      <j1 rule="para" parents="112 395"/>
    </justification>
  </clause>

  <clause id="662">
    <literal><![CDATA[
      ((x * y) \ x) \ z != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(412(a,1),395(a,1,1,1))].">
      <j1 rule="para" parents="412 395"/>
    </justification>
  </clause>

  <clause id="663">
    <literal><![CDATA[
      L(x,y \ z,y) != z \ y
    ]]></literal>
    <literal><![CDATA[
      (y \ z) \ 1 = x
    ]]></literal>
    <justification jstring="[para(408(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="408 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="664">
    <literal><![CDATA[
      T((x \ y) \ 1,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(408(a,1),197(a,1,2))].">
      <j1 rule="para" parents="408 197"/>
    </justification>
  </clause>

  <clause id="665">
    <literal><![CDATA[
      x * ((y * y) \ 1) = x / (y * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,534,a(flip),b,414,a(flip))].">
      <j1 rule="hyper" parents="134 534 414"/>
    </justification>
  </clause>

  <clause id="666">
    <literal><![CDATA[
      T(x \ (x / y),z) = L(T(y \ 1,z),y,x / y)
    ]]></literal>
    <justification jstring="[para(414(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="414 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="667">
    <literal><![CDATA[
      x * (y \ (y \ 1)) = x / (y * y)
    ]]></literal>
    <justification jstring="[para(501(a,1),665(a,1,2))].">
      <j1 rule="para" parents="501 665"/>
    </justification>
  </clause>

  <clause id="668">
    <literal><![CDATA[
      x / (y \ (y \ 1)) = x * (y * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,11,a(flip),b,667,a)].">
      <j1 rule="hyper" parents="131 11 667"/>
    </justification>
  </clause>

  <clause id="669">
    <literal><![CDATA[
      x * R(1 / y,y,y \ z) = x * ((y \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(134,a,421,a,b,9,a)].">
      <j1 rule="hyper" parents="134 421 9"/>
    </justification>
  </clause>

  <clause id="670">
    <literal><![CDATA[
      ((x \ y) / y) * (R(1 / x,x,x \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(133,a,421,a(flip),b,80,a)].">
      <j1 rule="hyper" parents="133 421 80"/>
    </justification>
  </clause>

  <clause id="671">
    <literal><![CDATA[
      T((x \ y) / y,z) = R(T(1 / x,z),x,x \ y)
    ]]></literal>
    <justification jstring="[para(421(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="421 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="672">
    <literal><![CDATA[
      T(1 / (x / y),y / x) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(422(a,1),196(a,1,2))].">
      <j1 rule="para" parents="422 196"/>
    </justification>
  </clause>

  <clause id="673">
    <literal><![CDATA[
      x / y != z * (u \ (u * (z \ w)))
    ]]></literal>
    <literal><![CDATA[
      w * y = x
    ]]></literal>
    <justification jstring="[para(9(a,2),426(a,2,2))].">
      <j1 rule="para" parents="9 426"/>
    </justification>
  </clause>

  <clause id="674">
    <literal><![CDATA[
      (R(x,y,z) * (y * z)) / z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * y) = w
    ]]></literal>
    <justification jstring="[para(107(a,2),429(a,1,1))].">
      <j1 rule="para" parents="107 429"/>
    </justification>
  </clause>

  <clause id="675">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(10(a,2),430(a,1,2))].">
      <j1 rule="para" parents="10 430"/>
    </justification>
  </clause>

  <clause id="676">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * (y * z)) = w
    ]]></literal>
    <justification jstring="[para(18(a,2),430(a,1,2))].">
      <j1 rule="para" parents="18 430"/>
    </justification>
  </clause>

  <clause id="678">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(179(a,1),430(a,1,2))].">
      <j1 rule="para" parents="179 430"/>
    </justification>
  </clause>

  <clause id="679">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ ((x * y) * z) = w
    ]]></literal>
    <justification jstring="[para(209(a,1),430(a,1,2))].">
      <j1 rule="para" parents="209 430"/>
    </justification>
  </clause>

  <clause id="680">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(176(a,1),434(a,1,1))].">
      <j1 rule="para" parents="176 434"/>
    </justification>
  </clause>

  <clause id="681">
    <literal><![CDATA[
      (x / (y \ x)) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(204(a,1),434(a,1,1))].">
      <j1 rule="para" parents="204 434"/>
    </justification>
  </clause>

  <clause id="682">
    <literal><![CDATA[
      R((x / y) / z,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z * y) = u
    ]]></literal>
    <justification jstring="[para(108(a,2),438(a,1))].">
      <j1 rule="para" parents="108 438"/>
    </justification>
  </clause>

  <clause id="683">
    <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),440(a,1))].">
      <j1 rule="para" parents="27 440"/>
    </justification>
  </clause>

  <clause id="684">
    <literal><![CDATA[
      x / ((y \ 1) * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(y,y \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(448(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="448 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="685">
    <literal><![CDATA[
      T(R(T(x,y),z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(T(R(x,z,u),w),y) = v5
    ]]></literal>
    <justification jstring="[para(27(a,2),453(a,1,1))].">
      <j1 rule="para" parents="27 453"/>
    </justification>
  </clause>

  <clause id="686">
    <literal><![CDATA[
      (x * y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ z,y,x) = u
    ]]></literal>
    <justification jstring="[para(529(a,1),359(a,1,1))].">
      <j1 rule="para" parents="529 359"/>
    </justification>
  </clause>

  <clause id="687">
    <literal><![CDATA[
      ((x * y) \ (x * z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      L(y \ z,y,x) \ u = w
    ]]></literal>
    <justification jstring="[para(529(a,1),395(a,1,1,1))].">
      <j1 rule="para" parents="529 395"/>
    </justification>
  </clause>

  <clause id="688">
    <literal><![CDATA[
      L(T((x \ 1) \ y,z),x \ 1,x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(560(a,1),25(a,2,1))].">
      <j1 rule="para" parents="560 25"/>
    </justification>
  </clause>

  <clause id="689">
    <literal><![CDATA[
      L(L((x \ 1) \ y,z,u),x \ 1,x) = L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(560(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="560 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="691">
    <literal><![CDATA[
      R(x / y,y,y \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(189,a,579,a,b,10,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="189 579 10"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="693">
    <literal><![CDATA[
      R(x / y,y,x \ z) \ z = y * (x \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),579(a,1,2))].">
      <j1 rule="para" parents="10 579"/>
    </justification>
  </clause>

  <clause id="694">
    <literal><![CDATA[
      (x * y) / (z * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x / z,z,y) = u
    ]]></literal>
    <justification jstring="[para(579(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="579 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="695">
    <literal><![CDATA[
      (x \ 1) \ R(y,x,x \ 1) = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(309,a,585,a),flip(a)].">
      <j1 rule="hyper" parents="309 585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="696">
    <literal><![CDATA[
      L(R(x,y,y \ 1),z,u) / (y \ 1) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(131,a,29,a(flip),b,585,a)].">
      <j1 rule="hyper" parents="131 29 585"/>
    </justification>
  </clause>

  <clause id="697">
    <literal><![CDATA[
      T(R(x,y,y \ 1),z) / (y \ 1) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(131,a,27,a(flip),b,585,a)].">
      <j1 rule="hyper" parents="131 27 585"/>
    </justification>
  </clause>

  <clause id="698">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(585(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="585 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="699">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,z * x) = R(z,x,x \ 1) \ ((z * x) * y)
    ]]></literal>
    <justification jstring="[para(585(a,1),99(a,2,1))].">
      <j1 rule="para" parents="585 99"/>
    </justification>
  </clause>

  <clause id="700">
    <literal><![CDATA[
      x / (y \ 1) != z * y
    ]]></literal>
    <literal><![CDATA[
      R(z,y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(588(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="588 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="701">
    <literal><![CDATA[
      R(T(x / (1 / y),z),1 / y,y) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(603(a,1),27(a,2,1))].">
      <j1 rule="para" parents="603 27"/>
    </justification>
  </clause>

  <clause id="702">
    <literal><![CDATA[
      (x / y) / (z * z) = x / ((z * z) * y)
    ]]></literal>
    <justification jstring="[hyper(601,a,605,a)].">
      <j1 rule="hyper" parents="601 605"/>
    </justification>
  </clause>

  <clause id="703">
    <literal><![CDATA[
      (x / (y * y)) / z = x / (z * (y * y))
    ]]></literal>
    <justification jstring="[hyper(598,a,605,a)].">
      <j1 rule="hyper" parents="598 605"/>
    </justification>
  </clause>

  <clause id="704">
    <literal><![CDATA[
      R(T((x / y) / z,u),z,y) = T(x / (z * y),u)
    ]]></literal>
    <justification jstring="[para(605(a,1),27(a,2,1))].">
      <j1 rule="para" parents="605 27"/>
    </justification>
  </clause>

  <clause id="705">
    <literal><![CDATA[
      (x * (x \ y)) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(165(a,2),613(a,1))].">
      <j1 rule="para" parents="165 613"/>
    </justification>
  </clause>

  <clause id="706">
    <literal><![CDATA[
      x * (y \ (y * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(170(a,2),613(a,1))].">
      <j1 rule="para" parents="170 613"/>
    </justification>
  </clause>

  <clause id="707">
    <literal><![CDATA[
      x * (y \ (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(z,y) = u
    ]]></literal>
    <justification jstring="[para(111(a,1),620(a,1,2,2))].">
      <j1 rule="para" parents="111 620"/>
    </justification>
  </clause>

  <clause id="708">
    <literal><![CDATA[
      ((x / y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(379(a,1),620(a,1))].">
      <j1 rule="para" parents="379 620"/>
    </justification>
  </clause>

  <clause id="709">
    <literal><![CDATA[
      x \ y != (z * u) / u
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(176(a,2),636(a,2))].">
      <j1 rule="para" parents="176 636"/>
    </justification>
  </clause>

  <clause id="710">
    <literal><![CDATA[
      x \ (y \ (y * (x * z))) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * z = w
    ]]></literal>
    <justification jstring="[para(9(a,2),637(a,1,2))].">
      <j1 rule="para" parents="9 637"/>
    </justification>
  </clause>

  <clause id="711">
    <literal><![CDATA[
      x \ (y * x) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * T(y,x) = u
    ]]></literal>
    <justification jstring="[para(111(a,1),637(a,1,2))].">
      <j1 rule="para" parents="111 637"/>
    </justification>
  </clause>

  <clause id="712">
    <literal><![CDATA[
      (x * y) \ x != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * L(y \ 1,y,x) = u
    ]]></literal>
    <justification jstring="[para(413(a,1),637(a,1,2))].">
      <j1 rule="para" parents="413 637"/>
    </justification>
  </clause>

  <clause id="714">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * L(z,y,x) = w
    ]]></literal>
    <justification jstring="[para(97(a,1),637(a,1,2))].">
      <j1 rule="para" parents="97 637"/>
    </justification>
  </clause>

  <clause id="715">
    <literal><![CDATA[
      (x * (x \ y)) \ z != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * (y \ z) = w
    ]]></literal>
    <justification jstring="[para(205(a,1),638(a,1,1))].">
      <j1 rule="para" parents="205 638"/>
    </justification>
  </clause>

  <clause id="716">
    <literal><![CDATA[
      (x * y) \ (x * z) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * L(y \ z,y,x) = w
    ]]></literal>
    <justification jstring="[para(529(a,1),638(a,1,1))].">
      <j1 rule="para" parents="529 638"/>
    </justification>
  </clause>

  <clause id="717">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(164(a,2),652(a,1))].">
      <j1 rule="para" parents="164 652"/>
    </justification>
  </clause>

  <clause id="718">
    <literal><![CDATA[
      x * (y \ (y * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(170(a,2),652(a,1))].">
      <j1 rule="para" parents="170 652"/>
    </justification>
  </clause>

  <clause id="719">
    <literal><![CDATA[
      (((x / y) / z) * z) * y != u * w
    ]]></literal>
    <literal><![CDATA[
      x / w = u
    ]]></literal>
    <justification jstring="[para(12(a,2),654(a,1,1))].">
      <j1 rule="para" parents="12 654"/>
    </justification>
  </clause>

  <clause id="720">
    <literal><![CDATA[
      (x * y) \ x != z * u
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) / u = z
    ]]></literal>
    <justification jstring="[para(413(a,1),657(a,1,2))].">
      <j1 rule="para" parents="413 657"/>
    </justification>
  </clause>

  <clause id="721">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ 1) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(691(a,1),27(a,2,1))].">
      <j1 rule="para" parents="691 27"/>
    </justification>
  </clause>

  <clause id="722">
    <literal><![CDATA[
      R(R(x / y,z,u),y,y \ 1) = R(x * (y \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(691(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="691 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="723">
    <literal><![CDATA[
      x * ((y * y) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x / (y * y) = z
    ]]></literal>
    <justification jstring="[para(691(a,1),601(a,1))].">
      <j1 rule="para" parents="691 601"/>
    </justification>
  </clause>

  <clause id="724">
    <literal><![CDATA[
      ((x \ y) \ y) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) * z = u
    ]]></literal>
    <justification jstring="[para(296(a,1),708(a,1,1,1))].">
      <j1 rule="para" parents="296 708"/>
    </justification>
  </clause>

  <clause id="725">
    <literal><![CDATA[
      (x * (y * y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * ((y * y) * z) = u
    ]]></literal>
    <justification jstring="[para(117(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="117 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="726">
    <literal><![CDATA[
      ((x * x) \ y) * (x * x) = T(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(270,a,124,a),flip(a)].">
      <j1 rule="hyper" parents="270 124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="727">
    <literal><![CDATA[
      (x \ (y \ 1)) * (z * z) = x \ (y \ (z * z))
    ]]></literal>
    <justification jstring="[hyper(128,a,460,a(flip),b,124,a),flip(a)].">
      <j1 rule="hyper" parents="128 460 124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="728">
    <literal><![CDATA[
      x \ (y * (z * (u * u))) = (x \ (y * z)) * (u * u)
    ]]></literal>
    <justification jstring="[hyper(128,a,33,a(flip),b,124,a)].">
      <j1 rule="hyper" parents="128 33 124"/>
    </justification>
  </clause>

  <clause id="729">
    <literal><![CDATA[
      (x \ (y / (z * z))) * (z * z) = x \ y
    ]]></literal>
    <justification jstring="[hyper(128,a,12,a(flip),b,124,a),flip(a)].">
      <j1 rule="hyper" parents="128 12 124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="730">
    <literal><![CDATA[
      ((x * y) \ x) * (y * y) = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,97,a,b,124,a),flip(a)].">
      <j1 rule="hyper" parents="34 97 124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="731">
    <literal><![CDATA[
      x \ (y * (z * z)) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * (z * z) = u
    ]]></literal>
    <justification jstring="[para(124(a,1),356(a,1,2))].">
      <j1 rule="para" parents="124 356"/>
    </justification>
  </clause>

  <clause id="732">
    <literal><![CDATA[
      (x \ y) * ((y \ x) * (y \ x)) = L(y \ x,y \ x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),730(a,1,1,1))].">
      <j1 rule="para" parents="10 730"/>
    </justification>
  </clause>

  <clause id="733">
    <literal><![CDATA[
      L((x * x) \ y,x * x,(z * x) \ z) = L(x,x,z) \ (((z * x) \ z) * y)
    ]]></literal>
    <justification jstring="[para(730(a,1),99(a,2,1))].">
      <j1 rule="para" parents="730 99"/>
    </justification>
  </clause>

  <clause id="734">
    <literal><![CDATA[
      x * (y * T(z,x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,97,a(flip),b,267,a)].">
      <j1 rule="hyper" parents="63 97 267"/>
    </justification>
  </clause>

  <clause id="735">
    <literal><![CDATA[
      x \ (L(y,z,x) * (x * z)) = z * T(y,x * z)
    ]]></literal>
    <justification jstring="[hyper(128,a,267,a(flip),b,97,a(flip))].">
      <j1 rule="hyper" parents="128 267 97"/>
    </justification>
  </clause>

  <clause id="736">
    <literal><![CDATA[
      (x * (L(y,z,u) * w)) \ ((x * w) * L(T(y,w),z,u)) = a(x,w,L(T(y,w),z,u))
    ]]></literal>
    <justification jstring="[para(267(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="267 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="737">
    <literal><![CDATA[
      x * L(x \ (y * x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(22(a,1),267(a,1,2,1))].">
      <j1 rule="para" parents="22 267"/>
    </justification>
  </clause>

  <clause id="738">
    <literal><![CDATA[
      x * L(L(T(y,x),z,u),w,v5) = L(L(y,z,u),w,v5) * x
    ]]></literal>
    <justification jstring="[para(25(a,2),267(a,1,2,1))].">
      <j1 rule="para" parents="25 267"/>
    </justification>
  </clause>

  <clause id="739">
    <literal><![CDATA[
      x * L(R(T(y,x),z,u),w,v5) = L(R(y,z,u),w,v5) * x
    ]]></literal>
    <justification jstring="[para(27(a,2),267(a,1,2,1))].">
      <j1 rule="para" parents="27 267"/>
    </justification>
  </clause>

  <clause id="740">
    <literal><![CDATA[
      L(x / y,z,u) * y = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(113(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="741">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(254(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="254 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="742">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ y,z,u) = L(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(112(a,1),267(a,1,2,1))].">
      <j1 rule="para" parents="112 267"/>
    </justification>
  </clause>

  <clause id="743">
    <literal><![CDATA[
      (x * y) * R(T(z,x * y),x,y) = (z * x) * y
    ]]></literal>
    <justification jstring="[hyper(347,a,107,a(flip),b,268,a),flip(a)].">
      <j1 rule="hyper" parents="347 107 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="744">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,107,a(flip),b,268,a)].">
      <j1 rule="hyper" parents="128 107 268"/>
    </justification>
  </clause>

  <clause id="745">
    <literal><![CDATA[
      x * R(T(T(y,x),z),u,w) = R(T(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),268(a,1,2,1))].">
      <j1 rule="para" parents="23 268"/>
    </justification>
  </clause>

  <clause id="746">
    <literal><![CDATA[
      R(x / y,z,u) * y = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(113(a,1),268(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="747">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(254(a,1),268(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="254 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="748">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(112(a,1),268(a,1,2,1))].">
      <j1 rule="para" parents="112 268"/>
    </justification>
  </clause>

  <clause id="749">
    <literal><![CDATA[
      T(x / y,(z / y) \ z) = y \ x
    ]]></literal>
    <justification jstring="[hyper(269,a,376,a,b,378,a)].">
      <j1 rule="hyper" parents="269 376 378"/>
    </justification>
  </clause>

  <clause id="750">
    <literal><![CDATA[
      L(T(x,y),y,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(269,a,251,a(flip),b,97,a),flip(a)].">
      <j1 rule="hyper" parents="269 251 97"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="751">
    <literal><![CDATA[
      (x * x) \ (y \ (z * (y * (x * x)))) = T(z,y * (x * x))
    ]]></literal>
    <justification jstring="[hyper(269,a,76,a(flip),b,32,a),flip(a)].">
      <j1 rule="hyper" parents="269 76 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="752">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a(flip),b,750,a)].">
      <j1 rule="hyper" parents="63 25 750"/>
    </justification>
  </clause>

  <clause id="753">
    <literal><![CDATA[
      L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(750(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="750 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="754">
    <literal><![CDATA[
      x * T(y,y * x) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(750(a,1),267(a,1,2))].">
      <j1 rule="para" parents="750 267"/>
    </justification>
  </clause>

  <clause id="755">
    <literal><![CDATA[
      T((x * y) / x,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,304,a,b,752,a)].">
      <j1 rule="hyper" parents="40 304 752"/>
    </justification>
  </clause>

  <clause id="756">
    <literal><![CDATA[
      L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),754(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="757">
    <literal><![CDATA[
      T(((x \ y) * x) / (x \ y),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),755(a,1,2))].">
      <j1 rule="para" parents="10 755"/>
    </justification>
  </clause>

  <clause id="758">
    <literal><![CDATA[
      T(T((x * y) / x,z),y * x) = T(L(y,x,y),z)
    ]]></literal>
    <justification jstring="[para(755(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="755 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="759">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) / x = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(305,a,278,a)].">
      <j1 rule="hyper" parents="305 278"/>
    </justification>
  </clause>

  <clause id="760">
    <literal><![CDATA[
      L(1 / x,x,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(40,a,519,a(flip),b,278,a),flip(a)].">
      <j1 rule="hyper" parents="40 519 278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="761">
    <literal><![CDATA[
      T(x,y) != L(y \ z,u,w)
    ]]></literal>
    <literal><![CDATA[
      L(z / y,u,w) = x
    ]]></literal>
    <justification jstring="[para(278(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="278 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="762">
    <literal><![CDATA[
      T(x \ T(y,y \ z),x \ ((y \ z) \ z)) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(468,a,335,a,b,xx)].">
      <j1 rule="hyper" parents="468 335"/>
    </justification>
  </clause>

  <clause id="763">
    <literal><![CDATA[
      T(T(x,x \ y),z) = T((x \ y) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(269,a,339,a,b,111,a)].">
      <j1 rule="hyper" parents="269 339 111"/>
    </justification>
  </clause>

  <clause id="764">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (((x \ y) \ y) * (z * u)) = L(u,z,T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(128,a,339,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="128 339 97"/>
    </justification>
  </clause>

  <clause id="765">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,(x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(339(a,2),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="339 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="766">
    <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(339(a,2),365(a,1,1))].">
      <j1 rule="para" parents="339 365"/>
    </justification>
  </clause>

  <clause id="768">
    <literal><![CDATA[
      T(x,y) / (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(111(a,1),449(a,1,2))].">
      <j1 rule="para" parents="111 449"/>
    </justification>
  </clause>

  <clause id="769">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,92,a(flip),b,450,a)].">
      <j1 rule="hyper" parents="347 92 450"/>
    </justification>
  </clause>

  <clause id="770">
    <literal><![CDATA[
      K(x \ (x * y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(70(a,1),769(a,1,1)),flip(a)].">
      <j1 rule="para" parents="70 769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="771">
    <literal><![CDATA[
      K((x / y) \ x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),770(a,1,1,2))].">
      <j1 rule="para" parents="12 770"/>
    </justification>
  </clause>

  <clause id="772">
    <literal><![CDATA[
      T(x,y * y) / (y * y) = (y * y) \ x
    ]]></literal>
    <justification jstring="[hyper(131,a,22,a,b,456,a(flip))].">
      <j1 rule="hyper" parents="131 22 456"/>
    </justification>
  </clause>

  <clause id="773">
    <literal><![CDATA[
      ((x * x) \ y) * (x * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x * x) = z
    ]]></literal>
    <justification jstring="[para(456(a,1),360(a,1))].">
      <j1 rule="para" parents="456 360"/>
    </justification>
  </clause>

  <clause id="774">
    <literal><![CDATA[
      x \ T(y,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ ((y \ z) \ z) = u
    ]]></literal>
    <justification jstring="[para(457(a,1),646(a,1))].">
      <j1 rule="para" parents="457 646"/>
    </justification>
  </clause>

  <clause id="775">
    <literal><![CDATA[
      (x * (y * (z * z))) \ u = (z * z) \ ((x * y) \ u)
    ]]></literal>
    <justification jstring="[para(33(a,1),459(a,1,1))].">
      <j1 rule="para" parents="33 459"/>
    </justification>
  </clause>

  <clause id="776">
    <literal><![CDATA[
      (x * x) \ ((y \ 1) \ z) = (y \ (x * x)) \ z
    ]]></literal>
    <justification jstring="[para(460(a,1),459(a,1,1)),flip(a)].">
      <j1 rule="para" parents="460 459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="777">
    <literal><![CDATA[
      (x / (y * y)) \ z = (y * y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(12(a,1),461(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="778">
    <literal><![CDATA[
      (x * x) * ((y \ (x * x)) \ z) = (y \ 1) \ z
    ]]></literal>
    <justification jstring="[para(460(a,1),461(a,1,2,1))].">
      <j1 rule="para" parents="460 461"/>
    </justification>
  </clause>

  <clause id="779">
    <literal><![CDATA[
      (x \ y) / (z * z) = x \ (y / (z * z))
    ]]></literal>
    <justification jstring="[hyper(128,a,172,a(flip),b,464,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 172 464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="780">
    <literal><![CDATA[
      (x * y) / (y * y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(300(a,1),464(a,2,2))].">
      <j1 rule="para" parents="300 464"/>
    </justification>
  </clause>

  <clause id="781">
    <literal><![CDATA[
      (x / y) * (y \ 1) = x / (y * y)
    ]]></literal>
    <justification jstring="[hyper(438,a,780,a),flip(a)].">
      <j1 rule="hyper" parents="438 780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="782">
    <literal><![CDATA[
      (x / (y \ 1)) * y = x * (y * y)
    ]]></literal>
    <justification jstring="[hyper(352,a,780,a),flip(a)].">
      <j1 rule="hyper" parents="352 780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="783">
    <literal><![CDATA[
      (x * (y \ 1)) \ (x * y) = y * y
    ]]></literal>
    <justification jstring="[hyper(214,a,780,a)].">
      <j1 rule="hyper" parents="214 780"/>
    </justification>
  </clause>

  <clause id="784">
    <literal><![CDATA[
      (x * y) * (y \ (y \ 1)) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,667,a,b,780,a)].">
      <j1 rule="hyper" parents="63 667 780"/>
    </justification>
  </clause>

  <clause id="785">
    <literal><![CDATA[
      R(x / y,y,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,108,a,b,780,a)].">
      <j1 rule="hyper" parents="63 108 780"/>
    </justification>
  </clause>

  <clause id="786">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,20,a,b,780,a),flip(a)].">
      <j1 rule="hyper" parents="63 20 780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="787">
    <literal><![CDATA[
      (x \ 1) \ R(y,x,x) = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(462,a,20,a,b,780,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="462 20 780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="788">
    <literal><![CDATA[
      R(x,y,y) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(131,a,20,a,b,780,a(flip))].">
      <j1 rule="hyper" parents="131 20 780"/>
    </justification>
  </clause>

  <clause id="789">
    <literal><![CDATA[
      (x * y) \ R(x,y,y) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,20,a,b,780,a(flip))].">
      <j1 rule="hyper" parents="128 20 780"/>
    </justification>
  </clause>

  <clause id="790">
    <literal><![CDATA[
      (x * y) \ (x * (y \ 1)) = y \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,780,a(flip),b,667,a)].">
      <j1 rule="hyper" parents="128 780 667"/>
    </justification>
  </clause>

  <clause id="791">
    <literal><![CDATA[
      T(x * (y \ 1),y * y) = (y * y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(780(a,1),113(a,1,1))].">
      <j1 rule="para" parents="780 113"/>
    </justification>
  </clause>

  <clause id="792">
    <literal><![CDATA[
      (x * (y * z)) / (z * z) = x * (y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(780(a,1),464(a,2,2))].">
      <j1 rule="para" parents="780 464"/>
    </justification>
  </clause>

  <clause id="793">
    <literal><![CDATA[
      R(T(x / y,z),y,y) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(785(a,1),27(a,2,1))].">
      <j1 rule="para" parents="785 27"/>
    </justification>
  </clause>

  <clause id="794">
    <literal><![CDATA[
      R(x,x \ y,x \ y) = y * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(80(a,1),785(a,1,1))].">
      <j1 rule="para" parents="80 785"/>
    </justification>
  </clause>

  <clause id="795">
    <literal><![CDATA[
      R(x,x,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,495,a(flip),b,786,a),flip(a)].">
      <j1 rule="hyper" parents="63 495 786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="796">
    <literal><![CDATA[
      R(x / y,y,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * (y \ 1) = z
    ]]></literal>
    <justification jstring="[para(786(a,1),353(a,1))].">
      <j1 rule="para" parents="786 353"/>
    </justification>
  </clause>

  <clause id="797">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = R(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[para(795(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="795 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="798">
    <literal><![CDATA[
      (x * (y * y)) / y = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(131,a,11,a(flip),b,781,a),flip(a)].">
      <j1 rule="hyper" parents="131 11 781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="799">
    <literal><![CDATA[
      (x \ 1) \ (y / (x * x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(y / x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(781(a,1),360(a,1,2))].">
      <j1 rule="para" parents="781 360"/>
    </justification>
  </clause>

  <clause id="800">
    <literal><![CDATA[
      (x * (y * y)) / y != z
    ]]></literal>
    <literal><![CDATA[
      x / (y \ 1) = z
    ]]></literal>
    <justification jstring="[para(782(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="782 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="801">
    <literal><![CDATA[
      (x * (y * y)) / y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ (x / (y \ 1)) = u
    ]]></literal>
    <justification jstring="[para(782(a,1),429(a,1,1))].">
      <j1 rule="para" parents="782 429"/>
    </justification>
  </clause>

  <clause id="802">
    <literal><![CDATA[
      (x * y) / (y * y) != z
    ]]></literal>
    <literal><![CDATA[
      x * (y \ 1) = z
    ]]></literal>
    <justification jstring="[para(783(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="783 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="803">
    <literal><![CDATA[
      (x / (y * y)) * z = x * ((y * y) \ z)
    ]]></literal>
    <justification jstring="[para(465(a,1),350(a,1,1))].">
      <j1 rule="para" parents="465 350"/>
    </justification>
  </clause>

  <clause id="804">
    <literal><![CDATA[
      T(x,x \ y) * z != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) * z = u
    ]]></literal>
    <justification jstring="[para(467(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="467 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="805">
    <literal><![CDATA[
      x / T(y,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x / ((y \ z) \ z) = u
    ]]></literal>
    <justification jstring="[para(473(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="473 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="806">
    <literal><![CDATA[
      T(x,(y \ z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      ((y \ z) \ z) \ (x * T(y,y \ z)) = u
    ]]></literal>
    <justification jstring="[para(478(a,1),386(a,1,1))].">
      <j1 rule="para" parents="478 386"/>
    </justification>
  </clause>

  <clause id="807">
    <literal><![CDATA[
      T(x / y,z) * y != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(490(a,1),280(a,1,1))].">
      <j1 rule="para" parents="490 280"/>
    </justification>
  </clause>

  <clause id="808">
    <literal><![CDATA[
      T(T(x / y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(490(a,1),362(a,1,1))].">
      <j1 rule="para" parents="490 362"/>
    </justification>
  </clause>

  <clause id="809">
    <literal><![CDATA[
      T((x * (y / z)) / x,z) = (x * (z \ y)) / x
    ]]></literal>
    <justification jstring="[para(113(a,1),504(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="113 504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="810">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(504(a,1),362(a,1,1))].">
      <j1 rule="para" parents="504 362"/>
    </justification>
  </clause>

  <clause id="812">
    <literal><![CDATA[
      x / (y * (x * x)) = (x \ 1) / y
    ]]></literal>
    <justification jstring="[para(300(a,1),703(a,1,1)),flip(a)].">
      <j1 rule="para" parents="300 703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="813">
    <literal><![CDATA[
      (x * (y / (z * z))) / u = (x * y) / (u * (z * z))
    ]]></literal>
    <justification jstring="[para(464(a,1),703(a,1,1))].">
      <j1 rule="para" parents="464 703"/>
    </justification>
  </clause>

  <clause id="814">
    <literal><![CDATA[
      (x * y) / (z * (y * y)) = (x * (y \ 1)) / z
    ]]></literal>
    <justification jstring="[para(780(a,1),703(a,1,1)),flip(a)].">
      <j1 rule="para" parents="780 703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="815">
    <literal><![CDATA[
      (x \ ((y * y) \ z)) * (y * y) = x \ T(z,y * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,726,a(flip),b,124,a),flip(a)].">
      <j1 rule="hyper" parents="128 726 124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="816">
    <literal><![CDATA[
      T((x \ 1) \ y,x * x) = (x \ y) * (x * x)
    ]]></literal>
    <justification jstring="[para(500(a,1),726(a,1,1)),flip(a)].">
      <j1 rule="para" parents="500 726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="817">
    <literal><![CDATA[
      (x \ y) / (z * z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ (y / (z * z)) = u
    ]]></literal>
    <justification jstring="[para(729(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="729 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="818">
    <literal><![CDATA[
      (x * (y / (z * z))) \ u = (z * z) * ((x * y) \ u)
    ]]></literal>
    <justification jstring="[para(464(a,1),777(a,1,1))].">
      <j1 rule="para" parents="464 777"/>
    </justification>
  </clause>

  <clause id="819">
    <literal><![CDATA[
      (x * x) * ((y * x) \ z) = (y * (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(780(a,1),777(a,1,1)),flip(a)].">
      <j1 rule="para" parents="780 777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="820">
    <literal><![CDATA[
      (x \ y) / (y * y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(300(a,1),779(a,2,2))].">
      <j1 rule="para" parents="300 779"/>
    </justification>
  </clause>

  <clause id="821">
    <literal><![CDATA[
      (x / y) \ (x \ 1) = y / (x * x)
    ]]></literal>
    <justification jstring="[para(83(a,1),820(a,1,1)),flip(a)].">
      <j1 rule="para" parents="83 820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="822">
    <literal><![CDATA[
      (x * x) * ((y \ x) \ z) = (y \ (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(820(a,1),777(a,1,1)),flip(a)].">
      <j1 rule="para" parents="820 777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="823">
    <literal><![CDATA[
      (x \ 1) / (y * (x \ 1)) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(220,a,780,a(flip),b,821,a)].">
      <j1 rule="hyper" parents="220 780 821"/>
    </justification>
  </clause>

  <clause id="824">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) \ 1) = y \ (x * ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(128,a,784,a(flip),b,165,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 784 165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="825">
    <literal><![CDATA[
      R(x,y,y) != z
    ]]></literal>
    <literal><![CDATA[
      (x * y) * (y \ 1) = z
    ]]></literal>
    <justification jstring="[para(11(a,1),796(a,1,1))].">
      <j1 rule="para" parents="11 796"/>
    </justification>
  </clause>

  <clause id="826">
    <literal><![CDATA[
      (x * (y \ (y \ 1))) * z = x * ((y * y) \ z)
    ]]></literal>
    <justification jstring="[para(667(a,2),803(a,1,1))].">
      <j1 rule="para" parents="667 803"/>
    </justification>
  </clause>

  <clause id="827">
    <literal><![CDATA[
      (x * (y / (z * z))) * u = (x * y) * ((z * z) \ u)
    ]]></literal>
    <justification jstring="[para(464(a,1),803(a,1,1))].">
      <j1 rule="para" parents="464 803"/>
    </justification>
  </clause>

  <clause id="828">
    <literal><![CDATA[
      (x * y) * ((y * y) \ z) = (x * (y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(780(a,1),803(a,1,1)),flip(a)].">
      <j1 rule="para" parents="780 803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="829">
    <literal><![CDATA[
      T(x,y * y) * ((y * y) \ z) = ((y * y) \ x) * z
    ]]></literal>
    <justification jstring="[para(772(a,1),803(a,1,1)),flip(a)].">
      <j1 rule="para" parents="772 803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="830">
    <literal><![CDATA[
      (x \ (y / (z * z))) * u = (x \ y) * ((z * z) \ u)
    ]]></literal>
    <justification jstring="[para(779(a,1),803(a,1,1))].">
      <j1 rule="para" parents="779 803"/>
    </justification>
  </clause>

  <clause id="831">
    <literal><![CDATA[
      (x \ y) * ((y * y) \ z) = (x \ (y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(820(a,1),803(a,1,1)),flip(a)].">
      <j1 rule="para" parents="820 803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="832">
    <literal><![CDATA[
      (x * y) / a(x / z,z,y) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,164,a(flip),b,86,a)].">
      <j1 rule="hyper" parents="131 164 86"/>
    </justification>
  </clause>

  <clause id="833">
    <literal><![CDATA[
      x \ ((y * (z * u)) * a(y,z,u)) = x \ ((y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(128,a,86,a,b,10,a)].">
      <j1 rule="hyper" parents="128 86 10"/>
    </justification>
  </clause>

  <clause id="834">
    <literal><![CDATA[
      (x * y) * a(x,z,z \ y) = (x * z) * (z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),86(a,1,1,2))].">
      <j1 rule="para" parents="10 86"/>
    </justification>
  </clause>

  <clause id="835">
    <literal><![CDATA[
      x * a(x,y,y \ 1) = (x * y) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(73(a,1),86(a,1,1))].">
      <j1 rule="para" parents="73 86"/>
    </justification>
  </clause>

  <clause id="836">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(86(a,1),356(a,1,2))].">
      <j1 rule="para" parents="86 356"/>
    </justification>
  </clause>

  <clause id="837">
    <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(86(a,1),99(a,2,1))].">
      <j1 rule="para" parents="86 99"/>
    </justification>
  </clause>

  <clause id="838">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(86(a,1),637(a,1,2))].">
      <j1 rule="para" parents="86 637"/>
    </justification>
  </clause>

  <clause id="839">
    <literal><![CDATA[
      x * L(L(y,z \ x,z),u,w) = z * ((z \ x) * L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(134,a,30,a,b,98,a)].">
      <j1 rule="hyper" parents="134 30 98"/>
    </justification>
  </clause>

  <clause id="840">
    <literal><![CDATA[
      L(T(x,y \ z),y \ z,y) = z \ (y * (x * (y \ z)))
    ]]></literal>
    <justification jstring="[para(111(a,1),98(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 98"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="841">
    <literal><![CDATA[
      x * L(y,z \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      z * ((z \ x) * y) = u
    ]]></literal>
    <justification jstring="[para(98(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="98 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="842">
    <literal><![CDATA[
      (x * y) / T(z * z,u) = x * (y / T(z * z,u))
    ]]></literal>
    <justification jstring="[hyper(220,a,554,a(flip),b,100,a(flip))].">
      <j1 rule="hyper" parents="220 554 100"/>
    </justification>
  </clause>

  <clause id="843">
    <literal><![CDATA[
      R(x,x \ y,(x \ y) \ z) = (y * ((x \ y) \ z)) / z
    ]]></literal>
    <justification jstring="[para(10(a,1),104(a,2,2))].">
      <j1 rule="para" parents="10 104"/>
    </justification>
  </clause>

  <clause id="844">
    <literal><![CDATA[
      R(x,x \ y,z) \ (y * z) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * ((x \ y) * z) = w
    ]]></literal>
    <justification jstring="[para(104(a,2),638(a,1,1))].">
      <j1 rule="para" parents="104 638"/>
    </justification>
  </clause>

  <clause id="845">
    <literal><![CDATA[
      (x * y) * (y \ (1 / y)) = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(133,a,599,a(flip),b,106,a),flip(a)].">
      <j1 rule="hyper" parents="133 599 106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="846">
    <literal><![CDATA[
      L(R(x,y,y \ z),u,w) * z = (L(x,u,w) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(133,a,29,a(flip),b,106,a)].">
      <j1 rule="hyper" parents="133 29 106"/>
    </justification>
  </clause>

  <clause id="847">
    <literal><![CDATA[
      R(x,y,y \ z) * z != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(106(a,1),280(a,1,1))].">
      <j1 rule="para" parents="106 280"/>
    </justification>
  </clause>

  <clause id="848">
    <literal><![CDATA[
      R(x,x,x \ y) = ((x \ 1) \ y) / y
    ]]></literal>
    <justification jstring="[para(495(a,1),106(a,1,1)),flip(a)].">
      <j1 rule="para" parents="495 106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="849">
    <literal><![CDATA[
      (x / y) * (1 / y) = x * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(353,a,845,a),flip(a)].">
      <j1 rule="hyper" parents="353 845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="850">
    <literal><![CDATA[
      R(x,1 / y,y) != z
    ]]></literal>
    <literal><![CDATA[
      (x * (1 / y)) * y = z
    ]]></literal>
    <justification jstring="[para(109(a,1),195(a,1)),flip(b)].">
      <j1 rule="para" parents="109 195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="851">
    <literal><![CDATA[
      (x * y) * (y \ (x \ 1)) = a(x,y,y \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(193,a,210,a,b,76,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="193 210 76"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="852">
    <literal><![CDATA[
      a(x,x \ y,(x \ y) \ 1) = x \ (y * ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[para(10(a,1),243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="853">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(585(a,1),243(a,1,2))].">
      <j1 rule="para" parents="585 243"/>
    </justification>
  </clause>

  <clause id="854">
    <literal><![CDATA[
      x * a(x,y,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(150,a,853,a)].">
      <j1 rule="hyper" parents="150 853"/>
    </justification>
  </clause>

  <clause id="855">
    <literal><![CDATA[
      L(x \ a(y,z,z \ 1),x,y) = (y * x) \ R(y,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(853(a,1),329(a,1,1,2))].">
      <j1 rule="para" parents="853 329"/>
    </justification>
  </clause>

  <clause id="856">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(854(a,1),356(a,1,2))].">
      <j1 rule="para" parents="854 356"/>
    </justification>
  </clause>

  <clause id="857">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = T(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,25,a(flip),b,263,a),flip(a)].">
      <j1 rule="hyper" parents="347 25 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      L(T(x,y),y,z / y) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[para(12(a,1),263(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="859">
    <literal><![CDATA[
      L(T(x,y \ z),y \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      z \ (y * (x * (y \ z))) = u
    ]]></literal>
    <justification jstring="[para(263(a,1),374(a,1))].">
      <j1 rule="para" parents="263 374"/>
    </justification>
  </clause>

  <clause id="861">
    <literal><![CDATA[
      x * R(T(y,x),z,z \ x) = (y * z) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,268,a,b,392,a)].">
      <j1 rule="hyper" parents="63 268 392"/>
    </justification>
  </clause>

  <clause id="862">
    <literal><![CDATA[
      x * R(x,y,y \ x) = (x * y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,273,a(flip),b,392,a)].">
      <j1 rule="hyper" parents="63 273 392"/>
    </justification>
  </clause>

  <clause id="863">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (z * ((y * x) \ y)) = T(z,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,22,a,b,409,a),flip(a)].">
      <j1 rule="hyper" parents="347 22 409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="864">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,415,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="134 415 18"/>
    </justification>
  </clause>

  <clause id="865">
    <literal><![CDATA[
      R(T(1 / x,x * y),x,y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(386,a,423,a),flip(a)].">
      <j1 rule="hyper" parents="386 423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="866">
    <literal><![CDATA[
      T(x / (y * x),y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(113(a,1),423(a,2,1))].">
      <j1 rule="para" parents="113 423"/>
    </justification>
  </clause>

  <clause id="867">
    <literal><![CDATA[
      (x / (y * x)) * y = y * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,866,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 866 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="868">
    <literal><![CDATA[
      R((x / y) \ 1,x / y,y) = T(y / x,x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),866(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="869">
    <literal><![CDATA[
      x * R(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y / (x * y)) * x = z
    ]]></literal>
    <justification jstring="[para(866(a,1),315(a,1,2))].">
      <j1 rule="para" parents="866 315"/>
    </justification>
  </clause>

  <clause id="870">
    <literal><![CDATA[
      x * ((T(y,x) \ z) \ z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y,T(y,x) \ z) = u
    ]]></literal>
    <justification jstring="[para(112(a,1),425(a,1,2))].">
      <j1 rule="para" parents="112 425"/>
    </justification>
  </clause>

  <clause id="871">
    <literal><![CDATA[
      (1 / x) * (x \ 1) != y * z
    ]]></literal>
    <literal><![CDATA[
      y \ (x \ (x \ 1)) = z
    ]]></literal>
    <justification jstring="[para(784(a,1),432(a,1))].">
      <j1 rule="para" parents="784 432"/>
    </justification>
  </clause>

  <clause id="872">
    <literal><![CDATA[
      x * T(x \ (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(22(a,1),435(a,1,2,1))].">
      <j1 rule="para" parents="22 435"/>
    </justification>
  </clause>

  <clause id="873">
    <literal><![CDATA[
      L(L(x \ 1,x,y) \ z,(y * x) \ y,y * x) = y \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(444(a,1),98(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="444 98"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="874">
    <literal><![CDATA[
      x \ (L(y,x \ z,x) * z) = (x \ z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,267,a(flip),b,476,a(flip))].">
      <j1 rule="hyper" parents="128 267 476"/>
    </justification>
  </clause>

  <clause id="875">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y \ x,y) = u
    ]]></literal>
    <justification jstring="[para(476(a,1),356(a,1,2))].">
      <j1 rule="para" parents="476 356"/>
    </justification>
  </clause>

  <clause id="876">
    <literal><![CDATA[
      x \ (y * L(z,x \ y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * z = u
    ]]></literal>
    <justification jstring="[para(476(a,2),356(a,1,2))].">
      <j1 rule="para" parents="476 356"/>
    </justification>
  </clause>

  <clause id="877">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,16,a,b,480,a)].">
      <j1 rule="hyper" parents="347 16 480"/>
    </justification>
  </clause>

  <clause id="878">
    <literal><![CDATA[
      L(T(x \ T(y,z),u),x,z) = T((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(480(a,1),25(a,2,1))].">
      <j1 rule="para" parents="480 25"/>
    </justification>
  </clause>

  <clause id="879">
    <literal><![CDATA[
      L((x * x) \ T(y,(z * x) \ z),x * x,(z * x) \ z) = L(x,x,z) \ (y * ((z * x) \ z))
    ]]></literal>
    <justification jstring="[para(730(a,1),480(a,2,1))].">
      <j1 rule="para" parents="730 480"/>
    </justification>
  </clause>

  <clause id="880">
    <literal><![CDATA[
      x \ (y * T(y \ x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(111(a,2),512(a,1,2))].">
      <j1 rule="para" parents="111 512"/>
    </justification>
  </clause>

  <clause id="881">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(z,y),y,x) = u
    ]]></literal>
    <justification jstring="[para(528(a,1),359(a,1,1))].">
      <j1 rule="para" parents="528 359"/>
    </justification>
  </clause>

  <clause id="882">
    <literal><![CDATA[
      L(x \ y,x,y / x) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(269,a,169,a(flip),b,532,a),flip(a)].">
      <j1 rule="hyper" parents="269 169 532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="884">
    <literal><![CDATA[
      (x / y) \ (L(z,y,x / y) * x) = y * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,267,a(flip),b,532,a(flip))].">
      <j1 rule="hyper" parents="128 267 532"/>
    </justification>
  </clause>

  <clause id="885">
    <literal><![CDATA[
      x \ ((1 / x) * y) = (x \ (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(551(a,1),538(a,1,2,2))].">
      <j1 rule="para" parents="551 538"/>
    </justification>
  </clause>

  <clause id="886">
    <literal><![CDATA[
      (x \ (1 / x)) * x = x \ 1
    ]]></literal>
    <justification jstring="[para(12(a,1),885(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="887">
    <literal><![CDATA[
      T(x \ (1 / x),x) = x \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(462,a,xx,b,886,a)].">
      <j1 rule="hyper" parents="462 886"/>
    </justification>
  </clause>

  <clause id="888">
    <literal><![CDATA[
      (x \ 1) / x = x \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(145,a,886,a)].">
      <j1 rule="hyper" parents="145 886"/>
    </justification>
  </clause>

  <clause id="889">
    <literal><![CDATA[
      (x * (y \ 1)) / L(y,y \ (1 / y),x) = x * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[para(886(a,1),212(a,1,1,2))].">
      <j1 rule="para" parents="886 212"/>
    </justification>
  </clause>

  <clause id="890">
    <literal><![CDATA[
      a(x,y,z) = L(((x * y) \ (x * (y * z))) \ z,(x * y) \ (x * (y * z)),x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,14,a,b,561,a)].">
      <j1 rule="hyper" parents="347 14 561"/>
    </justification>
  </clause>

  <clause id="891">
    <literal><![CDATA[
      L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(561(a,1),25(a,2,1))].">
      <j1 rule="para" parents="561 25"/>
    </justification>
  </clause>

  <clause id="892">
    <literal><![CDATA[
      L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(561(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="561 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="893">
    <literal><![CDATA[
      L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(561(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="561 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="894">
    <literal><![CDATA[
      L(L(x,y,z),z * y,u / (z * y)) = u \ ((u / (z * y)) * (z * (y * x)))
    ]]></literal>
    <justification jstring="[para(18(a,2),565(a,1,1))].">
      <j1 rule="para" parents="18 565"/>
    </justification>
  </clause>

  <clause id="895">
    <literal><![CDATA[
      L(x \ y,x,R(1 / z,z,z \ x)) = (z \ x) \ (((z \ x) / x) * y)
    ]]></literal>
    <justification jstring="[para(421(a,2),565(a,1,3))].">
      <j1 rule="para" parents="421 565"/>
    </justification>
  </clause>

  <clause id="896">
    <literal><![CDATA[
      x / ((y * y) \ z) = (x / z) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(220,a,534,a(flip),b,566,a(flip))].">
      <j1 rule="hyper" parents="220 534 566"/>
    </justification>
  </clause>

  <clause id="897">
    <literal><![CDATA[
      (x / (y * z)) * (y * y) = x / L(y \ z,y,y)
    ]]></literal>
    <justification jstring="[para(99(a,2),896(a,1,2)),flip(a)].">
      <j1 rule="para" parents="99 896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="898">
    <literal><![CDATA[
      R(x,x \ y,y \ z) \ z = (x \ y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),578(a,1,2))].">
      <j1 rule="para" parents="10 578"/>
    </justification>
  </clause>

  <clause id="899">
    <literal><![CDATA[
      R(x,x \ (y / z),z) \ y = (x \ (y / z)) * z
    ]]></literal>
    <justification jstring="[para(12(a,1),578(a,1,2))].">
      <j1 rule="para" parents="12 578"/>
    </justification>
  </clause>

  <clause id="900">
    <literal><![CDATA[
      (x * y) / ((z \ x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(z,z \ x,y) = u
    ]]></literal>
    <justification jstring="[para(578(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="578 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="901">
    <literal><![CDATA[
      R(1 / x,x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) / y = z
    ]]></literal>
    <justification jstring="[para(606(a,2),319(a,1))].">
      <j1 rule="para" parents="606 319"/>
    </justification>
  </clause>

  <clause id="902">
    <literal><![CDATA[
      (x * (y * y)) / z = x / (z / (y * y))
    ]]></literal>
    <justification jstring="[hyper(598,a,607,a),flip(a)].">
      <j1 rule="hyper" parents="598 607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="903">
    <literal><![CDATA[
      (x * (y \ (1 / y))) / z = x / (z / (y \ (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,599,a(flip),b,607,a),flip(a)].">
      <j1 rule="hyper" parents="63 599 607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="904">
    <literal><![CDATA[
      R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(607(a,1),27(a,2,1))].">
      <j1 rule="para" parents="607 27"/>
    </justification>
  </clause>

  <clause id="905">
    <literal><![CDATA[
      R(x / R(1 / y,y,z),z / (y * z),y * z) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[para(247(a,2),607(a,1,1,2))].">
      <j1 rule="para" parents="247 607"/>
    </justification>
  </clause>

  <clause id="906">
    <literal><![CDATA[
      (x * (y * y)) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / (z / (y * y)) = u
    ]]></literal>
    <justification jstring="[para(607(a,1),598(a,1))].">
      <j1 rule="para" parents="607 598"/>
    </justification>
  </clause>

  <clause id="907">
    <literal><![CDATA[
      (x * (y * (z * z))) / u = (x * y) / (u / (z * z))
    ]]></literal>
    <justification jstring="[para(33(a,1),902(a,1,1))].">
      <j1 rule="para" parents="33 902"/>
    </justification>
  </clause>

  <clause id="908">
    <literal><![CDATA[
      T(x,y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(x,y) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),632(a,1))].">
      <j1 rule="para" parents="22 632"/>
    </justification>
  </clause>

  <clause id="909">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),y) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) \ (y * z) = u
    ]]></literal>
    <justification jstring="[para(99(a,2),650(a,1))].">
      <j1 rule="para" parents="99 650"/>
    </justification>
  </clause>

  <clause id="910">
    <literal><![CDATA[
      R(x,T(y,x),(y * x) \ z) \ z = T(y,x) * ((y * x) \ z)
    ]]></literal>
    <justification jstring="[para(213(a,1),693(a,1,1,1))].">
      <j1 rule="para" parents="213 693"/>
    </justification>
  </clause>

  <clause id="911">
    <literal><![CDATA[
      (x / y) \ (1 / x) = y * (x \ (1 / x))
    ]]></literal>
    <justification jstring="[para(599(a,1),693(a,1,1))].">
      <j1 rule="para" parents="599 693"/>
    </justification>
  </clause>

  <clause id="912">
    <literal><![CDATA[
      (x \ y) * (y \ (1 / y)) = x \ (1 / y)
    ]]></literal>
    <justification jstring="[hyper(646,a,911,a),flip(a)].">
      <j1 rule="hyper" parents="646 911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="913">
    <literal><![CDATA[
      x * (y \ (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      x / (y * y) = z
    ]]></literal>
    <justification jstring="[para(501(a,1),723(a,1,2))].">
      <j1 rule="para" parents="501 723"/>
    </justification>
  </clause>

  <clause id="914">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = T(x / y,z) * y
    ]]></literal>
    <justification jstring="[hyper(131,a,793,a(flip),b,786,a)].">
      <j1 rule="hyper" parents="131 793 786"/>
    </justification>
  </clause>

  <clause id="915">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x) = R(y,x,x)
    ]]></literal>
    <justification jstring="[para(254(a,1),793(a,1,1)),flip(a)].">
      <j1 rule="para" parents="254 793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="916">
    <literal><![CDATA[
      ((x * y) * (x \ 1)) * x = x * R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,915,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 915 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="917">
    <literal><![CDATA[
      x * R(y,x,x) != z
    ]]></literal>
    <literal><![CDATA[
      ((x * y) * (x \ 1)) * x = z
    ]]></literal>
    <justification jstring="[para(915(a,1),315(a,1,2))].">
      <j1 rule="para" parents="915 315"/>
    </justification>
  </clause>

  <clause id="918">
    <literal><![CDATA[
      T(T(x,y),x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(11(a,1),810(a,1,1,1))].">
      <j1 rule="para" parents="11 810"/>
    </justification>
  </clause>

  <clause id="919">
    <literal><![CDATA[
      T(L(x,y \ z,y),y \ z) = z \ (y * (x * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(374,a,857,a),flip(a)].">
      <j1 rule="hyper" parents="374 857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="920">
    <literal><![CDATA[
      (1 / x) \ T(L(y,x,1 / x),x) = y * x
    ]]></literal>
    <justification jstring="[hyper(128,a,857,a(flip),b,184,a(flip))].">
      <j1 rule="hyper" parents="128 857 184"/>
    </justification>
  </clause>

  <clause id="921">
    <literal><![CDATA[
      T(L(x,y,z / y),y) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[para(12(a,1),857(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="922">
    <literal><![CDATA[
      x * R(x \ y,x,x) = (y * (x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),916(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="923">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(559(a,1),920(a,1,2,1))].">
      <j1 rule="para" parents="559 920"/>
    </justification>
  </clause>

  <clause id="924">
    <literal><![CDATA[
      L(x,y,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * (y * x) = z
    ]]></literal>
    <justification jstring="[para(184(a,1),151(a,2))].">
      <j1 rule="para" parents="184 151"/>
    </justification>
  </clause>

  <clause id="925">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (y * z) != v5
    ]]></literal>
    <literal><![CDATA[
      (L(x,u,w) * y) * z = v5
    ]]></literal>
    <justification jstring="[para(29(a,1),314(a,1,1))].">
      <j1 rule="para" parents="29 314"/>
    </justification>
  </clause>

  <clause id="927">
    <literal><![CDATA[
      R(x,y,T(z,y)) * (z * y) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * T(z,y) = u
    ]]></literal>
    <justification jstring="[para(111(a,1),314(a,1,2))].">
      <j1 rule="para" parents="111 314"/>
    </justification>
  </clause>

  <clause id="928">
    <literal><![CDATA[
      x * L(y,z,x / z) != u
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * y) = u
    ]]></literal>
    <justification jstring="[para(12(a,1),322(a,1,1))].">
      <j1 rule="para" parents="12 322"/>
    </justification>
  </clause>

  <clause id="929">
    <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),322(a,1,2))].">
      <j1 rule="para" parents="25 322"/>
    </justification>
  </clause>

  <clause id="930">
    <literal><![CDATA[
      (x * y) * L(L(z,y,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (y * L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(30(a,1),322(a,1,2))].">
      <j1 rule="para" parents="30 322"/>
    </justification>
  </clause>

  <clause id="931">
    <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(342(a,1),315(a,1,2))].">
      <j1 rule="para" parents="342 315"/>
    </justification>
  </clause>

  <clause id="932">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = R((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,27,a,b,343,a)].">
      <j1 rule="hyper" parents="63 27 343"/>
    </justification>
  </clause>

  <clause id="933">
    <literal><![CDATA[
      T(x,y \ z) != R((y \ z) \ z,u,w)
    ]]></literal>
    <literal><![CDATA[
      R(y,u,w) = x
    ]]></literal>
    <justification jstring="[para(343(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="343 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="934">
    <literal><![CDATA[
      ((x \ 1) * y) * (x * x) = x * T(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,33,a,b,496,a)].">
      <j1 rule="hyper" parents="63 33 496"/>
    </justification>
  </clause>

  <clause id="935">
    <literal><![CDATA[
      T(T(x,y \ 1),y * y) / (y * y) = y \ (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,772,a,b,498,a)].">
      <j1 rule="hyper" parents="63 772 498"/>
    </justification>
  </clause>

  <clause id="936">
    <literal><![CDATA[
      (x \ (y * y)) * T(z,y * y) = (x \ 1) * (z * (y * y))
    ]]></literal>
    <justification jstring="[hyper(639,a,516,a),flip(a)].">
      <j1 rule="hyper" parents="639 516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="937">
    <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(91(a,1),544(a,1,1)),flip(a)].">
      <j1 rule="para" parents="91 544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="938">
    <literal><![CDATA[
      K(x \ 1,x) * y != (x \ 1) * (x * z)
    ]]></literal>
    <literal><![CDATA[
      L(z,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(290(a,2),544(a,1,1))].">
      <j1 rule="para" parents="290 544"/>
    </justification>
  </clause>

  <clause id="939">
    <literal><![CDATA[
      T(x,x * x) != y
    ]]></literal>
    <literal><![CDATA[
      L(x,x,x) = y
    ]]></literal>
    <justification jstring="[para(22(a,2),545(a,1))].">
      <j1 rule="para" parents="22 545"/>
    </justification>
  </clause>

  <clause id="941">
    <literal><![CDATA[
      (x * y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ (x \ z),y,x) = u
    ]]></literal>
    <justification jstring="[para(76(a,1),545(a,1,2))].">
      <j1 rule="para" parents="76 545"/>
    </justification>
  </clause>

  <clause id="942">
    <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(97(a,1),545(a,1,2,2))].">
      <j1 rule="para" parents="97 545"/>
    </justification>
  </clause>

  <clause id="943">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (((x \ y) \ y) * (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,z,(x \ y) \ y) = w
    ]]></literal>
    <justification jstring="[para(339(a,2),545(a,1,1))].">
      <j1 rule="para" parents="339 545"/>
    </justification>
  </clause>

  <clause id="944">
    <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(86(a,1),545(a,1,2,2))].">
      <j1 rule="para" parents="86 545"/>
    </justification>
  </clause>

  <clause id="945">
    <literal><![CDATA[
      R(x / y,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) / (y * z) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),682(a,1,1,1))].">
      <j1 rule="para" parents="11 682"/>
    </justification>
  </clause>

  <clause id="946">
    <literal><![CDATA[
      x \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      L((y \ x) \ z,y \ x,y) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),686(a,1,1))].">
      <j1 rule="para" parents="10 686"/>
    </justification>
  </clause>

  <clause id="947">
    <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(108(a,2),740(a,1,1,1))].">
      <j1 rule="para" parents="108 740"/>
    </justification>
  </clause>

  <clause id="948">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) * (x \ y) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(408(a,1),740(a,2,2))].">
      <j1 rule="para" parents="408 740"/>
    </justification>
  </clause>

  <clause id="949">
    <literal><![CDATA[
      L((x * y) / x,z,u) = (x * L(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(145,a,741,a),flip(a)].">
      <j1 rule="hyper" parents="145 741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="950">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) = (x * (y * z)) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,97,a(flip),b,741,a),flip(a)].">
      <j1 rule="hyper" parents="131 97 741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="951">
    <literal><![CDATA[
      (x * L(y,z,u)) / x != w
    ]]></literal>
    <literal><![CDATA[
      L((x * y) / x,z,u) = w
    ]]></literal>
    <justification jstring="[para(741(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="741 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="952">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) / x = R(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,746,a)].">
      <j1 rule="hyper" parents="145 746"/>
    </justification>
  </clause>

  <clause id="953">
    <literal><![CDATA[
      ((x * y) / (z * y)) * z = z * R(z \ x,z,y)
    ]]></literal>
    <justification jstring="[para(108(a,1),746(a,1,1))].">
      <j1 rule="para" parents="108 746"/>
    </justification>
  </clause>

  <clause id="954">
    <literal><![CDATA[
      ((x * (y \ z)) / z) * y = y * R(y \ x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(606(a,1),746(a,1,1))].">
      <j1 rule="para" parents="606 746"/>
    </justification>
  </clause>

  <clause id="955">
    <literal><![CDATA[
      ((((x * y) * z) / (x * y)) * x) * y = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(314,a,747,a)].">
      <j1 rule="hyper" parents="314 747"/>
    </justification>
  </clause>

  <clause id="956">
    <literal><![CDATA[
      R((x * y) / x,z,u) = (x * R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(145,a,747,a),flip(a)].">
      <j1 rule="hyper" parents="145 747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="959">
    <literal><![CDATA[
      L(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(759(a,1),280(a,1,1))].">
      <j1 rule="para" parents="759 280"/>
    </justification>
  </clause>

  <clause id="960">
    <literal><![CDATA[
      T(L(x / y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(759(a,1),362(a,1,1))].">
      <j1 rule="para" parents="759 362"/>
    </justification>
  </clause>

  <clause id="961">
    <literal><![CDATA[
      (x * ((y * x) \ (y * z))) / x = L(z / x,x,y)
    ]]></literal>
    <justification jstring="[para(99(a,1),759(a,1,1,2))].">
      <j1 rule="para" parents="99 759"/>
    </justification>
  </clause>

  <clause id="962">
    <literal><![CDATA[
      L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z
    ]]></literal>
    <justification jstring="[para(329(a,1),759(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="329 759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="963">
    <literal><![CDATA[
      (x * ((1 / x) * y)) / x = L(y / x,x,1 / x)
    ]]></literal>
    <justification jstring="[para(559(a,1),759(a,1,1,2))].">
      <j1 rule="para" parents="559 759"/>
    </justification>
  </clause>

  <clause id="964">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[para(877(a,2),759(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="877 759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="965">
    <literal><![CDATA[
      (x * x) * ((y \ (x * x)) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      (y \ 1) \ z = u
    ]]></literal>
    <justification jstring="[para(776(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="776 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="966">
    <literal><![CDATA[
      (x * (y * (z \ 1))) / (z \ 1) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(131,a,792,a(flip),b,781,a)].">
      <j1 rule="hyper" parents="131 792 781"/>
    </justification>
  </clause>

  <clause id="967">
    <literal><![CDATA[
      T(x * (y * (z \ 1)),z * z) = (z * z) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[para(792(a,1),113(a,1,1))].">
      <j1 rule="para" parents="792 113"/>
    </justification>
  </clause>

  <clause id="968">
    <literal><![CDATA[
      (x * (y * z)) * ((z * z) \ u) = (x * (y * (z \ 1))) * u
    ]]></literal>
    <justification jstring="[para(792(a,1),803(a,1,1)),flip(a)].">
      <j1 rule="para" parents="792 803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="969">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / x = (y * (z / x)) / y
    ]]></literal>
    <justification jstring="[hyper(305,a,809,a)].">
      <j1 rule="hyper" parents="305 809"/>
    </justification>
  </clause>

  <clause id="970">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(134,a,809,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 809 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="971">
    <literal><![CDATA[
      x * ((y * (x \ z)) / y) != u
    ]]></literal>
    <literal><![CDATA[
      ((y * (z / x)) / y) * x = u
    ]]></literal>
    <justification jstring="[para(809(a,1),315(a,1,2))].">
      <j1 rule="para" parents="809 315"/>
    </justification>
  </clause>

  <clause id="972">
    <literal><![CDATA[
      T(((x * x) * (y / x)) / (x * x),x) = ((x \ 1) \ y) / (x * x)
    ]]></literal>
    <justification jstring="[para(495(a,1),809(a,2,1))].">
      <j1 rule="para" parents="495 809"/>
    </justification>
  </clause>

  <clause id="973">
    <literal><![CDATA[
      (x * x) \ ((y * (x \ 1)) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(138,a,819,a)].">
      <j1 rule="hyper" parents="138 819"/>
    </justification>
  </clause>

  <clause id="974">
    <literal><![CDATA[
      (x \ 1) * ((y * (x \ 1)) \ z) = x * ((y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(134,a,819,a(flip),b,494,a)].">
      <j1 rule="hyper" parents="134 819 494"/>
    </justification>
  </clause>

  <clause id="975">
    <literal><![CDATA[
      ((x * y) * (x * y)) * (y \ z) = (x \ ((x * y) \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(9(a,1),822(a,1,2,1))].">
      <j1 rule="para" parents="9 822"/>
    </justification>
  </clause>

  <clause id="976">
    <literal><![CDATA[
      (x \ (x \ 1)) \ y = (x * x) * y
    ]]></literal>
    <justification jstring="[para(190(a,1),822(a,1,2)),flip(a)].">
      <j1 rule="para" parents="190 822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="977">
    <literal><![CDATA[
      ((x * x) \ y) / y = x \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(375,a,976,a)].">
      <j1 rule="hyper" parents="375 976"/>
    </justification>
  </clause>

  <clause id="978">
    <literal><![CDATA[
      (x * x) * (y * (x \ (x \ 1))) = T(y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(360,a,976,a),flip(a)].">
      <j1 rule="hyper" parents="360 976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="979">
    <literal><![CDATA[
      (x \ (x \ 1)) * y = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(355,a,976,a)].">
      <j1 rule="hyper" parents="355 976"/>
    </justification>
  </clause>

  <clause id="980">
    <literal><![CDATA[
      x \ y != (z * z) * y
    ]]></literal>
    <literal><![CDATA[
      z \ (z \ 1) = x
    ]]></literal>
    <justification jstring="[para(976(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="976 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="981">
    <literal><![CDATA[
      (x \ (x \ 1)) * y != z
    ]]></literal>
    <literal><![CDATA[
      (x * x) \ y = z
    ]]></literal>
    <justification jstring="[para(977(a,1),280(a,1,1))].">
      <j1 rule="para" parents="977 280"/>
    </justification>
  </clause>

  <clause id="982">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) \ y = ((1 / x) \ x) * y
    ]]></literal>
    <justification jstring="[para(83(a,1),979(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="83 979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="983">
    <literal><![CDATA[
      (x * (y \ (y \ 1))) * z = x * ((y \ (y \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(979(a,2),826(a,2,2))].">
      <j1 rule="para" parents="979 826"/>
    </justification>
  </clause>

  <clause id="984">
    <literal><![CDATA[
      x * (((y \ x) * (y \ x)) \ z) = (y * ((y \ x) \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(628,a,828,a)].">
      <j1 rule="hyper" parents="628 828"/>
    </justification>
  </clause>

  <clause id="985">
    <literal><![CDATA[
      ((x \ 1) * (x \ 1)) \ y = (x * ((x \ 1) \ 1)) * y
    ]]></literal>
    <justification jstring="[hyper(232,a,828,a)].">
      <j1 rule="hyper" parents="232 828"/>
    </justification>
  </clause>

  <clause id="986">
    <literal><![CDATA[
      (x * y) * T(y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(518(a,2),828(a,1,2))].">
      <j1 rule="para" parents="518 828"/>
    </justification>
  </clause>

  <clause id="987">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ z) = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(500(a,1),828(a,1,2)),flip(a)].">
      <j1 rule="para" parents="500 828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="988">
    <literal><![CDATA[
      (x \ (y \ 1)) * ((y \ 1) \ z) = (x \ y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(500(a,1),831(a,1,2)),flip(a)].">
      <j1 rule="para" parents="500 831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="989">
    <literal><![CDATA[
      (1 / x) * ((x \ y) * x) = T((1 / x) * y,x)
    ]]></literal>
    <justification jstring="[hyper(150,a,923,a)].">
      <j1 rule="hyper" parents="150 923"/>
    </justification>
  </clause>

  <clause id="990">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) * x = (1 / x) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),923(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="991">
    <literal><![CDATA[
      T(x,x \ y) \ R(T(z,z \ u),w,v5) = ((x \ y) \ y) \ R((z \ u) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(128,a,932,a,b,396,a)].">
      <j1 rule="hyper" parents="128 932 396"/>
    </justification>
  </clause>

  <clause id="992">
    <literal><![CDATA[
      ((x \ 1) * y) * ((x * x) * z) = (x * T(y,x * x)) * z
    ]]></literal>
    <justification jstring="[para(934(a,1),32(a,1,1)),flip(a)].">
      <j1 rule="para" parents="934 32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="993">
    <literal><![CDATA[
      R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      ((x * y) * z) / (y * z) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),945(a,1,1))].">
      <j1 rule="para" parents="11 945"/>
    </justification>
  </clause>

  <clause id="994">
    <literal><![CDATA[
      R(R(x,y,z),y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (((x * y) * z) * u) / ((y * z) * u) = w
    ]]></literal>
    <justification jstring="[para(20(a,2),945(a,1,1))].">
      <j1 rule="para" parents="20 945"/>
    </justification>
  </clause>

  <clause id="995">
    <literal><![CDATA[
      R(x,x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * z) / ((x \ y) * z) = u
    ]]></literal>
    <justification jstring="[para(80(a,1),945(a,1,1))].">
      <j1 rule="para" parents="80 945"/>
    </justification>
  </clause>

  <clause id="996">
    <literal><![CDATA[
      L((x * (y \ (z \ u))) / x,y,z) = (x * ((z * y) \ u)) / x
    ]]></literal>
    <justification jstring="[para(329(a,1),949(a,2,1,2))].">
      <j1 rule="para" parents="329 949"/>
    </justification>
  </clause>

  <clause id="997">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z / y) = (x * (z \ (z / y))) / x
    ]]></literal>
    <justification jstring="[para(414(a,1),949(a,2,1,2))].">
      <j1 rule="para" parents="414 949"/>
    </justification>
  </clause>

  <clause id="998">
    <literal><![CDATA[
      L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x
    ]]></literal>
    <justification jstring="[para(561(a,1),949(a,2,1,2))].">
      <j1 rule="para" parents="561 949"/>
    </justification>
  </clause>

  <clause id="999">
    <literal><![CDATA[
      R(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * R(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(952(a,1),280(a,1,1))].">
      <j1 rule="para" parents="952 280"/>
    </justification>
  </clause>

  <clause id="1000">
    <literal><![CDATA[
      (x * R(y,x,x \ 1)) / x = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,691,a(flip),b,956,a),flip(a)].">
      <j1 rule="hyper" parents="63 691 956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1001">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * R(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(956(a,2),280(a,1,1))].">
      <j1 rule="para" parents="956 280"/>
    </justification>
  </clause>

  <clause id="1002">
    <literal><![CDATA[
      R((x * ((y / z) / u)) / x,u,z) = (x * (y / (u * z))) / x
    ]]></literal>
    <justification jstring="[para(605(a,1),956(a,2,1,2))].">
      <j1 rule="para" parents="605 956"/>
    </justification>
  </clause>

  <clause id="1003">
    <literal><![CDATA[
      R((x * (y / z)) / x,z,z \ 1) = (x * (y * (z \ 1))) / x
    ]]></literal>
    <justification jstring="[para(691(a,1),956(a,2,1,2))].">
      <j1 rule="para" parents="691 956"/>
    </justification>
  </clause>

  <clause id="1004">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (((x * y) / x) * z) * u = w
    ]]></literal>
    <justification jstring="[para(956(a,1),314(a,1,1))].">
      <j1 rule="para" parents="956 314"/>
    </justification>
  </clause>

  <clause id="1005">
    <literal><![CDATA[
      T((1 / x) * (x * y),x) = (1 / x) * (y * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),989(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1006">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((1 / x) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(128,a,990,a(flip),b,330,a)].">
      <j1 rule="hyper" parents="128 990 330"/>
    </justification>
  </clause>

  <clause id="1007">
    <literal><![CDATA[
      ((x \ y) * (x \ y)) \ (x \ (y * (x \ y))) = a(x,x \ y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,459,a(flip),b,88,a)].">
      <j1 rule="hyper" parents="63 459 88"/>
    </justification>
  </clause>

  <clause id="1008">
    <literal><![CDATA[
      a(x,R(1 / y,y,z),y * z) = (x * z) \ ((x * (z / (y * z))) * (y * z))
    ]]></literal>
    <justification jstring="[para(247(a,2),89(a,2,2)),flip(a)].">
      <j1 rule="para" parents="247 89"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1009">
    <literal><![CDATA[
      x / L(y,z,x / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      (x / (z * y)) * z = u
    ]]></literal>
    <justification jstring="[para(101(a,2),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="101 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1010">
    <literal><![CDATA[
      R(x,y,(x * y) \ z) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y * ((x * y) \ z) = u
    ]]></literal>
    <justification jstring="[para(105(a,2),359(a,1,1))].">
      <j1 rule="para" parents="105 359"/>
    </justification>
  </clause>

  <clause id="1011">
    <literal><![CDATA[
      (x * y) * L(L(z,T(x,y),y),u,w) = y * (T(x,y) * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(134,a,30,a,b,262,a)].">
      <j1 rule="hyper" parents="134 30 262"/>
    </justification>
  </clause>

  <clause id="1012">
    <literal><![CDATA[
      T(((x * y) * x) / (x * y),y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,504,a(flip),b,265,a)].">
      <j1 rule="hyper" parents="63 504 265"/>
    </justification>
  </clause>

  <clause id="1013">
    <literal><![CDATA[
      T(R(x,y,T(x,y)),z) * (x * y) = (x * y) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(265(a,1),485(a,1,1,1))].">
      <j1 rule="para" parents="265 485"/>
    </justification>
  </clause>

  <clause id="1014">
    <literal><![CDATA[
      L(L(x \ 1,y * x,z),x,y) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,99,a(flip),b,416,a),flip(a)].">
      <j1 rule="hyper" parents="347 99 416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1015">
    <literal><![CDATA[
      (x * y) * L((x * y) \ x,z,u) = x * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,416,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 416 18"/>
    </justification>
  </clause>

  <clause id="1016">
    <literal><![CDATA[
      (x * y) * L((x * y) \ x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * L(y \ 1,z,u)) = w
    ]]></literal>
    <justification jstring="[para(416(a,1),322(a,1,2))].">
      <j1 rule="para" parents="416 322"/>
    </justification>
  </clause>

  <clause id="1017">
    <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),436(a,1,2,1))].">
      <j1 rule="para" parents="22 436"/>
    </justification>
  </clause>

  <clause id="1018">
    <literal><![CDATA[
      x * L(L(T(y,x),z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(L(y,z,u),w,v5) * x = v6
    ]]></literal>
    <justification jstring="[para(25(a,2),436(a,1,2,1))].">
      <j1 rule="para" parents="25 436"/>
    </justification>
  </clause>

  <clause id="1019">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = T(x / (z * y),u) * (z * y)
    ]]></literal>
    <justification jstring="[para(605(a,1),472(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="605 472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1020">
    <literal><![CDATA[
      x * (y * T(z,x * y)) != u * (x * y)
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(477(a,1),271(a,1)),flip(b)].">
      <j1 rule="para" parents="477 271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1021">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(99(a,1),477(a,1,2,1))].">
      <j1 rule="para" parents="99 477"/>
    </justification>
  </clause>

  <clause id="1022">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u))
    ]]></literal>
    <justification jstring="[para(329(a,1),477(a,1,2,1))].">
      <j1 rule="para" parents="329 477"/>
    </justification>
  </clause>

  <clause id="1023">
    <literal><![CDATA[
      (x * y) * T(T(x,x * y),z) = x * (y * T(T(x,y),z))
    ]]></literal>
    <justification jstring="[para(750(a,1),477(a,1,2,1))].">
      <j1 rule="para" parents="750 477"/>
    </justification>
  </clause>

  <clause id="1024">
    <literal><![CDATA[
      (L(x \ y,x,z) * u) \ (((z * x) \ (z * y)) * (u * w)) = L(w,u,(z * x) \ (z * y))
    ]]></literal>
    <justification jstring="[para(563(a,2),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="563 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1025">
    <literal><![CDATA[
      (L(x \ y,x,z) * u) \ (((z * x) \ (z * y)) * (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(w,u,L(x \ y,x,z)) = v5
    ]]></literal>
    <justification jstring="[para(563(a,1),545(a,1,2))].">
      <j1 rule="para" parents="563 545"/>
    </justification>
  </clause>

  <clause id="1026">
    <literal><![CDATA[
      L(T(T(x,y) \ z,u),T(x,y),y) = T((x * y) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(570(a,1),25(a,2,1))].">
      <j1 rule="para" parents="570 25"/>
    </justification>
  </clause>

  <clause id="1027">
    <literal><![CDATA[
      L(R(T(x,y) \ z,u,w),T(x,y),y) = R((x * y) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(570(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="570 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1028">
    <literal><![CDATA[
      L(L(T(x,y) \ z,u,w),T(x,y),y) = L((x * y) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(570(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="570 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1029">
    <literal><![CDATA[
      R(x,T(y,x),T(z,y * x)) \ (z * (y * x)) = T(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,250,a(flip),b,577,a)].">
      <j1 rule="hyper" parents="63 250 577"/>
    </justification>
  </clause>

  <clause id="1030">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,268,a,b,583,a(flip))].">
      <j1 rule="hyper" parents="34 268 583"/>
    </justification>
  </clause>

  <clause id="1031">
    <literal><![CDATA[
      (T(x,x * y) * y) * T(x,y) = T(x,y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,1030,a(flip),b,265,a),flip(a)].">
      <j1 rule="hyper" parents="133 1030 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1033">
    <literal><![CDATA[
      T((x * y) / (z * y),z) = R(z \ x,z,y)
    ]]></literal>
    <justification jstring="[para(113(a,1),608(a,2,1))].">
      <j1 rule="para" parents="113 608"/>
    </justification>
  </clause>

  <clause id="1034">
    <literal><![CDATA[
      R(x,y,z) = T(((y * x) * z) / (y * z),y)
    ]]></literal>
    <justification jstring="[para(254(a,1),608(a,2,1)),flip(a)].">
      <j1 rule="para" parents="254 608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1035">
    <literal><![CDATA[
      R(T(x / y,y * z),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * z) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(608(a,1),386(a,1))].">
      <j1 rule="para" parents="608 386"/>
    </justification>
  </clause>

  <clause id="1036">
    <literal><![CDATA[
      T((x * (y \ z)) / z,y) = R(y \ x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),1033(a,1,1,2))].">
      <j1 rule="para" parents="10 1033"/>
    </justification>
  </clause>

  <clause id="1037">
    <literal><![CDATA[
      R(x \ (y / z),x,z) = T(y / (x * z),x)
    ]]></literal>
    <justification jstring="[para(12(a,1),1033(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 1033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1038">
    <literal><![CDATA[
      R((x / y) \ z,x / y,y) = T((z * y) / x,x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),1033(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 1033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1039">
    <literal><![CDATA[
      T(R(x \ y,x,z),x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T((x * z) \ (y * z),x) = u
    ]]></literal>
    <justification jstring="[para(1033(a,1),808(a,1,1))].">
      <j1 rule="para" parents="1033 808"/>
    </justification>
  </clause>

  <clause id="1040">
    <literal><![CDATA[
      T(((1 / x) * y) * x,1 / x) = R(y,1 / x,x)
    ]]></literal>
    <justification jstring="[para(194(a,1),1034(a,2,1)),flip(a)].">
      <j1 rule="para" parents="194 1034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1041">
    <literal><![CDATA[
      T(R(x,y,x),y * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1034(a,2),304(a,1,1))].">
      <j1 rule="para" parents="1034 304"/>
    </justification>
  </clause>

  <clause id="1042">
    <literal><![CDATA[
      R(T(x,y * x),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,27,a,b,1041,a)].">
      <j1 rule="hyper" parents="63 27 1041"/>
    </justification>
  </clause>

  <clause id="1043">
    <literal><![CDATA[
      L(R(x,y,x),z,u) * (y * x) = (y * x) * L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(1041(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1041 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1044">
    <literal><![CDATA[
      R(R(x,y,x),z,u) * (y * x) = (y * x) * R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(1041(a,1),268(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1041 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1045">
    <literal><![CDATA[
      R(x,y,z) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      T(z,y * z) = x
    ]]></literal>
    <justification jstring="[para(1041(a,1),162(a,1)),flip(a)].">
      <j1 rule="para" parents="1041 162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1046">
    <literal><![CDATA[
      R(T(x,y),y / x,x) = T(x,y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),1042(a,1,1,2))].">
      <j1 rule="para" parents="12 1042"/>
    </justification>
  </clause>

  <clause id="1047">
    <literal><![CDATA[
      R(x,y / z,z) != T(z,y / z)
    ]]></literal>
    <literal><![CDATA[
      T(z,y) = x
    ]]></literal>
    <justification jstring="[para(1046(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="1046 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1048">
    <literal><![CDATA[
      R(x,1 / x,x) = T(x,1 / x)
    ]]></literal>
    <justification jstring="[para(223(a,1),1046(a,1,1))].">
      <j1 rule="para" parents="223 1046"/>
    </justification>
  </clause>

  <clause id="1049">
    <literal><![CDATA[
      R((x * x) \ (y / (x \ z)),x * x,x \ z) = T(y / ((x \ 1) \ z),x * x)
    ]]></literal>
    <justification jstring="[para(495(a,1),1037(a,2,1,2))].">
      <j1 rule="para" parents="495 1037"/>
    </justification>
  </clause>

  <clause id="1050">
    <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(621(a,1),322(a,1,2))].">
      <j1 rule="para" parents="621 322"/>
    </justification>
  </clause>

  <clause id="1051">
    <literal><![CDATA[
      (x * (y * (z * z))) \ u != w
    ]]></literal>
    <literal><![CDATA[
      (z * z) \ ((x * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(33(a,1),625(a,1,1))].">
      <j1 rule="para" parents="33 625"/>
    </justification>
  </clause>

  <clause id="1052">
    <literal><![CDATA[
      x \ y != z * (u \ (u * w))
    ]]></literal>
    <literal><![CDATA[
      x * (z * w) = y
    ]]></literal>
    <justification jstring="[para(9(a,1),634(a,2,2,2,2))].">
      <j1 rule="para" parents="9 634"/>
    </justification>
  </clause>

  <clause id="1054">
    <literal><![CDATA[
      (x / y) * (y * T(y \ 1,z)) = x * T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[para(666(a,2),532(a,1,2)),flip(a)].">
      <j1 rule="para" parents="666 532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1055">
    <literal><![CDATA[
      T((x \ y) / y,z) * y = (T(1 / x,z) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(133,a,671,a,b,106,a)].">
      <j1 rule="hyper" parents="133 671 106"/>
    </justification>
  </clause>

  <clause id="1056">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,688,a(flip),b,289,a),flip(a)].">
      <j1 rule="hyper" parents="128 688 289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1057">
    <literal><![CDATA[
      T(x / (1 / y),z) * (1 / y) = T(x * y,z) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,701,a(flip),b,294,a),flip(a)].">
      <j1 rule="hyper" parents="131 701 294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1058">
    <literal><![CDATA[
      R(x \ y,x,x \ 1) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[para(113(a,1),721(a,1,1))].">
      <j1 rule="para" parents="113 721"/>
    </justification>
  </clause>

  <clause id="1059">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(254(a,1),721(a,1,1)),flip(a)].">
      <j1 rule="para" parents="254 721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1060">
    <literal><![CDATA[
      x \ (y * (z * (u * u))) != w
    ]]></literal>
    <literal><![CDATA[
      (x \ (y * z)) * (u * u) = w
    ]]></literal>
    <justification jstring="[para(33(a,1),731(a,1,2))].">
      <j1 rule="para" parents="33 731"/>
    </justification>
  </clause>

  <clause id="1061">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * (y * T(y \ 1,x * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,411,a(flip),b,734,a)].">
      <j1 rule="hyper" parents="347 411 734"/>
    </justification>
  </clause>

  <clause id="1062">
    <literal><![CDATA[
      R(T(x,(y * z) * a(x,y,z)),y * z,a(x,y,z)) = ((y * z) * a(x,y,z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(128,a,86,a(flip),b,743,a),flip(a)].">
      <j1 rule="hyper" parents="128 86 743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1063">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(T(z,x * y),x,y) = u
    ]]></literal>
    <justification jstring="[para(743(a,1),356(a,1,2))].">
      <j1 rule="para" parents="743 356"/>
    </justification>
  </clause>

  <clause id="1064">
    <literal><![CDATA[
      (x * y) * T(y,x) = (y * x) * y
    ]]></literal>
    <justification jstring="[para(1042(a,1),743(a,1,2))].">
      <j1 rule="para" parents="1042 743"/>
    </justification>
  </clause>

  <clause id="1065">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(353,a,1064,a),flip(a)].">
      <j1 rule="hyper" parents="353 1064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1066">
    <literal><![CDATA[
      T(x,y) = (y * x) \ ((x * y) * x)
    ]]></literal>
    <justification jstring="[hyper(138,a,1064,a),flip(a)].">
      <j1 rule="hyper" parents="138 1064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1067">
    <literal><![CDATA[
      ((x \ 1) * x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,71,a(flip),b,1064,a)].">
      <j1 rule="hyper" parents="128 71 1064"/>
    </justification>
  </clause>

  <clause id="1068">
    <literal><![CDATA[
      T(x,y) != x
    ]]></literal>
    <literal><![CDATA[
      x * y = y * x
    ]]></literal>
    <justification jstring="[para(1066(a,2),153(a,1))].">
      <j1 rule="para" parents="1066 153"/>
    </justification>
  </clause>

  <clause id="1069">
    <literal><![CDATA[
      K(x \ 1,x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(290(a,2),1067(a,1,1))].">
      <j1 rule="para" parents="290 1067"/>
    </justification>
  </clause>

  <clause id="1070">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(134,a,112,a(flip),b,1069,a)].">
      <j1 rule="hyper" parents="134 112 1069"/>
    </justification>
  </clause>

  <clause id="1071">
    <literal><![CDATA[
      (x * y) \ (y * T(x,y / x)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[para(1065(a,1),89(a,1,2))].">
      <j1 rule="para" parents="1065 89"/>
    </justification>
  </clause>

  <clause id="1072">
    <literal><![CDATA[
      R(T(x,y * z),y,z) != (y * z) \ u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(744(a,1),47(a,1))].">
      <j1 rule="para" parents="744 47"/>
    </justification>
  </clause>

  <clause id="1073">
    <literal><![CDATA[
      L(T(R(x,y,z),u),u,x) = R(T(x,x * u),y,z)
    ]]></literal>
    <justification jstring="[para(27(a,1),753(a,1,1))].">
      <j1 rule="para" parents="27 753"/>
    </justification>
  </clause>

  <clause id="1074">
    <literal><![CDATA[
      T(T((x * y) / x,z),y * x) = L(T(y,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,25,a,b,758,a),flip(a)].">
      <j1 rule="hyper" parents="347 25 758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1075">
    <literal><![CDATA[
      (x * T(y,(x / z) * z)) / a(x / z,z,T(y,(x / z) * z)) = L(y,z,x / z) * ((x / z) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,734,a(flip),b,832,a),flip(a)].">
      <j1 rule="hyper" parents="347 734 832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1076">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / T(x * z,a(x,y,y \ z)) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(131,a,834,a(flip),b,111,a)].">
      <j1 rule="hyper" parents="131 834 111"/>
    </justification>
  </clause>

  <clause id="1077">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(128,a,164,a(flip),b,861,a),flip(a)].">
      <j1 rule="hyper" parents="128 164 861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1078">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(408(a,1),874(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="408 874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1079">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[para(561(a,1),874(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="561 874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1080">
    <literal><![CDATA[
      (x * (y * (z * z))) / u != w
    ]]></literal>
    <literal><![CDATA[
      (x * y) / (u / (z * z)) = w
    ]]></literal>
    <justification jstring="[para(33(a,1),906(a,1,1))].">
      <j1 rule="para" parents="33 906"/>
    </justification>
  </clause>

  <clause id="1081">
    <literal><![CDATA[
      x \ ((x / y) * ((y \ z) * y)) = T(x \ ((x / y) * z),y)
    ]]></literal>
    <justification jstring="[para(565(a,1),921(a,1,1)),flip(a)].">
      <j1 rule="para" parents="565 921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1082">
    <literal><![CDATA[
      L(((x / y) \ z) / y,y,x / y) = (y * (x \ z)) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),962(a,2,1,2,1))].">
      <j1 rule="para" parents="12 962"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = (z * T(y,x * z)) / z
    ]]></literal>
    <justification jstring="[para(22(a,2),962(a,2,1,2))].">
      <j1 rule="para" parents="22 962"/>
    </justification>
  </clause>

  <clause id="1084">
    <literal><![CDATA[
      L((x \ (T(x,y) * y)) / y,y,x) = (y * K(T(x,y),y)) / y
    ]]></literal>
    <justification jstring="[para(261(a,1),962(a,2,1,2))].">
      <j1 rule="para" parents="261 962"/>
    </justification>
  </clause>

  <clause id="1085">
    <literal><![CDATA[
      (x * (y * (x \ 1))) / x = (x * (y / x)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(691(a,1),1000(a,1,1,2))].">
      <j1 rule="para" parents="691 1000"/>
    </justification>
  </clause>

  <clause id="1086">
    <literal><![CDATA[
      R(x \ y,x,x \ z) * z = z * T(z \ (y * (x \ z)),x)
    ]]></literal>
    <justification jstring="[hyper(133,a,1036,a(flip),b,490,a)].">
      <j1 rule="hyper" parents="133 1036 490"/>
    </justification>
  </clause>

  <clause id="1088">
    <literal><![CDATA[
      R(x,y,z) != L(T(R(u,y,z),w),w,u)
    ]]></literal>
    <literal><![CDATA[
      T(u,u * w) = x
    ]]></literal>
    <justification jstring="[para(1073(a,2),51(a,1)),flip(a)].">
      <j1 rule="para" parents="1073 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1089">
    <literal><![CDATA[
      T(T(x,y),x * x) = L(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[para(11(a,1),1074(a,1,1,1))].">
      <j1 rule="para" parents="11 1074"/>
    </justification>
  </clause>

  <clause id="1090">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ z) = (u * (u \ z)) \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,174,a,b,1077,a),flip(a)].">
      <j1 rule="hyper" parents="347 174 1077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1091">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (T(y / z,x) * z) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(133,a,1077,a(flip),b,106,a)].">
      <j1 rule="hyper" parents="133 1077 106"/>
    </justification>
  </clause>

  <clause id="1092">
    <literal><![CDATA[
      (x * ((y * y) \ z)) * ((y * y) * u) = (x * T(z,y * y)) * u
    ]]></literal>
    <justification jstring="[para(726(a,1),125(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="726 125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1093">
    <literal><![CDATA[
      a(x,y,z) != 1
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = x * (y * z)
    ]]></literal>
    <justification jstring="[para(68(a,1),154(a,1)),flip(a),flip(b)].">
      <j1 rule="para" parents="68 154"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1094">
    <literal><![CDATA[
      L(L(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(L(x,u,w),y,z) = v5
    ]]></literal>
    <justification jstring="[para(470(a,1),230(a,1))].">
      <j1 rule="para" parents="470 230"/>
    </justification>
  </clause>

  <clause id="1095">
    <literal><![CDATA[
      L((x * y) \ x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(L(y \ 1,z,u),y,x) = w
    ]]></literal>
    <justification jstring="[para(244(a,1),1094(a,1,1))].">
      <j1 rule="para" parents="244 1094"/>
    </justification>
  </clause>

  <clause id="1096">
    <literal><![CDATA[
      T(x / (x / y),z) * (x / y) != u
    ]]></literal>
    <literal><![CDATA[
      (x / y) * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(505(a,1),280(a,1,1))].">
      <j1 rule="para" parents="505 280"/>
    </justification>
  </clause>

  <clause id="1097">
    <literal><![CDATA[
      L(x \ (1 / x),y,z) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(544,a,602,a)].">
      <j1 rule="hyper" parents="544 602"/>
    </justification>
  </clause>

  <clause id="1098">
    <literal><![CDATA[
      (x * y) * (z \ (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * (z \ (1 / z))) = u
    ]]></literal>
    <justification jstring="[para(1097(a,1),322(a,1,2))].">
      <j1 rule="para" parents="1097 322"/>
    </justification>
  </clause>

  <clause id="1099">
    <literal><![CDATA[
      L(K(x \ (y \ z),x),y \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      z \ (y * ((x \ (y \ z)) * x)) = u
    ]]></literal>
    <justification jstring="[para(92(a,1),651(a,1,1))].">
      <j1 rule="para" parents="92 651"/>
    </justification>
  </clause>

  <clause id="1100">
    <literal><![CDATA[
      x \ (y * (z * (u * (w * w)))) = (x \ (y * (z * u))) * (w * w)
    ]]></literal>
    <justification jstring="[para(33(a,1),728(a,1,2,2))].">
      <j1 rule="para" parents="33 728"/>
    </justification>
  </clause>

  <clause id="1101">
    <literal><![CDATA[
      (x \ (y * (z \ 1))) * (u * u) = x \ (y * (z \ (u * u)))
    ]]></literal>
    <justification jstring="[para(460(a,1),728(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="460 728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1102">
    <literal><![CDATA[
      (x * (y * (z * (u * u)))) \ w = (u * u) \ ((x * (y * z)) \ w)
    ]]></literal>
    <justification jstring="[para(33(a,1),775(a,1,1,2))].">
      <j1 rule="para" parents="33 775"/>
    </justification>
  </clause>

  <clause id="1103">
    <literal><![CDATA[
      (x * (y * (z / (u * u)))) * w = (x * (y * z)) * ((u * u) \ w)
    ]]></literal>
    <justification jstring="[para(464(a,1),827(a,1,1,2))].">
      <j1 rule="para" parents="464 827"/>
    </justification>
  </clause>

  <clause id="1104">
    <literal><![CDATA[
      (x \ (y * z)) * ((z * z) \ u) = (x \ (y * (z \ 1))) * u
    ]]></literal>
    <justification jstring="[para(780(a,1),830(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="780 830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1105">
    <literal><![CDATA[
      (x * ((x \ y) * z)) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),836(a,1,2,1))].">
      <j1 rule="para" parents="10 836"/>
    </justification>
  </clause>

  <clause id="1106">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * z) * T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(111(a,1),836(a,1,1,2))].">
      <j1 rule="para" parents="111 836"/>
    </justification>
  </clause>

  <clause id="1107">
    <literal><![CDATA[
      (x \ y) / T(z * z,u) = x \ (y / T(z * z,u))
    ]]></literal>
    <justification jstring="[hyper(649,a,842,a),flip(a)].">
      <j1 rule="hyper" parents="649 842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1108">
    <literal><![CDATA[
      x / T(y * y,x) = (y * y) \ x
    ]]></literal>
    <justification jstring="[hyper(648,a,842,a),flip(a)].">
      <j1 rule="hyper" parents="648 842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1109">
    <literal><![CDATA[
      x \ ((1 / x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ (1 / x)) * y = z
    ]]></literal>
    <justification jstring="[para(551(a,1),876(a,1,2,2))].">
      <j1 rule="para" parents="551 876"/>
    </justification>
  </clause>

  <clause id="1110">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,484,a(flip),b,914,a),flip(a)].">
      <j1 rule="hyper" parents="347 484 914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1111">
    <literal><![CDATA[
      T((x * y) * (x \ 1),z) = (x * T(y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,485,a(flip),b,914,a),flip(a)].">
      <j1 rule="hyper" parents="133 485 914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1112">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) = T(1 / x,y) * x
    ]]></literal>
    <justification jstring="[para(7(a,1),914(a,1,1,1))].">
      <j1 rule="para" parents="7 914"/>
    </justification>
  </clause>

  <clause id="1113">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(1112(a,2),807(a,1))].">
      <j1 rule="para" parents="1112 807"/>
    </justification>
  </clause>

  <clause id="1114">
    <literal><![CDATA[
      (x * ((y * z) / y)) / x = (y * ((x * z) / x)) / y
    ]]></literal>
    <justification jstring="[para(9(a,1),969(a,1,1,2,1,2))].">
      <j1 rule="para" parents="9 969"/>
    </justification>
  </clause>

  <clause id="1115">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x * (z \ y)) / x) = u
    ]]></literal>
    <justification jstring="[para(969(a,1),280(a,1,1))].">
      <j1 rule="para" parents="969 280"/>
    </justification>
  </clause>

  <clause id="1116">
    <literal><![CDATA[
      R((x * (y / z)) / x,z,z \ 1) / (z \ 1) = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,588,a,b,970,a)].">
      <j1 rule="hyper" parents="63 588 970"/>
    </justification>
  </clause>

  <clause id="1117">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(80(a,1),970(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="80 970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1118">
    <literal><![CDATA[
      ((x * R(y / z,z,u)) / x) * (z * u) = (z * u) * ((x * ((z * u) \ (y * u))) / x)
    ]]></literal>
    <justification jstring="[para(108(a,2),970(a,1,1,1,2))].">
      <j1 rule="para" parents="108 970"/>
    </justification>
  </clause>

  <clause id="1119">
    <literal><![CDATA[
      (x * x) * (y / (x * x)) = T(y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(667(a,1),978(a,1,2))].">
      <j1 rule="para" parents="667 978"/>
    </justification>
  </clause>

  <clause id="1120">
    <literal><![CDATA[
      T(x \ y,y \ (y \ 1)) = (y * y) * (x \ (y \ 1))
    ]]></literal>
    <justification jstring="[para(820(a,1),1119(a,1,2)),flip(a)].">
      <j1 rule="para" parents="820 1119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1121">
    <literal><![CDATA[
      ((x * x) * y) / (z * (x * x)) = T(y,x \ (x \ 1)) / z
    ]]></literal>
    <justification jstring="[para(1119(a,1),813(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1119 813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1122">
    <literal><![CDATA[
      R(x,y \ (y \ 1),z) = x
    ]]></literal>
    <justification jstring="[hyper(594,a,983,a)].">
      <j1 rule="hyper" parents="594 983"/>
    </justification>
  </clause>

  <clause id="1123">
    <literal><![CDATA[
      R(x,y \ (y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(1122(a,1),51(a,2))].">
      <j1 rule="para" parents="1122 51"/>
    </justification>
  </clause>

  <clause id="1124">
    <literal><![CDATA[
      R(x,(1 / y) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(83(a,1),1122(a,1,2,2))].">
      <j1 rule="para" parents="83 1122"/>
    </justification>
  </clause>

  <clause id="1125">
    <literal><![CDATA[
      (x * ((1 / y) \ y)) * z = x * (((1 / y) \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,1124,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 1124 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1126">
    <literal><![CDATA[
      (x / ((1 / y) \ y)) \ z = ((1 / y) \ y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(1124(a,1),693(a,1,1))].">
      <j1 rule="para" parents="1124 693"/>
    </justification>
  </clause>

  <clause id="1127">
    <literal><![CDATA[
      ((1 / x) \ x) * (x \ y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(1124(a,1),898(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1124 898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1128">
    <literal><![CDATA[
      x / (x \ 1) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(131,a,83,a(flip),b,1127,a)].">
      <j1 rule="hyper" parents="131 83 1127"/>
    </justification>
  </clause>

  <clause id="1129">
    <literal><![CDATA[
      ((1 / x) \ x) \ y = x \ ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,9,a(flip),b,1127,a)].">
      <j1 rule="hyper" parents="128 9 1127"/>
    </justification>
  </clause>

  <clause id="1130">
    <literal><![CDATA[
      (1 / (1 / x)) \ (1 / x) = (1 / x) / x
    ]]></literal>
    <justification jstring="[para(83(a,1),1128(a,1,2)),flip(a)].">
      <j1 rule="para" parents="83 1128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1131">
    <literal><![CDATA[
      ((1 / x) \ x) \ y != z
    ]]></literal>
    <literal><![CDATA[
      (x \ (1 / x)) * y = z
    ]]></literal>
    <justification jstring="[para(1129(a,2),1109(a,1))].">
      <j1 rule="para" parents="1129 1109"/>
    </justification>
  </clause>

  <clause id="1132">
    <literal><![CDATA[
      ((x \ 1) * (x \ 1)) \ y = (((x \ 1) \ 1) * x) * y
    ]]></literal>
    <justification jstring="[para(346(a,2),985(a,2,1))].">
      <j1 rule="para" parents="346 985"/>
    </justification>
  </clause>

  <clause id="1133">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,786,a(flip),b,987,a),flip(a)].">
      <j1 rule="hyper" parents="347 786 987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1134">
    <literal><![CDATA[
      T(T(x / y,(x / y) * y) * y,T(x / y,y)) = x
    ]]></literal>
    <justification jstring="[hyper(269,a,1031,a,b,168,a(flip))].">
      <j1 rule="hyper" parents="269 1031 168"/>
    </justification>
  </clause>

  <clause id="1135">
    <literal><![CDATA[
      T(T(x,x * y) * y,T(x,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(269,a,1031,a,b,xx)].">
      <j1 rule="hyper" parents="269 1031"/>
    </justification>
  </clause>

  <clause id="1136">
    <literal><![CDATA[
      x \ T(x * (y * (x \ 1)),z) = T(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(872,a,1056,a),flip(a)].">
      <j1 rule="hyper" parents="872 1056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1137">
    <literal><![CDATA[
      x \ T(x * y,x \ 1) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(315,a,1056,a),flip(a)].">
      <j1 rule="hyper" parents="315 1056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1138">
    <literal><![CDATA[
      (x \ 1) \ (x \ T(x * y,z)) = T((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,1056,a)].">
      <j1 rule="hyper" parents="138 1056"/>
    </justification>
  </clause>

  <clause id="1139">
    <literal><![CDATA[
      x * (((x \ 1) \ y) * (x \ 1)) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(635,a,1056,a(flip))].">
      <j1 rule="hyper" parents="635 1056"/>
    </justification>
  </clause>

  <clause id="1140">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),1056(a,2,2,1))].">
      <j1 rule="para" parents="8 1056"/>
    </justification>
  </clause>

  <clause id="1141">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),1056(a,2,2,1))].">
      <j1 rule="para" parents="10 1056"/>
    </justification>
  </clause>

  <clause id="1142">
    <literal><![CDATA[
      T(x,y) * (x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,486,a(flip),b,1140,a)].">
      <j1 rule="hyper" parents="63 486 1140"/>
    </justification>
  </clause>

  <clause id="1143">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(807,a,1057,a)].">
      <j1 rule="hyper" parents="807 1057"/>
    </justification>
  </clause>

  <clause id="1144">
    <literal><![CDATA[
      T(((1 / x) * y) * x,z) / x = (1 / x) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,485,a(flip),b,1057,a),flip(a)].">
      <j1 rule="hyper" parents="63 485 1057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1145">
    <literal><![CDATA[
      T(1 / (1 / x),y) * (1 / x) = T(x,y) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1057(a,2,1,1))].">
      <j1 rule="para" parents="7 1057"/>
    </justification>
  </clause>

  <clause id="1146">
    <literal><![CDATA[
      T(x * y,z) / y != u
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * T((1 / y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(1057(a,1),807(a,1))].">
      <j1 rule="para" parents="1057 807"/>
    </justification>
  </clause>

  <clause id="1147">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(807,a,1145,a)].">
      <j1 rule="hyper" parents="807 1145"/>
    </justification>
  </clause>

  <clause id="1148">
    <literal><![CDATA[
      (1 / x) * T(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,487,a(flip),b,1145,a)].">
      <j1 rule="hyper" parents="63 487 1145"/>
    </justification>
  </clause>

  <clause id="1149">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / x) = T(1 / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(462,a,1145,a(flip),b,487,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="462 1145 487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1150">
    <literal><![CDATA[
      (T(x,y) / x) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(131,a,1145,a(flip),b,487,a(flip))].">
      <j1 rule="hyper" parents="131 1145 487"/>
    </justification>
  </clause>

  <clause id="1151">
    <literal><![CDATA[
      (1 / x) \ (T(x,y) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,1145,a(flip),b,487,a(flip))].">
      <j1 rule="hyper" parents="128 1145 487"/>
    </justification>
  </clause>

  <clause id="1152">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(1145(a,1),807(a,1))].">
      <j1 rule="para" parents="1145 807"/>
    </justification>
  </clause>

  <clause id="1153">
    <literal><![CDATA[
      T(x,x \ y) / x = (1 / x) * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,338,a(flip),b,1148,a),flip(a)].">
      <j1 rule="hyper" parents="63 338 1148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1154">
    <literal><![CDATA[
      T((T(x,y) * (1 / x)) / T(x,y),T(x,y) / x) = L(1 / x,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(1148(a,1),755(a,1,2))].">
      <j1 rule="para" parents="1148 755"/>
    </justification>
  </clause>

  <clause id="1155">
    <literal><![CDATA[
      (1 / x) * ((x \ y) \ y) = ((x \ y) \ y) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,337,a(flip),b,1153,a),flip(a)].">
      <j1 rule="hyper" parents="63 337 1153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1156">
    <literal><![CDATA[
      K(x,y) = ((y * x) \ y) * T(((y * x) \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,450,a,b,1078,a)].">
      <j1 rule="hyper" parents="347 450 1078"/>
    </justification>
  </clause>

  <clause id="1157">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) = ((x * y) \ x) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,450,a,b,1078,a),flip(a)].">
      <j1 rule="hyper" parents="128 450 1078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1158">
    <literal><![CDATA[
      T(x * ((y \ 1) \ 1),z) / ((y \ 1) \ 1) = y \ T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,1056,a(flip),b,1110,a),flip(a)].">
      <j1 rule="hyper" parents="347 1056 1110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1159">
    <literal><![CDATA[
      T((x * y) * (x \ 1),y) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(110(a,1),1111(a,2,1,2))].">
      <j1 rule="para" parents="110 1111"/>
    </justification>
  </clause>

  <clause id="1160">
    <literal><![CDATA[
      K((x * y) * (x \ 1),y) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,1159,a)].">
      <j1 rule="hyper" parents="55 1159"/>
    </justification>
  </clause>

  <clause id="1161">
    <literal><![CDATA[
      K(((1 / x) * y) * x,y) = 1
    ]]></literal>
    <justification jstring="[para(83(a,1),1160(a,1,1,2))].">
      <j1 rule="para" parents="83 1160"/>
    </justification>
  </clause>

  <clause id="1162">
    <literal><![CDATA[
      K(x * y,(1 / y) \ x) = 1
    ]]></literal>
    <justification jstring="[para(10(a,1),1161(a,1,1,1))].">
      <j1 rule="para" parents="10 1161"/>
    </justification>
  </clause>

  <clause id="1163">
    <literal><![CDATA[
      T(x * y,(1 / y) \ x) = x * y
    ]]></literal>
    <justification jstring="[hyper(56,a,1162,a)].">
      <j1 rule="hyper" parents="56 1162"/>
    </justification>
  </clause>

  <clause id="1164">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = (((x / y) \ 1) \ y) * ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(12(a,1),1137(a,1,2,1))].">
      <j1 rule="para" parents="12 1137"/>
    </justification>
  </clause>

  <clause id="1165">
    <literal><![CDATA[
      T((x \ 1) \ (x \ y),z) = (x \ 1) \ (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),1138(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1166">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(1138(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1138 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1167">
    <literal><![CDATA[
      (x \ T(y,z)) / (x \ 1) = T((x \ y) / (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(131,a,1141,a(flip),b,484,a)].">
      <j1 rule="hyper" parents="131 1141 484"/>
    </justification>
  </clause>

  <clause id="1168">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ (y / x),z) = T(y,z) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),1143(a,2,1,1))].">
      <j1 rule="para" parents="12 1143"/>
    </justification>
  </clause>

  <clause id="1169">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) = ((y * x) \ y) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(244(a,2),1157(a,1,1,1))].">
      <j1 rule="para" parents="244 1157"/>
    </justification>
  </clause>

  <clause id="1170">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(1165(a,2),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1165 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1171">
    <literal><![CDATA[
      x \ y != (z \ 1) * T((z \ 1) \ (z \ u),w)
    ]]></literal>
    <literal><![CDATA[
      x * (z \ T(u,w)) = y
    ]]></literal>
    <justification jstring="[para(1165(a,2),355(a,2,2))].">
      <j1 rule="para" parents="1165 355"/>
    </justification>
  </clause>

  <clause id="1172">
    <literal><![CDATA[
      ((1 / x) \ (y / x)) * (1 / x) = T(y,1 / x) / x
    ]]></literal>
    <justification jstring="[hyper(315,a,1168,a)].">
      <j1 rule="hyper" parents="315 1168"/>
    </justification>
  </clause>

  <clause id="1173">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(1172(a,1),93(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1172 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1174">
    <literal><![CDATA[
      (x * (T(y,x) * T(z,y * x))) \ (z * (y * x)) = a(x,T(y,x),T(z,y * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,250,a(flip),b,259,a)].">
      <j1 rule="hyper" parents="63 250 259"/>
    </justification>
  </clause>

  <clause id="1175">
    <literal><![CDATA[
      a(x,x,x \ (x \ y)) = y \ ((x \ 1) \ (x \ y))
    ]]></literal>
    <justification jstring="[para(495(a,1),328(a,1,2)),flip(a)].">
      <j1 rule="para" parents="495 328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1176">
    <literal><![CDATA[
      R((x * y) / (z * y),u,w) * (z * y) = (R(x / z,u,w) * z) * y
    ]]></literal>
    <justification jstring="[para(108(a,1),469(a,1,1,1))].">
      <j1 rule="para" parents="108 469"/>
    </justification>
  </clause>

  <clause id="1177">
    <literal><![CDATA[
      (R(x / (y / z),u,w) * (y / z)) * z = R((x * z) / y,u,w) * ((y / z) * z)
    ]]></literal>
    <justification jstring="[para(607(a,1),469(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="607 469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1178">
    <literal><![CDATA[
      x \ ((L(y,z,x) * x) * z) = z * T(R(y,x,z),x * z)
    ]]></literal>
    <justification jstring="[hyper(128,a,471,a(flip),b,734,a)].">
      <j1 rule="hyper" parents="128 471 734"/>
    </justification>
  </clause>

  <clause id="1179">
    <literal><![CDATA[
      (L(x,y,z) * u) * w != v5 * (u * w)
    ]]></literal>
    <literal><![CDATA[
      L(R(x,u,w),y,z) = v5
    ]]></literal>
    <justification jstring="[para(471(a,1),44(a,1))].">
      <j1 rule="para" parents="471 44"/>
    </justification>
  </clause>

  <clause id="1180">
    <literal><![CDATA[
      (x * y) * L(L(L(z,y,x),u,w),v5,v6) = x * (y * L(L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(30(a,1),474(a,1,2,1))].">
      <j1 rule="para" parents="30 474"/>
    </justification>
  </clause>

  <clause id="1181">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (x * z),u,w) = x * (y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(99(a,1),474(a,1,2,1))].">
      <j1 rule="para" parents="99 474"/>
    </justification>
  </clause>

  <clause id="1182">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(329(a,1),474(a,1,2,1))].">
      <j1 rule="para" parents="329 474"/>
    </justification>
  </clause>

  <clause id="1183">
    <literal><![CDATA[
      (x * y) * L(T(x,x * y),z,u) = x * (y * L(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(750(a,1),474(a,1,2,1))].">
      <j1 rule="para" parents="750 474"/>
    </justification>
  </clause>

  <clause id="1184">
    <literal><![CDATA[
      (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(244(a,1),475(a,1,2,1))].">
      <j1 rule="para" parents="244 475"/>
    </justification>
  </clause>

  <clause id="1185">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(99(a,1),475(a,1,2,1))].">
      <j1 rule="para" parents="99 475"/>
    </justification>
  </clause>

  <clause id="1186">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(329(a,1),475(a,1,2,1))].">
      <j1 rule="para" parents="329 475"/>
    </justification>
  </clause>

  <clause id="1187">
    <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(621(a,1),547(a,1,2))].">
      <j1 rule="para" parents="621 547"/>
    </justification>
  </clause>

  <clause id="1188">
    <literal><![CDATA[
      L(L(L(x,y,z) \ u,w,v5),L(x,y,z),z * y) = L((z * (y * x)) \ ((z * y) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(97(a,1),568(a,2,1,1))].">
      <j1 rule="para" parents="97 568"/>
    </justification>
  </clause>

  <clause id="1189">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (x * z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (y * L(y \ z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(568(a,1),322(a,1,2))].">
      <j1 rule="para" parents="568 322"/>
    </justification>
  </clause>

  <clause id="1190">
    <literal><![CDATA[
      K(x \ 1,x) \ ((y * (x \ 1)) * x) = R(T(y,K(x \ 1,x)),x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,597,a(flip),b,268,a)].">
      <j1 rule="hyper" parents="128 597 268"/>
    </justification>
  </clause>

  <clause id="1191">
    <literal><![CDATA[
      R(x \ T(x,y),K(x \ 1,T(x,y)),z) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(1142(a,1),614(a,1,1,1))].">
      <j1 rule="para" parents="1142 614"/>
    </justification>
  </clause>

  <clause id="1192">
    <literal><![CDATA[
      (1 / x) \ L(1 / x,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(407(a,1),617(a,1,2,1))].">
      <j1 rule="para" parents="407 617"/>
    </justification>
  </clause>

  <clause id="1193">
    <literal><![CDATA[
      (1 / x) \ L((1 / x) * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(559(a,1),617(a,1,2,1))].">
      <j1 rule="para" parents="559 617"/>
    </justification>
  </clause>

  <clause id="1194">
    <literal><![CDATA[
      (1 / (x \ y)) \ L(1 / (x \ y),x \ y,x) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(408(a,1),1192(a,2,2))].">
      <j1 rule="para" parents="408 1192"/>
    </justification>
  </clause>

  <clause id="1195">
    <literal><![CDATA[
      R(x / (1 / y),z,u) * (1 / y) = R(x * y,z,u) / y
    ]]></literal>
    <justification jstring="[para(603(a,1),618(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="603 618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1196">
    <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(622(a,1),322(a,1,2))].">
      <j1 rule="para" parents="622 322"/>
    </justification>
  </clause>

  <clause id="1197">
    <literal><![CDATA[
      K(x \ 1,x) * L(((x \ 1) * x) \ y,z,u) = (x \ 1) * (x * L(x \ ((x \ 1) \ y),z,u))
    ]]></literal>
    <justification jstring="[para(622(a,1),547(a,1,2))].">
      <j1 rule="para" parents="622 547"/>
    </justification>
  </clause>

  <clause id="1198">
    <literal><![CDATA[
      R(T(T(x,y),z),u,w) = T(T(R(x,u,w),z),y)
    ]]></literal>
    <justification jstring="[hyper(685,a,27,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="685 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1199">
    <literal><![CDATA[
      T(T(R(x / y,z,u),w),y) = R(T(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(113(a,1),1198(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="113 1198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1200">
    <literal><![CDATA[
      T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y)
    ]]></literal>
    <justification jstring="[para(108(a,1),1199(a,1,1,1))].">
      <j1 rule="para" parents="108 1199"/>
    </justification>
  </clause>

  <clause id="1201">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(128,a,689,a(flip),b,289,a),flip(a)].">
      <j1 rule="hyper" parents="128 689 289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1202">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = L(x / y,z,u) * y
    ]]></literal>
    <justification jstring="[para(691(a,1),696(a,1,1,1))].">
      <j1 rule="para" parents="691 696"/>
    </justification>
  </clause>

  <clause id="1203">
    <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(789(a,1),732(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="789 732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1204">
    <literal><![CDATA[
      (x \ 1) \ (x \ (x \ 1)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(871,a,509,a)].">
      <j1 rule="hyper" parents="871 509"/>
    </justification>
  </clause>

  <clause id="1205">
    <literal><![CDATA[
      x \ (y * T(y \ (x * z),u)) = (x \ y) * T((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[para(891(a,1),538(a,1,2,2))].">
      <j1 rule="para" parents="891 538"/>
    </justification>
  </clause>

  <clause id="1206">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,904,a(flip),b,109,a),flip(a)].">
      <j1 rule="hyper" parents="133 904 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1207">
    <literal><![CDATA[
      R(x / (x / y),z,u) * (x / y) != w
    ]]></literal>
    <literal><![CDATA[
      (x / y) * R(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(12(a,1),1001(a,1,1,1,1))].">
      <j1 rule="para" parents="12 1001"/>
    </justification>
  </clause>

  <clause id="1208">
    <literal><![CDATA[
      K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,1169,a,b,409,a),flip(a)].">
      <j1 rule="hyper" parents="134 1169 409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1209">
    <literal><![CDATA[
      R(T(x \ y,x * z),x,z) = T((x * z) \ (y * z),x)
    ]]></literal>
    <justification jstring="[para(113(a,1),1200(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 1200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1210">
    <literal><![CDATA[
      R(T(x \ 1,x * y),x,y) = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),1209(a,2,1,2))].">
      <j1 rule="para" parents="7 1209"/>
    </justification>
  </clause>

  <clause id="1211">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1209(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1212">
    <literal><![CDATA[
      T((x * y) \ (z * y),x) != R(u,x,y)
    ]]></literal>
    <literal><![CDATA[
      T(x \ z,x * y) = u
    ]]></literal>
    <justification jstring="[para(1209(a,1),51(a,1))].">
      <j1 rule="para" parents="1209 51"/>
    </justification>
  </clause>

  <clause id="1213">
    <literal><![CDATA[
      L(L(L(x \ 1,y,z),u,w),x,x) = L(L(T(x \ 1,x),y,z),u,w)
    ]]></literal>
    <justification jstring="[para(519(a,1),116(a,2,1,1))].">
      <j1 rule="para" parents="519 116"/>
    </justification>
  </clause>

  <clause id="1214">
    <literal><![CDATA[
      (x * x) \ ((y \ (z * y)) * (x * x)) = T(z,y * (x * x))
    ]]></literal>
    <justification jstring="[para(728(a,1),751(a,1,2))].">
      <j1 rule="para" parents="728 751"/>
    </justification>
  </clause>

  <clause id="1216">
    <literal><![CDATA[
      T(R(x,y,T(z,y)),u) * (z * y) != w
    ]]></literal>
    <literal><![CDATA[
      (T(x,u) * y) * T(z,y) = w
    ]]></literal>
    <justification jstring="[para(27(a,1),927(a,1,1))].">
      <j1 rule="para" parents="27 927"/>
    </justification>
  </clause>

  <clause id="1217">
    <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(99(a,1),929(a,1,2,1))].">
      <j1 rule="para" parents="99 929"/>
    </justification>
  </clause>

  <clause id="1218">
    <literal><![CDATA[
      x * (y * T(T(x,y),z)) = T(x,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(435,a,1023,a),flip(a)].">
      <j1 rule="hyper" parents="435 1023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1219">
    <literal><![CDATA[
      T(x,y) * (x * z) = x * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(266(a,1),1218(a,1,2)),flip(a)].">
      <j1 rule="para" parents="266 1218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1220">
    <literal><![CDATA[
      x \ (T(x,y) * z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(678,a,1219,a)].">
      <j1 rule="hyper" parents="678 1219"/>
    </justification>
  </clause>

  <clause id="1221">
    <literal><![CDATA[
      T(x,y) * (x \ (T(x,y) \ z)) = x \ z
    ]]></literal>
    <justification jstring="[hyper(675,a,1219,a),flip(a)].">
      <j1 rule="hyper" parents="675 1219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1222">
    <literal><![CDATA[
      (T(x,y) * z) / (T(x,y) * (x \ z)) = x
    ]]></literal>
    <justification jstring="[hyper(656,a,1219,a)].">
      <j1 rule="hyper" parents="656 1219"/>
    </justification>
  </clause>

  <clause id="1223">
    <literal><![CDATA[
      (x / y) * (T(x / y,z) * y) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[hyper(641,a,1219,a),flip(a)].">
      <j1 rule="hyper" parents="641 1219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1224">
    <literal><![CDATA[
      x * (T(x,y) * T(z,x)) = T(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(639,a,1219,a),flip(a)].">
      <j1 rule="hyper" parents="639 1219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1225">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,y) \ z)) = (x * (T(x,y) \ z)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(462,a,169,a(flip),b,1219,a)].">
      <j1 rule="hyper" parents="462 169 1219"/>
    </justification>
  </clause>

  <clause id="1226">
    <literal><![CDATA[
      x * (T(x,y) * (x \ z)) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(357,a,1219,a),flip(a)].">
      <j1 rule="hyper" parents="357 1219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1227">
    <literal><![CDATA[
      T(x,y) * (x * (T(x,y) \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(347,a,169,a(flip),b,1219,a),flip(a)].">
      <j1 rule="hyper" parents="347 169 1219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1228">
    <literal><![CDATA[
      T(x,y) \ (x * (T(x,y) * z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(138,a,1219,a)].">
      <j1 rule="hyper" parents="138 1219"/>
    </justification>
  </clause>

  <clause id="1229">
    <literal><![CDATA[
      T(x,y) \ (x * z) = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(128,a,169,a(flip),b,1219,a)].">
      <j1 rule="hyper" parents="128 169 1219"/>
    </justification>
  </clause>

  <clause id="1230">
    <literal><![CDATA[
      x * (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,73,a(flip),b,1219,a),flip(a)].">
      <j1 rule="hyper" parents="128 73 1219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1231">
    <literal><![CDATA[
      (T(x,y) * x) \ (x * (T(x,y) * z)) = L(z,x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(128,a,1219,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="128 1219 97"/>
    </justification>
  </clause>

  <clause id="1233">
    <literal><![CDATA[
      T(x,y) * (x * z) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(1219(a,2),43(a,1))].">
      <j1 rule="para" parents="1219 43"/>
    </justification>
  </clause>

  <clause id="1234">
    <literal><![CDATA[
      (x / y) * (T(x / y,y) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(113(a,1),1219(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 1219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1235">
    <literal><![CDATA[
      (T(x,y) \ x) / (T(x,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,1230,a)].">
      <j1 rule="hyper" parents="145 1230"/>
    </justification>
  </clause>

  <clause id="1236">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,1 / x) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(134,a,1230,a(flip),b,454,a),flip(a)].">
      <j1 rule="hyper" parents="134 1230 454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1237">
    <literal><![CDATA[
      (T(x,y) \ x) / T(x,T(x,y) \ 1) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(131,a,1230,a(flip),b,111,a)].">
      <j1 rule="hyper" parents="131 1230 111"/>
    </justification>
  </clause>

  <clause id="1238">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = (x / y) * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(113(a,1),1230(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 1230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1239">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(1230(a,1),362(a,1,1,1))].">
      <j1 rule="para" parents="1230 362"/>
    </justification>
  </clause>

  <clause id="1240">
    <literal><![CDATA[
      T((1 / x) * (T(x,y) \ x),x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(1230(a,1),1005(a,1,1,2))].">
      <j1 rule="para" parents="1230 1005"/>
    </justification>
  </clause>

  <clause id="1241">
    <literal><![CDATA[
      (T(x,y) \ T(x,z)) / (T(x,y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(1235(a,1),1167(a,2,1))].">
      <j1 rule="para" parents="1235 1167"/>
    </justification>
  </clause>

  <clause id="1243">
    <literal><![CDATA[
      T(x,y) \ (x \ z) = x \ (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(138,a,1221,a)].">
      <j1 rule="hyper" parents="138 1221"/>
    </justification>
  </clause>

  <clause id="1244">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(1221(a,1),324(a,1,2,2))].">
      <j1 rule="para" parents="1221 324"/>
    </justification>
  </clause>

  <clause id="1245">
    <literal><![CDATA[
      T(x,y) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1222(a,1),140(a,1,1)),flip(a),flip(b)].">
      <j1 rule="para" parents="1222 140"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1246">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(269,a,111,a,b,1227,a),flip(a)].">
      <j1 rule="hyper" parents="269 111 1227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1247">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ y) = T(y,T(x / y,y))
    ]]></literal>
    <justification jstring="[para(113(a,1),1246(a,1,2,1))].">
      <j1 rule="para" parents="113 1246"/>
    </justification>
  </clause>

  <clause id="1248">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(34,a,476,a,b,1224,a),flip(a)].">
      <j1 rule="hyper" parents="34 476 1224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1249">
    <literal><![CDATA[
      T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(148,a,1241,a)].">
      <j1 rule="hyper" parents="148 1241"/>
    </justification>
  </clause>

  <clause id="1250">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ y) = T(y,y \ x)
    ]]></literal>
    <justification jstring="[para(113(a,1),1247(a,2,2))].">
      <j1 rule="para" parents="113 1247"/>
    </justification>
  </clause>

  <clause id="1251">
    <literal><![CDATA[
      (x / y) \ T(y,y \ x) = (y \ x) \ y
    ]]></literal>
    <justification jstring="[hyper(138,a,1250,a)].">
      <j1 rule="hyper" parents="138 1250"/>
    </justification>
  </clause>

  <clause id="1252">
    <literal><![CDATA[
      ((x * y) / x) * (y \ x) = T(x,x \ (x * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),1250(a,1,2,1))].">
      <j1 rule="para" parents="9 1250"/>
    </justification>
  </clause>

  <clause id="1253">
    <literal><![CDATA[
      T(x,y) = ((x * y) / x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1252(a,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1254">
    <literal><![CDATA[
      ((x * y) / x) \ T(x,y) = y \ x
    ]]></literal>
    <justification jstring="[hyper(908,a,1253,a)].">
      <j1 rule="hyper" parents="908 1253"/>
    </justification>
  </clause>

  <clause id="1255">
    <literal><![CDATA[
      ((x * (x / y)) / x) * y = T(x,x / y)
    ]]></literal>
    <justification jstring="[hyper(347,a,217,a(flip),b,1253,a)].">
      <j1 rule="hyper" parents="347 217 1253"/>
    </justification>
  </clause>

  <clause id="1256">
    <literal><![CDATA[
      ((x * y) * x) / (x * y) = T(x * y,x) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,1253,a,b,170,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 1253 170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1257">
    <literal><![CDATA[
      T(x,y) / (y \ x) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,1253,a,b,xx)].">
      <j1 rule="hyper" parents="131 1253"/>
    </justification>
  </clause>

  <clause id="1258">
    <literal><![CDATA[
      ((x * R(y,y \ 1,x)) / x) * ((y \ 1) * x) = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[para(448(a,1),1253(a,2,2)),flip(a)].">
      <j1 rule="para" parents="448 1253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1259">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) = T(y,y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,970,a(flip),b,1255,a)].">
      <j1 rule="hyper" parents="63 970 1255"/>
    </justification>
  </clause>

  <clause id="1260">
    <literal><![CDATA[
      x \ T(y,y / x) = (y * (x \ y)) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,1255,a(flip),b,970,a(flip))].">
      <j1 rule="hyper" parents="128 1255 970"/>
    </justification>
  </clause>

  <clause id="1261">
    <literal><![CDATA[
      (x / y) * ((x * y) / x) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[para(83(a,1),1259(a,1,2,1,2))].">
      <j1 rule="para" parents="83 1259"/>
    </justification>
  </clause>

  <clause id="1262">
    <literal><![CDATA[
      T(x \ T(y,y / x),y) = x \ y
    ]]></literal>
    <justification jstring="[para(1260(a,2),254(a,1,1))].">
      <j1 rule="para" parents="1260 254"/>
    </justification>
  </clause>

  <clause id="1263">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,y / x) = z
    ]]></literal>
    <justification jstring="[para(1260(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1260 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1264">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[para(80(a,1),1262(a,1,1,2,2))].">
      <j1 rule="para" parents="80 1262"/>
    </justification>
  </clause>

  <clause id="1265">
    <literal><![CDATA[
      T(T(x * y,x) / y,x * y) = x
    ]]></literal>
    <justification jstring="[para(1256(a,1),254(a,1,1))].">
      <j1 rule="para" parents="1256 254"/>
    </justification>
  </clause>

  <clause id="1266">
    <literal><![CDATA[
      T(T(x * y,x) / y,y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[para(1256(a,1),1012(a,1,1))].">
      <j1 rule="para" parents="1256 1012"/>
    </justification>
  </clause>

  <clause id="1267">
    <literal><![CDATA[
      T(T(R(x,y,y \ 1),x * y) / (y \ 1),(x * y) * (y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(585(a,1),1265(a,1,1,1,1))].">
      <j1 rule="para" parents="585 1265"/>
    </justification>
  </clause>

  <clause id="1268">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(386,a,1266,a)].">
      <j1 rule="hyper" parents="386 1266"/>
    </justification>
  </clause>

  <clause id="1269">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(255(a,1),1261(a,1,2)),flip(a)].">
      <j1 rule="para" parents="255 1261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1270">
    <literal><![CDATA[
      (x / y) * (y * T(y \ x,z)) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(484(a,1),1223(a,1,2))].">
      <j1 rule="para" parents="484 1223"/>
    </justification>
  </clause>

  <clause id="1271">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[para(113(a,1),1238(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 1238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1272">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = (x \ 1) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1155,a(flip),b,1271,a)].">
      <j1 rule="hyper" parents="63 1155 1271"/>
    </justification>
  </clause>

  <clause id="1273">
    <literal><![CDATA[
      (x \ (x * y)) \ ((x * y) / x) = ((x * y) / x) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),1271(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1274">
    <literal><![CDATA[
      (1 / x) \ T(1 / x,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,8,a(flip),b,1270,a)].">
      <j1 rule="hyper" parents="128 8 1270"/>
    </justification>
  </clause>

  <clause id="1275">
    <literal><![CDATA[
      (x * T(x,y)) \ (x * (T(x,y) * z)) = L(z,x,T(x,y))
    ]]></literal>
    <justification jstring="[para(272(a,1),1231(a,1,1))].">
      <j1 rule="para" parents="272 1231"/>
    </justification>
  </clause>

  <clause id="1276">
    <literal><![CDATA[
      L(x,y,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(1275(a,1),545(a,1))].">
      <j1 rule="para" parents="1275 545"/>
    </justification>
  </clause>

  <clause id="1278">
    <literal><![CDATA[
      (x / y) \ (x * T(x \ (x / y),z)) = y * T(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,1054,a)].">
      <j1 rule="hyper" parents="138 1054"/>
    </justification>
  </clause>

  <clause id="1279">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(387(a,1),1054(a,1,2))].">
      <j1 rule="para" parents="387 1054"/>
    </justification>
  </clause>

  <clause id="1280">
    <literal><![CDATA[
      (T(1 / x,y) * x) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(807,a,1055,a),flip(a)].">
      <j1 rule="hyper" parents="807 1055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1281">
    <literal><![CDATA[
      K((x * y) \ x,x * y) = y * T(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(511,a,1061,a)].">
      <j1 rule="hyper" parents="511 1061"/>
    </justification>
  </clause>

  <clause id="1282">
    <literal><![CDATA[
      K((x * y) \ x,x * y) / y = T(1 / y,x * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,1281,a,b,484,a)].">
      <j1 rule="hyper" parents="131 1281 484"/>
    </justification>
  </clause>

  <clause id="1283">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) != (x * y) \ u
    ]]></literal>
    <literal><![CDATA[
      (z * x) * y = u
    ]]></literal>
    <justification jstring="[para(1211(a,2),1072(a,1))].">
      <j1 rule="para" parents="1211 1072"/>
    </justification>
  </clause>

  <clause id="1285">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (z * T(z \ y,x)) * (z \ x)
    ]]></literal>
    <justification jstring="[para(484(a,1),1091(a,2,1))].">
      <j1 rule="para" parents="484 1091"/>
    </justification>
  </clause>

  <clause id="1286">
    <literal><![CDATA[
      x \ ((L(y,z,x) * x) * z) = z * R(T(y,x * z),x,z)
    ]]></literal>
    <justification jstring="[para(27(a,2),1178(a,2,2))].">
      <j1 rule="para" parents="27 1178"/>
    </justification>
  </clause>

  <clause id="1287">
    <literal><![CDATA[
      L((1 / x) * (y * x),z,u) = (1 / x) * (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(134,a,737,a(flip),b,1193,a),flip(a)].">
      <j1 rule="hyper" parents="134 737 1193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1288">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ y,z,u) = R(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(999,a,1195,a)].">
      <j1 rule="hyper" parents="999 1195"/>
    </justification>
  </clause>

  <clause id="1289">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) * (1 / x) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1195(a,2,1,1))].">
      <j1 rule="para" parents="7 1195"/>
    </justification>
  </clause>

  <clause id="1290">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ 1,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(999,a,1289,a)].">
      <j1 rule="hyper" parents="999 1289"/>
    </justification>
  </clause>

  <clause id="1291">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(83(a,1),1290(a,1,2,1))].">
      <j1 rule="para" parents="83 1290"/>
    </justification>
  </clause>

  <clause id="1292">
    <literal><![CDATA[
      R(x \ 1,y,z) / (x \ 1) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,1291,a),flip(a)].">
      <j1 rule="hyper" parents="370 1291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1293">
    <literal><![CDATA[
      R(x,y,z) / x != R(x,y,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,R(x,y,z)) = u
    ]]></literal>
    <justification jstring="[para(1291(a,1),270(a,2)),flip(a)].">
      <j1 rule="para" parents="1291 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1294">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),1201(a,2,2,1))].">
      <j1 rule="para" parents="8 1201"/>
    </justification>
  </clause>

  <clause id="1295">
    <literal><![CDATA[
      L(x,y,z) * (x \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,742,a(flip),b,1294,a)].">
      <j1 rule="hyper" parents="63 742 1294"/>
    </justification>
  </clause>

  <clause id="1296">
    <literal><![CDATA[
      (x \ L(x,y,z)) / (x \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,1294,a(flip),b,742,a(flip))].">
      <j1 rule="hyper" parents="131 1294 742"/>
    </justification>
  </clause>

  <clause id="1297">
    <literal><![CDATA[
      (x \ 1) * L(T(x,x \ 1),y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(112(a,2),1294(a,1,2,1))].">
      <j1 rule="para" parents="112 1294"/>
    </justification>
  </clause>

  <clause id="1298">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,L(x,z,u)) = (x \ L(x,z,u)) \ (L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(1295(a,1),99(a,2,1))].">
      <j1 rule="para" parents="1295 99"/>
    </justification>
  </clause>

  <clause id="1299">
    <literal><![CDATA[
      L(x,y,z) * R(L(x,y,z) \ 1,L(x,y,z),x \ 1) = ((x \ 1) / (x \ L(x,y,z))) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1295(a,1),867(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1295 867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1300">
    <literal><![CDATA[
      x \ T(x * (x \ L(x,y,z)),u) = T(L(x,y,z),u) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1295(a,1),1136(a,1,2,1,2))].">
      <j1 rule="para" parents="1295 1136"/>
    </justification>
  </clause>

  <clause id="1301">
    <literal><![CDATA[
      x \ L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(1297(a,1),436(a,1))].">
      <j1 rule="para" parents="1297 436"/>
    </justification>
  </clause>

  <clause id="1302">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,740,a(flip),b,1202,a),flip(a)].">
      <j1 rule="hyper" parents="347 740 1202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1303">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      y * L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(1202(a,2),959(a,1))].">
      <j1 rule="para" parents="1202 959"/>
    </justification>
  </clause>

  <clause id="1304">
    <literal><![CDATA[
      (x * x) \ (T(y,z) * (x * x)) = T(y,z * (x * x))
    ]]></literal>
    <justification jstring="[para(22(a,2),1214(a,1,2,1))].">
      <j1 rule="para" parents="22 1214"/>
    </justification>
  </clause>

  <clause id="1305">
    <literal><![CDATA[
      T(T(x,y),z * z) = T(x,y * (z * z))
    ]]></literal>
    <justification jstring="[hyper(360,a,1304,a)].">
      <j1 rule="hyper" parents="360 1304"/>
    </justification>
  </clause>

  <clause id="1306">
    <literal><![CDATA[
      T(T(x,y * y),z) = T(x,z * (y * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,114,a(flip),b,1304,a)].">
      <j1 rule="hyper" parents="63 114 1304"/>
    </justification>
  </clause>

  <clause id="1307">
    <literal><![CDATA[
      T(x,y * (z * z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,y),z * z) = u
    ]]></literal>
    <justification jstring="[para(1304(a,1),360(a,1))].">
      <j1 rule="para" parents="1304 360"/>
    </justification>
  </clause>

  <clause id="1308">
    <literal><![CDATA[
      T(x / (y * y),z * (y * y)) = T((y * y) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(808,a,1305,a),flip(a)].">
      <j1 rule="hyper" parents="808 1305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1309">
    <literal><![CDATA[
      T(x,y * (x * x)) = L(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1089,a(flip),b,1305,a),flip(a)].">
      <j1 rule="hyper" parents="63 1089 1305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1310">
    <literal><![CDATA[
      T(T(x,y \ 1),y * y) = T(x,y)
    ]]></literal>
    <justification jstring="[para(240(a,1),1305(a,2,2))].">
      <j1 rule="para" parents="240 1305"/>
    </justification>
  </clause>

  <clause id="1311">
    <literal><![CDATA[
      x \ (y * (x \ 1)) = T(y,x) / (x * x)
    ]]></literal>
    <justification jstring="[para(1310(a,1),935(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1310 935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1312">
    <literal><![CDATA[
      T(x * y,y) / (y * y) = y \ R(x,y,y)
    ]]></literal>
    <justification jstring="[para(786(a,1),1311(a,1,2)),flip(a)].">
      <j1 rule="para" parents="786 1311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1313">
    <literal><![CDATA[
      (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(113(a,1),1234(a,1,2,1))].">
      <j1 rule="para" parents="113 1234"/>
    </justification>
  </clause>

  <clause id="1314">
    <literal><![CDATA[
      (x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(254(a,1),1234(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="254 1234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1315">
    <literal><![CDATA[
      ((x / y) \ x) * ((x / (x / y)) * z) = (x / (x / y)) * (y * z)
    ]]></literal>
    <justification jstring="[para(275(a,1),1234(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="275 1234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1316">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,82,a(flip),b,1313,a),flip(a)].">
      <j1 rule="hyper" parents="347 82 1313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1317">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,x) = x \ 1
    ]]></literal>
    <justification jstring="[para(290(a,2),1316(a,1,2))].">
      <j1 rule="para" parents="290 1316"/>
    </justification>
  </clause>

  <clause id="1318">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1273(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1319">
    <literal><![CDATA[
      (1 / x) \ ((y * (1 / x)) / y) = ((y * (1 / x)) / y) * x
    ]]></literal>
    <justification jstring="[hyper(644,a,1318,a),flip(a)].">
      <j1 rule="hyper" parents="644 1318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1320">
    <literal><![CDATA[
      K(x \ (x / y),x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(880,a,1278,a)].">
      <j1 rule="hyper" parents="880 1278"/>
    </justification>
  </clause>

  <clause id="1321">
    <literal><![CDATA[
      x * T(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ (y / x),y) = z
    ]]></literal>
    <justification jstring="[para(1278(a,1),880(a,1))].">
      <j1 rule="para" parents="1278 880"/>
    </justification>
  </clause>

  <clause id="1322">
    <literal><![CDATA[
      K(x \ (x / (1 / y)),x) = T(y,x) / y
    ]]></literal>
    <justification jstring="[hyper(347,a,1147,a(flip),b,1320,a),flip(a)].">
      <j1 rule="hyper" parents="347 1147 1320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1323">
    <literal><![CDATA[
      K(x \ (x / (y \ 1)),x) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,1140,a(flip),b,1320,a),flip(a)].">
      <j1 rule="hyper" parents="347 1140 1320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1324">
    <literal><![CDATA[
      T(x,y) = K(y \ (y / (1 / x)),y) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,1320,a,b,1147,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 1320 1147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1325">
    <literal><![CDATA[
      K(x \ (x / y),x) / y = T(1 / y,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,1320,a,b,484,a)].">
      <j1 rule="hyper" parents="131 1320 484"/>
    </justification>
  </clause>

  <clause id="1326">
    <literal><![CDATA[
      K(T(1 / x,T(x,y)),T(x,y)) = x * T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(1149(a,1),1320(a,1,1))].">
      <j1 rule="para" parents="1149 1320"/>
    </justification>
  </clause>

  <clause id="1327">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * x) = x * K(x \ (x / T(x,y)),x)
    ]]></literal>
    <justification jstring="[para(1320(a,2),1224(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1320 1224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1329">
    <literal><![CDATA[
      K(x \ (x / (((x * y) / x) \ 1)),x) = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[para(254(a,1),1323(a,2,2))].">
      <j1 rule="para" parents="254 1323"/>
    </justification>
  </clause>

  <clause id="1330">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(484(a,1),1280(a,1,1))].">
      <j1 rule="para" parents="484 1280"/>
    </justification>
  </clause>

  <clause id="1331">
    <literal><![CDATA[
      x \ (y \ ((L(z,x,y) * y) * x)) = R(T(z,y * x),y,x)
    ]]></literal>
    <justification jstring="[hyper(630,a,1286,a)].">
      <j1 rule="hyper" parents="630 1286"/>
    </justification>
  </clause>

  <clause id="1332">
    <literal><![CDATA[
      (1 / x) * (L(x \ 1,y,z) * x) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1316(a,1),1287(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1316 1287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1333">
    <literal><![CDATA[
      (x * y) \ x = (1 / y) * (L(y \ 1,y,x) * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,244,a(flip),b,1332,a)].">
      <j1 rule="hyper" parents="347 244 1332"/>
    </justification>
  </clause>

  <clause id="1334">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) * (x \ y) = (1 / (x \ y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(128,a,408,a(flip),b,1332,a),flip(a)].">
      <j1 rule="hyper" parents="128 408 1332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1335">
    <literal><![CDATA[
      (1 / x) * (((y * x) \ y) * x) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(244(a,1),1333(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="244 1333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1336">
    <literal><![CDATA[
      x * L(x \ (((y * x) \ y) * x),z,u) = (1 / x) \ L((y * x) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(1335(a,1),1193(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1335 1193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1337">
    <literal><![CDATA[
      L(x \ 1,y,z) / (x \ 1) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),1302(a,1,1,1))].">
      <j1 rule="para" parents="7 1302"/>
    </justification>
  </clause>

  <clause id="1338">
    <literal><![CDATA[
      L(x * y,z,u) / ((1 / y) \ 1) = (1 / y) * L((1 / y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(83(a,1),1302(a,1,1,1,2))].">
      <j1 rule="para" parents="83 1302"/>
    </justification>
  </clause>

  <clause id="1339">
    <literal><![CDATA[
      L(x \ 1,x,y) / (x \ 1) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,410,a(flip),b,1337,a),flip(a)].">
      <j1 rule="hyper" parents="347 410 1337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1340">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * (x \ 1) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,410,a(flip),b,1337,a)].">
      <j1 rule="hyper" parents="133 410 1337"/>
    </justification>
  </clause>

  <clause id="1341">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ L(x \ 1,x,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(214,a,1339,a)].">
      <j1 rule="hyper" parents="214 1339"/>
    </justification>
  </clause>

  <clause id="1342">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * (x \ 1) = (y * x) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,244,a(flip),b,1340,a),flip(a)].">
      <j1 rule="hyper" parents="347 244 1340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1343">
    <literal><![CDATA[
      L(x \ 1,x,y) \ ((x \ 1) * (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(1340(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1340 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1344">
    <literal><![CDATA[
      ((x * y) \ x) * K(y \ 1,y * ((x * y) \ x)) = (y \ 1) * (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(133,a,1342,a(flip),b,211,a)].">
      <j1 rule="hyper" parents="133 1342 211"/>
    </justification>
  </clause>

  <clause id="1345">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ L((x \ y) \ 1,x \ y,x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),1341(a,1,1,2,1))].">
      <j1 rule="para" parents="10 1341"/>
    </justification>
  </clause>

  <clause id="1346">
    <literal><![CDATA[
      T((x * y) / x,K(x \ (x / (((x * y) / x) \ 1)),x)) = (((x * y) / x) \ y) \ y
    ]]></literal>
    <justification jstring="[para(1329(a,2),112(a,1,2))].">
      <j1 rule="para" parents="1329 112"/>
    </justification>
  </clause>

  <clause id="1347">
    <literal><![CDATA[
      K((x / y) \ ((x / y) / (T(x / (x / y),z) \ 1)),x / y) = (((x / y) * T(y,z)) / (x / y)) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(505(a,1),1329(a,1,1,2,2,1))].">
      <j1 rule="para" parents="505 1329"/>
    </justification>
  </clause>

  <clause id="1348">
    <literal><![CDATA[
      (x * T(x \ (y \ x),z)) / (y \ x) = y * T(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1330,a)].">
      <j1 rule="hyper" parents="145 1330"/>
    </justification>
  </clause>

  <clause id="1349">
    <literal><![CDATA[
      (x * T(x \ (y \ x),z)) / (y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1330(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1330 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1350">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(387(a,1),1330(a,1,1))].">
      <j1 rule="para" parents="387 1330"/>
    </justification>
  </clause>

  <clause id="1351">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ z) = z * T(z \ ((x \ 1) \ z),y)
    ]]></literal>
    <justification jstring="[para(1140(a,1),1330(a,1,1))].">
      <j1 rule="para" parents="1140 1330"/>
    </justification>
  </clause>

  <clause id="1352">
    <literal><![CDATA[
      a(x,y * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(120(a,1),236(a,1))].">
      <j1 rule="para" parents="120 236"/>
    </justification>
  </clause>

  <clause id="1353">
    <literal><![CDATA[
      L(x \ (x \ 1),x * x,y \ 1) = (y \ (x * x)) \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(501(a,1),517(a,1,1))].">
      <j1 rule="para" parents="501 517"/>
    </justification>
  </clause>

  <clause id="1354">
    <literal><![CDATA[
      x * ((x \ y) * L((x \ y) \ z,u,w)) = y * L(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(561(a,1),839(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="561 839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1355">
    <literal><![CDATA[
      L((x \ y) / y,z,u) * y = (L(1 / x,z,u) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(421(a,1),846(a,1,1,1))].">
      <j1 rule="para" parents="421 846"/>
    </justification>
  </clause>

  <clause id="1356">
    <literal><![CDATA[
      (x * (y \ 1)) / y = x * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[para(551(a,1),889(a,1,2))].">
      <j1 rule="para" parents="551 889"/>
    </justification>
  </clause>

  <clause id="1357">
    <literal><![CDATA[
      x * ((x \ y) * R((x \ y) \ z,u,w)) = y * R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(134,a,892,a(flip),b,98,a),flip(a)].">
      <j1 rule="hyper" parents="134 892 98"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1358">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(1 \ (x * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(128,a,892,a(flip),b,289,a),flip(a)].">
      <j1 rule="hyper" parents="128 892 289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1359">
    <literal><![CDATA[
      x \ (y * R(y \ (x * z),u,w)) = (x \ y) * R((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(892(a,1),538(a,1,2,2))].">
      <j1 rule="para" parents="892 538"/>
    </justification>
  </clause>

  <clause id="1360">
    <literal><![CDATA[
      x \ (y * L(y \ (x * z),u,w)) = (x \ y) * L((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(893(a,1),538(a,1,2,2))].">
      <j1 rule="para" parents="893 538"/>
    </justification>
  </clause>

  <clause id="1361">
    <literal><![CDATA[
      x \ (y * L(y \ (x * z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(893(a,1),876(a,1,2,2))].">
      <j1 rule="para" parents="893 876"/>
    </justification>
  </clause>

  <clause id="1362">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) != u / (x * y)
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(950(a,2),46(a,1))].">
      <j1 rule="para" parents="950 46"/>
    </justification>
  </clause>

  <clause id="1363">
    <literal><![CDATA[
      L(((x * y) * T(z,y)) / (x * y),y,x) = (x * (z * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(111(a,1),950(a,2,1,2))].">
      <j1 rule="para" parents="111 950"/>
    </justification>
  </clause>

  <clause id="1364">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z))
    ]]></literal>
    <justification jstring="[hyper(134,a,996,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 996 18"/>
    </justification>
  </clause>

  <clause id="1365">
    <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(996(a,1),322(a,1,2))].">
      <j1 rule="para" parents="996 322"/>
    </justification>
  </clause>

  <clause id="1366">
    <literal><![CDATA[
      (x / y) * (y * ((z * (y \ 1)) / z)) = x * ((z * (x \ (x / y))) / z)
    ]]></literal>
    <justification jstring="[para(997(a,1),532(a,1,2)),flip(a)].">
      <j1 rule="para" parents="997 532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1367">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (y * z),u) = y * (T(x,y) * T(T(x,y) \ z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,1026,a(flip),b,262,a)].">
      <j1 rule="hyper" parents="134 1026 262"/>
    </justification>
  </clause>

  <clause id="1368">
    <literal><![CDATA[
      (x * y) * L(T(y,x),z,u) = (L(y,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,471,a(flip),b,1043,a),flip(a)].">
      <j1 rule="hyper" parents="63 471 1043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1369">
    <literal><![CDATA[
      L(T(x,1 / x),y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(655,a,1368,a)].">
      <j1 rule="hyper" parents="655 1368"/>
    </justification>
  </clause>

  <clause id="1370">
    <literal><![CDATA[
      (x * y) * R(T(y,x),z,u) = (R(y,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,469,a(flip),b,1044,a),flip(a)].">
      <j1 rule="hyper" parents="63 469 1044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1371">
    <literal><![CDATA[
      x \ (y * (z * (u * (w * w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      (x \ (y * (z * u))) * (w * w) = v5
    ]]></literal>
    <justification jstring="[para(33(a,1),1060(a,1,2,2))].">
      <j1 rule="para" parents="33 1060"/>
    </justification>
  </clause>

  <clause id="1372">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = T((z * y) / z,x * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,504,a(flip),b,1083,a),flip(a)].">
      <j1 rule="hyper" parents="347 504 1083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1373">
    <literal><![CDATA[
      L((T(x,y) * (x \ y)) / y,y,x) = (y * K(T(x,y),y)) / y
    ]]></literal>
    <justification jstring="[para(1220(a,1),1084(a,1,1,1))].">
      <j1 rule="para" parents="1220 1084"/>
    </justification>
  </clause>

  <clause id="1374">
    <literal><![CDATA[
      ((x \ y) * x) * (x \ z) = z * T(z \ (y * (x \ z)),x)
    ]]></literal>
    <justification jstring="[hyper(847,a,1086,a)].">
      <j1 rule="hyper" parents="847 1086"/>
    </justification>
  </clause>

  <clause id="1375">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      z \ (x * (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(1090(a,2),374(a,1))].">
      <j1 rule="para" parents="1090 374"/>
    </justification>
  </clause>

  <clause id="1376">
    <literal><![CDATA[
      R(T(x,y),z,z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      y \ ((x * z) * (z \ y)) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),1375(a,1,1,1))].">
      <j1 rule="para" parents="11 1375"/>
    </justification>
  </clause>

  <clause id="1377">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1145(a,1),1096(a,1))].">
      <j1 rule="para" parents="1145 1096"/>
    </justification>
  </clause>

  <clause id="1378">
    <literal><![CDATA[
      (1 / x) \ ((y * (1 / x)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = z
    ]]></literal>
    <justification jstring="[para(1319(a,2),1115(a,1))].">
      <j1 rule="para" parents="1319 1115"/>
    </justification>
  </clause>

  <clause id="1379">
    <literal><![CDATA[
      (x \ (y * y)) \ (x \ 1) = y \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(550,a,1353,a),flip(a)].">
      <j1 rule="hyper" parents="550 1353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1381">
    <literal><![CDATA[
      ((x * (y * z)) \ (x * y)) * (z * z) = L(L(z,z,y),y * z,x)
    ]]></literal>
    <justification jstring="[hyper(1060,a,542,a)].">
      <j1 rule="hyper" parents="1060 542"/>
    </justification>
  </clause>

  <clause id="1382">
    <literal><![CDATA[
      (x * x) \ ((y * z) \ (y * (z * ((x * x) * u)))) = L(L(u,x * x,z),z * (x * x),y)
    ]]></literal>
    <justification jstring="[hyper(1051,a,542,a)].">
      <j1 rule="hyper" parents="1051 542"/>
    </justification>
  </clause>

  <clause id="1384">
    <literal><![CDATA[
      ((x * y) * (z * (u * u))) / ((y * z) * (u * u)) = R(R(x,y,z),y * z,u * u)
    ]]></literal>
    <justification jstring="[para(33(a,1),591(a,1,1))].">
      <j1 rule="para" parents="33 591"/>
    </justification>
  </clause>

  <clause id="1385">
    <literal><![CDATA[
      K(x \ 1,x) * y != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      L(x \ z,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(10(a,1),938(a,2,2))].">
      <j1 rule="para" parents="10 938"/>
    </justification>
  </clause>

  <clause id="1386">
    <literal><![CDATA[
      T((x * x) * ((y / x) / (x * x)),x) = ((x \ 1) \ y) / (x * x)
    ]]></literal>
    <justification jstring="[para(464(a,1),972(a,1,1))].">
      <j1 rule="para" parents="464 972"/>
    </justification>
  </clause>

  <clause id="1387">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = (z * y) * T((z * y) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,484,a(flip),b,1019,a),flip(a)].">
      <j1 rule="hyper" parents="347 484 1019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1388">
    <literal><![CDATA[
      (x * (y * (z * (u * u)))) / (u * u) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(220,a,187,a(flip),b,1100,a)].">
      <j1 rule="hyper" parents="220 187 1100"/>
    </justification>
  </clause>

  <clause id="1389">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * (u * u)))) = L(z,y,x) * (u * u)
    ]]></literal>
    <justification jstring="[para(18(a,2),1100(a,2,1))].">
      <j1 rule="para" parents="18 1100"/>
    </justification>
  </clause>

  <clause id="1390">
    <literal><![CDATA[
      L(x * (y * y),z,u) = L(x,z,u) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(545,a,1389,a)].">
      <j1 rule="hyper" parents="545 1389"/>
    </justification>
  </clause>

  <clause id="1391">
    <literal><![CDATA[
      L(x,y,z) * (u * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x * (u * u),y,z) = w
    ]]></literal>
    <justification jstring="[para(1389(a,1),545(a,1))].">
      <j1 rule="para" parents="1389 545"/>
    </justification>
  </clause>

  <clause id="1393">
    <literal><![CDATA[
      L(x,y,z) * L(u * u,w,v5) = L(x * (u * u),y,z)
    ]]></literal>
    <justification jstring="[para(533(a,2),1390(a,2,2)),flip(a)].">
      <j1 rule="para" parents="533 1390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1394">
    <literal><![CDATA[
      L(x * (y * y),z,u) \ w = (y * y) \ (L(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(1390(a,2),459(a,1,1))].">
      <j1 rule="para" parents="1390 459"/>
    </justification>
  </clause>

  <clause id="1395">
    <literal><![CDATA[
      (x * L(y * (z * z),u,w)) \ v5 = (z * z) \ ((x * L(y,u,w)) \ v5)
    ]]></literal>
    <justification jstring="[para(1390(a,2),775(a,1,1,2))].">
      <j1 rule="para" parents="1390 775"/>
    </justification>
  </clause>

  <clause id="1397">
    <literal><![CDATA[
      (x * x) \ (L(y \ 1,z,u) \ w) = L(y \ (x * x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(460(a,1),1394(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="460 1394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1398">
    <literal><![CDATA[
      (x * x) \ (L((x * x) \ y,z,u) \ w) = L(T(y,x * x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(726(a,1),1394(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="726 1394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1399">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ 1)) / y) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(347,a,1318,a(flip),b,1117,a),flip(a)].">
      <j1 rule="hyper" parents="347 1318 1117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1400">
    <literal><![CDATA[
      x * (y * L(T(x,y),z,u)) = L(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(436,a,1183,a),flip(a)].">
      <j1 rule="hyper" parents="436 1183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1401">
    <literal><![CDATA[
      L(x,y,z) * (x * u) = x * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(267(a,1),1400(a,1,2)),flip(a)].">
      <j1 rule="para" parents="267 1400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1402">
    <literal><![CDATA[
      x \ (L(x,y,z) * u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(678,a,1401,a)].">
      <j1 rule="hyper" parents="678 1401"/>
    </justification>
  </clause>

  <clause id="1403">
    <literal><![CDATA[
      L(x,y,z) * (x \ (L(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(675,a,1401,a),flip(a)].">
      <j1 rule="hyper" parents="675 1401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1404">
    <literal><![CDATA[
      x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(357,a,1401,a),flip(a)].">
      <j1 rule="hyper" parents="357 1401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1405">
    <literal><![CDATA[
      L(x,y,z) * (x * (L(x,y,z) \ u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(347,a,169,a(flip),b,1401,a),flip(a)].">
      <j1 rule="hyper" parents="347 169 1401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1406">
    <literal><![CDATA[
      L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(138,a,1401,a)].">
      <j1 rule="hyper" parents="138 1401"/>
    </justification>
  </clause>

  <clause id="1407">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(128,a,169,a(flip),b,1401,a)].">
      <j1 rule="hyper" parents="128 169 1401"/>
    </justification>
  </clause>

  <clause id="1408">
    <literal><![CDATA[
      x * (L(x,y,z) \ (x \ u)) = L(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(128,a,76,a(flip),b,1401,a),flip(a)].">
      <j1 rule="hyper" parents="128 76 1401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1409">
    <literal><![CDATA[
      x * (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,73,a(flip),b,1401,a),flip(a)].">
      <j1 rule="hyper" parents="128 73 1401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1410">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) \ (L(x,y,z) * u) = T(x,L(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(462,a,169,a(flip),b,1401,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="462 169 1401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1411">
    <literal><![CDATA[
      x \ (L(x,y,z) * (u * x)) = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,251,a(flip),b,1401,a(flip))].">
      <j1 rule="hyper" parents="128 251 1401"/>
    </justification>
  </clause>

  <clause id="1412">
    <literal><![CDATA[
      x * (L(x,y,z) * ((x * x) \ u)) = L(x,y,z) * ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(497(a,1),1401(a,1,2)),flip(a)].">
      <j1 rule="para" parents="497 1401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1413">
    <literal><![CDATA[
      x * (L(x,y,z) * (x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) * u = w
    ]]></literal>
    <justification jstring="[para(1401(a,1),357(a,1))].">
      <j1 rule="para" parents="1401 357"/>
    </justification>
  </clause>

  <clause id="1414">
    <literal><![CDATA[
      (L(x,y,z) \ x) / (L(x,y,z) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,1409,a)].">
      <j1 rule="hyper" parents="145 1409"/>
    </justification>
  </clause>

  <clause id="1415">
    <literal><![CDATA[
      x \ (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(138,a,1409,a)].">
      <j1 rule="hyper" parents="138 1409"/>
    </justification>
  </clause>

  <clause id="1416">
    <literal><![CDATA[
      (x * y) * ((y * y) \ (L(x * (y \ 1),z,u) \ 1)) = L(x * (y \ 1),z,u) \ (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,828,a,b,1409,a)].">
      <j1 rule="hyper" parents="63 828 1409"/>
    </justification>
  </clause>

  <clause id="1417">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,1 / x) = (1 / x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(134,a,1409,a(flip),b,454,a),flip(a)].">
      <j1 rule="hyper" parents="134 1409 454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1418">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ ((L(x,y,z) \ 1) * x) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(1409(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1409 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1419">
    <literal><![CDATA[
      (x * y) \ (x * (L(y,z,u) \ y)) = L(L(y,z,u) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(1409(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1409 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1420">
    <literal><![CDATA[
      T((1 / x) * (L(x,y,z) \ x),x) = (1 / x) * ((L(x,y,z) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(1409(a,1),1005(a,1,1,2))].">
      <j1 rule="para" parents="1409 1005"/>
    </justification>
  </clause>

  <clause id="1421">
    <literal><![CDATA[
      L(x,y,z) \ T(L(x,y,z) * (L(x,y,z) \ x),u) = T(x,u) * (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(1409(a,1),1136(a,1,2,1,2))].">
      <j1 rule="para" parents="1409 1136"/>
    </justification>
  </clause>

  <clause id="1422">
    <literal><![CDATA[
      x * (L(x,y,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(1414(a,1),280(a,1,1))].">
      <j1 rule="para" parents="1414 280"/>
    </justification>
  </clause>

  <clause id="1423">
    <literal><![CDATA[
      L(x,y,z) \ (x \ u) = x \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(138,a,1403,a)].">
      <j1 rule="hyper" parents="138 1403"/>
    </justification>
  </clause>

  <clause id="1424">
    <literal><![CDATA[
      x * (L(x,y,z) \ (x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ u = w
    ]]></literal>
    <justification jstring="[para(1403(a,1),324(a,1,2,2))].">
      <j1 rule="para" parents="1403 324"/>
    </justification>
  </clause>

  <clause id="1425">
    <literal><![CDATA[
      L(x,y,z) * u != x * w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) * (x \ u) = w
    ]]></literal>
    <justification jstring="[para(1404(a,1),43(a,1))].">
      <j1 rule="para" parents="1404 43"/>
    </justification>
  </clause>

  <clause id="1426">
    <literal><![CDATA[
      x \ (L(x,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) * (x \ u) = w
    ]]></literal>
    <justification jstring="[para(1404(a,1),356(a,1,2))].">
      <j1 rule="para" parents="1404 356"/>
    </justification>
  </clause>

  <clause id="1427">
    <literal><![CDATA[
      (x / y) * (L(x / y,z,u) \ y) = L(x / y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,12,a(flip),b,1405,a),flip(a)].">
      <j1 rule="hyper" parents="128 12 1405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1428">
    <literal><![CDATA[
      L(L(x,y,z) \ u,x,L(x,y,z)) = (L(x,y,z) * x) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(128,a,1405,a(flip),b,97,a),flip(a)].">
      <j1 rule="hyper" parents="128 1405 97"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1429">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (L(x,y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(1405(a,1),356(a,1,2))].">
      <j1 rule="para" parents="1405 356"/>
    </justification>
  </clause>

  <clause id="1430">
    <literal><![CDATA[
      L(x,y,z) * (x * u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (L(x,y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(1406(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1406 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1431">
    <literal><![CDATA[
      T((x * y) / x,L(y,z,u) * x) = L((y * x) / x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1406(a,1),1372(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1406 1372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1432">
    <literal><![CDATA[
      T(L(x,y,z),x * (L(x,y,z) \ u)) = (L(x,y,z) \ (x * u)) \ (x * u)
    ]]></literal>
    <justification jstring="[para(1407(a,1),112(a,1,2))].">
      <j1 rule="para" parents="1407 112"/>
    </justification>
  </clause>

  <clause id="1433">
    <literal><![CDATA[
      (x / y) * (L(x / y,z,u) \ y) != w
    ]]></literal>
    <literal><![CDATA[
      L(x / y,z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(83(a,1),1424(a,1,2,2))].">
      <j1 rule="para" parents="83 1424"/>
    </justification>
  </clause>

  <clause id="1434">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (u * u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * u)) = w
    ]]></literal>
    <justification jstring="[para(456(a,1),1429(a,1))].">
      <j1 rule="para" parents="456 1429"/>
    </justification>
  </clause>

  <clause id="1435">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(8(a,1),1205(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 1205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1436">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ (x \ z),u) = x \ (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),1205(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 1205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1437">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z)
    ]]></literal>
    <justification jstring="[hyper(134,a,1320,a,b,1435,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 1320 1435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1438">
    <literal><![CDATA[
      (x \ y) * K(z \ (z / ((x \ y) \ (x \ 1))),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(1170,a,1437,a),flip(a)].">
      <j1 rule="hyper" parents="1170 1437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1439">
    <literal><![CDATA[
      (x / y) * K(z \ (z / ((x / y) \ (1 / y))),z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,1168,a(flip),b,1437,a),flip(a)].">
      <j1 rule="hyper" parents="63 1168 1437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1440">
    <literal><![CDATA[
      (x * y) * K(z \ (z / ((x * y) \ x)),z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1437(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1441">
    <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),1437(a,2,2,1,2,2))].">
      <j1 rule="para" parents="18 1437"/>
    </justification>
  </clause>

  <clause id="1443">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,484,a(flip),b,1206,a),flip(a)].">
      <j1 rule="hyper" parents="347 484 1206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1444">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1300(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1446">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),1444(a,2,2))].">
      <j1 rule="para" parents="25 1444"/>
    </justification>
  </clause>

  <clause id="1447">
    <literal><![CDATA[
      L(T(x,y),z,u) * (x \ 1) = x \ L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),1446(a,1,1))].">
      <j1 rule="para" parents="25 1446"/>
    </justification>
  </clause>

  <clause id="1448">
    <literal><![CDATA[
      ((x * y) / x) * (y * z) = y * (((x * y) / x) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1314(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1449">
    <literal><![CDATA[
      x * (((y * x) / y) * (x \ z)) = ((y * x) / y) * z
    ]]></literal>
    <justification jstring="[hyper(357,a,1448,a),flip(a)].">
      <j1 rule="hyper" parents="357 1448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1450">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(128,a,169,a(flip),b,1448,a)].">
      <j1 rule="hyper" parents="128 169 1448"/>
    </justification>
  </clause>

  <clause id="1451">
    <literal><![CDATA[
      x * (((y * x) / y) \ 1) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,73,a(flip),b,1448,a),flip(a)].">
      <j1 rule="hyper" parents="128 73 1448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1452">
    <literal><![CDATA[
      (((x / y) * T(y,z)) / (x / y)) \ T(y,z) = T(y,z) * (T(x / (x / y),z) \ 1)
    ]]></literal>
    <justification jstring="[para(505(a,1),1451(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="505 1451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1453">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((((x * y) / x) \ y) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(34,a,476,a,b,1449,a),flip(a)].">
      <j1 rule="hyper" parents="34 476 1449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1454">
    <literal><![CDATA[
      (x / (x / y)) * (y * z) = y * ((x / (x / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(708,a,1315,a),flip(a)].">
      <j1 rule="hyper" parents="708 1315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1455">
    <literal><![CDATA[
      (x / (x / y)) * (y \ 1) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(427,a,1454,a),flip(a)].">
      <j1 rule="hyper" parents="427 1454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1457">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,82,a(flip),b,1454,a),flip(a)].">
      <j1 rule="hyper" parents="347 82 1454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1459">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,1 / x) = x
    ]]></literal>
    <justification jstring="[para(292(a,2),1457(a,1,2))].">
      <j1 rule="para" parents="292 1457"/>
    </justification>
  </clause>

  <clause id="1460">
    <literal><![CDATA[
      (L(1 / x,y,z) * x) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(959,a,1355,a),flip(a)].">
      <j1 rule="hyper" parents="959 1355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1461">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(66(a,1),1358(a,2,2,1))].">
      <j1 rule="para" parents="66 1358"/>
    </justification>
  </clause>

  <clause id="1462">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(182(a,1),1358(a,2,2,1))].">
      <j1 rule="para" parents="182 1358"/>
    </justification>
  </clause>

  <clause id="1463">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,748,a(flip),b,1462,a)].">
      <j1 rule="hyper" parents="63 748 1462"/>
    </justification>
  </clause>

  <clause id="1464">
    <literal><![CDATA[
      (x \ 1) * R(T(x,x \ 1),y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(112(a,2),1462(a,1,2,1))].">
      <j1 rule="para" parents="112 1462"/>
    </justification>
  </clause>

  <clause id="1465">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = R(1 / x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(644,a,1463,a),flip(a)].">
      <j1 rule="hyper" parents="644 1463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1466">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(x \ 1,R(x,y,z)) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,1463,a(flip),b,211,a)].">
      <j1 rule="hyper" parents="133 1463 211"/>
    </justification>
  </clause>

  <clause id="1467">
    <literal><![CDATA[
      (x \ R(x,y,z)) / R(T(x,x \ 1),y,z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(131,a,1463,a(flip),b,268,a)].">
      <j1 rule="hyper" parents="131 1463 268"/>
    </justification>
  </clause>

  <clause id="1468">
    <literal><![CDATA[
      (x \ 1) \ (x \ R(x,y,z)) = R(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,1463,a(flip),b,268,a)].">
      <j1 rule="hyper" parents="128 1463 268"/>
    </justification>
  </clause>

  <clause id="1469">
    <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(1463(a,1),867(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1463 867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1470">
    <literal><![CDATA[
      R(x,y,z) * (x \ (1 / x)) = (x \ R(x,y,z)) / x
    ]]></literal>
    <justification jstring="[para(1463(a,1),1356(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1463 1356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1471">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,746,a(flip),b,1465,a),flip(a)].">
      <j1 rule="hyper" parents="347 746 1465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1472">
    <literal><![CDATA[
      (1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,419,a(flip),b,1465,a)].">
      <j1 rule="hyper" parents="134 419 1465"/>
    </justification>
  </clause>

  <clause id="1474">
    <literal><![CDATA[
      ((x / (y * x)) * y) \ (x / (y * x)) = T(1 / y,(x / (y * x)) * y)
    ]]></literal>
    <justification jstring="[hyper(462,a,247,a(flip),b,1472,a),flip(a)].">
      <j1 rule="hyper" parents="462 247 1472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1475">
    <literal><![CDATA[
      ((x \ y) / y) / (((x \ y) / (x * (x \ y))) * x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(131,a,421,a(flip),b,1472,a)].">
      <j1 rule="hyper" parents="131 421 1472"/>
    </justification>
  </clause>

  <clause id="1476">
    <literal><![CDATA[
      R(x,y,z) * ((x \ (1 / x)) * u) = ((x \ R(x,y,z)) / x) * u
    ]]></literal>
    <justification jstring="[para(1470(a,1),558(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1470 558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1477">
    <literal><![CDATA[
      x * R(x \ 1,y,y \ 1) = a(1 / x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(856,a,1471,a),flip(a)].">
      <j1 rule="hyper" parents="856 1471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1478">
    <literal><![CDATA[
      x * R(x \ 1,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(1 / x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(1471(a,1),856(a,1))].">
      <j1 rule="para" parents="1471 856"/>
    </justification>
  </clause>

  <clause id="1479">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ (x \ y),z,u) = x \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1461(a,2,2,1))].">
      <j1 rule="para" parents="10 1461"/>
    </justification>
  </clause>

  <clause id="1480">
    <literal><![CDATA[
      x \ R(x * (y * (x \ 1)),z,u) = (x \ 1) * R(T(y,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),1461(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="22 1461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1481">
    <literal><![CDATA[
      ((x \ y) / y) / (((x \ y) / y) * x) = 1 / x
    ]]></literal>
    <justification jstring="[para(10(a,1),1475(a,1,2,1,2))].">
      <j1 rule="para" parents="10 1475"/>
    </justification>
  </clause>

  <clause id="1482">
    <literal><![CDATA[
      (1 / x) \ ((x \ y) / y) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(214,a,1481,a)].">
      <j1 rule="hyper" parents="214 1481"/>
    </justification>
  </clause>

  <clause id="1483">
    <literal><![CDATA[
      (x \ 1) * R(1 / x,y,z) = x \ R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1204(a,1),1479(a,1,2,1))].">
      <j1 rule="para" parents="1204 1479"/>
    </justification>
  </clause>

  <clause id="1484">
    <literal><![CDATA[
      T((x * x) * (y / ((x * x) * x)),x) = ((x \ 1) \ y) / (x * x)
    ]]></literal>
    <justification jstring="[para(702(a,1),1386(a,1,1,2))].">
      <j1 rule="para" parents="702 1386"/>
    </justification>
  </clause>

  <clause id="1485">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y
    ]]></literal>
    <justification jstring="[para(11(a,1),1387(a,1,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 1387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1486">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[para(113(a,1),1387(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="113 1387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1487">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = (x * z) * T((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(484(a,1),1387(a,1,1))].">
      <j1 rule="para" parents="484 1387"/>
    </justification>
  </clause>

  <clause id="1488">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1022,a(flip),b,1486,a)].">
      <j1 rule="hyper" parents="63 1022 1486"/>
    </justification>
  </clause>

  <clause id="1489">
    <literal><![CDATA[
      ((x \ (x / y)) * x) * y = x * (y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,864,a(flip),b,1486,a),flip(a)].">
      <j1 rule="hyper" parents="63 864 1486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1490">
    <literal><![CDATA[
      x * ((y \ x) * T((y \ x) \ 1,x)) = ((x \ y) * x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(80(a,1),1489(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="80 1489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1491">
    <literal><![CDATA[
      ((x \ R(1 / y,y,x)) * x) * (y * x) = x * ((y * x) * T((y * x) \ 1,x))
    ]]></literal>
    <justification jstring="[para(247(a,2),1489(a,1,1,1,2))].">
      <j1 rule="para" parents="247 1489"/>
    </justification>
  </clause>

  <clause id="1492">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = x * (T((x \ y) * z,x) / z)
    ]]></literal>
    <justification jstring="[para(1143(a,1),1488(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1143 1488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1493">
    <literal><![CDATA[
      (x * x) \ (L(R(x / y,y,x) \ 1,z,u) \ w) = L(y * x,z,u) \ w
    ]]></literal>
    <justification jstring="[para(579(a,1),1397(a,2,1,1))].">
      <j1 rule="para" parents="579 1397"/>
    </justification>
  </clause>

  <clause id="1494">
    <literal><![CDATA[
      L(L(x,y,z) \ u,x,L(x,y,z)) = (x * L(x,y,z)) \ (x * u)
    ]]></literal>
    <justification jstring="[para(274(a,1),1428(a,2,1))].">
      <j1 rule="para" parents="274 1428"/>
    </justification>
  </clause>

  <clause id="1495">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ z,u)) * y = x * T(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(484(a,1),1443(a,1,1))].">
      <j1 rule="para" parents="484 1443"/>
    </justification>
  </clause>

  <clause id="1496">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(740(a,1),1460(a,1,1))].">
      <j1 rule="para" parents="740 1460"/>
    </justification>
  </clause>

  <clause id="1497">
    <literal><![CDATA[
      (T((x * y) / x,z) * x) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1485(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1498">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[para(484(a,1),1485(a,2,1))].">
      <j1 rule="para" parents="484 1485"/>
    </justification>
  </clause>

  <clause id="1499">
    <literal><![CDATA[
      (x * T(y,z)) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(485(a,1),1497(a,1,1))].">
      <j1 rule="para" parents="485 1497"/>
    </justification>
  </clause>

  <clause id="1500">
    <literal><![CDATA[
      (x * y) / T(y,z) = (x / T(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(717,a,1499,a)].">
      <j1 rule="hyper" parents="717 1499"/>
    </justification>
  </clause>

  <clause id="1501">
    <literal><![CDATA[
      (1 / T(x,y)) * x = x / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(655,a,1499,a),flip(a)].">
      <j1 rule="hyper" parents="655 1499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1502">
    <literal><![CDATA[
      ((x / T(y,z)) * y) * T(y,z) = x * y
    ]]></literal>
    <justification jstring="[hyper(353,a,1499,a),flip(a)].">
      <j1 rule="hyper" parents="353 1499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1503">
    <literal><![CDATA[
      ((x / y) * T(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,164,a(flip),b,1499,a),flip(a)].">
      <j1 rule="hyper" parents="347 164 1499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1504">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(138,a,1499,a)].">
      <j1 rule="hyper" parents="138 1499"/>
    </justification>
  </clause>

  <clause id="1505">
    <literal><![CDATA[
      (x * T(y,z)) / y = (x / y) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,164,a(flip),b,1499,a)].">
      <j1 rule="hyper" parents="131 164 1499"/>
    </justification>
  </clause>

  <clause id="1506">
    <literal><![CDATA[
      (x * (y * x)) / x = y * T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(131,a,111,a(flip),b,1499,a)].">
      <j1 rule="hyper" parents="131 111 1499"/>
    </justification>
  </clause>

  <clause id="1507">
    <literal><![CDATA[
      ((x / T(y,z)) / y) * T(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(719,a,1499,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="719 1499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1508">
    <literal><![CDATA[
      (x * (y / z)) * T(y / z,z) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(113(a,1),1499(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="113 1499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1509">
    <literal><![CDATA[
      ((x * y) * T(y,z)) \ (x * T(y,z)) = L(y \ 1,y,x * T(y,z))
    ]]></literal>
    <justification jstring="[para(1499(a,1),244(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1499 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1510">
    <literal><![CDATA[
      (1 / T(x,y)) \ (x / T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(138,a,1501,a)].">
      <j1 rule="hyper" parents="138 1501"/>
    </justification>
  </clause>

  <clause id="1511">
    <literal><![CDATA[
      (1 / T(x,y)) * x != z
    ]]></literal>
    <literal><![CDATA[
      x / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1510(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1510 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1512">
    <literal><![CDATA[
      (1 / T(x,y)) * T(x,z) = T(x,z) / T(x,y)
    ]]></literal>
    <justification jstring="[para(1510(a,1),1168(a,1,2,1))].">
      <j1 rule="para" parents="1510 1168"/>
    </justification>
  </clause>

  <clause id="1513">
    <literal><![CDATA[
      T(x,1 / T(x,y)) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1510(a,1),1172(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1510 1172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1514">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(133,a,1269,a,b,1500,a)].">
      <j1 rule="hyper" parents="133 1269 1500"/>
    </justification>
  </clause>

  <clause id="1516">
    <literal><![CDATA[
      (x * y) / T(y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      T(x / T(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(1500(a,2),270(a,2)),flip(a)].">
      <j1 rule="para" parents="1500 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1517">
    <literal><![CDATA[
      (x / y) * T(y,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,111,a(flip),b,1503,a),flip(a)].">
      <j1 rule="hyper" parents="131 111 1503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1518">
    <literal><![CDATA[
      T(x,y) \ ((x * y) / x) = T(y / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(462,a,xx,b,1517,a),flip(a)].">
      <j1 rule="hyper" parents="462 1517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1519">
    <literal><![CDATA[
      ((x \ y) * y) / (x \ y) = x * T(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(370,a,1517,a),flip(a)].">
      <j1 rule="hyper" parents="370 1517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1520">
    <literal><![CDATA[
      ((x * y) / x) / T(x,y) = y / x
    ]]></literal>
    <justification jstring="[hyper(145,a,1517,a)].">
      <j1 rule="hyper" parents="145 1517"/>
    </justification>
  </clause>

  <clause id="1521">
    <literal><![CDATA[
      T(x,y) = (y / x) \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(138,a,1517,a),flip(a)].">
      <j1 rule="hyper" parents="138 1517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1522">
    <literal><![CDATA[
      (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = (y * x) * T(L(x \ 1,x,y),y)
    ]]></literal>
    <justification jstring="[para(412(a,1),1517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="412 1517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1523">
    <literal><![CDATA[
      ((x * (y * x)) / x) / T(x,y * x) = y
    ]]></literal>
    <justification jstring="[hyper(347,a,11,a(flip),b,1520,a),flip(a)].">
      <j1 rule="hyper" parents="347 11 1520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1524">
    <literal><![CDATA[
      R(T(x,y * T(x,z)),y,T(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1504(a,1),1211(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1504 1211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1525">
    <literal><![CDATA[
      x * T(y,x * y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * (x * y)) / y = z
    ]]></literal>
    <justification jstring="[para(1523(a,1),280(a,1,1))].">
      <j1 rule="para" parents="1523 280"/>
    </justification>
  </clause>

  <clause id="1526">
    <literal><![CDATA[
      R(x,y,T(z,u)) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      T(z,y * T(z,u)) = x
    ]]></literal>
    <justification jstring="[para(1524(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="1524 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1528">
    <literal><![CDATA[
      (T(x,y) / T(x,z)) / T(x,y) = 1 / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1512,a)].">
      <j1 rule="hyper" parents="145 1512"/>
    </justification>
  </clause>

  <clause id="1529">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(1514(a,1),1224(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1514 1224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1530">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x * (x * y)) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(145,a,1529,a),flip(a)].">
      <j1 rule="hyper" parents="145 1529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1531">
    <literal><![CDATA[
      (x * (x * y)) / (y * x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1269,a(flip),b,1530,a),flip(a)].">
      <j1 rule="hyper" parents="63 1269 1530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1532">
    <literal><![CDATA[
      R(((x * (x * y)) / x) / y,y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,605,a,b,1531,a)].">
      <j1 rule="hyper" parents="63 605 1531"/>
    </justification>
  </clause>

  <clause id="1533">
    <literal><![CDATA[
      (x * (y / z)) * (z \ y) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(113(a,1),1508(a,1,2))].">
      <j1 rule="para" parents="113 1508"/>
    </justification>
  </clause>

  <clause id="1534">
    <literal><![CDATA[
      (x * (y \ (y * z))) * ((y * z) / y) = (x * ((y * z) / y)) * z
    ]]></literal>
    <justification jstring="[para(254(a,1),1508(a,1,2)),flip(a)].">
      <j1 rule="para" parents="254 1508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1535">
    <literal><![CDATA[
      ((x / (y \ z)) / (z / y)) * (y \ z) = x / (z / y)
    ]]></literal>
    <justification jstring="[hyper(719,a,1533,a),flip(a)].">
      <j1 rule="hyper" parents="719 1533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1536">
    <literal><![CDATA[
      (x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(717,a,1533,a)].">
      <j1 rule="hyper" parents="717 1533"/>
    </justification>
  </clause>

  <clause id="1537">
    <literal><![CDATA[
      (1 / (x / y)) * (y \ x) = (y \ x) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(655,a,1533,a),flip(a)].">
      <j1 rule="hyper" parents="655 1533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1538">
    <literal><![CDATA[
      (x * (y / z)) / (z \ y) = (x / (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(131,a,164,a(flip),b,1533,a)].">
      <j1 rule="hyper" parents="131 164 1533"/>
    </justification>
  </clause>

  <clause id="1539">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) / (y / x)) = T(1 / (y / x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(462,a,xx,b,1537,a),flip(a)].">
      <j1 rule="hyper" parents="462 1537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1540">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = x \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,1455,a(flip),b,1537,a),flip(a)].">
      <j1 rule="hyper" parents="63 1455 1537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1542">
    <literal><![CDATA[
      K(T(1 / (1 / x),x \ 1),x \ 1) = T(x,x \ 1) / x
    ]]></literal>
    <justification jstring="[para(1539(a,1),1322(a,1,1))].">
      <j1 rule="para" parents="1539 1322"/>
    </justification>
  </clause>

  <clause id="1543">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u))
    ]]></literal>
    <justification jstring="[hyper(347,a,1022,a(flip),b,1487,a),flip(a)].">
      <j1 rule="hyper" parents="347 1022 1487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1544">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[para(77(a,1),1487(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="77 1487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1545">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(1487(a,1),629(a,1))].">
      <j1 rule="para" parents="1487 629"/>
    </justification>
  </clause>

  <clause id="1546">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1022,a(flip),b,1544,a)].">
      <j1 rule="hyper" parents="63 1022 1544"/>
    </justification>
  </clause>

  <clause id="1547">
    <literal><![CDATA[
      T(x,x * T(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(269,a,864,a(flip),b,1544,a(flip))].">
      <j1 rule="hyper" parents="269 864 1544"/>
    </justification>
  </clause>

  <clause id="1548">
    <literal><![CDATA[
      R(x,(x * T(x \ 1,y)) / x,x) = T(x,(x * T(x \ 1,y)) / x)
    ]]></literal>
    <justification jstring="[para(1547(a,1),1046(a,1,1))].">
      <j1 rule="para" parents="1547 1046"/>
    </justification>
  </clause>

  <clause id="1549">
    <literal><![CDATA[
      T(x \ 1,T(x,y) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(486(a,1),1547(a,1,2))].">
      <j1 rule="para" parents="486 1547"/>
    </justification>
  </clause>

  <clause id="1550">
    <literal><![CDATA[
      T(x \ 1,x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1140(a,1),1547(a,1,2))].">
      <j1 rule="para" parents="1140 1547"/>
    </justification>
  </clause>

  <clause id="1551">
    <literal><![CDATA[
      T(1 / x,T(x,y) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(1147(a,1),1547(a,1,2))].">
      <j1 rule="para" parents="1147 1547"/>
    </justification>
  </clause>

  <clause id="1552">
    <literal><![CDATA[
      (x \ T(x,y)) * (x \ 1) = (x \ 1) * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(1068,a,1550,a),flip(a)].">
      <j1 rule="hyper" parents="1068 1550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1553">
    <literal><![CDATA[
      T(x \ T(x,y),x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,1550,a)].">
      <j1 rule="hyper" parents="54 1550"/>
    </justification>
  </clause>

  <clause id="1554">
    <literal><![CDATA[
      T((x * (1 / y)) / x,T(y,z) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(1551(a,1),504(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1551 504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1555">
    <literal><![CDATA[
      R(x \ 1,T(x,y),x \ 1) = T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(1549(a,1),1042(a,1,1))].">
      <j1 rule="para" parents="1549 1042"/>
    </justification>
  </clause>

  <clause id="1556">
    <literal><![CDATA[
      T((x * y) \ (y * x),y \ 1) = L(y \ T(y,x),y,x)
    ]]></literal>
    <justification jstring="[para(1553(a,1),878(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1553 878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1557">
    <literal><![CDATA[
      K(x,y) = T((y * x) \ (x * y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,877,a,b,1556,a)].">
      <j1 rule="hyper" parents="347 877 1556"/>
    </justification>
  </clause>

  <clause id="1558">
    <literal><![CDATA[
      T(K(x,y),x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[para(16(a,2),1557(a,2,1)),flip(a)].">
      <j1 rule="para" parents="16 1557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1559">
    <literal><![CDATA[
      T(x \ 1,K(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(54,a,1558,a)].">
      <j1 rule="hyper" parents="54 1558"/>
    </justification>
  </clause>

  <clause id="1560">
    <literal><![CDATA[
      (x \ 1) * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ 1) = z
    ]]></literal>
    <justification jstring="[para(1558(a,1),315(a,1,2))].">
      <j1 rule="para" parents="1558 315"/>
    </justification>
  </clause>

  <clause id="1561">
    <literal><![CDATA[
      T((x * y) \ x,K(y,z)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(1559(a,1),415(a,2,1))].">
      <j1 rule="para" parents="1559 415"/>
    </justification>
  </clause>

  <clause id="1562">
    <literal><![CDATA[
      T((x * y) \ x,K(y,z)) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(347,a,244,a(flip),b,1561,a),flip(a)].">
      <j1 rule="hyper" parents="347 244 1561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1563">
    <literal><![CDATA[
      T(K(x,y),(z * x) \ z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,1562,a)].">
      <j1 rule="hyper" parents="54 1562"/>
    </justification>
  </clause>

  <clause id="1564">
    <literal><![CDATA[
      T(K(x \ 1,y),x) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(183(a,1),1563(a,1,2))].">
      <j1 rule="para" parents="183 1563"/>
    </justification>
  </clause>

  <clause id="1565">
    <literal><![CDATA[
      K(x \ 1,y) * x = x * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1068,a,1564,a)].">
      <j1 rule="hyper" parents="1068 1564"/>
    </justification>
  </clause>

  <clause id="1566">
    <literal><![CDATA[
      (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = ((x \ 1) * T((x \ 1) \ 1,y)) * z
    ]]></literal>
    <justification jstring="[para(1351(a,2),1546(a,1,2))].">
      <j1 rule="para" parents="1351 1546"/>
    </justification>
  </clause>

  <clause id="1567">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * (y \ ((x \ y) * x))
    ]]></literal>
    <justification jstring="[para(1078(a,1),1490(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1078 1490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1568">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(92(a,1),1567(a,2,2))].">
      <j1 rule="para" parents="92 1567"/>
    </justification>
  </clause>

  <clause id="1569">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(y \ (y * x),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1568(a,1,1,1))].">
      <j1 rule="para" parents="9 1568"/>
    </justification>
  </clause>

  <clause id="1570">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1569(a,2,2,1))].">
      <j1 rule="para" parents="9 1569"/>
    </justification>
  </clause>

  <clause id="1571">
    <literal><![CDATA[
      (x * y) * L(x \ 1,x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,410,a,b,1570,a)].">
      <j1 rule="hyper" parents="63 410 1570"/>
    </justification>
  </clause>

  <clause id="1572">
    <literal><![CDATA[
      x \ (y * K(x / y,y)) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(128,a,1570,a(flip),b,164,a(flip))].">
      <j1 rule="hyper" parents="128 1570 164"/>
    </justification>
  </clause>

  <clause id="1574">
    <literal><![CDATA[
      (x * L(x,y,z)) \ (x * (L(x,y,z) * u)) = L(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),1494(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1575">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ (z * u)),w))) / u = ((x * y) / u) * T(((x * y) / u) \ z,w)
    ]]></literal>
    <justification jstring="[hyper(131,a,1022,a(flip),b,1495,a)].">
      <j1 rule="hyper" parents="131 1022 1495"/>
    </justification>
  </clause>

  <clause id="1576">
    <literal><![CDATA[
      (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,111,a(flip),b,1495,a),flip(a)].">
      <j1 rule="hyper" parents="131 111 1495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1577">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ 1,z)) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),1495(a,2,2,1,2))].">
      <j1 rule="para" parents="7 1495"/>
    </justification>
  </clause>

  <clause id="1578">
    <literal><![CDATA[
      (x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y
    ]]></literal>
    <justification jstring="[hyper(145,a,1577,a),flip(a)].">
      <j1 rule="hyper" parents="145 1577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1579">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) * z = y * T(y \ z,x)
    ]]></literal>
    <justification jstring="[para(1320(a,2),1577(a,1,1))].">
      <j1 rule="para" parents="1320 1577"/>
    </justification>
  </clause>

  <clause id="1580">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) = (y * T(y \ z,x)) / z
    ]]></literal>
    <justification jstring="[hyper(145,a,1579,a),flip(a)].">
      <j1 rule="hyper" parents="145 1579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1581">
    <literal><![CDATA[
      K((x * (y / z)) \ x,x * (y / z)) = (y * T(y \ z,x * (y / z))) / z
    ]]></literal>
    <justification jstring="[para(11(a,1),1580(a,1,1,2))].">
      <j1 rule="para" parents="11 1580"/>
    </justification>
  </clause>

  <clause id="1582">
    <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),1580(a,1,1,2,2))].">
      <j1 rule="para" parents="20 1580"/>
    </justification>
  </clause>

  <clause id="1583">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = ((y \ x) * ((y \ x) \ x)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(1264(a,1),1580(a,2,1,2))].">
      <j1 rule="para" parents="1264 1580"/>
    </justification>
  </clause>

  <clause id="1584">
    <literal><![CDATA[
      (x * L(x \ (y \ x),z,u)) / (y \ x) = y * L(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,1496,a)].">
      <j1 rule="hyper" parents="145 1496"/>
    </justification>
  </clause>

  <clause id="1585">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1022,a(flip),b,1498,a)].">
      <j1 rule="hyper" parents="63 1022 1498"/>
    </justification>
  </clause>

  <clause id="1586">
    <literal><![CDATA[
      ((x * y) * T((x * y) \ x,z)) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,864,a(flip),b,1498,a),flip(a)].">
      <j1 rule="hyper" parents="63 864 1498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1587">
    <literal><![CDATA[
      x * T(x \ (x \ (y * x)),z) = T(x * T(x \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(269,a,1498,a(flip),b,1022,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="269 1498 1022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1588">
    <literal><![CDATA[
      T(x * T(x \ y,z),x) = x * T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[para(22(a,2),1587(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1589">
    <literal><![CDATA[
      x \ T(x * T(x \ y,z),x) = T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(908,a,1588,a)].">
      <j1 rule="hyper" parents="908 1588"/>
    </justification>
  </clause>

  <clause id="1590">
    <literal><![CDATA[
      x * T(x \ T(y,x),x) = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[para(111(a,1),1588(a,1,1)),flip(a)].">
      <j1 rule="para" parents="111 1588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1591">
    <literal><![CDATA[
      T((x \ y) * x,x) = (x \ T(y,x)) * x
    ]]></literal>
    <justification jstring="[hyper(315,a,1590,a),flip(a)].">
      <j1 rule="hyper" parents="315 1590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1592">
    <literal><![CDATA[
      T((x \ y) * x,x) / x = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,1590,a(flip),b,111,a(flip))].">
      <j1 rule="hyper" parents="131 1590 111"/>
    </justification>
  </clause>

  <clause id="1593">
    <literal><![CDATA[
      x * (T((x \ y) * x,x) / x) = T(y,x)
    ]]></literal>
    <justification jstring="[para(1591(a,2),79(a,1,2,1))].">
      <j1 rule="para" parents="1591 79"/>
    </justification>
  </clause>

  <clause id="1594">
    <literal><![CDATA[
      T(x * y,y) / y = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1592(a,1,1,1,1))].">
      <j1 rule="para" parents="9 1592"/>
    </justification>
  </clause>

  <clause id="1595">
    <literal><![CDATA[
      x \ T(x * (y / x),x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(84(a,1),1592(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="84 1592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1596">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (T(y,x) / x)
    ]]></literal>
    <justification jstring="[para(84(a,1),1593(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="84 1593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1597">
    <literal><![CDATA[
      T(x * ((1 / x) * y),x) = x * ((1 / x) * T(y,x))
    ]]></literal>
    <justification jstring="[hyper(134,a,1144,a(flip),b,1594,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 1144 1594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1598">
    <literal><![CDATA[
      x \ T(x * T((x * y) / x,z),x) = T(x * T(y,z),x) / x
    ]]></literal>
    <justification jstring="[para(485(a,1),1594(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="485 1594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1599">
    <literal><![CDATA[
      x \ T(x * L((x * y) / x,z,u),x) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[para(741(a,1),1594(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="741 1594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1600">
    <literal><![CDATA[
      T(x \ T(x * y,x),z) = x \ T(x * T(y,z),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1589(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1601">
    <literal><![CDATA[
      x \ T(x * T(y / x,z),x) = T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[para(1595(a,1),1600(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1595 1600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1602">
    <literal><![CDATA[
      T(x * T(y / x,z),x) = x * T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(150,a,1601,a),flip(a)].">
      <j1 rule="hyper" parents="150 1601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1603">
    <literal><![CDATA[
      T(x * T(1 / x,y),x) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(226(a,1),1602(a,2,2,1,1))].">
      <j1 rule="para" parents="226 1602"/>
    </justification>
  </clause>

  <clause id="1604">
    <literal><![CDATA[
      (x * ((y * z) / y)) * z = (x * z) * ((y * z) / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),1534(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1606">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * y = y / ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(655,a,1604,a),flip(a)].">
      <j1 rule="hyper" parents="655 1604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1607">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,81,a(flip),b,1604,a),flip(a)].">
      <j1 rule="hyper" parents="131 81 1604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1608">
    <literal><![CDATA[
      ((x * (y \ 1)) / x) / (y \ 1) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(131,a,71,a(flip),b,1604,a)].">
      <j1 rule="hyper" parents="131 71 1604"/>
    </justification>
  </clause>

  <clause id="1610">
    <literal><![CDATA[
      ((x / y) * y) * ((x * y) / x) = T(x,x / (x / y)) * y
    ]]></literal>
    <justification jstring="[para(1261(a,1),1604(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1261 1604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1611">
    <literal><![CDATA[
      (1 / x) * ((y * ((z / x) \ z)) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[para(217(a,2),1607(a,1,2,1))].">
      <j1 rule="para" parents="217 1607"/>
    </justification>
  </clause>

  <clause id="1612">
    <literal><![CDATA[
      T(x,x / (x / y)) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(353,a,1610,a),flip(a)].">
      <j1 rule="hyper" parents="353 1610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1613">
    <literal><![CDATA[
      T(x,x / (x / y)) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1245,a,1612,a)].">
      <j1 rule="hyper" parents="1245 1612"/>
    </justification>
  </clause>

  <clause id="1615">
    <literal><![CDATA[
      ((x * y) / x) / (x \ y) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(145,a,1613,a)].">
      <j1 rule="hyper" parents="145 1613"/>
    </justification>
  </clause>

  <clause id="1616">
    <literal><![CDATA[
      x * ((y \ z) * T((y \ z) \ (x \ z),u)) = (x * T(x \ y,u)) * (y \ z)
    ]]></literal>
    <justification jstring="[para(80(a,1),1543(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="80 1543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1617">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(1543(a,1),629(a,1))].">
      <j1 rule="para" parents="1543 629"/>
    </justification>
  </clause>

  <clause id="1618">
    <literal><![CDATA[
      (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y
    ]]></literal>
    <justification jstring="[para(1056(a,1),1543(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1056 1543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1619">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ (x \ x),y))
    ]]></literal>
    <justification jstring="[para(1279(a,2),1543(a,1,1))].">
      <j1 rule="para" parents="1279 1543"/>
    </justification>
  </clause>

  <clause id="1620">
    <literal><![CDATA[
      L(x,L(y,z,u),y) = L(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(545,a,1574,a)].">
      <j1 rule="hyper" parents="545 1574"/>
    </justification>
  </clause>

  <clause id="1621">
    <literal><![CDATA[
      x * ((y \ (x \ (z * y))) * y) = (x * T(x \ z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(639,a,1585,a)].">
      <j1 rule="hyper" parents="639 1585"/>
    </justification>
  </clause>

  <clause id="1622">
    <literal><![CDATA[
      T(x * ((1 / x) * ((1 / x) \ (x \ (y * (1 / x))))),x) = (x * T(x \ y,x)) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1597,a,b,1585,a)].">
      <j1 rule="hyper" parents="63 1597 1585"/>
    </justification>
  </clause>

  <clause id="1624">
    <literal><![CDATA[
      T(x * T(y,z),x) / x = T(T(x * y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1601,a(flip),b,1598,a),flip(a)].">
      <j1 rule="hyper" parents="63 1601 1598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1625">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(68(a,1),1619(a,2,2,2,1,2))].">
      <j1 rule="para" parents="68 1619"/>
    </justification>
  </clause>

  <clause id="1627">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(387(a,1),1625(a,2,2))].">
      <j1 rule="para" parents="387 1625"/>
    </justification>
  </clause>

  <clause id="1628">
    <literal><![CDATA[
      (R(x,y \ 1,y) / y) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,597,a(flip),b,1627,a),flip(a)].">
      <j1 rule="hyper" parents="35 597 1627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1629">
    <literal><![CDATA[
      (L(x,y,z) * (z * y)) \ (x * (z * y)) = a(z,y,T(x,z * y))
    ]]></literal>
    <justification jstring="[para(734(a,1),260(a,1,1))].">
      <j1 rule="para" parents="734 260"/>
    </justification>
  </clause>

  <clause id="1630">
    <literal><![CDATA[
      (L(x,y \ z,y) * z) \ (x * (y * (y \ z))) = a(y,y \ z,T(x,y * (y \ z)))
    ]]></literal>
    <justification jstring="[para(10(a,1),1629(a,1,1,2))].">
      <j1 rule="para" parents="10 1629"/>
    </justification>
  </clause>

  <clause id="1631">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z)
    ]]></literal>
    <justification jstring="[hyper(134,a,998,a(flip),b,98,a),flip(a)].">
      <j1 rule="hyper" parents="134 998 98"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1632">
    <literal><![CDATA[
      x \ (y * ((z * (y \ (x * u))) / z)) = (x \ y) * ((z * ((x \ y) \ u)) / z)
    ]]></literal>
    <justification jstring="[para(998(a,1),538(a,1,2,2))].">
      <j1 rule="para" parents="998 538"/>
    </justification>
  </clause>

  <clause id="1633">
    <literal><![CDATA[
      R(x \ y,x \ y,a(x,x \ y,x \ y)) \ (x \ (y * (x \ y))) = (x \ y) * (((x \ y) * (x \ y)) \ (x \ (y * (x \ y))))
    ]]></literal>
    <justification jstring="[para(1007(a,1),581(a,1,1,3))].">
      <j1 rule="para" parents="1007 581"/>
    </justification>
  </clause>

  <clause id="1634">
    <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(570(a,1),1011(a,1,2,1))].">
      <j1 rule="para" parents="570 1011"/>
    </justification>
  </clause>

  <clause id="1635">
    <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(134,a,1027,a(flip),b,262,a)].">
      <j1 rule="hyper" parents="134 1027 262"/>
    </justification>
  </clause>

  <clause id="1636">
    <literal><![CDATA[
      (1 / (x \ y)) \ (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(408(a,1),1334(a,1,1)),flip(a)].">
      <j1 rule="para" parents="408 1334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1637">
    <literal><![CDATA[
      x \ (y * L(y \ x,x \ y,x)) = (1 / (y \ x)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,538,a,b,1636,a)].">
      <j1 rule="hyper" parents="347 538 1636"/>
    </justification>
  </clause>

  <clause id="1638">
    <literal><![CDATA[
      (1 / (x \ y)) * ((y \ x) * (x \ y)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(150,a,1636,a)].">
      <j1 rule="hyper" parents="150 1636"/>
    </justification>
  </clause>

  <clause id="1639">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(408(a,1),1345(a,1,2))].">
      <j1 rule="para" parents="408 1345"/>
    </justification>
  </clause>

  <clause id="1640">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) * ((x \ y) \ 1) = y \ x
    ]]></literal>
    <justification jstring="[hyper(150,a,1639,a)].">
      <j1 rule="hyper" parents="150 1639"/>
    </justification>
  </clause>

  <clause id="1641">
    <literal><![CDATA[
      L(T(((x * y) * z) / (x * y),y),y,x) = (x * (z * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(504(a,1),1363(a,1,1))].">
      <j1 rule="para" parents="504 1363"/>
    </justification>
  </clause>

  <clause id="1642">
    <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),1431(a,2,1))].">
      <j1 rule="para" parents="11 1431"/>
    </justification>
  </clause>

  <clause id="1643">
    <literal><![CDATA[
      x * T(y,L(y,z,u) * x) = L(y,x,L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,1642,a(flip),b,504,a),flip(a)].">
      <j1 rule="hyper" parents="133 1642 504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1644">
    <literal><![CDATA[
      L(T(x,y),y,L(x,z,u)) = T(x,L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(34,a,267,a,b,1643,a)].">
      <j1 rule="hyper" parents="34 267 1643"/>
    </justification>
  </clause>

  <clause id="1645">
    <literal><![CDATA[
      T(x,(x * T(x \ 1,y)) / x) = R(x,T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(490(a,1),1548(a,1,2)),flip(a)].">
      <j1 rule="para" parents="490 1548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1646">
    <literal><![CDATA[
      R(x,T(1 / x,y),x) = T(x,T(1 / x,y))
    ]]></literal>
    <justification jstring="[para(490(a,1),1645(a,1,2)),flip(a)].">
      <j1 rule="para" parents="490 1645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1647">
    <literal><![CDATA[
      x * (y \ T(y * (x \ z),x)) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / (y \ 1))) * x) * (y \ 1) = u
    ]]></literal>
    <justification jstring="[para(1056(a,1),1617(a,1,2))].">
      <j1 rule="para" parents="1056 1617"/>
    </justification>
  </clause>

  <clause id="1648">
    <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(1401(a,1),488(a,1,1))].">
      <j1 rule="para" parents="1401 488"/>
    </justification>
  </clause>

  <clause id="1649">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(999,a,1176,a)].">
      <j1 rule="hyper" parents="999 1176"/>
    </justification>
  </clause>

  <clause id="1651">
    <literal><![CDATA[
      R((x * y) / (x * z),u,w) * (x * z) = x * (z * R(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,746,a,b,1185,a)].">
      <j1 rule="hyper" parents="63 746 1185"/>
    </justification>
  </clause>

  <clause id="1652">
    <literal><![CDATA[
      (T(x,y) * z) * T(x,z) = (x * z) * T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(1216,a,1013,a)].">
      <j1 rule="hyper" parents="1216 1013"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(131,a,71,a(flip),b,1652,a)].">
      <j1 rule="hyper" parents="131 71 1652"/>
    </justification>
  </clause>

  <clause id="1654">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,1142,a(flip),b,1653,a),flip(a)].">
      <j1 rule="hyper" parents="347 1142 1653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1655">
    <literal><![CDATA[
      (((x * y) / x) * (y \ 1)) * x = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(1004,a,1258,a)].">
      <j1 rule="hyper" parents="1004 1258"/>
    </justification>
  </clause>

  <clause id="1656">
    <literal><![CDATA[
      (x \ ((y * x) / y)) * y = T(y,R(x,x \ 1,y))
    ]]></literal>
    <justification jstring="[para(1318(a,1),1655(a,1,1))].">
      <j1 rule="para" parents="1318 1655"/>
    </justification>
  </clause>

  <clause id="1657">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) / x = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(145,a,1656,a)].">
      <j1 rule="hyper" parents="145 1656"/>
    </justification>
  </clause>

  <clause id="1658">
    <literal><![CDATA[
      (1 / x) \ ((y * (1 / x)) / y) = T(y,R(1 / x,x,y)) / y
    ]]></literal>
    <justification jstring="[para(83(a,1),1657(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="83 1657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1659">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) / x = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(1378,a,1658,a),flip(a)].">
      <j1 rule="hyper" parents="1378 1658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1660">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(1 / x,x,y))
    ]]></literal>
    <justification jstring="[hyper(148,a,1659,a)].">
      <j1 rule="hyper" parents="148 1659"/>
    </justification>
  </clause>

  <clause id="1661">
    <literal><![CDATA[
      (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,R(1 / T(x,y),T(x,y),x))
    ]]></literal>
    <justification jstring="[para(1230(a,1),1660(a,1,1,2,1))].">
      <j1 rule="para" parents="1230 1660"/>
    </justification>
  </clause>

  <clause id="1662">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ y,z,u) = L(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(83(a,1),1338(a,1,2)),flip(a)].">
      <j1 rule="para" parents="83 1338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1663">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ 1,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1662(a,2,1,1))].">
      <j1 rule="para" parents="7 1662"/>
    </justification>
  </clause>

  <clause id="1664">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(83(a,1),1663(a,1,2,1))].">
      <j1 rule="para" parents="83 1663"/>
    </justification>
  </clause>

  <clause id="1665">
    <literal><![CDATA[
      (L(x,y,z) / x) / L(x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(145,a,1664,a)].">
      <j1 rule="hyper" parents="145 1664"/>
    </justification>
  </clause>

  <clause id="1666">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),1 / x) = (L(x,y,z) / x) \ ((1 / x) * u)
    ]]></literal>
    <justification jstring="[para(1664(a,1),99(a,2,1))].">
      <j1 rule="para" parents="1664 99"/>
    </justification>
  </clause>

  <clause id="1667">
    <literal><![CDATA[
      T((L(x,y,z) * (1 / x)) / L(x,y,z),L(x,y,z) / x) = L(1 / x,L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[para(1664(a,1),755(a,1,2))].">
      <j1 rule="para" parents="1664 755"/>
    </justification>
  </clause>

  <clause id="1668">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ 1,z,u) = x \ (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),1359(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 1359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1669">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * R((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) * R(((x * y) \ (x * (y * z))) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),1668(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 1668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1670">
    <literal><![CDATA[
      x \ ((y * x) * R((y * x) \ x,z,u)) = T(y,x) * R((x \ (y * x)) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),1668(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22 1668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1671">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),1360(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 1360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1672">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ (x \ z),u,w) = x \ (y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),1360(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 1360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1673">
    <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),1360(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14 1360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1674">
    <literal><![CDATA[
      x \ (y * L(y \ (x * z),u,w)) != (x \ y) * v5
    ]]></literal>
    <literal><![CDATA[
      L((x \ y) \ z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(1360(a,2),43(a,1))].">
      <j1 rule="para" parents="1360 43"/>
    </justification>
  </clause>

  <clause id="1675">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * L((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) * L(((x * y) \ (x * (y * z))) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),1671(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 1671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1676">
    <literal><![CDATA[
      x \ (y * L(y \ x,z,u)) != (x \ y) * w
    ]]></literal>
    <literal><![CDATA[
      L((x \ y) \ 1,z,u) = w
    ]]></literal>
    <justification jstring="[para(1671(a,1),43(a,1))].">
      <j1 rule="para" parents="1671 43"/>
    </justification>
  </clause>

  <clause id="1677">
    <literal><![CDATA[
      (x / y) \ (x * ((z * (x \ (x / y))) / z)) = y * ((z * (y \ 1)) / z)
    ]]></literal>
    <justification jstring="[hyper(138,a,1366,a)].">
      <j1 rule="hyper" parents="138 1366"/>
    </justification>
  </clause>

  <clause id="1678">
    <literal><![CDATA[
      T(1 / x,(y / (x * y)) * x) != z
    ]]></literal>
    <literal><![CDATA[
      L(x \ 1,x,y / (x * y)) = z
    ]]></literal>
    <justification jstring="[para(1474(a,1),443(a,1))].">
      <j1 rule="para" parents="1474 443"/>
    </justification>
  </clause>

  <clause id="1679">
    <literal><![CDATA[
      x \ R(x * (y * (x \ 1)),z,u) = R(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,268,a(flip),b,1480,a),flip(a)].">
      <j1 rule="hyper" parents="347 268 1480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1680">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y) * (T(x,y) \ x),z,u) = R(x,z,u) * (T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(1230(a,1),1679(a,1,2,1,2))].">
      <j1 rule="para" parents="1230 1679"/>
    </justification>
  </clause>

  <clause id="1681">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(864(a,1),1586(a,1,1))].">
      <j1 rule="para" parents="864 1586"/>
    </justification>
  </clause>

  <clause id="1682">
    <literal><![CDATA[
      a(L(x,y,z),x,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,L(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(1648(a,1),836(a,1))].">
      <j1 rule="para" parents="1648 836"/>
    </justification>
  </clause>

  <clause id="1683">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(746(a,1),1649(a,2,1))].">
      <j1 rule="para" parents="746 1649"/>
    </justification>
  </clause>

  <clause id="1684">
    <literal><![CDATA[
      (((x * y) / (x * z)) * x) * z = x * (z * R(z \ y,x,z))
    ]]></literal>
    <justification jstring="[hyper(314,a,1651,a)].">
      <j1 rule="hyper" parents="314 1651"/>
    </justification>
  </clause>

  <clause id="1685">
    <literal><![CDATA[
      R((x * y) / (x * z),u,w) * (x * z) = x * (R(y / z,u,w) * z)
    ]]></literal>
    <justification jstring="[para(746(a,2),1651(a,2,2))].">
      <j1 rule="para" parents="746 1651"/>
    </justification>
  </clause>

  <clause id="1686">
    <literal><![CDATA[
      (((x * (y * z)) / (x * y)) * x) * y = x * (y * R(z,x,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),1684(a,2,2,2,1))].">
      <j1 rule="para" parents="9 1684"/>
    </justification>
  </clause>

  <clause id="1687">
    <literal><![CDATA[
      (x \ y) \ (x \ (y * L(y \ z,u,w))) = L((x \ y) \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(138,a,1672,a)].">
      <j1 rule="hyper" parents="138 1672"/>
    </justification>
  </clause>

  <clause id="1688">
    <literal><![CDATA[
      L(x,y,z) != (u \ w) \ (u \ (w * L(w \ v5,y,z)))
    ]]></literal>
    <literal><![CDATA[
      (u \ w) \ (u \ v5) = x
    ]]></literal>
    <justification jstring="[para(1672(a,1),158(a,2,2))].">
      <j1 rule="para" parents="1672 158"/>
    </justification>
  </clause>

  <clause id="1689">
    <literal><![CDATA[
      (x / y) \ (x * ((x / y) / x)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),1677(a,1,2,2,1))].">
      <j1 rule="para" parents="10 1677"/>
    </justification>
  </clause>

  <clause id="1690">
    <literal><![CDATA[
      K(x,(x / y) / x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(513,a,1689,a)].">
      <j1 rule="hyper" parents="513 1689"/>
    </justification>
  </clause>

  <clause id="1691">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,(y / x) / y) = z
    ]]></literal>
    <justification jstring="[para(1689(a,1),513(a,1))].">
      <j1 rule="para" parents="1689 513"/>
    </justification>
  </clause>

  <clause id="1692">
    <literal><![CDATA[
      K(x,(x / (y \ 1)) / x) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(347,a,1399,a(flip),b,1690,a),flip(a)].">
      <j1 rule="hyper" parents="347 1399 1690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1693">
    <literal><![CDATA[
      (x \ y) * ((y * ((x \ y) \ 1)) / y) = K(y,x / y)
    ]]></literal>
    <justification jstring="[para(80(a,1),1690(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="80 1690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1694">
    <literal><![CDATA[
      x * ((T(x,y) * (x \ 1)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(1150(a,1),1690(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1150 1690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1695">
    <literal><![CDATA[
      T(x,y) * ((T(x,z) * (T(x,y) \ 1)) / T(x,z)) = K(T(x,z),1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1528(a,1),1690(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1528 1690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1696">
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = K(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[para(1665(a,1),1690(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1665 1690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1697">
    <literal><![CDATA[
      K(x,(x / ((T(x,y) \ 1) \ 1)) / x) = (T(x,y) \ 1) \ ((T(x,y) \ x) / x)
    ]]></literal>
    <justification jstring="[para(1230(a,1),1692(a,2,2,1))].">
      <j1 rule="para" parents="1230 1692"/>
    </justification>
  </clause>

  <clause id="1698">
    <literal><![CDATA[
      x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(486(a,2),1694(a,1,2,1))].">
      <j1 rule="para" parents="486 1694"/>
    </justification>
  </clause>

  <clause id="1699">
    <literal><![CDATA[
      x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1186,a(flip),b,1683,a)].">
      <j1 rule="hyper" parents="63 1186 1683"/>
    </justification>
  </clause>

  <clause id="1700">
    <literal><![CDATA[
      x * R(x \ (x \ (y * x)),z,u) = T(x * R(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(269,a,1683,a(flip),b,1186,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="269 1683 1186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1701">
    <literal><![CDATA[
      (x \ (y * z)) * R((x \ (y * z)) \ z,u,w) = x \ ((y * R(y \ x,u,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(128,a,1683,a(flip),b,1357,a),flip(a)].">
      <j1 rule="hyper" parents="128 1683 1357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1702">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),1683(a,1,2,1,2))].">
      <j1 rule="para" parents="7 1683"/>
    </justification>
  </clause>

  <clause id="1703">
    <literal><![CDATA[
      (x * R(x \ (x * y),z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1683(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1704">
    <literal><![CDATA[
      (x * R(y,z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1703(a,1,1,2,1))].">
      <j1 rule="para" parents="9 1703"/>
    </justification>
  </clause>

  <clause id="1705">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = x / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(655,a,1704,a),flip(a)].">
      <j1 rule="hyper" parents="655 1704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1706">
    <literal><![CDATA[
      ((x / R(y,z,u)) * y) * R(y,z,u) = x * y
    ]]></literal>
    <justification jstring="[hyper(353,a,1704,a),flip(a)].">
      <j1 rule="hyper" parents="353 1704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1707">
    <literal><![CDATA[
      (x * R(y,z,u)) \ ((x * y) * R(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(138,a,1704,a)].">
      <j1 rule="hyper" parents="138 1704"/>
    </justification>
  </clause>

  <clause id="1708">
    <literal><![CDATA[
      (x * R(y,z,u)) / y = (x / y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(131,a,164,a(flip),b,1704,a)].">
      <j1 rule="hyper" parents="131 164 1704"/>
    </justification>
  </clause>

  <clause id="1709">
    <literal><![CDATA[
      ((x / y) * R(y,z,u)) \ (x * R(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(128,a,164,a(flip),b,1704,a)].">
      <j1 rule="hyper" parents="128 164 1704"/>
    </justification>
  </clause>

  <clause id="1710">
    <literal><![CDATA[
      (x * y) / R(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / R(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(1706(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1706 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1712">
    <literal><![CDATA[
      R(T(x,y * R(x,z,u)),y,R(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1707(a,1),1211(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1707 1211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1713">
    <literal><![CDATA[
      (x * R(y,z,u)) / y != w
    ]]></literal>
    <literal><![CDATA[
      (x / y) * R(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(1709(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1709 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1714">
    <literal><![CDATA[
      (x * R(y / x,z,u)) \ (y * R(y / x,z,u)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[hyper(1035,a,1712,a)].">
      <j1 rule="hyper" parents="1035 1712"/>
    </justification>
  </clause>

  <clause id="1715">
    <literal><![CDATA[
      T(R(x,y,R(x,z,u)),y * R(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,27,a(flip),b,1712,a)].">
      <j1 rule="hyper" parents="63 27 1712"/>
    </justification>
  </clause>

  <clause id="1716">
    <literal><![CDATA[
      (x * R(y,z,u)) * T(y,x) = (y * x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(134,a,1712,a(flip),b,744,a)].">
      <j1 rule="hyper" parents="134 1712 744"/>
    </justification>
  </clause>

  <clause id="1718">
    <literal><![CDATA[
      x / R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = u
    ]]></literal>
    <justification jstring="[para(7(a,1),1710(a,1,1))].">
      <j1 rule="para" parents="7 1710"/>
    </justification>
  </clause>

  <clause id="1719">
    <literal><![CDATA[
      T(x * R(x \ y,z,u),x) = x * R(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),1700(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1720">
    <literal><![CDATA[
      x \ T(x * R(x \ y,z,u),x) = R(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(908,a,1719,a)].">
      <j1 rule="hyper" parents="908 1719"/>
    </justification>
  </clause>

  <clause id="1721">
    <literal><![CDATA[
      T(x * R(x \ 1,y,z),x) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(226(a,1),1719(a,2,2,1,2))].">
      <j1 rule="para" parents="226 1719"/>
    </justification>
  </clause>

  <clause id="1722">
    <literal><![CDATA[
      T(x,x * R(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,1721,a)].">
      <j1 rule="hyper" parents="54 1721"/>
    </justification>
  </clause>

  <clause id="1723">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * ((x * R(x \ 1,y,z)) / x)
    ]]></literal>
    <justification jstring="[para(1721(a,1),1596(a,2,2,1))].">
      <j1 rule="para" parents="1721 1596"/>
    </justification>
  </clause>

  <clause id="1724">
    <literal><![CDATA[
      T(x \ 1,R(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(748(a,1),1722(a,1,2))].">
      <j1 rule="para" parents="748 1722"/>
    </justification>
  </clause>

  <clause id="1725">
    <literal><![CDATA[
      T(x \ 1,x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1462(a,1),1722(a,1,2))].">
      <j1 rule="para" parents="1462 1722"/>
    </justification>
  </clause>

  <clause id="1726">
    <literal><![CDATA[
      T(T(x \ 1,y),x \ R(x,z,u)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1725(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1725 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1727">
    <literal><![CDATA[
      R(x \ 1,R(x,y,z),x \ 1) = T(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1724(a,1),1042(a,1,1))].">
      <j1 rule="para" parents="1724 1042"/>
    </justification>
  </clause>

  <clause id="1728">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1186,a(flip),b,1702,a)].">
      <j1 rule="hyper" parents="63 1186 1702"/>
    </justification>
  </clause>

  <clause id="1729">
    <literal><![CDATA[
      x * ((x * y) * R((x * y) \ y,z,u)) = (x * R(x \ 1,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1185,a(flip),b,1702,a)].">
      <j1 rule="hyper" parents="63 1185 1702"/>
    </justification>
  </clause>

  <clause id="1731">
    <literal><![CDATA[
      (x * R(y / x,z,u)) * (x \ y) = y * R(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(134,a,113,a(flip),b,1714,a)].">
      <j1 rule="hyper" parents="134 113 1714"/>
    </justification>
  </clause>

  <clause id="1732">
    <literal><![CDATA[
      R(1 / x,y,z) / (x \ 1) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,7,a(flip),b,1731,a)].">
      <j1 rule="hyper" parents="131 7 1731"/>
    </justification>
  </clause>

  <clause id="1733">
    <literal><![CDATA[
      (x * ((x \ y) / y)) * (x \ 1) = R(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(133,a,669,a(flip),b,1732,a)].">
      <j1 rule="hyper" parents="133 669 1732"/>
    </justification>
  </clause>

  <clause id="1734">
    <literal><![CDATA[
      (x / y) * R(1 / (x / y),x / y,y) = (y / x) / ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(422(a,1),1732(a,1,1)),flip(a)].">
      <j1 rule="para" parents="422 1732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1735">
    <literal><![CDATA[
      ((x \ y) / y) / (x \ 1) = x * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(131,a,421,a(flip),b,1733,a)].">
      <j1 rule="hyper" parents="131 421 1733"/>
    </justification>
  </clause>

  <clause id="1737">
    <literal><![CDATA[
      R(x * ((x \ y) / y),x \ 1,y) = (x \ y) / ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1735(a,1),605(a,1,1))].">
      <j1 rule="para" parents="1735 605"/>
    </justification>
  </clause>

  <clause id="1738">
    <literal><![CDATA[
      (x / y) / ((y / x) \ 1) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[para(422(a,1),1734(a,1,2)),flip(a)].">
      <j1 rule="para" parents="422 1734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1739">
    <literal><![CDATA[
      ((x / y) * (y / x)) * ((x / y) \ 1) = y / x
    ]]></literal>
    <justification jstring="[hyper(148,a,1738,a)].">
      <j1 rule="hyper" parents="148 1738"/>
    </justification>
  </clause>

  <clause id="1740">
    <literal><![CDATA[
      R((x * (y * z)) / (x * z),u,w) * (x * z) = x * (R(y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(11(a,1),1685(a,2,2,1,1))].">
      <j1 rule="para" parents="11 1685"/>
    </justification>
  </clause>

  <clause id="1741">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ (x \ z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x \ (y * L(y \ z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(1687(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1687 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1742">
    <literal><![CDATA[
      R(x,y,z) * (z * R(z \ (y * z),u,w)) = (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z
    ]]></literal>
    <justification jstring="[para(209(a,1),1699(a,1,2,2,1,2))].">
      <j1 rule="para" parents="209 1699"/>
    </justification>
  </clause>

  <clause id="1743">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (R(y,x,z) * z)
    ]]></literal>
    <justification jstring="[hyper(314,a,1740,a)].">
      <j1 rule="hyper" parents="314 1740"/>
    </justification>
  </clause>

  <clause id="1744">
    <literal><![CDATA[
      R(x,y,z) * (x * u) = x * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(11(a,1),1740(a,1,1,1))].">
      <j1 rule="para" parents="11 1740"/>
    </justification>
  </clause>

  <clause id="1745">
    <literal><![CDATA[
      x \ ((x * x) * y) = R(x,x,y) * y
    ]]></literal>
    <justification jstring="[hyper(679,a,1744,a)].">
      <j1 rule="hyper" parents="679 1744"/>
    </justification>
  </clause>

  <clause id="1746">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(678,a,1744,a)].">
      <j1 rule="hyper" parents="678 1744"/>
    </justification>
  </clause>

  <clause id="1747">
    <literal><![CDATA[
      R(x,y,z) * (x \ (R(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(675,a,1744,a),flip(a)].">
      <j1 rule="hyper" parents="675 1744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1748">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(x,y,z) * (x \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(656,a,1744,a)].">
      <j1 rule="hyper" parents="656 1744"/>
    </justification>
  </clause>

  <clause id="1749">
    <literal><![CDATA[
      x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[hyper(639,a,1744,a),flip(a)].">
      <j1 rule="hyper" parents="639 1744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1750">
    <literal><![CDATA[
      x * (R(x,x,y) * y) = (x * x) * y
    ]]></literal>
    <justification jstring="[hyper(314,a,1744,a),flip(a)].">
      <j1 rule="hyper" parents="314 1744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1751">
    <literal><![CDATA[
      R(x,y,z) \ (x * (R(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(138,a,1744,a)].">
      <j1 rule="hyper" parents="138 1744"/>
    </justification>
  </clause>

  <clause id="1752">
    <literal><![CDATA[
      (x * y) / (x * (R(x,z,u) \ y)) = R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(131,a,169,a(flip),b,1744,a)].">
      <j1 rule="hyper" parents="131 169 1744"/>
    </justification>
  </clause>

  <clause id="1753">
    <literal><![CDATA[
      R(x,y,z) \ (x * u) = x * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(128,a,169,a(flip),b,1744,a)].">
      <j1 rule="hyper" parents="128 169 1744"/>
    </justification>
  </clause>

  <clause id="1755">
    <literal><![CDATA[
      x * (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,73,a(flip),b,1744,a),flip(a)].">
      <j1 rule="hyper" parents="128 73 1744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1756">
    <literal><![CDATA[
      (R(x,y,z) * (x \ u)) \ (R(x,y,z) * u) = T(x,R(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(462,a,169,a(flip),b,1744,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="462 169 1744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1757">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * T(x,R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(316,a,1755,a)].">
      <j1 rule="hyper" parents="316 1755"/>
    </justification>
  </clause>

  <clause id="1758">
    <literal><![CDATA[
      x \ (R(x,y,z) \ x) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(138,a,1755,a)].">
      <j1 rule="hyper" parents="138 1755"/>
    </justification>
  </clause>

  <clause id="1759">
    <literal><![CDATA[
      L(R(x,y,z) \ 1,x,1 / x) = (1 / x) * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(134,a,1755,a(flip),b,454,a),flip(a)].">
      <j1 rule="hyper" parents="134 1755 454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1760">
    <literal><![CDATA[
      R(x,y,z) \ R(R(x,y,z) * (R(x,y,z) \ x),u,w) = R(x,u,w) * (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(1755(a,1),1679(a,1,2,1,2))].">
      <j1 rule="para" parents="1755 1679"/>
    </justification>
  </clause>

  <clause id="1761">
    <literal><![CDATA[
      x \ (R(x,y,z) * (1 / x)) = (x \ R(x,y,z)) / x
    ]]></literal>
    <justification jstring="[hyper(347,a,1470,a(flip),b,1746,a),flip(a)].">
      <j1 rule="hyper" parents="347 1470 1746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1762">
    <literal><![CDATA[
      R(x,y,z) * (x \ (y * z)) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1746(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1763">
    <literal><![CDATA[
      R(x,y,y \ z) * (x \ z) = x \ ((x * y) * (y \ z))
    ]]></literal>
    <justification jstring="[para(392(a,1),1746(a,1,2)),flip(a)].">
      <j1 rule="para" parents="392 1746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1764">
    <literal><![CDATA[
      R(x,y,z) * (x \ (x \ 1)) = x \ (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1463(a,1),1746(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1463 1746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1765">
    <literal><![CDATA[
      x * (R(x,y,z) \ (x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) \ u = w
    ]]></literal>
    <justification jstring="[para(1747(a,1),324(a,1,2,2))].">
      <j1 rule="para" parents="1747 324"/>
    </justification>
  </clause>

  <clause id="1766">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) * (x \ u) = w
    ]]></literal>
    <justification jstring="[para(1748(a,1),359(a,1,1))].">
      <j1 rule="para" parents="1748 359"/>
    </justification>
  </clause>

  <clause id="1768">
    <literal><![CDATA[
      R(x,y,z) = (x * ((x * y) * z)) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(209(a,1),1752(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="209 1752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1769">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (u * u) = x * (R(x,y,z) \ (u * u))
    ]]></literal>
    <justification jstring="[hyper(731,a,1753,a)].">
      <j1 rule="hyper" parents="731 1753"/>
    </justification>
  </clause>

  <clause id="1770">
    <literal><![CDATA[
      R(x,y,z) = (x \ ((x * y) * z)) / (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(145,a,1762,a),flip(a)].">
      <j1 rule="hyper" parents="145 1762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1771">
    <literal><![CDATA[
      R(x,x \ 1,y) * ((x * x) \ y) = x \ ((x * (x \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(499(a,1),1762(a,1,2))].">
      <j1 rule="para" parents="499 1762"/>
    </justification>
  </clause>

  <clause id="1773">
    <literal><![CDATA[
      R(x,y,x) * T(y,x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(269,a,107,a(flip),b,1749,a),flip(a)].">
      <j1 rule="hyper" parents="269 107 1749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1774">
    <literal><![CDATA[
      R(x,y,x) \ T(x * y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(138,a,1773,a)].">
      <j1 rule="hyper" parents="138 1773"/>
    </justification>
  </clause>

  <clause id="1775">
    <literal><![CDATA[
      x \ T(y * z,y) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      R(y,z,y) = x
    ]]></literal>
    <justification jstring="[para(1773(a,1),153(a,1,2))].">
      <j1 rule="para" parents="1773 153"/>
    </justification>
  </clause>

  <clause id="1776">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(T(1 / x,y),x) = T(x * T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(1646(a,1),1773(a,1,1))].">
      <j1 rule="para" parents="1646 1773"/>
    </justification>
  </clause>

  <clause id="1777">
    <literal><![CDATA[
      R(x,y,z) / (x * x) = x \ (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(913,a,1764,a)].">
      <j1 rule="hyper" parents="913 1764"/>
    </justification>
  </clause>

  <clause id="1778">
    <literal><![CDATA[
      (x \ (x \ R(x,y,z))) * u = R(x,y,z) * ((x * x) \ u)
    ]]></literal>
    <justification jstring="[para(1764(a,1),826(a,1,1))].">
      <j1 rule="para" parents="1764 826"/>
    </justification>
  </clause>

  <clause id="1779">
    <literal><![CDATA[
      (x \ (x \ R(x,y,z))) \ u = (x * x) * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(1777(a,1),777(a,1,1))].">
      <j1 rule="para" parents="1777 777"/>
    </justification>
  </clause>

  <clause id="1780">
    <literal><![CDATA[
      x \ ((x * (x \ y)) * ((x \ y) \ z)) = ((y * ((x \ y) \ z)) / z) * (x \ z)
    ]]></literal>
    <justification jstring="[para(843(a,1),1763(a,1,1)),flip(a)].">
      <j1 rule="para" parents="843 1763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1781">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(x \ 1,y) = T(x * T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(277(a,1),1776(a,1,2))].">
      <j1 rule="para" parents="277 1776"/>
    </justification>
  </clause>

  <clause id="1782">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,1603,a(flip),b,1781,a),flip(a)].">
      <j1 rule="hyper" parents="347 1603 1781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1783">
    <literal><![CDATA[
      (x * ((y * y) * z)) \ (x * ((y * y) * (z * u))) = L(u,z,x * (y * y))
    ]]></literal>
    <justification jstring="[para(32(a,1),121(a,1,2))].">
      <j1 rule="para" parents="32 121"/>
    </justification>
  </clause>

  <clause id="1784">
    <literal><![CDATA[
      ((x * y) * ((z * z) * u)) / (y * ((z * z) * u)) = R(x,y * (z * z),u)
    ]]></literal>
    <justification jstring="[para(125(a,1),122(a,1,1))].">
      <j1 rule="para" parents="125 122"/>
    </justification>
  </clause>

  <clause id="1785">
    <literal><![CDATA[
      a(x,y,(y * y) \ z) = (x * ((y \ 1) * z)) \ ((x * (y \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(828(a,1),522(a,1,2)),flip(a)].">
      <j1 rule="para" parents="828 522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1786">
    <literal><![CDATA[
      a(x,y,(y * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1785(a,2),836(a,1))].">
      <j1 rule="para" parents="1785 836"/>
    </justification>
  </clause>

  <clause id="1787">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,14,a,b,573,a)].">
      <j1 rule="hyper" parents="347 14 573"/>
    </justification>
  </clause>

  <clause id="1788">
    <literal><![CDATA[
      L(L(x,y,z) \ x,L(x,y,z),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      a(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(573(a,2),836(a,1))].">
      <j1 rule="para" parents="573 836"/>
    </justification>
  </clause>

  <clause id="1789">
    <literal><![CDATA[
      ((x * (y * (z \ 1))) / x) / (z \ 1) = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[para(1003(a,1),1116(a,1,1))].">
      <j1 rule="para" parents="1003 1116"/>
    </justification>
  </clause>

  <clause id="1790">
    <literal><![CDATA[
      ((x * (y * ((1 / z) \ 1))) / x) / z = (1 / z) * ((x * ((1 / z) \ y)) / x)
    ]]></literal>
    <justification jstring="[para(83(a,1),1789(a,1,2))].">
      <j1 rule="para" parents="83 1789"/>
    </justification>
  </clause>

  <clause id="1791">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ K(x \ 1,x))) / y) = ((y * x) / y) / ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1070(a,1),1789(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1070 1789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1792">
    <literal><![CDATA[
      (x * y) * L(L(T(x,x * y),z,u),w,v5) = x * (y * L(L(T(x,y),z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(750(a,1),1180(a,1,2,1,1))].">
      <j1 rule="para" parents="750 1180"/>
    </justification>
  </clause>

  <clause id="1793">
    <literal><![CDATA[
      T(T(R(x,y,y \ 1),x * y) / (y \ 1),R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(585(a,1),1267(a,1,2))].">
      <j1 rule="para" parents="585 1267"/>
    </justification>
  </clause>

  <clause id="1794">
    <literal><![CDATA[
      T(T(x,x * y) * y,R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(697(a,1),1793(a,1,1))].">
      <j1 rule="para" parents="697 1793"/>
    </justification>
  </clause>

  <clause id="1795">
    <literal><![CDATA[
      T(T(T(x,x * y) * y,z),R(x,y,y \ 1)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(1794(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1794 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1796">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,R(x / y,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(1134(a,1),1795(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1134 1795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1797">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(691(a,1),1796(a,2,2))].">
      <j1 rule="para" parents="691 1796"/>
    </justification>
  </clause>

  <clause id="1798">
    <literal><![CDATA[
      T(x,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(12(a,1),1797(a,1,1))].">
      <j1 rule="para" parents="12 1797"/>
    </justification>
  </clause>

  <clause id="1799">
    <literal><![CDATA[
      T(x,x * (y \ 1)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(113(a,1),1798(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 1798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1800">
    <literal><![CDATA[
      L(x \ 1,x \ 1,x \ 1) = T(x \ 1,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(939,a,1799,a)].">
      <j1 rule="hyper" parents="939 1799"/>
    </justification>
  </clause>

  <clause id="1801">
    <literal><![CDATA[
      L(x,y,z) != (L(u,y,z) \ (u * w)) \ (u * w)
    ]]></literal>
    <literal><![CDATA[
      T(u,u * (L(u,y,z) \ w)) = x
    ]]></literal>
    <justification jstring="[para(1432(a,1),159(a,1)),flip(a)].">
      <j1 rule="para" parents="1432 159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1802">
    <literal><![CDATA[
      (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,(1 * x) / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(609(a,1),1661(a,2,2))].">
      <j1 rule="para" parents="609 1661"/>
    </justification>
  </clause>

  <clause id="1803">
    <literal><![CDATA[
      (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(7(a,1),1802(a,2,2,1))].">
      <j1 rule="para" parents="7 1802"/>
    </justification>
  </clause>

  <clause id="1804">
    <literal><![CDATA[
      L(L(x,y,z * z),(z * z) * y,u) = L(x,y,u * (z * z))
    ]]></literal>
    <justification jstring="[hyper(942,a,1783,a)].">
      <j1 rule="hyper" parents="942 1783"/>
    </justification>
  </clause>

  <clause id="1805">
    <literal><![CDATA[
      R(x,y * (z * z),u) = R(x,y,(z * z) * u)
    ]]></literal>
    <justification jstring="[hyper(595,a,1784,a),flip(a)].">
      <j1 rule="hyper" parents="595 1784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1806">
    <literal><![CDATA[
      R(x,y * (z * (u * u)),w) = R(x,y * z,(u * u) * w)
    ]]></literal>
    <justification jstring="[para(33(a,1),1805(a,1,2))].">
      <j1 rule="para" parents="33 1805"/>
    </justification>
  </clause>

  <clause id="1807">
    <literal><![CDATA[
      L(a(x,y,y),x * (y * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * y) \ ((z * x) \ (z * ((x * y) * y))) = u
    ]]></literal>
    <justification jstring="[para(567(a,1),1051(a,1))].">
      <j1 rule="para" parents="567 1051"/>
    </justification>
  </clause>

  <clause id="1808">
    <literal><![CDATA[
      L(x,x,y) \ (((y * x) \ y) * z) = (x * x) \ z
    ]]></literal>
    <justification jstring="[hyper(550,a,733,a),flip(a)].">
      <j1 rule="hyper" parents="550 733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1810">
    <literal><![CDATA[
      (1 / x) \ L((y * x) \ y,z,u) = L((y * x) \ y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(1017,a,1336,a),flip(a)].">
      <j1 rule="hyper" parents="1017 1336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1811">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (x * u))) / z) = x * (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(9(a,1),1364(a,2,2,2,1,2,2))].">
      <j1 rule="para" parents="9 1364"/>
    </justification>
  </clause>

  <clause id="1812">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / z))
    ]]></literal>
    <justification jstring="[para(68(a,1),1364(a,2,2,2,1,2,2))].">
      <j1 rule="para" parents="68 1364"/>
    </justification>
  </clause>

  <clause id="1813">
    <literal><![CDATA[
      x \ T(x,x / (x * y)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(128,a,1259,a(flip),b,1812,a(flip))].">
      <j1 rule="hyper" parents="128 1259 1812"/>
    </justification>
  </clause>

  <clause id="1814">
    <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(97(a,1),1812(a,1,1))].">
      <j1 rule="para" parents="97 1812"/>
    </justification>
  </clause>

  <clause id="1815">
    <literal><![CDATA[
      T(x,x / (x * (y \ x))) = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(134,a,1693,a(flip),b,1813,a),flip(a)].">
      <j1 rule="hyper" parents="134 1693 1813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1816">
    <literal><![CDATA[
      x \ y != z * ((x * (z \ 1)) / x)
    ]]></literal>
    <literal><![CDATA[
      T(x,x / (x * z)) = y
    ]]></literal>
    <justification jstring="[para(1813(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="1813 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1817">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) = x * K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(105(a,2),1815(a,1,2))].">
      <j1 rule="para" parents="105 1815"/>
    </justification>
  </clause>

  <clause id="1818">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),1817(a,2,2,2))].">
      <j1 rule="para" parents="11 1817"/>
    </justification>
  </clause>

  <clause id="1819">
    <literal><![CDATA[
      T(x * T(x \ ((y * z) / y),u),y) = T(x,y) * T(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(269,a,1487,a,b,1367,a(flip))].">
      <j1 rule="hyper" parents="269 1487 1367"/>
    </justification>
  </clause>

  <clause id="1820">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(x * T(x \ y,z),y)
    ]]></literal>
    <justification jstring="[hyper(269,a,1498,a(flip),b,1367,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="269 1498 1367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1821">
    <literal><![CDATA[
      x * (T(y,x) * T(T(y,x) \ y,z)) = (y * x) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(16(a,2),1367(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16 1367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1822">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,T(y,x)) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(1248(a,1),1821(a,1,2))].">
      <j1 rule="para" parents="1248 1821"/>
    </justification>
  </clause>

  <clause id="1823">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ T(z,y),u) = T(x * T(x \ z,u),y)
    ]]></literal>
    <justification jstring="[para(255(a,1),1819(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="255 1819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1824">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(226(a,1),1823(a,1,2,1,2))].">
      <j1 rule="para" parents="226 1823"/>
    </justification>
  </clause>

  <clause id="1825">
    <literal><![CDATA[
      T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(1321,a,1824,a),flip(a)].">
      <j1 rule="hyper" parents="1321 1824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1826">
    <literal><![CDATA[
      T(x * T(x \ 1,T(x,y)),y) = (T(x,y) \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(315,a,1824,a),flip(a)].">
      <j1 rule="hyper" parents="315 1824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1827">
    <literal><![CDATA[
      T(x,y) \ T(x * T(x \ 1,z),y) = T(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,1824,a)].">
      <j1 rule="hyper" parents="138 1824"/>
    </justification>
  </clause>

  <clause id="1828">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * z = z * K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(134,a,1825,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 1825 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1829">
    <literal><![CDATA[
      T(x * T(x \ 1,y),x \ y) = K(y \ (x \ y),y)
    ]]></literal>
    <justification jstring="[para(296(a,1),1825(a,2,1,2))].">
      <j1 rule="para" parents="296 1825"/>
    </justification>
  </clause>

  <clause id="1830">
    <literal><![CDATA[
      K(x \ (x / T(x,y)),x) = T(K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(387(a,1),1825(a,1,1)),flip(a)].">
      <j1 rule="para" parents="387 1825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1832">
    <literal><![CDATA[
      K(x \ (x / T(L(y \ 1,y,x),z)),x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(1208(a,2),1825(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1208 1825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1833">
    <literal><![CDATA[
      T(L(x,y,z) * T(L(x,y,z) \ 1,x),x * (L(x,y,z) \ 1)) = K(x \ (L(x,y,z) \ x),x)
    ]]></literal>
    <justification jstring="[para(1409(a,2),1829(a,1,2))].">
      <j1 rule="para" parents="1409 1829"/>
    </justification>
  </clause>

  <clause id="1834">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(x * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1550(a,1),1827(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1550 1827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1835">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(1,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1834(a,2,2,1))].">
      <j1 rule="para" parents="10 1834"/>
    </justification>
  </clause>

  <clause id="1837">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(226(a,1),1835(a,2,2))].">
      <j1 rule="para" parents="226 1835"/>
    </justification>
  </clause>

  <clause id="1839">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = x / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,172,a(flip),b,1583,a),flip(a)].">
      <j1 rule="hyper" parents="347 172 1583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1841">
    <literal><![CDATA[
      (x \ T(x * (y / z),z)) * z = (x \ 1) * ((z \ ((x \ 1) \ y)) * z)
    ]]></literal>
    <justification jstring="[hyper(639,a,1618,a),flip(a)].">
      <j1 rule="hyper" parents="639 1618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1842">
    <literal><![CDATA[
      T((x \ (x * (y / x))) * x,x) = (x \ 1) * ((x \ ((x \ 1) \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1591,a,b,1841,a)].">
      <j1 rule="hyper" parents="63 1591 1841"/>
    </justification>
  </clause>

  <clause id="1843">
    <literal><![CDATA[
      T(x,y) = (y \ 1) * ((y \ ((y \ 1) \ x)) * y)
    ]]></literal>
    <justification jstring="[para(84(a,1),1842(a,1,1))].">
      <j1 rule="para" parents="84 1842"/>
    </justification>
  </clause>

  <clause id="1844">
    <literal><![CDATA[
      (x \ ((x \ 1) \ y)) * x = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(908,a,1843,a),flip(a)].">
      <j1 rule="hyper" parents="908 1843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1845">
    <literal><![CDATA[
      (x \ 1) * ((x \ y) * x) = T((x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1843(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1846">
    <literal><![CDATA[
      T((x \ 1) * (x * y),x) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(69(a,1),1843(a,2,2,1))].">
      <j1 rule="para" parents="69 1843"/>
    </justification>
  </clause>

  <clause id="1847">
    <literal><![CDATA[
      T((x \ 1) * y,x) != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * x = z
    ]]></literal>
    <justification jstring="[para(1845(a,1),43(a,1))].">
      <j1 rule="para" parents="1845 43"/>
    </justification>
  </clause>

  <clause id="1848">
    <literal><![CDATA[
      T(((x / y) \ 1) * x,x / y) = ((x / y) \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[para(83(a,1),1845(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 1845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1849">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * (K(y \ x,y) * x)
    ]]></literal>
    <justification jstring="[para(92(a,1),1845(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="92 1845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1850">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = L(K(x \ y,x),y,x \ 1)
    ]]></literal>
    <justification jstring="[para(1845(a,1),510(a,1,2))].">
      <j1 rule="para" parents="1845 510"/>
    </justification>
  </clause>

  <clause id="1851">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * x = x * ((x \ 1) * (y * x))
    ]]></literal>
    <justification jstring="[hyper(134,a,1846,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 1846 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1852">
    <literal><![CDATA[
      T((x \ 1) * (x * y),x) != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(1846(a,2),43(a,1))].">
      <j1 rule="para" parents="1846 43"/>
    </justification>
  </clause>

  <clause id="1853">
    <literal><![CDATA[
      L(x * y,y \ 1,y) / y = (y \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(131,a,289,a(flip),b,1851,a)].">
      <j1 rule="hyper" parents="131 289 1851"/>
    </justification>
  </clause>

  <clause id="1854">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ (x * 1))) / y)
    ]]></literal>
    <justification jstring="[para(1690(a,2),1631(a,1,2))].">
      <j1 rule="para" parents="1690 1631"/>
    </justification>
  </clause>

  <clause id="1855">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(8(a,1),1854(a,2,2,1,2,2))].">
      <j1 rule="para" parents="8 1854"/>
    </justification>
  </clause>

  <clause id="1856">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = y * K(z,(z / T(x,y)) / z)
    ]]></literal>
    <justification jstring="[para(22(a,2),1855(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1857">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ (x \ u))) / z) = x \ (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(10(a,1),1632(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 1632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1858">
    <literal><![CDATA[
      R(x,y,z) * (T(x,u) \ 1) = T(x,u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),1680(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1859">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ T(x,z)) / T(x,z)) = K(T(x,z),1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1249(a,1),1695(a,1,2,1))].">
      <j1 rule="para" parents="1249 1695"/>
    </justification>
  </clause>

  <clause id="1860">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(952(a,1),1723(a,2,2))].">
      <j1 rule="para" parents="952 1723"/>
    </justification>
  </clause>

  <clause id="1861">
    <literal><![CDATA[
      T(x * R(1 / x,y,z),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(952(a,1),1860(a,1,1,2))].">
      <j1 rule="para" parents="952 1860"/>
    </justification>
  </clause>

  <clause id="1862">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(247(a,1),1861(a,1,1,2))].">
      <j1 rule="para" parents="247 1861"/>
    </justification>
  </clause>

  <clause id="1863">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,418,a(flip),b,1862,a),flip(a)].">
      <j1 rule="hyper" parents="347 418 1862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1864">
    <literal><![CDATA[
      T(x,x * (y / (x * y))) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,1863,a)].">
      <j1 rule="hyper" parents="54 1863"/>
    </justification>
  </clause>

  <clause id="1865">
    <literal><![CDATA[
      T(x / y,(x / y) * (y / x)) = x / y
    ]]></literal>
    <justification jstring="[para(12(a,1),1864(a,1,2,2,2))].">
      <j1 rule="para" parents="12 1864"/>
    </justification>
  </clause>

  <clause id="1866">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(1865(a,1),277(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1865 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1867">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,113,a(flip),b,1866,a),flip(a)].">
      <j1 rule="hyper" parents="347 113 1866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1868">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = (y * (y \ x)) / x
    ]]></literal>
    <justification jstring="[para(1867(a,1),1581(a,2,1,2))].">
      <j1 rule="para" parents="1867 1581"/>
    </justification>
  </clause>

  <clause id="1869">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) * (x * u) = x * ((x * R(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1702(a,1),1729(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1702 1729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1870">
    <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(1462(a,1),1869(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1462 1869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1871">
    <literal><![CDATA[
      ((x * ((y \ x) \ z)) / z) * (y \ z) = y \ (x * ((y \ x) \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),1780(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1873">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ z)) / y) = ((y * (z * x)) / y) / x
    ]]></literal>
    <justification jstring="[para(83(a,1),1790(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="83 1790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1874">
    <literal><![CDATA[
      ((x * (x * y)) / x) / y = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(1263,a,1873,a),flip(a)].">
      <j1 rule="hyper" parents="1263 1873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1876">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = ((x * y) / x) / (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1874(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 1874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1877">
    <literal><![CDATA[
      R(T(x,x / (1 / y)),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(1874(a,1),1532(a,1,1))].">
      <j1 rule="para" parents="1874 1532"/>
    </justification>
  </clause>

  <clause id="1878">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(347,a,1615,a(flip),b,1876,a),flip(a)].">
      <j1 rule="hyper" parents="347 1615 1876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1879">
    <literal><![CDATA[
      T(x,x / (x / (x * y))) = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[para(9(a,1),1878(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1880">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = x / x
    ]]></literal>
    <justification jstring="[hyper(347,a,172,a(flip),b,1868,a),flip(a)].">
      <j1 rule="hyper" parents="347 172 1868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1882">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = 1
    ]]></literal>
    <justification jstring="[hyper(347,a,77,a(flip),b,1880,a),flip(a)].">
      <j1 rule="hyper" parents="347 77 1880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1884">
    <literal><![CDATA[
      T(1 / (x / y),(y / x) * (x / y)) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(1882(a,1),1282(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1882 1282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1885">
    <literal><![CDATA[
      K(1 / (x / y),(y / x) * (x / y)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,1884,a)].">
      <j1 rule="hyper" parents="55 1884"/>
    </justification>
  </clause>

  <clause id="1886">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * ((x * y) / y)) = 1
    ]]></literal>
    <justification jstring="[para(11(a,1),1885(a,1,1,2))].">
      <j1 rule="para" parents="11 1885"/>
    </justification>
  </clause>

  <clause id="1887">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * x) = 1
    ]]></literal>
    <justification jstring="[para(11(a,1),1886(a,1,2,2))].">
      <j1 rule="para" parents="11 1886"/>
    </justification>
  </clause>

  <clause id="1888">
    <literal><![CDATA[
      T(1 / x,(y / (x * y)) * x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(56,a,1887,a)].">
      <j1 rule="hyper" parents="56 1887"/>
    </justification>
  </clause>

  <clause id="1889">
    <literal><![CDATA[
      L(x \ 1,x,y / (x * y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(1678,a,1888,a)].">
      <j1 rule="hyper" parents="1678 1888"/>
    </justification>
  </clause>

  <clause id="1891">
    <literal><![CDATA[
      L(x \ 1,x,(x \ y) / y) = 1 / x
    ]]></literal>
    <justification jstring="[para(10(a,1),1889(a,1,3,2))].">
      <j1 rule="para" parents="10 1889"/>
    </justification>
  </clause>

  <clause id="1892">
    <literal><![CDATA[
      L(x \ 1,x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[para(300(a,1),1889(a,1,3))].">
      <j1 rule="para" parents="300 1889"/>
    </justification>
  </clause>

  <clause id="1893">
    <literal><![CDATA[
      L(x \ 1,x,R(1 / x,x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(247(a,2),1889(a,1,3))].">
      <j1 rule="para" parents="247 1889"/>
    </justification>
  </clause>

  <clause id="1894">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(220,a,1892,a(flip),b,244,a(flip))].">
      <j1 rule="hyper" parents="220 1892 244"/>
    </justification>
  </clause>

  <clause id="1895">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = (y * (1 / y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1892(a,1),1496(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1892 1496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1896">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,290,a,b,1894,a),flip(a)].">
      <j1 rule="hyper" parents="347 290 1894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1897">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,290,a,b,1894,a)].">
      <j1 rule="hyper" parents="133 290 1894"/>
    </justification>
  </clause>

  <clause id="1898">
    <literal><![CDATA[
      T(1 / (1 / x),x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(269,a,1537,a,b,1894,a(flip))].">
      <j1 rule="hyper" parents="269 1537 1894"/>
    </justification>
  </clause>

  <clause id="1899">
    <literal><![CDATA[
      T(T(1 / (1 / x),y),x \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1898(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1898 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1900">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1898(a,1),1542(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1898 1542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1901">
    <literal><![CDATA[
      x \ (1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1540,a(flip),b,1896,a)].">
      <j1 rule="hyper" parents="63 1540 1896"/>
    </justification>
  </clause>

  <clause id="1902">
    <literal><![CDATA[
      x * K(x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(134,a,1896,a(flip),b,1540,a(flip))].">
      <j1 rule="hyper" parents="134 1896 1540"/>
    </justification>
  </clause>

  <clause id="1903">
    <literal><![CDATA[
      K(x,x \ 1) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(148,a,1900,a)].">
      <j1 rule="hyper" parents="148 1900"/>
    </justification>
  </clause>

  <clause id="1904">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,337,a(flip),b,1900,a)].">
      <j1 rule="hyper" parents="63 337 1900"/>
    </justification>
  </clause>

  <clause id="1905">
    <literal><![CDATA[
      K(x,x \ 1) * x = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,1900,a(flip),b,337,a(flip))].">
      <j1 rule="hyper" parents="133 1900 337"/>
    </justification>
  </clause>

  <clause id="1906">
    <literal><![CDATA[
      (x \ 1) * K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(134,a,1904,a(flip),b,1272,a(flip))].">
      <j1 rule="hyper" parents="134 1904 1272"/>
    </justification>
  </clause>

  <clause id="1907">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(1560,a,1906,a)].">
      <j1 rule="hyper" parents="1560 1906"/>
    </justification>
  </clause>

  <clause id="1908">
    <literal><![CDATA[
      (1 / x) / L(y,(x \ 1) / y,K(x,x \ 1)) = K(x,x \ 1) * ((x \ 1) / y)
    ]]></literal>
    <justification jstring="[para(1907(a,1),530(a,1,1))].">
      <j1 rule="para" parents="1907 530"/>
    </justification>
  </clause>

  <clause id="1909">
    <literal><![CDATA[
      (((x \ y) / y) * x) * (1 / x) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(134,a,1891,a(flip),b,244,a(flip))].">
      <j1 rule="hyper" parents="134 1891 244"/>
    </justification>
  </clause>

  <clause id="1910">
    <literal><![CDATA[
      R(1 / x,x,y) / (1 / x) = R(1 / x,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(220,a,1893,a(flip),b,244,a(flip))].">
      <j1 rule="hyper" parents="220 1893 244"/>
    </justification>
  </clause>

  <clause id="1911">
    <literal><![CDATA[
      T(x,1 / x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(275(a,1),1899(a,1,1)),flip(a)].">
      <j1 rule="para" parents="275 1899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1912">
    <literal><![CDATA[
      T(x,1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,112,a(flip),b,1911,a),flip(a)].">
      <j1 rule="hyper" parents="347 112 1911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1913">
    <literal><![CDATA[
      R(x,1 / x,x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1048,a,b,1911,a)].">
      <j1 rule="hyper" parents="63 1048 1911"/>
    </justification>
  </clause>

  <clause id="1915">
    <literal><![CDATA[
      (x * T(y,y \ 1)) / x = T((x * y) / x,1 / y)
    ]]></literal>
    <justification jstring="[para(1911(a,1),504(a,1,1,2))].">
      <j1 rule="para" parents="1911 504"/>
    </justification>
  </clause>

  <clause id="1916">
    <literal><![CDATA[
      T(x \ 1,x) = ((x \ 1) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(80(a,1),1912(a,1,2))].">
      <j1 rule="para" parents="80 1912"/>
    </justification>
  </clause>

  <clause id="1917">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1912(a,1),1369(a,1,1,1))].">
      <j1 rule="para" parents="1912 1369"/>
    </justification>
  </clause>

  <clause id="1918">
    <literal><![CDATA[
      K(x,1 / x) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,619,a,b,1913,a)].">
      <j1 rule="hyper" parents="63 619 1913"/>
    </justification>
  </clause>

  <clause id="1919">
    <literal><![CDATA[
      T(x,x \ 1) \ 1 = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,336,a,b,1916,a)].">
      <j1 rule="hyper" parents="347 336 1916"/>
    </justification>
  </clause>

  <clause id="1920">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ 1 = (x * x) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,518,a(flip),b,1916,a),flip(a)].">
      <j1 rule="hyper" parents="63 518 1916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1921">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(131,a,112,a(flip),b,1918,a)].">
      <j1 rule="hyper" parents="131 112 1918"/>
    </justification>
  </clause>

  <clause id="1922">
    <literal><![CDATA[
      K(x,1 / x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,1903,a,b,1918,a),flip(a)].">
      <j1 rule="hyper" parents="35 1903 1918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1923">
    <literal><![CDATA[
      T(x,x \ 1) / x != y
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / x) = y
    ]]></literal>
    <justification jstring="[para(1918(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1918 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1924">
    <literal><![CDATA[
      K(x,x \ 1) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(452,a,1922,a),flip(a)].">
      <j1 rule="hyper" parents="452 1922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1925">
    <literal><![CDATA[
      x \ K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(128,a,1922,a(flip),b,292,a(flip))].">
      <j1 rule="hyper" parents="128 1922 292"/>
    </justification>
  </clause>

  <clause id="1926">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(80(a,1),1922(a,1,2)),flip(a)].">
      <j1 rule="para" parents="80 1922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1927">
    <literal><![CDATA[
      K(x,x \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(1922(a,1),452(a,1))].">
      <j1 rule="para" parents="1922 452"/>
    </justification>
  </clause>

  <clause id="1928">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,x \ 1) = x
    ]]></literal>
    <justification jstring="[para(1922(a,1),1459(a,1,2))].">
      <j1 rule="para" parents="1922 1459"/>
    </justification>
  </clause>

  <clause id="1929">
    <literal><![CDATA[
      L(x,y,z) \ K(x,x \ 1) = x * (L(x,y,z) \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(128,a,1924,a,b,1405,a)].">
      <j1 rule="hyper" parents="128 1924 1405"/>
    </justification>
  </clause>

  <clause id="1930">
    <literal><![CDATA[
      T((x * y) \ (K(x,x \ 1) * y),x) = R(T(1 / x,x * y),x,y)
    ]]></literal>
    <justification jstring="[para(1924(a,2),1211(a,1,1,2,1))].">
      <j1 rule="para" parents="1924 1211"/>
    </justification>
  </clause>

  <clause id="1931">
    <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(1924(a,2),1022(a,1,1))].">
      <j1 rule="para" parents="1924 1022"/>
    </justification>
  </clause>

  <clause id="1932">
    <literal><![CDATA[
      L(x,y,z) * K(x,x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      x * (L(x,y,z) * (1 / x)) = u
    ]]></literal>
    <justification jstring="[para(1924(a,2),1430(a,1,2))].">
      <j1 rule="para" parents="1924 1430"/>
    </justification>
  </clause>

  <clause id="1933">
    <literal><![CDATA[
      R(x,1 / x,y) * (x \ ((1 / x) * y)) = x \ (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1924(a,2),1762(a,2,2,1))].">
      <j1 rule="para" parents="1924 1762"/>
    </justification>
  </clause>

  <clause id="1934">
    <literal><![CDATA[
      x * (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1925(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1925 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1936">
    <literal><![CDATA[
      x * (y * (1 / y)) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(1925(a,1),357(a,1,2,2))].">
      <j1 rule="para" parents="1925 357"/>
    </justification>
  </clause>

  <clause id="1937">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x,x \ 1) \ (x * y),z,u) = x * ((1 / x) * R((x \ K(x,x \ 1)) \ y,z,u))
    ]]></literal>
    <justification jstring="[para(1925(a,1),1357(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1925 1357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1940">
    <literal><![CDATA[
      (x \ 1) / (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = y
    ]]></literal>
    <justification jstring="[para(749(a,1),1923(a,1,1))].">
      <j1 rule="para" parents="749 1923"/>
    </justification>
  </clause>

  <clause id="1941">
    <literal><![CDATA[
      T(1 / (1 / x),R(1 / x,x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(1293,a,1910,a)].">
      <j1 rule="hyper" parents="1293 1910"/>
    </justification>
  </clause>

  <clause id="1942">
    <literal><![CDATA[
      T(1 / (1 / x),y / (x * y)) = x
    ]]></literal>
    <justification jstring="[para(247(a,1),1941(a,1,2))].">
      <j1 rule="para" parents="247 1941"/>
    </justification>
  </clause>

  <clause id="1944">
    <literal><![CDATA[
      T(x,y / (x * y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1942(a,1),1899(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1942 1899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1945">
    <literal><![CDATA[
      T(x,y / (x * y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,112,a(flip),b,1944,a),flip(a)].">
      <j1 rule="hyper" parents="347 112 1944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1946">
    <literal><![CDATA[
      T(x,(x \ y) / y) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),1944(a,1,2,2))].">
      <j1 rule="para" parents="10 1944"/>
    </justification>
  </clause>

  <clause id="1947">
    <literal><![CDATA[
      T(x / y,y / x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(12(a,1),1945(a,1,2,2))].">
      <j1 rule="para" parents="12 1945"/>
    </justification>
  </clause>

  <clause id="1948">
    <literal><![CDATA[
      ((x \ y) / y) * T(x,x \ 1) = x * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(134,a,1946,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 1946 22"/>
    </justification>
  </clause>

  <clause id="1950">
    <literal><![CDATA[
      T(x / (y * x),y) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(11(a,1),1947(a,1,2))].">
      <j1 rule="para" parents="11 1947"/>
    </justification>
  </clause>

  <clause id="1951">
    <literal><![CDATA[
      R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,866,a(flip),b,1950,a)].">
      <j1 rule="hyper" parents="63 866 1950"/>
    </justification>
  </clause>

  <clause id="1952">
    <literal><![CDATA[
      T((x * y) / x,1 / y) = T((x * y) / x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(506,a,1915,a),flip(a)].">
      <j1 rule="hyper" parents="506 1915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1953">
    <literal><![CDATA[
      L(1 / x,y,z) * (1 / (1 / x)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(83(a,1),1917(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="83 1917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1954">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) != u
    ]]></literal>
    <literal><![CDATA[
      x \ L((x \ 1) \ 1,y,z) = u
    ]]></literal>
    <justification jstring="[para(1917(a,1),386(a,1,1))].">
      <j1 rule="para" parents="1917 386"/>
    </justification>
  </clause>

  <clause id="1955">
    <literal><![CDATA[
      T((x * T(y,x)) / x,T(y,x) \ 1) = T(y,1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(255(a,1),1952(a,1,1)),flip(a)].">
      <j1 rule="para" parents="255 1952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1956">
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1940,a,1896,a)].">
      <j1 rule="hyper" parents="1940 1896"/>
    </justification>
  </clause>

  <clause id="1957">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1922,a(flip),b,1956,a)].">
      <j1 rule="hyper" parents="63 1922 1956"/>
    </justification>
  </clause>

  <clause id="1958">
    <literal><![CDATA[
      K(1 / x,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(83(a,1),1957(a,1,2))].">
      <j1 rule="para" parents="83 1957"/>
    </justification>
  </clause>

  <clause id="1959">
    <literal><![CDATA[
      x * K(1 / x,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(134,a,1958,a,b,1901,a)].">
      <j1 rule="hyper" parents="134 1958 1901"/>
    </justification>
  </clause>

  <clause id="1960">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(80(a,1),1958(a,1,1)),flip(a)].">
      <j1 rule="para" parents="80 1958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1961">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ 1) = K(x,x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(1960(a,1),451(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1960 451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1962">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1926,a(flip),b,1961,a),flip(a)].">
      <j1 rule="hyper" parents="63 1926 1961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1963">
    <literal><![CDATA[
      T(x,1 / T(x,y)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(255(a,1),1955(a,1,1)),flip(a)].">
      <j1 rule="para" parents="255 1955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1964">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1963(a,1),1513(a,1,1))].">
      <j1 rule="para" parents="1963 1513"/>
    </justification>
  </clause>

  <clause id="1965">
    <literal><![CDATA[
      ((x * (1 / T(x,y))) / x) * T(x,y) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1964(a,1),1507(a,1,1,1))].">
      <j1 rule="para" parents="1964 1507"/>
    </justification>
  </clause>

  <clause id="1966">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = K(y,y \ 1) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1924(a,2),1895(a,2,1))].">
      <j1 rule="para" parents="1924 1895"/>
    </justification>
  </clause>

  <clause id="1969">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(1115,a,1965,a)].">
      <j1 rule="hyper" parents="1115 1965"/>
    </justification>
  </clause>

  <clause id="1970">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[hyper(134,a,1969,a(flip),b,1813,a)].">
      <j1 rule="hyper" parents="134 1969 1813"/>
    </justification>
  </clause>

  <clause id="1971">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1230(a,1),1969(a,1,2,1))].">
      <j1 rule="para" parents="1230 1969"/>
    </justification>
  </clause>

  <clause id="1972">
    <literal><![CDATA[
      (T(x,T(x,y) \ 1) / x) * x = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(1971(a,1),1803(a,1,1))].">
      <j1 rule="para" parents="1971 1803"/>
    </justification>
  </clause>

  <clause id="1973">
    <literal><![CDATA[
      T(x,x / (x * T(x,y))) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(323,a,1972,a)].">
      <j1 rule="hyper" parents="323 1972"/>
    </justification>
  </clause>

  <clause id="1975">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1970,a,b,1973,a)].">
      <j1 rule="hyper" parents="63 1970 1973"/>
    </justification>
  </clause>

  <clause id="1976">
    <literal><![CDATA[
      x * (T(x,y) * ((T(x,y) \ x) / x)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(1971(a,2),1975(a,1,2))].">
      <j1 rule="para" parents="1971 1975"/>
    </justification>
  </clause>

  <clause id="1977">
    <literal><![CDATA[
      T((x * y) \ (K(x,x \ 1) * y),x) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,865,a(flip),b,1930,a),flip(a)].">
      <j1 rule="hyper" parents="347 865 1930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1981">
    <literal><![CDATA[
      (x * (y * ((z * z) * u))) \ ((x * y) * ((z * z) * u)) = a(x,y * (z * z),u)
    ]]></literal>
    <justification jstring="[para(125(a,1),118(a,1,2))].">
      <j1 rule="para" parents="125 118"/>
    </justification>
  </clause>

  <clause id="1982">
    <literal><![CDATA[
      (x * ((y * y) * (z * u))) \ ((x * ((y * y) * z)) * u) = a(x * (y * y),z,u)
    ]]></literal>
    <justification jstring="[para(32(a,1),119(a,1,2,1))].">
      <j1 rule="para" parents="32 119"/>
    </justification>
  </clause>

  <clause id="1983">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(925,a,947,a),flip(a)].">
      <j1 rule="hyper" parents="925 947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1984">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(740(a,1),1983(a,2,1))].">
      <j1 rule="para" parents="740 1983"/>
    </justification>
  </clause>

  <clause id="1985">
    <literal><![CDATA[
      ((x * y) * L((x * y) \ x,z,u)) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(1016,a,1984,a),flip(a)].">
      <j1 rule="hyper" parents="1016 1984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1986">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ z,u,w)) * y = x * L(((x / y) * y) \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(353,a,1984,a),flip(a)].">
      <j1 rule="hyper" parents="353 1984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1987">
    <literal><![CDATA[
      x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1182,a(flip),b,1984,a)].">
      <j1 rule="hyper" parents="63 1182 1984"/>
    </justification>
  </clause>

  <clause id="1988">
    <literal><![CDATA[
      x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(269,a,1984,a(flip),b,1182,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="269 1984 1182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1989">
    <literal><![CDATA[
      (x \ (y * z)) * L((x \ (y * z)) \ z,u,w) = x \ ((y * L(y \ x,u,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(128,a,1984,a(flip),b,1354,a),flip(a)].">
      <j1 rule="hyper" parents="128 1984 1354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1990">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),1984(a,1,2,1,2))].">
      <j1 rule="para" parents="7 1984"/>
    </justification>
  </clause>

  <clause id="1991">
    <literal><![CDATA[
      (x * L(x \ (x * y),z,u)) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1984(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1992">
    <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),1984(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 1984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1993">
    <literal><![CDATA[
      (x * L(y,z,u)) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),1991(a,1,1,2,1))].">
      <j1 rule="para" parents="9 1991"/>
    </justification>
  </clause>

  <clause id="1994">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = (x / L(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(717,a,1993,a)].">
      <j1 rule="hyper" parents="717 1993"/>
    </justification>
  </clause>

  <clause id="1995">
    <literal><![CDATA[
      ((x / L(y,z,u)) * y) \ (x * y) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(680,a,1993,a)].">
      <j1 rule="hyper" parents="680 1993"/>
    </justification>
  </clause>

  <clause id="1996">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = x / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(655,a,1993,a),flip(a)].">
      <j1 rule="hyper" parents="655 1993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1997">
    <literal><![CDATA[
      T((x / y) * L(y,z,u),y) = y \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(462,a,164,a(flip),b,1993,a)].">
      <j1 rule="hyper" parents="462 164 1993"/>
    </justification>
  </clause>

  <clause id="1998">
    <literal><![CDATA[
      ((x / L(y,z,u)) * y) * L(y,z,u) = x * y
    ]]></literal>
    <justification jstring="[hyper(353,a,1993,a),flip(a)].">
      <j1 rule="hyper" parents="353 1993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1999">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) * y = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,164,a(flip),b,1993,a),flip(a)].">
      <j1 rule="hyper" parents="347 164 1993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2000">
    <literal><![CDATA[
      ((1 / L(x,y,z)) * x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(233,a,1993,a),flip(a)].">
      <j1 rule="hyper" parents="233 1993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2001">
    <literal><![CDATA[
      ((x * y) * L(y,z,u)) / y = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,1993,a)].">
      <j1 rule="hyper" parents="145 1993"/>
    </justification>
  </clause>

  <clause id="2002">
    <literal><![CDATA[
      (x * L(y,z,u)) \ ((x * y) * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(138,a,1993,a)].">
      <j1 rule="hyper" parents="138 1993"/>
    </justification>
  </clause>

  <clause id="2003">
    <literal><![CDATA[
      (x * L(y,z,u)) / y = (x / y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(131,a,164,a(flip),b,1993,a)].">
      <j1 rule="hyper" parents="131 164 1993"/>
    </justification>
  </clause>

  <clause id="2004">
    <literal><![CDATA[
      (x * (y * y)) / y = x * L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,97,a(flip),b,1993,a)].">
      <j1 rule="hyper" parents="131 97 1993"/>
    </justification>
  </clause>

  <clause id="2005">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) \ (x * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(128,a,164,a(flip),b,1993,a)].">
      <j1 rule="hyper" parents="128 164 1993"/>
    </justification>
  </clause>

  <clause id="2006">
    <literal><![CDATA[
      ((x * y) * L(y,z,u)) / (y * L(y,z,u)) = R(x,L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(1993(a,1),489(a,1,1))].">
      <j1 rule="para" parents="1993 489"/>
    </justification>
  </clause>

  <clause id="2007">
    <literal><![CDATA[
      L(x,x,y) = y \ (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(801,a,2004,a),flip(a)].">
      <j1 rule="hyper" parents="801 2004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2008">
    <literal><![CDATA[
      x * L(y,y,x) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(800,a,2004,a),flip(a)].">
      <j1 rule="hyper" parents="800 2004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2009">
    <literal><![CDATA[
      L(x,x,R(y,x,x)) = R(y,x,x) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(674,a,2004,a),flip(a)].">
      <j1 rule="hyper" parents="674 2004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2010">
    <literal><![CDATA[
      x * (y * L(z,z,y)) = x * (y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(2007(a,2),169(a,1,2,2))].">
      <j1 rule="para" parents="2007 169"/>
    </justification>
  </clause>

  <clause id="2011">
    <literal><![CDATA[
      (x * y) / L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / L(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(1995(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1995 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2012">
    <literal><![CDATA[
      ((x * y) / z) * L(z,y,x) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(131,a,97,a(flip),b,1999,a),flip(a)].">
      <j1 rule="hyper" parents="131 97 1999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2013">
    <literal><![CDATA[
      x * L(y,z,u) != w * y
    ]]></literal>
    <literal><![CDATA[
      (x / y) * L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(1999(a,1),44(a,1))].">
      <j1 rule="para" parents="1999 44"/>
    </justification>
  </clause>

  <clause id="2014">
    <literal><![CDATA[
      (x * L(y,z,u)) / y != w
    ]]></literal>
    <literal><![CDATA[
      (x / y) * L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(1999(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1999 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2015">
    <literal><![CDATA[
      R(T(x,y * L(x,z,u)),y,L(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2002(a,1),1211(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2002 1211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2016">
    <literal><![CDATA[
      x / y != (z / y) * L(y,u,w)
    ]]></literal>
    <literal><![CDATA[
      z * L(y,u,w) = x
    ]]></literal>
    <justification jstring="[para(2003(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="2003 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2017">
    <literal><![CDATA[
      ((x / L(y,z,u)) / y) * L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x / y = w
    ]]></literal>
    <justification jstring="[para(2003(a,1),438(a,1))].">
      <j1 rule="para" parents="2003 438"/>
    </justification>
  </clause>

  <clause id="2018">
    <literal><![CDATA[
      L(x,y,z) = ((z * y) / x) \ ((z * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(138,a,2012,a),flip(a)].">
      <j1 rule="hyper" parents="138 2012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2019">
    <literal><![CDATA[
      (x * L(y,z,u)) * T(y,x) = (y * x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(134,a,2015,a(flip),b,744,a)].">
      <j1 rule="hyper" parents="134 2015 744"/>
    </justification>
  </clause>

  <clause id="2020">
    <literal><![CDATA[
      (x / y) \ ((z * ((z \ x) * y)) / y) = L(y,z \ x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),2018(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 2018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2021">
    <literal><![CDATA[
      ((x * y) / z) * L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      (x * (y * z)) / z = u
    ]]></literal>
    <justification jstring="[para(2018(a,2),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2018 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2022">
    <literal><![CDATA[
      L(x,y,z) / x != u
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),2014(a,1,1))].">
      <j1 rule="para" parents="7 2014"/>
    </justification>
  </clause>

  <clause id="2023">
    <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),1988(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2024">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,u),x) = L(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(908,a,2023,a)].">
      <j1 rule="hyper" parents="908 2023"/>
    </justification>
  </clause>

  <clause id="2025">
    <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),2024(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 2024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2026">
    <literal><![CDATA[
      x \ T(x * L(y / x,z,u),x) = L(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[para(1595(a,1),2025(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1595 2025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2027">
    <literal><![CDATA[
      L(T(x * y,x) / x,z,u) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,1599,a(flip),b,2026,a),flip(a)].">
      <j1 rule="hyper" parents="63 1599 2026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2028">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1182,a(flip),b,1990,a)].">
      <j1 rule="hyper" parents="63 1182 1990"/>
    </justification>
  </clause>

  <clause id="2029">
    <literal><![CDATA[
      x * ((x * y) * L((x * y) \ y,z,u)) = (x * L(x \ 1,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1181,a(flip),b,1990,a)].">
      <j1 rule="hyper" parents="63 1181 1990"/>
    </justification>
  </clause>

  <clause id="2030">
    <literal><![CDATA[
      T(x,x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(269,a,1015,a(flip),b,1990,a(flip))].">
      <j1 rule="hyper" parents="269 1015 1990"/>
    </justification>
  </clause>

  <clause id="2031">
    <literal><![CDATA[
      K(x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,2030,a)].">
      <j1 rule="hyper" parents="55 2030"/>
    </justification>
  </clause>

  <clause id="2032">
    <literal><![CDATA[
      T(x,x * ((y * x) \ y)) = x
    ]]></literal>
    <justification jstring="[para(244(a,1),2030(a,1,2,2))].">
      <j1 rule="para" parents="244 2030"/>
    </justification>
  </clause>

  <clause id="2033">
    <literal><![CDATA[
      T(x \ y,(x \ y) * (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[para(408(a,1),2030(a,1,2,2))].">
      <j1 rule="para" parents="408 2030"/>
    </justification>
  </clause>

  <clause id="2034">
    <literal><![CDATA[
      T(x \ 1,L(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(742(a,1),2030(a,1,2))].">
      <j1 rule="para" parents="742 2030"/>
    </justification>
  </clause>

  <clause id="2035">
    <literal><![CDATA[
      T(x \ 1,x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1294(a,1),2030(a,1,2))].">
      <j1 rule="para" parents="1294 2030"/>
    </justification>
  </clause>

  <clause id="2036">
    <literal><![CDATA[
      T(1 / x,L(x,y,z) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(1663(a,1),2030(a,1,2))].">
      <j1 rule="para" parents="1663 2030"/>
    </justification>
  </clause>

  <clause id="2037">
    <literal><![CDATA[
      T(T(x,y),T(x,y) * ((T(x,y) / x) \ (1 / x))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1148(a,1),2032(a,1,2,2,1))].">
      <j1 rule="para" parents="1148 2032"/>
    </justification>
  </clause>

  <clause id="2038">
    <literal><![CDATA[
      T((x * (1 / y)) / x,L(y,z,u) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(2036(a,1),504(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2036 504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2039">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) * (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(2033(a,1),754(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2033 754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2040">
    <literal><![CDATA[
      R(x \ 1,L(x,y,z),x \ 1) = T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(2034(a,1),1042(a,1,1))].">
      <j1 rule="para" parents="2034 1042"/>
    </justification>
  </clause>

  <clause id="2041">
    <literal><![CDATA[
      T(T(x,y) * ((T(x,y) / x) \ (1 / x)),T(x,y)) = T(x,y) * ((T(x,y) / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(54,a,2037,a)].">
      <j1 rule="hyper" parents="54 2037"/>
    </justification>
  </clause>

  <clause id="2042">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,948,a,b,2039,a),flip(a)].">
      <j1 rule="hyper" parents="35 948 2039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2043">
    <literal><![CDATA[
      x \ (y * L(y \ x,x \ y,y \ x)) = (x \ y) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(2042(a,2),538(a,1,2,2))].">
      <j1 rule="para" parents="2042 538"/>
    </justification>
  </clause>

  <clause id="2044">
    <literal><![CDATA[
      R(x,L(y,z,u),y) = R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(595,a,2006,a),flip(a)].">
      <j1 rule="hyper" parents="595 2006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2045">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),x,x \ 1)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1892(a,1),2028(a,2,1,2))].">
      <j1 rule="para" parents="1892 2028"/>
    </justification>
  </clause>

  <clause id="2046">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1966(a,1),2045(a,1,2))].">
      <j1 rule="para" parents="1966 2045"/>
    </justification>
  </clause>

  <clause id="2047">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ L(y,1 / x,x)) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(34,a,97,a(flip),b,2046,a),flip(a)].">
      <j1 rule="hyper" parents="34 97 2046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2048">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1924(a,2),2046(a,2,1))].">
      <j1 rule="para" parents="1924 2046"/>
    </justification>
  </clause>

  <clause id="2049">
    <literal><![CDATA[
      K(x,x \ 1) * y != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = z
    ]]></literal>
    <justification jstring="[para(2048(a,1),43(a,1))].">
      <j1 rule="para" parents="2048 43"/>
    </justification>
  </clause>

  <clause id="2050">
    <literal><![CDATA[
      K(x,x \ 1) * y != (1 / x) * z
    ]]></literal>
    <literal><![CDATA[
      x \ L(z,1 / x,x) = y
    ]]></literal>
    <justification jstring="[para(2047(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="2047 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2052">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,y \ x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(1676,a,2043,a)].">
      <j1 rule="hyper" parents="1676 2043"/>
    </justification>
  </clause>

  <clause id="2053">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (x \ y) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(572,a,2052,a)].">
      <j1 rule="hyper" parents="572 2052"/>
    </justification>
  </clause>

  <clause id="2054">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) * (1 / (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(134,a,2052,a(flip),b,244,a(flip))].">
      <j1 rule="hyper" parents="134 2052 244"/>
    </justification>
  </clause>

  <clause id="2055">
    <literal><![CDATA[
      L(((x * y) \ x) \ 1,(x * y) \ x,y) = 1 / ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2052(a,1,3))].">
      <j1 rule="para" parents="9 2052"/>
    </justification>
  </clause>

  <clause id="2056">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / (x \ (x * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),2053(a,1,1,2))].">
      <j1 rule="para" parents="9 2053"/>
    </justification>
  </clause>

  <clause id="2057">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / y
    ]]></literal>
    <justification jstring="[para(9(a,1),2056(a,2,2))].">
      <j1 rule="para" parents="9 2056"/>
    </justification>
  </clause>

  <clause id="2058">
    <literal><![CDATA[
      ((x * y) \ x) / (1 / y) = ((x * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(222,a,2057,a)].">
      <j1 rule="hyper" parents="222 2057"/>
    </justification>
  </clause>

  <clause id="2059">
    <literal><![CDATA[
      (x * y) \ x = (L(y \ 1,y,x) * y) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(133,a,411,a,b,2058,a),flip(a)].">
      <j1 rule="hyper" parents="133 411 2058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2060">
    <literal><![CDATA[
      K(((x * y) \ x) \ (((x * y) \ x) * y),(x * y) \ x) * y = T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(2058(a,1),1324(a,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2058 1324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2061">
    <literal><![CDATA[
      L(x \ 1,x,y) / (1 / x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(720,a,2059,a)].">
      <j1 rule="hyper" parents="720 2059"/>
    </justification>
  </clause>

  <clause id="2062">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ x = 1 / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(572,a,2055,a)].">
      <j1 rule="hyper" parents="572 2055"/>
    </justification>
  </clause>

  <clause id="2063">
    <literal><![CDATA[
      (x * L(x \ (y / z),u,w)) * z = x * (z * L(z \ (x \ y),u,w))
    ]]></literal>
    <justification jstring="[para(12(a,1),1987(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 1987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2064">
    <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(111(a,1),1987(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="111 1987"/>
    </justification>
  </clause>

  <clause id="2065">
    <literal><![CDATA[
      (x * (y * L(y \ 1,z,u))) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(1015(a,1),1985(a,1,1))].">
      <j1 rule="para" parents="1015 1985"/>
    </justification>
  </clause>

  <clause id="2066">
    <literal><![CDATA[
      (x * y) * (y * L(y \ 1,y,1 / y)) = (x * (y * (1 / y))) * y
    ]]></literal>
    <justification jstring="[para(407(a,1),2065(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="407 2065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2067">
    <literal><![CDATA[
      (x * (y * (1 / y))) * y = (x * y) * (y * (1 / y))
    ]]></literal>
    <justification jstring="[para(407(a,1),2066(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="407 2066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2068">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = (x * y) * (y * (1 / y))
    ]]></literal>
    <justification jstring="[para(1924(a,2),2067(a,1,1,2))].">
      <j1 rule="para" parents="1924 2067"/>
    </justification>
  </clause>

  <clause id="2069">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = (x * y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1936,a,2068,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="1936 2068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2070">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ ((x * y) * K(y,y \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(138,a,2069,a)].">
      <j1 rule="hyper" parents="138 2069"/>
    </justification>
  </clause>

  <clause id="2071">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / y = (x / y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(131,a,164,a(flip),b,2069,a)].">
      <j1 rule="hyper" parents="131 164 2069"/>
    </justification>
  </clause>

  <clause id="2072">
    <literal><![CDATA[
      R(T(x,y * K(x,x \ 1)),y,K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2070(a,1),1211(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2070 1211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2074">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x * u) = x * ((x * L(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1990(a,1),2029(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1990 2029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2075">
    <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(1294(a,1),2074(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1294 2074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2076">
    <literal><![CDATA[
      T(x / ((y \ 1) \ z),y * y) = (y * y) \ (x / (y \ z))
    ]]></literal>
    <justification jstring="[hyper(601,a,1049,a),flip(a)].">
      <j1 rule="hyper" parents="601 1049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2078">
    <literal><![CDATA[
      (T(x,y) * (1 / x)) / T(x,y) = L(1 / x,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1554,a(flip),b,1154,a)].">
      <j1 rule="hyper" parents="63 1554 1154"/>
    </justification>
  </clause>

  <clause id="2080">
    <literal><![CDATA[
      T(L(1 / x,T(x,y),1 / x),x) = (T(x,y) * (x \ 1)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(2078(a,1),809(a,1,1))].">
      <j1 rule="para" parents="2078 809"/>
    </justification>
  </clause>

  <clause id="2081">
    <literal><![CDATA[
      (T(x,y) * (x \ 1)) / T(x,y) = L(x \ 1,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(960,a,2080,a),flip(a)].">
      <j1 rule="hyper" parents="960 2080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2082">
    <literal><![CDATA[
      x * L(x \ 1,T(x,y),1 / x) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(2081(a,1),1694(a,1,2))].">
      <j1 rule="para" parents="2081 1694"/>
    </justification>
  </clause>

  <clause id="2083">
    <literal><![CDATA[
      (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = y * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,477,a(flip),b,1522,a),flip(a)].">
      <j1 rule="hyper" parents="347 477 1522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2084">
    <literal><![CDATA[
      T(x,x * (y * T(y \ 1,x))) = x
    ]]></literal>
    <justification jstring="[para(2083(a,1),507(a,1,2))].">
      <j1 rule="para" parents="2083 507"/>
    </justification>
  </clause>

  <clause id="2085">
    <literal><![CDATA[
      x \ ((L(y \ 1,y,x) * x) / L(y \ 1,y,x)) = (x * (y * T(y \ 1,x))) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2083(a,1),1318(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2083 1318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2086">
    <literal><![CDATA[
      ((L(x \ 1,x,y) * y) / L(x \ 1,x,y)) / y = (1 / y) * (y * (x * T(x \ 1,y)))
    ]]></literal>
    <justification jstring="[para(2083(a,1),1607(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2083 1607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2087">
    <literal><![CDATA[
      T(x,x * K(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1156(a,2),2084(a,1,2,2))].">
      <j1 rule="para" parents="1156 2084"/>
    </justification>
  </clause>

  <clause id="2088">
    <literal><![CDATA[
      T(x,x * (y \ (z * T(z \ y,x)))) = x
    ]]></literal>
    <justification jstring="[para(1435(a,1),2084(a,1,2,2))].">
      <j1 rule="para" parents="1435 2084"/>
    </justification>
  </clause>

  <clause id="2089">
    <literal><![CDATA[
      T(x * K(y,x),x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(54,a,2087,a)].">
      <j1 rule="hyper" parents="54 2087"/>
    </justification>
  </clause>

  <clause id="2090">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ ((y \ x) * ((y \ x) \ x)))) = x
    ]]></literal>
    <justification jstring="[para(1264(a,1),2088(a,1,2,2,2,2))].">
      <j1 rule="para" parents="1264 2088"/>
    </justification>
  </clause>

  <clause id="2091">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ x)) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),2090(a,1,2,2,2))].">
      <j1 rule="para" parents="10 2090"/>
    </justification>
  </clause>

  <clause id="2092">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,z) \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2091(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2091 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2093">
    <literal><![CDATA[
      (x * x) / T(x,y) = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(220,a,2092,a(flip),b,1225,a(flip))].">
      <j1 rule="hyper" parents="220 2092 1225"/>
    </justification>
  </clause>

  <clause id="2094">
    <literal><![CDATA[
      T(x / T(x,y),x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(1516,a,2093,a)].">
      <j1 rule="hyper" parents="1516 2093"/>
    </justification>
  </clause>

  <clause id="2095">
    <literal><![CDATA[
      (x / T(x,y)) * x = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1500,a(flip),b,2093,a)].">
      <j1 rule="hyper" parents="63 1500 2093"/>
    </justification>
  </clause>

  <clause id="2096">
    <literal><![CDATA[
      T(((T(x,y) \ x) * x) / (T(x,y) \ x),(x * x) / T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(2093(a,2),755(a,1,2))].">
      <j1 rule="para" parents="2093 755"/>
    </justification>
  </clause>

  <clause id="2097">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,2094,a(flip),b,490,a),flip(a)].">
      <j1 rule="hyper" parents="133 2094 490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2099">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ 1,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x \ (y * L(y \ x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(68(a,1),1741(a,1,2,1,2))].">
      <j1 rule="para" parents="68 1741"/>
    </justification>
  </clause>

  <clause id="2100">
    <literal><![CDATA[
      a(x,y * (z * z),u) = a(x,y,(z * z) * u)
    ]]></literal>
    <justification jstring="[hyper(836,a,1981,a),flip(a)].">
      <j1 rule="hyper" parents="836 1981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2101">
    <literal><![CDATA[
      a(x,y * (z * z),(z * z) \ u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),2100(a,2,3))].">
      <j1 rule="para" parents="10 2100"/>
    </justification>
  </clause>

  <clause id="2102">
    <literal><![CDATA[
      a(x,y * (z * (u * u)),w) = a(x,y * z,(u * u) * w)
    ]]></literal>
    <justification jstring="[para(33(a,1),2100(a,1,2))].">
      <j1 rule="para" parents="33 2100"/>
    </justification>
  </clause>

  <clause id="2103">
    <literal><![CDATA[
      a(x,y \ z,((z \ y) * (z \ y)) * u) = a(x,L(z \ y,z \ y,z),u)
    ]]></literal>
    <justification jstring="[para(732(a,1),2100(a,1,2)),flip(a)].">
      <j1 rule="para" parents="732 2100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2104">
    <literal><![CDATA[
      a(x,y / (z * z),u) = a(x,y,(z * z) \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),2101(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 2101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2105">
    <literal><![CDATA[
      a(x,y * (z * (u * (w * w))),v5) = a(x,y * (z * u),(w * w) * v5)
    ]]></literal>
    <justification jstring="[para(33(a,1),2102(a,1,2,2))].">
      <j1 rule="para" parents="33 2102"/>
    </justification>
  </clause>

  <clause id="2106">
    <literal><![CDATA[
      a(x,y * ((z * z) \ u),(z * z) * w) = a(x,y * T(u,z * z),w)
    ]]></literal>
    <justification jstring="[para(726(a,1),2102(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="726 2102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2109">
    <literal><![CDATA[
      (L(x,y,z) * u) \ ((x * (x \ u)) * L(T(x,x \ u),y,z)) = a(x,x \ u,L(T(x,x \ u),y,z))
    ]]></literal>
    <justification jstring="[para(1404(a,1),736(a,1,1))].">
      <j1 rule="para" parents="1404 736"/>
    </justification>
  </clause>

  <clause id="2110">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * ((((x * y) \ (x * (y * z))) \ z) * ((x * y) \ (x * (y * z))))) = T(a(x,y,z),(x * y) \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(890(a,2),919(a,1,1)),flip(a)].">
      <j1 rule="para" parents="890 919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2111">
    <literal><![CDATA[
      L(x,y,T(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = w
    ]]></literal>
    <justification jstring="[para(764(a,1),943(a,1))].">
      <j1 rule="para" parents="764 943"/>
    </justification>
  </clause>

  <clause id="2112">
    <literal><![CDATA[
      (R(x / (y / z),u,w) * (y / z)) * z = R((x * z) / y,u,w) * y
    ]]></literal>
    <justification jstring="[hyper(347,a,168,a(flip),b,1177,a),flip(a)].">
      <j1 rule="hyper" parents="347 168 1177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2114">
    <literal><![CDATA[
      ((x / y) * R((x / y) \ z,u,w)) * y = R((z * y) / x,u,w) * x
    ]]></literal>
    <justification jstring="[para(746(a,1),2112(a,1,1))].">
      <j1 rule="para" parents="746 2112"/>
    </justification>
  </clause>

  <clause id="2115">
    <literal><![CDATA[
      ((x / y) * R((x / y) \ z,u,w)) * y = x * R(x \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,746,a(flip),b,2114,a),flip(a)].">
      <j1 rule="hyper" parents="347 746 2114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2116">
    <literal><![CDATA[
      ((x / y) * R((x / y) \ 1,z,u)) * y = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),2115(a,2,2,1,2))].">
      <j1 rule="para" parents="7 2115"/>
    </justification>
  </clause>

  <clause id="2117">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,z,u) = (x * R(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(145,a,2116,a),flip(a)].">
      <j1 rule="hyper" parents="145 2116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2118">
    <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),2117(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20 2117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2119">
    <literal><![CDATA[
      ((x * y) * (z * (u * u))) / (y * (z * (u * u))) = R(R(x,y,z),y * z,u * u)
    ]]></literal>
    <justification jstring="[para(33(a,1),1384(a,1,2))].">
      <j1 rule="para" parents="33 1384"/>
    </justification>
  </clause>

  <clause id="2120">
    <literal><![CDATA[
      T(x,y) * (L(x,z,u) \ 1) = L(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1421(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2121">
    <literal><![CDATA[
      L(x / y,z,u) \ T(x / y,y) = (y \ x) * (L(x / y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(113(a,1),2120(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 2120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2122">
    <literal><![CDATA[
      (x \ y) * (L(y / x,z,u) \ 1) = L(y / x,z,u) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),2121(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 2121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2123">
    <literal><![CDATA[
      L(x / (x / y),z,u) \ ((x / y) \ x) = y * (L(x / (x / y),z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(708,a,2122,a),flip(a)].">
      <j1 rule="hyper" parents="708 2122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2124">
    <literal><![CDATA[
      T(x,y) * (T(z / (z / x),y) \ 1) = T(z / (z / x),y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(505(a,1),1452(a,1,1)),flip(a)].">
      <j1 rule="para" parents="505 1452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2125">
    <literal><![CDATA[
      (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(1140(a,1),1566(a,2,1))].">
      <j1 rule="para" parents="1140 1566"/>
    </justification>
  </clause>

  <clause id="2126">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ ((x \ T(x,y)) \ (x \ 1))) = 1
    ]]></literal>
    <justification jstring="[hyper(127,a,10,a(flip),b,2125,a),flip(a)].">
      <j1 rule="hyper" parents="127 10 2125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2127">
    <literal><![CDATA[
      a(x,x \ y,T(z,x * (x \ y))) = (L(z,x \ y,x) * y) \ (z * y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1630(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 1630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2128">
    <literal><![CDATA[
      (L(x,y \ z,y) * z) \ (x * z) = a(y,y \ z,T(x,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),2127(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10 2127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2130">
    <literal><![CDATA[
      T(x * L(x \ ((y * z) / y),u,w),y) = T(x,y) * L(T(x,y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(269,a,1992,a,b,1634,a(flip))].">
      <j1 rule="hyper" parents="269 1992 1634"/>
    </justification>
  </clause>

  <clause id="2131">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ y,z,u) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(269,a,1984,a(flip),b,1634,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="269 1984 1634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2132">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ T(z,y),u,w) = T(x * L(x \ z,u,w),y)
    ]]></literal>
    <justification jstring="[para(255(a,1),2130(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="255 2130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2133">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(226(a,1),2132(a,1,2,1,2))].">
      <j1 rule="para" parents="226 2132"/>
    </justification>
  </clause>

  <clause id="2134">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ T(z,y),u,w) != v5 * v6
    ]]></literal>
    <literal><![CDATA[
      v5 \ T(x * L(x \ z,u,w),y) = v6
    ]]></literal>
    <justification jstring="[para(2132(a,2),908(a,1))].">
      <j1 rule="para" parents="2132 908"/>
    </justification>
  </clause>

  <clause id="2135">
    <literal><![CDATA[
      T(x,y) \ T(x * L(x \ 1,z,u),y) = L(T(x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(138,a,2133,a)].">
      <j1 rule="hyper" parents="138 2133"/>
    </justification>
  </clause>

  <clause id="2136">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),z),y) = T(x,y) * ((z * T(x,y)) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,410,a(flip),b,2133,a),flip(a)].">
      <j1 rule="hyper" parents="63 410 2133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2137">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,x,1 / x) = T(x * T(1 / x,1),y)
    ]]></literal>
    <justification jstring="[para(882(a,1),2133(a,2,1,2))].">
      <j1 rule="para" parents="882 2133"/>
    </justification>
  </clause>

  <clause id="2138">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x * L(x \ 1,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(2135(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2135 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2139">
    <literal><![CDATA[
      T(x \ y,z) \ T((x \ y) * (y \ x),z) = L(T(x \ y,z) \ 1,x \ y,x)
    ]]></literal>
    <justification jstring="[para(408(a,1),2135(a,1,2,1,2))].">
      <j1 rule="para" parents="408 2135"/>
    </justification>
  </clause>

  <clause id="2140">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),1 / x),y) = T(x,y) * ((T(x,y) / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(1148(a,1),2136(a,2,2,1))].">
      <j1 rule="para" parents="1148 2136"/>
    </justification>
  </clause>

  <clause id="2141">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * T(1 / x,1),y)
    ]]></literal>
    <justification jstring="[para(1236(a,1),2137(a,1,2))].">
      <j1 rule="para" parents="1236 2137"/>
    </justification>
  </clause>

  <clause id="2142">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(223(a,1),2141(a,2,1,2))].">
      <j1 rule="para" parents="223 2141"/>
    </justification>
  </clause>

  <clause id="2143">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[para(2082(a,1),2140(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2082 2140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2144">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ y,z,u) = T(x * R(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(269,a,1683,a(flip),b,1635,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="269 1683 1635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2145">
    <literal><![CDATA[
      T(x,x * y) * R(T(x,x * y) \ (x * y),z,u) = T(x * R(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),2144(a,2,1,2,1))].">
      <j1 rule="para" parents="9 2144"/>
    </justification>
  </clause>

  <clause id="2146">
    <literal><![CDATA[
      x \ ((y * x) * R((y * x) \ x,z,u)) = T(y,x) * R(T(y,x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),1670(a,2,2,1,1))].">
      <j1 rule="para" parents="22 1670"/>
    </justification>
  </clause>

  <clause id="2147">
    <literal><![CDATA[
      x \ ((y * R(y \ 1,z,u)) * x) = T(y,x) * R(T(y,x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(1702(a,1),2146(a,1,2))].">
      <j1 rule="para" parents="1702 2146"/>
    </justification>
  </clause>

  <clause id="2148">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(360,a,2147,a),flip(a)].">
      <j1 rule="hyper" parents="360 2147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2149">
    <literal><![CDATA[
      x * (T(y,x) * R(T(y,x) \ 1,z,u)) = (y * R(y \ 1,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(150,a,2147,a)].">
      <j1 rule="hyper" parents="150 2147"/>
    </justification>
  </clause>

  <clause id="2150">
    <literal><![CDATA[
      T(x * R(x \ 1,T(x,y),z),y) = (z / (T(x,y) * z)) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(869,a,2148,a),flip(a)].">
      <j1 rule="hyper" parents="869 2148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2151">
    <literal><![CDATA[
      T((x \ 1) * R((x \ 1) \ 1,y,z),x \ L(x,u,w)) = T(x \ 1,x \ L(x,u,w)) * R((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2035(a,1),2148(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2035 2148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2152">
    <literal><![CDATA[
      T(x * R(x \ 1,T(x,y),x \ 1),y) = ((x \ 1) / (x \ T(x,y))) * T(x,y)
    ]]></literal>
    <justification jstring="[para(1142(a,1),2150(a,2,1,2))].">
      <j1 rule="para" parents="1142 2150"/>
    </justification>
  </clause>

  <clause id="2153">
    <literal><![CDATA[
      x * (T(y,x) * R(T(y,x) \ 1,z,u)) = y * (x * R(x \ (y \ x),z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,1728,a,b,2149,a),flip(a)].">
      <j1 rule="hyper" parents="347 1728 2149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2154">
    <literal><![CDATA[
      ((x \ 1) / (x \ T(x,y))) * T(x,y) = T(x * T(x \ 1,T(x,y)),y)
    ]]></literal>
    <justification jstring="[para(1555(a,1),2152(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1555 2152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2155">
    <literal><![CDATA[
      (x \ 1) / (x \ T(x,y)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,1826,a(flip),b,2154,a),flip(a)].">
      <j1 rule="hyper" parents="35 1826 2154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2156">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2155(a,1),386(a,1,1))].">
      <j1 rule="para" parents="2155 386"/>
    </justification>
  </clause>

  <clause id="2157">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(2156,a,1837,a)].">
      <j1 rule="hyper" parents="2156 1837"/>
    </justification>
  </clause>

  <clause id="2158">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ ((1 / x) \ 1) = T(1 / x,y) \ 1
    ]]></literal>
    <justification jstring="[para(1274(a,1),2157(a,1,1))].">
      <j1 rule="para" parents="1274 2157"/>
    </justification>
  </clause>

  <clause id="2159">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ (T(x,y) \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(2157(a,1),2126(a,1,2,2))].">
      <j1 rule="para" parents="2157 2126"/>
    </justification>
  </clause>

  <clause id="2160">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = (x \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(138,a,2159,a),flip(a)].">
      <j1 rule="hyper" parents="138 2159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2161">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ x = T(1 / x,y) \ 1
    ]]></literal>
    <justification jstring="[para(83(a,1),2158(a,1,2))].">
      <j1 rule="para" parents="83 2158"/>
    </justification>
  </clause>

  <clause id="2162">
    <literal><![CDATA[
      x / (T(1 / x,y) \ 1) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(222,a,2161,a)].">
      <j1 rule="hyper" parents="222 2161"/>
    </justification>
  </clause>

  <clause id="2163">
    <literal><![CDATA[
      K(x \ (x / y),x) \ y = T(1 / y,x) \ 1
    ]]></literal>
    <justification jstring="[para(1320(a,2),2161(a,1,1))].">
      <j1 rule="para" parents="1320 2161"/>
    </justification>
  </clause>

  <clause id="2164">
    <literal><![CDATA[
      (x \ ((y \ x) * z)) * R((x \ ((y \ x) * z)) \ z,u,w) = x \ ((R(y,u,w) * (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(748(a,1),1701(a,2,2,1))].">
      <j1 rule="para" parents="748 1701"/>
    </justification>
  </clause>

  <clause id="2165">
    <literal><![CDATA[
      ((x * y) / x) / ((y \ 1) \ 1) = (y \ 1) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(388(a,1),1791(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="388 1791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2166">
    <literal><![CDATA[
      (T(x,y) \ 1) * ((y * T(x,y)) / y) = x / ((T(x,y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(255(a,1),2165(a,1,1)),flip(a)].">
      <j1 rule="para" parents="255 2165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2167">
    <literal><![CDATA[
      x / ((T(x,y) \ 1) \ 1) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(255(a,1),2166(a,1,2)),flip(a)].">
      <j1 rule="para" parents="255 2166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2168">
    <literal><![CDATA[
      (T(x,y) \ 1) \ ((T(x,y) \ x) / x) = K(x,((T(x,y) \ 1) * x) / x)
    ]]></literal>
    <justification jstring="[para(2167(a,1),1697(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2167 1697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2169">
    <literal><![CDATA[
      (T(x,y) \ 1) \ ((T(x,y) \ x) / x) = K(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),2168(a,2,2))].">
      <j1 rule="para" parents="11 2168"/>
    </justification>
  </clause>

  <clause id="2170">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x,T(x,y) \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(150,a,2169,a)].">
      <j1 rule="hyper" parents="150 2169"/>
    </justification>
  </clause>

  <clause id="2172">
    <literal><![CDATA[
      x * (y * L(L(T(x,y),z,u),w,v5)) = L(L(x,z,u),w,v5) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(1018,a,1792,a),flip(a)].">
      <j1 rule="hyper" parents="1018 1792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2173">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * (x * v5) = x * (L(L(x,y,z),u,w) * v5)
    ]]></literal>
    <justification jstring="[para(738(a,1),2172(a,1,2)),flip(a)].">
      <j1 rule="para" parents="738 2172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2174">
    <literal><![CDATA[
      x * (L(L(x,y,z),u,w) \ 1) = L(L(x,y,z),u,w) \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,73,a(flip),b,2173,a),flip(a)].">
      <j1 rule="hyper" parents="128 73 2173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2175">
    <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),1986(a,2,2,1,1))].">
      <j1 rule="para" parents="12 1986"/>
    </justification>
  </clause>

  <clause id="2176">
    <literal><![CDATA[
      (x * L(x \ (y * z),u,w)) / z = (x / z) * L((x / z) \ y,u,w)
    ]]></literal>
    <justification jstring="[hyper(145,a,2175,a)].">
      <j1 rule="hyper" parents="145 2175"/>
    </justification>
  </clause>

  <clause id="2177">
    <literal><![CDATA[
      (x / y) * L((x / y) \ 1,z,u) = (x * L(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),2176(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 2176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2178">
    <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),2176(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 2176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2179">
    <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),2177(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20 2177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2180">
    <literal><![CDATA[
      (x * L(x \ (y * x),z,u)) / y = (x / y) * L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(1521(a,2),2178(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1521 2178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2181">
    <literal><![CDATA[
      (x / y) * L(T(y,x),z,u) = (L(y,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(737(a,1),2180(a,1,1)),flip(a)].">
      <j1 rule="para" parents="737 2180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2182">
    <literal><![CDATA[
      K(x,(y * x) \ y) * x = T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(9(a,1),2060(a,1,1,1))].">
      <j1 rule="para" parents="9 2060"/>
    </justification>
  </clause>

  <clause id="2184">
    <literal><![CDATA[
      R(R(x,y,z),y * z,u * u) = R(x,y,z * (u * u))
    ]]></literal>
    <justification jstring="[hyper(595,a,2119,a),flip(a)].">
      <j1 rule="hyper" parents="595 2119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2185">
    <literal><![CDATA[
      R(x,y,z * (u * u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(598,a,2184,a),flip(a)].">
      <j1 rule="hyper" parents="598 2184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2186">
    <literal><![CDATA[
      R(x,y,z * (u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(2184(a,1),598(a,1))].">
      <j1 rule="para" parents="2184 598"/>
    </justification>
  </clause>

  <clause id="2188">
    <literal><![CDATA[
      R(x,y,z / (u * u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),2185(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12 2185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2190">
    <literal><![CDATA[
      R(x,y,z \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(240(a,1),2185(a,1,3)),flip(a)].">
      <j1 rule="para" parents="240 2185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2191">
    <literal><![CDATA[
      R(x,y,1 / z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(245(a,1),2185(a,1,3))].">
      <j1 rule="para" parents="245 2185"/>
    </justification>
  </clause>

  <clause id="2192">
    <literal><![CDATA[
      R(x,y,z \ (u * (w \ (v5 * v5)))) = R(x,y,z \ (u * (w \ 1)))
    ]]></literal>
    <justification jstring="[para(1101(a,1),2185(a,1,3))].">
      <j1 rule="para" parents="1101 2185"/>
    </justification>
  </clause>

  <clause id="2193">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(825,a,2190,a)].">
      <j1 rule="hyper" parents="825 2190"/>
    </justification>
  </clause>

  <clause id="2194">
    <literal><![CDATA[
      R(x / y,y,x) = 1 / (y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(659,a,2190,a),flip(a)].">
      <j1 rule="hyper" parents="659 2190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2195">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,2190,a(flip),b,2190,a),flip(a)].">
      <j1 rule="hyper" parents="347 2190 2190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2196">
    <literal><![CDATA[
      R(x / y,y,x) \ 1 = y * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2190(a,1),693(a,1,1))].">
      <j1 rule="para" parents="2190 693"/>
    </justification>
  </clause>

  <clause id="2197">
    <literal><![CDATA[
      R(x,x \ y,y) \ 1 = (x \ y) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(2190(a,1),898(a,1,1))].">
      <j1 rule="para" parents="2190 898"/>
    </justification>
  </clause>

  <clause id="2198">
    <literal><![CDATA[
      R(x,y,1 / z) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,2190,a,b,2191,a),flip(a)].">
      <j1 rule="hyper" parents="347 2190 2191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2199">
    <literal><![CDATA[
      R(x,y,1 / y) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(131,a,2191,a,b,786,a)].">
      <j1 rule="hyper" parents="131 2191 786"/>
    </justification>
  </clause>

  <clause id="2201">
    <literal><![CDATA[
      R(x,y,(1 / z) * (u * u)) = R(x,y,(u * u) \ z)
    ]]></literal>
    <justification jstring="[para(896(a,1),2191(a,1,3))].">
      <j1 rule="para" parents="896 2191"/>
    </justification>
  </clause>

  <clause id="2203">
    <literal><![CDATA[
      R(x,y,z * (u / (w * w))) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(464(a,1),2188(a,1,3))].">
      <j1 rule="para" parents="464 2188"/>
    </justification>
  </clause>

  <clause id="2204">
    <literal><![CDATA[
      R(x,y,z * (u \ 1)) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(780(a,1),2188(a,1,3))].">
      <j1 rule="para" parents="780 2188"/>
    </justification>
  </clause>

  <clause id="2205">
    <literal><![CDATA[
      R(x,y,z \ (u \ 1)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(820(a,1),2188(a,1,3))].">
      <j1 rule="para" parents="820 2188"/>
    </justification>
  </clause>

  <clause id="2206">
    <literal><![CDATA[
      R(x,y,z * (u * (w \ 1))) = R(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(792(a,1),2188(a,1,3))].">
      <j1 rule="para" parents="792 2188"/>
    </justification>
  </clause>

  <clause id="2207">
    <literal><![CDATA[
      R(x,y,z) * (y * ((z \ 1) \ 1)) = (x * y) * ((z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,2195,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="133 2195 20"/>
    </justification>
  </clause>

  <clause id="2208">
    <literal><![CDATA[
      T(R(x,y,1 / y),z) / (y \ 1) = T(x,z) * y
    ]]></literal>
    <justification jstring="[para(2198(a,2),697(a,1,1,1))].">
      <j1 rule="para" parents="2198 697"/>
    </justification>
  </clause>

  <clause id="2209">
    <literal><![CDATA[
      R(x / y,y,x) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      y * (x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2194(a,2),359(a,1,1))].">
      <j1 rule="para" parents="2194 359"/>
    </justification>
  </clause>

  <clause id="2210">
    <literal><![CDATA[
      R((x * (y * z)) / z,z \ 1,x * (y * (z \ 1))) \ 1 = (z \ 1) * ((x * (y * (z \ 1))) \ 1)
    ]]></literal>
    <justification jstring="[para(966(a,1),2196(a,1,1,1))].">
      <j1 rule="para" parents="966 2196"/>
    </justification>
  </clause>

  <clause id="2211">
    <literal><![CDATA[
      (x * x) \ (L(y * (x \ 1),z,u) \ w) = L(y * x,z,u) \ w
    ]]></literal>
    <justification jstring="[para(2196(a,1),1493(a,1,2,1,1))].">
      <j1 rule="para" parents="2196 1493"/>
    </justification>
  </clause>

  <clause id="2212">
    <literal><![CDATA[
      R(x,y,(z \ 1) * z) = x
    ]]></literal>
    <justification jstring="[hyper(598,a,2204,a),flip(a)].">
      <j1 rule="hyper" parents="598 2204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2213">
    <literal><![CDATA[
      R(x,y,L(z,u,w) \ z) = R(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1409(a,1),2204(a,1,3))].">
      <j1 rule="para" parents="1409 2204"/>
    </justification>
  </clause>

  <clause id="2214">
    <literal><![CDATA[
      R(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(290(a,2),2212(a,1,3))].">
      <j1 rule="para" parents="290 2212"/>
    </justification>
  </clause>

  <clause id="2215">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,2214,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 2214 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2216">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[para(83(a,1),2214(a,1,3,1))].">
      <j1 rule="para" parents="83 2214"/>
    </justification>
  </clause>

  <clause id="2217">
    <literal><![CDATA[
      (x \ 1) * K(y \ 1,y) = x \ K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2214(a,1),448(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2214 448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2218">
    <literal><![CDATA[
      R(x,y,K(1 / z,z)) = x
    ]]></literal>
    <justification jstring="[para(1958(a,2),2214(a,1,3))].">
      <j1 rule="para" parents="1958 2214"/>
    </justification>
  </clause>

  <clause id="2219">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1960(a,1),2214(a,1,3))].">
      <j1 rule="para" parents="1960 2214"/>
    </justification>
  </clause>

  <clause id="2220">
    <literal><![CDATA[
      (x * y) * K(z,1 / z) = x * (y * K(z,1 / z))
    ]]></literal>
    <justification jstring="[hyper(133,a,2216,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 2216 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2221">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(2216(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="2216 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2222">
    <literal><![CDATA[
      (x * y) * K(1 / z,z) = x * (y * K(1 / z,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,2218,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 2218 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2223">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * K(1 / u,u)) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(2218(a,1),616(a,1,1))].">
      <j1 rule="para" parents="2218 616"/>
    </justification>
  </clause>

  <clause id="2224">
    <literal><![CDATA[
      T(x,y * K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2072,a(flip),b,2219,a),flip(a)].">
      <j1 rule="hyper" parents="63 2072 2219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2225">
    <literal><![CDATA[
      x * ((x \ y) * K(z,z \ 1)) = y * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,2219,a(flip),b,104,a(flip))].">
      <j1 rule="hyper" parents="133 2219 104"/>
    </justification>
  </clause>

  <clause id="2226">
    <literal><![CDATA[
      (x * y) * K(z,z \ 1) = x * (y * K(z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(133,a,2219,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 2219 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2227">
    <literal><![CDATA[
      (x \ 1) * K(y,y \ 1) = x \ K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2219(a,1),448(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2219 448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2228">
    <literal><![CDATA[
      x \ (y * K(z,z \ 1)) = (x \ y) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(2219(a,1),578(a,1,1))].">
      <j1 rule="para" parents="2219 578"/>
    </justification>
  </clause>

  <clause id="2230">
    <literal><![CDATA[
      R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(240(a,1),2186(a,1,3))].">
      <j1 rule="para" parents="240 2186"/>
    </justification>
  </clause>

  <clause id="2231">
    <literal><![CDATA[
      R(x,y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(245(a,1),2186(a,1,3))].">
      <j1 rule="para" parents="245 2186"/>
    </justification>
  </clause>

  <clause id="2232">
    <literal><![CDATA[
      R(x,y,z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2198(a,1),2231(a,1))].">
      <j1 rule="para" parents="2198 2231"/>
    </justification>
  </clause>

  <clause id="2234">
    <literal><![CDATA[
      ((x \ 1) \ 1) * K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,388,a(flip),b,2217,a),flip(a)].">
      <j1 rule="hyper" parents="347 388 2217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2235">
    <literal><![CDATA[
      (x * ((y / z) \ 1)) * T(y / z,z / y) = R(x,(y / z) \ 1,y / z)
    ]]></literal>
    <justification jstring="[para(1947(a,2),2193(a,1,2))].">
      <j1 rule="para" parents="1947 2193"/>
    </justification>
  </clause>

  <clause id="2236">
    <literal><![CDATA[
      R(x,y,(z * z) \ u) = R(x,y,1 / u)
    ]]></literal>
    <justification jstring="[hyper(2186,a,2201,a),flip(a)].">
      <j1 rule="hyper" parents="2186 2201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2238">
    <literal><![CDATA[
      R(x,y,(z * z) \ u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,2191,a(flip),b,2236,a),flip(a)].">
      <j1 rule="hyper" parents="347 2191 2236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2239">
    <literal><![CDATA[
      R(x,y,(z * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(2236(a,2),2231(a,1))].">
      <j1 rule="para" parents="2236 2231"/>
    </justification>
  </clause>

  <clause id="2240">
    <literal><![CDATA[
      R(x,y,(z * z) * u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),2238(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9 2238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2241">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ u) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(500(a,1),2238(a,1,3)),flip(a)].">
      <j1 rule="para" parents="500 2238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2242">
    <literal><![CDATA[
      R(x,y,L(z \ u,z,z)) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(99(a,2),2238(a,1,3))].">
      <j1 rule="para" parents="99 2238"/>
    </justification>
  </clause>

  <clause id="2243">
    <literal><![CDATA[
      R(x,y,(z * (u \ 1)) \ w) = R(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[para(973(a,1),2238(a,1,3)),flip(a)].">
      <j1 rule="para" parents="973 2238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2244">
    <literal><![CDATA[
      R(x,y * (z * (u * u)),w) = R(x,y * z,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1806,a,b,2240,a)].">
      <j1 rule="hyper" parents="63 1806 2240"/>
    </justification>
  </clause>

  <clause id="2245">
    <literal><![CDATA[
      R(x,y * (z * z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1805,a,b,2240,a)].">
      <j1 rule="hyper" parents="63 1805 2240"/>
    </justification>
  </clause>

  <clause id="2247">
    <literal><![CDATA[
      R(x,y \ 1,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(240(a,1),2245(a,1,2)),flip(a)].">
      <j1 rule="para" parents="240 2245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2248">
    <literal><![CDATA[
      R(x,1 / y,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(245(a,1),2245(a,1,2))].">
      <j1 rule="para" parents="245 2245"/>
    </justification>
  </clause>

  <clause id="2249">
    <literal><![CDATA[
      R(x,(y / (z \ 1)) * z,u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(782(a,2),2245(a,1,2))].">
      <j1 rule="para" parents="782 2245"/>
    </justification>
  </clause>

  <clause id="2250">
    <literal><![CDATA[
      R(x,y \ (z * (u \ (w * w))),v5) = R(x,y \ (z * (u \ 1)),v5)
    ]]></literal>
    <justification jstring="[para(1101(a,1),2245(a,1,2))].">
      <j1 rule="para" parents="1101 2245"/>
    </justification>
  </clause>

  <clause id="2251">
    <literal><![CDATA[
      R(x,L(y * (z * z),u,w),v5) = R(x,L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(1390(a,2),2245(a,1,2))].">
      <j1 rule="para" parents="1390 2245"/>
    </justification>
  </clause>

  <clause id="2252">
    <literal><![CDATA[
      R(x,y \ 1,z \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2230,a,2247,a)].">
      <j1 rule="hyper" parents="2230 2247"/>
    </justification>
  </clause>

  <clause id="2253">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,20,a(flip),b,2247,a)].">
      <j1 rule="hyper" parents="347 20 2247"/>
    </justification>
  </clause>

  <clause id="2254">
    <literal><![CDATA[
      R(x * ((x \ y) / y),x,y) = (x \ y) / ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1737,a(flip),b,2247,a),flip(a)].">
      <j1 rule="hyper" parents="63 1737 2247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2255">
    <literal><![CDATA[
      R(x,x,y) = y / ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,241,a(flip),b,2247,a),flip(a)].">
      <j1 rule="hyper" parents="63 241 2247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2256">
    <literal><![CDATA[
      R(x,y,z) * ((y \ 1) * z) = (x * (y \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,2247,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="133 2247 20"/>
    </justification>
  </clause>

  <clause id="2257">
    <literal><![CDATA[
      R(x,x,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(2247(a,1),448(a,1,1))].">
      <j1 rule="para" parents="2247 448"/>
    </justification>
  </clause>

  <clause id="2258">
    <literal><![CDATA[
      R(x,x,y) * ((x * x) \ y) = x \ ((x * (x \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(2247(a,1),1771(a,1,1))].">
      <j1 rule="para" parents="2247 1771"/>
    </justification>
  </clause>

  <clause id="2259">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(850,a,2248,a)].">
      <j1 rule="hyper" parents="850 2248"/>
    </justification>
  </clause>

  <clause id="2260">
    <literal><![CDATA[
      R(x,1 / y,z) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,2247,a,b,2248,a),flip(a)].">
      <j1 rule="hyper" parents="347 2247 2248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2261">
    <literal><![CDATA[
      R(x,1 / y,1 / z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,2191,a(flip),b,2248,a),flip(a)].">
      <j1 rule="hyper" parents="347 2191 2248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2262">
    <literal><![CDATA[
      R(x / (1 / y),y,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(63,a,603,a(flip),b,2248,a),flip(a)].">
      <j1 rule="hyper" parents="63 603 2248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2263">
    <literal><![CDATA[
      T(x * (1 / y),y) = y \ R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(462,a,2248,a(flip),b,294,a)].">
      <j1 rule="hyper" parents="462 2248 294"/>
    </justification>
  </clause>

  <clause id="2264">
    <literal><![CDATA[
      R(x,y,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(131,a,2248,a(flip),b,294,a)].">
      <j1 rule="hyper" parents="131 2248 294"/>
    </justification>
  </clause>

  <clause id="2265">
    <literal><![CDATA[
      R(x,x,y) * (x \ ((1 / x) * y)) = x \ (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(2248(a,1),1933(a,1,1))].">
      <j1 rule="para" parents="2248 1933"/>
    </justification>
  </clause>

  <clause id="2266">
    <literal><![CDATA[
      R(x,1 / y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2248(a,2),2231(a,1))].">
      <j1 rule="para" parents="2248 2231"/>
    </justification>
  </clause>

  <clause id="2267">
    <literal><![CDATA[
      R(x \ 1,x,y) = y / (((x \ 1) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2247,a(flip),b,2255,a)].">
      <j1 rule="hyper" parents="63 2247 2255"/>
    </justification>
  </clause>

  <clause id="2268">
    <literal><![CDATA[
      x \ y != (z \ 1) * y
    ]]></literal>
    <literal><![CDATA[
      R(z,z,y) = x
    ]]></literal>
    <justification jstring="[para(2257(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="2257 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2269">
    <literal><![CDATA[
      x \ R(y,x \ 1,x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(462,a,2247,a,b,2259,a),flip(a)].">
      <j1 rule="hyper" parents="462 2247 2259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2270">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,2247,a,b,2259,a),flip(a)].">
      <j1 rule="hyper" parents="347 2247 2259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2272">
    <literal><![CDATA[
      R(x,y \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(131,a,2247,a,b,2259,a)].">
      <j1 rule="hyper" parents="131 2247 2259"/>
    </justification>
  </clause>

  <clause id="2273">
    <literal><![CDATA[
      R(x * (1 / y),y,y) = R(x,y,y) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,2259,a(flip),b,788,a),flip(a)].">
      <j1 rule="hyper" parents="133 2259 788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2274">
    <literal><![CDATA[
      R(x,y,y) / y != z
    ]]></literal>
    <literal><![CDATA[
      x * (1 / y) = z
    ]]></literal>
    <justification jstring="[para(2259(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2259 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2275">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(63,a,2247,a,b,2262,a)].">
      <j1 rule="hyper" parents="63 2247 2262"/>
    </justification>
  </clause>

  <clause id="2276">
    <literal><![CDATA[
      (x * y) / (y \ 1) = (x / (1 / y)) * y
    ]]></literal>
    <justification jstring="[hyper(131,a,2262,a(flip),b,786,a)].">
      <j1 rule="hyper" parents="131 2262 786"/>
    </justification>
  </clause>

  <clause id="2277">
    <literal><![CDATA[
      R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(2252(a,1),2232(a,1))].">
      <j1 rule="para" parents="2252 2232"/>
    </justification>
  </clause>

  <clause id="2278">
    <literal><![CDATA[
      R(1 / (1 / x),x \ 1,(1 / x) \ y) = ((1 / x) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(901,a,2260,a),flip(a)].">
      <j1 rule="hyper" parents="901 2260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2279">
    <literal><![CDATA[
      R(x,y \ 1,(z \ 1) \ 1) = R(x,1 / y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,2195,a,b,2260,a)].">
      <j1 rule="hyper" parents="347 2195 2260"/>
    </justification>
  </clause>

  <clause id="2280">
    <literal><![CDATA[
      R(x,y \ 1,z) * ((1 / y) * z) = (x * (1 / y)) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,2260,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="133 2260 20"/>
    </justification>
  </clause>

  <clause id="2281">
    <literal><![CDATA[
      x / y != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      R(z,y \ 1,y) = x
    ]]></literal>
    <justification jstring="[para(2272(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="2272 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2282">
    <literal><![CDATA[
      (x * (1 / y)) * y != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2272(a,1),280(a,1,1))].">
      <j1 rule="para" parents="2272 280"/>
    </justification>
  </clause>

  <clause id="2283">
    <literal><![CDATA[
      (x * (1 / y)) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(2272(a,1),1628(a,1,1))].">
      <j1 rule="para" parents="2272 1628"/>
    </justification>
  </clause>

  <clause id="2284">
    <literal><![CDATA[
      R(x,y * (z \ 1),u) = R(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),2249(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 2249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2285">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,w) = R(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(1414(a,1),2249(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1414 2249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2286">
    <literal><![CDATA[
      T((x / y) / (1 / y),y) = y \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(462,a,171,a(flip),b,2276,a(flip))].">
      <j1 rule="hyper" parents="462 171 2276"/>
    </justification>
  </clause>

  <clause id="2287">
    <literal><![CDATA[
      (x / (y \ 1)) / y = (x / y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(131,a,171,a(flip),b,2276,a(flip))].">
      <j1 rule="hyper" parents="131 171 2276"/>
    </justification>
  </clause>

  <clause id="2288">
    <literal><![CDATA[
      R(x,y * z,(u * u) \ w) = R(x,y * (z \ 1),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,2238,a,b,2284,a)].">
      <j1 rule="hyper" parents="347 2238 2284"/>
    </justification>
  </clause>

  <clause id="2289">
    <literal><![CDATA[
      R(x,R(y,z,u) \ y,w) = R(x,y * R(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(1755(a,1),2284(a,1,2))].">
      <j1 rule="para" parents="1755 2284"/>
    </justification>
  </clause>

  <clause id="2290">
    <literal><![CDATA[
      R(x,y,L(z \ u,z,z)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z * u) = w
    ]]></literal>
    <justification jstring="[para(99(a,2),2239(a,1,3))].">
      <j1 rule="para" parents="99 2239"/>
    </justification>
  </clause>

  <clause id="2291">
    <literal><![CDATA[
      R(x,y,L(z \ ((u \ w) / w),z,z)) = R(x,y,z * R(1 / u,u,u \ w))
    ]]></literal>
    <justification jstring="[para(669(a,2),2242(a,2,3))].">
      <j1 rule="para" parents="669 2242"/>
    </justification>
  </clause>

  <clause id="2292">
    <literal><![CDATA[
      R(x,y \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2253(a,1),595(a,1))].">
      <j1 rule="para" parents="2253 595"/>
    </justification>
  </clause>

  <clause id="2294">
    <literal><![CDATA[
      x / (((y \ 1) \ 1) * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(2255(a,1),2292(a,1))].">
      <j1 rule="para" parents="2255 2292"/>
    </justification>
  </clause>

  <clause id="2295">
    <literal><![CDATA[
      R(x,y \ 1,(z \ 1) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ u) = w
    ]]></literal>
    <justification jstring="[para(2241(a,2),2292(a,1))].">
      <j1 rule="para" parents="2241 2292"/>
    </justification>
  </clause>

  <clause id="2296">
    <literal><![CDATA[
      x / (((y \ 1) \ 1) * x) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1951,a(flip),b,2267,a),flip(a)].">
      <j1 rule="hyper" parents="63 1951 2267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2297">
    <literal><![CDATA[
      T(R(x \ 1,x,y),((x \ 1) \ 1) * y) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(2267(a,2),113(a,1,1))].">
      <j1 rule="para" parents="2267 113"/>
    </justification>
  </clause>

  <clause id="2298">
    <literal><![CDATA[
      x / (T(y,y \ 1) * x) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(112(a,2),2267(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="112 2267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2300">
    <literal><![CDATA[
      R(x,y * (z * (u * (w * w))),v5) = R(x,y * (z * u),v5)
    ]]></literal>
    <justification jstring="[para(33(a,1),2244(a,1,2,2))].">
      <j1 rule="para" parents="33 2244"/>
    </justification>
  </clause>

  <clause id="2301">
    <literal><![CDATA[
      R(x,1 / y,1 / (1 / z)) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(219(a,1),2279(a,1,3)),flip(a)].">
      <j1 rule="para" parents="219 2279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2302">
    <literal><![CDATA[
      R(x,y \ 1,T(z \ 1,z)) = R(x,1 / y,z \ 1)
    ]]></literal>
    <justification jstring="[para(1916(a,2),2279(a,1,3))].">
      <j1 rule="para" parents="1916 2279"/>
    </justification>
  </clause>

  <clause id="2303">
    <literal><![CDATA[
      (x / (1 / y)) * (y \ 1) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(353,a,2283,a),flip(a)].">
      <j1 rule="hyper" parents="353 2283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2304">
    <literal><![CDATA[
      R(x,1 / y,(1 / z) \ 1) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2198,a(flip),b,2301,a)].">
      <j1 rule="hyper" parents="63 2198 2301"/>
    </justification>
  </clause>

  <clause id="2305">
    <literal><![CDATA[
      (x * (y \ 1)) / (1 / y) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1536,a,b,2303,a)].">
      <j1 rule="hyper" parents="63 1536 2303"/>
    </justification>
  </clause>

  <clause id="2306">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y \ 1,y) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1535,a(flip),b,2303,a),flip(a)].">
      <j1 rule="hyper" parents="63 1535 2303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2307">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1340(a,1),2305(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1340 2305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2308">
    <literal><![CDATA[
      R(x * K(y \ 1,y),y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(2305(a,1),2275(a,1,1))].">
      <j1 rule="para" parents="2305 2275"/>
    </justification>
  </clause>

  <clause id="2309">
    <literal><![CDATA[
      (x * (y \ 1)) * z != u * ((y \ 1) * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2256(a,1),44(a,1))].">
      <j1 rule="para" parents="2256 44"/>
    </justification>
  </clause>

  <clause id="2310">
    <literal><![CDATA[
      R(x,y,z) * (((y \ 1) \ 1) * z) = (x * ((y \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(2247(a,1),2256(a,1,1))].">
      <j1 rule="para" parents="2247 2256"/>
    </justification>
  </clause>

  <clause id="2311">
    <literal><![CDATA[
      R(x,y,z * (L(u,w,v5) \ u)) = R(x,y,z * (u * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(1409(a,1),2206(a,1,3,2))].">
      <j1 rule="para" parents="1409 2206"/>
    </justification>
  </clause>

  <clause id="2312">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(544,a,2215,a)].">
      <j1 rule="hyper" parents="544 2215"/>
    </justification>
  </clause>

  <clause id="2313">
    <literal><![CDATA[
      (x * y) * K(y \ 1,y) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(1902(a,1),2215(a,2,2))].">
      <j1 rule="para" parents="1902 2215"/>
    </justification>
  </clause>

  <clause id="2314">
    <literal><![CDATA[
      x * (y * K(1 / z,(1 / z) \ 1)) = (x * y) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(1957(a,2),2215(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1957 2215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2315">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[para(2234(a,1),2215(a,2,2))].">
      <j1 rule="para" parents="2234 2215"/>
    </justification>
  </clause>

  <clause id="2316">
    <literal><![CDATA[
      (x / ((y \ 1) \ 1)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(353,a,2315,a),flip(a)].">
      <j1 rule="hyper" parents="353 2315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2318">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,1627,a,b,2316,a)].">
      <j1 rule="hyper" parents="35 1627 2316"/>
    </justification>
  </clause>

  <clause id="2319">
    <literal><![CDATA[
      T(x * ((y \ 1) \ 1),z) * K(y \ 1,y) = (y \ T(y * x,z)) * y
    ]]></literal>
    <justification jstring="[para(1158(a,1),2316(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1158 2316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2320">
    <literal><![CDATA[
      x * T(x \ (x / y),y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1279,a(flip),b,2318,a)].">
      <j1 rule="hyper" parents="63 1279 2318"/>
    </justification>
  </clause>

  <clause id="2321">
    <literal><![CDATA[
      T(x \ (x / y),y) = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(128,a,2318,a(flip),b,1279,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 2318 1279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2322">
    <literal><![CDATA[
      (x * y) / ((y \ 1) \ 1) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),2318(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 2318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2323">
    <literal><![CDATA[
      x * T(x \ (x / y),y) = x / T(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(112(a,2),2320(a,2,2))].">
      <j1 rule="para" parents="112 2320"/>
    </justification>
  </clause>

  <clause id="2324">
    <literal><![CDATA[
      x \ (x / ((y \ 1) \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x \ (x / y),y) = z
    ]]></literal>
    <justification jstring="[para(2320(a,1),356(a,1,2))].">
      <j1 rule="para" parents="2320 356"/>
    </justification>
  </clause>

  <clause id="2325">
    <literal><![CDATA[
      x * (y \ (y / ((x \ 1) \ 1))) = (y \ (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(134,a,2321,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 2321 22"/>
    </justification>
  </clause>

  <clause id="2326">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * ((y \ 1) \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(148,a,2322,a)].">
      <j1 rule="hyper" parents="148 2322"/>
    </justification>
  </clause>

  <clause id="2327">
    <literal><![CDATA[
      L(K(1 / x,x),y,z) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(544,a,2222,a)].">
      <j1 rule="hyper" parents="544 2222"/>
    </justification>
  </clause>

  <clause id="2328">
    <literal><![CDATA[
      (x \ (1 / (1 / y))) * K(y,y \ 1) = x \ y
    ]]></literal>
    <justification jstring="[hyper(128,a,1928,a(flip),b,2225,a),flip(a)].">
      <j1 rule="hyper" parents="128 1928 2225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2329">
    <literal><![CDATA[
      L(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(544,a,2226,a)].">
      <j1 rule="hyper" parents="544 2226"/>
    </justification>
  </clause>

  <clause id="2330">
    <literal><![CDATA[
      x * K(x,x \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(269,a,91,a(flip),b,2226,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="269 91 2226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2331">
    <literal><![CDATA[
      R(x * y,L(z,y,x),K(u,u \ 1)) \ (x * ((y * z) * K(u,u \ 1))) = L(z,y,x) * K(u,u \ 1)
    ]]></literal>
    <justification jstring="[para(2226(a,1),616(a,1,2))].">
      <j1 rule="para" parents="2226 616"/>
    </justification>
  </clause>

  <clause id="2332">
    <literal><![CDATA[
      (x * (y \ 1)) * K(y,y \ 1) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(1906(a,1),2226(a,2,2))].">
      <j1 rule="para" parents="1906 2226"/>
    </justification>
  </clause>

  <clause id="2333">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * K(y,y \ 1) = x * y
    ]]></literal>
    <justification jstring="[para(1928(a,1),2226(a,2,2))].">
      <j1 rule="para" parents="1928 2226"/>
    </justification>
  </clause>

  <clause id="2334">
    <literal><![CDATA[
      x * K(x,x \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,112,a(flip),b,2330,a),flip(a)].">
      <j1 rule="hyper" parents="347 112 2330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2335">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) = x \ T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,2330,a(flip),b,2225,a),flip(a)].">
      <j1 rule="hyper" parents="128 2330 2225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2336">
    <literal><![CDATA[
      (T(x,x \ 1) * y) / (K(x,x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      R(x,K(x,x \ 1),y) = z
    ]]></literal>
    <justification jstring="[para(2330(a,1),595(a,1,1,1))].">
      <j1 rule="para" parents="2330 595"/>
    </justification>
  </clause>

  <clause id="2337">
    <literal><![CDATA[
      x * (x * (1 / x)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1924(a,1),2330(a,1,2))].">
      <j1 rule="para" parents="1924 2330"/>
    </justification>
  </clause>

  <clause id="2338">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2330(a,1),2226(a,2,2))].">
      <j1 rule="para" parents="2330 2226"/>
    </justification>
  </clause>

  <clause id="2339">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) = x \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,2334,a(flip),b,2225,a),flip(a)].">
      <j1 rule="hyper" parents="128 2334 2225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2340">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2334(a,1),2226(a,2,2))].">
      <j1 rule="para" parents="2334 2226"/>
    </justification>
  </clause>

  <clause id="2341">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / y = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(717,a,2333,a)].">
      <j1 rule="hyper" parents="717 2333"/>
    </justification>
  </clause>

  <clause id="2342">
    <literal><![CDATA[
      (x / y) * T(y,y \ 1) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(353,a,2338,a),flip(a)].">
      <j1 rule="hyper" parents="353 2338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2343">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2069,a,b,2338,a)].">
      <j1 rule="hyper" parents="63 2069 2338"/>
    </justification>
  </clause>

  <clause id="2344">
    <literal><![CDATA[
      (x * y) * K(T(x,y),T(x,y) \ 1) = y * ((T(x,y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(629,a,2340,a)].">
      <j1 rule="hyper" parents="629 2340"/>
    </justification>
  </clause>

  <clause id="2345">
    <literal><![CDATA[
      (x / y) * ((y \ 1) \ 1) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(353,a,2340,a),flip(a)].">
      <j1 rule="hyper" parents="353 2340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2346">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2069,a,b,2340,a)].">
      <j1 rule="hyper" parents="63 2069 2340"/>
    </justification>
  </clause>

  <clause id="2347">
    <literal><![CDATA[
      (x / y) * K(y,y \ 1) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,2071,a(flip),b,2341,a)].">
      <j1 rule="hyper" parents="63 2071 2341"/>
    </justification>
  </clause>

  <clause id="2348">
    <literal><![CDATA[
      (x / ((y \ 1) \ 1)) * K(y,y \ 1) = x / y
    ]]></literal>
    <justification jstring="[hyper(131,a,473,a(flip),b,2343,a),flip(a)].">
      <j1 rule="hyper" parents="131 473 2343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2350">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * K(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,2326,a(flip),b,2346,a),flip(a)].">
      <j1 rule="hyper" parents="35 2326 2346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2351">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * K(y \ 1,y) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,2326,a,b,2346,a(flip))].">
      <j1 rule="hyper" parents="35 2326 2346"/>
    </justification>
  </clause>

  <clause id="2353">
    <literal><![CDATA[
      (x \ K(y,y \ 1)) * y = (x \ 1) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2227(a,1),2346(a,1,1))].">
      <j1 rule="para" parents="2227 2346"/>
    </justification>
  </clause>

  <clause id="2354">
    <literal><![CDATA[
      (x \ ((y \ 1) \ 1)) * K(y \ 1,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(35,a,2339,a,b,2350,a),flip(a)].">
      <j1 rule="hyper" parents="35 2339 2350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2355">
    <literal><![CDATA[
      (x \ y) * K(y \ 1,y) = x \ (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(35,a,2328,a,b,2350,a),flip(a)].">
      <j1 rule="hyper" parents="35 2328 2350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2356">
    <literal><![CDATA[
      (x / y) * y = (x * K(z,z \ 1)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,164,a,b,2350,a)].">
      <j1 rule="hyper" parents="35 164 2350"/>
    </justification>
  </clause>

  <clause id="2357">
    <literal><![CDATA[
      (x / (1 / y)) * K(y,y \ 1) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(2306(a,1),2350(a,1,1))].">
      <j1 rule="para" parents="2306 2350"/>
    </justification>
  </clause>

  <clause id="2358">
    <literal><![CDATA[
      T((K(x \ 1,x) * y) * K(x,x \ 1),K(x \ 1,x)) = y
    ]]></literal>
    <justification jstring="[hyper(269,a,2351,a,b,xx)].">
      <j1 rule="hyper" parents="269 2351"/>
    </justification>
  </clause>

  <clause id="2359">
    <literal><![CDATA[
      (x / (1 / (1 / y))) * K(y \ 1,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(35,a,2350,a,b,2347,a)].">
      <j1 rule="hyper" parents="35 2350 2347"/>
    </justification>
  </clause>

  <clause id="2362">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / (1 / y) = (x / y) / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(131,a,2359,a(flip),b,2303,a),flip(a)].">
      <j1 rule="hyper" parents="131 2359 2303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2363">
    <literal><![CDATA[
      R(x,y,((z * u) * u) \ w) = R(x,y,R(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[para(786(a,1),2243(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="786 2243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2364">
    <literal><![CDATA[
      R(x,L(y \ 1,z,u),w) = R(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(240(a,1),2251(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="240 2251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2365">
    <literal><![CDATA[
      R(x,y * (z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y * z,u) = w
    ]]></literal>
    <justification jstring="[para(2288(a,1),2239(a,1))].">
      <j1 rule="para" parents="2288 2239"/>
    </justification>
  </clause>

  <clause id="2366">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y * L(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(1409(a,1),2365(a,1,2))].">
      <j1 rule="para" parents="1409 2365"/>
    </justification>
  </clause>

  <clause id="2367">
    <literal><![CDATA[
      R(R(x,y,z),x * R(x,y,z),u) \ (x * u) = (R(x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[para(2289(a,1),578(a,1,1))].">
      <j1 rule="para" parents="2289 578"/>
    </justification>
  </clause>

  <clause id="2368">
    <literal><![CDATA[
      x / (T(y,y \ 1) * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(112(a,2),2294(a,1,2,1))].">
      <j1 rule="para" parents="112 2294"/>
    </justification>
  </clause>

  <clause id="2369">
    <literal><![CDATA[
      x / ((((y / x) \ 1) \ 1) * x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(12(a,1),2296(a,2,1,1,2))].">
      <j1 rule="para" parents="12 2296"/>
    </justification>
  </clause>

  <clause id="2370">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,T(z \ 1,z)) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(80(a,1),2302(a,2,2))].">
      <j1 rule="para" parents="80 2302"/>
    </justification>
  </clause>

  <clause id="2373">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(2356(a,1),323(a,1))].">
      <j1 rule="para" parents="2356 323"/>
    </justification>
  </clause>

  <clause id="2374">
    <literal><![CDATA[
      R(x,T(y,y \ 1),T(z \ 1,z)) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(112(a,2),2370(a,1,2))].">
      <j1 rule="para" parents="112 2370"/>
    </justification>
  </clause>

  <clause id="2375">
    <literal><![CDATA[
      R(x,x,y) * ((x * x) \ y) = x \ y
    ]]></literal>
    <justification jstring="[para(71(a,1),2258(a,2,2))].">
      <j1 rule="para" parents="71 2258"/>
    </justification>
  </clause>

  <clause id="2376">
    <literal><![CDATA[
      x \ (x \ R(x,x,y)) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,2375,a(flip),b,1778,a),flip(a)].">
      <j1 rule="hyper" parents="131 2375 1778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2377">
    <literal><![CDATA[
      x \ R(x,x,y) = x * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(150,a,2376,a),flip(a)].">
      <j1 rule="hyper" parents="150 2376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2378">
    <literal><![CDATA[
      x \ R(x,x,x * y) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),2377(a,2,2,1))].">
      <j1 rule="para" parents="9 2377"/>
    </justification>
  </clause>

  <clause id="2379">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ u) = w
    ]]></literal>
    <justification jstring="[para(2247(a,1),2295(a,1))].">
      <j1 rule="para" parents="2247 2295"/>
    </justification>
  </clause>

  <clause id="2380">
    <literal><![CDATA[
      R(((x \ (x / (y \ 1))) * x) * K(y \ 1,y),y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y
    ]]></literal>
    <justification jstring="[para(1489(a,1),2308(a,2,1))].">
      <j1 rule="para" parents="1489 2308"/>
    </justification>
  </clause>

  <clause id="2381">
    <literal><![CDATA[
      R(x,y * (z * (u \ 1)),w) = R(x,y * (z * u),w)
    ]]></literal>
    <justification jstring="[para(240(a,1),2300(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="240 2300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2382">
    <literal><![CDATA[
      R(x,y * (L(z,u,w) \ z),v5) = R(x,y * (z * L(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(1409(a,1),2381(a,1,2,2))].">
      <j1 rule="para" parents="1409 2381"/>
    </justification>
  </clause>

  <clause id="2383">
    <literal><![CDATA[
      T((K(x \ 1,x) * (y * z)) * K(x,x \ 1),K(x \ 1,x)) != u * z
    ]]></literal>
    <literal><![CDATA[
      u = y
    ]]></literal>
    <justification jstring="[para(2358(a,2),44(a,2)),flip(a)].">
      <j1 rule="para" parents="2358 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2384">
    <literal><![CDATA[
      (x * y) * ((z \ 1) \ 1) != u * (y * ((z \ 1) \ 1))
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2207(a,1),44(a,1))].">
      <j1 rule="para" parents="2207 44"/>
    </justification>
  </clause>

  <clause id="2385">
    <literal><![CDATA[
      R(x,x,y) * ((x \ (1 / x)) * y) = x \ (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(885(a,1),2265(a,1,2))].">
      <j1 rule="para" parents="885 2265"/>
    </justification>
  </clause>

  <clause id="2386">
    <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(2278(a,2),94(a,1,2,2))].">
      <j1 rule="para" parents="2278 94"/>
    </justification>
  </clause>

  <clause id="2387">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * z != u * (((y \ 1) \ 1) * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2310(a,1),44(a,1))].">
      <j1 rule="para" parents="2310 44"/>
    </justification>
  </clause>

  <clause id="2388">
    <literal><![CDATA[
      R(x,y,z \ (u * (w \ 1))) = R(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(9(a,1),2192(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="9 2192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2389">
    <literal><![CDATA[
      R(x,y,(z * ((u * u) * (w * (v5 \ 1)))) \ ((z * ((u * u) * w)) * v5)) = R(x,y,a(z * (u * u),w,v5 \ 1))
    ]]></literal>
    <justification jstring="[para(1982(a,1),2388(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1982 2388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2390">
    <literal><![CDATA[
      R(x,y \ (z * (u \ 1)),w) = R(x,y \ (z * u),w)
    ]]></literal>
    <justification jstring="[para(9(a,1),2250(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 2250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2392">
    <literal><![CDATA[
      R(T(x \ 1,((x \ 1) \ 1) * y),x,y) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,27,a,b,2297,a)].">
      <j1 rule="hyper" parents="63 27 2297"/>
    </justification>
  </clause>

  <clause id="2393">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,2061,a(flip),b,2307,a),flip(a)].">
      <j1 rule="hyper" parents="347 2061 2307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2394">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = ((y * x) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,411,a(flip),b,2393,a),flip(a)].">
      <j1 rule="hyper" parents="347 411 2393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2395">
    <literal><![CDATA[
      K((x * y) \ x,y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,2394,a)].">
      <j1 rule="hyper" parents="333 2394"/>
    </justification>
  </clause>

  <clause id="2396">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),2395(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 2395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2397">
    <literal><![CDATA[
      K(x \ (x / y),y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),2395(a,1,1,1))].">
      <j1 rule="para" parents="12 2395"/>
    </justification>
  </clause>

  <clause id="2398">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K((x * y) \ y,T(x,y))
    ]]></literal>
    <justification jstring="[para(111(a,1),2395(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="111 2395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2400">
    <literal><![CDATA[
      (x \ y) * K(y \ x,x \ y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(134,a,2396,a(flip),b,1901,a)].">
      <j1 rule="hyper" parents="134 2396 1901"/>
    </justification>
  </clause>

  <clause id="2401">
    <literal><![CDATA[
      L(K(x \ y,y \ x),z,u) = K((y \ x) \ 1,y \ x)
    ]]></literal>
    <justification jstring="[para(2396(a,1),2312(a,1,1))].">
      <j1 rule="para" parents="2396 2312"/>
    </justification>
  </clause>

  <clause id="2403">
    <literal><![CDATA[
      K(T(x / y,T(y,x)) \ 1,T(x / y,T(y,x))) = K(((y * x) / y) \ T(y,x),T(x / y,T(y,x)))
    ]]></literal>
    <justification jstring="[para(1517(a,1),2398(a,2,1,1))].">
      <j1 rule="para" parents="1517 2398"/>
    </justification>
  </clause>

  <clause id="2404">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(2401(a,1),401(a,1)),flip(b)].">
      <j1 rule="para" parents="2401 401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2405">
    <literal><![CDATA[
      L(K(x \ y,y \ x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,y \ x) = w
    ]]></literal>
    <justification jstring="[para(2401(a,2),2404(a,1))].">
      <j1 rule="para" parents="2401 2404"/>
    </justification>
  </clause>

  <clause id="2410">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * K(1 / u,u))) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(2222(a,1),2223(a,1,2))].">
      <j1 rule="para" parents="2222 2223"/>
    </justification>
  </clause>

  <clause id="2411">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * K(1 / u,u)))) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(2222(a,1),2410(a,1,2,2))].">
      <j1 rule="para" parents="2222 2410"/>
    </justification>
  </clause>

  <clause id="2412">
    <literal><![CDATA[
      L(x * K(1 / y,y),z,u) = L(x,z,u) * K(1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(545,a,2411,a)].">
      <j1 rule="hyper" parents="545 2411"/>
    </justification>
  </clause>

  <clause id="2413">
    <literal><![CDATA[
      R(x,y,L((z \ 1) \ ((z \ u) / u),z \ 1,z \ 1)) = R(x,y,z \ R(z \ 1,z,z \ u))
    ]]></literal>
    <justification jstring="[para(1483(a,1),2291(a,2,3))].">
      <j1 rule="para" parents="1483 2291"/>
    </justification>
  </clause>

  <clause id="2419">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (((z * (u / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(1004,a,1118,a),flip(a)].">
      <j1 rule="hyper" parents="1004 1118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2420">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (((z * (1 / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),2419(a,1,2,1,2,2))].">
      <j1 rule="para" parents="7 2419"/>
    </justification>
  </clause>

  <clause id="2421">
    <literal><![CDATA[
      (((x * ((y / z) / u)) / x) * u) * z = (u * z) * ((x * ((u * z) \ y)) / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),2419(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 2419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2422">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[para(970(a,1),2419(a,2,1))].">
      <j1 rule="para" parents="970 2419"/>
    </justification>
  </clause>

  <clause id="2423">
    <literal><![CDATA[
      ((x * (y / (z * y))) / x) * (z * y) = (((x * (1 / z)) / x) * z) * y
    ]]></literal>
    <justification jstring="[hyper(971,a,2420,a)].">
      <j1 rule="hyper" parents="971 2420"/>
    </justification>
  </clause>

  <clause id="2424">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y
    ]]></literal>
    <justification jstring="[para(970(a,1),2420(a,2,1))].">
      <j1 rule="para" parents="970 2420"/>
    </justification>
  </clause>

  <clause id="2425">
    <literal><![CDATA[
      ((x * ((y \ z) / (y * (y \ z)))) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(357,a,2423,a)].">
      <j1 rule="hyper" parents="357 2423"/>
    </justification>
  </clause>

  <clause id="2426">
    <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(107(a,1),2423(a,1,2))].">
      <j1 rule="para" parents="107 2423"/>
    </justification>
  </clause>

  <clause id="2427">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * x = x * (x * ((y * (x \ 1)) / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1812,a(flip),b,2424,a),flip(a)].">
      <j1 rule="hyper" parents="63 1812 2424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2428">
    <literal><![CDATA[
      T(x * ((y * (x \ 1)) / y),z) = K(y,(y / T(x,z)) / y)
    ]]></literal>
    <justification jstring="[hyper(269,a,2424,a(flip),b,1856,a(flip))].">
      <j1 rule="hyper" parents="269 2424 1856"/>
    </justification>
  </clause>

  <clause id="2429">
    <literal><![CDATA[
      T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,1690,a(flip),b,2428,a)].">
      <j1 rule="hyper" parents="347 1690 2428"/>
    </justification>
  </clause>

  <clause id="2430">
    <literal><![CDATA[
      (1 / x) * ((1 / x) * ((y * ((1 / x) \ 1)) / y)) = (((y * x) / y) / x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1611(a,1),2427(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1611 2427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2431">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(10(a,1),2429(a,2,1,2,1))].">
      <j1 rule="para" parents="10 2429"/>
    </justification>
  </clause>

  <clause id="2432">
    <literal><![CDATA[
      T(x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)),z) = T(x,z) * ((T(x,y) * (T(x,z) \ 1)) / T(x,y))
    ]]></literal>
    <justification jstring="[para(486(a,2),2429(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="486 2429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2433">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1230(a,1),2431(a,1,2,1))].">
      <j1 rule="para" parents="1230 2431"/>
    </justification>
  </clause>

  <clause id="2434">
    <literal><![CDATA[
      (1 / x) * (T(x,y) \ x) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(34,a,2142,a,b,2433,a)].">
      <j1 rule="hyper" parents="34 2142 2433"/>
    </justification>
  </clause>

  <clause id="2435">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(K(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1924(a,2),2433(a,2,1))].">
      <j1 rule="para" parents="1924 2433"/>
    </justification>
  </clause>

  <clause id="2436">
    <literal><![CDATA[
      (T(x,y) \ x) \ ((T(x,y) \ x) / x) = T(1 / x,T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(462,a,xx,b,2434,a),flip(a)].">
      <j1 rule="hyper" parents="462 2434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2437">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(2434(a,1),1240(a,1,1))].">
      <j1 rule="para" parents="2434 1240"/>
    </justification>
  </clause>

  <clause id="2438">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ x) * K(1 / z,(1 / z) \ 1)) = ((T(x,y) \ x) / x) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(2434(a,1),2314(a,2,1))].">
      <j1 rule="para" parents="2434 2314"/>
    </justification>
  </clause>

  <clause id="2439">
    <literal><![CDATA[
      x * T(K(x,x \ 1),y) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(2435(a,1),1976(a,1,2))].">
      <j1 rule="para" parents="2435 1976"/>
    </justification>
  </clause>

  <clause id="2440">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(1239,a,2437,a),flip(a)].">
      <j1 rule="hyper" parents="1239 2437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2441">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ (T(x,y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(2440(a,2),630(a,1))].">
      <j1 rule="para" parents="2440 630"/>
    </justification>
  </clause>

  <clause id="2442">
    <literal><![CDATA[
      (T(x,y) \ x) * T(T(1 / x,T(x,y) \ x),x) = ((T(x,y) \ x) / x) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2436(a,1),1279(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2436 1279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2443">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(353,a,2421,a),flip(a)].">
      <j1 rule="hyper" parents="353 2421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2444">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) != u
    ]]></literal>
    <literal><![CDATA[
      (x * ((z / y) / x)) * y = u
    ]]></literal>
    <justification jstring="[para(2421(a,1),353(a,1))].">
      <j1 rule="para" parents="2421 353"/>
    </justification>
  </clause>

  <clause id="2445">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(1263,a,2443,a),flip(a)].">
      <j1 rule="hyper" parents="1263 2443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2446">
    <literal><![CDATA[
      x * (y * ((x * (y \ (x \ z))) / x)) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1364,a(flip),b,2443,a)].">
      <j1 rule="hyper" parents="63 1364 2443"/>
    </justification>
  </clause>

  <clause id="2447">
    <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(604(a,2),2446(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="604 2446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2448">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((z * ((x * (z \ 1)) / x)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(2424(a,1),2446(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2424 2446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2449">
    <literal><![CDATA[
      T(x,x / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = z
    ]]></literal>
    <justification jstring="[para(1259(a,1),2444(a,1))].">
      <j1 rule="para" parents="1259 2444"/>
    </justification>
  </clause>

  <clause id="2450">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (((x / y) * y) \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[hyper(353,a,2422,a),flip(a)].">
      <j1 rule="hyper" parents="353 2422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2451">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * y = (x * y) * (y * ((z * (y \ 1)) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1812,a(flip),b,2422,a),flip(a)].">
      <j1 rule="hyper" parents="63 1812 2422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2452">
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ (u * y)))) / z)) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,1364,a(flip),b,2422,a)].">
      <j1 rule="hyper" parents="63 1364 2422"/>
    </justification>
  </clause>

  <clause id="2453">
    <literal><![CDATA[
      (x \ (y * x)) * ((z * ((x \ (y * x)) \ x)) / z) = T(y * ((z * (y \ x)) / z),x)
    ]]></literal>
    <justification jstring="[hyper(269,a,2422,a(flip),b,1631,a),flip(a)].">
      <j1 rule="hyper" parents="269 2422 1631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2454">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) * y = x * (y * ((x \ (z * y)) / y))
    ]]></literal>
    <justification jstring="[para(10(a,1),2452(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2455">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * z = (x * y) * (z * (L(y \ z,y,x) / z))
    ]]></literal>
    <justification jstring="[para(99(a,2),2454(a,2,2,2,1))].">
      <j1 rule="para" parents="99 2454"/>
    </justification>
  </clause>

  <clause id="2456">
    <literal><![CDATA[
      ((x * ((y \ z) / z)) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),2425(a,1,1,1,2,2))].">
      <j1 rule="para" parents="10 2425"/>
    </justification>
  </clause>

  <clause id="2457">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = ((x * (1 / y)) / x) * y
    ]]></literal>
    <justification jstring="[hyper(654,a,2456,a)].">
      <j1 rule="hyper" parents="654 2456"/>
    </justification>
  </clause>

  <clause id="2460">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(347,a,970,a(flip),b,2457,a),flip(a)].">
      <j1 rule="hyper" parents="347 970 2457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2462">
    <literal><![CDATA[
      (((x * y) / x) / y) * (1 / y) = (1 / y) * (((x * y) / x) / y)
    ]]></literal>
    <justification jstring="[para(1611(a,1),2430(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1611 2430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2463">
    <literal><![CDATA[
      ((1 / x) * (((y * x) / y) / x)) / (1 / x) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(145,a,2462,a)].">
      <j1 rule="hyper" parents="145 2462"/>
    </justification>
  </clause>

  <clause id="2465">
    <literal><![CDATA[
      R(((x * y) / x) / y,y,x) = ((1 / y) * ((x * y) / (y * x))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(2463(a,1),1002(a,1,1))].">
      <j1 rule="para" parents="2463 1002"/>
    </justification>
  </clause>

  <clause id="2466">
    <literal><![CDATA[
      ((1 / x) * ((y * x) / (x * y))) / (1 / x) = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(682,a,2465,a),flip(a)].">
      <j1 rule="hyper" parents="682 2465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2467">
    <literal><![CDATA[
      T((x * y) / (y * x),y * x) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(2466(a,1),809(a,1,1))].">
      <j1 rule="para" parents="2466 809"/>
    </justification>
  </clause>

  <clause id="2468">
    <literal><![CDATA[
      ((1 / x) * ((x * y) \ (y * x))) / (1 / x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(386,a,2467,a),flip(a)].">
      <j1 rule="hyper" parents="386 2467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2469">
    <literal><![CDATA[
      K(x,y) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(347,a,16,a,b,2468,a)].">
      <j1 rule="hyper" parents="347 16 2468"/>
    </justification>
  </clause>

  <clause id="2470">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) / (1 / x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(16(a,2),2469(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="16 2469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2471">
    <literal><![CDATA[
      T(1 / x,K(y,x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(298,a,2470,a)].">
      <j1 rule="hyper" parents="298 2470"/>
    </justification>
  </clause>

  <clause id="2474">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) * x = R(K(y,x),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2470(a,1),2275(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2470 2275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2476">
    <literal><![CDATA[
      K(1 / x,K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,2471,a)].">
      <j1 rule="hyper" parents="55 2471"/>
    </justification>
  </clause>

  <clause id="2477">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = T(1 / x,x)
    ]]></literal>
    <justification jstring="[para(2471(a,1),277(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2471 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2478">
    <literal><![CDATA[
      K(x,K(y,x \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(80(a,1),2476(a,1,1))].">
      <j1 rule="para" parents="80 2476"/>
    </justification>
  </clause>

  <clause id="2479">
    <literal><![CDATA[
      T(x,K(y,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,2478,a)].">
      <j1 rule="hyper" parents="56 2478"/>
    </justification>
  </clause>

  <clause id="2480">
    <literal><![CDATA[
      K(x,y \ 1) * y = y * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(189,a,16,a(flip),b,2478,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="189 16 2478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2481">
    <literal><![CDATA[
      L(x,y,z) * K(u,x \ 1) = K(u,x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2479(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2479 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2482">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,113,a(flip),b,2477,a),flip(a)].">
      <j1 rule="hyper" parents="347 113 2477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2483">
    <literal><![CDATA[
      T((x * y) \ x,K(z,y)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(2482(a,1),415(a,2,1))].">
      <j1 rule="para" parents="2482 415"/>
    </justification>
  </clause>

  <clause id="2484">
    <literal><![CDATA[
      T((x \ 1) * T((x \ 1) \ 1,y),K(z,x)) = (x \ 1) * T(T(x \ 1,K(z,x)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2482(a,1),1824(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2482 1824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2486">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = L((y \ x) \ 1,y \ x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),2483(a,1,1,1))].">
      <j1 rule="para" parents="10 2483"/>
    </justification>
  </clause>

  <clause id="2487">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,408,a(flip),b,2486,a),flip(a)].">
      <j1 rule="hyper" parents="347 408 2486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2488">
    <literal><![CDATA[
      K(x,y \ z) * (z \ y) = (z \ y) * K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(1068,a,2487,a),flip(a)].">
      <j1 rule="hyper" parents="1068 2487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2489">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = x * (L(x,y,z) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(1932,a,2481,a),flip(a)].">
      <j1 rule="hyper" parents="1932 2481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2493">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ L(x,y,z)) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(2049,a,2489,a)].">
      <j1 rule="hyper" parents="2049 2489"/>
    </justification>
  </clause>

  <clause id="2494">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ 1) * ((1 / x) \ L(1 / x,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(347,a,1953,a(flip),b,2493,a),flip(a)].">
      <j1 rule="hyper" parents="347 1953 2493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2499">
    <literal><![CDATA[
      T(x,y) * ((z * ((y \ (x * y)) \ y)) / z) = T(x * ((z * (x \ y)) / z),y)
    ]]></literal>
    <justification jstring="[para(22(a,2),2453(a,1,1))].">
      <j1 rule="para" parents="22 2453"/>
    </justification>
  </clause>

  <clause id="2500">
    <literal><![CDATA[
      T(x,y) * ((z * (T(x,y) \ y)) / z) = T(x * ((z * (x \ y)) / z),y)
    ]]></literal>
    <justification jstring="[para(22(a,2),2499(a,1,2,1,2,1))].">
      <j1 rule="para" parents="22 2499"/>
    </justification>
  </clause>

  <clause id="2501">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,x,y) \ (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(1429,a,1343,a)].">
      <j1 rule="hyper" parents="1429 1343"/>
    </justification>
  </clause>

  <clause id="2503">
    <literal><![CDATA[
      T(T(x,y) * T(T(x,y) \ x,x),(x * x) / T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(1519(a,1),2096(a,1,1))].">
      <j1 rule="para" parents="1519 2096"/>
    </justification>
  </clause>

  <clause id="2504">
    <literal><![CDATA[
      T(L(x,T(x,y) \ x,T(x,y)),(x * x) / T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(1248(a,1),2503(a,1,1))].">
      <j1 rule="para" parents="1248 2503"/>
    </justification>
  </clause>

  <clause id="2505">
    <literal><![CDATA[
      T(L(x,T(x,y) \ x,T(x,y)),x * (T(x,y) \ x)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(2093(a,1),2504(a,1,2))].">
      <j1 rule="para" parents="2093 2504"/>
    </justification>
  </clause>

  <clause id="2506">
    <literal><![CDATA[
      L(T(x,x * (T(x,y) \ x)),T(x,y) \ x,T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a,b,2505,a)].">
      <j1 rule="hyper" parents="63 25 2505"/>
    </justification>
  </clause>

  <clause id="2507">
    <literal><![CDATA[
      L(x,T(x,y) \ x,T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(2091(a,1),2506(a,1,1))].">
      <j1 rule="para" parents="2091 2506"/>
    </justification>
  </clause>

  <clause id="2508">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1248,a,b,2507,a)].">
      <j1 rule="hyper" parents="63 1248 2507"/>
    </justification>
  </clause>

  <clause id="2509">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,y) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(2507(a,1),1822(a,1,2))].">
      <j1 rule="para" parents="2507 1822"/>
    </justification>
  </clause>

  <clause id="2510">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2097,a(flip),b,2508,a),flip(a)].">
      <j1 rule="hyper" parents="63 2097 2508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2511">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = (x \ 1) * T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(863(a,1),2501(a,1,2)),flip(a)].">
      <j1 rule="para" parents="863 2501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2512">
    <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(290(a,2),1187(a,1,2,1,1))].">
      <j1 rule="para" parents="290 1187"/>
    </justification>
  </clause>

  <clause id="2513">
    <literal><![CDATA[
      (x * x) \ ((y * z) \ (y * (z * ((x * x) * u)))) = L(u,z * (x * x),y)
    ]]></literal>
    <justification jstring="[para(534(a,1),1382(a,2,1))].">
      <j1 rule="para" parents="534 1382"/>
    </justification>
  </clause>

  <clause id="2514">
    <literal><![CDATA[
      (x * x) \ L((x * x) * y,z,u) = L(y,z * (x * x),u)
    ]]></literal>
    <justification jstring="[para(18(a,2),2513(a,1,2))].">
      <j1 rule="para" parents="18 2513"/>
    </justification>
  </clause>

  <clause id="2515">
    <literal><![CDATA[
      ((x * y) / x) * T(((x * y) / x) \ z,u) = (x * (y * T(y \ T(z,x),u))) / x
    ]]></literal>
    <justification jstring="[para(22(a,2),1575(a,1,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2516">
    <literal><![CDATA[
      (x * T(x \ y,x)) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(76(a,1),1622(a,1,1)),flip(a)].">
      <j1 rule="para" parents="76 1622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2517">
    <literal><![CDATA[
      ((x \ y) * x) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(629,a,2516,a)].">
      <j1 rule="hyper" parents="629 2516"/>
    </justification>
  </clause>

  <clause id="2519">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2517(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2520">
    <literal><![CDATA[
      x \ R(x * y,x,x) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2263,a(flip),b,2519,a)].">
      <j1 rule="hyper" parents="63 2263 2519"/>
    </justification>
  </clause>

  <clause id="2521">
    <literal><![CDATA[
      R(x,y,z) * (R(x,u,w) \ 1) = R(x,u,w) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),1760(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2522">
    <literal><![CDATA[
      (x \ R(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ R(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1462(a,1),1870(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1462 1870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2523">
    <literal><![CDATA[
      (x \ 1) * ((x \ R(x,y,z)) \ 1) = (x \ R(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,73,a(flip),b,2522,a),flip(a)].">
      <j1 rule="hyper" parents="128 73 2522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2524">
    <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(1924(a,2),1931(a,1,2,1,1))].">
      <j1 rule="para" parents="1924 1931"/>
    </justification>
  </clause>

  <clause id="2525">
    <literal><![CDATA[
      T(T(x,y) * ((T(x,y) / x) \ (1 / x)),T(x,y)) = T(x,y) * (K(y \ (y / (1 / x)),y) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(1322(a,2),2041(a,2,2,1))].">
      <j1 rule="para" parents="1322 2041"/>
    </justification>
  </clause>

  <clause id="2526">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1294(a,1),2075(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1294 2075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2527">
    <literal><![CDATA[
      (x \ 1) * ((x \ L(x,y,z)) \ 1) = (x \ L(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,73,a(flip),b,2526,a),flip(a)].">
      <j1 rule="hyper" parents="128 73 2526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2528">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) != (x \ 1) * u
    ]]></literal>
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 = u
    ]]></literal>
    <justification jstring="[para(2527(a,1),43(a,1))].">
      <j1 rule="para" parents="2527 43"/>
    </justification>
  </clause>

  <clause id="2529">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = x \ (x * (y * T(y \ 1,x)))
    ]]></literal>
    <justification jstring="[para(2083(a,1),2085(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2083 2085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2530">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,9,a(flip),b,2529,a),flip(a)].">
      <j1 rule="hyper" parents="347 9 2529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2532">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = (y * (x \ T(x,y))) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(1140(a,1),2530(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1140 2530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2533">
    <literal><![CDATA[
      ((x * y) \ x) * T(((x * y) \ x) \ 1,x) = (x * K(y,x)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1156(a,2),2530(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1156 2530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2534">
    <literal><![CDATA[
      (x \ T(x,y)) / (y \ 1) = y * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(131,a,1140,a(flip),b,2532,a(flip))].">
      <j1 rule="hyper" parents="131 1140 2532"/>
    </justification>
  </clause>

  <clause id="2535">
    <literal><![CDATA[
      (x * K(y,x)) * (x \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1156,a,b,2533,a),flip(a)].">
      <j1 rule="hyper" parents="63 1156 2533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2537">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,1 / x) / x
    ]]></literal>
    <justification jstring="[hyper(377,a,2535,a),flip(a)].">
      <j1 rule="hyper" parents="377 2535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2540">
    <literal><![CDATA[
      ((L(x \ 1,x,y) * y) / L(x \ 1,x,y)) / y = L(x * T(x \ 1,y),y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(347,a,291,a(flip),b,2086,a),flip(a)].">
      <j1 rule="hyper" parents="347 291 2086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2541">
    <literal><![CDATA[
      L(x * T(x \ 1,y),y,1 / y) = (y * (x * T(x \ 1,y))) / y
    ]]></literal>
    <justification jstring="[para(2083(a,1),2540(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2083 2540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2542">
    <literal><![CDATA[
      (x * (((x * y) \ x) * T(((x * y) \ x) \ 1,x))) / x = L(K(y,x),x,1 / x)
    ]]></literal>
    <justification jstring="[para(1156(a,2),2541(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1156 2541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2543">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = (y * K(x,y)) / y
    ]]></literal>
    <justification jstring="[para(1156(a,2),2542(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1156 2542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2544">
    <literal><![CDATA[
      (T(x,y) \ x) * T(x \ 1,T(x,y) \ x) = ((T(x,y) \ x) / x) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(277(a,1),2442(a,1,2))].">
      <j1 rule="para" parents="277 2442"/>
    </justification>
  </clause>

  <clause id="2545">
    <literal><![CDATA[
      ((T(x,y) \ x) / x) * K(x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * (T(x,y) \ x) = z
    ]]></literal>
    <justification jstring="[para(2544(a,1),315(a,1))].">
      <j1 rule="para" parents="2544 315"/>
    </justification>
  </clause>

  <clause id="2546">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (x \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),2450(a,2,2,1,2,1))].">
      <j1 rule="para" parents="12 2450"/>
    </justification>
  </clause>

  <clause id="2547">
    <literal><![CDATA[
      (x * ((y * (x \ (z * u))) / y)) / u = (x / u) * ((y * ((x / u) \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(145,a,2546,a)].">
      <j1 rule="hyper" parents="145 2546"/>
    </justification>
  </clause>

  <clause id="2548">
    <literal><![CDATA[
      (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),2547(a,1,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 2547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2549">
    <literal><![CDATA[
      T((x \ 1) * T((x \ 1) \ 1,y),K(z,x)) = (x \ 1) * T((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2482(a,1),2484(a,2,2,1,1))].">
      <j1 rule="para" parents="2482 2484"/>
    </justification>
  </clause>

  <clause id="2550">
    <literal><![CDATA[
      T((x \ 1) * T((x \ 1) \ 1,y),K(z,x)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,1140,a(flip),b,2549,a),flip(a)].">
      <j1 rule="hyper" parents="347 1140 2549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2552">
    <literal><![CDATA[
      T(x \ T(x,y),K(z,x)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(1140(a,1),2550(a,1,1))].">
      <j1 rule="para" parents="1140 2550"/>
    </justification>
  </clause>

  <clause id="2553">
    <literal><![CDATA[
      T((x * y) \ (y * x),K(z,y)) = L(y \ T(y,x),y,x)
    ]]></literal>
    <justification jstring="[para(2552(a,1),878(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2552 878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2554">
    <literal><![CDATA[
      T((x * y) \ (y * x),K(z,y)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,877,a,b,2553,a),flip(a)].">
      <j1 rule="hyper" parents="347 877 2553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2555">
    <literal><![CDATA[
      T(K(x,y),K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(16(a,2),2554(a,1,1))].">
      <j1 rule="para" parents="16 2554"/>
    </justification>
  </clause>

  <clause id="2556">
    <literal><![CDATA[
      K(x,y) * K(z,x) = K(z,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1068,a,2555,a)].">
      <j1 rule="hyper" parents="1068 2555"/>
    </justification>
  </clause>

  <clause id="2557">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,2555,a)].">
      <j1 rule="hyper" parents="54 2555"/>
    </justification>
  </clause>

  <clause id="2558">
    <literal><![CDATA[
      K(x,y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2555(a,1),315(a,1,2))].">
      <j1 rule="para" parents="2555 315"/>
    </justification>
  </clause>

  <clause id="2559">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(w,x) = K(w,x) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2555(a,1),268(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2555 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2560">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2557(a,1),315(a,1,2))].">
      <j1 rule="para" parents="2557 315"/>
    </justification>
  </clause>

  <clause id="2561">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,u) = K(y,u) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(2557(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2557 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2562">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,w) = K(y,w) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2557(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2557 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2563">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,w) = K(y,w) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2557(a,1),268(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2557 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2564">
    <literal><![CDATA[
      K(x,y) * L(K(z,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(z,x),u,w) * K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(2557(a,1),436(a,1,2,1))].">
      <j1 rule="para" parents="2557 436"/>
    </justification>
  </clause>

  <clause id="2565">
    <literal><![CDATA[
      K(x,y) * R(K(z,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(K(z,x),u,w) * K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(2557(a,1),437(a,1,2,1))].">
      <j1 rule="para" parents="2557 437"/>
    </justification>
  </clause>

  <clause id="2566">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) \ L(1 / x,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1957(a,1),2494(a,1,1))].">
      <j1 rule="para" parents="1957 2494"/>
    </justification>
  </clause>

  <clause id="2567">
    <literal><![CDATA[
      K(x \ 1,x) * (x * L(x \ 1,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1192(a,1),2566(a,1,2))].">
      <j1 rule="para" parents="1192 2566"/>
    </justification>
  </clause>

  <clause id="2568">
    <literal><![CDATA[
      K(x \ 1,x) * (x * L(x \ 1,x,y)) = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,2307,a,b,2567,a),flip(a)].">
      <j1 rule="hyper" parents="347 2307 2567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2569">
    <literal><![CDATA[
      ((x \ 1) * x) * (x * L(x \ 1,x,y)) = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(290(a,1),2568(a,1,1))].">
      <j1 rule="para" parents="290 2568"/>
    </justification>
  </clause>

  <clause id="2570">
    <literal><![CDATA[
      ((x \ 1) * (x * L(x \ 1,x,y))) * x = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2065,a,b,2569,a)].">
      <j1 rule="hyper" parents="63 2065 2569"/>
    </justification>
  </clause>

  <clause id="2571">
    <literal><![CDATA[
      (x * y) \ x = (y \ 1) * (y * L(y \ 1,y,x))
    ]]></literal>
    <justification jstring="[hyper(35,a,2394,a(flip),b,2570,a)].">
      <j1 rule="hyper" parents="35 2394 2570"/>
    </justification>
  </clause>

  <clause id="2572">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * x) \ y)) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(244(a,1),2571(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="244 2571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2573">
    <literal><![CDATA[
      (x \ 1) \ ((y * x) \ y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(138,a,2572,a)].">
      <j1 rule="hyper" parents="138 2572"/>
    </justification>
  </clause>

  <clause id="2574">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,x,y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(128,a,244,a,b,2572,a)].">
      <j1 rule="hyper" parents="128 244 2572"/>
    </justification>
  </clause>

  <clause id="2575">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(127,a,2572,a(flip),b,1344,a),flip(a)].">
      <j1 rule="hyper" parents="127 2572 1344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2576">
    <literal><![CDATA[
      T(x,(y * x) \ y) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,2575,a(flip),b,2511,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 2575 2511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2577">
    <literal><![CDATA[
      T(x,(y * x) \ y) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,112,a,b,2576,a),flip(a)].">
      <j1 rule="hyper" parents="347 112 2576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2578">
    <literal><![CDATA[
      K(x,(y * x) \ y) = ((x \ 1) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,2576,a(flip),b,2182,a),flip(a)].">
      <j1 rule="hyper" parents="131 2576 2182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2579">
    <literal><![CDATA[
      T(x \ y,y \ x) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),2576(a,1,2,1))].">
      <j1 rule="para" parents="10 2576"/>
    </justification>
  </clause>

  <clause id="2581">
    <literal><![CDATA[
      T(1 / (1 / x),(y * x) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,1899,a,b,2577,a(flip))].">
      <j1 rule="hyper" parents="40 1899 2577"/>
    </justification>
  </clause>

  <clause id="2582">
    <literal><![CDATA[
      T(K(x,y),(x * y) \ (y * x)) = T(K(x,y),K(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(91(a,1),2577(a,1,2,1))].">
      <j1 rule="para" parents="91 2577"/>
    </justification>
  </clause>

  <clause id="2583">
    <literal><![CDATA[
      T(1 / (1 / (x \ y)),y \ x) = x \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),2581(a,1,2,1))].">
      <j1 rule="para" parents="10 2581"/>
    </justification>
  </clause>

  <clause id="2584">
    <literal><![CDATA[
      K(x,(y * x) \ y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,1904,a(flip),b,2578,a),flip(a)].">
      <j1 rule="hyper" parents="347 1904 2578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2585">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(10(a,1),2584(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2586">
    <literal><![CDATA[
      K(x,y \ (y / x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(12(a,1),2584(a,1,2,1))].">
      <j1 rule="para" parents="12 2584"/>
    </justification>
  </clause>

  <clause id="2587">
    <literal><![CDATA[
      K(x \ y,T(y,x) \ ((y * x) / y)) = K(x \ y,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1253(a,2),2584(a,1,2,1))].">
      <j1 rule="para" parents="1253 2584"/>
    </justification>
  </clause>

  <clause id="2588">
    <literal><![CDATA[
      K((x / y) \ x,z \ (z / y)) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,771,a,b,2586,a)].">
      <j1 rule="hyper" parents="63 771 2586"/>
    </justification>
  </clause>

  <clause id="2590">
    <literal><![CDATA[
      (x \ y) * (((y \ x) \ 1) \ 1) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(134,a,2579,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 2579 22"/>
    </justification>
  </clause>

  <clause id="2591">
    <literal><![CDATA[
      T(x \ (x / y),y) = ((x \ (x / y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(83(a,1),2579(a,1,2))].">
      <j1 rule="para" parents="83 2579"/>
    </justification>
  </clause>

  <clause id="2592">
    <literal><![CDATA[
      T(K(x \ (x / (y \ 1)),x),T(y,x) \ y) = ((y \ T(y,x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(1323(a,2),2579(a,1,1))].">
      <j1 rule="para" parents="1323 2579"/>
    </justification>
  </clause>

  <clause id="2593">
    <literal><![CDATA[
      T(1 / (1 / K(x \ (x / (y \ 1)),x)),T(y,x) \ y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(1323(a,2),2583(a,1,1,2,2))].">
      <j1 rule="para" parents="1323 2583"/>
    </justification>
  </clause>

  <clause id="2595">
    <literal><![CDATA[
      R(1 / x,x,(y * x) \ y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(447,a,2573,a)].">
      <j1 rule="hyper" parents="447 2573"/>
    </justification>
  </clause>

  <clause id="2596">
    <literal><![CDATA[
      R(1 / x,x,y \ (y / x)) = x \ 1
    ]]></literal>
    <justification jstring="[para(12(a,1),2595(a,1,3,1))].">
      <j1 rule="para" parents="12 2595"/>
    </justification>
  </clause>

  <clause id="2597">
    <literal><![CDATA[
      (x \ (x / y)) / (y * (x \ (x / y))) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,247,a(flip),b,2596,a)].">
      <j1 rule="hyper" parents="63 247 2596"/>
    </justification>
  </clause>

  <clause id="2598">
    <literal><![CDATA[
      (x \ y) * (1 / (x \ y)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(1927,a,2585,a)].">
      <j1 rule="hyper" parents="1927 2585"/>
    </justification>
  </clause>

  <clause id="2599">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ 1 = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,2321,a(flip),b,2591,a),flip(a)].">
      <j1 rule="hyper" parents="63 2321 2591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2600">
    <literal><![CDATA[
      1 / (x \ (x / ((y \ 1) \ 1))) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(220,a,2321,a(flip),b,2591,a(flip))].">
      <j1 rule="hyper" parents="220 2321 2591"/>
    </justification>
  </clause>

  <clause id="2601">
    <literal><![CDATA[
      x * (((x \ (x / y)) \ 1) \ 1) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,2591,a(flip),b,2321,a(flip))].">
      <j1 rule="hyper" parents="134 2591 2321"/>
    </justification>
  </clause>

  <clause id="2603">
    <literal><![CDATA[
      ((x \ (x / (1 / y))) \ 1) \ 1 = x \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(83(a,1),2599(a,2,2,2,1))].">
      <j1 rule="para" parents="83 2599"/>
    </justification>
  </clause>

  <clause id="2604">
    <literal><![CDATA[
      1 / (x \ (x / (y \ 1))) = (x \ (x / (1 / y))) \ 1
    ]]></literal>
    <justification jstring="[para(83(a,1),2600(a,1,2,2,2,1))].">
      <j1 rule="para" parents="83 2600"/>
    </justification>
  </clause>

  <clause id="2605">
    <literal><![CDATA[
      (x \ (x / (1 / (1 / y)))) \ 1 = 1 / (x \ (x / y))
    ]]></literal>
    <justification jstring="[para(219(a,1),2600(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="219 2600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2606">
    <literal><![CDATA[
      x / (((y \ x) \ 1) \ 1) = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(80(a,1),2601(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="80 2601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2607">
    <literal><![CDATA[
      x \ (x / ((y \ 1) \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ 1 = z
    ]]></literal>
    <justification jstring="[para(2601(a,1),356(a,1,2))].">
      <j1 rule="para" parents="2601 356"/>
    </justification>
  </clause>

  <clause id="2608">
    <literal><![CDATA[
      (x * (((x \ (x / y)) \ 1) \ 1)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2601(a,2),2316(a,1,1))].">
      <j1 rule="para" parents="2601 2316"/>
    </justification>
  </clause>

  <clause id="2609">
    <literal><![CDATA[
      1 / (1 / (x \ (x / y))) = x \ (x / (1 / (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(222,a,2605,a)].">
      <j1 rule="hyper" parents="222 2605"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (x / y)))) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(134,a,2609,a,b,xx)].">
      <j1 rule="hyper" parents="134 2609"/>
    </justification>
  </clause>

  <clause id="2611">
    <literal><![CDATA[
      (x / y) * K(y,y \ 1) = x * (1 / (1 / (x \ (x / y))))
    ]]></literal>
    <justification jstring="[hyper(347,a,2347,a,b,2610,a)].">
      <j1 rule="hyper" parents="347 2347 2610"/>
    </justification>
  </clause>

  <clause id="2612">
    <literal><![CDATA[
      x / (1 / (1 / (y \ x))) = x * (1 / (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[para(80(a,1),2610(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="80 2610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2613">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) \ x = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(214,a,2612,a)].">
      <j1 rule="hyper" parents="214 2612"/>
    </justification>
  </clause>

  <clause id="2615">
    <literal><![CDATA[
      (x * (1 / (1 / T(y,x)))) \ x = 1 / (1 / ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(22(a,2),2613(a,1,1,2,2,2))].">
      <j1 rule="para" parents="22 2613"/>
    </justification>
  </clause>

  <clause id="2616">
    <literal><![CDATA[
      T(K(x,y),K(x,y) \ 1) = T(K(x,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(16(a,2),2582(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16 2582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2617">
    <literal><![CDATA[
      T(K(x,y),K(y,x)) = (K(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(440,a,2616,a),flip(a)].">
      <j1 rule="hyper" parents="440 2616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2618">
    <literal><![CDATA[
      (K(x,y) \ 1) \ 1 = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2557,a(flip),b,2617,a),flip(a)].">
      <j1 rule="hyper" parents="63 2557 2617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2621">
    <literal><![CDATA[
      1 / (1 / K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2618(a,1),215(a,1,2,2))].">
      <j1 rule="para" parents="2618 215"/>
    </justification>
  </clause>

  <clause id="2622">
    <literal><![CDATA[
      (x * (y * z)) * (1 / (1 / ((x * (y * z)) \ ((x * (y * z)) / L(z,y,x))))) = (x * y) * K(L(z,y,x),L(z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(212(a,1),2611(a,1,1)),flip(a)].">
      <j1 rule="para" parents="212 2611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2623">
    <literal><![CDATA[
      K(x \ y,T(x / y,T(y,x))) = K(x \ y,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1518(a,1),2587(a,1,2))].">
      <j1 rule="para" parents="1518 2587"/>
    </justification>
  </clause>

  <clause id="2624">
    <literal><![CDATA[
      K(x \ y,T(x / y,T(y,x))) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,2585,a(flip),b,2623,a),flip(a)].">
      <j1 rule="hyper" parents="347 2585 2623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2625">
    <literal><![CDATA[
      T(K(x \ (x / (y \ 1)),x),T(y,x) \ y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(2621(a,1),2593(a,1,1))].">
      <j1 rule="para" parents="2621 2593"/>
    </justification>
  </clause>

  <clause id="2626">
    <literal><![CDATA[
      ((x \ T(x,y)) \ 1) \ 1 = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2592,a(flip),b,2625,a)].">
      <j1 rule="hyper" parents="63 2592 2625"/>
    </justification>
  </clause>

  <clause id="2627">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,1618,a(flip),b,2512,a),flip(a)].">
      <j1 rule="hyper" parents="347 1618 2512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2628">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = x * (T((x \ y) * x,z) / x)
    ]]></literal>
    <justification jstring="[para(1143(a,1),2524(a,2,2))].">
      <j1 rule="para" parents="1143 2524"/>
    </justification>
  </clause>

  <clause id="2630">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ x,y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(187(a,1),2628(a,2,2,1,1))].">
      <j1 rule="para" parents="187 2628"/>
    </justification>
  </clause>

  <clause id="2633">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * (K(x,x \ 1) \ 1) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(133,a,2630,a(flip),b,1110,a)].">
      <j1 rule="hyper" parents="133 2630 1110"/>
    </justification>
  </clause>

  <clause id="2634">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[para(1962(a,1),2633(a,1,2))].">
      <j1 rule="para" parents="1962 2633"/>
    </justification>
  </clause>

  <clause id="2635">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(1962(a,1),2634(a,2,1,2))].">
      <j1 rule="para" parents="1962 2634"/>
    </justification>
  </clause>

  <clause id="2636">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1902(a,1),2635(a,2,1))].">
      <j1 rule="para" parents="1902 2635"/>
    </justification>
  </clause>

  <clause id="2637">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * ((y * u) * T((y * u) \ y,z))
    ]]></literal>
    <justification jstring="[hyper(1217,a,1441,a),flip(a)].">
      <j1 rule="hyper" parents="1217 1441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2638">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * (y * (u * T(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(864(a,1),2637(a,2,2))].">
      <j1 rule="para" parents="864 2637"/>
    </justification>
  </clause>

  <clause id="2639">
    <literal><![CDATA[
      L(x * T(x \ 1,y),z,u) = K(y \ (y / L(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(544,a,2638,a)].">
      <j1 rule="hyper" parents="544 2638"/>
    </justification>
  </clause>

  <clause id="2640">
    <literal><![CDATA[
      L(x * T(x \ 1,L(x,y,z)),y,z) = K(L(x,y,z) \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,2397,a(flip),b,2639,a),flip(a)].">
      <j1 rule="hyper" parents="347 2397 2639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2641">
    <literal><![CDATA[
      L(x,y,z) * T(L(x,y,z) \ 1,u) = L(x * T(x \ 1,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,1320,a(flip),b,2639,a)].">
      <j1 rule="hyper" parents="347 1320 2639"/>
    </justification>
  </clause>

  <clause id="2642">
    <literal><![CDATA[
      L(x \ T(x,y),z,u) = K(y \ (y / L(x \ 1,z,u)),y)
    ]]></literal>
    <justification jstring="[para(1140(a,1),2639(a,1,1))].">
      <j1 rule="para" parents="1140 2639"/>
    </justification>
  </clause>

  <clause id="2643">
    <literal><![CDATA[
      L(x \ T(x,y * L(x \ 1,z,u)),z,u) = K((y * L(x \ 1,z,u)) \ y,y * L(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),2642(a,2,1,2))].">
      <j1 rule="para" parents="11 2642"/>
    </justification>
  </clause>

  <clause id="2644">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * z) * T((y * z) \ z,x)) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1498(a,1),1582(a,2,1))].">
      <j1 rule="para" parents="1498 1582"/>
    </justification>
  </clause>

  <clause id="2645">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * T(y \ 1,x)) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1544(a,1),2644(a,2,1,1))].">
      <j1 rule="para" parents="1544 2644"/>
    </justification>
  </clause>

  <clause id="2646">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(y \ (y / R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,20,a,b,2645,a)].">
      <j1 rule="hyper" parents="347 20 2645"/>
    </justification>
  </clause>

  <clause id="2647">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = ((x * T(x \ 1,R(x,y,z))) * y) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,2397,a(flip),b,2645,a(flip))].">
      <j1 rule="hyper" parents="133 2397 2645"/>
    </justification>
  </clause>

  <clause id="2648">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) != w
    ]]></literal>
    <literal><![CDATA[
      R(y * T(y \ 1,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(2645(a,2),595(a,1))].">
      <j1 rule="para" parents="2645 595"/>
    </justification>
  </clause>

  <clause id="2649">
    <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(347,a,1320,a(flip),b,2646,a)].">
      <j1 rule="hyper" parents="347 1320 2646"/>
    </justification>
  </clause>

  <clause id="2650">
    <literal><![CDATA[
      R(T(x,x \ 1) * T(T(x,x \ 1) \ 1,x \ R(x,y,z)),y,z) = K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1467(a,1),2646(a,2,1,2))].">
      <j1 rule="para" parents="1467 2646"/>
    </justification>
  </clause>

  <clause id="2651">
    <literal><![CDATA[
      R(x,y,z) * T(R(x,y,z) \ 1,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x * T(x \ 1,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(1320(a,1),2648(a,1))].">
      <j1 rule="para" parents="1320 2648"/>
    </justification>
  </clause>

  <clause id="2652">
    <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(2649(a,1),271(a,1)),flip(b)].">
      <j1 rule="para" parents="2649 271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2653">
    <literal><![CDATA[
      (L(x,y,z) * (1 / x)) / L(x,y,z) = L(1 / x,L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2038,a(flip),b,1667,a)].">
      <j1 rule="hyper" parents="63 2038 1667"/>
    </justification>
  </clause>

  <clause id="2655">
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = L(1 / x,L(x,y,z),1 / x) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,2653,a(flip),b,969,a),flip(a)].">
      <j1 rule="hyper" parents="133 2653 969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2656">
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = x * L(x \ 1,L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[hyper(347,a,740,a(flip),b,2655,a),flip(a)].">
      <j1 rule="hyper" parents="347 740 2655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2657">
    <literal><![CDATA[
      x * L(x \ 1,L(x,y,z),1 / x) = K(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1696,a(flip),b,2656,a),flip(a)].">
      <j1 rule="hyper" parents="63 1696 2656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2658">
    <literal><![CDATA[
      L(x,y,(z * u) \ (z * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(u \ w,u,z)) = v5
    ]]></literal>
    <justification jstring="[para(1024(a,1),1025(a,1))].">
      <j1 rule="para" parents="1024 1025"/>
    </justification>
  </clause>

  <clause id="2659">
    <literal><![CDATA[
      K(x \ 1,x) * L(K(x \ 1,x) \ y,z,u) = (x \ 1) * (x * L(x \ ((x \ 1) \ y),z,u))
    ]]></literal>
    <justification jstring="[para(290(a,2),1197(a,1,2,1,1))].">
      <j1 rule="para" parents="290 1197"/>
    </justification>
  </clause>

  <clause id="2660">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) \ (x * (y \ 1)) = (x * y) * (L(x * y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(2211(a,1),1416(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2211 1416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2661">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) \ (x * (y \ 1)) = L(x * y,z,u) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,1409,a(flip),b,2660,a),flip(a)].">
      <j1 rule="hyper" parents="347 1409 2660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2662">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ (L(x,y,z) * (x \ 1)) = L(L(x,y,z) * x,u,w) \ (L(x,y,z) * x)
    ]]></literal>
    <justification jstring="[para(1295(a,1),2661(a,1,1,1))].">
      <j1 rule="para" parents="1295 2661"/>
    </justification>
  </clause>

  <clause id="2663">
    <literal><![CDATA[
      T(L(x * T(x \ 1,x),y,z),x * (L(x,y,z) \ 1)) = K(x \ (L(x,y,z) \ x),x)
    ]]></literal>
    <justification jstring="[para(2641(a,1),1833(a,1,1))].">
      <j1 rule="para" parents="2641 1833"/>
    </justification>
  </clause>

  <clause id="2664">
    <literal><![CDATA[
      T(L(K(x \ 1,x),y,z),x * (L(x,y,z) \ 1)) = K(x \ (L(x,y,z) \ x),x)
    ]]></literal>
    <justification jstring="[para(387(a,1),2663(a,1,1,1))].">
      <j1 rule="para" parents="387 2663"/>
    </justification>
  </clause>

  <clause id="2665">
    <literal><![CDATA[
      T(L(K(x \ 1,x),y,z),L(x,y,z) \ x) = K(x \ (L(x,y,z) \ x),x)
    ]]></literal>
    <justification jstring="[para(1409(a,1),2664(a,1,2))].">
      <j1 rule="para" parents="1409 2664"/>
    </justification>
  </clause>

  <clause id="2666">
    <literal><![CDATA[
      L(T(K(x \ 1,x),L(x,y,z) \ x),y,z) = K(x \ (L(x,y,z) \ x),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a,b,2665,a)].">
      <j1 rule="hyper" parents="63 25 2665"/>
    </justification>
  </clause>

  <clause id="2667">
    <literal><![CDATA[
      L(T(K(x \ 1,x),L(x,y,z) \ x),y,z) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(1415(a,1),2666(a,2,1))].">
      <j1 rule="para" parents="1415 2666"/>
    </justification>
  </clause>

  <clause id="2668">
    <literal><![CDATA[
      K(x \ y,x) * R((y \ ((x \ y) * x)) \ x,z,u) = y \ ((R(x,z,u) * (x \ y)) * x)
    ]]></literal>
    <justification jstring="[para(92(a,1),2164(a,1,1))].">
      <j1 rule="para" parents="92 2164"/>
    </justification>
  </clause>

  <clause id="2669">
    <literal><![CDATA[
      K(x \ y,x) * R(K(x \ y,x) \ x,z,u) = y \ ((R(x,z,u) * (x \ y)) * x)
    ]]></literal>
    <justification jstring="[para(92(a,1),2668(a,1,2,1,1))].">
      <j1 rule="para" parents="92 2668"/>
    </justification>
  </clause>

  <clause id="2670">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ x) * K(1 / x,(1 / x) \ 1)) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(2545,a,2438,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2545 2438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2671">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ x) * K(x \ 1,x)) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(1957(a,1),2670(a,1,2,2))].">
      <j1 rule="para" parents="1957 2670"/>
    </justification>
  </clause>

  <clause id="2672">
    <literal><![CDATA[
      (1 / x) * (T(x,y) \ (1 / (1 / x))) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(2355(a,1),2671(a,1,2))].">
      <j1 rule="para" parents="2355 2671"/>
    </justification>
  </clause>

  <clause id="2673">
    <literal><![CDATA[
      K(x \ 1,x) * L(K(x \ 1,x) \ (y * x),z,u) = ((x \ 1) * L((x \ 1) \ y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,1987,a(flip),b,2659,a),flip(a)].">
      <j1 rule="hyper" parents="347 1987 2659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2674">
    <literal><![CDATA[
      K(x \ 1,x) * L(K(x \ 1,x) \ (y * x),z,u) = (x \ L(x * y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(1201(a,1),2673(a,2,1))].">
      <j1 rule="para" parents="1201 2673"/>
    </justification>
  </clause>

  <clause id="2675">
    <literal><![CDATA[
      (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z = R(x,y,z) * (z * R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(22(a,2),1742(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="22 1742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2676">
    <literal><![CDATA[
      (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z = R(x,y,z) * (R(y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(268(a,1),2675(a,2,2))].">
      <j1 rule="para" parents="268 2675"/>
    </justification>
  </clause>

  <clause id="2677">
    <literal><![CDATA[
      R((x * (y * z)) / z,z \ 1,x * (y * z)) \ 1 = (z \ 1) * ((x * (y * (z \ 1))) \ 1)
    ]]></literal>
    <justification jstring="[para(2206(a,1),2210(a,1,1))].">
      <j1 rule="para" parents="2206 2210"/>
    </justification>
  </clause>

  <clause id="2678">
    <literal><![CDATA[
      R((x * (y * z)) / z,z,x * (y * z)) \ 1 = (z \ 1) * ((x * (y * (z \ 1))) \ 1)
    ]]></literal>
    <justification jstring="[para(2247(a,1),2677(a,1,1))].">
      <j1 rule="para" parents="2247 2677"/>
    </justification>
  </clause>

  <clause id="2679">
    <literal><![CDATA[
      (x \ 1) * ((y * (z * (x \ 1))) \ 1) = x * ((y * (z * x)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2209,a,2678,a),flip(a)].">
      <j1 rule="hyper" parents="2209 2678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2680">
    <literal><![CDATA[
      a(x,x \ y,L(T(x,x \ y),z,u)) = (L(x,z,u) * y) \ (y * L(T(x,x \ y),z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),2109(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2682">
    <literal><![CDATA[
      K(T(x / y,T(y,x)) \ 1,T(x / y,T(y,x))) = K(x \ y,T(x / y,T(y,x)))
    ]]></literal>
    <justification jstring="[para(1254(a,1),2403(a,2,1))].">
      <j1 rule="para" parents="1254 2403"/>
    </justification>
  </clause>

  <clause id="2683">
    <literal><![CDATA[
      K(T(x / y,T(y,x)) \ 1,T(x / y,T(y,x))) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,2624,a(flip),b,2682,a),flip(a)].">
      <j1 rule="hyper" parents="347 2624 2682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2684">
    <literal><![CDATA[
      T(x,y) * (K(y \ (y / (1 / x)),y) \ (1 / x)) = T(x,y) * ((T(x,y) / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,2041,a(flip),b,2525,a),flip(a)].">
      <j1 rule="hyper" parents="63 2041 2525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2685">
    <literal><![CDATA[
      T(x,y) * (T(1 / (1 / x),y) \ 1) = T(x,y) * ((T(x,y) / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(2163(a,1),2684(a,1,2))].">
      <j1 rule="para" parents="2163 2684"/>
    </justification>
  </clause>

  <clause id="2686">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = T(1 / (1 / x),y) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2124,a(flip),b,2685,a),flip(a)].">
      <j1 rule="hyper" parents="63 2124 2685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2690">
    <literal><![CDATA[
      K((x * L(x \ 1,y,z)) \ x,x * L(x \ 1,y,z)) = L(x \ x,y,z)
    ]]></literal>
    <justification jstring="[para(2030(a,1),2643(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2030 2643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2691">
    <literal><![CDATA[
      K((x * L(x \ 1,y,z)) \ x,x * L(x \ 1,y,z)) = L(1,y,z)
    ]]></literal>
    <justification jstring="[para(68(a,1),2690(a,2,1))].">
      <j1 rule="para" parents="68 2690"/>
    </justification>
  </clause>

  <clause id="2692">
    <literal><![CDATA[
      K((x * L(x \ 1,y,z)) \ x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(347,a,556,a(flip),b,2691,a),flip(a)].">
      <j1 rule="hyper" parents="347 556 2691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2695">
    <literal><![CDATA[
      ((x * L(x \ 1,y,z)) \ x) * (x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(189,a,92,a,b,2692,a(flip))].">
      <j1 rule="hyper" parents="189 92 2692"/>
    </justification>
  </clause>

  <clause id="2696">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z)) = L(L(x,y,z) * x,u,w) \ (L(x,y,z) * x)
    ]]></literal>
    <justification jstring="[para(1295(a,1),2662(a,1,2))].">
      <j1 rule="para" parents="1295 2662"/>
    </justification>
  </clause>

  <clause id="2697">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z)) = L(x * L(x,y,z),u,w) \ (L(x,y,z) * x)
    ]]></literal>
    <justification jstring="[para(274(a,1),2696(a,2,1,1))].">
      <j1 rule="para" parents="274 2696"/>
    </justification>
  </clause>

  <clause id="2698">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z)) = L(x * L(x,y,z),u,w) \ (x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(274(a,1),2697(a,2,2))].">
      <j1 rule="para" parents="274 2697"/>
    </justification>
  </clause>

  <clause id="2699">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * K(u,u \ 1))) = L(z,y,x) * K(u,u \ 1)
    ]]></literal>
    <justification jstring="[para(2219(a,1),2331(a,1,1))].">
      <j1 rule="para" parents="2219 2331"/>
    </justification>
  </clause>

  <clause id="2701">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * K(u,u \ 1)))) = L(z,y,x) * K(u,u \ 1)
    ]]></literal>
    <justification jstring="[para(2226(a,1),2699(a,1,2,2))].">
      <j1 rule="para" parents="2226 2699"/>
    </justification>
  </clause>

  <clause id="2702">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) = L(x,z,u) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(545,a,2701,a)].">
      <j1 rule="hyper" parents="545 2701"/>
    </justification>
  </clause>

  <clause id="2703">
    <literal><![CDATA[
      x \ L(y * K(z,z \ 1),u,w) = (x \ L(y,u,w)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,2702,a,b,2225,a)].">
      <j1 rule="hyper" parents="128 2702 2225"/>
    </justification>
  </clause>

  <clause id="2704">
    <literal><![CDATA[
      L(x \ 1,y,z) * K(x,x \ 1) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1906(a,1),2702(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1906 2702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2705">
    <literal><![CDATA[
      K((1 / x) \ ((1 / x) * T((1 / x) \ 1,y)),1 / x) = (((1 / x) * T(x,y)) / (1 / x)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(2162(a,1),1347(a,1,1,2))].">
      <j1 rule="para" parents="2162 1347"/>
    </justification>
  </clause>

  <clause id="2706">
    <literal><![CDATA[
      (((1 / x) * T(x,y)) / (1 / x)) \ T(x,y) = K((1 / x) \ (T(x,y) / x),1 / x)
    ]]></literal>
    <justification jstring="[para(1147(a,1),2705(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1147 2705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2707">
    <literal><![CDATA[
      (((1 / x) * T(x,y)) / (1 / x)) \ T(x,y) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(1151(a,1),2706(a,2,1))].">
      <j1 rule="para" parents="1151 2706"/>
    </justification>
  </clause>

  <clause id="2708">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ T(x,y) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(505(a,1),2707(a,1,1))].">
      <j1 rule="para" parents="505 2707"/>
    </justification>
  </clause>

  <clause id="2709">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x,x \ 1) \ (x * y),z,u) = x * ((1 / x) * R((1 / x) \ y,z,u))
    ]]></literal>
    <justification jstring="[para(1925(a,1),1937(a,2,2,2,1,1))].">
      <j1 rule="para" parents="1925 1937"/>
    </justification>
  </clause>

  <clause id="2710">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x,x \ 1) \ (x * y),z,u) = x * (R(y * x,z,u) / x)
    ]]></literal>
    <justification jstring="[para(1288(a,1),2709(a,2,2))].">
      <j1 rule="para" parents="1288 2709"/>
    </justification>
  </clause>

  <clause id="2711">
    <literal><![CDATA[
      T(x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)),z) = T(x,z) * ((T(x,z) \ T(x,y)) / T(x,y))
    ]]></literal>
    <justification jstring="[para(1249(a,1),2432(a,2,2,1))].">
      <j1 rule="para" parents="1249 2432"/>
    </justification>
  </clause>

  <clause id="2712">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ T(x,z)) / T(x,z)) = T(K(T(x,z),1 / x),y)
    ]]></literal>
    <justification jstring="[para(1698(a,1),2711(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1698 2711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2713">
    <literal><![CDATA[
      K(T(x,y),1 / T(x,z)) = T(K(T(x,y),1 / x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1859,a(flip),b,2712,a)].">
      <j1 rule="hyper" parents="63 1859 2712"/>
    </justification>
  </clause>

  <clause id="2714">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1922,a(flip),b,2713,a)].">
      <j1 rule="hyper" parents="63 1922 2713"/>
    </justification>
  </clause>

  <clause id="2715">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = K(T(x,y),T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,2143,a,b,2714,a)].">
      <j1 rule="hyper" parents="347 2143 2714"/>
    </justification>
  </clause>

  <clause id="2716">
    <literal><![CDATA[
      (T(x,y) / x) \ (1 / x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,1924,a(flip),b,2715,a),flip(a)].">
      <j1 rule="hyper" parents="34 1924 2715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2717">
    <literal><![CDATA[
      (T(x,y) / x) * (1 / T(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(150,a,2716,a)].">
      <j1 rule="hyper" parents="150 2716"/>
    </justification>
  </clause>

  <clause id="2718">
    <literal><![CDATA[
      (T(T(x,x \ 1),y) / T(x,x \ 1)) \ (x \ 1) = 1 / T(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(296(a,1),2716(a,1,2))].">
      <j1 rule="para" parents="296 2716"/>
    </justification>
  </clause>

  <clause id="2719">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = z
    ]]></literal>
    <justification jstring="[para(2716(a,2),1934(a,1,2))].">
      <j1 rule="para" parents="2716 1934"/>
    </justification>
  </clause>

  <clause id="2720">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = z
    ]]></literal>
    <justification jstring="[para(2686(a,1),2719(a,1))].">
      <j1 rule="para" parents="2686 2719"/>
    </justification>
  </clause>

  <clause id="2721">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(2720,a,2708,a)].">
      <j1 rule="hyper" parents="2720 2708"/>
    </justification>
  </clause>

  <clause id="2722">
    <literal><![CDATA[
      (x * y) * K(T(x,y),1 / x) = y * ((T(x,y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2721(a,1),2344(a,1,2))].">
      <j1 rule="para" parents="2721 2344"/>
    </justification>
  </clause>

  <clause id="2723">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = 1 / T(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1654(a,1),2718(a,1,1))].">
      <j1 rule="para" parents="1654 2718"/>
    </justification>
  </clause>

  <clause id="2724">
    <literal><![CDATA[
      1 / T(T(x,x \ 1),y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,2157,a(flip),b,2723,a),flip(a)].">
      <j1 rule="hyper" parents="63 2157 2723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2725">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(214,a,2724,a),flip(a)].">
      <j1 rule="hyper" parents="214 2724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2726">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ 1 = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(385(a,1),2724(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="385 2724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2727">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,763,a(flip),b,2725,a)].">
      <j1 rule="hyper" parents="63 763 2725"/>
    </justification>
  </clause>

  <clause id="2728">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ 1 = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(749(a,1),2725(a,1,1)),flip(a)].">
      <j1 rule="para" parents="749 2725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2729">
    <literal><![CDATA[
      1 / (1 / T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(222,a,2726,a)].">
      <j1 rule="hyper" parents="222 2726"/>
    </justification>
  </clause>

  <clause id="2730">
    <literal><![CDATA[
      x * ((T(y,x) \ 1) \ 1) = ((y \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(134,a,2727,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 2727 22"/>
    </justification>
  </clause>

  <clause id="2731">
    <literal><![CDATA[
      T(((x / y) \ 1) \ 1,y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(113(a,1),2727(a,2,1,1))].">
      <j1 rule="para" parents="113 2727"/>
    </justification>
  </clause>

  <clause id="2732">
    <literal><![CDATA[
      (x / T(y,z)) * T((y \ 1) \ 1,z) = x * K(T(y,z),T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(2727(a,2),2345(a,1,2))].">
      <j1 rule="para" parents="2727 2345"/>
    </justification>
  </clause>

  <clause id="2733">
    <literal><![CDATA[
      T(x,y) * K(T(x,y) \ 1,T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1902,a,b,2729,a)].">
      <j1 rule="hyper" parents="63 1902 2729"/>
    </justification>
  </clause>

  <clause id="2734">
    <literal><![CDATA[
      T(1 / (1 / (x / y)),y) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[para(113(a,1),2729(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 2729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2735">
    <literal><![CDATA[
      (x * T(1 / (1 / y),x)) \ x = 1 / (1 / ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(2729(a,1),2615(a,1,1,2))].">
      <j1 rule="para" parents="2729 2615"/>
    </justification>
  </clause>

  <clause id="2736">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(870,a,2730,a)].">
      <j1 rule="hyper" parents="870 2730"/>
    </justification>
  </clause>

  <clause id="2737">
    <literal><![CDATA[
      (x * y) * K(T(x,y),1 / x) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,2722,a,b,2730,a)].">
      <j1 rule="hyper" parents="63 2722 2730"/>
    </justification>
  </clause>

  <clause id="2738">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) * y = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(113(a,1),2730(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="113 2730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2739">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = x * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,2334,a,b,2736,a),flip(a)].">
      <j1 rule="hyper" parents="347 2334 2736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2740">
    <literal><![CDATA[
      (T(x,y) \ x) / ((x \ 1) \ 1) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(2736(a,1),1237(a,1,2))].">
      <j1 rule="para" parents="2736 1237"/>
    </justification>
  </clause>

  <clause id="2741">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,2439,a,b,2739,a(flip))].">
      <j1 rule="hyper" parents="34 2439 2739"/>
    </justification>
  </clause>

  <clause id="2742">
    <literal><![CDATA[
      K(x,x \ 1) * y = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1068,a,2741,a)].">
      <j1 rule="hyper" parents="1068 2741"/>
    </justification>
  </clause>

  <clause id="2743">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,2741,a)].">
      <j1 rule="hyper" parents="54 2741"/>
    </justification>
  </clause>

  <clause id="2744">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,2741,a(flip),b,2435,a)].">
      <j1 rule="hyper" parents="128 2741 2435"/>
    </justification>
  </clause>

  <clause id="2747">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2743(a,1),315(a,1,2))].">
      <j1 rule="para" parents="2743 315"/>
    </justification>
  </clause>

  <clause id="2748">
    <literal><![CDATA[
      T(x,K(y,1 / y)) = x
    ]]></literal>
    <justification jstring="[para(1922(a,2),2743(a,1,2))].">
      <j1 rule="para" parents="1922 2743"/>
    </justification>
  </clause>

  <clause id="2749">
    <literal><![CDATA[
      T(x,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(1926(a,1),2743(a,1,2))].">
      <j1 rule="para" parents="1926 2743"/>
    </justification>
  </clause>

  <clause id="2751">
    <literal><![CDATA[
      K(x,1 / x) * y = y * K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(1852,a,2748,a),flip(a)].">
      <j1 rule="hyper" parents="1852 2748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2752">
    <literal><![CDATA[
      K(x \ 1,x) * (y * K(x,x \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(2383,a,2749,a)].">
      <j1 rule="hyper" parents="2383 2749"/>
    </justification>
  </clause>

  <clause id="2753">
    <literal><![CDATA[
      K(x \ 1,x) * y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1852,a,2749,a),flip(a)].">
      <j1 rule="hyper" parents="1852 2749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2754">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(63,a,2358,a(flip),b,2749,a),flip(a)].">
      <j1 rule="hyper" parents="63 2358 2749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2755">
    <literal><![CDATA[
      T(K(x \ 1,x),y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(54,a,2749,a)].">
      <j1 rule="hyper" parents="54 2749"/>
    </justification>
  </clause>

  <clause id="2756">
    <literal><![CDATA[
      T(x,(y \ 1) * y) = x
    ]]></literal>
    <justification jstring="[para(290(a,1),2749(a,1,2))].">
      <j1 rule="para" parents="290 2749"/>
    </justification>
  </clause>

  <clause id="2757">
    <literal><![CDATA[
      x * (K(y \ 1,y) * z) = x * (z * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(2749(a,1),251(a,1,2,2))].">
      <j1 rule="para" parents="2749 251"/>
    </justification>
  </clause>

  <clause id="2758">
    <literal><![CDATA[
      x \ y != K(z \ 1,z) * u
    ]]></literal>
    <literal><![CDATA[
      x * (u * K(z \ 1,z)) = y
    ]]></literal>
    <justification jstring="[para(2749(a,1),635(a,2,2))].">
      <j1 rule="para" parents="2749 635"/>
    </justification>
  </clause>

  <clause id="2759">
    <literal><![CDATA[
      K(x \ 1,x) \ ((y * (x \ 1)) * x) = R(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2749(a,1),1190(a,2,1))].">
      <j1 rule="para" parents="2749 1190"/>
    </justification>
  </clause>

  <clause id="2760">
    <literal><![CDATA[
      ((x \ 1) * x) * y = y * ((x \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(1852,a,2756,a),flip(a)].">
      <j1 rule="hyper" parents="1852 2756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2761">
    <literal><![CDATA[
      K(x \ (x / T(x,y)),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1830,a,b,2755,a)].">
      <j1 rule="hyper" parents="63 1830 2755"/>
    </justification>
  </clause>

  <clause id="2762">
    <literal><![CDATA[
      T((x \ 1) * x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(290(a,1),2755(a,1,1))].">
      <j1 rule="para" parents="290 2755"/>
    </justification>
  </clause>

  <clause id="2763">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,y) * x = z
    ]]></literal>
    <justification jstring="[para(2755(a,1),315(a,1,2))].">
      <j1 rule="para" parents="2755 315"/>
    </justification>
  </clause>

  <clause id="2764">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(2755(a,1),2667(a,1,1))].">
      <j1 rule="para" parents="2755 2667"/>
    </justification>
  </clause>

  <clause id="2765">
    <literal><![CDATA[
      K(x,x \ 1) * (y * K(x \ 1,x)) = y
    ]]></literal>
    <justification jstring="[hyper(347,a,2350,a(flip),b,2742,a),flip(a)].">
      <j1 rule="hyper" parents="347 2350 2742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2766">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ x) = y \ ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,2339,a(flip),b,2742,a),flip(a)].">
      <j1 rule="hyper" parents="347 2339 2742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2767">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,2338,a(flip),b,2742,a),flip(a)].">
      <j1 rule="hyper" parents="347 2338 2742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2768">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (x \ 1)) = y * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(347,a,2332,a(flip),b,2742,a),flip(a)].">
      <j1 rule="hyper" parents="347 2332 2742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2769">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = y * (z * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(347,a,2226,a(flip),b,2742,a),flip(a)].">
      <j1 rule="hyper" parents="347 2226 2742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2770">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) = (x \ z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,2742,a,b,2225,a)].">
      <j1 rule="hyper" parents="128 2742 2225"/>
    </justification>
  </clause>

  <clause id="2771">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[hyper(34,a,2350,a(flip),b,2742,a),flip(a)].">
      <j1 rule="hyper" parents="34 2350 2742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2772">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ ((z * y) * K(x,x \ 1)) = L(T(z,y),y,K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(2742(a,1),263(a,1,2))].">
      <j1 rule="para" parents="2742 263"/>
    </justification>
  </clause>

  <clause id="2773">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ ((z * y) * K(x,x \ 1)) = R(T(z,y * K(x,x \ 1)),y,K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(2742(a,2),744(a,1,1))].">
      <j1 rule="para" parents="2742 744"/>
    </justification>
  </clause>

  <clause id="2774">
    <literal><![CDATA[
      K(x,x \ 1) * y = y * (x * (1 / x))
    ]]></literal>
    <justification jstring="[para(1924(a,1),2742(a,2,2))].">
      <j1 rule="para" parents="1924 2742"/>
    </justification>
  </clause>

  <clause id="2775">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2742(a,2),2343(a,1,1))].">
      <j1 rule="para" parents="2742 2343"/>
    </justification>
  </clause>

  <clause id="2776">
    <literal><![CDATA[
      K(x,1 / x) * (y * z) = y * (z * K(x,1 / x))
    ]]></literal>
    <justification jstring="[hyper(347,a,2220,a(flip),b,2751,a),flip(a)].">
      <j1 rule="hyper" parents="347 2220 2751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2777">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * K(x,x \ 1) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(938,a,2752,a),flip(a)].">
      <j1 rule="hyper" parents="938 2752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2779">
    <literal><![CDATA[
      K(x \ 1,x) * (y * (1 / x)) = y * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2332(a,1),2752(a,1,2))].">
      <j1 rule="para" parents="2332 2752"/>
    </justification>
  </clause>

  <clause id="2780">
    <literal><![CDATA[
      K(x \ 1,x) * (y * x) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(2333(a,1),2752(a,1,2))].">
      <j1 rule="para" parents="2333 2752"/>
    </justification>
  </clause>

  <clause id="2781">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T(x,x \ 1)) = y * x
    ]]></literal>
    <justification jstring="[para(2338(a,1),2752(a,1,2))].">
      <j1 rule="para" parents="2338 2752"/>
    </justification>
  </clause>

  <clause id="2782">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (x \ 1)) = y / (1 / x)
    ]]></literal>
    <justification jstring="[para(2357(a,1),2752(a,1,2))].">
      <j1 rule="para" parents="2357 2752"/>
    </justification>
  </clause>

  <clause id="2783">
    <literal><![CDATA[
      K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(2702(a,2),2752(a,1,2))].">
      <j1 rule="para" parents="2702 2752"/>
    </justification>
  </clause>

  <clause id="2784">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,x \ 1) * y) = y
    ]]></literal>
    <justification jstring="[para(2742(a,2),2752(a,1,2))].">
      <j1 rule="para" parents="2742 2752"/>
    </justification>
  </clause>

  <clause id="2785">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ 1) = y \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,2217,a(flip),b,2753,a),flip(a)].">
      <j1 rule="hyper" parents="347 2217 2753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2786">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,2215,a(flip),b,2753,a),flip(a)].">
      <j1 rule="hyper" parents="347 2215 2753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2787">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * L(z,x,K(y \ 1,y)) = K(y \ 1,y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,2753,a(flip),b,212,a)].">
      <j1 rule="hyper" parents="133 2753 212"/>
    </justification>
  </clause>

  <clause id="2790">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ ((y * (x \ 1)) * x) = a(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2753(a,2),389(a,1,1))].">
      <j1 rule="para" parents="2753 389"/>
    </justification>
  </clause>

  <clause id="2791">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (K(z \ 1,z) * y)
    ]]></literal>
    <justification jstring="[para(2753(a,2),2215(a,2,2))].">
      <j1 rule="para" parents="2753 2215"/>
    </justification>
  </clause>

  <clause id="2793">
    <literal><![CDATA[
      K(x,x \ 1) * (K(x \ 1,x) * y) = y
    ]]></literal>
    <justification jstring="[hyper(63,a,2742,a,b,2754,a)].">
      <j1 rule="hyper" parents="63 2742 2754"/>
    </justification>
  </clause>

  <clause id="2794">
    <literal><![CDATA[
      K(x,x \ 1) \ y = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(128,a,2754,a(flip),b,2742,a)].">
      <j1 rule="hyper" parents="128 2754 2742"/>
    </justification>
  </clause>

  <clause id="2795">
    <literal><![CDATA[
      a(x \ 1,x,x \ 1) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(34,a,835,a,b,2760,a(flip))].">
      <j1 rule="hyper" parents="34 835 2760"/>
    </justification>
  </clause>

  <clause id="2796">
    <literal><![CDATA[
      a(x \ 1,x,x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,290,a,b,2795,a),flip(a)].">
      <j1 rule="hyper" parents="347 290 2795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2798">
    <literal><![CDATA[
      x * K(x \ (x / T(x,y)),x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(134,a,2761,a,b,1901,a)].">
      <j1 rule="hyper" parents="134 2761 1901"/>
    </justification>
  </clause>

  <clause id="2799">
    <literal><![CDATA[
      K(x \ 1,x) / T(x,y) = T(1 / T(x,y),x)
    ]]></literal>
    <justification jstring="[para(2761(a,1),1325(a,1,1))].">
      <j1 rule="para" parents="2761 1325"/>
    </justification>
  </clause>

  <clause id="2800">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      z * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(2765(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="2765 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2801">
    <literal><![CDATA[
      K(x \ 1,x) \ y = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(128,a,2771,a(flip),b,2753,a)].">
      <j1 rule="hyper" parents="128 2771 2753"/>
    </justification>
  </clause>

  <clause id="2802">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * z = x
    ]]></literal>
    <justification jstring="[para(2771(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2771 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2803">
    <literal><![CDATA[
      (x * (1 / x)) * y = y * (x * (1 / x))
    ]]></literal>
    <justification jstring="[para(1924(a,1),2774(a,1,1))].">
      <j1 rule="para" parents="1924 2774"/>
    </justification>
  </clause>

  <clause id="2804">
    <literal><![CDATA[
      K(x,x \ 1) * (K(x \ 1,x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(2794(a,1),286(a,1,2))].">
      <j1 rule="para" parents="2794 286"/>
    </justification>
  </clause>

  <clause id="2805">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x \ 1,x) * (x * y),z,u) = x * (R(y * x,z,u) / x)
    ]]></literal>
    <justification jstring="[para(2794(a,1),2710(a,1,2,1))].">
      <j1 rule="para" parents="2794 2710"/>
    </justification>
  </clause>

  <clause id="2806">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[para(2801(a,1),2627(a,1,2,1))].">
      <j1 rule="para" parents="2801 2627"/>
    </justification>
  </clause>

  <clause id="2807">
    <literal><![CDATA[
      K(x \ 1,x) * L(K(x,x \ 1) * (y * x),z,u) = (x \ L(x * y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(2801(a,1),2674(a,1,2,1))].">
      <j1 rule="para" parents="2801 2674"/>
    </justification>
  </clause>

  <clause id="2808">
    <literal><![CDATA[
      (x * (((x \ y) \ 1) \ 1)) / x = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(305,a,2731,a)].">
      <j1 rule="hyper" parents="305 2731"/>
    </justification>
  </clause>

  <clause id="2809">
    <literal><![CDATA[
      T(T(x / y,y / x),y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(1947(a,2),2731(a,1,1))].">
      <j1 rule="para" parents="1947 2731"/>
    </justification>
  </clause>

  <clause id="2810">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) / x = 1 / (1 / (y / x))
    ]]></literal>
    <justification jstring="[hyper(305,a,2734,a)].">
      <j1 rule="hyper" parents="305 2734"/>
    </justification>
  </clause>

  <clause id="2812">
    <literal><![CDATA[
      (T(x,y) \ 1) * ((x \ 1) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(148,a,2740,a)].">
      <j1 rule="hyper" parents="148 2740"/>
    </justification>
  </clause>

  <clause id="2813">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x,x \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[para(2740(a,1),2348(a,1,1))].">
      <j1 rule="para" parents="2740 2348"/>
    </justification>
  </clause>

  <clause id="2815">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2312,a(flip),b,2764,a),flip(a)].">
      <j1 rule="hyper" parents="63 2312 2764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2817">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(L(x,u,w) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,2312,a,b,2815,a)].">
      <j1 rule="hyper" parents="347 2312 2815"/>
    </justification>
  </clause>

  <clause id="2818">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(x \ 1,x) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(134,a,2815,a(flip),b,1418,a)].">
      <j1 rule="hyper" parents="134 2815 1418"/>
    </justification>
  </clause>

  <clause id="2819">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ y) / y) * x) = x * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(347,a,1948,a(flip),b,2767,a),flip(a)].">
      <j1 rule="hyper" parents="347 1948 2767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2820">
    <literal><![CDATA[
      T(x,y) \ (1 / (1 / x)) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(128,a,2798,a(flip),b,1327,a)].">
      <j1 rule="hyper" parents="128 2798 1327"/>
    </justification>
  </clause>

  <clause id="2821">
    <literal><![CDATA[
      T(x \ y,x / y) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(808,a,2809,a)].">
      <j1 rule="hyper" parents="808 2809"/>
    </justification>
  </clause>

  <clause id="2822">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x * y) \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(11(a,1),2821(a,1,2))].">
      <j1 rule="para" parents="11 2821"/>
    </justification>
  </clause>

  <clause id="2823">
    <literal><![CDATA[
      T(x \ (y \ x),y) = ((x \ (y \ x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(80(a,1),2821(a,1,2))].">
      <j1 rule="para" parents="80 2821"/>
    </justification>
  </clause>

  <clause id="2825">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(2820(a,1),2672(a,1,2))].">
      <j1 rule="para" parents="2820 2672"/>
    </justification>
  </clause>

  <clause id="2826">
    <literal><![CDATA[
      1 / T((x * y) \ y,x) = ((x * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(220,a,2822,a,b,xx)].">
      <j1 rule="hyper" parents="220 2822"/>
    </justification>
  </clause>

  <clause id="2827">
    <literal><![CDATA[
      1 / T(x \ (y \ x),y) = (x \ (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(220,a,2823,a,b,xx)].">
      <j1 rule="hyper" parents="220 2823"/>
    </justification>
  </clause>

  <clause id="2828">
    <literal><![CDATA[
      T(1 / (1 / ((x * y) \ y)),x) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(39,a,2726,a,b,2826,a(flip))].">
      <j1 rule="hyper" parents="39 2726 2826"/>
    </justification>
  </clause>

  <clause id="2829">
    <literal><![CDATA[
      ((x \ (y \ x)) \ 1) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      T(x \ (y \ x),y) = z
    ]]></literal>
    <justification jstring="[para(2827(a,1),359(a,1,1))].">
      <j1 rule="para" parents="2827 359"/>
    </justification>
  </clause>

  <clause id="2830">
    <literal><![CDATA[
      (x * y) \ (K(x,x \ 1) * y) = 1 / (1 / ((x * y) \ y))
    ]]></literal>
    <justification jstring="[hyper(40,a,1977,a,b,2828,a)].">
      <j1 rule="hyper" parents="40 1977 2828"/>
    </justification>
  </clause>

  <clause id="2831">
    <literal><![CDATA[
      x / (x * (((x \ y) \ 1) \ 1)) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2738(a,1),2369(a,1,2))].">
      <j1 rule="para" parents="2738 2369"/>
    </justification>
  </clause>

  <clause id="2832">
    <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(2757(a,2),836(a,1,2))].">
      <j1 rule="para" parents="2757 836"/>
    </justification>
  </clause>

  <clause id="2833">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * (x \ 1))) = y * (z * (1 / x))
    ]]></literal>
    <justification jstring="[para(2332(a,1),2769(a,2,2))].">
      <j1 rule="para" parents="2332 2769"/>
    </justification>
  </clause>

  <clause id="2834">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z / ((x \ 1) \ 1))) = y * (z / x)
    ]]></literal>
    <justification jstring="[para(2348(a,1),2769(a,2,2))].">
      <j1 rule="para" parents="2348 2769"/>
    </justification>
  </clause>

  <clause id="2835">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z / (1 / x))) = y * (z / (x \ 1))
    ]]></literal>
    <justification jstring="[para(2357(a,1),2769(a,2,2))].">
      <j1 rule="para" parents="2357 2769"/>
    </justification>
  </clause>

  <clause id="2836">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = y * (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2742(a,2),2769(a,2,2))].">
      <j1 rule="para" parents="2742 2769"/>
    </justification>
  </clause>

  <clause id="2837">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (K(x \ 1,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[para(2754(a,1),2769(a,2,2))].">
      <j1 rule="para" parents="2754 2769"/>
    </justification>
  </clause>

  <clause id="2838">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) = K(y,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,2742,a,b,2770,a),flip(a)].">
      <j1 rule="hyper" parents="347 2742 2770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2840">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = (x \ z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(678,a,2786,a)].">
      <j1 rule="hyper" parents="678 2786"/>
    </justification>
  </clause>

  <clause id="2841">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,2757,a,b,2786,a),flip(a)].">
      <j1 rule="hyper" parents="347 2757 2786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2842">
    <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(2786(a,1),567(a,1,1))].">
      <j1 rule="para" parents="2786 567"/>
    </justification>
  </clause>

  <clause id="2843">
    <literal><![CDATA[
      (x * T(x \ y,y \ x)) / x = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2579(a,2),2808(a,1,1,2))].">
      <j1 rule="para" parents="2579 2808"/>
    </justification>
  </clause>

  <clause id="2844">
    <literal><![CDATA[
      (x * (1 / (1 / y))) / x = 1 / (1 / ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(9(a,1),2810(a,1,1,2,2,2))].">
      <j1 rule="para" parents="9 2810"/>
    </justification>
  </clause>

  <clause id="2845">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / x = 1 / (1 / ((x / y) / x))
    ]]></literal>
    <justification jstring="[para(2610(a,1),2810(a,1,1))].">
      <j1 rule="para" parents="2610 2810"/>
    </justification>
  </clause>

  <clause id="2846">
    <literal><![CDATA[
      K(x,T(x,y) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,2170,a,b,2813,a)].">
      <j1 rule="hyper" parents="34 2170 2813"/>
    </justification>
  </clause>

  <clause id="2847">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,T(x,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,2741,a,b,2846,a)].">
      <j1 rule="hyper" parents="347 2741 2846"/>
    </justification>
  </clause>

  <clause id="2849">
    <literal><![CDATA[
      K(x,T(x,y) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2847(a,1),201(a,1)),flip(b)].">
      <j1 rule="para" parents="2847 201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2850">
    <literal><![CDATA[
      T(K(T(x,y),1 / x),z) = K(T(x,y),T(T(x,y),u) \ 1)
    ]]></literal>
    <justification jstring="[para(2721(a,1),2847(a,1,1))].">
      <j1 rule="para" parents="2721 2847"/>
    </justification>
  </clause>

  <clause id="2851">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) \ x = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(214,a,2831,a)].">
      <j1 rule="hyper" parents="214 2831"/>
    </justification>
  </clause>

  <clause id="2852">
    <literal><![CDATA[
      x / (x * ((y \ 1) \ 1)) = ((x / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),2831(a,1,2,2,1,1))].">
      <j1 rule="para" parents="9 2831"/>
    </justification>
  </clause>

  <clause id="2853">
    <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(2836(a,2),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2836 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2854">
    <literal><![CDATA[
      x \ (y * (K(z,z \ 1) * u)) = (x \ (y * u)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(2836(a,1),2770(a,1,2))].">
      <j1 rule="para" parents="2836 2770"/>
    </justification>
  </clause>

  <clause id="2855">
    <literal><![CDATA[
      R(x,x,y) * ((x \ (1 / x)) * y) = K(x,x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2385,a,b,2838,a)].">
      <j1 rule="hyper" parents="63 2385 2838"/>
    </justification>
  </clause>

  <clause id="2856">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      y \ K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2838(a,1),363(a,1))].">
      <j1 rule="para" parents="2838 363"/>
    </justification>
  </clause>

  <clause id="2857">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ z) * K(y,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(2838(a,2),2747(a,1))].">
      <j1 rule="para" parents="2838 2747"/>
    </justification>
  </clause>

  <clause id="2858">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,2753,a,b,2840,a),flip(a)].">
      <j1 rule="hyper" parents="347 2753 2840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2859">
    <literal><![CDATA[
      (x \ (1 / y)) * K(y \ 1,y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(1897(a,1),2840(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1897 2840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2860">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (K(x \ 1,x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(2841(a,1),2804(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2841 2804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2861">
    <literal><![CDATA[
      x \ (y * (K(z \ 1,z) * u)) = (x \ (y * u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(2841(a,1),2840(a,1,2))].">
      <j1 rule="para" parents="2841 2840"/>
    </justification>
  </clause>

  <clause id="2862">
    <literal><![CDATA[
      T(x / y,x \ y) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(493,a,2843,a)].">
      <j1 rule="hyper" parents="493 2843"/>
    </justification>
  </clause>

  <clause id="2863">
    <literal><![CDATA[
      1 / (1 / ((x / (y \ 1)) / x)) = (x / (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(80(a,1),2845(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="80 2845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2864">
    <literal><![CDATA[
      x * (((x \ (y \ x)) \ 1) \ 1) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(80(a,1),2851(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="80 2851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2865">
    <literal><![CDATA[
      1 / ((x / (y \ 1)) / x) = ((x / (1 / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(214,a,2863,a),flip(a)].">
      <j1 rule="hyper" parents="214 2863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2866">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) / y = (((x \ y) / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(131,a,2864,a(flip),b,2738,a)].">
      <j1 rule="hyper" parents="131 2864 2738"/>
    </justification>
  </clause>

  <clause id="2867">
    <literal><![CDATA[
      x * T(x \ (y \ x),y) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(2823(a,2),2864(a,1,2))].">
      <j1 rule="para" parents="2823 2864"/>
    </justification>
  </clause>

  <clause id="2868">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,1350,a,b,2867,a)].">
      <j1 rule="hyper" parents="63 1350 2867"/>
    </justification>
  </clause>

  <clause id="2869">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (x * y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(620,a,2868,a),flip(a)].">
      <j1 rule="hyper" parents="620 2868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2870">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = T(x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,336,a,b,2868,a),flip(a)].">
      <j1 rule="hyper" parents="347 336 2868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2871">
    <literal><![CDATA[
      x \ (K(x \ 1,x) * y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,2858,a,b,2868,a)].">
      <j1 rule="hyper" parents="63 2858 2868"/>
    </justification>
  </clause>

  <clause id="2872">
    <literal><![CDATA[
      (x \ y) * K(x \ 1,x) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,2753,a(flip),b,2868,a)].">
      <j1 rule="hyper" parents="63 2753 2868"/>
    </justification>
  </clause>

  <clause id="2873">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(34,a,2784,a,b,2868,a)].">
      <j1 rule="hyper" parents="34 2784 2868"/>
    </justification>
  </clause>

  <clause id="2874">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * K(x,x \ 1) = x \ y
    ]]></literal>
    <justification jstring="[hyper(34,a,2752,a,b,2868,a)].">
      <j1 rule="hyper" parents="34 2752 2868"/>
    </justification>
  </clause>

  <clause id="2875">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (x * y) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,2753,a(flip),b,2869,a),flip(a)].">
      <j1 rule="hyper" parents="347 2753 2869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2876">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (y * K(x \ 1,x)) = x * y
    ]]></literal>
    <justification jstring="[hyper(134,a,2753,a(flip),b,2869,a)].">
      <j1 rule="hyper" parents="134 2753 2869"/>
    </justification>
  </clause>

  <clause id="2877">
    <literal><![CDATA[
      T(x,x \ 1) * (K(x \ 1,x) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(38,a,466,a,b,2869,a)].">
      <j1 rule="hyper" parents="38 466 2869"/>
    </justification>
  </clause>

  <clause id="2878">
    <literal><![CDATA[
      K(x,x \ 1) * (T(x,x \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(34,a,2784,a,b,2870,a)].">
      <j1 rule="hyper" parents="34 2784 2870"/>
    </justification>
  </clause>

  <clause id="2880">
    <literal><![CDATA[
      K(x \ 1,x) * (T(x,x \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(134,a,466,a(flip),b,2871,a),flip(a)].">
      <j1 rule="hyper" parents="134 466 2871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2881">
    <literal><![CDATA[
      K(x \ 1,x) * (((x \ 1) \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(134,a,9,a(flip),b,2871,a),flip(a)].">
      <j1 rule="hyper" parents="134 9 2871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2882">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,2872,a(flip),b,2322,a)].">
      <j1 rule="hyper" parents="133 2872 2322"/>
    </justification>
  </clause>

  <clause id="2883">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (y / ((x \ 1) \ 1)) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(134,a,2318,a(flip),b,2875,a)].">
      <j1 rule="hyper" parents="134 2318 2875"/>
    </justification>
  </clause>

  <clause id="2884">
    <literal><![CDATA[
      x * (y * K(x,x \ 1)) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(2752(a,1),2877(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2752 2877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2885">
    <literal><![CDATA[
      x * (K(x,x \ 1) * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(2784(a,1),2877(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2784 2877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2886">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(2877(a,1),2837(a,1,2))].">
      <j1 rule="para" parents="2877 2837"/>
    </justification>
  </clause>

  <clause id="2887">
    <literal><![CDATA[
      (T(x,x \ 1) * y) / (K(x,x \ 1) * y) = x
    ]]></literal>
    <justification jstring="[hyper(220,a,170,a(flip),b,2878,a(flip))].">
      <j1 rule="hyper" parents="220 170 2878"/>
    </justification>
  </clause>

  <clause id="2888">
    <literal><![CDATA[
      T(x,x \ 1) * (x \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,2878,a(flip),b,2838,a)].">
      <j1 rule="hyper" parents="134 2878 2838"/>
    </justification>
  </clause>

  <clause id="2889">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(34,a,2752,a,b,2880,a)].">
      <j1 rule="hyper" parents="34 2752 2880"/>
    </justification>
  </clause>

  <clause id="2891">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(34,a,2784,a,b,2881,a)].">
      <j1 rule="hyper" parents="34 2784 2881"/>
    </justification>
  </clause>

  <clause id="2892">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(34,a,2752,a,b,2881,a)].">
      <j1 rule="hyper" parents="34 2752 2881"/>
    </justification>
  </clause>

  <clause id="2894">
    <literal><![CDATA[
      (1 / x) * (y * K(1 / x,(1 / x) \ 1)) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(749(a,1),2884(a,2,1))].">
      <j1 rule="para" parents="749 2884"/>
    </justification>
  </clause>

  <clause id="2895">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ ((K(x,x \ 1) * y) * x) = K(K(x,x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(2885(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2885 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2896">
    <literal><![CDATA[
      R(x,K(x,x \ 1),y) = x
    ]]></literal>
    <justification jstring="[hyper(2336,a,2887,a)].">
      <j1 rule="hyper" parents="2336 2887"/>
    </justification>
  </clause>

  <clause id="2897">
    <literal><![CDATA[
      R(1 / x,K(x \ 1,x),y) = 1 / x
    ]]></literal>
    <justification jstring="[para(1957(a,1),2896(a,1,2))].">
      <j1 rule="para" parents="1957 2896"/>
    </justification>
  </clause>

  <clause id="2898">
    <literal><![CDATA[
      R((1 / x) * T((1 / x) \ 1,y),K(x \ 1,x),z) = (1 / x) * T(R(1 / x,K(x \ 1,x),z) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2897(a,1),2649(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2897 2649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2899">
    <literal><![CDATA[
      x \ (y * K(x \ 1,x)) = T(x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(128,a,2765,a(flip),b,2888,a),flip(a)].">
      <j1 rule="hyper" parents="128 2765 2888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2900">
    <literal><![CDATA[
      ((((1 / x) \ y) / y) \ 1) \ 1 = ((x \ 1) \ y) / y
    ]]></literal>
    <justification jstring="[para(83(a,1),2866(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="83 2866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2901">
    <literal><![CDATA[
      T((x \ 1) * y,(x \ 1) \ 1) = (x \ 1) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(134,a,2882,a(flip),b,1137,a),flip(a)].">
      <j1 rule="hyper" parents="134 2882 1137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2902">
    <literal><![CDATA[
      (((x \ y) \ 1) \ 1) * (y / (((x \ y) \ 1) \ 1)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,207,a(flip),b,2883,a),flip(a)].">
      <j1 rule="hyper" parents="347 207 2883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2903">
    <literal><![CDATA[
      K(x \ 1,x) * R(y,x,x) = (y * (x \ 1)) * x
    ]]></literal>
    <justification jstring="[hyper(134,a,2247,a(flip),b,2759,a)].">
      <j1 rule="hyper" parents="134 2247 2759"/>
    </justification>
  </clause>

  <clause id="2904">
    <literal><![CDATA[
      T(x \ (y \ x),(y \ x) \ x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x \ (y \ x),y) = z
    ]]></literal>
    <justification jstring="[para(2579(a,2),2829(a,1))].">
      <j1 rule="para" parents="2579 2829"/>
    </justification>
  </clause>

  <clause id="2905">
    <literal><![CDATA[
      1 / (1 / ((x * y) \ y)) = ((1 / (1 / x)) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(650,a,2735,a),flip(a)].">
      <j1 rule="hyper" parents="650 2735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2906">
    <literal><![CDATA[
      (((1 / (1 / x)) * y) \ y) \ 1 = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(214,a,2905,a)].">
      <j1 rule="hyper" parents="214 2905"/>
    </justification>
  </clause>

  <clause id="2907">
    <literal><![CDATA[
      1 / (((x \ 1) * y) \ y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(80(a,1),2906(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="80 2906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2908">
    <literal><![CDATA[
      ((((1 / x) * y) \ y) \ 1) \ 1 = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(214,a,2907,a)].">
      <j1 rule="hyper" parents="214 2907"/>
    </justification>
  </clause>

  <clause id="2909">
    <literal><![CDATA[
      K(x \ 1,x) * (L(x,y,z) \ x) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(2763,a,2818,a)].">
      <j1 rule="hyper" parents="2763 2818"/>
    </justification>
  </clause>

  <clause id="2910">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) * K(x,x \ 1) = (L(x \ 1,y,z) \ 1) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1960(a,1),2818(a,1,2))].">
      <j1 rule="para" parents="1960 2818"/>
    </justification>
  </clause>

  <clause id="2911">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(2441,a,2825,a)].">
      <j1 rule="hyper" parents="2441 2825"/>
    </justification>
  </clause>

  <clause id="2912">
    <literal><![CDATA[
      (x \ T(x,y)) \ 1 = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,2160,a(flip),b,2911,a)].">
      <j1 rule="hyper" parents="63 2160 2911"/>
    </justification>
  </clause>

  <clause id="2913">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = ((x / y) \ (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[para(113(a,1),2912(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="113 2912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2914">
    <literal><![CDATA[
      (T(x,y) \ x) \ 1 = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(2912(a,1),2626(a,1,1))].">
      <j1 rule="para" parents="2912 2626"/>
    </justification>
  </clause>

  <clause id="2915">
    <literal><![CDATA[
      ((x / y) \ (y \ x)) \ 1 = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[para(113(a,1),2913(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 2913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2916">
    <literal><![CDATA[
      (x \ (x * y)) \ ((x * y) / x) = (((x * y) / x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),2915(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 2915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2917">
    <literal><![CDATA[
      ((x * y) \ y) * K(x,x \ 1) = 1 / (1 / ((x * y) \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,2770,a(flip),b,2830,a)].">
      <j1 rule="hyper" parents="63 2770 2830"/>
    </justification>
  </clause>

  <clause id="2918">
    <literal><![CDATA[
      K(T(x,y),T(T(x,y),z) \ 1) = K(T(x,y),1 / T(x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2713,a,b,2850,a),flip(a)].">
      <j1 rule="hyper" parents="63 2713 2850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2919">
    <literal><![CDATA[
      ((1 / x) * y) * K(x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,2314,a(flip),b,2894,a)].">
      <j1 rule="hyper" parents="63 2314 2894"/>
    </justification>
  </clause>

  <clause id="2920">
    <literal><![CDATA[
      (1 / x) * (y * K(x \ 1,x)) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1957(a,1),2894(a,1,2,2))].">
      <j1 rule="para" parents="1957 2894"/>
    </justification>
  </clause>

  <clause id="2921">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(2802,a,2919,a)].">
      <j1 rule="hyper" parents="2802 2919"/>
    </justification>
  </clause>

  <clause id="2922">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(2763,a,2919,a)].">
      <j1 rule="hyper" parents="2763 2919"/>
    </justification>
  </clause>

  <clause id="2923">
    <literal><![CDATA[
      (1 / x) * (K(x \ 1,x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,2791,a(flip),b,2919,a)].">
      <j1 rule="hyper" parents="63 2791 2919"/>
    </justification>
  </clause>

  <clause id="2924">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(35,a,2351,a,b,2919,a)].">
      <j1 rule="hyper" parents="35 2351 2919"/>
    </justification>
  </clause>

  <clause id="2925">
    <literal><![CDATA[
      ((x \ 1) \ 1) * ((x \ 1) * y) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,2919,a(flip),b,2875,a)].">
      <j1 rule="hyper" parents="134 2919 2875"/>
    </justification>
  </clause>

  <clause id="2926">
    <literal><![CDATA[
      ((1 / x) * y) / (1 / x) = ((x \ 1) * y) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(131,a,2919,a(flip),b,2303,a),flip(a)].">
      <j1 rule="hyper" parents="131 2919 2303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2927">
    <literal><![CDATA[
      K(x \ 1,x) \ ((x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(128,a,2919,a(flip),b,2753,a)].">
      <j1 rule="hyper" parents="128 2919 2753"/>
    </justification>
  </clause>

  <clause id="2928">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(128,a,10,a(flip),b,2920,a),flip(a)].">
      <j1 rule="hyper" parents="128 10 2920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2929">
    <literal><![CDATA[
      (x \ 1) * (y * ((x \ 1) \ 1)) = (1 / x) * (y * x)
    ]]></literal>
    <justification jstring="[para(2315(a,1),2920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2315 2920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2931">
    <literal><![CDATA[
      (x \ 1) * (K(x,x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(2771(a,1),2920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2771 2920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2932">
    <literal><![CDATA[
      x \ L(y,1 / x,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(2050,a,2921,a)].">
      <j1 rule="hyper" parents="2050 2921"/>
    </justification>
  </clause>

  <clause id="2933">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(357,a,2921,a),flip(a)].">
      <j1 rule="hyper" parents="357 2921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2934">
    <literal><![CDATA[
      (x \ 1) \ ((1 / x) * y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(128,a,2921,a(flip),b,2836,a(flip))].">
      <j1 rule="hyper" parents="128 2921 2836"/>
    </justification>
  </clause>

  <clause id="2935">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (x * ((1 / y) * z)) = L((y \ 1) * z,K(y,y \ 1),x)
    ]]></literal>
    <justification jstring="[para(2921(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2921 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2936">
    <literal><![CDATA[
      L(x,1 / y,y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(38,a,455,a,b,2932,a),flip(a)].">
      <j1 rule="hyper" parents="38 455 2932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2937">
    <literal><![CDATA[
      L(x,T(y,y \ z) \ 1,T(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,1 / T(y,y \ z),(y \ z) \ z) = u
    ]]></literal>
    <justification jstring="[para(2936(a,1),2111(a,1))].">
      <j1 rule="para" parents="2936 2111"/>
    </justification>
  </clause>

  <clause id="2938">
    <literal><![CDATA[
      L(x \ y,x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(1385,a,2922,a)].">
      <j1 rule="hyper" parents="1385 2922"/>
    </justification>
  </clause>

  <clause id="2939">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(938,a,2922,a),flip(a)].">
      <j1 rule="hyper" parents="938 2922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2940">
    <literal><![CDATA[
      (x \ 1) * ((1 / x) \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(357,a,2922,a),flip(a)].">
      <j1 rule="hyper" parents="357 2922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2941">
    <literal><![CDATA[
      ((x \ 1) * y) / L(T(1 / x,y),y,K(x \ 1,x)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(2922(a,1),528(a,1,1))].">
      <j1 rule="para" parents="2922 528"/>
    </justification>
  </clause>

  <clause id="2943">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,(x \ 1) \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(347,a,208,a(flip),b,2938,a),flip(a)].">
      <j1 rule="hyper" parents="347 208 2938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2944">
    <literal><![CDATA[
      L(T(x,y),y,y \ 1) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[para(22(a,2),2938(a,1,1))].">
      <j1 rule="para" parents="22 2938"/>
    </justification>
  </clause>

  <clause id="2945">
    <literal><![CDATA[
      x * ((1 / x) * (y * x)) = L(y,x,x \ 1) * x
    ]]></literal>
    <justification jstring="[para(2938(a,1),737(a,1,2))].">
      <j1 rule="para" parents="2938 737"/>
    </justification>
  </clause>

  <clause id="2946">
    <literal><![CDATA[
      (1 / x) \ L(y,x,x \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(138,a,2939,a)].">
      <j1 rule="hyper" parents="138 2939"/>
    </justification>
  </clause>

  <clause id="2947">
    <literal><![CDATA[
      L(x \ y,x,x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * y = z
    ]]></literal>
    <justification jstring="[para(2939(a,1),357(a,1))].">
      <j1 rule="para" parents="2939 357"/>
    </justification>
  </clause>

  <clause id="2948">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x = a(1 / y,y,x)
    ]]></literal>
    <justification jstring="[para(2939(a,1),246(a,1,1))].">
      <j1 rule="para" parents="2939 246"/>
    </justification>
  </clause>

  <clause id="2949">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,1 / y)
    ]]></literal>
    <justification jstring="[para(2939(a,1),332(a,1,1))].">
      <j1 rule="para" parents="2939 332"/>
    </justification>
  </clause>

  <clause id="2950">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = ((y \ 1) * (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(2939(a,1),2908(a,1,1,1,1))].">
      <j1 rule="para" parents="2939 2908"/>
    </justification>
  </clause>

  <clause id="2951">
    <literal><![CDATA[
      (1 / x) \ y != x * z
    ]]></literal>
    <literal><![CDATA[
      L(z,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(2946(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="2946 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2952">
    <literal><![CDATA[
      (1 / (1 / x)) \ L(y,1 / x,x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(83(a,1),2946(a,1,2,3))].">
      <j1 rule="para" parents="83 2946"/>
    </justification>
  </clause>

  <clause id="2953">
    <literal><![CDATA[
      (1 / x) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2946(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2946 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2954">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(128,a,10,a(flip),b,2923,a),flip(a)].">
      <j1 rule="hyper" parents="128 10 2923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2955">
    <literal><![CDATA[
      (x \ 1) * (y * T(x,x \ 1)) = (1 / x) * (y * x)
    ]]></literal>
    <justification jstring="[para(2781(a,1),2923(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2781 2923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2956">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(2924(a,1),2224(a,1,2))].">
      <j1 rule="para" parents="2924 2224"/>
    </justification>
  </clause>

  <clause id="2957">
    <literal><![CDATA[
      T(x \ 1,((x \ 1) \ 1) * y) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(80(a,1),2956(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="80 2956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2958">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / x) \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(2802,a,2928,a)].">
      <j1 rule="hyper" parents="2802 2928"/>
    </justification>
  </clause>

  <clause id="2959">
    <literal><![CDATA[
      ((1 / x) \ y) * K(x,x \ 1) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(35,a,2351,a,b,2928,a)].">
      <j1 rule="hyper" parents="35 2351 2928"/>
    </justification>
  </clause>

  <clause id="2960">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,2928,a(flip),b,2305,a)].">
      <j1 rule="hyper" parents="133 2928 2305"/>
    </justification>
  </clause>

  <clause id="2961">
    <literal><![CDATA[
      (1 / x) \ (y * (1 / x)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(269,a,2779,a(flip),b,2940,a),flip(a)].">
      <j1 rule="hyper" parents="269 2779 2940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2962">
    <literal><![CDATA[
      T(x,1 / y) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(360,a,2961,a)].">
      <j1 rule="hyper" parents="360 2961"/>
    </justification>
  </clause>

  <clause id="2963">
    <literal><![CDATA[
      T(x / (1 / y),y \ 1) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[para(12(a,1),2961(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 2961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2965">
    <literal><![CDATA[
      T(((1 / x) * y) * x,x \ 1) = R(y,1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1040,a(flip),b,2962,a),flip(a)].">
      <j1 rule="hyper" parents="63 1040 2962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2966">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(80(a,1),2962(a,1,2)),flip(a)].">
      <j1 rule="para" parents="80 2962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2967">
    <literal><![CDATA[
      T(x,1 / (1 / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(83(a,1),2962(a,2,2))].">
      <j1 rule="para" parents="83 2962"/>
    </justification>
  </clause>

  <clause id="2968">
    <literal><![CDATA[
      T(x / ((y \ 1) \ 1),y) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(386,a,2966,a),flip(a)].">
      <j1 rule="hyper" parents="386 2966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2969">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(y,x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,2966,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 2966 22"/>
    </justification>
  </clause>

  <clause id="2970">
    <literal><![CDATA[
      T(x,T(y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(112(a,2),2966(a,1,2))].">
      <j1 rule="para" parents="112 2966"/>
    </justification>
  </clause>

  <clause id="2973">
    <literal><![CDATA[
      T(x,x \ 1) * T(y,x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,2970,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 2970 22"/>
    </justification>
  </clause>

  <clause id="2974">
    <literal><![CDATA[
      L(x,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * (y * x) = z
    ]]></literal>
    <justification jstring="[para(9(a,1),2947(a,1,1))].">
      <j1 rule="para" parents="9 2947"/>
    </justification>
  </clause>

  <clause id="2975">
    <literal><![CDATA[
      K(x,x \ 1) * (y * ((1 / x) \ z)) = y * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2954(a,1),2837(a,1,2,2))].">
      <j1 rule="para" parents="2954 2837"/>
    </justification>
  </clause>

  <clause id="2976">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ ((x \ 1) \ y) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(2954(a,1),2871(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2954 2871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2977">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ y) / y) * x) = (x \ 1) \ ((x \ y) / y)
    ]]></literal>
    <justification jstring="[para(1482(a,1),2958(a,1,2))].">
      <j1 rule="para" parents="1482 2958"/>
    </justification>
  </clause>

  <clause id="2978">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) \ y = z
    ]]></literal>
    <justification jstring="[para(2959(a,1),2373(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2959 2373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2979">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(y,x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,338,a,b,2969,a),flip(a)].">
      <j1 rule="hyper" parents="347 338 2969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2980">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(T(x,y) \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(347,a,2812,a(flip),b,2969,a),flip(a)].">
      <j1 rule="hyper" parents="347 2812 2969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2981">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ R(y,x,x) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(128,a,1133,a(flip),b,2969,a)].">
      <j1 rule="hyper" parents="128 1133 2969"/>
    </justification>
  </clause>

  <clause id="2982">
    <literal><![CDATA[
      (T(x,x \ 1) \ 1) \ R(y,T(x,x \ 1),T(x,x \ 1) \ 1) = T(((x \ 1) \ 1) * T(y,x),T(x,x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2979(a,2),695(a,2,1))].">
      <j1 rule="para" parents="2979 695"/>
    </justification>
  </clause>

  <clause id="2983">
    <literal><![CDATA[
      (1 / (1 / x)) \ L(y,x \ 1,x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(2936(a,1),2952(a,1,2))].">
      <j1 rule="para" parents="2936 2952"/>
    </justification>
  </clause>

  <clause id="2984">
    <literal><![CDATA[
      T(((1 / x) * y) * x,x \ 1) = R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,2248,a(flip),b,2965,a),flip(a)].">
      <j1 rule="hyper" parents="347 2248 2965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2985">
    <literal><![CDATA[
      T((K(x,x \ 1) * y) * x,x \ 1) = R((x \ 1) \ y,1 / x,x)
    ]]></literal>
    <justification jstring="[para(2933(a,1),2965(a,1,1,1))].">
      <j1 rule="para" parents="2933 2965"/>
    </justification>
  </clause>

  <clause id="2986">
    <literal><![CDATA[
      ((x \ 1) \ 1) * R(y,x,x) = R(x * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,915,a(flip),b,2981,a)].">
      <j1 rule="hyper" parents="134 915 2981"/>
    </justification>
  </clause>

  <clause id="2987">
    <literal><![CDATA[
      T(x,x \ 1) * R(y,x,x) = R(x * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(724,a,2986,a)].">
      <j1 rule="hyper" parents="724 2986"/>
    </justification>
  </clause>

  <clause id="2988">
    <literal><![CDATA[
      L(x,1 / y,(1 / y) \ 1) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2951,a,2983,a)].">
      <j1 rule="hyper" parents="2951 2983"/>
    </justification>
  </clause>

  <clause id="2989">
    <literal><![CDATA[
      L(x,x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(189,a,2983,a,b,12,a(flip))].">
      <j1 rule="hyper" parents="189 2983 12"/>
    </justification>
  </clause>

  <clause id="2990">
    <literal><![CDATA[
      L(R(x,y,z),x \ 1,x) = R(1 / (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(2989(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2989 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2991">
    <literal><![CDATA[
      R(T(x \ 1,x * y),x,y) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(2957(a,1),2392(a,1,1))].">
      <j1 rule="para" parents="2957 2392"/>
    </justification>
  </clause>

  <clause id="2992">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,1210,a(flip),b,2991,a)].">
      <j1 rule="hyper" parents="63 1210 2991"/>
    </justification>
  </clause>

  <clause id="2993">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ y = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[para(112(a,2),2992(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="112 2992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2994">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * T(x,x \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(34,a,2781,a,b,2909,a)].">
      <j1 rule="hyper" parents="34 2781 2909"/>
    </justification>
  </clause>

  <clause id="2995">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) * (L(x,u,w) \ x) = (L(x,u,w) \ 1) * x
    ]]></literal>
    <justification jstring="[para(2815(a,2),2909(a,1,1))].">
      <j1 rule="para" parents="2815 2909"/>
    </justification>
  </clause>

  <clause id="2996">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ 1 = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2916(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2997">
    <literal><![CDATA[
      1 / (x \ ((y * x) / y)) != z
    ]]></literal>
    <literal><![CDATA[
      ((y * x) / y) \ x = z
    ]]></literal>
    <justification jstring="[para(2996(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2996 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2998">
    <literal><![CDATA[
      K(x \ (y * x),(y * x) \ x) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,2400,a,b,2917,a)].">
      <j1 rule="hyper" parents="34 2400 2917"/>
    </justification>
  </clause>

  <clause id="2999">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),1 / T(x,z))
    ]]></literal>
    <justification jstring="[hyper(2849,a,2918,a)].">
      <j1 rule="hyper" parents="2849 2918"/>
    </justification>
  </clause>

  <clause id="3001">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),x \ 1)
    ]]></literal>
    <justification jstring="[para(296(a,1),2999(a,2,2))].">
      <j1 rule="para" parents="296 2999"/>
    </justification>
  </clause>

  <clause id="3002">
    <literal><![CDATA[
      K(T(x,y),1 / x) = K(T(x,y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2721,a(flip),b,3001,a)].">
      <j1 rule="hyper" parents="63 2721 3001"/>
    </justification>
  </clause>

  <clause id="3003">
    <literal><![CDATA[
      (x * y) * K(T(x,y),x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(3002(a,1),2737(a,1,2))].">
      <j1 rule="para" parents="3002 2737"/>
    </justification>
  </clause>

  <clause id="3004">
    <literal><![CDATA[
      K(T(x,y),x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,2892,a,b,3003,a),flip(a)].">
      <j1 rule="hyper" parents="34 2892 3003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3005">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,3001,a,b,3004,a)].">
      <j1 rule="hyper" parents="63 3001 3004"/>
    </justification>
  </clause>

  <clause id="3009">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,3005,a(flip),b,1924,a(flip))].">
      <j1 rule="hyper" parents="128 3005 1924"/>
    </justification>
  </clause>

  <clause id="3010">
    <literal><![CDATA[
      (x * (T(y,z) \ 1)) * K(y,y \ 1) = x * (1 / T(y,z))
    ]]></literal>
    <justification jstring="[para(3005(a,1),2332(a,1,2))].">
      <j1 rule="para" parents="3005 2332"/>
    </justification>
  </clause>

  <clause id="3011">
    <literal><![CDATA[
      (1 / T(x,y)) * x = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,3009,a(flip),b,2744,a(flip))].">
      <j1 rule="hyper" parents="133 3009 2744"/>
    </justification>
  </clause>

  <clause id="3012">
    <literal><![CDATA[
      x / T(x,y) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(1511,a,3011,a)].">
      <j1 rule="hyper" parents="1511 3011"/>
    </justification>
  </clause>

  <clause id="3013">
    <literal><![CDATA[
      T(1 / T(x,y),x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(269,a,3011,a,b,1230,a)].">
      <j1 rule="hyper" parents="269 3011 1230"/>
    </justification>
  </clause>

  <clause id="3014">
    <literal><![CDATA[
      (T(x,y) \ x) * T(x,y) = x
    ]]></literal>
    <justification jstring="[hyper(133,a,3011,a(flip),b,1501,a(flip))].">
      <j1 rule="hyper" parents="133 3011 1501"/>
    </justification>
  </clause>

  <clause id="3015">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      x / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(3011(a,1),1511(a,1))].">
      <j1 rule="para" parents="3011 1511"/>
    </justification>
  </clause>

  <clause id="3016">
    <literal><![CDATA[
      (T(x,y) \ x) \ x = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(214,a,3012,a)].">
      <j1 rule="hyper" parents="214 3012"/>
    </justification>
  </clause>

  <clause id="3017">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,1839,a,b,3012,a)].">
      <j1 rule="hyper" parents="63 1839 3012"/>
    </justification>
  </clause>

  <clause id="3018">
    <literal><![CDATA[
      (T(x,y) \ x) * x = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(3012(a,1),2095(a,1,1))].">
      <j1 rule="para" parents="3012 2095"/>
    </justification>
  </clause>

  <clause id="3019">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,2510,a,b,3014,a)].">
      <j1 rule="hyper" parents="63 2510 3014"/>
    </justification>
  </clause>

  <clause id="3021">
    <literal><![CDATA[
      (x * y) * T(K(y,x),x) = y * x
    ]]></literal>
    <justification jstring="[para(3019(a,1),2509(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3019 2509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3023">
    <literal><![CDATA[
      (T(x,y) \ 1) * T(x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,3013,a(flip),b,2799,a)].">
      <j1 rule="hyper" parents="133 3013 2799"/>
    </justification>
  </clause>

  <clause id="3024">
    <literal><![CDATA[
      T(K(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(333,a,3021,a),flip(a)].">
      <j1 rule="hyper" parents="333 3021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3025">
    <literal><![CDATA[
      K(x,y) * y = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1068,a,3024,a)].">
      <j1 rule="hyper" parents="1068 3024"/>
    </justification>
  </clause>

  <clause id="3026">
    <literal><![CDATA[
      (x * K(y,x)) / x = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(305,a,3024,a)].">
      <j1 rule="hyper" parents="305 3024"/>
    </justification>
  </clause>

  <clause id="3027">
    <literal><![CDATA[
      T(x,K(y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,3024,a)].">
      <j1 rule="hyper" parents="54 3024"/>
    </justification>
  </clause>

  <clause id="3028">
    <literal><![CDATA[
      (x * K(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(3024(a,1),318(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="3024 318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3029">
    <literal><![CDATA[
      L(K(x,y),z,u) * y = y * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3024(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3024 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3030">
    <literal><![CDATA[
      T(x,K(y,R(x,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(162,a,3027,a)].">
      <j1 rule="hyper" parents="162 3027"/>
    </justification>
  </clause>

  <clause id="3031">
    <literal><![CDATA[
      T(x,K(y,L(x,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(159,a,3027,a)].">
      <j1 rule="hyper" parents="159 3027"/>
    </justification>
  </clause>

  <clause id="3032">
    <literal><![CDATA[
      T(x,K(y,T(x,z))) = x
    ]]></literal>
    <justification jstring="[hyper(156,a,3027,a)].">
      <j1 rule="hyper" parents="156 3027"/>
    </justification>
  </clause>

  <clause id="3033">
    <literal><![CDATA[
      K(x,K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,3027,a)].">
      <j1 rule="hyper" parents="55 3027"/>
    </justification>
  </clause>

  <clause id="3034">
    <literal><![CDATA[
      T(T(x,y),K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3027(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3027 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3035">
    <literal><![CDATA[
      K(x,y) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3027(a,1),315(a,1,2))].">
      <j1 rule="para" parents="3027 315"/>
    </justification>
  </clause>

  <clause id="3036">
    <literal><![CDATA[
      T(x,y) * K(z,x) = K(z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3027(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3027 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3037">
    <literal><![CDATA[
      L(x,y,z) * K(u,x) = K(u,x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3027(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3027 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3038">
    <literal><![CDATA[
      R(x,y,z) * K(u,x) = K(u,x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3027(a,1),268(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3027 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3039">
    <literal><![CDATA[
      K(x,y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3027(a,1),435(a,1,2,1))].">
      <j1 rule="para" parents="3027 435"/>
    </justification>
  </clause>

  <clause id="3040">
    <literal><![CDATA[
      T(T(x,y),z) * K(u,x) = K(u,x) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(3027(a,1),482(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3027 482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3041">
    <literal><![CDATA[
      T(x,y \ T(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1323(a,1),3027(a,1,2))].">
      <j1 rule="para" parents="1323 3027"/>
    </justification>
  </clause>

  <clause id="3043">
    <literal><![CDATA[
      K(x,T(y,z)) * y = y * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(1068,a,3032,a),flip(a)].">
      <j1 rule="hyper" parents="1068 3032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3044">
    <literal><![CDATA[
      (x \ T(x,y)) * y = y * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(1068,a,3041,a),flip(a)].">
      <j1 rule="hyper" parents="1068 3041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3045">
    <literal><![CDATA[
      T(x,y) * (z \ T(z,x)) = (z \ T(z,x)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3041(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3041 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3046">
    <literal><![CDATA[
      T(T(x,y),K(z,R(x,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3030(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3030 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3047">
    <literal><![CDATA[
      K(x,L(y,z,u)) * y = y * K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(1068,a,3031,a),flip(a)].">
      <j1 rule="hyper" parents="1068 3031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3049">
    <literal><![CDATA[
      (x * K(y,x)) / L(z,x / z,K(y,x)) = K(y,x) * (x / z)
    ]]></literal>
    <justification jstring="[para(3025(a,1),530(a,1,1))].">
      <j1 rule="para" parents="3025 530"/>
    </justification>
  </clause>

  <clause id="3050">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2543,a,b,3026,a)].">
      <j1 rule="hyper" parents="63 2543 3026"/>
    </justification>
  </clause>

  <clause id="3051">
    <literal><![CDATA[
      L((T(x,y) * (x \ y)) / y,y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1373,a,b,3026,a)].">
      <j1 rule="hyper" parents="63 1373 3026"/>
    </justification>
  </clause>

  <clause id="3052">
    <literal><![CDATA[
      T(K(x,y),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3026(a,1),362(a,1,1))].">
      <j1 rule="para" parents="3026 362"/>
    </justification>
  </clause>

  <clause id="3053">
    <literal><![CDATA[
      K(x,y) * T(T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      T(T(y,z),u) * K(x,y) = w
    ]]></literal>
    <justification jstring="[para(3034(a,1),435(a,1,2,1))].">
      <j1 rule="para" parents="3034 435"/>
    </justification>
  </clause>

  <clause id="3054">
    <literal><![CDATA[
      (1 / x) * (x * K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(924,a,3050,a)].">
      <j1 rule="hyper" parents="924 3050"/>
    </justification>
  </clause>

  <clause id="3055">
    <literal><![CDATA[
      (1 / x) \ K(y,x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,3050,a(flip),b,291,a)].">
      <j1 rule="hyper" parents="128 3050 291"/>
    </justification>
  </clause>

  <clause id="3056">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,3054,a(flip),b,208,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 3054 208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3058">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(397,a,3023,a)].">
      <j1 rule="hyper" parents="397 3023"/>
    </justification>
  </clause>

  <clause id="3060">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2683,a(flip),b,3058,a),flip(a)].">
      <j1 rule="hyper" parents="63 2683 3058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3061">
    <literal><![CDATA[
      K(x \ 1,x) * (T(x,y) \ z) = ((T(x,y) \ 1) \ 1) \ z
    ]]></literal>
    <justification jstring="[para(3058(a,1),2868(a,1,1))].">
      <j1 rule="para" parents="3058 2868"/>
    </justification>
  </clause>

  <clause id="3062">
    <literal><![CDATA[
      T(x,y) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(3058(a,1),2733(a,1,2))].">
      <j1 rule="para" parents="3058 2733"/>
    </justification>
  </clause>

  <clause id="3063">
    <literal><![CDATA[
      T(x,L(K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(270,a,3029,a)].">
      <j1 rule="hyper" parents="270 3029"/>
    </justification>
  </clause>

  <clause id="3065">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,2998,a(flip),b,3060,a),flip(a)].">
      <j1 rule="hyper" parents="347 2998 3060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3069">
    <literal><![CDATA[
      x * (T(x,y) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,2636,a,b,3062,a)].">
      <j1 rule="hyper" parents="35 2636 3062"/>
    </justification>
  </clause>

  <clause id="3071">
    <literal><![CDATA[
      T(x,y) / x = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(138,a,3069,a),flip(a)].">
      <j1 rule="hyper" parents="138 3069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3072">
    <literal><![CDATA[
      (x \ T(x,y)) * x = T(x,y)
    ]]></literal>
    <justification jstring="[para(3069(a,1),84(a,1,1,2))].">
      <j1 rule="para" parents="3069 84"/>
    </justification>
  </clause>

  <clause id="3074">
    <literal><![CDATA[
      (1 / x) * T(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1377,a,3071,a)].">
      <j1 rule="hyper" parents="1377 3071"/>
    </justification>
  </clause>

  <clause id="3075">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1152,a,3071,a)].">
      <j1 rule="hyper" parents="1152 3071"/>
    </justification>
  </clause>

  <clause id="3076">
    <literal><![CDATA[
      (x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1113,a,3071,a),flip(a)].">
      <j1 rule="hyper" parents="1113 3071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3077">
    <literal><![CDATA[
      x \ T(x,R(y,y \ 1,x)) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1657,a(flip),b,3071,a),flip(a)].">
      <j1 rule="hyper" parents="63 1657 3071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3078">
    <literal><![CDATA[
      T(x,x \ T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,296,a,b,3071,a)].">
      <j1 rule="hyper" parents="36 296 3071"/>
    </justification>
  </clause>

  <clause id="3079">
    <literal><![CDATA[
      (x \ T(x,y)) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(3071(a,1),280(a,1,1))].">
      <j1 rule="para" parents="3071 280"/>
    </justification>
  </clause>

  <clause id="3080">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = (T(x,y) * z) / (x * z)
    ]]></literal>
    <justification jstring="[para(3071(a,1),108(a,1,1))].">
      <j1 rule="para" parents="3071 108"/>
    </justification>
  </clause>

  <clause id="3081">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (T(x / y,z) * y) / x
    ]]></literal>
    <justification jstring="[para(3071(a,1),607(a,1,1))].">
      <j1 rule="para" parents="3071 607"/>
    </justification>
  </clause>

  <clause id="3083">
    <literal><![CDATA[
      (x \ T(x,y)) * (1 / T(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(3071(a,1),2717(a,1,1))].">
      <j1 rule="para" parents="3071 2717"/>
    </justification>
  </clause>

  <clause id="3084">
    <literal><![CDATA[
      T(x,K(y \ (y / (x \ 1)),y)) = x
    ]]></literal>
    <justification jstring="[para(1323(a,2),3078(a,1,2))].">
      <j1 rule="para" parents="1323 3078"/>
    </justification>
  </clause>

  <clause id="3085">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = u
    ]]></literal>
    <justification jstring="[para(3072(a,1),595(a,1,1,1))].">
      <j1 rule="para" parents="3072 595"/>
    </justification>
  </clause>

  <clause id="3086">
    <literal><![CDATA[
      T(1 / x,T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(269,a,3074,a,b,1142,a)].">
      <j1 rule="hyper" parents="269 3074 1142"/>
    </justification>
  </clause>

  <clause id="3087">
    <literal><![CDATA[
      T(1 / (1 / x),T(1 / x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,83,a(flip),b,3086,a),flip(a)].">
      <j1 rule="hyper" parents="347 83 3086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3088">
    <literal><![CDATA[
      T(x \ 1,T(x,y)) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3086(a,1),277(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3086 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3089">
    <literal><![CDATA[
      T(x / (y * x),T(y,z)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(3086(a,1),423(a,2,1))].">
      <j1 rule="para" parents="3086 423"/>
    </justification>
  </clause>

  <clause id="3090">
    <literal><![CDATA[
      x * T(x \ 1,T(x,y)) = K(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(3086(a,1),1326(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3086 1326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3091">
    <literal><![CDATA[
      (((x * y) / x) \ y) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[hyper(134,a,3084,a(flip),b,1346,a(flip))].">
      <j1 rule="hyper" parents="134 3084 1346"/>
    </justification>
  </clause>

  <clause id="3092">
    <literal><![CDATA[
      T(x,T(1 / x,y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3087(a,1),1899(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3087 1899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3096">
    <literal><![CDATA[
      T(x,x \ 1) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(3092(a,1),1782(a,1,1))].">
      <j1 rule="para" parents="3092 1782"/>
    </justification>
  </clause>

  <clause id="3097">
    <literal><![CDATA[
      (((L(x,y,y \ 1) * y) / y) \ ((1 / y) * (x * y))) * ((y * ((1 / y) * (x * y))) / y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[para(2945(a,1),3091(a,1,1,1,1))].">
      <j1 rule="para" parents="2945 3091"/>
    </justification>
  </clause>

  <clause id="3100">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(3076(a,1),877(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3076 877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3101">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = T(x \ 1,y) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(3076(a,1),2912(a,1,1))].">
      <j1 rule="para" parents="3076 2912"/>
    </justification>
  </clause>

  <clause id="3103">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = x * T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3088(a,1),3090(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3088 3090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3104">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,387,a(flip),b,3103,a),flip(a)].">
      <j1 rule="hyper" parents="347 387 3103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3107">
    <literal><![CDATA[
      R(x \ T(x,y),K(x \ 1,x),z) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(3104(a,1),1191(a,1,1,2))].">
      <j1 rule="para" parents="3104 1191"/>
    </justification>
  </clause>

  <clause id="3110">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ x = 1 / (y \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[hyper(220,a,3077,a(flip),b,2914,a),flip(a)].">
      <j1 rule="hyper" parents="220 3077 2914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3111">
    <literal><![CDATA[
      T(x \ 1,T(x,y) \ x) = x \ 1
    ]]></literal>
    <justification jstring="[para(3017(a,1),2482(a,1,2))].">
      <j1 rule="para" parents="3017 2482"/>
    </justification>
  </clause>

  <clause id="3112">
    <literal><![CDATA[
      R(K(x \ (x / ((y \ x) / T(x,y))),x),x \ 1,x) = ((1 / x) * (T(x,y) \ x)) * x
    ]]></literal>
    <justification jstring="[para(3017(a,1),2474(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3017 2474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3113">
    <literal><![CDATA[
      T(T(x,y) \ x,x \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(54,a,3111,a)].">
      <j1 rule="hyper" parents="54 3111"/>
    </justification>
  </clause>

  <clause id="3114">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(270,a,3045,a)].">
      <j1 rule="hyper" parents="270 3045"/>
    </justification>
  </clause>

  <clause id="3115">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) * (y * z) = T(y,y \ 1) * z
    ]]></literal>
    <justification jstring="[para(3065(a,2),2886(a,1,1))].">
      <j1 rule="para" parents="3065 2886"/>
    </justification>
  </clause>

  <clause id="3116">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(804,a,3096,a)].">
      <j1 rule="hyper" parents="804 3096"/>
    </justification>
  </clause>

  <clause id="3119">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ x = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(2997,a,3110,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2997 3110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3120">
    <literal><![CDATA[
      (T(x,y) \ T(x,z)) * K(x,x \ 1) = T(x,z) * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1249(a,1),3010(a,1,1))].">
      <j1 rule="para" parents="1249 3010"/>
    </justification>
  </clause>

  <clause id="3121">
    <literal><![CDATA[
      K(x \ 1,x) * (T(x,y) \ z) = T((x \ 1) \ 1,y) \ z
    ]]></literal>
    <justification jstring="[para(2727(a,2),3061(a,2,1))].">
      <j1 rule="para" parents="2727 3061"/>
    </justification>
  </clause>

  <clause id="3122">
    <literal><![CDATA[
      L(x \ (K(y \ 1,y) \ ((x * (y \ 1)) * y)),x,K(y \ 1,y)) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(941,a,2790,a)].">
      <j1 rule="hyper" parents="941 2790"/>
    </justification>
  </clause>

  <clause id="3123">
    <literal><![CDATA[
      ((x * (y * (K(z,z \ 1) * u))) \ ((x * y) * u)) * K(z,z \ 1) = a(x,y,K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(836,a,2854,a),flip(a)].">
      <j1 rule="hyper" parents="836 2854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3124">
    <literal><![CDATA[
      (x \ (y * ((z \ 1) \ 1))) * K(z \ 1,z) = x \ (y * z)
    ]]></literal>
    <justification jstring="[para(1070(a,1),2861(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1070 2861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3125">
    <literal><![CDATA[
      (((x \ y) \ 1) \ 1) * (y * (((y \ x) \ 1) \ 1)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(2606(a,1),2902(a,1,2))].">
      <j1 rule="para" parents="2606 2902"/>
    </justification>
  </clause>

  <clause id="3126">
    <literal><![CDATA[
      (x \ 1) \ ((x \ y) / y) = x * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2819,a(flip),b,2977,a),flip(a)].">
      <j1 rule="hyper" parents="63 2819 2977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3127">
    <literal><![CDATA[
      T(x,y) \ T(x,x \ 1) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,2889,a,b,3120,a),flip(a)].">
      <j1 rule="hyper" parents="35 2889 3120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3128">
    <literal><![CDATA[
      T(x,y) \ ((x \ 1) \ 1) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(774,a,3127,a)].">
      <j1 rule="hyper" parents="774 3127"/>
    </justification>
  </clause>

  <clause id="3129">
    <literal><![CDATA[
      (x * (1 / T(x,y))) * K(x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(3128(a,1),2354(a,1,1))].">
      <j1 rule="para" parents="3128 2354"/>
    </justification>
  </clause>

  <clause id="3130">
    <literal><![CDATA[
      (x \ 1) * (x * (1 / T(x,y))) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(3129(a,1),2920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3129 2920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3131">
    <literal><![CDATA[
      L((1 / T(x,y)) * x,x \ 1,x) = ((1 / x) * (T(x,y) \ x)) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,3130,a(flip),b,1853,a),flip(a)].">
      <j1 rule="hyper" parents="133 3130 1853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3132">
    <literal><![CDATA[
      x * K((x \ y) \ 1,x \ y) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,2876,a,b,3125,a)].">
      <j1 rule="hyper" parents="34 2876 3125"/>
    </justification>
  </clause>

  <clause id="3133">
    <literal><![CDATA[
      T(x * T(y,y \ 1),y \ 1) = R((y \ 1) \ x,1 / y,y)
    ]]></literal>
    <justification jstring="[para(2775(a,1),2985(a,1,1))].">
      <j1 rule="para" parents="2775 2985"/>
    </justification>
  </clause>

  <clause id="3134">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (y * T(y \ x,z)) / x
    ]]></literal>
    <justification jstring="[para(484(a,1),3081(a,2,1))].">
      <j1 rule="para" parents="484 3081"/>
    </justification>
  </clause>

  <clause id="3135">
    <literal><![CDATA[
      ((1 / x) * (T(x,y) \ x)) * x = L(T(x,y) \ x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3011(a,1),3131(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3011 3131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3136">
    <literal><![CDATA[
      (T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1) = z * T((T(x,z) \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[para(297(a,1),2732(a,1,1)),flip(a)].">
      <j1 rule="para" parents="297 2732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3149">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ (y * T(x,x \ 1)) = K(K(x,x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(2775(a,1),2895(a,1,2))].">
      <j1 rule="para" parents="2775 2895"/>
    </justification>
  </clause>

  <clause id="3150">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,T(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(365,a,3149,a),flip(a)].">
      <j1 rule="hyper" parents="365 3149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3151">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(112(a,1),3150(a,2,2))].">
      <j1 rule="para" parents="112 3150"/>
    </justification>
  </clause>

  <clause id="3152">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,(x \ 1) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[para(2793(a,1),3151(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2793 3151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3153">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,(x \ 1) \ 1) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,16,a(flip),b,3152,a),flip(a)].">
      <j1 rule="hyper" parents="347 16 3152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3154">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,(x \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(3153(a,2),365(a,1))].">
      <j1 rule="para" parents="3153 365"/>
    </justification>
  </clause>

  <clause id="3155">
    <literal><![CDATA[
      K(x \ 1,x) * L(y * T(x,x \ 1),z,u) = (x \ L(x * y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(2767(a,1),2807(a,1,2,1))].">
      <j1 rule="para" parents="2767 2807"/>
    </justification>
  </clause>

  <clause id="3156">
    <literal><![CDATA[
      K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = (x \ L(x * (y / x),z,u)) * x
    ]]></literal>
    <justification jstring="[para(2342(a,1),3155(a,1,2,1))].">
      <j1 rule="para" parents="2342 3155"/>
    </justification>
  </clause>

  <clause id="3157">
    <literal><![CDATA[
      L(x \ R(x,y \ 1,y),x,K(y \ 1,y)) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2759(a,1),3122(a,1,1,2))].">
      <j1 rule="para" parents="2759 3122"/>
    </justification>
  </clause>

  <clause id="3158">
    <literal><![CDATA[
      x \ L(x * (y / x),z,u) = L(y,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,2783,a(flip),b,3156,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 2783 3156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3159">
    <literal><![CDATA[
      L(x * (y / x),z,u) = x * (L(y,z,u) / x)
    ]]></literal>
    <justification jstring="[hyper(150,a,3158,a),flip(a)].">
      <j1 rule="hyper" parents="150 3158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3160">
    <literal><![CDATA[
      L(x * y,z,u) / y = y \ L(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),3158(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 3158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3161">
    <literal><![CDATA[
      L(x,y,z) / x = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(192(a,1),3158(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="192 3158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3162">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2022,a,3161,a)].">
      <j1 rule="hyper" parents="2022 3161"/>
    </justification>
  </clause>

  <clause id="3163">
    <literal><![CDATA[
      (x \ L(x,y,z)) * x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(148,a,3161,a)].">
      <j1 rule="hyper" parents="148 3161"/>
    </justification>
  </clause>

  <clause id="3164">
    <literal><![CDATA[
      R(x \ L(x,y,z),x,L(x,y,z) \ u) \ u = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(3161(a,1),693(a,1,1,1))].">
      <j1 rule="para" parents="3161 693"/>
    </justification>
  </clause>

  <clause id="3165">
    <literal><![CDATA[
      ((x * (y \ L(y,z,u))) * y) / L(y,z,u) = R(x,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(220,a,3163,a(flip),b,209,a)].">
      <j1 rule="hyper" parents="220 3163 209"/>
    </justification>
  </clause>

  <clause id="3166">
    <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(3163(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3163 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3168">
    <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(3163(a,1),99(a,2,1))].">
      <j1 rule="para" parents="3163 99"/>
    </justification>
  </clause>

  <clause id="3169">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(3163(a,1),2517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3163 2517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3170">
    <literal><![CDATA[
      R(x,y \ 1,L(y,z,u)) * (y \ L(y,z,u)) = (x * (1 / y)) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(3162(a,1),2280(a,1,2))].">
      <j1 rule="para" parents="3162 2280"/>
    </justification>
  </clause>

  <clause id="3172">
    <literal><![CDATA[
      (x \ 1) \ L((x \ 1) * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(1303,a,3160,a),flip(a)].">
      <j1 rule="hyper" parents="1303 3160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3173">
    <literal><![CDATA[
      (x \ L(x * y,z,u)) * x = L(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(148,a,3160,a)].">
      <j1 rule="hyper" parents="148 3160"/>
    </justification>
  </clause>

  <clause id="3174">
    <literal><![CDATA[
      (x * x) \ L((x * x) * y,z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(35,a,1390,a(flip),b,3173,a),flip(a)].">
      <j1 rule="hyper" parents="35 1390 3173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3175">
    <literal><![CDATA[
      L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),3173(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 3173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3176">
    <literal><![CDATA[
      L((x * x) * y,z,u) = (x * x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(150,a,3174,a),flip(a)].">
      <j1 rule="hyper" parents="150 3174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3177">
    <literal><![CDATA[
      L(x / (y * y),z,u) = L(x,z,u) / (y * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3158,a(flip),b,3174,a),flip(a)].">
      <j1 rule="hyper" parents="63 3158 3174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3178">
    <literal><![CDATA[
      L(x,y * (z * z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2514,a(flip),b,3174,a)].">
      <j1 rule="hyper" parents="63 2514 3174"/>
    </justification>
  </clause>

  <clause id="3179">
    <literal><![CDATA[
      L((x * x) * (x \ y),x,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(38,a,99,a(flip),b,3174,a),flip(a)].">
      <j1 rule="hyper" parents="38 99 3174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3180">
    <literal><![CDATA[
      L((x * x) * y,x,x) = x * (x * y)
    ]]></literal>
    <justification jstring="[hyper(38,a,18,a(flip),b,3174,a),flip(a)].">
      <j1 rule="hyper" parents="38 18 3174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3181">
    <literal><![CDATA[
      L((x * x) \ y,z,u) = (x * x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),3174(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 3174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3182">
    <literal><![CDATA[
      (x * x) * L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L((x * x) * y,z,u) = w
    ]]></literal>
    <justification jstring="[para(3174(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3174 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3183">
    <literal><![CDATA[
      (x * x) \ L((x \ 1) \ y,z,u) = L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(495(a,1),3174(a,1,2,1))].">
      <j1 rule="para" parents="495 3174"/>
    </justification>
  </clause>

  <clause id="3184">
    <literal><![CDATA[
      (x * x) \ ((y * z) \ (y * ((z * x) * x))) = L(a(z,x,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(1807,a,3178,a)].">
      <j1 rule="hyper" parents="1807 3178"/>
    </justification>
  </clause>

  <clause id="3186">
    <literal><![CDATA[
      L(x,y / (z * z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),3178(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 3178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3187">
    <literal><![CDATA[
      L(x,y * (z * (u * u)),w) = L(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(33(a,1),3178(a,1,2))].">
      <j1 rule="para" parents="33 3178"/>
    </justification>
  </clause>

  <clause id="3188">
    <literal><![CDATA[
      L(x,y \ 1,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(240(a,1),3178(a,1,2)),flip(a)].">
      <j1 rule="para" parents="240 3178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3189">
    <literal><![CDATA[
      L(x,1 / y,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(245(a,1),3178(a,1,2))].">
      <j1 rule="para" parents="245 3178"/>
    </justification>
  </clause>

  <clause id="3190">
    <literal><![CDATA[
      L(x,y * (1 / z),u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(479(a,1),3178(a,1,2))].">
      <j1 rule="para" parents="479 3178"/>
    </justification>
  </clause>

  <clause id="3191">
    <literal><![CDATA[
      L(x,L(y * (z * z),u,w),v5) = L(x,L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(1390(a,2),3178(a,1,2))].">
      <j1 rule="para" parents="1390 3178"/>
    </justification>
  </clause>

  <clause id="3192">
    <literal><![CDATA[
      L((x \ 1) \ y,x,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(645,a,3188,a),flip(a)].">
      <j1 rule="hyper" parents="645 3188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3193">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,3188,a(flip),b,3188,a),flip(a)].">
      <j1 rule="hyper" parents="347 3188 3188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3194">
    <literal><![CDATA[
      L(x,x \ 1,y) = y \ (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(347,a,2007,a(flip),b,3188,a),flip(a)].">
      <j1 rule="hyper" parents="347 2007 3188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3195">
    <literal><![CDATA[
      L(x \ 1,x \ 1,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(347,a,1892,a(flip),b,3188,a),flip(a)].">
      <j1 rule="hyper" parents="347 1892 3188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3196">
    <literal><![CDATA[
      L(x \ 1,x \ 1,y) = (y * x) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,244,a(flip),b,3188,a),flip(a)].">
      <j1 rule="hyper" parents="347 244 3188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3197">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,289,a,b,3188,a)].">
      <j1 rule="hyper" parents="63 289 3188"/>
    </justification>
  </clause>

  <clause id="3198">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) = L(R(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2990,a(flip),b,3188,a)].">
      <j1 rule="hyper" parents="63 2990 3188"/>
    </justification>
  </clause>

  <clause id="3199">
    <literal><![CDATA[
      L(x,x,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2989,a(flip),b,3188,a),flip(a)].">
      <j1 rule="hyper" parents="63 2989 3188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3200">
    <literal><![CDATA[
      L(L((x \ 1) \ y,z,u),x,x) = L(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,689,a(flip),b,3188,a),flip(a)].">
      <j1 rule="hyper" parents="63 689 3188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3201">
    <literal><![CDATA[
      L(x,y,y) / ((y \ 1) * x) = y
    ]]></literal>
    <justification jstring="[hyper(131,a,3188,a(flip),b,289,a)].">
      <j1 rule="hyper" parents="131 3188 289"/>
    </justification>
  </clause>

  <clause id="3202">
    <literal><![CDATA[
      x \ L(y,x,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(128,a,3188,a(flip),b,289,a)].">
      <j1 rule="hyper" parents="128 3188 289"/>
    </justification>
  </clause>

  <clause id="3203">
    <literal><![CDATA[
      L(x,y,z) != (z * (y \ 1)) \ u
    ]]></literal>
    <literal><![CDATA[
      (y \ 1) \ (z \ u) = x
    ]]></literal>
    <justification jstring="[para(3188(a,1),623(a,1))].">
      <j1 rule="para" parents="3188 623"/>
    </justification>
  </clause>

  <clause id="3204">
    <literal><![CDATA[
      L((x \ 1) \ y,x,x) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(3188(a,1),645(a,1))].">
      <j1 rule="para" parents="3188 645"/>
    </justification>
  </clause>

  <clause id="3205">
    <literal><![CDATA[
      L(x,x,x) \ 1 = 1 / x
    ]]></literal>
    <justification jstring="[hyper(132,a,3199,a,b,172,a)].">
      <j1 rule="hyper" parents="132 3199 172"/>
    </justification>
  </clause>

  <clause id="3206">
    <literal><![CDATA[
      L(x,1 / y,z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,3188,a,b,3189,a),flip(a)].">
      <j1 rule="hyper" parents="347 3188 3189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3207">
    <literal><![CDATA[
      L(x,1 / (1 / y),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,3189,a(flip),b,3189,a),flip(a)].">
      <j1 rule="hyper" parents="347 3189 3189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3208">
    <literal><![CDATA[
      (x * (1 / y)) * L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x * ((1 / y) * z) = u
    ]]></literal>
    <justification jstring="[para(3189(a,1),322(a,1,2))].">
      <j1 rule="para" parents="3189 322"/>
    </justification>
  </clause>

  <clause id="3210">
    <literal><![CDATA[
      ((x \ 1) \ y) * L((x \ 1) \ y,x,x) = (x * y) * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(133,a,3192,a(flip),b,299,a),flip(a)].">
      <j1 rule="hyper" parents="133 3192 299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3211">
    <literal><![CDATA[
      L(T(x,y \ 1),y,y) = y * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(22(a,2),3192(a,1,1))].">
      <j1 rule="para" parents="22 3192"/>
    </justification>
  </clause>

  <clause id="3212">
    <literal><![CDATA[
      (x \ 1) * (x * (y * (x \ 1))) = L(y,x,x) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(3192(a,1),737(a,1,2))].">
      <j1 rule="para" parents="3192 737"/>
    </justification>
  </clause>

  <clause id="3213">
    <literal><![CDATA[
      (x \ 1) * (x * (y * (x \ 1))) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x) * (x \ 1) = z
    ]]></literal>
    <justification jstring="[para(3192(a,1),1017(a,1,2))].">
      <j1 rule="para" parents="3192 1017"/>
    </justification>
  </clause>

  <clause id="3215">
    <literal><![CDATA[
      ((x \ 1) \ y) \ (L((x \ 1) \ y,x,x) \ z) = (x * y) \ (((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(3192(a,1),1423(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3192 1423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3216">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,x,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(2934(a,1),3192(a,1,1))].">
      <j1 rule="para" parents="2934 3192"/>
    </justification>
  </clause>

  <clause id="3217">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * x = L(y * x,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1851,a,b,3197,a)].">
      <j1 rule="hyper" parents="63 1851 3197"/>
    </justification>
  </clause>

  <clause id="3218">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((x \ 1) * u)) = L(x,y,z) \ L(u,x,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,3197,a(flip),b,1405,a),flip(a)].">
      <j1 rule="hyper" parents="128 3197 1405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3219">
    <literal><![CDATA[
      (x * x) * ((x \ 1) * y) = (x \ 1) \ L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,3197,a(flip),b,302,a),flip(a)].">
      <j1 rule="hyper" parents="128 3197 302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3220">
    <literal><![CDATA[
      x \ L(y,x,x) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(3197(a,1),356(a,1,2))].">
      <j1 rule="para" parents="3197 356"/>
    </justification>
  </clause>

  <clause id="3221">
    <literal><![CDATA[
      L(T(x \ 1,y),y,x) = (x * y) \ L(y,x,x)
    ]]></literal>
    <justification jstring="[para(3197(a,1),263(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3197 263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3222">
    <literal><![CDATA[
      x * ((x \ (y * y)) * z) = L((y * y) * z,x,x)
    ]]></literal>
    <justification jstring="[para(516(a,1),3197(a,1,2))].">
      <j1 rule="para" parents="516 3197"/>
    </justification>
  </clause>

  <clause id="3223">
    <literal><![CDATA[
      L((x * (y \ 1)) \ z,y,y) = y * (y * ((x * y) \ z))
    ]]></literal>
    <justification jstring="[para(974(a,1),3197(a,1,2)),flip(a)].">
      <j1 rule="para" parents="974 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3224">
    <literal><![CDATA[
      x * (R(x,x,y) \ y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[para(2257(a,2),3197(a,1,2))].">
      <j1 rule="para" parents="2257 3197"/>
    </justification>
  </clause>

  <clause id="3225">
    <literal><![CDATA[
      x \ y != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      L(z,x,x) = y
    ]]></literal>
    <justification jstring="[para(3201(a,1),221(a,1,1))].">
      <j1 rule="para" parents="3201 221"/>
    </justification>
  </clause>

  <clause id="3226">
    <literal><![CDATA[
      x * ((x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x) = z
    ]]></literal>
    <justification jstring="[para(3201(a,1),280(a,1,1))].">
      <j1 rule="para" parents="3201 280"/>
    </justification>
  </clause>

  <clause id="3227">
    <literal><![CDATA[
      x \ (y \ L(((y \ 1) \ x) * z,y,y)) = L(z,(y \ 1) \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,3202,a,b,476,a)].">
      <j1 rule="hyper" parents="128 3202 476"/>
    </justification>
  </clause>

  <clause id="3228">
    <literal><![CDATA[
      L(x,y * (z / (u * u)),w) = L(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(464(a,1),3186(a,1,2))].">
      <j1 rule="para" parents="464 3186"/>
    </justification>
  </clause>

  <clause id="3229">
    <literal><![CDATA[
      L(x,y * (z \ 1),u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(780(a,1),3186(a,1,2))].">
      <j1 rule="para" parents="780 3186"/>
    </justification>
  </clause>

  <clause id="3230">
    <literal><![CDATA[
      L(x,y \ (z \ 1),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(820(a,1),3186(a,1,2))].">
      <j1 rule="para" parents="820 3186"/>
    </justification>
  </clause>

  <clause id="3233">
    <literal><![CDATA[
      L(x,T(y,y \ 1),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(112(a,2),3193(a,1,2))].">
      <j1 rule="para" parents="112 3193"/>
    </justification>
  </clause>

  <clause id="3235">
    <literal><![CDATA[
      R(x,x,x \ y) \ y = L(x \ y,x,x)
    ]]></literal>
    <justification jstring="[hyper(1765,a,3224,a)].">
      <j1 rule="hyper" parents="1765 3224"/>
    </justification>
  </clause>

  <clause id="3236">
    <literal><![CDATA[
      x * (y * (R(y,y,z) \ z)) = x * L(z,y,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,3224,a,b,9,a)].">
      <j1 rule="hyper" parents="134 3224 9"/>
    </justification>
  </clause>

  <clause id="3237">
    <literal><![CDATA[
      (x * T(y,y \ 1)) * L(z,y,x) = x * (T(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(134,a,3233,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 3233 18"/>
    </justification>
  </clause>

  <clause id="3239">
    <literal><![CDATA[
      (x \ (x / (1 / y))) \ 1 = 1 / L(y,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(220,a,3194,a,b,2603,a),flip(a)].">
      <j1 rule="hyper" parents="220 3194 2603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3240">
    <literal><![CDATA[
      T(x \ 1,x \ (x \ 1)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(63,a,1800,a(flip),b,3195,a)].">
      <j1 rule="hyper" parents="63 1800 3195"/>
    </justification>
  </clause>

  <clause id="3241">
    <literal><![CDATA[
      x \ (x / ((y \ 1) \ 1)) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,2007,a(flip),b,3196,a)].">
      <j1 rule="hyper" parents="63 2007 3196"/>
    </justification>
  </clause>

  <clause id="3242">
    <literal><![CDATA[
      L(x,y * (1 / y),z) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,534,a(flip),b,3190,a),flip(a)].">
      <j1 rule="hyper" parents="347 534 3190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3243">
    <literal><![CDATA[
      (x * (y * (1 / y))) \ z = (y * (1 / y)) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(623,a,3242,a),flip(a)].">
      <j1 rule="hyper" parents="623 3242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3245">
    <literal><![CDATA[
      L(x,K(y,y \ 1),z) = x
    ]]></literal>
    <justification jstring="[para(1924(a,2),3242(a,1,2))].">
      <j1 rule="para" parents="1924 3242"/>
    </justification>
  </clause>

  <clause id="3246">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = x * (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(1362,a,3245,a),flip(a)].">
      <j1 rule="hyper" parents="1362 3245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3248">
    <literal><![CDATA[
      (x * ((1 / y) * z)) / ((y \ 1) * z) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(220,a,3245,a(flip),b,2935,a)].">
      <j1 rule="hyper" parents="220 3245 2935"/>
    </justification>
  </clause>

  <clause id="3249">
    <literal><![CDATA[
      L((x * x) * y,x,x) != z
    ]]></literal>
    <literal><![CDATA[
      x * (x * y) = z
    ]]></literal>
    <justification jstring="[para(494(a,1),3204(a,1,1))].">
      <j1 rule="para" parents="494 3204"/>
    </justification>
  </clause>

  <clause id="3250">
    <literal><![CDATA[
      L(x,y * (1 / z),u) = L(x,y * (z \ 1),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,3190,a,b,3229,a)].">
      <j1 rule="hyper" parents="347 3190 3229"/>
    </justification>
  </clause>

  <clause id="3251">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,w) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(1409(a,1),3229(a,1,2))].">
      <j1 rule="para" parents="1409 3229"/>
    </justification>
  </clause>

  <clause id="3252">
    <literal><![CDATA[
      L((x \ (y \ 1)) \ z,x \ y,x) = (y \ 1) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(651,a,3230,a),flip(a)].">
      <j1 rule="hyper" parents="651 3230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3253">
    <literal><![CDATA[
      (x \ 1) * L(y,z \ x,z) = z * ((z \ (x \ 1)) * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,3230,a(flip),b,98,a)].">
      <j1 rule="hyper" parents="134 3230 98"/>
    </justification>
  </clause>

  <clause id="3254">
    <literal><![CDATA[
      L((x \ (y \ 1)) \ z,x \ y,x) != u
    ]]></literal>
    <literal><![CDATA[
      (y \ 1) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(3230(a,1),651(a,1))].">
      <j1 rule="para" parents="3230 651"/>
    </justification>
  </clause>

  <clause id="3255">
    <literal><![CDATA[
      L(x \ y,x,x) = (((x \ 1) \ y) / y) \ y
    ]]></literal>
    <justification jstring="[para(848(a,1),3235(a,1,1)),flip(a)].">
      <j1 rule="para" parents="848 3235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3256">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ 1 = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(2607,a,3241,a)].">
      <j1 rule="hyper" parents="2607 3241"/>
    </justification>
  </clause>

  <clause id="3257">
    <literal><![CDATA[
      T(x \ (x / y),y) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(2324,a,3241,a)].">
      <j1 rule="hyper" parents="2324 3241"/>
    </justification>
  </clause>

  <clause id="3258">
    <literal><![CDATA[
      x / (((x \ y) \ 1) \ 1) = x * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(134,a,174,a(flip),b,3241,a),flip(a)].">
      <j1 rule="hyper" parents="134 174 3241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3259">
    <literal><![CDATA[
      1 / ((x * y) \ x) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(220,a,3241,a(flip),b,2599,a)].">
      <j1 rule="hyper" parents="220 3241 2599"/>
    </justification>
  </clause>

  <clause id="3260">
    <literal><![CDATA[
      (x * (1 / y)) \ x = x \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(83(a,1),3241(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="83 3241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3261">
    <literal><![CDATA[
      (x \ (x / y)) * y = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(3241(a,1),2325(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3241 2325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3262">
    <literal><![CDATA[
      T(x \ (x / y),y) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,244,a,b,3257,a),flip(a)].">
      <j1 rule="hyper" parents="347 244 3257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3263">
    <literal><![CDATA[
      x / T(y,y \ 1) = x * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(3257(a,1),2323(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3257 2323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3264">
    <literal><![CDATA[
      L(1 / x,x,y) = y \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(761,a,3262,a)].">
      <j1 rule="hyper" parents="761 3262"/>
    </justification>
  </clause>

  <clause id="3265">
    <literal><![CDATA[
      (x / y) / L(1 / y,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(220,a,3264,a,b,xx)].">
      <j1 rule="hyper" parents="220 3264"/>
    </justification>
  </clause>

  <clause id="3266">
    <literal><![CDATA[
      x * L(1 / y,y,x) = x / y
    ]]></literal>
    <justification jstring="[hyper(134,a,3264,a,b,xx)].">
      <j1 rule="hyper" parents="134 3264"/>
    </justification>
  </clause>

  <clause id="3267">
    <literal><![CDATA[
      L(1 / T(x,x \ y),T(x,x \ y),y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[para(296(a,1),3264(a,2,2))].">
      <j1 rule="para" parents="296 3264"/>
    </justification>
  </clause>

  <clause id="3268">
    <literal><![CDATA[
      L(1 / (x * y),x * y,y) = y \ R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(247(a,2),3264(a,2,2))].">
      <j1 rule="para" parents="247 3264"/>
    </justification>
  </clause>

  <clause id="3270">
    <literal><![CDATA[
      L(1 / x,x,R(y,x,x)) = R(y,x,x) \ (y * (1 / x))
    ]]></literal>
    <justification jstring="[para(2264(a,1),3264(a,2,2))].">
      <j1 rule="para" parents="2264 3264"/>
    </justification>
  </clause>

  <clause id="3271">
    <literal><![CDATA[
      (x \ (x / y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      L(1 / y,y,x) * z = u
    ]]></literal>
    <justification jstring="[para(3265(a,1),708(a,1,1,1))].">
      <j1 rule="para" parents="3265 708"/>
    </justification>
  </clause>

  <clause id="3272">
    <literal><![CDATA[
      ((x \ y) \ 1) \ 1 = (x * (y \ x)) \ x
    ]]></literal>
    <justification jstring="[para(80(a,1),3256(a,1,1,1,2))].">
      <j1 rule="para" parents="80 3256"/>
    </justification>
  </clause>

  <clause id="3273">
    <literal><![CDATA[
      R(x,y,(z * ((u \ (u / w)) \ 1)) \ v5) = R(x,y,(z * ((u * w) \ u)) \ v5)
    ]]></literal>
    <justification jstring="[para(3256(a,1),2243(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="3256 2243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3274">
    <literal><![CDATA[
      (x * ((x * y) \ x)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3256(a,1),2608(a,1,1,2))].">
      <j1 rule="para" parents="3256 2608"/>
    </justification>
  </clause>

  <clause id="3275">
    <literal><![CDATA[
      (((x \ y) \ 1) \ 1) * L((((x \ y) \ 1) \ 1) \ x,z,u) = L(x * (y \ x),z,u) * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3258(a,1),740(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3258 740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3276">
    <literal><![CDATA[
      x / T(x \ y,y \ x) = x * (y \ x)
    ]]></literal>
    <justification jstring="[para(2579(a,2),3258(a,1,2))].">
      <j1 rule="para" parents="2579 3258"/>
    </justification>
  </clause>

  <clause id="3277">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ R(1 / ((x * y) \ x),z,u) = ((x * y) \ x) * R(((x * y) \ x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(3259(a,1),1471(a,1,1))].">
      <j1 rule="para" parents="3259 1471"/>
    </justification>
  </clause>

  <clause id="3280">
    <literal><![CDATA[
      L(x,x,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,2007,a,b,3260,a)].">
      <j1 rule="hyper" parents="347 2007 3260"/>
    </justification>
  </clause>

  <clause id="3281">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(220,a,3194,a,b,3260,a)].">
      <j1 rule="hyper" parents="220 3194 3260"/>
    </justification>
  </clause>

  <clause id="3282">
    <literal><![CDATA[
      x / L(y,y,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(220,a,2007,a,b,3260,a)].">
      <j1 rule="hyper" parents="220 2007 3260"/>
    </justification>
  </clause>

  <clause id="3283">
    <literal><![CDATA[
      R(x,y,(z * ((1 / u) \ 1)) \ z) = R(x,y,z \ (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3260(a,1),2243(a,2,3))].">
      <j1 rule="para" parents="3260 2243"/>
    </justification>
  </clause>

  <clause id="3284">
    <literal><![CDATA[
      L(1 / x,x,y) = (y * (1 / (1 / x))) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,3189,a(flip),b,3280,a)].">
      <j1 rule="hyper" parents="63 3189 3280"/>
    </justification>
  </clause>

  <clause id="3285">
    <literal><![CDATA[
      (x * (1 / x)) / x = 1 / L(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,3282,a(flip),b,1996,a)].">
      <j1 rule="hyper" parents="131 3282 1996"/>
    </justification>
  </clause>

  <clause id="3286">
    <literal><![CDATA[
      ((x * (1 / y)) * y) * L(y,y,x) = x * y
    ]]></literal>
    <justification jstring="[para(3282(a,1),1998(a,1,1,1))].">
      <j1 rule="para" parents="3282 1998"/>
    </justification>
  </clause>

  <clause id="3288">
    <literal><![CDATA[
      K(x \ (x / L(y,y \ 1,x)),z) = K(1 / y,z)
    ]]></literal>
    <justification jstring="[para(3281(a,2),770(a,1,1,2))].">
      <j1 rule="para" parents="3281 770"/>
    </justification>
  </clause>

  <clause id="3289">
    <literal><![CDATA[
      (x * (y \ x)) * L(((x \ y) \ 1) \ 1,z,u) = x * ((y \ x) * L((y \ x) \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(3272(a,2),1015(a,1,2,1))].">
      <j1 rule="para" parents="3272 1015"/>
    </justification>
  </clause>

  <clause id="3290">
    <literal><![CDATA[
      T(L(x,y,y),y \ 1) = y * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a(flip),b,3211,a)].">
      <j1 rule="hyper" parents="63 25 3211"/>
    </justification>
  </clause>

  <clause id="3291">
    <literal><![CDATA[
      L((x \ y) * x,x,x) = ((x \ 1) * y) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),3217(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 3217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3292">
    <literal><![CDATA[
      L(L(x \ 1,y * x,y * x),x,y) = ((((y * x) \ 1) \ y) / y) \ y
    ]]></literal>
    <justification jstring="[hyper(1095,a,3255,a)].">
      <j1 rule="hyper" parents="1095 3255"/>
    </justification>
  </clause>

  <clause id="3294">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(347,a,2613,a(flip),b,3284,a),flip(a)].">
      <j1 rule="hyper" parents="347 2613 3284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3295">
    <literal><![CDATA[
      R(x,y,y) * L(y,y,x) = x * y
    ]]></literal>
    <justification jstring="[para(2259(a,1),3286(a,1,1))].">
      <j1 rule="para" parents="2259 3286"/>
    </justification>
  </clause>

  <clause id="3296">
    <literal><![CDATA[
      R(x,y,y) \ (x * y) = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(138,a,3295,a)].">
      <j1 rule="hyper" parents="138 3295"/>
    </justification>
  </clause>

  <clause id="3297">
    <literal><![CDATA[
      R(x / y,y,y) \ x = L(y,y,x / y)
    ]]></literal>
    <justification jstring="[hyper(128,a,12,a(flip),b,3295,a)].">
      <j1 rule="hyper" parents="128 12 3295"/>
    </justification>
  </clause>

  <clause id="3298">
    <literal><![CDATA[
      R(x,1 / y,1 / y) \ (x * (1 / y)) = L(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3189,a(flip),b,3296,a),flip(a)].">
      <j1 rule="hyper" parents="347 3189 3296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3299">
    <literal><![CDATA[
      L(x,x,y / x) = (y * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(785(a,1),3297(a,1,1)),flip(a)].">
      <j1 rule="para" parents="785 3297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3300">
    <literal><![CDATA[
      x * (T(y * y,z) \ 1) = x / T(y * y,z)
    ]]></literal>
    <justification jstring="[hyper(220,a,554,a(flip),b,3299,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="220 554 3299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3302">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(228,a,3175,a),flip(a)].">
      <j1 rule="hyper" parents="228 3175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3303">
    <literal><![CDATA[
      L((x \ y) * x,z,u) != w * x
    ]]></literal>
    <literal><![CDATA[
      x \ L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(3175(a,2),44(a,1))].">
      <j1 rule="para" parents="3175 44"/>
    </justification>
  </clause>

  <clause id="3304">
    <literal><![CDATA[
      L((x \ (y \ (z \ u))) * x,y,z) = (x \ ((z * y) \ u)) * x
    ]]></literal>
    <justification jstring="[para(329(a,1),3175(a,2,1,2))].">
      <j1 rule="para" parents="329 3175"/>
    </justification>
  </clause>

  <clause id="3305">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ z)) * x,y \ 1,y) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(560(a,1),3175(a,2,1,2))].">
      <j1 rule="para" parents="560 3175"/>
    </justification>
  </clause>

  <clause id="3306">
    <literal><![CDATA[
      L((x \ ((y \ z) \ u)) * x,y \ z,y) = (x \ (z \ (y * u))) * x
    ]]></literal>
    <justification jstring="[para(561(a,1),3175(a,2,1,2))].">
      <j1 rule="para" parents="561 3175"/>
    </justification>
  </clause>

  <clause id="3307">
    <literal><![CDATA[
      T(L(x,y,z),L(x,y,z) \ x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(383,a,3302,a)].">
      <j1 rule="hyper" parents="383 3302"/>
    </justification>
  </clause>

  <clause id="3308">
    <literal><![CDATA[
      x / L(x,y,z) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(145,a,3302,a)].">
      <j1 rule="hyper" parents="145 3302"/>
    </justification>
  </clause>

  <clause id="3309">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,3302,a)].">
      <j1 rule="hyper" parents="138 3302"/>
    </justification>
  </clause>

  <clause id="3310">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(35,a,2000,a,b,3302,a)].">
      <j1 rule="hyper" parents="35 2000 3302"/>
    </justification>
  </clause>

  <clause id="3311">
    <literal><![CDATA[
      L(x,y,z) / L(L(x,u,w),y,z) = L(L(x,y,z),u,w) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,3302,a(flip),b,166,a)].">
      <j1 rule="hyper" parents="131 3302 166"/>
    </justification>
  </clause>

  <clause id="3312">
    <literal><![CDATA[
      x * L(y,z,u) != y
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) \ y = x
    ]]></literal>
    <justification jstring="[para(3302(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="3302 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3313">
    <literal><![CDATA[
      x / L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(3302(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3302 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3314">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ x != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3302(a,1),356(a,1,2))].">
      <j1 rule="para" parents="3302 356"/>
    </justification>
  </clause>

  <clause id="3315">
    <literal><![CDATA[
      R(L(x,y,z) \ x,L(x,y,z),x \ u) = u / (L(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[para(3308(a,1),604(a,1,1))].">
      <j1 rule="para" parents="3308 604"/>
    </justification>
  </clause>

  <clause id="3316">
    <literal><![CDATA[
      T(1 / L(x,y,z),x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(269,a,3310,a,b,1409,a)].">
      <j1 rule="hyper" parents="269 3310 1409"/>
    </justification>
  </clause>

  <clause id="3317">
    <literal><![CDATA[
      T(x,L(x,y,z) \ x) = x
    ]]></literal>
    <justification jstring="[hyper(159,a,3307,a)].">
      <j1 rule="hyper" parents="159 3307"/>
    </justification>
  </clause>

  <clause id="3318">
    <literal><![CDATA[
      (L(x,y,z) \ x) * x = x * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(1068,a,3317,a),flip(a)].">
      <j1 rule="hyper" parents="1068 3317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3320">
    <literal><![CDATA[
      (x * x) * L((x * x) \ y,z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),3176(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3321">
    <literal><![CDATA[
      L(((1 / x) * (1 / x)) * y,z,u) = (x \ (1 / x)) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(307(a,1),3176(a,2,1))].">
      <j1 rule="para" parents="307 3176"/>
    </justification>
  </clause>

  <clause id="3322">
    <literal><![CDATA[
      L(x,y,z) / (x * x) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(300(a,1),3177(a,1,1)),flip(a)].">
      <j1 rule="para" parents="300 3177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3323">
    <literal><![CDATA[
      L(x / (y * y),z,u) \ w = (y * y) * (L(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(3177(a,2),777(a,1,1))].">
      <j1 rule="para" parents="3177 777"/>
    </justification>
  </clause>

  <clause id="3324">
    <literal><![CDATA[
      L(x \ 1,y,z) * ((x * x) * u) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(133,a,3322,a(flip),b,465,a)].">
      <j1 rule="hyper" parents="133 3322 465"/>
    </justification>
  </clause>

  <clause id="3325">
    <literal><![CDATA[
      (x * x) * (L(x,y,z) \ u) = L(x \ 1,y,z) \ u
    ]]></literal>
    <justification jstring="[para(3322(a,1),777(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3322 777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3326">
    <literal><![CDATA[
      L(x,y,z) * ((x * x) \ u) = L(x \ 1,y,z) * u
    ]]></literal>
    <justification jstring="[para(3322(a,1),803(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3322 803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3327">
    <literal><![CDATA[
      (x * L(y,z,u)) * ((y * y) \ w) = (x * L(y \ 1,z,u)) * w
    ]]></literal>
    <justification jstring="[para(3322(a,1),827(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3322 827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3328">
    <literal><![CDATA[
      R(x,y,L(z \ 1,u,w)) = R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(3322(a,1),2188(a,1,3))].">
      <j1 rule="para" parents="3322 2188"/>
    </justification>
  </clause>

  <clause id="3329">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(3322(a,1),3186(a,1,2))].">
      <j1 rule="para" parents="3322 3186"/>
    </justification>
  </clause>

  <clause id="3330">
    <literal><![CDATA[
      L(x,y * (z * z),u) = (w * w) * L((w * w) \ x,y,u)
    ]]></literal>
    <justification jstring="[hyper(134,a,3178,a(flip),b,3181,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 3178 3181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3331">
    <literal><![CDATA[
      (x * x) * L((x * x) \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(3181(a,2),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3181 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3332">
    <literal><![CDATA[
      L(x,y * (z * (u * (w \ 1))),v5) = L(x,y * (z * (u * w)),v5)
    ]]></literal>
    <justification jstring="[para(792(a,1),3228(a,1,2,2))].">
      <j1 rule="para" parents="792 3228"/>
    </justification>
  </clause>

  <clause id="3333">
    <literal><![CDATA[
      L(x,R(y,z,z) / z,u) = L(x,y * ((1 / z) / (w * w)),u)
    ]]></literal>
    <justification jstring="[para(2264(a,2),3228(a,2,2)),flip(a)].">
      <j1 rule="para" parents="2264 3228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3334">
    <literal><![CDATA[
      x * (R(y,y,z) \ (y * z)) = x * L(z,y,y)
    ]]></literal>
    <justification jstring="[para(1753(a,2),3236(a,1,2))].">
      <j1 rule="para" parents="1753 3236"/>
    </justification>
  </clause>

  <clause id="3336">
    <literal><![CDATA[
      x * (x * L(x \ y,z,u)) = L(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(1189,a,3320,a)].">
      <j1 rule="hyper" parents="1189 3320"/>
    </justification>
  </clause>

  <clause id="3337">
    <literal><![CDATA[
      x * (x * L(x \ 1,y,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1016,a,3320,a)].">
      <j1 rule="hyper" parents="1016 3320"/>
    </justification>
  </clause>

  <clause id="3338">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * x = L(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,1984,a(flip),b,3320,a)].">
      <j1 rule="hyper" parents="63 1984 3320"/>
    </justification>
  </clause>

  <clause id="3339">
    <literal><![CDATA[
      x * L(x \ (y / x),z,u) = L(y,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,3320,a(flip),b,1992,a),flip(a)].">
      <j1 rule="hyper" parents="131 3320 1992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3340">
    <literal><![CDATA[
      L(x * y,z,u) / y = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(131,a,3320,a(flip),b,1984,a(flip))].">
      <j1 rule="hyper" parents="131 3320 1984"/>
    </justification>
  </clause>

  <clause id="3341">
    <literal><![CDATA[
      x * L(x \ (x \ y),z,u) = x \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(128,a,3320,a(flip),b,1182,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 3320 1182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3342">
    <literal><![CDATA[
      x \ L(x * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(128,a,3320,a(flip),b,1181,a(flip))].">
      <j1 rule="hyper" parents="128 3320 1181"/>
    </justification>
  </clause>

  <clause id="3343">
    <literal><![CDATA[
      x * L(x \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,3320,a(flip),b,1015,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 3320 1015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3344">
    <literal><![CDATA[
      x \ (x \ L(x,y,z)) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(3337(a,1),69(a,1,2,2))].">
      <j1 rule="para" parents="3337 69"/>
    </justification>
  </clause>

  <clause id="3345">
    <literal><![CDATA[
      x \ L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * L(x \ 1,y,z) = u
    ]]></literal>
    <justification jstring="[para(3337(a,1),356(a,1,2))].">
      <j1 rule="para" parents="3337 356"/>
    </justification>
  </clause>

  <clause id="3346">
    <literal><![CDATA[
      x * (x * ((y * x) \ y)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[para(244(a,1),3337(a,1,2,2))].">
      <j1 rule="para" parents="244 3337"/>
    </justification>
  </clause>

  <clause id="3347">
    <literal><![CDATA[
      (x \ 1) * (x \ L(x,y,z)) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1294(a,1),3337(a,1,2))].">
      <j1 rule="para" parents="1294 3337"/>
    </justification>
  </clause>

  <clause id="3348">
    <literal><![CDATA[
      x \ L(x,x,y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(138,a,3346,a)].">
      <j1 rule="hyper" parents="138 3346"/>
    </justification>
  </clause>

  <clause id="3349">
    <literal><![CDATA[
      L(x,x,y) \ (x * (x * (((y * x) \ y) * z))) != u
    ]]></literal>
    <literal><![CDATA[
      L(L(z,(y * x) \ y,x),x * ((y * x) \ y),x) = u
    ]]></literal>
    <justification jstring="[para(3346(a,1),942(a,1,1))].">
      <j1 rule="para" parents="3346 942"/>
    </justification>
  </clause>

  <clause id="3350">
    <literal><![CDATA[
      x \ L(x,x,y) = (y \ (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,3261,a,b,3348,a),flip(a)].">
      <j1 rule="hyper" parents="347 3261 3348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3351">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * x = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,3348,a(flip),b,3161,a)].">
      <j1 rule="hyper" parents="133 3348 3161"/>
    </justification>
  </clause>

  <clause id="3352">
    <literal><![CDATA[
      R(R(x,y,(z * y) \ z),y * ((z * y) \ z),y) = (((x * y) * ((z * y) \ z)) * y) / L(y,y,z)
    ]]></literal>
    <justification jstring="[para(3351(a,1),591(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3351 591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3353">
    <literal><![CDATA[
      T(x * L(x \ 1,y,z),u) = T(x,u) \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(2138,a,3343,a)].">
      <j1 rule="hyper" parents="2138 3343"/>
    </justification>
  </clause>

  <clause id="3354">
    <literal><![CDATA[
      (x \ y) \ L(x \ y,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(2099,a,3343,a),flip(a)].">
      <j1 rule="hyper" parents="2099 3343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3355">
    <literal><![CDATA[
      x * (y * L(y \ (x \ 1),z,u)) = (x * y) \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(1196,a,3343,a)].">
      <j1 rule="hyper" parents="1196 3343"/>
    </justification>
  </clause>

  <clause id="3356">
    <literal><![CDATA[
      (1 / x) \ L(1 / x,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1192,a,b,3343,a)].">
      <j1 rule="hyper" parents="63 1192 3343"/>
    </justification>
  </clause>

  <clause id="3357">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1294,a(flip),b,3343,a),flip(a)].">
      <j1 rule="hyper" parents="63 1294 3343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3358">
    <literal><![CDATA[
      x * (L(x,y,z) * L(x \ 1,u,w)) = L(x,y,z) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(134,a,3343,a(flip),b,1406,a),flip(a)].">
      <j1 rule="hyper" parents="134 3343 1406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3359">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,3343,a(flip),b,1584,a)].">
      <j1 rule="hyper" parents="133 3343 1584"/>
    </justification>
  </clause>

  <clause id="3360">
    <literal><![CDATA[
      ((x / y) \ L(x / y,z,u)) * y = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,3343,a(flip),b,2177,a(flip))].">
      <j1 rule="hyper" parents="133 3343 2177"/>
    </justification>
  </clause>

  <clause id="3361">
    <literal><![CDATA[
      (x * L((x \ 1) * (y * y),z,u)) \ w = (y * y) \ ((x \ L(x,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(3343(a,1),1395(a,2,2,1))].">
      <j1 rule="para" parents="3343 1395"/>
    </justification>
  </clause>

  <clause id="3362">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x \ L(x,z,u)) * y
    ]]></literal>
    <justification jstring="[para(3343(a,1),2028(a,2,1))].">
      <j1 rule="para" parents="3343 2028"/>
    </justification>
  </clause>

  <clause id="3363">
    <literal><![CDATA[
      (x * y) * (y * L(y \ 1,z,u)) = (x * (y \ L(y,z,u))) * y
    ]]></literal>
    <justification jstring="[para(3343(a,1),2065(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3343 2065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3365">
    <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(3343(a,1),2099(a,1))].">
      <j1 rule="para" parents="3343 2099"/>
    </justification>
  </clause>

  <clause id="3366">
    <literal><![CDATA[
      x * L(x \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3344(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3344 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3367">
    <literal><![CDATA[
      x \ (y * L(y \ (x * ((x \ y) \ L(x \ y,z,u))),w,v5)) = (x \ y) * L(L((x \ y) \ 1,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(3344(a,1),1360(a,2,2,1))].">
      <j1 rule="para" parents="3344 1360"/>
    </justification>
  </clause>

  <clause id="3368">
    <literal><![CDATA[
      R(x,y,L(z \ 1,u,w)) = R(x,y,L(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,2190,a,b,3328,a),flip(a)].">
      <j1 rule="hyper" parents="347 2190 3328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3369">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u),w) = L(x,L(y,z,u) \ 1,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,3188,a,b,3329,a),flip(a)].">
      <j1 rule="hyper" parents="347 3188 3329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3370">
    <literal><![CDATA[
      L(x,L(1 / y,z,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(83(a,1),3329(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 3329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3371">
    <literal><![CDATA[
      R(x,x,y) \ (x * (x * y)) = x * L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1753,a,b,3334,a)].">
      <j1 rule="hyper" parents="63 1753 3334"/>
    </justification>
  </clause>

  <clause id="3372">
    <literal><![CDATA[
      L(x * (x * y),z,u) = x * (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),3336(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 3336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3373">
    <literal><![CDATA[
      x * (x * ((y * x) \ (y * z))) = L(x * z,x,y)
    ]]></literal>
    <justification jstring="[para(99(a,1),3336(a,1,2,2))].">
      <j1 rule="para" parents="99 3336"/>
    </justification>
  </clause>

  <clause id="3374">
    <literal><![CDATA[
      L(x * (y * x),z,u) = x * (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(737(a,1),3336(a,1,2)),flip(a)].">
      <j1 rule="para" parents="737 3336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3375">
    <literal><![CDATA[
      x * (x * ((1 / x) * y)) = L(x * y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2938(a,1),3336(a,1,2,2))].">
      <j1 rule="para" parents="2938 3336"/>
    </justification>
  </clause>

  <clause id="3376">
    <literal><![CDATA[
      L((x * y) * x,z,u) = (x * L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(9(a,1),3338(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 3338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3377">
    <literal><![CDATA[
      L(x * y,z,u) / y != w
    ]]></literal>
    <literal><![CDATA[
      y * L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(3338(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3338 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3378">
    <literal><![CDATA[
      (x * ((1 / x) * y)) * x = L(y * x,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2938(a,1),3338(a,1,1,2))].">
      <j1 rule="para" parents="2938 3338"/>
    </justification>
  </clause>

  <clause id="3379">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ x,z,u) = L(y,z,u) / (x \ y)
    ]]></literal>
    <justification jstring="[para(80(a,1),3339(a,1,2,1,2))].">
      <j1 rule="para" parents="80 3339"/>
    </justification>
  </clause>

  <clause id="3380">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(1303,a,3340,a),flip(a)].">
      <j1 rule="hyper" parents="1303 3340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3381">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x * L(x \ y,z,u) = w
    ]]></literal>
    <justification jstring="[para(3340(a,1),1303(a,1))].">
      <j1 rule="para" parents="3340 1303"/>
    </justification>
  </clause>

  <clause id="3382">
    <literal><![CDATA[
      L(x \ (x \ y),z,u) = x \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(138,a,3341,a),flip(a)].">
      <j1 rule="hyper" parents="138 3341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3383">
    <literal><![CDATA[
      x * L(L(x \ 1,y,z),u,w) = x \ L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3344(a,1),3341(a,1,2,1))].">
      <j1 rule="para" parents="3344 3341"/>
    </justification>
  </clause>

  <clause id="3384">
    <literal><![CDATA[
      (x / y) * L((x / y) \ (y \ 1),z,u) = (x / y) \ L(x / (y * y),z,u)
    ]]></literal>
    <justification jstring="[para(781(a,1),3342(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="781 3342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3385">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3347(a,1),356(a,1,2))].">
      <j1 rule="para" parents="3347 356"/>
    </justification>
  </clause>

  <clause id="3386">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ L(1 / ((x * y) \ x),z,u) = ((x * y) \ x) \ L((x * y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(3259(a,1),3356(a,1,1))].">
      <j1 rule="para" parents="3259 3356"/>
    </justification>
  </clause>

  <clause id="3387">
    <literal><![CDATA[
      R(x,x,L(y,x,x)) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,580,a,b,3371,a)].">
      <j1 rule="hyper" parents="39 580 3371"/>
    </justification>
  </clause>

  <clause id="3388">
    <literal><![CDATA[
      R(x,x,x \ y) = R(x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(2290,a,3387,a),flip(a)].">
      <j1 rule="hyper" parents="2290 3387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3389">
    <literal><![CDATA[
      R(x,x,x * y) = ((x \ 1) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,848,a(flip),b,3388,a),flip(a)].">
      <j1 rule="hyper" parents="63 848 3388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3390">
    <literal><![CDATA[
      R(x,x,x * y) * y = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(133,a,3388,a(flip),b,848,a(flip))].">
      <j1 rule="hyper" parents="133 3388 848"/>
    </justification>
  </clause>

  <clause id="3391">
    <literal><![CDATA[
      (x * y) \ (x * L(y * (y * z),u,w)) = L(y * L(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(3372(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3372 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3392">
    <literal><![CDATA[
      L(x * (x * (y \ (z \ u))),y,z) = x * (x * ((z * y) \ u))
    ]]></literal>
    <justification jstring="[para(329(a,1),3372(a,2,2,2))].">
      <j1 rule="para" parents="329 3372"/>
    </justification>
  </clause>

  <clause id="3393">
    <literal><![CDATA[
      x * L(x \ (x \ y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x \ L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(3382(a,2),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3382 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3394">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2639,a,b,3288,a)].">
      <j1 rule="hyper" parents="63 2639 3288"/>
    </justification>
  </clause>

  <clause id="3396">
    <literal><![CDATA[
      x \ (x / (x \ y)) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3264,a(flip),b,3294,a)].">
      <j1 rule="hyper" parents="63 3264 3294"/>
    </justification>
  </clause>

  <clause id="3397">
    <literal><![CDATA[
      x * (1 / (1 / (y \ x))) = x / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(134,a,3294,a(flip),b,3264,a(flip))].">
      <j1 rule="hyper" parents="134 3294 3264"/>
    </justification>
  </clause>

  <clause id="3398">
    <literal><![CDATA[
      (1 / (x \ y)) \ (1 / (1 / (y \ x))) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(3294(a,1),1194(a,1,2))].">
      <j1 rule="para" parents="3294 1194"/>
    </justification>
  </clause>

  <clause id="3399">
    <literal><![CDATA[
      (x \ (x / (x \ y))) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      1 / (y \ x) = z
    ]]></literal>
    <justification jstring="[para(3396(a,2),359(a,1,1))].">
      <j1 rule="para" parents="3396 359"/>
    </justification>
  </clause>

  <clause id="3400">
    <literal><![CDATA[
      (x \ y) / ((x \ y) \ ((x \ y) * (y \ x))) = (x \ y) * (1 / (1 / (1 / (y \ x))))
    ]]></literal>
    <justification jstring="[para(2053(a,1),3397(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2053 3397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3401">
    <literal><![CDATA[
      x * (y * ((x * y) \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      (x * y) \ L(x * y,y,x) = z
    ]]></literal>
    <justification jstring="[para(97(a,1),3366(a,1))].">
      <j1 rule="para" parents="97 3366"/>
    </justification>
  </clause>

  <clause id="3402">
    <literal><![CDATA[
      x * (y * L(y \ (x \ 1),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (x * y) \ L(x * y,z,u) = w
    ]]></literal>
    <justification jstring="[para(1182(a,1),3366(a,1))].">
      <j1 rule="para" parents="1182 3366"/>
    </justification>
  </clause>

  <clause id="3403">
    <literal><![CDATA[
      K(1 / x,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3100,a(flip),b,3394,a),flip(a)].">
      <j1 rule="hyper" parents="63 3100 3394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3404">
    <literal><![CDATA[
      L((1 / x) * T((1 / x) \ 1,y),x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(83(a,1),3394(a,1,2))].">
      <j1 rule="para" parents="83 3394"/>
    </justification>
  </clause>

  <clause id="3405">
    <literal><![CDATA[
      (x * (y \ 1)) \ ((y \ 1) * x) = K(1 / y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,16,a(flip),b,3403,a)].">
      <j1 rule="hyper" parents="347 16 3403"/>
    </justification>
  </clause>

  <clause id="3406">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1173,a(flip),b,3403,a),flip(a)].">
      <j1 rule="hyper" parents="63 1173 3403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3407">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(80(a,1),3403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="80 3403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3408">
    <literal><![CDATA[
      K(T(x \ y,y \ x),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2579(a,2),3407(a,1,1))].">
      <j1 rule="para" parents="2579 3407"/>
    </justification>
  </clause>

  <clause id="3409">
    <literal><![CDATA[
      K(1 / x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(3405(a,1),365(a,1))].">
      <j1 rule="para" parents="3405 365"/>
    </justification>
  </clause>

  <clause id="3411">
    <literal><![CDATA[
      x \ L((x \ 1) \ 1,y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1954,a,3169,a)].">
      <j1 rule="hyper" parents="1954 3169"/>
    </justification>
  </clause>

  <clause id="3412">
    <literal><![CDATA[
      L((x \ 1) \ y,x,x \ 1) = (x * x) * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,2938,a(flip),b,3183,a),flip(a)].">
      <j1 rule="hyper" parents="134 2938 3183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3413">
    <literal><![CDATA[
      L(x,L((y * z) * z,u,w),v5) = L(x,L(R(y,z,z),u,w),v5)
    ]]></literal>
    <justification jstring="[para(107(a,1),3191(a,1,2,1))].">
      <j1 rule="para" parents="107 3191"/>
    </justification>
  </clause>

  <clause id="3415">
    <literal><![CDATA[
      (x * (1 / x)) \ (x \ y) = T(x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(2337(a,1),3243(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2337 3243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3417">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,2836,a,b,3246,a),flip(a)].">
      <j1 rule="hyper" parents="347 2836 3246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3418">
    <literal><![CDATA[
      (1 / (1 / x)) * (K(x,x \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[para(1928(a,1),3246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1928 3246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3419">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(128,a,10,a(flip),b,3418,a),flip(a)].">
      <j1 rule="hyper" parents="128 10 3418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3420">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(63,a,2836,a,b,3418,a)].">
      <j1 rule="hyper" parents="63 2836 3418"/>
    </justification>
  </clause>

  <clause id="3421">
    <literal><![CDATA[
      x * (y * K(x \ 1,x)) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(2765(a,1),3418(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2765 3418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3422">
    <literal><![CDATA[
      x * (K(x \ 1,x) * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(2793(a,1),3418(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2793 3418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3423">
    <literal><![CDATA[
      x \ (K(x,x \ 1) * y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,2838,a,b,3419,a)].">
      <j1 rule="hyper" parents="63 2838 3419"/>
    </justification>
  </clause>

  <clause id="3424">
    <literal><![CDATA[
      K(x,1 / x) * (x \ y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(1922(a,2),3419(a,1,1))].">
      <j1 rule="para" parents="1922 3419"/>
    </justification>
  </clause>

  <clause id="3425">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = L(x,x,x) \ y
    ]]></literal>
    <justification jstring="[para(3199(a,2),3419(a,2,1))].">
      <j1 rule="para" parents="3199 3419"/>
    </justification>
  </clause>

  <clause id="3426">
    <literal><![CDATA[
      R(x,x,y) * ((x \ (1 / x)) * y) = L(x,x,x) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,2855,a,b,3425,a)].">
      <j1 rule="hyper" parents="63 2855 3425"/>
    </justification>
  </clause>

  <clause id="3427">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(2800,a,3420,a)].">
      <j1 rule="hyper" parents="2800 3420"/>
    </justification>
  </clause>

  <clause id="3428">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * y) = x * K(y \ (1 / (1 / x)),y)
    ]]></literal>
    <justification jstring="[para(330(a,1),3420(a,1,2))].">
      <j1 rule="para" parents="330 3420"/>
    </justification>
  </clause>

  <clause id="3429">
    <literal><![CDATA[
      (1 / (1 / x)) * (y / (1 / (1 / x))) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(2359(a,1),3421(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2359 3421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3430">
    <literal><![CDATA[
      T(x,y) * (K(x \ 1,x) * z) = (1 / (1 / T(x,y))) * z
    ]]></literal>
    <justification jstring="[para(3058(a,1),3422(a,1,2,1))].">
      <j1 rule="para" parents="3058 3422"/>
    </justification>
  </clause>

  <clause id="3431">
    <literal><![CDATA[
      x * (K(x \ 1,x) * y) = L(x,x,x) * y
    ]]></literal>
    <justification jstring="[para(3199(a,2),3422(a,2,1))].">
      <j1 rule="para" parents="3199 3422"/>
    </justification>
  </clause>

  <clause id="3432">
    <literal><![CDATA[
      x * (y \ K(x \ 1,x)) = L(x,x,x) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(2785(a,1),3431(a,1,2))].">
      <j1 rule="para" parents="2785 3431"/>
    </justification>
  </clause>

  <clause id="3433">
    <literal><![CDATA[
      K(x,x \ 1) * L(y,x \ 1,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,2983,a(flip),b,3423,a),flip(a)].">
      <j1 rule="hyper" parents="134 2983 3423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3434">
    <literal><![CDATA[
      (x \ y) * K(x,1 / x) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,2751,a(flip),b,3424,a)].">
      <j1 rule="hyper" parents="63 2751 3424"/>
    </justification>
  </clause>

  <clause id="3435">
    <literal><![CDATA[
      ((1 / (1 / x)) * y) * (1 / x) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,3427,a(flip),b,2305,a)].">
      <j1 rule="hyper" parents="133 3427 2305"/>
    </justification>
  </clause>

  <clause id="3436">
    <literal><![CDATA[
      ((x \ y) * z) * K(y \ x,x \ y) = (1 / (1 / (x \ y))) * z
    ]]></literal>
    <justification jstring="[para(2396(a,1),3427(a,1,2))].">
      <j1 rule="para" parents="2396 3427"/>
    </justification>
  </clause>

  <clause id="3438">
    <literal><![CDATA[
      L(x \ 1,y,z) * ((x \ 1) \ u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(495(a,1),3324(a,1,2))].">
      <j1 rule="para" parents="495 3324"/>
    </justification>
  </clause>

  <clause id="3439">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(134,a,3325,a(flip),b,494,a)].">
      <j1 rule="hyper" parents="134 3325 494"/>
    </justification>
  </clause>

  <clause id="3440">
    <literal><![CDATA[
      L(x,y,z) * ((x \ 1) * u) = x * (L(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[para(3326(a,1),1412(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3326 1412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3441">
    <literal><![CDATA[
      R(x,y,L(z \ 1,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(3368(a,2),2232(a,1))].">
      <j1 rule="para" parents="3368 2232"/>
    </justification>
  </clause>

  <clause id="3442">
    <literal><![CDATA[
      x \ L(T(x,x \ 1),y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(112(a,2),3411(a,1,2,1))].">
      <j1 rule="para" parents="112 3411"/>
    </justification>
  </clause>

  <clause id="3446">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[para(2328(a,1),3417(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2328 3417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3447">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ x) * z) = (y \ ((x \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(2339(a,1),3417(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2339 3417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3448">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = K(x,x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[para(2742(a,2),3417(a,1,1))].">
      <j1 rule="para" parents="2742 3417"/>
    </justification>
  </clause>

  <clause id="3449">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) * y) * z) = ((1 / x) * y) * z
    ]]></literal>
    <justification jstring="[para(2924(a,1),3417(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2924 3417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3450">
    <literal><![CDATA[
      ((x \ R(x,x,y)) / x) * y = L(x,x,x) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,1476,a(flip),b,3426,a)].">
      <j1 rule="hyper" parents="63 1476 3426"/>
    </justification>
  </clause>

  <clause id="3451">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 / (1 / x))) * y) * (1 / x)
    ]]></literal>
    <justification jstring="[para(330(a,1),3435(a,1,1)),flip(a)].">
      <j1 rule="para" parents="330 3435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3452">
    <literal><![CDATA[
      R(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2387,a,3448,a)].">
      <j1 rule="hyper" parents="2387 3448"/>
    </justification>
  </clause>

  <clause id="3453">
    <literal><![CDATA[
      L(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(544,a,3448,a)].">
      <j1 rule="hyper" parents="544 3448"/>
    </justification>
  </clause>

  <clause id="3454">
    <literal><![CDATA[
      (K(x,x \ 1) * y) / z = K(x,x \ 1) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(131,a,168,a(flip),b,3448,a)].">
      <j1 rule="hyper" parents="131 168 3448"/>
    </justification>
  </clause>

  <clause id="3455">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ (K(x,x \ 1) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(128,a,169,a(flip),b,3448,a)].">
      <j1 rule="hyper" parents="128 169 3448"/>
    </justification>
  </clause>

  <clause id="3456">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ (K(x,x \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      y \ z = u
    ]]></literal>
    <justification jstring="[para(3453(a,1),569(a,1)),flip(a)].">
      <j1 rule="para" parents="3453 569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3457">
    <literal><![CDATA[
      L(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[para(1922(a,2),3453(a,1,3))].">
      <j1 rule="para" parents="1922 3453"/>
    </justification>
  </clause>

  <clause id="3458">
    <literal><![CDATA[
      L(x,y,z * (1 / z)) = x
    ]]></literal>
    <justification jstring="[para(1924(a,1),3453(a,1,3))].">
      <j1 rule="para" parents="1924 3453"/>
    </justification>
  </clause>

  <clause id="3459">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(1926(a,1),3453(a,1,3))].">
      <j1 rule="para" parents="1926 3453"/>
    </justification>
  </clause>

  <clause id="3460">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) / y) = (1 / x) / y
    ]]></literal>
    <justification jstring="[para(3453(a,1),1908(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3453 1908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3461">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = K(x,1 / x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1362,a,3457,a),flip(a)].">
      <j1 rule="hyper" parents="1362 3457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3462">
    <literal><![CDATA[
      K(x,1 / x) * (1 / y) = K(x,1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(220,a,3457,a(flip),b,3280,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="220 3457 3280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3463">
    <literal><![CDATA[
      ((x * (1 / x)) * y) \ z = y \ ((x * (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[hyper(623,a,3458,a),flip(a)].">
      <j1 rule="hyper" parents="623 3458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3464">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * z = K(x \ 1,x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1362,a,3459,a),flip(a)].">
      <j1 rule="hyper" parents="1362 3459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3465">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ (K(x \ 1,x) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(569,a,3459,a),flip(a)].">
      <j1 rule="hyper" parents="569 3459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3466">
    <literal><![CDATA[
      x \ R(x,y \ 1,y) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3157,a(flip),b,3459,a),flip(a)].">
      <j1 rule="hyper" parents="63 3157 3459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3467">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z = K(x \ 1,x) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(220,a,3459,a(flip),b,100,a(flip))].">
      <j1 rule="hyper" parents="220 3459 100"/>
    </justification>
  </clause>

  <clause id="3468">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3459(a,1),50(a,2))].">
      <j1 rule="para" parents="3459 50"/>
    </justification>
  </clause>

  <clause id="3469">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(3459(a,1),2787(a,1,2))].">
      <j1 rule="para" parents="3459 2787"/>
    </justification>
  </clause>

  <clause id="3470">
    <literal><![CDATA[
      ((x \ 1) * y) / T(1 / x,y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(3459(a,1),2941(a,1,2))].">
      <j1 rule="para" parents="3459 2941"/>
    </justification>
  </clause>

  <clause id="3472">
    <literal><![CDATA[
      ((x \ 1) / y) * K(x,x \ 1) = (1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(2747,a,3460,a)].">
      <j1 rule="hyper" parents="2747 3460"/>
    </justification>
  </clause>

  <clause id="3473">
    <literal><![CDATA[
      K(x,x \ 1) * (x / y) = ((x \ 1) \ 1) / y
    ]]></literal>
    <justification jstring="[para(1905(a,1),3454(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1905 3454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3474">
    <literal><![CDATA[
      (x / y) * K(x,x \ 1) = ((x \ 1) \ 1) / y
    ]]></literal>
    <justification jstring="[hyper(2747,a,3473,a)].">
      <j1 rule="hyper" parents="2747 3473"/>
    </justification>
  </clause>

  <clause id="3475">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ z = x \ (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2765(a,1),3455(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2765 3455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3476">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = y \ (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2793(a,1),3455(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2793 3455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3477">
    <literal><![CDATA[
      R(K(x,1 / x),y,z) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(2387,a,3461,a)].">
      <j1 rule="hyper" parents="2387 3461"/>
    </justification>
  </clause>

  <clause id="3478">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = y * (z * K(x,1 / x))
    ]]></literal>
    <justification jstring="[hyper(347,a,2776,a(flip),b,3461,a),flip(a)].">
      <j1 rule="hyper" parents="347 2776 3461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3479">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = (y * z) * K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(347,a,2751,a(flip),b,3461,a),flip(a)].">
      <j1 rule="hyper" parents="347 2751 3461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3480">
    <literal><![CDATA[
      K(x,1 / x) * ((x \ y) * z) = ((1 / (1 / x)) \ y) * z
    ]]></literal>
    <justification jstring="[para(3424(a,1),3461(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3424 3461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3481">
    <literal><![CDATA[
      R(K(x,1 / x),y,z) = ((x \ 1) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(347,a,1921,a,b,3477,a),flip(a)].">
      <j1 rule="hyper" parents="347 1921 3477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3482">
    <literal><![CDATA[
      ((K(x \ 1,x) * (y * z)) * u) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(3464(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3464 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3483">
    <literal><![CDATA[
      K(x \ 1,x) * ((y / (x \ 1)) * z) = (y / (1 / x)) * z
    ]]></literal>
    <justification jstring="[para(2782(a,1),3464(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2782 3464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3484">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ y) * z) = (((x \ 1) \ 1) \ y) * z
    ]]></literal>
    <justification jstring="[para(2868(a,1),3464(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2868 3464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3485">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = x \ (K(y \ 1,y) * z)
    ]]></literal>
    <justification jstring="[para(2752(a,1),3465(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2752 3465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3486">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (K(z \ 1,z) * u) = (x * y) \ u
    ]]></literal>
    <justification jstring="[para(2786(a,1),3465(a,1,1))].">
      <j1 rule="para" parents="2786 3465"/>
    </justification>
  </clause>

  <clause id="3487">
    <literal><![CDATA[
      ((x \ 1) * y) \ (K(x \ 1,x) * z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(2922(a,1),3465(a,1,1))].">
      <j1 rule="para" parents="2922 3465"/>
    </justification>
  </clause>

  <clause id="3488">
    <literal><![CDATA[
      (K(x \ 1,x) * (y * (z * u))) \ (((y * K(x \ 1,x)) * z) * u) = a(y * K(x \ 1,x),z,u)
    ]]></literal>
    <justification jstring="[para(3469(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3469 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3489">
    <literal><![CDATA[
      (K(x \ 1,x) * (y * z)) \ ((y * K(x \ 1,x)) * (z * u)) = L(u,z,y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(3469(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3469 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3490">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (K(z \ 1,z) * (y * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * K(z \ 1,z),x) = u
    ]]></literal>
    <justification jstring="[para(3469(a,1),365(a,1,2))].">
      <j1 rule="para" parents="3469 365"/>
    </justification>
  </clause>

  <clause id="3491">
    <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(3469(a,1),545(a,1,2,2))].">
      <j1 rule="para" parents="3469 545"/>
    </justification>
  </clause>

  <clause id="3492">
    <literal><![CDATA[
      x * K(((y \ 1) * x) \ (K(y \ 1,y) * x),(y \ 1) * x) = ((1 / y) * T((1 / y) \ 1,(y \ 1) * x)) * x
    ]]></literal>
    <justification jstring="[para(3470(a,1),1828(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3470 1828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3494">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ z = K(y,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,2838,a(flip),b,3475,a),flip(a)].">
      <j1 rule="hyper" parents="347 2838 3475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3495">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ u = (x * y) \ (K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(2215(a,1),3475(a,1,1))].">
      <j1 rule="para" parents="2215 3475"/>
    </justification>
  </clause>

  <clause id="3496">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = K(x,x \ 1) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,2838,a(flip),b,3476,a),flip(a)].">
      <j1 rule="hyper" parents="347 2838 3476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3497">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = (y \ z) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,2770,a(flip),b,3476,a),flip(a)].">
      <j1 rule="hyper" parents="347 2770 3476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3498">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ 1 = y \ K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,175,a(flip),b,3476,a),flip(a)].">
      <j1 rule="hyper" parents="347 175 3476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3499">
    <literal><![CDATA[
      L(x,y,y \ 1) \ K(y,y \ 1) = ((y \ 1) * (y * x)) \ 1
    ]]></literal>
    <justification jstring="[para(547(a,1),3498(a,1,1)),flip(a)].">
      <j1 rule="para" parents="547 3498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3500">
    <literal><![CDATA[
      (x * K(y,1 / y)) / z = K(y,1 / y) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(131,a,164,a(flip),b,3479,a)].">
      <j1 rule="hyper" parents="131 164 3479"/>
    </justification>
  </clause>

  <clause id="3501">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,2858,a(flip),b,3485,a),flip(a)].">
      <j1 rule="hyper" parents="347 2858 3485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3503">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (1 / y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(1897(a,1),3485(a,2,2))].">
      <j1 rule="para" parents="1897 3485"/>
    </justification>
  </clause>

  <clause id="3504">
    <literal><![CDATA[
      L(1 / x,y,z) \ (1 / x) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(2704(a,1),3503(a,1,1))].">
      <j1 rule="para" parents="2704 3503"/>
    </justification>
  </clause>

  <clause id="3505">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ y) \ z) = ((1 / x) \ y) \ z
    ]]></literal>
    <justification jstring="[para(2928(a,1),3494(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2928 3494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3506">
    <literal><![CDATA[
      K(x,x \ 1) * ((x * y) \ z) = ((1 / (1 / x)) * y) \ z
    ]]></literal>
    <justification jstring="[para(3427(a,1),3494(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3427 3494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3507">
    <literal><![CDATA[
      x / (K(y,y \ 1) * z) = K(y \ 1,y) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(220,a,217,a(flip),b,3496,a)].">
      <j1 rule="hyper" parents="220 217 3496"/>
    </justification>
  </clause>

  <clause id="3508">
    <literal><![CDATA[
      R(x / (y / K(z,1 / z)),y / K(z,1 / z),K(z,1 / z)) = K(z,1 / z) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,607,a,b,3500,a)].">
      <j1 rule="hyper" parents="63 607 3500"/>
    </justification>
  </clause>

  <clause id="3509">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * x) \ z) = (y * ((x \ 1) \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(2340(a,1),3501(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2340 3501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3510">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = K(x \ 1,x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(2742(a,2),3501(a,1,1))].">
      <j1 rule="para" parents="2742 3501"/>
    </justification>
  </clause>

  <clause id="3511">
    <literal><![CDATA[
      K(x \ 1,x) * (((x \ 1) * y) \ z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(2924(a,1),3501(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2924 3501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3512">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = (y \ z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,2753,a(flip),b,3510,a),flip(a)].">
      <j1 rule="hyper" parents="347 2753 3510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3513">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * z)) \ u = ((x * z) \ u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2836(a,1),3512(a,1,1))].">
      <j1 rule="para" parents="2836 3512"/>
    </justification>
  </clause>

  <clause id="3514">
    <literal><![CDATA[
      (x \ 1) * y != z * ((z \ (x \ 1)) * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,z \ x,z) = y
    ]]></literal>
    <justification jstring="[para(3253(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="3253 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3515">
    <literal><![CDATA[
      (x / (1 / y)) * ((1 / y) * z) = (x / (y \ 1)) * ((y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,2357,a(flip),b,3248,a),flip(a)].">
      <j1 rule="hyper" parents="133 2357 3248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3516">
    <literal><![CDATA[
      R(x,y,y) \ (x * (1 / y)) = L(1 / y,y,x)
    ]]></literal>
    <justification jstring="[para(2261(a,1),3298(a,1,1))].">
      <j1 rule="para" parents="2261 3298"/>
    </justification>
  </clause>

  <clause id="3517">
    <literal><![CDATA[
      (x / (y * y)) * ((y * y) * (L(x,z,u) \ 1)) = L(x / (y * y),z,u) \ (x / (y * y))
    ]]></literal>
    <justification jstring="[hyper(134,a,3323,a(flip),b,1415,a)].">
      <j1 rule="hyper" parents="134 3323 1415"/>
    </justification>
  </clause>

  <clause id="3518">
    <literal><![CDATA[
      L(x,y * (z * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(3330(a,2),3331(a,1))].">
      <j1 rule="para" parents="3330 3331"/>
    </justification>
  </clause>

  <clause id="3519">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(240(a,1),3518(a,1,2))].">
      <j1 rule="para" parents="240 3518"/>
    </justification>
  </clause>

  <clause id="3520">
    <literal><![CDATA[
      L(x,1 / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(245(a,1),3518(a,1,2))].">
      <j1 rule="para" parents="245 3518"/>
    </justification>
  </clause>

  <clause id="3521">
    <literal><![CDATA[
      L(x,y * (1 / z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,u) = w
    ]]></literal>
    <justification jstring="[para(479(a,1),3518(a,1,2))].">
      <j1 rule="para" parents="479 3518"/>
    </justification>
  </clause>

  <clause id="3522">
    <literal><![CDATA[
      L(x,L(y * (z * z),u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,L(y,u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(1390(a,2),3518(a,1,2))].">
      <j1 rule="para" parents="1390 3518"/>
    </justification>
  </clause>

  <clause id="3523">
    <literal><![CDATA[
      L(x,1 / (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3189(a,2),3520(a,1))].">
      <j1 rule="para" parents="3189 3520"/>
    </justification>
  </clause>

  <clause id="3524">
    <literal><![CDATA[
      L(x,y \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3206(a,1),3520(a,1))].">
      <j1 rule="para" parents="3206 3520"/>
    </justification>
  </clause>

  <clause id="3525">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (L(x,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      L((x \ 1) \ u,x,L(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(1298(a,1),3524(a,1))].">
      <j1 rule="para" parents="1298 3524"/>
    </justification>
  </clause>

  <clause id="3526">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3188(a,2),3524(a,1))].">
      <j1 rule="para" parents="3188 3524"/>
    </justification>
  </clause>

  <clause id="3527">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,L(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(3369(a,2),3524(a,1))].">
      <j1 rule="para" parents="3369 3524"/>
    </justification>
  </clause>

  <clause id="3528">
    <literal><![CDATA[
      L(x,y * (z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,u) = w
    ]]></literal>
    <justification jstring="[para(3250(a,1),3521(a,1))].">
      <j1 rule="para" parents="3250 3521"/>
    </justification>
  </clause>

  <clause id="3529">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * L(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(1409(a,1),3528(a,1,2))].">
      <j1 rule="para" parents="1409 3528"/>
    </justification>
  </clause>

  <clause id="3530">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,u) = T(x \ L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(3343(a,1),3353(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3343 3353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3531">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,u) = y \ ((x \ L(x,z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,22,a(flip),b,3530,a),flip(a)].">
      <j1 rule="hyper" parents="347 22 3530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3532">
    <literal><![CDATA[
      T(x \ L(x,y,z),L(x,u,w) \ x) = x \ L(T(x,L(x,u,w) \ x),y,z)
    ]]></literal>
    <justification jstring="[para(3317(a,1),3530(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3317 3530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3533">
    <literal><![CDATA[
      (x \ y) \ L(x \ y,x \ y,x) = (1 / (y \ x)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,1637,a(flip),b,3354,a),flip(a)].">
      <j1 rule="hyper" parents="347 1637 3354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3534">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(134,a,1407,a(flip),b,3354,a)].">
      <j1 rule="hyper" parents="134 1407 3354"/>
    </justification>
  </clause>

  <clause id="3535">
    <literal><![CDATA[
      (1 / x) \ ((y * y) * L((y * y) \ (1 / x),z,u)) = (x * (y * y)) \ L((1 / x) \ (y * y),z,u)
    ]]></literal>
    <justification jstring="[para(458(a,1),3354(a,1,1)),flip(a)].">
      <j1 rule="para" parents="458 3354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3536">
    <literal><![CDATA[
      (x \ y) \ ((z * x) \ (z * y)) = x \ (y * L(y \ x,x,z))
    ]]></literal>
    <justification jstring="[para(99(a,1),3354(a,1,2))].">
      <j1 rule="para" parents="99 3354"/>
    </justification>
  </clause>

  <clause id="3537">
    <literal><![CDATA[
      x * ((x \ L(x,y,z)) * (x \ u)) = (x \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(3359(a,2),3362(a,1,2))].">
      <j1 rule="para" parents="3359 3362"/>
    </justification>
  </clause>

  <clause id="3538">
    <literal><![CDATA[
      L((x \ 1) \ (x \ y),z,u) = (x \ 1) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(128,a,3341,a(flip),b,3380,a),flip(a)].">
      <j1 rule="hyper" parents="128 3341 3380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3539">
    <literal><![CDATA[
      x * L(x \ (y * (x \ 1)),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) * (x \ 1) = w
    ]]></literal>
    <justification jstring="[para(3380(a,1),1017(a,1))].">
      <j1 rule="para" parents="3380 1017"/>
    </justification>
  </clause>

  <clause id="3540">
    <literal><![CDATA[
      x * L(L(x \ 1,y,z),u,w) = x \ L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,166,a,b,3383,a)].">
      <j1 rule="hyper" parents="63 166 3383"/>
    </justification>
  </clause>

  <clause id="3543">
    <literal><![CDATA[
      T(x,y) * (K(x \ 1,x) * z) = T(1 / (1 / x),y) * z
    ]]></literal>
    <justification jstring="[para(2729(a,1),3430(a,2,1))].">
      <j1 rule="para" parents="2729 3430"/>
    </justification>
  </clause>

  <clause id="3544">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ u) = (x \ 1) \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(128,a,1403,a(flip),b,3438,a)].">
      <j1 rule="hyper" parents="128 1403 3438"/>
    </justification>
  </clause>

  <clause id="3545">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) * (x \ u)) = L(x \ 1,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(134,a,3438,a(flip),b,1402,a)].">
      <j1 rule="hyper" parents="134 3438 1402"/>
    </justification>
  </clause>

  <clause id="3546">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,x \ y,x) \ z) = ((x \ y) \ 1) * ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[para(408(a,1),3439(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="408 3439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3547">
    <literal><![CDATA[
      (x \ 1) * ((x \ 1) * (L(x \ 1,y,z) \ u)) = x * (L(x,y,z) \ ((x \ 1) * u))
    ]]></literal>
    <justification jstring="[para(1407(a,1),3439(a,1,2))].">
      <j1 rule="para" parents="1407 3439"/>
    </justification>
  </clause>

  <clause id="3548">
    <literal><![CDATA[
      x * (L(x \ 1,y,z) * (K(x,x \ 1) * u)) = L(x,y,z) * ((1 / x) * u)
    ]]></literal>
    <justification jstring="[para(2931(a,1),3440(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2931 3440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3549">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ 1)) * z) = (1 / x) * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(134,a,3447,a(flip),b,2934,a)].">
      <j1 rule="hyper" parents="134 3447 2934"/>
    </justification>
  </clause>

  <clause id="3550">
    <literal><![CDATA[
      (((x \ 1) * y) * z) * K(x,x \ 1) = ((1 / x) * y) * z
    ]]></literal>
    <justification jstring="[hyper(2747,a,3449,a)].">
      <j1 rule="hyper" parents="2747 3449"/>
    </justification>
  </clause>

  <clause id="3551">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,u) != w \ v5
    ]]></literal>
    <literal><![CDATA[
      w * T(x \ L(x,z,u),y) = v5
    ]]></literal>
    <justification jstring="[para(3531(a,2),711(a,1))].">
      <j1 rule="para" parents="3531 711"/>
    </justification>
  </clause>

  <clause id="3552">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * u) = x * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),3537(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 3537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3553">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * T(x,u)) = x * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(256(a,1),3537(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="256 3537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3554">
    <literal><![CDATA[
      T(x \ 1,y) * (K((x \ 1) \ 1,x \ 1) * z) = T(1 / x,y) * z
    ]]></literal>
    <justification jstring="[para(80(a,1),3543(a,2,1,1,2))].">
      <j1 rule="para" parents="80 3543"/>
    </justification>
  </clause>

  <clause id="3555">
    <literal><![CDATA[
      ((1 / x) \ 1) \ (L(1 / x,y,z) \ u) = L(x,y,z) \ ((1 / x) \ u)
    ]]></literal>
    <justification jstring="[para(83(a,1),3544(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="83 3544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3556">
    <literal><![CDATA[
      L(x \ 1,y,z) * (x * u) = (x \ 1) * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),3545(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 3545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3557">
    <literal><![CDATA[
      L(x \ 1,y,z) * x = (x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(188(a,1),3545(a,1,2)),flip(a)].">
      <j1 rule="para" parents="188 3545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3558">
    <literal><![CDATA[
      (x * T(y,y \ 1)) * z != x * (T(y,y \ 1) * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(3237(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="3237 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3559">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ u)) * z) = x * (y * ((z \ (y \ (x \ u))) * z))
    ]]></literal>
    <justification jstring="[hyper(134,a,3304,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 3304 18"/>
    </justification>
  </clause>

  <clause id="3560">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,3305,a(flip),b,289,a),flip(a)].">
      <j1 rule="hyper" parents="128 3305 289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3561">
    <literal><![CDATA[
      L(x,R(y,z,z) / z,u) = L(x,y * (1 / ((w * w) * z)),u)
    ]]></literal>
    <justification jstring="[para(702(a,1),3333(a,2,2,2))].">
      <j1 rule="para" parents="702 3333"/>
    </justification>
  </clause>

  <clause id="3562">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1147(a,1),3404(a,1,1))].">
      <j1 rule="para" parents="1147 3404"/>
    </justification>
  </clause>

  <clause id="3563">
    <literal><![CDATA[
      K(1 / (1 / x),y) * x = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,3562,a(flip),b,964,a(flip))].">
      <j1 rule="hyper" parents="133 3562 964"/>
    </justification>
  </clause>

  <clause id="3564">
    <literal><![CDATA[
      T(K(1 / (1 / x),y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(269,a,3563,a,b,xx)].">
      <j1 rule="hyper" parents="269 3563"/>
    </justification>
  </clause>

  <clause id="3565">
    <literal><![CDATA[
      T(K(1 / (x \ 1),y),T(x,x \ 1)) = K(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(296(a,1),3564(a,1,1,1,2))].">
      <j1 rule="para" parents="296 3564"/>
    </justification>
  </clause>

  <clause id="3566">
    <literal><![CDATA[
      T(K(x,y),T(x,x \ 1)) = K(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(80(a,1),3565(a,1,1,1))].">
      <j1 rule="para" parents="80 3565"/>
    </justification>
  </clause>

  <clause id="3567">
    <literal><![CDATA[
      K(T(x,x \ 1),y) = T(K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2970,a(flip),b,3566,a),flip(a)].">
      <j1 rule="hyper" parents="63 2970 3566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3568">
    <literal><![CDATA[
      T(K(x,y),x) = K((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[para(112(a,1),3567(a,1,1)),flip(a)].">
      <j1 rule="para" parents="112 3567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3569">
    <literal><![CDATA[
      T(K(x,y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3407,a(flip),b,3568,a),flip(a)].">
      <j1 rule="hyper" parents="347 3407 3568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3571">
    <literal><![CDATA[
      T(x,K(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,3569,a)].">
      <j1 rule="hyper" parents="54 3569"/>
    </justification>
  </clause>

  <clause id="3572">
    <literal><![CDATA[
      T(K(x,y),z) * x = x * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3569(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3569 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3573">
    <literal><![CDATA[
      R(K(x,y),z,u) * x = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3569(a,1),268(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3569 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3574">
    <literal><![CDATA[
      T((x \ y) \ y,K((x \ y) \ y,z)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,112,a,b,3571,a),flip(a)].">
      <j1 rule="hyper" parents="347 112 3571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3575">
    <literal><![CDATA[
      T(T(x,y),K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3571(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3571 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3576">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3571(a,1),315(a,1,2))].">
      <j1 rule="para" parents="3571 315"/>
    </justification>
  </clause>

  <clause id="3577">
    <literal><![CDATA[
      T(x,y) * K(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3571(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3571 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3578">
    <literal><![CDATA[
      T(T(T(x,y),z),K(x,u)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(3571(a,1),115(a,2,1,1))].">
      <j1 rule="para" parents="3571 115"/>
    </justification>
  </clause>

  <clause id="3579">
    <literal><![CDATA[
      L(x,y,z) * K(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3571(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3571 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3580">
    <literal><![CDATA[
      T((x * y) / x,K(y,z)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(3571(a,1),504(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3571 504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3581">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * (y * K(y,z))) = L(y,K(y,z),x)
    ]]></literal>
    <justification jstring="[para(3571(a,1),263(a,2,1))].">
      <j1 rule="para" parents="3571 263"/>
    </justification>
  </clause>

  <clause id="3582">
    <literal><![CDATA[
      K(x,y) * T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3571(a,1),435(a,1,2,1))].">
      <j1 rule="para" parents="3571 435"/>
    </justification>
  </clause>

  <clause id="3583">
    <literal><![CDATA[
      T(K(x,y),T(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,3575,a)].">
      <j1 rule="hyper" parents="54 3575"/>
    </justification>
  </clause>

  <clause id="3587">
    <literal><![CDATA[
      T(x,T(K(x,y),z)) = x
    ]]></literal>
    <justification jstring="[hyper(270,a,3572,a)].">
      <j1 rule="hyper" parents="270 3572"/>
    </justification>
  </clause>

  <clause id="3589">
    <literal><![CDATA[
      T(K(x,y),(z * x) / z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,3580,a)].">
      <j1 rule="hyper" parents="54 3580"/>
    </justification>
  </clause>

  <clause id="3590">
    <literal><![CDATA[
      T(K(x \ y,z),y / x) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),3589(a,1,2,1))].">
      <j1 rule="para" parents="10 3589"/>
    </justification>
  </clause>

  <clause id="3591">
    <literal><![CDATA[
      T(x / y,K(y \ x,z)) = x / y
    ]]></literal>
    <justification jstring="[hyper(54,a,3590,a)].">
      <j1 rule="hyper" parents="54 3590"/>
    </justification>
  </clause>

  <clause id="3592">
    <literal><![CDATA[
      (x * y) * R(K(x * y,z),y,T(x,y)) = (K(x * y,z) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(927,a,3573,a),flip(a)].">
      <j1 rule="hyper" parents="927 3573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3593">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(127,a,3573,a,b,91,a),flip(a)].">
      <j1 rule="hyper" parents="127 3573 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3594">
    <literal><![CDATA[
      L(x,R(y,z,z) / z,u) = L(x,y * ((w * w) * z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,3190,a(flip),b,3561,a),flip(a)].">
      <j1 rule="hyper" parents="347 3190 3561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3595">
    <literal><![CDATA[
      L(x,y * ((z * z) * u),w) = L(x,y * (1 / u),w)
    ]]></literal>
    <justification jstring="[para(2264(a,1),3594(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2264 3594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3596">
    <literal><![CDATA[
      L(x,y * ((z * z) * u),w) = L(x,y * u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,3190,a(flip),b,3595,a),flip(a)].">
      <j1 rule="hyper" parents="347 3190 3595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3597">
    <literal><![CDATA[
      L(x,y * ((z * z) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * u,w) = v5
    ]]></literal>
    <justification jstring="[para(3595(a,2),3521(a,1))].">
      <j1 rule="para" parents="3595 3521"/>
    </justification>
  </clause>

  <clause id="3598">
    <literal><![CDATA[
      L(x,y * ((z * z) \ u),w) = L(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),3596(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 3596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3599">
    <literal><![CDATA[
      L(x,(y \ 1) * z,u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(302(a,1),3596(a,1,2)),flip(a)].">
      <j1 rule="para" parents="302 3596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3600">
    <literal><![CDATA[
      L(x,y * ((z \ 1) \ u),w) = L(x,y * (z \ u),w)
    ]]></literal>
    <justification jstring="[para(495(a,1),3596(a,1,2,2))].">
      <j1 rule="para" parents="495 3596"/>
    </justification>
  </clause>

  <clause id="3601">
    <literal><![CDATA[
      L(x,(1 / y) * z,u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(83(a,1),3599(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 3599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3602">
    <literal><![CDATA[
      L(x,y * ((z * z) * u),w) = L(x,(1 / y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,3596,a,b,3601,a)].">
      <j1 rule="hyper" parents="347 3596 3601"/>
    </justification>
  </clause>

  <clause id="3603">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),w) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(3162(a,1),3601(a,1,2))].">
      <j1 rule="para" parents="3162 3601"/>
    </justification>
  </clause>

  <clause id="3604">
    <literal><![CDATA[
      L(x,(y * y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),3598(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 3598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3605">
    <literal><![CDATA[
      L(x,(y \ (z \ 1)) * u,w) = L(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(831(a,1),3598(a,1,2))].">
      <j1 rule="para" parents="831 3598"/>
    </justification>
  </clause>

  <clause id="3606">
    <literal><![CDATA[
      L(L(x,y,z * z),y,u) = L(x,y,u * (z * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,1804,a(flip),b,3604,a),flip(a)].">
      <j1 rule="hyper" parents="63 1804 3604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3607">
    <literal><![CDATA[
      L(x,(y * y) \ z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),3604(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 3604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3608">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(495(a,1),3604(a,1,2))].">
      <j1 rule="para" parents="495 3604"/>
    </justification>
  </clause>

  <clause id="3609">
    <literal><![CDATA[
      L(x,y * (y * z),u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(97(a,1),3604(a,1,2))].">
      <j1 rule="para" parents="97 3604"/>
    </justification>
  </clause>

  <clause id="3610">
    <literal><![CDATA[
      L(x,(y \ (z * z)) \ u,w) = L(x,(y \ 1) \ u,w)
    ]]></literal>
    <justification jstring="[para(778(a,1),3604(a,1,2)),flip(a)].">
      <j1 rule="para" parents="778 3604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3611">
    <literal><![CDATA[
      L(x,(y * z) * (z \ y),u) = L(x,a(y,z,z \ y),u)
    ]]></literal>
    <justification jstring="[para(834(a,1),3604(a,1,2))].">
      <j1 rule="para" parents="834 3604"/>
    </justification>
  </clause>

  <clause id="3612">
    <literal><![CDATA[
      L(x,(y * y) \ (z \ u),w) = L(x,z \ (u \ 1),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,3230,a,b,3607,a),flip(a)].">
      <j1 rule="hyper" parents="347 3230 3607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3613">
    <literal><![CDATA[
      L(x,L(y \ z,y,y),u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(99(a,2),3607(a,1,2))].">
      <j1 rule="para" parents="99 3607"/>
    </justification>
  </clause>

  <clause id="3615">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),y * L(y,z,u),x) = x / ((y \ L(y,z,u)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,3603,a(flip),b,2007,a(flip))].">
      <j1 rule="hyper" parents="134 3603 2007"/>
    </justification>
  </clause>

  <clause id="3616">
    <literal><![CDATA[
      L(x,(y \ (z * z)) \ u,w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,3608,a(flip),b,3610,a),flip(a)].">
      <j1 rule="hyper" parents="347 3608 3610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3617">
    <literal><![CDATA[
      L(x,y * ((z \ 1) \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * (z \ u),w) = v5
    ]]></literal>
    <justification jstring="[para(495(a,1),3597(a,1,2,2))].">
      <j1 rule="para" parents="495 3597"/>
    </justification>
  </clause>

  <clause id="3618">
    <literal><![CDATA[
      L(x,(1 / y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,u) = w
    ]]></literal>
    <justification jstring="[para(3602(a,1),3597(a,1))].">
      <j1 rule="para" parents="3602 3597"/>
    </justification>
  </clause>

  <clause id="3619">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * L(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(3162(a,1),3618(a,1,2))].">
      <j1 rule="para" parents="3162 3618"/>
    </justification>
  </clause>

  <clause id="3620">
    <literal><![CDATA[
      L(x,(y \ (y / z)) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z * L(z,z,y),u) = w
    ]]></literal>
    <justification jstring="[para(3350(a,1),3619(a,1,2))].">
      <j1 rule="para" parents="3350 3619"/>
    </justification>
  </clause>

  <clause id="3621">
    <literal><![CDATA[
      R(x,y,z \ (z / (u \ 1))) = R(x,y,(z * u) \ z)
    ]]></literal>
    <justification jstring="[para(83(a,1),3283(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="83 3283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3623">
    <literal><![CDATA[
      L((x \ (1 / x)) * y,z,u) = (x \ (1 / x)) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(307(a,1),3321(a,1,1,1))].">
      <j1 rule="para" parents="307 3321"/>
    </justification>
  </clause>

  <clause id="3624">
    <literal><![CDATA[
      L(x * (y \ (1 / y)),z,u) = L(x,z,u) * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(34,a,3374,a(flip),b,3623,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 3374 3623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3625">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * y = (x * y) * (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(3343(a,1),3363(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3343 3363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3626">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = (T(y,x \ 1) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(2962(a,1),3406(a,2,1,1))].">
      <j1 rule="para" parents="2962 3406"/>
    </justification>
  </clause>

  <clause id="3627">
    <literal><![CDATA[
      ((x \ (x / y)) * z) * K(y,y \ 1) = (1 / (1 / (x \ (x / y)))) * z
    ]]></literal>
    <justification jstring="[para(2588(a,1),3436(a,1,2))].">
      <j1 rule="para" parents="2588 3436"/>
    </justification>
  </clause>

  <clause id="3628">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * z,y \ 1,y) = y * ((1 / y) * ((x \ y) * z))
    ]]></literal>
    <justification jstring="[hyper(134,a,3549,a(flip),b,455,a),flip(a)].">
      <j1 rule="hyper" parents="134 3549 455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3629">
    <literal><![CDATA[
      L(x,y,z) \ (x * ((x \ L(x,y,z)) * u)) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(3552(a,1),3166(a,1,2))].">
      <j1 rule="para" parents="3552 3166"/>
    </justification>
  </clause>

  <clause id="3630">
    <literal><![CDATA[
      T(x \ 1,y) * (K(x,x \ 1) * z) = T(1 / x,y) * z
    ]]></literal>
    <justification jstring="[para(1960(a,1),3554(a,1,2,1))].">
      <j1 rule="para" parents="1960 3554"/>
    </justification>
  </clause>

  <clause id="3631">
    <literal><![CDATA[
      T(x \ 1,y) * (T(x \ 1,(x \ 1) \ 1) \ z) = T(1 / x,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2870(a,1),3554(a,1,2))].">
      <j1 rule="para" parents="2870 3554"/>
    </justification>
  </clause>

  <clause id="3632">
    <literal><![CDATA[
      K(x,x \ 1) * (T(1 / x,y) \ z) = T(x \ 1,y) \ z
    ]]></literal>
    <justification jstring="[hyper(128,a,10,a(flip),b,3630,a),flip(a)].">
      <j1 rule="hyper" parents="128 10 3630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3633">
    <literal><![CDATA[
      T(1 / x,y) * ((1 / x) \ z) = T(x \ 1,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2958(a,1),3630(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2958 3630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3634">
    <literal><![CDATA[
      (T(x \ 1,y) \ z) * K(x \ 1,x) = T(1 / x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(2800,a,3632,a)].">
      <j1 rule="hyper" parents="2800 3632"/>
    </justification>
  </clause>

  <clause id="3635">
    <literal><![CDATA[
      (1 / x) * (T(x \ 1,y) * ((x \ 1) \ z)) = T(1 / x,y) * z
    ]]></literal>
    <justification jstring="[hyper(134,a,3633,a(flip),b,1220,a)].">
      <j1 rule="hyper" parents="134 3633 1220"/>
    </justification>
  </clause>

  <clause id="3636">
    <literal><![CDATA[
      L(x,y,z) \ ((1 / x) \ u) = x \ (L(1 / x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(395,a,3555,a),flip(a)].">
      <j1 rule="hyper" parents="395 3555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3637">
    <literal><![CDATA[
      x \ (L(1 / x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(83(a,1),3636(a,1,2)),flip(a)].">
      <j1 rule="para" parents="83 3636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3638">
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 = x * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(150,a,3637,a),flip(a)].">
      <j1 rule="hyper" parents="150 3637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3639">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (L(x * L(x,y,z),u,w) \ (x * L(x,y,z))) = L(1 / (x \ L(x,y,z)),u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(134,a,2698,a(flip),b,3637,a)].">
      <j1 rule="hyper" parents="134 2698 3637"/>
    </justification>
  </clause>

  <clause id="3640">
    <literal><![CDATA[
      x * (L(x,y,z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 = u
    ]]></literal>
    <justification jstring="[para(3637(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3637 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3641">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) \ u != w \ v5
    ]]></literal>
    <literal><![CDATA[
      w * ((L(1 / x,y,z) \ 1) \ u) = v5
    ]]></literal>
    <justification jstring="[para(3637(a,1),715(a,1,1,2))].">
      <j1 rule="para" parents="3637 715"/>
    </justification>
  </clause>

  <clause id="3642">
    <literal><![CDATA[
      L(x,x,y) \ x = x \ ((y \ (y / x)) \ 1)
    ]]></literal>
    <justification jstring="[para(3264(a,1),3637(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3264 3637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3643">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,x \ L(1 / x,y,z),x) != w
    ]]></literal>
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) \ (x * u) = w
    ]]></literal>
    <justification jstring="[para(3637(a,1),3254(a,1,1,1))].">
      <j1 rule="para" parents="3637 3254"/>
    </justification>
  </clause>

  <clause id="3644">
    <literal><![CDATA[
      (x \ (x / y)) \ 1 = y * (L(y,y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(134,a,3642,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="134 3642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3645">
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 = (L(x,y,z) \ x) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,3318,a,b,3638,a),flip(a)].">
      <j1 rule="hyper" parents="347 3318 3638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3646">
    <literal><![CDATA[
      1 / (x * (L(x,y,z) \ x)) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(222,a,3638,a)].">
      <j1 rule="hyper" parents="222 3638"/>
    </justification>
  </clause>

  <clause id="3647">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (L(1 / x,y,z) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(128,a,3638,a,b,3318,a)].">
      <j1 rule="hyper" parents="128 3638 3318"/>
    </justification>
  </clause>

  <clause id="3648">
    <literal><![CDATA[
      1 / (x * (L(x,y,z) \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      L(1 / x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3638(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3638 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3649">
    <literal><![CDATA[
      x \ (L(1 / x,y,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(3638(a,2),356(a,1,2))].">
      <j1 rule="para" parents="3638 356"/>
    </justification>
  </clause>

  <clause id="3650">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (1 / (1 / (x \ (x / (y \ 1))))) * z
    ]]></literal>
    <justification jstring="[para(1926(a,1),3627(a,1,2))].">
      <j1 rule="para" parents="1926 3627"/>
    </justification>
  </clause>

  <clause id="3651">
    <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(1429,a,3629,a)].">
      <j1 rule="hyper" parents="1429 3629"/>
    </justification>
  </clause>

  <clause id="3652">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),y) = L(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(875,a,3629,a)].">
      <j1 rule="hyper" parents="875 3629"/>
    </justification>
  </clause>

  <clause id="3653">
    <literal><![CDATA[
      L(x,y * L(y,z,u),y) = L(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(3619,a,3652,a)].">
      <j1 rule="hyper" parents="3619 3652"/>
    </justification>
  </clause>

  <clause id="3654">
    <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),3651(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 3651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3655">
    <literal><![CDATA[
      L(x * y,x,x \ L(x,z,u)) = x * L(y,x,x \ L(x,z,u))
    ]]></literal>
    <justification jstring="[para(3166(a,1),3651(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3166 3651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3656">
    <literal><![CDATA[
      L(x / y,y,y \ L(y,z,u)) = L(x,y,y \ L(y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(34,a,3159,a(flip),b,3655,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 3159 3655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3658">
    <literal><![CDATA[
      (K(x \ 1,x) * ((y * z) * u)) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(3464(a,1),3482(a,1,1))].">
      <j1 rule="para" parents="3464 3482"/>
    </justification>
  </clause>

  <clause id="3659">
    <literal><![CDATA[
      L(x \ y,x \ y,x) \ (x \ y) = ((x \ y) \ 1) * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1422,a,3546,a)].">
      <j1 rule="hyper" parents="1422 3546"/>
    </justification>
  </clause>

  <clause id="3660">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((y \ x) \ (x \ y)) = (x \ (x / (x \ y))) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,3644,a,b,3546,a),flip(a)].">
      <j1 rule="hyper" parents="63 3644 3546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3661">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((y \ x) \ (x \ y)) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(3399,a,3660,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3399 3660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3662">
    <literal><![CDATA[
      (x * y) * R(K(x * y,z),y,T(x,y)) = (K(y * T(x,y),z) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(111(a,2),3592(a,2,1,1,1))].">
      <j1 rule="para" parents="111 3592"/>
    </justification>
  </clause>

  <clause id="3663">
    <literal><![CDATA[
      K(x \ 1,x) * (((y * z) * u) / (z * u)) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3467,a(flip),b,3658,a)].">
      <j1 rule="hyper" parents="63 3467 3658"/>
    </justification>
  </clause>

  <clause id="3664">
    <literal><![CDATA[
      R(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(20(a,2),3663(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 3663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3665">
    <literal><![CDATA[
      R(K(x \ 1,x) * y,x,x) = (y * (x \ 1)) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,2903,a(flip),b,3664,a),flip(a)].">
      <j1 rule="hyper" parents="347 2903 3664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3666">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) = R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(134,a,3664,a,b,2794,a)].">
      <j1 rule="hyper" parents="134 3664 2794"/>
    </justification>
  </clause>

  <clause id="3667">
    <literal><![CDATA[
      R(x * y,z,u) / y = y \ R(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(128,a,3666,a(flip),b,2805,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 3666 2805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3668">
    <literal><![CDATA[
      K(x,x \ 1) * R(x \ 1,y,z) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1897(a,1),3666(a,1,2,1))].">
      <j1 rule="para" parents="1897 3666"/>
    </justification>
  </clause>

  <clause id="3669">
    <literal><![CDATA[
      (x \ R(x * y,z,u)) * x = R(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(148,a,3667,a)].">
      <j1 rule="hyper" parents="148 3667"/>
    </justification>
  </clause>

  <clause id="3670">
    <literal><![CDATA[
      (x \ y) \ R((x \ y) * x,z,u) = R(y,z,u) / (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3667(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3671">
    <literal><![CDATA[
      x \ R(x * (y / x),z,u) = R(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),3667(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 3667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3672">
    <literal><![CDATA[
      x \ R(x * y,x,x) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) * (1 / x) = z
    ]]></literal>
    <justification jstring="[para(3667(a,1),2274(a,1))].">
      <j1 rule="para" parents="3667 2274"/>
    </justification>
  </clause>

  <clause id="3673">
    <literal><![CDATA[
      R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),3669(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 3669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3674">
    <literal><![CDATA[
      R(x * (y / x),z,u) = x * (R(y,z,u) / x)
    ]]></literal>
    <justification jstring="[hyper(150,a,3671,a),flip(a)].">
      <j1 rule="hyper" parents="150 3671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3675">
    <literal><![CDATA[
      R(x,y,z) / x = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(192(a,1),3671(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="192 3671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3678">
    <literal><![CDATA[
      (x \ R(x,y,z)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(148,a,3675,a)].">
      <j1 rule="hyper" parents="148 3675"/>
    </justification>
  </clause>

  <clause id="3679">
    <literal><![CDATA[
      x * (R(x,y,z) / x) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,3675,a,b,xx)].">
      <j1 rule="hyper" parents="134 3675"/>
    </justification>
  </clause>

  <clause id="3680">
    <literal><![CDATA[
      R(x,y,z) \ (R(x,y,z) / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,3675,a,b,1463,a)].">
      <j1 rule="hyper" parents="128 3675 1463"/>
    </justification>
  </clause>

  <clause id="3681">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1291,a,b,3675,a)].">
      <j1 rule="hyper" parents="63 1291 3675"/>
    </justification>
  </clause>

  <clause id="3682">
    <literal><![CDATA[
      (x \ 1) \ R(x \ 1,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1292,a(flip),b,3675,a),flip(a)].">
      <j1 rule="hyper" parents="63 1292 3675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3683">
    <literal><![CDATA[
      T(x,x \ R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,296,a,b,3675,a)].">
      <j1 rule="hyper" parents="36 296 3675"/>
    </justification>
  </clause>

  <clause id="3684">
    <literal><![CDATA[
      (x \ R(x,y,z)) / R(x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(131,a,3675,a(flip),b,1291,a)].">
      <j1 rule="hyper" parents="131 3675 1291"/>
    </justification>
  </clause>

  <clause id="3685">
    <literal><![CDATA[
      T(x \ R(x,y,z),x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3675(a,1),113(a,1,1))].">
      <j1 rule="para" parents="3675 113"/>
    </justification>
  </clause>

  <clause id="3686">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,u) = (R(x,y,z) * u) / (x * u)
    ]]></literal>
    <justification jstring="[para(3675(a,1),108(a,1,1))].">
      <j1 rule="para" parents="3675 108"/>
    </justification>
  </clause>

  <clause id="3687">
    <literal><![CDATA[
      R(T(x \ R(x,y,z),x * u),x,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x * u) \ (R(x,y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(3675(a,1),1035(a,1,1,1))].">
      <j1 rule="para" parents="3675 1035"/>
    </justification>
  </clause>

  <clause id="3688">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(3675(a,1),610(a,1,1))].">
      <j1 rule="para" parents="3675 610"/>
    </justification>
  </clause>

  <clause id="3689">
    <literal><![CDATA[
      R(x,y,z) / x != u
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3683(a,1),345(a,1,2))].">
      <j1 rule="para" parents="3683 345"/>
    </justification>
  </clause>

  <clause id="3690">
    <literal><![CDATA[
      R(x,y,z) / (x * x) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ R(x,y,z)) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(3678(a,1),802(a,1,1))].">
      <j1 rule="para" parents="3678 802"/>
    </justification>
  </clause>

  <clause id="3691">
    <literal><![CDATA[
      L(x,y,y \ R(y,z,u)) * ((y \ R(y,z,u)) * y) = (y \ R(y,z,u)) * (y * T(x,R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(3678(a,1),734(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3678 734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3692">
    <literal><![CDATA[
      R(R(x,y,z),u,w) / x = x \ R(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3679(a,1),3671(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3679 3671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3693">
    <literal><![CDATA[
      x * T(x \ 1,R(x,y,z)) = K(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(3680(a,1),1320(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3680 1320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3695">
    <literal><![CDATA[
      (x \ 1) \ R(x \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * R(x \ 1,y,z) = u
    ]]></literal>
    <justification jstring="[para(3681(a,1),370(a,1))].">
      <j1 rule="para" parents="3681 370"/>
    </justification>
  </clause>

  <clause id="3696">
    <literal><![CDATA[
      (x \ (1 / x)) * R(x,y,z) = x \ (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(3681(a,1),885(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3681 885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3697">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(x \ 1,x) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3681(a,1),2919(a,1,1))].">
      <j1 rule="para" parents="3681 2919"/>
    </justification>
  </clause>

  <clause id="3698">
    <literal><![CDATA[
      (R(x,y,z) \ x) * R(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(229,a,3673,a),flip(a)].">
      <j1 rule="hyper" parents="229 3673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3699">
    <literal><![CDATA[
      R((x \ (y / z)) * x,z,z \ 1) = (x \ (y * (z \ 1))) * x
    ]]></literal>
    <justification jstring="[para(691(a,1),3673(a,2,1,2))].">
      <j1 rule="para" parents="691 3673"/>
    </justification>
  </clause>

  <clause id="3700">
    <literal><![CDATA[
      R((x \ (1 / y)) * x,y,x) * (y * x) = x * ((y * x) * T((y * x) \ 1,x))
    ]]></literal>
    <justification jstring="[para(3673(a,2),1491(a,1,1))].">
      <j1 rule="para" parents="3673 1491"/>
    </justification>
  </clause>

  <clause id="3701">
    <literal><![CDATA[
      R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(2275(a,1),3673(a,2,1,2))].">
      <j1 rule="para" parents="2275 3673"/>
    </justification>
  </clause>

  <clause id="3702">
    <literal><![CDATA[
      x / R(x,y,z) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(145,a,3698,a)].">
      <j1 rule="hyper" parents="145 3698"/>
    </justification>
  </clause>

  <clause id="3703">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,3698,a)].">
      <j1 rule="hyper" parents="138 3698"/>
    </justification>
  </clause>

  <clause id="3704">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(1718,a,3702,a)].">
      <j1 rule="hyper" parents="1718 3702"/>
    </justification>
  </clause>

  <clause id="3705">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ (x \ 1) = R(x,y,z) / (x * x)
    ]]></literal>
    <justification jstring="[para(3702(a,1),821(a,1,1))].">
      <j1 rule="para" parents="3702 821"/>
    </justification>
  </clause>

  <clause id="3706">
    <literal><![CDATA[
      (x / R(x,y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      (R(x,y,z) \ x) * u = w
    ]]></literal>
    <justification jstring="[para(3703(a,1),370(a,1,1,2))].">
      <j1 rule="para" parents="3703 370"/>
    </justification>
  </clause>

  <clause id="3707">
    <literal><![CDATA[
      T(1 / R(x,y,z),x) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(269,a,3704,a,b,1755,a)].">
      <j1 rule="hyper" parents="269 3704 1755"/>
    </justification>
  </clause>

  <clause id="3708">
    <literal><![CDATA[
      ((x \ y) \ 1) \ R((x \ y) \ 1,z,u) = x \ (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,1668,a(flip),b,3682,a),flip(a)].">
      <j1 rule="hyper" parents="347 1668 3682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3709">
    <literal><![CDATA[
      R(x,y,z \ R(z \ 1,u,w)) = R(x,y,z * R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(3682(a,1),2241(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3682 2241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3710">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = (K(x \ 1,R(x,y,z)) * y) * z
    ]]></literal>
    <justification jstring="[para(3693(a,1),2647(a,2,1,1))].">
      <j1 rule="para" parents="3693 2647"/>
    </justification>
  </clause>

  <clause id="3711">
    <literal><![CDATA[
      ((x \ 1) / x) * R(x,y,z) = x \ (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(888(a,2),3696(a,1,1))].">
      <j1 rule="para" parents="888 3696"/>
    </justification>
  </clause>

  <clause id="3712">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ (x \ 1) = x \ (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,1777,a(flip),b,3705,a),flip(a)].">
      <j1 rule="hyper" parents="347 1777 3705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3713">
    <literal><![CDATA[
      (x \ (x \ R(x,y,z))) * x = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,3711,a(flip),b,1708,a)].">
      <j1 rule="hyper" parents="133 3711 1708"/>
    </justification>
  </clause>

  <clause id="3714">
    <literal><![CDATA[
      T(x \ (x \ R(x,y,z)),x) = (x * x) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(269,a,3713,a,b,497,a)].">
      <j1 rule="hyper" parents="269 3713 497"/>
    </justification>
  </clause>

  <clause id="3715">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,1466,a,b,3697,a)].">
      <j1 rule="hyper" parents="34 1466 3697"/>
    </justification>
  </clause>

  <clause id="3716">
    <literal><![CDATA[
      L(x,y,K(z \ 1,R(z,u,w))) = x
    ]]></literal>
    <justification jstring="[para(3715(a,2),3459(a,1,3))].">
      <j1 rule="para" parents="3715 3459"/>
    </justification>
  </clause>

  <clause id="3718">
    <literal><![CDATA[
      (K(x \ 1,R(x,y,z)) * u) * w = K(x \ 1,R(x,y,z)) * (u * w)
    ]]></literal>
    <justification jstring="[hyper(1362,a,3716,a),flip(a)].">
      <j1 rule="hyper" parents="1362 3716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3719">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (x \ 1) = x \ (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(3690,a,1777,a)].">
      <j1 rule="hyper" parents="3690 1777"/>
    </justification>
  </clause>

  <clause id="3720">
    <literal><![CDATA[
      (x \ R(x,x,y)) \ ((x \ y) / y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,2376,a(flip),b,3719,a)].">
      <j1 rule="hyper" parents="128 2376 3719"/>
    </justification>
  </clause>

  <clause id="3721">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = ((x \ (y / z)) * x) * z
    ]]></literal>
    <justification jstring="[hyper(131,a,3699,a(flip),b,585,a)].">
      <j1 rule="hyper" parents="131 3699 585"/>
    </justification>
  </clause>

  <clause id="3722">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(131,a,3701,a(flip),b,2270,a),flip(a)].">
      <j1 rule="hyper" parents="131 3701 2270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3723">
    <literal><![CDATA[
      T((R(x \ R(x,y,z),x,y * z) \ 1) \ 1,x * (y * z)) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(3688(a,2),2731(a,1,1,1,1))].">
      <j1 rule="para" parents="3688 2731"/>
    </justification>
  </clause>

  <clause id="3724">
    <literal><![CDATA[
      R(x,y,L((z \ 1) \ ((z \ u) / u),z \ 1,z \ 1)) = R(x,y,z * R(z \ 1,z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2413,a,b,3709,a)].">
      <j1 rule="hyper" parents="63 2413 3709"/>
    </justification>
  </clause>

  <clause id="3725">
    <literal><![CDATA[
      x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(63,a,1492,a(flip),b,3722,a)].">
      <j1 rule="hyper" parents="63 1492 3722"/>
    </justification>
  </clause>

  <clause id="3726">
    <literal><![CDATA[
      R(x,y,L(y,z,u)) * (y \ L(y,z,u)) = (x * (1 / y)) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(2247(a,1),3170(a,1,1))].">
      <j1 rule="para" parents="2247 3170"/>
    </justification>
  </clause>

  <clause id="3727">
    <literal><![CDATA[
      R(x,y,(z \ L(z,z,u)) \ w) = R(x,y,(z * ((u \ (u / z)) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(3348(a,2),3273(a,2,3,1)),flip(a)].">
      <j1 rule="para" parents="3348 3273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3728">
    <literal><![CDATA[
      (x * x) \ ((x \ L(x,y,z)) \ u) = (x * L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(240(a,1),3361(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="240 3361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3729">
    <literal><![CDATA[
      (x * x) * ((x * L(x,y,z)) \ u) = (x \ L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(150,a,3728,a)].">
      <j1 rule="hyper" parents="150 3728"/>
    </justification>
  </clause>

  <clause id="3730">
    <literal><![CDATA[
      R(x,y,(z \ L(z,u,w)) \ v5) = R(x,y,(z * L(z,u,w)) \ v5)
    ]]></literal>
    <justification jstring="[para(3728(a,1),2238(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3728 2238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3731">
    <literal><![CDATA[
      x * K(y \ (1 / (1 / x)),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,3446,a(flip),b,3428,a),flip(a)].">
      <j1 rule="hyper" parents="63 3446 3428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3732">
    <literal><![CDATA[
      x \ L(T(x,L(x,y,z) \ x),y,z) = ((x \ L(x,y,z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,2579,a(flip),b,3532,a),flip(a)].">
      <j1 rule="hyper" parents="63 2579 3532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3733">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ 1) \ 1 = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3317(a,1),3732(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3317 3732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3734">
    <literal><![CDATA[
      1 / (x \ L(x,y,z)) = (x \ L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(222,a,3733,a)].">
      <j1 rule="hyper" parents="222 3733"/>
    </justification>
  </clause>

  <clause id="3735">
    <literal><![CDATA[
      T((x * y) \ (R(x,z,u) * y),x) != w
    ]]></literal>
    <literal><![CDATA[
      (x * y) \ (R(x,z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(1209(a,1),3687(a,1))].">
      <j1 rule="para" parents="1209 3687"/>
    </justification>
  </clause>

  <clause id="3736">
    <literal><![CDATA[
      ((x \ 1) \ y) \ ((x * y) \ z) = (x * y) \ (((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(3192(a,1),3215(a,1,2,1))].">
      <j1 rule="para" parents="3192 3215"/>
    </justification>
  </clause>

  <clause id="3737">
    <literal><![CDATA[
      x * ((L(1 / y,z,u) \ 1) \ w) = x * ((y * (L(y,z,u) \ y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(3641,a,9,a(flip))].">
      <j1 rule="hyper" parents="3641 9"/>
    </justification>
  </clause>

  <clause id="3738">
    <literal><![CDATA[
      x * ((L(1 / y,z,u) \ 1) \ w) = x * ((L(y,z,u) \ (y * y)) \ w)
    ]]></literal>
    <justification jstring="[para(1407(a,2),3737(a,2,2,1))].">
      <j1 rule="para" parents="1407 3737"/>
    </justification>
  </clause>

  <clause id="3739">
    <literal><![CDATA[
      x * ((y * y) \ ((L(y,z,u) \ 1) \ w)) = x * ((L(1 / y,z,u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(776(a,2),3738(a,2,2)),flip(a)].">
      <j1 rule="para" parents="776 3738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3740">
    <literal><![CDATA[
      (x \ 1) * ((L(x,y,z) \ 1) \ u) = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(525,a,3739,a)].">
      <j1 rule="hyper" parents="525 3739"/>
    </justification>
  </clause>

  <clause id="3741">
    <literal><![CDATA[
      x * ((y * x) * T((y * x) \ 1,x)) = (((x \ (1 / y)) * x) * y) * x
    ]]></literal>
    <justification jstring="[hyper(314,a,3700,a),flip(a)].">
      <j1 rule="hyper" parents="314 3700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3742">
    <literal><![CDATA[
      x * (y * (x * T(x \ (y \ 1),x))) = (((x \ (1 / y)) * x) * y) * x
    ]]></literal>
    <justification jstring="[para(1022(a,1),3741(a,1,2))].">
      <j1 rule="para" parents="1022 3741"/>
    </justification>
  </clause>

  <clause id="3743">
    <literal><![CDATA[
      (((x \ (1 / y)) * x) * y) * x = x * (y * ((x \ (y \ 1)) * x))
    ]]></literal>
    <justification jstring="[para(111(a,1),3742(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 3742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3744">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,3718,a(flip),b,3710,a),flip(a)].">
      <j1 rule="hyper" parents="35 3718 3710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3745">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3715,a(flip),b,3744,a),flip(a)].">
      <j1 rule="hyper" parents="347 3715 3744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3748">
    <literal><![CDATA[
      (x \ (1 / R(y,z,u))) * K(y \ 1,y) = x \ (R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(3745(a,1),2859(a,1,2))].">
      <j1 rule="para" parents="3745 2859"/>
    </justification>
  </clause>

  <clause id="3749">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = (x \ 1) \ (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2978,a,3748,a)].">
      <j1 rule="hyper" parents="2978 3748"/>
    </justification>
  </clause>

  <clause id="3750">
    <literal><![CDATA[
      (x \ y) * (1 / (1 / (1 / (y \ x)))) = (x \ y) / (y \ x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3400(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 3400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3752">
    <literal><![CDATA[
      R((x \ (1 / (1 / y))) * x,1 / y,(1 / y) \ 1) / ((1 / y) \ 1) = (y * K(x \ (1 / (1 / y)),x)) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,588,a,b,3451,a)].">
      <j1 rule="hyper" parents="347 588 3451"/>
    </justification>
  </clause>

  <clause id="3753">
    <literal><![CDATA[
      (x \ 1) * (x * (L(x,y,z) \ u)) = x * (L(x,y,z) \ ((x \ 1) * u))
    ]]></literal>
    <justification jstring="[para(3439(a,1),3547(a,1,2))].">
      <j1 rule="para" parents="3439 3547"/>
    </justification>
  </clause>

  <clause id="3754">
    <literal><![CDATA[
      x * (x * (L(x,y,z) \ ((x \ 1) * u))) != w
    ]]></literal>
    <literal><![CDATA[
      L(x * (L(x,y,z) \ u),x,x) = w
    ]]></literal>
    <justification jstring="[para(3753(a,1),3226(a,1,2))].">
      <j1 rule="para" parents="3753 3226"/>
    </justification>
  </clause>

  <clause id="3755">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (1 / ((x \ (x / (1 / y))) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(2604(a,1),3650(a,2,1,2))].">
      <j1 rule="para" parents="2604 3650"/>
    </justification>
  </clause>

  <clause id="3756">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (x \ (x / (1 / y))) * z
    ]]></literal>
    <justification jstring="[hyper(347,a,208,a(flip),b,3755,a),flip(a)].">
      <j1 rule="hyper" parents="347 208 3755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3758">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y
    ]]></literal>
    <justification jstring="[para(3756(a,1),2380(a,1,1))].">
      <j1 rule="para" parents="3756 2380"/>
    </justification>
  </clause>

  <clause id="3759">
    <literal><![CDATA[
      R(K(x \ (x / ((y \ x) / T(x,y))),x),x \ 1,x) = L(T(x,y) \ x,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3135,a(flip),b,3112,a),flip(a)].">
      <j1 rule="hyper" parents="347 3135 3112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3760">
    <literal><![CDATA[
      R(T(x,y) \ x,x \ 1,x) = L(T(x,y) \ x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3017(a,1),3759(a,1,1))].">
      <j1 rule="para" parents="3017 3759"/>
    </justification>
  </clause>

  <clause id="3761">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[para(1140(a,1),3758(a,2,1,2))].">
      <j1 rule="para" parents="1140 3758"/>
    </justification>
  </clause>

  <clause id="3762">
    <literal><![CDATA[
      (x \ (x * y)) * x = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,3701,a(flip),b,3761,a)].">
      <j1 rule="hyper" parents="63 3701 3761"/>
    </justification>
  </clause>

  <clause id="3763">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * y = y * x
    ]]></literal>
    <justification jstring="[para(9(a,1),3762(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3764">
    <literal><![CDATA[
      x * (y \ T(y,x)) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(145,a,3763,a),flip(a)].">
      <j1 rule="hyper" parents="145 3763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3765">
    <literal><![CDATA[
      (x \ y) * (x \ T(x,x \ y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(131,a,10,a(flip),b,3763,a),flip(a)].">
      <j1 rule="hyper" parents="131 10 3763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3766">
    <literal><![CDATA[
      x \ ((y * x) / y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(138,a,3764,a)].">
      <j1 rule="hyper" parents="138 3764"/>
    </justification>
  </clause>

  <clause id="3767">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(128,a,255,a(flip),b,3764,a)].">
      <j1 rule="hyper" parents="128 255 3764"/>
    </justification>
  </clause>

  <clause id="3768">
    <literal><![CDATA[
      (x / y) \ T(x / y,y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(128,a,171,a(flip),b,3764,a),flip(a)].">
      <j1 rule="hyper" parents="128 171 3764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3769">
    <literal><![CDATA[
      (x \ T(x,y)) * y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,3044,a,b,3764,a)].">
      <j1 rule="hyper" parents="63 3044 3764"/>
    </justification>
  </clause>

  <clause id="3770">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,3764,a(flip),b,2534,a)].">
      <j1 rule="hyper" parents="133 3764 2534"/>
    </justification>
  </clause>

  <clause id="3771">
    <literal><![CDATA[
      ((x * y) / x) / y = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,3764,a(flip),b,3044,a)].">
      <j1 rule="hyper" parents="131 3764 3044"/>
    </justification>
  </clause>

  <clause id="3772">
    <literal><![CDATA[
      ((x \ 1) * y) / (x \ 1) = y * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(3076(a,1),3764(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3076 3764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3774">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(38,a,3077,a,b,3766,a(flip))].">
      <j1 rule="hyper" parents="38 3077 3766"/>
    </justification>
  </clause>

  <clause id="3775">
    <literal><![CDATA[
      ((x * y) / x) \ y = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(3774(a,1),3119(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3774 3119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3776">
    <literal><![CDATA[
      R(T(x,y) \ x,y,z) = (T(y,T(x,y)) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(3767(a,2),3080(a,1,1))].">
      <j1 rule="para" parents="3767 3080"/>
    </justification>
  </clause>

  <clause id="3777">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(3769(a,1),209(a,1,2,1))].">
      <j1 rule="para" parents="3769 209"/>
    </justification>
  </clause>

  <clause id="3778">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = y \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,1608,a(flip),b,3771,a)].">
      <j1 rule="hyper" parents="63 1608 3771"/>
    </justification>
  </clause>

  <clause id="3779">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[para(3771(a,1),693(a,1,1,1))].">
      <j1 rule="para" parents="3771 693"/>
    </justification>
  </clause>

  <clause id="3780">
    <literal><![CDATA[
      T(x,x \ y) \ x = (y / x) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3775(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 3775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3781">
    <literal><![CDATA[
      T(x,T(y,x)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(255(a,1),3775(a,1,1)),flip(a)].">
      <j1 rule="para" parents="255 3775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3782">
    <literal><![CDATA[
      (((x * y) / x) * T(((x * y) / x) \ z,y)) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(3775(a,1),1285(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3775 1285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3783">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(3775(a,1),1453(a,1,2,2,1))].">
      <j1 rule="para" parents="3775 1453"/>
    </justification>
  </clause>

  <clause id="3784">
    <literal><![CDATA[
      (T(x,y) \ x) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[para(3775(a,1),3091(a,1,1))].">
      <j1 rule="para" parents="3775 3091"/>
    </justification>
  </clause>

  <clause id="3785">
    <literal><![CDATA[
      (x \ T(x,y)) \ y = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(3781(a,1),3016(a,1,1))].">
      <j1 rule="para" parents="3781 3016"/>
    </justification>
  </clause>

  <clause id="3786">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ y = T(y,T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(3076(a,1),3785(a,1,1))].">
      <j1 rule="para" parents="3076 3785"/>
    </justification>
  </clause>

  <clause id="3787">
    <literal><![CDATA[
      (x \ y) * (x \ ((x \ y) \ y)) = y / x
    ]]></literal>
    <justification jstring="[para(112(a,1),3765(a,1,2,2))].">
      <j1 rule="para" parents="112 3765"/>
    </justification>
  </clause>

  <clause id="3788">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x * y) / x) * ((y \ 1) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y \ 1,(x * y) / x) = u
    ]]></literal>
    <justification jstring="[para(3770(a,1),545(a,1,1))].">
      <j1 rule="para" parents="3770 545"/>
    </justification>
  </clause>

  <clause id="3789">
    <literal><![CDATA[
      (x \ y) \ (y / x) = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(138,a,3787,a)].">
      <j1 rule="hyper" parents="138 3787"/>
    </justification>
  </clause>

  <clause id="3790">
    <literal><![CDATA[
      (x / y) \ (y \ x) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[para(113(a,1),3768(a,1,2))].">
      <j1 rule="para" parents="113 3768"/>
    </justification>
  </clause>

  <clause id="3791">
    <literal><![CDATA[
      T(x,x \ y) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3780,a,b,3790,a)].">
      <j1 rule="hyper" parents="63 3780 3790"/>
    </justification>
  </clause>

  <clause id="3792">
    <literal><![CDATA[
      x / (x / y) = y * (T(y,y \ x) \ y)
    ]]></literal>
    <justification jstring="[hyper(134,a,3780,a,b,3790,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 3780 3790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3794">
    <literal><![CDATA[
      K(x,(x / y) / x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1691,a,3778,a)].">
      <j1 rule="hyper" parents="1691 3778"/>
    </justification>
  </clause>

  <clause id="3795">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = T(y,x \ 1) / y
    ]]></literal>
    <justification jstring="[hyper(347,a,3071,a,b,3778,a),flip(a)].">
      <j1 rule="hyper" parents="347 3071 3778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3796">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2460,a,b,3778,a)].">
      <j1 rule="hyper" parents="63 2460 3778"/>
    </justification>
  </clause>

  <clause id="3797">
    <literal><![CDATA[
      T(x,x / (x * y)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1816,a,3778,a(flip))].">
      <j1 rule="hyper" parents="1816 3778"/>
    </justification>
  </clause>

  <clause id="3798">
    <literal><![CDATA[
      x * K(x,(x / y) / x) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,1690,a,b,3778,a(flip))].">
      <j1 rule="hyper" parents="134 1690 3778"/>
    </justification>
  </clause>

  <clause id="3799">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,(x / T(y,z)) / x)
    ]]></literal>
    <justification jstring="[para(3778(a,1),2428(a,1,1))].">
      <j1 rule="para" parents="3778 2428"/>
    </justification>
  </clause>

  <clause id="3800">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((x \ T(x,z \ 1)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(3778(a,1),2448(a,2,2,1))].">
      <j1 rule="para" parents="3778 2448"/>
    </justification>
  </clause>

  <clause id="3801">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2449,a,3797,a)].">
      <j1 rule="hyper" parents="2449 3797"/>
    </justification>
  </clause>

  <clause id="3804">
    <literal><![CDATA[
      T(x * ((x / y) / x),y) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(462,a,3797,a(flip),b,2445,a)].">
      <j1 rule="hyper" parents="462 3797 2445"/>
    </justification>
  </clause>

  <clause id="3805">
    <literal><![CDATA[
      T(x,y \ 1) / y = x * ((x / y) / x)
    ]]></literal>
    <justification jstring="[hyper(131,a,3797,a(flip),b,2445,a)].">
      <j1 rule="hyper" parents="131 3797 2445"/>
    </justification>
  </clause>

  <clause id="3806">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,(y \ x) / x)
    ]]></literal>
    <justification jstring="[para(296(a,1),3798(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="296 3798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3807">
    <literal><![CDATA[
      T(x,y) / (y \ 1) = x * ((x / (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(131,a,2966,a(flip),b,3801,a)].">
      <j1 rule="hyper" parents="131 2966 3801"/>
    </justification>
  </clause>

  <clause id="3808">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(80(a,1),3805(a,2,2,1))].">
      <j1 rule="para" parents="80 3805"/>
    </justification>
  </clause>

  <clause id="3809">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x * ((x / (1 / y)) / x)
    ]]></literal>
    <justification jstring="[para(83(a,1),3805(a,1,1,2))].">
      <j1 rule="para" parents="83 3805"/>
    </justification>
  </clause>

  <clause id="3810">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[para(3805(a,2),244(a,2,1))].">
      <j1 rule="para" parents="3805 244"/>
    </justification>
  </clause>

  <clause id="3812">
    <literal><![CDATA[
      ((x * (1 / y)) / x) * y = T(x,y \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(971,a,3795,a)].">
      <j1 rule="hyper" parents="971 3795"/>
    </justification>
  </clause>

  <clause id="3813">
    <literal><![CDATA[
      T(((x / y) / x) * ((x \ 1) \ 1),y) * K(x \ 1,x) = (x \ (y \ T(x,y \ 1))) * x
    ]]></literal>
    <justification jstring="[para(3804(a,1),2319(a,2,1,2))].">
      <j1 rule="para" parents="3804 2319"/>
    </justification>
  </clause>

  <clause id="3814">
    <literal><![CDATA[
      ((x * (1 / y)) / x) * y = T(x,1 / y) / x
    ]]></literal>
    <justification jstring="[para(2962(a,2),3812(a,2,1))].">
      <j1 rule="para" parents="2962 3812"/>
    </justification>
  </clause>

  <clause id="3817">
    <literal><![CDATA[
      (((x * y) \ 1) * x) / ((x * y) \ 1) = x * (((x \ (1 / y)) * x) * y)
    ]]></literal>
    <justification jstring="[para(1486(a,1),3772(a,2,2))].">
      <j1 rule="para" parents="1486 3772"/>
    </justification>
  </clause>

  <clause id="3818">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = x \ T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,3794,a(flip),b,3799,a),flip(a)].">
      <j1 rule="hyper" parents="347 3794 3799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3819">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ x) / x) = z
    ]]></literal>
    <justification jstring="[para(3806(a,2),43(a,1))].">
      <j1 rule="para" parents="3806 43"/>
    </justification>
  </clause>

  <clause id="3820">
    <literal><![CDATA[
      T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = x \ T(x,R(z \ 1,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(3089(a,1),3818(a,2,2,2,1))].">
      <j1 rule="para" parents="3089 3818"/>
    </justification>
  </clause>

  <clause id="3821">
    <literal><![CDATA[
      L((T(x,T(y,x)) * z) / (x * z),T(y,x),x) = R((y * x) \ (x * y),x,z)
    ]]></literal>
    <justification jstring="[para(3776(a,1),1027(a,1,1))].">
      <j1 rule="para" parents="3776 1027"/>
    </justification>
  </clause>

  <clause id="3825">
    <literal><![CDATA[
      ((1 / (x * y)) * x) / (1 / (x * y)) = x * (((x \ (1 / y)) * x) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2926,a,b,3817,a)].">
      <j1 rule="hyper" parents="63 2926 3817"/>
    </justification>
  </clause>

  <clause id="3827">
    <literal><![CDATA[
      L((T(x,T(y,x)) * z) / (x * z),T(y,x),x) = R(K(x,y),x,z)
    ]]></literal>
    <justification jstring="[para(16(a,2),3821(a,2,1))].">
      <j1 rule="para" parents="16 3821"/>
    </justification>
  </clause>

  <clause id="3828">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,T(x,y) \ x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(3775(a,1),3783(a,2,2))].">
      <j1 rule="para" parents="3775 3783"/>
    </justification>
  </clause>

  <clause id="3829">
    <literal><![CDATA[
      (T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1) = z * T(T((x \ 1) \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(2727(a,2),3136(a,2,2,1))].">
      <j1 rule="para" parents="2727 3136"/>
    </justification>
  </clause>

  <clause id="3830">
    <literal><![CDATA[
      (x * (y \ x)) * L(((x \ y) \ 1) \ 1,z,u) = x * ((y \ x) \ L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(3343(a,1),3289(a,2,2))].">
      <j1 rule="para" parents="3343 3289"/>
    </justification>
  </clause>

  <clause id="3832">
    <literal><![CDATA[
      x * ((y * y) \ ((y * y) * (L(x,z,u) \ 1))) = L(x / (y * y),z,u) \ (x / (y * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,803,a(flip),b,3517,a)].">
      <j1 rule="hyper" parents="63 803 3517"/>
    </justification>
  </clause>

  <clause id="3833">
    <literal><![CDATA[
      T((x / y) * K(x,x \ 1),y) * K(x \ 1,x) = (x \ (y \ T(x,y \ 1))) * x
    ]]></literal>
    <justification jstring="[para(2345(a,1),3813(a,1,1,1))].">
      <j1 rule="para" parents="2345 3813"/>
    </justification>
  </clause>

  <clause id="3834">
    <literal><![CDATA[
      T(((x \ 1) \ 1) / y,y) * K(x \ 1,x) = (x \ (y \ T(x,y \ 1))) * x
    ]]></literal>
    <justification jstring="[para(3474(a,1),3833(a,1,1,1))].">
      <j1 rule="para" parents="3474 3833"/>
    </justification>
  </clause>

  <clause id="3835">
    <literal><![CDATA[
      (x \ ((y \ 1) \ 1)) * K(y \ 1,y) = (y \ (x \ T(y,x \ 1))) * y
    ]]></literal>
    <justification jstring="[para(113(a,1),3834(a,1,1))].">
      <j1 rule="para" parents="113 3834"/>
    </justification>
  </clause>

  <clause id="3836">
    <literal><![CDATA[
      x \ (y \ T(x,y \ 1)) = (y \ x) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,2354,a(flip),b,3835,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 2354 3835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3837">
    <literal><![CDATA[
      x \ T(y,x \ 1) = y * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(150,a,3836,a),flip(a)].">
      <j1 rule="hyper" parents="150 3836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3838">
    <literal><![CDATA[
      x * R(1 / y,y,y \ x) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,421,a,b,3836,a)].">
      <j1 rule="hyper" parents="134 421 3836"/>
    </justification>
  </clause>

  <clause id="3839">
    <literal><![CDATA[
      x \ T(R(x,y,z),x \ 1) = R(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(134,a,3684,a(flip),b,3836,a),flip(a)].">
      <j1 rule="hyper" parents="134 3684 3836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3840">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(3836(a,1),76(a,1,2,2))].">
      <j1 rule="para" parents="3836 76"/>
    </justification>
  </clause>

  <clause id="3841">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(83(a,1),3837(a,2,2,1))].">
      <j1 rule="para" parents="83 3837"/>
    </justification>
  </clause>

  <clause id="3842">
    <literal><![CDATA[
      (x \ 1) \ T(y,x) = y * (((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[para(2966(a,1),3837(a,1,2))].">
      <j1 rule="para" parents="2966 3837"/>
    </justification>
  </clause>

  <clause id="3843">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),3840(a,1,2,2,1))].">
      <j1 rule="para" parents="9 3840"/>
    </justification>
  </clause>

  <clause id="3844">
    <literal><![CDATA[
      (((x / y) \ 1) \ y) * ((x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1164,a(flip),b,3841,a)].">
      <j1 rule="hyper" parents="63 1164 3841"/>
    </justification>
  </clause>

  <clause id="3845">
    <literal><![CDATA[
      x * R(1 / (1 / y),1 / y,(1 / y) \ x) = (1 / y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(83(a,1),3838(a,2,2,2))].">
      <j1 rule="para" parents="83 3838"/>
    </justification>
  </clause>

  <clause id="3846">
    <literal><![CDATA[
      x \ R(T(x,x \ 1),y,z) = R(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(27(a,2),3839(a,1,2))].">
      <j1 rule="para" parents="27 3839"/>
    </justification>
  </clause>

  <clause id="3847">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = (x * y) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(34,a,1139,a,b,3843,a)].">
      <j1 rule="hyper" parents="34 1139 3843"/>
    </justification>
  </clause>

  <clause id="3848">
    <literal><![CDATA[
      ((x \ 1) * y) * (y / ((x \ 1) * y)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(34,a,2901,a(flip),b,3843,a),flip(a)].">
      <j1 rule="hyper" parents="34 2901 3843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3849">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(((y / x) \ 1) \ x,(y / x) \ 1) = z
    ]]></literal>
    <justification jstring="[para(3844(a,1),512(a,1,2))].">
      <j1 rule="para" parents="3844 512"/>
    </justification>
  </clause>

  <clause id="3850">
    <literal><![CDATA[
      ((x \ 1) * y) * R(x,x \ 1,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(241(a,2),3848(a,1,2))].">
      <j1 rule="para" parents="241 3848"/>
    </justification>
  </clause>

  <clause id="3851">
    <literal><![CDATA[
      ((((x \ 1) * y) * x) / ((x \ 1) * y)) * (x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,3850,a(flip),b,955,a),flip(a)].">
      <j1 rule="hyper" parents="131 3850 955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3852">
    <literal><![CDATA[
      x * R(1 / (1 / y),y \ 1,(1 / y) \ x) = (1 / y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(2260(a,1),3845(a,1,2))].">
      <j1 rule="para" parents="2260 3845"/>
    </justification>
  </clause>

  <clause id="3853">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,3770,a(flip),b,3851,a)].">
      <j1 rule="hyper" parents="63 3770 3851"/>
    </justification>
  </clause>

  <clause id="3854">
    <literal><![CDATA[
      L(K(x \ y,x),y,x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,1850,a(flip),b,3853,a)].">
      <j1 rule="hyper" parents="63 1850 3853"/>
    </justification>
  </clause>

  <clause id="3855">
    <literal><![CDATA[
      ((x \ (x * y)) * x) / (x * y) = L(K(y,x),x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),3854(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3856">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3855(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3857">
    <literal><![CDATA[
      (T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1) = T((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[hyper(347,a,266,a(flip),b,3829,a),flip(a)].">
      <j1 rule="hyper" parents="347 266 3829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3858">
    <literal><![CDATA[
      (T(x,y) * z) * K(T(x,z),T(x,z) \ 1) = T((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(3005(a,1),3857(a,1,2))].">
      <j1 rule="para" parents="3005 3857"/>
    </justification>
  </clause>

  <clause id="3859">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,x \ 1) = T((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(3005(a,1),3858(a,1,2))].">
      <j1 rule="para" parents="3005 3858"/>
    </justification>
  </clause>

  <clause id="3861">
    <literal><![CDATA[
      (1 / x) * (T(((1 / x) \ 1) \ 1,y) * z) = (x \ 1) * (T(1 / x,y) * z)
    ]]></literal>
    <justification jstring="[para(3859(a,1),2894(a,1,2))].">
      <j1 rule="para" parents="3859 2894"/>
    </justification>
  </clause>

  <clause id="3863">
    <literal><![CDATA[
      (1 / x) * (T(x \ 1,y) * z) = (x \ 1) * (T(1 / x,y) * z)
    ]]></literal>
    <justification jstring="[para(83(a,1),3861(a,1,2,1,1,1))].">
      <j1 rule="para" parents="83 3861"/>
    </justification>
  </clause>

  <clause id="3864">
    <literal><![CDATA[
      K(x \ 1,x) * (T(1 / x,y) * z) = T(x \ 1,y) * z
    ]]></literal>
    <justification jstring="[hyper(34,a,2923,a,b,3863,a)].">
      <j1 rule="hyper" parents="34 2923 3863"/>
    </justification>
  </clause>

  <clause id="3865">
    <literal><![CDATA[
      (T(1 / x,y) * z) / (T(1 / x,y) * ((x \ 1) \ z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(131,a,3635,a(flip),b,3863,a(flip))].">
      <j1 rule="hyper" parents="131 3635 3863"/>
    </justification>
  </clause>

  <clause id="3866">
    <literal><![CDATA[
      L(x / (y * y),z,u) \ (x / (y * y)) = x * (L(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(620,a,3832,a),flip(a)].">
      <j1 rule="hyper" parents="620 3832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3868">
    <literal><![CDATA[
      L(x / (y * y),z,u) \ (x / (y * y)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(3866(a,2),1422(a,1))].">
      <j1 rule="para" parents="3866 1422"/>
    </justification>
  </clause>

  <clause id="3870">
    <literal><![CDATA[
      (K(x \ 1,x) * (y * z)) \ (K(x \ 1,x) * (y * (z * u))) = L(u,z,y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(3469(a,1),3489(a,1,2))].">
      <j1 rule="para" parents="3469 3489"/>
    </justification>
  </clause>

  <clause id="3871">
    <literal><![CDATA[
      K(x * K(y \ 1,y),z) = (z * x) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(3490,a,3486,a)].">
      <j1 rule="hyper" parents="3490 3486"/>
    </justification>
  </clause>

  <clause id="3872">
    <literal><![CDATA[
      K(x * K(y \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,16,a,b,3871,a),flip(a)].">
      <j1 rule="hyper" parents="347 16 3871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3873">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2283(a,1),3872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2283 3872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3874">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2306(a,1),3872(a,1,1))].">
      <j1 rule="para" parents="2306 3872"/>
    </justification>
  </clause>

  <clause id="3875">
    <literal><![CDATA[
      K(x * (1 / (1 / y)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2313(a,1),3872(a,1,1))].">
      <j1 rule="para" parents="2313 3872"/>
    </justification>
  </clause>

  <clause id="3876">
    <literal><![CDATA[
      K(x * ((y \ 1) \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2315(a,1),3872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2315 3872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3877">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(2753(a,2),3872(a,1,1))].">
      <j1 rule="para" parents="2753 3872"/>
    </justification>
  </clause>

  <clause id="3878">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(2771(a,1),3872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2771 3872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3879">
    <literal><![CDATA[
      K(x \ (1 / y),z) = K(x \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2859(a,1),3872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2859 3872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3880">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2872(a,1),3872(a,1,1))].">
      <j1 rule="para" parents="2872 3872"/>
    </justification>
  </clause>

  <clause id="3881">
    <literal><![CDATA[
      K((1 / x) * y,z) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(2919(a,1),3872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2919 3872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3882">
    <literal><![CDATA[
      K(x \ (y * ((z \ 1) \ 1)),u) = K(x \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(3124(a,1),3872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3124 3872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3883">
    <literal><![CDATA[
      K((K(x,x \ 1) * y) \ z,u) = K(y \ z,u)
    ]]></literal>
    <justification jstring="[para(3512(a,2),3872(a,1,1))].">
      <j1 rule="para" parents="3512 3872"/>
    </justification>
  </clause>

  <clause id="3884">
    <literal><![CDATA[
      K(T(1 / x,y) \ z,u) = K(T(x \ 1,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3634(a,1),3872(a,1,1))].">
      <j1 rule="para" parents="3634 3872"/>
    </justification>
  </clause>

  <clause id="3885">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3154,a,3877,a),flip(a)].">
      <j1 rule="hyper" parents="3154 3877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3886">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3877(a,1),3154(a,1))].">
      <j1 rule="para" parents="3877 3154"/>
    </justification>
  </clause>

  <clause id="3887">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,u) = K(((x \ 1) * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3511(a,1),3877(a,1,1))].">
      <j1 rule="para" parents="3511 3877"/>
    </justification>
  </clause>

  <clause id="3889">
    <literal><![CDATA[
      K(x,y) = (T(y,y \ 1) * x) \ (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,765,a,b,3885,a),flip(a)].">
      <j1 rule="hyper" parents="63 765 3885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3890">
    <literal><![CDATA[
      K(x,1 / y) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(83(a,1),3885(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 3885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3891">
    <literal><![CDATA[
      K(x,1 / (1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(219(a,1),3885(a,1,2)),flip(a)].">
      <j1 rule="para" parents="219 3885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3892">
    <literal><![CDATA[
      K(x,T(y,1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1912(a,2),3885(a,1,2))].">
      <j1 rule="para" parents="1912 3885"/>
    </justification>
  </clause>

  <clause id="3893">
    <literal><![CDATA[
      K(x,T(y / z,z / y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(1947(a,2),3885(a,1,2))].">
      <j1 rule="para" parents="1947 3885"/>
    </justification>
  </clause>

  <clause id="3894">
    <literal><![CDATA[
      K(x,T(1 / y,z)) = K(x,T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(2728(a,1),3885(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2728 3885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3895">
    <literal><![CDATA[
      K(x,T(y / z,y \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(2862(a,2),3885(a,1,2))].">
      <j1 rule="para" parents="2862 3885"/>
    </justification>
  </clause>

  <clause id="3896">
    <literal><![CDATA[
      K(x,((1 / y) \ z) / z) = K(x,((y \ 1) \ z) / z)
    ]]></literal>
    <justification jstring="[para(2900(a,1),3885(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2900 3885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3898">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[para(3890(a,1),2537(a,2,1))].">
      <j1 rule="para" parents="3890 2537"/>
    </justification>
  </clause>

  <clause id="3899">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,1 / x)
    ]]></literal>
    <justification jstring="[para(3890(a,2),3056(a,2,2))].">
      <j1 rule="para" parents="3890 3056"/>
    </justification>
  </clause>

  <clause id="3902">
    <literal><![CDATA[
      K(x \ (K(y,y \ 1) * z),u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(2838(a,2),3878(a,1,1))].">
      <j1 rule="para" parents="2838 3878"/>
    </justification>
  </clause>

  <clause id="3903">
    <literal><![CDATA[
      K(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / y) = z
    ]]></literal>
    <justification jstring="[para(83(a,1),3886(a,1,2,1))].">
      <j1 rule="para" parents="83 3886"/>
    </justification>
  </clause>

  <clause id="3904">
    <literal><![CDATA[
      K(x,T(y,y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(112(a,2),3886(a,1,2))].">
      <j1 rule="para" parents="112 3886"/>
    </justification>
  </clause>

  <clause id="3905">
    <literal><![CDATA[
      K(x,T(y / z,z / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(1947(a,2),3886(a,1,2))].">
      <j1 rule="para" parents="1947 3886"/>
    </justification>
  </clause>

  <clause id="3906">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,(z \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(3877(a,2),3886(a,1))].">
      <j1 rule="para" parents="3877 3886"/>
    </justification>
  </clause>

  <clause id="3908">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),u) = K(x * ((y * z) \ z),u)
    ]]></literal>
    <justification jstring="[para(2822(a,2),3876(a,1,1,2))].">
      <j1 rule="para" parents="2822 3876"/>
    </justification>
  </clause>

  <clause id="3909">
    <literal><![CDATA[
      K(x \ ((1 / x) \ y),z) = K(x \ ((x \ 1) \ y),z)
    ]]></literal>
    <justification jstring="[para(2976(a,1),3880(a,1,1))].">
      <j1 rule="para" parents="2976 3880"/>
    </justification>
  </clause>

  <clause id="3911">
    <literal><![CDATA[
      K((1 / (1 / x)) * (x \ y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(378(a,1),3881(a,2,1))].">
      <j1 rule="para" parents="378 3881"/>
    </justification>
  </clause>

  <clause id="3912">
    <literal><![CDATA[
      K((((x \ 1) \ 1) \ y) \ z,u) = K((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[para(2873(a,1),3883(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2873 3883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3914">
    <literal><![CDATA[
      K((((1 / x) \ y) \ z) \ u,w) = K((((x \ 1) \ y) \ z) \ u,w)
    ]]></literal>
    <justification jstring="[para(3505(a,1),3883(a,1,1,1))].">
      <j1 rule="para" parents="3505 3883"/>
    </justification>
  </clause>

  <clause id="3915">
    <literal><![CDATA[
      K(x \ (y * (1 / z)),u) = K(x \ (y * (z \ 1)),u)
    ]]></literal>
    <justification jstring="[para(2768(a,1),3902(a,1,1,2))].">
      <j1 rule="para" parents="2768 3902"/>
    </justification>
  </clause>

  <clause id="3917">
    <literal><![CDATA[
      K(x \ R(1 / y,z,u),w) = K(x \ R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(3668(a,1),3902(a,1,1,2))].">
      <j1 rule="para" parents="3668 3902"/>
    </justification>
  </clause>

  <clause id="3918">
    <literal><![CDATA[
      K(x \ ((y \ 1) * y),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),3882(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 3882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3919">
    <literal><![CDATA[
      K(x \ (y * (((y \ z) \ 1) \ 1)),u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),3882(a,2,1,2))].">
      <j1 rule="para" parents="10 3882"/>
    </justification>
  </clause>

  <clause id="3920">
    <literal><![CDATA[
      K(((x \ 1) * (x * y)) \ z,u) = K(L(y,x,x \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(2939(a,1),3887(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2939 3887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3921">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = z
    ]]></literal>
    <justification jstring="[para(3889(a,2),766(a,1))].">
      <j1 rule="para" parents="3889 766"/>
    </justification>
  </clause>

  <clause id="3922">
    <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(63,a,2386,a,b,3896,a)].">
      <j1 rule="hyper" parents="63 2386 3896"/>
    </justification>
  </clause>

  <clause id="3923">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((x \ 1) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1006,a,b,3909,a)].">
      <j1 rule="hyper" parents="63 1006 3909"/>
    </justification>
  </clause>

  <clause id="3924">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(3885(a,1),3906(a,1))].">
      <j1 rule="para" parents="3885 3906"/>
    </justification>
  </clause>

  <clause id="3925">
    <literal><![CDATA[
      K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(1897(a,1),3924(a,1,1))].">
      <j1 rule="para" parents="1897 3924"/>
    </justification>
  </clause>

  <clause id="3926">
    <literal><![CDATA[
      K(x * (1 / (1 / y)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(2780(a,1),3924(a,1,1))].">
      <j1 rule="para" parents="2780 3924"/>
    </justification>
  </clause>

  <clause id="3927">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(2868(a,1),3924(a,1,1))].">
      <j1 rule="para" parents="2868 3924"/>
    </justification>
  </clause>

  <clause id="3928">
    <literal><![CDATA[
      K((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ 1) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(2954(a,1),3924(a,1,1))].">
      <j1 rule="para" parents="2954 3924"/>
    </justification>
  </clause>

  <clause id="3929">
    <literal><![CDATA[
      K((x * ((y \ 1) \ 1)) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(3509(a,1),3924(a,1,1))].">
      <j1 rule="para" parents="3509 3924"/>
    </justification>
  </clause>

  <clause id="3930">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(3511(a,1),3924(a,1,1))].">
      <j1 rule="para" parents="3511 3924"/>
    </justification>
  </clause>

  <clause id="3931">
    <literal><![CDATA[
      K(x * (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ 1),z) = u
    ]]></literal>
    <justification jstring="[para(80(a,1),3926(a,1,1,2,2))].">
      <j1 rule="para" parents="80 3926"/>
    </justification>
  </clause>

  <clause id="3932">
    <literal><![CDATA[
      K((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((1 / x) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(83(a,1),3927(a,1,1,1,1))].">
      <j1 rule="para" parents="83 3927"/>
    </justification>
  </clause>

  <clause id="3933">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u \ 1,u)) = L(x,y,z * K(u \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(942,a,3870,a)].">
      <j1 rule="hyper" parents="942 3870"/>
    </justification>
  </clause>

  <clause id="3934">
    <literal><![CDATA[
      L(x,y,z * K(u \ 1,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3468,a,3933,a),flip(a)].">
      <j1 rule="hyper" parents="3468 3933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3936">
    <literal><![CDATA[
      L(x,y,1 / z) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(1317(a,1),3934(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1317 3934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3937">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2234(a,1),3934(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2234 3934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3938">
    <literal><![CDATA[
      L(x,y,z * (1 / u)) = L(x,y,z * (u \ 1))
    ]]></literal>
    <justification jstring="[para(2283(a,1),3934(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2283 3934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3939">
    <literal><![CDATA[
      L(x,y,z / (1 / u)) = L(x,y,z / (u \ 1))
    ]]></literal>
    <justification jstring="[para(2306(a,1),3934(a,1,3))].">
      <j1 rule="para" parents="2306 3934"/>
    </justification>
  </clause>

  <clause id="3940">
    <literal><![CDATA[
      L(x,y,z * ((u \ 1) \ 1)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(2315(a,1),3934(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2315 3934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3941">
    <literal><![CDATA[
      L(x,y,K(z,z \ 1) * u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(2771(a,1),3934(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2771 3934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3942">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ 1) \ u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(2872(a,1),3934(a,1,3))].">
      <j1 rule="para" parents="2872 3934"/>
    </justification>
  </clause>

  <clause id="3943">
    <literal><![CDATA[
      L(x,y,(1 / z) \ u) = L(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(2928(a,1),3934(a,1,3))].">
      <j1 rule="para" parents="2928 3934"/>
    </justification>
  </clause>

  <clause id="3945">
    <literal><![CDATA[
      L(x,1 / y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(3936(a,2),3520(a,1))].">
      <j1 rule="para" parents="3936 3520"/>
    </justification>
  </clause>

  <clause id="3946">
    <literal><![CDATA[
      L(x,y,(z * z) \ z) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(1920(a,1),3937(a,1,3))].">
      <j1 rule="para" parents="1920 3937"/>
    </justification>
  </clause>

  <clause id="3947">
    <literal><![CDATA[
      L(x,y,z * (u * K(w,w \ 1))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(2769(a,1),3941(a,1,3))].">
      <j1 rule="para" parents="2769 3941"/>
    </justification>
  </clause>

  <clause id="3948">
    <literal><![CDATA[
      L(x,y,R(1 / z,u,w)) = L(x,y,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(3668(a,1),3941(a,1,3))].">
      <j1 rule="para" parents="3668 3941"/>
    </justification>
  </clause>

  <clause id="3949">
    <literal><![CDATA[
      L(x,y,z * ((u * w) \ u)) = L(x,y,z * (u \ (u / w)))
    ]]></literal>
    <justification jstring="[para(3256(a,1),3940(a,1,3,2))].">
      <j1 rule="para" parents="3256 3940"/>
    </justification>
  </clause>

  <clause id="3950">
    <literal><![CDATA[
      L(x,y,((z * u) \ z) \ w) = L(x,y,(z \ (z / u)) \ w)
    ]]></literal>
    <justification jstring="[para(3256(a,1),3942(a,1,3,1))].">
      <j1 rule="para" parents="3256 3942"/>
    </justification>
  </clause>

  <clause id="3951">
    <literal><![CDATA[
      L(x,y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(3189(a,1),3945(a,1))].">
      <j1 rule="para" parents="3189 3945"/>
    </justification>
  </clause>

  <clause id="3952">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(2949(a,2),3951(a,1))].">
      <j1 rule="para" parents="2949 3951"/>
    </justification>
  </clause>

  <clause id="3954">
    <literal><![CDATA[
      K(x,((y \ 1) \ x) / x) = ((1 / y) \ x) \ ((1 / y) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(3852(a,1),3922(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3852 3922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3955">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3923,a(flip),b,3954,a)].">
      <j1 rule="hyper" parents="347 3923 3954"/>
    </justification>
  </clause>

  <clause id="3956">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ L(1 / ((x * y) \ x),z,u) = (x * y) \ (x * L(x \ (x * y),z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,3354,a(flip),b,3386,a),flip(a)].">
      <j1 rule="hyper" parents="347 3354 3386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3957">
    <literal><![CDATA[
      R(x,y,L((z \ 1) \ ((z \ u) / u),z,z \ 1)) = R(x,y,z * R(z \ 1,z,z \ u))
    ]]></literal>
    <justification jstring="[para(3188(a,1),3724(a,1,3))].">
      <j1 rule="para" parents="3188 3724"/>
    </justification>
  </clause>

  <clause id="3958">
    <literal><![CDATA[
      R(x,y,(z * z) * ((1 / z) * ((z \ u) / u))) = R(x,y,z * R(z \ 1,z,z \ u))
    ]]></literal>
    <justification jstring="[para(3412(a,1),3957(a,1,3))].">
      <j1 rule="para" parents="3412 3957"/>
    </justification>
  </clause>

  <clause id="3959">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ L(1 / ((x * y) \ x),z,u) = (x * y) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),3956(a,2,2,2,1))].">
      <j1 rule="para" parents="9 3956"/>
    </justification>
  </clause>

  <clause id="3960">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ L((x \ (x / y)) \ 1,z,u) = (x * y) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(3259(a,1),3959(a,1,2,1))].">
      <j1 rule="para" parents="3259 3959"/>
    </justification>
  </clause>

  <clause id="3961">
    <literal><![CDATA[
      (x \ (x / y)) \ L(x \ (x / y),z,u) = (x * y) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(3385,a,3960,a)].">
      <j1 rule="hyper" parents="3385 3960"/>
    </justification>
  </clause>

  <clause id="3962">
    <literal><![CDATA[
      x \ ((x / y) * L((x / y) \ x,z,u)) = (x * y) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(3365,a,3961,a)].">
      <j1 rule="hyper" parents="3365 3961"/>
    </justification>
  </clause>

  <clause id="3963">
    <literal><![CDATA[
      (x * y) \ (x * L(y,z,u)) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(83(a,1),3962(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="83 3962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3964">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),y,x) = (x / y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(716,a,3963,a)].">
      <j1 rule="hyper" parents="716 3963"/>
    </justification>
  </clause>

  <clause id="3965">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) = u \ ((u / x) * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(686,a,3963,a)].">
      <j1 rule="hyper" parents="686 3963"/>
    </justification>
  </clause>

  <clause id="3966">
    <literal><![CDATA[
      (x * y) * (x \ ((x / y) * L(y,z,u))) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(150,a,3963,a)].">
      <j1 rule="hyper" parents="150 3963"/>
    </justification>
  </clause>

  <clause id="3967">
    <literal><![CDATA[
      (x * y) \ (((x * y) / z) * L(z,y,x)) = ((x * y) * z) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[para(97(a,1),3963(a,1,2)),flip(a)].">
      <j1 rule="para" parents="97 3963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3968">
    <literal><![CDATA[
      x \ ((x / y) * L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(y \ L(y,z,u),y,x) = w
    ]]></literal>
    <justification jstring="[para(3963(a,1),686(a,1))].">
      <j1 rule="para" parents="3963 686"/>
    </justification>
  </clause>

  <clause id="3969">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) \ w = (u \ ((u / x) * L(x,y,z))) \ w
    ]]></literal>
    <justification jstring="[para(3963(a,1),564(a,2,1))].">
      <j1 rule="para" parents="3963 564"/>
    </justification>
  </clause>

  <clause id="3970">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,z * y) = (z * y) \ ((z * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(128,a,2012,a(flip),b,3964,a),flip(a)].">
      <j1 rule="hyper" parents="128 2012 3964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3971">
    <literal><![CDATA[
      x / L(y \ L(y,z,u),y,x) = x * (1 / (1 / (((x / y) * L(y,z,u)) \ x)))
    ]]></literal>
    <justification jstring="[para(3965(a,2),3397(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3965 3397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3972">
    <literal><![CDATA[
      (x * x) * (x \ L(x,y,z)) = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(191(a,1),3966(a,1,2,2))].">
      <j1 rule="para" parents="191 3966"/>
    </justification>
  </clause>

  <clause id="3973">
    <literal><![CDATA[
      (x * y) \ (x * L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x \ ((x / y) * L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(3966(a,1),356(a,1,2))].">
      <j1 rule="para" parents="3966 356"/>
    </justification>
  </clause>

  <clause id="3974">
    <literal><![CDATA[
      (x \ 1) \ L(x,y,z) = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(526,a,3972,a)].">
      <j1 rule="hyper" parents="526 3972"/>
    </justification>
  </clause>

  <clause id="3975">
    <literal><![CDATA[
      R(x,y,z \ L(z,u,w)) = R(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(3972(a,1),2240(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3972 2240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3976">
    <literal><![CDATA[
      R(1 / x,x,L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(447,a,3974,a)].">
      <j1 rule="hyper" parents="447 3974"/>
    </justification>
  </clause>

  <clause id="3977">
    <literal><![CDATA[
      x \ L(y,z,u) != y * L(y,z,u)
    ]]></literal>
    <literal><![CDATA[
      y \ 1 = x
    ]]></literal>
    <justification jstring="[para(3974(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="3974 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3978">
    <literal><![CDATA[
      R(x,y,z * L(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(3974(a,1),2379(a,1,3))].">
      <j1 rule="para" parents="3974 2379"/>
    </justification>
  </clause>

  <clause id="3979">
    <literal><![CDATA[
      R(x,y,(1 / z) \ L(1 / z,z,u)) = R(x,y,(1 / z) * (u \ (u / z)))
    ]]></literal>
    <justification jstring="[para(3264(a,1),3975(a,2,3,2))].">
      <j1 rule="para" parents="3264 3975"/>
    </justification>
  </clause>

  <clause id="3980">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (y * z)) = (x * y) \ ((x * (y * z)) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,574,a(flip),b,3970,a)].">
      <j1 rule="hyper" parents="63 574 3970"/>
    </justification>
  </clause>

  <clause id="3981">
    <literal><![CDATA[
      (x * y) \ ((x * (y * (y \ z))) / (y \ z)) = ((x * y) * (y \ z)) \ (x * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),3980(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 3980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3982">
    <literal><![CDATA[
      R(x,y,z \ L(z,z,u)) = R(x,y,(1 / z) * (u \ (u / z)))
    ]]></literal>
    <justification jstring="[para(3356(a,1),3979(a,1,3))].">
      <j1 rule="para" parents="3356 3979"/>
    </justification>
  </clause>

  <clause id="3983">
    <literal><![CDATA[
      ((x * y) * (y \ z)) \ (x * z) = (x * y) \ ((x * z) / (y \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),3981(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 3981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3984">
    <literal><![CDATA[
      ((x / y) * y) \ (((x / y) * z) / (y \ z)) = (x * (y \ z)) \ ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(12(a,1),3983(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 3983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3986">
    <literal><![CDATA[
      (x * (y \ z)) \ ((x / y) * z) = x \ (((x / y) * z) / (y \ z))
    ]]></literal>
    <justification jstring="[para(12(a,1),3984(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 3984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3987">
    <literal><![CDATA[
      R(T(x,y * K(z,z \ 1)),y,K(z,z \ 1)) = L(T(x,y),y,K(z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,2772,a(flip),b,2773,a),flip(a)].">
      <j1 rule="hyper" parents="63 2772 2773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3988">
    <literal><![CDATA[
      R(T(x,y * K(z,z \ 1)),y,K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3453,a(flip),b,3987,a),flip(a)].">
      <j1 rule="hyper" parents="347 3453 3987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3990">
    <literal><![CDATA[
      T(x,y * K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2219,a(flip),b,3988,a)].">
      <j1 rule="hyper" parents="63 2219 3988"/>
    </justification>
  </clause>

  <clause id="3992">
    <literal><![CDATA[
      T(x,y * K(z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1926(a,1),3990(a,1,2,2))].">
      <j1 rule="para" parents="1926 3990"/>
    </justification>
  </clause>

  <clause id="3993">
    <literal><![CDATA[
      T(x,y * (z * K(u,u \ 1))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(2226(a,1),3990(a,1,2))].">
      <j1 rule="para" parents="2226 3990"/>
    </justification>
  </clause>

  <clause id="3994">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(2332(a,1),3990(a,1,2))].">
      <j1 rule="para" parents="2332 3990"/>
    </justification>
  </clause>

  <clause id="3996">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(2357(a,1),3990(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2357 3990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3997">
    <literal><![CDATA[
      T(x,K(y \ 1,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2754(a,1),3990(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2754 3990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3998">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2874(a,1),3990(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2874 3990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4001">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2959(a,1),3990(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2959 3990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4003">
    <literal><![CDATA[
      T(x,y * (K(z \ 1,z) * u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(2791(a,1),3992(a,1,2))].">
      <j1 rule="para" parents="2791 3992"/>
    </justification>
  </clause>

  <clause id="4004">
    <literal><![CDATA[
      T(x,y \ (1 / z)) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(2859(a,1),3992(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2859 3992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4005">
    <literal><![CDATA[
      T(x,y * (((y \ z) \ 1) \ 1)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(3132(a,1),3992(a,1,2))].">
      <j1 rule="para" parents="3132 3992"/>
    </justification>
  </clause>

  <clause id="4006">
    <literal><![CDATA[
      T(x,T(1 / y,z) \ u) = T(x,T(y \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[para(3634(a,1),3992(a,1,2))].">
      <j1 rule="para" parents="3634 3992"/>
    </justification>
  </clause>

  <clause id="4007">
    <literal><![CDATA[
      T(x,T(y,y \ 1) \ z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2870(a,1),3997(a,1,2))].">
      <j1 rule="para" parents="2870 3997"/>
    </justification>
  </clause>

  <clause id="4008">
    <literal><![CDATA[
      T(x,(y / (1 / z)) * u) = T(x,(y / (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(3483(a,1),3997(a,1,2))].">
      <j1 rule="para" parents="3483 3997"/>
    </justification>
  </clause>

  <clause id="4009">
    <literal><![CDATA[
      T(x,x * (1 / y)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,1799,a(flip),b,3994,a),flip(a)].">
      <j1 rule="hyper" parents="347 1799 3994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4010">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ u) = T(x,(z / (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(1951(a,2),3998(a,1,2,1))].">
      <j1 rule="para" parents="1951 3998"/>
    </justification>
  </clause>

  <clause id="4011">
    <literal><![CDATA[
      T(x,y * (((z \ 1) \ 1) \ u)) = T(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(2874(a,1),3993(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2874 3993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4012">
    <literal><![CDATA[
      T(x,y * (((1 / z) * u) * w)) = T(x,y * (((z \ 1) * u) * w))
    ]]></literal>
    <justification jstring="[para(3550(a,1),3993(a,1,2,2))].">
      <j1 rule="para" parents="3550 3993"/>
    </justification>
  </clause>

  <clause id="4013">
    <literal><![CDATA[
      T(x,y * ((((z \ 1) \ 1) \ u) * w)) = T(x,y * ((z \ u) * w))
    ]]></literal>
    <justification jstring="[para(3484(a,1),4003(a,1,2,2))].">
      <j1 rule="para" parents="3484 4003"/>
    </justification>
  </clause>

  <clause id="4014">
    <literal><![CDATA[
      T(x,y * (T(1 / z,u) * w)) = T(x,y * (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[para(3864(a,1),4003(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3864 4003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4016">
    <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(3448(a,1),2853(a,1,1,2))].">
      <j1 rule="para" parents="3448 2853"/>
    </justification>
  </clause>

  <clause id="4017">
    <literal><![CDATA[
      (K(x \ 1,x) * (y * (z * u))) \ ((K(x \ 1,x) * (y * z)) * u) = a(y * K(x \ 1,x),z,u)
    ]]></literal>
    <justification jstring="[para(3469(a,1),3488(a,1,2,1))].">
      <j1 rule="para" parents="3469 3488"/>
    </justification>
  </clause>

  <clause id="4018">
    <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(3448(a,1),4016(a,1,2))].">
      <j1 rule="para" parents="3448 4016"/>
    </justification>
  </clause>

  <clause id="4019">
    <literal><![CDATA[
      (K(x \ 1,x) * (y * (z * u))) \ (K(x \ 1,x) * ((y * z) * u)) = a(y * K(x \ 1,x),z,u)
    ]]></literal>
    <justification jstring="[para(3464(a,1),4017(a,1,2))].">
      <j1 rule="para" parents="3464 4017"/>
    </justification>
  </clause>

  <clause id="4020">
    <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(2857,a,4018,a)].">
      <j1 rule="hyper" parents="2857 4018"/>
    </justification>
  </clause>

  <clause id="4021">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),K(u \ 1,u)) = a(x * K(u \ 1,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(944,a,4019,a)].">
      <j1 rule="hyper" parents="944 4019"/>
    </justification>
  </clause>

  <clause id="4022">
    <literal><![CDATA[
      a(x * K(y \ 1,y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(3468,a,4021,a),flip(a)].">
      <j1 rule="hyper" parents="3468 4021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4024">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1317(a,1),4022(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1317 4022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4025">
    <literal><![CDATA[
      a((L(x,y,z) \ 1) * x,u,w) = a(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(2818(a,1),4022(a,1,1))].">
      <j1 rule="para" parents="2818 4022"/>
    </justification>
  </clause>

  <clause id="4026">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x = a(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2948,a,b,4024,a)].">
      <j1 rule="hyper" parents="63 2948 4024"/>
    </justification>
  </clause>

  <clause id="4027">
    <literal><![CDATA[
      a((x * y) \ 1,x,y) / y = (1 / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(131,a,4024,a(flip),b,293,a)].">
      <j1 rule="hyper" parents="131 4024 293"/>
    </justification>
  </clause>

  <clause id="4028">
    <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(4027(a,2),3769(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4027 3769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4029">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = x * (((x \ (1 / y)) * x) * y)
    ]]></literal>
    <justification jstring="[para(4027(a,2),3825(a,1,1))].">
      <j1 rule="para" parents="4027 3825"/>
    </justification>
  </clause>

  <clause id="4030">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) != x * z
    ]]></literal>
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = z
    ]]></literal>
    <justification jstring="[para(4029(a,2),43(a,1))].">
      <j1 rule="para" parents="4029 43"/>
    </justification>
  </clause>

  <clause id="4031">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = ((x * y) * T((x * y) \ 1,x)) * x
    ]]></literal>
    <justification jstring="[para(1274(a,1),4028(a,2,1))].">
      <j1 rule="para" parents="1274 4028"/>
    </justification>
  </clause>

  <clause id="4032">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = (((x \ (1 / y)) * x) * y) * x
    ]]></literal>
    <justification jstring="[para(1486(a,1),4031(a,2,1))].">
      <j1 rule="para" parents="1486 4031"/>
    </justification>
  </clause>

  <clause id="4033">
    <literal><![CDATA[
      (a((x * y) \ 1,x,y) / y) / (1 / (x * y)) = x * (y * ((x \ (y \ 1)) * x))
    ]]></literal>
    <justification jstring="[hyper(347,a,3743,a(flip),b,4032,a),flip(a)].">
      <j1 rule="hyper" parents="347 3743 4032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4034">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = y * ((x \ (y \ 1)) * x)
    ]]></literal>
    <justification jstring="[hyper(4030,a,4033,a)].">
      <j1 rule="hyper" parents="4030 4033"/>
    </justification>
  </clause>

  <clause id="4035">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ 1)) * y) = ((y \ x) * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(80(a,1),4034(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="80 4034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4036">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = (1 / y) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3549,a(flip),b,4035,a),flip(a)].">
      <j1 rule="hyper" parents="63 3549 4035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4037">
    <literal><![CDATA[
      T(1 / x,(y \ x) * y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(269,a,3549,a(flip),b,4035,a(flip))].">
      <j1 rule="hyper" parents="269 3549 4035"/>
    </justification>
  </clause>

  <clause id="4038">
    <literal><![CDATA[
      T(1 / (x * y),y * x) = (x * y) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),4037(a,1,2,1))].">
      <j1 rule="para" parents="9 4037"/>
    </justification>
  </clause>

  <clause id="4039">
    <literal><![CDATA[
      (1 / (x * y)) * (y * x) = (y * x) * ((x * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,4038,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 4038 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4040">
    <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(3513(a,1),4020(a,1,1))].">
      <j1 rule="para" parents="3513 4020"/>
    </justification>
  </clause>

  <clause id="4041">
    <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),4040(a,1,1,1))].">
      <j1 rule="para" parents="14 4040"/>
    </justification>
  </clause>

  <clause id="4042">
    <literal><![CDATA[
      a(x,K(y,y \ 1) * z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2350,a(flip),b,4041,a),flip(a)].">
      <j1 rule="hyper" parents="63 2350 4041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4044">
    <literal><![CDATA[
      a(x,1 / y,z) = a(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(1907(a,1),4042(a,1,2))].">
      <j1 rule="para" parents="1907 4042"/>
    </justification>
  </clause>

  <clause id="4045">
    <literal><![CDATA[
      a(x,y * K(z \ 1,z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(2765(a,1),4042(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2765 4042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4046">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ R((x \ (x / y)) \ 1,z,u) = ((x * y) \ x) * R(((x * y) \ x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(3259(a,1),3277(a,1,2,1))].">
      <j1 rule="para" parents="3259 3277"/>
    </justification>
  </clause>

  <clause id="4047">
    <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(3491,a,3495,a),flip(a)].">
      <j1 rule="hyper" parents="3491 3495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4048">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = (u * y) \ (u * (y * x))
    ]]></literal>
    <justification jstring="[para(2837(a,1),4047(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2837 4047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4049">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,18,a,b,4048,a),flip(a)].">
      <j1 rule="hyper" parents="347 18 4048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4051">
    <literal><![CDATA[
      L(x,T(1 / y,z) \ u,w) = L(x,T(y \ 1,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(3634(a,1),4049(a,1,2))].">
      <j1 rule="para" parents="3634 4049"/>
    </justification>
  </clause>

  <clause id="4052">
    <literal><![CDATA[
      L(x,T((y \ 1) \ 1,z) \ u,w) = L(x,T(y,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(80(a,1),4051(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="80 4051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4053">
    <literal><![CDATA[
      (1 / x) \ ((y * y) * L((y * y) \ (1 / x),z,u)) = (x * (y * y)) \ L(x * (y * y),z,u)
    ]]></literal>
    <justification jstring="[para(458(a,1),3535(a,2,2,1))].">
      <j1 rule="para" parents="458 3535"/>
    </justification>
  </clause>

  <clause id="4054">
    <literal><![CDATA[
      (1 / x) \ ((y * y) * L((y * y) \ (1 / x),z,u)) = (y * y) \ (x \ L(x * (y * y),z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,459,a(flip),b,4053,a),flip(a)].">
      <j1 rule="hyper" parents="347 459 4053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4055">
    <literal><![CDATA[
      (x * x) \ (y \ L(y * (x * x),z,u)) = (1 / y) \ L(1 / y,z,u)
    ]]></literal>
    <justification jstring="[para(3320(a,1),4054(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3320 4054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4056">
    <literal><![CDATA[
      (x * x) \ (y \ L(y * (x * x),z,u)) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,3356,a(flip),b,4055,a),flip(a)].">
      <j1 rule="hyper" parents="347 3356 4055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4058">
    <literal><![CDATA[
      (x * x) \ (y * L(y \ (x * x),z,u)) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(3342(a,1),4056(a,1,2))].">
      <j1 rule="para" parents="3342 4056"/>
    </justification>
  </clause>

  <clause id="4059">
    <literal><![CDATA[
      R(x,y,z * L(z \ (u * u),w,v5)) = R(x,y,z \ L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(4058(a,1),2238(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4058 2238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4061">
    <literal><![CDATA[
      R(x,y,z * L(z \ (u * u),w,v5)) = R(x,y,z * L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,3975,a(flip),b,4059,a),flip(a)].">
      <j1 rule="hyper" parents="347 3975 4059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4062">
    <literal><![CDATA[
      R(x,x,y * L(y,z,u)) * ((x * x) \ (y * L(y \ (w * w),z,u))) = x \ (y * L(y \ (w * w),z,u))
    ]]></literal>
    <justification jstring="[para(4061(a,1),2375(a,1,1))].">
      <j1 rule="para" parents="4061 2375"/>
    </justification>
  </clause>

  <clause id="4063">
    <literal><![CDATA[
      ((x * (y * T(y \ T(z,x),y))) / x) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(2515(a,1),3782(a,1,1))].">
      <j1 rule="para" parents="2515 3782"/>
    </justification>
  </clause>

  <clause id="4064">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(111(a,1),4063(a,1,1,1,2))].">
      <j1 rule="para" parents="111 4063"/>
    </justification>
  </clause>

  <clause id="4065">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(3775(a,1),4064(a,1,2))].">
      <j1 rule="para" parents="3775 4064"/>
    </justification>
  </clause>

  <clause id="4066">
    <literal><![CDATA[
      ((x * y) \ x) * R(((x * y) \ x) \ 1,z,u) = (x \ (x / y)) * R((x \ (x / y)) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(3695,a,4046,a),flip(a)].">
      <j1 rule="hyper" parents="3695 4046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4067">
    <literal><![CDATA[
      (x \ (x / y)) * R((x \ (x / y)) \ 1,z,u) = (x * y) \ (x * R(x \ (x * y),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1668,a(flip),b,4066,a),flip(a)].">
      <j1 rule="hyper" parents="63 1668 4066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4068">
    <literal><![CDATA[
      (x \ (x / y)) * R((x \ (x / y)) \ 1,z,u) = (x * y) \ (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),4067(a,2,2,2,1))].">
      <j1 rule="para" parents="9 4067"/>
    </justification>
  </clause>

  <clause id="4069">
    <literal><![CDATA[
      x \ ((x / y) * R((x / y) \ x,z,u)) = (x * y) \ (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,1668,a(flip),b,4068,a)].">
      <j1 rule="hyper" parents="63 1668 4068"/>
    </justification>
  </clause>

  <clause id="4070">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,u)) = x \ ((x / y) * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(83(a,1),4069(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="83 4069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4071">
    <literal><![CDATA[
      x * L(y \ R(y,z,u),y,x) = (x / y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(716,a,4070,a)].">
      <j1 rule="hyper" parents="716 4070"/>
    </justification>
  </clause>

  <clause id="4072">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,u) = u \ ((u / x) * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(686,a,4070,a)].">
      <j1 rule="hyper" parents="686 4070"/>
    </justification>
  </clause>

  <clause id="4073">
    <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(2861(a,1),2832(a,1))].">
      <j1 rule="para" parents="2861 2832"/>
    </justification>
  </clause>

  <clause id="4074">
    <literal><![CDATA[
      R((1 / x) * T((1 / x) \ 1,y),K(x \ 1,x),z) = (1 / x) * T((1 / x) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2897(a,1),2898(a,2,2,1,1))].">
      <j1 rule="para" parents="2897 2898"/>
    </justification>
  </clause>

  <clause id="4075">
    <literal><![CDATA[
      R((1 / x) * T((1 / x) \ 1,y),K(x \ 1,x),z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3075,a(flip),b,4074,a),flip(a)].">
      <j1 rule="hyper" parents="347 3075 4074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4077">
    <literal><![CDATA[
      R(x \ T(x,y),K(x \ 1,x),z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3075(a,1),4075(a,1,1))].">
      <j1 rule="para" parents="3075 4075"/>
    </justification>
  </clause>

  <clause id="4078">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(4077(a,1),3107(a,1,1))].">
      <j1 rule="para" parents="4077 3107"/>
    </justification>
  </clause>

  <clause id="4079">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,x) * z
    ]]></literal>
    <justification jstring="[para(3104(a,1),4078(a,2,1))].">
      <j1 rule="para" parents="3104 4078"/>
    </justification>
  </clause>

  <clause id="4081">
    <literal><![CDATA[
      (x \ T(x,y)) * (z * K(x \ 1,x)) = ((x \ 1) * T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(2758,a,4079,a)].">
      <j1 rule="hyper" parents="2758 4079"/>
    </justification>
  </clause>

  <clause id="4084">
    <literal><![CDATA[
      L(x * (y \ x),z,u) * (((x \ y) \ 1) \ 1) = ((x \ y) \ 1) * L(((x \ y) \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(3381,a,3275,a),flip(a)].">
      <j1 rule="hyper" parents="3381 3275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4085">
    <literal><![CDATA[
      L(x * (y \ x),z,u) * (((x \ y) \ 1) \ 1) = (x \ y) * L((x \ y) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,3380,a(flip),b,4084,a),flip(a)].">
      <j1 rule="hyper" parents="347 3380 4084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4086">
    <literal><![CDATA[
      L(L(x,(y * z) \ y,z),z * ((y * z) \ y),z) = z * (L(z,z,y) \ (z * (((y * z) \ y) * x)))
    ]]></literal>
    <justification jstring="[hyper(3349,a,1407,a)].">
      <j1 rule="hyper" parents="3349 1407"/>
    </justification>
  </clause>

  <clause id="4087">
    <literal><![CDATA[
      L(L(x,(y * z) \ y,z),z * ((y * z) \ y),z) = z * (z * (L(z,z,y) \ (((y * z) \ y) * x)))
    ]]></literal>
    <justification jstring="[para(1407(a,1),4086(a,2,2))].">
      <j1 rule="para" parents="1407 4086"/>
    </justification>
  </clause>

  <clause id="4088">
    <literal><![CDATA[
      L(L(x,(y * z) \ y,z),z * ((y * z) \ y),z) = z * (z * ((z * z) \ x))
    ]]></literal>
    <justification jstring="[para(1808(a,1),4087(a,2,2,2))].">
      <j1 rule="para" parents="1808 4087"/>
    </justification>
  </clause>

  <clause id="4089">
    <literal><![CDATA[
      L(L(x,(y * z) \ y,z),z * ((y * z) \ y),z) = z * ((z \ 1) * x)
    ]]></literal>
    <justification jstring="[para(497(a,1),4088(a,2,2))].">
      <j1 rule="para" parents="497 4088"/>
    </justification>
  </clause>

  <clause id="4091">
    <literal><![CDATA[
      L(L(x,(y * z) \ y,z),z * ((y * z) \ y),z) = L(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,3197,a(flip),b,4089,a),flip(a)].">
      <j1 rule="hyper" parents="347 3197 4089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4092">
    <literal><![CDATA[
      x \ (y * L(y \ (x * (x \ (y * L(y \ x,z,u)))),w,v5)) = (x \ y) * L(L((x \ y) \ 1,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(3354(a,1),3367(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="3354 3367"/>
    </justification>
  </clause>

  <clause id="4093">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (L(x * L(x,y,z),u,w) \ (x * L(x,y,z))) = L((x \ L(x,y,z)) \ 1,u,w) \ 1
    ]]></literal>
    <justification jstring="[para(3734(a,1),3639(a,2,1,1))].">
      <j1 rule="para" parents="3734 3639"/>
    </justification>
  </clause>

  <clause id="4094">
    <literal><![CDATA[
      x \ (y * L(y \ (x * x),z,u)) = R(x,x,y * L(y,z,u)) * (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(4058(a,1),4062(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4058 4062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4095">
    <literal><![CDATA[
      R(x,x,y * L(y,z,u)) * (y \ L(y,z,u)) = (x \ y) * L((x \ y) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(1361,a,4094,a),flip(a)].">
      <j1 rule="hyper" parents="1361 4094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4096">
    <literal><![CDATA[
      (x \ y) * L(L((x \ y) \ 1,z,u),w,v5) = x \ (y * L(L(y \ x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(74(a,1),4092(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="74 4092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4097">
    <literal><![CDATA[
      (x \ y) \ L(L(x \ y,z,u),w,v5) = x \ (y * L(L(y \ x,w,v5),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,3540,a(flip),b,4096,a)].">
      <j1 rule="hyper" parents="63 3540 4096"/>
    </justification>
  </clause>

  <clause id="4099">
    <literal><![CDATA[
      ((x * y) \ (x * (y * z))) \ L(L((x * y) \ (x * (y * z)),u,w),v5,v6) = (x * y) \ ((x * (y * z)) * L(L(L(L(z \ 1,z,y),y * z,x),v5,v6),u,w))
    ]]></literal>
    <justification jstring="[para(446(a,2),4097(a,2,2,2,1,1))].">
      <j1 rule="para" parents="446 4097"/>
    </justification>
  </clause>

  <clause id="4100">
    <literal><![CDATA[
      (L(x,y,y \ 1) \ ((1 / y) * (x * y))) * ((y * ((1 / y) * (x * y))) / y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[para(11(a,1),3097(a,1,1,1))].">
      <j1 rule="para" parents="11 3097"/>
    </justification>
  </clause>

  <clause id="4101">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(35,a,3784,a,b,4100,a),flip(a)].">
      <j1 rule="hyper" parents="35 3784 4100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4104">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(3952,a,4101,a)].">
      <j1 rule="hyper" parents="3952 4101"/>
    </justification>
  </clause>

  <clause id="4105">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(y \ 1) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[para(2956(a,1),4104(a,2,1))].">
      <j1 rule="para" parents="2956 4104"/>
    </justification>
  </clause>

  <clause id="4106">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) \ x = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3856,a(flip),b,4105,a),flip(a)].">
      <j1 rule="hyper" parents="63 3856 4105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4107">
    <literal><![CDATA[
      T((x \ 1) * R((x \ 1) \ 1,y,z),x \ L(x,u,w)) = (x \ 1) * R((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2035(a,1),2151(a,2,1))].">
      <j1 rule="para" parents="2035 2151"/>
    </justification>
  </clause>

  <clause id="4108">
    <literal><![CDATA[
      T((x \ 1) * R((x \ 1) \ 1,y,z),x \ L(x,u,w)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,1462,a(flip),b,4107,a),flip(a)].">
      <j1 rule="hyper" parents="347 1462 4107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4110">
    <literal><![CDATA[
      T(x \ R(x,y,z),x \ L(x,u,w)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1462(a,1),4108(a,1,1))].">
      <j1 rule="para" parents="1462 4108"/>
    </justification>
  </clause>

  <clause id="4111">
    <literal><![CDATA[
      T(x \ L(x,y,z),x \ R(x,u,w)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,4110,a)].">
      <j1 rule="hyper" parents="54 4110"/>
    </justification>
  </clause>

  <clause id="4112">
    <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(2215(a,1),2842(a,1,1,2))].">
      <j1 rule="para" parents="2215 2842"/>
    </justification>
  </clause>

  <clause id="4113">
    <literal><![CDATA[
      x * K(((y \ 1) * x) \ (K(y \ 1,y) * x),(y \ 1) * x) = (y \ T(y,(y \ 1) * x)) * x
    ]]></literal>
    <justification jstring="[para(3075(a,1),3492(a,2,1))].">
      <j1 rule="para" parents="3075 3492"/>
    </justification>
  </clause>

  <clause id="4114">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((1 / x) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(3487(a,1),4113(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3487 4113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4115">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((x \ 1) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(3887(a,1),4114(a,2,2))].">
      <j1 rule="para" parents="3887 4114"/>
    </justification>
  </clause>

  <clause id="4116">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,(x \ 1) * y)) * y
    ]]></literal>
    <justification jstring="[hyper(347,a,330,a(flip),b,4115,a)].">
      <j1 rule="hyper" parents="347 330 4115"/>
    </justification>
  </clause>

  <clause id="4117">
    <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(63,a,2840,a(flip),b,4112,a)].">
      <j1 rule="hyper" parents="63 2840 4112"/>
    </justification>
  </clause>

  <clause id="4118">
    <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(4073,a,4117,a),flip(a)].">
      <j1 rule="hyper" parents="4073 4117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4119">
    <literal><![CDATA[
      a(x,y,z * K(u \ 1,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3468,a,4118,a),flip(a)].">
      <j1 rule="hyper" parents="3468 4118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4120">
    <literal><![CDATA[
      a(x,y,z * K(u \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(4118(a,1),3468(a,1))].">
      <j1 rule="para" parents="4118 3468"/>
    </justification>
  </clause>

  <clause id="4122">
    <literal><![CDATA[
      a(x,y,1 / z) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(1317(a,1),4119(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1317 4119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4123">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(2771(a,1),4119(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2771 4119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4124">
    <literal><![CDATA[
      a(x,y,(1 / z) * u) = a(x,y,(z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(2919(a,1),4119(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2919 4119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4125">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) \ 1) = a(x,y,(1 / u) * (z * z))
    ]]></literal>
    <justification jstring="[para(896(a,1),4122(a,1,3)),flip(a)].">
      <j1 rule="para" parents="896 4122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4126">
    <literal><![CDATA[
      ((x * (y * (K(z,z \ 1) * u))) \ ((x * y) * u)) * K(z,z \ 1) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3123,a,b,4123,a)].">
      <j1 rule="hyper" parents="63 3123 4123"/>
    </justification>
  </clause>

  <clause id="4127">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) \ 1) = a(x,y,(u \ 1) * (z * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,4124,a(flip),b,4125,a),flip(a)].">
      <j1 rule="hyper" parents="347 4124 4125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4128">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) \ 1) = a(x,y,u \ (z * z))
    ]]></literal>
    <justification jstring="[para(460(a,1),4127(a,2,3))].">
      <j1 rule="para" parents="460 4127"/>
    </justification>
  </clause>

  <clause id="4130">
    <literal><![CDATA[
      ((x * (y * (z * K(u,u \ 1)))) \ ((x * y) * z)) * K(u,u \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2742(a,1),4126(a,1,1,1,2,2))].">
      <j1 rule="para" parents="2742 4126"/>
    </justification>
  </clause>

  <clause id="4131">
    <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(347,a,2446,a(flip),b,2447,a),flip(a)].">
      <j1 rule="hyper" parents="347 2446 2447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4132">
    <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(3674(a,2),4131(a,1,1))].">
      <j1 rule="para" parents="3674 4131"/>
    </justification>
  </clause>

  <clause id="4133">
    <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(4132(a,1),314(a,1))].">
      <j1 rule="para" parents="4132 314"/>
    </justification>
  </clause>

  <clause id="4134">
    <literal><![CDATA[
      ((x * ((x / y) / x)) * y) * (x \ z) = x * ((x \ T(x,y \ 1)) * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(4133,a,3800,a)].">
      <j1 rule="hyper" parents="4133 3800"/>
    </justification>
  </clause>

  <clause id="4135">
    <literal><![CDATA[
      x * ((x \ T(x,y \ 1)) * (x \ z)) = T(x,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[para(3801(a,1),4134(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3801 4134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4136">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) * (x \ z) = x * ((x \ T(x,y)) * (x \ z))
    ]]></literal>
    <justification jstring="[para(2966(a,1),4135(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2966 4135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4137">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * (x \ z)) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(2966(a,1),4136(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2966 4136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4138">
    <literal><![CDATA[
      T(x,y) * (x \ (x * z)) = x * ((x \ T(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),4137(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 4137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4139">
    <literal><![CDATA[
      (T(x,y) * z) / ((x \ T(x,y)) * z) = x
    ]]></literal>
    <justification jstring="[hyper(718,a,4138,a)].">
      <j1 rule="hyper" parents="718 4138"/>
    </justification>
  </clause>

  <clause id="4140">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(620,a,4138,a),flip(a)].">
      <j1 rule="hyper" parents="620 4138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4141">
    <literal><![CDATA[
      R(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(900,a,4139,a)].">
      <j1 rule="hyper" parents="900 4139"/>
    </justification>
  </clause>

  <clause id="4142">
    <literal><![CDATA[
      (x \ T(x,y)) * z = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(36,a,1222,a,b,4139,a),flip(a)].">
      <j1 rule="hyper" parents="36 1222 4139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4145">
    <literal><![CDATA[
      (x \ T(x,y)) * (x * (T(x,y) \ z)) = z
    ]]></literal>
    <justification jstring="[hyper(34,a,1227,a(flip),b,4140,a),flip(a)].">
      <j1 rule="hyper" parents="34 1227 4140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4146">
    <literal><![CDATA[
      L(x,y \ T(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(34,a,476,a,b,4140,a(flip))].">
      <j1 rule="hyper" parents="34 476 4140"/>
    </justification>
  </clause>

  <clause id="4148">
    <literal><![CDATA[
      x * ((T(y,x) \ y) * z) = T(x,T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(3767(a,2),4140(a,1,2,1))].">
      <j1 rule="para" parents="3767 4140"/>
    </justification>
  </clause>

  <clause id="4149">
    <literal><![CDATA[
      T(x,y) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(3769(a,1),4140(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3769 4140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4151">
    <literal><![CDATA[
      L(x,y \ T(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4146(a,1),50(a,2))].">
      <j1 rule="para" parents="4146 50"/>
    </justification>
  </clause>

  <clause id="4152">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * T(z,x * (x \ T(x,y)))) = z * (x * (x \ T(x,y)))
    ]]></literal>
    <justification jstring="[para(4146(a,1),734(a,2,1))].">
      <j1 rule="para" parents="4146 734"/>
    </justification>
  </clause>

  <clause id="4153">
    <literal><![CDATA[
      L(x,T(y,T(z,y)) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(3781(a,2),4146(a,1,2))].">
      <j1 rule="para" parents="3781 4146"/>
    </justification>
  </clause>

  <clause id="4154">
    <literal><![CDATA[
      L(x,T(y,z) \ y,(y * z) / y) = x
    ]]></literal>
    <justification jstring="[para(254(a,1),4153(a,1,2,1,2))].">
      <j1 rule="para" parents="254 4153"/>
    </justification>
  </clause>

  <clause id="4155">
    <literal><![CDATA[
      T(x,y) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1245,a,4149,a)].">
      <j1 rule="hyper" parents="1245 4149"/>
    </justification>
  </clause>

  <clause id="4156">
    <literal><![CDATA[
      (x * (x * y)) / x = T(x,x * y) * y
    ]]></literal>
    <justification jstring="[hyper(1233,a,4149,a),flip(a)].">
      <j1 rule="hyper" parents="1233 4149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4157">
    <literal><![CDATA[
      T(x,x / (x / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1612,a,b,4149,a)].">
      <j1 rule="hyper" parents="35 1612 4149"/>
    </justification>
  </clause>

  <clause id="4158">
    <literal><![CDATA[
      T(x,x \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),4149(a,2,2,1))].">
      <j1 rule="para" parents="10 4149"/>
    </justification>
  </clause>

  <clause id="4159">
    <literal><![CDATA[
      T(x / y,y) * y = (x / y) * (x / (x / y))
    ]]></literal>
    <justification jstring="[para(12(a,1),4149(a,2,2,1))].">
      <j1 rule="para" parents="12 4149"/>
    </justification>
  </clause>

  <clause id="4160">
    <literal><![CDATA[
      T(x,T(y,x)) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[para(255(a,1),4149(a,2,2))].">
      <j1 rule="para" parents="255 4149"/>
    </justification>
  </clause>

  <clause id="4161">
    <literal><![CDATA[
      T(x,y) = (x / y) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1261,a,b,4157,a),flip(a)].">
      <j1 rule="hyper" parents="63 1261 4157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4162">
    <literal><![CDATA[
      T(x,x / (1 / y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1879,a(flip),b,4157,a)].">
      <j1 rule="hyper" parents="63 1879 4157"/>
    </justification>
  </clause>

  <clause id="4163">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,1269,a(flip),b,4157,a)].">
      <j1 rule="hyper" parents="63 1269 4157"/>
    </justification>
  </clause>

  <clause id="4164">
    <literal><![CDATA[
      T(x,T(y,x)) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,4157,a(flip),b,1530,a(flip))].">
      <j1 rule="hyper" parents="133 4157 1530"/>
    </justification>
  </clause>

  <clause id="4165">
    <literal><![CDATA[
      T(x,y) / ((x * y) / x) = x / y
    ]]></literal>
    <justification jstring="[hyper(131,a,4157,a(flip),b,1261,a)].">
      <j1 rule="hyper" parents="131 4157 1261"/>
    </justification>
  </clause>

  <clause id="4166">
    <literal><![CDATA[
      T(x,x / y) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(80(a,1),4157(a,1,2,2))].">
      <j1 rule="para" parents="80 4157"/>
    </justification>
  </clause>

  <clause id="4167">
    <literal><![CDATA[
      T(x,(y \ x) \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(215(a,1),4157(a,1,2)),flip(a)].">
      <j1 rule="para" parents="215 4157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4168">
    <literal><![CDATA[
      T(x,x * (1 / y)) = T(x,x / y)
    ]]></literal>
    <justification jstring="[hyper(347,a,4009,a,b,4166,a)].">
      <j1 rule="hyper" parents="347 4009 4166"/>
    </justification>
  </clause>

  <clause id="4169">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) = T(y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1259,a,b,4166,a)].">
      <j1 rule="hyper" parents="63 1259 4166"/>
    </justification>
  </clause>

  <clause id="4170">
    <literal><![CDATA[
      T(x,y \ x) / y = (x * (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,4166,a(flip),b,1255,a)].">
      <j1 rule="hyper" parents="131 4166 1255"/>
    </justification>
  </clause>

  <clause id="4171">
    <literal><![CDATA[
      T(x \ T(y,x \ y),y) = x \ y
    ]]></literal>
    <justification jstring="[para(4166(a,1),1262(a,1,1,2))].">
      <j1 rule="para" parents="4166 1262"/>
    </justification>
  </clause>

  <clause id="4172">
    <literal><![CDATA[
      T(x,T(y,y \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(112(a,2),4167(a,1,2))].">
      <j1 rule="para" parents="112 4167"/>
    </justification>
  </clause>

  <clause id="4173">
    <literal><![CDATA[
      T(x / y,T(y,x)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(269,a,1517,a,b,4155,a)].">
      <j1 rule="hyper" parents="269 1517 4155"/>
    </justification>
  </clause>

  <clause id="4174">
    <literal><![CDATA[
      T(x,T(y,x * y)) = y \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(269,a,1506,a(flip),b,4155,a)].">
      <j1 rule="hyper" parents="269 1506 4155"/>
    </justification>
  </clause>

  <clause id="4175">
    <literal><![CDATA[
      T(x,y) \ ((x * y) / x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(138,a,4155,a)].">
      <j1 rule="hyper" parents="138 4155"/>
    </justification>
  </clause>

  <clause id="4176">
    <literal><![CDATA[
      L(((x * y) / x) / y,y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4155(a,1),3051(a,1,1,1))].">
      <j1 rule="para" parents="4155 3051"/>
    </justification>
  </clause>

  <clause id="4177">
    <literal><![CDATA[
      T(x \ y,T(x,y)) = T(x \ y,x)
    ]]></literal>
    <justification jstring="[para(4173(a,1),277(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4173 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4178">
    <literal><![CDATA[
      T(x / y,(x * y) / x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(269,a,4161,a(flip),b,1253,a(flip))].">
      <j1 rule="hyper" parents="269 4161 1253"/>
    </justification>
  </clause>

  <clause id="4179">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(4162(a,1),1877(a,1,1))].">
      <j1 rule="para" parents="4162 1877"/>
    </justification>
  </clause>

  <clause id="4180">
    <literal><![CDATA[
      ((x * y) * y) / (x * y) = x \ T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,204,a(flip),b,4165,a),flip(a)].">
      <j1 rule="hyper" parents="36 204 4165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4181">
    <literal><![CDATA[
      T(x,T(y,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,22,a,b,4174,a),flip(a)].">
      <j1 rule="hyper" parents="347 22 4174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4182">
    <literal><![CDATA[
      x \ ((T(y,x) \ y) * z) = ((y * x) / y) \ z
    ]]></literal>
    <justification jstring="[hyper(128,a,4154,a(flip),b,3828,a),flip(a)].">
      <j1 rule="hyper" parents="128 4154 3828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4183">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,170,a(flip),b,4142,a)].">
      <j1 rule="hyper" parents="131 170 4142"/>
    </justification>
  </clause>

  <clause id="4184">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(128,a,170,a(flip),b,4142,a)].">
      <j1 rule="hyper" parents="128 170 4142"/>
    </justification>
  </clause>

  <clause id="4185">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(128,a,75,a(flip),b,4142,a)].">
      <j1 rule="hyper" parents="128 75 4142"/>
    </justification>
  </clause>

  <clause id="4186">
    <literal><![CDATA[
      T(x,y) * (x \ (z * K(x \ 1,x))) = ((x \ 1) * T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,4081,a(flip),b,4142,a),flip(a)].">
      <j1 rule="hyper" parents="63 4081 4142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4187">
    <literal><![CDATA[
      x * (T(x,y) \ (1 / x)) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,3083,a,b,4145,a),flip(a)].">
      <j1 rule="hyper" parents="34 3083 4145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4188">
    <literal><![CDATA[
      (x \ T(x,y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(4145(a,1),356(a,1,2))].">
      <j1 rule="para" parents="4145 356"/>
    </justification>
  </clause>

  <clause id="4189">
    <literal><![CDATA[
      T(T(x,x * y) * y,x) = x * y
    ]]></literal>
    <justification jstring="[para(4156(a,1),254(a,1,1))].">
      <j1 rule="para" parents="4156 254"/>
    </justification>
  </clause>

  <clause id="4190">
    <literal><![CDATA[
      T(x,x \ (y \ x)) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(128,a,3837,a,b,4158,a)].">
      <j1 rule="hyper" parents="128 3837 4158"/>
    </justification>
  </clause>

  <clause id="4191">
    <literal><![CDATA[
      (x \ T(x,x \ y)) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4142,a,b,4158,a)].">
      <j1 rule="hyper" parents="63 4142 4158"/>
    </justification>
  </clause>

  <clause id="4192">
    <literal><![CDATA[
      T(x,x \ y) * y = x * (x * (y / x))
    ]]></literal>
    <justification jstring="[hyper(134,a,4158,a(flip),b,1220,a),flip(a)].">
      <j1 rule="hyper" parents="134 4158 1220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4193">
    <literal><![CDATA[
      (x * (y / x)) \ (T(x,x \ y) * ((x \ y) * z)) = L(z,x \ y,T(x,x \ y))
    ]]></literal>
    <justification jstring="[para(4158(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4158 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4194">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3085,a,4183,a)].">
      <j1 rule="hyper" parents="3085 4183"/>
    </justification>
  </clause>

  <clause id="4195">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(4183(a,1),359(a,1,1))].">
      <j1 rule="para" parents="4183 359"/>
    </justification>
  </clause>

  <clause id="4197">
    <literal><![CDATA[
      R(K(x,y),x,z) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4183(a,1),3827(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4183 3827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4199">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = (y / x) \ T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3134,a(flip),b,4194,a)].">
      <j1 rule="hyper" parents="63 3134 4194"/>
    </justification>
  </clause>

  <clause id="4200">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(4185(a,2),1244(a,1))].">
      <j1 rule="para" parents="4185 1244"/>
    </justification>
  </clause>

  <clause id="4201">
    <literal><![CDATA[
      L(x \ T(x,y),y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(3771(a,1),4176(a,1,1))].">
      <j1 rule="para" parents="3771 4176"/>
    </justification>
  </clause>

  <clause id="4202">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,4163,a(flip),b,4179,a),flip(a)].">
      <j1 rule="hyper" parents="347 4163 4179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4203">
    <literal><![CDATA[
      (x * y) * T(x,T(y,x)) = R(x,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(4202(a,1),268(a,1,2))].">
      <j1 rule="para" parents="4202 268"/>
    </justification>
  </clause>

  <clause id="4204">
    <literal><![CDATA[
      (T(x,y) \ x) * (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(34,a,4164,a(flip),b,4148,a),flip(a)].">
      <j1 rule="hyper" parents="34 4164 4148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4205">
    <literal><![CDATA[
      K(x,y) = T(T(y,x) \ y,y * x)
    ]]></literal>
    <justification jstring="[hyper(269,a,4204,a,b,91,a),flip(a)].">
      <j1 rule="hyper" parents="269 4204 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4206">
    <literal><![CDATA[
      (x * y) / (y * x) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(145,a,4204,a)].">
      <j1 rule="hyper" parents="145 4204"/>
    </justification>
  </clause>

  <clause id="4207">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = (y * (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,4204,a(flip),b,168,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 4204 168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4209">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,4106,a,b,4206,a(flip))].">
      <j1 rule="hyper" parents="39 4106 4206"/>
    </justification>
  </clause>

  <clause id="4210">
    <literal><![CDATA[
      x \ y != (z * y) / (y * z)
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = x
    ]]></literal>
    <justification jstring="[para(4206(a,2),48(a,1)),flip(a)].">
      <j1 rule="para" parents="4206 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4211">
    <literal><![CDATA[
      T(x,y / x) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * (y / x)) = z
    ]]></literal>
    <justification jstring="[para(4206(a,1),438(a,1))].">
      <j1 rule="para" parents="4206 438"/>
    </justification>
  </clause>

  <clause id="4212">
    <literal><![CDATA[
      T(x,T((x \ 1) * y,x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(1845(a,1),4209(a,1,2))].">
      <j1 rule="para" parents="1845 4209"/>
    </justification>
  </clause>

  <clause id="4213">
    <literal><![CDATA[
      (x / y) * (x / (x / y)) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(113(a,1),4159(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 4159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4214">
    <literal><![CDATA[
      T(x \ T(x * y,y),x) = R(y,x,y)
    ]]></literal>
    <justification jstring="[para(4180(a,1),1034(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4180 1034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4215">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(150,a,4182,a)].">
      <j1 rule="hyper" parents="150 4182"/>
    </justification>
  </clause>

  <clause id="4216">
    <literal><![CDATA[
      x \ (y * (T(y,x) \ y)) = ((y * x) / y) \ y
    ]]></literal>
    <justification jstring="[para(3018(a,1),4182(a,1,2))].">
      <j1 rule="para" parents="3018 4182"/>
    </justification>
  </clause>

  <clause id="4217">
    <literal><![CDATA[
      (x * (y / x)) / y = (x \ y) \ (y / x)
    ]]></literal>
    <justification jstring="[para(113(a,1),4207(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 4207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4218">
    <literal><![CDATA[
      (x * (y / x)) / y = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3789,a(flip),b,4217,a),flip(a)].">
      <j1 rule="hyper" parents="347 3789 4217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4219">
    <literal><![CDATA[
      (x \ (y \ x)) \ (y \ x) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(38,a,3796,a(flip),b,4218,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="38 3796 4218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4220">
    <literal><![CDATA[
      T(x,x \ (y \ x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(384,a,4219,a)].">
      <j1 rule="hyper" parents="384 4219"/>
    </justification>
  </clause>

  <clause id="4221">
    <literal><![CDATA[
      (x \ y) / T(y,x \ 1) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(222,a,4219,a)].">
      <j1 rule="hyper" parents="222 4219"/>
    </justification>
  </clause>

  <clause id="4222">
    <literal><![CDATA[
      ((x \ 1) \ y) / T(y,x) = y \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(220,a,2966,a(flip),b,4219,a)].">
      <j1 rule="hyper" parents="220 2966 4219"/>
    </justification>
  </clause>

  <clause id="4223">
    <literal><![CDATA[
      (x \ (y \ x)) * T(x,y \ 1) = y \ x
    ]]></literal>
    <justification jstring="[hyper(150,a,4219,a)].">
      <j1 rule="hyper" parents="150 4219"/>
    </justification>
  </clause>

  <clause id="4224">
    <literal><![CDATA[
      T(x * y,(x * y) \ y) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),4220(a,1,2,2))].">
      <j1 rule="para" parents="9 4220"/>
    </justification>
  </clause>

  <clause id="4225">
    <literal><![CDATA[
      T(x,(x / y) \ 1) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(83(a,1),4220(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="83 4220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4226">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = T(x,y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(4220(a,1),3791(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4220 3791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4227">
    <literal><![CDATA[
      (x / y) \ T(x,x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4225(a,1),3841(a,1,2))].">
      <j1 rule="para" parents="4225 3841"/>
    </justification>
  </clause>

  <clause id="4228">
    <literal><![CDATA[
      ((x * y) \ (y \ (x * y))) * T(x * y,y \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,22,a,b,4223,a),flip(a)].">
      <j1 rule="hyper" parents="347 22 4223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4229">
    <literal><![CDATA[
      (x \ ((1 / y) \ x)) * T(x,y) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[para(83(a,1),4223(a,1,2,2))].">
      <j1 rule="para" parents="83 4223"/>
    </justification>
  </clause>

  <clause id="4230">
    <literal><![CDATA[
      ((x \ y) \ y) / (x * (y / x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(220,a,4227,a(flip),b,335,a(flip))].">
      <j1 rule="hyper" parents="220 4227 335"/>
    </justification>
  </clause>

  <clause id="4231">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,x \ (y * x)) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),4227(a,2,2))].">
      <j1 rule="para" parents="11 4227"/>
    </justification>
  </clause>

  <clause id="4232">
    <literal><![CDATA[
      ((x / y) * ((x * (y / x)) / T(x,x \ y))) * ((x / y) \ 1) = R(1 / (x / y),x / y,(x / y) \ T(x,x \ y))
    ]]></literal>
    <justification jstring="[para(4227(a,1),1733(a,1,1,2,1))].">
      <j1 rule="para" parents="4227 1733"/>
    </justification>
  </clause>

  <clause id="4233">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = ((x * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(133,a,11,a(flip),b,4230,a)].">
      <j1 rule="hyper" parents="133 11 4230"/>
    </justification>
  </clause>

  <clause id="4234">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,3779,a,b,4215,a)].">
      <j1 rule="hyper" parents="63 3779 4215"/>
    </justification>
  </clause>

  <clause id="4235">
    <literal><![CDATA[
      T(x * y,x \ 1) = ((x * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(440,a,4224,a),flip(a)].">
      <j1 rule="hyper" parents="440 4224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4236">
    <literal><![CDATA[
      T(x * y,x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      ((x * y) \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(4224(a,1),440(a,1))].">
      <j1 rule="para" parents="4224 440"/>
    </justification>
  </clause>

  <clause id="4237">
    <literal><![CDATA[
      T((x \ 1) * y,x) = (((x \ 1) * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,2966,a(flip),b,4235,a)].">
      <j1 rule="hyper" parents="63 2966 4235"/>
    </justification>
  </clause>

  <clause id="4238">
    <literal><![CDATA[
      (x \ 1) * (((x * y) \ y) \ y) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,4235,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 4235 22"/>
    </justification>
  </clause>

  <clause id="4239">
    <literal><![CDATA[
      T((1 / x) * y,x) = (((1 / x) * y) \ y) \ y
    ]]></literal>
    <justification jstring="[para(83(a,1),4235(a,1,2))].">
      <j1 rule="para" parents="83 4235"/>
    </justification>
  </clause>

  <clause id="4240">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,T(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(22(a,2),4231(a,1,2,2))].">
      <j1 rule="para" parents="22 4231"/>
    </justification>
  </clause>

  <clause id="4241">
    <literal><![CDATA[
      ((((x / y) \ 1) * x) \ x) \ x = ((x / y) \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1848,a(flip),b,4237,a),flip(a)].">
      <j1 rule="hyper" parents="63 1848 4237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4243">
    <literal><![CDATA[
      T((x \ 1) * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (((x \ 1) * y) \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(2966(a,1),4236(a,1))].">
      <j1 rule="para" parents="2966 4236"/>
    </justification>
  </clause>

  <clause id="4244">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(2221,a,4197,a),flip(a)].">
      <j1 rule="hyper" parents="2221 4197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4245">
    <literal><![CDATA[
      L(x \ T(x,T(y,x)),T(y,x),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4197(a,1),406(a,1)),flip(b)].">
      <j1 rule="para" parents="4197 406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4247">
    <literal><![CDATA[
      R(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,4197,a,b,4244,a)].">
      <j1 rule="hyper" parents="347 4197 4244"/>
    </justification>
  </clause>

  <clause id="4248">
    <literal><![CDATA[
      (K(x,y) * x) * z = K(x,y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,4247,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 4247 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4249">
    <literal><![CDATA[
      K(x,y) * (1 / x) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,4247,a(flip),b,2259,a),flip(a)].">
      <j1 rule="hyper" parents="131 4247 2259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4250">
    <literal><![CDATA[
      L(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(544,a,4248,a)].">
      <j1 rule="hyper" parents="544 4248"/>
    </justification>
  </clause>

  <clause id="4251">
    <literal><![CDATA[
      L(x,y \ 1,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(3519,a,4250,a)].">
      <j1 rule="hyper" parents="3519 4250"/>
    </justification>
  </clause>

  <clause id="4252">
    <literal><![CDATA[
      L(x,y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4250(a,1),50(a,2))].">
      <j1 rule="para" parents="4250 50"/>
    </justification>
  </clause>

  <clause id="4253">
    <literal><![CDATA[
      ((x \ y) / y) \ T((x \ y) / y,z) = x * T(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1349,a,4199,a),flip(a)].">
      <j1 rule="hyper" parents="1349 4199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4256">
    <literal><![CDATA[
      K(T(x,T(y,x)),T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4201(a,1),4245(a,1))].">
      <j1 rule="para" parents="4201 4245"/>
    </justification>
  </clause>

  <clause id="4257">
    <literal><![CDATA[
      R(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(4197(a,2),4245(a,1))].">
      <j1 rule="para" parents="4197 4245"/>
    </justification>
  </clause>

  <clause id="4258">
    <literal><![CDATA[
      T(x,y \ 1) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[para(4220(a,1),4190(a,1,1))].">
      <j1 rule="para" parents="4220 4190"/>
    </justification>
  </clause>

  <clause id="4259">
    <literal><![CDATA[
      T(L(x,y,y \ 1),(1 / y) \ 1) \ ((1 / y) \ T(L(x,y,y \ 1),(1 / y) \ 1)) = L(x,y,y \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(2946(a,1),4258(a,2,2))].">
      <j1 rule="para" parents="2946 4258"/>
    </justification>
  </clause>

  <clause id="4260">
    <literal><![CDATA[
      ((x * y) \ T(x,y)) * T(x * y,y \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(22(a,2),4228(a,1,1,2))].">
      <j1 rule="para" parents="22 4228"/>
    </justification>
  </clause>

  <clause id="4261">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3768,a(flip),b,4253,a)].">
      <j1 rule="hyper" parents="63 3768 4253"/>
    </justification>
  </clause>

  <clause id="4262">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = (y * T(y \ 1,x)) \ x
    ]]></literal>
    <justification jstring="[para(4253(a,1),3785(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4253 3785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4263">
    <literal><![CDATA[
      T(x,y \ 1) \ x = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4226,a(flip),b,4261,a)].">
      <j1 rule="hyper" parents="63 4226 4261"/>
    </justification>
  </clause>

  <clause id="4265">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,1140,a(flip),b,4263,a),flip(a)].">
      <j1 rule="hyper" parents="347 1140 4263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4266">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(2966(a,1),4265(a,1,1))].">
      <j1 rule="para" parents="2966 4265"/>
    </justification>
  </clause>

  <clause id="4267">
    <literal><![CDATA[
      T(x,y / x) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(347,a,3768,a(flip),b,4266,a),flip(a)].">
      <j1 rule="hyper" parents="347 3768 4266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4268">
    <literal><![CDATA[
      (x * y) / x = y * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(134,a,4266,a,b,3766,a),flip(a)].">
      <j1 rule="hyper" parents="134 4266 3766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4269">
    <literal><![CDATA[
      (T(x,y / z) \ x) * y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,4266,a,b,4199,a)].">
      <j1 rule="hyper" parents="133 4266 4199"/>
    </justification>
  </clause>

  <clause id="4270">
    <literal><![CDATA[
      T(x,T(y,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,3781,a,b,4266,a)].">
      <j1 rule="hyper" parents="39 3781 4266"/>
    </justification>
  </clause>

  <clause id="4271">
    <literal><![CDATA[
      x * ((T(y,x) \ y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4266(a,2),4140(a,1,2,1))].">
      <j1 rule="para" parents="4266 4140"/>
    </justification>
  </clause>

  <clause id="4272">
    <literal><![CDATA[
      T(x,y) * (x \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[para(4266(a,2),4142(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4266 4142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4273">
    <literal><![CDATA[
      K(x,y) = T(x \ T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(4266(a,1),4205(a,2,1))].">
      <j1 rule="para" parents="4266 4205"/>
    </justification>
  </clause>

  <clause id="4274">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4202,a,b,4270,a)].">
      <j1 rule="hyper" parents="63 4202 4270"/>
    </justification>
  </clause>

  <clause id="4275">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4163,a,b,4270,a)].">
      <j1 rule="hyper" parents="63 4163 4270"/>
    </justification>
  </clause>

  <clause id="4276">
    <literal><![CDATA[
      T(x,(x \ 1) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4212,a(flip),b,4270,a),flip(a)].">
      <j1 rule="hyper" parents="63 4212 4270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4277">
    <literal><![CDATA[
      T((T(x,y) * y) / T(x,y),x) = y
    ]]></literal>
    <justification jstring="[hyper(40,a,304,a,b,4270,a)].">
      <j1 rule="hyper" parents="40 304 4270"/>
    </justification>
  </clause>

  <clause id="4278">
    <literal><![CDATA[
      T(x / T(y,x),y) = y \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(462,a,4270,a(flip),b,4163,a)].">
      <j1 rule="hyper" parents="462 4270 4163"/>
    </justification>
  </clause>

  <clause id="4279">
    <literal><![CDATA[
      T(x,y) / y = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,4270,a(flip),b,4163,a)].">
      <j1 rule="hyper" parents="131 4270 4163"/>
    </justification>
  </clause>

  <clause id="4280">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ x) = y
    ]]></literal>
    <justification jstring="[hyper(131,a,4270,a(flip),b,1246,a)].">
      <j1 rule="hyper" parents="131 4270 1246"/>
    </justification>
  </clause>

  <clause id="4281">
    <literal><![CDATA[
      T(x,y) \ y = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,4270,a(flip),b,1246,a),flip(a)].">
      <j1 rule="hyper" parents="128 4270 1246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4282">
    <literal><![CDATA[
      T(T(x,y),T(z,x)) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(4270(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4270 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4284">
    <literal><![CDATA[
      T(x,L(T(y,x),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),4270(a,1,2))].">
      <j1 rule="para" parents="25 4270"/>
    </justification>
  </clause>

  <clause id="4285">
    <literal><![CDATA[
      T(x,y / x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),4270(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 4270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4286">
    <literal><![CDATA[
      T(x \ y,(x \ y) \ y) = T(x \ y,x)
    ]]></literal>
    <justification jstring="[para(112(a,1),4270(a,1,2))].">
      <j1 rule="para" parents="112 4270"/>
    </justification>
  </clause>

  <clause id="4287">
    <literal><![CDATA[
      T(x,y) * T(T(y,x),z) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4270(a,1),266(a,1,2,1))].">
      <j1 rule="para" parents="4270 266"/>
    </justification>
  </clause>

  <clause id="4288">
    <literal><![CDATA[
      T(x,y) * L(T(y,x),z,u) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4270(a,1),267(a,1,2,1))].">
      <j1 rule="para" parents="4270 267"/>
    </justification>
  </clause>

  <clause id="4289">
    <literal><![CDATA[
      T(x,y) * R(T(y,x),z,u) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4270(a,1),268(a,1,2,1))].">
      <j1 rule="para" parents="4270 268"/>
    </justification>
  </clause>

  <clause id="4290">
    <literal><![CDATA[
      T(x,y) * T(T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(4270(a,1),435(a,1,2,1))].">
      <j1 rule="para" parents="4270 435"/>
    </justification>
  </clause>

  <clause id="4292">
    <literal><![CDATA[
      T(x,y) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[para(4270(a,1),4160(a,1,1))].">
      <j1 rule="para" parents="4270 4160"/>
    </justification>
  </clause>

  <clause id="4293">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,y) = x * y
    ]]></literal>
    <justification jstring="[para(4270(a,1),4240(a,1,2))].">
      <j1 rule="para" parents="4270 4240"/>
    </justification>
  </clause>

  <clause id="4294">
    <literal><![CDATA[
      R(x,y,x) * (x * y) = (x * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4270(a,1),4203(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4270 4203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4295">
    <literal><![CDATA[
      (x * y) / T(y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1500,a,b,4275,a)].">
      <j1 rule="hyper" parents="63 1500 4275"/>
    </justification>
  </clause>

  <clause id="4296">
    <literal><![CDATA[
      ((x / T(y,x)) * z) \ T(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      L(z \ y,z,x / T(y,x)) = u
    ]]></literal>
    <justification jstring="[para(4275(a,1),686(a,1,2))].">
      <j1 rule="para" parents="4275 686"/>
    </justification>
  </clause>

  <clause id="4297">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(134,a,4279,a(flip),b,1595,a),flip(a)].">
      <j1 rule="hyper" parents="134 4279 1595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4298">
    <literal><![CDATA[
      T(x,L(y,z,u)) / L(y,z,u) = x / L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),4279(a,2,2))].">
      <j1 rule="para" parents="25 4279"/>
    </justification>
  </clause>

  <clause id="4299">
    <literal><![CDATA[
      (x / T(y,x)) \ z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4279(a,1),221(a,1,1))].">
      <j1 rule="para" parents="4279 221"/>
    </justification>
  </clause>

  <clause id="4300">
    <literal><![CDATA[
      T(x,y) * (x \ T(y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(150,a,4281,a)].">
      <j1 rule="hyper" parents="150 4281"/>
    </justification>
  </clause>

  <clause id="4301">
    <literal><![CDATA[
      T(x,x \ y) \ y = T(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(38,a,1243,a(flip),b,4281,a(flip))].">
      <j1 rule="hyper" parents="38 1243 4281"/>
    </justification>
  </clause>

  <clause id="4302">
    <literal><![CDATA[
      T(x,y) \ ((T(y,x) \ x) * y) = K(y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4281(a,2),92(a,1,2,1))].">
      <j1 rule="para" parents="4281 92"/>
    </justification>
  </clause>

  <clause id="4303">
    <literal><![CDATA[
      (T(x,y) * ((x \ T(y,x)) * z)) \ (y * z) = a(T(x,y),T(x,y) \ y,z)
    ]]></literal>
    <justification jstring="[para(4281(a,1),88(a,1,1,2,1))].">
      <j1 rule="para" parents="4281 88"/>
    </justification>
  </clause>

  <clause id="4304">
    <literal><![CDATA[
      T(x,y) * L(x \ T(y,x),z,u) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[para(4281(a,1),2131(a,1,2,1))].">
      <j1 rule="para" parents="4281 2131"/>
    </justification>
  </clause>

  <clause id="4305">
    <literal><![CDATA[
      T(x,x * y) * R(x \ T(x * y,x),z,u) = T(x * R(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(4281(a,1),2145(a,1,2,1))].">
      <j1 rule="para" parents="4281 2145"/>
    </justification>
  </clause>

  <clause id="4306">
    <literal><![CDATA[
      T(x,y / x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,112,a(flip),b,4285,a),flip(a)].">
      <j1 rule="hyper" parents="347 112 4285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4307">
    <literal><![CDATA[
      (x * (y / x)) / T(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(220,a,4285,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="220 4285 22"/>
    </justification>
  </clause>

  <clause id="4309">
    <literal><![CDATA[
      (x * y) \ (y * T(x,x \ y)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[para(4285(a,1),1071(a,1,2,2))].">
      <j1 rule="para" parents="4285 1071"/>
    </justification>
  </clause>

  <clause id="4310">
    <literal><![CDATA[
      T(x,y) \ (x * y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(138,a,4292,a)].">
      <j1 rule="hyper" parents="138 4292"/>
    </justification>
  </clause>

  <clause id="4311">
    <literal><![CDATA[
      R(x,T(y,z),T(z,y)) * (y * z) = (x * T(y,z)) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,4292,a(flip),b,209,a)].">
      <j1 rule="hyper" parents="134 4292 209"/>
    </justification>
  </clause>

  <clause id="4312">
    <literal><![CDATA[
      (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4292(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4292 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4313">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y))
    ]]></literal>
    <justification jstring="[para(4292(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4292 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4315">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) != (x * y) * u
    ]]></literal>
    <literal><![CDATA[
      L(z,T(y,x),T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(4292(a,1),544(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4292 544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4316">
    <literal><![CDATA[
      ((x * y) * z) / (T(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(T(x,y),T(y,x),z) = u
    ]]></literal>
    <justification jstring="[para(4292(a,1),595(a,1,1,1))].">
      <j1 rule="para" parents="4292 595"/>
    </justification>
  </clause>

  <clause id="4317">
    <literal><![CDATA[
      (T(x,y) * (y * x)) / T(x,y) = T(y,x) * T(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[hyper(133,a,4295,a(flip),b,1520,a),flip(a)].">
      <j1 rule="hyper" parents="133 4295 1520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4318">
    <literal><![CDATA[
      (x * R(y,z,u)) / R(T(y,x),z,u) = T(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(27(a,2),4295(a,1,2))].">
      <j1 rule="para" parents="27 4295"/>
    </justification>
  </clause>

  <clause id="4320">
    <literal><![CDATA[
      T(x \ y,x) = ((x \ y) \ y) \ y
    ]]></literal>
    <justification jstring="[para(80(a,1),4306(a,1,2))].">
      <j1 rule="para" parents="80 4306"/>
    </justification>
  </clause>

  <clause id="4321">
    <literal><![CDATA[
      (x * (y / x)) * x = y * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(4306(a,1),1065(a,2,2))].">
      <j1 rule="para" parents="4306 1065"/>
    </justification>
  </clause>

  <clause id="4322">
    <literal><![CDATA[
      T(x,x * (y / x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1047,a,4274,a),flip(a)].">
      <j1 rule="hyper" parents="1047 4274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4323">
    <literal><![CDATA[
      T(x,y * x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(1045,a,4274,a)].">
      <j1 rule="hyper" parents="1045 4274"/>
    </justification>
  </clause>

  <clause id="4324">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),4274(a,1,1,2))].">
      <j1 rule="para" parents="10 4274"/>
    </justification>
  </clause>

  <clause id="4325">
    <literal><![CDATA[
      T(x,(x \ y) * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),4322(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 4322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4326">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * (y / x),x)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4322(a,1),4300(a,1,1))].">
      <j1 rule="para" parents="4322 4300"/>
    </justification>
  </clause>

  <clause id="4327">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,752,a,b,4323,a)].">
      <j1 rule="hyper" parents="347 752 4323"/>
    </justification>
  </clause>

  <clause id="4329">
    <literal><![CDATA[
      R(T(x,y * R(x,z,u)),z,u) = T(R(x,z,u),R(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,27,a,b,4323,a)].">
      <j1 rule="hyper" parents="63 27 4323"/>
    </justification>
  </clause>

  <clause id="4330">
    <literal><![CDATA[
      T(T(x,x * y),z) = T(T(x,z),y * x)
    ]]></literal>
    <justification jstring="[para(4323(a,1),23(a,1,1))].">
      <j1 rule="para" parents="4323 23"/>
    </justification>
  </clause>

  <clause id="4331">
    <literal><![CDATA[
      x * T(y,x * y) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(4323(a,2),754(a,1,2))].">
      <j1 rule="para" parents="4323 754"/>
    </justification>
  </clause>

  <clause id="4332">
    <literal><![CDATA[
      T(x,T(y,y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4323(a,1),4181(a,1,2))].">
      <j1 rule="para" parents="4323 4181"/>
    </justification>
  </clause>

  <clause id="4333">
    <literal><![CDATA[
      T(T(x,y),(x \ z) * x) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(4325(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4325 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4334">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * ((x \ y) * x) = z
    ]]></literal>
    <justification jstring="[para(4325(a,1),315(a,1,2))].">
      <j1 rule="para" parents="4325 315"/>
    </justification>
  </clause>

  <clause id="4335">
    <literal><![CDATA[
      (((x \ y) * x) / T(x,y)) * x = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[para(4325(a,1),4275(a,1,1,2))].">
      <j1 rule="para" parents="4325 4275"/>
    </justification>
  </clause>

  <clause id="4336">
    <literal><![CDATA[
      T(x,x * y) * L(T(y,x),z,u) = L(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[para(4332(a,1),267(a,1,2,1))].">
      <j1 rule="para" parents="4332 267"/>
    </justification>
  </clause>

  <clause id="4337">
    <literal><![CDATA[
      T(x,x * y) * R(T(y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(y,z,u) * T(x,x * y) = w
    ]]></literal>
    <justification jstring="[para(4332(a,1),437(a,1,2,1))].">
      <j1 rule="para" parents="4332 437"/>
    </justification>
  </clause>

  <clause id="4338">
    <literal><![CDATA[
      T((x * y) / x,x * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,304,a,b,4327,a)].">
      <j1 rule="hyper" parents="40 304 4327"/>
    </justification>
  </clause>

  <clause id="4339">
    <literal><![CDATA[
      ((x \ y) * x) / (x \ y) = y / (y / x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3792,a,b,4268,a),flip(a)].">
      <j1 rule="hyper" parents="347 3792 4268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4340">
    <literal><![CDATA[
      ((x * y) / x) \ x = y \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(4268(a,2),4216(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4268 4216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4341">
    <literal><![CDATA[
      x \ T(x,T(y,(y \ 1) * x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,3818,a(flip),b,4273,a)].">
      <j1 rule="hyper" parents="347 3818 4273"/>
    </justification>
  </clause>

  <clause id="4342">
    <literal><![CDATA[
      T(x \ 1,(x \ 1) \ y) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2957,a(flip),b,4276,a),flip(a)].">
      <j1 rule="hyper" parents="63 2957 4276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4343">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,x \ y)) * y
    ]]></literal>
    <justification jstring="[para(4276(a,1),4116(a,2,1,2))].">
      <j1 rule="para" parents="4276 4116"/>
    </justification>
  </clause>

  <clause id="4344">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4277(a,1),810(a,1,1))].">
      <j1 rule="para" parents="4277 810"/>
    </justification>
  </clause>

  <clause id="4345">
    <literal><![CDATA[
      T(x,L(T(y,x),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(25(a,2),4344(a,1,2))].">
      <j1 rule="para" parents="25 4344"/>
    </justification>
  </clause>

  <clause id="4346">
    <literal><![CDATA[
      T(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y / x) = z
    ]]></literal>
    <justification jstring="[para(113(a,1),4344(a,1,2))].">
      <j1 rule="para" parents="113 4344"/>
    </justification>
  </clause>

  <clause id="4347">
    <literal><![CDATA[
      T(T(x,y),T(z,x)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,23,a,b,4282,a),flip(a)].">
      <j1 rule="hyper" parents="347 23 4282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4348">
    <literal><![CDATA[
      T(x,x \ y) / y = x / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(375,a,4293,a)].">
      <j1 rule="hyper" parents="375 4293"/>
    </justification>
  </clause>

  <clause id="4349">
    <literal><![CDATA[
      T(x,y) / (x * y) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(222,a,4293,a)].">
      <j1 rule="hyper" parents="222 4293"/>
    </justification>
  </clause>

  <clause id="4350">
    <literal><![CDATA[
      T(x \ (y \ x),x) = T(x,y \ 1) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(4220(a,1),4301(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4220 4301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4351">
    <literal><![CDATA[
      T(T(x \ y,z),x) = T(((x \ y) \ y) \ y,z)
    ]]></literal>
    <justification jstring="[para(4320(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4320 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4352">
    <literal><![CDATA[
      T(x \ y,x) != z \ y
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(4320(a,2),48(a,1))].">
      <j1 rule="para" parents="4320 48"/>
    </justification>
  </clause>

  <clause id="4353">
    <literal><![CDATA[
      L((((x \ y) \ z) \ z) \ z,x \ y,x) = T(y \ (x * z),x \ y)
    ]]></literal>
    <justification jstring="[para(4320(a,1),891(a,1,1))].">
      <j1 rule="para" parents="4320 891"/>
    </justification>
  </clause>

  <clause id="4354">
    <literal><![CDATA[
      T(x,y) * T(T(y,z),x) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,4347,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 4347 22"/>
    </justification>
  </clause>

  <clause id="4355">
    <literal><![CDATA[
      T(T(x,y),z / x) = T(T(x,y),x \ z)
    ]]></literal>
    <justification jstring="[para(113(a,1),4347(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 4347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4356">
    <literal><![CDATA[
      T(x,y) / (x * y) = R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,247,a,b,4349,a),flip(a)].">
      <j1 rule="hyper" parents="347 247 4349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4357">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,112,a(flip),b,4324,a),flip(a)].">
      <j1 rule="hyper" parents="347 112 4324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4358">
    <literal><![CDATA[
      (x * (y * x)) / x = L(x,y,x) * y
    ]]></literal>
    <justification jstring="[hyper(1525,a,4331,a)].">
      <j1 rule="hyper" parents="1525 4331"/>
    </justification>
  </clause>

  <clause id="4359">
    <literal><![CDATA[
      (x * T(y,z * y)) / (L(y,z,y) * z) = R(x / z,z,T(y,z * y))
    ]]></literal>
    <justification jstring="[hyper(220,a,4331,a(flip),b,579,a)].">
      <j1 rule="hyper" parents="220 4331 579"/>
    </justification>
  </clause>

  <clause id="4360">
    <literal><![CDATA[
      (L(x,y,x) * y) * x = x * (y * x)
    ]]></literal>
    <justification jstring="[hyper(133,a,4331,a(flip),b,1506,a)].">
      <j1 rule="hyper" parents="133 4331 1506"/>
    </justification>
  </clause>

  <clause id="4361">
    <literal><![CDATA[
      L(x,y,x) \ ((x * (y * x)) / x) = y
    ]]></literal>
    <justification jstring="[hyper(128,a,1506,a,b,4331,a(flip))].">
      <j1 rule="hyper" parents="128 1506 4331"/>
    </justification>
  </clause>

  <clause id="4362">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x * y) = R(L(y,x,y),x,x)
    ]]></literal>
    <justification jstring="[para(4338(a,1),793(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4338 793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4363">
    <literal><![CDATA[
      R(1 / x,x,T(y,x)) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(768,a,4356,a)].">
      <j1 rule="hyper" parents="768 4356"/>
    </justification>
  </clause>

  <clause id="4364">
    <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(4356(a,1),2117(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4356 2117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4365">
    <literal><![CDATA[
      R(T(T(x,y),z),x \ y,x) = T((x \ y) \ y,z)
    ]]></literal>
    <justification jstring="[para(4357(a,1),27(a,2,1))].">
      <j1 rule="para" parents="4357 27"/>
    </justification>
  </clause>

  <clause id="4366">
    <literal><![CDATA[
      R(x,x \ y,x) * y = y * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(4357(a,1),268(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4357 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4367">
    <literal><![CDATA[
      T((x * y) / x,L(x,y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(269,a,2012,a,b,4358,a(flip))].">
      <j1 rule="hyper" parents="269 2012 4358"/>
    </justification>
  </clause>

  <clause id="4368">
    <literal><![CDATA[
      T(L(x,y,x) * y,x) = y * x
    ]]></literal>
    <justification jstring="[para(4358(a,1),254(a,1,1))].">
      <j1 rule="para" parents="4358 254"/>
    </justification>
  </clause>

  <clause id="4369">
    <literal><![CDATA[
      T(x,L(y,x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4367(a,1),304(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4367 304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4370">
    <literal><![CDATA[
      L(x,y,x) * T(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      y * L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(4369(a,1),315(a,1,2))].">
      <j1 rule="para" parents="4369 315"/>
    </justification>
  </clause>

  <clause id="4371">
    <literal><![CDATA[
      T((x \ y) * T(x,y),x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(756(a,1),4368(a,1,1))].">
      <j1 rule="para" parents="756 4368"/>
    </justification>
  </clause>

  <clause id="4372">
    <literal><![CDATA[
      L(R(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[hyper(1179,a,4360,a)].">
      <j1 rule="hyper" parents="1179 4360"/>
    </justification>
  </clause>

  <clause id="4373">
    <literal><![CDATA[
      R(L(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[hyper(594,a,4360,a)].">
      <j1 rule="hyper" parents="594 4360"/>
    </justification>
  </clause>

  <clause id="4374">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,535,a,b,4372,a)].">
      <j1 rule="hyper" parents="41 535 4372"/>
    </justification>
  </clause>

  <clause id="4375">
    <literal><![CDATA[
      L(T(R(x,y,x),z),y,x) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4372(a,1),25(a,2,1))].">
      <j1 rule="para" parents="4372 25"/>
    </justification>
  </clause>

  <clause id="4376">
    <literal><![CDATA[
      L(R(R(x,y,x),z,u),y,x) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(4372(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4372 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4377">
    <literal><![CDATA[
      R(x,y,z) != z
    ]]></literal>
    <literal><![CDATA[
      L(z,y,z) = x
    ]]></literal>
    <justification jstring="[para(4373(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="4373 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4378">
    <literal><![CDATA[
      x * R(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(150,a,4374,a)].">
      <j1 rule="hyper" parents="150 4374"/>
    </justification>
  </clause>

  <clause id="4379">
    <literal><![CDATA[
      R(x,y,T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1268,a(flip),b,4374,a)].">
      <j1 rule="hyper" parents="63 1268 4374"/>
    </justification>
  </clause>

  <clause id="4380">
    <literal><![CDATA[
      R(x,x \ y,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),4374(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 4374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4381">
    <literal><![CDATA[
      R(x / y,y,x / y) = y \ T(x,x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),4374(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 4374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4382">
    <literal><![CDATA[
      R(x,y,x) != y \ z
    ]]></literal>
    <literal><![CDATA[
      T(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(4374(a,1),47(a,1))].">
      <j1 rule="para" parents="4374 47"/>
    </justification>
  </clause>

  <clause id="4383">
    <literal><![CDATA[
      (x * y) \ (x * T(z * y,z)) = L(R(z,y,z),y,x)
    ]]></literal>
    <justification jstring="[para(4374(a,1),99(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4374 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4384">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4270(a,1),4379(a,1,3))].">
      <j1 rule="para" parents="4270 4379"/>
    </justification>
  </clause>

  <clause id="4385">
    <literal><![CDATA[
      x \ T(y * x,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(y,x,y) = z
    ]]></literal>
    <justification jstring="[para(4378(a,1),356(a,1,2))].">
      <j1 rule="para" parents="4378 356"/>
    </justification>
  </clause>

  <clause id="4386">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4378(a,1),1716(a,1,1))].">
      <j1 rule="para" parents="4378 1716"/>
    </justification>
  </clause>

  <clause id="4387">
    <literal><![CDATA[
      L(R(T(x,y),z,x),z,x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(27(a,2),4375(a,1,1))].">
      <j1 rule="para" parents="27 4375"/>
    </justification>
  </clause>

  <clause id="4388">
    <literal><![CDATA[
      x / (y * (x / y)) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(4211,a,4267,a)].">
      <j1 rule="hyper" parents="4211 4267"/>
    </justification>
  </clause>

  <clause id="4389">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,4215,a,b,4272,a)].">
      <j1 rule="hyper" parents="347 4215 4272"/>
    </justification>
  </clause>

  <clause id="4390">
    <literal><![CDATA[
      T(x * (y / x),x) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(462,a,xx,b,4321,a)].">
      <j1 rule="hyper" parents="462 4321"/>
    </justification>
  </clause>

  <clause id="4391">
    <literal><![CDATA[
      (x * T(y,y \ x)) / y = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(131,a,338,a,b,4321,a)].">
      <j1 rule="hyper" parents="131 338 4321"/>
    </justification>
  </clause>

  <clause id="4392">
    <literal><![CDATA[
      T(x / (x / y),y \ x) = y
    ]]></literal>
    <justification jstring="[para(4339(a,1),254(a,1,1))].">
      <j1 rule="para" parents="4339 254"/>
    </justification>
  </clause>

  <clause id="4394">
    <literal><![CDATA[
      T(x / (x / y),x) = L(y,y \ x,y)
    ]]></literal>
    <justification jstring="[para(4339(a,1),757(a,1,1))].">
      <j1 rule="para" parents="4339 757"/>
    </justification>
  </clause>

  <clause id="4395">
    <literal><![CDATA[
      T(x / (x / (x / y)),y) = x / y
    ]]></literal>
    <justification jstring="[para(83(a,1),4392(a,1,2))].">
      <j1 rule="para" parents="83 4392"/>
    </justification>
  </clause>

  <clause id="4396">
    <literal><![CDATA[
      (x * (y / x)) / x = y / (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(305,a,4395,a)].">
      <j1 rule="hyper" parents="305 4395"/>
    </justification>
  </clause>

  <clause id="4397">
    <literal><![CDATA[
      x * T(x / (x / y),x) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,4394,a,b,98,a)].">
      <j1 rule="hyper" parents="134 4394 98"/>
    </justification>
  </clause>

  <clause id="4398">
    <literal><![CDATA[
      L(x \ y,(x \ y) \ y,x \ y) = T(y / x,y)
    ]]></literal>
    <justification jstring="[para(80(a,1),4394(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="80 4394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4399">
    <literal><![CDATA[
      T(x,y \ 1) / (y \ x) = x / ((x \ (y \ x)) * x)
    ]]></literal>
    <justification jstring="[para(4220(a,1),4348(a,1,1))].">
      <j1 rule="para" parents="4220 4348"/>
    </justification>
  </clause>

  <clause id="4400">
    <literal><![CDATA[
      R(1 / x,x,y / x) = R(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),4363(a,1,3)),flip(a)].">
      <j1 rule="para" parents="113 4363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4401">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,(x \ y) * x)
    ]]></literal>
    <justification jstring="[para(4371(a,1),4270(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4371 4270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4402">
    <literal><![CDATA[
      (x * (y \ x)) / (x / y) = (x / y) * (x / (x / y))
    ]]></literal>
    <justification jstring="[para(749(a,1),4391(a,1,1,2))].">
      <j1 rule="para" parents="749 4391"/>
    </justification>
  </clause>

  <clause id="4403">
    <literal><![CDATA[
      R(x,x \ y,x) * y = (x * (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,4321,a,b,4366,a),flip(a)].">
      <j1 rule="hyper" parents="347 4321 4366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4404">
    <literal><![CDATA[
      R(x / y,y,x / y) = y \ T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(4166(a,1),4381(a,2,2))].">
      <j1 rule="para" parents="4166 4381"/>
    </justification>
  </clause>

  <clause id="4405">
    <literal><![CDATA[
      R(x,y / x,x) = R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,584,a,b,4403,a)].">
      <j1 rule="hyper" parents="35 584 4403"/>
    </justification>
  </clause>

  <clause id="4406">
    <literal><![CDATA[
      R(x,y / x,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,4380,a(flip),b,4405,a),flip(a)].">
      <j1 rule="hyper" parents="347 4380 4405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4407">
    <literal><![CDATA[
      R(x,(x * y) / x,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4405(a,2,2))].">
      <j1 rule="para" parents="9 4405"/>
    </justification>
  </clause>

  <clause id="4408">
    <literal><![CDATA[
      R(x,T(y,x),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(255(a,1),4407(a,1,2)),flip(a)].">
      <j1 rule="para" parents="255 4407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4409">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4384,a,b,4408,a)].">
      <j1 rule="hyper" parents="63 4384 4408"/>
    </justification>
  </clause>

  <clause id="4410">
    <literal><![CDATA[
      R(R(x,y,z),T(u,x),T(x,u)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(4409(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4409 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4411">
    <literal><![CDATA[
      (x \ (y * x)) \ T(y * x,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(11(a,1),4406(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 4406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4412">
    <literal><![CDATA[
      T((x / y) * y,x / y) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(4382,a,4404,a)].">
      <j1 rule="hyper" parents="4382 4404"/>
    </justification>
  </clause>

  <clause id="4413">
    <literal><![CDATA[
      (T(x,(y / z) / (1 / z)) \ x) * (y / z) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(347,a,1168,a(flip),b,4269,a),flip(a)].">
      <j1 rule="hyper" parents="347 1168 4269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4414">
    <literal><![CDATA[
      T(x,y) \ (y * x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(128,a,4292,a(flip),b,4287,a)].">
      <j1 rule="hyper" parents="128 4292 4287"/>
    </justification>
  </clause>

  <clause id="4415">
    <literal><![CDATA[
      L(T(x,y),z,u) \ (y * L(x,z,u)) = T(T(y,L(x,z,u)),L(x,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),4414(a,1,1))].">
      <j1 rule="para" parents="25 4414"/>
    </justification>
  </clause>

  <clause id="4416">
    <literal><![CDATA[
      T(x \ 1,x * y) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(440,a,4342,a),flip(a)].">
      <j1 rule="hyper" parents="440 4342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4417">
    <literal><![CDATA[
      x / T(y \ 1,y * x) = (y \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(220,a,4342,a(flip),b,112,a(flip))].">
      <j1 rule="hyper" parents="220 4342 112"/>
    </justification>
  </clause>

  <clause id="4418">
    <literal><![CDATA[
      T(x \ 1,x * y) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(4342(a,1),440(a,1))].">
      <j1 rule="para" parents="4342 440"/>
    </justification>
  </clause>

  <clause id="4419">
    <literal><![CDATA[
      T(x \ 1,x * y) * R((((x \ 1) \ y) \ y) \ 1,z,u) = T((x \ 1) * R((x \ 1) \ 1,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(4416(a,1),2148(a,1,2,1,1))].">
      <j1 rule="para" parents="4416 2148"/>
    </justification>
  </clause>

  <clause id="4420">
    <literal><![CDATA[
      (x \ y) / T(x \ 1,y) = (x \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),4417(a,1,2,2))].">
      <j1 rule="para" parents="10 4417"/>
    </justification>
  </clause>

  <clause id="4421">
    <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(134,a,4354,a(flip),b,884,a),flip(a)].">
      <j1 rule="hyper" parents="134 4354 884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4422">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = T(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1450,a,b,4389,a)].">
      <j1 rule="hyper" parents="63 1450 4389"/>
    </justification>
  </clause>

  <clause id="4423">
    <literal><![CDATA[
      x \ (y * ((x \ y) \ y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4297,a(flip),b,4390,a),flip(a)].">
      <j1 rule="hyper" parents="63 4297 4390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4424">
    <literal><![CDATA[
      R(1 / x,x,x \ y) \ (y / x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4400(a,1),420(a,1,1))].">
      <j1 rule="para" parents="4400 420"/>
    </justification>
  </clause>

  <clause id="4425">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,4325,a(flip),b,4401,a),flip(a)].">
      <j1 rule="hyper" parents="347 4325 4401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4426">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,y)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4425(a,1),1524(a,1,1))].">
      <j1 rule="para" parents="4425 1524"/>
    </justification>
  </clause>

  <clause id="4427">
    <literal><![CDATA[
      R(T(T(x,y),(x \ z) * x),x \ z,x) = T((x \ z) \ z,y)
    ]]></literal>
    <justification jstring="[para(4333(a,2),4365(a,1,1))].">
      <j1 rule="para" parents="4333 4365"/>
    </justification>
  </clause>

  <clause id="4428">
    <literal><![CDATA[
      ((x \ y) / y) * (x * (y / x)) = y / x
    ]]></literal>
    <justification jstring="[para(4424(a,1),670(a,1,2))].">
      <j1 rule="para" parents="4424 670"/>
    </justification>
  </clause>

  <clause id="4429">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = T(x,T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,3786,a(flip),b,4262,a),flip(a)].">
      <j1 rule="hyper" parents="347 3786 4262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4430">
    <literal><![CDATA[
      T(x,T(y \ 1,x)) = T(x,(y \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(4344,a,4429,a),flip(a)].">
      <j1 rule="hyper" parents="4344 4429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4431">
    <literal><![CDATA[
      T(x,(y \ z) / z) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4344,a,4430,a),flip(a)].">
      <j1 rule="hyper" parents="4344 4430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4432">
    <literal><![CDATA[
      T(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(4430(a,1),4344(a,1))].">
      <j1 rule="para" parents="4430 4344"/>
    </justification>
  </clause>

  <clause id="4434">
    <literal><![CDATA[
      T(x,y / (z * y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),4431(a,1,2,1))].">
      <j1 rule="para" parents="9 4431"/>
    </justification>
  </clause>

  <clause id="4435">
    <literal><![CDATA[
      T(x,(y / z) \ 1) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(83(a,1),4431(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 4431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4436">
    <literal><![CDATA[
      T(x / (y * x),y \ 1) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(367,a,4434,a)].">
      <j1 rule="hyper" parents="367 4434"/>
    </justification>
  </clause>

  <clause id="4439">
    <literal><![CDATA[
      T(x,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(68(a,1),4432(a,1,2,1))].">
      <j1 rule="para" parents="68 4432"/>
    </justification>
  </clause>

  <clause id="4440">
    <literal><![CDATA[
      T(x,y) * T(y,y * x) = L(y,x,y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(750(a,1),4288(a,1,2))].">
      <j1 rule="para" parents="750 4288"/>
    </justification>
  </clause>

  <clause id="4441">
    <literal><![CDATA[
      T(x,y) * T(y,y * x) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(4370,a,4440,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4370 4440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4442">
    <literal><![CDATA[
      (x * (R(x,y,z) * T(u,x))) \ ((u * x) * R(T(x,u),y,z)) = a(x,T(u,x),R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(4289(a,1),259(a,1,1,2))].">
      <j1 rule="para" parents="4289 259"/>
    </justification>
  </clause>

  <clause id="4443">
    <literal><![CDATA[
      R(x,y,x) * T(x * y,x) = T(x * y,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4274(a,1),4289(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4274 4289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4444">
    <literal><![CDATA[
      T(x,y) * (T(y,x) / x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(1595(a,1),4326(a,1,2))].">
      <j1 rule="para" parents="1595 4326"/>
    </justification>
  </clause>

  <clause id="4445">
    <literal><![CDATA[
      T(x,y) * z != x * (y / x)
    ]]></literal>
    <literal><![CDATA[
      T(y,x) / x = z
    ]]></literal>
    <justification jstring="[para(4444(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="4444 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4446">
    <literal><![CDATA[
      T(x,y) * (y / T(x,y)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4279(a,1),4444(a,1,2))].">
      <j1 rule="para" parents="4279 4444"/>
    </justification>
  </clause>

  <clause id="4447">
    <literal><![CDATA[
      T((x / (y * y)) * (y * y),x / (y * y)) = T(y * y,x) * (x / T(y * y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,253,a,b,4446,a)].">
      <j1 rule="hyper" parents="347 253 4446"/>
    </justification>
  </clause>

  <clause id="4448">
    <literal><![CDATA[
      T(x,y) * z != x * (y / x)
    ]]></literal>
    <literal><![CDATA[
      y / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4446(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="4446 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4449">
    <literal><![CDATA[
      ((x \ y) * x) / T(x,y) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,1591,a(flip),b,4335,a),flip(a)].">
      <j1 rule="hyper" parents="35 1591 4335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4450">
    <literal><![CDATA[
      (x \ T(y,x)) * T(x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(148,a,4449,a)].">
      <j1 rule="hyper" parents="148 4449"/>
    </justification>
  </clause>

  <clause id="4452">
    <literal><![CDATA[
      x \ T(x,T(y,y \ x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4276(a,1),4341(a,1,2,2,1))].">
      <j1 rule="para" parents="4276 4341"/>
    </justification>
  </clause>

  <clause id="4453">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(150,a,4452,a),flip(a)].">
      <j1 rule="hyper" parents="150 4452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4454">
    <literal><![CDATA[
      K(x,(y \ x) / x) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3819,a,4453,a)].">
      <j1 rule="hyper" parents="3819 4453"/>
    </justification>
  </clause>

  <clause id="4455">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,3955,a,b,4454,a)].">
      <j1 rule="hyper" parents="63 3955 4454"/>
    </justification>
  </clause>

  <clause id="4456">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3885,a(flip),b,4455,a),flip(a)].">
      <j1 rule="hyper" parents="347 3885 4455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4457">
    <literal><![CDATA[
      K(x \ ((1 / x) \ y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3909,a,b,4456,a)].">
      <j1 rule="hyper" parents="63 3909 4456"/>
    </justification>
  </clause>

  <clause id="4458">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4457(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 4457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4459">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(80(a,1),4458(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="80 4458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4460">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x * y) = L(R(y,x,x),x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,29,a(flip),b,4362,a),flip(a)].">
      <j1 rule="hyper" parents="347 29 4362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4461">
    <literal><![CDATA[
      L(R(x,y,x),y,x) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(4383(a,1),368(a,1))].">
      <j1 rule="para" parents="4383 368"/>
    </justification>
  </clause>

  <clause id="4462">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = x / ((x \ ((y \ 1) \ x)) * x)
    ]]></literal>
    <justification jstring="[para(2966(a,1),4399(a,1,1))].">
      <j1 rule="para" parents="2966 4399"/>
    </justification>
  </clause>

  <clause id="4463">
    <literal><![CDATA[
      (x * (y \ x)) / (x / y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(347,a,4213,a(flip),b,4402,a),flip(a)].">
      <j1 rule="hyper" parents="347 4213 4402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4464">
    <literal><![CDATA[
      (x * (y / x)) * (y / (y / x)) = y * ((y / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(133,a,218,a(flip),b,4463,a)].">
      <j1 rule="hyper" parents="133 218 4463"/>
    </justification>
  </clause>

  <clause id="4465">
    <literal><![CDATA[
      (x * (y / x)) * (y / (y / x)) = y * x
    ]]></literal>
    <justification jstring="[hyper(347,a,217,a(flip),b,4464,a),flip(a)].">
      <j1 rule="hyper" parents="347 217 4464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4467">
    <literal><![CDATA[
      (x * y) * ((y * x) / ((y * x) / x)) = (y * x) * x
    ]]></literal>
    <justification jstring="[para(11(a,1),4465(a,1,1,2))].">
      <j1 rule="para" parents="11 4465"/>
    </justification>
  </clause>

  <clause id="4468">
    <literal><![CDATA[
      (x * y) * ((y * x) / y) = (y * x) * x
    ]]></literal>
    <justification jstring="[para(11(a,1),4467(a,1,2,2))].">
      <j1 rule="para" parents="11 4467"/>
    </justification>
  </clause>

  <clause id="4469">
    <literal><![CDATA[
      x * (((y \ x) * y) / (y \ x)) = ((y \ x) * y) * y
    ]]></literal>
    <justification jstring="[hyper(628,a,4468,a)].">
      <j1 rule="hyper" parents="628 4468"/>
    </justification>
  </clause>

  <clause id="4470">
    <literal><![CDATA[
      ((x \ y) * x) * x = y * (y / (y / x))
    ]]></literal>
    <justification jstring="[para(4339(a,1),4469(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4339 4469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4471">
    <literal><![CDATA[
      ((x \ T(y,x)) * T(x,y)) * T(x,y) = y * (y / (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(4281(a,1),4470(a,1,1,1))].">
      <j1 rule="para" parents="4281 4470"/>
    </justification>
  </clause>

  <clause id="4472">
    <literal><![CDATA[
      (x * R(x * K(y,x),z,u)) / R(x * K(y,x),z,u) = T(x,R(x * K(y,x),z,u))
    ]]></literal>
    <justification jstring="[para(2089(a,1),4318(a,1,2,1))].">
      <j1 rule="para" parents="2089 4318"/>
    </justification>
  </clause>

  <clause id="4473">
    <literal><![CDATA[
      (T(x,y) / ((y \ 1) \ x)) \ x = (x \ ((y \ 1) \ x)) * x
    ]]></literal>
    <justification jstring="[hyper(132,a,4462,a,b,172,a)].">
      <j1 rule="hyper" parents="132 4462 172"/>
    </justification>
  </clause>

  <clause id="4474">
    <literal><![CDATA[
      (R(x,y,z) * T(u,x)) * T(x,u) = R(R(x,u,x),y,z) * (u * x)
    ]]></literal>
    <justification jstring="[para(4410(a,1),4311(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4410 4311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4475">
    <literal><![CDATA[
      ((x \ y) * x) * T((x \ y) \ y,z) = (T(x,z) * (x \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(134,a,4427,a(flip),b,744,a)].">
      <j1 rule="hyper" parents="134 4427 744"/>
    </justification>
  </clause>

  <clause id="4476">
    <literal><![CDATA[
      T(x,y) * (T(x,x \ 1) \ z) = ((x \ 1) * T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(2899(a,1),4186(a,1,2))].">
      <j1 rule="para" parents="2899 4186"/>
    </justification>
  </clause>

  <clause id="4477">
    <literal><![CDATA[
      (((x \ 1) \ 1) * T(x \ 1,y)) * z = T(1 / x,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3631,a(flip),b,4476,a),flip(a)].">
      <j1 rule="hyper" parents="63 3631 4476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4478">
    <literal><![CDATA[
      (T(x,y) * (y * x)) / T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y * x) * T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4317(a,2),4290(a,1))].">
      <j1 rule="para" parents="4317 4290"/>
    </justification>
  </clause>

  <clause id="4479">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(347,a,4191,a(flip),b,4343,a),flip(a)].">
      <j1 rule="hyper" parents="347 4191 4343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4480">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) = y * (y / (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(4450(a,1),4471(a,1,1))].">
      <j1 rule="para" parents="4450 4471"/>
    </justification>
  </clause>

  <clause id="4481">
    <literal><![CDATA[
      x * (x / (x / T(y,x))) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(4334,a,4480,a),flip(a)].">
      <j1 rule="hyper" parents="4334 4480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4482">
    <literal><![CDATA[
      x / (x / T(y,x)) = T(x / (x / y),x)
    ]]></literal>
    <justification jstring="[hyper(34,a,4397,a,b,4481,a),flip(a)].">
      <j1 rule="hyper" parents="34 4397 4481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4483">
    <literal><![CDATA[
      T(x / (x / y),x) \ x = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(214,a,4482,a)].">
      <j1 rule="hyper" parents="214 4482"/>
    </justification>
  </clause>

  <clause id="4484">
    <literal><![CDATA[
      x / T(y \ x,x) = T(x / y,x) \ x
    ]]></literal>
    <justification jstring="[para(80(a,1),4483(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="80 4483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4485">
    <literal><![CDATA[
      L(x,x \ y,x) \ y = y / T(x,y)
    ]]></literal>
    <justification jstring="[para(4394(a,1),4483(a,1,1))].">
      <j1 rule="para" parents="4394 4483"/>
    </justification>
  </clause>

  <clause id="4486">
    <literal><![CDATA[
      ((x \ y) * x) * T(T(x,x \ y),z) = (T(x,z) * (x \ y)) * x
    ]]></literal>
    <justification jstring="[para(112(a,2),4475(a,1,2,1))].">
      <j1 rule="para" parents="112 4475"/>
    </justification>
  </clause>

  <clause id="4487">
    <literal><![CDATA[
      (x * y) * T(T(y,y \ (y * x)),z) = (T(y,z) * (y \ (y * x))) * y
    ]]></literal>
    <justification jstring="[para(9(a,1),4486(a,1,1,1))].">
      <j1 rule="para" parents="9 4486"/>
    </justification>
  </clause>

  <clause id="4488">
    <literal><![CDATA[
      (R(x,y,z) * T(u,x)) * T(x,u) = (R(x,y,z) * u) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,469,a(flip),b,4474,a),flip(a)].">
      <j1 rule="hyper" parents="347 469 4474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4489">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (R(x,y,x) * y) * x
    ]]></literal>
    <justification jstring="[para(1773(a,1),4488(a,1,1))].">
      <j1 rule="para" parents="1773 4488"/>
    </justification>
  </clause>

  <clause id="4490">
    <literal><![CDATA[
      (R(x,y,x) * y) * x = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4386,a(flip),b,4489,a),flip(a)].">
      <j1 rule="hyper" parents="63 4386 4489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4491">
    <literal><![CDATA[
      (R(x,y,x) * y) \ (R(x,y,x) * T(x * y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(128,a,4443,a,b,4489,a(flip))].">
      <j1 rule="hyper" parents="128 4443 4489"/>
    </justification>
  </clause>

  <clause id="4492">
    <literal><![CDATA[
      (R(x,y,x) * y) \ ((x * y) * R(x,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(128,a,4386,a(flip),b,4489,a(flip))].">
      <j1 rule="hyper" parents="128 4386 4489"/>
    </justification>
  </clause>

  <clause id="4493">
    <literal><![CDATA[
      (R(x,y,x) * y) \ ((x * y) * R(x,y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(4490(a,1),358(a,1,2))].">
      <j1 rule="para" parents="4490 358"/>
    </justification>
  </clause>

  <clause id="4494">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,4383,a(flip),b,4491,a)].">
      <j1 rule="hyper" parents="63 4383 4491"/>
    </justification>
  </clause>

  <clause id="4495">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,y,x)) = (R(x,z,x) * z) \ ((x * z) * R(x,z,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,4492,a,b,4494,a),flip(a)].">
      <j1 rule="hyper" parents="347 4492 4494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4496">
    <literal><![CDATA[
      T(1 / x,y) * ((x \ 1) \ z) = (x * T(1 / x,y)) * z
    ]]></literal>
    <justification jstring="[para(3116(a,1),4477(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3116 4477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4497">
    <literal><![CDATA[
      (T(1 / x,y) * z) / ((x * T(1 / x,y)) * z) = x \ 1
    ]]></literal>
    <justification jstring="[para(4496(a,1),3865(a,1,2))].">
      <j1 rule="para" parents="4496 3865"/>
    </justification>
  </clause>

  <clause id="4498">
    <literal><![CDATA[
      T(1 / x,y) * ((x * T(1 / x,y)) \ z) = (x \ 1) * z
    ]]></literal>
    <justification jstring="[para(4497(a,1),350(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4497 350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4499">
    <literal><![CDATA[
      (x \ 1) \ T(1 / x,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(428,a,4498,a)].">
      <j1 rule="hyper" parents="428 4498"/>
    </justification>
  </clause>

  <clause id="4500">
    <literal><![CDATA[
      (T(x,y) * (x \ (x * z))) * x = (z * x) * T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),4487(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 4487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4501">
    <literal><![CDATA[
      (x * y) * T(T(y,x),z) = (T(y,z) * x) * y
    ]]></literal>
    <justification jstring="[para(9(a,1),4500(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 4500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4502">
    <literal><![CDATA[
      (x * y) * T(T(y,z),x) = (T(y,z) * x) * y
    ]]></literal>
    <justification jstring="[para(23(a,1),4501(a,1,2))].">
      <j1 rule="para" parents="23 4501"/>
    </justification>
  </clause>

  <clause id="4504">
    <literal><![CDATA[
      R(T(T(x,y),z * x),z,x) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(34,a,743,a,b,4502,a)].">
      <j1 rule="hyper" parents="34 743 4502"/>
    </justification>
  </clause>

  <clause id="4505">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(4495(a,2),4493(a,1))].">
      <j1 rule="para" parents="4495 4493"/>
    </justification>
  </clause>

  <clause id="4506">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * T(z,T(x,y))) = z * (x * (x \ T(x,y)))
    ]]></literal>
    <justification jstring="[para(10(a,1),4152(a,1,2,2,2))].">
      <j1 rule="para" parents="10 4152"/>
    </justification>
  </clause>

  <clause id="4508">
    <literal><![CDATA[
      (1 / x) * (x * (x \ T(x,y))) = x * ((x \ T(x,y)) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(3086(a,1),4506(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3086 4506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4509">
    <literal><![CDATA[
      (1 / x) * (x * (x \ T(x,y))) = x * ((x \ 1) * (x \ T(x,y)))
    ]]></literal>
    <justification jstring="[para(1552(a,1),4508(a,2,2))].">
      <j1 rule="para" parents="1552 4508"/>
    </justification>
  </clause>

  <clause id="4510">
    <literal><![CDATA[
      (1 / x) * (x * (x \ T(x,y))) = L(x \ T(x,y),x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,289,a(flip),b,4509,a),flip(a)].">
      <j1 rule="hyper" parents="347 289 4509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4511">
    <literal><![CDATA[
      L(x \ T(x,y),x \ 1,x) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(357,a,4510,a),flip(a)].">
      <j1 rule="hyper" parents="357 4510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4513">
    <literal><![CDATA[
      L(x \ T(x,y),x \ 1,x) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3074,a(flip),b,4511,a),flip(a)].">
      <j1 rule="hyper" parents="347 3074 4511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4514">
    <literal><![CDATA[
      L(x \ (x * K(x,y)),x \ 1,x) = x \ T(x,R(y,x,(y * x) \ x))
    ]]></literal>
    <justification jstring="[para(1818(a,1),4513(a,1,1,2))].">
      <j1 rule="para" parents="1818 4513"/>
    </justification>
  </clause>

  <clause id="4515">
    <literal><![CDATA[
      x \ T(x,R(y,x,(y * x) \ x)) = L(K(x,y),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4514(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 4514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4517">
    <literal><![CDATA[
      L(K(x,y),x \ 1,x) = x \ (x * K(x,y))
    ]]></literal>
    <justification jstring="[para(1818(a,1),4515(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1818 4515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4518">
    <literal><![CDATA[
      L(K(x,y),x \ 1,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,9,a(flip),b,4517,a),flip(a)].">
      <j1 rule="hyper" parents="347 9 4517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4520">
    <literal><![CDATA[
      (x \ 1) * K(x,y) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,4518,a(flip),b,289,a),flip(a)].">
      <j1 rule="hyper" parents="128 4518 289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4521">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1560,a,4520,a)].">
      <j1 rule="hyper" parents="1560 4520"/>
    </justification>
  </clause>

  <clause id="4522">
    <literal><![CDATA[
      T(x * x,y) * (y / T(x * x,y)) = T(y,y / (x * x))
    ]]></literal>
    <justification jstring="[para(12(a,1),4447(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 4447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4523">
    <literal><![CDATA[
      T(x,R(x * K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(283,a,4472,a),flip(a)].">
      <j1 rule="hyper" parents="283 4472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4525">
    <literal><![CDATA[
      (R(x,y,z) * (u * x)) \ ((u * x) * R(T(x,u),y,z)) = a(x,T(u,x),R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(1749(a,1),4442(a,1,1))].">
      <j1 rule="para" parents="1749 4442"/>
    </justification>
  </clause>

  <clause id="4526">
    <literal><![CDATA[
      (R(x,y,z) * (u * x)) \ ((R(x,y,z) * u) * x) = a(x,T(u,x),R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(1370(a,1),4525(a,1,2))].">
      <j1 rule="para" parents="1370 4525"/>
    </justification>
  </clause>

  <clause id="4527">
    <literal><![CDATA[
      a(x,T(y,x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(836,a,4526,a),flip(a)].">
      <j1 rule="hyper" parents="836 4526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4528">
    <literal><![CDATA[
      T(x \ 1,x * y) * R((((x \ 1) \ y) \ y) \ 1,z,u) = T(x \ R(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(1462(a,1),4419(a,2,1))].">
      <j1 rule="para" parents="1462 4419"/>
    </justification>
  </clause>

  <clause id="4529">
    <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(4356(a,1),4364(a,2,2,1,1))].">
      <j1 rule="para" parents="4356 4364"/>
    </justification>
  </clause>

  <clause id="4530">
    <literal><![CDATA[
      T(x \ 1,x) \ R(y,T(x,x \ 1),T(x,x \ 1) \ 1) = T(((x \ 1) \ 1) * T(y,x),T(x,x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1919(a,1),2982(a,1,1))].">
      <j1 rule="para" parents="1919 2982"/>
    </justification>
  </clause>

  <clause id="4531">
    <literal><![CDATA[
      T(x \ 1,x) \ R(y,T(x,x \ 1),T(x \ 1,x)) = T(((x \ 1) \ 1) * T(y,x),T(x,x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(1919(a,1),4530(a,1,2,3))].">
      <j1 rule="para" parents="1919 4530"/>
    </justification>
  </clause>

  <clause id="4532">
    <literal><![CDATA[
      T(((x \ 1) \ 1) * T(y,x),T(x,x \ 1) \ 1) = T(x \ 1,x) \ R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2374(a,1),4531(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2374 4531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4533">
    <literal><![CDATA[
      T(x * T(y,y \ 1),T(y,y \ 1) \ 1) = T(y \ 1,y) \ R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2979(a,1),4532(a,1,1))].">
      <j1 rule="para" parents="2979 4532"/>
    </justification>
  </clause>

  <clause id="4534">
    <literal><![CDATA[
      T(x \ 1,x) \ R(T(x,y) \ 1,x,x \ 1) = T(T(x,y) \ x,T(x,x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2980(a,1),4532(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2980 4532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4535">
    <literal><![CDATA[
      T(x \ 1,x) \ R(y,x,x \ 1) = T(y * T(x,x \ 1),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,4007,a(flip),b,4533,a),flip(a)].">
      <j1 rule="hyper" parents="63 4007 4533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4536">
    <literal><![CDATA[
      T(x \ 1,x) \ R(y,x,x \ 1) = R((x \ 1) \ y,1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3133,a(flip),b,4535,a),flip(a)].">
      <j1 rule="hyper" parents="347 3133 4535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4537">
    <literal><![CDATA[
      T(x \ 1,x) \ R(y,x,x \ 1) = R((x \ 1) \ y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,2260,a(flip),b,4536,a),flip(a)].">
      <j1 rule="hyper" parents="347 2260 4536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4538">
    <literal><![CDATA[
      R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(T(x,y) \ x,T(x,x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,4537,a(flip),b,4534,a)].">
      <j1 rule="hyper" parents="63 4537 4534"/>
    </justification>
  </clause>

  <clause id="4539">
    <literal><![CDATA[
      R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(T(x,y) \ x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,4007,a(flip),b,4538,a),flip(a)].">
      <j1 rule="hyper" parents="347 4007 4538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4540">
    <literal><![CDATA[
      R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(347,a,3113,a(flip),b,4539,a),flip(a)].">
      <j1 rule="hyper" parents="347 3113 4539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4541">
    <literal><![CDATA[
      R(T(x,y) \ x,x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(2911(a,1),4540(a,1,1))].">
      <j1 rule="para" parents="2911 4540"/>
    </justification>
  </clause>

  <clause id="4542">
    <literal><![CDATA[
      L(T(x,y) \ x,x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,3760,a(flip),b,4541,a)].">
      <j1 rule="hyper" parents="63 3760 4541"/>
    </justification>
  </clause>

  <clause id="4543">
    <literal><![CDATA[
      L(T(x,y) \ x,T(x,y),y) = L((x * y) \ (y * x),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(4542(a,1),1028(a,1,1))].">
      <j1 rule="para" parents="4542 1028"/>
    </justification>
  </clause>

  <clause id="4544">
    <literal><![CDATA[
      L((x * y) \ (y * x),x \ 1,x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(909,a,4543,a),flip(a)].">
      <j1 rule="hyper" parents="909 4543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4545">
    <literal><![CDATA[
      K(x,y) = L((y * x) \ (x * y),y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,16,a,b,4544,a)].">
      <j1 rule="hyper" parents="347 16 4544"/>
    </justification>
  </clause>

  <clause id="4546">
    <literal><![CDATA[
      L(K(x,y),y \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(16(a,2),4545(a,2,1)),flip(a)].">
      <j1 rule="para" parents="16 4545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4547">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,4546,a(flip),b,289,a),flip(a)].">
      <j1 rule="hyper" parents="128 4546 289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4548">
    <literal><![CDATA[
      ((x * (y \ 1)) * K(z,y)) / (y \ K(z,y)) = R(x,y \ 1,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(220,a,4547,a(flip),b,209,a)].">
      <j1 rule="hyper" parents="220 4547 209"/>
    </justification>
  </clause>

  <clause id="4549">
    <literal><![CDATA[
      R((x \ (1 / (1 / y))) * x,y \ 1,y) / ((1 / y) \ 1) = (y * K(x \ (1 / (1 / y)),x)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(2304(a,1),3752(a,1,1))].">
      <j1 rule="para" parents="2304 3752"/>
    </justification>
  </clause>

  <clause id="4550">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 * x)) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(3701(a,1),4549(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3701 4549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4551">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),4550(a,2,1,1,2))].">
      <j1 rule="para" parents="7 4550"/>
    </justification>
  </clause>

  <clause id="4552">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[para(83(a,1),4551(a,2,2))].">
      <j1 rule="para" parents="83 4551"/>
    </justification>
  </clause>

  <clause id="4553">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[para(3731(a,1),4552(a,1,1))].">
      <j1 rule="para" parents="3731 4552"/>
    </justification>
  </clause>

  <clause id="4554">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,4036,a(flip),b,4553,a)].">
      <j1 rule="hyper" parents="63 4036 4553"/>
    </justification>
  </clause>

  <clause id="4555">
    <literal><![CDATA[
      R(1 / (x / y),x / y,(x / y) \ T(x,x \ y)) = ((x / y) * (y / x)) * ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(4307(a,1),4232(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4307 4232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4556">
    <literal><![CDATA[
      R(1 / (x / y),x / y,(x / y) \ T(x,x \ y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(347,a,1739,a(flip),b,4555,a),flip(a)].">
      <j1 rule="hyper" parents="347 1739 4555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4557">
    <literal><![CDATA[
      R(1 / (x / y),x / y,x * (y / x)) = y / x
    ]]></literal>
    <justification jstring="[para(4227(a,1),4556(a,1,3))].">
      <j1 rule="para" parents="4227 4556"/>
    </justification>
  </clause>

  <clause id="4558">
    <literal><![CDATA[
      ((x / y) \ (1 / (y / x))) * R(1 / (y / x),y / x,y * (x / y)) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[para(4557(a,1),3698(a,1,1,1))].">
      <j1 rule="para" parents="4557 3698"/>
    </justification>
  </clause>

  <clause id="4559">
    <literal><![CDATA[
      ((x / y) \ (1 / (y / x))) * (x / y) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[para(4557(a,1),4558(a,1,2))].">
      <j1 rule="para" parents="4557 4558"/>
    </justification>
  </clause>

  <clause id="4560">
    <literal><![CDATA[
      T(x / y,(x / y) \ (1 / (y / x))) = x / y
    ]]></literal>
    <justification jstring="[hyper(383,a,4559,a)].">
      <j1 rule="hyper" parents="383 4559"/>
    </justification>
  </clause>

  <clause id="4561">
    <literal><![CDATA[
      T(x / y,(x / y) \ ((y / x) \ 1)) = x / y
    ]]></literal>
    <justification jstring="[hyper(63,a,4004,a(flip),b,4560,a)].">
      <j1 rule="hyper" parents="63 4004 4560"/>
    </justification>
  </clause>

  <clause id="4562">
    <literal><![CDATA[
      ((x / y) \ ((y / x) \ 1)) * (x / y) = (y / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(134,a,4561,a(flip),b,112,a(flip))].">
      <j1 rule="hyper" parents="134 4561 112"/>
    </justification>
  </clause>

  <clause id="4563">
    <literal><![CDATA[
      T(L(x,y,y \ 1),y) \ ((1 / y) \ T(L(x,y,y \ 1),(1 / y) \ 1)) = L(x,y,y \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(83(a,1),4259(a,1,1,2))].">
      <j1 rule="para" parents="83 4259"/>
    </justification>
  </clause>

  <clause id="4564">
    <literal><![CDATA[
      L(T(x,y),y,y \ 1) \ ((1 / y) \ T(L(x,y,y \ 1),(1 / y) \ 1)) = L(x,y,y \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(25(a,2),4563(a,1,1))].">
      <j1 rule="para" parents="25 4563"/>
    </justification>
  </clause>

  <clause id="4565">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ T(L(y,x,x \ 1),(1 / x) \ 1)) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(2944(a,1),4564(a,1,1))].">
      <j1 rule="para" parents="2944 4564"/>
    </justification>
  </clause>

  <clause id="4566">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ T(L(y,x,x \ 1),x)) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(83(a,1),4565(a,1,2,2,2))].">
      <j1 rule="para" parents="83 4565"/>
    </justification>
  </clause>

  <clause id="4567">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ L(T(y,x),x,x \ 1)) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(25(a,2),4566(a,1,2,2))].">
      <j1 rule="para" parents="25 4566"/>
    </justification>
  </clause>

  <clause id="4568">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ ((1 / x) * (y * x))) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(2944(a,1),4567(a,1,2,2))].">
      <j1 rule="para" parents="2944 4567"/>
    </justification>
  </clause>

  <clause id="4569">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * x) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),4568(a,1,2))].">
      <j1 rule="para" parents="9 4568"/>
    </justification>
  </clause>

  <clause id="4571">
    <literal><![CDATA[
      R(T(x,x \ 1) * T(T(x \ 1,x),x \ R(x,y,z)),y,z) = K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1919(a,1),2650(a,1,1,2,1))].">
      <j1 rule="para" parents="1919 2650"/>
    </justification>
  </clause>

  <clause id="4572">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R(T(x,x \ 1) * T(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(1726(a,1),4571(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1726 4571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4574">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R((x \ 1) * T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(2973(a,1),4572(a,2,1))].">
      <j1 rule="para" parents="2973 4572"/>
    </justification>
  </clause>

  <clause id="4575">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R(1,y,z)
    ]]></literal>
    <justification jstring="[para(249(a,1),4574(a,2,1))].">
      <j1 rule="para" parents="249 4574"/>
    </justification>
  </clause>

  <clause id="4576">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(347,a,403,a(flip),b,4575,a),flip(a)].">
      <j1 rule="hyper" parents="347 403 4575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4579">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(189,a,92,a,b,4576,a(flip))].">
      <j1 rule="hyper" parents="189 92 4576"/>
    </justification>
  </clause>

  <clause id="4580">
    <literal><![CDATA[
      (x \ 1) / (x \ R(x,y,z)) = (x \ R(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,4579,a)].">
      <j1 rule="hyper" parents="145 4579"/>
    </justification>
  </clause>

  <clause id="4581">
    <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(3296(a,1),1203(a,2,1))].">
      <j1 rule="para" parents="3296 1203"/>
    </justification>
  </clause>

  <clause id="4582">
    <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(789(a,1),4581(a,2,2,2))].">
      <j1 rule="para" parents="789 4581"/>
    </justification>
  </clause>

  <clause id="4583">
    <literal><![CDATA[
      L((x * y) \ R(x,y,y),(x * y) \ R(x,y,y),x * y) = L(y * ((y \ 1) * (y \ 1)),y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,1390,a,b,4582,a),flip(a)].">
      <j1 rule="hyper" parents="347 1390 4582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4585">
    <literal><![CDATA[
      L((x * y) \ R(x,y,y),(x * y) \ R(x,y,y),x * y) = L(L(y \ 1,y,y),y,x)
    ]]></literal>
    <justification jstring="[para(3197(a,1),4583(a,2,1))].">
      <j1 rule="para" parents="3197 4583"/>
    </justification>
  </clause>

  <clause id="4586">
    <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(519(a,1),4585(a,2,1))].">
      <j1 rule="para" parents="519 4585"/>
    </justification>
  </clause>

  <clause id="4587">
    <literal><![CDATA[
      L(x \ 1,(y * x) \ R(y,x,x),y * x) = L(T(x \ 1,x),x,y)
    ]]></literal>
    <justification jstring="[para(789(a,1),4586(a,1,1))].">
      <j1 rule="para" parents="789 4586"/>
    </justification>
  </clause>

  <clause id="4588">
    <literal><![CDATA[
      L(x \ 1,x \ 1,y * x) = L(T(x \ 1,x),x,y)
    ]]></literal>
    <justification jstring="[para(789(a,1),4587(a,1,2))].">
      <j1 rule="para" parents="789 4587"/>
    </justification>
  </clause>

  <clause id="4590">
    <literal><![CDATA[
      L(T(x \ 1,x),x,y) = L(x \ 1,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(3524,a,4588,a),flip(a)].">
      <j1 rule="hyper" parents="3524 4588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4592">
    <literal><![CDATA[
      L((1 / x) \ 1,1 / x,y * (1 / x)) = L(T(x,1 / x),1 / x,y)
    ]]></literal>
    <justification jstring="[para(83(a,1),4590(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="83 4590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4593">
    <literal><![CDATA[
      L((1 / x) \ 1,1 / x,y * (1 / x)) = L(T(x,x \ 1),1 / x,y)
    ]]></literal>
    <justification jstring="[para(1911(a,1),4592(a,2,1))].">
      <j1 rule="para" parents="1911 4592"/>
    </justification>
  </clause>

  <clause id="4594">
    <literal><![CDATA[
      L((1 / x) \ 1,1 / x,y * (1 / x)) = L(T(x,x \ 1),x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3189,a(flip),b,4593,a),flip(a)].">
      <j1 rule="hyper" parents="347 3189 4593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4595">
    <literal><![CDATA[
      L(x,1 / x,y * (1 / x)) = L(T(x,x \ 1),x,y)
    ]]></literal>
    <justification jstring="[para(83(a,1),4594(a,1,1))].">
      <j1 rule="para" parents="83 4594"/>
    </justification>
  </clause>

  <clause id="4596">
    <literal><![CDATA[
      L(x,1 / x,y * (x \ 1)) = L(T(x,x \ 1),x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3938,a(flip),b,4595,a)].">
      <j1 rule="hyper" parents="63 3938 4595"/>
    </justification>
  </clause>

  <clause id="4597">
    <literal><![CDATA[
      L(T(x,x \ 1),x,y) = L(x,x,y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(3520,a,4596,a),flip(a)].">
      <j1 rule="hyper" parents="3520 4596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4598">
    <literal><![CDATA[
      L((x \ 1) \ 1,x,y) = L(x,x,y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(112(a,1),4597(a,1,1))].">
      <j1 rule="para" parents="112 4597"/>
    </justification>
  </clause>

  <clause id="4599">
    <literal><![CDATA[
      L((x \ 1) \ 1,x,y * x) = L(x,x,R(y,x,x))
    ]]></literal>
    <justification jstring="[para(786(a,1),4598(a,2,3))].">
      <j1 rule="para" parents="786 4598"/>
    </justification>
  </clause>

  <clause id="4600">
    <literal><![CDATA[
      L((x \ 1) \ 1,x,y * x) = R(y,x,x) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,2009,a(flip),b,4599,a),flip(a)].">
      <j1 rule="hyper" parents="347 2009 4599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4601">
    <literal><![CDATA[
      L((x \ 1) \ 1,x,y * x) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3296,a(flip),b,4600,a),flip(a)].">
      <j1 rule="hyper" parents="347 3296 4600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4602">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * R((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) * R(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),1669(a,2,2,1,1))].">
      <j1 rule="para" parents="18 1669"/>
    </justification>
  </clause>

  <clause id="4603">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * R((y * z) \ y,u,w))) = L(z,y,x) * R(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(1185(a,1),4602(a,1,2))].">
      <j1 rule="para" parents="1185 4602"/>
    </justification>
  </clause>

  <clause id="4604">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * R(z \ 1,u,w)))) = L(z,y,x) * R(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(1184(a,1),4603(a,1,2,2))].">
      <j1 rule="para" parents="1184 4603"/>
    </justification>
  </clause>

  <clause id="4605">
    <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(545,a,4604,a),flip(a)].">
      <j1 rule="hyper" parents="545 4604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4606">
    <literal><![CDATA[
      L(x * R(x \ 1,L(x,y,z),x \ 1),y,z) = ((x \ 1) / (x \ L(x,y,z))) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1299,a(flip),b,4605,a),flip(a)].">
      <j1 rule="hyper" parents="63 1299 4605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4607">
    <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(4378(a,1),4605(a,2,1))].">
      <j1 rule="para" parents="4378 4605"/>
    </justification>
  </clause>

  <clause id="4608">
    <literal><![CDATA[
      L(T((x \ 1) * x,x \ 1),y,z) = a(1 / L(x,y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1478,a,4607,a),flip(a)].">
      <j1 rule="hyper" parents="1478 4607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4609">
    <literal><![CDATA[
      a(1 / L(x,y,z),x,x \ 1) = L(K(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(2762(a,1),4608(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2762 4608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4610">
    <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(131,a,4609,a(flip),b,1477,a)].">
      <j1 rule="hyper" parents="131 4609 1477"/>
    </justification>
  </clause>

  <clause id="4612">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) / R(L(x,u,w) \ 1,x,x \ 1) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(2817(a,1),4610(a,1,1))].">
      <j1 rule="para" parents="2817 4610"/>
    </justification>
  </clause>

  <clause id="4614">
    <literal><![CDATA[
      ((x \ 1) / (x \ L(x,y,z))) * L(x,y,z) = L(x * T(x \ 1,L(x,y,z)),y,z)
    ]]></literal>
    <justification jstring="[para(2040(a,1),4606(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2040 4606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4615">
    <literal><![CDATA[
      ((x \ 1) / (x \ L(x,y,z))) * L(x,y,z) = K(L(x,y,z) \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,2640,a(flip),b,4614,a),flip(a)].">
      <j1 rule="hyper" parents="347 2640 4614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4616">
    <literal><![CDATA[
      (x \ 1) / (x \ L(x,y,z)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,290,a(flip),b,4615,a),flip(a)].">
      <j1 rule="hyper" parents="35 290 4615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4617">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ (x \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(214,a,4616,a)].">
      <j1 rule="hyper" parents="214 4616"/>
    </justification>
  </clause>

  <clause id="4618">
    <literal><![CDATA[
      x / ((1 / x) \ L(1 / x,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(83(a,1),4616(a,1,1))].">
      <j1 rule="para" parents="83 4616"/>
    </justification>
  </clause>

  <clause id="4619">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ (x \ 1) = (x \ 1) \ L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,3357,a,b,4617,a),flip(a)].">
      <j1 rule="hyper" parents="347 3357 4617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4620">
    <literal><![CDATA[
      x / (x * L(x \ 1,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1192(a,1),4618(a,1,2))].">
      <j1 rule="para" parents="1192 4618"/>
    </justification>
  </clause>

  <clause id="4621">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * (x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(148,a,4620,a)].">
      <j1 rule="hyper" parents="148 4620"/>
    </justification>
  </clause>

  <clause id="4622">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ x = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,2695,a,b,4621,a)].">
      <j1 rule="hyper" parents="35 2695 4621"/>
    </justification>
  </clause>

  <clause id="4623">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = (L(x,y,z) / x) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(1663(a,1),4622(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1663 4622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4624">
    <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),1673(a,1,1))].">
      <j1 rule="para" parents="18 1673"/>
    </justification>
  </clause>

  <clause id="4625">
    <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),4624(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="18 4624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4626">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * L((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) * L(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),1675(a,2,2,1,1))].">
      <j1 rule="para" parents="18 1675"/>
    </justification>
  </clause>

  <clause id="4627">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * L((y * z) \ y,u,w))) = L(z,y,x) * L(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(1181(a,1),4626(a,1,2))].">
      <j1 rule="para" parents="1181 4626"/>
    </justification>
  </clause>

  <clause id="4628">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * L(z \ 1,u,w)))) = L(z,y,x) * L(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(1015(a,1),4627(a,1,2,2))].">
      <j1 rule="para" parents="1015 4627"/>
    </justification>
  </clause>

  <clause id="4629">
    <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(545,a,4628,a),flip(a)].">
      <j1 rule="hyper" parents="545 4628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4630">
    <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="[hyper(347,a,3343,a(flip),b,4628,a),flip(a)].">
      <j1 rule="hyper" parents="347 3343 4628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4631">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ 1,x,1 / x) = L(x * T(1 / x,1),y,z)
    ]]></literal>
    <justification jstring="[para(882(a,1),4629(a,2,1,2))].">
      <j1 rule="para" parents="882 4629"/>
    </justification>
  </clause>

  <clause id="4632">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) / x) \ ((1 / x) * 1)) = L(x * L(x \ 1,L(x,y,z),1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(1666(a,1),4629(a,1,2))].">
      <j1 rule="para" parents="1666 4629"/>
    </justification>
  </clause>

  <clause id="4633">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = L(x * T(1 / x,1),y,z)
    ]]></literal>
    <justification jstring="[para(1417(a,1),4631(a,1,2))].">
      <j1 rule="para" parents="1417 4631"/>
    </justification>
  </clause>

  <clause id="4634">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = L(x * (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(223(a,1),4633(a,2,1,2))].">
      <j1 rule="para" parents="223 4633"/>
    </justification>
  </clause>

  <clause id="4635">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = L(K(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1924(a,2),4634(a,2,1))].">
      <j1 rule="para" parents="1924 4634"/>
    </justification>
  </clause>

  <clause id="4636">
    <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(3343(a,1),4630(a,1,2,2,2))].">
      <j1 rule="para" parents="3343 4630"/>
    </justification>
  </clause>

  <clause id="4637">
    <literal><![CDATA[
      L(x,y,z) * L(x \ L(x,u,w),y,z) = L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(714,a,4636,a)].">
      <j1 rule="hyper" parents="714 4636"/>
    </justification>
  </clause>

  <clause id="4638">
    <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(545,a,4636,a),flip(a)].">
      <j1 rule="hyper" parents="545 4636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4639">
    <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(4636(a,1),545(a,1))].">
      <j1 rule="para" parents="4636 545"/>
    </justification>
  </clause>

  <clause id="4640">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,u,w),y,z) = L(x \ L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,30,a,b,4637,a)].">
      <j1 rule="hyper" parents="128 30 4637"/>
    </justification>
  </clause>

  <clause id="4641">
    <literal><![CDATA[
      ((x * y) \ x) \ L(L(y \ 1,y,x),z,u) = L((y \ 1) \ L(y \ 1,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,445,a,b,4637,a)].">
      <j1 rule="hyper" parents="34 445 4637"/>
    </justification>
  </clause>

  <clause id="4642">
    <literal><![CDATA[
      L(L(x,y,z),u,w) / L(x,y,z) = L(x \ L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3161,a,b,4638,a)].">
      <j1 rule="hyper" parents="63 3161 4638"/>
    </justification>
  </clause>

  <clause id="4643">
    <literal><![CDATA[
      ((x * y) \ x) \ L(L(y \ 1,y,x),z,u) = L(y \ L(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(3357(a,1),4641(a,2,1))].">
      <j1 rule="para" parents="3357 4641"/>
    </justification>
  </clause>

  <clause id="4644">
    <literal><![CDATA[
      L(x * L(x \ 1,L(x,y,z),1 / x),y,z) = L(x,y,z) * ((L(x,y,z) / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(8(a,1),4632(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8 4632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4645">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) / x) \ (1 / x)) = L(K(L(x,y,z),1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(2657(a,1),4644(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2657 4644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4646">
    <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(97(a,1),1814(a,1,2,1,2,1))].">
      <j1 rule="para" parents="97 1814"/>
    </justification>
  </clause>

  <clause id="4647">
    <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(63,a,1811,a(flip),b,4646,a),flip(a)].">
      <j1 rule="hyper" parents="63 1811 4646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4648">
    <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(1812(a,1),4647(a,2,2))].">
      <j1 rule="para" parents="1812 4647"/>
    </justification>
  </clause>

  <clause id="4649">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * ((u * (z \ 1)) / u)))) = L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)
    ]]></literal>
    <justification jstring="[hyper(138,a,4648,a)].">
      <j1 rule="hyper" parents="138 4648"/>
    </justification>
  </clause>

  <clause id="4650">
    <literal><![CDATA[
      L(x,y,z) * ((u * (L(x,y,z) \ 1)) / u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x * ((u * (x \ 1)) / u),y,z) = w
    ]]></literal>
    <justification jstring="[para(4649(a,1),545(a,1))].">
      <j1 rule="para" parents="4649 545"/>
    </justification>
  </clause>

  <clause id="4651">
    <literal><![CDATA[
      L(x * ((y * (x \ 1)) / y),z,u) = y \ T(y,L(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(4650,a,3778,a)].">
      <j1 rule="hyper" parents="4650 3778"/>
    </justification>
  </clause>

  <clause id="4652">
    <literal><![CDATA[
      L(x,y,z) * (1 / L(x,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)),y,z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),4650(a,1,2,1))].">
      <j1 rule="para" parents="10 4650"/>
    </justification>
  </clause>

  <clause id="4653">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = x \ T(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(3778(a,1),4651(a,1,1))].">
      <j1 rule="para" parents="3778 4651"/>
    </justification>
  </clause>

  <clause id="4654">
    <literal><![CDATA[
      L(x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)),y,z) = K(L(x,y,z),L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(4652,a,1924,a(flip))].">
      <j1 rule="hyper" parents="4652 1924"/>
    </justification>
  </clause>

  <clause id="4655">
    <literal><![CDATA[
      L(K(L(x,y,z),1 / x),y,z) = K(L(x,y,z),L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(1696(a,1),4654(a,1,1))].">
      <j1 rule="para" parents="1696 4654"/>
    </justification>
  </clause>

  <clause id="4656">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) / x) \ (1 / x)) = K(L(x,y,z),L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,4645,a,b,4655,a)].">
      <j1 rule="hyper" parents="63 4645 4655"/>
    </justification>
  </clause>

  <clause id="4657">
    <literal><![CDATA[
      (L(x,y,z) / x) \ (1 / x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,1924,a(flip),b,4656,a),flip(a)].">
      <j1 rule="hyper" parents="34 1924 4656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4658">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4623,a,b,4657,a)].">
      <j1 rule="hyper" parents="63 4623 4657"/>
    </justification>
  </clause>

  <clause id="4659">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(220,a,4657,a(flip),b,4623,a),flip(a)].">
      <j1 rule="hyper" parents="220 4657 4623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4660">
    <literal><![CDATA[
      1 / L(x \ 1,y,z) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(80(a,1),4658(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="80 4658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4661">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ ((1 / x) \ 1) = x * (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(4658(a,1),2123(a,2,2))].">
      <j1 rule="para" parents="4658 2123"/>
    </justification>
  </clause>

  <clause id="4662">
    <literal><![CDATA[
      L(L(x,x,x),y,z) \ 1 = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3199(a,2),4658(a,1,1,1))].">
      <j1 rule="para" parents="3199 4658"/>
    </justification>
  </clause>

  <clause id="4663">
    <literal><![CDATA[
      x \ 1 != 1 / L(y,z,u)
    ]]></literal>
    <literal><![CDATA[
      L(L(y,y,y),z,u) = x
    ]]></literal>
    <justification jstring="[para(4662(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="4662 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4664">
    <literal><![CDATA[
      1 / (1 / L(x \ 1,y,z)) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(80(a,1),4659(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="80 4659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4665">
    <literal><![CDATA[
      L(1 / (1 / (x \ (y \ z))),x,y) = 1 / (1 / ((y * x) \ z))
    ]]></literal>
    <justification jstring="[para(329(a,1),4659(a,2,2,2))].">
      <j1 rule="para" parents="329 4659"/>
    </justification>
  </clause>

  <clause id="4666">
    <literal><![CDATA[
      T(1 / (1 / L(x,y,z)),1 / x) = L((1 / x) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(4659(a,1),278(a,1,1))].">
      <j1 rule="para" parents="4659 278"/>
    </justification>
  </clause>

  <clause id="4667">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) \ 1 = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(214,a,4660,a)].">
      <j1 rule="hyper" parents="214 4660"/>
    </justification>
  </clause>

  <clause id="4668">
    <literal><![CDATA[
      1 / (1 / L(L(x \ 1,y,z),u,w)) = L(L(1 / x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(4664(a,1),4659(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4664 4659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4669">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) = (L(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(80(a,1),4667(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="80 4667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4670">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) \ 1 = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(3638(a,1),4667(a,1,1))].">
      <j1 rule="para" parents="3638 4667"/>
    </justification>
  </clause>

  <clause id="4671">
    <literal><![CDATA[
      L((((x \ y) \ z) \ 1) \ 1,x \ y,x) = ((y \ (x * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(561(a,1),4669(a,2,1,1))].">
      <j1 rule="para" parents="561 4669"/>
    </justification>
  </clause>

  <clause id="4672">
    <literal><![CDATA[
      T(1 / (1 / L(x,y,z)),1 / x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),4666(a,2,1))].">
      <j1 rule="para" parents="83 4666"/>
    </justification>
  </clause>

  <clause id="4673">
    <literal><![CDATA[
      T(T(1 / (1 / L(x,y,z)),u),1 / x) = T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(4672(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4672 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4674">
    <literal><![CDATA[
      (x * y) * (1 / (1 / ((x * y) \ z))) = x * (y * (1 / (1 / (y \ (x \ z)))))
    ]]></literal>
    <justification jstring="[hyper(134,a,4665,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 4665 18"/>
    </justification>
  </clause>

  <clause id="4675">
    <literal><![CDATA[
      K(x,L(L(1 / y,z,u),w,v5)) = K(x,L(L(y \ 1,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(4668(a,1),3891(a,1,2))].">
      <j1 rule="para" parents="4668 3891"/>
    </justification>
  </clause>

  <clause id="4676">
    <literal><![CDATA[
      L(T((x \ y) \ z,z \ (x \ y)),x \ y,x) = ((y \ (x * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2579(a,2),4671(a,1,1))].">
      <j1 rule="para" parents="2579 4671"/>
    </justification>
  </clause>

  <clause id="4677">
    <literal><![CDATA[
      T(x \ (y * z),z \ (y \ x)) = ((x \ (y * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,891,a(flip),b,4676,a)].">
      <j1 rule="hyper" parents="63 891 4676"/>
    </justification>
  </clause>

  <clause id="4678">
    <literal><![CDATA[
      T(a(x,y,z),z \ ((x * y) \ (x * (y * z)))) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(14(a,2),4677(a,1,1))].">
      <j1 rule="para" parents="14 4677"/>
    </justification>
  </clause>

  <clause id="4679">
    <literal><![CDATA[
      (x * y) * (1 / (1 / ((x * y) \ (x * z)))) = x * (y * (1 / (1 / (y \ z))))
    ]]></literal>
    <justification jstring="[para(9(a,1),4674(a,2,2,2,2,2,2))].">
      <j1 rule="para" parents="9 4674"/>
    </justification>
  </clause>

  <clause id="4680">
    <literal><![CDATA[
      T(a(x,y,z),z \ L(z,y,x)) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(18(a,2),4678(a,1,2,2))].">
      <j1 rule="para" parents="18 4678"/>
    </justification>
  </clause>

  <clause id="4681">
    <literal><![CDATA[
      T(a(x,y,z),z \ L(z,y,x)) = (a(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(14(a,2),4680(a,2,1,1))].">
      <j1 rule="para" parents="14 4680"/>
    </justification>
  </clause>

  <clause id="4682">
    <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),2118(a,2,2,1,1))].">
      <j1 rule="para" parents="20 2118"/>
    </justification>
  </clause>

  <clause id="4683">
    <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(1683(a,1),4682(a,1,1))].">
      <j1 rule="para" parents="1683 4682"/>
    </justification>
  </clause>

  <clause id="4684">
    <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(1702(a,1),4683(a,1,1,1))].">
      <j1 rule="para" parents="1702 4683"/>
    </justification>
  </clause>

  <clause id="4685">
    <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(595,a,4684,a),flip(a)].">
      <j1 rule="hyper" parents="595 4684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4686">
    <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(63,a,4529,a,b,4685,a)].">
      <j1 rule="hyper" parents="63 4529 4685"/>
    </justification>
  </clause>

  <clause id="4687">
    <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(63,a,1469,a(flip),b,4685,a),flip(a)].">
      <j1 rule="hyper" parents="63 1469 4685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4688">
    <literal><![CDATA[
      R(x,y,z) * R(R(x,y,z) \ 1,x,x \ 1) = R(x * T(1 * (x \ 1),x),y,z)
    ]]></literal>
    <justification jstring="[para(1058(a,1),4685(a,2,1,2))].">
      <j1 rule="para" parents="1058 4685"/>
    </justification>
  </clause>

  <clause id="4689">
    <literal><![CDATA[
      R(x * T(1 * (x \ 1),x),y,z) = a(1 / R(x,y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1478,a,4688,a),flip(a)].">
      <j1 rule="hyper" parents="1478 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4690">
    <literal><![CDATA[
      a(1 / R(x,y,z),x,x \ 1) = R(x * T(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),4689(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 4689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4691">
    <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(1727(a,1),4687(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1727 4687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4692">
    <literal><![CDATA[
      (x \ 1) / (x \ R(x,y,z)) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(2652,a,4691,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2652 4691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4693">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,4580,a(flip),b,4692,a)].">
      <j1 rule="hyper" parents="63 4580 4692"/>
    </justification>
  </clause>

  <clause id="4694">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,4693,a(flip),b,2523,a)].">
      <j1 rule="hyper" parents="128 4693 2523"/>
    </justification>
  </clause>

  <clause id="4695">
    <literal><![CDATA[
      ((1 / x) \ R(1 / x,y,z)) \ x = R(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(83(a,1),4693(a,1,2))].">
      <j1 rule="para" parents="83 4693"/>
    </justification>
  </clause>

  <clause id="4696">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) \ x = R(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1471(a,1),4695(a,1,1))].">
      <j1 rule="para" parents="1471 4695"/>
    </justification>
  </clause>

  <clause id="4697">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) \ 1 = (R(x,y,z) / x) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(1290(a,1),4696(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1290 4696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4698">
    <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(1290(a,1),4686(a,2,1))].">
      <j1 rule="para" parents="1290 4686"/>
    </justification>
  </clause>

  <clause id="4699">
    <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(4310(a,1),4698(a,1,1,2,1))].">
      <j1 rule="para" parents="4310 4698"/>
    </justification>
  </clause>

  <clause id="4700">
    <literal><![CDATA[
      (R(x,y,z) * T(u,x)) / (u * x) = R(R(x,y,z) / x,x,u)
    ]]></literal>
    <justification jstring="[para(4289(a,1),4699(a,1,1))].">
      <j1 rule="para" parents="4289 4699"/>
    </justification>
  </clause>

  <clause id="4701">
    <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),2179(a,2,2,1,1))].">
      <j1 rule="para" parents="20 2179"/>
    </justification>
  </clause>

  <clause id="4702">
    <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(1984(a,1),4701(a,1,1))].">
      <j1 rule="para" parents="1984 4701"/>
    </justification>
  </clause>

  <clause id="4703">
    <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(1990(a,1),4702(a,1,1,1))].">
      <j1 rule="para" parents="1990 4702"/>
    </justification>
  </clause>

  <clause id="4704">
    <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(595,a,4703,a),flip(a)].">
      <j1 rule="hyper" parents="595 4703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4705">
    <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(882(a,1),4704(a,2,1,2))].">
      <j1 rule="para" parents="882 4704"/>
    </justification>
  </clause>

  <clause id="4706">
    <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(1759(a,1),4705(a,1,2))].">
      <j1 rule="para" parents="1759 4705"/>
    </justification>
  </clause>

  <clause id="4707">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(x * (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(223(a,1),4706(a,2,1,2))].">
      <j1 rule="para" parents="223 4706"/>
    </justification>
  </clause>

  <clause id="4708">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(K(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1924(a,2),4707(a,2,1))].">
      <j1 rule="para" parents="1924 4707"/>
    </justification>
  </clause>

  <clause id="4709">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,3452,a(flip),b,4708,a),flip(a)].">
      <j1 rule="hyper" parents="347 3452 4708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4711">
    <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(107(a,1),2426(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 2426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4712">
    <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(347,a,970,a(flip),b,4711,a),flip(a)].">
      <j1 rule="hyper" parents="347 970 4711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4713">
    <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(347,a,2422,a(flip),b,4712,a),flip(a)].">
      <j1 rule="hyper" parents="347 2422 4712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4714">
    <literal><![CDATA[
      ((((x * (y / (z * y))) / x) * (z * y)) * u) / (y * u) = ((x * (1 / R(z,y,u))) / x) * R(z,y,u)
    ]]></literal>
    <justification jstring="[hyper(131,a,2419,a(flip),b,4712,a)].">
      <j1 rule="hyper" parents="131 2419 4712"/>
    </justification>
  </clause>

  <clause id="4715">
    <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(970(a,1),4713(a,1,1))].">
      <j1 rule="para" parents="970 4713"/>
    </justification>
  </clause>

  <clause id="4716">
    <literal><![CDATA[
      (((((x * (1 / y)) / x) * y) * z) * u) / (z * u) = ((x * (1 / R(y,z,u))) / x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(2423(a,1),4714(a,1,1,1))].">
      <j1 rule="para" parents="2423 4714"/>
    </justification>
  </clause>

  <clause id="4717">
    <literal><![CDATA[
      ((x * (1 / R(y,z,u))) / x) * R(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(((x * (1 / y)) / x) * y,z,u) = w
    ]]></literal>
    <justification jstring="[para(4716(a,1),595(a,1))].">
      <j1 rule="para" parents="4716 595"/>
    </justification>
  </clause>

  <clause id="4718">
    <literal><![CDATA[
      R(((x * (1 / y)) / x) * y,z,u) = T(x,1 / R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(4717,a,3814,a)].">
      <j1 rule="hyper" parents="4717 3814"/>
    </justification>
  </clause>

  <clause id="4719">
    <literal><![CDATA[
      R((K(x,1 / x) / x) * x,y,z) = T(x,1 / R(x,y,z)) / x
    ]]></literal>
    <justification jstring="[para(292(a,2),4718(a,1,1,1,1))].">
      <j1 rule="para" parents="292 4718"/>
    </justification>
  </clause>

  <clause id="4720">
    <literal><![CDATA[
      T(x,1 / R(x,y,z)) / x = R(K(x,1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),4719(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 4719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4721">
    <literal><![CDATA[
      T(x,1 / R(x,y,z)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(37,a,3481,a(flip),b,4720,a),flip(a)].">
      <j1 rule="hyper" parents="37 3481 4720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4723">
    <literal><![CDATA[
      T(x,R(x,y,z) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(4439,a,4721,a)].">
      <j1 rule="hyper" parents="4439 4721"/>
    </justification>
  </clause>

  <clause id="4725">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) = (R(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4723(a,1),334(a,1,1))].">
      <j1 rule="para" parents="4723 334"/>
    </justification>
  </clause>

  <clause id="4726">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * ((x \ 1) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(4723(a,1),1757(a,1,2))].">
      <j1 rule="para" parents="4723 1757"/>
    </justification>
  </clause>

  <clause id="4727">
    <literal><![CDATA[
      (R(1 / x,y,z) \ 1) \ 1 = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),4725(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="83 4725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4728">
    <literal><![CDATA[
      (R(1 / (1 / x),y,z) \ 1) \ 1 = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(219(a,1),4725(a,1,1)),flip(a)].">
      <j1 rule="para" parents="219 4725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4729">
    <literal><![CDATA[
      T(R(((x \ R(x,y,z)) \ 1) \ 1,x,y * z),x * (y * z)) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4725(a,2),3723(a,1,1))].">
      <j1 rule="para" parents="4725 3723"/>
    </justification>
  </clause>

  <clause id="4730">
    <literal><![CDATA[
      K(x * R(1 / y,z,u),w) = K(x * R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(4727(a,1),3876(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4727 3876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4731">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) \ 1 = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(222,a,4728,a),flip(a)].">
      <j1 rule="hyper" parents="222 4728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4732">
    <literal><![CDATA[
      (R(x,y,z) / x) \ (1 / x) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4697,a(flip),b,4731,a)].">
      <j1 rule="hyper" parents="63 4697 4731"/>
    </justification>
  </clause>

  <clause id="4733">
    <literal><![CDATA[
      R(T(1 / (1 / x),y),z,u) \ 1 = 1 / R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2729(a,1),4731(a,1,1,1))].">
      <j1 rule="para" parents="2729 4731"/>
    </justification>
  </clause>

  <clause id="4734">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * ((x \ 1) \ 1) = (1 / R(x,y,z)) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,3704,a,b,4726,a),flip(a)].">
      <j1 rule="hyper" parents="347 3704 4726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4736">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),1 / x,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(865(a,1),4733(a,1,1)),flip(a)].">
      <j1 rule="para" parents="865 4733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4737">
    <literal><![CDATA[
      R(x,y,z) \ K(x,x \ 1) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,2353,a,b,4734,a(flip))].">
      <j1 rule="hyper" parents="35 2353 4734"/>
    </justification>
  </clause>

  <clause id="4738">
    <literal><![CDATA[
      R(x,y,z) * (1 / R(x,y,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(150,a,4737,a)].">
      <j1 rule="hyper" parents="150 4737"/>
    </justification>
  </clause>

  <clause id="4739">
    <literal><![CDATA[
      (1 / x) * (R(x,y,z) \ x) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,4709,a,b,4738,a)].">
      <j1 rule="hyper" parents="34 4709 4738"/>
    </justification>
  </clause>

  <clause id="4740">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(138,a,4739,a)].">
      <j1 rule="hyper" parents="138 4739"/>
    </justification>
  </clause>

  <clause id="4741">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,3749,a(flip),b,4740,a)].">
      <j1 rule="hyper" parents="63 3749 4740"/>
    </justification>
  </clause>

  <clause id="4742">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,4694,a(flip),b,4741,a)].">
      <j1 rule="hyper" parents="63 4694 4741"/>
    </justification>
  </clause>

  <clause id="4743">
    <literal><![CDATA[
      1 / (R(x,y,z) \ x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(220,a,4741,a(flip),b,4694,a(flip))].">
      <j1 rule="hyper" parents="220 4741 4694"/>
    </justification>
  </clause>

  <clause id="4744">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(2260(a,1),4736(a,1,2))].">
      <j1 rule="para" parents="2260 4736"/>
    </justification>
  </clause>

  <clause id="4745">
    <literal><![CDATA[
      1 / R(T(x,(x \ 1) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(2956(a,1),4744(a,1,2,1))].">
      <j1 rule="para" parents="2956 4744"/>
    </justification>
  </clause>

  <clause id="4746">
    <literal><![CDATA[
      (((1 / x) * (y * x)) \ (y * x)) \ 1 = 1 / R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(4209(a,1),4745(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4209 4745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4747">
    <literal><![CDATA[
      1 / R(T(x,y),x \ 1,y * x) = (L(y,x,x \ 1) \ (x * y)) \ 1
    ]]></literal>
    <justification jstring="[para(4569(a,1),4746(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4569 4746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4748">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = R(T(y,x),y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(214,a,4747,a)].">
      <j1 rule="hyper" parents="214 4747"/>
    </justification>
  </clause>

  <clause id="4749">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) \ (x * y) = R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2950,a(flip),b,4748,a)].">
      <j1 rule="hyper" parents="63 2950 4748"/>
    </justification>
  </clause>

  <clause id="4750">
    <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(2424(a,1),4715(a,2,1))].">
      <j1 rule="para" parents="2424 4715"/>
    </justification>
  </clause>

  <clause id="4751">
    <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(35,a,107,a,b,4750,a),flip(a)].">
      <j1 rule="hyper" parents="35 107 4750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4752">
    <literal><![CDATA[
      R(x * ((y * (x \ 1)) / y),z,u) = K(y,(y / R(x,z,u)) / y)
    ]]></literal>
    <justification jstring="[hyper(1691,a,4751,a),flip(a)].">
      <j1 rule="hyper" parents="1691 4751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4753">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = K(x,(x / R(y,z,u)) / x)
    ]]></literal>
    <justification jstring="[para(3778(a,1),4752(a,1,1))].">
      <j1 rule="para" parents="3778 4752"/>
    </justification>
  </clause>

  <clause id="4754">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = x \ T(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,3794,a(flip),b,4753,a),flip(a)].">
      <j1 rule="hyper" parents="347 3794 4753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4755">
    <literal><![CDATA[
      T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,(z \ 1) \ 1),z,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3820,a,b,4754,a)].">
      <j1 rule="hyper" parents="347 3820 4754"/>
    </justification>
  </clause>

  <clause id="4756">
    <literal><![CDATA[
      T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,z),z,y)
    ]]></literal>
    <justification jstring="[para(2966(a,1),4755(a,2,1,2))].">
      <j1 rule="para" parents="2966 4755"/>
    </justification>
  </clause>

  <clause id="4757">
    <literal><![CDATA[
      T(x \ T(x,(y * z) / z),T(y,u)) = R(x \ T(x,y),y,z)
    ]]></literal>
    <justification jstring="[para(4435(a,1),4756(a,1,1,2))].">
      <j1 rule="para" parents="4435 4756"/>
    </justification>
  </clause>

  <clause id="4758">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = R(x \ T(x,y),y,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),4757(a,1,1,2,2))].">
      <j1 rule="para" parents="11 4757"/>
    </justification>
  </clause>

  <clause id="4759">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3114,a(flip),b,4758,a),flip(a)].">
      <j1 rule="hyper" parents="63 3114 4758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4760">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(4759(a,1),3777(a,1,1))].">
      <j1 rule="para" parents="4759 3777"/>
    </justification>
  </clause>

  <clause id="4761">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[para(4759(a,1),4234(a,1,1))].">
      <j1 rule="para" parents="4759 4234"/>
    </justification>
  </clause>

  <clause id="4762">
    <literal><![CDATA[
      (T(x,y) \ x) * (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(4195,a,4761,a),flip(a)].">
      <j1 rule="hyper" parents="4195 4761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4763">
    <literal><![CDATA[
      (T(x,y) \ x) * z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(4188,a,4761,a),flip(a)].">
      <j1 rule="hyper" parents="4188 4761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4765">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(63,a,4272,a,b,4762,a)].">
      <j1 rule="hyper" parents="63 4272 4762"/>
    </justification>
  </clause>

  <clause id="4766">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(269,a,4762,a(flip),b,4215,a),flip(a)].">
      <j1 rule="hyper" parents="269 4762 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4767">
    <literal><![CDATA[
      T(x,y) \ (y * z) = x \ (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(128,a,4762,a(flip),b,4272,a)].">
      <j1 rule="hyper" parents="128 4762 4272"/>
    </justification>
  </clause>

  <clause id="4768">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(4762(a,1),4271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4762 4271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4769">
    <literal><![CDATA[
      T(x,y) * (x \ z) = y * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4272,a,b,4763,a)].">
      <j1 rule="hyper" parents="63 4272 4763"/>
    </justification>
  </clause>

  <clause id="4770">
    <literal><![CDATA[
      x * (T(x,(y / z) / (1 / z)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(63,a,4413,a(flip),b,4763,a),flip(a)].">
      <j1 rule="hyper" parents="63 4413 4763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4771">
    <literal><![CDATA[
      x * T(x \ y,z) = z * (T(z,y / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4269,a(flip),b,4763,a)].">
      <j1 rule="hyper" parents="63 4269 4763"/>
    </justification>
  </clause>

  <clause id="4772">
    <literal><![CDATA[
      x \ (T(y,x) * (y \ z)) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(128,a,4272,a,b,4763,a(flip))].">
      <j1 rule="hyper" parents="128 4272 4763"/>
    </justification>
  </clause>

  <clause id="4776">
    <literal><![CDATA[
      ((x * y) / x) * (x * z) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(134,a,4765,a(flip),b,4422,a)].">
      <j1 rule="hyper" parents="134 4765 4422"/>
    </justification>
  </clause>

  <clause id="4777">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(4765(a,2),613(a,1))].">
      <j1 rule="para" parents="4765 613"/>
    </justification>
  </clause>

  <clause id="4778">
    <literal><![CDATA[
      T(x,y) * ((x \ T(y,x)) * z) = y * L(z,x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(538(a,1),4765(a,1,2))].">
      <j1 rule="para" parents="538 4765"/>
    </justification>
  </clause>

  <clause id="4779">
    <literal><![CDATA[
      ((x * y) / x) * T(x,y) = T(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(150,a,4766,a)].">
      <j1 rule="hyper" parents="150 4766"/>
    </justification>
  </clause>

  <clause id="4781">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) = (x * y) * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,97,a,b,4768,a),flip(a)].">
      <j1 rule="hyper" parents="347 97 4768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4782">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y))
    ]]></literal>
    <justification jstring="[para(4768(a,1),4313(a,1,2))].">
      <j1 rule="para" parents="4768 4313"/>
    </justification>
  </clause>

  <clause id="4783">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4768(a,1),4312(a,1,1))].">
      <j1 rule="para" parents="4768 4312"/>
    </justification>
  </clause>

  <clause id="4784">
    <literal><![CDATA[
      T(x,y) \ (T(y,x) \ z) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(128,a,1221,a(flip),b,4769,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 1221 4769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4785">
    <literal><![CDATA[
      L(x,y \ 1,(z * y) / z) = y * ((y \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(3788,a,4760,a)].">
      <j1 rule="hyper" parents="3788 4760"/>
    </justification>
  </clause>

  <clause id="4786">
    <literal><![CDATA[
      (x \ T(x,x \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(85(a,1),4760(a,1,2))].">
      <j1 rule="para" parents="85 4760"/>
    </justification>
  </clause>

  <clause id="4788">
    <literal><![CDATA[
      T(x,x \ (x \ y)) \ y = (x \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(4200,a,4786,a)].">
      <j1 rule="hyper" parents="4200 4786"/>
    </justification>
  </clause>

  <clause id="4789">
    <literal><![CDATA[
      (x \ ((x \ y) \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(112(a,1),4786(a,1,1,2))].">
      <j1 rule="para" parents="112 4786"/>
    </justification>
  </clause>

  <clause id="4790">
    <literal><![CDATA[
      x / ((y \ x) * y) = y \ ((y \ x) \ x)
    ]]></literal>
    <justification jstring="[hyper(222,a,4789,a)].">
      <j1 rule="hyper" parents="222 4789"/>
    </justification>
  </clause>

  <clause id="4791">
    <literal><![CDATA[
      (x * (y / x)) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,4218,a,b,4790,a)].">
      <j1 rule="hyper" parents="347 4218 4790"/>
    </justification>
  </clause>

  <clause id="4792">
    <literal><![CDATA[
      x \ T(x * y,z) = z * (T(z,y / (x \ 1)) \ y)
    ]]></literal>
    <justification jstring="[hyper(1166,a,4771,a)].">
      <j1 rule="hyper" parents="1166 4771"/>
    </justification>
  </clause>

  <clause id="4794">
    <literal><![CDATA[
      (x \ y) * (T(x,x \ y) * z) = (y / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),4776(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 4776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4795">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = y * (T(x,y) * a(x,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(854(a,1),4776(a,1,2))].">
      <j1 rule="para" parents="854 4776"/>
    </justification>
  </clause>

  <clause id="4796">
    <literal><![CDATA[
      L(x,T(y,z),T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(4315,a,4781,a)].">
      <j1 rule="hyper" parents="4315 4781"/>
    </justification>
  </clause>

  <clause id="4797">
    <literal><![CDATA[
      L(T(x,y),T(y,x),T(x,y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,750,a(flip),b,4796,a),flip(a)].">
      <j1 rule="hyper" parents="347 750 4796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4798">
    <literal><![CDATA[
      L(x,T(y,z),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4782(a,1),545(a,1))].">
      <j1 rule="para" parents="4782 545"/>
    </justification>
  </clause>

  <clause id="4799">
    <literal><![CDATA[
      L(x,T(y,y \ z),T((y / z) \ 1,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(y / z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(4225(a,1),4798(a,1,2))].">
      <j1 rule="para" parents="4225 4798"/>
    </justification>
  </clause>

  <clause id="4800">
    <literal><![CDATA[
      L(x,y \ 1,(z * y) / z) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,289,a(flip),b,4785,a),flip(a)].">
      <j1 rule="hyper" parents="347 289 4785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4801">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * z) = L(z,T(x,y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(255(a,1),4785(a,1,3)),flip(a)].">
      <j1 rule="para" parents="255 4785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4802">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,T(y,z)) = L(x,T(y,z) \ 1,y)
    ]]></literal>
    <justification jstring="[para(255(a,1),4800(a,1,3)),flip(a)].">
      <j1 rule="para" parents="255 4800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4805">
    <literal><![CDATA[
      L(x,1 / T(y,y \ z),(y \ z) \ z) = L(x,T(y,y \ z) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2937,a,4802,a)].">
      <j1 rule="hyper" parents="2937 4802"/>
    </justification>
  </clause>

  <clause id="4806">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(836,a,4783,a),flip(a)].">
      <j1 rule="hyper" parents="836 4783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4807">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4783(a,1),836(a,1))].">
      <j1 rule="para" parents="4783 836"/>
    </justification>
  </clause>

  <clause id="4808">
    <literal><![CDATA[
      a(T(x,T(y,x)),T(T(y,x),x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,4527,a(flip),b,4806,a),flip(a)].">
      <j1 rule="hyper" parents="347 4527 4806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4809">
    <literal><![CDATA[
      a(T(x * (y / x),x),T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x * (y / x),x,z) = u
    ]]></literal>
    <justification jstring="[para(4322(a,1),4807(a,1,2))].">
      <j1 rule="para" parents="4322 4807"/>
    </justification>
  </clause>

  <clause id="4810">
    <literal><![CDATA[
      x * (T(x,(y / z) / (z \ 1)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[para(3996(a,1),4770(a,1,2,1))].">
      <j1 rule="para" parents="3996 4770"/>
    </justification>
  </clause>

  <clause id="4811">
    <literal><![CDATA[
      x \ T(x * (y / x),z) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,4792,a,b,4810,a)].">
      <j1 rule="hyper" parents="63 4792 4810"/>
    </justification>
  </clause>

  <clause id="4812">
    <literal><![CDATA[
      T(x * (y / x),z) = x * (T(y,z) / x)
    ]]></literal>
    <justification jstring="[hyper(134,a,4810,a(flip),b,4792,a),flip(a)].">
      <j1 rule="hyper" parents="134 4810 4792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4813">
    <literal><![CDATA[
      (x \ T(x * (y / x),z)) * x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,4792,a,b,4810,a(flip))].">
      <j1 rule="hyper" parents="133 4792 4810"/>
    </justification>
  </clause>

  <clause id="4814">
    <literal><![CDATA[
      T(x * y,z) / y = y \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),4811(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 4811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4815">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,z) = T(y,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(80(a,1),4811(a,1,2,1,2))].">
      <j1 rule="para" parents="80 4811"/>
    </justification>
  </clause>

  <clause id="4817">
    <literal><![CDATA[
      T((x \ y) * x,z) / x = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),4811(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 4811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4820">
    <literal><![CDATA[
      T(T(x,y),z) / x = x \ T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(3069(a,1),4811(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3069 4811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4821">
    <literal><![CDATA[
      x * (T(y * x,z) / x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),4812(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 4812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4822">
    <literal><![CDATA[
      T(x * (y / x),y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(110(a,1),4812(a,2,2,1))].">
      <j1 rule="para" parents="110 4812"/>
    </justification>
  </clause>

  <clause id="4823">
    <literal><![CDATA[
      T(x * ((y / z) / x),z) = x * ((z \ y) / x)
    ]]></literal>
    <justification jstring="[para(113(a,1),4812(a,2,2,1))].">
      <j1 rule="para" parents="113 4812"/>
    </justification>
  </clause>

  <clause id="4826">
    <literal><![CDATA[
      T(x * (y / x),z / y) = x * (T(y,y \ z) / x)
    ]]></literal>
    <justification jstring="[para(4285(a,1),4812(a,2,2,1))].">
      <j1 rule="para" parents="4285 4812"/>
    </justification>
  </clause>

  <clause id="4827">
    <literal><![CDATA[
      T(x * (y / x),y) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(4822(a,2),4791(a,1,1))].">
      <j1 rule="para" parents="4822 4791"/>
    </justification>
  </clause>

  <clause id="4828">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2806,a,b,4813,a)].">
      <j1 rule="hyper" parents="63 2806 4813"/>
    </justification>
  </clause>

  <clause id="4829">
    <literal><![CDATA[
      (x \ T(x * y,z)) * x = T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),4813(a,1,1,2,1,2))].">
      <j1 rule="para" parents="11 4813"/>
    </justification>
  </clause>

  <clause id="4830">
    <literal><![CDATA[
      T((x \ y) * x,z) = (x \ T(y,z)) * x
    ]]></literal>
    <justification jstring="[para(79(a,1),4813(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 4813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4831">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(1146,a,4814,a)].">
      <j1 rule="hyper" parents="1146 4814"/>
    </justification>
  </clause>

  <clause id="4832">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(347,a,1056,a,b,4814,a)].">
      <j1 rule="hyper" parents="347 1056 4814"/>
    </justification>
  </clause>

  <clause id="4834">
    <literal><![CDATA[
      T(x \ T(x * y,z),x) = x \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(4814(a,1),113(a,1,1))].">
      <j1 rule="para" parents="4814 113"/>
    </justification>
  </clause>

  <clause id="4836">
    <literal><![CDATA[
      x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[para(4814(a,1),3725(a,1,2))].">
      <j1 rule="para" parents="4814 3725"/>
    </justification>
  </clause>

  <clause id="4838">
    <literal><![CDATA[
      T(x,y) / L(x,z,u) = L(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3302(a,1),4817(a,1,1,1))].">
      <j1 rule="para" parents="3302 4817"/>
    </justification>
  </clause>

  <clause id="4839">
    <literal><![CDATA[
      T(x,T(y * x,z)) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(4821(a,1),4322(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4821 4322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4840">
    <literal><![CDATA[
      (x \ T(L(y,x,x),z)) * x = T(((x \ 1) * y) * x,z)
    ]]></literal>
    <justification jstring="[para(3197(a,1),4829(a,1,1,2,1))].">
      <j1 rule="para" parents="3197 4829"/>
    </justification>
  </clause>

  <clause id="4841">
    <literal><![CDATA[
      x * ((y \ T(z,x)) * y) = ((y \ z) * y) * x
    ]]></literal>
    <justification jstring="[hyper(134,a,4830,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 4830 22"/>
    </justification>
  </clause>

  <clause id="4842">
    <literal><![CDATA[
      T((x \ y) * x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(110(a,1),4830(a,2,1,2))].">
      <j1 rule="para" parents="110 4830"/>
    </justification>
  </clause>

  <clause id="4843">
    <literal><![CDATA[
      T((x \ (y / z)) * x,z) = (x \ (z \ y)) * x
    ]]></literal>
    <justification jstring="[para(113(a,1),4830(a,2,1,2))].">
      <j1 rule="para" parents="113 4830"/>
    </justification>
  </clause>

  <clause id="4845">
    <literal><![CDATA[
      ((x * T((y \ z) * y,x)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(4830(a,2),4065(a,1,1,1,2))].">
      <j1 rule="para" parents="4830 4065"/>
    </justification>
  </clause>

  <clause id="4846">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = z * (x * ((z \ y) / x))
    ]]></literal>
    <justification jstring="[hyper(134,a,4823,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 4823 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4847">
    <literal><![CDATA[
      T((x * x) * (y / ((x * x) * z)),z) = (x * x) * ((z \ y) / (x * x))
    ]]></literal>
    <justification jstring="[para(702(a,1),4823(a,1,1,2))].">
      <j1 rule="para" parents="702 4823"/>
    </justification>
  </clause>

  <clause id="4848">
    <literal><![CDATA[
      x / ((((y \ 1) * x) \ x) * ((y \ 1) * x)) = T((y \ x) * y,x) / x
    ]]></literal>
    <justification jstring="[para(3848(a,1),4827(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3848 4827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4849">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[para(113(a,1),4841(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="113 4841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4851">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) / x = (y \ (z / x)) * y
    ]]></literal>
    <justification jstring="[hyper(305,a,4843,a)].">
      <j1 rule="hyper" parents="305 4843"/>
    </justification>
  </clause>

  <clause id="4852">
    <literal><![CDATA[
      T(x,y) != (z \ (y \ u)) * z
    ]]></literal>
    <literal><![CDATA[
      (z \ (u / y)) * z = x
    ]]></literal>
    <justification jstring="[para(4843(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="4843 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4853">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(347,a,1257,a(flip),b,4815,a),flip(a)].">
      <j1 rule="hyper" parents="347 1257 4815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4854">
    <literal><![CDATA[
      T(x * (y / x),z / y) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,4812,a,b,4826,a),flip(a)].">
      <j1 rule="hyper" parents="347 4812 4826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,z) = T(y,z) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,2752,a,b,4828,a),flip(a)].">
      <j1 rule="hyper" parents="34 2752 4828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4857">
    <literal><![CDATA[
      x \ T(x * y,1 / x) = ((1 / x) \ y) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(315,a,4831,a),flip(a)].">
      <j1 rule="hyper" parents="315 4831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4858">
    <literal><![CDATA[
      (1 / x) * (y * T(y \ ((1 / x) \ z),u)) = (x \ T(x * (z / y),u)) * y
    ]]></literal>
    <justification jstring="[para(4831(a,1),1543(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4831 1543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4859">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = ((u * ((y / x) / u)) * x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(4133,a,4846,a),flip(a)].">
      <j1 rule="hyper" parents="4133 4846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4860">
    <literal><![CDATA[
      (x * (((y * z) / y) / x)) * y = y * (x * (z / x))
    ]]></literal>
    <justification jstring="[para(9(a,1),4846(a,2,2,2,1))].">
      <j1 rule="para" parents="9 4846"/>
    </justification>
  </clause>

  <clause id="4861">
    <literal><![CDATA[
      (x * ((y / (y * z)) / x)) * (y * z) = (y * z) * (x * (L(z \ 1,z,y) / x))
    ]]></literal>
    <justification jstring="[para(244(a,2),4846(a,2,2,2,1))].">
      <j1 rule="para" parents="244 4846"/>
    </justification>
  </clause>

  <clause id="4862">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3721,a,b,4849,a)].">
      <j1 rule="hyper" parents="63 3721 4849"/>
    </justification>
  </clause>

  <clause id="4863">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = y * ((x \ (y \ z)) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1486,a,b,4849,a)].">
      <j1 rule="hyper" parents="63 1486 4849"/>
    </justification>
  </clause>

  <clause id="4864">
    <literal><![CDATA[
      ((x \ R(1 / y,y,z)) * x) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(247(a,2),4849(a,1,1,1,2))].">
      <j1 rule="para" parents="247 4849"/>
    </justification>
  </clause>

  <clause id="4865">
    <literal><![CDATA[
      (x * ((y \ z) * y)) / x = (y \ ((x * z) / x)) * y
    ]]></literal>
    <justification jstring="[para(9(a,1),4851(a,1,1,2,1,2))].">
      <j1 rule="para" parents="9 4851"/>
    </justification>
  </clause>

  <clause id="4866">
    <literal><![CDATA[
      (x \ ((y * (x * z)) / y)) * x = (y * (z * x)) / y
    ]]></literal>
    <justification jstring="[para(69(a,1),4851(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="69 4851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4867">
    <literal><![CDATA[
      T(x * (y / x),(y / z) \ 1) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4435,a,b,4854,a)].">
      <j1 rule="hyper" parents="63 4435 4854"/>
    </justification>
  </clause>

  <clause id="4868">
    <literal><![CDATA[
      T(x * K(y,y \ 1),z) = T(x,z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2742(a,1),4856(a,1,1))].">
      <j1 rule="para" parents="2742 4856"/>
    </justification>
  </clause>

  <clause id="4869">
    <literal><![CDATA[
      T(((x \ 1) \ 1) \ y,z) * K(x,x \ 1) = T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2873(a,1),4856(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2873 4856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4870">
    <literal><![CDATA[
      T((x / y) * K(z,z \ 1),y) = (y \ x) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(113(a,1),4868(a,2,1))].">
      <j1 rule="para" parents="113 4868"/>
    </justification>
  </clause>

  <clause id="4871">
    <literal><![CDATA[
      (x \ L(T(y,z),x,x)) * x = T(((x \ 1) * y) * x,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),4840(a,1,1,2))].">
      <j1 rule="para" parents="25 4840"/>
    </justification>
  </clause>

  <clause id="4872">
    <literal><![CDATA[
      T(((x \ 1) * y) * x,z) = ((x \ 1) * T(y,z)) * x
    ]]></literal>
    <justification jstring="[para(3202(a,1),4871(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3202 4871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4873">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(1647,a,4836,a)].">
      <j1 rule="hyper" parents="1647 4836"/>
    </justification>
  </clause>

  <clause id="4874">
    <literal><![CDATA[
      T(x,T(((y \ 1) \ 1) \ z,u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(4869(a,1),3990(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4869 3990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4875">
    <literal><![CDATA[
      T(x,T((1 / y) \ z,u)) = T(x,T((y \ 1) \ z,u))
    ]]></literal>
    <justification jstring="[para(83(a,1),4874(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="83 4874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4876">
    <literal><![CDATA[
      T((x / y) * K(z,z \ 1),y) != u * K(z,z \ 1)
    ]]></literal>
    <literal><![CDATA[
      y \ x = u
    ]]></literal>
    <justification jstring="[para(4870(a,2),44(a,1))].">
      <j1 rule="para" parents="4870 44"/>
    </justification>
  </clause>

  <clause id="4877">
    <literal><![CDATA[
      (x * L(y,z \ T(x,z),z)) \ (x * y) = a(T(z,x),T(z,x) \ x,y)
    ]]></literal>
    <justification jstring="[para(4778(a,1),4303(a,1,1))].">
      <j1 rule="para" parents="4778 4303"/>
    </justification>
  </clause>

  <clause id="4878">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,4849,a(flip),b,4873,a)].">
      <j1 rule="hyper" parents="63 4849 4873"/>
    </justification>
  </clause>

  <clause id="4879">
    <literal><![CDATA[
      ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3560,a(flip),b,4878,a),flip(a)].">
      <j1 rule="hyper" parents="63 3560 4878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4880">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * x = (y \ (z * x)) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,3560,a(flip),b,4878,a(flip))].">
      <j1 rule="hyper" parents="133 3560 4878"/>
    </justification>
  </clause>

  <clause id="4881">
    <literal><![CDATA[
      a(T(x,y),T(T(y,x),x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(4270(a,1),4808(a,1,1))].">
      <j1 rule="para" parents="4270 4808"/>
    </justification>
  </clause>

  <clause id="4882">
    <literal><![CDATA[
      T((x * x) * (y / ((x * x) * z)),z) = T(z \ y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(347,a,1119,a(flip),b,4847,a),flip(a)].">
      <j1 rule="hyper" parents="347 1119 4847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4883">
    <literal><![CDATA[
      ((x \ 1) \ y) / (x * x) = T(x \ y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,1484,a(flip),b,4882,a)].">
      <j1 rule="hyper" parents="63 1484 4882"/>
    </justification>
  </clause>

  <clause id="4884">
    <literal><![CDATA[
      T(x \ y,x \ (x \ 1)) = (x \ 1) \ (y / (x * x))
    ]]></literal>
    <justification jstring="[hyper(817,a,4883,a),flip(a)].">
      <j1 rule="hyper" parents="817 4883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4885">
    <literal><![CDATA[
      T(x \ y,x \ (x \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      T(y / x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(4884(a,2),799(a,1))].">
      <j1 rule="para" parents="4884 799"/>
    </justification>
  </clause>

  <clause id="4886">
    <literal><![CDATA[
      T((x \ y) * x,y) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(4479(a,1),4848(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4479 4848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4887">
    <literal><![CDATA[
      ((x \ y) * x) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(4842(a,1),4886(a,1,1))].">
      <j1 rule="para" parents="4842 4886"/>
    </justification>
  </clause>

  <clause id="4888">
    <literal><![CDATA[
      ((x \ y) * x) / y = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(347,a,4388,a(flip),b,4887,a),flip(a)].">
      <j1 rule="hyper" parents="347 4388 4887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4889">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4554,a,b,4888,a)].">
      <j1 rule="hyper" parents="63 4554 4888"/>
    </justification>
  </clause>

  <clause id="4890">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * x,y \ 1,y) = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[para(4889(a,1),3628(a,2,2))].">
      <j1 rule="para" parents="4889 3628"/>
    </justification>
  </clause>

  <clause id="4891">
    <literal><![CDATA[
      (x \ (1 \ (y * 1))) * x = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3306,a(flip),b,4890,a)].">
      <j1 rule="hyper" parents="63 3306 4890"/>
    </justification>
  </clause>

  <clause id="4892">
    <literal><![CDATA[
      x * (y \ (x / (x / y))) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(182(a,1),4891(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="182 4891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4893">
    <literal><![CDATA[
      x \ (y / (y / x)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,330,a,b,4892,a),flip(a)].">
      <j1 rule="hyper" parents="34 330 4892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4894">
    <literal><![CDATA[
      x / (x / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(150,a,4893,a),flip(a)].">
      <j1 rule="hyper" parents="150 4893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4895">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4889,a,b,4893,a)].">
      <j1 rule="hyper" parents="63 4889 4893"/>
    </justification>
  </clause>

  <clause id="4896">
    <literal><![CDATA[
      ((x \ y) * x) / y = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4888,a,b,4893,a)].">
      <j1 rule="hyper" parents="63 4888 4893"/>
    </justification>
  </clause>

  <clause id="4898">
    <literal><![CDATA[
      K(x \ y,x) * y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,4893,a(flip),b,4888,a)].">
      <j1 rule="hyper" parents="133 4893 4888"/>
    </justification>
  </clause>

  <clause id="4899">
    <literal><![CDATA[
      K(x \ y,x) * (x * (y / x)) = y
    ]]></literal>
    <justification jstring="[hyper(133,a,4893,a(flip),b,4388,a)].">
      <j1 rule="hyper" parents="133 4893 4388"/>
    </justification>
  </clause>

  <clause id="4900">
    <literal><![CDATA[
      x \ K((x \ 1) \ y,x \ 1) = y / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(347,a,3056,a(flip),b,4894,a)].">
      <j1 rule="hyper" parents="347 3056 4894"/>
    </justification>
  </clause>

  <clause id="4901">
    <literal><![CDATA[
      x / (x / y) != y * z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(4894(a,2),43(a,1))].">
      <j1 rule="para" parents="4894 43"/>
    </justification>
  </clause>

  <clause id="4903">
    <literal><![CDATA[
      T(x * K(x \ y,x),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(4894(a,1),4394(a,1,1))].">
      <j1 rule="para" parents="4894 4394"/>
    </justification>
  </clause>

  <clause id="4904">
    <literal><![CDATA[
      T(x,K(y \ x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(269,a,330,a,b,4898,a)].">
      <j1 rule="hyper" parents="269 330 4898"/>
    </justification>
  </clause>

  <clause id="4905">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(4898(a,1),1849(a,2,2))].">
      <j1 rule="para" parents="4898 1849"/>
    </justification>
  </clause>

  <clause id="4906">
    <literal><![CDATA[
      T(x * y,K(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(9(a,1),4904(a,1,2,1))].">
      <j1 rule="para" parents="9 4904"/>
    </justification>
  </clause>

  <clause id="4907">
    <literal><![CDATA[
      K(x,y) \ (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(441,a,4906,a)].">
      <j1 rule="hyper" parents="441 4906"/>
    </justification>
  </clause>

  <clause id="4908">
    <literal><![CDATA[
      K(x,y) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(222,a,4907,a),flip(a)].">
      <j1 rule="hyper" parents="222 4907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4909">
    <literal><![CDATA[
      K(x,y) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[hyper(150,a,4907,a)].">
      <j1 rule="hyper" parents="150 4907"/>
    </justification>
  </clause>

  <clause id="4910">
    <literal><![CDATA[
      K(x * y,R(z,x,y)) * ((z * x) * y) = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,107,a(flip),b,4907,a)].">
      <j1 rule="hyper" parents="134 107 4907"/>
    </justification>
  </clause>

  <clause id="4911">
    <literal><![CDATA[
      K(L(x,y,z),z * y) * (z * (y * x)) = L(x,y,z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,97,a(flip),b,4907,a)].">
      <j1 rule="hyper" parents="134 97 4907"/>
    </justification>
  </clause>

  <clause id="4912">
    <literal><![CDATA[
      K(x,x \ y) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),4907(a,1,2))].">
      <j1 rule="para" parents="10 4907"/>
    </justification>
  </clause>

  <clause id="4913">
    <literal><![CDATA[
      K(x,y) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,4206,a(flip),b,4908,a),flip(a)].">
      <j1 rule="hyper" parents="347 4206 4908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4914">
    <literal><![CDATA[
      T(x,y) = x / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(220,a,4908,a,b,4206,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="220 4908 4206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4915">
    <literal><![CDATA[
      T(x,y) * K(y,x) = x
    ]]></literal>
    <justification jstring="[hyper(134,a,4908,a,b,4206,a(flip))].">
      <j1 rule="hyper" parents="134 4908 4206"/>
    </justification>
  </clause>

  <clause id="4916">
    <literal><![CDATA[
      K(x,y) != z \ y
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4908(a,2),4210(a,2)),flip(a)].">
      <j1 rule="para" parents="4908 4210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4917">
    <literal><![CDATA[
      (x * y) \ T((x * y) * K(y,x),z) = T(y * x,z) / (x * y)
    ]]></literal>
    <justification jstring="[para(4908(a,2),4811(a,1,2,1,2))].">
      <j1 rule="para" parents="4908 4811"/>
    </justification>
  </clause>

  <clause id="4918">
    <literal><![CDATA[
      K(x,y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(347,a,3775,a,b,4913,a),flip(a)].">
      <j1 rule="hyper" parents="347 3775 4913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4919">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,3101,a,b,4913,a)].">
      <j1 rule="hyper" parents="347 3101 4913"/>
    </justification>
  </clause>

  <clause id="4920">
    <literal><![CDATA[
      K(x,y) = y / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3012,a,b,4913,a),flip(a)].">
      <j1 rule="hyper" parents="347 3012 4913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4921">
    <literal><![CDATA[
      K(x,y) = (1 / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(347,a,3011,a,b,4913,a),flip(a)].">
      <j1 rule="hyper" parents="347 3011 4913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4922">
    <literal><![CDATA[
      K(x,y) = y * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,1230,a,b,4913,a),flip(a)].">
      <j1 rule="hyper" parents="347 1230 4913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4923">
    <literal><![CDATA[
      T(T(x,y),z) \ T(x,z) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,173,a,b,4913,a)].">
      <j1 rule="hyper" parents="347 173 4913"/>
    </justification>
  </clause>

  <clause id="4924">
    <literal><![CDATA[
      K(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,4266,a(flip),b,4913,a),flip(a)].">
      <j1 rule="hyper" parents="347 4266 4913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4925">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,4263,a(flip),b,4913,a)].">
      <j1 rule="hyper" parents="347 4263 4913"/>
    </justification>
  </clause>

  <clause id="4926">
    <literal><![CDATA[
      (x \ y) / ((x \ y) / y) = y * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,4913,a,b,4226,a),flip(a)].">
      <j1 rule="hyper" parents="134 4913 4226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4927">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(134,a,4913,a,b,2911,a)].">
      <j1 rule="hyper" parents="134 4913 2911"/>
    </justification>
  </clause>

  <clause id="4928">
    <literal><![CDATA[
      x / (x / y) = y * K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,4913,a,b,4267,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 4913 4267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4929">
    <literal><![CDATA[
      T(x,y) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,4913,a,b,4266,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 4913 4266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4931">
    <literal><![CDATA[
      K(x,y) * T(y,x) = y
    ]]></literal>
    <justification jstring="[hyper(133,a,4913,a,b,3012,a)].">
      <j1 rule="hyper" parents="133 4913 3012"/>
    </justification>
  </clause>

  <clause id="4932">
    <literal><![CDATA[
      K(x,y) / y = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,4913,a,b,3011,a)].">
      <j1 rule="hyper" parents="131 4913 3011"/>
    </justification>
  </clause>

  <clause id="4933">
    <literal><![CDATA[
      K(x,y * y) / (y * y) = T(y * y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(131,a,4913,a,b,460,a)].">
      <j1 rule="hyper" parents="131 4913 460"/>
    </justification>
  </clause>

  <clause id="4934">
    <literal><![CDATA[
      T(x,y) \ 1 = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,4913,a,b,1230,a),flip(a)].">
      <j1 rule="hyper" parents="128 4913 1230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4935">
    <literal><![CDATA[
      x \ K(x \ 1,y) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,4913,a,b,4263,a(flip))].">
      <j1 rule="hyper" parents="128 4913 4263"/>
    </justification>
  </clause>

  <clause id="4936">
    <literal><![CDATA[
      L(T(x,y),z,u) \ L(x,z,u) = K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),4913(a,2,1)),flip(a)].">
      <j1 rule="para" parents="25 4913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4937">
    <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),4913(a,2,1)),flip(a)].">
      <j1 rule="para" parents="27 4913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4938">
    <literal><![CDATA[
      x / K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4913(a,2),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4913 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4939">
    <literal><![CDATA[
      T(x,y) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[para(4913(a,2),3016(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4913 3016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4940">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y / T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4913(a,2),3015(a,1))].">
      <j1 rule="para" parents="4913 3015"/>
    </justification>
  </clause>

  <clause id="4941">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4913(a,2),4215(a,2,1))].">
      <j1 rule="para" parents="4913 4215"/>
    </justification>
  </clause>

  <clause id="4942">
    <literal><![CDATA[
      (x * y) / x = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(4913(a,2),4268(a,2,2))].">
      <j1 rule="para" parents="4913 4268"/>
    </justification>
  </clause>

  <clause id="4943">
    <literal><![CDATA[
      x * (K(x,y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4913(a,2),4271(a,1,2,1))].">
      <j1 rule="para" parents="4913 4271"/>
    </justification>
  </clause>

  <clause id="4944">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4913(a,2),4272(a,2,1))].">
      <j1 rule="para" parents="4913 4272"/>
    </justification>
  </clause>

  <clause id="4945">
    <literal><![CDATA[
      K(x / y,z) * x = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(4913(a,2),4269(a,1,1))].">
      <j1 rule="para" parents="4913 4269"/>
    </justification>
  </clause>

  <clause id="4946">
    <literal><![CDATA[
      K(x,y) * (T(y,x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(4913(a,2),4762(a,1,1))].">
      <j1 rule="para" parents="4913 4762"/>
    </justification>
  </clause>

  <clause id="4947">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(4913(a,2),4763(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4913 4763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4948">
    <literal><![CDATA[
      ((x \ y) \ y) * K(y / x,x) = x
    ]]></literal>
    <justification jstring="[hyper(133,a,4306,a(flip),b,4914,a(flip))].">
      <j1 rule="hyper" parents="133 4306 4914"/>
    </justification>
  </clause>

  <clause id="4949">
    <literal><![CDATA[
      (x \ y) * K(x,y / x) = y / x
    ]]></literal>
    <justification jstring="[hyper(133,a,113,a(flip),b,4914,a(flip))].">
      <j1 rule="hyper" parents="133 113 4914"/>
    </justification>
  </clause>

  <clause id="4950">
    <literal><![CDATA[
      T(x,y) != x / z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4914(a,2),45(a,1))].">
      <j1 rule="para" parents="4914 45"/>
    </justification>
  </clause>

  <clause id="4951">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4914(a,2),359(a,1,1))].">
      <j1 rule="para" parents="4914 359"/>
    </justification>
  </clause>

  <clause id="4952">
    <literal><![CDATA[
      T(x,y) != x
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = 1
    ]]></literal>
    <justification jstring="[para(4915(a,1),137(a,1)),flip(a),flip(b)].">
      <j1 rule="para" parents="4915 137"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4953">
    <literal><![CDATA[
      x * (y * K(x,y)) = T(x,y) * y
    ]]></literal>
    <justification jstring="[para(4915(a,1),4768(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4915 4768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4954">
    <literal><![CDATA[
      K(x,y) != y / z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4920(a,2),45(a,1))].">
      <j1 rule="para" parents="4920 45"/>
    </justification>
  </clause>

  <clause id="4956">
    <literal><![CDATA[
      K(x * (1 / y),x) = x / T(x,x / y)
    ]]></literal>
    <justification jstring="[para(4168(a,1),4920(a,2,2))].">
      <j1 rule="para" parents="4168 4920"/>
    </justification>
  </clause>

  <clause id="4957">
    <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(4920(a,2),4421(a,2,1))].">
      <j1 rule="para" parents="4920 4421"/>
    </justification>
  </clause>

  <clause id="4958">
    <literal><![CDATA[
      x \ T(x,y \ 1) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(3903,a,4924,a),flip(a)].">
      <j1 rule="hyper" parents="3903 4924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4959">
    <literal><![CDATA[
      T(T(x,y),x \ 1) = (x \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(462,a,4924,a,b,1142,a)].">
      <j1 rule="hyper" parents="462 4924 1142"/>
    </justification>
  </clause>

  <clause id="4960">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,4653,a,b,4924,a)].">
      <j1 rule="hyper" parents="347 4653 4924"/>
    </justification>
  </clause>

  <clause id="4962">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,4199,a,b,4924,a)].">
      <j1 rule="hyper" parents="347 4199 4924"/>
    </justification>
  </clause>

  <clause id="4963">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,4183,a,b,4924,a)].">
      <j1 rule="hyper" parents="347 4183 4924"/>
    </justification>
  </clause>

  <clause id="4964">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,3818,a,b,4924,a)].">
      <j1 rule="hyper" parents="347 3818 4924"/>
    </justification>
  </clause>

  <clause id="4965">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,3778,a,b,4924,a)].">
      <j1 rule="hyper" parents="347 3778 4924"/>
    </justification>
  </clause>

  <clause id="4966">
    <literal><![CDATA[
      K(x,y) = ((x * y) / x) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,3770,a,b,4924,a),flip(a)].">
      <j1 rule="hyper" parents="347 3770 4924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4967">
    <literal><![CDATA[
      K(x,y) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3766,a,b,4924,a),flip(a)].">
      <j1 rule="hyper" parents="347 3766 4924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4968">
    <literal><![CDATA[
      K(x,y) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3074,a,b,4924,a),flip(a)].">
      <j1 rule="hyper" parents="347 3074 4924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4969">
    <literal><![CDATA[
      K(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(347,a,3071,a,b,4924,a),flip(a)].">
      <j1 rule="hyper" parents="347 3071 4924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4970">
    <literal><![CDATA[
      K(x,y) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,1142,a,b,4924,a),flip(a)].">
      <j1 rule="hyper" parents="347 1142 4924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4971">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,1274,a(flip),b,4924,a)].">
      <j1 rule="hyper" parents="347 1274 4924"/>
    </justification>
  </clause>

  <clause id="4972">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(134,a,4924,a,b,3767,a)].">
      <j1 rule="hyper" parents="134 4924 3767"/>
    </justification>
  </clause>

  <clause id="4973">
    <literal><![CDATA[
      (x \ y) \ y = x * K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(134,a,4924,a,b,335,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 4924 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4974">
    <literal><![CDATA[
      K(x,y) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,4924,a,b,4183,a)].">
      <j1 rule="hyper" parents="133 4924 4183"/>
    </justification>
  </clause>

  <clause id="4975">
    <literal><![CDATA[
      K(x,y \ 1) * (y \ x) = x * ((y \ x) / x)
    ]]></literal>
    <justification jstring="[hyper(133,a,4924,a,b,3796,a)].">
      <j1 rule="hyper" parents="133 4924 3796"/>
    </justification>
  </clause>

  <clause id="4976">
    <literal><![CDATA[
      (x * y) / x = K(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,4924,a,b,3771,a),flip(a)].">
      <j1 rule="hyper" parents="133 4924 3771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4977">
    <literal><![CDATA[
      T(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,4924,a,b,3071,a),flip(a)].">
      <j1 rule="hyper" parents="133 4924 3071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4978">
    <literal><![CDATA[
      K(x,y) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(131,a,4924,a,b,3074,a)].">
      <j1 rule="hyper" parents="131 4924 3074"/>
    </justification>
  </clause>

  <clause id="4979">
    <literal><![CDATA[
      x \ K(y,x \ 1) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(128,a,4924,a,b,3778,a)].">
      <j1 rule="hyper" parents="128 4924 3778"/>
    </justification>
  </clause>

  <clause id="4980">
    <literal><![CDATA[
      ((x * y) / x) \ K(x,y) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,4924,a,b,3770,a)].">
      <j1 rule="hyper" parents="128 4924 3770"/>
    </justification>
  </clause>

  <clause id="4981">
    <literal><![CDATA[
      T(x,y) = (1 / x) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,4924,a,b,3074,a),flip(a)].">
      <j1 rule="hyper" parents="128 4924 3074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4982">
    <literal><![CDATA[
      L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(25(a,2),4924(a,2,2)),flip(a)].">
      <j1 rule="para" parents="25 4924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4983">
    <literal><![CDATA[
      R(x,y,z) \ R(T(x,u),y,z) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(27(a,2),4924(a,2,2)),flip(a)].">
      <j1 rule="para" parents="27 4924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4984">
    <literal><![CDATA[
      x * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4924(a,2),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4924 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4986">
    <literal><![CDATA[
      T(x,y) * (x \ K(T(x,y),z)) = x \ T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(4924(a,2),1221(a,1,2,2))].">
      <j1 rule="para" parents="4924 1221"/>
    </justification>
  </clause>

  <clause id="4987">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4924(a,2),3079(a,1,1))].">
      <j1 rule="para" parents="4924 3079"/>
    </justification>
  </clause>

  <clause id="4988">
    <literal><![CDATA[
      x * L(x \ K(x,y),z,u) = x \ L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4924(a,2),3341(a,1,2,1,2))].">
      <j1 rule="para" parents="4924 3341"/>
    </justification>
  </clause>

  <clause id="4989">
    <literal><![CDATA[
      (x * K(y,x)) * y = y * x
    ]]></literal>
    <justification jstring="[para(4924(a,2),3763(a,1,1,2))].">
      <j1 rule="para" parents="4924 3763"/>
    </justification>
  </clause>

  <clause id="4990">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(4924(a,2),3765(a,1,2))].">
      <j1 rule="para" parents="4924 3765"/>
    </justification>
  </clause>

  <clause id="4991">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3990(a,1),4924(a,2,2))].">
      <j1 rule="para" parents="3990 4924"/>
    </justification>
  </clause>

  <clause id="4993">
    <literal><![CDATA[
      R(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(4924(a,2),4141(a,1,2))].">
      <j1 rule="para" parents="4924 4141"/>
    </justification>
  </clause>

  <clause id="4994">
    <literal><![CDATA[
      L(x,K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4924(a,2),4151(a,1,2))].">
      <j1 rule="para" parents="4924 4151"/>
    </justification>
  </clause>

  <clause id="4995">
    <literal><![CDATA[
      K(x,y) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[para(4924(a,2),4184(a,1,1))].">
      <j1 rule="para" parents="4924 4184"/>
    </justification>
  </clause>

  <clause id="4996">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[para(4924(a,2),4185(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4924 4185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4997">
    <literal><![CDATA[
      K(x,x \ y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4924(a,2),4191(a,1,1))].">
      <j1 rule="para" parents="4924 4191"/>
    </justification>
  </clause>

  <clause id="4998">
    <literal><![CDATA[
      x \ T(x,x * y) = K(x,y * x)
    ]]></literal>
    <justification jstring="[para(4323(a,1),4924(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4323 4924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4999">
    <literal><![CDATA[
      K(a(x,y,z),z \ L(z,y,x)) = a(x,y,z) \ ((a(x,y,z) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(4681(a,1),4924(a,2,2))].">
      <j1 rule="para" parents="4681 4924"/>
    </justification>
  </clause>

  <clause id="5000">
    <literal><![CDATA[
      K(x,y) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(4924(a,2),4760(a,1,1))].">
      <j1 rule="para" parents="4924 4760"/>
    </justification>
  </clause>

  <clause id="5001">
    <literal><![CDATA[
      R(T(x,y),K(x,z),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4993(a,1),27(a,2,1))].">
      <j1 rule="para" parents="4993 27"/>
    </justification>
  </clause>

  <clause id="5002">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) * w = L(x,y,z) * (K(x,u) * w)
    ]]></literal>
    <justification jstring="[para(4993(a,1),471(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4993 471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5004">
    <literal><![CDATA[
      (x * y) * L(K(y,z),y,x) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,4929,a,b,327,a),flip(a)].">
      <j1 rule="hyper" parents="134 4929 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5005">
    <literal><![CDATA[
      T(x,y) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4929(a,2),43(a,1))].">
      <j1 rule="para" parents="4929 43"/>
    </justification>
  </clause>

  <clause id="5006">
    <literal><![CDATA[
      x \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4929(a,2),356(a,1,2))].">
      <j1 rule="para" parents="4929 356"/>
    </justification>
  </clause>

  <clause id="5007">
    <literal><![CDATA[
      L(K(x,y) \ z,K(x,y),x) = T(x,y) \ (x * z)
    ]]></literal>
    <justification jstring="[para(4929(a,2),99(a,2,1))].">
      <j1 rule="para" parents="4929 99"/>
    </justification>
  </clause>

  <clause id="5008">
    <literal><![CDATA[
      (x * y) * K(y,z) != u * T(y,z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(4929(a,2),594(a,2,2))].">
      <j1 rule="para" parents="4929 594"/>
    </justification>
  </clause>

  <clause id="5010">
    <literal><![CDATA[
      T(x * y,z) / a(x,y,K(x * y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * K(x * y,z)) = u
    ]]></literal>
    <justification jstring="[para(4929(a,2),325(a,1,1))].">
      <j1 rule="para" parents="4929 325"/>
    </justification>
  </clause>

  <clause id="5011">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * T(y,z)) = L(y,K(y,z),x)
    ]]></literal>
    <justification jstring="[para(4929(a,2),3581(a,1,2,2))].">
      <j1 rule="para" parents="4929 3581"/>
    </justification>
  </clause>

  <clause id="5012">
    <literal><![CDATA[
      K(x,y / x) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(113(a,1),4931(a,1,2))].">
      <j1 rule="para" parents="113 4931"/>
    </justification>
  </clause>

  <clause id="5013">
    <literal><![CDATA[
      x / T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4931(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4931 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5014">
    <literal><![CDATA[
      K(x \ y,x) * R(T(x,x \ y),z,u) = y \ ((R(x,z,u) * (x \ y)) * x)
    ]]></literal>
    <justification jstring="[para(4939(a,2),2669(a,1,2,1))].">
      <j1 rule="para" parents="4939 2669"/>
    </justification>
  </clause>

  <clause id="5015">
    <literal><![CDATA[
      T(1 / x,y) * x = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,1112,a(flip),b,4969,a)].">
      <j1 rule="hyper" parents="347 1112 4969"/>
    </justification>
  </clause>

  <clause id="5017">
    <literal><![CDATA[
      (x \ y) \ y = K(x,x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,4969,a,b,337,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 4969 337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5018">
    <literal><![CDATA[
      K(x,1 / y) / y = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,4969,a,b,3814,a)].">
      <j1 rule="hyper" parents="131 4969 3814"/>
    </justification>
  </clause>

  <clause id="5019">
    <literal><![CDATA[
      K(x,y \ 1) / y = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,4969,a,b,3812,a)].">
      <j1 rule="hyper" parents="131 4969 3812"/>
    </justification>
  </clause>

  <clause id="5022">
    <literal><![CDATA[
      R(T(x,y),z,u) / R(x,z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(27(a,2),4969(a,2,1)),flip(a)].">
      <j1 rule="para" parents="27 4969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5025">
    <literal><![CDATA[
      K(x,x \ y) * x = T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(4346,a,4977,a),flip(a)].">
      <j1 rule="hyper" parents="4346 4977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5026">
    <literal><![CDATA[
      K(T(x,y),z) * T(x,y) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(453,a,4977,a),flip(a)].">
      <j1 rule="hyper" parents="453 4977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5027">
    <literal><![CDATA[
      K(x / y,y) * (x / y) = y \ x
    ]]></literal>
    <justification jstring="[hyper(386,a,4977,a),flip(a)].">
      <j1 rule="hyper" parents="386 4977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5028">
    <literal><![CDATA[
      K(L(x,y,z),u) * L(x,y,z) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,25,a,b,4977,a),flip(a)].">
      <j1 rule="hyper" parents="63 25 4977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5030">
    <literal><![CDATA[
      x * (K(y,x) * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(134,a,4977,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 4977 22"/>
    </justification>
  </clause>

  <clause id="5031">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4977(a,2),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4977 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5032">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) = (K(y,z) * x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(4977(a,2),99(a,2,2))].">
      <j1 rule="para" parents="4977 99"/>
    </justification>
  </clause>

  <clause id="5033">
    <literal><![CDATA[
      T(x,y) \ (K(x,y) * (z * x)) = L(T(z,x),x,K(x,y))
    ]]></literal>
    <justification jstring="[para(4977(a,2),263(a,1,1))].">
      <j1 rule="para" parents="4977 263"/>
    </justification>
  </clause>

  <clause id="5034">
    <literal><![CDATA[
      (x * K(y,z)) * y != u * T(y,z)
    ]]></literal>
    <literal><![CDATA[
      R(x,K(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(4977(a,2),594(a,2,2))].">
      <j1 rule="para" parents="4977 594"/>
    </justification>
  </clause>

  <clause id="5035">
    <literal><![CDATA[
      (K(x,y) * z) \ T(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      L(z \ x,z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(4977(a,2),686(a,1,2))].">
      <j1 rule="para" parents="4977 686"/>
    </justification>
  </clause>

  <clause id="5036">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4977(a,2),3576(a,1))].">
      <j1 rule="para" parents="4977 3576"/>
    </justification>
  </clause>

  <clause id="5037">
    <literal><![CDATA[
      ((x * y) / x) \ 1 = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,4918,a,b,1451,a),flip(a)].">
      <j1 rule="hyper" parents="128 4918 1451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5039">
    <literal><![CDATA[
      K(x,y) != 1
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = y
    ]]></literal>
    <justification jstring="[para(4921(a,2),140(a,1)),flip(b)].">
      <j1 rule="para" parents="4921 140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5040">
    <literal><![CDATA[
      ((x * (1 / T(y,z))) * y) / K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,1 / T(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(4921(a,2),595(a,1,2))].">
      <j1 rule="para" parents="4921 595"/>
    </justification>
  </clause>

  <clause id="5041">
    <literal><![CDATA[
      (x * y) \ (x * K(z,y)) = L(T(y,z) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(4922(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4922 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5042">
    <literal><![CDATA[
      x * (T(y,z) \ 1) = x * (y \ K(z,y))
    ]]></literal>
    <justification jstring="[para(4922(a,2),170(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4922 170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5043">
    <literal><![CDATA[
      L(T(x \ y,z) \ 1,x \ y,x) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[para(4922(a,2),98(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4922 98"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5044">
    <literal><![CDATA[
      T(x,y) = 1 / (x \ K(y,x))
    ]]></literal>
    <justification jstring="[hyper(222,a,4934,a),flip(a)].">
      <j1 rule="hyper" parents="222 4934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5045">
    <literal><![CDATA[
      1 / (x \ K(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4934(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4934 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5046">
    <literal><![CDATA[
      T(x,y) * L(x \ K(y,x),z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(4934(a,1),2133(a,1,2,1))].">
      <j1 rule="para" parents="4934 2133"/>
    </justification>
  </clause>

  <clause id="5047">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (x \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(4934(a,1),2725(a,2,1))].">
      <j1 rule="para" parents="4934 2725"/>
    </justification>
  </clause>

  <clause id="5048">
    <literal><![CDATA[
      (x * y) * K(T(y,x),x * y) = T(y,x * y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4478,a,4942,a),flip(a)].">
      <j1 rule="hyper" parents="4478 4942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5049">
    <literal><![CDATA[
      (x \ y) \ (y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(649,a,4942,a)].">
      <j1 rule="hyper" parents="649 4942"/>
    </justification>
  </clause>

  <clause id="5050">
    <literal><![CDATA[
      T((x * y) / x,z) = T(y,z) * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(506,a,4942,a)].">
      <j1 rule="hyper" parents="506 4942"/>
    </justification>
  </clause>

  <clause id="5051">
    <literal><![CDATA[
      x \ K(y,1 / x) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(347,a,3899,a(flip),b,4942,a)].">
      <j1 rule="hyper" parents="347 3899 4942"/>
    </justification>
  </clause>

  <clause id="5052">
    <literal><![CDATA[
      K(x,y) = (1 / y) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(134,a,4942,a,b,3055,a),flip(a)].">
      <j1 rule="hyper" parents="134 4942 3055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5054">
    <literal><![CDATA[
      (x \ K(y,x \ 1)) * y = y * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,3056,a(flip),b,4942,a)].">
      <j1 rule="hyper" parents="133 3056 4942"/>
    </justification>
  </clause>

  <clause id="5055">
    <literal><![CDATA[
      (x * y) \ ((x * y) / x) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,4942,a,b,1571,a)].">
      <j1 rule="hyper" parents="128 4942 1571"/>
    </justification>
  </clause>

  <clause id="5056">
    <literal><![CDATA[
      (x * y) * K(y,x * y) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,4358,a(flip),b,4942,a),flip(a)].">
      <j1 rule="hyper" parents="63 4358 4942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5057">
    <literal><![CDATA[
      (x * x) \ (y / (y / (x * x))) = K(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(128,a,902,a(flip),b,4942,a(flip))].">
      <j1 rule="hyper" parents="128 902 4942"/>
    </justification>
  </clause>

  <clause id="5058">
    <literal><![CDATA[
      T(x * K(y,x),y) = x
    ]]></literal>
    <justification jstring="[para(4942(a,1),254(a,1,1))].">
      <j1 rule="para" parents="4942 254"/>
    </justification>
  </clause>

  <clause id="5059">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4942(a,1),304(a,1,1,1))].">
      <j1 rule="para" parents="4942 304"/>
    </justification>
  </clause>

  <clause id="5060">
    <literal><![CDATA[
      ((x * y) * z) / R(x,y,z) = (y * z) * K(R(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),4942(a,1,1))].">
      <j1 rule="para" parents="107 4942"/>
    </justification>
  </clause>

  <clause id="5061">
    <literal><![CDATA[
      R(x * K(y,x),y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(4942(a,1),108(a,1,1))].">
      <j1 rule="para" parents="4942 108"/>
    </justification>
  </clause>

  <clause id="5062">
    <literal><![CDATA[
      R(x / y,y,K(z,x)) \ ((z * x) / z) = y * K(z,x)
    ]]></literal>
    <justification jstring="[para(4942(a,2),579(a,1,2))].">
      <j1 rule="para" parents="4942 579"/>
    </justification>
  </clause>

  <clause id="5063">
    <literal><![CDATA[
      T(x * K(y,x),z) * y = y * T(x,z)
    ]]></literal>
    <justification jstring="[para(4942(a,1),485(a,1,1,1))].">
      <j1 rule="para" parents="4942 485"/>
    </justification>
  </clause>

  <clause id="5064">
    <literal><![CDATA[
      T(x * K(y,x),z) = (y * T(x,z)) / y
    ]]></literal>
    <justification jstring="[para(4942(a,1),504(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4942 504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5065">
    <literal><![CDATA[
      a(x,y,z) * K(x * (y * z),a(x,y,z)) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(86(a,1),4942(a,1,1)),flip(a)].">
      <j1 rule="para" parents="86 4942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5066">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(4942(a,1),810(a,1,1,1))].">
      <j1 rule="para" parents="4942 810"/>
    </justification>
  </clause>

  <clause id="5067">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * y = y * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(4942(a,1),741(a,1,1,1))].">
      <j1 rule="para" parents="4942 741"/>
    </justification>
  </clause>

  <clause id="5068">
    <literal><![CDATA[
      L(x * K(y,x),z,u) = (y * L(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(4942(a,1),949(a,1,1))].">
      <j1 rule="para" parents="4942 949"/>
    </justification>
  </clause>

  <clause id="5069">
    <literal><![CDATA[
      R(x * K(y,x),z,u) = (y * R(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(4942(a,1),956(a,1,1))].">
      <j1 rule="para" parents="4942 956"/>
    </justification>
  </clause>

  <clause id="5070">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4942(a,1),1034(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4942 1034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5071">
    <literal><![CDATA[
      L(x * K(y * z,x),z,y) = (y * (z * x)) / (y * z)
    ]]></literal>
    <justification jstring="[para(4942(a,1),950(a,1,1))].">
      <j1 rule="para" parents="4942 950"/>
    </justification>
  </clause>

  <clause id="5073">
    <literal><![CDATA[
      ((x * y) * R(y,z,u)) / (x * R(y,z,u)) = y * K(x * R(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(1704(a,1),4942(a,1,1))].">
      <j1 rule="para" parents="1704 4942"/>
    </justification>
  </clause>

  <clause id="5074">
    <literal><![CDATA[
      ((x * y) * L(y,z,u)) / (x * L(y,z,u)) = y * K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(1993(a,1),4942(a,1,1))].">
      <j1 rule="para" parents="1993 4942"/>
    </justification>
  </clause>

  <clause id="5075">
    <literal><![CDATA[
      (T(x,y) * y) / T(x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,4277,a,b,5058,a)].">
      <j1 rule="hyper" parents="40 4277 5058"/>
    </justification>
  </clause>

  <clause id="5076">
    <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(40,a,1715,a,b,5058,a),flip(a)].">
      <j1 rule="hyper" parents="40 1715 5058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5077">
    <literal><![CDATA[
      T(L(x * K(y,x),z,u),y) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(5058(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5058 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5078">
    <literal><![CDATA[
      T(R(x * K(y,x),z,u),y) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(5058(a,1),27(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5058 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5079">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      z * K(y,z) = x
    ]]></literal>
    <justification jstring="[para(5058(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="5058 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5080">
    <literal><![CDATA[
      (x * y) / x != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5058(a,1),318(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="5058 318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5081">
    <literal><![CDATA[
      T(x * K(y,x),(x * K(y,x)) * y) = L(x,y,x * K(y,x))
    ]]></literal>
    <justification jstring="[para(5058(a,1),750(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5058 750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5082">
    <literal><![CDATA[
      R(T(x * K(y,x),z),u,w) * y = y * R(T(x,z),u,w)
    ]]></literal>
    <justification jstring="[para(5058(a,1),745(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5058 745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5083">
    <literal><![CDATA[
      T(x * K(y \ 1,x),y) = T(x,y * y)
    ]]></literal>
    <justification jstring="[para(5058(a,1),1310(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5058 1310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5084">
    <literal><![CDATA[
      T(1 / (1 / (x * K(y,x))),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(5058(a,1),2729(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5058 2729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5085">
    <literal><![CDATA[
      T(K(x,y) * y,x) = y
    ]]></literal>
    <justification jstring="[para(3025(a,2),5058(a,1,1))].">
      <j1 rule="para" parents="3025 5058"/>
    </justification>
  </clause>

  <clause id="5087">
    <literal><![CDATA[
      T(K(x,y \ 1) / y,x) = 1 / y
    ]]></literal>
    <justification jstring="[para(3898(a,1),5058(a,1,1))].">
      <j1 rule="para" parents="3898 5058"/>
    </justification>
  </clause>

  <clause id="5088">
    <literal><![CDATA[
      T(x,L(y * K(x,y),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5058(a,1),4284(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5058 4284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5089">
    <literal><![CDATA[
      ((x \ (y * K(z,y))) * x) * z = z * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(5058(a,1),4841(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5058 4841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5091">
    <literal><![CDATA[
      x * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) / y = z
    ]]></literal>
    <justification jstring="[para(4967(a,2),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4967 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5092">
    <literal><![CDATA[
      K(1 / x,y) / x = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,4970,a,b,217,a(flip))].">
      <j1 rule="hyper" parents="131 4970 217"/>
    </justification>
  </clause>

  <clause id="5093">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * K(y,z)) = L(y \ 1,T(y,z),x)
    ]]></literal>
    <justification jstring="[para(4970(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4970 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5095">
    <literal><![CDATA[
      K(x,T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,4915,a,b,4972,a),flip(a)].">
      <j1 rule="hyper" parents="34 4915 4972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5096">
    <literal><![CDATA[
      K(x,x \ (y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),5095(a,1,2))].">
      <j1 rule="para" parents="22 5095"/>
    </justification>
  </clause>

  <clause id="5097">
    <literal><![CDATA[
      K(x,L(T(y,x),z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),5095(a,1,2))].">
      <j1 rule="para" parents="25 5095"/>
    </justification>
  </clause>

  <clause id="5098">
    <literal><![CDATA[
      K(x,y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),5095(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 5095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5099">
    <literal><![CDATA[
      K(x,(x * y) / x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(254(a,1),5095(a,1,2)),flip(a)].">
      <j1 rule="para" parents="254 5095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5101">
    <literal><![CDATA[
      K(x,L(y / x,z,u)) = K(x,L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(278(a,1),5095(a,1,2)),flip(a)].">
      <j1 rule="para" parents="278 5095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5102">
    <literal><![CDATA[
      K(x,y) \ T(y,x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[para(5095(a,1),4939(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5095 4939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5103">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(y,(x * z) / x)
    ]]></literal>
    <justification jstring="[hyper(131,a,1114,a,b,4976,a(flip))].">
      <j1 rule="hyper" parents="131 1114 4976"/>
    </justification>
  </clause>

  <clause id="5104">
    <literal><![CDATA[
      (x / y) / (y \ x) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(131,a,172,a(flip),b,4976,a(flip))].">
      <j1 rule="hyper" parents="131 172 4976"/>
    </justification>
  </clause>

  <clause id="5105">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * ((y * z) / y)) = L(z,K(y,z),x)
    ]]></literal>
    <justification jstring="[para(4976(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4976 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5106">
    <literal><![CDATA[
      R(K(x,y) / z,z,y) = ((x * y) / x) / (z * y)
    ]]></literal>
    <justification jstring="[para(4976(a,2),108(a,2,1))].">
      <j1 rule="para" parents="4976 108"/>
    </justification>
  </clause>

  <clause id="5107">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * (z * K(y,z))) * y) = a(x,z * K(y,z),y)
    ]]></literal>
    <justification jstring="[para(4989(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4989 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5108">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y * K(x,y)) = x * (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(4989(a,1),4293(a,1,1,2))].">
      <j1 rule="para" parents="4989 4293"/>
    </justification>
  </clause>

  <clause id="5109">
    <literal><![CDATA[
      x * (T(y,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y \ K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5044(a,2),644(a,1,2,1))].">
      <j1 rule="para" parents="5044 644"/>
    </justification>
  </clause>

  <clause id="5110">
    <literal><![CDATA[
      x \ (y * (x / y)) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,94,a,b,5098,a)].">
      <j1 rule="hyper" parents="63 94 5098"/>
    </justification>
  </clause>

  <clause id="5111">
    <literal><![CDATA[
      x * K(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(134,a,5098,a(flip),b,94,a)].">
      <j1 rule="hyper" parents="134 5098 94"/>
    </justification>
  </clause>

  <clause id="5112">
    <literal><![CDATA[
      K(x,R(y / x,z,u)) = K(x,R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(952(a,1),5099(a,1,2))].">
      <j1 rule="para" parents="952 5099"/>
    </justification>
  </clause>

  <clause id="5113">
    <literal><![CDATA[
      T(T(x,y),z) \ T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),4951(a,1,1))].">
      <j1 rule="para" parents="23 4951"/>
    </justification>
  </clause>

  <clause id="5114">
    <literal><![CDATA[
      L(T(x,y),z,u) \ L(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,L(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(25(a,2),4951(a,1,1))].">
      <j1 rule="para" parents="25 4951"/>
    </justification>
  </clause>

  <clause id="5115">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(3403(a,1),4984(a,1,2))].">
      <j1 rule="para" parents="3403 4984"/>
    </justification>
  </clause>

  <clause id="5116">
    <literal><![CDATA[
      (R(T(x,y),z,u) * K(x,w)) * v5 = R(T(x,y),z,u) * (K(x,w) * v5)
    ]]></literal>
    <justification jstring="[para(5001(a,1),469(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5001 469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5117">
    <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),5006(a,1,2))].">
      <j1 rule="para" parents="25 5006"/>
    </justification>
  </clause>

  <clause id="5118">
    <literal><![CDATA[
      x \ L(T(x,y),y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(750(a,2),5006(a,1,2))].">
      <j1 rule="para" parents="750 5006"/>
    </justification>
  </clause>

  <clause id="5119">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(4199(a,2),5006(a,1))].">
      <j1 rule="para" parents="4199 5006"/>
    </justification>
  </clause>

  <clause id="5121">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2651,a,4925,a)].">
      <j1 rule="hyper" parents="2651 4925"/>
    </justification>
  </clause>

  <clause id="5122">
    <literal><![CDATA[
      x * (y * T(y \ (x \ 1),z)) = K((x * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1050,a,4925,a)].">
      <j1 rule="hyper" parents="1050 4925"/>
    </justification>
  </clause>

  <clause id="5124">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K((x / y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1578,a(flip),b,4925,a)].">
      <j1 rule="hyper" parents="63 1578 4925"/>
    </justification>
  </clause>

  <clause id="5125">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1435,a(flip),b,4925,a)].">
      <j1 rule="hyper" parents="63 1435 4925"/>
    </justification>
  </clause>

  <clause id="5126">
    <literal><![CDATA[
      (x / y) * K(y \ 1,z) = x * T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(134,a,4925,a(flip),b,1278,a)].">
      <j1 rule="hyper" parents="134 4925 1278"/>
    </justification>
  </clause>

  <clause id="5127">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K((y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,4925,a(flip),b,1435,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 4925 1435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5128">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(133,a,4925,a(flip),b,1348,a)].">
      <j1 rule="hyper" parents="133 4925 1348"/>
    </justification>
  </clause>

  <clause id="5129">
    <literal><![CDATA[
      K((x / y) \ 1,z) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,4925,a(flip),b,1578,a(flip))].">
      <j1 rule="hyper" parents="133 4925 1578"/>
    </justification>
  </clause>

  <clause id="5130">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(4925(a,1),864(a,2,2))].">
      <j1 rule="para" parents="4925 864"/>
    </justification>
  </clause>

  <clause id="5131">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * K(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(4925(a,1),1061(a,2,2))].">
      <j1 rule="para" parents="4925 1061"/>
    </justification>
  </clause>

  <clause id="5132">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(4925(a,1),1544(a,2,1))].">
      <j1 rule="para" parents="4925 1544"/>
    </justification>
  </clause>

  <clause id="5133">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(4925(a,1),1546(a,2,1))].">
      <j1 rule="para" parents="4925 1546"/>
    </justification>
  </clause>

  <clause id="5134">
    <literal><![CDATA[
      K((x * y) \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = z
    ]]></literal>
    <justification jstring="[para(4925(a,1),1545(a,1))].">
      <j1 rule="para" parents="4925 1545"/>
    </justification>
  </clause>

  <clause id="5135">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(4925(a,1),1681(a,2,2))].">
      <j1 rule="para" parents="4925 1681"/>
    </justification>
  </clause>

  <clause id="5138">
    <literal><![CDATA[
      K(x / y,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,4894,a(flip),b,4928,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 4894 4928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5139">
    <literal><![CDATA[
      (x * (y / x)) \ x = y \ (y / (y / x))
    ]]></literal>
    <justification jstring="[para(4928(a,2),1572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4928 1572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5140">
    <literal><![CDATA[
      K((x * y) / x,x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,770,a(flip),b,5138,a),flip(a)].">
      <j1 rule="hyper" parents="347 770 5138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5141">
    <literal><![CDATA[
      x * K(x / y,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,5138,a,b,92,a)].">
      <j1 rule="hyper" parents="134 5138 92"/>
    </justification>
  </clause>

  <clause id="5143">
    <literal><![CDATA[
      K(x \ (y * x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(11(a,1),5138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 5138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5144">
    <literal><![CDATA[
      K((x \ y) \ y,x \ y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(80(a,1),5138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="80 5138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5146">
    <literal><![CDATA[
      K(T(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(255(a,1),5140(a,1,1)),flip(a)].">
      <j1 rule="para" parents="255 5140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5147">
    <literal><![CDATA[
      (x * y) * K(x,y) = T(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,5146,a(flip),b,261,a)].">
      <j1 rule="hyper" parents="134 5146 261"/>
    </justification>
  </clause>

  <clause id="5148">
    <literal><![CDATA[
      T(x,y) * K(x,y) = T(T(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(134,a,5146,a(flip),b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 5146 4924"/>
    </justification>
  </clause>

  <clause id="5149">
    <literal><![CDATA[
      K(R(x,y,x),y * x) = K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(1041(a,1),5146(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1041 5146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5150">
    <literal><![CDATA[
      K(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5146(a,1),4256(a,1))].">
      <j1 rule="para" parents="5146 4256"/>
    </justification>
  </clause>

  <clause id="5151">
    <literal><![CDATA[
      T(x * y,K(x,y)) = x * y
    ]]></literal>
    <justification jstring="[para(5143(a,1),4904(a,1,2))].">
      <j1 rule="para" parents="5143 4904"/>
    </justification>
  </clause>

  <clause id="5152">
    <literal><![CDATA[
      K(x,L(T(y,x),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(25(a,2),5150(a,1,2))].">
      <j1 rule="para" parents="25 5150"/>
    </justification>
  </clause>

  <clause id="5153">
    <literal><![CDATA[
      K(x,y) \ (x \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(675,a,4943,a),flip(a)].">
      <j1 rule="hyper" parents="675 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5154">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(639,a,4943,a),flip(a)].">
      <j1 rule="hyper" parents="639 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5155">
    <literal><![CDATA[
      T(x,y) * (K(x,y) \ z) = x * z
    ]]></literal>
    <justification jstring="[hyper(357,a,4943,a),flip(a)].">
      <j1 rule="hyper" parents="357 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5156">
    <literal><![CDATA[
      ((x \ y) \ y) * z = x * (K(x,x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,339,a(flip),b,4943,a)].">
      <j1 rule="hyper" parents="347 339 4943"/>
    </justification>
  </clause>

  <clause id="5157">
    <literal><![CDATA[
      x \ (T(x,y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(138,a,4943,a)].">
      <j1 rule="hyper" parents="138 4943"/>
    </justification>
  </clause>

  <clause id="5159">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(128,a,10,a(flip),b,4943,a),flip(a)].">
      <j1 rule="hyper" parents="128 10 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5160">
    <literal><![CDATA[
      K(x,y) * K(y,x) = 1
    ]]></literal>
    <justification jstring="[hyper(127,a,4915,a(flip),b,4943,a),flip(a)].">
      <j1 rule="hyper" parents="127 4915 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5161">
    <literal><![CDATA[
      ((x * y) / x) \ z = K(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(34,a,4389,a,b,4943,a)].">
      <j1 rule="hyper" parents="34 4389 4943"/>
    </justification>
  </clause>

  <clause id="5162">
    <literal><![CDATA[
      K(x,y) * (z * x) = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,1224,a,b,4943,a),flip(a)].">
      <j1 rule="hyper" parents="34 1224 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5163">
    <literal><![CDATA[
      K(x,y) * T(y,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,4441,a(flip),b,4943,a),flip(a)].">
      <j1 rule="hyper" parents="34 4441 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5164">
    <literal><![CDATA[
      K(x * y,x) * T(x,y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,4386,a(flip),b,4943,a),flip(a)].">
      <j1 rule="hyper" parents="34 4386 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5165">
    <literal><![CDATA[
      (x \ y) * (K(y,z) * K(y,z)) = x \ (T(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,4943,a(flip),b,124,a),flip(a)].">
      <j1 rule="hyper" parents="128 4943 124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5166">
    <literal><![CDATA[
      (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(4943(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4943 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5168">
    <literal><![CDATA[
      T(x,y) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4943(a,1),43(a,1))].">
      <j1 rule="para" parents="4943 43"/>
    </justification>
  </clause>

  <clause id="5169">
    <literal><![CDATA[
      x \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4943(a,1),356(a,1,2))].">
      <j1 rule="para" parents="4943 356"/>
    </justification>
  </clause>

  <clause id="5170">
    <literal><![CDATA[
      (x * y) \ (x * (T(y,z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(y,z) * u,y,x) = w
    ]]></literal>
    <justification jstring="[para(4943(a,1),545(a,1,2,2))].">
      <j1 rule="para" parents="4943 545"/>
    </justification>
  </clause>

  <clause id="5171">
    <literal><![CDATA[
      T(x,y) * (K(x,y) * z) = T(T(x,y),y) * z
    ]]></literal>
    <justification jstring="[para(5146(a,1),4943(a,1,2,1))].">
      <j1 rule="para" parents="5146 4943"/>
    </justification>
  </clause>

  <clause id="5172">
    <literal><![CDATA[
      1 / K(x,y) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,5160,a)].">
      <j1 rule="hyper" parents="145 5160"/>
    </justification>
  </clause>

  <clause id="5173">
    <literal><![CDATA[
      K(x,y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(138,a,5160,a)].">
      <j1 rule="hyper" parents="138 5160"/>
    </justification>
  </clause>

  <clause id="5175">
    <literal><![CDATA[
      K(x,y) * z != 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5160(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="5160 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5177">
    <literal><![CDATA[
      K(x,y) != z \ 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5160(a,1),153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5160 153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5178">
    <literal><![CDATA[
      1 / K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5160(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5160 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5179">
    <literal><![CDATA[
      K(x,y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5160(a,1),356(a,1,2))].">
      <j1 rule="para" parents="5160 356"/>
    </justification>
  </clause>

  <clause id="5181">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(5172(a,1),3189(a,1,2))].">
      <j1 rule="para" parents="5172 3189"/>
    </justification>
  </clause>

  <clause id="5182">
    <literal><![CDATA[
      L(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(5172(a,1),3520(a,1,2))].">
      <j1 rule="para" parents="5172 3520"/>
    </justification>
  </clause>

  <clause id="5184">
    <literal><![CDATA[
      a(x,x,x) \ 1 = K(x,x * x)
    ]]></literal>
    <justification jstring="[para(95(a,1),5173(a,1,1))].">
      <j1 rule="para" parents="95 5173"/>
    </justification>
  </clause>

  <clause id="5185">
    <literal><![CDATA[
      T(K(x,y),z) * R(T(K(x,y),z) \ 1,u,w) = T(K(x,y) * R(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(5173(a,1),2148(a,2,1,2,1))].">
      <j1 rule="para" parents="5173 2148"/>
    </justification>
  </clause>

  <clause id="5187">
    <literal><![CDATA[
      K(x,y) \ (y * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(4777,a,4944,a)].">
      <j1 rule="hyper" parents="4777 4944"/>
    </justification>
  </clause>

  <clause id="5188">
    <literal><![CDATA[
      ((x \ y) \ y) * (x \ z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(804,a,4944,a)].">
      <j1 rule="hyper" parents="804 4944"/>
    </justification>
  </clause>

  <clause id="5189">
    <literal><![CDATA[
      T(x,y) \ (K(x,y) * z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(138,a,4944,a)].">
      <j1 rule="hyper" parents="138 4944"/>
    </justification>
  </clause>

  <clause id="5191">
    <literal><![CDATA[
      x * (K(x,y) * (x \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,4943,a,b,4944,a)].">
      <j1 rule="hyper" parents="63 4943 4944"/>
    </justification>
  </clause>

  <clause id="5192">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,4422,a,b,4944,a)].">
      <j1 rule="hyper" parents="63 4422 4944"/>
    </justification>
  </clause>

  <clause id="5193">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,486,a,b,4944,a)].">
      <j1 rule="hyper" parents="63 486 4944"/>
    </justification>
  </clause>

  <clause id="5194">
    <literal><![CDATA[
      ((x \ y) \ y) \ (K(x,x \ y) * z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(34,a,396,a,b,4944,a)].">
      <j1 rule="hyper" parents="34 396 4944"/>
    </justification>
  </clause>

  <clause id="5195">
    <literal><![CDATA[
      ((x * y) / x) * (K(y,x) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(134,a,4944,a(flip),b,4422,a)].">
      <j1 rule="hyper" parents="134 4944 4422"/>
    </justification>
  </clause>

  <clause id="5196">
    <literal><![CDATA[
      (x * y) / (T(x,z) * y) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,4765,a(flip),b,4944,a(flip))].">
      <j1 rule="hyper" parents="131 4765 4944"/>
    </justification>
  </clause>

  <clause id="5197">
    <literal><![CDATA[
      (x * (y / x)) / y = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(131,a,4158,a(flip),b,4944,a(flip))].">
      <j1 rule="hyper" parents="131 4158 4944"/>
    </justification>
  </clause>

  <clause id="5198">
    <literal><![CDATA[
      x \ (K(y,x) * z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(128,a,4944,a(flip),b,4769,a(flip))].">
      <j1 rule="hyper" parents="128 4944 4769"/>
    </justification>
  </clause>

  <clause id="5199">
    <literal><![CDATA[
      L(T(x,y),z,u) * (L(x,z,u) \ w) = K(L(x,z,u),y) * w
    ]]></literal>
    <justification jstring="[para(25(a,2),4944(a,1,1))].">
      <j1 rule="para" parents="25 4944"/>
    </justification>
  </clause>

  <clause id="5200">
    <literal><![CDATA[
      K(x,y) * (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4944(a,1),620(a,1))].">
      <j1 rule="para" parents="4944 620"/>
    </justification>
  </clause>

  <clause id="5201">
    <literal><![CDATA[
      K(x,y) * (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) / (x * x) = z
    ]]></literal>
    <justification jstring="[para(4944(a,1),913(a,1))].">
      <j1 rule="para" parents="4944 913"/>
    </justification>
  </clause>

  <clause id="5202">
    <literal><![CDATA[
      T(x,y) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4944(a,2),3035(a,1))].">
      <j1 rule="para" parents="4944 3035"/>
    </justification>
  </clause>

  <clause id="5203">
    <literal><![CDATA[
      K(x,y) * T(x,z) = T(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4924(a,2),4944(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4924 4944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5206">
    <literal><![CDATA[
      K(x,y) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(4946(a,1),356(a,1,2))].">
      <j1 rule="para" parents="4946 356"/>
    </justification>
  </clause>

  <clause id="5207">
    <literal><![CDATA[
      L(L(x,y,T(z,u)),T(z,u) * y,K(u,z)) = (z * y) \ (K(u,z) * (T(z,u) * (y * x)))
    ]]></literal>
    <justification jstring="[para(4946(a,1),542(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4946 542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5208">
    <literal><![CDATA[
      K(x,y) * T(T(y,x),z) = y * K(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4929(a,2),4946(a,1,2))].">
      <j1 rule="para" parents="4929 4946"/>
    </justification>
  </clause>

  <clause id="5209">
    <literal><![CDATA[
      K(x,y) * (y \ z) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(1244,a,4947,a),flip(a)].">
      <j1 rule="hyper" parents="1244 4947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5210">
    <literal><![CDATA[
      T(x,y) \ (x * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,1229,a,b,4947,a)].">
      <j1 rule="hyper" parents="63 1229 4947"/>
    </justification>
  </clause>

  <clause id="5211">
    <literal><![CDATA[
      K(x,y) * (1 / y) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4187,a(flip),b,4947,a),flip(a)].">
      <j1 rule="hyper" parents="63 4187 4947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5212">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(220,a,4947,a(flip),b,1229,a)].">
      <j1 rule="hyper" parents="220 4947 1229"/>
    </justification>
  </clause>

  <clause id="5213">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(134,a,4947,a(flip),b,1229,a)].">
      <j1 rule="hyper" parents="134 4947 1229"/>
    </justification>
  </clause>

  <clause id="5214">
    <literal><![CDATA[
      K((x / y) / (y \ 1),z) = (T(x,z) / y) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(131,a,4810,a(flip),b,4947,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="131 4810 4947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5215">
    <literal><![CDATA[
      K(x,y) * (T(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(4947(a,1),620(a,1))].">
      <j1 rule="para" parents="4947 620"/>
    </justification>
  </clause>

  <clause id="5216">
    <literal><![CDATA[
      x \ (y * (K(z,y \ x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(y \ x,z) \ u,y \ x,y) = w
    ]]></literal>
    <justification jstring="[para(4947(a,1),875(a,1,2,2))].">
      <j1 rule="para" parents="4947 875"/>
    </justification>
  </clause>

  <clause id="5217">
    <literal><![CDATA[
      K(x,y) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(4947(a,1),1244(a,1))].">
      <j1 rule="para" parents="4947 1244"/>
    </justification>
  </clause>

  <clause id="5218">
    <literal><![CDATA[
      K(x,y) * L(T(y,x),z,u) = y * T(y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(3530(a,1),4947(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3530 4947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5219">
    <literal><![CDATA[
      (x / T(y,x)) * ((y \ T(x,y)) \ z) = K(y,x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(4278(a,1),4947(a,1,2,1))].">
      <j1 rule="para" parents="4278 4947"/>
    </justification>
  </clause>

  <clause id="5220">
    <literal><![CDATA[
      K(x,y) * (K(z,T(y,x)) * u) = y * (T(T(y,x),z) \ u)
    ]]></literal>
    <justification jstring="[para(4947(a,1),4946(a,1,2))].">
      <j1 rule="para" parents="4947 4946"/>
    </justification>
  </clause>

  <clause id="5221">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) * K(1 / x,x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4948(a,1),2412(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4948 2412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5222">
    <literal><![CDATA[
      ((x * y) * (z * K(y,z))) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(220,a,4953,a(flip),b,209,a)].">
      <j1 rule="hyper" parents="220 4953 209"/>
    </justification>
  </clause>

  <clause id="5224">
    <literal><![CDATA[
      K(x,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(4958(a,1),5006(a,1))].">
      <j1 rule="para" parents="4958 5006"/>
    </justification>
  </clause>

  <clause id="5225">
    <literal><![CDATA[
      (T(R(x,y,z),u) * (y * z)) / ((x * y) * z) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(107(a,1),4963(a,1,2))].">
      <j1 rule="para" parents="107 4963"/>
    </justification>
  </clause>

  <clause id="5226">
    <literal><![CDATA[
      (x * T(x \ y,y)) * (y \ 1) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[para(1519(a,1),4966(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1519 4966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5228">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K(1 / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1578,a(flip),b,4971,a)].">
      <j1 rule="hyper" parents="63 1578 4971"/>
    </justification>
  </clause>

  <clause id="5229">
    <literal><![CDATA[
      K(1 / x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(4971(a,1),493(a,1,1))].">
      <j1 rule="para" parents="4971 493"/>
    </justification>
  </clause>

  <clause id="5231">
    <literal><![CDATA[
      K(x,y) * (x * (T(y,x) * z)) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,4768,a(flip),b,4974,a),flip(a)].">
      <j1 rule="hyper" parents="347 4768 4974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5233">
    <literal><![CDATA[
      K(x,y) \ x = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,4915,a(flip),b,4974,a)].">
      <j1 rule="hyper" parents="128 4915 4974"/>
    </justification>
  </clause>

  <clause id="5234">
    <literal><![CDATA[
      (T(x,y) * z) * L(u,x * z,K(x,y)) = K(x,y) * ((x * z) * u)
    ]]></literal>
    <justification jstring="[hyper(133,a,4974,a(flip),b,212,a)].">
      <j1 rule="hyper" parents="133 4974 212"/>
    </justification>
  </clause>

  <clause id="5235">
    <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),4974(a,2,1))].">
      <j1 rule="para" parents="25 4974"/>
    </justification>
  </clause>

  <clause id="5236">
    <literal><![CDATA[
      K(R(x,y,z),u) * (R(x,y,z) * w) = R(T(x,u),y,z) * w
    ]]></literal>
    <justification jstring="[para(27(a,2),4974(a,2,1))].">
      <j1 rule="para" parents="27 4974"/>
    </justification>
  </clause>

  <clause id="5237">
    <literal><![CDATA[
      K(x / y,y) * ((x / y) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[para(113(a,1),4974(a,2,1))].">
      <j1 rule="para" parents="113 4974"/>
    </justification>
  </clause>

  <clause id="5238">
    <literal><![CDATA[
      T(x,y) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4974(a,1),357(a,1))].">
      <j1 rule="para" parents="4974 357"/>
    </justification>
  </clause>

  <clause id="5239">
    <literal><![CDATA[
      K(x,y) * (R(z,u,w) * x) = T(x,y) * R(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(268(a,1),4974(a,1,2))].">
      <j1 rule="para" parents="268 4974"/>
    </justification>
  </clause>

  <clause id="5240">
    <literal><![CDATA[
      T(x,y) * T(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (z * x) = u
    ]]></literal>
    <justification jstring="[para(4974(a,1),639(a,1))].">
      <j1 rule="para" parents="4974 639"/>
    </justification>
  </clause>

  <clause id="5241">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),x * z,u) = w
    ]]></literal>
    <justification jstring="[para(4974(a,1),595(a,1,1,1))].">
      <j1 rule="para" parents="4974 595"/>
    </justification>
  </clause>

  <clause id="5242">
    <literal><![CDATA[
      L(T(x,K(x,y) \ z),K(x,y) \ z,K(x,y)) = z \ (T(x,y) * (K(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(4974(a,1),840(a,2,2))].">
      <j1 rule="para" parents="4974 840"/>
    </justification>
  </clause>

  <clause id="5243">
    <literal><![CDATA[
      (T(x,y) * z) \ (K(x,y) * (x * (z * u))) = L(L(u,z,x),x * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(4974(a,1),542(a,1,1))].">
      <j1 rule="para" parents="4974 542"/>
    </justification>
  </clause>

  <clause id="5244">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) = T(x,y) * (T(x,z) \ u)
    ]]></literal>
    <justification jstring="[para(4947(a,1),4974(a,1,2))].">
      <j1 rule="para" parents="4947 4974"/>
    </justification>
  </clause>

  <clause id="5245">
    <literal><![CDATA[
      K(x,y) = x / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(220,a,4942,a,b,5233,a),flip(a)].">
      <j1 rule="hyper" parents="220 4942 5233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5249">
    <literal><![CDATA[
      K(x,y) / x = 1 / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(131,a,5245,a,b,1606,a)].">
      <j1 rule="hyper" parents="131 5245 1606"/>
    </justification>
  </clause>

  <clause id="5250">
    <literal><![CDATA[
      (x \ y) / (y / x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),5245(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 5245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5251">
    <literal><![CDATA[
      (x / y) \ K(y,y \ x) = (y \ x) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),4980(a,1,1,1))].">
      <j1 rule="para" parents="10 4980"/>
    </justification>
  </clause>

  <clause id="5252">
    <literal><![CDATA[
      K(x \ y,x) * (y / x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(134,a,4990,a(flip),b,5233,a)].">
      <j1 rule="hyper" parents="134 4990 5233"/>
    </justification>
  </clause>

  <clause id="5254">
    <literal><![CDATA[
      T(x \ y,R(y / x,z,u)) = x \ y
    ]]></literal>
    <justification jstring="[para(4990(a,1),4523(a,1,2,1))].">
      <j1 rule="para" parents="4990 4523"/>
    </justification>
  </clause>

  <clause id="5255">
    <literal><![CDATA[
      K(x,y / z) \ y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4771,a,b,4996,a),flip(a)].">
      <j1 rule="hyper" parents="63 4771 4996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5256">
    <literal><![CDATA[
      K(x,y) \ z = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,4947,a(flip),b,4996,a),flip(a)].">
      <j1 rule="hyper" parents="63 4947 4996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5257">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(462,a,4996,a(flip),b,4947,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="462 4996 4947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5258">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) = K(z,x / y)
    ]]></literal>
    <justification jstring="[hyper(220,a,4771,a,b,4996,a(flip))].">
      <j1 rule="hyper" parents="220 4771 4996"/>
    </justification>
  </clause>

  <clause id="5259">
    <literal><![CDATA[
      x / (K(y,z) * x) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(220,a,4947,a(flip),b,4996,a(flip))].">
      <j1 rule="hyper" parents="220 4947 4996"/>
    </justification>
  </clause>

  <clause id="5260">
    <literal><![CDATA[
      K(x,y / (z \ 1)) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(134,a,4792,a,b,4996,a(flip))].">
      <j1 rule="hyper" parents="134 4792 4996"/>
    </justification>
  </clause>

  <clause id="5261">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) = z
    ]]></literal>
    <justification jstring="[hyper(134,a,4947,a(flip),b,4996,a(flip))].">
      <j1 rule="hyper" parents="134 4947 4996"/>
    </justification>
  </clause>

  <clause id="5262">
    <literal><![CDATA[
      (K(x,y) \ z) / z = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,4996,a(flip),b,4947,a(flip))].">
      <j1 rule="hyper" parents="131 4996 4947"/>
    </justification>
  </clause>

  <clause id="5263">
    <literal><![CDATA[
      K(x,y) \ (K(y,x) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(128,a,4996,a(flip),b,4947,a(flip))].">
      <j1 rule="hyper" parents="128 4996 4947"/>
    </justification>
  </clause>

  <clause id="5264">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(z,T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(4996(a,1),707(a,1))].">
      <j1 rule="para" parents="4996 707"/>
    </justification>
  </clause>

  <clause id="5265">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(635,a,5256,a)].">
      <j1 rule="hyper" parents="635 5256"/>
    </justification>
  </clause>

  <clause id="5266">
    <literal><![CDATA[
      K(x,y) \ T(T(x,z),u) = T(T(x,z),u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3040,a,b,5256,a),flip(a)].">
      <j1 rule="hyper" parents="347 3040 5256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5267">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(220,a,4521,a(flip),b,5256,a)].">
      <j1 rule="hyper" parents="220 4521 5256"/>
    </justification>
  </clause>

  <clause id="5268">
    <literal><![CDATA[
      K(x,y) * (y \ K(y,x)) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(134,a,4521,a(flip),b,5256,a)].">
      <j1 rule="hyper" parents="134 4521 5256"/>
    </justification>
  </clause>

  <clause id="5269">
    <literal><![CDATA[
      K(x,y) * (K(z,y) * K(y,x)) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,2556,a(flip),b,5256,a)].">
      <j1 rule="hyper" parents="134 2556 5256"/>
    </justification>
  </clause>

  <clause id="5270">
    <literal><![CDATA[
      (K(x,y) \ z) * L(u,z,K(y,x)) = K(y,x) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(133,a,5256,a,b,212,a)].">
      <j1 rule="hyper" parents="133 5256 212"/>
    </justification>
  </clause>

  <clause id="5271">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z \ 1,z) = a(K(y,x),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3466,a(flip),b,5256,a),flip(a)].">
      <j1 rule="hyper" parents="63 3466 5256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5272">
    <literal><![CDATA[
      x * (K(y,z) * (K(z,y) * (x \ u))) = u
    ]]></literal>
    <justification jstring="[hyper(134,a,5256,a(flip),b,9,a(flip))].">
      <j1 rule="hyper" parents="134 5256 9"/>
    </justification>
  </clause>

  <clause id="5273">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * u = z
    ]]></literal>
    <justification jstring="[para(5256(a,1),150(a,1))].">
      <j1 rule="para" parents="5256 150"/>
    </justification>
  </clause>

  <clause id="5274">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(5256(a,1),286(a,1,2))].">
      <j1 rule="para" parents="5256 286"/>
    </justification>
  </clause>

  <clause id="5275">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(5256(a,1),287(a,1,2))].">
      <j1 rule="para" parents="5256 287"/>
    </justification>
  </clause>

  <clause id="5276">
    <literal><![CDATA[
      x / (K(y,z) * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(5256(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5256 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5277">
    <literal><![CDATA[
      L(x \ (K(y,z) * u),x,K(z,y)) = (K(z,y) * x) \ u
    ]]></literal>
    <justification jstring="[para(5256(a,1),329(a,1,1,2))].">
      <j1 rule="para" parents="5256 329"/>
    </justification>
  </clause>

  <clause id="5278">
    <literal><![CDATA[
      L(K(x,y) * (z \ u),K(y,x),z) = (z * K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(5256(a,1),329(a,1,1))].">
      <j1 rule="para" parents="5256 329"/>
    </justification>
  </clause>

  <clause id="5279">
    <literal><![CDATA[
      x \ y != K(z,u) * (K(u,z) * w)
    ]]></literal>
    <literal><![CDATA[
      x * w = y
    ]]></literal>
    <justification jstring="[para(5256(a,1),355(a,2,2))].">
      <j1 rule="para" parents="5256 355"/>
    </justification>
  </clause>

  <clause id="5280">
    <literal><![CDATA[
      T((x \ K(y,z)) \ 1,K(z,y) * x) = (x \ K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(5256(a,1),664(a,1,2))].">
      <j1 rule="para" parents="5256 664"/>
    </justification>
  </clause>

  <clause id="5281">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5256(a,1),392(a,1,1,3))].">
      <j1 rule="para" parents="5256 392"/>
    </justification>
  </clause>

  <clause id="5282">
    <literal><![CDATA[
      x * (K(y,z) * (K(z,y) * (x \ u))) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ u = v5
    ]]></literal>
    <justification jstring="[para(5256(a,1),675(a,1,2,2))].">
      <j1 rule="para" parents="5256 675"/>
    </justification>
  </clause>

  <clause id="5283">
    <literal><![CDATA[
      R(K(x,y) * R(K(y,x),z,u),K(y,x),z * u) = ((K(y,x) * z) * u) / (K(y,x) * (z * u))
    ]]></literal>
    <justification jstring="[para(5256(a,1),3688(a,1,1))].">
      <j1 rule="para" parents="5256 3688"/>
    </justification>
  </clause>

  <clause id="5285">
    <literal><![CDATA[
      K(x,y) != z / u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5259(a,1),45(a,1))].">
      <j1 rule="para" parents="5259 45"/>
    </justification>
  </clause>

  <clause id="5286">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5259(a,1),359(a,1,1))].">
      <j1 rule="para" parents="5259 359"/>
    </justification>
  </clause>

  <clause id="5287">
    <literal><![CDATA[
      a(x,y * K(z \ 1,z),u) = K(w,v5) * (K(v5,w) * a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,4045,a,b,5261,a)].">
      <j1 rule="hyper" parents="347 4045 5261"/>
    </justification>
  </clause>

  <clause id="5288">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(134,a,5261,a(flip),b,209,a)].">
      <j1 rule="hyper" parents="134 5261 209"/>
    </justification>
  </clause>

  <clause id="5289">
    <literal><![CDATA[
      L((K(x,y) * z) \ u,K(x,y) * z,K(y,x)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(5261(a,1),99(a,2,1))].">
      <j1 rule="para" parents="5261 99"/>
    </justification>
  </clause>

  <clause id="5290">
    <literal><![CDATA[
      L(x,y,K(z,u)) != (K(z,u) * y) \ w
    ]]></literal>
    <literal><![CDATA[
      y \ (K(u,z) * w) = x
    ]]></literal>
    <justification jstring="[para(5261(a,1),569(a,2,2))].">
      <j1 rule="para" parents="5261 569"/>
    </justification>
  </clause>

  <clause id="5291">
    <literal><![CDATA[
      (x * y) \ ((x * K(z,u)) * (K(u,z) * y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,K(z,u),K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(5261(a,1),836(a,1,1,2))].">
      <j1 rule="para" parents="5261 836"/>
    </justification>
  </clause>

  <clause id="5292">
    <literal><![CDATA[
      L(T(x,x \ (K(y,z) * u)),x \ (K(y,z) * u),K(z,y)) = (K(z,y) * (x \ (K(y,z) * u))) \ u
    ]]></literal>
    <justification jstring="[para(5261(a,1),382(a,2,2))].">
      <j1 rule="para" parents="5261 382"/>
    </justification>
  </clause>

  <clause id="5293">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(5262(a,1),280(a,1,1))].">
      <j1 rule="para" parents="5262 280"/>
    </justification>
  </clause>

  <clause id="5295">
    <literal><![CDATA[
      T(x * (y / x),z) / T(y,z) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,4812,a,b,4997,a)].">
      <j1 rule="hyper" parents="131 4812 4997"/>
    </justification>
  </clause>

  <clause id="5296">
    <literal><![CDATA[
      (x * (y / x)) \ (K(x,x \ y) * (y * z)) = L(z,y,K(x,x \ y))
    ]]></literal>
    <justification jstring="[para(4997(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4997 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5297">
    <literal><![CDATA[
      K(x,y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5006,a,4998,a),flip(a)].">
      <j1 rule="hyper" parents="5006 4998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5298">
    <literal><![CDATA[
      K(x,x * (y / x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),5297(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 5297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5299">
    <literal><![CDATA[
      K(x * (y * z),a(x,y,z) * (x * (y * z))) = K(x * (y * z),(x * y) * z)
    ]]></literal>
    <justification jstring="[para(86(a,1),5297(a,2,2))].">
      <j1 rule="para" parents="86 5297"/>
    </justification>
  </clause>

  <clause id="5302">
    <literal><![CDATA[
      (x \ y) \ K(x \ y,x) = (y / x) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),5037(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5303">
    <literal><![CDATA[
      L(x \ y,z,u) \ K(L(x \ y,z,u),x) = L(y / x,z,u) \ 1
    ]]></literal>
    <justification jstring="[para(759(a,1),5037(a,1,1)),flip(a)].">
      <j1 rule="para" parents="759 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5304">
    <literal><![CDATA[
      (x * y) \ K(x * y,y) = (L(y,x,y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(4358(a,1),5037(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4358 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5305">
    <literal><![CDATA[
      (x * K(y,x)) \ 1 = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(4942(a,1),5037(a,1,1))].">
      <j1 rule="para" parents="4942 5037"/>
    </justification>
  </clause>

  <clause id="5306">
    <literal><![CDATA[
      ((x * (y / x)) / x) \ 1 = (y / x) \ K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(5138(a,1),5037(a,2,2))].">
      <j1 rule="para" parents="5138 5037"/>
    </justification>
  </clause>

  <clause id="5307">
    <literal><![CDATA[
      T(1 / x,(y * x) / y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(269,a,5052,a(flip),b,4966,a(flip))].">
      <j1 rule="hyper" parents="269 5052 4966"/>
    </justification>
  </clause>

  <clause id="5308">
    <literal><![CDATA[
      T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(5079,a,5059,a)].">
      <j1 rule="hyper" parents="5079 5059"/>
    </justification>
  </clause>

  <clause id="5309">
    <literal><![CDATA[
      T(x * K(y * R(x,z,u),x),y) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(40,a,1715,a,b,5059,a),flip(a)].">
      <j1 rule="hyper" parents="40 1715 5059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5311">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T(z * K(y,z),u) = x
    ]]></literal>
    <justification jstring="[para(5059(a,1),49(a,2)),flip(b)].">
      <j1 rule="para" parents="5059 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5313">
    <literal><![CDATA[
      K(((x / y) \ 1) \ y,(x / y) \ 1) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(3849,a,5110,a)].">
      <j1 rule="hyper" parents="3849 5110"/>
    </justification>
  </clause>

  <clause id="5314">
    <literal><![CDATA[
      x * K(y,y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      y * (x / y) = z
    ]]></literal>
    <justification jstring="[para(5110(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5110 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5315">
    <literal><![CDATA[
      T(x,K(y,y \ x)) = x
    ]]></literal>
    <justification jstring="[hyper(269,a,5111,a,b,4997,a)].">
      <j1 rule="hyper" parents="269 5111 4997"/>
    </justification>
  </clause>

  <clause id="5316">
    <literal><![CDATA[
      (x * (y / x)) \ (y * (K(x,x \ y) * z)) = L(z,K(x,x \ y),y)
    ]]></literal>
    <justification jstring="[para(5111(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5111 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5317">
    <literal><![CDATA[
      x * (y / x) != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(5111(a,1),43(a,1))].">
      <j1 rule="para" parents="5111 43"/>
    </justification>
  </clause>

  <clause id="5318">
    <literal><![CDATA[
      R(x,x \ y,K(z,z \ y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(5111(a,1),578(a,1,2))].">
      <j1 rule="para" parents="5111 578"/>
    </justification>
  </clause>

  <clause id="5319">
    <literal><![CDATA[
      (x * ((y \ x) \ z)) * K(z,z \ (x * ((y \ x) \ z))) = z * R(y,y \ x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[para(843(a,2),5111(a,2,2))].">
      <j1 rule="para" parents="843 5111"/>
    </justification>
  </clause>

  <clause id="5320">
    <literal><![CDATA[
      T(x,y) * K(x * y,(x * y) \ T(x,y)) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(4349(a,1),5111(a,2,2))].">
      <j1 rule="para" parents="4349 5111"/>
    </justification>
  </clause>

  <clause id="5321">
    <literal><![CDATA[
      K(x,y) * (x \ (y \ z)) = x \ (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(134,a,4784,a(flip),b,5153,a)].">
      <j1 rule="hyper" parents="134 4784 5153"/>
    </justification>
  </clause>

  <clause id="5322">
    <literal><![CDATA[
      K(x,y) \ (T(y,x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(38,a,5263,a,b,5153,a)].">
      <j1 rule="hyper" parents="38 5263 5153"/>
    </justification>
  </clause>

  <clause id="5323">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ z = u
    ]]></literal>
    <justification jstring="[para(5153(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5153 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5324">
    <literal><![CDATA[
      x * (K(y,z) * (T(y,z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y \ u) = w
    ]]></literal>
    <justification jstring="[para(5153(a,1),357(a,1,2,2))].">
      <j1 rule="para" parents="5153 357"/>
    </justification>
  </clause>

  <clause id="5326">
    <literal><![CDATA[
      x * (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(5155(a,1),620(a,1))].">
      <j1 rule="para" parents="5155 620"/>
    </justification>
  </clause>

  <clause id="5327">
    <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),5159(a,1,2,1))].">
      <j1 rule="para" parents="27 5159"/>
    </justification>
  </clause>

  <clause id="5328">
    <literal><![CDATA[
      L((T(x,y) \ z) \ u,T(x,y) \ z,K(x,y)) = (x \ z) \ (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(5159(a,1),99(a,2,1))].">
      <j1 rule="para" parents="5159 99"/>
    </justification>
  </clause>

  <clause id="5329">
    <literal><![CDATA[
      L(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(4994,a,5181,a),flip(a)].">
      <j1 rule="hyper" parents="4994 5181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5330">
    <literal><![CDATA[
      L(x,K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5181(a,1),4994(a,1))].">
      <j1 rule="para" parents="5181 4994"/>
    </justification>
  </clause>

  <clause id="5331">
    <literal><![CDATA[
      (x * K(y,x)) * z = x * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(1362,a,5329,a),flip(a)].">
      <j1 rule="hyper" parents="1362 5329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5332">
    <literal><![CDATA[
      (x * K(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,x) * z) = u
    ]]></literal>
    <justification jstring="[para(5329(a,1),322(a,1,2))].">
      <j1 rule="para" parents="5329 322"/>
    </justification>
  </clause>

  <clause id="5337">
    <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),5196(a,1,2,1))].">
      <j1 rule="para" parents="27 5196"/>
    </justification>
  </clause>

  <clause id="5339">
    <literal><![CDATA[
      T(x / y,z) \ x = K(z,x / y) * y
    ]]></literal>
    <justification jstring="[hyper(644,a,5209,a),flip(a)].">
      <j1 rule="hyper" parents="644 5209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5340">
    <literal><![CDATA[
      ((x \ y) \ y) \ z = K(x \ y,x) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,336,a(flip),b,5209,a)].">
      <j1 rule="hyper" parents="347 336 5209"/>
    </justification>
  </clause>

  <clause id="5341">
    <literal><![CDATA[
      x * (K(y,x) * (x \ z)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(134,a,5209,a,b,5198,a)].">
      <j1 rule="hyper" parents="134 5209 5198"/>
    </justification>
  </clause>

  <clause id="5342">
    <literal><![CDATA[
      T(x,y) * (y \ z) = x * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(134,a,5209,a(flip),b,5157,a),flip(a)].">
      <j1 rule="hyper" parents="134 5209 5157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5343">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (L(y,z,u) \ w) = L(T(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(25(a,2),5209(a,2,1))].">
      <j1 rule="para" parents="25 5209"/>
    </justification>
  </clause>

  <clause id="5344">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (R(y,z,u) \ w) = R(T(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(27(a,2),5209(a,2,1))].">
      <j1 rule="para" parents="27 5209"/>
    </justification>
  </clause>

  <clause id="5345">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) \ y) = ((x * x) \ x) \ y
    ]]></literal>
    <justification jstring="[para(518(a,1),5209(a,2,1))].">
      <j1 rule="para" parents="518 5209"/>
    </justification>
  </clause>

  <clause id="5347">
    <literal><![CDATA[
      K(x,T(y,z)) * K(z,y) = T(T(y,z),x) \ y
    ]]></literal>
    <justification jstring="[para(4913(a,2),5209(a,1,2))].">
      <j1 rule="para" parents="4913 5209"/>
    </justification>
  </clause>

  <clause id="5348">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4924(a,2),5209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4924 5209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5349">
    <literal><![CDATA[
      K(x,y) * (T(y,x) \ z) = T(T(y,x),x) \ z
    ]]></literal>
    <justification jstring="[para(5095(a,1),5209(a,1,1))].">
      <j1 rule="para" parents="5095 5209"/>
    </justification>
  </clause>

  <clause id="5350">
    <literal><![CDATA[
      T(x,y) \ (T(x,z) * u) = K(y,x) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[para(5157(a,1),5209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5157 5209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5352">
    <literal><![CDATA[
      T(x,y) \ (x * L(K(y,x) \ 1,z,u)) = K(y,x) \ L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,3343,a(flip),b,5210,a),flip(a)].">
      <j1 rule="hyper" parents="347 3343 5210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5353">
    <literal><![CDATA[
      K(x,y) * (y * z) = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(134,a,5210,a(flip),b,5198,a),flip(a)].">
      <j1 rule="hyper" parents="134 5210 5198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5354">
    <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),5210(a,1,1))].">
      <j1 rule="para" parents="25 5210"/>
    </justification>
  </clause>

  <clause id="5355">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(5210(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5210 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5356">
    <literal><![CDATA[
      T(x,y) * (1 / y) = x * (1 / T(y,x))
    ]]></literal>
    <justification jstring="[hyper(134,a,5211,a(flip),b,5157,a),flip(a)].">
      <j1 rule="hyper" parents="134 5211 5157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5357">
    <literal><![CDATA[
      ((x * y) * z) / (K(u,R(x,y,z)) * (y * z)) = T(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(107(a,1),5212(a,1,1))].">
      <j1 rule="para" parents="107 5212"/>
    </justification>
  </clause>

  <clause id="5358">
    <literal><![CDATA[
      R(x,y,z * K(u,z)) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(5212(a,1),2188(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5212 2188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5359">
    <literal><![CDATA[
      L(x,y * K(z,y),u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(5212(a,1),3186(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5212 3186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5360">
    <literal><![CDATA[
      T(x,y) / (K(z,x) * K(x,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4929(a,2),5212(a,1,1))].">
      <j1 rule="para" parents="4929 5212"/>
    </justification>
  </clause>

  <clause id="5361">
    <literal><![CDATA[
      K(x,y) * (x / y) = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(4448,a,5213,a),flip(a)].">
      <j1 rule="hyper" parents="4448 5213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5362">
    <literal><![CDATA[
      K(x,y) * (x / y) = T(x,y) / y
    ]]></literal>
    <justification jstring="[hyper(4445,a,5213,a),flip(a)].">
      <j1 rule="hyper" parents="4445 5213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5363">
    <literal><![CDATA[
      (K(x,y) * z) * K(T(y,x),K(x,y) * z) = (y * z) / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,5213,a(flip),b,4989,a),flip(a)].">
      <j1 rule="hyper" parents="131 5213 4989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5364">
    <literal><![CDATA[
      R(x,y,z * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(5213(a,1),2186(a,1,3))].">
      <j1 rule="para" parents="5213 2186"/>
    </justification>
  </clause>

  <clause id="5365">
    <literal><![CDATA[
      x * (y * (K(x,y) * z)) = T(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(5213(a,1),4768(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5213 4768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5366">
    <literal><![CDATA[
      T(x,y) * (K(y,T(x,y)) * z) = x * z
    ]]></literal>
    <justification jstring="[para(5095(a,2),5213(a,1,2,1))].">
      <j1 rule="para" parents="5095 5213"/>
    </justification>
  </clause>

  <clause id="5367">
    <literal><![CDATA[
      K(R(x,y,y \ 1),y) / R(x,y,y \ 1) = 1 / ((y * x) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(1000(a,1),5249(a,2,2))].">
      <j1 rule="para" parents="1000 5249"/>
    </justification>
  </clause>

  <clause id="5368">
    <literal><![CDATA[
      1 / (x * K(y,x)) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(4942(a,1),5249(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4942 5249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5370">
    <literal><![CDATA[
      K(x \ y,x) * (y / x) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(5250(a,1),280(a,1,1))].">
      <j1 rule="para" parents="5250 280"/>
    </justification>
  </clause>

  <clause id="5371">
    <literal><![CDATA[
      K(x,y) * (z * R(T(K(y,x),z),u,w)) = (K(x,y) * R(K(x,y) \ 1,u,w)) * z
    ]]></literal>
    <justification jstring="[para(5257(a,1),1728(a,1,2,2,1))].">
      <j1 rule="para" parents="5257 1728"/>
    </justification>
  </clause>

  <clause id="5372">
    <literal><![CDATA[
      K(x,y) * (z * L(T(K(y,x),z),u,w)) = (K(x,y) * L(K(x,y) \ 1,u,w)) * z
    ]]></literal>
    <justification jstring="[para(5257(a,1),2028(a,1,2,2,1))].">
      <j1 rule="para" parents="5257 2028"/>
    </justification>
  </clause>

  <clause id="5373">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5268(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5268 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5375">
    <literal><![CDATA[
      (x / T(y,x)) * L(z,x / y,K(x,y)) = K(x,y) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,5361,a(flip),b,212,a)].">
      <j1 rule="hyper" parents="133 5361 212"/>
    </justification>
  </clause>

  <clause id="5376">
    <literal><![CDATA[
      (K(x,y) / x) \ 1 = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(214,a,5368,a)].">
      <j1 rule="hyper" parents="214 5368"/>
    </justification>
  </clause>

  <clause id="5377">
    <literal><![CDATA[
      1 / ((x \ 1) * K(y,x \ 1)) = K(1 / x,y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(3403(a,2),5368(a,2,1))].">
      <j1 rule="para" parents="3403 5368"/>
    </justification>
  </clause>

  <clause id="5378">
    <literal><![CDATA[
      T(K(x * (1 / y),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(3898(a,1),5070(a,1,1))].">
      <j1 rule="para" parents="3898 5070"/>
    </justification>
  </clause>

  <clause id="5379">
    <literal><![CDATA[
      T(x,x * y) * K(y,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(3039,a,5163,a)].">
      <j1 rule="hyper" parents="3039 5163"/>
    </justification>
  </clause>

  <clause id="5380">
    <literal><![CDATA[
      K(x,y) = T(y,y * x) \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,5163,a(flip),b,3036,a),flip(a)].">
      <j1 rule="hyper" parents="128 5163 3036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5381">
    <literal><![CDATA[
      T(x,y) * K(x * y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(3039,a,5164,a)].">
      <j1 rule="hyper" parents="3039 5164"/>
    </justification>
  </clause>

  <clause id="5382">
    <literal><![CDATA[
      K(x,x * y) * K(y,x) = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,5379,a(flip),b,4943,a),flip(a)].">
      <j1 rule="hyper" parents="128 5379 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5383">
    <literal><![CDATA[
      T(x,y \ x) * K(y \ 1,x) = L(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(1799(a,1),5379(a,1,1))].">
      <j1 rule="para" parents="1799 5379"/>
    </justification>
  </clause>

  <clause id="5384">
    <literal><![CDATA[
      T(x,x * y) * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(5380(a,2),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5380 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5385">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,5381,a(flip),b,4943,a),flip(a)].">
      <j1 rule="hyper" parents="128 5381 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5387">
    <literal><![CDATA[
      x * ((y \ (x \ 1)) * y) = K(y \ (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(370,a,4895,a)].">
      <j1 rule="hyper" parents="370 4895"/>
    </justification>
  </clause>

  <clause id="5388">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) * R(R(x * T(x \ 1,y),z,u) \ 1,w,v5) = R((x * T(x \ 1,y)) * R(K(y,x \ 1),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(4919(a,1),4685(a,2,1,2,1))].">
      <j1 rule="para" parents="4919 4685"/>
    </justification>
  </clause>

  <clause id="5389">
    <literal><![CDATA[
      (x \ y) * ((y / x) \ z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),4941(a,1,2,1,1))].">
      <j1 rule="para" parents="10 4941"/>
    </justification>
  </clause>

  <clause id="5390">
    <literal><![CDATA[
      x * ((y / (y / x)) \ z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(4339(a,1),4941(a,1,2,1))].">
      <j1 rule="para" parents="4339 4941"/>
    </justification>
  </clause>

  <clause id="5391">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) / z = K(z / (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(131,a,1022,a(flip),b,4945,a)].">
      <j1 rule="hyper" parents="131 1022 4945"/>
    </justification>
  </clause>

  <clause id="5392">
    <literal><![CDATA[
      (x * (y * T(y \ z,u))) / (x * z) = K((x * z) / (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(131,a,1021,a(flip),b,4945,a)].">
      <j1 rule="hyper" parents="131 1021 4945"/>
    </justification>
  </clause>

  <clause id="5393">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x / y) = u
    ]]></literal>
    <justification jstring="[para(4945(a,1),5276(a,1,2))].">
      <j1 rule="para" parents="4945 5276"/>
    </justification>
  </clause>

  <clause id="5394">
    <literal><![CDATA[
      K(x * (1 / y),x) = K(x / y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,4920,a,b,4956,a),flip(a)].">
      <j1 rule="hyper" parents="347 4920 4956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5396">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2548,a(flip),b,4965,a)].">
      <j1 rule="hyper" parents="63 2548 4965"/>
    </justification>
  </clause>

  <clause id="5398">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = y * ((x * (y \ z)) / x)
    ]]></literal>
    <justification jstring="[hyper(133,a,4965,a(flip),b,2548,a(flip))].">
      <j1 rule="hyper" parents="133 4965 2548"/>
    </justification>
  </clause>

  <clause id="5399">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(4965(a,1),1812(a,2,2))].">
      <j1 rule="para" parents="4965 1812"/>
    </justification>
  </clause>

  <clause id="5400">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = K(z,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(4965(a,1),2424(a,2,1))].">
      <j1 rule="para" parents="4965 2424"/>
    </justification>
  </clause>

  <clause id="5401">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * y = (x * y) * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(4965(a,1),2451(a,2,2))].">
      <j1 rule="para" parents="4965 2451"/>
    </justification>
  </clause>

  <clause id="5402">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) * (z * u) = ((y * z) * ((x * ((y * z) \ z)) / x)) * u
    ]]></literal>
    <justification jstring="[para(4965(a,1),4715(a,1,1))].">
      <j1 rule="para" parents="4965 4715"/>
    </justification>
  </clause>

  <clause id="5403">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,4924,a,b,4991,a),flip(a)].">
      <j1 rule="hyper" parents="347 4924 4991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5404">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(2332(a,1),5403(a,1,2))].">
      <j1 rule="para" parents="2332 5403"/>
    </justification>
  </clause>

  <clause id="5405">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2340(a,1),5403(a,1,2))].">
      <j1 rule="para" parents="2340 5403"/>
    </justification>
  </clause>

  <clause id="5406">
    <literal><![CDATA[
      K(x,y / (1 / z)) = K(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(2357(a,1),5403(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2357 5403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5407">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2742(a,2),5403(a,1,2))].">
      <j1 rule="para" parents="2742 5403"/>
    </justification>
  </clause>

  <clause id="5408">
    <literal><![CDATA[
      K(x,K(y \ 1,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2754(a,1),5403(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2754 5403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5409">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ 1) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(2770(a,2),5403(a,1,2))].">
      <j1 rule="para" parents="2770 5403"/>
    </justification>
  </clause>

  <clause id="5410">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2892(a,1),5403(a,1,2))].">
      <j1 rule="para" parents="2892 5403"/>
    </justification>
  </clause>

  <clause id="5411">
    <literal><![CDATA[
      K(x,(y \ 1) * (y * z)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(2777(a,1),5403(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2777 5403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5412">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2924(a,1),5403(a,1,2))].">
      <j1 rule="para" parents="2924 5403"/>
    </justification>
  </clause>

  <clause id="5413">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2959(a,1),5403(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2959 5403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5414">
    <literal><![CDATA[
      K(x,(1 / y) / z) = K(x,(y \ 1) / z)
    ]]></literal>
    <justification jstring="[para(3472(a,1),5403(a,1,2))].">
      <j1 rule="para" parents="3472 5403"/>
    </justification>
  </clause>

  <clause id="5415">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3497(a,2),5403(a,1,2))].">
      <j1 rule="para" parents="3497 5403"/>
    </justification>
  </clause>

  <clause id="5416">
    <literal><![CDATA[
      K(x,T(y * K(z,z \ 1),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(4868(a,2),5403(a,1,2))].">
      <j1 rule="para" parents="4868 5403"/>
    </justification>
  </clause>

  <clause id="5417">
    <literal><![CDATA[
      K(x,K(y,1 / y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1922(a,2),5407(a,1,2,1))].">
      <j1 rule="para" parents="1922 5407"/>
    </justification>
  </clause>

  <clause id="5418">
    <literal><![CDATA[
      K(x,y * (z * (1 / u))) = K(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(2833(a,1),5407(a,1,2))].">
      <j1 rule="para" parents="2833 5407"/>
    </justification>
  </clause>

  <clause id="5419">
    <literal><![CDATA[
      K(x,y * (z / ((u \ 1) \ 1))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(2834(a,1),5407(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2834 5407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5421">
    <literal><![CDATA[
      K(x,y * ((1 / z) \ u)) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(2975(a,1),5407(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2975 5407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5422">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[para(3467(a,2),5408(a,1,2))].">
      <j1 rule="para" parents="3467 5408"/>
    </justification>
  </clause>

  <clause id="5423">
    <literal><![CDATA[
      K(x,y / (K(z,z \ 1) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(3507(a,2),5408(a,1,2))].">
      <j1 rule="para" parents="3507 5408"/>
    </justification>
  </clause>

  <clause id="5424">
    <literal><![CDATA[
      K(x,(K(y,y \ 1) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3510(a,2),5408(a,1,2))].">
      <j1 rule="para" parents="3510 5408"/>
    </justification>
  </clause>

  <clause id="5425">
    <literal><![CDATA[
      K(x,((1 / y) * z) \ u) = K(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(3511(a,1),5408(a,1,2))].">
      <j1 rule="para" parents="3511 5408"/>
    </justification>
  </clause>

  <clause id="5426">
    <literal><![CDATA[
      K(x,y * (z * K(u,1 / u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2776(a,1),5417(a,1,2))].">
      <j1 rule="para" parents="2776 5417"/>
    </justification>
  </clause>

  <clause id="5427">
    <literal><![CDATA[
      K(x,K(y,1 / y) / z) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(3462(a,1),5417(a,1,2))].">
      <j1 rule="para" parents="3462 5417"/>
    </justification>
  </clause>

  <clause id="5428">
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(355,a,5000,a),flip(a)].">
      <j1 rule="hyper" parents="355 5000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5429">
    <literal><![CDATA[
      K(x,y) * (y * z) = ((x * y) / x) * z
    ]]></literal>
    <justification jstring="[hyper(150,a,5000,a)].">
      <j1 rule="hyper" parents="150 5000"/>
    </justification>
  </clause>

  <clause id="5430">
    <literal><![CDATA[
      K(x,x \ y) \ ((y / x) * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),5000(a,1,2,1,1))].">
      <j1 rule="para" parents="10 5000"/>
    </justification>
  </clause>

  <clause id="5432">
    <literal><![CDATA[
      T(x * K(x * y,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,4294,a,b,5063,a),flip(a)].">
      <j1 rule="hyper" parents="35 4294 5063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5433">
    <literal><![CDATA[
      T(R(x,y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = u
    ]]></literal>
    <justification jstring="[para(5432(a,1),453(a,1,1))].">
      <j1 rule="para" parents="5432 453"/>
    </justification>
  </clause>

  <clause id="5434">
    <literal><![CDATA[
      T(x,y) \ T(x * K(z,x),y) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(128,a,5064,a,b,4942,a(flip))].">
      <j1 rule="hyper" parents="128 5064 4942"/>
    </justification>
  </clause>

  <clause id="5435">
    <literal><![CDATA[
      L(T(x * K(y * z,x),u),z,y) = (y * (z * T(x,u))) / (y * z)
    ]]></literal>
    <justification jstring="[para(5064(a,2),950(a,1,1))].">
      <j1 rule="para" parents="5064 950"/>
    </justification>
  </clause>

  <clause id="5436">
    <literal><![CDATA[
      ((T(x,(1 / y) \ z) * (z * y)) / T(x,(1 / y) \ z)) / y = (1 / y) * (((1 / y) \ z) * K(x,(1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(5075(a,1),1873(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5075 1873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5437">
    <literal><![CDATA[
      L(x,y,z) * K(u,L(x,y,z)) = L(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(5079,a,5077,a)].">
      <j1 rule="hyper" parents="5079 5077"/>
    </justification>
  </clause>

  <clause id="5438">
    <literal><![CDATA[
      R(x,y,z) * K(u,R(x,y,z)) = R(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(5079,a,5078,a)].">
      <j1 rule="hyper" parents="5079 5078"/>
    </justification>
  </clause>

  <clause id="5439">
    <literal><![CDATA[
      x * ((y * (x / y)) \ y) = x / (x / y)
    ]]></literal>
    <justification jstring="[hyper(134,a,5139,a,b,xx)].">
      <j1 rule="hyper" parents="134 5139"/>
    </justification>
  </clause>

  <clause id="5441">
    <literal><![CDATA[
      K(x \ y,x) * ((x \ y) \ z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),5161(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5443">
    <literal><![CDATA[
      (x / (x / y)) \ z = K(y,y \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(4339(a,1),5161(a,1,1))].">
      <j1 rule="para" parents="4339 5161"/>
    </justification>
  </clause>

  <clause id="5444">
    <literal><![CDATA[
      (x * K(y,x)) \ z = K(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(4942(a,1),5161(a,1,1))].">
      <j1 rule="para" parents="4942 5161"/>
    </justification>
  </clause>

  <clause id="5445">
    <literal><![CDATA[
      K(x \ 1,y) * ((x \ 1) \ z) = (x \ K(y,x \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(4979(a,2),5161(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4979 5161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5446">
    <literal><![CDATA[
      x * (K(x,y) * T(z,x)) = K(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,4943,a,b,5162,a)].">
      <j1 rule="hyper" parents="347 4943 5162"/>
    </justification>
  </clause>

  <clause id="5448">
    <literal><![CDATA[
      x * (K(x,y) * K(x,z)) = K(x,y) * T(x,z)
    ]]></literal>
    <justification jstring="[para(4924(a,2),5191(a,1,2,2))].">
      <j1 rule="para" parents="4924 5191"/>
    </justification>
  </clause>

  <clause id="5449">
    <literal><![CDATA[
      ((x * y) / x) * z = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(134,a,5261,a(flip),b,5192,a)].">
      <j1 rule="hyper" parents="134 5261 5192"/>
    </justification>
  </clause>

  <clause id="5450">
    <literal><![CDATA[
      ((R(x,y,z) * (x \ u)) / (x \ u)) \ (R((x \ u) \ u,y,z) * w) = K(R((x \ u) \ u,y,z),x \ u) * w
    ]]></literal>
    <justification jstring="[para(748(a,1),5192(a,1,1,1))].">
      <j1 rule="para" parents="748 5192"/>
    </justification>
  </clause>

  <clause id="5451">
    <literal><![CDATA[
      (x / y) * (K(y \ x,y) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),5195(a,1,1,1))].">
      <j1 rule="para" parents="10 5195"/>
    </justification>
  </clause>

  <clause id="5454">
    <literal><![CDATA[
      K(x,y) * T(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3577,a(flip),b,5203,a)].">
      <j1 rule="hyper" parents="347 3577 5203"/>
    </justification>
  </clause>

  <clause id="5455">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) / T(x,y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,3577,a(flip),b,5203,a)].">
      <j1 rule="hyper" parents="131 3577 5203"/>
    </justification>
  </clause>

  <clause id="5456">
    <literal><![CDATA[
      K(x,(y \ z) / (y \ 1)) * (y \ T(z,x)) = y \ z
    ]]></literal>
    <justification jstring="[hyper(1171,a,5255,a)].">
      <j1 rule="hyper" parents="1171 5255"/>
    </justification>
  </clause>

  <clause id="5457">
    <literal><![CDATA[
      x / (((y \ (x * z)) * y) / z) = K(y,x / (y / z))
    ]]></literal>
    <justification jstring="[hyper(220,a,1576,a(flip),b,5255,a)].">
      <j1 rule="hyper" parents="220 1576 5255"/>
    </justification>
  </clause>

  <clause id="5458">
    <literal><![CDATA[
      x * T(x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) * y = u
    ]]></literal>
    <justification jstring="[para(5255(a,1),5286(a,1))].">
      <j1 rule="para" parents="5255 5286"/>
    </justification>
  </clause>

  <clause id="5459">
    <literal><![CDATA[
      R(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(2384,a,5331,a)].">
      <j1 rule="hyper" parents="2384 5331"/>
    </justification>
  </clause>

  <clause id="5460">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ ((x * K(y,x)) * (z * u)) = L(u,z,x * K(y,x))
    ]]></literal>
    <justification jstring="[para(5331(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5331 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5461">
    <literal><![CDATA[
      (x / (x / y)) * z = y * (K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(4894(a,2),5331(a,1,1))].">
      <j1 rule="para" parents="4894 5331"/>
    </justification>
  </clause>

  <clause id="5462">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(4990(a,1),5331(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4990 5331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5463">
    <literal><![CDATA[
      (T(x,y) * K(z,x)) * u = T(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(5459(a,1),472(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5459 472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5464">
    <literal><![CDATA[
      (R(x,y,z) * K(u,x)) * w = R(x,y,z) * (K(u,x) * w)
    ]]></literal>
    <justification jstring="[para(5459(a,1),469(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5459 469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5465">
    <literal><![CDATA[
      K(x,y / z) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (T(y / z,x) \ y) = w
    ]]></literal>
    <justification jstring="[para(5339(a,1),630(a,1))].">
      <j1 rule="para" parents="5339 630"/>
    </justification>
  </clause>

  <clause id="5466">
    <literal><![CDATA[
      (x * K(y,x)) * (x \ z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,5331,a,b,5341,a)].">
      <j1 rule="hyper" parents="63 5331 5341"/>
    </justification>
  </clause>

  <clause id="5467">
    <literal><![CDATA[
      x * (K(y,x) * (L(x,z,u) \ 1)) = K(y,x) * (L(x,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(1415(a,1),5341(a,1,2,2))].">
      <j1 rule="para" parents="1415 5341"/>
    </justification>
  </clause>

  <clause id="5468">
    <literal><![CDATA[
      T(x,y) \ T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(5348(a,2),2558(a,1))].">
      <j1 rule="para" parents="5348 2558"/>
    </justification>
  </clause>

  <clause id="5470">
    <literal><![CDATA[
      R(K(x,y),y * z,u) * ((y * z) * u) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[hyper(133,a,5353,a(flip),b,576,a),flip(a)].">
      <j1 rule="hyper" parents="133 5353 576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5471">
    <literal><![CDATA[
      x * (K(y,x) * (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5353(a,1),357(a,1))].">
      <j1 rule="para" parents="5353 357"/>
    </justification>
  </clause>

  <clause id="5472">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ (K(y,x) * (x * (z * u))) = L(L(u,z,x),x * z,K(y,x))
    ]]></literal>
    <justification jstring="[para(5353(a,1),542(a,1,1))].">
      <j1 rule="para" parents="5353 542"/>
    </justification>
  </clause>

  <clause id="5473">
    <literal><![CDATA[
      L((1 / T(x,y)) \ z,1 / T(x,y),y) = (T(y,x) * (1 / x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(5356(a,2),99(a,2,1))].">
      <j1 rule="para" parents="5356 99"/>
    </justification>
  </clause>

  <clause id="5474">
    <literal><![CDATA[
      L(x,T(y \ z,y),u) = L(x,z / y,u)
    ]]></literal>
    <justification jstring="[para(4990(a,1),5359(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4990 5359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5475">
    <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(5058(a,1),5360(a,1,1))].">
      <j1 rule="para" parents="5058 5360"/>
    </justification>
  </clause>

  <clause id="5476">
    <literal><![CDATA[
      K(x,((y * z) \ y) * u) = K(x,(y \ (y / z)) * u)
    ]]></literal>
    <justification jstring="[para(3256(a,1),5410(a,1,2,1))].">
      <j1 rule="para" parents="3256 5410"/>
    </justification>
  </clause>

  <clause id="5477">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ z) = K(y,y \ x) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),5428(a,1,1,1))].">
      <j1 rule="para" parents="10 5428"/>
    </justification>
  </clause>

  <clause id="5478">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(128,a,5429,a(flip),b,5353,a(flip))].">
      <j1 rule="hyper" parents="128 5429 5353"/>
    </justification>
  </clause>

  <clause id="5479">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),5429(a,2,1,1))].">
      <j1 rule="para" parents="10 5429"/>
    </justification>
  </clause>

  <clause id="5480">
    <literal><![CDATA[
      K(x \ y,x) * (x * z) = (y / (y / x)) * z
    ]]></literal>
    <justification jstring="[para(4339(a,1),5429(a,2,1))].">
      <j1 rule="para" parents="4339 5429"/>
    </justification>
  </clause>

  <clause id="5481">
    <literal><![CDATA[
      (K(x,y) * y) * z = K(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(4976(a,1),5429(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4976 5429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5482">
    <literal><![CDATA[
      ((x * y) / x) * z = (y * (K(x,y) * z)) * 1
    ]]></literal>
    <justification jstring="[hyper(347,a,8,a,b,5449,a),flip(a)].">
      <j1 rule="hyper" parents="347 8 5449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5483">
    <literal><![CDATA[
      K(x,y) * (K((x * y) / x,z) * u) = y \ (T((x * y) / x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(128,a,4943,a(flip),b,5449,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 4943 5449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5484">
    <literal><![CDATA[
      (x * (K(y * z,x) * y)) * z = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5449(a,1),955(a,1,1))].">
      <j1 rule="para" parents="5449 955"/>
    </justification>
  </clause>

  <clause id="5485">
    <literal><![CDATA[
      (x / y) * (K(y,y \ x) * z) = ((y * (x / y)) / y) * z
    ]]></literal>
    <justification jstring="[para(5098(a,1),5449(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5098 5449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5486">
    <literal><![CDATA[
      ((x * y) / x) * (x / y) = y * (x / T(y,x))
    ]]></literal>
    <justification jstring="[para(5361(a,1),5449(a,2,2))].">
      <j1 rule="para" parents="5361 5449"/>
    </justification>
  </clause>

  <clause id="5487">
    <literal><![CDATA[
      T(x,y) / (K(x,y) * T(x,z)) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(220,a,5454,a,b,5256,a)].">
      <j1 rule="hyper" parents="220 5454 5256"/>
    </justification>
  </clause>

  <clause id="5488">
    <literal><![CDATA[
      T(x * K(y,x),x \ y) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(462,a,4977,a,b,5466,a)].">
      <j1 rule="hyper" parents="462 4977 5466"/>
    </justification>
  </clause>

  <clause id="5489">
    <literal><![CDATA[
      (x * K(y,x)) \ z = x \ (K(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(128,a,10,a(flip),b,5466,a)].">
      <j1 rule="hyper" parents="128 10 5466"/>
    </justification>
  </clause>

  <clause id="5490">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ z,u) = L(x,z / y,u)
    ]]></literal>
    <justification jstring="[para(4320(a,1),5474(a,1,2))].">
      <j1 rule="para" parents="4320 5474"/>
    </justification>
  </clause>

  <clause id="5491">
    <literal><![CDATA[
      (x \ y) \ ((y / x) * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),5478(a,1,2,1,1))].">
      <j1 rule="para" parents="10 5478"/>
    </justification>
  </clause>

  <clause id="5492">
    <literal><![CDATA[
      x \ ((y / (y / x)) * z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(4339(a,1),5478(a,1,2,1))].">
      <j1 rule="para" parents="4339 5478"/>
    </justification>
  </clause>

  <clause id="5493">
    <literal><![CDATA[
      R(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2384,a,5481,a)].">
      <j1 rule="hyper" parents="2384 5481"/>
    </justification>
  </clause>

  <clause id="5494">
    <literal><![CDATA[
      L(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(544,a,5481,a)].">
      <j1 rule="hyper" parents="544 5481"/>
    </justification>
  </clause>

  <clause id="5495">
    <literal><![CDATA[
      a(K(x,y),y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(127,a,5481,a(flip),b,86,a),flip(a)].">
      <j1 rule="hyper" parents="127 5481 86"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5496">
    <literal><![CDATA[
      L(x,y,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5494(a,1),50(a,2))].">
      <j1 rule="para" parents="5494 50"/>
    </justification>
  </clause>

  <clause id="5498">
    <literal><![CDATA[
      a(K(x,y),y,z) = u \ u
    ]]></literal>
    <justification jstring="[hyper(347,a,68,a,b,5495,a),flip(a)].">
      <j1 rule="hyper" parents="347 68 5495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5499">
    <literal><![CDATA[
      R(K(x,y),y \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2277,a,5493,a)].">
      <j1 rule="hyper" parents="2277 5493"/>
    </justification>
  </clause>

  <clause id="5500">
    <literal><![CDATA[
      (K(x,y \ 1) * y) * z = K(x,y \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,5493,a(flip),b,2253,a),flip(a)].">
      <j1 rule="hyper" parents="133 5493 2253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5501">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),y,u) = z
    ]]></literal>
    <justification jstring="[para(5493(a,1),2186(a,1))].">
      <j1 rule="para" parents="5493 2186"/>
    </justification>
  </clause>

  <clause id="5503">
    <literal><![CDATA[
      a(K(x,y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(5498(a,2),185(a,1))].">
      <j1 rule="para" parents="5498 185"/>
    </justification>
  </clause>

  <clause id="5504">
    <literal><![CDATA[
      (x * K(y,x)) \ y = x \ (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(5233(a,1),5489(a,2,2))].">
      <j1 rule="para" parents="5233 5489"/>
    </justification>
  </clause>

  <clause id="5505">
    <literal><![CDATA[
      L(1 / x,x,x * y) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3264,a,b,5055,a)].">
      <j1 rule="hyper" parents="63 3264 5055"/>
    </justification>
  </clause>

  <clause id="5506">
    <literal><![CDATA[
      L(x \ 1,x,x \ y) = L(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),5505(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 5505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5507">
    <literal><![CDATA[
      ((x \ y) * x) \ (x \ y) = L(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(572,a,5506,a)].">
      <j1 rule="hyper" parents="572 5506"/>
    </justification>
  </clause>

  <clause id="5508">
    <literal><![CDATA[
      L(x \ 1,x,x \ y) = y \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3264,a(flip),b,5506,a),flip(a)].">
      <j1 rule="hyper" parents="347 3264 5506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5509">
    <literal><![CDATA[
      L((1 / (1 / x)) \ 1,1 / (1 / x),(1 / (1 / x)) \ y) = L((x * (1 / x)) / x,1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(4396(a,2),5506(a,2,1))].">
      <j1 rule="para" parents="4396 5506"/>
    </justification>
  </clause>

  <clause id="5510">
    <literal><![CDATA[
      ((x \ y) * x) \ (x \ y) = y \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(572,a,5508,a)].">
      <j1 rule="hyper" parents="572 5508"/>
    </justification>
  </clause>

  <clause id="5511">
    <literal><![CDATA[
      x * L(y \ 1,y,y \ z) = x * (z \ (z / y))
    ]]></literal>
    <justification jstring="[hyper(134,a,5508,a,b,9,a)].">
      <j1 rule="hyper" parents="134 5508 9"/>
    </justification>
  </clause>

  <clause id="5512">
    <literal><![CDATA[
      (x \ y) / (y \ (y / x)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(220,a,5508,a(flip),b,244,a(flip))].">
      <j1 rule="hyper" parents="220 5508 244"/>
    </justification>
  </clause>

  <clause id="5513">
    <literal><![CDATA[
      x * (x * (y \ (y / x))) = L(x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(5508(a,1),3337(a,1,2,2))].">
      <j1 rule="para" parents="5508 3337"/>
    </justification>
  </clause>

  <clause id="5514">
    <literal><![CDATA[
      x \ (x / y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * L(y \ 1,y,y \ x) = u
    ]]></literal>
    <justification jstring="[para(5510(a,1),712(a,1))].">
      <j1 rule="para" parents="5510 712"/>
    </justification>
  </clause>

  <clause id="5515">
    <literal><![CDATA[
      ((x \ y) * x) \ (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ (y / x) = z
    ]]></literal>
    <justification jstring="[para(5512(a,1),359(a,1,1))].">
      <j1 rule="para" parents="5512 359"/>
    </justification>
  </clause>

  <clause id="5516">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(5381(a,1),5169(a,1,2))].">
      <j1 rule="para" parents="5381 5169"/>
    </justification>
  </clause>

  <clause id="5517">
    <literal><![CDATA[
      K(x \ 1,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x \ 1,y) * (x * x) = z
    ]]></literal>
    <justification jstring="[para(240(a,1),5200(a,1,2))].">
      <j1 rule="para" parents="240 5200"/>
    </justification>
  </clause>

  <clause id="5518">
    <literal><![CDATA[
      K(x,y) * (K(z,T(y,x)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      y * (T(T(y,x),z) \ u) = w
    ]]></literal>
    <justification jstring="[para(4947(a,1),5215(a,1,2))].">
      <j1 rule="para" parents="4947 5215"/>
    </justification>
  </clause>

  <clause id="5519">
    <literal><![CDATA[
      K(x,y) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      y * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(5213(a,1),5215(a,1,2))].">
      <j1 rule="para" parents="5213 5215"/>
    </justification>
  </clause>

  <clause id="5520">
    <literal><![CDATA[
      K(x,y / z) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(y / z,x) \ y = u
    ]]></literal>
    <justification jstring="[para(83(a,1),5217(a,1,2))].">
      <j1 rule="para" parents="83 5217"/>
    </justification>
  </clause>

  <clause id="5521">
    <literal><![CDATA[
      K(x,y) * L(1 / z,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ (y / z) = u
    ]]></literal>
    <justification jstring="[para(3264(a,2),5217(a,1,2))].">
      <j1 rule="para" parents="3264 5217"/>
    </justification>
  </clause>

  <clause id="5522">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,(x * y) \ y) = z
    ]]></literal>
    <justification jstring="[para(3847(a,2),5317(a,1))].">
      <j1 rule="para" parents="3847 5317"/>
    </justification>
  </clause>

  <clause id="5523">
    <literal><![CDATA[
      T(x \ y,z) * ((y \ x) * K(z,x \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * (y \ x) = u
    ]]></literal>
    <justification jstring="[para(2488(a,1),5355(a,1,2))].">
      <j1 rule="para" parents="2488 5355"/>
    </justification>
  </clause>

  <clause id="5524">
    <literal><![CDATA[
      K(x,y) * K(y,y * x) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(2560,a,5382,a)].">
      <j1 rule="hyper" parents="2560 5382"/>
    </justification>
  </clause>

  <clause id="5525">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2560,a,5385,a)].">
      <j1 rule="hyper" parents="2560 5385"/>
    </justification>
  </clause>

  <clause id="5526">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5385(a,1),2560(a,1))].">
      <j1 rule="para" parents="5385 2560"/>
    </justification>
  </clause>

  <clause id="5527">
    <literal><![CDATA[
      K(x,y) * K(y,x * y) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[para(5297(a,2),5524(a,1,2))].">
      <j1 rule="para" parents="5297 5524"/>
    </justification>
  </clause>

  <clause id="5528">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = K(y,x) * K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),5525(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5529">
    <literal><![CDATA[
      K(x \ (y \ x),x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(4901,a,4926,a)].">
      <j1 rule="hyper" parents="4901 4926"/>
    </justification>
  </clause>

  <clause id="5530">
    <literal><![CDATA[
      K((x / y) \ 1,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(83(a,1),5529(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="83 5529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5531">
    <literal><![CDATA[
      (x * K(y,z * z)) * ((z * z) \ u) = (x * (T(z * z,y) \ 1)) * u
    ]]></literal>
    <justification jstring="[para(4933(a,1),827(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4933 827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5532">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = T(K(x,y \ 1),z)
    ]]></literal>
    <justification jstring="[para(4924(a,2),4964(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4924 4964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5535">
    <literal><![CDATA[
      K(x,T(1 / y,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(83(a,1),5532(a,2,1,2))].">
      <j1 rule="para" parents="83 5532"/>
    </justification>
  </clause>

  <clause id="5536">
    <literal><![CDATA[
      K(x,1 / T(1 / y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(3903,a,5535,a)].">
      <j1 rule="hyper" parents="3903 5535"/>
    </justification>
  </clause>

  <clause id="5537">
    <literal><![CDATA[
      K(x,1 / T(y,z)) = T(K(x,1 / y),z)
    ]]></literal>
    <justification jstring="[para(2726(a,1),5535(a,1,2))].">
      <j1 rule="para" parents="2726 5535"/>
    </justification>
  </clause>

  <clause id="5538">
    <literal><![CDATA[
      K(x,R(T(K(x,y),z),u,w)) = 1
    ]]></literal>
    <justification jstring="[para(5535(a,1),3593(a,1,2,1))].">
      <j1 rule="para" parents="5535 3593"/>
    </justification>
  </clause>

  <clause id="5539">
    <literal><![CDATA[
      (x \ T(y,x \ 1)) / (x \ y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(131,a,3837,a,b,4975,a)].">
      <j1 rule="hyper" parents="131 3837 4975"/>
    </justification>
  </clause>

  <clause id="5540">
    <literal><![CDATA[
      K((x * x) \ y,x * x) = K(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4893,a(flip),b,5057,a)].">
      <j1 rule="hyper" parents="63 4893 5057"/>
    </justification>
  </clause>

  <clause id="5541">
    <literal><![CDATA[
      L((x * y) / x,z,u) = L(y * K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(35,a,741,a,b,5067,a)].">
      <j1 rule="hyper" parents="35 741 5067"/>
    </justification>
  </clause>

  <clause id="5542">
    <literal><![CDATA[
      L(x * K(y,x),z,u) / L(x,z,u) = K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,5068,a,b,4976,a(flip))].">
      <j1 rule="hyper" parents="131 5068 4976"/>
    </justification>
  </clause>

  <clause id="5543">
    <literal><![CDATA[
      T(L(x * K(y,x),z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(5068(a,2),362(a,1,1))].">
      <j1 rule="para" parents="5068 362"/>
    </justification>
  </clause>

  <clause id="5544">
    <literal><![CDATA[
      L(x * K(y,x),z,u) \ L(x,z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(5068(a,2),4918(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5068 4918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5545">
    <literal><![CDATA[
      L(x,y,z) / L(x * K(u,x),y,z) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5068(a,2),5245(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5068 5245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5546">
    <literal><![CDATA[
      R(x,y,z) \ R(x * K(u,x),y,z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,5069,a,b,4942,a(flip))].">
      <j1 rule="hyper" parents="128 5069 4942"/>
    </justification>
  </clause>

  <clause id="5547">
    <literal><![CDATA[
      R(x * K(y,x),z,u) \ y = R(x,z,u) \ ((R(x,z,u) * y) / R(x,z,u))
    ]]></literal>
    <justification jstring="[para(5069(a,2),4340(a,1,1))].">
      <j1 rule="para" parents="5069 4340"/>
    </justification>
  </clause>

  <clause id="5548">
    <literal><![CDATA[
      R(x * K(y,x),z,u) \ R(x,z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(5069(a,2),4918(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5069 4918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5549">
    <literal><![CDATA[
      T(1 / (K(x,y) / x),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(5368(a,1),5084(a,1,1,2))].">
      <j1 rule="para" parents="5368 5084"/>
    </justification>
  </clause>

  <clause id="5550">
    <literal><![CDATA[
      (1 / (K(x,y) / x)) * y = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(134,a,5549,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 5549 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5551">
    <literal><![CDATA[
      K((x / y) \ 1,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4962,a(flip),b,5124,a),flip(a)].">
      <j1 rule="hyper" parents="63 4962 5124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5552">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[para(1168(a,1),5124(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1168 5124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5553">
    <literal><![CDATA[
      (x * (y * T(y \ z,u))) / (x * z) = K(((x * y) / (x * z)) \ 1,u)
    ]]></literal>
    <justification jstring="[para(1021(a,1),5124(a,1,1))].">
      <j1 rule="para" parents="1021 5124"/>
    </justification>
  </clause>

  <clause id="5554">
    <literal><![CDATA[
      K(1 / (x / y),z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(3925,a,5551,a)].">
      <j1 rule="hyper" parents="3925 5551"/>
    </justification>
  </clause>

  <clause id="5555">
    <literal><![CDATA[
      K(x / (y * x),z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),5551(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 5551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5556">
    <literal><![CDATA[
      K((x \ y) / y,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(80(a,1),5551(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="80 5551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5557">
    <literal><![CDATA[
      K(x \ 1,y) * (z / (x * z)) = T(z / (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(133,a,5555,a(flip),b,4969,a(flip))].">
      <j1 rule="hyper" parents="133 5555 4969"/>
    </justification>
  </clause>

  <clause id="5558">
    <literal><![CDATA[
      K(x / (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / y,z) = u
    ]]></literal>
    <justification jstring="[para(5555(a,2),3925(a,1))].">
      <j1 rule="para" parents="5555 3925"/>
    </justification>
  </clause>

  <clause id="5559">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(5555(a,1),5141(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5555 5141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5560">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((x \ (y / z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(1576(a,1),5125(a,1,2))].">
      <j1 rule="para" parents="1576 5125"/>
    </justification>
  </clause>

  <clause id="5561">
    <literal><![CDATA[
      T(x,y) \ T(z * T(z \ x,u),y) = K((T(x,y) \ T(z,y)) \ 1,u)
    ]]></literal>
    <justification jstring="[para(1823(a,1),5125(a,1,2))].">
      <j1 rule="para" parents="1823 5125"/>
    </justification>
  </clause>

  <clause id="5562">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = y * K((y \ (x * z)) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1545,a,5127,a)].">
      <j1 rule="hyper" parents="1545 5127"/>
    </justification>
  </clause>

  <clause id="5563">
    <literal><![CDATA[
      (x \ y) * K(((x \ y) \ (x \ 1)) \ 1,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(1170,a,5127,a),flip(a)].">
      <j1 rule="hyper" parents="1170 5127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5564">
    <literal><![CDATA[
      (x * y) * K(((x * y) \ y) \ 1,z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(872,a,5127,a),flip(a)].">
      <j1 rule="hyper" parents="872 5127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5565">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) / y = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,5127,a(flip),b,484,a)].">
      <j1 rule="hyper" parents="131 5127 484"/>
    </justification>
  </clause>

  <clause id="5568">
    <literal><![CDATA[
      K(x,y) * T(K(y,x) * z,u) = z * K((z \ K(x,y)) \ 1,u)
    ]]></literal>
    <justification jstring="[para(5256(a,1),5127(a,1,2,1))].">
      <j1 rule="para" parents="5256 5127"/>
    </justification>
  </clause>

  <clause id="5569">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) * (y / x) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(347,a,1168,a(flip),b,5129,a),flip(a)].">
      <j1 rule="hyper" parents="347 1168 5129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5570">
    <literal><![CDATA[
      K(((x \ 1) / (x \ y)) \ 1,z) * (x \ y) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,1141,a(flip),b,5129,a),flip(a)].">
      <j1 rule="hyper" parents="347 1141 5129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5571">
    <literal><![CDATA[
      K(((x \ 1) / (x \ y)) \ 1,z) \ (x \ T(y,z)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(128,a,1141,a(flip),b,5129,a)].">
      <j1 rule="hyper" parents="128 1141 5129"/>
    </justification>
  </clause>

  <clause id="5572">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) = K(z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(220,a,5129,a(flip),b,5256,a)].">
      <j1 rule="hyper" parents="220 5129 5256"/>
    </justification>
  </clause>

  <clause id="5573">
    <literal><![CDATA[
      K((x / (x * y)) \ 1,z) * (x * y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5129(a,2,2,1))].">
      <j1 rule="para" parents="9 5129"/>
    </justification>
  </clause>

  <clause id="5576">
    <literal><![CDATA[
      T(T(x,y),z) * K(y,x) = x * K(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(3053,a,5208,a)].">
      <j1 rule="hyper" parents="3053 5208"/>
    </justification>
  </clause>

  <clause id="5577">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),z) = (T(y * x,z) / x) / y
    ]]></literal>
    <justification jstring="[para(1143(a,1),5228(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1143 5228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5578">
    <literal><![CDATA[
      K(x \ y,x) * ((y / x) * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[para(5138(a,1),5237(a,1,1))].">
      <j1 rule="para" parents="5138 5237"/>
    </justification>
  </clause>

  <clause id="5579">
    <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(5308(a,1),356(a,1,2))].">
      <j1 rule="para" parents="5308 356"/>
    </justification>
  </clause>

  <clause id="5580">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) \ z) = x \ (T(T(x,y),y) \ z)
    ]]></literal>
    <justification jstring="[hyper(128,a,5349,a(flip),b,4947,a),flip(a)].">
      <j1 rule="hyper" parents="128 5349 4947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5581">
    <literal><![CDATA[
      (T(x,y) * (y * z)) \ ((x * y) * (K(x,y) * z)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(5365(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5365 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5582">
    <literal><![CDATA[
      K(x,y) * T(y,y * x) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,y) = z
    ]]></literal>
    <justification jstring="[para(3036(a,1),5384(a,1))].">
      <j1 rule="para" parents="3036 5384"/>
    </justification>
  </clause>

  <clause id="5587">
    <literal><![CDATA[
      K(x,y \ (z * (1 / u))) = K(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(2768(a,1),5409(a,1,2,2))].">
      <j1 rule="para" parents="2768 5409"/>
    </justification>
  </clause>

  <clause id="5588">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ 1) * u)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(2891(a,1),5409(a,1,2,2))].">
      <j1 rule="para" parents="2891 5409"/>
    </justification>
  </clause>

  <clause id="5589">
    <literal><![CDATA[
      K(x,y \ ((1 / z) * u)) = K(x,y \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(2921(a,1),5409(a,1,2,2))].">
      <j1 rule="para" parents="2921 5409"/>
    </justification>
  </clause>

  <clause id="5590">
    <literal><![CDATA[
      K(x,y \ (z * ((1 / u) \ w))) = K(x,y \ (z * ((u \ 1) \ w)))
    ]]></literal>
    <justification jstring="[para(2975(a,1),5409(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2975 5409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5591">
    <literal><![CDATA[
      K(x,(y * (1 / z)) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(2779(a,1),5415(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2779 5415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5592">
    <literal><![CDATA[
      K(x,T((1 / y) * z,u)) = K(x,T((y \ 1) * z,u))
    ]]></literal>
    <justification jstring="[para(2924(a,1),5416(a,1,2,1))].">
      <j1 rule="para" parents="2924 5416"/>
    </justification>
  </clause>

  <clause id="5593">
    <literal><![CDATA[
      K(x,(y * (1 / z)) / u) = K(x,(y * (z \ 1)) / u)
    ]]></literal>
    <justification jstring="[para(2779(a,1),5422(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2779 5422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5594">
    <literal><![CDATA[
      K(x,((1 / y) * z) / u) = K(x,((y \ 1) * z) / u)
    ]]></literal>
    <justification jstring="[para(2922(a,1),5422(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2922 5422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5596">
    <literal><![CDATA[
      K(x,y / (z * (1 / u))) = K(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(2768(a,1),5423(a,1,2,2))].">
      <j1 rule="para" parents="2768 5423"/>
    </justification>
  </clause>

  <clause id="5597">
    <literal><![CDATA[
      K(x,y / (((z \ 1) \ 1) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(2891(a,1),5423(a,1,2,2))].">
      <j1 rule="para" parents="2891 5423"/>
    </justification>
  </clause>

  <clause id="5598">
    <literal><![CDATA[
      K(x,(y * (z / (1 / u))) \ w) = K(x,(y * (z / (u \ 1))) \ w)
    ]]></literal>
    <justification jstring="[para(2835(a,1),5424(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2835 5424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5599">
    <literal><![CDATA[
      K(x,y * (K(z,1 / z) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(2751(a,2),5426(a,1,2,2))].">
      <j1 rule="para" parents="2751 5426"/>
    </justification>
  </clause>

  <clause id="5600">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * z = u
    ]]></literal>
    <justification jstring="[para(5430(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5430 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5602">
    <literal><![CDATA[
      T(x,y) \ T(z * T(z \ x,x),y) = K((x \ z) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(5127(a,2),5434(a,1,2,1))].">
      <j1 rule="para" parents="5127 5434"/>
    </justification>
  </clause>

  <clause id="5603">
    <literal><![CDATA[
      K(x,x \ y) * ((y / x) \ z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(5273,a,5441,a)].">
      <j1 rule="hyper" parents="5273 5441"/>
    </justification>
  </clause>

  <clause id="5604">
    <literal><![CDATA[
      K(x \ y,x) * T(z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(707,a,5441,a)].">
      <j1 rule="hyper" parents="707 5441"/>
    </justification>
  </clause>

  <clause id="5605">
    <literal><![CDATA[
      T(x,x \ y) \ ((x \ y) \ z) = x \ ((y / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(128,a,5441,a(flip),b,4947,a),flip(a)].">
      <j1 rule="hyper" parents="128 5441 4947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5606">
    <literal><![CDATA[
      K(x \ y,x) * L(z,z,x \ y) = (y / x) \ ((x \ y) / (z \ 1))
    ]]></literal>
    <justification jstring="[para(2007(a,2),5441(a,1,2))].">
      <j1 rule="para" parents="2007 5441"/>
    </justification>
  </clause>

  <clause id="5608">
    <literal><![CDATA[
      K(x \ y,x) * ((y / (y / x)) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(134,a,5443,a,b,5256,a)].">
      <j1 rule="hyper" parents="134 5443 5256"/>
    </justification>
  </clause>

  <clause id="5610">
    <literal><![CDATA[
      K(x / y,(x / y) \ x) * z = y \ ((x / (x / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(380,a,5462,a),flip(a)].">
      <j1 rule="hyper" parents="380 5462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5611">
    <literal><![CDATA[
      ((x / y) \ K(y,y \ x)) * R(((x / y) \ K(y,y \ x)) \ z,u,w) = (y \ x) \ R(K(y,y \ x) \ ((x / y) * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(34,a,1357,a,b,5477,a)].">
      <j1 rule="hyper" parents="34 1357 5477"/>
    </justification>
  </clause>

  <clause id="5613">
    <literal><![CDATA[
      ((x \ y) \ y) * ((x \ y) * z) = x * ((y / x) * z)
    ]]></literal>
    <justification jstring="[para(5479(a,1),5156(a,2,2))].">
      <j1 rule="para" parents="5479 5156"/>
    </justification>
  </clause>

  <clause id="5615">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(5480(a,1),3924(a,1,1))].">
      <j1 rule="para" parents="5480 3924"/>
    </justification>
  </clause>

  <clause id="5616">
    <literal><![CDATA[
      (x / y) * ((x / (x / y)) * z) = (y \ x) * (y * z)
    ]]></literal>
    <justification jstring="[para(5480(a,1),5451(a,1,2))].">
      <j1 rule="para" parents="5480 5451"/>
    </justification>
  </clause>

  <clause id="5617">
    <literal><![CDATA[
      (x \ y) * (y / T(x \ y,y)) = ((y * (x \ y)) / y) * x
    ]]></literal>
    <justification jstring="[hyper(643,a,5486,a),flip(a)].">
      <j1 rule="hyper" parents="643 5486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5618">
    <literal><![CDATA[
      T(x * (y / x),x) = ((y * x) / y) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(347,a,4297,a,b,5486,a)].">
      <j1 rule="hyper" parents="347 4297 5486"/>
    </justification>
  </clause>

  <clause id="5619">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * z = u
    ]]></literal>
    <justification jstring="[para(5491(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5491 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5620">
    <literal><![CDATA[
      (x * K(y,x)) / L((y * x) / y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x * K(y,x),z,u) \ (x * K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(5541(a,2),3313(a,1,2))].">
      <j1 rule="para" parents="5541 3313"/>
    </justification>
  </clause>

  <clause id="5621">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5258,a(flip),b,5572,a),flip(a)].">
      <j1 rule="hyper" parents="63 5258 5572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5622">
    <literal><![CDATA[
      K(x,1 / (y / z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(3903,a,5621,a)].">
      <j1 rule="hyper" parents="3903 5621"/>
    </justification>
  </clause>

  <clause id="5623">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),5621(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 5621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5624">
    <literal><![CDATA[
      K(x,(y / (z * y)) \ 1) = K(x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),5621(a,2,2))].">
      <j1 rule="para" parents="11 5621"/>
    </justification>
  </clause>

  <clause id="5625">
    <literal><![CDATA[
      K(x,(y \ z) / z) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(80(a,1),5621(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="80 5621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5626">
    <literal><![CDATA[
      K(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / (z / y)) = u
    ]]></literal>
    <justification jstring="[para(5621(a,1),3903(a,1))].">
      <j1 rule="para" parents="5621 3903"/>
    </justification>
  </clause>

  <clause id="5627">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(11(a,1),5622(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 5622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5628">
    <literal><![CDATA[
      K(x * y,x \ 1) * ((x * y) \ y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(5623(a,1),5012(a,1,1))].">
      <j1 rule="para" parents="5623 5012"/>
    </justification>
  </clause>

  <clause id="5632">
    <literal><![CDATA[
      K(x,y / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(5627(a,2),5224(a,1))].">
      <j1 rule="para" parents="5627 5224"/>
    </justification>
  </clause>

  <clause id="5634">
    <literal><![CDATA[
      (x \ y) * T(z,y / x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) * (z * (y / x)) = u
    ]]></literal>
    <justification jstring="[para(5578(a,1),639(a,1))].">
      <j1 rule="para" parents="5578 639"/>
    </justification>
  </clause>

  <clause id="5636">
    <literal><![CDATA[
      K(x,y * (((1 / (1 / z)) \ u) * w)) = K(x,y * ((z \ u) * w))
    ]]></literal>
    <justification jstring="[para(3480(a,1),5599(a,1,2,2))].">
      <j1 rule="para" parents="3480 5599"/>
    </justification>
  </clause>

  <clause id="5637">
    <literal><![CDATA[
      (x / (x / y)) \ ((x / y) \ z) = y \ ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(128,a,5603,a(flip),b,5390,a),flip(a)].">
      <j1 rule="hyper" parents="128 5603 5390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5639">
    <literal><![CDATA[
      K(x \ y,x) * ((x \ y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) \ z = u
    ]]></literal>
    <justification jstring="[para(5603(a,1),5274(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5603 5274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5640">
    <literal><![CDATA[
      T(x * (y / x),x) != z * (y / x)
    ]]></literal>
    <literal><![CDATA[
      (y * x) / y = z
    ]]></literal>
    <justification jstring="[para(5618(a,2),44(a,1))].">
      <j1 rule="para" parents="5618 44"/>
    </justification>
  </clause>

  <clause id="5641">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * L(T(z,u),y,x)) = L(K(L(z,y,x),u),L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(4982(a,1),573(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4982 573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5642">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = R(x,y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3683(a,1),4983(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3683 4983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5643">
    <literal><![CDATA[
      (((x \ (x \ 1)) * y) * z) / ((x \ (x \ 1)) * z) = y * K(x \ (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(1123,a,5061,a),flip(a)].">
      <j1 rule="hyper" parents="1123 5061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5644">
    <literal><![CDATA[
      K((x / y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(5124(a,1),5119(a,1))].">
      <j1 rule="para" parents="5124 5119"/>
    </justification>
  </clause>

  <clause id="5645">
    <literal><![CDATA[
      T(x,y) / (x * x) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5201,a,4521,a)].">
      <j1 rule="hyper" parents="5201 4521"/>
    </justification>
  </clause>

  <clause id="5646">
    <literal><![CDATA[
      T(x,y) * ((x * x) \ z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(5645(a,1),803(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5645 803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5647">
    <literal><![CDATA[
      T(x,y) * L(T(z,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (L(z,u,w) * x) = v5
    ]]></literal>
    <justification jstring="[para(25(a,2),5240(a,1,2))].">
      <j1 rule="para" parents="25 5240"/>
    </justification>
  </clause>

  <clause id="5648">
    <literal><![CDATA[
      T(x,T(1 / y,z) \ x) * K(T(y \ 1,z) \ 1,x) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(3884(a,1),5383(a,1,2))].">
      <j1 rule="para" parents="3884 5383"/>
    </justification>
  </clause>

  <clause id="5649">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x / (z * y)) = u
    ]]></literal>
    <justification jstring="[para(4863(a,1),5393(a,1,2))].">
      <j1 rule="para" parents="4863 5393"/>
    </justification>
  </clause>

  <clause id="5650">
    <literal><![CDATA[
      K(x,(y / z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(5572(a,1),5393(a,1))].">
      <j1 rule="para" parents="5572 5393"/>
    </justification>
  </clause>

  <clause id="5651">
    <literal><![CDATA[
      K(x,R(y / z,z,u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * u) / (y * u)) = w
    ]]></literal>
    <justification jstring="[para(108(a,2),5650(a,1,2,1))].">
      <j1 rule="para" parents="108 5650"/>
    </justification>
  </clause>

  <clause id="5652">
    <literal><![CDATA[
      T(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(4972(a,1),5543(a,1,1,1))].">
      <j1 rule="para" parents="4972 5543"/>
    </justification>
  </clause>

  <clause id="5653">
    <literal><![CDATA[
      K((1 / x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ 1) * y,z) = u
    ]]></literal>
    <justification jstring="[para(80(a,1),5615(a,1,1,1,2))].">
      <j1 rule="para" parents="80 5615"/>
    </justification>
  </clause>

  <clause id="5654">
    <literal><![CDATA[
      x \ K(x * y,x \ 1) = y / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(4459(a,1),4900(a,1,2))].">
      <j1 rule="para" parents="4459 4900"/>
    </justification>
  </clause>

  <clause id="5655">
    <literal><![CDATA[
      (x \ K(x * y,x \ 1)) \ y = y / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(132,a,5654,a,b,172,a)].">
      <j1 rule="hyper" parents="132 5654 172"/>
    </justification>
  </clause>

  <clause id="5656">
    <literal><![CDATA[
      L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(4924(a,2),4960(a,1,1))].">
      <j1 rule="para" parents="4924 4960"/>
    </justification>
  </clause>

  <clause id="5658">
    <literal><![CDATA[
      K(x,L(x,y,z) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,2329,a(flip),b,5656,a),flip(a)].">
      <j1 rule="hyper" parents="63 2329 5656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5659">
    <literal><![CDATA[
      L(x,y,z) \ K(x,L(x,y,z) \ 1) = (1 / x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(128,a,5656,a(flip),b,4635,a)].">
      <j1 rule="hyper" parents="128 5656 4635"/>
    </justification>
  </clause>

  <clause id="5660">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3885(a,1),5656(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3885 5656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5661">
    <literal><![CDATA[
      K(x,1 / L(y \ 1,z,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(3903,a,5660,a)].">
      <j1 rule="hyper" parents="3903 5660"/>
    </justification>
  </clause>

  <clause id="5662">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) = 1 / L(K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(220,a,5660,a(flip),b,5173,a),flip(a)].">
      <j1 rule="hyper" parents="220 5660 5173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5663">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,y) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(408(a,1),5660(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="408 5660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5664">
    <literal><![CDATA[
      K(x,L(L(y \ 1,z,u),w,v5) \ 1) = L(L(K(x,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(5660(a,1),5656(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5660 5656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5665">
    <literal><![CDATA[
      L(K(x,1 / y),z,u) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[para(83(a,1),5661(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="83 5661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5666">
    <literal><![CDATA[
      x * ((x \ y) * K(z,x \ y)) = y * K(z,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,5663,a(flip),b,98,a),flip(a)].">
      <j1 rule="hyper" parents="134 5663 98"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5667">
    <literal><![CDATA[
      x \ L(T(x,x \ 1),y,z) = x * L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1925(a,1),4988(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1925 4988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5668">
    <literal><![CDATA[
      ((x \ y) * x) * K(z,(x \ y) * x) = (x \ (y * K(z,y))) * x
    ]]></literal>
    <justification jstring="[hyper(35,a,4989,a,b,5089,a)].">
      <j1 rule="hyper" parents="35 4989 5089"/>
    </justification>
  </clause>

  <clause id="5669">
    <literal><![CDATA[
      a(1 / R(x,y,z),x,x \ 1) = K(R(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4690,a,b,5121,a)].">
      <j1 rule="hyper" parents="63 4690 5121"/>
    </justification>
  </clause>

  <clause id="5671">
    <literal><![CDATA[
      R(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(4925(a,1),5121(a,1,1))].">
      <j1 rule="para" parents="4925 5121"/>
    </justification>
  </clause>

  <clause id="5672">
    <literal><![CDATA[
      R(K(x \ 1,y),z,u) = K(1 / R(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3403,a,b,5671,a),flip(a)].">
      <j1 rule="hyper" parents="347 3403 5671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5673">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5493,a(flip),b,5671,a),flip(a)].">
      <j1 rule="hyper" parents="63 5493 5671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5675">
    <literal><![CDATA[
      K(R(1 / x,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),5671(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="83 5671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5676">
    <literal><![CDATA[
      R(K((x / y) \ 1,z),y,u) = K(((x * u) / (y * u)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(108(a,1),5671(a,2,1,1))].">
      <j1 rule="para" parents="108 5671"/>
    </justification>
  </clause>

  <clause id="5677">
    <literal><![CDATA[
      K(R(x \ 1,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3407(a,1),5671(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3407 5671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5678">
    <literal><![CDATA[
      K(((x * (y * z)) / z) \ 1,z / (y * z)) = K((x / R(1 / y,y,z)) \ 1,z / (y * z))
    ]]></literal>
    <justification jstring="[para(905(a,1),5673(a,1,1,1))].">
      <j1 rule="para" parents="905 5673"/>
    </justification>
  </clause>

  <clause id="5679">
    <literal><![CDATA[
      R(K(x \ 1,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(R(x,z,u) \ 1,y) = w
    ]]></literal>
    <justification jstring="[para(5672(a,2),3409(a,1))].">
      <j1 rule="para" parents="5672 3409"/>
    </justification>
  </clause>

  <clause id="5680">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ 1) = R(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(5675(a,1),5173(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5675 5173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5681">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) * w = R(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(5677(a,1),5256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5677 5256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5682">
    <literal><![CDATA[
      x * ((y \ (x \ 1)) * y) = K((x * y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(639,a,5122,a)].">
      <j1 rule="hyper" parents="639 5122"/>
    </justification>
  </clause>

  <clause id="5683">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (y \ 1) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1616,a(flip),b,5122,a)].">
      <j1 rule="hyper" parents="63 1616 5122"/>
    </justification>
  </clause>

  <clause id="5684">
    <literal><![CDATA[
      x * (y \ T(y * (x \ 1),z)) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(1056(a,1),5122(a,1,2))].">
      <j1 rule="para" parents="1056 5122"/>
    </justification>
  </clause>

  <clause id="5685">
    <literal><![CDATA[
      x \ ((x / y) * K(y \ 1,z)) = T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(613,a,5126,a)].">
      <j1 rule="hyper" parents="613 5126"/>
    </justification>
  </clause>

  <clause id="5689">
    <literal><![CDATA[
      (x * K(y \ 1,x)) / ((x \ (y \ x)) * x) = y
    ]]></literal>
    <justification jstring="[hyper(131,a,5130,a(flip),b,4863,a(flip))].">
      <j1 rule="hyper" parents="131 5130 4863"/>
    </justification>
  </clause>

  <clause id="5690">
    <literal><![CDATA[
      (x * K((x / y) \ 1,x)) / ((x \ y) * x) = x / y
    ]]></literal>
    <justification jstring="[para(83(a,1),5689(a,1,2,1,2))].">
      <j1 rule="para" parents="83 5689"/>
    </justification>
  </clause>

  <clause id="5691">
    <literal><![CDATA[
      (R(x,y,y \ 1) \ (x * y)) * ((x * y) * (y \ 1)) = (x * y) * K((y \ 1) \ 1,(x * y) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(585(a,1),5131(a,1,1,1))].">
      <j1 rule="para" parents="585 5131"/>
    </justification>
  </clause>

  <clause id="5692">
    <literal><![CDATA[
      (x * y) \ (K(x \ 1,z) * y) = T((x * y) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,5132,a)].">
      <j1 rule="hyper" parents="138 5132"/>
    </justification>
  </clause>

  <clause id="5693">
    <literal><![CDATA[
      ((1 / x) * y) * T(((1 / x) * y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[para(83(a,1),5132(a,2,1,1))].">
      <j1 rule="para" parents="83 5132"/>
    </justification>
  </clause>

  <clause id="5694">
    <literal><![CDATA[
      x * (K(x \ 1,y) * (x \ z)) = K(x \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(5128(a,2),5133(a,1,2))].">
      <j1 rule="para" parents="5128 5133"/>
    </justification>
  </clause>

  <clause id="5695">
    <literal><![CDATA[
      K(((x \ 1) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5551,a,b,5214,a)].">
      <j1 rule="hyper" parents="63 5551 5214"/>
    </justification>
  </clause>

  <clause id="5696">
    <literal><![CDATA[
      (R(x,y,z) / (x * x)) \ K(T(x \ (x \ R(x,y,z)),x),x * x) = (((x * x) * (R(x,y,z) / (x * x))) / (x * x)) \ 1
    ]]></literal>
    <justification jstring="[para(3714(a,2),5306(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3714 5306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5697">
    <literal><![CDATA[
      (x * (y * ((z * (y \ (x \ u))) / z))) / u = K(z,((x * y) / u) \ 1)
    ]]></literal>
    <justification jstring="[para(1364(a,1),5396(a,1,1))].">
      <j1 rule="para" parents="1364 5396"/>
    </justification>
  </clause>

  <clause id="5698">
    <literal><![CDATA[
      T(x * ((y * (x \ z)) / y),z) / z = K(y,(T(x,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(2500(a,1),5396(a,1,1))].">
      <j1 rule="para" parents="2500 5396"/>
    </justification>
  </clause>

  <clause id="5699">
    <literal><![CDATA[
      K(x,y \ 1) * (y \ z) = z * ((x * (z \ (y \ z))) / x)
    ]]></literal>
    <justification jstring="[para(80(a,1),5398(a,1,1,2,1))].">
      <j1 rule="para" parents="80 5398"/>
    </justification>
  </clause>

  <clause id="5700">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * ((1 / u) \ K(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(5037(a,2),5421(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5037 5421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5701">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(4862(a,1),5457(a,1,2))].">
      <j1 rule="para" parents="4862 5457"/>
    </justification>
  </clause>

  <clause id="5702">
    <literal><![CDATA[
      T(x,x * y) * (K(y,x) * z) = L(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(5379(a,1),5463(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5379 5463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5703">
    <literal><![CDATA[
      (x * K(y,x \ 1)) * z = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[para(2480(a,1),5500(a,1,1))].">
      <j1 rule="para" parents="2480 5500"/>
    </justification>
  </clause>

  <clause id="5704">
    <literal><![CDATA[
      T(x,y \ (z * (1 / u))) = T(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(132,a,5587,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 5587 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5705">
    <literal><![CDATA[
      K(x,y \ (T(1 / z,u) * w)) = K(x,y \ (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[para(2728(a,1),5588(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2728 5588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5706">
    <literal><![CDATA[
      K(x,y \ (z * ((1 / z) * u))) = K(x,y \ (z * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[para(2925(a,1),5588(a,1,2,2))].">
      <j1 rule="para" parents="2925 5588"/>
    </justification>
  </clause>

  <clause id="5707">
    <literal><![CDATA[
      T(x,y \ ((1 / z) * u)) = T(x,y \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(132,a,5589,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 5589 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5708">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * (z * u))) = K(x,y \ L(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(2939(a,1),5589(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2939 5589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5709">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,T(K(z \ y,z),u))
    ]]></literal>
    <justification jstring="[para(4895(a,1),5592(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4895 5592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5710">
    <literal><![CDATA[
      T(x * ((y / x) * (x \ y)),(x \ y) \ y) = ((x \ y) * (x \ y)) * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(5613(a,1),253(a,1,1))].">
      <j1 rule="para" parents="5613 253"/>
    </justification>
  </clause>

  <clause id="5711">
    <literal><![CDATA[
      (1 / x) * (L(x,x,x) * y) = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(3199(a,2),5616(a,1,2,1))].">
      <j1 rule="para" parents="3199 5616"/>
    </justification>
  </clause>

  <clause id="5712">
    <literal><![CDATA[
      L(x,x,x) * x = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,240,a(flip),b,5711,a),flip(a)].">
      <j1 rule="hyper" parents="128 240 5711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5713">
    <literal><![CDATA[
      x * T(x,x * x) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,4331,a,b,5712,a)].">
      <j1 rule="hyper" parents="63 4331 5712"/>
    </justification>
  </clause>

  <clause id="5714">
    <literal><![CDATA[
      (x * K(x \ y,x)) / ((x \ y) * x) = x / y
    ]]></literal>
    <justification jstring="[para(5530(a,1),5690(a,1,1,2))].">
      <j1 rule="para" parents="5530 5690"/>
    </justification>
  </clause>

  <clause id="5715">
    <literal><![CDATA[
      (x / (x / y)) / ((y \ x) * y) = y / x
    ]]></literal>
    <justification jstring="[para(4894(a,2),5714(a,1,1))].">
      <j1 rule="para" parents="4894 5714"/>
    </justification>
  </clause>

  <clause id="5716">
    <literal><![CDATA[
      x * (((x * y) \ y) * (x * y)) = y / (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(133,a,11,a(flip),b,5715,a)].">
      <j1 rule="hyper" parents="133 11 5715"/>
    </justification>
  </clause>

  <clause id="5717">
    <literal><![CDATA[
      T((x * y) \ y,T(x,z)) = (x * y) \ (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(3104(a,1),5692(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3104 5692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5718">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K((1 / x) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(83(a,1),5694(a,1,2,1,1))].">
      <j1 rule="para" parents="83 5694"/>
    </justification>
  </clause>

  <clause id="5719">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(3407(a,1),5694(a,1,2,1))].">
      <j1 rule="para" parents="3407 5694"/>
    </justification>
  </clause>

  <clause id="5720">
    <literal><![CDATA[
      L(T(x * K(y * z,x),u),z,y) = T((y * (z * x)) / (y * z),u)
    ]]></literal>
    <justification jstring="[para(5071(a,1),25(a,2,1))].">
      <j1 rule="para" parents="5071 25"/>
    </justification>
  </clause>

  <clause id="5721">
    <literal><![CDATA[
      (K(x,y) \ z) \ (K(x,y) \ (z * u)) = L(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(128,a,5256,a,b,5270,a)].">
      <j1 rule="hyper" parents="128 5256 5270"/>
    </justification>
  </clause>

  <clause id="5722">
    <literal><![CDATA[
      L(K(x,y) * (K(z,u) * w),K(y,x),K(u,z)) = (K(u,z) * K(y,x)) \ w
    ]]></literal>
    <justification jstring="[para(5256(a,1),5277(a,1,1))].">
      <j1 rule="para" parents="5256 5277"/>
    </justification>
  </clause>

  <clause id="5723">
    <literal><![CDATA[
      (x * K(y,x)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(5278(a,1),5330(a,1))].">
      <j1 rule="para" parents="5278 5330"/>
    </justification>
  </clause>

  <clause id="5724">
    <literal><![CDATA[
      T((1 / x) * K(y * R(1 / x,x,z),1 / x),y) = R(1 / x,y,z / (x * z))
    ]]></literal>
    <justification jstring="[para(247(a,1),5309(a,2,3))].">
      <j1 rule="para" parents="247 5309"/>
    </justification>
  </clause>

  <clause id="5725">
    <literal><![CDATA[
      K(1 / x,L(x,y,z)) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,2412,a(flip),b,5437,a),flip(a)].">
      <j1 rule="hyper" parents="34 2412 5437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5726">
    <literal><![CDATA[
      L(x * K(y,x),z,u) / L(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,L(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(5437(a,1),3028(a,1,1))].">
      <j1 rule="para" parents="5437 3028"/>
    </justification>
  </clause>

  <clause id="5727">
    <literal><![CDATA[
      L(x / (x / y),z,u) = L(y,z,u) * K(y \ x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(4894(a,2),5437(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4894 5437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5728">
    <literal><![CDATA[
      T(x \ 1,y) * (x * x) = x * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(5517,a,1565,a)].">
      <j1 rule="hyper" parents="5517 1565"/>
    </justification>
  </clause>

  <clause id="5729">
    <literal><![CDATA[
      (x \ 1) * (y \ ((x \ 1) \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * (y \ x) = z
    ]]></literal>
    <justification jstring="[para(2766(a,1),5619(a,1,2))].">
      <j1 rule="para" parents="2766 5619"/>
    </justification>
  </clause>

  <clause id="5730">
    <literal><![CDATA[
      K(x \ y,x) * T(z,x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) \ (z * (x \ y)) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),5639(a,1,2))].">
      <j1 rule="para" parents="22 5639"/>
    </justification>
  </clause>

  <clause id="5732">
    <literal><![CDATA[
      (x \ y) \ K(x \ y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (y / x) \ 1 = z
    ]]></literal>
    <justification jstring="[para(4521(a,1),5639(a,1))].">
      <j1 rule="para" parents="4521 5639"/>
    </justification>
  </clause>

  <clause id="5733">
    <literal><![CDATA[
      (1 / R(x,y,z)) * K(R(x,y,z) \ 1,x) = ((1 / R(x,y,z)) * x) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,5669,a(flip),b,243,a)].">
      <j1 rule="hyper" parents="134 5669 243"/>
    </justification>
  </clause>

  <clause id="5734">
    <literal><![CDATA[
      L(x \ y,x,K(z,u)) = (K(u,z) \ x) \ (K(u,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(1688,a,5721,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="1688 5721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5735">
    <literal><![CDATA[
      L(x \ (y * z),x,K(z,y)) = (K(y,z) \ x) \ (z * y)
    ]]></literal>
    <justification jstring="[para(4907(a,1),5734(a,2,2))].">
      <j1 rule="para" parents="4907 5734"/>
    </justification>
  </clause>

  <clause id="5736">
    <literal><![CDATA[
      L(x \ T(y,z),x,K(y,z)) = (K(z,y) \ x) \ T(T(y,z),z)
    ]]></literal>
    <justification jstring="[para(5102(a,1),5734(a,2,2))].">
      <j1 rule="para" parents="5102 5734"/>
    </justification>
  </clause>

  <clause id="5737">
    <literal><![CDATA[
      (K(x,y) * L(x,z,u)) * w = L(x,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(3579(a,1),5002(a,1,1))].">
      <j1 rule="para" parents="3579 5002"/>
    </justification>
  </clause>

  <clause id="5738">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(4925(a,1),5135(a,1,1,2))].">
      <j1 rule="para" parents="4925 5135"/>
    </justification>
  </clause>

  <clause id="5740">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ ((x * y) * K(y \ 1,z)) = y
    ]]></literal>
    <justification jstring="[hyper(138,a,5738,a)].">
      <j1 rule="hyper" parents="138 5738"/>
    </justification>
  </clause>

  <clause id="5741">
    <literal><![CDATA[
      (x * K(y \ 1,z)) / y = (x / y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,164,a(flip),b,5738,a)].">
      <j1 rule="hyper" parents="131 164 5738"/>
    </justification>
  </clause>

  <clause id="5742">
    <literal><![CDATA[
      R(T(x,y * K(x \ 1,z)),y,K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5740(a,1),1211(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5740 1211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5743">
    <literal><![CDATA[
      (T(x,y \ 1) / y) * K(y \ 1,x) = x / y
    ]]></literal>
    <justification jstring="[para(4915(a,1),5741(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4915 5741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5744">
    <literal><![CDATA[
      (T(x,y \ 1) / y) \ (x / y) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(138,a,5743,a)].">
      <j1 rule="hyper" parents="138 5743"/>
    </justification>
  </clause>

  <clause id="5745">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3626,a,b,5744,a)].">
      <j1 rule="hyper" parents="63 3626 5744"/>
    </justification>
  </clause>

  <clause id="5746">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(11(a,1),5745(a,1,2,2))].">
      <j1 rule="para" parents="11 5745"/>
    </justification>
  </clause>

  <clause id="5747">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(3925,a,5746,a)].">
      <j1 rule="hyper" parents="3925 5746"/>
    </justification>
  </clause>

  <clause id="5748">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5413,a(flip),b,5746,a)].">
      <j1 rule="hyper" parents="63 5413 5746"/>
    </justification>
  </clause>

  <clause id="5749">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(134,a,5747,a(flip),b,5110,a),flip(a)].">
      <j1 rule="hyper" parents="134 5747 5110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5750">
    <literal><![CDATA[
      (x \ 1) * (y / (x \ 1)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(134,a,5748,a(flip),b,5110,a),flip(a)].">
      <j1 rule="hyper" parents="134 5748 5110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5751">
    <literal><![CDATA[
      x * K((1 / y) \ 1,x * (1 / y)) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3429,a(flip),b,5749,a),flip(a)].">
      <j1 rule="hyper" parents="63 3429 5749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5752">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = y * K(1 / x,y * x)
    ]]></literal>
    <justification jstring="[para(3403(a,2),5749(a,2,2))].">
      <j1 rule="para" parents="3403 5749"/>
    </justification>
  </clause>

  <clause id="5753">
    <literal><![CDATA[
      x * (y * K(x \ 1,y * x)) = L(y / (x \ 1),x,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,5750,a(flip),b,3202,a)].">
      <j1 rule="hyper" parents="134 5750 3202"/>
    </justification>
  </clause>

  <clause id="5754">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * K(u \ 1,(1 / z) * u)) * w)) = T(x,y * (((u \ 1) * ((1 / z) / (u \ 1))) * w))
    ]]></literal>
    <justification jstring="[para(5750(a,2),4012(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5750 4012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5755">
    <literal><![CDATA[
      x * K(y,x * (1 / y)) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(83(a,1),5751(a,1,2,1))].">
      <j1 rule="para" parents="83 5751"/>
    </justification>
  </clause>

  <clause id="5756">
    <literal><![CDATA[
      K(x,y * (1 / x)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(34,a,5111,a,b,5755,a),flip(a)].">
      <j1 rule="hyper" parents="34 5111 5755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5758">
    <literal><![CDATA[
      x * K(y,x * (y \ 1)) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(5404(a,1),5755(a,1,2))].">
      <j1 rule="para" parents="5404 5755"/>
    </justification>
  </clause>

  <clause id="5759">
    <literal><![CDATA[
      K(x * (1 / y),y) = 1 / K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(220,a,5756,a(flip),b,5173,a),flip(a)].">
      <j1 rule="hyper" parents="220 5756 5173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5760">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,x) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),5758(a,1,2,2))].">
      <j1 rule="para" parents="12 5758"/>
    </justification>
  </clause>

  <clause id="5761">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,5172,a(flip),b,5759,a),flip(a)].">
      <j1 rule="hyper" parents="347 5172 5759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5762">
    <literal><![CDATA[
      K(x * (1 / y),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(5759(a,2),5178(a,1))].">
      <j1 rule="para" parents="5759 5178"/>
    </justification>
  </clause>

  <clause id="5763">
    <literal><![CDATA[
      K(x * (y \ 1),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(3931,a,5761,a)].">
      <j1 rule="hyper" parents="3931 5761"/>
    </justification>
  </clause>

  <clause id="5764">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,5138,a,b,5761,a),flip(a)].">
      <j1 rule="hyper" parents="347 5138 5761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5765">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,4458,a,b,5761,a)].">
      <j1 rule="hyper" parents="347 4458 5761"/>
    </justification>
  </clause>

  <clause id="5766">
    <literal><![CDATA[
      K(((1 / x) \ y) * (1 / x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,4457,a(flip),b,5761,a),flip(a)].">
      <j1 rule="hyper" parents="347 4457 5761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5767">
    <literal><![CDATA[
      K(x \ y,x) * (y * (1 / x)) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(133,a,5761,a(flip),b,4969,a(flip))].">
      <j1 rule="hyper" parents="133 5761 4969"/>
    </justification>
  </clause>

  <clause id="5768">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(80(a,1),5761(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="80 5761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5769">
    <literal><![CDATA[
      x * K(x * (y \ 1),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,5763,a,b,92,a)].">
      <j1 rule="hyper" parents="134 5763 92"/>
    </justification>
  </clause>

  <clause id="5770">
    <literal><![CDATA[
      K(x / (1 / y),1 / y) = K(x * y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(3926,a,5764,a),flip(a)].">
      <j1 rule="hyper" parents="3926 5764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5771">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,1 / x) = K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3875,a(flip),b,5765,a),flip(a)].">
      <j1 rule="hyper" parents="347 3875 5765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5772">
    <literal><![CDATA[
      K(T(x,1 / y) / y,y) = K(x / y,y)
    ]]></literal>
    <justification jstring="[para(1172(a,1),5766(a,1,1))].">
      <j1 rule="para" parents="1172 5766"/>
    </justification>
  </clause>

  <clause id="5773">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = y * K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[para(83(a,1),5769(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="83 5769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5774">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = y * K(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3876(a,1),5769(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3876 5769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5775">
    <literal><![CDATA[
      K(T(x / (1 / (1 / y)),1 / (1 / y)) / (1 / y),1 / y) = K((x / y) / (y \ 1),1 / y)
    ]]></literal>
    <justification jstring="[para(2362(a,1),5772(a,2,1))].">
      <j1 rule="para" parents="2362 5772"/>
    </justification>
  </clause>

  <clause id="5776">
    <literal><![CDATA[
      K(x * y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K((y \ 1) \ x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(80(a,1),5762(a,1,1,2))].">
      <j1 rule="para" parents="80 5762"/>
    </justification>
  </clause>

  <clause id="5777">
    <literal><![CDATA[
      K(x * y,y \ 1) = K(y * x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,4459,a(flip),b,5768,a),flip(a)].">
      <j1 rule="hyper" parents="63 4459 5768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5778">
    <literal><![CDATA[
      K(1 / x,y / (1 / x)) = K(1 / x,y * x)
    ]]></literal>
    <justification jstring="[hyper(34,a,331,a,b,5752,a(flip))].">
      <j1 rule="hyper" parents="34 331 5752"/>
    </justification>
  </clause>

  <clause id="5779">
    <literal><![CDATA[
      K((x \ y) * x,1 / x) = K(y,1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3911,a(flip),b,5771,a),flip(a)].">
      <j1 rule="hyper" parents="63 3911 5771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5780">
    <literal><![CDATA[
      (x \ y) * (K(y,z) * K(y,z)) = x \ T(T(y,z),z)
    ]]></literal>
    <justification jstring="[para(5148(a,1),5165(a,2,2))].">
      <j1 rule="para" parents="5148 5165"/>
    </justification>
  </clause>

  <clause id="5781">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * z) = y * (T(T(y,x),x) \ z)
    ]]></literal>
    <justification jstring="[para(5095(a,1),5220(a,1,2,1))].">
      <j1 rule="para" parents="5095 5220"/>
    </justification>
  </clause>

  <clause id="5782">
    <literal><![CDATA[
      K(x,x * y) * (R(y,z,u) * x) = R(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(4337,a,5239,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4337 5239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5783">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) = 1 / (x \ K(y,1 / x))
    ]]></literal>
    <justification jstring="[para(3899(a,1),5377(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3899 5377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5784">
    <literal><![CDATA[
      K(x,((y * z) / y) \ 1) = (y * K(x,z \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,5399,a(flip),b,5398,a),flip(a)].">
      <j1 rule="hyper" parents="131 5399 5398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5785">
    <literal><![CDATA[
      (x * y) * (x / (x * y)) = x * K(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),5399(a,1,2,1))].">
      <j1 rule="para" parents="10 5399"/>
    </justification>
  </clause>

  <clause id="5786">
    <literal><![CDATA[
      (x * y) * (z * (L(y \ z,y,x) / z)) = (x * K(z,y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(5399(a,1),2455(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5399 2455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5787">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = x * K(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(83(a,1),5785(a,2,2,2))].">
      <j1 rule="para" parents="83 5785"/>
    </justification>
  </clause>

  <clause id="5788">
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ y))) / z)) = K(z,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(1365,a,5400,a)].">
      <j1 rule="hyper" parents="1365 5400"/>
    </justification>
  </clause>

  <clause id="5789">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(5433,a,27,a(flip))].">
      <j1 rule="hyper" parents="5433 27"/>
    </justification>
  </clause>

  <clause id="5792">
    <literal><![CDATA[
      (K(x,y) * R(y,z,u)) * w = R(y,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(3038(a,1),5464(a,1,1))].">
      <j1 rule="para" parents="3038 5464"/>
    </justification>
  </clause>

  <clause id="5793">
    <literal><![CDATA[
      K(x,y * ((z / u) * (K(u,u \ z) * (1 / w)))) = K(x,y * (((u * (z / u)) / u) * (w \ 1)))
    ]]></literal>
    <justification jstring="[para(5485(a,2),5418(a,1,2,2))].">
      <j1 rule="para" parents="5485 5418"/>
    </justification>
  </clause>

  <clause id="5794">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) = x \ (((y \ (x / z)) * y) * z)
    ]]></literal>
    <justification jstring="[para(3721(a,1),5560(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3721 5560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5795">
    <literal><![CDATA[
      x \ (((y \ (x / z)) * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(5562(a,2),356(a,1,2))].">
      <j1 rule="para" parents="5562 356"/>
    </justification>
  </clause>

  <clause id="5796">
    <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),5563(a,2,2))].">
      <j1 rule="para" parents="27 5563"/>
    </justification>
  </clause>

  <clause id="5798">
    <literal><![CDATA[
      K(x / y,(x / y) \ x) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,5492,a(flip),b,5610,a),flip(a)].">
      <j1 rule="hyper" parents="35 5492 5610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5800">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = ((y * ((x \ y) \ y)) / y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(112(a,2),5617(a,1,2,2,1))].">
      <j1 rule="para" parents="112 5617"/>
    </justification>
  </clause>

  <clause id="5801">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(347,a,68,a(flip),b,5642,a),flip(a)].">
      <j1 rule="hyper" parents="347 68 5642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5802">
    <literal><![CDATA[
      T(x \ R(x,y,z),R(x,u,w)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(5039,a,5801,a)].">
      <j1 rule="hyper" parents="5039 5801"/>
    </justification>
  </clause>

  <clause id="5804">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5226,a(flip),b,5683,a),flip(a)].">
      <j1 rule="hyper" parents="63 5226 5683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5805">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) * (x \ 1) = K((y * (x \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(5127(a,1),5683(a,1,1))].">
      <j1 rule="para" parents="5127 5683"/>
    </justification>
  </clause>

  <clause id="5806">
    <literal><![CDATA[
      K(x \ y,y) / (y \ T(y * (x \ 1),y)) = x
    ]]></literal>
    <justification jstring="[hyper(131,a,5804,a(flip),b,5684,a)].">
      <j1 rule="hyper" parents="131 5804 5684"/>
    </justification>
  </clause>

  <clause id="5807">
    <literal><![CDATA[
      K(((1 / x) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[para(83(a,1),5684(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="83 5684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5808">
    <literal><![CDATA[
      x * (y \ K((y * (x \ 1)) \ 1,z)) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(5684(a,1),75(a,1,2,2))].">
      <j1 rule="para" parents="5684 75"/>
    </justification>
  </clause>

  <clause id="5809">
    <literal><![CDATA[
      K(x,((y \ 1) / (z / y)) \ 1) * (T(z,x) / y) = z / y
    ]]></literal>
    <justification jstring="[hyper(5285,a,5695,a)].">
      <j1 rule="hyper" parents="5285 5695"/>
    </justification>
  </clause>

  <clause id="5810">
    <literal><![CDATA[
      T((x * y) \ y,T(x,z)) = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,5692,a(flip),b,5717,a),flip(a)].">
      <j1 rule="hyper" parents="347 5692 5717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5811">
    <literal><![CDATA[
      x * (K(y,x \ 1) * (x \ z)) = K(y,x \ 1) * z
    ]]></literal>
    <justification jstring="[para(5699(a,2),5788(a,1,2))].">
      <j1 rule="para" parents="5699 5788"/>
    </justification>
  </clause>

  <clause id="5812">
    <literal><![CDATA[
      K(x,y \ 1) * (y * z) = y * (K(x,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5811(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 5811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5814">
    <literal><![CDATA[
      1 \ (x * (K(y,x \ 1) * z)) = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,66,a,b,5812,a)].">
      <j1 rule="hyper" parents="347 66 5812"/>
    </justification>
  </clause>

  <clause id="5815">
    <literal><![CDATA[
      (x * K(y,x \ 1)) * z = x * (K(y,x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5703,a,b,5812,a)].">
      <j1 rule="hyper" parents="63 5703 5812"/>
    </justification>
  </clause>

  <clause id="5817">
    <literal><![CDATA[
      L(x,K(y,z \ 1),z) = x
    ]]></literal>
    <justification jstring="[hyper(544,a,5815,a)].">
      <j1 rule="hyper" parents="544 5815"/>
    </justification>
  </clause>

  <clause id="5818">
    <literal><![CDATA[
      L(x,K(y \ 1,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(5182,a,5817,a)].">
      <j1 rule="hyper" parents="5182 5817"/>
    </justification>
  </clause>

  <clause id="5819">
    <literal><![CDATA[
      L(x,K(y,z),z \ 1) = x
    ]]></literal>
    <justification jstring="[para(3152(a,1),5817(a,1,2))].">
      <j1 rule="para" parents="3152 5817"/>
    </justification>
  </clause>

  <clause id="5820">
    <literal><![CDATA[
      L(x,K(y,z),u / (z * u)) = x
    ]]></literal>
    <justification jstring="[para(5624(a,1),5817(a,1,2))].">
      <j1 rule="para" parents="5624 5817"/>
    </justification>
  </clause>

  <clause id="5821">
    <literal><![CDATA[
      L(x,K(y,z),1 / y) = x
    ]]></literal>
    <justification jstring="[para(83(a,1),5818(a,1,2,1))].">
      <j1 rule="para" parents="83 5818"/>
    </justification>
  </clause>

  <clause id="5822">
    <literal><![CDATA[
      ((x \ 1) * K(y,x)) \ z = K(y,x) \ ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(623,a,5819,a),flip(a)].">
      <j1 rule="hyper" parents="623 5819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5823">
    <literal><![CDATA[
      ((x / (y * x)) * K(z,y)) \ u = K(y,z) * ((x / (y * x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5278,a(flip),b,5820,a)].">
      <j1 rule="hyper" parents="63 5278 5820"/>
    </justification>
  </clause>

  <clause id="5824">
    <literal><![CDATA[
      K(x,y) \ ((y \ 1) \ z) = (y \ K(x,y)) \ z
    ]]></literal>
    <justification jstring="[para(4547(a,1),5822(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4547 5822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5825">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ z) = (x \ K(y,x)) \ z
    ]]></literal>
    <justification jstring="[hyper(5286,a,5824,a)].">
      <j1 rule="hyper" parents="5286 5824"/>
    </justification>
  </clause>

  <clause id="5826">
    <literal><![CDATA[
      (x \ K(y,x)) \ L((x \ 1) * z,u,w) = K(x,y) * (x * L(x \ z,u,w))
    ]]></literal>
    <justification jstring="[para(3172(a,1),5825(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3172 5825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5827">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ z) = (T(x,y) \ 1) \ z
    ]]></literal>
    <justification jstring="[para(4934(a,2),5825(a,2,1))].">
      <j1 rule="para" parents="4934 5825"/>
    </justification>
  </clause>

  <clause id="5828">
    <literal><![CDATA[
      R(x,y,z) * (K(u,x) * w) != v5 * (R(x,y,z) * w)
    ]]></literal>
    <literal><![CDATA[
      R(K(u,x),R(x,y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(5792(a,1),594(a,1))].">
      <j1 rule="para" parents="5792 594"/>
    </justification>
  </clause>

  <clause id="5829">
    <literal><![CDATA[
      x * (y \ K(y \ x,x)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[para(5804(a,1),5808(a,1,2,2))].">
      <j1 rule="para" parents="5804 5808"/>
    </justification>
  </clause>

  <clause id="5830">
    <literal><![CDATA[
      ((x * (K(y \ x,x) * (y \ 1))) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(5829(a,1),1789(a,2,2,1))].">
      <j1 rule="para" parents="5829 1789"/>
    </justification>
  </clause>

  <clause id="5831">
    <literal><![CDATA[
      T(x \ y,z) \ T((x \ y) * (y \ x),z) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,2139,a,b,5043,a)].">
      <j1 rule="hyper" parents="63 2139 5043"/>
    </justification>
  </clause>

  <clause id="5832">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(T(x,w),y,z) * u) != v5
    ]]></literal>
    <literal><![CDATA[
      K(w,R(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(5236(a,1),5276(a,1,2))].">
      <j1 rule="para" parents="5236 5276"/>
    </justification>
  </clause>

  <clause id="5833">
    <literal><![CDATA[
      (L(x,y,z) \ u) / (L(T(x,w),y,z) \ u) = K(L(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(220,a,5343,a(flip),b,5256,a)].">
      <j1 rule="hyper" parents="220 5343 5256"/>
    </justification>
  </clause>

  <clause id="5834">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(3873(a,1),5378(a,1,1,1))].">
      <j1 rule="para" parents="3873 5378"/>
    </justification>
  </clause>

  <clause id="5835">
    <literal><![CDATA[
      K(x,y / (x / (z \ 1))) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[hyper(5649,a,5701,a),flip(a)].">
      <j1 rule="hyper" parents="5649 5701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5836">
    <literal><![CDATA[
      R(K(x \ y,x),y,z) = K(((x * z) / (y * z)) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5530(a,1),5676(a,1,1))].">
      <j1 rule="para" parents="5530 5676"/>
    </justification>
  </clause>

  <clause id="5837">
    <literal><![CDATA[
      R(K(x \ (y / z),x),y / z,z) = K(((x * z) / y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),5836(a,2,1,1,2))].">
      <j1 rule="para" parents="12 5836"/>
    </justification>
  </clause>

  <clause id="5838">
    <literal><![CDATA[
      L(L(x / (x / y),z,u),w,v5) \ L(L(y,z,u),w,v5) = K(L(L(y,z,u),w,v5),y \ x)
    ]]></literal>
    <justification jstring="[para(5727(a,2),5544(a,1,1,1))].">
      <j1 rule="para" parents="5727 5544"/>
    </justification>
  </clause>

  <clause id="5839">
    <literal><![CDATA[
      L(x \ (y * z),x,K(T(y,y * z) * z,y)) = (K(y,T(y,y * z) * z) \ x) \ T(T(T(y,y * z) * z,y),y)
    ]]></literal>
    <justification jstring="[para(4189(a,1),5736(a,1,1,2))].">
      <j1 rule="para" parents="4189 5736"/>
    </justification>
  </clause>

  <clause id="5840">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,2198,a(flip),b,5834,a),flip(a)].">
      <j1 rule="hyper" parents="347 2198 5834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5841">
    <literal><![CDATA[
      R(K(x \ (y / z),x),y / z,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / (x * z),x) = u
    ]]></literal>
    <justification jstring="[para(5837(a,2),5644(a,1))].">
      <j1 rule="para" parents="5837 5644"/>
    </justification>
  </clause>

  <clause id="5842">
    <literal><![CDATA[
      T(x * y,z) / (y * x) = (y * x) \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(91(a,1),4917(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="91 4917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5843">
    <literal><![CDATA[
      T(x * L(x \ 1,y,z),u) != T(x,u) * w
    ]]></literal>
    <literal><![CDATA[
      L(x \ K(u,x),y,z) = w
    ]]></literal>
    <justification jstring="[para(5046(a,1),43(a,1))].">
      <j1 rule="para" parents="5046 43"/>
    </justification>
  </clause>

  <clause id="5844">
    <literal><![CDATA[
      (x * y) * K(R(y,x,y),x * y) = ((y * x) / R(y,x,y)) * y
    ]]></literal>
    <justification jstring="[hyper(1710,a,5060,a),flip(a)].">
      <j1 rule="hyper" parents="1710 5060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5845">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(472(a,1),5225(a,1,1))].">
      <j1 rule="para" parents="472 5225"/>
    </justification>
  </clause>

  <clause id="5846">
    <literal><![CDATA[
      K(R(x,y,z),u) * ((x * y) * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(148,a,5845,a)].">
      <j1 rule="hyper" parents="148 5845"/>
    </justification>
  </clause>

  <clause id="5847">
    <literal><![CDATA[
      ((x * y) * z) / ((T(x,u) * y) * z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(220,a,5846,a(flip),b,5256,a)].">
      <j1 rule="hyper" parents="220 5846 5256"/>
    </justification>
  </clause>

  <clause id="5848">
    <literal><![CDATA[
      a(x,y * K(z \ 1,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(5287(a,2),2804(a,1)),flip(b)].">
      <j1 rule="para" parents="5287 2804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5849">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(1960(a,1),5848(a,1,2,2))].">
      <j1 rule="para" parents="1960 5848"/>
    </justification>
  </clause>

  <clause id="5850">
    <literal><![CDATA[
      a(x,(y \ 1) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(2334(a,1),5849(a,1,2))].">
      <j1 rule="para" parents="2334 5849"/>
    </justification>
  </clause>

  <clause id="5851">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = (x * (K(z,u) * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(5193(a,1),5392(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5193 5392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5852">
    <literal><![CDATA[
      K(x,y) * (z * K((z \ K(y,x)) \ 1,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(5273,a,5568,a)].">
      <j1 rule="hyper" parents="5273 5568"/>
    </justification>
  </clause>

  <clause id="5853">
    <literal><![CDATA[
      K(x,y * ((z \ L(u,1 / z,z)) * w)) = K(x,y * (((1 / z) * u) * w))
    ]]></literal>
    <justification jstring="[para(2952(a,1),5636(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2952 5636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5854">
    <literal><![CDATA[
      T(((x * y) / x) * (y \ z),z) / z = K(x,(T(y \ z,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(1117(a,1),5698(a,1,1,1))].">
      <j1 rule="para" parents="1117 5698"/>
    </justification>
  </clause>

  <clause id="5855">
    <literal><![CDATA[
      K(x,y \ (z * ((1 / z) * u))) = K(x,y \ L(u,z,z))
    ]]></literal>
    <justification jstring="[para(3197(a,1),5706(a,2,2,2))].">
      <j1 rule="para" parents="3197 5706"/>
    </justification>
  </clause>

  <clause id="5856">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(83(a,1),5718(a,2,1,1))].">
      <j1 rule="para" parents="83 5718"/>
    </justification>
  </clause>

  <clause id="5857">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5856(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 5856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5859">
    <literal><![CDATA[
      (K(x,y) * ((1 / x) * z)) / (K(x,y) * z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(652,a,5857,a)].">
      <j1 rule="hyper" parents="652 5857"/>
    </justification>
  </clause>

  <clause id="5860">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,y) * ((1 / x) * z)) = T(1 / x,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(462,a,5857,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="462 5857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5861">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) = u
    ]]></literal>
    <justification jstring="[para(5859(a,1),280(a,1,1))].">
      <j1 rule="para" parents="5859 280"/>
    </justification>
  </clause>

  <clause id="5862">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(3407(a,1),5719(a,2,1))].">
      <j1 rule="para" parents="3407 5719"/>
    </justification>
  </clause>

  <clause id="5863">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ T(y,x)) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(128,a,4931,a(flip),b,5862,a),flip(a)].">
      <j1 rule="hyper" parents="128 4931 5862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5864">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) = (x \ 1) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5862(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 5862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5865">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = T(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(220,a,5863,a(flip),b,5827,a(flip))].">
      <j1 rule="hyper" parents="220 5863 5827"/>
    </justification>
  </clause>

  <clause id="5866">
    <literal><![CDATA[
      (x \ ((y \ 1) \ x)) * x = (T(y,x) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(5865(a,1),4473(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5865 4473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5867">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ y = (y \ (x \ y)) * y
    ]]></literal>
    <justification jstring="[para(83(a,1),5866(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 5866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5868">
    <literal><![CDATA[
      x / ((x \ (y \ x)) * x) = T(1 / y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(222,a,5867,a)].">
      <j1 rule="hyper" parents="222 5867"/>
    </justification>
  </clause>

  <clause id="5869">
    <literal><![CDATA[
      T(1 / (x / y),x) \ 1 = x / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(83(a,1),5868(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="83 5868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5870">
    <literal><![CDATA[
      x * (K(x,y) * ((x \ 1) * z)) = L(K(x,y) * z,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,5864,a,b,455,a)].">
      <j1 rule="hyper" parents="134 5864 455"/>
    </justification>
  </clause>

  <clause id="5871">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ 1) * (K(x,z) * y)) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(220,a,5864,a(flip),b,5256,a)].">
      <j1 rule="hyper" parents="220 5864 5256"/>
    </justification>
  </clause>

  <clause id="5872">
    <literal><![CDATA[
      ((x \ 1) * (K(y,x) * z)) / ((x \ 1) * z) = K(y,x)
    ]]></literal>
    <justification jstring="[para(5261(a,1),5871(a,1,2,2))].">
      <j1 rule="para" parents="5261 5871"/>
    </justification>
  </clause>

  <clause id="5873">
    <literal><![CDATA[
      L(K(x,y) * z,x \ 1,x) = T(x,y) * ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(5326,a,5870,a),flip(a)].">
      <j1 rule="hyper" parents="5326 5870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5874">
    <literal><![CDATA[
      L(K(x,y) * z,x,x) = T(x,y) * ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(3524,a,5873,a)].">
      <j1 rule="hyper" parents="3524 5873"/>
    </justification>
  </clause>

  <clause id="5875">
    <literal><![CDATA[
      T(x,y) * ((x \ 1) * (K(y,x) * z)) = L(z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(5261(a,1),5873(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5261 5873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5876">
    <literal><![CDATA[
      L(K(x,y) * L((x \ 1) \ ((x \ 1) \ z),u,w),x,x) = T(x,y) * ((x \ 1) \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(3341(a,1),5874(a,2,2))].">
      <j1 rule="para" parents="3341 5874"/>
    </justification>
  </clause>

  <clause id="5877">
    <literal><![CDATA[
      K(R(x,R(y,z,u),x),R(x,R(y,z,u),x) * y) * T(x * R(y,z,u),x) = R(y,z,u) * T(R(x,R(y,z,u),x),R(x,R(y,z,u),x) * y)
    ]]></literal>
    <justification jstring="[para(4378(a,1),5782(a,1,2))].">
      <j1 rule="para" parents="4378 5782"/>
    </justification>
  </clause>

  <clause id="5878">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = x * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(5761(a,1),5787(a,2,2))].">
      <j1 rule="para" parents="5761 5787"/>
    </justification>
  </clause>

  <clause id="5879">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(347,a,330,a(flip),b,5878,a),flip(a)].">
      <j1 rule="hyper" parents="347 330 5878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5880">
    <literal><![CDATA[
      K((x * ((1 / y) \ 1)) \ 1,z) / y = (1 / y) * K(((1 / y) \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(377,a,5805,a)].">
      <j1 rule="hyper" parents="377 5805"/>
    </justification>
  </clause>

  <clause id="5881">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ y,z)) * (y \ 1) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5683,a,b,5807,a)].">
      <j1 rule="hyper" parents="63 5683 5807"/>
    </justification>
  </clause>

  <clause id="5882">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = (y * x) * K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(5149(a,1),5844(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5149 5844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5883">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = T(x,y * x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,5048,a(flip),b,5882,a),flip(a)].">
      <j1 rule="hyper" parents="347 5048 5882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5884">
    <literal><![CDATA[
      T(x,(x \ y) * x) * T(x \ y,x) = (y / R(x,x \ y,x)) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),5883(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5885">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * (K(u,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(5285,a,5851,a)].">
      <j1 rule="hyper" parents="5285 5851"/>
    </justification>
  </clause>

  <clause id="5886">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * T(K(y,x) \ z,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5127(a,2),5852(a,1,2))].">
      <j1 rule="para" parents="5127 5852"/>
    </justification>
  </clause>

  <clause id="5887">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,x)),u) = K(x,y) * (T(z,u) * K(y,x))
    ]]></literal>
    <justification jstring="[para(5564(a,1),5852(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5564 5852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5888">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * (K(y,x) * w)) = R(y,z,u) * w
    ]]></literal>
    <justification jstring="[para(1748(a,1),5885(a,1,1,2))].">
      <j1 rule="para" parents="1748 5885"/>
    </justification>
  </clause>

  <clause id="5889">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(z,(x * u) / (x * (y \ u)))) = (x * u) \ (K(z,(x * u) / (x * (y \ u))) * ((x * K(y,z)) * u))
    ]]></literal>
    <justification jstring="[para(5885(a,1),567(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5885 567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5890">
    <literal><![CDATA[
      R(x,y,z) * (K(x,u) * w) = K(x,u) * (R(x,y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(5273,a,5888,a),flip(a)].">
      <j1 rule="hyper" parents="5273 5888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5891">
    <literal><![CDATA[
      R(x,y,z) * (K(u,x) * w) = K(u,x) * (R(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(5261(a,1),5888(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5261 5888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5892">
    <literal><![CDATA[
      K(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,73,a(flip),b,5890,a),flip(a)].">
      <j1 rule="hyper" parents="128 73 5890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5893">
    <literal><![CDATA[
      K(x,y) \ T(K(x,y) * z,u) = K(y,x) * T(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(138,a,5886,a)].">
      <j1 rule="hyper" parents="138 5886"/>
    </justification>
  </clause>

  <clause id="5894">
    <literal><![CDATA[
      (K(x,y) * T(K(x,y) \ z,u)) * K(y,x) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(133,a,5893,a(flip),b,4814,a)].">
      <j1 rule="hyper" parents="133 5893 4814"/>
    </justification>
  </clause>

  <clause id="5895">
    <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),5894(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 5894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5896">
    <literal><![CDATA[
      L(K(x \ y,x) * z,K(x,x \ y),y) = (x * (y / x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(5261(a,1),5316(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5261 5316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5897">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      y * (T(T(y,x),x) \ z) = u
    ]]></literal>
    <justification jstring="[para(5095(a,1),5518(a,1,2,1))].">
      <j1 rule="para" parents="5095 5518"/>
    </justification>
  </clause>

  <clause id="5898">
    <literal><![CDATA[
      K(x * y,(x * y) \ y) = K(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(5522,a,5774,a)].">
      <j1 rule="hyper" parents="5522 5774"/>
    </justification>
  </clause>

  <clause id="5899">
    <literal><![CDATA[
      K(x,x * y) * (L(y,z,u) * x) = L(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5647,a,4336,a)].">
      <j1 rule="hyper" parents="5647 4336"/>
    </justification>
  </clause>

  <clause id="5901">
    <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(4378(a,1),5899(a,1,2))].">
      <j1 rule="para" parents="4378 5899"/>
    </justification>
  </clause>

  <clause id="5902">
    <literal><![CDATA[
      (x * (y * T(z,u))) / (x * y) = T((x * (y * z)) / (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5435,a(flip),b,5720,a)].">
      <j1 rule="hyper" parents="63 5435 5720"/>
    </justification>
  </clause>

  <clause id="5903">
    <literal><![CDATA[
      T((x * (y * z)) / (x * y),y) = (x * (z * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(111(a,1),5902(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="111 5902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5904">
    <literal><![CDATA[
      T((x * (y * z)) / (x * y),y) != u / (x * y)
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(5903(a,2),46(a,1))].">
      <j1 rule="para" parents="5903 46"/>
    </justification>
  </clause>

  <clause id="5905">
    <literal><![CDATA[
      (x * y) * L(z * ((y \ z) / z),y,x) = (x * K(z,y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3159(a,2),5786(a,1,2))].">
      <j1 rule="para" parents="3159 5786"/>
    </justification>
  </clause>

  <clause id="5906">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(5794(a,2),5795(a,1))].">
      <j1 rule="para" parents="5794 5795"/>
    </justification>
  </clause>

  <clause id="5907">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y = T(y,x) * T(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4325(a,1),5884(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4325 5884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5908">
    <literal><![CDATA[
      x * (y * (z * ((y \ z) / z))) = (x * K(z,y \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(322,a,5905,a)].">
      <j1 rule="hyper" parents="322 5905"/>
    </justification>
  </clause>

  <clause id="5909">
    <literal><![CDATA[
      (x * K(y,z \ 1)) * y = x * T(y,z \ 1)
    ]]></literal>
    <justification jstring="[para(3840(a,1),5908(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3840 5908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5912">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,(z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3885(a,1),5909(a,1,1,2))].">
      <j1 rule="para" parents="3885 5909"/>
    </justification>
  </clause>

  <clause id="5914">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(2966(a,1),5912(a,2,2))].">
      <j1 rule="para" parents="2966 5912"/>
    </justification>
  </clause>

  <clause id="5915">
    <literal><![CDATA[
      R(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(5034,a,5914,a)].">
      <j1 rule="hyper" parents="5034 5914"/>
    </justification>
  </clause>

  <clause id="5916">
    <literal><![CDATA[
      T(x * K(y,z),y) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(462,a,xx,b,5914,a)].">
      <j1 rule="hyper" parents="462 5914"/>
    </justification>
  </clause>

  <clause id="5917">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * y = T(y,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3036,a,b,5914,a),flip(a)].">
      <j1 rule="hyper" parents="347 3036 5914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5919">
    <literal><![CDATA[
      (x * T(y,z)) / y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,5914,a)].">
      <j1 rule="hyper" parents="145 5914"/>
    </justification>
  </clause>

  <clause id="5920">
    <literal><![CDATA[
      (1 / x) * K(x,y) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,4968,a,b,5914,a),flip(a)].">
      <j1 rule="hyper" parents="131 4968 5914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5922">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(131,a,12,a(flip),b,5914,a),flip(a)].">
      <j1 rule="hyper" parents="131 12 5914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5923">
    <literal><![CDATA[
      ((x * y) * K(L(z,y,x),u)) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,477,a(flip),b,5914,a)].">
      <j1 rule="hyper" parents="128 477 5914"/>
    </justification>
  </clause>

  <clause id="5924">
    <literal><![CDATA[
      (x * y) * K(T(x,y),z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(35,a,1652,a,b,5914,a),flip(a)].">
      <j1 rule="hyper" parents="35 1652 5914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5925">
    <literal><![CDATA[
      (x / y) * T(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,1503,a,b,5914,a)].">
      <j1 rule="hyper" parents="35 1503 5914"/>
    </justification>
  </clause>

  <clause id="5926">
    <literal><![CDATA[
      (x * y) * K(y,z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,1499,a,b,5914,a),flip(a)].">
      <j1 rule="hyper" parents="35 1499 5914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5927">
    <literal><![CDATA[
      (x * (y / z)) * K(y / z,z) = x * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1508,a(flip),b,5914,a),flip(a)].">
      <j1 rule="hyper" parents="35 1508 5914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5928">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ ((x * (y * K(z,u))) * z) = a(x,y * K(z,u),z)
    ]]></literal>
    <justification jstring="[para(5914(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5914 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5929">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = y
    ]]></literal>
    <justification jstring="[para(5914(a,1),358(a,1,2))].">
      <j1 rule="para" parents="5914 358"/>
    </justification>
  </clause>

  <clause id="5930">
    <literal><![CDATA[
      x * T(y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      T(x * K(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(5914(a,1),270(a,2)),flip(a)].">
      <j1 rule="para" parents="5914 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5931">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x * K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(5914(a,1),443(a,1,1))].">
      <j1 rule="para" parents="5914 443"/>
    </justification>
  </clause>

  <clause id="5932">
    <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(5914(a,1),545(a,1,2,2))].">
      <j1 rule="para" parents="5914 545"/>
    </justification>
  </clause>

  <clause id="5934">
    <literal><![CDATA[
      (T(x,y) \ 1) * y = (x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(4927(a,1),5914(a,1,1))].">
      <j1 rule="para" parents="4927 5914"/>
    </justification>
  </clause>

  <clause id="5936">
    <literal><![CDATA[
      (x / y) \ (x * K(y,z)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,5919,a(flip),b,1505,a(flip))].">
      <j1 rule="hyper" parents="128 5919 1505"/>
    </justification>
  </clause>

  <clause id="5937">
    <literal><![CDATA[
      (K(x,y) / x) * L(z,K(x,y),1 / x) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,5920,a(flip),b,212,a)].">
      <j1 rule="hyper" parents="133 5920 212"/>
    </justification>
  </clause>

  <clause id="5938">
    <literal><![CDATA[
      T(x / T(y,z),K(y,z)) = K(z,y) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(269,a,5922,a,b,5261,a)].">
      <j1 rule="hyper" parents="269 5922 5261"/>
    </justification>
  </clause>

  <clause id="5939">
    <literal><![CDATA[
      (x / ((y * y) \ y)) * K(y \ 1,y) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(518(a,1),5922(a,1,1,2))].">
      <j1 rule="para" parents="518 5922"/>
    </justification>
  </clause>

  <clause id="5940">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(681,a,5925,a)].">
      <j1 rule="hyper" parents="681 5925"/>
    </justification>
  </clause>

  <clause id="5941">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(370,a,5925,a)].">
      <j1 rule="hyper" parents="370 5925"/>
    </justification>
  </clause>

  <clause id="5942">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ z) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,338,a(flip),b,5925,a)].">
      <j1 rule="hyper" parents="63 338 5925"/>
    </justification>
  </clause>

  <clause id="5943">
    <literal><![CDATA[
      (x * K(y,z)) / y = (x / y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,5925,a(flip),b,5914,a)].">
      <j1 rule="hyper" parents="131 5925 5914"/>
    </justification>
  </clause>

  <clause id="5944">
    <literal><![CDATA[
      (x * K(y,z)) / (x / y) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(131,a,5925,a(flip),b,487,a)].">
      <j1 rule="hyper" parents="131 5925 487"/>
    </justification>
  </clause>

  <clause id="5945">
    <literal><![CDATA[
      ((x / y) * K(y,z)) \ (x * K(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(128,a,5925,a(flip),b,5914,a)].">
      <j1 rule="hyper" parents="128 5925 5914"/>
    </justification>
  </clause>

  <clause id="5946">
    <literal><![CDATA[
      x \ (y * K(x \ y,z)) = T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,5925,a(flip),b,208,a(flip))].">
      <j1 rule="hyper" parents="128 5925 208"/>
    </justification>
  </clause>

  <clause id="5947">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,u) = R(x,y,z) * T(y * z,u)
    ]]></literal>
    <justification jstring="[para(20(a,2),5925(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20 5925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5948">
    <literal><![CDATA[
      x * K(y \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5925(a,1),370(a,1))].">
      <j1 rule="para" parents="5925 370"/>
    </justification>
  </clause>

  <clause id="5949">
    <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(5925(a,1),1137(a,1,2,1))].">
      <j1 rule="para" parents="5925 1137"/>
    </justification>
  </clause>

  <clause id="5950">
    <literal><![CDATA[
      R(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(5008,a,5926,a)].">
      <j1 rule="hyper" parents="5008 5926"/>
    </justification>
  </clause>

  <clause id="5951">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = T(z * x,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(462,a,xx,b,5926,a),flip(a)].">
      <j1 rule="hyper" parents="462 5926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5953">
    <literal><![CDATA[
      (T(x,y) * T(y,x)) * K(T(y,x),z) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,4287,a(flip),b,5926,a),flip(a)].">
      <j1 rule="hyper" parents="347 4287 5926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5954">
    <literal><![CDATA[
      (x * y) * K(y,y \ z) = x * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,338,a(flip),b,5926,a),flip(a)].">
      <j1 rule="hyper" parents="347 338 5926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5955">
    <literal><![CDATA[
      K(x,y) * (z * T(y,x)) = T(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(269,a,5926,a,b,5261,a),flip(a)].">
      <j1 rule="hyper" parents="269 5926 5261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5956">
    <literal><![CDATA[
      (x * y) \ (x * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,5926,a)].">
      <j1 rule="hyper" parents="138 5926"/>
    </justification>
  </clause>

  <clause id="5957">
    <literal><![CDATA[
      x * ((y * z) * K(z,x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,5926,a,b,735,a)].">
      <j1 rule="hyper" parents="134 5926 735"/>
    </justification>
  </clause>

  <clause id="5959">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,5004,a,b,5926,a)].">
      <j1 rule="hyper" parents="34 5004 5926"/>
    </justification>
  </clause>

  <clause id="5960">
    <literal><![CDATA[
      (x / y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(5926(a,1),353(a,1))].">
      <j1 rule="para" parents="5926 353"/>
    </justification>
  </clause>

  <clause id="5961">
    <literal><![CDATA[
      R(x * y,K(y,x),K(x,z)) \ (y * T(x,z)) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(5926(a,1),614(a,1,2))].">
      <j1 rule="para" parents="5926 614"/>
    </justification>
  </clause>

  <clause id="5962">
    <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(5926(a,1),591(a,1,1))].">
      <j1 rule="para" parents="5926 591"/>
    </justification>
  </clause>

  <clause id="5964">
    <literal><![CDATA[
      R(x,y,K(y \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(2292,a,5950,a)].">
      <j1 rule="hyper" parents="2292 5950"/>
    </justification>
  </clause>

  <clause id="5965">
    <literal><![CDATA[
      (x * R(R(x,y,K(y,z)) \ (x * y),u,w)) * K(y,z) = R(x,y,K(y,z)) * (R(y,u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[para(5950(a,1),2676(a,1,1,1))].">
      <j1 rule="para" parents="5950 2676"/>
    </justification>
  </clause>

  <clause id="5967">
    <literal><![CDATA[
      a(x,y,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,5959,a)].">
      <j1 rule="hyper" parents="53 5959"/>
    </justification>
  </clause>

  <clause id="5970">
    <literal><![CDATA[
      x * a(y,z,K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(134,a,5967,a,b,68,a)].">
      <j1 rule="hyper" parents="134 5967 68"/>
    </justification>
  </clause>

  <clause id="5971">
    <literal><![CDATA[
      (1 / x) \ K(x \ 1,y) = x * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(5964(a,1),420(a,1,1))].">
      <j1 rule="para" parents="5964 420"/>
    </justification>
  </clause>

  <clause id="5972">
    <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(5936(a,1),5539(a,1,2))].">
      <j1 rule="para" parents="5936 5539"/>
    </justification>
  </clause>

  <clause id="5973">
    <literal><![CDATA[
      (x * y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(5956(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5956 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5975">
    <literal><![CDATA[
      (x * (y / x)) \ (K(x,x \ y) * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(4997(a,1),5956(a,1,1))].">
      <j1 rule="para" parents="4997 5956"/>
    </justification>
  </clause>

  <clause id="5977">
    <literal><![CDATA[
      T(K(x,y),x * z) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(269,a,4974,a,b,5924,a)].">
      <j1 rule="hyper" parents="269 4974 5924"/>
    </justification>
  </clause>

  <clause id="5979">
    <literal><![CDATA[
      (x * K(y,x)) * K(x,z) = T(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(3027(a,1),5924(a,1,2,1))].">
      <j1 rule="para" parents="3027 5924"/>
    </justification>
  </clause>

  <clause id="5981">
    <literal><![CDATA[
      K(T(x,x \ y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(10(a,1),5977(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 5977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5982">
    <literal><![CDATA[
      K((x \ y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(112(a,1),5981(a,1,1))].">
      <j1 rule="para" parents="112 5981"/>
    </justification>
  </clause>

  <clause id="5983">
    <literal><![CDATA[
      K((x \ y) \ y,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3024,a(flip),b,5982,a),flip(a)].">
      <j1 rule="hyper" parents="347 3024 5982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5984">
    <literal><![CDATA[
      K(x / y,x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[para(83(a,1),5983(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="83 5983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5985">
    <literal><![CDATA[
      K(x * (1 / y),x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5394,a,b,5984,a)].">
      <j1 rule="hyper" parents="63 5394 5984"/>
    </justification>
  </clause>

  <clause id="5986">
    <literal><![CDATA[
      K(x * (y \ 1),x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(3931,a,5985,a)].">
      <j1 rule="hyper" parents="3931 5985"/>
    </justification>
  </clause>

  <clause id="5988">
    <literal><![CDATA[
      K((x \ y) \ 1,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5125,a(flip),b,5940,a)].">
      <j1 rule="hyper" parents="63 5125 5940"/>
    </justification>
  </clause>

  <clause id="5990">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = z \ (y * (x * T(x \ (y \ z),u)))
    ]]></literal>
    <justification jstring="[para(5940(a,1),561(a,1,1))].">
      <j1 rule="para" parents="5940 561"/>
    </justification>
  </clause>

  <clause id="5991">
    <literal><![CDATA[
      x \ (y \ T(y * x,z)) = K((y \ 1) \ x,z)
    ]]></literal>
    <justification jstring="[para(1056(a,1),5940(a,1,2))].">
      <j1 rule="para" parents="1056 5940"/>
    </justification>
  </clause>

  <clause id="5992">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((y \ z) \ x,z)
    ]]></literal>
    <justification jstring="[para(1079(a,1),5940(a,1,2))].">
      <j1 rule="para" parents="1079 5940"/>
    </justification>
  </clause>

  <clause id="5993">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((y / z) \ x,y)
    ]]></literal>
    <justification jstring="[para(1576(a,1),5940(a,1,2))].">
      <j1 rule="para" parents="1576 5940"/>
    </justification>
  </clause>

  <clause id="5994">
    <literal><![CDATA[
      K(1 / (x \ y),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(3925,a,5988,a)].">
      <j1 rule="hyper" parents="3925 5988"/>
    </justification>
  </clause>

  <clause id="5996">
    <literal><![CDATA[
      K((x * y) \ x,z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5988(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 5988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5998">
    <literal><![CDATA[
      K(x \ (x / y),z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),5988(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="83 5988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6001">
    <literal><![CDATA[
      K((K(x,y) * z) \ 1,u) = K(z \ K(y,x),u)
    ]]></literal>
    <justification jstring="[para(5256(a,1),5988(a,1,1,1))].">
      <j1 rule="para" parents="5256 5988"/>
    </justification>
  </clause>

  <clause id="6002">
    <literal><![CDATA[
      (x * K(y \ x,z)) / y = T(x / y,z)
    ]]></literal>
    <justification jstring="[para(5988(a,1),5565(a,1,1,2))].">
      <j1 rule="para" parents="5988 5565"/>
    </justification>
  </clause>

  <clause id="6003">
    <literal><![CDATA[
      T(x,(y \ z) \ x) * K(z \ y,x) = L(x,(y \ z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5988(a,1),5383(a,1,2))].">
      <j1 rule="para" parents="5988 5383"/>
    </justification>
  </clause>

  <clause id="6004">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = z * K(y \ x,z * (x \ y))
    ]]></literal>
    <justification jstring="[para(5988(a,1),5749(a,2,2))].">
      <j1 rule="para" parents="5988 5749"/>
    </justification>
  </clause>

  <clause id="6005">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5988(a,1),5563(a,1,2))].">
      <j1 rule="para" parents="5988 5563"/>
    </justification>
  </clause>

  <clause id="6010">
    <literal><![CDATA[
      K(x \ (x / (y \ z)),u) = y \ (z * T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,5125,a,b,5998,a),flip(a)].">
      <j1 rule="hyper" parents="347 5125 5998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6013">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(u \ (u / (y \ x)),z)
    ]]></literal>
    <justification jstring="[hyper(134,a,5998,a,b,5125,a),flip(a)].">
      <j1 rule="hyper" parents="134 5998 5125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6017">
    <literal><![CDATA[
      K(x / y,z) * x = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(5458,a,5941,a)].">
      <j1 rule="hyper" parents="5458 5941"/>
    </justification>
  </clause>

  <clause id="6018">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(1166,a,5941,a)].">
      <j1 rule="hyper" parents="1166 5941"/>
    </justification>
  </clause>

  <clause id="6020">
    <literal><![CDATA[
      x * (y * K((x \ 1) \ y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,5941,a(flip),b,1056,a(flip))].">
      <j1 rule="hyper" parents="134 5941 1056"/>
    </justification>
  </clause>

  <clause id="6021">
    <literal><![CDATA[
      (x * K(y \ x,z)) * (y \ 1) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(133,a,5941,a(flip),b,1110,a)].">
      <j1 rule="hyper" parents="133 5941 1110"/>
    </justification>
  </clause>

  <clause id="6022">
    <literal><![CDATA[
      (x * K((y \ 1) \ x,z)) * y = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,5941,a(flip),b,4832,a(flip))].">
      <j1 rule="hyper" parents="133 5941 4832"/>
    </justification>
  </clause>

  <clause id="6023">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5941(a,2),356(a,1,2))].">
      <j1 rule="para" parents="5941 356"/>
    </justification>
  </clause>

  <clause id="6024">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(y * K(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(5941(a,1),1820(a,2,1))].">
      <j1 rule="para" parents="5941 1820"/>
    </justification>
  </clause>

  <clause id="6026">
    <literal><![CDATA[
      T(x,((y * K((1 / z) \ y,u)) / (z \ 1)) * w) = T(x,T(y / (1 / z),u) * w)
    ]]></literal>
    <justification jstring="[para(6002(a,1),4008(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6002 4008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6027">
    <literal><![CDATA[
      K(L(x,y,z) / u,x) = K(u \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(35,a,3037,a(flip),b,6017,a),flip(a)].">
      <j1 rule="hyper" parents="35 3037 6017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6028">
    <literal><![CDATA[
      L(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(5929,a,5011,a)].">
      <j1 rule="hyper" parents="5929 5011"/>
    </justification>
  </clause>

  <clause id="6030">
    <literal><![CDATA[
      L(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(5182,a,6028,a)].">
      <j1 rule="hyper" parents="5182 6028"/>
    </justification>
  </clause>

  <clause id="6031">
    <literal><![CDATA[
      L(T(x,y),K(x,z),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6028(a,1),25(a,2,1))].">
      <j1 rule="para" parents="6028 25"/>
    </justification>
  </clause>

  <clause id="6032">
    <literal><![CDATA[
      (x * K(y,z)) * L(y,u,w) = x * (K(y,z) * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(6028(a,1),474(a,1,2,1))].">
      <j1 rule="para" parents="6028 474"/>
    </justification>
  </clause>

  <clause id="6035">
    <literal><![CDATA[
      L(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(4924(a,1),6028(a,1,2))].">
      <j1 rule="para" parents="4924 6028"/>
    </justification>
  </clause>

  <clause id="6036">
    <literal><![CDATA[
      (x * ((y * z) / y)) / z = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(220,a,6030,a(flip),b,5105,a)].">
      <j1 rule="hyper" parents="220 6030 5105"/>
    </justification>
  </clause>

  <clause id="6037">
    <literal><![CDATA[
      L(x,K(y,T(x,z)),u) = x
    ]]></literal>
    <justification jstring="[hyper(157,a,6030,a(flip))].">
      <j1 rule="hyper" parents="157 6030"/>
    </justification>
  </clause>

  <clause id="6038">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,u) = x * (K(y,z) * T(z,u))
    ]]></literal>
    <justification jstring="[para(6030(a,1),477(a,1,2,1))].">
      <j1 rule="para" parents="6030 477"/>
    </justification>
  </clause>

  <clause id="6039">
    <literal><![CDATA[
      (x * K(y,z)) * L(z,u,w) = x * (K(y,z) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(6030(a,1),474(a,1,2,1))].">
      <j1 rule="para" parents="6030 474"/>
    </justification>
  </clause>

  <clause id="6041">
    <literal><![CDATA[
      L(L(T(x,y),z,u),K(x,w),v5) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(6031(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6031 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6042">
    <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(6031(a,1),930(a,1,2,1))].">
      <j1 rule="para" parents="6031 930"/>
    </justification>
  </clause>

  <clause id="6043">
    <literal><![CDATA[
      (x / ((y * z) / y)) * K(y,z) = x / z
    ]]></literal>
    <justification jstring="[hyper(438,a,6036,a),flip(a)].">
      <j1 rule="hyper" parents="438 6036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6044">
    <literal><![CDATA[
      (x \ 1) * ((y * x) / y) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,4927,a(flip),b,6036,a),flip(a)].">
      <j1 rule="hyper" parents="133 4927 6036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6045">
    <literal><![CDATA[
      (x * (y / z)) / (z \ y) = x * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),6036(a,1,1,2,1))].">
      <j1 rule="para" parents="10 6036"/>
    </justification>
  </clause>

  <clause id="6046">
    <literal><![CDATA[
      (x * (y * K(z,y))) / y = x * K(z,y)
    ]]></literal>
    <justification jstring="[para(4942(a,1),6036(a,1,1,2))].">
      <j1 rule="para" parents="4942 6036"/>
    </justification>
  </clause>

  <clause id="6047">
    <literal><![CDATA[
      (x / (y / z)) * K(z,z \ y) = x / (z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),6043(a,1,1,2,1))].">
      <j1 rule="para" parents="10 6043"/>
    </justification>
  </clause>

  <clause id="6048">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((((y * z) / y) \ K(y,z)) * ((y * z) / y))) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(6043(a,1),1081(a,2,1,2))].">
      <j1 rule="para" parents="6043 1081"/>
    </justification>
  </clause>

  <clause id="6050">
    <literal><![CDATA[
      (x / ((y * z) / y)) \ T(x / z,1 / (x / ((y * z) / y))) = ((1 / (x / ((y * z) / y))) \ K(y,z)) * (1 / (x / ((y * z) / y)))
    ]]></literal>
    <justification jstring="[para(6043(a,1),4857(a,1,2,1))].">
      <j1 rule="para" parents="6043 4857"/>
    </justification>
  </clause>

  <clause id="6051">
    <literal><![CDATA[
      (x * K(y,z)) * z = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(148,a,6046,a)].">
      <j1 rule="hyper" parents="148 6046"/>
    </justification>
  </clause>

  <clause id="6052">
    <literal><![CDATA[
      (x * y) * (z * K(y,z)) = (x * T(y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,5926,a(flip),b,6046,a),flip(a)].">
      <j1 rule="hyper" parents="133 5926 6046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6055">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * K(x,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(y / x,z,u) * T(x,w) = v5
    ]]></literal>
    <justification jstring="[para(740(a,1),5973(a,1,1))].">
      <j1 rule="para" parents="740 5973"/>
    </justification>
  </clause>

  <clause id="6057">
    <literal><![CDATA[
      (x * (y / z)) * K(z \ y,z) = x * (z \ y)
    ]]></literal>
    <justification jstring="[para(5138(a,1),5927(a,1,2))].">
      <j1 rule="para" parents="5138 5927"/>
    </justification>
  </clause>

  <clause id="6059">
    <literal><![CDATA[
      T(x / (x / y),z) != u / (x / y)
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(5944(a,1),46(a,1))].">
      <j1 rule="para" parents="5944 46"/>
    </justification>
  </clause>

  <clause id="6060">
    <literal><![CDATA[
      T(x * y,K(y,z)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(5264,a,5951,a),flip(a)].">
      <j1 rule="hyper" parents="5264 5951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6061">
    <literal><![CDATA[
      T(x * y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(5951(a,1),5264(a,1))].">
      <j1 rule="para" parents="5951 5264"/>
    </justification>
  </clause>

  <clause id="6062">
    <literal><![CDATA[
      T(x * L(y,z,u),K(L(y,z,u),w)) = L(y,z,u) * T(x,L(T(y,w),z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),6060(a,2,2,2))].">
      <j1 rule="para" parents="25 6060"/>
    </justification>
  </clause>

  <clause id="6063">
    <literal><![CDATA[
      (x * K(y,x)) \ L(x,y,x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(128,a,5379,a(flip),b,5979,a)].">
      <j1 rule="hyper" parents="128 5379 5979"/>
    </justification>
  </clause>

  <clause id="6064">
    <literal><![CDATA[
      (x \ 1) \ T((x \ 1) * y,z) = y * K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,3880,a(flip),b,5991,a),flip(a)].">
      <j1 rule="hyper" parents="134 3880 5991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6065">
    <literal><![CDATA[
      T(x,y) / (z \ x) = z * K(((z \ x) \ 1) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4815,a(flip),b,6018,a)].">
      <j1 rule="hyper" parents="63 4815 6018"/>
    </justification>
  </clause>

  <clause id="6068">
    <literal><![CDATA[
      T(x * K((y \ 1) \ x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6018(a,1),4834(a,1,1))].">
      <j1 rule="para" parents="6018 4834"/>
    </justification>
  </clause>

  <clause id="6070">
    <literal><![CDATA[
      (x * T(y,y \ z)) * (y \ z) = (x * y) * (z / y)
    ]]></literal>
    <justification jstring="[hyper(133,a,5926,a(flip),b,6045,a)].">
      <j1 rule="hyper" parents="133 5926 6045"/>
    </justification>
  </clause>

  <clause id="6071">
    <literal><![CDATA[
      (x / (y \ z)) * (z / y) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1538,a(flip),b,6045,a)].">
      <j1 rule="hyper" parents="63 1538 6045"/>
    </justification>
  </clause>

  <clause id="6072">
    <literal><![CDATA[
      ((x * T(y,z)) * z) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[para(6052(a,1),5222(a,1,1))].">
      <j1 rule="para" parents="6052 5222"/>
    </justification>
  </clause>

  <clause id="6074">
    <literal><![CDATA[
      (x * (y \ z)) / K(y \ z,y) = x * (z / y)
    ]]></literal>
    <justification jstring="[hyper(145,a,6057,a)].">
      <j1 rule="hyper" parents="145 6057"/>
    </justification>
  </clause>

  <clause id="6075">
    <literal><![CDATA[
      (x * (y \ z)) * K(y,y \ z) = x * (z / y)
    ]]></literal>
    <justification jstring="[para(11(a,1),6071(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 6071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6076">
    <literal><![CDATA[
      (x * (y \ z)) * T(y,y \ z) = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,6075,a(flip),b,5919,a),flip(a)].">
      <j1 rule="hyper" parents="133 6075 5919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6077">
    <literal><![CDATA[
      ((x * y) * (z / u)) / ((y * (u \ z)) * K(u,u \ z)) = R(R(x,y,u \ z),y * (u \ z),K(u,u \ z))
    ]]></literal>
    <justification jstring="[para(6075(a,1),591(a,1,1))].">
      <j1 rule="para" parents="6075 591"/>
    </justification>
  </clause>

  <clause id="6079">
    <literal><![CDATA[
      x \ (y * (z * T(z \ (y \ x),u))) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * z) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(1022(a,1),6023(a,1,2))].">
      <j1 rule="para" parents="1022 6023"/>
    </justification>
  </clause>

  <clause id="6080">
    <literal><![CDATA[
      K((x \ y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5125(a,1),6023(a,1))].">
      <j1 rule="para" parents="5125 6023"/>
    </justification>
  </clause>

  <clause id="6081">
    <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),6080(a,1,1,1))].">
      <j1 rule="para" parents="22 6080"/>
    </justification>
  </clause>

  <clause id="6082">
    <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(99(a,2),6080(a,1,1,1))].">
      <j1 rule="para" parents="99 6080"/>
    </justification>
  </clause>

  <clause id="6087">
    <literal><![CDATA[
      ((x / y) * (y * y)) * K(y \ 1,y) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(896(a,1),5939(a,1,1))].">
      <j1 rule="para" parents="896 5939"/>
    </justification>
  </clause>

  <clause id="6088">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((z / y) \ x,z)
    ]]></literal>
    <justification jstring="[para(4879(a,1),5993(a,1,2))].">
      <j1 rule="para" parents="4879 5993"/>
    </justification>
  </clause>

  <clause id="6089">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),x \ y,(x \ y) \ 1) / (x \ T(y,z)) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(220,a,6005,a(flip),b,2946,a)].">
      <j1 rule="hyper" parents="220 6005 2946"/>
    </justification>
  </clause>

  <clause id="6090">
    <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(6005(a,1),4193(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6005 4193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6091">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),u) = z \ ((y * z) * T((y * z) \ z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),6010(a,1,1,2,2))].">
      <j1 rule="para" parents="22 6010"/>
    </justification>
  </clause>

  <clause id="6094">
    <literal><![CDATA[
      (x * (y * z)) * T((x * (y * z)) \ (x * y),u) = (x * y) * K(w \ (w / L(z,y,x)),u)
    ]]></literal>
    <justification jstring="[para(18(a,2),6013(a,2,2,1,2,2))].">
      <j1 rule="para" parents="18 6013"/>
    </justification>
  </clause>

  <clause id="6095">
    <literal><![CDATA[
      x * (K(y \ x,x) * (y \ 1)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(5332,a,6021,a)].">
      <j1 rule="hyper" parents="5332 6021"/>
    </justification>
  </clause>

  <clause id="6096">
    <literal><![CDATA[
      R(x,K(y,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(594,a,6038,a)].">
      <j1 rule="hyper" parents="594 6038"/>
    </justification>
  </clause>

  <clause id="6097">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,y) = x * z
    ]]></literal>
    <justification jstring="[para(4931(a,1),6038(a,2,2))].">
      <j1 rule="para" parents="4931 6038"/>
    </justification>
  </clause>

  <clause id="6098">
    <literal><![CDATA[
      (x / T(y,z)) / K(z,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(719,a,6097,a),flip(a)].">
      <j1 rule="hyper" parents="719 6097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6099">
    <literal><![CDATA[
      (x * y) / T(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,6097,a)].">
      <j1 rule="hyper" parents="145 6097"/>
    </justification>
  </clause>

  <clause id="6100">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * z) = T(z,y)
    ]]></literal>
    <justification jstring="[hyper(138,a,6097,a)].">
      <j1 rule="hyper" parents="138 6097"/>
    </justification>
  </clause>

  <clause id="6101">
    <literal><![CDATA[
      (x / T(y,x)) * K(z,y) = T(x,y) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,4275,a(flip),b,6097,a),flip(a)].">
      <j1 rule="hyper" parents="131 4275 6097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6102">
    <literal><![CDATA[
      (x / y) * K(z,y) = x / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,12,a(flip),b,6097,a),flip(a)].">
      <j1 rule="hyper" parents="131 12 6097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6103">
    <literal><![CDATA[
      x / T(y \ x,z) = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(131,a,10,a(flip),b,6097,a)].">
      <j1 rule="hyper" parents="131 10 6097"/>
    </justification>
  </clause>

  <clause id="6104">
    <literal><![CDATA[
      (x * K(y,x \ z)) \ z = T(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,10,a(flip),b,6097,a)].">
      <j1 rule="hyper" parents="128 10 6097"/>
    </justification>
  </clause>

  <clause id="6106">
    <literal><![CDATA[
      (x \ y) * K(y,x) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,4450,a,b,6097,a),flip(a)].">
      <j1 rule="hyper" parents="35 4450 6097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6107">
    <literal><![CDATA[
      (x / T(y,z)) * y = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1502,a,b,6097,a)].">
      <j1 rule="hyper" parents="35 1502 6097"/>
    </justification>
  </clause>

  <clause id="6108">
    <literal><![CDATA[
      (x * y) / ((y \ z) \ z) = x * K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,473,a,b,6097,a)].">
      <j1 rule="hyper" parents="35 473 6097"/>
    </justification>
  </clause>

  <clause id="6109">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,5914,a(flip),b,6097,a),flip(a)].">
      <j1 rule="hyper" parents="35 5914 6097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6110">
    <literal><![CDATA[
      (T(x,y) * z) * K(y,T(x,z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(35,a,1652,a(flip),b,6097,a),flip(a)].">
      <j1 rule="hyper" parents="35 1652 6097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6111">
    <literal><![CDATA[
      (x * T(y,z)) * K(z,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(35,a,1499,a(flip),b,6097,a),flip(a)].">
      <j1 rule="hyper" parents="35 1499 6097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6112">
    <literal><![CDATA[
      x * T(y,z) != u * y
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(6097(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="6097 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6113">
    <literal><![CDATA[
      (x * y) / T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6097(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6097 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6114">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(z,y) = u
    ]]></literal>
    <justification jstring="[para(6097(a,1),356(a,1,2))].">
      <j1 rule="para" parents="6097 356"/>
    </justification>
  </clause>

  <clause id="6115">
    <literal><![CDATA[
      (x * T(y,z)) * T(z,y) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(5926(a,1),6097(a,1,1))].">
      <j1 rule="para" parents="5926 6097"/>
    </justification>
  </clause>

  <clause id="6116">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(462,a,xx,b,6109,a)].">
      <j1 rule="hyper" parents="462 6109"/>
    </justification>
  </clause>

  <clause id="6117">
    <literal><![CDATA[
      x / K(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(353,a,6109,a),flip(a)].">
      <j1 rule="hyper" parents="353 6109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6118">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) = (a(x,y,u) * K(w,v5)) * K(v5,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,4123,a,b,6109,a)].">
      <j1 rule="hyper" parents="347 4123 6109"/>
    </justification>
  </clause>

  <clause id="6121">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(269,a,6109,a,b,5261,a)].">
      <j1 rule="hyper" parents="269 6109 5261"/>
    </justification>
  </clause>

  <clause id="6123">
    <literal><![CDATA[
      (x * K(y,z)) \ x = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(138,a,6109,a)].">
      <j1 rule="hyper" parents="138 6109"/>
    </justification>
  </clause>

  <clause id="6125">
    <literal><![CDATA[
      (x / (y \ z)) * K(y \ z,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[hyper(35,a,6047,a,b,6109,a),flip(a)].">
      <j1 rule="hyper" parents="35 6047 6109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6126">
    <literal><![CDATA[
      x / ((y * z) / y) = (x / z) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,6043,a,b,6109,a)].">
      <j1 rule="hyper" parents="35 6043 6109"/>
    </justification>
  </clause>

  <clause id="6127">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,(x \ 1) \ (x \ y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(35,a,6005,a,b,6109,a),flip(a)].">
      <j1 rule="hyper" parents="35 6005 6109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6128">
    <literal><![CDATA[
      (x * ((y \ z) \ z)) * K(y \ z,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(35,a,5954,a,b,6109,a),flip(a)].">
      <j1 rule="hyper" parents="35 5954 6109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6129">
    <literal><![CDATA[
      L(x,y,z) * K(x,1 / x) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,5221,a,b,6109,a),flip(a)].">
      <j1 rule="hyper" parents="35 5221 6109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6130">
    <literal><![CDATA[
      (x \ K(x,y)) * K(y,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,4520,a,b,6109,a),flip(a)].">
      <j1 rule="hyper" parents="35 4520 6109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6131">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * K(y,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,2556,a,b,6109,a),flip(a)].">
      <j1 rule="hyper" parents="35 2556 6109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6133">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * K(y,x) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,2556,a(flip),b,6109,a),flip(a)].">
      <j1 rule="hyper" parents="35 2556 6109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6134">
    <literal><![CDATA[
      x * L(y,K(z,u),x * K(u,z)) = (x * K(u,z)) * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,6109,a(flip),b,212,a)].">
      <j1 rule="hyper" parents="133 6109 212"/>
    </justification>
  </clause>

  <clause id="6135">
    <literal><![CDATA[
      (x * K(y,z)) / z = x / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,6109,a(flip),b,5925,a),flip(a)].">
      <j1 rule="hyper" parents="131 6109 5925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6136">
    <literal><![CDATA[
      L(K(x,y),z * K(y,x),u) = (u * (z * K(y,x))) \ (u * z)
    ]]></literal>
    <justification jstring="[para(6109(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="6109 18"/>
    </justification>
  </clause>

  <clause id="6138">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(6109(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="6109 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6139">
    <literal><![CDATA[
      K(x,y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      u * K(y,x) = z
    ]]></literal>
    <justification jstring="[para(6109(a,1),153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6109 153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6140">
    <literal><![CDATA[
      x / K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6109(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6109 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6141">
    <literal><![CDATA[
      (x * K(y,z)) \ x != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6109(a,1),356(a,1,2))].">
      <j1 rule="para" parents="6109 356"/>
    </justification>
  </clause>

  <clause id="6142">
    <literal><![CDATA[
      x \ ((x * K(y,z)) * (K(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,K(z,y),x * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(6109(a,1),545(a,1,1))].">
      <j1 rule="para" parents="6109 545"/>
    </justification>
  </clause>

  <clause id="6143">
    <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(6109(a,1),836(a,1,1,2))].">
      <j1 rule="para" parents="6109 836"/>
    </justification>
  </clause>

  <clause id="6144">
    <literal><![CDATA[
      (x * y) / K(z,y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,5926,a(flip),b,6117,a),flip(a)].">
      <j1 rule="hyper" parents="347 5926 6117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6145">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(6117(a,1),280(a,1,1))].">
      <j1 rule="para" parents="6117 280"/>
    </justification>
  </clause>

  <clause id="6146">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(6117(a,1),282(a,1))].">
      <j1 rule="para" parents="6117 282"/>
    </justification>
  </clause>

  <clause id="6147">
    <literal><![CDATA[
      x / K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = K(z,y) \ u
    ]]></literal>
    <justification jstring="[para(6117(a,2),309(a,1))].">
      <j1 rule="para" parents="6117 309"/>
    </justification>
  </clause>

  <clause id="6148">
    <literal><![CDATA[
      R((x * K(y,z)) / u,u,K(z,y)) != w
    ]]></literal>
    <literal><![CDATA[
      x / (u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(6117(a,1),682(a,1,1,1))].">
      <j1 rule="para" parents="6117 682"/>
    </justification>
  </clause>

  <clause id="6149">
    <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(6117(a,1),682(a,1,1))].">
      <j1 rule="para" parents="6117 682"/>
    </justification>
  </clause>

  <clause id="6150">
    <literal><![CDATA[
      R(x * K(y,z),K(z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      (x * u) / (K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(6117(a,1),945(a,1,1))].">
      <j1 rule="para" parents="6117 945"/>
    </justification>
  </clause>

  <clause id="6151">
    <literal><![CDATA[
      R(x / (y * K(1 / z,z)),y / K(z,1 / z),K(z,1 / z)) = K(z,1 / z) * (x / y)
    ]]></literal>
    <justification jstring="[para(6117(a,1),3508(a,1,1,2))].">
      <j1 rule="para" parents="6117 3508"/>
    </justification>
  </clause>

  <clause id="6152">
    <literal><![CDATA[
      x / (K(y,z) \ 1) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(5173(a,2),6117(a,1,2))].">
      <j1 rule="para" parents="5173 6117"/>
    </justification>
  </clause>

  <clause id="6153">
    <literal><![CDATA[
      K(x,1 / (K(y,z) / u)) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6117(a,1),5622(a,2,2))].">
      <j1 rule="para" parents="6117 5622"/>
    </justification>
  </clause>

  <clause id="6155">
    <literal><![CDATA[
      (x * y) / K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6117(a,2),5973(a,1))].">
      <j1 rule="para" parents="6117 5973"/>
    </justification>
  </clause>

  <clause id="6156">
    <literal><![CDATA[
      ((x * K(y,z)) \ x) \ u = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(6123(a,2),5256(a,1,1))].">
      <j1 rule="para" parents="6123 5256"/>
    </justification>
  </clause>

  <clause id="6157">
    <literal><![CDATA[
      R(x,y,x) \ T(x,y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(5381(a,1),6123(a,1,1))].">
      <j1 rule="para" parents="5381 6123"/>
    </justification>
  </clause>

  <clause id="6158">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(5525(a,1),6123(a,1,1))].">
      <j1 rule="para" parents="5525 6123"/>
    </justification>
  </clause>

  <clause id="6159">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y = K(z,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(5127(a,2),6123(a,1,1))].">
      <j1 rule="para" parents="5127 6123"/>
    </justification>
  </clause>

  <clause id="6160">
    <literal><![CDATA[
      (x / y) \ (x / T(y,z)) = K(z,y)
    ]]></literal>
    <justification jstring="[para(5922(a,1),6123(a,1,1))].">
      <j1 rule="para" parents="5922 6123"/>
    </justification>
  </clause>

  <clause id="6161">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(5926(a,1),6123(a,1,1))].">
      <j1 rule="para" parents="5926 6123"/>
    </justification>
  </clause>

  <clause id="6162">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y = K(z,x \ y)
    ]]></literal>
    <justification jstring="[para(5941(a,2),6123(a,1,1))].">
      <j1 rule="para" parents="5941 6123"/>
    </justification>
  </clause>

  <clause id="6163">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y = K(z,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(6018(a,2),6123(a,1,1))].">
      <j1 rule="para" parents="6018 6123"/>
    </justification>
  </clause>

  <clause id="6164">
    <literal><![CDATA[
      (L(x,y,z) \ T(x,u)) * K(w,L(x,y,z)) = T(x,u) / T(L(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(133,a,4838,a(flip),b,6098,a)].">
      <j1 rule="hyper" parents="133 4838 6098"/>
    </justification>
  </clause>

  <clause id="6165">
    <literal><![CDATA[
      (x \ T(T(x,y),z)) * K(u,x) = T(T(x,y),z) / T(x,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,4820,a(flip),b,6098,a)].">
      <j1 rule="hyper" parents="133 4820 6098"/>
    </justification>
  </clause>

  <clause id="6166">
    <literal><![CDATA[
      (x * (y * y)) * K(z,y \ (y \ 1)) = x / T(y \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(133,a,668,a(flip),b,6098,a)].">
      <j1 rule="hyper" parents="133 668 6098"/>
    </justification>
  </clause>

  <clause id="6167">
    <literal><![CDATA[
      (x / y) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6098(a,1),280(a,1,1))].">
      <j1 rule="para" parents="6098 280"/>
    </justification>
  </clause>

  <clause id="6168">
    <literal><![CDATA[
      x \ y != (z / u) * K(w,u)
    ]]></literal>
    <literal><![CDATA[
      x * (z / T(u,w)) = y
    ]]></literal>
    <justification jstring="[para(6098(a,1),636(a,2,1))].">
      <j1 rule="para" parents="6098 636"/>
    </justification>
  </clause>

  <clause id="6169">
    <literal><![CDATA[
      R(x * K(y,z),K(u,w),u) = (x * z) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,5915,a,b,6099,a)].">
      <j1 rule="hyper" parents="347 5915 6099"/>
    </justification>
  </clause>

  <clause id="6170">
    <literal><![CDATA[
      (x / T(y,z)) \ (x * K(z,y)) = y
    ]]></literal>
    <justification jstring="[hyper(128,a,6099,a(flip),b,1500,a(flip))].">
      <j1 rule="hyper" parents="128 6099 1500"/>
    </justification>
  </clause>

  <clause id="6171">
    <literal><![CDATA[
      T(x * K(x * y,y),y) = y \ T(x * y,y)
    ]]></literal>
    <justification jstring="[para(6099(a,1),4278(a,1,1))].">
      <j1 rule="para" parents="6099 4278"/>
    </justification>
  </clause>

  <clause id="6173">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * z) = T(z,y)
    ]]></literal>
    <justification jstring="[para(5926(a,1),6100(a,1,1))].">
      <j1 rule="para" parents="5926 6100"/>
    </justification>
  </clause>

  <clause id="6174">
    <literal><![CDATA[
      x * (K(y,x) * K(z,y)) = (y * x) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5449,a(flip),b,6102,a)].">
      <j1 rule="hyper" parents="63 5449 6102"/>
    </justification>
  </clause>

  <clause id="6175">
    <literal><![CDATA[
      x / ((y \ z) \ z) = (x / y) * K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(805,a,6102,a(flip))].">
      <j1 rule="hyper" parents="805 6102"/>
    </justification>
  </clause>

  <clause id="6176">
    <literal><![CDATA[
      K(x \ y,x) * K(z,y / x) = x \ (y / T(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,6102,a(flip),b,5461,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 6102 5461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6177">
    <literal><![CDATA[
      (x / L(y,z,u)) * K(w,L(y,z,u)) = x / L(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),6102(a,2,2))].">
      <j1 rule="para" parents="25 6102"/>
    </justification>
  </clause>

  <clause id="6178">
    <literal><![CDATA[
      x \ T(x * y,x) = y * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),6106(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 6106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6179">
    <literal><![CDATA[
      (x \ T(y,x)) \ ((x \ y) * (K(y,x) * z)) = L(z,K(y,x),x \ y)
    ]]></literal>
    <justification jstring="[para(6106(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6106 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6180">
    <literal><![CDATA[
      T((x * y) / T(z,y),z) = z \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(462,a,5926,a(flip),b,6107,a)].">
      <j1 rule="hyper" parents="462 5926 6107"/>
    </justification>
  </clause>

  <clause id="6181">
    <literal><![CDATA[
      (x * T(y,z)) / z = (x * y) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,5926,a(flip),b,6107,a)].">
      <j1 rule="hyper" parents="131 5926 6107"/>
    </justification>
  </clause>

  <clause id="6182">
    <literal><![CDATA[
      R(x / T(y,z),y,y \ 1) = (x * K(z,y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,6107,a(flip),b,588,a),flip(a)].">
      <j1 rule="hyper" parents="133 6107 588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6183">
    <literal><![CDATA[
      x * K(y,z) != u * z
    ]]></literal>
    <literal><![CDATA[
      x / T(z,y) = u
    ]]></literal>
    <justification jstring="[para(6107(a,1),44(a,1))].">
      <j1 rule="para" parents="6107 44"/>
    </justification>
  </clause>

  <clause id="6184">
    <literal><![CDATA[
      (x * K(y,z)) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / T(z,y) = u
    ]]></literal>
    <justification jstring="[para(6107(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6107 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6186">
    <literal><![CDATA[
      x \ (y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / T(x,z),x) = u
    ]]></literal>
    <justification jstring="[para(6107(a,1),360(a,1,2))].">
      <j1 rule="para" parents="6107 360"/>
    </justification>
  </clause>

  <clause id="6187">
    <literal><![CDATA[
      L(L(x \ 1,x,y / T(x,z)) \ u,(y * K(z,x)) \ (y / T(x,z)),(y / T(x,z)) * x) = (y / T(x,z)) \ (((y / T(x,z)) * x) * u)
    ]]></literal>
    <justification jstring="[para(6107(a,1),873(a,1,2,1))].">
      <j1 rule="para" parents="6107 873"/>
    </justification>
  </clause>

  <clause id="6189">
    <literal><![CDATA[
      (x * K(y,z)) * z = (x * z) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6099(a,1),6107(a,1,1))].">
      <j1 rule="para" parents="6099 6107"/>
    </justification>
  </clause>

  <clause id="6191">
    <literal><![CDATA[
      T(x * T(y,z),K(z,y)) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(269,a,6111,a,b,5261,a)].">
      <j1 rule="hyper" parents="269 6111 5261"/>
    </justification>
  </clause>

  <clause id="6192">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * T(y,x) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,5917,a(flip),b,6111,a),flip(a)].">
      <j1 rule="hyper" parents="35 5917 6111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6193">
    <literal><![CDATA[
      x * K(y,z) != u * z
    ]]></literal>
    <literal><![CDATA[
      u * T(z,y) = x
    ]]></literal>
    <justification jstring="[para(6111(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="6111 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6194">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6111(a,1),356(a,1,2))].">
      <j1 rule="para" parents="6111 356"/>
    </justification>
  </clause>

  <clause id="6195">
    <literal><![CDATA[
      R(x / (y \ K(y,z)),y \ K(y,z),K(z,y)) = (x * K(z,y)) / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(220,a,6130,a(flip),b,579,a),flip(a)].">
      <j1 rule="hyper" parents="220 6130 579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6196">
    <literal><![CDATA[
      (x * K(y,z / y)) / (z / y) = x / (y \ z)
    ]]></literal>
    <justification jstring="[para(113(a,1),6135(a,2,2))].">
      <j1 rule="para" parents="113 6135"/>
    </justification>
  </clause>

  <clause id="6197">
    <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(6135(a,1),5960(a,1,1))].">
      <j1 rule="para" parents="6135 5960"/>
    </justification>
  </clause>

  <clause id="6198">
    <literal><![CDATA[
      R(x,K(y,z),K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,788,a,b,6152,a)].">
      <j1 rule="hyper" parents="37 788 6152"/>
    </justification>
  </clause>

  <clause id="6199">
    <literal><![CDATA[
      ((x / T(y,z)) * K(y,z)) \ (x / T(y,u)) = K(u,y)
    ]]></literal>
    <justification jstring="[para(5922(a,2),6160(a,1,1))].">
      <j1 rule="para" parents="5922 6160"/>
    </justification>
  </clause>

  <clause id="6201">
    <literal><![CDATA[
      R(x * K(y,x),z,u) \ R(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(R(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(5438(a,1),6141(a,1,1))].">
      <j1 rule="para" parents="5438 6141"/>
    </justification>
  </clause>

  <clause id="6202">
    <literal><![CDATA[
      (T(x,y) * z) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(5924(a,1),6141(a,1,1))].">
      <j1 rule="para" parents="5924 6141"/>
    </justification>
  </clause>

  <clause id="6203">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(5941(a,2),6141(a,1,1))].">
      <j1 rule="para" parents="5941 6141"/>
    </justification>
  </clause>

  <clause id="6205">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / K(z,y) = u
    ]]></literal>
    <justification jstring="[para(12(a,1),6145(a,1,1))].">
      <j1 rule="para" parents="12 6145"/>
    </justification>
  </clause>

  <clause id="6207">
    <literal><![CDATA[
      R(x * x,x \ y,x * x) \ T(x * x,x \ y) = K(x * x,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(495(a,1),6157(a,2,2))].">
      <j1 rule="para" parents="495 6157"/>
    </justification>
  </clause>

  <clause id="6209">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * z)) = T(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(128,a,97,a(flip),b,6115,a)].">
      <j1 rule="hyper" parents="128 97 6115"/>
    </justification>
  </clause>

  <clause id="6210">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) = R(x,T(y,z),T(z,y))
    ]]></literal>
    <justification jstring="[hyper(131,a,6115,a(flip),b,4311,a)].">
      <j1 rule="hyper" parents="131 6115 4311"/>
    </justification>
  </clause>

  <clause id="6211">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(6116(a,2),5286(a,1))].">
      <j1 rule="para" parents="6116 5286"/>
    </justification>
  </clause>

  <clause id="6212">
    <literal><![CDATA[
      L(x * K(y,z),u,w) * K(z,y) = K(z,y) * L(K(y,z) * x,u,w)
    ]]></literal>
    <justification jstring="[para(6121(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6121 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6213">
    <literal><![CDATA[
      (x / ((y * z) / y)) * z = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,6126,a,b,5943,a)].">
      <j1 rule="hyper" parents="133 6126 5943"/>
    </justification>
  </clause>

  <clause id="6214">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),6126(a,2,1))].">
      <j1 rule="para" parents="11 6126"/>
    </justification>
  </clause>

  <clause id="6215">
    <literal><![CDATA[
      x / (y / (y / z)) = (x / z) * K(z,y / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),6126(a,1,2,1))].">
      <j1 rule="para" parents="12 6126"/>
    </justification>
  </clause>

  <clause id="6217">
    <literal><![CDATA[
      x / (y * K(z,y)) = (x / y) * K(y,z)
    ]]></literal>
    <justification jstring="[para(4942(a,1),6126(a,1,2))].">
      <j1 rule="para" parents="4942 6126"/>
    </justification>
  </clause>

  <clause id="6220">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(1022(a,1),6162(a,1,1))].">
      <j1 rule="para" parents="1022 6162"/>
    </justification>
  </clause>

  <clause id="6221">
    <literal><![CDATA[
      ((x * T(x \ y,z)) * u) \ (y * u) = K(z,(x * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(1498(a,1),6162(a,1,1))].">
      <j1 rule="para" parents="1498 6162"/>
    </justification>
  </clause>

  <clause id="6222">
    <literal><![CDATA[
      T(x * T(x \ y,z),u) \ T(y,u) = K(z,T(x,u) \ T(y,u))
    ]]></literal>
    <justification jstring="[para(1823(a,1),6162(a,1,1))].">
      <j1 rule="para" parents="1823 6162"/>
    </justification>
  </clause>

  <clause id="6223">
    <literal><![CDATA[
      K((x \ 1) \ y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,6018,a(flip),b,6178,a(flip))].">
      <j1 rule="hyper" parents="34 6018 6178"/>
    </justification>
  </clause>

  <clause id="6224">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(z,K(x * y,x))) = L(T(K(x * y,x),z) \ 1,K(x * y,x),y)
    ]]></literal>
    <justification jstring="[para(6178(a,2),5041(a,1,1))].">
      <j1 rule="para" parents="6178 5041"/>
    </justification>
  </clause>

  <clause id="6225">
    <literal><![CDATA[
      K((1 / x) \ y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(3932,a,6223,a)].">
      <j1 rule="hyper" parents="3932 6223"/>
    </justification>
  </clause>

  <clause id="6226">
    <literal><![CDATA[
      K((x \ 1) * y,x \ 1) = K(x \ y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3927,a,6223,a),flip(a)].">
      <j1 rule="hyper" parents="3927 6223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6227">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * (y * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6051,a(flip),b,6189,a),flip(a)].">
      <j1 rule="hyper" parents="63 6051 6189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6228">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x / ((z * y) / z),y) = y \ u
    ]]></literal>
    <justification jstring="[para(6213(a,1),309(a,1))].">
      <j1 rule="para" parents="6213 309"/>
    </justification>
  </clause>

  <clause id="6231">
    <literal><![CDATA[
      (x * y) / z != x * K(y,u)
    ]]></literal>
    <literal><![CDATA[
      (u * y) / u = z
    ]]></literal>
    <justification jstring="[para(6214(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="6214 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6233">
    <literal><![CDATA[
      (x * y) / (y * K(z,y)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(4942(a,1),6214(a,1,2))].">
      <j1 rule="para" parents="4942 6214"/>
    </justification>
  </clause>

  <clause id="6234">
    <literal><![CDATA[
      (x * (y * K(z,y))) / (y * K(u,y)) = (x * K(z,y)) * K(y,u)
    ]]></literal>
    <justification jstring="[para(6046(a,1),6217(a,2,1))].">
      <j1 rule="para" parents="6046 6217"/>
    </justification>
  </clause>

  <clause id="6235">
    <literal><![CDATA[
      R(x,y,K(z,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(2309,a,6227,a)].">
      <j1 rule="hyper" parents="2309 6227"/>
    </justification>
  </clause>

  <clause id="6236">
    <literal><![CDATA[
      R(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(594,a,6227,a)].">
      <j1 rule="hyper" parents="594 6227"/>
    </justification>
  </clause>

  <clause id="6237">
    <literal><![CDATA[
      L(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(544,a,6227,a)].">
      <j1 rule="hyper" parents="544 6227"/>
    </justification>
  </clause>

  <clause id="6238">
    <literal><![CDATA[
      (x / y) * (y * K(z,y)) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(353,a,6227,a),flip(a)].">
      <j1 rule="hyper" parents="353 6227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6239">
    <literal><![CDATA[
      (x * (y * K(z,y))) * z = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,6227,a(flip),b,5919,a)].">
      <j1 rule="hyper" parents="133 6227 5919"/>
    </justification>
  </clause>

  <clause id="6240">
    <literal><![CDATA[
      a(x,y,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(127,a,6227,a(flip),b,86,a),flip(a)].">
      <j1 rule="hyper" parents="127 6227 86"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6242">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * ((z * y) / z)
    ]]></literal>
    <justification jstring="[para(4942(a,2),6227(a,2,2))].">
      <j1 rule="para" parents="4942 6227"/>
    </justification>
  </clause>

  <clause id="6243">
    <literal><![CDATA[
      R(x,y \ 1,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(2277,a,6236,a)].">
      <j1 rule="hyper" parents="2277 6236"/>
    </justification>
  </clause>

  <clause id="6244">
    <literal><![CDATA[
      (x * y) * K(z,y \ 1) = x * (y * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(133,a,6236,a(flip),b,2253,a),flip(a)].">
      <j1 rule="hyper" parents="133 6236 2253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6246">
    <literal><![CDATA[
      L(K(x,y),y \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3519,a,6237,a)].">
      <j1 rule="hyper" parents="3519 6237"/>
    </justification>
  </clause>

  <clause id="6247">
    <literal><![CDATA[
      L(K(x,y),y,z) = L(K(x,y),y,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,6237,a,b,6237,a)].">
      <j1 rule="hyper" parents="347 6237 6237"/>
    </justification>
  </clause>

  <clause id="6250">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5663,a(flip),b,6237,a)].">
      <j1 rule="hyper" parents="63 5663 6237"/>
    </justification>
  </clause>

  <clause id="6251">
    <literal><![CDATA[
      1 / L(K(x,y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = u
    ]]></literal>
    <justification jstring="[para(6237(a,2),5178(a,1,2))].">
      <j1 rule="para" parents="6237 5178"/>
    </justification>
  </clause>

  <clause id="6252">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,y) = x * (y \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(133,a,6243,a(flip),b,4548,a),flip(a)].">
      <j1 rule="hyper" parents="133 6243 4548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6253">
    <literal><![CDATA[
      a(x,y \ 1,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,6246,a)].">
      <j1 rule="hyper" parents="53 6246"/>
    </justification>
  </clause>

  <clause id="6255">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,u) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,5663,a(flip),b,6247,a),flip(a)].">
      <j1 rule="hyper" parents="347 5663 6247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6256">
    <literal><![CDATA[
      L(K(x,y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6247(a,1),401(a,1)),flip(b)].">
      <j1 rule="para" parents="6247 401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6257">
    <literal><![CDATA[
      K(x,1 / (y \ z)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(3903,a,6250,a)].">
      <j1 rule="hyper" parents="3903 6250"/>
    </justification>
  </clause>

  <clause id="6258">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(132,a,6250,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 6250 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6259">
    <literal><![CDATA[
      K(x,(y * z) \ y) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),6250(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6260">
    <literal><![CDATA[
      K(x,((y * z) \ y) \ 1) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),6250(a,2,2))].">
      <j1 rule="para" parents="9 6250"/>
    </justification>
  </clause>

  <clause id="6262">
    <literal><![CDATA[
      K(x,(y \ (y / z)) \ 1) = K(x,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),6250(a,2,2))].">
      <j1 rule="para" parents="83 6250"/>
    </justification>
  </clause>

  <clause id="6265">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(5256(a,1),6250(a,1,2,1))].">
      <j1 rule="para" parents="5256 6250"/>
    </justification>
  </clause>

  <clause id="6266">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) \ 1) = L(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6250(a,1),5656(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6250 5656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6267">
    <literal><![CDATA[
      R(x,y \ z,K(u,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(6250(a,1),6235(a,1,3))].">
      <j1 rule="para" parents="6250 6235"/>
    </justification>
  </clause>

  <clause id="6268">
    <literal><![CDATA[
      x \ (y * K(z,y \ x)) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * ((x \ y) * K(z,y \ x)) = w
    ]]></literal>
    <justification jstring="[para(6267(a,1),844(a,1,1))].">
      <j1 rule="para" parents="6267 844"/>
    </justification>
  </clause>

  <clause id="6269">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(5663(a,1),6256(a,1))].">
      <j1 rule="para" parents="5663 6256"/>
    </justification>
  </clause>

  <clause id="6270">
    <literal><![CDATA[
      K(x,1 / (y \ x)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(347,a,5098,a,b,6257,a),flip(a)].">
      <j1 rule="hyper" parents="347 5098 6257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6271">
    <literal><![CDATA[
      T(x,1 / (y \ z)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(132,a,6257,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 6257 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6272">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ (y * z)) = K(x,1 / L(u,z,y))
    ]]></literal>
    <justification jstring="[para(18(a,2),6257(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18 6257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6273">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(83(a,1),6257(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="83 6257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6274">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (x \ y),y \ x)
    ]]></literal>
    <justification jstring="[para(6257(a,1),5773(a,2,2))].">
      <j1 rule="para" parents="6257 5773"/>
    </justification>
  </clause>

  <clause id="6275">
    <literal><![CDATA[
      ((x \ y) \ 1) * T(z,y \ x) = z * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,6258,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 6258 22"/>
    </justification>
  </clause>

  <clause id="6276">
    <literal><![CDATA[
      T(x,(y * z) \ y) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),6258(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6277">
    <literal><![CDATA[
      T(x,((y * z) \ y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),6258(a,2,2))].">
      <j1 rule="para" parents="9 6258"/>
    </justification>
  </clause>

  <clause id="6279">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(83(a,1),6258(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 6258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6280">
    <literal><![CDATA[
      T(x,x \ y) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(6258(a,1),3808(a,1,1))].">
      <j1 rule="para" parents="6258 3808"/>
    </justification>
  </clause>

  <clause id="6281">
    <literal><![CDATA[
      T(x,y \ z) / ((z \ y) \ x) = x / ((x \ ((z \ y) \ x)) * x)
    ]]></literal>
    <justification jstring="[para(6258(a,1),4399(a,1,1))].">
      <j1 rule="para" parents="6258 4399"/>
    </justification>
  </clause>

  <clause id="6283">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) \ z,((x * y) \ x) \ 1) = K(z * ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[hyper(5776,a,6260,a)].">
      <j1 rule="hyper" parents="5776 6260"/>
    </justification>
  </clause>

  <clause id="6284">
    <literal><![CDATA[
      L(K(x,y),y,z) = K(x,((u * y) \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,6237,a,b,6260,a)].">
      <j1 rule="hyper" parents="347 6237 6260"/>
    </justification>
  </clause>

  <clause id="6285">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,1 / z)
    ]]></literal>
    <justification jstring="[para(83(a,1),6271(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="83 6271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6286">
    <literal><![CDATA[
      (x / y) * K(x,1 / y) = x * ((x / y) / x)
    ]]></literal>
    <justification jstring="[hyper(134,a,6273,a(flip),b,5110,a)].">
      <j1 rule="hyper" parents="134 6273 5110"/>
    </justification>
  </clause>

  <clause id="6287">
    <literal><![CDATA[
      K(x,L(1 / y,y,z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(3264(a,2),6273(a,1,2))].">
      <j1 rule="para" parents="3264 6273"/>
    </justification>
  </clause>

  <clause id="6288">
    <literal><![CDATA[
      K(x,y \ (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6273(a,2),5224(a,1))].">
      <j1 rule="para" parents="6273 5224"/>
    </justification>
  </clause>

  <clause id="6289">
    <literal><![CDATA[
      T(x * y,y \ 1) = ((x * y) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(440,a,6276,a),flip(a)].">
      <j1 rule="hyper" parents="440 6276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6290">
    <literal><![CDATA[
      ((x * y) \ x) * T(z,y \ 1) = z * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(134,a,6276,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 6276 22"/>
    </justification>
  </clause>

  <clause id="6291">
    <literal><![CDATA[
      T(x,a(y * z,(y * z) \ y,z)) = T(x,(((y * z) \ y) * z) \ 1)
    ]]></literal>
    <justification jstring="[para(88(a,1),6276(a,1,2))].">
      <j1 rule="para" parents="88 6276"/>
    </justification>
  </clause>

  <clause id="6292">
    <literal><![CDATA[
      L((x * x) \ T(y,x \ 1),x * x,(z * x) \ z) = L(x,x,z) \ (y * ((z * x) \ z))
    ]]></literal>
    <justification jstring="[para(6276(a,1),879(a,1,1,2))].">
      <j1 rule="para" parents="6276 879"/>
    </justification>
  </clause>

  <clause id="6293">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * T(z,y) = z * (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(134,a,6277,a(flip),b,2961,a)].">
      <j1 rule="hyper" parents="134 6277 2961"/>
    </justification>
  </clause>

  <clause id="6294">
    <literal><![CDATA[
      (x \ (x / y)) * T(x,y \ 1) = x / y
    ]]></literal>
    <justification jstring="[hyper(134,a,6279,a(flip),b,112,a(flip))].">
      <j1 rule="hyper" parents="134 6279 112"/>
    </justification>
  </clause>

  <clause id="6295">
    <literal><![CDATA[
      ((x / y) * (x \ (x / y))) / (x / y) = x \ T(x / y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,6279,a(flip),b,4169,a),flip(a)].">
      <j1 rule="hyper" parents="128 6279 4169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6296">
    <literal><![CDATA[
      T(x,(x / y) / x) = T(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(4346,a,6285,a)].">
      <j1 rule="hyper" parents="4346 6285"/>
    </justification>
  </clause>

  <clause id="6297">
    <literal><![CDATA[
      T(x,y \ (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6285(a,2),4439(a,1))].">
      <j1 rule="para" parents="6285 4439"/>
    </justification>
  </clause>

  <clause id="6298">
    <literal><![CDATA[
      (x / y) * ((z * y) / z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[para(4942(a,2),6238(a,1,2))].">
      <j1 rule="para" parents="4942 6238"/>
    </justification>
  </clause>

  <clause id="6299">
    <literal><![CDATA[
      x * K(y,z \ x) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(628,a,6242,a)].">
      <j1 rule="hyper" parents="628 6242"/>
    </justification>
  </clause>

  <clause id="6300">
    <literal><![CDATA[
      (x * ((y * z) / y)) * y = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,6242,a(flip),b,5919,a)].">
      <j1 rule="hyper" parents="133 6242 5919"/>
    </justification>
  </clause>

  <clause id="6302">
    <literal><![CDATA[
      T(x,x \ (y * x)) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),6280(a,2,2))].">
      <j1 rule="para" parents="11 6280"/>
    </justification>
  </clause>

  <clause id="6303">
    <literal><![CDATA[
      T(x,y / x) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4285(a,2),6280(a,1,1))].">
      <j1 rule="para" parents="4285 6280"/>
    </justification>
  </clause>

  <clause id="6304">
    <literal><![CDATA[
      x / T(x * y,y \ 1) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(220,a,6289,a,b,409,a)].">
      <j1 rule="hyper" parents="220 6289 409"/>
    </justification>
  </clause>

  <clause id="6305">
    <literal><![CDATA[
      T(x * (y \ 1),y) = ((x * (y \ 1)) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,2966,a(flip),b,6289,a)].">
      <j1 rule="hyper" parents="63 2966 6289"/>
    </justification>
  </clause>

  <clause id="6306">
    <literal><![CDATA[
      x / T(x * (y \ z),z \ y) = (x * (y \ z)) \ x
    ]]></literal>
    <justification jstring="[hyper(220,a,6258,a(flip),b,6289,a(flip))].">
      <j1 rule="hyper" parents="220 6258 6289"/>
    </justification>
  </clause>

  <clause id="6307">
    <literal><![CDATA[
      (x \ 1) * (((y * x) \ y) \ y) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,6289,a(flip),b,695,a)].">
      <j1 rule="hyper" parents="134 6289 695"/>
    </justification>
  </clause>

  <clause id="6308">
    <literal><![CDATA[
      T(x * (1 / y),y) = ((x * (1 / y)) \ x) \ x
    ]]></literal>
    <justification jstring="[para(83(a,1),6289(a,1,2))].">
      <j1 rule="para" parents="83 6289"/>
    </justification>
  </clause>

  <clause id="6309">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * T(x,y) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(2966(a,1),6294(a,1,2))].">
      <j1 rule="para" parents="2966 6294"/>
    </justification>
  </clause>

  <clause id="6310">
    <literal><![CDATA[
      L(x,(y / z) * ((u * u) * z),w) = L(x,y * K(u * u,z),w)
    ]]></literal>
    <justification jstring="[para(6298(a,1),3228(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6298 3228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6311">
    <literal><![CDATA[
      x / T(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * K(z,T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(4931(a,1),6113(a,1,1))].">
      <j1 rule="para" parents="4931 6113"/>
    </justification>
  </clause>

  <clause id="6312">
    <literal><![CDATA[
      K(x,y) * K(z,y * x) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) / T(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(4908(a,2),6167(a,1,1))].">
      <j1 rule="para" parents="4908 6167"/>
    </justification>
  </clause>

  <clause id="6313">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) / T(x,z) = u
    ]]></literal>
    <justification jstring="[para(4969(a,2),6167(a,1,1))].">
      <j1 rule="para" parents="4969 6167"/>
    </justification>
  </clause>

  <clause id="6314">
    <literal><![CDATA[
      x * (K(y,x) * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) / T(y,z) = u
    ]]></literal>
    <justification jstring="[para(5449(a,1),6167(a,1))].">
      <j1 rule="para" parents="5449 6167"/>
    </justification>
  </clause>

  <clause id="6315">
    <literal><![CDATA[
      (x * T(y,z)) / z != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) / T(z,y) = u
    ]]></literal>
    <justification jstring="[para(5926(a,1),6184(a,1,1))].">
      <j1 rule="para" parents="5926 6184"/>
    </justification>
  </clause>

  <clause id="6316">
    <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(99(a,2),6269(a,1,2,1))].">
      <j1 rule="para" parents="99 6269"/>
    </justification>
  </clause>

  <clause id="6317">
    <literal><![CDATA[
      K(x,1 / (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3890(a,2),6269(a,1))].">
      <j1 rule="para" parents="3890 6269"/>
    </justification>
  </clause>

  <clause id="6318">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(5256(a,1),6269(a,1,2,1))].">
      <j1 rule="para" parents="5256 6269"/>
    </justification>
  </clause>

  <clause id="6319">
    <literal><![CDATA[
      K(x,((y * z) \ y) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(6284(a,1),401(a,1)),flip(b)].">
      <j1 rule="para" parents="6284 401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6321">
    <literal><![CDATA[
      K(x,(y * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),6288(a,1,2,2))].">
      <j1 rule="para" parents="11 6288"/>
    </justification>
  </clause>

  <clause id="6322">
    <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(463(a,1),6288(a,1,2,2))].">
      <j1 rule="para" parents="463 6288"/>
    </justification>
  </clause>

  <clause id="6323">
    <literal><![CDATA[
      K(x,((y * z) * u) \ (y * (z * u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(y,z,u) \ 1) = w
    ]]></literal>
    <justification jstring="[para(210(a,1),6288(a,1,2,2))].">
      <j1 rule="para" parents="210 6288"/>
    </justification>
  </clause>

  <clause id="6324">
    <literal><![CDATA[
      T(x,(y * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),6297(a,1,2,2))].">
      <j1 rule="para" parents="11 6297"/>
    </justification>
  </clause>

  <clause id="6325">
    <literal><![CDATA[
      x / T(x * (y / x),y \ x) = L((y / x) \ 1,y / x,x)
    ]]></literal>
    <justification jstring="[para(4867(a,1),6304(a,1,2))].">
      <j1 rule="para" parents="4867 6304"/>
    </justification>
  </clause>

  <clause id="6326">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(5261(a,1),6319(a,1,2,1,1))].">
      <j1 rule="para" parents="5261 6319"/>
    </justification>
  </clause>

  <clause id="6328">
    <literal><![CDATA[
      (x * (y * y)) * K(y \ (y \ 1),y) = x / ((y \ 1) / y)
    ]]></literal>
    <justification jstring="[para(668(a,1),6125(a,1,1))].">
      <j1 rule="para" parents="668 6125"/>
    </justification>
  </clause>

  <clause id="6329">
    <literal><![CDATA[
      K(x,1 / ((y * (1 / z)) / y)) = K(x,z * K(1 / z,y))
    ]]></literal>
    <justification jstring="[para(5018(a,1),6153(a,1,2,2))].">
      <j1 rule="para" parents="5018 6153"/>
    </justification>
  </clause>

  <clause id="6330">
    <literal><![CDATA[
      T(x,K(y,(x \ z) \ 1)) / (z * T(z \ x,y)) = (x * (x / (z * T(z \ x,y)))) / x
    ]]></literal>
    <justification jstring="[para(6159(a,1),4170(a,1,1,2))].">
      <j1 rule="para" parents="6159 4170"/>
    </justification>
  </clause>

  <clause id="6331">
    <literal><![CDATA[
      x * (K(y,x) * K(y * x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[hyper(347,a,4279,a,b,6174,a),flip(a)].">
      <j1 rule="hyper" parents="347 4279 6174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6332">
    <literal><![CDATA[
      x * (K(R(y,z,u),x) * K(w,R(y,z,u))) = (R(y,z,u) * x) / R(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(27(a,2),6174(a,2,2))].">
      <j1 rule="para" parents="27 6174"/>
    </justification>
  </clause>

  <clause id="6333">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) / (1 / x) = (x \ y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(3434(a,1),6196(a,1,1))].">
      <j1 rule="para" parents="3434 6196"/>
    </justification>
  </clause>

  <clause id="6334">
    <literal><![CDATA[
      K(x,1 / x) * (y / x) = y / (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(347,a,2751,a,b,6215,a)].">
      <j1 rule="hyper" parents="347 2751 6215"/>
    </justification>
  </clause>

  <clause id="6337">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K((x \ y) \ z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6269,a,6226,a)].">
      <j1 rule="hyper" parents="6269 6226"/>
    </justification>
  </clause>

  <clause id="6338">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / ((y * K(z,y)) * z) = R(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[hyper(131,a,6239,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="131 6239 107"/>
    </justification>
  </clause>

  <clause id="6339">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z * K(y,z),y)
    ]]></literal>
    <justification jstring="[para(6239(a,1),5107(a,1,2))].">
      <j1 rule="para" parents="6239 5107"/>
    </justification>
  </clause>

  <clause id="6340">
    <literal><![CDATA[
      (x * (y \ 1)) \ (x * (T(y,z) \ 1)) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,5042,a,b,6252,a)].">
      <j1 rule="hyper" parents="128 5042 6252"/>
    </justification>
  </clause>

  <clause id="6341">
    <literal><![CDATA[
      T(x,(x / y) / x) / ((x / y) \ x) = (x / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(347,a,6303,a,b,6286,a)].">
      <j1 rule="hyper" parents="347 6303 6286"/>
    </justification>
  </clause>

  <clause id="6342">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,2443,a(flip),b,6299,a)].">
      <j1 rule="hyper" parents="347 2443 6299"/>
    </justification>
  </clause>

  <clause id="6343">
    <literal><![CDATA[
      x * K(y,1 / (x \ z)) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(6257(a,2),6299(a,1,2))].">
      <j1 rule="para" parents="6257 6299"/>
    </justification>
  </clause>

  <clause id="6344">
    <literal><![CDATA[
      T(x,T(y,x)) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(22(a,2),6302(a,1,1,2))].">
      <j1 rule="para" parents="22 6302"/>
    </justification>
  </clause>

  <clause id="6345">
    <literal><![CDATA[
      T(x,y) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(4270(a,1),6344(a,1,1))].">
      <j1 rule="para" parents="4270 6344"/>
    </justification>
  </clause>

  <clause id="6346">
    <literal><![CDATA[
      ((x \ y) * x) \ x = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6345,a),flip(a)].">
      <j1 rule="hyper" parents="373 6345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6347">
    <literal><![CDATA[
      (x * y) \ T(x,y) = (y * x) \ x
    ]]></literal>
    <justification jstring="[hyper(214,a,6345,a)].">
      <j1 rule="hyper" parents="214 6345"/>
    </justification>
  </clause>

  <clause id="6348">
    <literal><![CDATA[
      T(x,y) = (x * y) * ((y * x) \ x)
    ]]></literal>
    <justification jstring="[hyper(148,a,6345,a),flip(a)].">
      <j1 rule="hyper" parents="148 6345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6349">
    <literal><![CDATA[
      T(x * y,z) * ((y * x) \ x) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,6347,a(flip),b,5189,a)].">
      <j1 rule="hyper" parents="134 6347 5189"/>
    </justification>
  </clause>

  <clause id="6351">
    <literal><![CDATA[
      ((x * y) \ y) * T(y * x,x \ 1) = T(y,x)
    ]]></literal>
    <justification jstring="[para(6347(a,1),4260(a,1,1))].">
      <j1 rule="para" parents="6347 4260"/>
    </justification>
  </clause>

  <clause id="6352">
    <literal><![CDATA[
      L(T(x,x \ 1),x \ 1,y) \ y = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[para(417(a,2),6305(a,2,1)),flip(a)].">
      <j1 rule="para" parents="417 6305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6353">
    <literal><![CDATA[
      x / T(x * (1 / y),y) = (x * (1 / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(220,a,6308,a,b,xx)].">
      <j1 rule="hyper" parents="220 6308"/>
    </justification>
  </clause>

  <clause id="6354">
    <literal><![CDATA[
      T(x * (1 / y),y) = L(y,y,x) \ x
    ]]></literal>
    <justification jstring="[para(3280(a,2),6308(a,2,1))].">
      <j1 rule="para" parents="3280 6308"/>
    </justification>
  </clause>

  <clause id="6355">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * x = (x / (y \ 1)) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,6309,a(flip),b,6144,a),flip(a)].">
      <j1 rule="hyper" parents="133 6309 6144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6356">
    <literal><![CDATA[
      (x / y) * (z * K(y,1 / y)) = (x / (1 / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(6334(a,1),3478(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6334 3478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6359">
    <literal><![CDATA[
      (x * (T(y,z) \ 1)) * K(y,z) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(39,a,6123,a,b,6340,a)].">
      <j1 rule="hyper" parents="39 6123 6340"/>
    </justification>
  </clause>

  <clause id="6360">
    <literal><![CDATA[
      (x * (T(y,z) \ 1)) * T(y,z) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,6359,a(flip),b,5919,a),flip(a)].">
      <j1 rule="hyper" parents="133 6359 5919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6361">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z != w
    ]]></literal>
    <literal><![CDATA[
      K(u,(x * y) \ z) = w
    ]]></literal>
    <justification jstring="[para(1022(a,1),6203(a,1,1))].">
      <j1 rule="para" parents="1022 6203"/>
    </justification>
  </clause>

  <clause id="6362">
    <literal><![CDATA[
      R(x,T(y,z),T(z,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(595,a,6210,a),flip(a)].">
      <j1 rule="hyper" parents="595 6210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6363">
    <literal><![CDATA[
      R(x,T(y,z),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(6210(a,1),595(a,1))].">
      <j1 rule="para" parents="6210 595"/>
    </justification>
  </clause>

  <clause id="6365">
    <literal><![CDATA[
      R(T(x,y),T(z,u),T(u,z)) = T(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,27,a(flip),b,6362,a),flip(a)].">
      <j1 rule="hyper" parents="347 27 6362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6366">
    <literal><![CDATA[
      T(R(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      R(T(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(6365(a,1),6363(a,1))].">
      <j1 rule="para" parents="6365 6363"/>
    </justification>
  </clause>

  <clause id="6367">
    <literal><![CDATA[
      T(K(x,(y \ z) \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(K(x,z \ y),u),z \ y,v5) = w
    ]]></literal>
    <justification jstring="[para(6255(a,1),5652(a,1,1))].">
      <j1 rule="para" parents="6255 5652"/>
    </justification>
  </clause>

  <clause id="6368">
    <literal><![CDATA[
      (x \ 1) * (y * K(x \ y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T((x \ 1) * y,z) = u
    ]]></literal>
    <justification jstring="[para(6064(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6064 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6369">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = (1 / z) * K((((1 / z) \ x) \ 1) \ (z \ 1),y)
    ]]></literal>
    <justification jstring="[para(3879(a,1),6065(a,2,2))].">
      <j1 rule="para" parents="3879 6065"/>
    </justification>
  </clause>

  <clause id="6370">
    <literal><![CDATA[
      T(x * K(x * y,y \ 1),y) = y \ T(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[para(5768(a,1),6068(a,1,1,2))].">
      <j1 rule="para" parents="5768 6068"/>
    </justification>
  </clause>

  <clause id="6371">
    <literal><![CDATA[
      (x * (y \ z)) * T(y,y \ z) = R(x,z / y,y) * z
    ]]></literal>
    <justification jstring="[hyper(347,a,584,a,b,6076,a),flip(a)].">
      <j1 rule="hyper" parents="347 584 6076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6372">
    <literal><![CDATA[
      (x / y) * ((y * y) * K(y \ 1,y)) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(725,a,6087,a)].">
      <j1 rule="hyper" parents="725 6087"/>
    </justification>
  </clause>

  <clause id="6373">
    <literal><![CDATA[
      K(x,x \ 1) * (((y / x) * (x * x)) \ z) = (y / (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(6087(a,1),3494(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6087 3494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6374">
    <literal><![CDATA[
      K((x / y) \ z,x) = K((y \ x) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5992,a(flip),b,6088,a),flip(a)].">
      <j1 rule="hyper" parents="63 5992 6088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6375">
    <literal><![CDATA[
      K(x,1 / x) * (y * L(x,z,u)) = y * L((x \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(6129(a,1),2776(a,2,2))].">
      <j1 rule="para" parents="6129 2776"/>
    </justification>
  </clause>

  <clause id="6376">
    <literal><![CDATA[
      L(K(x,y \ z),z,z \ 1) = K(x,((1 / z) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(2938(a,1),6266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2938 6266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6377">
    <literal><![CDATA[
      x * (y \ R(y,x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[para(5385(a,1),6331(a,1,2))].">
      <j1 rule="para" parents="5385 6331"/>
    </justification>
  </clause>

  <clause id="6378">
    <literal><![CDATA[
      (x \ R(x,y \ 1,x)) / (T(x * (y \ 1),x) / x) != z
    ]]></literal>
    <literal><![CDATA[
      R(y,y \ 1,x \ R(x,y \ 1,x)) = z
    ]]></literal>
    <justification jstring="[para(6377(a,1),684(a,1,2))].">
      <j1 rule="para" parents="6377 684"/>
    </justification>
  </clause>

  <clause id="6379">
    <literal><![CDATA[
      T(x / (1 / (1 / y)),1 / (1 / y)) / (1 / y) = (y \ x) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(113(a,2),6333(a,1,1))].">
      <j1 rule="para" parents="113 6333"/>
    </justification>
  </clause>

  <clause id="6380">
    <literal><![CDATA[
      x \ (y * ((z * (y \ x)) / z)) = K(z,1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(138,a,6343,a)].">
      <j1 rule="hyper" parents="138 6343"/>
    </justification>
  </clause>

  <clause id="6381">
    <literal><![CDATA[
      (x / y) * (y * (y * K(y \ 1,y))) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(2215(a,1),6372(a,1,2))].">
      <j1 rule="para" parents="2215 6372"/>
    </justification>
  </clause>

  <clause id="6382">
    <literal><![CDATA[
      x \ (R(1 / y,y,x) * ((z * (y * x)) / z)) = K(z,1 / (x \ R(1 / y,y,x)))
    ]]></literal>
    <justification jstring="[para(420(a,1),6380(a,1,2,2,1,2))].">
      <j1 rule="para" parents="420 6380"/>
    </justification>
  </clause>

  <clause id="6383">
    <literal><![CDATA[
      x * (x * K(x \ 1,x)) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,80,a(flip),b,6381,a),flip(a)].">
      <j1 rule="hyper" parents="128 80 6381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6384">
    <literal><![CDATA[
      x * (1 / (1 / x)) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[para(1902(a,1),6383(a,1,2))].">
      <j1 rule="para" parents="1902 6383"/>
    </justification>
  </clause>

  <clause id="6385">
    <literal><![CDATA[
      (x / y) * ((1 / y) \ y) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(6383(a,1),6381(a,1,2))].">
      <j1 rule="para" parents="6383 6381"/>
    </justification>
  </clause>

  <clause id="6386">
    <literal><![CDATA[
      (x * y) / (y \ 1) = x * ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[para(11(a,1),6385(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 6385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6387">
    <literal><![CDATA[
      x * ((1 / (1 / y)) \ (1 / y)) = (x * (1 / y)) / y
    ]]></literal>
    <justification jstring="[para(83(a,1),6386(a,1,2)),flip(a)].">
      <j1 rule="para" parents="83 6386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6388">
    <literal><![CDATA[
      (x * (1 / y)) / y = x * ((1 / y) / y)
    ]]></literal>
    <justification jstring="[para(1130(a,1),6387(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1130 6387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6390">
    <literal><![CDATA[
      K(x,L(L(y \ 1,y,z),z * y,u)) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[para(446(a,2),6272(a,1,2))].">
      <j1 rule="para" parents="446 6272"/>
    </justification>
  </clause>

  <clause id="6391">
    <literal><![CDATA[
      L(T(x,x \ 1),x,y) \ y = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[para(3188(a,1),6352(a,1,1))].">
      <j1 rule="para" parents="3188 6352"/>
    </justification>
  </clause>

  <clause id="6393">
    <literal><![CDATA[
      L(K(x,y \ z),z,z \ 1) = K(x,((z \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,5425,a(flip),b,6376,a),flip(a)].">
      <j1 rule="hyper" parents="347 5425 6376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6394">
    <literal><![CDATA[
      K(x,((y \ 1) * (y / z)) \ 1) = L(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[para(83(a,1),6393(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="83 6393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6395">
    <literal><![CDATA[
      (x * y) * K(T(y,x),z) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4292(a,1),5953(a,1,1))].">
      <j1 rule="para" parents="4292 5953"/>
    </justification>
  </clause>

  <clause id="6396">
    <literal><![CDATA[
      x \ T(x * K(y \ x,z),x) = K(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,6024,a(flip),b,5941,a(flip))].">
      <j1 rule="hyper" parents="128 6024 5941"/>
    </justification>
  </clause>

  <clause id="6397">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = x \ T(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(83(a,1),6396(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 6396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6398">
    <literal><![CDATA[
      R(x,K(y,z),L(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(594,a,6039,a)].">
      <j1 rule="hyper" parents="594 6039"/>
    </justification>
  </clause>

  <clause id="6399">
    <literal><![CDATA[
      (x * T(y,L(z * K(y,z),y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,5077,a(flip),b,6209,a),flip(a)].">
      <j1 rule="hyper" parents="347 5077 6209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6400">
    <literal><![CDATA[
      (x * (y * (z * T(z \ (y \ (x \ u)),w)))) \ u = K(w,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(1022(a,1),6220(a,1,1,2))].">
      <j1 rule="para" parents="1022 6220"/>
    </justification>
  </clause>

  <clause id="6401">
    <literal><![CDATA[
      (x * (((y \ ((x \ z) * u)) * y) / u)) \ z = K(y,(x * (y / u)) \ z)
    ]]></literal>
    <justification jstring="[para(1576(a,1),6220(a,1,1,2))].">
      <j1 rule="para" parents="1576 6220"/>
    </justification>
  </clause>

  <clause id="6402">
    <literal><![CDATA[
      x * ((y * y) * K(y \ (y \ 1),y)) = x / ((y \ 1) / y)
    ]]></literal>
    <justification jstring="[hyper(725,a,6328,a)].">
      <j1 rule="hyper" parents="725 6328"/>
    </justification>
  </clause>

  <clause id="6403">
    <literal><![CDATA[
      K(x,(y / (1 / (1 / z))) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(6356(a,1),5426(a,1,2))].">
      <j1 rule="para" parents="6356 5426"/>
    </justification>
  </clause>

  <clause id="6404">
    <literal><![CDATA[
      x * (y * (y * K(y \ (y \ 1),y))) = x / ((y \ 1) / y)
    ]]></literal>
    <justification jstring="[para(6227(a,1),6402(a,1,2))].">
      <j1 rule="para" parents="6227 6402"/>
    </justification>
  </clause>

  <clause id="6405">
    <literal><![CDATA[
      x * (y * (y * K(y \ (y \ 1),y))) = x / (y \ (1 / y))
    ]]></literal>
    <justification jstring="[para(888(a,1),6404(a,2,2))].">
      <j1 rule="para" parents="888 6404"/>
    </justification>
  </clause>

  <clause id="6406">
    <literal><![CDATA[
      R(x,y,z * K(y,z)) = R(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(595,a,6072,a),flip(a)].">
      <j1 rule="hyper" parents="595 6072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6407">
    <literal><![CDATA[
      R(x,T(y,z),z) = R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(5364,a,6406,a),flip(a)].">
      <j1 rule="hyper" parents="5364 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6408">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = x / T(x * ((x / y) / x),y)
    ]]></literal>
    <justification jstring="[para(83(a,1),6325(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="83 6325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6409">
    <literal><![CDATA[
      a(x,y * K(z,y),z) = a(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(1106,a,6339,a),flip(a)].">
      <j1 rule="hyper" parents="1106 6339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6410">
    <literal><![CDATA[
      a(x,y \ z,T(y,y \ z)) = a(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(4990(a,1),6409(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4990 6409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6411">
    <literal><![CDATA[
      K(x,L(L(1 / y,y,z),z * y,u)) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4675,a,b,6390,a)].">
      <j1 rule="hyper" parents="63 4675 6390"/>
    </justification>
  </clause>

  <clause id="6412">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),u) = z \ ((y * T(y \ 1,u)) * z)
    ]]></literal>
    <justification jstring="[para(1544(a,1),6091(a,2,2))].">
      <j1 rule="para" parents="1544 6091"/>
    </justification>
  </clause>

  <clause id="6413">
    <literal><![CDATA[
      T(x * T(x \ 1,y),z) = K(u \ (u / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,22,a,b,6412,a)].">
      <j1 rule="hyper" parents="347 22 6412"/>
    </justification>
  </clause>

  <clause id="6419">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),u) = T(K(y \ 1,u),z)
    ]]></literal>
    <justification jstring="[para(4925(a,1),6413(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4925 6413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6421">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5998,a(flip),b,6419,a)].">
      <j1 rule="hyper" parents="63 5998 6419"/>
    </justification>
  </clause>

  <clause id="6422">
    <literal><![CDATA[
      K(T(1 / x,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(83(a,1),6421(a,2,1,1))].">
      <j1 rule="para" parents="83 6421"/>
    </justification>
  </clause>

  <clause id="6423">
    <literal><![CDATA[
      K(T(x \ 1,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(3407(a,1),6421(a,2,1))].">
      <j1 rule="para" parents="3407 6421"/>
    </justification>
  </clause>

  <clause id="6424">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) \ 1,w) = T(K(z \ K(y,x),w),u)
    ]]></literal>
    <justification jstring="[para(6001(a,1),6421(a,2,1))].">
      <j1 rule="para" parents="6001 6421"/>
    </justification>
  </clause>

  <clause id="6425">
    <literal><![CDATA[
      K(1 / T(x,y),z) = T(K(1 / x,z),y)
    ]]></literal>
    <justification jstring="[para(2726(a,1),6422(a,1,1))].">
      <j1 rule="para" parents="2726 6422"/>
    </justification>
  </clause>

  <clause id="6426">
    <literal><![CDATA[
      K(((x \ 1) * y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(6081,a,6423,a)].">
      <j1 rule="hyper" parents="6081 6423"/>
    </justification>
  </clause>

  <clause id="6427">
    <literal><![CDATA[
      T(K(x \ K(x,y),z),y) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(5085(a,1),6424(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5085 6424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6428">
    <literal><![CDATA[
      K(x \ K(x,y),z) * y = y * K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,6427,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 6427 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6429">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(6118(a,2),2373(a,1)),flip(b)].">
      <j1 rule="para" parents="6118 2373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6430">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1905(a,1),6429(a,1,3))].">
      <j1 rule="para" parents="1905 6429"/>
    </justification>
  </clause>

  <clause id="6431">
    <literal><![CDATA[
      x / (K(y,z) * T(z,u)) = (x / T(z,u)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6149,a,6096,a)].">
      <j1 rule="hyper" parents="6149 6096"/>
    </justification>
  </clause>

  <clause id="6432">
    <literal><![CDATA[
      (x / T(y,y * z)) * K(y,z) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(5163(a,1),6431(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5163 6431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6433">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,y * z) = x / R(y,z,y)
    ]]></literal>
    <justification jstring="[para(5164(a,1),6431(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5164 6431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6434">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,y * z) = (x / R(y,z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,6433,a(flip),b,5919,a),flip(a)].">
      <j1 rule="hyper" parents="133 6433 5919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6435">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,z * y) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(6197,a,6434,a)].">
      <j1 rule="hyper" parents="6197 6434"/>
    </justification>
  </clause>

  <clause id="6436">
    <literal><![CDATA[
      (x / R(y,z,y)) * y != u
    ]]></literal>
    <literal><![CDATA[
      (x * K(z,y)) * K(y,y * z) = u
    ]]></literal>
    <justification jstring="[para(6434(a,1),6197(a,1))].">
      <j1 rule="para" parents="6434 6197"/>
    </justification>
  </clause>

  <clause id="6437">
    <literal><![CDATA[
      x * ((y * y) * K(z,y \ (y \ 1))) = x / T(y \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(725,a,6166,a)].">
      <j1 rule="hyper" parents="725 6166"/>
    </justification>
  </clause>

  <clause id="6438">
    <literal><![CDATA[
      (((x / y) * T(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u))
    ]]></literal>
    <justification jstring="[para(83(a,1),6221(a,1,1,1,2,1))].">
      <j1 rule="para" parents="83 6221"/>
    </justification>
  </clause>

  <clause id="6439">
    <literal><![CDATA[
      K(x,T(y \ z,u) \ T(z,u)) = T(K(y,x) * z,u) \ T(z,u)
    ]]></literal>
    <justification jstring="[para(5193(a,1),6222(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5193 6222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6440">
    <literal><![CDATA[
      ((x / y) * L(1 / y,y,x)) / (x / y) = x \ T(x / y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3264(a,2),6295(a,1,1,2))].">
      <j1 rule="para" parents="3264 6295"/>
    </justification>
  </clause>

  <clause id="6441">
    <literal><![CDATA[
      L(x,(y / z) * z,u) = L(x,y * K(w * w,z),u)
    ]]></literal>
    <justification jstring="[hyper(3597,a,6310,a)].">
      <j1 rule="hyper" parents="3597 6310"/>
    </justification>
  </clause>

  <clause id="6443">
    <literal><![CDATA[
      L(x,y * K(z * z,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),6441(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 6441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6444">
    <literal><![CDATA[
      L(x,K(y * y,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(550,a,6443,a),flip(a)].">
      <j1 rule="hyper" parents="550 6443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6446">
    <literal><![CDATA[
      L(x,K(y,z * z),u) = x
    ]]></literal>
    <justification jstring="[hyper(5182,a,6444,a)].">
      <j1 rule="hyper" parents="5182 6444"/>
    </justification>
  </clause>

  <clause id="6447">
    <literal><![CDATA[
      (x * K(y,z * z)) * u = x * (K(y,z * z) * u)
    ]]></literal>
    <justification jstring="[hyper(1362,a,6446,a),flip(a)].">
      <j1 rule="hyper" parents="1362 6446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6448">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(6316,a,6266,a),flip(a)].">
      <j1 rule="hyper" parents="6316 6266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6449">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(6266(a,1),6316(a,1))].">
      <j1 rule="para" parents="6266 6316"/>
    </justification>
  </clause>

  <clause id="6450">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),u,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),6448(a,2,2,1))].">
      <j1 rule="para" parents="10 6448"/>
    </justification>
  </clause>

  <clause id="6451">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),6448(a,2,2,2))].">
      <j1 rule="para" parents="10 6448"/>
    </justification>
  </clause>

  <clause id="6452">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,L(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(99(a,2),6448(a,2,2))].">
      <j1 rule="para" parents="99 6448"/>
    </justification>
  </clause>

  <clause id="6453">
    <literal><![CDATA[
      K(x,L(y \ z,y,K(z,u))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(4252,a,6452,a),flip(a)].">
      <j1 rule="hyper" parents="4252 6452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6454">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6448,a(flip),b,6452,a),flip(a)].">
      <j1 rule="hyper" parents="63 6448 6452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6455">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ T(y,z)) = K(x,u \ y)
    ]]></literal>
    <justification jstring="[para(5032(a,1),6453(a,1,2))].">
      <j1 rule="para" parents="5032 6453"/>
    </justification>
  </clause>

  <clause id="6456">
    <literal><![CDATA[
      K(x \ (y \ z),(y \ z) \ x) = K(x \ (y \ z),z \ (y * x))
    ]]></literal>
    <justification jstring="[hyper(2405,a,6450,a)].">
      <j1 rule="hyper" parents="2405 6450"/>
    </justification>
  </clause>

  <clause id="6457">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,5959,a(flip),b,6450,a)].">
      <j1 rule="hyper" parents="63 5959 6450"/>
    </justification>
  </clause>

  <clause id="6458">
    <literal><![CDATA[
      (x * y) * K(z,u \ (x * y)) = x * (y * K(z,(x \ u) \ y))
    ]]></literal>
    <justification jstring="[hyper(134,a,6450,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 6450 18"/>
    </justification>
  </clause>

  <clause id="6459">
    <literal><![CDATA[
      T(K(x,y \ (z * u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(T(K(x,(z \ y) \ u),w),u,z) = v5
    ]]></literal>
    <justification jstring="[para(6450(a,1),5652(a,1,1))].">
      <j1 rule="para" parents="6450 5652"/>
    </justification>
  </clause>

  <clause id="6460">
    <literal><![CDATA[
      K(x,(y \ x) \ x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,5096,a(flip),b,6457,a),flip(a)].">
      <j1 rule="hyper" parents="347 5096 6457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6461">
    <literal><![CDATA[
      T(x,(y \ z) \ x) = T(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[hyper(132,a,6457,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 6457 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6462">
    <literal><![CDATA[
      K(x,(y * z) \ (z * x)) = K(x,T(y,z) \ x)
    ]]></literal>
    <justification jstring="[para(22(a,2),6457(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="22 6457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6463">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ x) = K(x,u \ (K(z,y) * x))
    ]]></literal>
    <justification jstring="[para(5256(a,1),6457(a,1,2,1))].">
      <j1 rule="para" parents="5256 6457"/>
    </justification>
  </clause>

  <clause id="6464">
    <literal><![CDATA[
      K(x,((y * K(z,y)) \ u) \ x) = K(x,u \ (y * (K(z,y) * x)))
    ]]></literal>
    <justification jstring="[para(5331(a,1),6457(a,2,2,2))].">
      <j1 rule="para" parents="5331 6457"/>
    </justification>
  </clause>

  <clause id="6465">
    <literal><![CDATA[
      K(x,x / y) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(83(a,1),6460(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 6460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6466">
    <literal><![CDATA[
      K(x,T(y,y \ x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(112(a,2),6460(a,1,2))].">
      <j1 rule="para" parents="112 6460"/>
    </justification>
  </clause>

  <clause id="6467">
    <literal><![CDATA[
      T(x,y \ (z * x)) * K(y \ z,x) = L(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6461(a,1),6003(a,1,1))].">
      <j1 rule="para" parents="6461 6003"/>
    </justification>
  </clause>

  <clause id="6468">
    <literal><![CDATA[
      K(x,L(y \ z,y,u / y)) = K(x,u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[para(12(a,1),6454(a,2,2,1))].">
      <j1 rule="para" parents="12 6454"/>
    </justification>
  </clause>

  <clause id="6469">
    <literal><![CDATA[
      K(x,L(y \ (((z * u) \ z) \ z),y,u \ 1)) = K(x,((u \ 1) * y) \ R(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[para(6307(a,1),6454(a,2,2,2))].">
      <j1 rule="para" parents="6307 6454"/>
    </justification>
  </clause>

  <clause id="6470">
    <literal><![CDATA[
      L(K(x,R(y,z,y) \ (z \ u)),z \ u,z) = K(x,T(y * z,y) \ u)
    ]]></literal>
    <justification jstring="[para(4378(a,1),6451(a,2,2,1))].">
      <j1 rule="para" parents="4378 6451"/>
    </justification>
  </clause>

  <clause id="6471">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(u * K(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(5256(a,1),6451(a,1,1,2))].">
      <j1 rule="para" parents="5256 6451"/>
    </justification>
  </clause>

  <clause id="6472">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(6452(a,1),6449(a,1))].">
      <j1 rule="para" parents="6452 6449"/>
    </justification>
  </clause>

  <clause id="6473">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K((x \ y) \ z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,6250,a(flip),b,6337,a),flip(a)].">
      <j1 rule="hyper" parents="347 6250 6337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6474">
    <literal><![CDATA[
      T(x,1 / y) / ((x / y) \ x) = (x / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(6296(a,1),6341(a,1,1))].">
      <j1 rule="para" parents="6296 6341"/>
    </justification>
  </clause>

  <clause id="6475">
    <literal><![CDATA[
      (x / y) * K(x,1 / y) = T(x,1 / y) / y
    ]]></literal>
    <justification jstring="[para(83(a,1),6474(a,1,2)),flip(a)].">
      <j1 rule="para" parents="83 6474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6476">
    <literal><![CDATA[
      K(x,x \ 1) * ((x * x) \ ((y / x) \ z)) = (y / (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(459(a,1),6373(a,1,2))].">
      <j1 rule="para" parents="459 6373"/>
    </justification>
  </clause>

  <clause id="6477">
    <literal><![CDATA[
      (x * T(y \ (y \ 1),z)) \ x = (y * y) * K(z,y \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(128,a,11,a(flip),b,6437,a)].">
      <j1 rule="hyper" parents="128 11 6437"/>
    </justification>
  </clause>

  <clause id="6478">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,T(x \ z,u) \ T(z,u)) = T(z,u)
    ]]></literal>
    <justification jstring="[hyper(134,a,6439,a,b,xx)].">
      <j1 rule="hyper" parents="134 6439"/>
    </justification>
  </clause>

  <clause id="6479">
    <literal><![CDATA[
      (x \ (y \ z)) \ K(x \ (y \ z),z \ (y * x)) = 1 / (x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(128,a,6456,a(flip),b,2598,a)].">
      <j1 rule="hyper" parents="128 6456 2598"/>
    </justification>
  </clause>

  <clause id="6481">
    <literal><![CDATA[
      (x * y) * z != x * (y * K(u,(x \ w) \ y))
    ]]></literal>
    <literal><![CDATA[
      K(u,w \ (x * y)) = z
    ]]></literal>
    <justification jstring="[para(6458(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="6458 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6482">
    <literal><![CDATA[
      x * (y * K(z,(x \ 1) \ y)) = (x * y) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(66(a,1),6458(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="66 6458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6483">
    <literal><![CDATA[
      (x * y) * z != x * (y * K(u,(x \ 1) \ y))
    ]]></literal>
    <literal><![CDATA[
      K(u,x * y) = z
    ]]></literal>
    <justification jstring="[para(6482(a,2),43(a,1)),flip(a)].">
      <j1 rule="para" parents="6482 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6484">
    <literal><![CDATA[
      K(x,(K(y,z) * (y \ u)) \ x) = K(x,u \ (y * (K(z,y) * x)))
    ]]></literal>
    <justification jstring="[para(5444(a,1),6464(a,1,2,1))].">
      <j1 rule="para" parents="5444 6464"/>
    </justification>
  </clause>

  <clause id="6485">
    <literal><![CDATA[
      ((1 / (1 / x)) * x) \ ((y / x) \ z) = (y / (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,3506,a(flip),b,6476,a)].">
      <j1 rule="hyper" parents="63 3506 6476"/>
    </justification>
  </clause>

  <clause id="6486">
    <literal><![CDATA[
      (x * (1 / (1 / x))) \ ((y / x) \ z) = (y / (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(514(a,1),6485(a,1,1))].">
      <j1 rule="para" parents="514 6485"/>
    </justification>
  </clause>

  <clause id="6487">
    <literal><![CDATA[
      ((1 / x) \ x) \ ((y / x) \ z) = (y / (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(6384(a,1),6486(a,1,1))].">
      <j1 rule="para" parents="6384 6486"/>
    </justification>
  </clause>

  <clause id="6488">
    <literal><![CDATA[
      (x \ (1 / x)) * ((y / x) \ z) = (y / (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[hyper(1131,a,6487,a)].">
      <j1 rule="hyper" parents="1131 6487"/>
    </justification>
  </clause>

  <clause id="6489">
    <literal><![CDATA[
      (1 / x) * ((y / x) \ z) = x * ((y / (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(134,a,6487,a(flip),b,1129,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 6487 1129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6490">
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = K((y / (z \ 1)) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(5906,a,5988,a)].">
      <j1 rule="hyper" parents="5906 5988"/>
    </justification>
  </clause>

  <clause id="6491">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K((x * y) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(6080,a,6490,a),flip(a)].">
      <j1 rule="hyper" parents="6080 6490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6492">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * z) = (K(x,y) / x) * z
    ]]></literal>
    <justification jstring="[para(5821(a,1),5937(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5821 5937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6493">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) = (K(x,y) / x) * z
    ]]></literal>
    <justification jstring="[hyper(5861,a,6492,a)].">
      <j1 rule="hyper" parents="5861 6492"/>
    </justification>
  </clause>

  <clause id="6494">
    <literal><![CDATA[
      (K(x,y) / x) * (x * (T(y,x) * z)) = (1 / x) * (x * (y * z))
    ]]></literal>
    <justification jstring="[para(5231(a,1),6492(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5231 6492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6495">
    <literal><![CDATA[
      (K(x,y) / x) * (x * (T(y,x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(y * z,x,x \ 1) = u
    ]]></literal>
    <justification jstring="[para(6494(a,2),2953(a,1))].">
      <j1 rule="para" parents="6494 2953"/>
    </justification>
  </clause>

  <clause id="6496">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / (y * T(z,y)) = R(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[para(5914(a,1),6338(a,1,2))].">
      <j1 rule="para" parents="5914 6338"/>
    </justification>
  </clause>

  <clause id="6497">
    <literal><![CDATA[
      R(x,y * K(z,y),z) = R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(595,a,6496,a),flip(a)].">
      <j1 rule="hyper" parents="595 6496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6498">
    <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(1079(a,1),6361(a,1,1,2))].">
      <j1 rule="para" parents="1079 6361"/>
    </justification>
  </clause>

  <clause id="6499">
    <literal><![CDATA[
      (x * ((x \ y) * K(z \ (x \ y),u))) \ y != w
    ]]></literal>
    <literal><![CDATA[
      K(u,(x * z) \ y) = w
    ]]></literal>
    <justification jstring="[para(5941(a,1),6361(a,1,1,2))].">
      <j1 rule="para" parents="5941 6361"/>
    </justification>
  </clause>

  <clause id="6500">
    <literal><![CDATA[
      L(((x / y) * (1 / y)) / (x / y),y,x) = x \ T(x / y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(951,a,6440,a)].">
      <j1 rule="hyper" parents="951 6440"/>
    </justification>
  </clause>

  <clause id="6501">
    <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(6428(a,2),6471(a,2,2,1))].">
      <j1 rule="para" parents="6428 6471"/>
    </justification>
  </clause>

  <clause id="6502">
    <literal><![CDATA[
      L((x * (y \ (1 / y))) / (x / y),y,x) = x \ T(x / y,y \ 1)
    ]]></literal>
    <justification jstring="[para(849(a,1),6500(a,1,1,1))].">
      <j1 rule="para" parents="849 6500"/>
    </justification>
  </clause>

  <clause id="6503">
    <literal><![CDATA[
      (x * (1 / T(y,z))) * T(y,z) = R(x,1 / T(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(5040,a,6144,a),flip(a)].">
      <j1 rule="hyper" parents="5040 6144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6504">
    <literal><![CDATA[
      R(x,1 / T(y,z),y) / y = (x * (1 / T(y,z))) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,6503,a(flip),b,5914,a)].">
      <j1 rule="hyper" parents="131 6503 5914"/>
    </justification>
  </clause>

  <clause id="6505">
    <literal><![CDATA[
      R(x,1 / T(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,T(y,z) \ 1,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6503(a,1),2282(a,1))].">
      <j1 rule="para" parents="6503 2282"/>
    </justification>
  </clause>

  <clause id="6506">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = (x * (1 / T(y,z))) * K(y,z)
    ]]></literal>
    <justification jstring="[para(2260(a,1),6504(a,1,1))].">
      <j1 rule="para" parents="2260 6504"/>
    </justification>
  </clause>

  <clause id="6507">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,T(y,z) \ 1,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(2260(a,1),6505(a,1))].">
      <j1 rule="para" parents="2260 6505"/>
    </justification>
  </clause>

  <clause id="6508">
    <literal><![CDATA[
      R(K(x,y),x * z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(5241,a,5845,a)].">
      <j1 rule="hyper" parents="5241 5845"/>
    </justification>
  </clause>

  <clause id="6509">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),6508(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 6508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6510">
    <literal><![CDATA[
      K(R(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,600,a(flip),b,6509,a),flip(a)].">
      <j1 rule="hyper" parents="347 600 6509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6511">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) * (y * z) = (K(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,6509,a,b,20,a(flip))].">
      <j1 rule="hyper" parents="133 6509 20"/>
    </justification>
  </clause>

  <clause id="6512">
    <literal><![CDATA[
      K((x * y) / ((z \ x) * y),u) = R(K(z,u),x,y)
    ]]></literal>
    <justification jstring="[para(104(a,1),6509(a,1,1))].">
      <j1 rule="para" parents="104 6509"/>
    </justification>
  </clause>

  <clause id="6513">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = (w * R(K(y,x),z,u)) \ w
    ]]></literal>
    <justification jstring="[para(6509(a,1),6123(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6509 6123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6514">
    <literal><![CDATA[
      R(K(x / y,z),x,u) = K((x * u) / (y * u),z)
    ]]></literal>
    <justification jstring="[para(83(a,1),6512(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 6512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6515">
    <literal><![CDATA[
      R(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),6514(a,2,1,2))].">
      <j1 rule="para" parents="12 6514"/>
    </justification>
  </clause>

  <clause id="6516">
    <literal><![CDATA[
      K((x * y) / z,x) = K(x / (z / y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5493,a(flip),b,6515,a),flip(a)].">
      <j1 rule="hyper" parents="63 5493 6515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6517">
    <literal><![CDATA[
      K((x * y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,5984,a(flip),b,6516,a),flip(a)].">
      <j1 rule="hyper" parents="347 5984 6516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6518">
    <literal><![CDATA[
      T(x,y) * K(x * y,(y * x) \ x) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(6347(a,1),5320(a,1,2,2))].">
      <j1 rule="para" parents="6347 5320"/>
    </justification>
  </clause>

  <clause id="6519">
    <literal><![CDATA[
      T(x,y) \ (x * L(K(x,y),z,u)) = K(y,x) \ L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5173(a,1),5352(a,1,2,2,1))].">
      <j1 rule="para" parents="5173 5352"/>
    </justification>
  </clause>

  <clause id="6520">
    <literal><![CDATA[
      (x * K(y,z \ 1)) * z = (x * z) * K(y,z \ 1)
    ]]></literal>
    <justification jstring="[para(5399(a,1),5401(a,1,1))].">
      <j1 rule="para" parents="5399 5401"/>
    </justification>
  </clause>

  <clause id="6523">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,(y \ 1) \ 1) = (x * K(z,y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(3885(a,1),6520(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3885 6520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6524">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = (x * (z \ 1)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(3885(a,1),6523(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3885 6523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6525">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (z \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,6252,a(flip),b,6524,a),flip(a)].">
      <j1 rule="hyper" parents="347 6252 6524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6526">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,5042,a,b,6525,a),flip(a)].">
      <j1 rule="hyper" parents="347 5042 6525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6527">
    <literal><![CDATA[
      R(x / T(y,z),y,y \ 1) = x * (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,6182,a,b,6526,a)].">
      <j1 rule="hyper" parents="63 6182 6526"/>
    </justification>
  </clause>

  <clause id="6528">
    <literal><![CDATA[
      x \ T(x * (y \ 1),y) = T(y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,6021,a(flip),b,6526,a(flip))].">
      <j1 rule="hyper" parents="128 6021 6526"/>
    </justification>
  </clause>

  <clause id="6529">
    <literal><![CDATA[
      (x * K(y,z)) * (T(y,z) \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(6109(a,1),6526(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6109 6526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6530">
    <literal><![CDATA[
      x \ T(x * (y \ 1),y) = ((y \ x) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,336,a(flip),b,6528,a),flip(a)].">
      <j1 rule="hyper" parents="347 336 6528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6531">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,z) = x / (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(131,a,12,a(flip),b,6529,a),flip(a)].">
      <j1 rule="hyper" parents="131 12 6529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6532">
    <literal><![CDATA[
      T((x \ 1) * y,x) = (((x \ y) \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,6530,a(flip),b,4814,a),flip(a)].">
      <j1 rule="hyper" parents="133 6530 4814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6533">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * x = x / (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,6355,a,b,6531,a)].">
      <j1 rule="hyper" parents="63 6355 6531"/>
    </justification>
  </clause>

  <clause id="6534">
    <literal><![CDATA[
      x / (T(y,x) \ 1) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5760,a(flip),b,6531,a),flip(a)].">
      <j1 rule="hyper" parents="63 5760 6531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6535">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) \ y = (((x \ y) \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(4243,a,6532,a)].">
      <j1 rule="hyper" parents="4243 6532"/>
    </justification>
  </clause>

  <clause id="6536">
    <literal><![CDATA[
      x / (y \ K(x,y)) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(4934(a,1),6534(a,1,2))].">
      <j1 rule="para" parents="4934 6534"/>
    </justification>
  </clause>

  <clause id="6537">
    <literal><![CDATA[
      x \ (y / (x \ K(y,x))) = (y / (x \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,6536,a,b,xx)].">
      <j1 rule="hyper" parents="128 6536"/>
    </justification>
  </clause>

  <clause id="6538">
    <literal><![CDATA[
      (x * T(y,z)) * (T(y,z) \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),6527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 6527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6539">
    <literal><![CDATA[
      (x * T(y,z)) * (y \ K(z,y)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5109,a,6538,a)].">
      <j1 rule="hyper" parents="5109 6538"/>
    </justification>
  </clause>

  <clause id="6540">
    <literal><![CDATA[
      (x * y) * (x \ K(y,x)) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(629,a,6539,a)].">
      <j1 rule="hyper" parents="629 6539"/>
    </justification>
  </clause>

  <clause id="6541">
    <literal><![CDATA[
      (x * y) * (x \ K(y,x)) = R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,2190,a(flip),b,6540,a),flip(a)].">
      <j1 rule="hyper" parents="347 2190 6540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6542">
    <literal><![CDATA[
      ((((x / y) \ 1) * x) \ x) \ x = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(83(a,1),6535(a,2,1,1,1))].">
      <j1 rule="para" parents="83 6535"/>
    </justification>
  </clause>

  <clause id="6543">
    <literal><![CDATA[
      ((x / y) \ 1) * (y * (x / y)) = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,4241,a(flip),b,6542,a)].">
      <j1 rule="hyper" parents="63 4241 6542"/>
    </justification>
  </clause>

  <clause id="6544">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,y * (z / y),(z / y) \ 1)) = K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u))
    ]]></literal>
    <justification jstring="[para(6543(a,1),6454(a,2,2,1))].">
      <j1 rule="para" parents="6543 6454"/>
    </justification>
  </clause>

  <clause id="6545">
    <literal><![CDATA[
      x * (K(y,z * z) * ((z * z) \ u)) = (x * (T(z * z,y) \ 1)) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,6447,a(flip),b,5531,a)].">
      <j1 rule="hyper" parents="63 6447 5531"/>
    </justification>
  </clause>

  <clause id="6546">
    <literal><![CDATA[
      (K(x,y) * (((1 / x) * z) * T(((1 / x) * z) \ z,u))) / (K(x,y) * z) = K((1 / x) \ 1,u)
    ]]></literal>
    <justification jstring="[para(5859(a,1),5553(a,2,1,1))].">
      <j1 rule="para" parents="5859 5553"/>
    </justification>
  </clause>

  <clause id="6547">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K((x \ z) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,5602,a(flip),b,5561,a),flip(a)].">
      <j1 rule="hyper" parents="63 5602 5561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6548">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K(z \ x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,5988,a(flip),b,6547,a),flip(a)].">
      <j1 rule="hyper" parents="347 5988 6547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6549">
    <literal><![CDATA[
      K(T(x,y) \ T(z,y),z) = K(x \ z,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(6080,a,6548,a)].">
      <j1 rule="hyper" parents="6080 6548"/>
    </justification>
  </clause>

  <clause id="6550">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = 1 / K(y \ x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(220,a,6549,a(flip),b,5173,a),flip(a)].">
      <j1 rule="hyper" parents="220 6549 5173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6551">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,((x * y) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),5697(a,1,1,2,2,1))].">
      <j1 rule="para" parents="10 5697"/>
    </justification>
  </clause>

  <clause id="6552">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,z / (x * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,5621,a(flip),b,6551,a),flip(a)].">
      <j1 rule="hyper" parents="347 5621 6551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6553">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z / (x * y)) = u
    ]]></literal>
    <justification jstring="[para(6551(a,2),5650(a,1))].">
      <j1 rule="para" parents="6551 5650"/>
    </justification>
  </clause>

  <clause id="6554">
    <literal><![CDATA[
      R(K(x,(y / z) / (u * x)),y / z,z) = ((u * (x * ((u \ (y / z)) / x))) * z) / y
    ]]></literal>
    <justification jstring="[para(6552(a,1),607(a,1,1))].">
      <j1 rule="para" parents="6552 607"/>
    </justification>
  </clause>

  <clause id="6555">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = T(K(x,y) * z,z) / z
    ]]></literal>
    <justification jstring="[para(5428(a,1),5854(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5428 5854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6556">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = z \ T(z * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,4814,a(flip),b,6555,a),flip(a)].">
      <j1 rule="hyper" parents="347 4814 6555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6557">
    <literal><![CDATA[
      K(x,y / T(z \ y,y)) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(5650,a,6556,a)].">
      <j1 rule="hyper" parents="5650 6556"/>
    </justification>
  </clause>

  <clause id="6558">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(4484(a,1),6557(a,1,2))].">
      <j1 rule="para" parents="4484 6557"/>
    </justification>
  </clause>

  <clause id="6559">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = K(y,T(x / z,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,6397,a,b,6558,a)].">
      <j1 rule="hyper" parents="347 6397 6558"/>
    </justification>
  </clause>

  <clause id="6560">
    <literal><![CDATA[
      L(T(1 / x,y),y,K(x,z)) = T(1 / x,K(x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(881,a,5860,a)].">
      <j1 rule="hyper" parents="881 5860"/>
    </justification>
  </clause>

  <clause id="6561">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = L(x \ 1,T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(5931,a,5093,a)].">
      <j1 rule="hyper" parents="5931 5093"/>
    </justification>
  </clause>

  <clause id="6562">
    <literal><![CDATA[
      K(x,L(y \ L(y,z,u),y,u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(u,z,y) \ 1) = w
    ]]></literal>
    <justification jstring="[para(574(a,2),6323(a,1,2))].">
      <j1 rule="para" parents="574 6323"/>
    </justification>
  </clause>

  <clause id="6563">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(4879(a,1),6401(a,1,1,2))].">
      <j1 rule="para" parents="4879 6401"/>
    </justification>
  </clause>

  <clause id="6564">
    <literal><![CDATA[
      K(x,((y / z) * u) \ (y * u)) = ((y * K(z,x)) * u) \ (y * u)
    ]]></literal>
    <justification jstring="[para(5925(a,1),6438(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5925 6438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6565">
    <literal><![CDATA[
      ((x * K(y,z)) * u) * K(z,((x / y) * u) \ (x * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(134,a,6564,a,b,xx)].">
      <j1 rule="hyper" parents="134 6564"/>
    </justification>
  </clause>

  <clause id="6566">
    <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(6032(a,1),6564(a,2,1))].">
      <j1 rule="para" parents="6032 6564"/>
    </justification>
  </clause>

  <clause id="6567">
    <literal><![CDATA[
      ((x * K(y,z)) * K(y,u)) * K(z,y) = x * K(y,u)
    ]]></literal>
    <justification jstring="[para(5945(a,1),6565(a,1,2,2))].">
      <j1 rule="para" parents="5945 6565"/>
    </justification>
  </clause>

  <clause id="6568">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) = (x * z) \ ((x * K(y,u)) * z)
    ]]></literal>
    <justification jstring="[para(6565(a,1),6123(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6565 6123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6569">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = (x * K(u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6109(a,1),6567(a,1,1,1))].">
      <j1 rule="para" parents="6109 6567"/>
    </justification>
  </clause>

  <clause id="6571">
    <literal><![CDATA[
      ((x * K(y,z)) * K(u,y)) * y = (x * K(u,y)) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,6569,a,b,5919,a)].">
      <j1 rule="hyper" parents="133 6569 5919"/>
    </justification>
  </clause>

  <clause id="6572">
    <literal><![CDATA[
      ((x * K(y,z)) * K(z,u)) / z = (x * K(z,u)) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,6569,a(flip),b,6107,a)].">
      <j1 rule="hyper" parents="131 6569 6107"/>
    </justification>
  </clause>

  <clause id="6573">
    <literal><![CDATA[
      (x * K(y,z)) * (y * K(u,y)) = (x * K(u,y)) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6051,a(flip),b,6571,a)].">
      <j1 rule="hyper" parents="63 6051 6571"/>
    </justification>
  </clause>

  <clause id="6574">
    <literal><![CDATA[
      ((x * K(y,z)) / z) * K(z,u) = (x * K(z,u)) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5943,a(flip),b,6572,a)].">
      <j1 rule="hyper" parents="63 5943 6572"/>
    </justification>
  </clause>

  <clause id="6575">
    <literal><![CDATA[
      (x * K(y,z)) * (y * K(u,y)) = x * (K(u,y) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,6038,a(flip),b,6573,a),flip(a)].">
      <j1 rule="hyper" parents="347 6038 6573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6576">
    <literal><![CDATA[
      (x * K(y,z)) / T(y,u) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6135(a,1),6574(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6135 6574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6577">
    <literal><![CDATA[
      (1 / T(x,y)) * K(x,z) = K(x,z) / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(319,a,6576,a),flip(a)].">
      <j1 rule="hyper" parents="319 6576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6578">
    <literal><![CDATA[
      (x * K(y,z)) * (y * K(u,y)) = x * (T(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(3036(a,2),6575(a,2,2))].">
      <j1 rule="para" parents="3036 6575"/>
    </justification>
  </clause>

  <clause id="6579">
    <literal><![CDATA[
      (x * (T(y * y,z) \ 1)) * u = x * (T(y * y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5209(a,1),6545(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5209 6545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6580">
    <literal><![CDATA[
      (x / T(y * y,z)) * u = x * (T(y * y,z) \ u)
    ]]></literal>
    <justification jstring="[para(3300(a,1),6579(a,1,1))].">
      <j1 rule="para" parents="3300 6579"/>
    </justification>
  </clause>

  <clause id="6581">
    <literal><![CDATA[
      K(x,L(y * ((z * y) \ z),y \ 1,z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,a(z,y,y \ 1) \ 1) = u
    ]]></literal>
    <justification jstring="[para(2574(a,1),6562(a,1,2,1))].">
      <j1 rule="para" parents="2574 6562"/>
    </justification>
  </clause>

  <clause id="6582">
    <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(4920(a,2),4957(a,1,1,3))].">
      <j1 rule="para" parents="4920 4957"/>
    </justification>
  </clause>

  <clause id="6583">
    <literal><![CDATA[
      T(T(x * K(y * R(x,z,u),x),w),y) = R(T(y \ (y * x),w),y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(5073(a,1),1200(a,1,1,1))].">
      <j1 rule="para" parents="5073 1200"/>
    </justification>
  </clause>

  <clause id="6584">
    <literal><![CDATA[
      R(x * K(y,x),y,L(x,z,u)) = x * K(y * L(x,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5061,a,b,5074,a)].">
      <j1 rule="hyper" parents="63 5061 5074"/>
    </justification>
  </clause>

  <clause id="6585">
    <literal><![CDATA[
      T(x * K(y * L(x,z,u),x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(5074(a,1),1034(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5074 1034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6586">
    <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(63,a,5308,a,b,6585,a)].">
      <j1 rule="hyper" parents="63 5308 6585"/>
    </justification>
  </clause>

  <clause id="6587">
    <literal><![CDATA[
      (x / (y * K(z,y))) * R(y * K(z,y),z,L(y,u,w)) = (x * (y * K(z * L(y,u,w),y))) / (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(6584(a,1),1708(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6584 1708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6588">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ (x * (K(y,x) * (z * u))) = L(u,z,x * K(y,x))
    ]]></literal>
    <justification jstring="[para(5331(a,1),5460(a,1,2))].">
      <j1 rule="para" parents="5331 5460"/>
    </justification>
  </clause>

  <clause id="6589">
    <literal><![CDATA[
      L((1 / T(x,y)) \ z,T(x,y),y) = (T(y,x) * (1 / x)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(3520,a,5473,a)].">
      <j1 rule="hyper" parents="3520 5473"/>
    </justification>
  </clause>

  <clause id="6592">
    <literal><![CDATA[
      K(x,y * (((1 / z) * u) * w)) = K(x,y * (((z \ 1) * u) * w))
    ]]></literal>
    <justification jstring="[para(2932(a,1),5853(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2932 5853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6593">
    <literal><![CDATA[
      K(x,y * ((((K(z,u) / z) \ 1) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(5550(a,1),6592(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5550 6592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6594">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(6079,a,5990,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="6079 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6595">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(5990(a,2),6079(a,1))].">
      <j1 rule="para" parents="5990 6079"/>
    </justification>
  </clause>

  <clause id="6596">
    <literal><![CDATA[
      x \ (y * ((z \ (y \ x)) * z)) = K((y * z) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(1099,a,6594,a)].">
      <j1 rule="hyper" parents="1099 6594"/>
    </justification>
  </clause>

  <clause id="6597">
    <literal><![CDATA[
      x * ((x \ y) * K(z \ (x \ y),u)) = y * K((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(134,a,6594,a(flip),b,98,a),flip(a)].">
      <j1 rule="hyper" parents="134 6594 98"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6598">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K((y * (x \ 1)) \ z,x)
    ]]></literal>
    <justification jstring="[para(6223(a,1),6594(a,1,1))].">
      <j1 rule="para" parents="6223 6594"/>
    </justification>
  </clause>

  <clause id="6599">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ u),y),z \ u,z) = K((z * (y / x)) \ u,y)
    ]]></literal>
    <justification jstring="[para(6374(a,1),6594(a,1,1))].">
      <j1 rule="para" parents="6374 6594"/>
    </justification>
  </clause>

  <clause id="6600">
    <literal><![CDATA[
      K((x * (y / z)) \ u,y) = K((x * (z \ y)) \ u,y)
    ]]></literal>
    <justification jstring="[hyper(6595,a,6599,a),flip(a)].">
      <j1 rule="hyper" parents="6595 6599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6601">
    <literal><![CDATA[
      K((x * (y / x)) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),6600(a,2,1,1))].">
      <j1 rule="para" parents="10 6600"/>
    </justification>
  </clause>

  <clause id="6602">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(80(a,1),6601(a,1,1,1,2))].">
      <j1 rule="para" parents="80 6601"/>
    </justification>
  </clause>

  <clause id="6603">
    <literal><![CDATA[
      T(x,((y \ x) * y) \ z) = (u * K(x \ z,x)) \ (u * x)
    ]]></literal>
    <justification jstring="[para(6602(a,1),6100(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6602 6100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6604">
    <literal><![CDATA[
      T(x,((y \ x) * y) \ z) = T(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,6100,a(flip),b,6603,a),flip(a)].">
      <j1 rule="hyper" parents="347 6100 6603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6605">
    <literal><![CDATA[
      T((x \ y) * x,((z \ y) * z) \ u) = (x \ T(y,y \ u)) * x
    ]]></literal>
    <justification jstring="[para(6604(a,1),4830(a,2,1,2))].">
      <j1 rule="para" parents="6604 4830"/>
    </justification>
  </clause>

  <clause id="6606">
    <literal><![CDATA[
      T(x,x \ T(y,y \ x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(6346(a,1),6604(a,1,2))].">
      <j1 rule="para" parents="6346 6604"/>
    </justification>
  </clause>

  <clause id="6607">
    <literal><![CDATA[
      T(x,x \ y) / T(y,y \ x) = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(220,a,6606,a(flip),b,112,a(flip))].">
      <j1 rule="hyper" parents="220 6606 112"/>
    </justification>
  </clause>

  <clause id="6608">
    <literal><![CDATA[
      T(x,x \ y) / ((y \ x) \ x) = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(805,a,6607,a)].">
      <j1 rule="hyper" parents="805 6607"/>
    </justification>
  </clause>

  <clause id="6609">
    <literal><![CDATA[
      x \ T(y,y \ x) = y / ((y \ ((x \ y) \ y)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6281,a(flip),b,6608,a),flip(a)].">
      <j1 rule="hyper" parents="63 6281 6608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6610">
    <literal><![CDATA[
      T(1 / (x \ y),y) \ 1 = x \ T(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,5868,a(flip),b,6609,a)].">
      <j1 rule="hyper" parents="347 5868 6609"/>
    </justification>
  </clause>

  <clause id="6611">
    <literal><![CDATA[
      (x \ T(y,y \ x)) \ 1 = T((x \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(6610(a,1),2728(a,1,1))].">
      <j1 rule="para" parents="6610 2728"/>
    </justification>
  </clause>

  <clause id="6612">
    <literal><![CDATA[
      (((x \ y) * x) \ x) \ 1 = T((y \ x) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6346(a,2),6611(a,1,1))].">
      <j1 rule="para" parents="6346 6611"/>
    </justification>
  </clause>

  <clause id="6613">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) = ((y * x) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),6612(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 6612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6614">
    <literal><![CDATA[
      T((x \ y) * x,((z \ y) * z) \ u) = T((x \ y) * x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,4830,a,b,6605,a),flip(a)].">
      <j1 rule="hyper" parents="347 4830 6605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6615">
    <literal><![CDATA[
      x / T((y \ z) * y,z \ x) != u
    ]]></literal>
    <literal><![CDATA[
      ((y \ z) * y) \ x = u
    ]]></literal>
    <justification jstring="[para(6614(a,1),345(a,1,2))].">
      <j1 rule="para" parents="6614 345"/>
    </justification>
  </clause>

  <clause id="6616">
    <literal><![CDATA[
      T(x \ y,z) * ((y \ x) * K(z,x \ y)) = T((x \ y) * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(6268,a,5831,a(flip))].">
      <j1 rule="hyper" parents="6268 5831"/>
    </justification>
  </clause>

  <clause id="6617">
    <literal><![CDATA[
      T((x \ y) * (y \ x),z) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(5523,a,6616,a),flip(a)].">
      <j1 rule="hyper" parents="5523 6616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6618">
    <literal><![CDATA[
      K(x,(y \ z) * (z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(4952,a,6617,a)].">
      <j1 rule="hyper" parents="4952 6617"/>
    </justification>
  </clause>

  <clause id="6619">
    <literal><![CDATA[
      T(x,(y \ z) * (z \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,6617,a)].">
      <j1 rule="hyper" parents="54 6617"/>
    </justification>
  </clause>

  <clause id="6620">
    <literal><![CDATA[
      x / ((y \ z) * (z \ y)) = ((y \ z) * (z \ y)) \ x
    ]]></literal>
    <justification jstring="[hyper(220,a,6617,a(flip),b,4306,a(flip))].">
      <j1 rule="hyper" parents="220 6617 4306"/>
    </justification>
  </clause>

  <clause id="6621">
    <literal><![CDATA[
      K(x,y * ((z * y) \ z)) = 1
    ]]></literal>
    <justification jstring="[para(9(a,1),6618(a,1,2,1))].">
      <j1 rule="para" parents="9 6618"/>
    </justification>
  </clause>

  <clause id="6622">
    <literal><![CDATA[
      K(x,(y \ (y / z)) * z) = 1
    ]]></literal>
    <justification jstring="[para(83(a,1),6618(a,1,2,2))].">
      <j1 rule="para" parents="83 6618"/>
    </justification>
  </clause>

  <clause id="6623">
    <literal><![CDATA[
      T(x,y * ((z * y) \ z)) = x
    ]]></literal>
    <justification jstring="[para(9(a,1),6619(a,1,2,1))].">
      <j1 rule="para" parents="9 6619"/>
    </justification>
  </clause>

  <clause id="6624">
    <literal><![CDATA[
      T(x,y * (z \ (z / y))) = x
    ]]></literal>
    <justification jstring="[para(83(a,1),6619(a,1,2,1))].">
      <j1 rule="para" parents="83 6619"/>
    </justification>
  </clause>

  <clause id="6625">
    <literal><![CDATA[
      T(x * ((y * x) \ y),z) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(5039,a,6621,a)].">
      <j1 rule="hyper" parents="5039 6621"/>
    </justification>
  </clause>

  <clause id="6626">
    <literal><![CDATA[
      x / (y * (z \ (z / y))) = (y * (z \ (z / y))) \ x
    ]]></literal>
    <justification jstring="[hyper(4876,a,6624,a),flip(a)].">
      <j1 rule="hyper" parents="4876 6624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6627">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),z) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(244(a,2),6625(a,1,1,2))].">
      <j1 rule="para" parents="244 6625"/>
    </justification>
  </clause>

  <clause id="6628">
    <literal><![CDATA[
      (x * (y \ (y / x))) \ (y \ (y / x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,2597,a(flip),b,6626,a),flip(a)].">
      <j1 rule="hyper" parents="63 2597 6626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6629">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = x / (y \ T(x,y \ 1))
    ]]></literal>
    <justification jstring="[para(3804(a,1),6408(a,2,2))].">
      <j1 rule="para" parents="3804 6408"/>
    </justification>
  </clause>

  <clause id="6630">
    <literal><![CDATA[
      x / (y \ T(x,y \ 1)) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,3810,a(flip),b,6629,a),flip(a)].">
      <j1 rule="hyper" parents="63 3810 6629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6631">
    <literal><![CDATA[
      (T(x,(y \ 1) \ 1) / (y \ 1)) \ x = x / ((y \ 1) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(2966(a,1),6630(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2966 6630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6632">
    <literal><![CDATA[
      x / ((y \ 1) \ T(x,y)) = (T(x,y) / (y \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(2966(a,1),6631(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2966 6631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6633">
    <literal><![CDATA[
      ((T(x,y) / (y \ 1)) \ x) \ x = (y \ 1) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(214,a,6632,a)].">
      <j1 rule="hyper" parents="214 6632"/>
    </justification>
  </clause>

  <clause id="6634">
    <literal><![CDATA[
      (x * y) \ (y * (K(x,y) * (x * z))) = L(z,x,y * K(x,y))
    ]]></literal>
    <justification jstring="[para(5030(a,1),6588(a,1,1))].">
      <j1 rule="para" parents="5030 6588"/>
    </justification>
  </clause>

  <clause id="6635">
    <literal><![CDATA[
      x * (K(y * y,x) * ((y * y) * z)) = ((y * y) * x) * z
    ]]></literal>
    <justification jstring="[hyper(134,a,534,a(flip),b,6634,a),flip(a)].">
      <j1 rule="hyper" parents="134 534 6634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6636">
    <literal><![CDATA[
      (x * y) \ (y * (T(x,y) * z)) = L(z,x,y * K(x,y))
    ]]></literal>
    <justification jstring="[para(4974(a,1),6634(a,1,2,2))].">
      <j1 rule="para" parents="4974 6634"/>
    </justification>
  </clause>

  <clause id="6637">
    <literal><![CDATA[
      ((x \ T(x * (y / z),u)) * z) / y = K(y / ((1 / x) * z),u)
    ]]></literal>
    <justification jstring="[para(4858(a,1),5391(a,1,1))].">
      <j1 rule="para" parents="4858 5391"/>
    </justification>
  </clause>

  <clause id="6638">
    <literal><![CDATA[
      T(x,x \ y) \ R(T(x,x \ y),z,u) = x \ (y \ ((R(x,z,u) * (x \ y)) * x))
    ]]></literal>
    <justification jstring="[hyper(128,a,5014,a(flip),b,4947,a),flip(a)].">
      <j1 rule="hyper" parents="128 5014 4947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6639">
    <literal><![CDATA[
      K(a(x,y,z),x * (y * z)) * (((x * y) * z) / (x * (y * z))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,5065,a(flip),b,5233,a)].">
      <j1 rule="hyper" parents="134 5065 5233"/>
    </justification>
  </clause>

  <clause id="6640">
    <literal><![CDATA[
      L(T(x \ 1,y) \ z,x \ 1,x) = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(5216,a,5814,a)].">
      <j1 rule="hyper" parents="5216 5814"/>
    </justification>
  </clause>

  <clause id="6641">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(z,u)) = (T(z,u) * y) \ (T(z,u) * (y * x))
    ]]></literal>
    <justification jstring="[para(4974(a,1),5243(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4974 5243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6642">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(z,u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,18,a,b,6641,a),flip(a)].">
      <j1 rule="hyper" parents="347 18 6641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6643">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(6641(a,2),545(a,1))].">
      <j1 rule="para" parents="6641 545"/>
    </justification>
  </clause>

  <clause id="6644">
    <literal><![CDATA[
      L(L(x,y * z,K(y,u)),z,y) = L(x,z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(1094,a,6642,a)].">
      <j1 rule="hyper" parents="1094 6642"/>
    </justification>
  </clause>

  <clause id="6645">
    <literal><![CDATA[
      L(x,y,T(y,z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(550,a,6642,a),flip(a)].">
      <j1 rule="hyper" parents="550 6642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6646">
    <literal><![CDATA[
      L(x,T(y,z),y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(1276,a,6645,a)].">
      <j1 rule="hyper" parents="1276 6645"/>
    </justification>
  </clause>

  <clause id="6647">
    <literal><![CDATA[
      L(x,(y \ z) \ z,y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(112(a,1),6646(a,1,2))].">
      <j1 rule="para" parents="112 6646"/>
    </justification>
  </clause>

  <clause id="6648">
    <literal><![CDATA[
      (((x * x) \ y) * z) / ((x \ (x \ 1)) * z) = y * K(x \ (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(979(a,1),5643(a,1,1,1))].">
      <j1 rule="para" parents="979 5643"/>
    </justification>
  </clause>

  <clause id="6649">
    <literal><![CDATA[
      (((x * x) \ y) * z) / ((x * x) \ z) = y * K(x \ (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(979(a,1),6648(a,1,2))].">
      <j1 rule="para" parents="979 6648"/>
    </justification>
  </clause>

  <clause id="6650">
    <literal><![CDATA[
      ((((x * x) \ y) * z) / z) * (x * x) = y * K(x \ (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,896,a(flip),b,6649,a)].">
      <j1 rule="hyper" parents="63 896 6649"/>
    </justification>
  </clause>

  <clause id="6651">
    <literal><![CDATA[
      ((x * x) \ y) * (x * x) = y * K(x \ (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(323,a,6650,a),flip(a)].">
      <j1 rule="hyper" parents="323 6650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6652">
    <literal><![CDATA[
      x * K(y \ (y \ 1),x) = T(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(773,a,6651,a),flip(a)].">
      <j1 rule="hyper" parents="773 6651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6653">
    <literal><![CDATA[
      K(x \ (x \ 1),y) = K(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(34,a,4929,a(flip),b,6652,a),flip(a)].">
      <j1 rule="hyper" parents="34 4929 6652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6654">
    <literal><![CDATA[
      x * (y * T(y,y * y)) = x / (y \ (1 / y))
    ]]></literal>
    <justification jstring="[para(6652(a,1),6405(a,1,2,2))].">
      <j1 rule="para" parents="6652 6405"/>
    </justification>
  </clause>

  <clause id="6655">
    <literal><![CDATA[
      x / (y \ (1 / y)) = x * ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[para(5713(a,1),6654(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5713 6654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6656">
    <literal><![CDATA[
      x / ((1 / y) \ y) = x * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(352,a,6655,a),flip(a)].">
      <j1 rule="hyper" parents="352 6655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6657">
    <literal><![CDATA[
      (x * (y \ (1 / y))) / z = x / (z * ((1 / y) \ y))
    ]]></literal>
    <justification jstring="[para(6655(a,1),903(a,2,2))].">
      <j1 rule="para" parents="6655 903"/>
    </justification>
  </clause>

  <clause id="6658">
    <literal><![CDATA[
      (x * (y \ (1 / y))) \ z = ((1 / y) \ y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(6656(a,1),1126(a,1,1))].">
      <j1 rule="para" parents="6656 1126"/>
    </justification>
  </clause>

  <clause id="6659">
    <literal><![CDATA[
      L(x / ((x / y) * ((1 / y) \ y)),y,x) = x \ T(x / y,y \ 1)
    ]]></literal>
    <justification jstring="[para(6657(a,1),6502(a,1,1))].">
      <j1 rule="para" parents="6657 6502"/>
    </justification>
  </clause>

  <clause id="6660">
    <literal><![CDATA[
      ((1 / x) \ x) * ((y * x) \ z) = (y * (1 / x)) \ z
    ]]></literal>
    <justification jstring="[para(845(a,1),6658(a,1,1)),flip(a)].">
      <j1 rule="para" parents="845 6658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6661">
    <literal><![CDATA[
      L(x * (y \ (1 / y)),z,u) \ w = ((1 / y) \ y) * (L(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(3624(a,2),6658(a,1,1))].">
      <j1 rule="para" parents="3624 6658"/>
    </justification>
  </clause>

  <clause id="6662">
    <literal><![CDATA[
      L(x / (x / (y \ 1)),y,x) = x \ T(x / y,y \ 1)
    ]]></literal>
    <justification jstring="[para(6385(a,1),6659(a,1,1,2))].">
      <j1 rule="para" parents="6385 6659"/>
    </justification>
  </clause>

  <clause id="6663">
    <literal><![CDATA[
      ((1 / x) \ x) * (L(x,y,z) \ u) = L(1 / x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(10(a,1),6661(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 6661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6664">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(5971(a,1),5700(a,2,2,2))].">
      <j1 rule="para" parents="5971 5700"/>
    </justification>
  </clause>

  <clause id="6665">
    <literal><![CDATA[
      (x \ K(y,x)) \ L((x \ 1) * z,u,w) = T(x,y) * L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,4974,a(flip),b,5826,a),flip(a)].">
      <j1 rule="hyper" parents="347 4974 5826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6666">
    <literal><![CDATA[
      (1 / x) * K(((1 / x) \ y) \ 1,z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(83(a,1),5880(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="83 5880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6668">
    <literal><![CDATA[
      (1 / x) * K(y \ (1 / x),z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(5988(a,1),6666(a,1,2))].">
      <j1 rule="para" parents="5988 6666"/>
    </justification>
  </clause>

  <clause id="6669">
    <literal><![CDATA[
      (1 / x) * K(y \ (x \ 1),z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(3879(a,1),6668(a,1,2))].">
      <j1 rule="para" parents="3879 6668"/>
    </justification>
  </clause>

  <clause id="6670">
    <literal><![CDATA[
      (T(x * y,z) / y) * (x \ 1) = (1 / y) * (x \ T(x * y,z))
    ]]></literal>
    <justification jstring="[para(1143(a,1),5881(a,1,1))].">
      <j1 rule="para" parents="1143 5881"/>
    </justification>
  </clause>

  <clause id="6671">
    <literal><![CDATA[
      (1 / x) * ((x \ y) \ T((x \ y) * x,x)) = (x \ T(y,x)) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1592(a,1),6670(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1592 6670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6673">
    <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(5926(a,1),5962(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5926 5962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6674">
    <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(6673(a,2),595(a,1))].">
      <j1 rule="para" parents="6673 595"/>
    </justification>
  </clause>

  <clause id="6675">
    <literal><![CDATA[
      R(R(x,y * z,K(z,u)),y,z) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(6674,a,31,a),flip(a)].">
      <j1 rule="hyper" parents="6674 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6676">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) \ z,y) = K(z * ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[hyper(6319,a,6283,a)].">
      <j1 rule="hyper" parents="6319 6283"/>
    </justification>
  </clause>

  <clause id="6678">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = (1 / z) * K((((z \ 1) \ x) \ 1) \ (z \ 1),y)
    ]]></literal>
    <justification jstring="[para(3914(a,1),6369(a,2,2))].">
      <j1 rule="para" parents="3914 6369"/>
    </justification>
  </clause>

  <clause id="6679">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(5088(a,1),6399(a,1,1,2))].">
      <j1 rule="para" parents="5088 6399"/>
    </justification>
  </clause>

  <clause id="6680">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (T(y,z) * z)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(4953(a,1),6679(a,1,2,2))].">
      <j1 rule="para" parents="4953 6679"/>
    </justification>
  </clause>

  <clause id="6681">
    <literal><![CDATA[
      (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(111(a,1),6400(a,1,1,2,2))].">
      <j1 rule="para" parents="111 6400"/>
    </justification>
  </clause>

  <clause id="6682">
    <literal><![CDATA[
      ((x * y) * ((z \ ((x * y) \ u)) * z)) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(3559(a,2),6681(a,1,1))].">
      <j1 rule="para" parents="3559 6681"/>
    </justification>
  </clause>

  <clause id="6683">
    <literal><![CDATA[
      (x \ T(y,x)) * ((x \ y) \ 1) = (1 / x) * ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(4853(a,1),6671(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4853 6671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6684">
    <literal><![CDATA[
      K(x,y) = (y \ T(x,y)) * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,5052,a,b,6683,a)].">
      <j1 rule="hyper" parents="347 5052 6683"/>
    </justification>
  </clause>

  <clause id="6685">
    <literal><![CDATA[
      (x \ T(x * y,x)) * (y \ 1) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),6684(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6686">
    <literal><![CDATA[
      (x \ T(x * K(y,z),x)) * (K(z,y) * 1) = K(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(5256(a,1),6685(a,1,2))].">
      <j1 rule="para" parents="5256 6685"/>
    </justification>
  </clause>

  <clause id="6687">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * (K(z,x) * 1) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(6558(a,2),6686(a,1,1))].">
      <j1 rule="para" parents="6558 6686"/>
    </justification>
  </clause>

  <clause id="6688">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(640,a,6687,a)].">
      <j1 rule="hyper" parents="640 6687"/>
    </justification>
  </clause>

  <clause id="6689">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = K(((((z \ 1) \ x) \ 1) * z) \ 1,y) / z
    ]]></literal>
    <justification jstring="[hyper(347,a,6669,a(flip),b,6678,a),flip(a)].">
      <j1 rule="hyper" parents="347 6669 6678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6690">
    <literal><![CDATA[
      (x * y) * (z * (L(y \ 1,y,x) / z)) = (x * y) * (z * (((x * y) \ x) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4846,a(flip),b,4861,a),flip(a)].">
      <j1 rule="hyper" parents="63 4846 4861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6691">
    <literal><![CDATA[
      R((x \ (1 / y)) * x,y,z) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(3673(a,2),4864(a,1,1))].">
      <j1 rule="para" parents="3673 4864"/>
    </justification>
  </clause>

  <clause id="6692">
    <literal><![CDATA[
      L(T(x,K(y,x) * z),K(x,y) \ z,K(x,y)) = z \ (T(x,y) * (K(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(5256(a,1),5242(a,1,1,2))].">
      <j1 rule="para" parents="5256 5242"/>
    </justification>
  </clause>

  <clause id="6693">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) * (z * u) = (K(x,y \ 1) * z) * u
    ]]></literal>
    <justification jstring="[para(5400(a,1),5402(a,2,1))].">
      <j1 rule="para" parents="5400 5402"/>
    </justification>
  </clause>

  <clause id="6694">
    <literal><![CDATA[
      R(K(x,y \ 1),z,u) = K(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,107,a,b,6693,a)].">
      <j1 rule="hyper" parents="35 107 6693"/>
    </justification>
  </clause>

  <clause id="6695">
    <literal><![CDATA[
      K(x,R(y,x,z) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,4248,a(flip),b,6693,a),flip(a)].">
      <j1 rule="hyper" parents="35 4248 6693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6696">
    <literal><![CDATA[
      K(x,R(R(y,x,z),u,w) \ 1) = K(x,R(y,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(31(a,1),6695(a,1,2,1))].">
      <j1 rule="para" parents="31 6695"/>
    </justification>
  </clause>

  <clause id="6697">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ 1) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(83(a,1),6694(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="83 6694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6698">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3885(a,1),6694(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3885 6694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6699">
    <literal><![CDATA[
      K(x,R(y / z,u,w) \ 1) = R(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[para(5621(a,1),6694(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5621 6694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6700">
    <literal><![CDATA[
      K(x,R(y \ z,u,w) \ 1) = R(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6250(a,1),6694(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6250 6694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6701">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 = R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5680,a(flip),b,6697,a)].">
      <j1 rule="hyper" parents="63 5680 6697"/>
    </justification>
  </clause>

  <clause id="6702">
    <literal><![CDATA[
      (R(K(x,y),z,u) \ K(R(K(x,y),z,u) * w,R(K(y,x),z,u))) \ w = w / (R(K(x,y),z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(6701(a,1),5655(a,1,1,2,2))].">
      <j1 rule="para" parents="6701 5655"/>
    </justification>
  </clause>

  <clause id="6703">
    <literal><![CDATA[
      R(K(x,y),z,u) \ w = R(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(6698(a,1),5681(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6698 5681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6704">
    <literal><![CDATA[
      R(K(x,y),z,u) \ (z * u) = (K(y,x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(347,a,107,a(flip),b,6703,a),flip(a)].">
      <j1 rule="hyper" parents="347 107 6703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6705">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      R(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(6703(a,2),141(a,1)),flip(b)].">
      <j1 rule="para" parents="6703 141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6706">
    <literal><![CDATA[
      R(K(x,y / z),y,u) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(5651,a,6699,a),flip(a)].">
      <j1 rule="hyper" parents="5651 6699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6707">
    <literal><![CDATA[
      R(K(x,y / z),y,z \ 1) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(693(a,1),6699(a,1,2)),flip(a)].">
      <j1 rule="para" parents="693 6699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6708">
    <literal><![CDATA[
      R(K(x,y / z),y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * u) / (z * u)) = w
    ]]></literal>
    <justification jstring="[para(6699(a,1),5651(a,1))].">
      <j1 rule="para" parents="6699 5651"/>
    </justification>
  </clause>

  <clause id="6709">
    <literal><![CDATA[
      R(K(x,(y / z) / u),y / z,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(12(a,1),6706(a,2,2,1))].">
      <j1 rule="para" parents="12 6706"/>
    </justification>
  </clause>

  <clause id="6710">
    <literal><![CDATA[
      R(K(x,y / (z / u)),y,u) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),6706(a,2,2,2))].">
      <j1 rule="para" parents="12 6706"/>
    </justification>
  </clause>

  <clause id="6711">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(80(a,1),6706(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="80 6706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6712">
    <literal><![CDATA[
      R(K(x,R(y,z,u) \ y),y,w) = K(x,(y * w) / (R(y,z,u) * w))
    ]]></literal>
    <justification jstring="[para(3702(a,1),6706(a,1,1,2))].">
      <j1 rule="para" parents="3702 6706"/>
    </justification>
  </clause>

  <clause id="6713">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(104(a,2),6711(a,1,2))].">
      <j1 rule="para" parents="104 6711"/>
    </justification>
  </clause>

  <clause id="6714">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) \ x = R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,6513,a(flip),b,6713,a)].">
      <j1 rule="hyper" parents="63 6513 6713"/>
    </justification>
  </clause>

  <clause id="6715">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) * R(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[hyper(134,a,6713,a(flip),b,6513,a(flip))].">
      <j1 rule="hyper" parents="134 6713 6513"/>
    </justification>
  </clause>

  <clause id="6716">
    <literal><![CDATA[
      R(K(x,y),y * z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),6713(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 6713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6717">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,T(z,y),u))
    ]]></literal>
    <justification jstring="[para(22(a,2),6713(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="22 6713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6718">
    <literal><![CDATA[
      R(K(x,R(y,z,u)),(y * z) * u,w) = K(x,R(R(y,z,u),z * u,w))
    ]]></literal>
    <justification jstring="[para(209(a,1),6713(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="209 6713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6719">
    <literal><![CDATA[
      K(R(x,y * z,u) \ 1,y) = K(x \ 1,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(5679,a,6716,a)].">
      <j1 rule="hyper" parents="5679 6716"/>
    </justification>
  </clause>

  <clause id="6720">
    <literal><![CDATA[
      K(x * y,R(x,y,z)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(4257,a,6716,a),flip(a)].">
      <j1 rule="hyper" parents="4257 6716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6721">
    <literal><![CDATA[
      K(x,R(y,z,u)) * ((y * z) * u) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[para(6716(a,1),5470(a,1,1))].">
      <j1 rule="para" parents="6716 5470"/>
    </justification>
  </clause>

  <clause id="6722">
    <literal><![CDATA[
      T(K(x,R(y,z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(T(K(x,y),w),y * z,u) = v5
    ]]></literal>
    <justification jstring="[para(6716(a,1),6366(a,1,1))].">
      <j1 rule="para" parents="6716 6366"/>
    </justification>
  </clause>

  <clause id="6723">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,(((y * z) * u) / ((x * z) * u)) \ 1)
    ]]></literal>
    <justification jstring="[para(612(a,1),6696(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="612 6696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6724">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * u) / ((y \ z) * u)) = w
    ]]></literal>
    <justification jstring="[para(80(a,1),6708(a,1,1,2))].">
      <j1 rule="para" parents="80 6708"/>
    </justification>
  </clause>

  <clause id="6725">
    <literal><![CDATA[
      (x * (K(y,x) * z)) * u != w * ((x * z) * u)
    ]]></literal>
    <literal><![CDATA[
      K(y,R(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(6721(a,1),44(a,1))].">
      <j1 rule="para" parents="6721 44"/>
    </justification>
  </clause>

  <clause id="6726">
    <literal><![CDATA[
      ((1 / R(x,y,z)) * x) * (x \ 1) = T(1 / R(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(5115,a,5733,a),flip(a)].">
      <j1 rule="hyper" parents="5115 5733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6727">
    <literal><![CDATA[
      (x / R(x,y,z)) * (x \ 1) = T(1 / R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(1705(a,1),6726(a,1,1))].">
      <j1 rule="para" parents="1705 6726"/>
    </justification>
  </clause>

  <clause id="6728">
    <literal><![CDATA[
      (x / R(x,y,z)) * (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,3707,a(flip),b,6727,a),flip(a)].">
      <j1 rule="hyper" parents="347 3707 6727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6729">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(3706,a,6728,a)].">
      <j1 rule="hyper" parents="3706 6728"/>
    </justification>
  </clause>

  <clause id="6730">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(R(x,y,z) \ x,x \ 1) = u
    ]]></literal>
    <justification jstring="[para(6729(a,1),360(a,1,2))].">
      <j1 rule="para" parents="6729 360"/>
    </justification>
  </clause>

  <clause id="6731">
    <literal><![CDATA[
      T(R(x,y,z) \ x,x \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(6730,a,4741,a)].">
      <j1 rule="hyper" parents="6730 4741"/>
    </justification>
  </clause>

  <clause id="6732">
    <literal><![CDATA[
      K(R(x,y,z) \ x,x \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,6731,a)].">
      <j1 rule="hyper" parents="55 6731"/>
    </justification>
  </clause>

  <clause id="6733">
    <literal><![CDATA[
      T(1 / x,R(x,y,z) \ x) = 1 / x
    ]]></literal>
    <justification jstring="[para(6732(a,1),5087(a,1,1,1))].">
      <j1 rule="para" parents="6732 5087"/>
    </justification>
  </clause>

  <clause id="6734">
    <literal><![CDATA[
      T((1 / x) * R((1 / x) \ 1,y,z),R(x,u,w) \ x) = (1 / x) * R(T(1 / x,R(x,u,w) \ x) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(6733(a,1),2148(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6733 2148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6736">
    <literal><![CDATA[
      (x * x) \ T(x * x,x \ y) = K(x * x,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(586(a,1),6207(a,1,1))].">
      <j1 rule="para" parents="586 6207"/>
    </justification>
  </clause>

  <clause id="6738">
    <literal><![CDATA[
      K(x * x,(x \ 1) \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(6736(a,1),5006(a,1))].">
      <j1 rule="para" parents="6736 5006"/>
    </justification>
  </clause>

  <clause id="6739">
    <literal><![CDATA[
      K(x,(y * (x / z)) \ u) = K(x,(y * (z \ x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(6498,a,6563,a),flip(a)].">
      <j1 rule="hyper" parents="6498 6563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6740">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),6739(a,2,2,1))].">
      <j1 rule="para" parents="10 6739"/>
    </justification>
  </clause>

  <clause id="6741">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ x)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(80(a,1),6739(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="80 6739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6742">
    <literal><![CDATA[
      T(T(x * K(y * R(x,z,u),x),w),y) = R(T(x,w),y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),6583(a,2,1,1))].">
      <j1 rule="para" parents="9 6583"/>
    </justification>
  </clause>

  <clause id="6743">
    <literal><![CDATA[
      (x * y) * L(z * ((y \ 1) / z),y,x) = (x * y) * (z * (((x * y) \ x) / z))
    ]]></literal>
    <justification jstring="[para(3159(a,2),6690(a,1,2))].">
      <j1 rule="para" parents="3159 6690"/>
    </justification>
  </clause>

  <clause id="6744">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = (((z \ (1 / x)) * z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(314,a,6691,a),flip(a)].">
      <j1 rule="hyper" parents="314 6691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6745">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,5621,a(flip),b,6723,a),flip(a)].">
      <j1 rule="hyper" parents="347 5621 6723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6746">
    <literal><![CDATA[
      R(K(x,x / y),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6699,a(flip),b,6745,a)].">
      <j1 rule="hyper" parents="63 6699 6745"/>
    </justification>
  </clause>

  <clause id="6747">
    <literal><![CDATA[
      R(K(x,y \ x),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(6465(a,1),6746(a,1,1))].">
      <j1 rule="para" parents="6465 6746"/>
    </justification>
  </clause>

  <clause id="6748">
    <literal><![CDATA[
      K(x,((x * y) * z) / ((u * y) * z)) = K(R(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6508,a(flip),b,6747,a),flip(a)].">
      <j1 rule="hyper" parents="63 6508 6747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6749">
    <literal><![CDATA[
      K(R(x,x \ y,z),u \ x) = K(x,(y * z) / ((u * (x \ y)) * z))
    ]]></literal>
    <justification jstring="[para(10(a,1),6748(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 6748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6750">
    <literal><![CDATA[
      K(x,((y * z) * R(x,y,z)) / ((u * (K(y * z,x) * y)) * z)) = K(R(x,K(y * z,x) * y,z),u \ x)
    ]]></literal>
    <justification jstring="[para(5484(a,1),6748(a,1,2,1))].">
      <j1 rule="para" parents="5484 6748"/>
    </justification>
  </clause>

  <clause id="6751">
    <literal><![CDATA[
      K(x,(y * z) / ((u * (x \ y)) * z)) = R(K(x,u \ x),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6509,a(flip),b,6749,a),flip(a)].">
      <j1 rule="hyper" parents="63 6509 6749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6754">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * (y * (z * ((y \ 1) / z)))
    ]]></literal>
    <justification jstring="[hyper(322,a,6743,a),flip(a)].">
      <j1 rule="hyper" parents="322 6743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6755">
    <literal><![CDATA[
      (x \ (y * (T(z,x) \ z))) * x = ((x \ y) * x) * (T(z,x) \ z)
    ]]></literal>
    <justification jstring="[para(255(a,1),4845(a,1,1)),flip(a)].">
      <j1 rule="para" parents="255 4845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6757">
    <literal><![CDATA[
      ((x \ y) * x) * (T(z,x) \ z) = (x \ (y * K(x,z))) * x
    ]]></literal>
    <justification jstring="[para(4913(a,2),6755(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4913 6755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6758">
    <literal><![CDATA[
      (x \ (y * K(x,z))) * x = ((x \ y) * x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4913(a,2),6757(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4913 6757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6759">
    <literal><![CDATA[
      (x \ (y * K(x,z))) * x = (x \ y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,5926,a(flip),b,6758,a),flip(a)].">
      <j1 rule="hyper" parents="347 5926 6758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6760">
    <literal><![CDATA[
      x \ (y * K(x,z)) = (x \ y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,5914,a,b,6759,a),flip(a)].">
      <j1 rule="hyper" parents="35 5914 6759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6761">
    <literal><![CDATA[
      x * ((x \ y) * K(x,z)) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(150,a,6760,a)].">
      <j1 rule="hyper" parents="150 6760"/>
    </justification>
  </clause>

  <clause id="6762">
    <literal><![CDATA[
      x \ (y * K(x,z)) != u * K(x,z)
    ]]></literal>
    <literal><![CDATA[
      x \ y = u
    ]]></literal>
    <justification jstring="[para(6760(a,2),44(a,1))].">
      <j1 rule="para" parents="6760 44"/>
    </justification>
  </clause>

  <clause id="6763">
    <literal><![CDATA[
      (x \ (y / z)) * K(x,z) = x \ (y / T(z,x))
    ]]></literal>
    <justification jstring="[para(6102(a,1),6760(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6102 6760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6765">
    <literal><![CDATA[
      (x * y) * K(x,z) = x * (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),6761(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6766">
    <literal><![CDATA[
      K(x,(x \ 1) \ y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(6483,a,6765,a),flip(a)].">
      <j1 rule="hyper" parents="6483 6765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6767">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(6481,a,6765,a),flip(a)].">
      <j1 rule="hyper" parents="6481 6765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6768">
    <literal><![CDATA[
      L(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3558,a,6765,a)].">
      <j1 rule="hyper" parents="3558 6765"/>
    </justification>
  </clause>

  <clause id="6769">
    <literal><![CDATA[
      R(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(2387,a,6765,a)].">
      <j1 rule="hyper" parents="2387 6765"/>
    </justification>
  </clause>

  <clause id="6770">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,5154,a,b,6765,a)].">
      <j1 rule="hyper" parents="347 5154 6765"/>
    </justification>
  </clause>

  <clause id="6771">
    <literal><![CDATA[
      (x * (y * K(x,z))) * x = (x * y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,6765,a(flip),b,5919,a)].">
      <j1 rule="hyper" parents="133 6765 5919"/>
    </justification>
  </clause>

  <clause id="6772">
    <literal><![CDATA[
      (x * (y * K(x,z))) / T(x,z) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,6765,a(flip),b,5925,a)].">
      <j1 rule="hyper" parents="131 6765 5925"/>
    </justification>
  </clause>

  <clause id="6773">
    <literal><![CDATA[
      R(R(x / y,y,z),y * z,K(y,u)) = ((x * z) * K(y,u)) / (y * (z * K(y,u)))
    ]]></literal>
    <justification jstring="[para(6765(a,1),612(a,2,2))].">
      <j1 rule="para" parents="6765 612"/>
    </justification>
  </clause>

  <clause id="6775">
    <literal><![CDATA[
      (x * (y * K(x,z))) / x = ((x * y) / x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(6765(a,1),5943(a,1,1))].">
      <j1 rule="para" parents="6765 5943"/>
    </justification>
  </clause>

  <clause id="6776">
    <literal><![CDATA[
      x * (L(x \ y,z,u) * K(x,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(y / x,z,u) * T(x,w) = v5
    ]]></literal>
    <justification jstring="[para(6765(a,1),6055(a,1))].">
      <j1 rule="para" parents="6765 6055"/>
    </justification>
  </clause>

  <clause id="6777">
    <literal><![CDATA[
      R(T(x,y),z,K(x,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6769(a,1),27(a,2,1))].">
      <j1 rule="para" parents="6769 27"/>
    </justification>
  </clause>

  <clause id="6778">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,u) = T(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[para(6769(a,1),472(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6769 472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6779">
    <literal><![CDATA[
      (R(x,y,z) * u) * K(x,w) = R(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(6769(a,1),469(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6769 469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6780">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(x,w) = L(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(6769(a,1),471(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6769 471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6781">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,u) = K(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[para(6769(a,1),6511(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6769 6511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6782">
    <literal><![CDATA[
      R(x,y,T(x,z)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(6769(a,1),6675(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6769 6675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6784">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6451,a(flip),b,6768,a)].">
      <j1 rule="hyper" parents="63 6451 6768"/>
    </justification>
  </clause>

  <clause id="6785">
    <literal><![CDATA[
      (x * y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(6768(a,1),322(a,1,2))].">
      <j1 rule="para" parents="6768 322"/>
    </justification>
  </clause>

  <clause id="6788">
    <literal><![CDATA[
      R(x,y,x * K(z,x)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5358,a,b,6782,a)].">
      <j1 rule="hyper" parents="63 5358 6782"/>
    </justification>
  </clause>

  <clause id="6789">
    <literal><![CDATA[
      R(T(x,y),z,T(x,u)) = T(R(x,z,x),y)
    ]]></literal>
    <justification jstring="[para(6782(a,1),27(a,2,1))].">
      <j1 rule="para" parents="6782 27"/>
    </justification>
  </clause>

  <clause id="6790">
    <literal><![CDATA[
      R(x / y,z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(113(a,1),6782(a,1,3)),flip(a)].">
      <j1 rule="para" parents="113 6782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6791">
    <literal><![CDATA[
      R(x,y,(x \ z) \ z) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(112(a,1),6782(a,1,3))].">
      <j1 rule="para" parents="112 6782"/>
    </justification>
  </clause>

  <clause id="6793">
    <literal><![CDATA[
      R(T(x,y),z,T(x,u)) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(6777(a,1),6675(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6777 6675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6794">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,y) = K(x,(y * (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(6766(a,1),6451(a,1,1))].">
      <j1 rule="para" parents="6766 6451"/>
    </justification>
  </clause>

  <clause id="6795">
    <literal><![CDATA[
      R(x \ y,z,y / x) = R(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(4990(a,1),6788(a,1,3))].">
      <j1 rule="para" parents="4990 6788"/>
    </justification>
  </clause>

  <clause id="6796">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(6784(a,1),6342(a,2,2))].">
      <j1 rule="para" parents="6784 6342"/>
    </justification>
  </clause>

  <clause id="6797">
    <literal><![CDATA[
      R(T(x,y),z,T(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(T(x,y),z,x) = w
    ]]></literal>
    <justification jstring="[para(6789(a,2),6366(a,1))].">
      <j1 rule="para" parents="6789 6366"/>
    </justification>
  </clause>

  <clause id="6798">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,z)) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,4357,a(flip),b,6793,a),flip(a)].">
      <j1 rule="hyper" parents="347 4357 6793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6800">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,4274,a(flip),b,6793,a),flip(a)].">
      <j1 rule="hyper" parents="347 4274 6793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6801">
    <literal><![CDATA[
      R(T(x,y),z,x) \ T(T(x,y) * z,T(x,y)) = T(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(6793(a,1),1774(a,1,1))].">
      <j1 rule="para" parents="6793 1774"/>
    </justification>
  </clause>

  <clause id="6802">
    <literal><![CDATA[
      T(x,y * T(x,z)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(1526,a,6800,a)].">
      <j1 rule="hyper" parents="1526 6800"/>
    </justification>
  </clause>

  <clause id="6805">
    <literal><![CDATA[
      T(x,x * (y / T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),6802(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 6802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6807">
    <literal><![CDATA[
      T(x \ (y / z),K(x,z)) = T(x,z) \ (y / T(z,x))
    ]]></literal>
    <justification jstring="[hyper(269,a,6763,a,b,5159,a)].">
      <j1 rule="hyper" parents="269 6763 5159"/>
    </justification>
  </clause>

  <clause id="6808">
    <literal><![CDATA[
      (x \ 1) \ ((x \ y) / T(y,x \ 1)) = (x * ((x \ y) / y)) * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(3126(a,1),6763(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3126 6763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6809">
    <literal><![CDATA[
      T((x * y) / x,T(x,z)) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(269,a,5925,a,b,6770,a)].">
      <j1 rule="hyper" parents="269 5925 6770"/>
    </justification>
  </clause>

  <clause id="6810">
    <literal><![CDATA[
      T(x * y,K(x,z)) = x * T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(269,a,6770,a(flip),b,4974,a)].">
      <j1 rule="hyper" parents="269 6770 4974"/>
    </justification>
  </clause>

  <clause id="6811">
    <literal><![CDATA[
      T(x,K(y,z)) * y = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,6809,a(flip),b,504,a)].">
      <j1 rule="hyper" parents="133 6809 504"/>
    </justification>
  </clause>

  <clause id="6812">
    <literal><![CDATA[
      T(x / y,T(y,z)) = T(y \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),6809(a,1,1,1))].">
      <j1 rule="para" parents="10 6809"/>
    </justification>
  </clause>

  <clause id="6813">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(255(a,1),6809(a,1,1)),flip(a)].">
      <j1 rule="para" parents="255 6809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6814">
    <literal><![CDATA[
      T(T(x,K(y,z)),y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6809(a,1),304(a,1,1))].">
      <j1 rule="para" parents="6809 304"/>
    </justification>
  </clause>

  <clause id="6815">
    <literal><![CDATA[
      K(x,y) * T(z,T(x,y)) = T(z,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,6813,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 6813 22"/>
    </justification>
  </clause>

  <clause id="6816">
    <literal><![CDATA[
      T(x,T(y,z)) / T(x,y) = K(T(x,y),K(y,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,6813,a(flip),b,4977,a(flip))].">
      <j1 rule="hyper" parents="131 6813 4977"/>
    </justification>
  </clause>

  <clause id="6817">
    <literal><![CDATA[
      T(T(T(x,y),z),K(y,u)) = T(T(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(6813(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6813 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6818">
    <literal><![CDATA[
      T(T(x,T(y,z)),K(T(y,z),u)) = T(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[para(23(a,1),6813(a,2,2))].">
      <j1 rule="para" parents="23 6813"/>
    </justification>
  </clause>

  <clause id="6819">
    <literal><![CDATA[
      T(x,T(y,z)) != T(u,K(y,z))
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(6813(a,1),49(a,1))].">
      <j1 rule="para" parents="6813 49"/>
    </justification>
  </clause>

  <clause id="6820">
    <literal><![CDATA[
      T(x,T(y,z)) \ (T(x,y) * (T(T(x,y),K(y,z)) * u)) = T(x,y) * u
    ]]></literal>
    <justification jstring="[para(6813(a,1),1228(a,1,1))].">
      <j1 rule="para" parents="6813 1228"/>
    </justification>
  </clause>

  <clause id="6821">
    <literal><![CDATA[
      L(K(T(x,y),K(y,z)) \ u,K(T(x,y),K(y,z)),T(x,y)) = T(x,T(y,z)) \ (T(x,y) * u)
    ]]></literal>
    <justification jstring="[para(6813(a,1),5007(a,2,1))].">
      <j1 rule="para" parents="6813 5007"/>
    </justification>
  </clause>

  <clause id="6822">
    <literal><![CDATA[
      T(x,K(y,x * y)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,4181,a(flip),b,6814,a),flip(a)].">
      <j1 rule="hyper" parents="40 4181 6814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6823">
    <literal><![CDATA[
      T(x \ y,K(x,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(40,a,4177,a(flip),b,6814,a),flip(a)].">
      <j1 rule="hyper" parents="40 4177 6814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6824">
    <literal><![CDATA[
      T(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6814(a,1),453(a,1))].">
      <j1 rule="para" parents="6814 453"/>
    </justification>
  </clause>

  <clause id="6825">
    <literal><![CDATA[
      T(x / y,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6814(a,1),808(a,1))].">
      <j1 rule="para" parents="6814 808"/>
    </justification>
  </clause>

  <clause id="6826">
    <literal><![CDATA[
      T(x \ 1,T(y,x)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(2482(a,1),6814(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2482 6814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6827">
    <literal><![CDATA[
      T(x * K(y,z),T(z,y)) = T(K(y,z) * x,z)
    ]]></literal>
    <justification jstring="[para(6121(a,1),6814(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6121 6814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6828">
    <literal><![CDATA[
      K(x,K(y,x * y)) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,6822,a)].">
      <j1 rule="hyper" parents="55 6822"/>
    </justification>
  </clause>

  <clause id="6829">
    <literal><![CDATA[
      T(x / y,K(y,x)) = x / y
    ]]></literal>
    <justification jstring="[para(12(a,1),6822(a,1,2,2))].">
      <j1 rule="para" parents="12 6822"/>
    </justification>
  </clause>

  <clause id="6830">
    <literal><![CDATA[
      K(x,K(y,y * x)) = 1
    ]]></literal>
    <justification jstring="[para(5297(a,1),6828(a,1,2))].">
      <j1 rule="para" parents="5297 6828"/>
    </justification>
  </clause>

  <clause id="6831">
    <literal><![CDATA[
      K(x,K(y,y * x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(6830(a,2),135(a,1,1))].">
      <j1 rule="para" parents="6830 135"/>
    </justification>
  </clause>

  <clause id="6832">
    <literal><![CDATA[
      K(x,y) * (x \ y) = (x \ y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1068,a,6823,a),flip(a)].">
      <j1 rule="hyper" parents="1068 6823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6833">
    <literal><![CDATA[
      K(x,y) * (y / x) = (y / x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1068,a,6829,a),flip(a)].">
      <j1 rule="hyper" parents="1068 6829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6835">
    <literal><![CDATA[
      T(x * y,K(y,z)) = T(x,K(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(347,a,6060,a,b,6811,a)].">
      <j1 rule="hyper" parents="347 6060 6811"/>
    </justification>
  </clause>

  <clause id="6836">
    <literal><![CDATA[
      x / ((x * y) / x) = K(y,x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(347,a,6126,a,b,6833,a)].">
      <j1 rule="hyper" parents="347 6126 6833"/>
    </justification>
  </clause>

  <clause id="6838">
    <literal><![CDATA[
      (x * (y * T(x,z))) \ ((x * y) * T(x,z)) = a(x,y * K(x,z),x)
    ]]></literal>
    <justification jstring="[para(6771(a,1),5928(a,1,2))].">
      <j1 rule="para" parents="6771 5928"/>
    </justification>
  </clause>

  <clause id="6839">
    <literal><![CDATA[
      (L(x,y,z) * (u * K(L(x,y,z),w))) / L(T(x,w),y,z) = (L(x,y,z) * u) / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),6772(a,1,2))].">
      <j1 rule="para" parents="25 6772"/>
    </justification>
  </clause>

  <clause id="6840">
    <literal><![CDATA[
      (R(x,y,z) * (u * K(R(x,y,z),w))) / R(T(x,w),y,z) = (R(x,y,z) * u) / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(27(a,2),6772(a,1,2))].">
      <j1 rule="para" parents="27 6772"/>
    </justification>
  </clause>

  <clause id="6841">
    <literal><![CDATA[
      (x * (y * K(z,x))) / x = (x * y) / T(x,z)
    ]]></literal>
    <justification jstring="[para(6109(a,1),6772(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6109 6772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6842">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(6829(a,2),6790(a,1,1))].">
      <j1 rule="para" parents="6829 6790"/>
    </justification>
  </clause>

  <clause id="6843">
    <literal><![CDATA[
      T(T(x * K(y,z),u),T(z,y)) = T(T(K(y,z) * x,z),u)
    ]]></literal>
    <justification jstring="[para(6827(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6827 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6844">
    <literal><![CDATA[
      (x * y) * K(z,x) = x * (y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(37,a,6135,a,b,6841,a)].">
      <j1 rule="hyper" parents="37 6135 6841"/>
    </justification>
  </clause>

  <clause id="6845">
    <literal><![CDATA[
      L(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3558,a,6844,a)].">
      <j1 rule="hyper" parents="3558 6844"/>
    </justification>
  </clause>

  <clause id="6846">
    <literal><![CDATA[
      R(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(2387,a,6844,a)].">
      <j1 rule="hyper" parents="2387 6844"/>
    </justification>
  </clause>

  <clause id="6847">
    <literal><![CDATA[
      x \ (y * K(z,x)) = (x \ y) * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(705,a,6844,a)].">
      <j1 rule="hyper" parents="705 6844"/>
    </justification>
  </clause>

  <clause id="6848">
    <literal><![CDATA[
      (x * (y * K(z,x))) * z = (x * y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,6844,a(flip),b,5919,a)].">
      <j1 rule="hyper" parents="133 6844 5919"/>
    </justification>
  </clause>

  <clause id="6849">
    <literal><![CDATA[
      a(x,y,K(z,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(127,a,6844,a(flip),b,86,a),flip(a)].">
      <j1 rule="hyper" parents="127 6844 86"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6850">
    <literal><![CDATA[
      R(x,y,K(z,T(x,u))) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,27,a(flip),b,6846,a(flip))].">
      <j1 rule="hyper" parents="40 27 6846"/>
    </justification>
  </clause>

  <clause id="6851">
    <literal><![CDATA[
      (T(x,y) * z) * K(u,x) = T(x,y) * (z * K(u,x))
    ]]></literal>
    <justification jstring="[para(6846(a,1),472(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6846 472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6852">
    <literal><![CDATA[
      R(x,y,T(K(z,x),u)) = x
    ]]></literal>
    <justification jstring="[para(1832(a,1),6846(a,1,3))].">
      <j1 rule="para" parents="1832 6846"/>
    </justification>
  </clause>

  <clause id="6853">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,x) = K(x,y) * (z * K(u,x))
    ]]></literal>
    <justification jstring="[para(6846(a,1),6511(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6846 6511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6854">
    <literal><![CDATA[
      ((x * y) / x) * z = (y * (K(x,y) * z)) * a(u,w,K(v5,u))
    ]]></literal>
    <justification jstring="[para(6849(a,2),5482(a,2,2))].">
      <j1 rule="para" parents="6849 5482"/>
    </justification>
  </clause>

  <clause id="6855">
    <literal><![CDATA[
      K((x * y) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(6595,a,6845,a)].">
      <j1 rule="hyper" parents="6595 6845"/>
    </justification>
  </clause>

  <clause id="6858">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(w,T(x,v5)) = L(x,y,z) * (u * K(w,T(x,v5)))
    ]]></literal>
    <justification jstring="[para(6850(a,1),471(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6850 471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6859">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,T(x,w)) = K(x,y) * (z * K(u,T(x,w)))
    ]]></literal>
    <justification jstring="[para(6850(a,1),6511(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6850 6511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6860">
    <literal><![CDATA[
      x \ (y * T(K(z,x),u)) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(6852(a,1),578(a,1,1))].">
      <j1 rule="para" parents="6852 578"/>
    </justification>
  </clause>

  <clause id="6861">
    <literal><![CDATA[
      (x \ y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / T(x,z),x) = u
    ]]></literal>
    <justification jstring="[para(6847(a,1),6186(a,1))].">
      <j1 rule="para" parents="6847 6186"/>
    </justification>
  </clause>

  <clause id="6862">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = K(y \ (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(5134,a,6855,a)].">
      <j1 rule="hyper" parents="5134 6855"/>
    </justification>
  </clause>

  <clause id="6863">
    <literal><![CDATA[
      K((x \ y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),6855(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 6855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6864">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = K(x \ (z \ 1),z) * y
    ]]></literal>
    <justification jstring="[para(6862(a,1),6744(a,2,1))].">
      <j1 rule="para" parents="6862 6744"/>
    </justification>
  </clause>

  <clause id="6865">
    <literal><![CDATA[
      T(T(x,y) / T(L(x,z,u),w),L(x,z,u)) = T(x,y) / T(L(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(6861,a,6164,a)].">
      <j1 rule="hyper" parents="6861 6164"/>
    </justification>
  </clause>

  <clause id="6866">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(269,a,6778,a,b,4974,a)].">
      <j1 rule="hyper" parents="269 6778 4974"/>
    </justification>
  </clause>

  <clause id="6867">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,6765,a,b,6866,a),flip(a)].">
      <j1 rule="hyper" parents="347 6765 6866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6868">
    <literal><![CDATA[
      T(x,K(y,z)) != y * (u * K(y,z))
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * u = x
    ]]></literal>
    <justification jstring="[para(6866(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="6866 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6869">
    <literal><![CDATA[
      (x * T(T(y,z) * K(y,z),K(y,z))) * u = (x * y) * ((K(y,z) * K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(6866(a,2),125(a,1,1,2))].">
      <j1 rule="para" parents="6866 125"/>
    </justification>
  </clause>

  <clause id="6870">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(6867(a,2),6785(a,1))].">
      <j1 rule="para" parents="6867 6785"/>
    </justification>
  </clause>

  <clause id="6871">
    <literal><![CDATA[
      L(K(x,y),z,K(x,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3558,a,6781,a)].">
      <j1 rule="hyper" parents="3558 6781"/>
    </justification>
  </clause>

  <clause id="6872">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(269,a,6781,a,b,xx)].">
      <j1 rule="hyper" parents="269 6781"/>
    </justification>
  </clause>

  <clause id="6873">
    <literal><![CDATA[
      (K(x,y) \ z) * K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(269,a,165,a(flip),b,6781,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="269 165 6781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6875">
    <literal><![CDATA[
      L(T(K(x,y),z),u,K(x,w)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6871(a,1),25(a,2,1))].">
      <j1 rule="para" parents="6871 25"/>
    </justification>
  </clause>

  <clause id="6877">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,6117,a,b,6872,a),flip(a)].">
      <j1 rule="hyper" parents="347 6117 6872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6878">
    <literal><![CDATA[
      T(T(K(x,y) * z,u),K(x,y)) = T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(6872(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6872 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6879">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[para(5256(a,2),6872(a,1,1))].">
      <j1 rule="para" parents="5256 6872"/>
    </justification>
  </clause>

  <clause id="6880">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(5261(a,1),6872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5261 6872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6881">
    <literal><![CDATA[
      T((x \ K(y,x)) \ z,K(x,y)) = ((x \ 1) \ z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5825(a,1),6872(a,1,1))].">
      <j1 rule="para" parents="5825 6872"/>
    </justification>
  </clause>

  <clause id="6882">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,y)) = T(z * K(x,y),x)
    ]]></literal>
    <justification jstring="[para(6872(a,1),6814(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6872 6814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6883">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) = z / K(x,y)
    ]]></literal>
    <justification jstring="[para(5256(a,2),6877(a,1,1))].">
      <j1 rule="para" parents="5256 6877"/>
    </justification>
  </clause>

  <clause id="6884">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6877(a,2),6140(a,1))].">
      <j1 rule="para" parents="6877 6140"/>
    </justification>
  </clause>

  <clause id="6885">
    <literal><![CDATA[
      T(x,K(y,z)) * K(z,y) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(6138,a,6880,a)].">
      <j1 rule="hyper" parents="6138 6880"/>
    </justification>
  </clause>

  <clause id="6887">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(6880(a,1),628(a,1))].">
      <j1 rule="para" parents="6880 628"/>
    </justification>
  </clause>

  <clause id="6888">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(483,a,6885,a)].">
      <j1 rule="hyper" parents="483 6885"/>
    </justification>
  </clause>

  <clause id="6889">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,4989,a,b,6885,a)].">
      <j1 rule="hyper" parents="35 4989 6885"/>
    </justification>
  </clause>

  <clause id="6890">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(269,a,6885,a(flip),b,4943,a),flip(a)].">
      <j1 rule="hyper" parents="269 6885 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6891">
    <literal><![CDATA[
      ((T(x,K(y,z)) * (K(z,y) * u)) * w) / (L(u,K(z,y),T(x,K(y,z))) * w) = R(K(z,y) * x,L(u,K(z,y),T(x,K(y,z))),w)
    ]]></literal>
    <justification jstring="[para(6885(a,1),543(a,2,1))].">
      <j1 rule="para" parents="6885 543"/>
    </justification>
  </clause>

  <clause id="6892">
    <literal><![CDATA[
      ((x * K(y,z)) * (L(u,K(y,z),x) * w)) \ ((x * (T(u,K(z,y)) * K(y,z))) * w) = a(x * K(y,z),L(u,K(y,z),x),w)
    ]]></literal>
    <justification jstring="[para(6885(a,2),540(a,1,2,1,2))].">
      <j1 rule="para" parents="6885 540"/>
    </justification>
  </clause>

  <clause id="6893">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(6885(a,1),6145(a,1,1))].">
      <j1 rule="para" parents="6885 6145"/>
    </justification>
  </clause>

  <clause id="6895">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(6888(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="6888 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6896">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(6888(a,1),6814(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6888 6814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6897">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(34,a,4929,a(flip),b,6889,a),flip(a)].">
      <j1 rule="hyper" parents="34 4929 6889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6898">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(134,a,6897,a(flip),b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 6897 4924"/>
    </justification>
  </clause>

  <clause id="6899">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6897(a,1),5179(a,1,1))].">
      <j1 rule="para" parents="6897 5179"/>
    </justification>
  </clause>

  <clause id="6900">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) * w = u
    ]]></literal>
    <justification jstring="[para(6897(a,1),5273(a,1,1))].">
      <j1 rule="para" parents="6897 5273"/>
    </justification>
  </clause>

  <clause id="6901">
    <literal><![CDATA[
      T((x * y) \ y,K(z,x)) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(40,a,5810,a,b,6896,a),flip(a)].">
      <j1 rule="hyper" parents="40 5810 6896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6902">
    <literal><![CDATA[
      T(x,T(y,z)) != T(u,y)
    ]]></literal>
    <literal><![CDATA[
      T(u,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(6896(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="6896 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6904">
    <literal><![CDATA[
      T(x,T(x * y,y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(6822(a,1),6896(a,1,1))].">
      <j1 rule="para" parents="6822 6896"/>
    </justification>
  </clause>

  <clause id="6905">
    <literal><![CDATA[
      T(K(x * y,x),y) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(6831,a,6890,a),flip(a)].">
      <j1 rule="hyper" parents="6831 6890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6907">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(5273,a,6898,a)].">
      <j1 rule="hyper" parents="5273 6898"/>
    </justification>
  </clause>

  <clause id="6908">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(34,a,4922,a(flip),b,6907,a)].">
      <j1 rule="hyper" parents="34 4922 6907"/>
    </justification>
  </clause>

  <clause id="6909">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(5173(a,1),6899(a,1))].">
      <j1 rule="para" parents="5173 6899"/>
    </justification>
  </clause>

  <clause id="6910">
    <literal><![CDATA[
      (x * y) * K(z,x \ (z \ (x * y))) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4860,a(flip),b,6796,a),flip(a)].">
      <j1 rule="hyper" parents="63 4860 6796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6911">
    <literal><![CDATA[
      x * K(y,z \ (y \ x)) = z * (y * ((z \ x) / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,4846,a(flip),b,6796,a),flip(a)].">
      <j1 rule="hyper" parents="63 4846 6796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6912">
    <literal><![CDATA[
      x * (y * ((x \ 1) / y)) = K(y,x \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(126,a,6796,a(flip),b,4846,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 6796 4846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6913">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * K(z,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(6912(a,1),6754(a,2,2))].">
      <j1 rule="para" parents="6912 6754"/>
    </justification>
  </clause>

  <clause id="6914">
    <literal><![CDATA[
      L(K(x,y),z,T(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3558,a,6851,a)].">
      <j1 rule="hyper" parents="3558 6851"/>
    </justification>
  </clause>

  <clause id="6915">
    <literal><![CDATA[
      T(x,y) \ (z * K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      (T(x,y) \ z) * K(u,x) = w
    ]]></literal>
    <justification jstring="[para(6914(a,1),876(a,1,2,2))].">
      <j1 rule="para" parents="6914 876"/>
    </justification>
  </clause>

  <clause id="6916">
    <literal><![CDATA[
      L(K(x,y),z,K(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3558,a,6853,a)].">
      <j1 rule="hyper" parents="3558 6853"/>
    </justification>
  </clause>

  <clause id="6919">
    <literal><![CDATA[
      K(x,(R(x,y,z) \ u) \ w) = K(x,u \ (R(x,y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(6481,a,6779,a),flip(a)].">
      <j1 rule="hyper" parents="6481 6779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6920">
    <literal><![CDATA[
      L(K(x,y),z,L(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3558,a,6780,a)].">
      <j1 rule="hyper" parents="3558 6780"/>
    </justification>
  </clause>

  <clause id="6921">
    <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(6780(a,1),6141(a,1,1))].">
      <j1 rule="para" parents="6780 6141"/>
    </justification>
  </clause>

  <clause id="6922">
    <literal><![CDATA[
      T((x \ K(y,x)) \ L((x \ 1) * (z / (x \ 1)),u,w),K(x,y)) = (L(z,u,w) / (x \ 1)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(3158(a,1),6881(a,2,1))].">
      <j1 rule="para" parents="3158 6881"/>
    </justification>
  </clause>

  <clause id="6923">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) \ T(K(z,y) * x,T(x,K(y,z))) = T(K(z,y),T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(6885(a,1),6801(a,1,2,1))].">
      <j1 rule="para" parents="6885 6801"/>
    </justification>
  </clause>

  <clause id="6924">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = y / (K(z \ (x \ 1),x) * y)
    ]]></literal>
    <justification jstring="[para(6864(a,1),5701(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6864 5701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6925">
    <literal><![CDATA[
      K(x,(y * z) \ (x \ y)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(34,a,6911,a,b,6913,a(flip))].">
      <j1 rule="hyper" parents="34 6911 6913"/>
    </justification>
  </clause>

  <clause id="6926">
    <literal><![CDATA[
      (x * K(y,z \ (y \ 1))) \ x != u
    ]]></literal>
    <literal><![CDATA[
      K((w * z) \ (y \ w),y) = u
    ]]></literal>
    <justification jstring="[para(6925(a,1),6141(a,1,1,2))].">
      <j1 rule="para" parents="6925 6141"/>
    </justification>
  </clause>

  <clause id="6927">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ (x \ 1)) = u
    ]]></literal>
    <justification jstring="[para(6924(a,2),5276(a,1))].">
      <j1 rule="para" parents="6924 5276"/>
    </justification>
  </clause>

  <clause id="6928">
    <literal><![CDATA[
      K(x,y / (x * (z * y))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ (x \ 1)) = u
    ]]></literal>
    <justification jstring="[para(5835(a,1),6927(a,1))].">
      <j1 rule="para" parents="5835 6927"/>
    </justification>
  </clause>

  <clause id="6929">
    <literal><![CDATA[
      a(x,y * K(x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(6838(a,1),836(a,1))].">
      <j1 rule="para" parents="6838 836"/>
    </justification>
  </clause>

  <clause id="6930">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = K(y \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(6926,a,6199,a)].">
      <j1 rule="hyper" parents="6926 6199"/>
    </justification>
  </clause>

  <clause id="6931">
    <literal><![CDATA[
      K((x \ y) \ (z \ 1),z) = K(y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[para(10(a,1),6930(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 6930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6932">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ 1),z),z \ 1,u) = K(y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6246,a,b,6931,a)].">
      <j1 rule="hyper" parents="63 6246 6931"/>
    </justification>
  </clause>

  <clause id="6933">
    <literal><![CDATA[
      T(x,T(y,z)) \ (T(x,y) * (T(x,T(y,z)) * u)) = T(x,y) * u
    ]]></literal>
    <justification jstring="[para(6813(a,1),6820(a,1,2,2,1))].">
      <j1 rule="para" parents="6813 6820"/>
    </justification>
  </clause>

  <clause id="6934">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,L(y,w,v5)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(3558,a,6858,a)].">
      <j1 rule="hyper" parents="3558 6858"/>
    </justification>
  </clause>

  <clause id="6935">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(398(a,1),6934(a,1,3))].">
      <j1 rule="para" parents="398 6934"/>
    </justification>
  </clause>

  <clause id="6936">
    <literal><![CDATA[
      T(T(x,y) / L(T(x,z),u,w),L(x,u,w)) = T(x,y) / T(L(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(25(a,2),6865(a,1,1,2))].">
      <j1 rule="para" parents="25 6865"/>
    </justification>
  </clause>

  <clause id="6937">
    <literal><![CDATA[
      T(T(x,y) / L(T(x,z),u,w),L(x,u,w)) = T(x,y) / L(T(x,z),u,w)
    ]]></literal>
    <justification jstring="[para(25(a,2),6936(a,2,2))].">
      <j1 rule="para" parents="25 6936"/>
    </justification>
  </clause>

  <clause id="6938">
    <literal><![CDATA[
      T(K(x,y),z) * R(T(K(y,x),z),u,w) = T(K(x,y) * R(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(6908(a,1),5185(a,1,2,1))].">
      <j1 rule="para" parents="6908 5185"/>
    </justification>
  </clause>

  <clause id="6939">
    <literal><![CDATA[
      (K(x,y) * R(K(x,y) \ 1,z,u)) * w = K(x,y) * (R(K(y,x),z,u) * w)
    ]]></literal>
    <justification jstring="[para(268(a,1),5371(a,1,2)),flip(a)].">
      <j1 rule="para" parents="268 5371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6940">
    <literal><![CDATA[
      (K(x,y) * R(K(y,x),z,u)) * w = K(x,y) * (R(K(y,x),z,u) * w)
    ]]></literal>
    <justification jstring="[para(5173(a,1),6939(a,1,1,2,1))].">
      <j1 rule="para" parents="5173 6939"/>
    </justification>
  </clause>

  <clause id="6941">
    <literal><![CDATA[
      (K(x,y) * L(K(x,y) \ 1,z,u)) * w = K(x,y) * (L(K(y,x),z,u) * w)
    ]]></literal>
    <justification jstring="[para(267(a,1),5372(a,1,2)),flip(a)].">
      <j1 rule="para" parents="267 5372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6942">
    <literal><![CDATA[
      (K(x,y) * L(K(y,x),z,u)) * w = K(x,y) * (L(K(y,x),z,u) * w)
    ]]></literal>
    <justification jstring="[para(5173(a,1),6941(a,1,1,2,1))].">
      <j1 rule="para" parents="5173 6941"/>
    </justification>
  </clause>

  <clause id="6943">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ (x * (K(y,x) * (z * u))) = L(L(u,z,x),x * z,K(y,x))
    ]]></literal>
    <justification jstring="[para(5353(a,1),5472(a,1,2))].">
      <j1 rule="para" parents="5353 5472"/>
    </justification>
  </clause>

  <clause id="6944">
    <literal><![CDATA[
      T(x * ((x \ y) * (y / x)),(x \ y) \ y) = ((x \ y) * (x \ y)) * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(509(a,1),5710(a,1,1,2))].">
      <j1 rule="para" parents="509 5710"/>
    </justification>
  </clause>

  <clause id="6945">
    <literal><![CDATA[
      T(K(x * R(1 / y,y,z),y \ 1) / y,x) = R(1 / y,x,z / (y * z))
    ]]></literal>
    <justification jstring="[para(3898(a,1),5724(a,1,1))].">
      <j1 rule="para" parents="3898 5724"/>
    </justification>
  </clause>

  <clause id="6946">
    <literal><![CDATA[
      T(K(x * R(y \ 1,y,z),y \ 1) / y,x) = R(1 / y,x,z / (y * z))
    ]]></literal>
    <justification jstring="[para(4730(a,1),6945(a,1,1,1))].">
      <j1 rule="para" parents="4730 6945"/>
    </justification>
  </clause>

  <clause id="6947">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(347,a,1871,a(flip),b,5800,a),flip(a)].">
      <j1 rule="hyper" parents="347 1871 5800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6948">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,4423,a(flip),b,6947,a),flip(a)].">
      <j1 rule="hyper" parents="347 4423 6947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6949">
    <literal><![CDATA[
      (T(x * (y \ 1),x) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(6095(a,1),5830(a,1,1,1))].">
      <j1 rule="para" parents="6095 5830"/>
    </justification>
  </clause>

  <clause id="6950">
    <literal><![CDATA[
      K(x,y * (((z * K(u,z)) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(5376(a,1),6593(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5376 6593"/>
    </justification>
  </clause>

  <clause id="6951">
    <literal><![CDATA[
      K(x,y * ((z * (1 / (1 / u))) * w)) = K(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[para(4989(a,1),6950(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4989 6950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6952">
    <literal><![CDATA[
      ((x \ y) \ y) \ R((x \ y) \ y,z,u) = x \ (y \ ((R(x,z,u) * (x \ y)) * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,991,a(flip),b,6638,a)].">
      <j1 rule="hyper" parents="63 991 6638"/>
    </justification>
  </clause>

  <clause id="6953">
    <literal><![CDATA[
      (x * T(T(T(y,z),z),K(y,z))) * u = (x * y) * ((K(y,z) * K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(5148(a,1),6869(a,1,1,2,1))].">
      <j1 rule="para" parents="5148 6869"/>
    </justification>
  </clause>

  <clause id="6954">
    <literal><![CDATA[
      (x * y) * ((K(y,z) * K(y,z)) * u) = (x * T(T(y,z),z)) * u
    ]]></literal>
    <justification jstring="[para(3578(a,1),6953(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3578 6953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6956">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,z)) = L(x,y,z * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6588,a(flip),b,6943,a),flip(a)].">
      <j1 rule="hyper" parents="63 6588 6943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6957">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[hyper(347,a,6636,a,b,6956,a),flip(a)].">
      <j1 rule="hyper" parents="347 6636 6956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6958">
    <literal><![CDATA[
      L(L(x,y,z \ u),(z \ u) * y,K(z,z \ u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(4990(a,1),6956(a,2,3))].">
      <j1 rule="para" parents="4990 6956"/>
    </justification>
  </clause>

  <clause id="6959">
    <literal><![CDATA[
      L(x,y \ z,z / y) = L(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(550,a,6958,a),flip(a)].">
      <j1 rule="hyper" parents="550 6958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6960">
    <literal><![CDATA[
      L(x,(y \ z) \ z,(y \ z) \ z) = L(x,(y \ z) \ z,y)
    ]]></literal>
    <justification jstring="[para(80(a,1),6959(a,1,3)),flip(a)].">
      <j1 rule="para" parents="80 6959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6961">
    <literal><![CDATA[
      L(x,(y \ z) \ z,(y \ z) \ z) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,6647,a(flip),b,6960,a),flip(a)].">
      <j1 rule="hyper" parents="347 6647 6960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6963">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K((R(x,y,z) \ 1) \ 1,u) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(4693(a,1),5796(a,1,2,1,1))].">
      <j1 rule="para" parents="4693 5796"/>
    </justification>
  </clause>

  <clause id="6964">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(R(x,y,z),u) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3407(a,1),6963(a,1,2))].">
      <j1 rule="para" parents="3407 6963"/>
    </justification>
  </clause>

  <clause id="6965">
    <literal><![CDATA[
      R(K(x,y),R(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5828,a,5891,a)].">
      <j1 rule="hyper" parents="5828 5891"/>
    </justification>
  </clause>

  <clause id="6966">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) = (v5 * K(y,x)) \ v5
    ]]></literal>
    <justification jstring="[para(6965(a,1),6714(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6965 6714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6967">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,6199,a(flip),b,6966,a),flip(a)].">
      <j1 rule="hyper" parents="347 6199 6966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6968">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) = K(x,R(x,y,z) / (w / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6710,a(flip),b,6967,a)].">
      <j1 rule="hyper" parents="63 6710 6967"/>
    </justification>
  </clause>

  <clause id="6969">
    <literal><![CDATA[
      ((x * (y * ((x \ (z / u)) / y))) * u) / z = K(y,z / ((x * y) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6709,a(flip),b,6554,a),flip(a)].">
      <j1 rule="hyper" parents="63 6709 6554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6970">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = (x * (u * ((x \ y) / u))) * (y \ z)
    ]]></literal>
    <justification jstring="[para(4846(a,1),4859(a,2,1))].">
      <j1 rule="para" parents="4846 4859"/>
    </justification>
  </clause>

  <clause id="6971">
    <literal><![CDATA[
      L(L(x,y,T(z,u)),T(z,u) * y,K(u,z)) = (z * y) \ (z * (y * x))
    ]]></literal>
    <justification jstring="[para(4946(a,1),5207(a,2,2))].">
      <j1 rule="para" parents="4946 5207"/>
    </justification>
  </clause>

  <clause id="6972">
    <literal><![CDATA[
      L(L(x,y,T(z,u)),T(z,u) * y,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(6971(a,2),545(a,1))].">
      <j1 rule="para" parents="6971 545"/>
    </justification>
  </clause>

  <clause id="6974">
    <literal><![CDATA[
      L(K(L(x,y,z),u),L(x,y,z),z * y) = (z * (y * x)) \ (z * (y * T(x,u)))
    ]]></literal>
    <justification jstring="[para(97(a,1),5641(a,1,2)),flip(a)].">
      <j1 rule="para" parents="97 5641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6975">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,5959,a(flip),b,6974,a(flip))].">
      <j1 rule="hyper" parents="134 5959 6974"/>
    </justification>
  </clause>

  <clause id="6976">
    <literal><![CDATA[
      (x * (y * z)) / K(L(y,z,x),z) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,251,a(flip),b,6975,a)].">
      <j1 rule="hyper" parents="131 251 6975"/>
    </justification>
  </clause>

  <clause id="6977">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(6140,a,6976,a)].">
      <j1 rule="hyper" parents="6140 6976"/>
    </justification>
  </clause>

  <clause id="6978">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = K(z,L(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(128,a,6976,a(flip),b,6117,a(flip))].">
      <j1 rule="hyper" parents="128 6976 6117"/>
    </justification>
  </clause>

  <clause id="6979">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * (z * y)) = w
    ]]></literal>
    <justification jstring="[para(6977(a,2),613(a,1))].">
      <j1 rule="para" parents="6977 613"/>
    </justification>
  </clause>

  <clause id="6980">
    <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(347,a,4830,a,b,5949,a)].">
      <j1 rule="hyper" parents="347 4830 5949"/>
    </justification>
  </clause>

  <clause id="6981">
    <literal><![CDATA[
      L(x \ (y * (x \ 1)),x * x,(z * x) \ z) = L(x,x,z) \ (y * ((z * x) \ z))
    ]]></literal>
    <justification jstring="[para(498(a,1),6292(a,1,1))].">
      <j1 rule="para" parents="498 6292"/>
    </justification>
  </clause>

  <clause id="6983">
    <literal><![CDATA[
      L(x,x,y) \ (z * ((y * x) \ y)) = x \ (z * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(550,a,6981,a),flip(a)].">
      <j1 rule="hyper" parents="550 6981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6985">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * ((z / u) \ z)) \ z) / y))
    ]]></literal>
    <justification jstring="[para(83(a,1),6970(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="83 6970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6986">
    <literal><![CDATA[
      (x / y) \ T(x * K(y,z),(x / y) \ 1) = T(x * (y / x),z)
    ]]></literal>
    <justification jstring="[para(3844(a,1),6980(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3844 6980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6987">
    <literal><![CDATA[
      K(x * K(y,z),(x / y) \ 1) = T(x * (y / x),z) / T(y,z)
    ]]></literal>
    <justification jstring="[para(6986(a,1),5972(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6986 5972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6988">
    <literal><![CDATA[
      K(x * K(y,z),(x / y) \ 1) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,5295,a(flip),b,6987,a),flip(a)].">
      <j1 rule="hyper" parents="347 5295 6987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6989">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,z / (y * z)) = K(((x * (y * z)) / z) \ 1,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5632,a,5678,a),flip(a)].">
      <j1 rule="hyper" parents="5632 5678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6991">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,z / (y * z)) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,5551,a(flip),b,6989,a),flip(a)].">
      <j1 rule="hyper" parents="347 5551 6989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6992">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5632,a,6991,a)].">
      <j1 rule="hyper" parents="5632 6991"/>
    </justification>
  </clause>

  <clause id="6993">
    <literal><![CDATA[
      K(R(1 / x,x,y) / z,x \ 1) = K(y / (z * (x * y)),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(5644,a,6992,a)].">
      <j1 rule="hyper" parents="5644 6992"/>
    </justification>
  </clause>

  <clause id="6995">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),w) = x * ((y * u) * T((y * u) \ y,w))
    ]]></literal>
    <justification jstring="[hyper(1217,a,6094,a),flip(a)].">
      <j1 rule="hyper" parents="1217 6094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6996">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),w) = x * (y * (u * T(u \ 1,w)))
    ]]></literal>
    <justification jstring="[para(864(a,1),6995(a,2,2))].">
      <j1 rule="para" parents="864 6995"/>
    </justification>
  </clause>

  <clause id="6998">
    <literal><![CDATA[
      (x * y) * K(1 / L(z,y,x),u) = x * (y * (z * T(z \ 1,u)))
    ]]></literal>
    <justification jstring="[para(66(a,1),6996(a,1,2,1))].">
      <j1 rule="para" parents="66 6996"/>
    </justification>
  </clause>

  <clause id="6999">
    <literal><![CDATA[
      (x * y) * K(1 / L(z,y,x),u) = x * (y * K(1 / z,u))
    ]]></literal>
    <justification jstring="[para(4971(a,1),6998(a,2,2,2))].">
      <j1 rule="para" parents="4971 6998"/>
    </justification>
  </clause>

  <clause id="7000">
    <literal><![CDATA[
      L(K(1 / x,y),z,u) = K(1 / L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(544,a,6999,a)].">
      <j1 rule="hyper" parents="544 6999"/>
    </justification>
  </clause>

  <clause id="7001">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = L(K(1 / x,x),y,z)
    ]]></literal>
    <justification jstring="[para(5725(a,1),7000(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5725 7000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7002">
    <literal><![CDATA[
      K(1 / L(x \ y,z,u),w) = L(K(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(5994(a,1),7000(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5994 7000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7003">
    <literal><![CDATA[
      K(L(x \ y,z,u) \ 1,w) = L(K(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[hyper(3409,a,7002,a)].">
      <j1 rule="hyper" parents="3409 7002"/>
    </justification>
  </clause>

  <clause id="7004">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z)
    ]]></literal>
    <justification jstring="[hyper(6082,a,7003,a),flip(a)].">
      <j1 rule="hyper" parents="6082 7003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7005">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(66(a,1),7003(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="66 7003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7006">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(66(a,1),7003(a,2,1,1))].">
      <j1 rule="para" parents="66 7003"/>
    </justification>
  </clause>

  <clause id="7007">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((u * x) \ (u * y),z) = w
    ]]></literal>
    <justification jstring="[para(7003(a,1),6082(a,1))].">
      <j1 rule="para" parents="7003 6082"/>
    </justification>
  </clause>

  <clause id="7008">
    <literal><![CDATA[
      (x * y) \ (x * (y * K(z \ 1,u))) = K(L(z,y,x) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18,a(flip),b,7005,a)].">
      <j1 rule="hyper" parents="63 18 7005"/>
    </justification>
  </clause>

  <clause id="7009">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,(x \ 1) * L((x \ 1) \ 1,u,w)) = L(1,y,z)
    ]]></literal>
    <justification jstring="[para(2031(a,1),7005(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2031 7005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7010">
    <literal><![CDATA[
      K(L(K(x,y),z,u) \ 1,w) = L(K(K(y,x),w),z,u)
    ]]></literal>
    <justification jstring="[para(5173(a,1),7005(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5173 7005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7011">
    <literal><![CDATA[
      K(L(T(1 / x,y),z,u) \ 1,w) = L(T(K(x,w),y),z,u)
    ]]></literal>
    <justification jstring="[para(6422(a,1),7005(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6422 7005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7012">
    <literal><![CDATA[
      1 / L(K(x,y),z,u) = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5662,a(flip),b,7006,a)].">
      <j1 rule="hyper" parents="63 5662 7006"/>
    </justification>
  </clause>

  <clause id="7013">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) * w = L(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(7006(a,1),5256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7006 5256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7014">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = (w * L(K(y,x),z,u)) \ w
    ]]></literal>
    <justification jstring="[para(7006(a,1),6123(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7006 6123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7015">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(214,a,7012,a)].">
      <j1 rule="hyper" parents="214 7012"/>
    </justification>
  </clause>

  <clause id="7016">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(7012(a,1),359(a,1,1))].">
      <j1 rule="para" parents="7012 359"/>
    </justification>
  </clause>

  <clause id="7017">
    <literal><![CDATA[
      L(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7012(a,1),6251(a,1))].">
      <j1 rule="para" parents="7012 6251"/>
    </justification>
  </clause>

  <clause id="7018">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ y) \ x) = u
    ]]></literal>
    <justification jstring="[para(6450(a,1),7017(a,1))].">
      <j1 rule="para" parents="6450 7017"/>
    </justification>
  </clause>

  <clause id="7019">
    <literal><![CDATA[
      1 / L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(7015(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7015 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7020">
    <literal><![CDATA[
      L(K(x \ y,z),y,y \ 1) = K(((y \ 1) * x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,3918,a(flip),b,7004,a),flip(a)].">
      <j1 rule="hyper" parents="347 3918 7004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7021">
    <literal><![CDATA[
      K((K(x,y) * z) \ (K(x,y) * u),x) = K(z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6916,a(flip),b,7004,a),flip(a)].">
      <j1 rule="hyper" parents="63 6916 7004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7022">
    <literal><![CDATA[
      L(K((x \ y) \ z,u),z,x) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),7004(a,2,1,1))].">
      <j1 rule="para" parents="10 7004"/>
    </justification>
  </clause>

  <clause id="7023">
    <literal><![CDATA[
      K((x * (y / z)) \ (x * y),u) = L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(83(a,1),7004(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="83 7004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7024">
    <literal><![CDATA[
      L(K(x \ T(y,z),u),T(y,z),z) = K((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(111(a,1),7004(a,2,1,2))].">
      <j1 rule="para" parents="111 7004"/>
    </justification>
  </clause>

  <clause id="7025">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K(L(x \ y,x,u),z)
    ]]></literal>
    <justification jstring="[para(99(a,2),7004(a,2,1))].">
      <j1 rule="para" parents="99 7004"/>
    </justification>
  </clause>

  <clause id="7026">
    <literal><![CDATA[
      L(K((K(x,y) * z) \ u,w),u,K(y,x)) = K(z \ (K(y,x) * u),w)
    ]]></literal>
    <justification jstring="[para(5261(a,1),7004(a,2,1,1))].">
      <j1 rule="para" parents="5261 7004"/>
    </justification>
  </clause>

  <clause id="7027">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K((z * (x \ 1)) \ (z * y),x)
    ]]></literal>
    <justification jstring="[para(6223(a,1),7004(a,1,1))].">
      <j1 rule="para" parents="6223 7004"/>
    </justification>
  </clause>

  <clause id="7028">
    <literal><![CDATA[
      L(K(L(x,y,z) \ x,u),x,z * y) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(1787(a,2),7025(a,2,1))].">
      <j1 rule="para" parents="1787 7025"/>
    </justification>
  </clause>

  <clause id="7029">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(2938(a,1),7025(a,2,1))].">
      <j1 rule="para" parents="2938 7025"/>
    </justification>
  </clause>

  <clause id="7030">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(y \ (x * z),z)
    ]]></literal>
    <justification jstring="[hyper(6256,a,7022,a)].">
      <j1 rule="hyper" parents="6256 7022"/>
    </justification>
  </clause>

  <clause id="7031">
    <literal><![CDATA[
      K((x \ y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6935,a(flip),b,7022,a)].">
      <j1 rule="hyper" parents="63 6935 7022"/>
    </justification>
  </clause>

  <clause id="7032">
    <literal><![CDATA[
      K(x \ (y * (z \ 1)),z) = K(x \ (z \ y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6932,a(flip),b,7022,a),flip(a)].">
      <j1 rule="hyper" parents="63 6932 7022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7033">
    <literal><![CDATA[
      K((x \ y) \ z,u \ (x * z)) = K(y \ (x * z),(x \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6450,a(flip),b,7022,a)].">
      <j1 rule="hyper" parents="63 6450 7022"/>
    </justification>
  </clause>

  <clause id="7035">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,z) = u
    ]]></literal>
    <justification jstring="[para(7022(a,1),6256(a,1))].">
      <j1 rule="para" parents="7022 6256"/>
    </justification>
  </clause>

  <clause id="7036">
    <literal><![CDATA[
      K(x \ (y * z),z) / (z \ T(z * ((y \ x) \ 1),z)) = y \ x
    ]]></literal>
    <justification jstring="[para(7030(a,1),5806(a,1,1))].">
      <j1 rule="para" parents="7030 5806"/>
    </justification>
  </clause>

  <clause id="7037">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(100(a,2),7023(a,1,1))].">
      <j1 rule="para" parents="100 7023"/>
    </justification>
  </clause>

  <clause id="7038">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = (z * y) \ (z * (y * K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,18,a(flip),b,7037,a),flip(a)].">
      <j1 rule="hyper" parents="347 18 7037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7039">
    <literal><![CDATA[
      L(K(x,y),z * x,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(11(a,1),7037(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 7037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7040">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(7037(a,1),5173(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7037 5173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7041">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(6256,a,7039,a),flip(a)].">
      <j1 rule="hyper" parents="6256 7039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7042">
    <literal><![CDATA[
      K(L(x,y,L(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,6920,a(flip),b,7039,a),flip(a)].">
      <j1 rule="hyper" parents="63 6920 7039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7043">
    <literal><![CDATA[
      K(L(x,y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6845,a(flip),b,7039,a),flip(a)].">
      <j1 rule="hyper" parents="63 6845 7039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7044">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6768,a(flip),b,7039,a),flip(a)].">
      <j1 rule="hyper" parents="63 6768 7039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7045">
    <literal><![CDATA[
      K(L(L(x,y,z),u,w),z) = K(L(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(30(a,1),7043(a,1,1))].">
      <j1 rule="para" parents="30 7043"/>
    </justification>
  </clause>

  <clause id="7046">
    <literal><![CDATA[
      K(L(x,y,z),R(z,u,w)) = R(z,u,w) \ R(z * K(x,z),u,w)
    ]]></literal>
    <justification jstring="[para(7043(a,1),5546(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7043 5546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7048">
    <literal><![CDATA[
      K((x * (y / x)) \ (y * z),y) = K(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[para(5896(a,1),7043(a,1,1))].">
      <j1 rule="para" parents="5896 7043"/>
    </justification>
  </clause>

  <clause id="7049">
    <literal><![CDATA[
      K(L(x,y,x),z) = u / (K(z,x) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,5259,a,b,7044,a),flip(a)].">
      <j1 rule="hyper" parents="347 5259 7044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7050">
    <literal><![CDATA[
      T(x,L(y,z,y)) = x / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(220,a,7044,a(flip),b,4913,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="220 7044 4913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7051">
    <literal><![CDATA[
      L(x,y,x) * K(x,z) = L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,7044,a(flip),b,4982,a)].">
      <j1 rule="hyper" parents="134 7044 4982"/>
    </justification>
  </clause>

  <clause id="7052">
    <literal><![CDATA[
      K(R(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4494(a,1),7044(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4494 7044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7053">
    <literal><![CDATA[
      (x * K(y,x)) * L(y,z,y) = L(y,z,y) * x
    ]]></literal>
    <justification jstring="[para(7044(a,1),4989(a,1,1,2))].">
      <j1 rule="para" parents="7044 4989"/>
    </justification>
  </clause>

  <clause id="7054">
    <literal><![CDATA[
      K(x,y) * L(x,z,x) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7044(a,1),5028(a,1,1))].">
      <j1 rule="para" parents="7044 5028"/>
    </justification>
  </clause>

  <clause id="7056">
    <literal><![CDATA[
      K(x,y) * R(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,7052,a(flip),b,5022,a)].">
      <j1 rule="hyper" parents="133 7052 5022"/>
    </justification>
  </clause>

  <clause id="7057">
    <literal><![CDATA[
      (K(x,y) * z) * x = K(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(7052(a,1),6511(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7052 6511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7058">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(6798(a,1),7052(a,1,1))].">
      <j1 rule="para" parents="6798 7052"/>
    </justification>
  </clause>

  <clause id="7059">
    <literal><![CDATA[
      T(x,L(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,4914,a,b,7050,a),flip(a)].">
      <j1 rule="hyper" parents="347 4914 7050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7060">
    <literal><![CDATA[
      T(x,L(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(7050(a,2),4938(a,1))].">
      <j1 rule="para" parents="7050 4938"/>
    </justification>
  </clause>

  <clause id="7061">
    <literal><![CDATA[
      T(x / L(y,z,y),y) = L(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(386,a,7059,a),flip(a)].">
      <j1 rule="hyper" parents="386 7059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7064">
    <literal><![CDATA[
      T(x,T(y / z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4398(a,1),7059(a,1,2))].">
      <j1 rule="para" parents="4398 7059"/>
    </justification>
  </clause>

  <clause id="7065">
    <literal><![CDATA[
      T(x,R(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4494(a,1),7059(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4494 7059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7066">
    <literal><![CDATA[
      T(x / R(y,z,y),y) = R(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(386,a,7065,a),flip(a)].">
      <j1 rule="hyper" parents="386 7065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7067">
    <literal><![CDATA[
      T(x / y,R(y,z,y)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(347,a,113,a(flip),b,7065,a),flip(a)].">
      <j1 rule="hyper" parents="347 113 7065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7068">
    <literal><![CDATA[
      R(x,y,x) * T(z,x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,7065,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 7065 22"/>
    </justification>
  </clause>

  <clause id="7069">
    <literal><![CDATA[
      T(x,T(y,y \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4426(a,1),7065(a,1,2))].">
      <j1 rule="para" parents="4426 7065"/>
    </justification>
  </clause>

  <clause id="7070">
    <literal><![CDATA[
      T(x,(y \ z) \ z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6798(a,1),7065(a,1,2))].">
      <j1 rule="para" parents="6798 7065"/>
    </justification>
  </clause>

  <clause id="7071">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = (z / x) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,7067,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 7067 22"/>
    </justification>
  </clause>

  <clause id="7072">
    <literal><![CDATA[
      K(T(x,y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5982,a(flip),b,7058,a),flip(a)].">
      <j1 rule="hyper" parents="63 5982 7058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7073">
    <literal><![CDATA[
      K(T(R(x,x \ y,y \ z),z),u) = K(((x \ y) * (y \ z)) \ z,u)
    ]]></literal>
    <justification jstring="[para(898(a,1),7058(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="898 7058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7074">
    <literal><![CDATA[
      K(T(x * K(y,z),x),u) = K(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(6156(a,1),7058(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6156 7058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7075">
    <literal><![CDATA[
      K((x * (y \ z)) \ (x * z),u) = L(K(T(y,z),u),z,x)
    ]]></literal>
    <justification jstring="[para(7058(a,1),7004(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7058 7004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7076">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(134,a,7072,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="134 7072 22"/>
    </justification>
  </clause>

  <clause id="7077">
    <literal><![CDATA[
      T(K(x,y),x \ z) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5981,a(flip),b,7072,a),flip(a)].">
      <j1 rule="hyper" parents="63 5981 7072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7078">
    <literal><![CDATA[
      T(K(x,y),z) * T(x,z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(133,a,7072,a(flip),b,4969,a(flip))].">
      <j1 rule="hyper" parents="133 7072 4969"/>
    </justification>
  </clause>

  <clause id="7079">
    <literal><![CDATA[
      T(K(x * y,z),K(x,y)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(5151(a,1),7072(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5151 7072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7080">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7072(a,1),5173(a,1,1))].">
      <j1 rule="para" parents="7072 5173"/>
    </justification>
  </clause>

  <clause id="7081">
    <literal><![CDATA[
      T(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(4398(a,1),7060(a,1,2))].">
      <j1 rule="para" parents="4398 7060"/>
    </justification>
  </clause>

  <clause id="7082">
    <literal><![CDATA[
      T(x,T((y \ 1) / z,y)) = T(x,(z * (y * y)) \ y)
    ]]></literal>
    <justification jstring="[para(812(a,1),7064(a,1,2,1))].">
      <j1 rule="para" parents="812 7064"/>
    </justification>
  </clause>

  <clause id="7083">
    <literal><![CDATA[
      T((x \ y) \ 1,T(x,y)) = T((x \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6826,a(flip),b,7069,a),flip(a)].">
      <j1 rule="hyper" parents="63 6826 7069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7084">
    <literal><![CDATA[
      ((x \ y) \ y) \ (z * T(x,x \ y)) = T(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(806,a,7070,a)].">
      <j1 rule="hyper" parents="806 7070"/>
    </justification>
  </clause>

  <clause id="7085">
    <literal><![CDATA[
      T(x * ((x \ y) * (y / x)),T(x,y)) = ((x \ y) * (x \ y)) * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6944,a(flip),b,7070,a),flip(a)].">
      <j1 rule="hyper" parents="63 6944 7070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7086">
    <literal><![CDATA[
      x / K(y,T(z,x)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(6205,a,7076,a)].">
      <j1 rule="hyper" parents="6205 7076"/>
    </justification>
  </clause>

  <clause id="7087">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,T(x,z)) = z
    ]]></literal>
    <justification jstring="[hyper(6138,a,7076,a)].">
      <j1 rule="hyper" parents="6138 7076"/>
    </justification>
  </clause>

  <clause id="7088">
    <literal><![CDATA[
      x * (y * K(T(x,y),z)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,7076,a,b,5157,a)].">
      <j1 rule="hyper" parents="134 7076 5157"/>
    </justification>
  </clause>

  <clause id="7089">
    <literal><![CDATA[
      K(x / y,z) * y = y * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(113(a,1),7076(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 7076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7090">
    <literal><![CDATA[
      (K(x,y) * z) \ z = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7076(a,1),6123(a,1,1))].">
      <j1 rule="para" parents="7076 6123"/>
    </justification>
  </clause>

  <clause id="7091">
    <literal><![CDATA[
      K(x,T(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6908,a(flip),b,7080,a),flip(a)].">
      <j1 rule="hyper" parents="63 6908 7080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7092">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(134,a,7080,a(flip),b,4934,a(flip))].">
      <j1 rule="hyper" parents="134 7080 4934"/>
    </justification>
  </clause>

  <clause id="7093">
    <literal><![CDATA[
      K(T(x,y),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,7072,a,b,7091,a)].">
      <j1 rule="hyper" parents="347 7072 7091"/>
    </justification>
  </clause>

  <clause id="7094">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,6898,a,b,7091,a)].">
      <j1 rule="hyper" parents="347 6898 7091"/>
    </justification>
  </clause>

  <clause id="7095">
    <literal><![CDATA[
      K(1 / T(x,y),z) = K(1 / x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,6425,a,b,7091,a)].">
      <j1 rule="hyper" parents="347 6425 7091"/>
    </justification>
  </clause>

  <clause id="7096">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K(x \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,6421,a,b,7091,a)].">
      <j1 rule="hyper" parents="347 6421 7091"/>
    </justification>
  </clause>

  <clause id="7097">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,5982,a,b,7091,a)].">
      <j1 rule="hyper" parents="347 5982 7091"/>
    </justification>
  </clause>

  <clause id="7098">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,5532,a,b,7091,a),flip(a)].">
      <j1 rule="hyper" parents="347 5532 7091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7099">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,5257,a,b,7091,a)].">
      <j1 rule="hyper" parents="347 5257 7091"/>
    </justification>
  </clause>

  <clause id="7100">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7077,a(flip),b,7091,a),flip(a)].">
      <j1 rule="hyper" parents="347 7077 7091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7101">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,5977,a(flip),b,7091,a),flip(a)].">
      <j1 rule="hyper" parents="347 5977 7091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7102">
    <literal><![CDATA[
      K(x \ 1,T(y,x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,1564,a(flip),b,7091,a),flip(a)].">
      <j1 rule="hyper" parents="347 1564 7091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7103">
    <literal><![CDATA[
      x * K(y,T(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(134,a,7091,a,b,9,a)].">
      <j1 rule="hyper" parents="134 7091 9"/>
    </justification>
  </clause>

  <clause id="7104">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(134,a,7091,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="134 7091 22"/>
    </justification>
  </clause>

  <clause id="7105">
    <literal><![CDATA[
      K(x,T(y,z)) / K(x,y) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(131,a,7091,a,b,6890,a)].">
      <j1 rule="hyper" parents="131 7091 6890"/>
    </justification>
  </clause>

  <clause id="7106">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = K(x,T(R(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(6722,a,7091,a(flip))].">
      <j1 rule="hyper" parents="6722 7091"/>
    </justification>
  </clause>

  <clause id="7107">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[hyper(6459,a,7091,a(flip))].">
      <j1 rule="hyper" parents="6459 7091"/>
    </justification>
  </clause>

  <clause id="7108">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,w) = K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(6367,a,7091,a(flip))].">
      <j1 rule="hyper" parents="6367 7091"/>
    </justification>
  </clause>

  <clause id="7109">
    <literal><![CDATA[
      x * T(K(x,y),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,7091,a(flip),b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 7091 4924"/>
    </justification>
  </clause>

  <clause id="7110">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u * x
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7091(a,2),271(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7091 271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7111">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(7091(a,2),315(a,1,2))].">
      <j1 rule="para" parents="7091 315"/>
    </justification>
  </clause>

  <clause id="7112">
    <literal><![CDATA[
      x * (y * K(z,T(u,y))) = x * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(7091(a,2),251(a,1,2,2))].">
      <j1 rule="para" parents="7091 251"/>
    </justification>
  </clause>

  <clause id="7113">
    <literal><![CDATA[
      x * L(K(y,T(z,x)),u,w) = L(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(7091(a,2),267(a,1,2,1))].">
      <j1 rule="para" parents="7091 267"/>
    </justification>
  </clause>

  <clause id="7114">
    <literal><![CDATA[
      L(x \ K(y,T(z,u)),x,u) = (u * x) \ (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(7091(a,2),480(a,1,1,2))].">
      <j1 rule="para" parents="7091 480"/>
    </justification>
  </clause>

  <clause id="7115">
    <literal><![CDATA[
      x * (y * K(z,T(u,y))) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(7091(a,2),639(a,1,2,2))].">
      <j1 rule="para" parents="7091 639"/>
    </justification>
  </clause>

  <clause id="7117">
    <literal><![CDATA[
      L(K(x,T(y,z \ u)),z \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      u \ (z * (K(x,y) * (z \ u))) = w
    ]]></literal>
    <justification jstring="[para(7091(a,2),859(a,1,1))].">
      <j1 rule="para" parents="7091 859"/>
    </justification>
  </clause>

  <clause id="7118">
    <literal><![CDATA[
      T(K(x,y),y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(7091(a,1),3904(a,1))].">
      <j1 rule="para" parents="7091 3904"/>
    </justification>
  </clause>

  <clause id="7119">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,K(z \ y,T(z,u)))
    ]]></literal>
    <justification jstring="[para(7091(a,2),5709(a,2,2))].">
      <j1 rule="para" parents="7091 5709"/>
    </justification>
  </clause>

  <clause id="7120">
    <literal><![CDATA[
      x \ (y * K(z,T(x,u))) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(7091(a,2),6860(a,1,2,2))].">
      <j1 rule="para" parents="7091 6860"/>
    </justification>
  </clause>

  <clause id="7121">
    <literal><![CDATA[
      K(x,T(y,z)) * R(T(K(y,x),z),u,w) = T(K(x,y) * R(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(7091(a,2),6938(a,1,1))].">
      <j1 rule="para" parents="7091 6938"/>
    </justification>
  </clause>

  <clause id="7122">
    <literal><![CDATA[
      K(x,T(y,z)) \ 1 = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7091(a,2),7080(a,1,1))].">
      <j1 rule="para" parents="7091 7080"/>
    </justification>
  </clause>

  <clause id="7123">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = T(K(x,K(y,z)),u)
    ]]></literal>
    <justification jstring="[para(7091(a,2),7091(a,1,2))].">
      <j1 rule="para" parents="7091 7091"/>
    </justification>
  </clause>

  <clause id="7124">
    <literal><![CDATA[
      x * K(T(y,z),u) = x * K(y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,7093,a,b,9,a)].">
      <j1 rule="hyper" parents="134 7093 9"/>
    </justification>
  </clause>

  <clause id="7125">
    <literal><![CDATA[
      T(K(x,y),x * z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5977,a,b,7093,a)].">
      <j1 rule="hyper" parents="63 5977 7093"/>
    </justification>
  </clause>

  <clause id="7126">
    <literal><![CDATA[
      x / K(y,T(z,u)) = x * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(220,a,7093,a(flip),b,6123,a)].">
      <j1 rule="hyper" parents="220 7093 6123"/>
    </justification>
  </clause>

  <clause id="7127">
    <literal><![CDATA[
      x / K(y,T(x,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(220,a,7093,a(flip),b,4913,a(flip))].">
      <j1 rule="hyper" parents="220 7093 4913"/>
    </justification>
  </clause>

  <clause id="7128">
    <literal><![CDATA[
      (x / y) * K(z,T(y,u)) = x / T(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,7093,a(flip),b,6160,a)].">
      <j1 rule="hyper" parents="134 7093 6160"/>
    </justification>
  </clause>

  <clause id="7129">
    <literal><![CDATA[
      K(x,T(y,z)) \ u = K(y,T(x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(133,a,7093,a(flip),b,5262,a),flip(a)].">
      <j1 rule="hyper" parents="133 7093 5262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7130">
    <literal><![CDATA[
      T(x,T(y,z)) \ 1 = x \ K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,7093,a(flip),b,4922,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 7093 4922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7131">
    <literal><![CDATA[
      K(T(x,y),T(z,u)) = K(x,T(T(z,y),u))
    ]]></literal>
    <justification jstring="[para(23(a,1),7093(a,2,2))].">
      <j1 rule="para" parents="23 7093"/>
    </justification>
  </clause>

  <clause id="7132">
    <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),7093(a,1,1))].">
      <j1 rule="para" parents="25 7093"/>
    </justification>
  </clause>

  <clause id="7133">
    <literal><![CDATA[
      K(T(x,y),L(z,u,w)) = K(x,L(T(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),7093(a,2,2))].">
      <j1 rule="para" parents="25 7093"/>
    </justification>
  </clause>

  <clause id="7134">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(196(a,1),7093(a,1,1)),flip(a)].">
      <j1 rule="para" parents="196 7093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7135">
    <literal><![CDATA[
      K(x / y,T(z,y)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(113(a,1),7093(a,1,1)),flip(a)].">
      <j1 rule="para" parents="113 7093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7136">
    <literal><![CDATA[
      K(T(x,y),z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(113(a,1),7093(a,2,2))].">
      <j1 rule="para" parents="113 7093"/>
    </justification>
  </clause>

  <clause id="7137">
    <literal><![CDATA[
      K(x,T(y,T(T(x,z),u))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(231(a,1),7093(a,1,1)),flip(a)].">
      <j1 rule="para" parents="231 7093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7138">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(254(a,1),7093(a,1,1)),flip(a)].">
      <j1 rule="para" parents="254 7093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7139">
    <literal><![CDATA[
      K(L(x,y,z),T(u,x)) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(199(a,1),7093(a,1,1)),flip(a)].">
      <j1 rule="para" parents="199 7093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7140">
    <literal><![CDATA[
      K(T(x,(1 / y) \ z),z * y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(1163(a,1),7093(a,2,2))].">
      <j1 rule="para" parents="1163 7093"/>
    </justification>
  </clause>

  <clause id="7141">
    <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(1715(a,1),7093(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1715 7093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7142">
    <literal><![CDATA[
      K(T(x,y),K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(3569(a,1),7093(a,2,2))].">
      <j1 rule="para" parents="3569 7093"/>
    </justification>
  </clause>

  <clause id="7143">
    <literal><![CDATA[
      K(x,T(y,K(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3571(a,1),7093(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3571 7093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7145">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5315(a,1),7093(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5315 7093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7146">
    <literal><![CDATA[
      K(x,T(y,z)) * (y \ u) = T(y,T(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(7093(a,1),5209(a,1,1))].">
      <j1 rule="para" parents="7093 5209"/>
    </justification>
  </clause>

  <clause id="7147">
    <literal><![CDATA[
      (x * y) / (K(z,T(x,u)) * y) = T(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(7093(a,1),5212(a,1,2,1))].">
      <j1 rule="para" parents="7093 5212"/>
    </justification>
  </clause>

  <clause id="7148">
    <literal><![CDATA[
      1 / (x \ K(y,T(x,z))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7093(a,1),5045(a,1,2,2))].">
      <j1 rule="para" parents="7093 5045"/>
    </justification>
  </clause>

  <clause id="7149">
    <literal><![CDATA[
      K(x,T(y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7093(a,1),5286(a,1,1))].">
      <j1 rule="para" parents="7093 5286"/>
    </justification>
  </clause>

  <clause id="7151">
    <literal><![CDATA[
      K(x,T(y,z)) \ (y * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7093(a,1),5206(a,1,1))].">
      <j1 rule="para" parents="7093 5206"/>
    </justification>
  </clause>

  <clause id="7152">
    <literal><![CDATA[
      T(x,y) * (x \ K(x,T(z,y))) = x \ T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(7093(a,1),4986(a,1,2,2))].">
      <j1 rule="para" parents="7093 4986"/>
    </justification>
  </clause>

  <clause id="7153">
    <literal><![CDATA[
      x * K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w * K(z,T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(7093(a,1),6138(a,1,2))].">
      <j1 rule="para" parents="7093 6138"/>
    </justification>
  </clause>

  <clause id="7154">
    <literal><![CDATA[
      x / K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(z,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(7093(a,1),6140(a,1,2))].">
      <j1 rule="para" parents="7093 6140"/>
    </justification>
  </clause>

  <clause id="7155">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ x != w
    ]]></literal>
    <literal><![CDATA[
      K(z,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(7093(a,1),6141(a,1,1,2))].">
      <j1 rule="para" parents="7093 6141"/>
    </justification>
  </clause>

  <clause id="7156">
    <literal><![CDATA[
      a(x,y,K(z,T(y,u))) = 1
    ]]></literal>
    <justification jstring="[para(7093(a,1),6240(a,1,3))].">
      <j1 rule="para" parents="7093 6240"/>
    </justification>
  </clause>

  <clause id="7157">
    <literal><![CDATA[
      R(x,y \ 1,K(z,T(y,u))) = x
    ]]></literal>
    <justification jstring="[para(7093(a,1),6243(a,1,3))].">
      <j1 rule="para" parents="7093 6243"/>
    </justification>
  </clause>

  <clause id="7158">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ (x * z) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(7093(a,1),6114(a,1,1,2))].">
      <j1 rule="para" parents="7093 6114"/>
    </justification>
  </clause>

  <clause id="7159">
    <literal><![CDATA[
      x \ (y * K(z,T(x,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(y / T(x,T(z,u)),x) = w
    ]]></literal>
    <justification jstring="[para(7093(a,1),6186(a,1,2,2))].">
      <j1 rule="para" parents="7093 6186"/>
    </justification>
  </clause>

  <clause id="7160">
    <literal><![CDATA[
      (x * y) * K(y,T(z,x)) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7093(a,1),6395(a,1,2))].">
      <j1 rule="para" parents="7093 6395"/>
    </justification>
  </clause>

  <clause id="7161">
    <literal><![CDATA[
      (x * y) * K(z,T(y,u)) = x * (y * K(z,T(y,u)))
    ]]></literal>
    <justification jstring="[hyper(1093,a,7156,a)].">
      <j1 rule="hyper" parents="1093 7156"/>
    </justification>
  </clause>

  <clause id="7162">
    <literal><![CDATA[
      R(x,(y * K(z,y)) \ 1,K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(5058(a,1),7157(a,1,3,2))].">
      <j1 rule="para" parents="5058 7157"/>
    </justification>
  </clause>

  <clause id="7163">
    <literal><![CDATA[
      (K(x,y) * z) * K(T(y,z),x) = z
    ]]></literal>
    <justification jstring="[para(7093(a,2),7087(a,1,2))].">
      <j1 rule="para" parents="7093 7087"/>
    </justification>
  </clause>

  <clause id="7164">
    <literal><![CDATA[
      (K(x,y) \ z) \ z = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5256(a,2),7090(a,1,1))].">
      <j1 rule="para" parents="5256 7090"/>
    </justification>
  </clause>

  <clause id="7165">
    <literal><![CDATA[
      K(x / y,T(z,x)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),7097(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="83 7097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7166">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7091,a,b,7100,a),flip(a)].">
      <j1 rule="hyper" parents="347 7091 7100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7167">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7093,a(flip),b,7101,a),flip(a)].">
      <j1 rule="hyper" parents="347 7093 7101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7168">
    <literal><![CDATA[
      K(x,T(y,x * y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,5146,a(flip),b,7101,a),flip(a)].">
      <j1 rule="hyper" parents="347 5146 7101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7169">
    <literal><![CDATA[
      x * (y * K(x,T(z,y))) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,7104,a,b,5157,a)].">
      <j1 rule="hyper" parents="134 7104 5157"/>
    </justification>
  </clause>

  <clause id="7170">
    <literal><![CDATA[
      x \ (y * K(z,T(x,y))) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(128,a,7104,a,b,4947,a)].">
      <j1 rule="hyper" parents="128 7104 4947"/>
    </justification>
  </clause>

  <clause id="7171">
    <literal><![CDATA[
      (K(x,y) * z) / T(y,z) = z / T(T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(131,a,7104,a(flip),b,6107,a)].">
      <j1 rule="hyper" parents="131 7104 6107"/>
    </justification>
  </clause>

  <clause id="7172">
    <literal><![CDATA[
      x * K(y,T(T(z,x),u)) = K(y,T(z,u)) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),7104(a,1,2,2))].">
      <j1 rule="para" parents="23 7104"/>
    </justification>
  </clause>

  <clause id="7173">
    <literal><![CDATA[
      x * K(y,L(T(z,x),u,w)) = K(y,L(z,u,w)) * x
    ]]></literal>
    <justification jstring="[para(25(a,2),7104(a,1,2,2))].">
      <j1 rule="para" parents="25 7104"/>
    </justification>
  </clause>

  <clause id="7174">
    <literal><![CDATA[
      K(x,y) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7104(a,1),43(a,1))].">
      <j1 rule="para" parents="7104 43"/>
    </justification>
  </clause>

  <clause id="7175">
    <literal><![CDATA[
      K(x,y / z) * z = z * K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),7104(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 7104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7176">
    <literal><![CDATA[
      K(x \ y,z) * K(u,y / x) = K(u,y / x) * K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(3591(a,1),7104(a,1,2,2))].">
      <j1 rule="para" parents="3591 7104"/>
    </justification>
  </clause>

  <clause id="7177">
    <literal><![CDATA[
      x * K(y,K(z,T(u,x))) = K(y,K(z,u)) * x
    ]]></literal>
    <justification jstring="[para(7091(a,2),7104(a,1,2,2))].">
      <j1 rule="para" parents="7091 7104"/>
    </justification>
  </clause>

  <clause id="7178">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = x * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,6813,a,b,7109,a)].">
      <j1 rule="hyper" parents="347 6813 7109"/>
    </justification>
  </clause>

  <clause id="7179">
    <literal><![CDATA[
      K(x,T(x * y,y)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(3052,a,7125,a),flip(a)].">
      <j1 rule="hyper" parents="3052 7125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7180">
    <literal><![CDATA[
      K(x,T(x * y,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(7125(a,1),3052(a,1))].">
      <j1 rule="para" parents="7125 3052"/>
    </justification>
  </clause>

  <clause id="7181">
    <literal><![CDATA[
      K(x \ (y \ x),z) = K(y \ 1,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,5556,a(flip),b,7135,a),flip(a)].">
      <j1 rule="hyper" parents="63 5556 7135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7182">
    <literal><![CDATA[
      K(x / y,L(y,z,u)) = K(y \ x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(199(a,1),7135(a,1,2))].">
      <j1 rule="para" parents="199 7135"/>
    </justification>
  </clause>

  <clause id="7184">
    <literal><![CDATA[
      K(x,y / T(x,z)) = K(x,T(x,z) \ y)
    ]]></literal>
    <justification jstring="[para(198(a,1),7136(a,1,1))].">
      <j1 rule="para" parents="198 7136"/>
    </justification>
  </clause>

  <clause id="7185">
    <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(7136(a,1),6167(a,1,2))].">
      <j1 rule="para" parents="7136 6167"/>
    </justification>
  </clause>

  <clause id="7186">
    <literal><![CDATA[
      T(x,T(y,T(T(x,z),u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,7137,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 7137 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7187">
    <literal><![CDATA[
      L(x,T(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(7138(a,1),5494(a,1,3))].">
      <j1 rule="para" parents="7138 5494"/>
    </justification>
  </clause>

  <clause id="7188">
    <literal><![CDATA[
      L(x,T(y,z),K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(7138(a,1),5496(a,1,3))].">
      <j1 rule="para" parents="7138 5496"/>
    </justification>
  </clause>

  <clause id="7189">
    <literal><![CDATA[
      R(x,K(y,z),L(T(z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(7138(a,1),6398(a,1,2))].">
      <j1 rule="para" parents="7138 6398"/>
    </justification>
  </clause>

  <clause id="7191">
    <literal><![CDATA[
      K(x,y) * (T(x,z) * T(y,x)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[para(7187(a,1),6582(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7187 6582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7192">
    <literal><![CDATA[
      K(x,K(y,z)) * T(x,y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,7142,a(flip),b,6816,a)].">
      <j1 rule="hyper" parents="133 7142 6816"/>
    </justification>
  </clause>

  <clause id="7193">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) = K(x,z * K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(6121(a,1),7145(a,1,2))].">
      <j1 rule="para" parents="6121 7145"/>
    </justification>
  </clause>

  <clause id="7194">
    <literal><![CDATA[
      (x * (y / z)) * K(z \ y,u) != w
    ]]></literal>
    <literal><![CDATA[
      x * T(y / z,T(u,y)) = w
    ]]></literal>
    <justification jstring="[para(7165(a,1),5973(a,1,2))].">
      <j1 rule="para" parents="7165 5973"/>
    </justification>
  </clause>

  <clause id="7195">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,7166,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 7166 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7196">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,7166,a(flip),b,4924,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 7166 4924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7197">
    <literal><![CDATA[
      K(x,T(y / (x * z),z)) = K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),7167(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 7167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7199">
    <literal><![CDATA[
      T(x * K(y,x),T(z,T(x,u))) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[para(5058(a,1),7186(a,1,2,2,1))].">
      <j1 rule="para" parents="5058 7186"/>
    </justification>
  </clause>

  <clause id="7200">
    <literal><![CDATA[
      x \ (((y \ x) * y) * L(T(y,z),u,w)) = K(y \ x,y) * L(T(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(7189(a,1),615(a,1,1))].">
      <j1 rule="para" parents="7189 615"/>
    </justification>
  </clause>

  <clause id="7201">
    <literal><![CDATA[
      L(x,y,z) \ L(T(x,T(u,w)),y,z) = K(L(x,y,z),T(u,x \ w))
    ]]></literal>
    <justification jstring="[para(7195(a,1),4982(a,1,2,1))].">
      <j1 rule="para" parents="7195 4982"/>
    </justification>
  </clause>

  <clause id="7202">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,5297,a(flip),b,7041,a),flip(a)].">
      <j1 rule="hyper" parents="347 5297 7041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7203">
    <literal><![CDATA[
      K(x,y) * (L(y,z,y) \ u) = L(T(y,x),z,y) \ u
    ]]></literal>
    <justification jstring="[hyper(36,a,5833,a,b,7049,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 5833 7049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7204">
    <literal><![CDATA[
      K(L(x,y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7049(a,2),5276(a,1))].">
      <j1 rule="para" parents="7049 5276"/>
    </justification>
  </clause>

  <clause id="7205">
    <literal><![CDATA[
      K(x \ (x * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(552(a,1),7204(a,1,1))].">
      <j1 rule="para" parents="552 7204"/>
    </justification>
  </clause>

  <clause id="7206">
    <literal><![CDATA[
      K(T(x / y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(4398(a,1),7204(a,1,1))].">
      <j1 rule="para" parents="4398 7204"/>
    </justification>
  </clause>

  <clause id="7207">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(R(x,u,x),y) = z
    ]]></literal>
    <justification jstring="[para(4494(a,1),7204(a,1,1))].">
      <j1 rule="para" parents="4494 7204"/>
    </justification>
  </clause>

  <clause id="7208">
    <literal><![CDATA[
      L(K(x,y),z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7037(a,1),7204(a,1))].">
      <j1 rule="para" parents="7037 7204"/>
    </justification>
  </clause>

  <clause id="7209">
    <literal><![CDATA[
      K(x,(x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(6451(a,1),7208(a,1))].">
      <j1 rule="para" parents="6451 7208"/>
    </justification>
  </clause>

  <clause id="7210">
    <literal><![CDATA[
      T(K(x,y),(z * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6276(a,2),7118(a,1))].">
      <j1 rule="para" parents="6276 7118"/>
    </justification>
  </clause>

  <clause id="7211">
    <literal><![CDATA[
      R(x,y \ K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(5305(a,1),7162(a,1,2))].">
      <j1 rule="para" parents="5305 7162"/>
    </justification>
  </clause>

  <clause id="7212">
    <literal><![CDATA[
      (x * K(y,z)) / (z \ 1) = x / (z \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6195,a(flip),b,7211,a)].">
      <j1 rule="hyper" parents="63 6195 7211"/>
    </justification>
  </clause>

  <clause id="7213">
    <literal><![CDATA[
      K((x / y) \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(12(a,1),7205(a,1,1,2))].">
      <j1 rule="para" parents="12 7205"/>
    </justification>
  </clause>

  <clause id="7214">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,x) = x \ L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,7054,a(flip),b,4944,a)].">
      <j1 rule="hyper" parents="128 7054 4944"/>
    </justification>
  </clause>

  <clause id="7215">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,7056,a(flip),b,4944,a)].">
      <j1 rule="hyper" parents="128 7056 4944"/>
    </justification>
  </clause>

  <clause id="7216">
    <literal><![CDATA[
      L(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(3558,a,7057,a)].">
      <j1 rule="hyper" parents="3558 7057"/>
    </justification>
  </clause>

  <clause id="7217">
    <literal><![CDATA[
      (K(x,y) * z) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,5162,a(flip),b,7057,a),flip(a)].">
      <j1 rule="hyper" parents="347 5162 7057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7218">
    <literal><![CDATA[
      T(K(x,y) * z,x) = K(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(269,a,7057,a,b,5446,a)].">
      <j1 rule="hyper" parents="269 7057 5446"/>
    </justification>
  </clause>

  <clause id="7219">
    <literal><![CDATA[
      (K(x,y) * z) / x = K(x,y) * (z / x)
    ]]></literal>
    <justification jstring="[hyper(131,a,168,a(flip),b,7057,a)].">
      <j1 rule="hyper" parents="131 168 7057"/>
    </justification>
  </clause>

  <clause id="7220">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x \ 1,x,K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(7057(a,1),443(a,1,1))].">
      <j1 rule="para" parents="7057 443"/>
    </justification>
  </clause>

  <clause id="7221">
    <literal><![CDATA[
      (x * (K(y,x) * z)) * y = K(y,x) * ((x * z) * y)
    ]]></literal>
    <justification jstring="[para(5353(a,1),7057(a,1,1))].">
      <j1 rule="para" parents="5353 7057"/>
    </justification>
  </clause>

  <clause id="7222">
    <literal><![CDATA[
      L(T(x,y),z,K(x,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7216(a,1),25(a,2,1))].">
      <j1 rule="para" parents="7216 25"/>
    </justification>
  </clause>

  <clause id="7223">
    <literal><![CDATA[
      (K(x,y) * z) * R(x,u,w) = K(x,y) * (z * R(x,u,w))
    ]]></literal>
    <justification jstring="[para(7216(a,1),475(a,1,2,1))].">
      <j1 rule="para" parents="7216 475"/>
    </justification>
  </clause>

  <clause id="7224">
    <literal><![CDATA[
      L(x,y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(7216(a,1),6644(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7216 6644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7226">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) = T(L(x,z,x),y)
    ]]></literal>
    <justification jstring="[para(7224(a,1),25(a,2,1))].">
      <j1 rule="para" parents="7224 25"/>
    </justification>
  </clause>

  <clause id="7228">
    <literal><![CDATA[
      x \ (T(y,z) * (K(y,z) \ x)) = T(y,K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6692,a(flip),b,7222,a)].">
      <j1 rule="hyper" parents="63 6692 7222"/>
    </justification>
  </clause>

  <clause id="7229">
    <literal><![CDATA[
      (K(x,y) * (x \ z)) \ (K(x,y) * z) = T(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,382,a(flip),b,7222,a)].">
      <j1 rule="hyper" parents="63 382 7222"/>
    </justification>
  </clause>

  <clause id="7230">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7222(a,1),6644(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7222 6644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7231">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = y * (L(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(134,a,7061,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 7061 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7232">
    <literal><![CDATA[
      R(R(x,y,x) / x,x,z) = (z * R(x,y,x)) / (z * x)
    ]]></literal>
    <justification jstring="[para(7068(a,1),4700(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7068 4700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7233">
    <literal><![CDATA[
      K(x / (y \ z),z \ y) = K((y \ z) \ x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(35,a,2488,a,b,7089,a),flip(a)].">
      <j1 rule="hyper" parents="35 2488 7089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7234">
    <literal><![CDATA[
      K(x,K(y,z)) * T(z,y) = T(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(7092(a,1),6192(a,1,1))].">
      <j1 rule="para" parents="7092 6192"/>
    </justification>
  </clause>

  <clause id="7235">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(113(a,1),7098(a,2,2,1))].">
      <j1 rule="para" parents="113 7098"/>
    </justification>
  </clause>

  <clause id="7236">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(128,a,5924,a(flip),b,7124,a(flip))].">
      <j1 rule="hyper" parents="128 5924 7124"/>
    </justification>
  </clause>

  <clause id="7237">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(126,a,7126,a(flip),b,6550,a),flip(a)].">
      <j1 rule="hyper" parents="126 7126 6550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7238">
    <literal><![CDATA[
      R(x,y,z) * (x \ K(u,T(x,w))) = T(x,T(u,w)) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(7130(a,1),1858(a,1,2))].">
      <j1 rule="para" parents="7130 1858"/>
    </justification>
  </clause>

  <clause id="7239">
    <literal><![CDATA[
      T(x / y,z) \ x = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(5520,a,7175,a)].">
      <j1 rule="hyper" parents="5520 7175"/>
    </justification>
  </clause>

  <clause id="7240">
    <literal><![CDATA[
      x \ (T(y / x,z) \ y) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(5465,a,7175,a)].">
      <j1 rule="hyper" parents="5465 7175"/>
    </justification>
  </clause>

  <clause id="7241">
    <literal><![CDATA[
      x / (y * K(z,y \ x)) = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(220,a,7175,a(flip),b,5339,a)].">
      <j1 rule="hyper" parents="220 7175 5339"/>
    </justification>
  </clause>

  <clause id="7242">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * y = y * K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5621(a,2),7175(a,1,1))].">
      <j1 rule="para" parents="5621 7175"/>
    </justification>
  </clause>

  <clause id="7243">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = K(z,(x * (1 / y)) \ x) * T(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(6353(a,1),7175(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6353 7175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7244">
    <literal><![CDATA[
      T(T(x,1 / y),K(1 / y,z)) = x * K(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[para(5537(a,2),7178(a,2,2))].">
      <j1 rule="para" parents="5537 7178"/>
    </justification>
  </clause>

  <clause id="7245">
    <literal><![CDATA[
      K(R(x,y,(x * y) \ z) \ 1,T(u,z)) = K(z \ (y * ((x * y) \ z)),u)
    ]]></literal>
    <justification jstring="[para(581(a,1),7181(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="581 7181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7246">
    <literal><![CDATA[
      T(x,y) * K(x,K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(3582,a,7192,a)].">
      <j1 rule="hyper" parents="3582 7192"/>
    </justification>
  </clause>

  <clause id="7247">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,6192,a,b,7192,a)].">
      <j1 rule="hyper" parents="35 6192 7192"/>
    </justification>
  </clause>

  <clause id="7248">
    <literal><![CDATA[
      T(x,T(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7196(a,2),4984(a,1))].">
      <j1 rule="para" parents="7196 4984"/>
    </justification>
  </clause>

  <clause id="7249">
    <literal><![CDATA[
      x / R(y,y \ x,y) = K(y,x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(35,a,5907,a,b,7217,a)].">
      <j1 rule="hyper" parents="35 5907 7217"/>
    </justification>
  </clause>

  <clause id="7250">
    <literal><![CDATA[
      (T(x,y) * (x \ z)) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[para(4944(a,2),7217(a,1,1))].">
      <j1 rule="para" parents="4944 7217"/>
    </justification>
  </clause>

  <clause id="7251">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ z,x) = (x \ z) * x
    ]]></literal>
    <justification jstring="[para(5159(a,1),7217(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5159 7217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7252">
    <literal><![CDATA[
      K(x,y) \ T(K(x,y) * z,x) = T(z,x)
    ]]></literal>
    <justification jstring="[hyper(908,a,7218,a)].">
      <j1 rule="hyper" parents="908 7218"/>
    </justification>
  </clause>

  <clause id="7253">
    <literal><![CDATA[
      T(x * K(y,z),z) = T(x,z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,5887,a(flip),b,7218,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 5887 7218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7254">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,x) = T(z,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),7218(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 7218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7255">
    <literal><![CDATA[
      T(K(x \ y,x) * z,x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) \ (z * (x \ y)) = u
    ]]></literal>
    <justification jstring="[para(7218(a,2),5730(a,1))].">
      <j1 rule="para" parents="7218 5730"/>
    </justification>
  </clause>

  <clause id="7256">
    <literal><![CDATA[
      K(x,y) * ((x * z) / x) = (T(x,y) * z) / x
    ]]></literal>
    <justification jstring="[para(4974(a,1),7219(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4974 7219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7257">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(x,y),z,x) = w
    ]]></literal>
    <justification jstring="[para(7226(a,2),5652(a,1))].">
      <j1 rule="para" parents="7226 5652"/>
    </justification>
  </clause>

  <clause id="7259">
    <literal><![CDATA[
      T(x,L(T(y,z),u,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7230(a,1),7059(a,1,2))].">
      <j1 rule="para" parents="7230 7059"/>
    </justification>
  </clause>

  <clause id="7260">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(35,a,7192,a,b,7234,a)].">
      <j1 rule="hyper" parents="35 7192 7234"/>
    </justification>
  </clause>

  <clause id="7261">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,6897,a,b,7260,a)].">
      <j1 rule="hyper" parents="347 6897 7260"/>
    </justification>
  </clause>

  <clause id="7262">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(134,a,7260,a,b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 7260 4924"/>
    </justification>
  </clause>

  <clause id="7263">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,7260,a,b,7105,a)].">
      <j1 rule="hyper" parents="133 7260 7105"/>
    </justification>
  </clause>

  <clause id="7264">
    <literal><![CDATA[
      K(x,K(y,z)) \ K(y,x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(7260(a,1),4939(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7260 4939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7265">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7260(a,1),6890(a,1,1))].">
      <j1 rule="para" parents="7260 6890"/>
    </justification>
  </clause>

  <clause id="7266">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7260(a,1),6898(a,1,2))].">
      <j1 rule="para" parents="7260 6898"/>
    </justification>
  </clause>

  <clause id="7267">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7260(a,1),7094(a,1,2))].">
      <j1 rule="para" parents="7260 7094"/>
    </justification>
  </clause>

  <clause id="7268">
    <literal><![CDATA[
      R(K(K(x,y),z \ 1),u,w) = K(x,K(y,R(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,6694,a,b,7261,a)].">
      <j1 rule="hyper" parents="63 6694 7261"/>
    </justification>
  </clause>

  <clause id="7269">
    <literal><![CDATA[
      (x * K(y,z)) * K(y,K(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(134,a,7261,a(flip),b,5956,a)].">
      <j1 rule="hyper" parents="134 7261 5956"/>
    </justification>
  </clause>

  <clause id="7270">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) = T(K(x,y),z) * u
    ]]></literal>
    <justification jstring="[hyper(133,a,7261,a(flip),b,4963,a)].">
      <j1 rule="hyper" parents="133 7261 4963"/>
    </justification>
  </clause>

  <clause id="7272">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(7261(a,1),4984(a,1,2))].">
      <j1 rule="para" parents="7261 4984"/>
    </justification>
  </clause>

  <clause id="7273">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(7261(a,1),5173(a,1,1))].">
      <j1 rule="para" parents="7261 5173"/>
    </justification>
  </clause>

  <clause id="7274">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ u) = T(z,K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(7261(a,1),5209(a,1,1))].">
      <j1 rule="para" parents="7261 5209"/>
    </justification>
  </clause>

  <clause id="7275">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) \ u = w
    ]]></literal>
    <justification jstring="[para(7261(a,1),5217(a,1,1))].">
      <j1 rule="para" parents="7261 5217"/>
    </justification>
  </clause>

  <clause id="7276">
    <literal><![CDATA[
      (x / y) * K(z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      x / T(y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(7261(a,1),6167(a,1,2))].">
      <j1 rule="para" parents="7261 6167"/>
    </justification>
  </clause>

  <clause id="7277">
    <literal><![CDATA[
      (K(x,y) / z) * K(x,K(y,1 / z)) = T(K(x,y),1 / z) / z
    ]]></literal>
    <justification jstring="[para(7261(a,1),6475(a,1,2))].">
      <j1 rule="para" parents="7261 6475"/>
    </justification>
  </clause>

  <clause id="7278">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(7261(a,1),6909(a,1))].">
      <j1 rule="para" parents="7261 6909"/>
    </justification>
  </clause>

  <clause id="7279">
    <literal><![CDATA[
      K(x,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(6899,a,7273,a)].">
      <j1 rule="hyper" parents="6899 7273"/>
    </justification>
  </clause>

  <clause id="7280">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(5179,a,7273,a)].">
      <j1 rule="hyper" parents="5179 7273"/>
    </justification>
  </clause>

  <clause id="7281">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7273(a,1),6899(a,1))].">
      <j1 rule="para" parents="7273 6899"/>
    </justification>
  </clause>

  <clause id="7282">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7261,a,b,7279,a)].">
      <j1 rule="hyper" parents="347 7261 7279"/>
    </justification>
  </clause>

  <clause id="7283">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,7260,a,b,7279,a),flip(a)].">
      <j1 rule="hyper" parents="347 7260 7279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7284">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * u) = T(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(133,a,7279,a,b,4963,a)].">
      <j1 rule="hyper" parents="133 7279 4963"/>
    </justification>
  </clause>

  <clause id="7285">
    <literal><![CDATA[
      K(x,K(y,z)) * y = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,7279,a,b,4969,a(flip))].">
      <j1 rule="hyper" parents="133 7279 4969"/>
    </justification>
  </clause>

  <clause id="7287">
    <literal><![CDATA[
      K(x,K(y,z)) * y != u
    ]]></literal>
    <literal><![CDATA[
      T(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7279(a,1),4987(a,1,1))].">
      <j1 rule="para" parents="7279 4987"/>
    </justification>
  </clause>

  <clause id="7288">
    <literal><![CDATA[
      x * (K(y,K(x,z)) * u) = T(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(7279(a,1),4943(a,1,2,1))].">
      <j1 rule="para" parents="7279 4943"/>
    </justification>
  </clause>

  <clause id="7289">
    <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(7279(a,1),5304(a,1,2))].">
      <j1 rule="para" parents="7279 5304"/>
    </justification>
  </clause>

  <clause id="7290">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7279(a,1),7262(a,1,2))].">
      <j1 rule="para" parents="7279 7262"/>
    </justification>
  </clause>

  <clause id="7291">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,7260,a,b,7280,a),flip(a)].">
      <j1 rule="hyper" parents="347 7260 7280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7292">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,7260,a,b,7282,a),flip(a)].">
      <j1 rule="hyper" parents="347 7260 7282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7293">
    <literal><![CDATA[
      K(x,K(y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7280,a(flip),b,7282,a)].">
      <j1 rule="hyper" parents="63 7280 7282"/>
    </justification>
  </clause>

  <clause id="7294">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(y,x)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,7282,a(flip),b,4908,a(flip))].">
      <j1 rule="hyper" parents="133 7282 4908"/>
    </justification>
  </clause>

  <clause id="7295">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(7282(a,1),6909(a,1))].">
      <j1 rule="para" parents="7282 6909"/>
    </justification>
  </clause>

  <clause id="7296">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7282(a,2),7262(a,1,2))].">
      <j1 rule="para" parents="7282 7262"/>
    </justification>
  </clause>

  <clause id="7297">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7092,a,b,7283,a)].">
      <j1 rule="hyper" parents="347 7092 7283"/>
    </justification>
  </clause>

  <clause id="7298">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,7283,a,b,7273,a)].">
      <j1 rule="hyper" parents="134 7283 7273"/>
    </justification>
  </clause>

  <clause id="7299">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,(x \ 1) \ y))
    ]]></literal>
    <justification jstring="[hyper(134,a,7283,a,b,5991,a),flip(a)].">
      <j1 rule="hyper" parents="134 7283 5991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7300">
    <literal><![CDATA[
      x * T(x \ y,K(z,u)) = y * K(z,K(u,x \ y))
    ]]></literal>
    <justification jstring="[hyper(134,a,7283,a,b,5940,a),flip(a)].">
      <j1 rule="hyper" parents="134 7283 5940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7301">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,7283,a,b,7105,a)].">
      <j1 rule="hyper" parents="133 7283 7105"/>
    </justification>
  </clause>

  <clause id="7302">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * u) = T(z,K(x,y)) * u
    ]]></literal>
    <justification jstring="[hyper(133,a,7283,a,b,4963,a)].">
      <j1 rule="hyper" parents="133 7283 4963"/>
    </justification>
  </clause>

  <clause id="7303">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) * (u / z) = T(u,K(x,y)) / z
    ]]></literal>
    <justification jstring="[hyper(133,a,7283,a,b,5552,a(flip))].">
      <j1 rule="hyper" parents="133 7283 5552"/>
    </justification>
  </clause>

  <clause id="7304">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(133,a,7283,a,b,4969,a(flip))].">
      <j1 rule="hyper" parents="133 7283 4969"/>
    </justification>
  </clause>

  <clause id="7306">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) * u = w
    ]]></literal>
    <justification jstring="[para(7283(a,2),5200(a,1,1))].">
      <j1 rule="para" parents="7283 5200"/>
    </justification>
  </clause>

  <clause id="7308">
    <literal><![CDATA[
      (x * K(y,K(z,u))) / K(y,z) = x / T(K(y,z),u)
    ]]></literal>
    <justification jstring="[para(7283(a,2),6135(a,1,1,2))].">
      <j1 rule="para" parents="7283 6135"/>
    </justification>
  </clause>

  <clause id="7309">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,T(y,u)))
    ]]></literal>
    <justification jstring="[para(7093(a,1),7283(a,1,2))].">
      <j1 rule="para" parents="7093 7283"/>
    </justification>
  </clause>

  <clause id="7310">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7283(a,1),7094(a,1,2))].">
      <j1 rule="para" parents="7283 7094"/>
    </justification>
  </clause>

  <clause id="7311">
    <literal><![CDATA[
      K(x,y) * K(y,K(x,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7283(a,2),7094(a,1,2))].">
      <j1 rule="para" parents="7283 7094"/>
    </justification>
  </clause>

  <clause id="7312">
    <literal><![CDATA[
      K(x,K(y,z)) / y = 1 / T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,7291,a(flip),b,4921,a(flip))].">
      <j1 rule="hyper" parents="131 7291 4921"/>
    </justification>
  </clause>

  <clause id="7313">
    <literal><![CDATA[
      K(x,K(y,z)) * (y \ u) = T(y,K(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(7291(a,1),5209(a,1,1))].">
      <j1 rule="para" parents="7291 5209"/>
    </justification>
  </clause>

  <clause id="7314">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7291(a,1),6909(a,1))].">
      <j1 rule="para" parents="7291 6909"/>
    </justification>
  </clause>

  <clause id="7315">
    <literal><![CDATA[
      x / K(y,K(z,u)) = x * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(220,a,7292,a(flip),b,6123,a)].">
      <j1 rule="hyper" parents="220 7292 6123"/>
    </justification>
  </clause>

  <clause id="7316">
    <literal><![CDATA[
      (x / y) * K(y,K(z,u)) = x / T(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,7292,a(flip),b,6160,a)].">
      <j1 rule="hyper" parents="134 7292 6160"/>
    </justification>
  </clause>

  <clause id="7317">
    <literal><![CDATA[
      K(x,y) * K(z,K(x,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(134,a,7292,a(flip),b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 7292 4924"/>
    </justification>
  </clause>

  <clause id="7318">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(133,a,7292,a(flip),b,5262,a),flip(a)].">
      <j1 rule="hyper" parents="133 7292 5262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7319">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,K(y,z)) * u) = u
    ]]></literal>
    <justification jstring="[hyper(133,a,7292,a(flip),b,5259,a)].">
      <j1 rule="hyper" parents="133 7292 5259"/>
    </justification>
  </clause>

  <clause id="7320">
    <literal><![CDATA[
      x \ (K(x,K(y,z)) * u) = T(x,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(7292(a,1),5198(a,1,2,1))].">
      <j1 rule="para" parents="7292 5198"/>
    </justification>
  </clause>

  <clause id="7321">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ u) = T(x,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(7292(a,1),5209(a,1,1))].">
      <j1 rule="para" parents="7292 5209"/>
    </justification>
  </clause>

  <clause id="7322">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) * w = u
    ]]></literal>
    <justification jstring="[para(7292(a,1),5273(a,1,1))].">
      <j1 rule="para" parents="7292 5273"/>
    </justification>
  </clause>

  <clause id="7323">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,K(y,z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      w = u
    ]]></literal>
    <justification jstring="[para(7292(a,1),5274(a,1,1))].">
      <j1 rule="para" parents="7292 5274"/>
    </justification>
  </clause>

  <clause id="7324">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,K(y,z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(7292(a,1),5275(a,1,1))].">
      <j1 rule="para" parents="7292 5275"/>
    </justification>
  </clause>

  <clause id="7325">
    <literal><![CDATA[
      K(x,K(y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7292(a,1),5286(a,1,1))].">
      <j1 rule="para" parents="7292 5286"/>
    </justification>
  </clause>

  <clause id="7326">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(7292(a,1),5293(a,1,1))].">
      <j1 rule="para" parents="7292 5293"/>
    </justification>
  </clause>

  <clause id="7327">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(7292(a,1),5217(a,1,1))].">
      <j1 rule="para" parents="7292 5217"/>
    </justification>
  </clause>

  <clause id="7328">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7292(a,1),6909(a,1))].">
      <j1 rule="para" parents="7292 6909"/>
    </justification>
  </clause>

  <clause id="7329">
    <literal><![CDATA[
      K(x,K(y,z)) * x = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(133,a,7293,a,b,4969,a(flip))].">
      <j1 rule="hyper" parents="133 7293 4969"/>
    </justification>
  </clause>

  <clause id="7330">
    <literal><![CDATA[
      T(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(132,a,7293,a,b,5455,a)].">
      <j1 rule="hyper" parents="132 7293 5455"/>
    </justification>
  </clause>

  <clause id="7331">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) = K(x,(T(u,y) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(5552(a,1),7293(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5552 7293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7332">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,T(K(z,y),u))
    ]]></literal>
    <justification jstring="[para(7072(a,1),7293(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7072 7293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7333">
    <literal><![CDATA[
      K(x,y) * K(z,K(x,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7293(a,1),7094(a,1,2))].">
      <j1 rule="para" parents="7293 7094"/>
    </justification>
  </clause>

  <clause id="7334">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(6895,a,7330,a)].">
      <j1 rule="hyper" parents="6895 7330"/>
    </justification>
  </clause>

  <clause id="7335">
    <literal><![CDATA[
      T(K(x,y) \ z,K(x,y)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(6887,a,7330,a),flip(a)].">
      <j1 rule="hyper" parents="6887 7330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7336">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6884,a,7330,a),flip(a)].">
      <j1 rule="hyper" parents="6884 7330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7337">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(6211,a,7330,a),flip(a)].">
      <j1 rule="hyper" parents="6211 7330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7338">
    <literal><![CDATA[
      T(x * y,K(z,y)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6061,a,7330,a),flip(a)].">
      <j1 rule="hyper" parents="6061 7330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7339">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(T(x,u),K(z,y))
    ]]></literal>
    <justification jstring="[hyper(453,a,7330,a)].">
      <j1 rule="hyper" parents="453 7330"/>
    </justification>
  </clause>

  <clause id="7340">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,6880,a,b,7330,a)].">
      <j1 rule="hyper" parents="347 6880 7330"/>
    </justification>
  </clause>

  <clause id="7341">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,5265,a,b,7330,a)].">
      <j1 rule="hyper" parents="347 5265 7330"/>
    </justification>
  </clause>

  <clause id="7342">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,6813,a(flip),b,7330,a),flip(a)].">
      <j1 rule="hyper" parents="347 6813 7330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7343">
    <literal><![CDATA[
      T(x * T(y,z),K(y,z)) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,6191,a(flip),b,7330,a),flip(a)].">
      <j1 rule="hyper" parents="347 6191 7330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7344">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,7330,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="134 7330 22"/>
    </justification>
  </clause>

  <clause id="7345">
    <literal><![CDATA[
      K(x,y) \ T(z,K(x,y)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,7330,a,b,5265,a)].">
      <j1 rule="hyper" parents="128 7330 5265"/>
    </justification>
  </clause>

  <clause id="7346">
    <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(7330(a,1),453(a,1,1))].">
      <j1 rule="para" parents="7330 453"/>
    </justification>
  </clause>

  <clause id="7347">
    <literal><![CDATA[
      T(x,K(y,z)) * (T(K(z,y),x) * u) = x * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(7330(a,1),4768(a,1,1))].">
      <j1 rule="para" parents="7330 4768"/>
    </justification>
  </clause>

  <clause id="7348">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(7330(a,1),6211(a,1))].">
      <j1 rule="para" parents="7330 6211"/>
    </justification>
  </clause>

  <clause id="7349">
    <literal><![CDATA[
      T(T(x,K(y,z)),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7330(a,1),6814(a,1,1))].">
      <j1 rule="para" parents="7330 6814"/>
    </justification>
  </clause>

  <clause id="7350">
    <literal><![CDATA[
      T(x,K(y,z)) * z = z * T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7330(a,1),6811(a,1,1))].">
      <j1 rule="para" parents="7330 6811"/>
    </justification>
  </clause>

  <clause id="7351">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[para(7330(a,1),6885(a,1,1))].">
      <j1 rule="para" parents="7330 6885"/>
    </justification>
  </clause>

  <clause id="7352">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(7330(a,1),6895(a,1))].">
      <j1 rule="para" parents="7330 6895"/>
    </justification>
  </clause>

  <clause id="7353">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7330(a,1),6884(a,1))].">
      <j1 rule="para" parents="7330 6884"/>
    </justification>
  </clause>

  <clause id="7354">
    <literal><![CDATA[
      T(x * (y * K(x,z)),K(x,z)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(6868,a,7334,a),flip(a)].">
      <j1 rule="hyper" parents="6868 7334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7355">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(810,a,7334,a),flip(a)].">
      <j1 rule="hyper" parents="810 7334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7356">
    <literal><![CDATA[
      T(T(x,T(y,z)),K(y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6817,a(flip),b,7334,a)].">
      <j1 rule="hyper" parents="63 6817 7334"/>
    </justification>
  </clause>

  <clause id="7357">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (K(x,y) * u) = T(R(z,K(x,y),u),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(40,a,1034,a(flip),b,7334,a)].">
      <j1 rule="hyper" parents="40 1034 7334"/>
    </justification>
  </clause>

  <clause id="7358">
    <literal><![CDATA[
      T(K(x,y),z) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,7334,a(flip),b,4414,a)].">
      <j1 rule="hyper" parents="134 7334 4414"/>
    </justification>
  </clause>

  <clause id="7359">
    <literal><![CDATA[
      K(x,y) * z != u * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(7334(a,1),271(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7334 271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7360">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(7334(a,1),318(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="7334 318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7361">
    <literal><![CDATA[
      T(T(T(x,K(y,z)),u),K(y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(7296(a,1),5066(a,1,1,1))].">
      <j1 rule="para" parents="7296 5066"/>
    </justification>
  </clause>

  <clause id="7362">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7329(a,1),4987(a,1))].">
      <j1 rule="para" parents="7329 4987"/>
    </justification>
  </clause>

  <clause id="7363">
    <literal><![CDATA[
      T(T(x,y / z),K(y,y / z)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,7064,a(flip),b,7342,a),flip(a)].">
      <j1 rule="hyper" parents="347 7064 7342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7364">
    <literal><![CDATA[
      T(x * K(y,x),T(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(5058(a,1),7342(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5058 7342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7365">
    <literal><![CDATA[
      T(x,T(y,z)) * K(y,z) = K(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7342(a,1),6885(a,1,1))].">
      <j1 rule="para" parents="7342 6885"/>
    </justification>
  </clause>

  <clause id="7366">
    <literal><![CDATA[
      K(x,T(y,T(z,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7342(a,1),7143(a,1,2))].">
      <j1 rule="para" parents="7342 7143"/>
    </justification>
  </clause>

  <clause id="7368">
    <literal><![CDATA[
      T(x,K(y,z)) * T(y,z) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,7356,a(flip),b,114,a),flip(a)].">
      <j1 rule="hyper" parents="134 7356 114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7369">
    <literal><![CDATA[
      T(T(K(x,y),z),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(483,a,7358,a)].">
      <j1 rule="hyper" parents="483 7358"/>
    </justification>
  </clause>

  <clause id="7370">
    <literal><![CDATA[
      T(K(x \ y,z),x) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,7089,a,b,7358,a),flip(a)].">
      <j1 rule="hyper" parents="35 7089 7358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7371">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,7104,a(flip),b,7358,a),flip(a)].">
      <j1 rule="hyper" parents="35 7104 7358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7372">
    <literal><![CDATA[
      K(T(x,y),z) * y = y * K(x,z)
    ]]></literal>
    <justification jstring="[para(7072(a,2),7358(a,1,1))].">
      <j1 rule="para" parents="7072 7358"/>
    </justification>
  </clause>

  <clause id="7373">
    <literal><![CDATA[
      K(x,T(y,z)) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[para(7091(a,2),7358(a,1,1))].">
      <j1 rule="para" parents="7091 7358"/>
    </justification>
  </clause>

  <clause id="7374">
    <literal><![CDATA[
      T(K(1 / T(x,y),z),y) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,6425,a(flip),b,7369,a),flip(a)].">
      <j1 rule="hyper" parents="40 6425 7369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7375">
    <literal><![CDATA[
      T(K(x,1 / T(y,z)),z) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(40,a,5537,a(flip),b,7369,a),flip(a)].">
      <j1 rule="hyper" parents="40 5537 7369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7376">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) * z = z * L(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7369(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7369 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7377">
    <literal><![CDATA[
      R(T(K(x,y),z),u,w) * z = z * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7369(a,1),268(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7369 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7378">
    <literal><![CDATA[
      (x * K(y,z)) / x = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(305,a,7371,a)].">
      <j1 rule="hyper" parents="305 7371"/>
    </justification>
  </clause>

  <clause id="7379">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7091,a,b,7371,a)].">
      <j1 rule="hyper" parents="63 7091 7371"/>
    </justification>
  </clause>

  <clause id="7380">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7072,a,b,7371,a)].">
      <j1 rule="hyper" parents="63 7072 7371"/>
    </justification>
  </clause>

  <clause id="7382">
    <literal><![CDATA[
      T(x,y) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      K(z,T(u,y)) = x
    ]]></literal>
    <justification jstring="[para(7371(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="7371 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7383">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) * x = u
    ]]></literal>
    <justification jstring="[para(7371(a,1),315(a,1,2))].">
      <j1 rule="para" parents="7371 315"/>
    </justification>
  </clause>

  <clause id="7384">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * z = z * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7371(a,1),268(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7371 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7385">
    <literal><![CDATA[
      (K(x,T(y,z * u)) * z) * u = (z * u) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(7371(a,1),743(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7371 743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7386">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7371(a,1),7078(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7371 7078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7387">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,7379,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 7379 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7388">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7165,a(flip),b,7379,a)].">
      <j1 rule="hyper" parents="63 7165 7379"/>
    </justification>
  </clause>

  <clause id="7389">
    <literal><![CDATA[
      K((x * y) / x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,7138,a(flip),b,7379,a),flip(a)].">
      <j1 rule="hyper" parents="63 7138 7379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7390">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7135,a(flip),b,7379,a)].">
      <j1 rule="hyper" parents="63 7135 7379"/>
    </justification>
  </clause>

  <clause id="7391">
    <literal><![CDATA[
      K(x,T(L(T(y,z),u,w),z)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),7379(a,1,2,1))].">
      <j1 rule="para" parents="25 7379"/>
    </justification>
  </clause>

  <clause id="7392">
    <literal><![CDATA[
      K(x,T(y \ z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(113(a,1),7379(a,1,2,1))].">
      <j1 rule="para" parents="113 7379"/>
    </justification>
  </clause>

  <clause id="7393">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(254(a,1),7379(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="254 7379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7394">
    <literal><![CDATA[
      K(x,y * K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5058(a,1),7379(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5058 7379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7395">
    <literal><![CDATA[
      T(x,T(y,z)) * z = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(7379(a,1),7169(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7379 7169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7396">
    <literal><![CDATA[
      x * K(T(x,y),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,7380,a,b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 7380 4924"/>
    </justification>
  </clause>

  <clause id="7398">
    <literal><![CDATA[
      K(x,T(y,z)) \ z = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,7380,a(flip),b,7099,a),flip(a)].">
      <j1 rule="hyper" parents="134 7380 7099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7399">
    <literal><![CDATA[
      K(L(T(x,y),z,u),T(w,y)) = K(L(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(25(a,2),7380(a,1,1))].">
      <j1 rule="para" parents="25 7380"/>
    </justification>
  </clause>

  <clause id="7400">
    <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),7380(a,1,2))].">
      <j1 rule="para" parents="25 7380"/>
    </justification>
  </clause>

  <clause id="7401">
    <literal><![CDATA[
      K(R(T(x,y),z,u),T(w,y)) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(27(a,2),7380(a,1,1))].">
      <j1 rule="para" parents="27 7380"/>
    </justification>
  </clause>

  <clause id="7402">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(113(a,1),7380(a,1,2))].">
      <j1 rule="para" parents="113 7380"/>
    </justification>
  </clause>

  <clause id="7403">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(254(a,1),7380(a,1,2)),flip(a)].">
      <j1 rule="para" parents="254 7380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7404">
    <literal><![CDATA[
      K(T(x,x * y) * y,z) = K(x * y,T(z,T(x,y)))
    ]]></literal>
    <justification jstring="[para(1135(a,1),7380(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1135 7380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7405">
    <literal><![CDATA[
      K(x \ y,T(z,(y * x) / y)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[para(4178(a,1),7380(a,1,1))].">
      <j1 rule="para" parents="4178 7380"/>
    </justification>
  </clause>

  <clause id="7406">
    <literal><![CDATA[
      K(T(x,x * y) * y,z) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(4189(a,1),7380(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4189 7380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7407">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,K(y,u)) = x
    ]]></literal>
    <justification jstring="[para(7380(a,1),4251(a,1,3))].">
      <j1 rule="para" parents="7380 4251"/>
    </justification>
  </clause>

  <clause id="7408">
    <literal><![CDATA[
      K(x * K(y,x),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(5058(a,1),7380(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5058 7380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7409">
    <literal><![CDATA[
      K(x,y * K(z,y)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(5058(a,1),7380(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5058 7380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7410">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7380(a,1),5347(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7380 5347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7411">
    <literal><![CDATA[
      K(x,y) * (R(T(y,z),u,w) * (K(T(y,z),T(x,z)) * v5)) = R(T(y,z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(7380(a,1),5888(a,1,1))].">
      <j1 rule="para" parents="7380 5888"/>
    </justification>
  </clause>

  <clause id="7412">
    <literal><![CDATA[
      R(x,K(y,z),T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(7380(a,1),5915(a,1,2))].">
      <j1 rule="para" parents="7380 5915"/>
    </justification>
  </clause>

  <clause id="7414">
    <literal><![CDATA[
      T(x,T(y,z)) * z = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7380(a,1),5924(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7380 5924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7415">
    <literal><![CDATA[
      R(K(x,y),T(y,z) * u,w) = K(T(x,z),R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(7380(a,1),6716(a,1,1))].">
      <j1 rule="para" parents="7380 6716"/>
    </justification>
  </clause>

  <clause id="7416">
    <literal><![CDATA[
      L(K(x,y),z * T(x,u),w) = K(L(T(x,u),z,w),T(y,u))
    ]]></literal>
    <justification jstring="[para(7380(a,1),7039(a,1,1))].">
      <j1 rule="para" parents="7380 7039"/>
    </justification>
  </clause>

  <clause id="7417">
    <literal><![CDATA[
      x / (K(y,z) * T(y,u)) = (x / T(y,u)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6149,a,7412,a)].">
      <j1 rule="hyper" parents="6149 7412"/>
    </justification>
  </clause>

  <clause id="7419">
    <literal><![CDATA[
      T(x,T(y \ z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(113(a,1),7387(a,1,2,1))].">
      <j1 rule="para" parents="113 7387"/>
    </justification>
  </clause>

  <clause id="7421">
    <literal><![CDATA[
      T(x,T(T(y \ z,u),y)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(277(a,1),7387(a,1,2,1))].">
      <j1 rule="para" parents="277 7387"/>
    </justification>
  </clause>

  <clause id="7422">
    <literal><![CDATA[
      T(x,y * K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5058(a,1),7387(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5058 7387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7423">
    <literal><![CDATA[
      T(x,L(y * K(z,y),u,w)) = T(x,T(L(y,u,w),z))
    ]]></literal>
    <justification jstring="[para(5077(a,1),7387(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5077 7387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7424">
    <literal><![CDATA[
      T(x,T(y,T(z,x))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,7366,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 7366 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7425">
    <literal><![CDATA[
      K(x \ y,T(z,(x \ y) \ T(y,x))) = K(x \ y,T(z,x * K(y,x)))
    ]]></literal>
    <justification jstring="[para(5488(a,1),7366(a,1,2,2))].">
      <j1 rule="para" parents="5488 7366"/>
    </justification>
  </clause>

  <clause id="7426">
    <literal><![CDATA[
      (x \ y) * K(y / x,z) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[para(7370(a,1),7109(a,1,2))].">
      <j1 rule="para" parents="7370 7109"/>
    </justification>
  </clause>

  <clause id="7427">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(y,x)) = z
    ]]></literal>
    <justification jstring="[hyper(5273,a,7372,a)].">
      <j1 rule="hyper" parents="5273 7372"/>
    </justification>
  </clause>

  <clause id="7428">
    <literal><![CDATA[
      x / (x * K(y,z)) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(220,a,7372,a(flip),b,5256,a)].">
      <j1 rule="hyper" parents="220 7372 5256"/>
    </justification>
  </clause>

  <clause id="7429">
    <literal><![CDATA[
      (x * y) / (y * K(z,x)) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(220,a,7372,a(flip),b,5210,a)].">
      <j1 rule="hyper" parents="220 7372 5210"/>
    </justification>
  </clause>

  <clause id="7430">
    <literal><![CDATA[
      K(x,y \ z) * y = y * K(x,z / y)
    ]]></literal>
    <justification jstring="[para(7136(a,1),7372(a,1,1))].">
      <j1 rule="para" parents="7136 7372"/>
    </justification>
  </clause>

  <clause id="7431">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) * z = z * K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(7131(a,1),7372(a,1,1))].">
      <j1 rule="para" parents="7131 7372"/>
    </justification>
  </clause>

  <clause id="7432">
    <literal><![CDATA[
      K(T(x,y),z) * (y * K(z,x)) = y
    ]]></literal>
    <justification jstring="[hyper(5273,a,7373,a)].">
      <j1 rule="hyper" parents="5273 7373"/>
    </justification>
  </clause>

  <clause id="7433">
    <literal><![CDATA[
      x * T(x \ y,T(z,y)) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4945,a(flip),b,7373,a)].">
      <j1 rule="hyper" parents="63 4945 7373"/>
    </justification>
  </clause>

  <clause id="7434">
    <literal><![CDATA[
      R(x / K(y,T(z,u)),K(y,T(z,u)),u) = (x * u) / (u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(220,a,7373,a(flip),b,579,a),flip(a)].">
      <j1 rule="hyper" parents="220 7373 579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7435">
    <literal><![CDATA[
      (x * K(y,z)) / (y \ x) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(131,a,7373,a(flip),b,4944,a)].">
      <j1 rule="hyper" parents="131 7373 4944"/>
    </justification>
  </clause>

  <clause id="7436">
    <literal><![CDATA[
      K(x,T(y,z)) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (z * K(x,y)) / w = u
    ]]></literal>
    <justification jstring="[para(7373(a,2),652(a,1))].">
      <j1 rule="para" parents="7373 652"/>
    </justification>
  </clause>

  <clause id="7437">
    <literal><![CDATA[
      (x * K(y,z)) / (u * x) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(y,T(z,x)) / u,u,x) = w
    ]]></literal>
    <justification jstring="[para(7373(a,1),694(a,1,1))].">
      <j1 rule="para" parents="7373 694"/>
    </justification>
  </clause>

  <clause id="7438">
    <literal><![CDATA[
      R(T(K(x,T(y,z)),z * u),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(7373(a,1),744(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7373 744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7439">
    <literal><![CDATA[
      (x * K(T(y,z),u)) * (K(u,T(y,z)) * z) = R(x,K(T(y,z),u),z * K(u,y)) * z
    ]]></literal>
    <justification jstring="[para(7373(a,1),5288(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="7373 5288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7440">
    <literal><![CDATA[
      K(x \ y,z) * y = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(7165(a,1),7373(a,1,1))].">
      <j1 rule="para" parents="7165 7373"/>
    </justification>
  </clause>

  <clause id="7441">
    <literal><![CDATA[
      K(x,((y * z) / y) \ 1) = K(x,T(z \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,5784,a,b,7378,a)].">
      <j1 rule="hyper" parents="63 5784 7378"/>
    </justification>
  </clause>

  <clause id="7442">
    <literal><![CDATA[
      K(x,T(y,z)) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7378(a,1),280(a,1,1))].">
      <j1 rule="para" parents="7378 280"/>
    </justification>
  </clause>

  <clause id="7443">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7378(a,1),362(a,1,1))].">
      <j1 rule="para" parents="7378 362"/>
    </justification>
  </clause>

  <clause id="7444">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) / x = L(K(y,T(z,x)),u,w)
    ]]></literal>
    <justification jstring="[para(7378(a,1),949(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7378 949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7445">
    <literal><![CDATA[
      L(T(K(x,T(y,z * u)),u),u,z) = (z * (K(x,y) * u)) / (z * u)
    ]]></literal>
    <justification jstring="[para(7378(a,1),1641(a,1,1,1))].">
      <j1 rule="para" parents="7378 1641"/>
    </justification>
  </clause>

  <clause id="7446">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(y,z) * u) = K(y,T(z,x)) * u
    ]]></literal>
    <justification jstring="[para(7378(a,1),5429(a,2,1))].">
      <j1 rule="para" parents="7378 5429"/>
    </justification>
  </clause>

  <clause id="7447">
    <literal><![CDATA[
      L(K(x \ y,T(z,u * y)),y,u) = K((u * y) / (u * x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7004,a,b,7388,a)].">
      <j1 rule="hyper" parents="63 7004 7388"/>
    </justification>
  </clause>

  <clause id="7449">
    <literal><![CDATA[
      K(x / (x / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7388(a,1),7213(a,1))].">
      <j1 rule="para" parents="7388 7213"/>
    </justification>
  </clause>

  <clause id="7450">
    <literal><![CDATA[
      L(x * K((y * z) / y,x),u,w) / L(x,u,w) = K(z,T(L(x,u,w),y))
    ]]></literal>
    <justification jstring="[hyper(63,a,5542,a,b,7389,a)].">
      <j1 rule="hyper" parents="63 5542 7389"/>
    </justification>
  </clause>

  <clause id="7451">
    <literal><![CDATA[
      K(((x * y) * z) / (x * (y * z)),u) = K(a(x,y,z),T(u,x * (y * z)))
    ]]></literal>
    <justification jstring="[para(86(a,1),7389(a,1,1,1))].">
      <j1 rule="para" parents="86 7389"/>
    </justification>
  </clause>

  <clause id="7452">
    <literal><![CDATA[
      K(L((x \ y) / z,z,x),u) = K((x * z) \ y,T(u,z))
    ]]></literal>
    <justification jstring="[para(962(a,2),7389(a,1,1))].">
      <j1 rule="para" parents="962 7389"/>
    </justification>
  </clause>

  <clause id="7453">
    <literal><![CDATA[
      K(x \ T(x * y,y),z) = K(y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(4180(a,1),7389(a,1,1))].">
      <j1 rule="para" parents="4180 7389"/>
    </justification>
  </clause>

  <clause id="7454">
    <literal><![CDATA[
      x \ (T((y * x) / y,z) * u) = K(y,x) * (K(x,T(z,y)) * u)
    ]]></literal>
    <justification jstring="[para(7389(a,1),5483(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7389 5483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7455">
    <literal><![CDATA[
      K((x \ y) \ 1,T(z,y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5988,a,b,7390,a)].">
      <j1 rule="hyper" parents="63 5988 7390"/>
    </justification>
  </clause>

  <clause id="7456">
    <literal><![CDATA[
      x * T(x \ y,T(z,x)) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,7390,a(flip),b,5940,a),flip(a)].">
      <j1 rule="hyper" parents="134 7390 5940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7457">
    <literal><![CDATA[
      K(x \ y,T(T(z,x),u)) = K(y / x,T(z,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),7390(a,1,2))].">
      <j1 rule="para" parents="23 7390"/>
    </justification>
  </clause>

  <clause id="7458">
    <literal><![CDATA[
      K(x \ y,T(z,x)) / (x \ y) = (1 / (x \ y)) * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(7390(a,1),5920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7390 5920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7459">
    <literal><![CDATA[
      (x * K(x / y,z)) / y = T(x / y,T(z,y))
    ]]></literal>
    <justification jstring="[para(7390(a,1),6002(a,1,1,2))].">
      <j1 rule="para" parents="7390 6002"/>
    </justification>
  </clause>

  <clause id="7460">
    <literal><![CDATA[
      K((x * y) / x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7390(a,1),7205(a,1))].">
      <j1 rule="para" parents="7390 7205"/>
    </justification>
  </clause>

  <clause id="7461">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,T(a(y,z,u),y * (z * u)))
    ]]></literal>
    <justification jstring="[para(14(a,2),7392(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14 7392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7462">
    <literal><![CDATA[
      K(x,(y * (z * u)) / (y * z)) = K(x,T(L(u,z,y),y * z))
    ]]></literal>
    <justification jstring="[para(18(a,2),7392(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18 7392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7463">
    <literal><![CDATA[
      K(x,T((y * z) \ (y * u),z)) = K(x,L(u / z,z,y))
    ]]></literal>
    <justification jstring="[para(961(a,1),7393(a,1,2)),flip(a)].">
      <j1 rule="para" parents="961 7393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7464">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5103,a,b,7403,a)].">
      <j1 rule="hyper" parents="63 5103 7403"/>
    </justification>
  </clause>

  <clause id="7465">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(7043(a,1),7408(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7043 7408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7466">
    <literal><![CDATA[
      x / (K(T(y,z),x) * K(x * K(z,x),z)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(7409(a,1),5475(a,1,2,1))].">
      <j1 rule="para" parents="7409 5475"/>
    </justification>
  </clause>

  <clause id="7467">
    <literal><![CDATA[
      T(x,T(y * z,u) / y) = T(x,y \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4834(a,1),7419(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4834 7419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7468">
    <literal><![CDATA[
      T(x * (y \ z),K(y \ z,y)) = (y \ z) * T(x,z / y)
    ]]></literal>
    <justification jstring="[para(7419(a,1),6060(a,2,2))].">
      <j1 rule="para" parents="7419 6060"/>
    </justification>
  </clause>

  <clause id="7469">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ K(y,x) = T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(4418,a,7422,a)].">
      <j1 rule="hyper" parents="4418 7422"/>
    </justification>
  </clause>

  <clause id="7470">
    <literal><![CDATA[
      T(x,T(y,z / x)) = T(x,T(y,x \ z))
    ]]></literal>
    <justification jstring="[para(113(a,1),7424(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 7424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7472">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(7282(a,2),7278(a,1))].">
      <j1 rule="para" parents="7282 7278"/>
    </justification>
  </clause>

  <clause id="7473">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,T(y,u))) = w
    ]]></literal>
    <justification jstring="[para(7093(a,1),7295(a,1,2))].">
      <j1 rule="para" parents="7093 7295"/>
    </justification>
  </clause>

  <clause id="7474">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7092(a,2),7314(a,1))].">
      <j1 rule="para" parents="7092 7314"/>
    </justification>
  </clause>

  <clause id="7475">
    <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(7093(a,1),7328(a,1,2))].">
      <j1 rule="para" parents="7093 7328"/>
    </justification>
  </clause>

  <clause id="7476">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(5265(a,2),7362(a,1))].">
      <j1 rule="para" parents="5265 7362"/>
    </justification>
  </clause>

  <clause id="7477">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7072(a,2),7443(a,1))].">
      <j1 rule="para" parents="7072 7443"/>
    </justification>
  </clause>

  <clause id="7478">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7091(a,2),7443(a,1))].">
      <j1 rule="para" parents="7091 7443"/>
    </justification>
  </clause>

  <clause id="7479">
    <literal><![CDATA[
      T(K(x \ y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7135(a,1),7443(a,1,1))].">
      <j1 rule="para" parents="7135 7443"/>
    </justification>
  </clause>

  <clause id="7480">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7379(a,1),7443(a,1,1))].">
      <j1 rule="para" parents="7379 7443"/>
    </justification>
  </clause>

  <clause id="7481">
    <literal><![CDATA[
      K(x / y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(7370(a,1),7443(a,1))].">
      <j1 rule="para" parents="7370 7443"/>
    </justification>
  </clause>

  <clause id="7483">
    <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),7477(a,1,2))].">
      <j1 rule="para" parents="23 7477"/>
    </justification>
  </clause>

  <clause id="7484">
    <literal><![CDATA[
      K(T(x,y),R(T(z,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(27(a,2),7477(a,1,2))].">
      <j1 rule="para" parents="27 7477"/>
    </justification>
  </clause>

  <clause id="7485">
    <literal><![CDATA[
      K(x \ y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(113(a,1),7477(a,1,1))].">
      <j1 rule="para" parents="113 7477"/>
    </justification>
  </clause>

  <clause id="7486">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(238(a,1),7477(a,1,1))].">
      <j1 rule="para" parents="238 7477"/>
    </justification>
  </clause>

  <clause id="7487">
    <literal><![CDATA[
      K(x \ y,T(z,y \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3408(a,1),7477(a,1))].">
      <j1 rule="para" parents="3408 7477"/>
    </justification>
  </clause>

  <clause id="7488">
    <literal><![CDATA[
      K(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7379(a,1),7477(a,1))].">
      <j1 rule="para" parents="7379 7477"/>
    </justification>
  </clause>

  <clause id="7489">
    <literal><![CDATA[
      K(T(x,y),z / y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(7392(a,1),7477(a,1))].">
      <j1 rule="para" parents="7392 7477"/>
    </justification>
  </clause>

  <clause id="7490">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(23(a,1),7478(a,1,2,1))].">
      <j1 rule="para" parents="23 7478"/>
    </justification>
  </clause>

  <clause id="7491">
    <literal><![CDATA[
      K(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(113(a,1),7478(a,1,2,1))].">
      <j1 rule="para" parents="113 7478"/>
    </justification>
  </clause>

  <clause id="7492">
    <literal><![CDATA[
      K(x \ y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7165(a,1),7478(a,1))].">
      <j1 rule="para" parents="7165 7478"/>
    </justification>
  </clause>

  <clause id="7493">
    <literal><![CDATA[
      K(x / y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(7388(a,1),7478(a,1))].">
      <j1 rule="para" parents="7388 7478"/>
    </justification>
  </clause>

  <clause id="7494">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6421(a,2),7480(a,1))].">
      <j1 rule="para" parents="6421 7480"/>
    </justification>
  </clause>

  <clause id="7495">
    <literal><![CDATA[
      K(x,T(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7100(a,2),7480(a,1))].">
      <j1 rule="para" parents="7100 7480"/>
    </justification>
  </clause>

  <clause id="7496">
    <literal><![CDATA[
      K(x,T(y,x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7101(a,2),7488(a,1))].">
      <j1 rule="para" parents="7101 7488"/>
    </justification>
  </clause>

  <clause id="7497">
    <literal><![CDATA[
      K(x,y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7409(a,2),7488(a,1))].">
      <j1 rule="para" parents="7409 7488"/>
    </justification>
  </clause>

  <clause id="7498">
    <literal><![CDATA[
      L(K(x,T(y,z)),x,u) = (x * z) \ (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,5959,a,b,7236,a)].">
      <j1 rule="hyper" parents="347 5959 7236"/>
    </justification>
  </clause>

  <clause id="7499">
    <literal><![CDATA[
      x / T(y \ x,z) = T(x / y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(347,a,6103,a,b,7239,a)].">
      <j1 rule="hyper" parents="347 6103 7239"/>
    </justification>
  </clause>

  <clause id="7500">
    <literal><![CDATA[
      L(x,y,z) * K(u,L(x,y,z) \ x) = T(L(x,y,z) \ x,u) \ x
    ]]></literal>
    <justification jstring="[para(3308(a,1),7239(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3308 7239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7502">
    <literal><![CDATA[
      (T(x / y,z) \ x) \ x = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(7239(a,2),6104(a,1,1))].">
      <j1 rule="para" parents="7239 6104"/>
    </justification>
  </clause>

  <clause id="7503">
    <literal><![CDATA[
      (x * y) \ (T(R(z * K(x,z),x,y),u) \ ((x * z) * y)) = K(u,(x * y) \ ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(5061(a,2),7240(a,1,2,1,1))].">
      <j1 rule="para" parents="5061 7240"/>
    </justification>
  </clause>

  <clause id="7504">
    <literal><![CDATA[
      (x * y) / (x * K(z,y)) = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),7241(a,1,2,2,2))].">
      <j1 rule="para" parents="9 7241"/>
    </justification>
  </clause>

  <clause id="7505">
    <literal><![CDATA[
      T(T(x * K(y,x \ z),u),(x * K(y,x \ z)) \ z) = T(T(x * K(y,x \ z),u),T(z / x,y))
    ]]></literal>
    <justification jstring="[para(7241(a,1),4355(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7241 4355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7506">
    <literal><![CDATA[
      x / ((x * y) * K(z,y \ 1)) = T(x / (x * y),z)
    ]]></literal>
    <justification jstring="[para(6259(a,1),7241(a,1,2,2))].">
      <j1 rule="para" parents="6259 7241"/>
    </justification>
  </clause>

  <clause id="7507">
    <literal><![CDATA[
      x / (T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x)) = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[para(6353(a,1),7241(a,2,1))].">
      <j1 rule="para" parents="6353 7241"/>
    </justification>
  </clause>

  <clause id="7508">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(2558,a,7247,a)].">
      <j1 rule="hyper" parents="2558 7247"/>
    </justification>
  </clause>

  <clause id="7509">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7247(a,1),5274(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7247 5274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7510">
    <literal><![CDATA[
      T(x * K(y,z),y) = T(x,y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,7252,a(flip),b,4814,a),flip(a)].">
      <j1 rule="hyper" parents="133 7252 4814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7511">
    <literal><![CDATA[
      K(x,y) * T(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y) * z,x) = u
    ]]></literal>
    <justification jstring="[para(7252(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7252 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7513">
    <literal><![CDATA[
      T(L(x / y,z,u) * K(w,y),y) = L(y \ x,z,u) * K(w,y)
    ]]></literal>
    <justification jstring="[para(278(a,1),7253(a,2,1))].">
      <j1 rule="para" parents="278 7253"/>
    </justification>
  </clause>

  <clause id="7514">
    <literal><![CDATA[
      T(T(x,y) * K(z,y),K(y,u)) = T(x * K(z,y),T(y,u))
    ]]></literal>
    <justification jstring="[para(7253(a,1),6813(a,1,1))].">
      <j1 rule="para" parents="7253 6813"/>
    </justification>
  </clause>

  <clause id="7515">
    <literal><![CDATA[
      T(K(x,y) * z,y) = K(x,y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,7254,a(flip),b,5893,a),flip(a)].">
      <j1 rule="hyper" parents="134 7254 5893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7516">
    <literal><![CDATA[
      K(x,(y * K(x,z)) \ u) = (y * T(y \ u,x)) \ u
    ]]></literal>
    <justification jstring="[para(7254(a,1),6220(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7254 6220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7517">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = u
    ]]></literal>
    <justification jstring="[para(7263(a,1),6141(a,1,1))].">
      <j1 rule="para" parents="7263 6141"/>
    </justification>
  </clause>

  <clause id="7518">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) \ K(y,x) = T(K(y,x),T(z,y \ u))
    ]]></literal>
    <justification jstring="[para(7166(a,1),7264(a,1,1,2))].">
      <j1 rule="para" parents="7166 7264"/>
    </justification>
  </clause>

  <clause id="7519">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = K(x,K(y,z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7143(a,1),7265(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7143 7265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7520">
    <literal><![CDATA[
      T(K(x,y),z) != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7266(a,1),43(a,1))].">
      <j1 rule="para" parents="7266 43"/>
    </justification>
  </clause>

  <clause id="7521">
    <literal><![CDATA[
      K(x,T(y,z)) != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7267(a,1),43(a,1))].">
      <j1 rule="para" parents="7267 43"/>
    </justification>
  </clause>

  <clause id="7522">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(2558,a,7297,a)].">
      <j1 rule="hyper" parents="2558 7297"/>
    </justification>
  </clause>

  <clause id="7523">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(y,K(u,T(x,z)))
    ]]></literal>
    <justification jstring="[hyper(7314,a,7309,a)].">
      <j1 rule="hyper" parents="7314 7309"/>
    </justification>
  </clause>

  <clause id="7524">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,T(x,u))) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(7309(a,2),7266(a,1,2))].">
      <j1 rule="para" parents="7309 7266"/>
    </justification>
  </clause>

  <clause id="7525">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,7311,a(flip),b,5348,a)].">
      <j1 rule="hyper" parents="134 7311 5348"/>
    </justification>
  </clause>

  <clause id="7527">
    <literal><![CDATA[
      R(K(x,y),z,u) \ R(T(K(x,y),w),z,u) = K(w,R(K(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(7317(a,1),5546(a,1,2,1))].">
      <j1 rule="para" parents="7317 5546"/>
    </justification>
  </clause>

  <clause id="7528">
    <literal><![CDATA[
      T(T(x,y) \ z,K(x,y)) = (x \ z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(5153(a,1),7335(a,1,1))].">
      <j1 rule="para" parents="5153 7335"/>
    </justification>
  </clause>

  <clause id="7529">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,x) = K(y,x) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(7336(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7336 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7530">
    <literal><![CDATA[
      K(x,y) * (z / K(x,y)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),7337(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 7337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7531">
    <literal><![CDATA[
      K(K(x,y),z) * T(u,K(x,y)) = T(K(x,y),z) * (u * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(134,a,7341,a(flip),b,4995,a)].">
      <j1 rule="hyper" parents="134 7341 4995"/>
    </justification>
  </clause>

  <clause id="7532">
    <literal><![CDATA[
      L(x,(K(y,z) \ 1) * (u * K(z,y)),w) = L(x,T(u,K(y,z)),w)
    ]]></literal>
    <justification jstring="[para(7341(a,1),3599(a,2,2))].">
      <j1 rule="para" parents="7341 3599"/>
    </justification>
  </clause>

  <clause id="7533">
    <literal><![CDATA[
      K(x,T(y,z)) * (u * K(y,T(x,z))) = T(u,K(x,T(y,z)))
    ]]></literal>
    <justification jstring="[para(7093(a,1),7341(a,1,2,2))].">
      <j1 rule="para" parents="7093 7341"/>
    </justification>
  </clause>

  <clause id="7534">
    <literal><![CDATA[
      K(x,y) \ z != u * K(y,x)
    ]]></literal>
    <literal><![CDATA[
      T(u,K(x,y)) = z
    ]]></literal>
    <justification jstring="[para(7345(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="7345 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7535">
    <literal><![CDATA[
      T(x * y,K(z,y)) = T(x,K(z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(347,a,7338,a,b,7350,a)].">
      <j1 rule="hyper" parents="347 7338 7350"/>
    </justification>
  </clause>

  <clause id="7536">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(7355(a,1),321(a,1))].">
      <j1 rule="para" parents="7355 321"/>
    </justification>
  </clause>

  <clause id="7537">
    <literal><![CDATA[
      T(x \ y,K(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(6823(a,1),7536(a,1,1))].">
      <j1 rule="para" parents="6823 7536"/>
    </justification>
  </clause>

  <clause id="7538">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(7330(a,1),7536(a,1,1))].">
      <j1 rule="para" parents="7330 7536"/>
    </justification>
  </clause>

  <clause id="7539">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7356(a,1),7536(a,1,1))].">
      <j1 rule="para" parents="7356 7536"/>
    </justification>
  </clause>

  <clause id="7540">
    <literal><![CDATA[
      T(x / y,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(6812(a,2),7537(a,1))].">
      <j1 rule="para" parents="6812 7537"/>
    </justification>
  </clause>

  <clause id="7541">
    <literal><![CDATA[
      T(x / L(y,z,u),L(T(y,x),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(25(a,2),7540(a,1,2))].">
      <j1 rule="para" parents="25 7540"/>
    </justification>
  </clause>

  <clause id="7542">
    <literal><![CDATA[
      K(1 / T(T(x,y),y),z) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6425,a,b,7374,a)].">
      <j1 rule="hyper" parents="63 6425 7374"/>
    </justification>
  </clause>

  <clause id="7543">
    <literal><![CDATA[
      K(x,1 / T(T(y,z),z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5537,a,b,7375,a)].">
      <j1 rule="hyper" parents="63 5537 7375"/>
    </justification>
  </clause>

  <clause id="7544">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,5454,a,b,7386,a),flip(a)].">
      <j1 rule="hyper" parents="347 5454 7386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7545">
    <literal><![CDATA[
      (x * K(T(y,z),T(u,z))) / T(u,z) = x / (K(u,y) * T(u,z))
    ]]></literal>
    <justification jstring="[para(7386(a,1),6135(a,2,2))].">
      <j1 rule="para" parents="7386 6135"/>
    </justification>
  </clause>

  <clause id="7546">
    <literal><![CDATA[
      R(K(x,y),T(y,T(z,u)) * u,w) = K(x,R(y,u * K(y,z),w))
    ]]></literal>
    <justification jstring="[para(7395(a,2),6716(a,1,2))].">
      <j1 rule="para" parents="7395 6716"/>
    </justification>
  </clause>

  <clause id="7547">
    <literal><![CDATA[
      (x * y) \ ((x * K(z,u / x)) * y) != w
    ]]></literal>
    <literal><![CDATA[
      R(T(K(z,x \ u),x * y),x,y) = w
    ]]></literal>
    <justification jstring="[para(7430(a,1),1063(a,1,2,1))].">
      <j1 rule="para" parents="7430 1063"/>
    </justification>
  </clause>

  <clause id="7548">
    <literal><![CDATA[
      K(x \ (y \ z),y) * z = z * K(z / (y * x),y)
    ]]></literal>
    <justification jstring="[para(6855(a,1),7440(a,1,1))].">
      <j1 rule="para" parents="6855 7440"/>
    </justification>
  </clause>

  <clause id="7549">
    <literal><![CDATA[
      R(x,y \ z,K(y / z,u)) = x
    ]]></literal>
    <justification jstring="[para(7455(a,1),5964(a,1,3))].">
      <j1 rule="para" parents="7455 5964"/>
    </justification>
  </clause>

  <clause id="7550">
    <literal><![CDATA[
      x \ (y * K(x / y,z)) = (x \ y) * K(x / y,z)
    ]]></literal>
    <justification jstring="[para(7549(a,1),578(a,1,1))].">
      <j1 rule="para" parents="7549 578"/>
    </justification>
  </clause>

  <clause id="7551">
    <literal><![CDATA[
      T(x,T(y,z / x)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7195,a(flip),b,7470,a),flip(a)].">
      <j1 rule="hyper" parents="347 7195 7470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7552">
    <literal><![CDATA[
      T(x,T(y,y / x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(110(a,1),7551(a,2,2))].">
      <j1 rule="para" parents="110 7551"/>
    </justification>
  </clause>

  <clause id="7553">
    <literal><![CDATA[
      T(x \ y,T(z,y)) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[para(80(a,1),7551(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="80 7551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7554">
    <literal><![CDATA[
      T(K(x,y) * z,T(z,K(y,x))) = T(K(x,y) * z,z)
    ]]></literal>
    <justification jstring="[para(5259(a,1),7552(a,1,2,2))].">
      <j1 rule="para" parents="5259 7552"/>
    </justification>
  </clause>

  <clause id="7555">
    <literal><![CDATA[
      x / T((y \ x) \ x,z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(80(a,1),7499(a,2,1,1))].">
      <j1 rule="para" parents="80 7499"/>
    </justification>
  </clause>

  <clause id="7558">
    <literal><![CDATA[
      T((x \ y) \ y,z) = (T(x,z) \ y) \ y
    ]]></literal>
    <justification jstring="[para(80(a,1),7502(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="80 7502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7559">
    <literal><![CDATA[
      x \ (y * T(x,z)) = T(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5916,a(flip),b,7510,a)].">
      <j1 rule="hyper" parents="63 5916 7510"/>
    </justification>
  </clause>

  <clause id="7560">
    <literal><![CDATA[
      T((x / y) * K(y,z),y) = (y \ x) * K(y,z)
    ]]></literal>
    <justification jstring="[para(113(a,1),7510(a,2,1))].">
      <j1 rule="para" parents="113 7510"/>
    </justification>
  </clause>

  <clause id="7561">
    <literal><![CDATA[
      x \ T(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7510(a,2),5169(a,1,2))].">
      <j1 rule="para" parents="7510 5169"/>
    </justification>
  </clause>

  <clause id="7562">
    <literal><![CDATA[
      K(x,y) * T(K(x * y,x),y) = T(x \ R(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(5385(a,1),7515(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5385 7515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7563">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7522(a,1),6145(a,1,1))].">
      <j1 rule="para" parents="7522 6145"/>
    </justification>
  </clause>

  <clause id="7564">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7510,a,b,7525,a)].">
      <j1 rule="hyper" parents="63 7510 7525"/>
    </justification>
  </clause>

  <clause id="7565">
    <literal><![CDATA[
      T(x \ y,K(z,x)) = x \ T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(35,a,4830,a(flip),b,7535,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 4830 7535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7566">
    <literal><![CDATA[
      T(T(x,y) * z,K(y,z)) = T(x,T(y,z)) * z
    ]]></literal>
    <justification jstring="[para(6813(a,1),7535(a,2,1))].">
      <j1 rule="para" parents="6813 7535"/>
    </justification>
  </clause>

  <clause id="7567">
    <literal><![CDATA[
      K(1 / T(T(x,x * y),y),z) = K(1 / L(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(752(a,1),7542(a,1,1,2,1))].">
      <j1 rule="para" parents="752 7542"/>
    </justification>
  </clause>

  <clause id="7568">
    <literal><![CDATA[
      K(x,1 / ((y * z) / y)) = K(x,1 / T(z,y))
    ]]></literal>
    <justification jstring="[para(254(a,1),7543(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="254 7543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7569">
    <literal><![CDATA[
      K(x,1 / T(y,z / y)) = K(x,1 / (z / (z / y)))
    ]]></literal>
    <justification jstring="[para(275(a,1),7543(a,1,2,2,1))].">
      <j1 rule="para" parents="275 7543"/>
    </justification>
  </clause>

  <clause id="7570">
    <literal><![CDATA[
      (T(T(x,y),T(z,y)) * u) / (T(K(x,y),T(x,z)) * u) = R(T(x,z),T(K(x,y),T(x,z)),u)
    ]]></literal>
    <justification jstring="[para(7544(a,2),264(a,1,1,1))].">
      <j1 rule="para" parents="7544 264"/>
    </justification>
  </clause>

  <clause id="7571">
    <literal><![CDATA[
      x / T(T(y,y \ x),z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(112(a,2),7555(a,1,2,1))].">
      <j1 rule="para" parents="112 7555"/>
    </justification>
  </clause>

  <clause id="7572">
    <literal><![CDATA[
      x / T(T(x,y),z) = T(T(x,y),z) \ x
    ]]></literal>
    <justification jstring="[para(3016(a,1),7555(a,1,2,1))].">
      <j1 rule="para" parents="3016 7555"/>
    </justification>
  </clause>

  <clause id="7573">
    <literal><![CDATA[
      T(T(x,x \ y),z) = (T(x,z) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,763,a,b,7558,a)].">
      <j1 rule="hyper" parents="63 763 7558"/>
    </justification>
  </clause>

  <clause id="7574">
    <literal><![CDATA[
      T(T(x,y),x \ z) = (T(x,y) \ z) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,341,a,b,7558,a)].">
      <j1 rule="hyper" parents="63 341 7558"/>
    </justification>
  </clause>

  <clause id="7578">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z)) = x * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(5311,a,7564,a)].">
      <j1 rule="hyper" parents="5311 7564"/>
    </justification>
  </clause>

  <clause id="7579">
    <literal><![CDATA[
      T(x * K(y / z,x),z \ y) = T(x,K(z \ y,y))
    ]]></literal>
    <justification jstring="[para(7388(a,1),7564(a,1,1,2))].">
      <j1 rule="para" parents="7388 7564"/>
    </justification>
  </clause>

  <clause id="7580">
    <literal><![CDATA[
      x * T(x \ y,K(z,x)) != u * w
    ]]></literal>
    <literal><![CDATA[
      T(y,K(z,x)) / w = u
    ]]></literal>
    <justification jstring="[para(7565(a,2),390(a,1,2))].">
      <j1 rule="para" parents="7565 390"/>
    </justification>
  </clause>

  <clause id="7581">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,y) \ y) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[para(7571(a,1),6948(a,1,2))].">
      <j1 rule="para" parents="7571 6948"/>
    </justification>
  </clause>

  <clause id="7582">
    <literal><![CDATA[
      x / T(T(x,y),z) = T(T(x,z),y) \ x
    ]]></literal>
    <justification jstring="[hyper(347,a,173,a,b,7572,a),flip(a)].">
      <j1 rule="hyper" parents="347 173 7572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7583">
    <literal><![CDATA[
      T(x,T(T(y,z),y \ u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(7574(a,2),7070(a,1,2))].">
      <j1 rule="para" parents="7574 7070"/>
    </justification>
  </clause>

  <clause id="7584">
    <literal><![CDATA[
      K(x,y) * K(z,T(y,x)) = T(T(y,z),x) \ y
    ]]></literal>
    <justification jstring="[hyper(6311,a,7582,a)].">
      <j1 rule="hyper" parents="6311 7582"/>
    </justification>
  </clause>

  <clause id="7585">
    <literal><![CDATA[
      T(x,T(y * K(z,y \ u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ u,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(6103(a,1),7081(a,1,2,1))].">
      <j1 rule="para" parents="6103 7081"/>
    </justification>
  </clause>

  <clause id="7586">
    <literal><![CDATA[
      K(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7143(a,1),7111(a,1,2))].">
      <j1 rule="para" parents="7143 7111"/>
    </justification>
  </clause>

  <clause id="7587">
    <literal><![CDATA[
      K(x / y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x) = z
    ]]></literal>
    <justification jstring="[para(5146(a,1),7206(a,1))].">
      <j1 rule="para" parents="5146 7206"/>
    </justification>
  </clause>

  <clause id="7588">
    <literal><![CDATA[
      K((x * y) / z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K((z / y) \ x,x) = u
    ]]></literal>
    <justification jstring="[para(6516(a,2),7587(a,1))].">
      <j1 rule="para" parents="6516 7587"/>
    </justification>
  </clause>

  <clause id="7589">
    <literal><![CDATA[
      K(x / ((y * z) \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(((y * z) \ y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(7370(a,1),7210(a,1))].">
      <j1 rule="para" parents="7370 7210"/>
    </justification>
  </clause>

  <clause id="7590">
    <literal><![CDATA[
      T(x * y,T(z,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6276(a,1),7248(a,1,2))].">
      <j1 rule="para" parents="6276 7248"/>
    </justification>
  </clause>

  <clause id="7591">
    <literal><![CDATA[
      x / R(y,y \ x,y) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[hyper(347,a,5444,a,b,7249,a),flip(a)].">
      <j1 rule="hyper" parents="347 5444 7249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7592">
    <literal><![CDATA[
      K(L((x \ y) / z,z,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * z) \ y,T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(962(a,2),7460(a,1,1))].">
      <j1 rule="para" parents="962 7460"/>
    </justification>
  </clause>

  <clause id="7593">
    <literal><![CDATA[
      K(x * K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(4942(a,1),7460(a,1,1))].">
      <j1 rule="para" parents="4942 7460"/>
    </justification>
  </clause>

  <clause id="7594">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7408,a(flip),b,7465,a),flip(a)].">
      <j1 rule="hyper" parents="347 7408 7465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7595">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ (x * u)))
    ]]></literal>
    <justification jstring="[para(561(a,1),7594(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="561 7594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7596">
    <literal><![CDATA[
      K(x / y,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(199(a,1),7481(a,1,2))].">
      <j1 rule="para" parents="199 7481"/>
    </justification>
  </clause>

  <clause id="7597">
    <literal><![CDATA[
      K(R(x / y,y,z),T(u,y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * z) \ (x * z),u) = w
    ]]></literal>
    <justification jstring="[para(108(a,2),7481(a,1,1))].">
      <j1 rule="para" parents="108 7481"/>
    </justification>
  </clause>

  <clause id="7599">
    <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(197(a,1),7485(a,1,2))].">
      <j1 rule="para" parents="197 7485"/>
    </justification>
  </clause>

  <clause id="7600">
    <literal><![CDATA[
      K((x / y) \ z,y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z / (x / y),y \ x) = u
    ]]></literal>
    <justification jstring="[para(508(a,1),7485(a,1,2))].">
      <j1 rule="para" parents="508 7485"/>
    </justification>
  </clause>

  <clause id="7601">
    <literal><![CDATA[
      K(T(x,y),z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z \ y)) = u
    ]]></literal>
    <justification jstring="[para(5625(a,1),7489(a,1))].">
      <j1 rule="para" parents="5625 7489"/>
    </justification>
  </clause>

  <clause id="7602">
    <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(4834(a,1),7491(a,1,2))].">
      <j1 rule="para" parents="4834 7491"/>
    </justification>
  </clause>

  <clause id="7603">
    <literal><![CDATA[
      K(((x \ y) \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7097(a,2),7492(a,1))].">
      <j1 rule="para" parents="7097 7492"/>
    </justification>
  </clause>

  <clause id="7604">
    <literal><![CDATA[
      K(R(x / y,z,u) / w,y \ x) != v5
    ]]></literal>
    <literal><![CDATA[
      K(w \ R(x / y,z,u),y \ x) = v5
    ]]></literal>
    <justification jstring="[para(5254(a,1),7493(a,1,2))].">
      <j1 rule="para" parents="5254 7493"/>
    </justification>
  </clause>

  <clause id="7605">
    <literal><![CDATA[
      K(x * y,T(z,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6276(a,1),7495(a,1,2))].">
      <j1 rule="para" parents="6276 7495"/>
    </justification>
  </clause>

  <clause id="7606">
    <literal><![CDATA[
      x / ((y \ x) \ T(x,y)) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[para(4380(a,1),7591(a,1,2))].">
      <j1 rule="para" parents="4380 7591"/>
    </justification>
  </clause>

  <clause id="7607">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,7015,a(flip),b,7040,a),flip(a)].">
      <j1 rule="hyper" parents="347 7015 7040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7608">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(7040(a,2),7016(a,1))].">
      <j1 rule="para" parents="7040 7016"/>
    </justification>
  </clause>

  <clause id="7609">
    <literal><![CDATA[
      (x * y) * K(z,L(u,y / u,x)) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,7607,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="134 7607 18"/>
    </justification>
  </clause>

  <clause id="7610">
    <literal><![CDATA[
      L(K(x,y),z * y,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),7607(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 7607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7611">
    <literal><![CDATA[
      L(K(x,y),z * T(y,u),w) = K(x,L(y,z * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(5919(a,1),7607(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5919 7607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7612">
    <literal><![CDATA[
      K(x,L(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7208,a,7610,a),flip(a)].">
      <j1 rule="hyper" parents="7208 7610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7613">
    <literal><![CDATA[
      K(x,L(y,y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(550,a,7610,a),flip(a)].">
      <j1 rule="hyper" parents="550 7610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7615">
    <literal><![CDATA[
      K(x,L(y,z,K(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6871,a(flip),b,7610,a),flip(a)].">
      <j1 rule="hyper" parents="63 6871 7610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7616">
    <literal><![CDATA[
      K(x,L(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6845,a(flip),b,7610,a),flip(a)].">
      <j1 rule="hyper" parents="63 6845 7610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7617">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,y,z)) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(41,a,2312,a,b,7610,a)].">
      <j1 rule="hyper" parents="41 2312 7610"/>
    </justification>
  </clause>

  <clause id="7618">
    <literal><![CDATA[
      K(x,L(y,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7610(a,1),550(a,1))].">
      <j1 rule="para" parents="7610 550"/>
    </justification>
  </clause>

  <clause id="7619">
    <literal><![CDATA[
      K(x,L(L(y,z,x),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),7612(a,1,2))].">
      <j1 rule="para" parents="30 7612"/>
    </justification>
  </clause>

  <clause id="7620">
    <literal><![CDATA[
      K(x,T((x \ y) \ z,u)) = K(x,T(y \ (x * z),u))
    ]]></literal>
    <justification jstring="[para(891(a,1),7612(a,1,2)),flip(a)].">
      <j1 rule="para" parents="891 7612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7621">
    <literal><![CDATA[
      L(x * K(y,x),z,y) = L(x,z,y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7612(a,1),5437(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7612 5437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7622">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ (x * z)) = K(x,K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(5896(a,1),7612(a,1,2))].">
      <j1 rule="para" parents="5896 7612"/>
    </justification>
  </clause>

  <clause id="7623">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) = L(K(x,u),y * x,z)
    ]]></literal>
    <justification jstring="[para(7612(a,1),7039(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7612 7039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7624">
    <literal><![CDATA[
      T(x,L(y,y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,7613,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 7613 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7625">
    <literal><![CDATA[
      K(x,K(y,L(z,z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(7613(a,2),7293(a,1,2))].">
      <j1 rule="para" parents="7613 7293"/>
    </justification>
  </clause>

  <clause id="7626">
    <literal><![CDATA[
      K(x,T(y / z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4398(a,1),7616(a,1,2))].">
      <j1 rule="para" parents="4398 7616"/>
    </justification>
  </clause>

  <clause id="7627">
    <literal><![CDATA[
      K(x,R(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4494(a,1),7616(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4494 7616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7628">
    <literal><![CDATA[
      K(x,T(y,y * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4797(a,1),7616(a,1,2))].">
      <j1 rule="para" parents="4797 7616"/>
    </justification>
  </clause>

  <clause id="7629">
    <literal><![CDATA[
      L(x,x,y) * T(z,x) = z * L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,7624,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 7624 22"/>
    </justification>
  </clause>

  <clause id="7630">
    <literal><![CDATA[
      T(x,L(y,y \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3188(a,2),7624(a,1,2))].">
      <j1 rule="para" parents="3188 7624"/>
    </justification>
  </clause>

  <clause id="7631">
    <literal><![CDATA[
      R(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6713,a(flip),b,7627,a)].">
      <j1 rule="hyper" parents="63 6713 7627"/>
    </justification>
  </clause>

  <clause id="7632">
    <literal><![CDATA[
      R(x * K(y,x),z,x) = R(x,z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,7627,a(flip),b,5546,a),flip(a)].">
      <j1 rule="hyper" parents="134 7627 5546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7633">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4426(a,1),7627(a,1,2))].">
      <j1 rule="para" parents="4426 7627"/>
    </justification>
  </clause>

  <clause id="7634">
    <literal><![CDATA[
      K(x,T(R(y,z,y),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(6789(a,1),7627(a,1,2))].">
      <j1 rule="para" parents="6789 7627"/>
    </justification>
  </clause>

  <clause id="7635">
    <literal><![CDATA[
      K(x,R(T(y,z),u,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6793(a,1),7627(a,1,2))].">
      <j1 rule="para" parents="6793 7627"/>
    </justification>
  </clause>

  <clause id="7636">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6798(a,1),7627(a,1,2))].">
      <j1 rule="para" parents="6798 7627"/>
    </justification>
  </clause>

  <clause id="7637">
    <literal><![CDATA[
      K(R(x,y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6508,a(flip),b,7631,a)].">
      <j1 rule="hyper" parents="63 6508 7631"/>
    </justification>
  </clause>

  <clause id="7638">
    <literal><![CDATA[
      (K(x,y) * z) * y = K(x,y) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,7631,a(flip),b,2253,a),flip(a)].">
      <j1 rule="hyper" parents="133 7631 2253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7639">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ (K(x,y) * u))
    ]]></literal>
    <justification jstring="[para(5289(a,1),7615(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5289 7615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7640">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) = T(x,L(y,y \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,7387,a,b,7630,a)].">
      <j1 rule="hyper" parents="347 7387 7630"/>
    </justification>
  </clause>

  <clause id="7642">
    <literal><![CDATA[
      K(x,y / z) * K(x,K(y,y / z)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7310,a,b,7626,a)].">
      <j1 rule="hyper" parents="63 7310 7626"/>
    </justification>
  </clause>

  <clause id="7643">
    <literal><![CDATA[
      K(T(x,y),y / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7093,a,b,7626,a)].">
      <j1 rule="hyper" parents="63 7093 7626"/>
    </justification>
  </clause>

  <clause id="7644">
    <literal><![CDATA[
      K(x \ 1,x / y) = K(x \ 1,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7102,a(flip),b,7626,a)].">
      <j1 rule="hyper" parents="63 7102 7626"/>
    </justification>
  </clause>

  <clause id="7645">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7091,a(flip),b,7626,a)].">
      <j1 rule="hyper" parents="63 7091 7626"/>
    </justification>
  </clause>

  <clause id="7646">
    <literal><![CDATA[
      K(x,y \ z) * z = z * K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(133,a,7626,a(flip),b,7378,a)].">
      <j1 rule="hyper" parents="133 7626 7378"/>
    </justification>
  </clause>

  <clause id="7647">
    <literal><![CDATA[
      K(x,T(R(y / z,z,y \ u),u)) = K(x,(z * (y \ u)) \ u)
    ]]></literal>
    <justification jstring="[para(604(a,2),7626(a,1,2,1))].">
      <j1 rule="para" parents="604 7626"/>
    </justification>
  </clause>

  <clause id="7648">
    <literal><![CDATA[
      T(K(x,y \ z),z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(7626(a,1),7371(a,1,1))].">
      <j1 rule="para" parents="7626 7371"/>
    </justification>
  </clause>

  <clause id="7650">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K((y * z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(7492,a,7628,a),flip(a)].">
      <j1 rule="hyper" parents="7492 7628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7651">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) * (y \ w))) = K(x,T(y,L(y,z,u) * w))
    ]]></literal>
    <justification jstring="[para(1404(a,1),7628(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1404 7628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7652">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ y))
    ]]></literal>
    <justification jstring="[para(1799(a,1),7628(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1799 7628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7653">
    <literal><![CDATA[
      K(x,T(y,z * y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4323(a,2),7628(a,1,2))].">
      <j1 rule="para" parents="4323 7628"/>
    </justification>
  </clause>

  <clause id="7654">
    <literal><![CDATA[
      (x * y) * K(z,T(x,y)) = K(z,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(7628(a,1),7104(a,1,2))].">
      <j1 rule="para" parents="7628 7104"/>
    </justification>
  </clause>

  <clause id="7655">
    <literal><![CDATA[
      K(x \ (y \ z),T(y,z)) = K((y \ z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(7492,a,7633,a),flip(a)].">
      <j1 rule="hyper" parents="7492 7633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7656">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7091,a(flip),b,7633,a),flip(a)].">
      <j1 rule="hyper" parents="347 7091 7633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7657">
    <literal><![CDATA[
      K(x,T(y * z,y \ 1)) = K(x,T(y * z,z))
    ]]></literal>
    <justification jstring="[para(4224(a,1),7633(a,1,2))].">
      <j1 rule="para" parents="4224 7633"/>
    </justification>
  </clause>

  <clause id="7658">
    <literal><![CDATA[
      ((x \ y) * K(z,T(x,y))) \ y = T((x \ y) \ y,z)
    ]]></literal>
    <justification jstring="[para(7636(a,1),6104(a,1,1,2))].">
      <j1 rule="para" parents="7636 6104"/>
    </justification>
  </clause>

  <clause id="7659">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = L(K(x,T(z,u)),u,y)
    ]]></literal>
    <justification jstring="[para(7636(a,1),6448(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7636 6448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7660">
    <literal><![CDATA[
      L(K(x,T(y,z)),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * (y \ z)) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(7636(a,1),6449(a,1,1))].">
      <j1 rule="para" parents="7636 6449"/>
    </justification>
  </clause>

  <clause id="7661">
    <literal><![CDATA[
      K(x,T(T(y / z,u),y)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(7502(a,1),7636(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7502 7636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7662">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(238(a,1),7643(a,1,1))].">
      <j1 rule="para" parents="238 7643"/>
    </justification>
  </clause>

  <clause id="7663">
    <literal><![CDATA[
      K(x,T(y \ z,z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(7382,a,7645,a)].">
      <j1 rule="hyper" parents="7382 7645"/>
    </justification>
  </clause>

  <clause id="7664">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7091,a(flip),b,7653,a)].">
      <j1 rule="hyper" parents="63 7091 7653"/>
    </justification>
  </clause>

  <clause id="7665">
    <literal><![CDATA[
      K(x,T(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7656(a,2),7480(a,1))].">
      <j1 rule="para" parents="7656 7480"/>
    </justification>
  </clause>

  <clause id="7666">
    <literal><![CDATA[
      K(x,T((y \ z) \ z,u)) = K(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(6798(a,1),7634(a,1,2,1))].">
      <j1 rule="para" parents="6798 7634"/>
    </justification>
  </clause>

  <clause id="7667">
    <literal><![CDATA[
      L(x,x,y) * (z * x) = x * (z * L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(134,a,7629,a(flip),b,1411,a),flip(a)].">
      <j1 rule="hyper" parents="134 7629 1411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7668">
    <literal><![CDATA[
      L(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(3558,a,7638,a)].">
      <j1 rule="hyper" parents="3558 7638"/>
    </justification>
  </clause>

  <clause id="7669">
    <literal><![CDATA[
      T(K(x,y) * z,y) = T(y,x) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(269,a,7638,a,b,4947,a)].">
      <j1 rule="hyper" parents="269 7638 4947"/>
    </justification>
  </clause>

  <clause id="7670">
    <literal><![CDATA[
      (K(x,y) * T(z * K(y,z),u)) * y = K(x,y) * (y * T(z,u))
    ]]></literal>
    <justification jstring="[para(5063(a,1),7638(a,2,2))].">
      <j1 rule="para" parents="5063 7638"/>
    </justification>
  </clause>

  <clause id="7671">
    <literal><![CDATA[
      L(x,K(y,T(x,z)),u) = L(x,w,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,6037,a,b,7668,a)].">
      <j1 rule="hyper" parents="347 6037 7668"/>
    </justification>
  </clause>

  <clause id="7672">
    <literal><![CDATA[
      L(L(x,y,z),u,K(w,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(7668(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7668 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7673">
    <literal><![CDATA[
      (K(x,y) * z) * T(y,u) = K(x,y) * (z * T(y,u))
    ]]></literal>
    <justification jstring="[para(7668(a,1),477(a,1,2,1))].">
      <j1 rule="para" parents="7668 477"/>
    </justification>
  </clause>

  <clause id="7674">
    <literal><![CDATA[
      L(x \ y,z,y / x) = L(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6958,a(flip),b,7672,a)].">
      <j1 rule="hyper" parents="63 6958 7672"/>
    </justification>
  </clause>

  <clause id="7675">
    <literal><![CDATA[
      L(x,y,x * K(z,x)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6956,a(flip),b,7672,a)].">
      <j1 rule="hyper" parents="63 6956 7672"/>
    </justification>
  </clause>

  <clause id="7676">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ y)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6258(a,1),7652(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6258 7652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7677">
    <literal><![CDATA[
      T(K(x,y \ z) * y,y \ z) = T(y \ z,x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),7669(a,2,2))].">
      <j1 rule="para" parents="10 7669"/>
    </justification>
  </clause>

  <clause id="7678">
    <literal><![CDATA[
      T(K(x,y) * (z / y),y) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[para(12(a,1),7669(a,2,2))].">
      <j1 rule="para" parents="12 7669"/>
    </justification>
  </clause>

  <clause id="7679">
    <literal><![CDATA[
      T(K(x,y) * (z * (1 / y)),y) = T(y,x) \ R(z,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2270(a,1),7669(a,2,2))].">
      <j1 rule="para" parents="2270 7669"/>
    </justification>
  </clause>

  <clause id="7680">
    <literal><![CDATA[
      T(K(x,y) * (z / T(y,u)),y) = T(y,x) \ (z * K(u,y))
    ]]></literal>
    <justification jstring="[para(6107(a,1),7669(a,2,2))].">
      <j1 rule="para" parents="6107 7669"/>
    </justification>
  </clause>

  <clause id="7681">
    <literal><![CDATA[
      L(x,y,K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(7671(a,1),401(a,1))].">
      <j1 rule="para" parents="7671 401"/>
    </justification>
  </clause>

  <clause id="7682">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(7640(a,2),7060(a,1))].">
      <j1 rule="para" parents="7640 7060"/>
    </justification>
  </clause>

  <clause id="7683">
    <literal><![CDATA[
      T(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(113(a,1),7682(a,1,2,1))].">
      <j1 rule="para" parents="113 7682"/>
    </justification>
  </clause>

  <clause id="7684">
    <literal><![CDATA[
      T(x,((y \ z) \ z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(4320(a,1),7683(a,1,2))].">
      <j1 rule="para" parents="4320 7683"/>
    </justification>
  </clause>

  <clause id="7685">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = (z / x) * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4990(a,1),7053(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4990 7053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7687">
    <literal><![CDATA[
      K(K(x,y) * z,u) * z = z * K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(7074(a,1),7372(a,1,1))].">
      <j1 rule="para" parents="7074 7372"/>
    </justification>
  </clause>

  <clause id="7688">
    <literal><![CDATA[
      T(x,y) * T(z,x) = z * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(5973,a,7160,a),flip(a)].">
      <j1 rule="hyper" parents="5973 7160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7689">
    <literal><![CDATA[
      T(K(x,y),z * x) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(269,a,5162,a,b,7160,a)].">
      <j1 rule="hyper" parents="269 5162 7160"/>
    </justification>
  </clause>

  <clause id="7690">
    <literal><![CDATA[
      K(x,T(y,z * x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7480,a,7689,a)].">
      <j1 rule="hyper" parents="7480 7689"/>
    </justification>
  </clause>

  <clause id="7692">
    <literal><![CDATA[
      K(L(x,y,x),T(z,u)) = K(x,T(z,u * x))
    ]]></literal>
    <justification jstring="[hyper(347,a,7044,a,b,7690,a)].">
      <j1 rule="hyper" parents="347 7044 7690"/>
    </justification>
  </clause>

  <clause id="7693">
    <literal><![CDATA[
      K(x,T(y,z / x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),7690(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 7690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7694">
    <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(86(a,1),7690(a,1,2,2))].">
      <j1 rule="para" parents="86 7690"/>
    </justification>
  </clause>

  <clause id="7695">
    <literal><![CDATA[
      K(x,K(y,T(z,u / x))) = K(z,K(x,T(y,u)))
    ]]></literal>
    <justification jstring="[para(7693(a,1),7309(a,2,2))].">
      <j1 rule="para" parents="7693 7309"/>
    </justification>
  </clause>

  <clause id="7696">
    <literal><![CDATA[
      T(T(x,y) * K(z,x),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(5930,a,7688,a)].">
      <j1 rule="hyper" parents="5930 7688"/>
    </justification>
  </clause>

  <clause id="7697">
    <literal><![CDATA[
      K(x,y) * (z * x) = z * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(5240,a,7688,a)].">
      <j1 rule="hyper" parents="5240 7688"/>
    </justification>
  </clause>

  <clause id="7698">
    <literal><![CDATA[
      L((x * y) \ z,x * y,K(y,u)) = (x * T(y,T(u,x))) \ (K(y,u) * z)
    ]]></literal>
    <justification jstring="[para(7697(a,1),99(a,2,1))].">
      <j1 rule="para" parents="7697 99"/>
    </justification>
  </clause>

  <clause id="7699">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * x) = z * T(x,y)
    ]]></literal>
    <justification jstring="[para(7387(a,1),7697(a,2,2))].">
      <j1 rule="para" parents="7387 7697"/>
    </justification>
  </clause>

  <clause id="7700">
    <literal><![CDATA[
      (x * T(y,z)) / (x * y) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(145,a,7699,a)].">
      <j1 rule="hyper" parents="145 7699"/>
    </justification>
  </clause>

  <clause id="7701">
    <literal><![CDATA[
      K(x,T(y,z)) \ (z * y) = z * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7129,a,b,7699,a)].">
      <j1 rule="hyper" parents="63 7129 7699"/>
    </justification>
  </clause>

  <clause id="7702">
    <literal><![CDATA[
      T(x,T(y,z)) * (z * x) = x * (z * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(134,a,7699,a(flip),b,5157,a),flip(a)].">
      <j1 rule="hyper" parents="134 7699 5157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7703">
    <literal><![CDATA[
      (x * T(y,z)) / T(x,y) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(131,a,7699,a(flip),b,5162,a(flip))].">
      <j1 rule="hyper" parents="131 7699 5162"/>
    </justification>
  </clause>

  <clause id="7704">
    <literal><![CDATA[
      (x * T(y,z)) / (x * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7699(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7699 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7705">
    <literal><![CDATA[
      T(K(x,y),z) * (z * x) = z * T(x,y)
    ]]></literal>
    <justification jstring="[para(7091(a,1),7699(a,1,1))].">
      <j1 rule="para" parents="7091 7699"/>
    </justification>
  </clause>

  <clause id="7706">
    <literal><![CDATA[
      T(K(x,y),z) * ((x \ z) * x) = (x \ z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7100(a,1),7699(a,1,1))].">
      <j1 rule="para" parents="7100 7699"/>
    </justification>
  </clause>

  <clause id="7707">
    <literal><![CDATA[
      K(x,T(y,z)) * ((z * y) * x) = (z * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7653(a,1),7699(a,1,1))].">
      <j1 rule="para" parents="7653 7699"/>
    </justification>
  </clause>

  <clause id="7708">
    <literal><![CDATA[
      (x * T(y,z \ y)) / T(x,y) = T(y,T(y * (z \ 1),x))
    ]]></literal>
    <justification jstring="[para(1799(a,1),7703(a,1,1,2))].">
      <j1 rule="para" parents="1799 7703"/>
    </justification>
  </clause>

  <clause id="7709">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,T(T(z,u),u * x))
    ]]></literal>
    <justification jstring="[hyper(7478,a,7692,a)].">
      <j1 rule="hyper" parents="7478 7692"/>
    </justification>
  </clause>

  <clause id="7710">
    <literal><![CDATA[
      K(x,T(y,z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7692(a,1),7204(a,1))].">
      <j1 rule="para" parents="7692 7204"/>
    </justification>
  </clause>

  <clause id="7711">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ (y * x),y)) = u
    ]]></literal>
    <justification jstring="[para(7663(a,1),7710(a,1))].">
      <j1 rule="para" parents="7663 7710"/>
    </justification>
  </clause>

  <clause id="7712">
    <literal><![CDATA[
      T(x / T(T(y,x),z),y) = y \ (K(z,y) * T(x,y))
    ]]></literal>
    <justification jstring="[para(7171(a,1),6180(a,1,1))].">
      <j1 rule="para" parents="7171 6180"/>
    </justification>
  </clause>

  <clause id="7713">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * (y * x)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[para(5162(a,2),7191(a,1,2))].">
      <j1 rule="para" parents="5162 7191"/>
    </justification>
  </clause>

  <clause id="7716">
    <literal><![CDATA[
      K(x,T(y / (x * z),z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(347,a,6784,a(flip),b,7197,a),flip(a)].">
      <j1 rule="hyper" parents="347 6784 7197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7718">
    <literal><![CDATA[
      T(x,y) / (y \ 1) = x / (y \ K(y,x))
    ]]></literal>
    <justification jstring="[para(4929(a,2),7212(a,1,1))].">
      <j1 rule="para" parents="4929 7212"/>
    </justification>
  </clause>

  <clause id="7719">
    <literal><![CDATA[
      (T(x,y) / (y \ 1)) \ x = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(132,a,7718,a,b,172,a)].">
      <j1 rule="hyper" parents="132 7718 172"/>
    </justification>
  </clause>

  <clause id="7720">
    <literal><![CDATA[
      x \ (x / (y \ K(y,x))) = (x / (y \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,7718,a(flip),b,3807,a(flip))].">
      <j1 rule="hyper" parents="128 7718 3807"/>
    </justification>
  </clause>

  <clause id="7721">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(7719(a,1),6633(a,1,1))].">
      <j1 rule="para" parents="7719 6633"/>
    </justification>
  </clause>

  <clause id="7722">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = (x \ ((x \ 1) \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,1844,a,b,7721,a),flip(a)].">
      <j1 rule="hyper" parents="347 1844 7721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7723">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = y * (((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3842,a(flip),b,7721,a),flip(a)].">
      <j1 rule="hyper" parents="347 3842 7721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7724">
    <literal><![CDATA[
      x \ ((y \ K(y,x)) \ x) = ((y \ 1) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(128,a,7721,a,b,3842,a(flip))].">
      <j1 rule="hyper" parents="128 7721 3842"/>
    </justification>
  </clause>

  <clause id="7725">
    <literal><![CDATA[
      K(x,y) * (x \ L(x,z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      x \ L(T(x,y),z,x) = u
    ]]></literal>
    <justification jstring="[para(7214(a,1),5323(a,1,2))].">
      <j1 rule="para" parents="7214 5323"/>
    </justification>
  </clause>

  <clause id="7726">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(7235(a,2),6269(a,1))].">
      <j1 rule="para" parents="7235 6269"/>
    </justification>
  </clause>

  <clause id="7727">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,y)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(7174,a,7242,a)].">
      <j1 rule="hyper" parents="7174 7242"/>
    </justification>
  </clause>

  <clause id="7729">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(80(a,1),7727(a,1,2,1,1))].">
      <j1 rule="para" parents="80 7727"/>
    </justification>
  </clause>

  <clause id="7730">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7098,a(flip),b,7729,a)].">
      <j1 rule="hyper" parents="63 7098 7729"/>
    </justification>
  </clause>

  <clause id="7731">
    <literal><![CDATA[
      K(x,y \ K(z,y)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(4934(a,1),7730(a,1,2))].">
      <j1 rule="para" parents="4934 7730"/>
    </justification>
  </clause>

  <clause id="7732">
    <literal><![CDATA[
      T(T(x,y) * (x \ z),x) = T(x,y) * (x \ T(z,x))
    ]]></literal>
    <justification jstring="[hyper(269,a,7250,a,b,1226,a)].">
      <j1 rule="hyper" parents="269 7250 1226"/>
    </justification>
  </clause>

  <clause id="7733">
    <literal><![CDATA[
      T(T(x,y) \ T(x * z,u),x) = T(x,y) \ T(z * x,u)
    ]]></literal>
    <justification jstring="[hyper(128,a,4829,a(flip),b,7251,a),flip(a)].">
      <j1 rule="hyper" parents="128 4829 7251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7734">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,z) = (T(x,y) * z) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,6242,a,b,7256,a)].">
      <j1 rule="hyper" parents="63 6242 7256"/>
    </justification>
  </clause>

  <clause id="7735">
    <literal><![CDATA[
      K(x,y) * (z * K(x,z)) = (T(x,y) * z) / x
    ]]></literal>
    <justification jstring="[para(4942(a,1),7256(a,1,2))].">
      <j1 rule="para" parents="4942 7256"/>
    </justification>
  </clause>

  <clause id="7736">
    <literal><![CDATA[
      K(x,K(y,z)) \ (K(u,T(y,K(x,z))) * w) = y * (T(T(y,K(x,z)),u) \ w)
    ]]></literal>
    <justification jstring="[hyper(128,a,4947,a(flip),b,7284,a)].">
      <j1 rule="hyper" parents="128 4947 7284"/>
    </justification>
  </clause>

  <clause id="7737">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / K(x,y)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(6117(a,2),7294(a,1,2))].">
      <j1 rule="para" parents="6117 7294"/>
    </justification>
  </clause>

  <clause id="7738">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,y) * u) = T(T(z,y),K(x,y)) * u
    ]]></literal>
    <justification jstring="[para(5095(a,1),7302(a,1,1,2))].">
      <j1 rule="para" parents="5095 7302"/>
    </justification>
  </clause>

  <clause id="7739">
    <literal><![CDATA[
      K(x,K(y,z)) \ (K(u,T(y,K(x,z))) * w) = y \ (((u * T(y,K(x,z))) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(128,a,5478,a(flip),b,7313,a)].">
      <j1 rule="hyper" parents="128 5478 7313"/>
    </justification>
  </clause>

  <clause id="7740">
    <literal><![CDATA[
      T(x * T(y,z),K(y,z)) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,5162,a(flip),b,7343,a),flip(a)].">
      <j1 rule="hyper" parents="347 5162 7343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7741">
    <literal><![CDATA[
      K(x * T(y,z),T(u,K(y,z))) = K(K(y,z) * (x * y),u)
    ]]></literal>
    <justification jstring="[para(7343(a,1),7093(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7343 7093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7742">
    <literal><![CDATA[
      T(x,y) * (z * K(y,x)) = T(x * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6109(a,1),7354(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6109 7354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7743">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = K(z \ y,z) * T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(7419(a,1),7365(a,1,1))].">
      <j1 rule="para" parents="7419 7365"/>
    </justification>
  </clause>

  <clause id="7744">
    <literal><![CDATA[
      T(x,K(y,z)) * T(y,z) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,5162,a,b,7368,a),flip(a)].">
      <j1 rule="hyper" parents="347 5162 7368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7745">
    <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(1644(a,1),7399(a,1,1))].">
      <j1 rule="para" parents="1644 7399"/>
    </justification>
  </clause>

  <clause id="7746">
    <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(63,a,7607,a(flip),b,7400,a)].">
      <j1 rule="hyper" parents="63 7607 7400"/>
    </justification>
  </clause>

  <clause id="7747">
    <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(1644(a,1),7400(a,1,2))].">
      <j1 rule="para" parents="1644 7400"/>
    </justification>
  </clause>

  <clause id="7748">
    <literal><![CDATA[
      K(R(T(x,y),z,u),L(y,w,v5)) = K(R(x,z,u),L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(199(a,1),7401(a,1,2))].">
      <j1 rule="para" parents="199 7401"/>
    </justification>
  </clause>

  <clause id="7749">
    <literal><![CDATA[
      K(x \ y,T(z,x * K(y,x))) = K(y / x,z)
    ]]></literal>
    <justification jstring="[para(4942(a,1),7405(a,1,2,2))].">
      <j1 rule="para" parents="4942 7405"/>
    </justification>
  </clause>

  <clause id="7750">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7544(a,1),7410(a,1,1))].">
      <j1 rule="para" parents="7544 7410"/>
    </justification>
  </clause>

  <clause id="7751">
    <literal><![CDATA[
      T(x,T(T(y * K(z,y \ u),w),T(u / y,z))) = T(x,T(u / T(u / y,z),w))
    ]]></literal>
    <justification jstring="[para(7239(a,1),7421(a,1,2,1,1))].">
      <j1 rule="para" parents="7239 7421"/>
    </justification>
  </clause>

  <clause id="7752">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = y * T(y \ T(x,y),T(z,T(x,y)))
    ]]></literal>
    <justification jstring="[para(4279(a,1),7433(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4279 7433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7753">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z / (z * y))
    ]]></literal>
    <justification jstring="[hyper(5650,a,7441,a),flip(a)].">
      <j1 rule="hyper" parents="5650 7441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7754">
    <literal><![CDATA[
      K(x,y / (y * z)) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7729,a(flip),b,7753,a),flip(a)].">
      <j1 rule="hyper" parents="63 7729 7753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7755">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(10(a,1),7753(a,2,2,2))].">
      <j1 rule="para" parents="10 7753"/>
    </justification>
  </clause>

  <clause id="7756">
    <literal><![CDATA[
      K(x,T(T(y,z),z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(z * x,x) / z,y) = u
    ]]></literal>
    <justification jstring="[para(7453(a,1),7485(a,1))].">
      <j1 rule="para" parents="7453 7485"/>
    </justification>
  </clause>

  <clause id="7757">
    <literal><![CDATA[
      T(x * K(x / K(y,z),u),K(z,y)) = K(z,y) \ T(x / K(y,z),T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(6147,a,7459,a)].">
      <j1 rule="hyper" parents="6147 7459"/>
    </justification>
  </clause>

  <clause id="7758">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w / R(T(x,y),z,u)) = v5
    ]]></literal>
    <justification jstring="[para(113(a,1),7486(a,1,2))].">
      <j1 rule="para" parents="113 7486"/>
    </justification>
  </clause>

  <clause id="7759">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(T(x,z),u,w) / y) = v5
    ]]></literal>
    <justification jstring="[para(7626(a,1),7486(a,1))].">
      <j1 rule="para" parents="7626 7486"/>
    </justification>
  </clause>

  <clause id="7760">
    <literal><![CDATA[
      T((x * y) / x,z) != (x * y) / u
    ]]></literal>
    <literal><![CDATA[
      x * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(7504(a,1),45(a,1))].">
      <j1 rule="para" parents="7504 45"/>
    </justification>
  </clause>

  <clause id="7761">
    <literal><![CDATA[
      T((x / y) * K(y,z),y) != u * K(y,z)
    ]]></literal>
    <literal><![CDATA[
      y \ x = u
    ]]></literal>
    <justification jstring="[para(7560(a,2),44(a,1))].">
      <j1 rule="para" parents="7560 44"/>
    </justification>
  </clause>

  <clause id="7762">
    <literal><![CDATA[
      K(x,1 / T(1 / y,z)) = K(x,y * K(1 / y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6329,a(flip),b,7568,a),flip(a)].">
      <j1 rule="hyper" parents="63 6329 7568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7763">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z)) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7578(a,2),43(a,1))].">
      <j1 rule="para" parents="7578 43"/>
    </justification>
  </clause>

  <clause id="7764">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7578(a,1),5066(a,1,1))].">
      <j1 rule="para" parents="7578 5066"/>
    </justification>
  </clause>

  <clause id="7765">
    <literal><![CDATA[
      T(x,T(T(y,z),y * u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(9(a,1),7583(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 7583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7766">
    <literal><![CDATA[
      ((x * K(y,x)) \ y) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(214,a,7606,a)].">
      <j1 rule="hyper" parents="214 7606"/>
    </justification>
  </clause>

  <clause id="7767">
    <literal><![CDATA[
      (R(x \ y,z,x \ y) / (x \ y)) * (y / x) = R((x \ y) * K(x,x \ y),z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,6071,a,b,7632,a)].">
      <j1 rule="hyper" parents="347 6071 7632"/>
    </justification>
  </clause>

  <clause id="7768">
    <literal><![CDATA[
      ((x \ y) * z) * K(x,T(x \ y,z)) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(347,a,5479,a(flip),b,7654,a),flip(a)].">
      <j1 rule="hyper" parents="347 5479 7654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7769">
    <literal><![CDATA[
      K(x \ (y \ z),y) * z = z * K((y \ z) / x,y)
    ]]></literal>
    <justification jstring="[para(7655(a,1),7104(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7655 7104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7770">
    <literal><![CDATA[
      K(x,T(R(y \ z,y,u),z * u)) = K(x,T((y * u) \ (z * u),y))
    ]]></literal>
    <justification jstring="[para(1033(a,1),7661(a,1,2,1))].">
      <j1 rule="para" parents="1033 7661"/>
    </justification>
  </clause>

  <clause id="7771">
    <literal><![CDATA[
      K(x,T(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(7661(a,1),7478(a,1))].">
      <j1 rule="para" parents="7661 7478"/>
    </justification>
  </clause>

  <clause id="7772">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(x * z) / y) = u
    ]]></literal>
    <justification jstring="[para(7167(a,1),7771(a,1))].">
      <j1 rule="para" parents="7167 7771"/>
    </justification>
  </clause>

  <clause id="7773">
    <literal><![CDATA[
      K(x,T(y,z \ (u * y))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(6461(a,1),7676(a,1,2))].">
      <j1 rule="para" parents="6461 7676"/>
    </justification>
  </clause>

  <clause id="7774">
    <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(7695(a,2),7281(a,1))].">
      <j1 rule="para" parents="7695 7281"/>
    </justification>
  </clause>

  <clause id="7775">
    <literal><![CDATA[
      K(x,y) * (y * T(x,z)) = T(x,T(z,y)) * y
    ]]></literal>
    <justification jstring="[para(7699(a,1),7713(a,1,2))].">
      <j1 rule="para" parents="7699 7713"/>
    </justification>
  </clause>

  <clause id="7776">
    <literal><![CDATA[
      (x / ((x \ y) \ 1)) / x = x \ (x / ((y / x) \ 1))
    ]]></literal>
    <justification jstring="[para(5302(a,1),7720(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5302 7720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7777">
    <literal><![CDATA[
      (T(x,y) * z) / T(x,z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(35,a,5922,a,b,7734,a)].">
      <j1 rule="hyper" parents="35 5922 7734"/>
    </justification>
  </clause>

  <clause id="7778">
    <literal><![CDATA[
      (K(x,y) * z) \ (T(x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(214,a,7777,a)].">
      <j1 rule="hyper" parents="214 7777"/>
    </justification>
  </clause>

  <clause id="7779">
    <literal><![CDATA[
      (1 / T(x,y)) \ (T(y,x) * (1 / x)) = T(y,1 / x)
    ]]></literal>
    <justification jstring="[para(5211(a,1),7778(a,1,1))].">
      <j1 rule="para" parents="5211 7778"/>
    </justification>
  </clause>

  <clause id="7780">
    <literal><![CDATA[
      x * (K(y,x) * K(y,x)) = (T(y,x) * x) / y
    ]]></literal>
    <justification jstring="[hyper(5519,a,7735,a)].">
      <j1 rule="hyper" parents="5519 7735"/>
    </justification>
  </clause>

  <clause id="7781">
    <literal><![CDATA[
      K(x,1) * ((y \ R(y,z,u)) / K(x,R(y,w,v5))) = K(R(y,w,v5),x) * (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(5801(a,1),7737(a,1,1,2))].">
      <j1 rule="para" parents="5801 7737"/>
    </justification>
  </clause>

  <clause id="7782">
    <literal><![CDATA[
      K(x,y) * (K(x * y,z) * x) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7079(a,1),7744(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7079 7744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7783">
    <literal><![CDATA[
      (K(x,y) * T(x,K(z,u))) \ x = K(z,K(u,x)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7261(a,1),7750(a,2,1))].">
      <j1 rule="para" parents="7261 7750"/>
    </justification>
  </clause>

  <clause id="7784">
    <literal><![CDATA[
      (x \ (y * K(x,y))) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5504(a,1),7766(a,1,1))].">
      <j1 rule="para" parents="5504 7766"/>
    </justification>
  </clause>

  <clause id="7785">
    <literal><![CDATA[
      K(x,T(y \ z,u \ z)) = K(x,T(y \ z,u \ y))
    ]]></literal>
    <justification jstring="[para(10(a,1),7773(a,1,2,2,2))].">
      <j1 rule="para" parents="10 7773"/>
    </justification>
  </clause>

  <clause id="7786">
    <literal><![CDATA[
      (x \ ((x * y) / x)) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4942(a,2),7784(a,1,1,2))].">
      <j1 rule="para" parents="4942 7784"/>
    </justification>
  </clause>

  <clause id="7787">
    <literal><![CDATA[
      K((1 / x) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(6256,a,7029,a),flip(a)].">
      <j1 rule="hyper" parents="6256 7029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7788">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,3881,a(flip),b,7029,a),flip(a)].">
      <j1 rule="hyper" parents="347 3881 7029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7789">
    <literal><![CDATA[
      K((x \ 1) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(5653,a,7787,a)].">
      <j1 rule="hyper" parents="5653 7787"/>
    </justification>
  </clause>

  <clause id="7790">
    <literal><![CDATA[
      K(T(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) * u = w
    ]]></literal>
    <justification jstring="[para(5256(a,1),7149(a,1))].">
      <j1 rule="para" parents="5256 7149"/>
    </justification>
  </clause>

  <clause id="7791">
    <literal><![CDATA[
      x * K(T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(y,T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(6117(a,1),7154(a,1))].">
      <j1 rule="para" parents="6117 7154"/>
    </justification>
  </clause>

  <clause id="7792">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6110(a,1),7155(a,1,1))].">
      <j1 rule="para" parents="6110 7155"/>
    </justification>
  </clause>

  <clause id="7793">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(7267(a,1),7272(a,1))].">
      <j1 rule="para" parents="7267 7272"/>
    </justification>
  </clause>

  <clause id="7794">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,T(x,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(7309(a,2),7272(a,1,2))].">
      <j1 rule="para" parents="7309 7272"/>
    </justification>
  </clause>

  <clause id="7795">
    <literal><![CDATA[
      K(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,z \ y),z) = u
    ]]></literal>
    <justification jstring="[para(7392(a,1),7793(a,1))].">
      <j1 rule="para" parents="7392 7793"/>
    </justification>
  </clause>

  <clause id="7796">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(7342(a,1),7361(a,1))].">
      <j1 rule="para" parents="7342 7361"/>
    </justification>
  </clause>

  <clause id="7797">
    <literal><![CDATA[
      T(K(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(2557(a,1),7796(a,1,1))].">
      <j1 rule="para" parents="2557 7796"/>
    </justification>
  </clause>

  <clause id="7798">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(z * K(x,y),x) = u
    ]]></literal>
    <justification jstring="[para(6121(a,1),7796(a,1,1))].">
      <j1 rule="para" parents="6121 7796"/>
    </justification>
  </clause>

  <clause id="7799">
    <literal><![CDATA[
      T(K(x,y \ z),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y \ z),y) = u
    ]]></literal>
    <justification jstring="[para(7069(a,1),7797(a,1))].">
      <j1 rule="para" parents="7069 7797"/>
    </justification>
  </clause>

  <clause id="7800">
    <literal><![CDATA[
      K(x / y,T(z,x \ y)) = K(y \ x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(7487,a,7457,a),flip(a)].">
      <j1 rule="hyper" parents="7487 7457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7801">
    <literal><![CDATA[
      K(x / y,T(z,x \ y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7390,a(flip),b,7800,a),flip(a)].">
      <j1 rule="hyper" parents="347 7390 7800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7802">
    <literal><![CDATA[
      T(x / y,T(z,x \ y)) = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,7801,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 7801 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7803">
    <literal><![CDATA[
      K(x,y) * L(T(z,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y) * L(z,u,w),x) = v5
    ]]></literal>
    <justification jstring="[para(25(a,2),7511(a,1,2))].">
      <j1 rule="para" parents="25 7511"/>
    </justification>
  </clause>

  <clause id="7804">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7263(a,1),7586(a,1))].">
      <j1 rule="para" parents="7263 7586"/>
    </justification>
  </clause>

  <clause id="7805">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((x / z) \ y,y) = u
    ]]></literal>
    <justification jstring="[para(7650(a,2),7588(a,1))].">
      <j1 rule="para" parents="7650 7588"/>
    </justification>
  </clause>

  <clause id="7806">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ (y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),z,y) = w
    ]]></literal>
    <justification jstring="[para(100(a,1),7608(a,1,2))].">
      <j1 rule="para" parents="100 7608"/>
    </justification>
  </clause>

  <clause id="7807">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,7039,a(flip),b,7623,a),flip(a)].">
      <j1 rule="hyper" parents="347 7039 7623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7808">
    <literal><![CDATA[
      L(K(x,y),z * x,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(7623(a,1),7618(a,1))].">
      <j1 rule="para" parents="7623 7618"/>
    </justification>
  </clause>

  <clause id="7809">
    <literal><![CDATA[
      T(x,T(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(7070(a,1),7684(a,1))].">
      <j1 rule="para" parents="7070 7684"/>
    </justification>
  </clause>

  <clause id="7811">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ z) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),7726(a,1,2,1,1))].">
      <j1 rule="para" parents="11 7726"/>
    </justification>
  </clause>

  <clause id="7813">
    <literal><![CDATA[
      K((x \ 1) * y,T(x \ 1,z)) = K(x \ y,T(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6935,a(flip),b,7788,a),flip(a)].">
      <j1 rule="hyper" parents="63 6935 7788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7814">
    <literal><![CDATA[
      T(K(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7072(a,1),7790(a,1,1))].">
      <j1 rule="para" parents="7072 7790"/>
    </justification>
  </clause>

  <clause id="7815">
    <literal><![CDATA[
      x * T(K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(7072(a,1),7791(a,1,2))].">
      <j1 rule="para" parents="7072 7791"/>
    </justification>
  </clause>

  <clause id="7816">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ y) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(7811,a,7755,a)].">
      <j1 rule="hyper" parents="7811 7755"/>
    </justification>
  </clause>

  <clause id="7817">
    <literal><![CDATA[
      K(x,(y * z) \ z) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(7811,a,7729,a)].">
      <j1 rule="hyper" parents="7811 7729"/>
    </justification>
  </clause>

  <clause id="7818">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(7811,a,xx),flip(a)].">
      <j1 rule="hyper" parents="7811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7819">
    <literal><![CDATA[
      K(x,y \ T(z,z \ y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(6346(a,1),7816(a,1,2))].">
      <j1 rule="para" parents="6346 7816"/>
    </justification>
  </clause>

  <clause id="7820">
    <literal><![CDATA[
      T(x,(y * z) \ z) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(132,a,7817,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 7817 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7821">
    <literal><![CDATA[
      K(x,(y / z) / y) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[para(749(a,1),7819(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="749 7819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7822">
    <literal><![CDATA[
      K(x,(y / z) / y) = K(x,y / (y * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7754,a,b,7821,a),flip(a)].">
      <j1 rule="hyper" parents="347 7754 7821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7823">
    <literal><![CDATA[
      K(L(K(x,y),z,u) \ 1,w) = L(K(y,K(x,w)),z,u)
    ]]></literal>
    <justification jstring="[para(7261(a,1),7010(a,2,1))].">
      <j1 rule="para" parents="7261 7010"/>
    </justification>
  </clause>

  <clause id="7824">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K(z / (y \ x),y)
    ]]></literal>
    <justification jstring="[hyper(7492,a,7031,a),flip(a)].">
      <j1 rule="hyper" parents="7492 7031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7825">
    <literal><![CDATA[
      T(x,T((y \ 1) / z,y)) = T(x,(y * y) \ (z \ y))
    ]]></literal>
    <justification jstring="[para(459(a,1),7082(a,2,2))].">
      <j1 rule="para" parents="459 7082"/>
    </justification>
  </clause>

  <clause id="7826">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(27(a,2),7106(a,2,2))].">
      <j1 rule="para" parents="27 7106"/>
    </justification>
  </clause>

  <clause id="7827">
    <literal><![CDATA[
      (x \ R(x,y,z)) * T(K(u,x),w) = R(x,y,z) * (x \ K(u,T(x,w)))
    ]]></literal>
    <justification jstring="[hyper(1766,a,7120,a),flip(a)].">
      <j1 rule="hyper" parents="1766 7120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7828">
    <literal><![CDATA[
      K(x,y) * K(x,T(z,y)) = x \ T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(5238,a,7152,a)].">
      <j1 rule="hyper" parents="5238 7152"/>
    </justification>
  </clause>

  <clause id="7829">
    <literal><![CDATA[
      K(x,y) * K(x,T(z,y)) = T(T(x,y),z) / x
    ]]></literal>
    <justification jstring="[hyper(347,a,4820,a,b,7828,a),flip(a)].">
      <j1 rule="hyper" parents="347 4820 7828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7830">
    <literal><![CDATA[
      K(x,y) * K(T(x,y),z) = T(T(x,y),z) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,7124,a,b,7829,a)].">
      <j1 rule="hyper" parents="63 7124 7829"/>
    </justification>
  </clause>

  <clause id="7831">
    <literal><![CDATA[
      x * K(y,L(T(z,x),u,w)) != v5 * v6
    ]]></literal>
    <literal><![CDATA[
      v5 \ (K(y,L(z,u,w)) * x) = v6
    ]]></literal>
    <justification jstring="[para(7173(a,2),613(a,1))].">
      <j1 rule="para" parents="7173 613"/>
    </justification>
  </clause>

  <clause id="7832">
    <literal><![CDATA[
      x * K(y,(1 / x) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(2944(a,1),7173(a,1,2,2))].">
      <j1 rule="para" parents="2944 7173"/>
    </justification>
  </clause>

  <clause id="7834">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = x * (L(x,z,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(134,a,7203,a(flip),b,5210,a)].">
      <j1 rule="hyper" parents="134 7203 5210"/>
    </justification>
  </clause>

  <clause id="7835">
    <literal><![CDATA[
      K(x,R(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6725,a,7221,a)].">
      <j1 rule="hyper" parents="6725 7221"/>
    </justification>
  </clause>

  <clause id="7836">
    <literal><![CDATA[
      T(x,R(y,z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,7835,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 7835 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7837">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (z / x))
    ]]></literal>
    <justification jstring="[para(607(a,1),7835(a,1,2))].">
      <j1 rule="para" parents="607 7835"/>
    </justification>
  </clause>

  <clause id="7838">
    <literal><![CDATA[
      K(x,R(y,z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2190(a,2),7835(a,1,2))].">
      <j1 rule="para" parents="2190 7835"/>
    </justification>
  </clause>

  <clause id="7840">
    <literal><![CDATA[
      T(x,T((y * x) / z,u)) = T(x,T(y / (z / x),u))
    ]]></literal>
    <justification jstring="[para(904(a,1),7836(a,1,2))].">
      <j1 rule="para" parents="904 7836"/>
    </justification>
  </clause>

  <clause id="7843">
    <literal><![CDATA[
      R(K(x,y),z,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6713,a(flip),b,7838,a)].">
      <j1 rule="hyper" parents="63 6713 7838"/>
    </justification>
  </clause>

  <clause id="7844">
    <literal><![CDATA[
      (K(x,y) * z) * (x \ 1) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(133,a,7843,a(flip),b,2253,a),flip(a)].">
      <j1 rule="hyper" parents="133 7843 2253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7846">
    <literal><![CDATA[
      T(x,K(y,x) * z) = z \ (x * z)
    ]]></literal>
    <justification jstring="[para(5155(a,1),7228(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5155 7228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7847">
    <literal><![CDATA[
      T(x,K(y,x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,22,a,b,7846,a),flip(a)].">
      <j1 rule="hyper" parents="347 22 7846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7848">
    <literal><![CDATA[
      T(x,K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(7846(a,2),360(a,1))].">
      <j1 rule="para" parents="7846 360"/>
    </justification>
  </clause>

  <clause id="7850">
    <literal><![CDATA[
      T(x,T(x,y) * z) = T(x,x * z)
    ]]></literal>
    <justification jstring="[para(4946(a,1),7847(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4946 7847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7851">
    <literal><![CDATA[
      T(x,K(x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5261(a,1),7847(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5261 7847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7853">
    <literal><![CDATA[
      T(x,y * T(z,x)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(5573(a,1),7847(a,1,2))].">
      <j1 rule="para" parents="5573 7847"/>
    </justification>
  </clause>

  <clause id="7854">
    <literal><![CDATA[
      T(x,y * K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7372(a,1),7847(a,1,2))].">
      <j1 rule="para" parents="7372 7847"/>
    </justification>
  </clause>

  <clause id="7855">
    <literal><![CDATA[
      T(x,y * K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7432(a,1),7847(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7432 7847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7856">
    <literal><![CDATA[
      T(x,K(x,y) * L(K(z,x),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,3063,a(flip),b,7851,a),flip(a)].">
      <j1 rule="hyper" parents="347 3063 7851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7857">
    <literal><![CDATA[
      K(x,K(x,y) * z) = x \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,7851,a(flip),b,4929,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 7851 4929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7858">
    <literal><![CDATA[
      T(x,y) * K(z,T(x,K(x,u) * y)) = T(x * K(z,x),K(x,u) * y)
    ]]></literal>
    <justification jstring="[para(7851(a,1),5308(a,1,1))].">
      <j1 rule="para" parents="7851 5308"/>
    </justification>
  </clause>

  <clause id="7859">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K((K(y,z) * u) / x,y) = w
    ]]></literal>
    <justification jstring="[para(7851(a,1),7492(a,1,2))].">
      <j1 rule="para" parents="7851 7492"/>
    </justification>
  </clause>

  <clause id="7860">
    <literal><![CDATA[
      K(T(x,y),(y * K(z,x)) \ u) = K(x,u / (y * K(z,x)))
    ]]></literal>
    <justification jstring="[para(7854(a,1),7402(a,1,1))].">
      <j1 rule="para" parents="7854 7402"/>
    </justification>
  </clause>

  <clause id="7863">
    <literal><![CDATA[
      (x * K(y,z)) * L(T(y,x),u,w) = L(y,u,w) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(7855(a,1),267(a,1,2,1))].">
      <j1 rule="para" parents="7855 267"/>
    </justification>
  </clause>

  <clause id="7865">
    <literal><![CDATA[
      T(x * K(y,z),L(T(y,x),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x * K(y,z),L(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(7855(a,1),4345(a,1,2,1))].">
      <j1 rule="para" parents="7855 4345"/>
    </justification>
  </clause>

  <clause id="7866">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y) = x * (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(7855(a,1),5108(a,1,2))].">
      <j1 rule="para" parents="7855 5108"/>
    </justification>
  </clause>

  <clause id="7867">
    <literal><![CDATA[
      T(x,y * (z * x)) = T(x,y * (x * z))
    ]]></literal>
    <justification jstring="[para(6977(a,1),7855(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6977 7855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7868">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(y,x)) = K(u / (x * K(y,z)),y)
    ]]></literal>
    <justification jstring="[para(7855(a,1),7390(a,1,2))].">
      <j1 rule="para" parents="7855 7390"/>
    </justification>
  </clause>

  <clause id="7869">
    <literal><![CDATA[
      T(T(x,y),T(x,z) * u) = T(T(x,x * u),y)
    ]]></literal>
    <justification jstring="[para(7850(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7850 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7870">
    <literal><![CDATA[
      K(x,K(x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,4924,a,b,7857,a),flip(a)].">
      <j1 rule="hyper" parents="347 4924 7857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7871">
    <literal><![CDATA[
      K(x,K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7857(a,2),5006(a,1))].">
      <j1 rule="para" parents="7857 5006"/>
    </justification>
  </clause>

  <clause id="7873">
    <literal><![CDATA[
      K(x,T(x,y) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(4974(a,1),7870(a,1,2))].">
      <j1 rule="para" parents="4974 7870"/>
    </justification>
  </clause>

  <clause id="7874">
    <literal><![CDATA[
      K(x,K(y,x) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5256(a,2),7870(a,1,2))].">
      <j1 rule="para" parents="5256 7870"/>
    </justification>
  </clause>

  <clause id="7875">
    <literal><![CDATA[
      K(x,T(x,y) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(5159(a,1),7870(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5159 7870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7876">
    <literal><![CDATA[
      K(x,T(y,x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5209(a,1),7870(a,1,2))].">
      <j1 rule="para" parents="5209 7870"/>
    </justification>
  </clause>

  <clause id="7877">
    <literal><![CDATA[
      K(x,y \ T(y * z,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5260(a,1),7870(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5260 7870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7878">
    <literal><![CDATA[
      K(x,(y / x) \ z) = K(x,(x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(5603(a,1),7870(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5603 7870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7879">
    <literal><![CDATA[
      K(x,y \ T(z,x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5456(a,1),7870(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5456 7870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7880">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(6697(a,1),7870(a,1,2,1))].">
      <j1 rule="para" parents="6697 7870"/>
    </justification>
  </clause>

  <clause id="7881">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[para(7870(a,1),7279(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7870 7279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7882">
    <literal><![CDATA[
      K(x,y * K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7373(a,1),7870(a,1,2))].">
      <j1 rule="para" parents="7373 7870"/>
    </justification>
  </clause>

  <clause id="7883">
    <literal><![CDATA[
      K(x,y * K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7427(a,1),7870(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7427 7870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7885">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = K(x,y) * K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7874(a,1),7266(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7874 7266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7886">
    <literal><![CDATA[
      K(x,K(y,x * K(y,z))) = 1
    ]]></literal>
    <justification jstring="[para(7882(a,2),3033(a,1,2))].">
      <j1 rule="para" parents="7882 3033"/>
    </justification>
  </clause>

  <clause id="7887">
    <literal><![CDATA[
      K(x,y * L(K(x,z),u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5660(a,1),7882(a,1,2,2))].">
      <j1 rule="para" parents="5660 7882"/>
    </justification>
  </clause>

  <clause id="7888">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[para(6047(a,1),7882(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6047 7882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7889">
    <literal><![CDATA[
      K(x,T(K(y,x) * z,u)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(6478(a,1),7882(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6478 7882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7890">
    <literal><![CDATA[
      K(x * K(y,z),z) = 1 / K(z,x)
    ]]></literal>
    <justification jstring="[hyper(220,a,7883,a(flip),b,5173,a),flip(a)].">
      <j1 rule="hyper" parents="220 7883 5173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7891">
    <literal><![CDATA[
      R(K(x,y),y * K(z,x),u) = K(x,y * K(z,x))
    ]]></literal>
    <justification jstring="[para(7883(a,1),5493(a,1,1))].">
      <j1 rule="para" parents="7883 5493"/>
    </justification>
  </clause>

  <clause id="7892">
    <literal><![CDATA[
      K(x,y \ R(T(z,x),u,w)) = K(x,y \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(5796(a,1),7883(a,1,2))].">
      <j1 rule="para" parents="5796 7883"/>
    </justification>
  </clause>

  <clause id="7893">
    <literal><![CDATA[
      K(x,T(x * K(y,z),y)) = K(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(7510(a,2),7873(a,1,2))].">
      <j1 rule="para" parents="7510 7873"/>
    </justification>
  </clause>

  <clause id="7894">
    <literal><![CDATA[
      K(x,y / T(x,z)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7184,a,b,7875,a)].">
      <j1 rule="hyper" parents="63 7184 7875"/>
    </justification>
  </clause>

  <clause id="7896">
    <literal><![CDATA[
      K(x,y \ (z / x)) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(113(a,1),7879(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 7879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7897">
    <literal><![CDATA[
      K(x * K(y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,5172,a(flip),b,7890,a),flip(a)].">
      <j1 rule="hyper" parents="347 5172 7890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7898">
    <literal><![CDATA[
      K(x * K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7890(a,2),5178(a,1))].">
      <j1 rule="para" parents="7890 5178"/>
    </justification>
  </clause>

  <clause id="7899">
    <literal><![CDATA[
      K(x * y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[para(91(a,1),7897(a,1,1))].">
      <j1 rule="para" parents="91 7897"/>
    </justification>
  </clause>

  <clause id="7900">
    <literal><![CDATA[
      K(x * T(y,z),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(1440(a,1),7897(a,1,1))].">
      <j1 rule="para" parents="1440 7897"/>
    </justification>
  </clause>

  <clause id="7901">
    <literal><![CDATA[
      K(x \ T(y,z),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(1438(a,1),7897(a,1,1))].">
      <j1 rule="para" parents="1438 7897"/>
    </justification>
  </clause>

  <clause id="7902">
    <literal><![CDATA[
      K(x * (y / z),z) = K(x * (z \ y),z)
    ]]></literal>
    <justification jstring="[para(5927(a,1),7897(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5927 7897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7903">
    <literal><![CDATA[
      K(x * K(y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6109(a,1),7897(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6109 7897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7904">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(6111(a,1),7897(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6111 7897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7905">
    <literal><![CDATA[
      K(x * K(y,T(z,u)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7093(a,1),7897(a,1,1,2))].">
      <j1 rule="para" parents="7093 7897"/>
    </justification>
  </clause>

  <clause id="7906">
    <literal><![CDATA[
      K(x * K(y,z \ u),u / z) = K(x,u / z)
    ]]></literal>
    <justification jstring="[para(7136(a,1),7897(a,1,1,2))].">
      <j1 rule="para" parents="7136 7897"/>
    </justification>
  </clause>

  <clause id="7907">
    <literal><![CDATA[
      K(K(x,y) * z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(7163(a,1),7897(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7163 7897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7908">
    <literal><![CDATA[
      K(x * (y \ 1),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,6226,a(flip),b,7899,a),flip(a)].">
      <j1 rule="hyper" parents="347 6226 7899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7909">
    <literal><![CDATA[
      K(x * (y / x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),7899(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 7899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7910">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(7899(a,2),5385(a,1,2))].">
      <j1 rule="para" parents="7899 5385"/>
    </justification>
  </clause>

  <clause id="7911">
    <literal><![CDATA[
      K(x * y,y) * K(y,x) = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[para(7899(a,2),5525(a,1,1))].">
      <j1 rule="para" parents="7899 5525"/>
    </justification>
  </clause>

  <clause id="7912">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5660(a,1),7903(a,1,1,2))].">
      <j1 rule="para" parents="5660 7903"/>
    </justification>
  </clause>

  <clause id="7913">
    <literal><![CDATA[
      K(R(x,y,z),u * K(x,w)) = R(x * K(u,x),y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(7903(a,1),5548(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7903 5548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7916">
    <literal><![CDATA[
      K(T(x,y) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(4974(a,1),7907(a,1,1))].">
      <j1 rule="para" parents="4974 7907"/>
    </justification>
  </clause>

  <clause id="7917">
    <literal><![CDATA[
      K(x * (K(y,z) * u),z) = K(x * u,z)
    ]]></literal>
    <justification jstring="[para(5885(a,1),7907(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5885 7907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7918">
    <literal><![CDATA[
      L(K(x,y),K(y,z) * x,u) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[para(7907(a,1),5959(a,1,1))].">
      <j1 rule="para" parents="7907 5959"/>
    </justification>
  </clause>

  <clause id="7919">
    <literal><![CDATA[
      K(R(K(x,y),z,u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(6697(a,1),7907(a,1,1,1))].">
      <j1 rule="para" parents="6697 7907"/>
    </justification>
  </clause>

  <clause id="7920">
    <literal><![CDATA[
      K(K(x,y) * z,T(x,u)) = K(z,T(x,u))
    ]]></literal>
    <justification jstring="[para(7380(a,1),7907(a,1,1,1))].">
      <j1 rule="para" parents="7380 7907"/>
    </justification>
  </clause>

  <clause id="7922">
    <literal><![CDATA[
      (x / T(y,x)) * ((y \ T(x,y)) \ z) = K(y,y \ x) * z
    ]]></literal>
    <justification jstring="[para(7894(a,1),5219(a,2,1))].">
      <j1 rule="para" parents="7894 5219"/>
    </justification>
  </clause>

  <clause id="7923">
    <literal><![CDATA[
      K((1 / ((x * y) \ x)) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[para(6293(a,1),7900(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6293 7900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7924">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (R(z,u,z) \ y),z)
    ]]></literal>
    <justification jstring="[para(7066(a,1),7900(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7066 7900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7925">
    <literal><![CDATA[
      T(x,y) \ ((T(y,x) \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4302,a,b,7901,a)].">
      <j1 rule="hyper" parents="63 4302 7901"/>
    </justification>
  </clause>

  <clause id="7926">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),7901(a,1,1,2))].">
      <j1 rule="para" parents="22 7901"/>
    </justification>
  </clause>

  <clause id="7927">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,7899,a(flip),b,7904,a),flip(a)].">
      <j1 rule="hyper" parents="347 7899 7904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7928">
    <literal><![CDATA[
      K(T(x,T(y,z)) * u,y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(5564(a,1),7905(a,1,1))].">
      <j1 rule="para" parents="5564 7905"/>
    </justification>
  </clause>

  <clause id="7930">
    <literal><![CDATA[
      K(x * (y / T(x,z)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),7927(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 7927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7931">
    <literal><![CDATA[
      T(x,(x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(y / x) * z) = u
    ]]></literal>
    <justification jstring="[para(5237(a,1),7848(a,1,2))].">
      <j1 rule="para" parents="5237 7848"/>
    </justification>
  </clause>

  <clause id="7932">
    <literal><![CDATA[
      K(x,(K(x,y) * z) * u) = K(x,z * u)
    ]]></literal>
    <justification jstring="[para(107(a,1),7880(a,1,2))].">
      <j1 rule="para" parents="107 7880"/>
    </justification>
  </clause>

  <clause id="7933">
    <literal><![CDATA[
      K(x,K(R(x,y,z),u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(6508(a,1),7880(a,1,2,1))].">
      <j1 rule="para" parents="6508 7880"/>
    </justification>
  </clause>

  <clause id="7934">
    <literal><![CDATA[
      K(x,y * (z * K(x,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(97(a,1),7887(a,1,2))].">
      <j1 rule="para" parents="97 7887"/>
    </justification>
  </clause>

  <clause id="7935">
    <literal><![CDATA[
      K(x * y,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,y) = z
    ]]></literal>
    <justification jstring="[para(91(a,1),7898(a,1,1))].">
      <j1 rule="para" parents="91 7898"/>
    </justification>
  </clause>

  <clause id="7936">
    <literal><![CDATA[
      K(x \ T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(1438(a,1),7898(a,1,1))].">
      <j1 rule="para" parents="1438 7898"/>
    </justification>
  </clause>

  <clause id="7937">
    <literal><![CDATA[
      K(K(x,y) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(7076(a,1),7898(a,1,1))].">
      <j1 rule="para" parents="7076 7898"/>
    </justification>
  </clause>

  <clause id="7938">
    <literal><![CDATA[
      K(x * (y * K(z,u)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(97(a,1),7912(a,1,1))].">
      <j1 rule="para" parents="97 7912"/>
    </justification>
  </clause>

  <clause id="7939">
    <literal><![CDATA[
      K(x * K(L(y,z,u),w),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7039(a,1),7912(a,1,1,2))].">
      <j1 rule="para" parents="7039 7912"/>
    </justification>
  </clause>

  <clause id="7940">
    <literal><![CDATA[
      K((K(x,y) * z) * u,x) = K(z * u,x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7919(a,1,1))].">
      <j1 rule="para" parents="107 7919"/>
    </justification>
  </clause>

  <clause id="7941">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(6508(a,1),7919(a,1,1,1))].">
      <j1 rule="para" parents="6508 7919"/>
    </justification>
  </clause>

  <clause id="7942">
    <literal><![CDATA[
      K(x,R(x,y,z) * u) = K(x,u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(4909(a,1),7933(a,1,2))].">
      <j1 rule="para" parents="4909 7933"/>
    </justification>
  </clause>

  <clause id="7943">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,(R(x,z,u) \ y) \ w)
    ]]></literal>
    <justification jstring="[para(5603(a,1),7933(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5603 7933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7944">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) * w) = K(x,R(x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(5236(a,1),7933(a,1,2))].">
      <j1 rule="para" parents="5236 7933"/>
    </justification>
  </clause>

  <clause id="7945">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) \ w) = K(x,R(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(5327(a,1),7933(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5327 7933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7946">
    <literal><![CDATA[
      K(x,T(y,T(z,R(x,u,w)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7234(a,1),7933(a,1,2))].">
      <j1 rule="para" parents="7234 7933"/>
    </justification>
  </clause>

  <clause id="7947">
    <literal><![CDATA[
      K(x,y * K(z,R(x,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7427(a,1),7933(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7427 7933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7950">
    <literal><![CDATA[
      K(K(x,y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(5256(a,2),7937(a,1,1))].">
      <j1 rule="para" parents="5256 7937"/>
    </justification>
  </clause>

  <clause id="7951">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) \ z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(5603(a,1),7937(a,1,1))].">
      <j1 rule="para" parents="5603 7937"/>
    </justification>
  </clause>

  <clause id="7952">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) = K(u * L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(91(a,1),7939(a,1,1))].">
      <j1 rule="para" parents="91 7939"/>
    </justification>
  </clause>

  <clause id="7953">
    <literal><![CDATA[
      K(K(L(x,y,z),u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(7104(a,1),7939(a,1,1))].">
      <j1 rule="para" parents="7104 7939"/>
    </justification>
  </clause>

  <clause id="7954">
    <literal><![CDATA[
      K(R(x,y,z) * u,x) = K(u * R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(4909(a,1),7941(a,1,1))].">
      <j1 rule="para" parents="4909 7941"/>
    </justification>
  </clause>

  <clause id="7955">
    <literal><![CDATA[
      K(T(x,R(y,z,u)) * w,y) = K(x * w,y)
    ]]></literal>
    <justification jstring="[para(4946(a,1),7941(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4946 7941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7956">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,T(x,v5)) = K(w,T(x,v5))
    ]]></literal>
    <justification jstring="[para(7401(a,1),7941(a,1,1,1))].">
      <j1 rule="para" parents="7401 7941"/>
    </justification>
  </clause>

  <clause id="7957">
    <literal><![CDATA[
      K(x,y / (z / R(x,u,w))) = K(x,y / (R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(6125(a,1),7947(a,1,2))].">
      <j1 rule="para" parents="6125 7947"/>
    </justification>
  </clause>

  <clause id="7958">
    <literal><![CDATA[
      K(x,T(y,K(L(x,z,u),w) * v5)) = K(x * K(v5,x),y)
    ]]></literal>
    <justification jstring="[para(7953(a,1),7408(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7953 7408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7959">
    <literal><![CDATA[
      T(x * K(y,T(x,z * (u * x))),y) = T(x,K(y,z * (x * u)))
    ]]></literal>
    <justification jstring="[para(7867(a,2),7564(a,1,1,2,2))].">
      <j1 rule="para" parents="7867 7564"/>
    </justification>
  </clause>

  <clause id="7960">
    <literal><![CDATA[
      K(x,(y / x) \ z) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,6767,a(flip),b,7878,a),flip(a)].">
      <j1 rule="hyper" parents="347 6767 7878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7961">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,7279,a,b,7881,a),flip(a)].">
      <j1 rule="hyper" parents="347 7279 7881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7963">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7837,a,b,7888,a)].">
      <j1 rule="hyper" parents="63 7837 7888"/>
    </justification>
  </clause>

  <clause id="7964">
    <literal><![CDATA[
      K(T(x,y),K(z,x) * u) = K(x,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7093,a,b,7889,a)].">
      <j1 rule="hyper" parents="63 7093 7889"/>
    </justification>
  </clause>

  <clause id="7965">
    <literal><![CDATA[
      K(x,T(T(x,y) \ z,u)) = K(x,T(x \ z,u))
    ]]></literal>
    <justification jstring="[para(5209(a,1),7889(a,1,2,1))].">
      <j1 rule="para" parents="5209 7889"/>
    </justification>
  </clause>

  <clause id="7966">
    <literal><![CDATA[
      K(x,T(y * K(x,z),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(7432(a,1),7889(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7432 7889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7967">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,y \ (z / x))
    ]]></literal>
    <justification jstring="[hyper(347,a,6784,a,b,7896,a)].">
      <j1 rule="hyper" parents="347 6784 7896"/>
    </justification>
  </clause>

  <clause id="7968">
    <literal><![CDATA[
      K(x * (K(y,z) * u),y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(5261(a,1),7917(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5261 7917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7971">
    <literal><![CDATA[
      K(x * y,T(y,z)) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4909(a,1),7920(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4909 7920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7972">
    <literal><![CDATA[
      K(T(x,y) * z,T(x,u)) = K(x * z,T(x,u))
    ]]></literal>
    <justification jstring="[para(4974(a,1),7920(a,1,1))].">
      <j1 rule="para" parents="4974 7920"/>
    </justification>
  </clause>

  <clause id="7973">
    <literal><![CDATA[
      K(x * T(y,z),T(y,u)) = K(x * y,T(y,u))
    ]]></literal>
    <justification jstring="[para(7699(a,1),7920(a,1,1))].">
      <j1 rule="para" parents="7699 7920"/>
    </justification>
  </clause>

  <clause id="7974">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6863,a(flip),b,7926,a),flip(a)].">
      <j1 rule="hyper" parents="63 6863 7926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7975">
    <literal><![CDATA[
      T(x * K(y * R(x,z,u),x),T(y,T(x,w))) = R(x,T(y,T(x,w)),R(x,z,u))
    ]]></literal>
    <justification jstring="[para(7928(a,1),5309(a,1,1,2))].">
      <j1 rule="para" parents="7928 5309"/>
    </justification>
  </clause>

  <clause id="7976">
    <literal><![CDATA[
      K(x,(T(y,x) * z) * u) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(4946(a,1),7932(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4946 7932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7977">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) * u) = K(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[para(5456(a,1),7932(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5456 7932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7978">
    <literal><![CDATA[
      K(x,(T(y,x) / z) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(5809(a,1),7932(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5809 7932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7979">
    <literal><![CDATA[
      T(x,y * (z * K(x,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(132,a,7934,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 7934 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7981">
    <literal><![CDATA[
      K(x,y * (z * K(u,x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(6109(a,1),7934(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6109 7934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7982">
    <literal><![CDATA[
      K(x,y * (z / T(u,x))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(6102(a,1),7934(a,1,2,2))].">
      <j1 rule="para" parents="6102 7934"/>
    </justification>
  </clause>

  <clause id="7983">
    <literal><![CDATA[
      K(x,y * (K(x,z) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(7104(a,1),7934(a,1,2,2))].">
      <j1 rule="para" parents="7104 7934"/>
    </justification>
  </clause>

  <clause id="7984">
    <literal><![CDATA[
      K(x * (y / T(z,u)),u) = K(x * (y / z),u)
    ]]></literal>
    <justification jstring="[para(6102(a,1),7938(a,1,1,2))].">
      <j1 rule="para" parents="6102 7938"/>
    </justification>
  </clause>

  <clause id="7985">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (y / T(z,u)),z)
    ]]></literal>
    <justification jstring="[para(6433(a,1),7938(a,1,1,2))].">
      <j1 rule="para" parents="6433 7938"/>
    </justification>
  </clause>

  <clause id="7986">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(x,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(7295,a,7961,a)].">
      <j1 rule="hyper" parents="7295 7961"/>
    </justification>
  </clause>

  <clause id="7987">
    <literal><![CDATA[
      K(x,K(y,T(x,z) * u)) = K(x,K(y,x * u))
    ]]></literal>
    <justification jstring="[para(4974(a,1),7961(a,1,2,2))].">
      <j1 rule="para" parents="4974 7961"/>
    </justification>
  </clause>

  <clause id="7988">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(5603(a,1),7961(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5603 7961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7989">
    <literal><![CDATA[
      K(x,K(y,z * K(u,x))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7427(a,1),7961(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7427 7961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7990">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,T(z,x)) = (y * z) / T(y,x)
    ]]></literal>
    <justification jstring="[para(7964(a,1),5363(a,1,2))].">
      <j1 rule="para" parents="7964 5363"/>
    </justification>
  </clause>

  <clause id="7991">
    <literal><![CDATA[
      K(x,T(y / (z / x),u)) = K(x,T(y / (x \ z),u))
    ]]></literal>
    <justification jstring="[para(6047(a,1),7966(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6047 7966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7992">
    <literal><![CDATA[
      K(x,(x * y) \ (z * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(11(a,1),7967(a,2,2,2))].">
      <j1 rule="para" parents="11 7967"/>
    </justification>
  </clause>

  <clause id="7993">
    <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(7968(a,1),5545(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7968 5545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7994">
    <literal><![CDATA[
      K(x * (K(y,z) * u),R(y,w,v5)) = R(y,w,v5) \ R(y * K(x * u,y),w,v5)
    ]]></literal>
    <justification jstring="[para(7968(a,1),5546(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7968 5546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7995">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6863,a(flip),b,7974,a),flip(a)].">
      <j1 rule="hyper" parents="63 6863 7974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7996">
    <literal><![CDATA[
      T(x,L(x,y,z) * (z * y)) = T(x,z * (y * x))
    ]]></literal>
    <justification jstring="[para(5957(a,1),7979(a,1,2))].">
      <j1 rule="para" parents="5957 7979"/>
    </justification>
  </clause>

  <clause id="7997">
    <literal><![CDATA[
      T(x,y * (K(x,z) * u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(7104(a,1),7979(a,1,2,2))].">
      <j1 rule="para" parents="7104 7979"/>
    </justification>
  </clause>

  <clause id="7998">
    <literal><![CDATA[
      T(x,y * T(z,K(x,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(7290(a,1),7979(a,1,2,2))].">
      <j1 rule="para" parents="7290 7979"/>
    </justification>
  </clause>

  <clause id="7999">
    <literal><![CDATA[
      K(x / y,z * (y * (x / y))) = K(x / y,z * x)
    ]]></literal>
    <justification jstring="[para(331(a,1),7981(a,1,2,2))].">
      <j1 rule="para" parents="331 7981"/>
    </justification>
  </clause>

  <clause id="8000">
    <literal><![CDATA[
      K(x,y * (z * L(K(u,x),w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(7006(a,1),7981(a,1,2,2,2))].">
      <j1 rule="para" parents="7006 7981"/>
    </justification>
  </clause>

  <clause id="8002">
    <literal><![CDATA[
      K(x,y * (T(z,x) \ u)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(5209(a,1),7983(a,1,2,2))].">
      <j1 rule="para" parents="5209 7983"/>
    </justification>
  </clause>

  <clause id="8003">
    <literal><![CDATA[
      K(x,y * (z * (K(u,x) * w))) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(5885(a,1),7983(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5885 7983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8004">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,7283,a(flip),b,7986,a),flip(a)].">
      <j1 rule="hyper" parents="347 7283 7986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8006">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(u,x)) = T(z * K(u,x),K(x,y))
    ]]></literal>
    <justification jstring="[para(7989(a,1),7304(a,1,1))].">
      <j1 rule="para" parents="7989 7304"/>
    </justification>
  </clause>

  <clause id="8007">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(10(a,1),7992(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 7992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8008">
    <literal><![CDATA[
      K(x \ (y * z),z) = K(x \ (z * y),z)
    ]]></literal>
    <justification jstring="[para(9(a,1),7995(a,1,1,2,1))].">
      <j1 rule="para" parents="9 7995"/>
    </justification>
  </clause>

  <clause id="8010">
    <literal><![CDATA[
      R(x,K(y,z) * u,K(u,K(y,w))) = x
    ]]></literal>
    <justification jstring="[para(8004(a,1),5950(a,1,3))].">
      <j1 rule="para" parents="8004 5950"/>
    </justification>
  </clause>

  <clause id="8011">
    <literal><![CDATA[
      K(x * K(y,z),K(y,u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7373(a,1),8004(a,1,1))].">
      <j1 rule="para" parents="7373 8004"/>
    </justification>
  </clause>

  <clause id="8012">
    <literal><![CDATA[
      R(x,K(y,z),T(u,K(y,w))) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(6674,a,8010,a)].">
      <j1 rule="hyper" parents="6674 8010"/>
    </justification>
  </clause>

  <clause id="8013">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * K(u,K(y,z)) = x * (u * K(y,z))
    ]]></literal>
    <justification jstring="[para(8010(a,1),596(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8010 596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8015">
    <literal><![CDATA[
      T(x,(x \ y) \ z) = T(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(132,a,8007,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 8007 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8016">
    <literal><![CDATA[
      K(x,(y / x) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,7878,a,b,8007,a)].">
      <j1 rule="hyper" parents="63 7878 8007"/>
    </justification>
  </clause>

  <clause id="8017">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6767,a(flip),b,8007,a),flip(a)].">
      <j1 rule="hyper" parents="63 6767 8007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8018">
    <literal><![CDATA[
      K(x,y \ (((x \ y) * z) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8007(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8019">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (x \ y)) \ u)
    ]]></literal>
    <justification jstring="[para(8007(a,1),6451(a,1,1))].">
      <j1 rule="para" parents="8007 6451"/>
    </justification>
  </clause>

  <clause id="8020">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ (u * y))) = K(x,T(y,(y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(8007(a,1),7267(a,1,2,2))].">
      <j1 rule="para" parents="8007 7267"/>
    </justification>
  </clause>

  <clause id="8022">
    <literal><![CDATA[
      K(x,T(y,(y \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(8015(a,2),7773(a,1,2))].">
      <j1 rule="para" parents="8015 7773"/>
    </justification>
  </clause>

  <clause id="8023">
    <literal><![CDATA[
      T(x,(y / x) \ z) = T(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(132,a,8016,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 8016 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8024">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (y / x)) \ u)
    ]]></literal>
    <justification jstring="[para(8016(a,1),6451(a,1,1))].">
      <j1 rule="para" parents="8016 6451"/>
    </justification>
  </clause>

  <clause id="8025">
    <literal><![CDATA[
      K(x,y \ ((x \ z) * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),8017(a,2,2,2))].">
      <j1 rule="para" parents="10 8017"/>
    </justification>
  </clause>

  <clause id="8026">
    <literal><![CDATA[
      L(T(x,y \ (z * x)),u,w) \ L(x,u,w) = K((y / x) \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(8023(a,1),4936(a,1,1,1))].">
      <j1 rule="para" parents="8023 4936"/>
    </justification>
  </clause>

  <clause id="8027">
    <literal><![CDATA[
      T(x,y \ ((x \ z) * x)) = x * K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(134,a,8025,a(flip),b,4924,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 8025 4924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8028">
    <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(5914(a,1),7910(a,1,2,1))].">
      <j1 rule="para" parents="5914 7910"/>
    </justification>
  </clause>

  <clause id="8029">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(22(a,1),7936(a,1,1,2))].">
      <j1 rule="para" parents="22 7936"/>
    </justification>
  </clause>

  <clause id="8030">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(113(a,1),7946(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 7946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8031">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y) = T(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(347,a,4953,a(flip),b,7866,a),flip(a)].">
      <j1 rule="hyper" parents="347 4953 7866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8033">
    <literal><![CDATA[
      K(x * T(y,z \ u),u / z) = K(x * y,u / z)
    ]]></literal>
    <justification jstring="[para(1440(a,1),7906(a,1,1))].">
      <j1 rule="para" parents="1440 7906"/>
    </justification>
  </clause>

  <clause id="8034">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[para(7908(a,1),5840(a,1,1,1))].">
      <j1 rule="para" parents="7908 5840"/>
    </justification>
  </clause>

  <clause id="8035">
    <literal><![CDATA[
      (T(x,y) \ y) * x != z * K(x \ y,x)
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(7925(a,1),143(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7925 143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8036">
    <literal><![CDATA[
      K((L(x,y,z) \ u) * L(x,y,z),x) = K(u,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),7952(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 7952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8037">
    <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(7972(a,1),5434(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7972 5434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8038">
    <literal><![CDATA[
      K(x,(T(T(y,x),z) / u) * w) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[para(23(a,1),7978(a,1,2,1,1))].">
      <j1 rule="para" parents="23 7978"/>
    </justification>
  </clause>

  <clause id="8039">
    <literal><![CDATA[
      K(x * (((y \ 1) \ z) / z),y) = K(x * (z \ ((y \ 1) \ z)),y)
    ]]></literal>
    <justification jstring="[para(4222(a,1),7984(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4222 7984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8040">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6407,a,b,8012,a)].">
      <j1 rule="hyper" parents="63 6407 8012"/>
    </justification>
  </clause>

  <clause id="8041">
    <literal><![CDATA[
      R(x,K(y,z),T(K(z,y) * u,K(y,w))) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(8012(a,2),5281(a,1,1))].">
      <j1 rule="para" parents="8012 5281"/>
    </justification>
  </clause>

  <clause id="8043">
    <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(8022(a,2),7521(a,1))].">
      <j1 rule="para" parents="8022 7521"/>
    </justification>
  </clause>

  <clause id="8044">
    <literal><![CDATA[
      K(x,y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7891(a,1),406(a,1)),flip(b)].">
      <j1 rule="para" parents="7891 406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8045">
    <literal><![CDATA[
      K(x,y \ T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(1438(a,1),8044(a,1,2))].">
      <j1 rule="para" parents="1438 8044"/>
    </justification>
  </clause>

  <clause id="8046">
    <literal><![CDATA[
      K(x,T(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(5564(a,1),8044(a,1,2))].">
      <j1 rule="para" parents="5564 8044"/>
    </justification>
  </clause>

  <clause id="8047">
    <literal><![CDATA[
      K(x,y \ (x \ (z * x))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(22(a,1),8045(a,1,2,2))].">
      <j1 rule="para" parents="22 8045"/>
    </justification>
  </clause>

  <clause id="8048">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(7808,a,7918,a)].">
      <j1 rule="hyper" parents="7808 7918"/>
    </justification>
  </clause>

  <clause id="8049">
    <literal><![CDATA[
      K(K(x,y) * z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(7918(a,1),401(a,1)),flip(b)].">
      <j1 rule="para" parents="7918 401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8050">
    <literal><![CDATA[
      K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,x) = z
    ]]></literal>
    <justification jstring="[para(4909(a,1),8049(a,1,1))].">
      <j1 rule="para" parents="4909 8049"/>
    </justification>
  </clause>

  <clause id="8052">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,7907,a(flip),b,8048,a),flip(a)].">
      <j1 rule="hyper" parents="347 7907 8048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8054">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(K(y,z) \ (x \ u),y)
    ]]></literal>
    <justification jstring="[para(329(a,1),8052(a,1,1))].">
      <j1 rule="para" parents="329 8052"/>
    </justification>
  </clause>

  <clause id="8057">
    <literal><![CDATA[
      K(x,(x * y) \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(6784(a,2),8047(a,1))].">
      <j1 rule="para" parents="6784 8047"/>
    </justification>
  </clause>

  <clause id="8058">
    <literal><![CDATA[
      (K(x \ y,z) * ((x \ y) \ u)) \ (K(x \ y,z) * u) = (x * K((x \ y) \ u,x \ y)) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,6104,a,b,7229,a),flip(a)].">
      <j1 rule="hyper" parents="347 6104 7229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8059">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K(z / (x \ y),y \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,6473,a,b,7233,a)].">
      <j1 rule="hyper" parents="347 6473 7233"/>
    </justification>
  </clause>

  <clause id="8060">
    <literal><![CDATA[
      (x * K(y,z)) * T(K(z,y),u) = x * K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(6109(a,1),7269(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6109 7269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8061">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(7814,a,7270,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="7814 7270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8062">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7270(a,2),7814(a,1))].">
      <j1 rule="para" parents="7270 7814"/>
    </justification>
  </clause>

  <clause id="8063">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ (z * L(K(x,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      z = v5
    ]]></literal>
    <justification jstring="[para(7376(a,1),356(a,1,2))].">
      <j1 rule="para" parents="7376 356"/>
    </justification>
  </clause>

  <clause id="8064">
    <literal><![CDATA[
      T(R(K(x,y),z,u),w) * w = w * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(27(a,1),7377(a,1,1))].">
      <j1 rule="para" parents="27 7377"/>
    </justification>
  </clause>

  <clause id="8065">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * (z * K(y,v5)) = (z * K(y,v5)) * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7855(a,1),7384(a,1,1,1,2))].">
      <j1 rule="para" parents="7855 7384"/>
    </justification>
  </clause>

  <clause id="8066">
    <literal><![CDATA[
      K(x * y,T(z,T(x,y))) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,7406,a(flip),b,7404,a),flip(a)].">
      <j1 rule="hyper" parents="63 7406 7404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8067">
    <literal><![CDATA[
      T(x,y) * K(x * y,T(z,x)) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8066(a,1),7104(a,1,2))].">
      <j1 rule="para" parents="8066 7104"/>
    </justification>
  </clause>

  <clause id="8068">
    <literal><![CDATA[
      T(x,L(y * K(z,y),u,w)) = T(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),7423(a,2,2))].">
      <j1 rule="para" parents="25 7423"/>
    </justification>
  </clause>

  <clause id="8069">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(y,x) * u) = K(y,T(x,z)) * u
    ]]></literal>
    <justification jstring="[para(7260(a,1),7446(a,1,1))].">
      <j1 rule="para" parents="7260 7446"/>
    </justification>
  </clause>

  <clause id="8070">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = K(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(7293(a,1),7446(a,1,1))].">
      <j1 rule="para" parents="7293 7446"/>
    </justification>
  </clause>

  <clause id="8071">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ K(y,x) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3088,a(flip),b,7469,a),flip(a)].">
      <j1 rule="hyper" parents="347 3088 7469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8073">
    <literal><![CDATA[
      x / (x * (y * K(z,y \ 1))) = T(x / (x * y),z)
    ]]></literal>
    <justification jstring="[para(6244(a,1),7506(a,1,2))].">
      <j1 rule="para" parents="6244 7506"/>
    </justification>
  </clause>

  <clause id="8074">
    <literal><![CDATA[
      K(x,(y * K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,6162,a(flip),b,7516,a),flip(a)].">
      <j1 rule="hyper" parents="347 6162 7516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8075">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(91(a,1),8074(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="91 8074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8076">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(6075(a,1),8074(a,1,2,1))].">
      <j1 rule="para" parents="6075 8074"/>
    </justification>
  </clause>

  <clause id="8077">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(6109(a,1),8074(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6109 8074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8078">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * (x * z)) \ u)
    ]]></literal>
    <justification jstring="[para(6977(a,1),8074(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6977 8074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8079">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7087(a,1),8074(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7087 8074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8080">
    <literal><![CDATA[
      K(x,(K(x,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7104(a,1),8074(a,1,2,1))].">
      <j1 rule="para" parents="7104 8074"/>
    </justification>
  </clause>

  <clause id="8082">
    <literal><![CDATA[
      1 / K((x * y) \ z,x) = K(x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,5172,a,b,8075,a)].">
      <j1 rule="hyper" parents="347 5172 8075"/>
    </justification>
  </clause>

  <clause id="8083">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,6784,a(flip),b,8075,a),flip(a)].">
      <j1 rule="hyper" parents="347 6784 8075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8084">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = (y * T(y \ u,x)) \ u
    ]]></literal>
    <justification jstring="[hyper(347,a,6162,a,b,8077,a),flip(a)].">
      <j1 rule="hyper" parents="347 6162 8077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8085">
    <literal><![CDATA[
      K(T(x,y),(z * K(u,x)) \ w) = K(T(x,y),z \ w)
    ]]></literal>
    <justification jstring="[para(7138(a,1),8077(a,1,2,1,2))].">
      <j1 rule="para" parents="7138 8077"/>
    </justification>
  </clause>

  <clause id="8086">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[hyper(132,a,8079,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 8079 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8087">
    <literal><![CDATA[
      K(x,y \ T(x,z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6455,a(flip),b,8080,a),flip(a)].">
      <j1 rule="hyper" parents="63 6455 8080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8088">
    <literal><![CDATA[
      K(x,(y * z) \ ((K(x,u) * y) * z)) = K(x,a(K(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(14(a,2),8080(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14 8080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8089">
    <literal><![CDATA[
      K(x,(y * (K(z,x) * u)) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(5885(a,1),8080(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5885 8080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8090">
    <literal><![CDATA[
      K(x,T(y \ x,z)) = K(x,T(y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7237,a(flip),b,8087,a)].">
      <j1 rule="hyper" parents="63 7237 8087"/>
    </justification>
  </clause>

  <clause id="8091">
    <literal><![CDATA[
      K(x,L(x \ y,x,z)) = K(x,z \ (x \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6454,a,b,8083,a)].">
      <j1 rule="hyper" parents="63 6454 8083"/>
    </justification>
  </clause>

  <clause id="8092">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(T(z,x),x,y))
    ]]></literal>
    <justification jstring="[para(263(a,1),8083(a,1,2)),flip(a)].">
      <j1 rule="para" parents="263 8083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8093">
    <literal><![CDATA[
      L(K(x,y \ (x \ z)),u * x,w) = K(L(x,u,w),(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(8083(a,1),7039(a,1,1))].">
      <j1 rule="para" parents="8083 7039"/>
    </justification>
  </clause>

  <clause id="8095">
    <literal><![CDATA[
      K(x,(y * z) \ (z * x)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,6462,a,b,8090,a)].">
      <j1 rule="hyper" parents="347 6462 8090"/>
    </justification>
  </clause>

  <clause id="8096">
    <literal><![CDATA[
      T(x,T(y \ x,z)) = T(x,T(y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(132,a,8090,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 8090 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8097">
    <literal><![CDATA[
      T(x,T((1 / y) \ x,z)) * K(T(y \ 1,z) \ 1,x) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(8096(a,2),5648(a,1,1))].">
      <j1 rule="para" parents="8096 5648"/>
    </justification>
  </clause>

  <clause id="8098">
    <literal><![CDATA[
      K((x * y) \ z,y) = K((y * x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,5172,a,b,8082,a)].">
      <j1 rule="hyper" parents="36 5172 8082"/>
    </justification>
  </clause>

  <clause id="8099">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,6855,a(flip),b,8098,a),flip(a)].">
      <j1 rule="hyper" parents="347 6855 8098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8100">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,7926,a(flip),b,8099,a),flip(a)].">
      <j1 rule="hyper" parents="347 7926 8099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8101">
    <literal><![CDATA[
      x * K(y \ (z \ x),z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[hyper(134,a,8099,a(flip),b,6596,a)].">
      <j1 rule="hyper" parents="134 8099 6596"/>
    </justification>
  </clause>

  <clause id="8102">
    <literal><![CDATA[
      L(x * K(y \ (x \ z),x),u,w) / L(x,u,w) = K((y * x) \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(8099(a,1),5542(a,1,1,1,2))].">
      <j1 rule="para" parents="8099 5542"/>
    </justification>
  </clause>

  <clause id="8103">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(8099(a,2),8029(a,1))].">
      <j1 rule="para" parents="8099 8029"/>
    </justification>
  </clause>

  <clause id="8104">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,z \ ((y \ z) * x))
    ]]></literal>
    <justification jstring="[para(10(a,1),8095(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 8095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8105">
    <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(4229(a,1),8091(a,2,2,2,2))].">
      <j1 rule="para" parents="4229 8091"/>
    </justification>
  </clause>

  <clause id="8106">
    <literal><![CDATA[
      K((x * y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ (y \ z),y) = u
    ]]></literal>
    <justification jstring="[para(7995(a,1),8103(a,1))].">
      <j1 rule="para" parents="7995 8103"/>
    </justification>
  </clause>

  <clause id="8107">
    <literal><![CDATA[
      K((x * y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ z),x) = u
    ]]></literal>
    <justification jstring="[para(8098(a,1),8106(a,1))].">
      <j1 rule="para" parents="8098 8106"/>
    </justification>
  </clause>

  <clause id="8108">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ z),x) = u
    ]]></literal>
    <justification jstring="[para(6491(a,2),8107(a,1))].">
      <j1 rule="para" parents="6491 8107"/>
    </justification>
  </clause>

  <clause id="8109">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7265,a(flip),b,7519,a),flip(a)].">
      <j1 rule="hyper" parents="347 7265 7519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8110">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),K(u,y) \ z)
    ]]></literal>
    <justification jstring="[para(6883(a,1),8109(a,1,2))].">
      <j1 rule="para" parents="6883 8109"/>
    </justification>
  </clause>

  <clause id="8111">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,T(x,x * u))) = T(K(x,y),T(z,u * x))
    ]]></literal>
    <justification jstring="[para(4323(a,1),7524(a,1,2,2,2))].">
      <j1 rule="para" parents="4323 7524"/>
    </justification>
  </clause>

  <clause id="8112">
    <literal><![CDATA[
      (x \ y) * K(x / y,y) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,1572,a(flip),b,7550,a),flip(a)].">
      <j1 rule="hyper" parents="63 1572 7550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8115">
    <literal><![CDATA[
      T(K(x,y),z / (1 / y)) = K(x,1 / (z / (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(63,a,5536,a(flip),b,7569,a)].">
      <j1 rule="hyper" parents="63 5536 7569"/>
    </justification>
  </clause>

  <clause id="8116">
    <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(7581(a,1),755(a,1,2))].">
      <j1 rule="para" parents="7581 755"/>
    </justification>
  </clause>

  <clause id="8117">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(7771,a,7620,a),flip(a)].">
      <j1 rule="hyper" parents="7771 7620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8118">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) * u != u * w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z / (x \ y),u)) = w
    ]]></literal>
    <justification jstring="[para(8117(a,2),7174(a,1,1))].">
      <j1 rule="para" parents="8117 7174"/>
    </justification>
  </clause>

  <clause id="8119">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8079,a(flip),b,7639,a),flip(a)].">
      <j1 rule="hyper" parents="63 8079 7639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8121">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,x) * w))) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(5885(a,1),8119(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5885 8119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8122">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,y)) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(39,a,7558,a(flip),b,7658,a),flip(a)].">
      <j1 rule="hyper" parents="39 7558 7658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8123">
    <literal><![CDATA[
      K(x * K(y,z),(x / u) \ 1) = K(K(y,z) * x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(35,a,7242,a,b,7687,a)].">
      <j1 rule="hyper" parents="35 7242 7687"/>
    </justification>
  </clause>

  <clause id="8124">
    <literal><![CDATA[
      K(x,T(y,K(y * T(x,y),z))) * ((K(y * T(x,y),z) * y) * x) = (x * y) * R(K(x * y,z),y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,3662,a,b,7707,a),flip(a)].">
      <j1 rule="hyper" parents="347 3662 7707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8125">
    <literal><![CDATA[
      (K(x,T(y,z)) * (z * (y * x))) \ ((z * y) * T(x,y)) = L(a(z,y,x),z * (y * x),K(x,T(y,z)))
    ]]></literal>
    <justification jstring="[para(7707(a,1),567(a,1,2))].">
      <j1 rule="para" parents="7707 567"/>
    </justification>
  </clause>

  <clause id="8126">
    <literal><![CDATA[
      T(x / T(T(y,x),z),y) = T(y,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,5198,a(flip),b,7712,a),flip(a)].">
      <j1 rule="hyper" parents="347 5198 7712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8127">
    <literal><![CDATA[
      T(T(x,y) / T(T(L(x,z,u),T(x,y)),w),L(x,z,u)) = T(L(x,z,u),w) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(239(a,1),8126(a,2,2))].">
      <j1 rule="para" parents="239 8126"/>
    </justification>
  </clause>

  <clause id="8128">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * z,x)) = T(T(x,y) * z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),7732(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 7732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8129">
    <literal><![CDATA[
      K(x,y * K(1 / y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5536,a(flip),b,7762,a),flip(a)].">
      <j1 rule="hyper" parents="63 5536 7762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8130">
    <literal><![CDATA[
      K(x,y * K(1 / y,z * y)) = T(K(x,y),z / (1 / y))
    ]]></literal>
    <justification jstring="[para(5778(a,1),8129(a,1,2,2))].">
      <j1 rule="para" parents="5778 8129"/>
    </justification>
  </clause>

  <clause id="8131">
    <literal><![CDATA[
      K((x \ y) / z,x) = K(y / (x * z),x)
    ]]></literal>
    <justification jstring="[hyper(34,a,7548,a(flip),b,7769,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 7548 7769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8132">
    <literal><![CDATA[
      x * ((x / ((x \ y) \ 1)) / x) = x / ((y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,7776,a,b,xx)].">
      <j1 rule="hyper" parents="134 7776"/>
    </justification>
  </clause>

  <clause id="8133">
    <literal><![CDATA[
      (1 / T(x,y)) \ (T(y,x) * (1 / x)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,2962,a(flip),b,7779,a),flip(a)].">
      <j1 rule="hyper" parents="347 2962 7779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8134">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(L(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(7015(a,1),7823(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7015 7823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8135">
    <literal><![CDATA[
      R(K(x,T(y,z)),y * u,w) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(7091(a,2),7826(a,1,1))].">
      <j1 rule="para" parents="7091 7826"/>
    </justification>
  </clause>

  <clause id="8136">
    <literal><![CDATA[
      L(x \ 1,y,K(x,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(3558,a,7844,a)].">
      <j1 rule="hyper" parents="3558 7844"/>
    </justification>
  </clause>

  <clause id="8137">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[para(8136(a,1),1014(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8136 1014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8138">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,7266,a(flip),b,7885,a),flip(a)].">
      <j1 rule="hyper" parents="347 7266 7885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8139">
    <literal><![CDATA[
      T((x \ R(T(y,z),u,w)) * K(z,x \ R(y,u,w)),z) = x \ R(T(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(7892(a,1),5058(a,1,1,2))].">
      <j1 rule="para" parents="7892 5058"/>
    </justification>
  </clause>

  <clause id="8141">
    <literal><![CDATA[
      K(x,y) * (z * K(y,T(z,x))) = (y * z) / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7161,a(flip),b,7990,a)].">
      <j1 rule="hyper" parents="63 7161 7990"/>
    </justification>
  </clause>

  <clause id="8143">
    <literal><![CDATA[
      T(x,T(y / (z / x),u)) = T(x,T(y / (x \ z),u))
    ]]></literal>
    <justification jstring="[hyper(132,a,7991,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 7991 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8145">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K(z * ((x \ y) \ 1),x / y)
    ]]></literal>
    <justification jstring="[para(6275(a,1),8033(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6275 8033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8146">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(7950,a,8054,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="7950 8054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8147">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * (z * y)) \ u,z)
    ]]></literal>
    <justification jstring="[para(6977(a,1),8146(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6977 8146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8148">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ u,y)
    ]]></literal>
    <justification jstring="[para(7087(a,1),8146(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7087 8146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8149">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,x) = K(z \ u,x)
    ]]></literal>
    <justification jstring="[para(7104(a,1),8146(a,1,1,1))].">
      <j1 rule="para" parents="7104 8146"/>
    </justification>
  </clause>

  <clause id="8150">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(7380(a,1),8146(a,1,1,1,2))].">
      <j1 rule="para" parents="7380 8146"/>
    </justification>
  </clause>

  <clause id="8151">
    <literal><![CDATA[
      K(x \ K(y,z),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5996,a(flip),b,8148,a),flip(a)].">
      <j1 rule="hyper" parents="63 5996 8148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8153">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) * (y \ K(u,z)) = T(y \ K(u,z),K(x,z))
    ]]></literal>
    <justification jstring="[para(8151(a,1),7285(a,1,1,2))].">
      <j1 rule="para" parents="8151 7285"/>
    </justification>
  </clause>

  <clause id="8154">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7021,a(flip),b,8149,a),flip(a)].">
      <j1 rule="hyper" parents="63 7021 8149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8156">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(5261(a,1),8154(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5261 8154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8157">
    <literal><![CDATA[
      K(x \ (y / z),z \ y) = K(x \ (z \ y),z \ y)
    ]]></literal>
    <justification jstring="[para(5252(a,1),8154(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5252 8154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8158">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(7380(a,1),8154(a,1,1,2,1))].">
      <j1 rule="para" parents="7380 8154"/>
    </justification>
  </clause>

  <clause id="8159">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(7373(a,1),8154(a,1,1,2))].">
      <j1 rule="para" parents="7373 8154"/>
    </justification>
  </clause>

  <clause id="8160">
    <literal><![CDATA[
      K(x \ (y / (z * y)),z \ 1) = K(x \ ((z * y) \ y),z \ 1)
    ]]></literal>
    <justification jstring="[para(5628(a,1),8156(a,1,1,2))].">
      <j1 rule="para" parents="5628 8156"/>
    </justification>
  </clause>

  <clause id="8161">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(x \ (y * (u * z)),u)
    ]]></literal>
    <justification jstring="[para(6977(a,1),8159(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6977 8159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8162">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),T(z,w)) = K(x \ y,T(z,w))
    ]]></literal>
    <justification jstring="[para(7380(a,1),8159(a,1,1,2,2))].">
      <j1 rule="para" parents="7380 8159"/>
    </justification>
  </clause>

  <clause id="8163">
    <literal><![CDATA[
      (x \ R(x,y,x)) * T(K(y,x),z) = K(y * x,x) * K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(7911(a,1),8060(a,1,1))].">
      <j1 rule="para" parents="7911 8060"/>
    </justification>
  </clause>

  <clause id="8164">
    <literal><![CDATA[
      T(R(K(x,y),z,u) \ w,R(K(x,y),z,u)) = w / R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(269,a,8064,a(flip),b,4158,a(flip))].">
      <j1 rule="hyper" parents="269 8064 4158"/>
    </justification>
  </clause>

  <clause id="8165">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * (x \ z)) \ u)) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(8076(a,1),5267(a,1,2,2))].">
      <j1 rule="para" parents="8076 5267"/>
    </justification>
  </clause>

  <clause id="8166">
    <literal><![CDATA[
      L(K(x,(y * (x * z)) \ u),w * x,v5) = K(L(x,w,v5),(y * (z * x)) \ u)
    ]]></literal>
    <justification jstring="[para(8078(a,1),7039(a,1,1))].">
      <j1 rule="para" parents="8078 7039"/>
    </justification>
  </clause>

  <clause id="8167">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(8084(a,2),6203(a,1))].">
      <j1 rule="para" parents="8084 6203"/>
    </justification>
  </clause>

  <clause id="8168">
    <literal><![CDATA[
      K(x,(T(y,x) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(5564(a,1),8167(a,1,2,1))].">
      <j1 rule="para" parents="5564 8167"/>
    </justification>
  </clause>

  <clause id="8169">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = y * K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,4849,a,b,8101,a)].">
      <j1 rule="hyper" parents="347 4849 8101"/>
    </justification>
  </clause>

  <clause id="8170">
    <literal><![CDATA[
      (x * K((y \ 1) \ (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,8101,a,b,4878,a(flip))].">
      <j1 rule="hyper" parents="133 8101 4878"/>
    </justification>
  </clause>

  <clause id="8171">
    <literal><![CDATA[
      (x * y) * K(x \ (z \ (x * y)),z) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8101(a,2,2,1,2))].">
      <j1 rule="para" parents="9 8101"/>
    </justification>
  </clause>

  <clause id="8172">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(8101(a,1),6141(a,1,1))].">
      <j1 rule="para" parents="8101 6141"/>
    </justification>
  </clause>

  <clause id="8173">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,8138,a(flip),b,8110,a),flip(a)].">
      <j1 rule="hyper" parents="347 8138 8110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8175">
    <literal><![CDATA[
      T(K(x,y),z * K(y,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6117(a,1),8173(a,1,2))].">
      <j1 rule="para" parents="6117 8173"/>
    </justification>
  </clause>

  <clause id="8176">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u * K(z,w)) = R(x,K(y,z),u * K(z,w))
    ]]></literal>
    <justification jstring="[para(8175(a,1),8040(a,1,2))].">
      <j1 rule="para" parents="8175 8040"/>
    </justification>
  </clause>

  <clause id="8177">
    <literal><![CDATA[
      K(x,L(L(y,z,K(u,x)),K(u,x) * z,w)) = K(x,(w * (K(u,x) * z)) \ (w * (z * y)))
    ]]></literal>
    <justification jstring="[para(542(a,1),8121(a,1,2))].">
      <j1 rule="para" parents="542 8121"/>
    </justification>
  </clause>

  <clause id="8178">
    <literal><![CDATA[
      K(x,y \ (z * (u * x))) = K(x,y \ (z * (x * u)))
    ]]></literal>
    <justification jstring="[para(4909(a,1),8121(a,1,2,2,2))].">
      <j1 rule="para" parents="4909 8121"/>
    </justification>
  </clause>

  <clause id="8179">
    <literal><![CDATA[
      K(x,y \ (z * (u / x))) = K(x,y \ (z * (x \ u)))
    ]]></literal>
    <justification jstring="[para(5027(a,1),8121(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5027 8121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8180">
    <literal><![CDATA[
      T(T(x,y) * R(x \ z,u,w),x) = T(x,y) * R(x \ T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(1720(a,1),8128(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1720 8128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8181">
    <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(2024(a,1),8128(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2024 8128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8182">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ u,w)) = R(K(x,T(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),8135(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 8135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8183">
    <literal><![CDATA[
      K(x,y) * (R(z,u,w) * K(y,R(T(z,x),u,w))) = (y * R(z,u,w)) / T(y,x)
    ]]></literal>
    <justification jstring="[para(27(a,2),8141(a,1,2,2,2))].">
      <j1 rule="para" parents="27 8141"/>
    </justification>
  </clause>

  <clause id="8184">
    <literal><![CDATA[
      T(x,T((y * x) / z,u)) = T(x,T(y / (x \ z),u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7840,a,b,8143,a)].">
      <j1 rule="hyper" parents="63 7840 8143"/>
    </justification>
  </clause>

  <clause id="8185">
    <literal><![CDATA[
      K(((x \ 1) * (y * x)) \ z,x) = K(L(y,x,x \ 1) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3920,a(flip),b,8147,a),flip(a)].">
      <j1 rule="hyper" parents="347 3920 8147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8186">
    <literal><![CDATA[
      R((x \ y) * K(z \ (x \ y),x \ y),u,w) \ R(x \ y,u,w) = K(R(x \ y,u,w),z \ (y / x))
    ]]></literal>
    <justification jstring="[para(8157(a,1),5548(a,1,1,1,2))].">
      <j1 rule="para" parents="8157 5548"/>
    </justification>
  </clause>

  <clause id="8187">
    <literal><![CDATA[
      K(x \ (y * z),T(z,u)) = K(x \ (z * y),T(z,u))
    ]]></literal>
    <justification jstring="[para(4909(a,1),8158(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4909 8158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8188">
    <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(542(a,1),8161(a,2,1))].">
      <j1 rule="para" parents="542 8161"/>
    </justification>
  </clause>

  <clause id="8189">
    <literal><![CDATA[
      (x * y) * K(y \ (z \ (x * y)),z) = ((z \ x) * z) * y
    ]]></literal>
    <justification jstring="[para(11(a,1),8169(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 8169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8190">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ (z * (x \ u))) = K(x,(z * (u / x)) \ (y \ (z * (u / x))))
    ]]></literal>
    <justification jstring="[hyper(63,a,7817,a(flip),b,8179,a),flip(a)].">
      <j1 rule="hyper" parents="63 7817 8179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8191">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,600,a(flip),b,8182,a),flip(a)].">
      <j1 rule="hyper" parents="347 600 8182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8192">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7091,a(flip),b,8191,a),flip(a)].">
      <j1 rule="hyper" parents="347 7091 8191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8193">
    <literal><![CDATA[
      K(x \ (y * (z * K(y,u))),T(y,w)) = K(x \ (z * T(y,u)),T(y,w))
    ]]></literal>
    <justification jstring="[para(5914(a,1),8187(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5914 8187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8194">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,2327,a(flip),b,7001,a),flip(a)].">
      <j1 rule="hyper" parents="347 2327 7001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8196">
    <literal><![CDATA[
      L(x,y,z) * K(1 / x,x) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(8194(a,1),1959(a,1,2))].">
      <j1 rule="para" parents="8194 1959"/>
    </justification>
  </clause>

  <clause id="8197">
    <literal><![CDATA[
      K(1 / x,x) \ (R(1 / L(x,y,z),L(x,y,z),K(1 / x,x)) * ((u * (1 / (1 / L(x,y,z)))) / u)) = K(u,1 / (K(1 / x,x) \ R(1 / L(x,y,z),L(x,y,z),K(1 / x,x))))
    ]]></literal>
    <justification jstring="[para(8196(a,1),6382(a,1,2,2,1,2))].">
      <j1 rule="para" parents="8196 6382"/>
    </justification>
  </clause>

  <clause id="8198">
    <literal><![CDATA[
      K((((x \ y) \ 1) * (x \ 1)) \ 1,z) / (x \ T(y,z)) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[para(7020(a,1),6089(a,1,1))].">
      <j1 rule="para" parents="7020 6089"/>
    </justification>
  </clause>

  <clause id="8199">
    <literal><![CDATA[
      K(L(x,y / x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(7038(a,2),545(a,1))].">
      <j1 rule="para" parents="7038 545"/>
    </justification>
  </clause>

  <clause id="8200">
    <literal><![CDATA[
      R(x \ R(x,y,x),x,z) = (z * R(x,y,x)) / (z * x)
    ]]></literal>
    <justification jstring="[para(3675(a,1),7232(a,1,1))].">
      <j1 rule="para" parents="3675 7232"/>
    </justification>
  </clause>

  <clause id="8201">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * z != v5 * v6
    ]]></literal>
    <literal><![CDATA[
      (z * K(x,L(y,u,w))) / v6 = v5
    ]]></literal>
    <justification jstring="[para(25(a,2),7436(a,1,1,2))].">
      <j1 rule="para" parents="25 7436"/>
    </justification>
  </clause>

  <clause id="8202">
    <literal><![CDATA[
      T(K(x,y) * z,x) / z = K(z,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7561,a,4814,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="7561 4814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8203">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = T(x \ R(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(6905(a,1),7562(a,1,2))].">
      <j1 rule="para" parents="6905 7562"/>
    </justification>
  </clause>

  <clause id="8204">
    <literal><![CDATA[
      T(x \ R(x,y,x),y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5385,a(flip),b,8203,a),flip(a)].">
      <j1 rule="hyper" parents="63 5385 8203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8205">
    <literal><![CDATA[
      (x * (y \ R(y,x,y))) / x = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(305,a,8204,a)].">
      <j1 rule="hyper" parents="305 8204"/>
    </justification>
  </clause>

  <clause id="8206">
    <literal><![CDATA[
      (T(x * y,x) / x) / y = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(6377(a,1),8205(a,1,1))].">
      <j1 rule="para" parents="6377 8205"/>
    </justification>
  </clause>

  <clause id="8207">
    <literal><![CDATA[
      (x \ R(x,y \ 1,x)) / (T(x * (y \ 1),x) / x) = y
    ]]></literal>
    <justification jstring="[hyper(131,a,8206,a(flip),b,6949,a(flip))].">
      <j1 rule="hyper" parents="131 8206 6949"/>
    </justification>
  </clause>

  <clause id="8208">
    <literal><![CDATA[
      K(1 / T(T(x,y),y * x),z) = K(1 / L(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(4330(a,1),7567(a,1,1,2))].">
      <j1 rule="para" parents="4330 7567"/>
    </justification>
  </clause>

  <clause id="8209">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,y) = K(x,y) * (z * K(u,y))
    ]]></literal>
    <justification jstring="[para(7668(a,1),7609(a,1,2,2))].">
      <j1 rule="para" parents="7668 7609"/>
    </justification>
  </clause>

  <clause id="8210">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (u * K(y,x))) = T(K(z,x) * u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(134,a,8209,a(flip),b,7345,a)].">
      <j1 rule="hyper" parents="134 8209 7345"/>
    </justification>
  </clause>

  <clause id="8211">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,y,z)) * (L(x,u,w) \ x) = (L(x,u,w) \ 1) * x
    ]]></literal>
    <justification jstring="[para(7617(a,2),2995(a,1,1))].">
      <j1 rule="para" parents="7617 2995"/>
    </justification>
  </clause>

  <clause id="8212">
    <literal><![CDATA[
      L(K(x,T(y,z)),z,L(y,u,w)) = K(x,T(y,L(y,u,w) * (y \ z)))
    ]]></literal>
    <justification jstring="[para(1410(a,1),7659(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1410 7659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8213">
    <literal><![CDATA[
      T(x * K(y,x),K(z,y)) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7330(a,1),7763(a,1))].">
      <j1 rule="para" parents="7330 7763"/>
    </justification>
  </clause>

  <clause id="8214">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(7772,a,8117,a)].">
      <j1 rule="hyper" parents="7772 8117"/>
    </justification>
  </clause>

  <clause id="8215">
    <literal><![CDATA[
      K(x,(x \ y) / (x \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(10(a,1),8214(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 8214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8216">
    <literal><![CDATA[
      K(x,(x \ y) / (z / x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7888,a,b,8215,a)].">
      <j1 rule="hyper" parents="63 7888 8215"/>
    </justification>
  </clause>

  <clause id="8217">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(11(a,1),8216(a,1,2,2))].">
      <j1 rule="para" parents="11 8216"/>
    </justification>
  </clause>

  <clause id="8218">
    <literal><![CDATA[
      K(x,(x * y) / (z * x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8217(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 8217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8219">
    <literal><![CDATA[
      K(x / (y \ z),y) = K((z / x) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(7805,a,7824,a),flip(a)].">
      <j1 rule="hyper" parents="7805 7824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8220">
    <literal><![CDATA[
      (x * K((y / z) \ u,u)) \ x = K(u,z / (u \ y))
    ]]></literal>
    <justification jstring="[para(8219(a,1),6123(a,1,1,2))].">
      <j1 rule="para" parents="8219 6123"/>
    </justification>
  </clause>

  <clause id="8221">
    <literal><![CDATA[
      K(x,y / (x \ z)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(6141,a,8220,a),flip(a)].">
      <j1 rule="hyper" parents="6141 8220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8222">
    <literal><![CDATA[
      K(x,y / (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(8220(a,1),6141(a,1))].">
      <j1 rule="para" parents="8220 6141"/>
    </justification>
  </clause>

  <clause id="8223">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8214,a,b,8221,a)].">
      <j1 rule="hyper" parents="63 8214 8221"/>
    </justification>
  </clause>

  <clause id="8224">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8117,a,b,8221,a)].">
      <j1 rule="hyper" parents="63 8117 8221"/>
    </justification>
  </clause>

  <clause id="8225">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7963,a,b,8221,a)].">
      <j1 rule="hyper" parents="63 7963 8221"/>
    </justification>
  </clause>

  <clause id="8226">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7888,a,b,8221,a)].">
      <j1 rule="hyper" parents="63 7888 8221"/>
    </justification>
  </clause>

  <clause id="8227">
    <literal><![CDATA[
      K(x,((x * y) / z) \ x) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),8221(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8228">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),z / u,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[para(8221(a,1),6709(a,1,1))].">
      <j1 rule="para" parents="8221 6709"/>
    </justification>
  </clause>

  <clause id="8229">
    <literal><![CDATA[
      K(x,(L(y,z,u) / y) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(1994(a,1),8223(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1994 8223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8230">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),y) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(7795,a,8225,a)].">
      <j1 rule="hyper" parents="7795 8225"/>
    </justification>
  </clause>

  <clause id="8231">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(7711,a,8225,a)].">
      <j1 rule="hyper" parents="7711 8225"/>
    </justification>
  </clause>

  <clause id="8232">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(132,a,8225,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 8225 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8233">
    <literal><![CDATA[
      K(x,(K(y,x * z) * (y \ (x * z))) \ x) = K(x,R(y,y \ (x * z),y) / z)
    ]]></literal>
    <justification jstring="[para(7249(a,1),8227(a,1,2,1))].">
      <j1 rule="para" parents="7249 8227"/>
    </justification>
  </clause>

  <clause id="8234">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) * u = u * K(x,T((y / z) \ x,u))
    ]]></literal>
    <justification jstring="[para(8224(a,2),7104(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8224 7104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8235">
    <literal><![CDATA[
      K(x,T((y / z) \ x,y)) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(7382,a,8230,a)].">
      <j1 rule="hyper" parents="7382 8230"/>
    </justification>
  </clause>

  <clause id="8236">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * x)) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(80(a,1),8235(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="80 8235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8237">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8104,a,b,8236,a)].">
      <j1 rule="hyper" parents="63 8104 8236"/>
    </justification>
  </clause>

  <clause id="8238">
    <literal><![CDATA[
      K(x,y \ (x * (z \ y))) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,8017,a(flip),b,8236,a)].">
      <j1 rule="hyper" parents="63 8017 8236"/>
    </justification>
  </clause>

  <clause id="8239">
    <literal><![CDATA[
      K(x,(y \ (z * (u \ y))) \ K(z,T(u \ z,y))) = K(x,z \ ((y \ (z * (u \ y))) \ z))
    ]]></literal>
    <justification jstring="[para(8238(a,1),7731(a,1,2,2))].">
      <j1 rule="para" parents="8238 7731"/>
    </justification>
  </clause>

  <clause id="8240">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(7963(a,2),8222(a,1))].">
      <j1 rule="para" parents="7963 8222"/>
    </justification>
  </clause>

  <clause id="8241">
    <literal><![CDATA[
      K(x,(x * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(8214(a,2),8222(a,1))].">
      <j1 rule="para" parents="8214 8222"/>
    </justification>
  </clause>

  <clause id="8242">
    <literal><![CDATA[
      K(x,T(y,K(L(x,z,u),w) * v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,7408,a(flip),b,7958,a),flip(a)].">
      <j1 rule="hyper" parents="347 7408 7958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8243">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) * (u * z))) = K(x,T(y,u * (z * x)))
    ]]></literal>
    <justification jstring="[para(4911(a,1),8242(a,1,2,2))].">
      <j1 rule="para" parents="4911 8242"/>
    </justification>
  </clause>

  <clause id="8244">
    <literal><![CDATA[
      (T(x,y) \ y) * ((x \ y) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(8035,a,6128,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8035 6128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8245">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,5097,a(flip),b,8092,a),flip(a)].">
      <j1 rule="hyper" parents="347 5097 8092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8246">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z,x,y)) = u
    ]]></literal>
    <justification jstring="[para(8092(a,2),5152(a,1))].">
      <j1 rule="para" parents="8092 5152"/>
    </justification>
  </clause>

  <clause id="8247">
    <literal><![CDATA[
      K(((x \ 1) \ y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(8108,a,6374,a),flip(a)].">
      <j1 rule="hyper" parents="8108 6374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8248">
    <literal><![CDATA[
      K((x \ 1) \ (y \ z),y) = K((x \ y) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3912,a(flip),b,8247,a),flip(a)].">
      <j1 rule="hyper" parents="63 3912 8247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8249">
    <literal><![CDATA[
      K((x \ y) \ (z * y),y) = K((x \ 1) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(8029,a,8248,a),flip(a)].">
      <j1 rule="hyper" parents="8029 8248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8250">
    <literal><![CDATA[
      T(x,(y \ x) \ (z * x)) = 1 / (x \ K((y \ 1) \ z,x))
    ]]></literal>
    <justification jstring="[para(8249(a,1),5044(a,2,2,2))].">
      <j1 rule="para" parents="8249 5044"/>
    </justification>
  </clause>

  <clause id="8251">
    <literal><![CDATA[
      K(1 / T(x,y),T(z,y * x)) = K(1 / L(x,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7095,a(flip),b,8208,a)].">
      <j1 rule="hyper" parents="63 7095 8208"/>
    </justification>
  </clause>

  <clause id="8252">
    <literal><![CDATA[
      K(1 / x,T(T(y,z * x),z)) = K(1 / L(x,z,x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7095,a(flip),b,8251,a)].">
      <j1 rule="hyper" parents="63 7095 8251"/>
    </justification>
  </clause>

  <clause id="8253">
    <literal><![CDATA[
      K(1 / x,T(T(y,z),z * x)) = K(1 / L(x,z,x),y)
    ]]></literal>
    <justification jstring="[para(23(a,1),8252(a,1,2))].">
      <j1 rule="para" parents="23 8252"/>
    </justification>
  </clause>

  <clause id="8254">
    <literal><![CDATA[
      L(T(K(x,y),z),z,K(x,u)) = K(T(1 / x,K(x,u) * z) \ 1,y)
    ]]></literal>
    <justification jstring="[para(6560(a,1),7011(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6560 7011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8255">
    <literal><![CDATA[
      L(K(x,y),z,u) \ w = L(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(5660(a,1),7013(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5660 7013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8256">
    <literal><![CDATA[
      L(K(x,y),z,u) * (L(K(y,x),z,u) * w) = w
    ]]></literal>
    <justification jstring="[hyper(358,a,8255,a)].">
      <j1 rule="hyper" parents="358 8255"/>
    </justification>
  </clause>

  <clause id="8257">
    <literal><![CDATA[
      L(K(x,y),z,u) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) * w = v5
    ]]></literal>
    <justification jstring="[para(8256(a,1),356(a,1,2))].">
      <j1 rule="para" parents="8256 356"/>
    </justification>
  </clause>

  <clause id="8258">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5660,a(flip),b,7014,a),flip(a)].">
      <j1 rule="hyper" parents="63 5660 7014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8259">
    <literal><![CDATA[
      x / L(K(y,z),u,w) = x * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(220,a,5660,a(flip),b,7014,a(flip))].">
      <j1 rule="hyper" parents="220 5660 7014"/>
    </justification>
  </clause>

  <clause id="8263">
    <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(8258(a,1),143(a,1,2))].">
      <j1 rule="para" parents="8258 143"/>
    </justification>
  </clause>

  <clause id="8264">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) = L(K(u,z),y,x)
    ]]></literal>
    <justification jstring="[para(97(a,1),8258(a,1,1))].">
      <j1 rule="para" parents="97 8258"/>
    </justification>
  </clause>

  <clause id="8265">
    <literal><![CDATA[
      (x * ((x \ y) * K(z,u))) \ y = L(K(u,z),x \ y,x)
    ]]></literal>
    <justification jstring="[para(476(a,1),8258(a,1,1))].">
      <j1 rule="para" parents="476 8258"/>
    </justification>
  </clause>

  <clause id="8266">
    <literal><![CDATA[
      L(K(x,y),z * K(y,x),u) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6136,a,b,8264,a)].">
      <j1 rule="hyper" parents="63 6136 8264"/>
    </justification>
  </clause>

  <clause id="8267">
    <literal><![CDATA[
      L(K(x,y),z,L(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(8264(a,1),6921(a,1))].">
      <j1 rule="para" parents="8264 6921"/>
    </justification>
  </clause>

  <clause id="8268">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * u) = L(K(z,T(y,u)),u,x)
    ]]></literal>
    <justification jstring="[para(7076(a,1),8264(a,1,1,2))].">
      <j1 rule="para" parents="7076 8264"/>
    </justification>
  </clause>

  <clause id="8269">
    <literal><![CDATA[
      K(x,L(y,z,L(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8267,a,7610,a),flip(a)].">
      <j1 rule="hyper" parents="8267 7610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8270">
    <literal><![CDATA[
      K(L(x,y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(8267,a,7039,a),flip(a)].">
      <j1 rule="hyper" parents="8267 7039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8271">
    <literal><![CDATA[
      L(K(x,y),z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(398(a,1),8267(a,1,3))].">
      <j1 rule="para" parents="398 8267"/>
    </justification>
  </clause>

  <clause id="8272">
    <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(4353(a,1),8270(a,1,1))].">
      <j1 rule="para" parents="4353 8270"/>
    </justification>
  </clause>

  <clause id="8273">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(8265(a,1),6499(a,1))].">
      <j1 rule="para" parents="8265 6499"/>
    </justification>
  </clause>

  <clause id="8274">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(K(z \ x,z) * y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6601,a(flip),b,7048,a)].">
      <j1 rule="hyper" parents="63 6601 7048"/>
    </justification>
  </clause>

  <clause id="8275">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(7205,a,8274,a),flip(a)].">
      <j1 rule="hyper" parents="7205 8274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8277">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(8274(a,1),7205(a,1))].">
      <j1 rule="para" parents="8274 7205"/>
    </justification>
  </clause>

  <clause id="8279">
    <literal><![CDATA[
      (K(x \ y,x) * z) * K(z,y) = T(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,8275,a(flip),b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 8275 4924"/>
    </justification>
  </clause>

  <clause id="8280">
    <literal><![CDATA[
      K(K(x,y) * z,x * y) = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(5143(a,1),8275(a,1,1,1))].">
      <j1 rule="para" parents="5143 8275"/>
    </justification>
  </clause>

  <clause id="8281">
    <literal><![CDATA[
      K(T(x,y) * z,y * x) = K(x * z,y * x)
    ]]></literal>
    <justification jstring="[para(4946(a,1),8280(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4946 8280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8282">
    <literal><![CDATA[
      K(K(x,y) * z,x * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x * y) = u
    ]]></literal>
    <justification jstring="[para(5143(a,1),8277(a,1,1,1))].">
      <j1 rule="para" parents="5143 8277"/>
    </justification>
  </clause>

  <clause id="8283">
    <literal><![CDATA[
      K(((x \ y) \ y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(5340(a,2),8277(a,1,1))].">
      <j1 rule="para" parents="5340 8277"/>
    </justification>
  </clause>

  <clause id="8284">
    <literal><![CDATA[
      K((x \ y) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) * z,y) = u
    ]]></literal>
    <justification jstring="[para(5578(a,1),8277(a,1,1))].">
      <j1 rule="para" parents="5578 8277"/>
    </justification>
  </clause>

  <clause id="8285">
    <literal><![CDATA[
      R(K(x,y),z,R(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2387,a,7223,a)].">
      <j1 rule="hyper" parents="2387 7223"/>
    </justification>
  </clause>

  <clause id="8286">
    <literal><![CDATA[
      (x * (K(y,x) * z)) * R(y,u,w) = K(y,x) * ((x * z) * R(y,u,w))
    ]]></literal>
    <justification jstring="[para(5353(a,1),7223(a,1,1))].">
      <j1 rule="para" parents="5353 7223"/>
    </justification>
  </clause>

  <clause id="8287">
    <literal><![CDATA[
      (x * (K(x,y) * (z * R(x,u,w)))) \ ((T(x,y) * z) * R(x,u,w)) = a(x,K(x,y) * z,R(x,u,w))
    ]]></literal>
    <justification jstring="[para(7223(a,1),5166(a,1,1,2))].">
      <j1 rule="para" parents="7223 5166"/>
    </justification>
  </clause>

  <clause id="8288">
    <literal><![CDATA[
      K(x,R(y,z,R(x,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6716,a(flip),b,8285,a)].">
      <j1 rule="hyper" parents="63 6716 8285"/>
    </justification>
  </clause>

  <clause id="8289">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (w / R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6710,a(flip),b,8285,a)].">
      <j1 rule="hyper" parents="63 6710 8285"/>
    </justification>
  </clause>

  <clause id="8290">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,6508,a(flip),b,8285,a)].">
      <j1 rule="hyper" parents="63 6508 8285"/>
    </justification>
  </clause>

  <clause id="8291">
    <literal><![CDATA[
      K(x,T((y * R(x,z,u)) / w,w / R(x,z,u))) = K(x,(w / R(x,z,u)) \ y)
    ]]></literal>
    <justification jstring="[para(1038(a,1),8288(a,1,2))].">
      <j1 rule="para" parents="1038 8288"/>
    </justification>
  </clause>

  <clause id="8292">
    <literal><![CDATA[
      T(T(x,1 / y),K(1 / y,z)) = T(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,4929,a,b,7244,a),flip(a)].">
      <j1 rule="hyper" parents="347 4929 7244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8293">
    <literal><![CDATA[
      T(x,1 / T(y,z)) = T(x,T(1 / y,z))
    ]]></literal>
    <justification jstring="[hyper(7539,a,8292,a),flip(a)].">
      <j1 rule="hyper" parents="7539 8292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8294">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(7261(a,1),7268(a,1,1))].">
      <j1 rule="para" parents="7261 7268"/>
    </justification>
  </clause>

  <clause id="8295">
    <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),7299(a,1,2,1))].">
      <j1 rule="para" parents="12 7299"/>
    </justification>
  </clause>

  <clause id="8296">
    <literal><![CDATA[
      T(x,K(y,z)) * (K(z,T(y,x)) * u) = x * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(7091(a,2),7347(a,1,2,1))].">
      <j1 rule="para" parents="7091 7347"/>
    </justification>
  </clause>

  <clause id="8297">
    <literal><![CDATA[
      R(K(x,y),T(y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(7415(a,2),7484(a,1))].">
      <j1 rule="para" parents="7415 7484"/>
    </justification>
  </clause>

  <clause id="8298">
    <literal><![CDATA[
      L(K(x,y),z * T(x,u),w) = K(L(x,z,w),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,7399,a(flip),b,7416,a),flip(a)].">
      <j1 rule="hyper" parents="347 7399 7416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8300">
    <literal><![CDATA[
      L(K(x,y),x * z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(111(a,1),8298(a,1,2))].">
      <j1 rule="para" parents="111 8298"/>
    </justification>
  </clause>

  <clause id="8301">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(249(a,1),8298(a,1,2)),flip(a)].">
      <j1 rule="para" parents="249 8298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8302">
    <literal><![CDATA[
      K(L(x,y,z),x * y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(6256,a,8300,a),flip(a)].">
      <j1 rule="hyper" parents="6256 8300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8303">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7610,a(flip),b,8300,a),flip(a)].">
      <j1 rule="hyper" parents="63 7610 8300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8304">
    <literal><![CDATA[
      K(L(x,y,z),(z \ u) \ (x * y)) = K(x,u \ (z * (x * y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6450,a(flip),b,8300,a),flip(a)].">
      <j1 rule="hyper" parents="63 6450 8300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8305">
    <literal><![CDATA[
      K(L(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,549,a(flip),b,8301,a),flip(a)].">
      <j1 rule="hyper" parents="347 549 8301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8306">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(L(x,T(x,y) \ 1,u),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7399,a(flip),b,8305,a),flip(a)].">
      <j1 rule="hyper" parents="63 7399 8305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8307">
    <literal><![CDATA[
      K(L(x,T(x,y) \ 1,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(7477,a,8306,a),flip(a)].">
      <j1 rule="hyper" parents="7477 8306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8308">
    <literal><![CDATA[
      K(L(x,T(x,y) \ 1,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(8306(a,1),7477(a,1))].">
      <j1 rule="para" parents="8306 7477"/>
    </justification>
  </clause>

  <clause id="8310">
    <literal><![CDATA[
      K(L(x,x \ K(y,x),z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(4934(a,1),8307(a,1,1,2))].">
      <j1 rule="para" parents="4934 8307"/>
    </justification>
  </clause>

  <clause id="8311">
    <literal><![CDATA[
      L(K(x,y),K(z,x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8301,a(flip),b,8310,a)].">
      <j1 rule="hyper" parents="63 8301 8310"/>
    </justification>
  </clause>

  <clause id="8312">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,8311,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 8311 18"/>
    </justification>
  </clause>

  <clause id="8313">
    <literal><![CDATA[
      L(L(K(x,y),z,u),K(w,x),v5) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8311(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8311 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8314">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,z) * K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(8311(a,1),322(a,1,2))].">
      <j1 rule="para" parents="8311 322"/>
    </justification>
  </clause>

  <clause id="8315">
    <literal><![CDATA[
      (x * K(y,z)) * R(K(z,u),w,v5) = x * (K(y,z) * R(K(z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(8311(a,1),475(a,1,2,1))].">
      <j1 rule="para" parents="8311 475"/>
    </justification>
  </clause>

  <clause id="8316">
    <literal><![CDATA[
      x / L(L(K(y,z),u,w),K(v5,y),v6) = x * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(220,a,8313,a,b,8258,a)].">
      <j1 rule="hyper" parents="220 8313 8258"/>
    </justification>
  </clause>

  <clause id="8317">
    <literal><![CDATA[
      (x * (K(y,z) * K(z,u))) * K(u,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6138,a,8312,a)].">
      <j1 rule="hyper" parents="6138 8312"/>
    </justification>
  </clause>

  <clause id="8318">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(594,a,8312,a)].">
      <j1 rule="hyper" parents="594 8312"/>
    </justification>
  </clause>

  <clause id="8319">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(u,y) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6569,a,b,8312,a)].">
      <j1 rule="hyper" parents="63 6569 8312"/>
    </justification>
  </clause>

  <clause id="8320">
    <literal><![CDATA[
      x * (K(y,z) * K(z,z * y)) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,6435,a(flip),b,8312,a),flip(a)].">
      <j1 rule="hyper" parents="63 6435 8312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8321">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(2556(a,2),8312(a,2,2))].">
      <j1 rule="para" parents="2556 8312"/>
    </justification>
  </clause>

  <clause id="8322">
    <literal><![CDATA[
      R(x,T(K(y,z),u),K(z,w)) = x
    ]]></literal>
    <justification jstring="[para(1832(a,1),8318(a,1,2))].">
      <j1 rule="para" parents="1832 8318"/>
    </justification>
  </clause>

  <clause id="8323">
    <literal><![CDATA[
      (x * R(R(x,K(y,z),K(z,u)) \ (x * K(y,z)),w,v5)) * K(z,u) = R(x,K(y,z),K(z,u)) * (R(K(y,z),w,v5) * K(z,u))
    ]]></literal>
    <justification jstring="[para(8318(a,1),2676(a,1,1,1))].">
      <j1 rule="para" parents="8318 2676"/>
    </justification>
  </clause>

  <clause id="8324">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(8318(a,1),5961(a,1,1))].">
      <j1 rule="para" parents="8318 5961"/>
    </justification>
  </clause>

  <clause id="8325">
    <literal><![CDATA[
      R(x,L(K(y,z),u,w),K(z,v5)) = x
    ]]></literal>
    <justification jstring="[para(7006(a,1),8318(a,1,2))].">
      <j1 rule="para" parents="7006 8318"/>
    </justification>
  </clause>

  <clause id="8326">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) * K(z,v5) = x * (L(K(y,z),u,w) * K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(133,a,8325,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 8325 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8327">
    <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(8325(a,1),616(a,1,1))].">
      <j1 rule="para" parents="8325 616"/>
    </justification>
  </clause>

  <clause id="8328">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) = K(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,2556,a,b,8324,a),flip(a)].">
      <j1 rule="hyper" parents="347 2556 8324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8329">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,x / y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4309,a(flip),b,8324,a),flip(a)].">
      <j1 rule="hyper" parents="63 4309 8324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8330">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (u * L(T(x,w),y,z)) = K(u,L(x,y,z)) * K(L(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(25(a,2),8324(a,1,2,2))].">
      <j1 rule="para" parents="25 8324"/>
    </justification>
  </clause>

  <clause id="8332">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5528,a,b,8329,a)].">
      <j1 rule="hyper" parents="63 5528 8329"/>
    </justification>
  </clause>

  <clause id="8333">
    <literal><![CDATA[
      a(x,y / x,x) \ K(y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(8329(a,1),6123(a,1,1))].">
      <j1 rule="para" parents="8329 6123"/>
    </justification>
  </clause>

  <clause id="8334">
    <literal><![CDATA[
      a(x,(x * y) / x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),8332(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8335">
    <literal><![CDATA[
      x \ R(x,T(y,x),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(255(a,1),8334(a,1,2)),flip(a)].">
      <j1 rule="para" parents="255 8334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8336">
    <literal><![CDATA[
      x \ R(x,y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(4408(a,1),8335(a,1,2))].">
      <j1 rule="para" parents="4408 8335"/>
    </justification>
  </clause>

  <clause id="8337">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5526,a,8336,a)].">
      <j1 rule="hyper" parents="5526 8336"/>
    </justification>
  </clause>

  <clause id="8338">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5516,a,8336,a)].">
      <j1 rule="hyper" parents="5516 8336"/>
    </justification>
  </clause>

  <clause id="8339">
    <literal><![CDATA[
      x * a(x,y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(150,a,8336,a)].">
      <j1 rule="hyper" parents="150 8336"/>
    </justification>
  </clause>

  <clause id="8340">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7215,a,b,8336,a)].">
      <j1 rule="hyper" parents="63 7215 8336"/>
    </justification>
  </clause>

  <clause id="8341">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5528,a(flip),b,8336,a)].">
      <j1 rule="hyper" parents="63 5528 8336"/>
    </justification>
  </clause>

  <clause id="8342">
    <literal><![CDATA[
      a(x,y,x) * x = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,8336,a(flip),b,3675,a)].">
      <j1 rule="hyper" parents="133 8336 3675"/>
    </justification>
  </clause>

  <clause id="8343">
    <literal><![CDATA[
      a(x,y,x) != x \ z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(8336(a,1),47(a,1))].">
      <j1 rule="para" parents="8336 47"/>
    </justification>
  </clause>

  <clause id="8344">
    <literal><![CDATA[
      x * a(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(8336(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8336 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8345">
    <literal><![CDATA[
      a(x,y,x) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(8336(a,1),6158(a,1,1))].">
      <j1 rule="para" parents="8336 6158"/>
    </justification>
  </clause>

  <clause id="8346">
    <literal><![CDATA[
      T(x * y,x) / x = y * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(8336(a,1),6377(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8336 6377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8347">
    <literal><![CDATA[
      T(x,T(y,z)) \ R(x,u,x) = K(y,T(x,z)) * a(x,u,x)
    ]]></literal>
    <justification jstring="[para(8336(a,1),7146(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8336 7146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8348">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = R(a(y,z,y),y,x)
    ]]></literal>
    <justification jstring="[para(8336(a,1),8200(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8336 8200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8349">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(8339(a,1),356(a,1,2))].">
      <j1 rule="para" parents="8339 356"/>
    </justification>
  </clause>

  <clause id="8350">
    <literal><![CDATA[
      a(x,x,x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(35,a,2259,a,b,8342,a),flip(a)].">
      <j1 rule="hyper" parents="35 2259 8342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8351">
    <literal><![CDATA[
      K(x,x \ 1) = a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,1924,a,b,8350,a)].">
      <j1 rule="hyper" parents="347 1924 8350"/>
    </justification>
  </clause>

  <clause id="8352">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(6138,a,8337,a)].">
      <j1 rule="hyper" parents="6138 8337"/>
    </justification>
  </clause>

  <clause id="8353">
    <literal><![CDATA[
      K(x,x * y) * a(x,y,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5273,a,8337,a)].">
      <j1 rule="hyper" parents="5273 8337"/>
    </justification>
  </clause>

  <clause id="8354">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[para(8337(a,1),5269(a,1,2))].">
      <j1 rule="para" parents="8337 5269"/>
    </justification>
  </clause>

  <clause id="8355">
    <literal><![CDATA[
      a(x,y,x) * K(x,x * y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8337(a,1),6131(a,1,1))].">
      <j1 rule="para" parents="8337 6131"/>
    </justification>
  </clause>

  <clause id="8356">
    <literal><![CDATA[
      K(x,y) / K(x,x * y) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(6205,a,8338,a)].">
      <j1 rule="hyper" parents="6205 8338"/>
    </justification>
  </clause>

  <clause id="8357">
    <literal><![CDATA[
      a(x,y,x) \ K(x,y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(8338(a,1),6123(a,1,1))].">
      <j1 rule="para" parents="8338 6123"/>
    </justification>
  </clause>

  <clause id="8358">
    <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(134,a,7690,a(flip),b,8345,a)].">
      <j1 rule="hyper" parents="134 7690 8345"/>
    </justification>
  </clause>

  <clause id="8359">
    <literal><![CDATA[
      a(x,y \ 1,x) \ K(y \ x,x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(5986(a,1),8345(a,1,2))].">
      <j1 rule="para" parents="5986 8345"/>
    </justification>
  </clause>

  <clause id="8360">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(10(a,1),8346(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 8346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8361">
    <literal><![CDATA[
      T(x * a(y,x,y),y) = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[para(8346(a,1),113(a,1,1))].">
      <j1 rule="para" parents="8346 113"/>
    </justification>
  </clause>

  <clause id="8362">
    <literal><![CDATA[
      R(x * a(y,x,y),z,u) * y = y * R(y \ T(y * x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8346(a,1),746(a,1,1,1))].">
      <j1 rule="para" parents="8346 746"/>
    </justification>
  </clause>

  <clause id="8363">
    <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(8346(a,2),262(a,1,2,2))].">
      <j1 rule="para" parents="8346 262"/>
    </justification>
  </clause>

  <clause id="8364">
    <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(8346(a,2),541(a,1,2,2))].">
      <j1 rule="para" parents="8346 541"/>
    </justification>
  </clause>

  <clause id="8365">
    <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(8346(a,2),942(a,1,2,2,2))].">
      <j1 rule="para" parents="8346 942"/>
    </justification>
  </clause>

  <clause id="8366">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(5525(a,2),8349(a,1))].">
      <j1 rule="para" parents="5525 8349"/>
    </justification>
  </clause>

  <clause id="8367">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,7899,a,b,8352,a),flip(a)].">
      <j1 rule="hyper" parents="347 7899 8352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8368">
    <literal><![CDATA[
      a(1 / ((x * y) \ x),T(z,y),1 / ((x * y) \ x)) * K(T(z,y),1 / ((x * y) \ x)) = K(z * (1 / ((x * y) \ x)),1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(6293(a,1),8352(a,2,1))].">
      <j1 rule="para" parents="6293 8352"/>
    </justification>
  </clause>

  <clause id="8369">
    <literal><![CDATA[
      K(x,y) * a(x,x \ y,x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),8353(a,1,1,2))].">
      <j1 rule="para" parents="10 8353"/>
    </justification>
  </clause>

  <clause id="8370">
    <literal><![CDATA[
      a(x,x \ y,x) * K(x,y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),8355(a,1,2,2))].">
      <j1 rule="para" parents="10 8355"/>
    </justification>
  </clause>

  <clause id="8372">
    <literal><![CDATA[
      a(x,y,x) * T(x,z) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,8340,a(flip),b,3675,a)].">
      <j1 rule="hyper" parents="133 8340 3675"/>
    </justification>
  </clause>

  <clause id="8373">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(x / y,z,x / y) * (x / y)
    ]]></literal>
    <justification jstring="[para(6829(a,1),8372(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6829 8372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8374">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * K(z,y) = x * K(u,y)
    ]]></literal>
    <justification jstring="[para(2556(a,2),8317(a,1,1,2))].">
      <j1 rule="para" parents="2556 8317"/>
    </justification>
  </clause>

  <clause id="8375">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(2556(a,2),8319(a,2,2))].">
      <j1 rule="para" parents="2556 8319"/>
    </justification>
  </clause>

  <clause id="8376">
    <literal><![CDATA[
      T(L(x,K(y,z),K(z,u)) * K(y,z),K(z,u)) = K(y,z) * T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(269,a,8321,a,b,734,a)].">
      <j1 rule="hyper" parents="269 8321 734"/>
    </justification>
  </clause>

  <clause id="8377">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(u,y)) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6102(a,1),8321(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6102 8321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8378">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * (K(z,y) * K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,8317,a,b,8374,a(flip))].">
      <j1 rule="hyper" parents="35 8317 8374"/>
    </justification>
  </clause>

  <clause id="8379">
    <literal><![CDATA[
      L(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(544,a,8375,a)].">
      <j1 rule="hyper" parents="544 8375"/>
    </justification>
  </clause>

  <clause id="8381">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * K(u,y)) = T(z,K(x,y)) * K(u,y)
    ]]></literal>
    <justification jstring="[para(7340(a,1),8375(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7340 8375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8382">
    <literal><![CDATA[
      L(K(x,T(y,z)),K(y,u),w) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7380(a,1),8379(a,1,2))].">
      <j1 rule="para" parents="7380 8379"/>
    </justification>
  </clause>

  <clause id="8383">
    <literal><![CDATA[
      x / (K(y,z) * K(u,y)) = x * (K(z,y) * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(353,a,8378,a),flip(a)].">
      <j1 rule="hyper" parents="353 8378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8384">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * w != x
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * K(y,u) = w
    ]]></literal>
    <justification jstring="[para(8378(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="8378 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8385">
    <literal><![CDATA[
      x / (K(y,z) * K(u,y)) = x * (K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[para(2556(a,2),8383(a,2,2))].">
      <j1 rule="para" parents="2556 8383"/>
    </justification>
  </clause>

  <clause id="8386">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x * (y \ L(y,z,y))
    ]]></literal>
    <justification jstring="[para(5524(a,1),8320(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5524 8320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8387">
    <literal><![CDATA[
      R(x,y,x) \ x = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(433,a,8386,a)].">
      <j1 rule="hyper" parents="433 8386"/>
    </justification>
  </clause>

  <clause id="8388">
    <literal><![CDATA[
      x / R(x,y,x) = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(126,a,8386,a(flip),b,1705,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="126 8386 1705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8389">
    <literal><![CDATA[
      x \ (x \ L(x,y,x)) = R(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,8387,a(flip),b,1755,a)].">
      <j1 rule="hyper" parents="128 8387 1755"/>
    </justification>
  </clause>

  <clause id="8390">
    <literal><![CDATA[
      (x * ((y \ L(y,z,y)) \ 1)) * T(y / R(y,z,y),R(y,z,y) / y) = R(x,(y / R(y,z,y)) \ 1,y / R(y,z,y))
    ]]></literal>
    <justification jstring="[para(8388(a,1),2235(a,1,1,2,1))].">
      <j1 rule="para" parents="8388 2235"/>
    </justification>
  </clause>

  <clause id="8391">
    <literal><![CDATA[
      L(x \ 1,y,x) = R(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,3344,a(flip),b,8389,a)].">
      <j1 rule="hyper" parents="63 3344 8389"/>
    </justification>
  </clause>

  <clause id="8392">
    <literal><![CDATA[
      ((x * (y * K(z,y))) / x) / ((x * y) / x) = K(T(z,x),y)
    ]]></literal>
    <justification jstring="[para(4942(a,1),7464(a,1,1,1,2))].">
      <j1 rule="para" parents="4942 7464"/>
    </justification>
  </clause>

  <clause id="8393">
    <literal><![CDATA[
      T(K(x,y),T(z,x \ u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7264,a(flip),b,7518,a),flip(a)].">
      <j1 rule="hyper" parents="63 7264 7518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8394">
    <literal><![CDATA[
      T(K(x,y),T(z,x * u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),8393(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8396">
    <literal><![CDATA[
      K(x,x \ (x * y)) = K(x,K(z \ x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6740,a(flip),b,7622,a)].">
      <j1 rule="hyper" parents="63 6740 7622"/>
    </justification>
  </clause>

  <clause id="8398">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8396(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8399">
    <literal><![CDATA[
      K(x,y * K(z \ x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7193,a(flip),b,8398,a)].">
      <j1 rule="hyper" parents="63 7193 8398"/>
    </justification>
  </clause>

  <clause id="8400">
    <literal><![CDATA[
      K(x * y,K(y,x) * z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8398(a,1,2,1,1))].">
      <j1 rule="para" parents="9 8398"/>
    </justification>
  </clause>

  <clause id="8402">
    <literal><![CDATA[
      K(x,((y \ x) \ x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5340(a,2),8398(a,1,2))].">
      <j1 rule="para" parents="5340 8398"/>
    </justification>
  </clause>

  <clause id="8403">
    <literal><![CDATA[
      K(x,(x / y) * z) = K(x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(5578(a,1),8398(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5578 8398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8405">
    <literal><![CDATA[
      K(x,y * (x / z)) = K(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[para(6057(a,1),8399(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6057 8399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8406">
    <literal><![CDATA[
      K(x,y / (x / z)) = K(x,y / (z \ x))
    ]]></literal>
    <justification jstring="[para(6125(a,1),8399(a,1,2))].">
      <j1 rule="para" parents="6125 8399"/>
    </justification>
  </clause>

  <clause id="8407">
    <literal><![CDATA[
      K(x,y \ T(z,((y \ 1) \ (y \ z)) \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(6127(a,1),8399(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6127 8399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8408">
    <literal><![CDATA[
      T(x * y,K(y,x) * z) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(132,a,8400,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 8400 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8409">
    <literal><![CDATA[
      (x * K(y,z * (u \ y))) \ x = K(z * (y / u),y)
    ]]></literal>
    <justification jstring="[para(8405(a,1),6123(a,1,1,2))].">
      <j1 rule="para" parents="8405 6123"/>
    </justification>
  </clause>

  <clause id="8410">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(134,a,8408,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 8408 22"/>
    </justification>
  </clause>

  <clause id="8411">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(8408(a,1),315(a,1,2))].">
      <j1 rule="para" parents="8408 315"/>
    </justification>
  </clause>

  <clause id="8412">
    <literal><![CDATA[
      K(x * (y / z),y) = K(x * (z \ y),y)
    ]]></literal>
    <justification jstring="[hyper(6141,a,8409,a),flip(a)].">
      <j1 rule="hyper" parents="6141 8409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8413">
    <literal><![CDATA[
      T(K(x,y) * (z / T(y,u)),y) != w
    ]]></literal>
    <literal><![CDATA[
      (T(y,x) \ z) * K(u,y) = w
    ]]></literal>
    <justification jstring="[para(7680(a,2),6915(a,1))].">
      <j1 rule="para" parents="7680 6915"/>
    </justification>
  </clause>

  <clause id="8414">
    <literal><![CDATA[
      T(x,T(x * (y \ 1),z)) = T(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7703,a(flip),b,7708,a),flip(a)].">
      <j1 rule="hyper" parents="63 7703 7708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8415">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,y) * u) = T(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(7342(a,1),7738(a,2,1))].">
      <j1 rule="para" parents="7342 7738"/>
    </justification>
  </clause>

  <clause id="8416">
    <literal><![CDATA[
      K(x * T(R(y,z,u),w),T(T(y,v5),K(R(y,z,u),w))) = K(x * R(y,z,u),T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,7956,a(flip),b,7741,a),flip(a)].">
      <j1 rule="hyper" parents="347 7956 7741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8417">
    <literal><![CDATA[
      K(x,L(y,z / T(y,u),w)) = L(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(7380(a,1),7746(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7380 7746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8418">
    <literal><![CDATA[
      L(K(x,y),z * T(y,u),w) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[para(11(a,1),8417(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 8417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8419">
    <literal><![CDATA[
      L(K(x,y),y * z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(213(a,1),8417(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="213 8417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8420">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(296(a,1),8417(a,1,2,2))].">
      <j1 rule="para" parents="296 8417"/>
    </justification>
  </clause>

  <clause id="8423">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(x,L(y,K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(7777(a,1),8417(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7777 8417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8424">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * ((y * z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(134,a,8419,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 8419 18"/>
    </justification>
  </clause>

  <clause id="8425">
    <literal><![CDATA[
      L(K(x,y / z),y,u) = K(x,L(y / z,z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),8419(a,1,2))].">
      <j1 rule="para" parents="12 8419"/>
    </justification>
  </clause>

  <clause id="8426">
    <literal><![CDATA[
      K(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z),y) = u
    ]]></literal>
    <justification jstring="[para(8419(a,1),7808(a,1))].">
      <j1 rule="para" parents="8419 7808"/>
    </justification>
  </clause>

  <clause id="8427">
    <literal><![CDATA[
      L(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6035(a,1),8420(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6035 8420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8429">
    <literal><![CDATA[
      (x * T(y,z)) * K(u,y) = x * (T(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(134,a,8427,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 8427 18"/>
    </justification>
  </clause>

  <clause id="8430">
    <literal><![CDATA[
      K(x,L(y,z * K(y,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,7611,a(flip),b,8418,a)].">
      <j1 rule="hyper" parents="63 7611 8418"/>
    </justification>
  </clause>

  <clause id="8432">
    <literal><![CDATA[
      K(x,L(y * y,z,u)) = K(x,y * y)
    ]]></literal>
    <justification jstring="[para(533(a,1),8430(a,1,2)),flip(a)].">
      <j1 rule="para" parents="533 8430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8433">
    <literal><![CDATA[
      K(x,L(y,K(y,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(7104(a,1),8430(a,1,2,2))].">
      <j1 rule="para" parents="7104 8430"/>
    </justification>
  </clause>

  <clause id="8437">
    <literal><![CDATA[
      (K(x,K(y,z)) * T(x,K(u,w))) \ x = K(u,K(w,x)) * K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(7280(a,1),7783(a,2,2))].">
      <j1 rule="para" parents="7280 7783"/>
    </justification>
  </clause>

  <clause id="8438">
    <literal><![CDATA[
      K(x,(y * z) \ (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,z \ u),u,y) = w
    ]]></literal>
    <justification jstring="[para(80(a,1),7806(a,1,2,1,2))].">
      <j1 rule="para" parents="80 7806"/>
    </justification>
  </clause>

  <clause id="8439">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / (y * K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8085,a(flip),b,7860,a)].">
      <j1 rule="hyper" parents="63 8085 7860"/>
    </justification>
  </clause>

  <clause id="8441">
    <literal><![CDATA[
      K(x,y / (z * K(u,x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7402,a(flip),b,8439,a),flip(a)].">
      <j1 rule="hyper" parents="63 7402 8439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8442">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[para(91(a,1),8441(a,1,2,2))].">
      <j1 rule="para" parents="91 8441"/>
    </justification>
  </clause>

  <clause id="8443">
    <literal><![CDATA[
      K(x,y / (T(z,x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(5564(a,1),8441(a,1,2,2))].">
      <j1 rule="para" parents="5564 8441"/>
    </justification>
  </clause>

  <clause id="8444">
    <literal><![CDATA[
      K(x,y / (z * K(x,u))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(6109(a,1),8441(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6109 8441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8445">
    <literal><![CDATA[
      K(x,y / (K(z,x) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(7076(a,1),8441(a,1,2,2))].">
      <j1 rule="para" parents="7076 8441"/>
    </justification>
  </clause>

  <clause id="8446">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(6928,a,8442,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="6928 8442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8447">
    <literal><![CDATA[
      K(x,R(y / x,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[para(108(a,2),8442(a,2,2)),flip(a)].">
      <j1 rule="para" parents="108 8442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8448">
    <literal><![CDATA[
      K(x,y / ((z * K(u,x)) * w)) = K(x,y / (z * w))
    ]]></literal>
    <justification jstring="[para(6565(a,1),8444(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6565 8444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8449">
    <literal><![CDATA[
      K(x,(y / z) \ (x \ 1)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[para(12(a,1),8446(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 8446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8450">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,((y \ z) / z) \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(4428(a,1),8446(a,1,2,2,1))].">
      <j1 rule="para" parents="4428 8446"/>
    </justification>
  </clause>

  <clause id="8451">
    <literal><![CDATA[
      K(x,R(x \ y,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,5112,a(flip),b,8447,a)].">
      <j1 rule="hyper" parents="63 5112 8447"/>
    </justification>
  </clause>

  <clause id="8452">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(91(a,1),8448(a,1,2,2,1))].">
      <j1 rule="para" parents="91 8448"/>
    </justification>
  </clause>

  <clause id="8453">
    <literal><![CDATA[
      K(x,y / (((x \ z) * x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(330(a,1),8448(a,1,2,2,1))].">
      <j1 rule="para" parents="330 8448"/>
    </justification>
  </clause>

  <clause id="8454">
    <literal><![CDATA[
      K(x,y / ((K(x,z) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(7163(a,1),8448(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7163 8448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8455">
    <literal><![CDATA[
      K(x,y / ((z * (K(u,x) * w)) * v5)) = K(x,y / ((z * w) * v5))
    ]]></literal>
    <justification jstring="[para(5885(a,1),8454(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5885 8454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8456">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / (x * K(z,u)),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8150,a(flip),b,7868,a)].">
      <j1 rule="hyper" parents="63 8150 7868"/>
    </justification>
  </clause>

  <clause id="8457">
    <literal><![CDATA[
      K(x / (y * K(z,u)),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(7485,a,8456,a),flip(a)].">
      <j1 rule="hyper" parents="7485 8456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8459">
    <literal><![CDATA[
      K(x / ((y * K(z,u)) * w),u) = K(x / (y * w),u)
    ]]></literal>
    <justification jstring="[para(6565(a,1),8457(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6565 8457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8460">
    <literal><![CDATA[
      K(x / ((K(y,z) * u) * w),y) = K(x / (u * w),y)
    ]]></literal>
    <justification jstring="[para(7163(a,1),8459(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7163 8459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8461">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * (K(y,x) * z)) = (y / T(x,y)) * L(z,K(y,x),x \ y)
    ]]></literal>
    <justification jstring="[para(6179(a,1),7922(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6179 7922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8463">
    <literal><![CDATA[
      K(x * (R(y,z,y) \ u),y) = K(x * (u / T(y,z)),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7985,a(flip),b,7924,a),flip(a)].">
      <j1 rule="hyper" parents="63 7985 7924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8464">
    <literal><![CDATA[
      K(x * (R(x,y,x) \ z),x) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,7930,a(flip),b,8463,a),flip(a)].">
      <j1 rule="hyper" parents="347 7930 8463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8465">
    <literal><![CDATA[
      K(R(x,y,x) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),8464(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8466">
    <literal><![CDATA[
      K(x * R(y,z,y),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7954,a(flip),b,8465,a)].">
      <j1 rule="hyper" parents="63 7954 8465"/>
    </justification>
  </clause>

  <clause id="8467">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = 1 / (x \ K(x * y,x))
    ]]></literal>
    <justification jstring="[para(8466(a,1),5044(a,2,2,2))].">
      <j1 rule="para" parents="8466 5044"/>
    </justification>
  </clause>

  <clause id="8468">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,5044,a,b,8467,a),flip(a)].">
      <j1 rule="hyper" parents="347 5044 8467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8469">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = x * K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,4929,a(flip),b,8468,a),flip(a)].">
      <j1 rule="hyper" parents="347 4929 8468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8470">
    <literal><![CDATA[
      K(x,y * R(x,z,x)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5005,a,8469,a)].">
      <j1 rule="hyper" parents="5005 8469"/>
    </justification>
  </clause>

  <clause id="8471">
    <literal><![CDATA[
      K(x,R(x,y,x) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7942,a,b,8470,a)].">
      <j1 rule="hyper" parents="63 7942 8470"/>
    </justification>
  </clause>

  <clause id="8472">
    <literal><![CDATA[
      K(R(x,y,x),R(x,z,x) * u) = K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(7207,a,8471,a)].">
      <j1 rule="hyper" parents="7207 8471"/>
    </justification>
  </clause>

  <clause id="8473">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) = T(x,K(z,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(7306,a,8006,a),flip(a)].">
      <j1 rule="hyper" parents="7306 8006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8474">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) * K(u,y) = T(x * K(u,y),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7514,a(flip),b,8473,a),flip(a)].">
      <j1 rule="hyper" parents="63 7514 8473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8475">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,u)) = K(x,y) * T(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,5895,a(flip),b,8473,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 5895 8473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8476">
    <literal><![CDATA[
      T(x * K(L(y \ 1,z,u) \ 1,w),K(w,v5)) = T(x,K(w,v5)) * L(K(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(7006(a,1),8473(a,2,2))].">
      <j1 rule="para" parents="7006 8473"/>
    </justification>
  </clause>

  <clause id="8477">
    <literal><![CDATA[
      K(x,K(y,z)) * T(y,K(x,u)) = T(T(y,K(x,z)),K(x,u))
    ]]></literal>
    <justification jstring="[para(7285(a,1),8475(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7285 8475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8478">
    <literal><![CDATA[
      K(x,(T(T(y * z,x),z \ 1) / u) * w) = K(x,((((y * z) \ y) \ y) / u) * w)
    ]]></literal>
    <justification jstring="[para(6289(a,1),8038(a,2,2,1,1))].">
      <j1 rule="para" parents="6289 8038"/>
    </justification>
  </clause>

  <clause id="8479">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,x \ (x * y)) = K(z / ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),8059(a,2,2))].">
      <j1 rule="para" parents="9 8059"/>
    </justification>
  </clause>

  <clause id="8480">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,z \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6988,a(flip),b,8123,a),flip(a)].">
      <j1 rule="hyper" parents="63 6988 8123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8481">
    <literal><![CDATA[
      T(K(x,y),z / (1 / y)) = T(K(x,y),z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8129,a(flip),b,8130,a),flip(a)].">
      <j1 rule="hyper" parents="63 8129 8130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8482">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,1 / (z / (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(63,a,8115,a(flip),b,8481,a),flip(a)].">
      <j1 rule="hyper" parents="63 8115 8481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8483">
    <literal><![CDATA[
      K(x,1 / (y / (y / (1 / z)))) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7664,a(flip),b,8482,a),flip(a)].">
      <j1 rule="hyper" parents="63 7664 8482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8484">
    <literal><![CDATA[
      (x * K((y \ z) \ x,z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(8248(a,1),8170(a,1,1,2))].">
      <j1 rule="para" parents="8248 8170"/>
    </justification>
  </clause>

  <clause id="8485">
    <literal><![CDATA[
      K(x,(((x \ y) * x) * z) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(8189(a,1),8077(a,1,2,1))].">
      <j1 rule="para" parents="8189 8077"/>
    </justification>
  </clause>

  <clause id="8486">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(3161(a,1),8229(a,1,2,1))].">
      <j1 rule="para" parents="3161 8229"/>
    </justification>
  </clause>

  <clause id="8487">
    <literal><![CDATA[
      T(x,(y \ x) \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(y \ 1) \ z) = u
    ]]></literal>
    <justification jstring="[para(8250(a,2),5045(a,1))].">
      <j1 rule="para" parents="8250 5045"/>
    </justification>
  </clause>

  <clause id="8488">
    <literal><![CDATA[
      T(x,(y \ 1) \ (x \ z)) = x * K(x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(8487,a,8027,a)].">
      <j1 rule="hyper" parents="8487 8027"/>
    </justification>
  </clause>

  <clause id="8489">
    <literal><![CDATA[
      K(x,(y \ 1) \ (x \ z)) = K(x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(5005,a,8488,a)].">
      <j1 rule="hyper" parents="5005 8488"/>
    </justification>
  </clause>

  <clause id="8490">
    <literal><![CDATA[
      K(x,(y \ x) \ (z * x)) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(8047,a,8489,a),flip(a)].">
      <j1 rule="hyper" parents="8047 8489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8491">
    <literal><![CDATA[
      K(x,(y \ x) \ (x * z)) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8489(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8492">
    <literal><![CDATA[
      T(K(x \ y,x) * z,y) = K(x \ y,x) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(5973,a,8279,a),flip(a)].">
      <j1 rule="hyper" parents="5973 8279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8493">
    <literal><![CDATA[
      T(K(x \ (y * x),x) * z,y * x) = K(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(5143(a,1),8492(a,2,1))].">
      <j1 rule="para" parents="5143 8492"/>
    </justification>
  </clause>

  <clause id="8494">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (R(x,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(347,a,7957,a(flip),b,8289,a),flip(a)].">
      <j1 rule="hyper" parents="347 7957 8289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8495">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(y * z,y)) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,6432,a(flip),b,8377,a),flip(a)].">
      <j1 rule="hyper" parents="347 6432 8377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8496">
    <literal><![CDATA[
      (x / y) * a(y,z,y) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(8338(a,1),8495(a,1,2))].">
      <j1 rule="para" parents="8338 8495"/>
    </justification>
  </clause>

  <clause id="8497">
    <literal><![CDATA[
      a(x,y,x) * L(x,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(133,a,191,a(flip),b,8496,a(flip))].">
      <j1 rule="hyper" parents="133 191 8496"/>
    </justification>
  </clause>

  <clause id="8498">
    <literal><![CDATA[
      (x * y) / L(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),8496(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 8496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8499">
    <literal><![CDATA[
      L(x,y,x) \ x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(3312,a,8497,a)].">
      <j1 rule="hyper" parents="3312 8497"/>
    </justification>
  </clause>

  <clause id="8500">
    <literal><![CDATA[
      a(x,y,x) \ x = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(138,a,8497,a)].">
      <j1 rule="hyper" parents="138 8497"/>
    </justification>
  </clause>

  <clause id="8501">
    <literal><![CDATA[
      L(x,y,x) != z \ x
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(8497(a,1),153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8497 153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8502">
    <literal><![CDATA[
      a(x,y,x) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(8497(a,1),356(a,1,2))].">
      <j1 rule="para" parents="8497 356"/>
    </justification>
  </clause>

  <clause id="8504">
    <literal><![CDATA[
      a(x,y,x) \ (x * L(x \ a(x,y,x),z,u)) = L(x,y,x) \ L(a(x,y,x) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(8500(a,1),3354(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8500 3354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8506">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(2011,a,8498,a)].">
      <j1 rule="hyper" parents="2011 8498"/>
    </justification>
  </clause>

  <clause id="8507">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (x * y) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(214,a,8498,a)].">
      <j1 rule="hyper" parents="214 8498"/>
    </justification>
  </clause>

  <clause id="8508">
    <literal><![CDATA[
      x * (L(x,y,x) \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7231,a(flip),b,8506,a)].">
      <j1 rule="hyper" parents="63 7231 8506"/>
    </justification>
  </clause>

  <clause id="8509">
    <literal><![CDATA[
      (x * L(y,z,y)) * a(y,z,y) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),8506(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 8506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8510">
    <literal><![CDATA[
      ((x * y) * a(T(y,x),z,T(y,x))) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(1064(a,1),8507(a,1,2))].">
      <j1 rule="para" parents="1064 8507"/>
    </justification>
  </clause>

  <clause id="8511">
    <literal><![CDATA[
      (x \ y) * a(x,z,x) = L(x,z,x) \ y
    ]]></literal>
    <justification jstring="[hyper(1424,a,8508,a),flip(a)].">
      <j1 rule="hyper" parents="1424 8508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8512">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = z / a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(653,a,8508,a),flip(a)].">
      <j1 rule="hyper" parents="653 8508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8513">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = u * a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7834,a,b,8508,a)].">
      <j1 rule="hyper" parents="63 7834 8508"/>
    </justification>
  </clause>

  <clause id="8514">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = u * a(T(x,y),z,T(x,y))
    ]]></literal>
    <justification jstring="[para(7230(a,1),8508(a,1,2,1))].">
      <j1 rule="para" parents="7230 8508"/>
    </justification>
  </clause>

  <clause id="8515">
    <literal><![CDATA[
      x * (y / a(x,z,x)) = L(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,84,a(flip),b,8511,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 84 8511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8516">
    <literal><![CDATA[
      (x / y) \ (x / a(y,z,y)) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,8512,a(flip),b,7685,a(flip))].">
      <j1 rule="hyper" parents="128 8512 7685"/>
    </justification>
  </clause>

  <clause id="8517">
    <literal><![CDATA[
      K(T(x,y),z) * ((y * z) / y) = (y * (z * K(x,z))) / y
    ]]></literal>
    <justification jstring="[hyper(148,a,8392,a)].">
      <j1 rule="hyper" parents="148 8392"/>
    </justification>
  </clause>

  <clause id="8518">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,8433,a(flip),b,8423,a),flip(a)].">
      <j1 rule="hyper" parents="347 8433 8423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8520">
    <literal><![CDATA[
      L(K(x,L(y,x,z)),T(y,u) * w,v5) = K(L(x,y,z),L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(8303(a,1),8518(a,1,1))].">
      <j1 rule="para" parents="8303 8518"/>
    </justification>
  </clause>

  <clause id="8521">
    <literal><![CDATA[
      T(x * K(y,z),T(z,u)) = T(x,T(z,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6813(a,1),8474(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6813 8474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8522">
    <literal><![CDATA[
      T(x,T(y,z)) * K(z,y) = T(K(z,y) * x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6827,a(flip),b,8521,a),flip(a)].">
      <j1 rule="hyper" parents="63 6827 8521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8523">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,u)) = K(x,y) * T(z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,5895,a(flip),b,8521,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 5895 8521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8524">
    <literal><![CDATA[
      K(x,L(y,z,u) \ (y * x)) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6457,a(flip),b,8486,a)].">
      <j1 rule="hyper" parents="63 6457 8486"/>
    </justification>
  </clause>

  <clause id="8525">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z,y))) / x) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(220,a,8517,a(flip),b,5256,a)].">
      <j1 rule="hyper" parents="220 8517 5256"/>
    </justification>
  </clause>

  <clause id="8526">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z,y))) / x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8517(a,1),5276(a,1,2))].">
      <j1 rule="para" parents="8517 5276"/>
    </justification>
  </clause>

  <clause id="8527">
    <literal><![CDATA[
      K(x,(x / L(y,z,u)) * y) = K(x,y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(1407(a,1),8524(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1407 8524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8528">
    <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(8460(a,1),8525(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8460 8525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8529">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x \ 1,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(7008(a,1),545(a,1))].">
      <j1 rule="para" parents="7008 545"/>
    </justification>
  </clause>

  <clause id="8530">
    <literal><![CDATA[
      L(K(x,T((y \ z) \ u,w)),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[para(7091(a,2),7107(a,1,1))].">
      <j1 rule="para" parents="7091 7107"/>
    </justification>
  </clause>

  <clause id="8531">
    <literal><![CDATA[
      L(K(x,T(y \ z,u)),y \ z,w) = K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(7091(a,2),7108(a,1,1))].">
      <j1 rule="para" parents="7091 7108"/>
    </justification>
  </clause>

  <clause id="8532">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),T(w,y * R(x,z,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(7141(a,2),7488(a,1))].">
      <j1 rule="para" parents="7141 7488"/>
    </justification>
  </clause>

  <clause id="8533">
    <literal><![CDATA[
      T(x / T(y,T(z,x)),y) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(7159,a,7170,a)].">
      <j1 rule="hyper" parents="7159 7170"/>
    </justification>
  </clause>

  <clause id="8534">
    <literal><![CDATA[
      T(x / T(y,z),y) = T(y,T(z,x)) \ x
    ]]></literal>
    <justification jstring="[para(7387(a,1),8533(a,1,1,2))].">
      <j1 rule="para" parents="7387 8533"/>
    </justification>
  </clause>

  <clause id="8535">
    <literal><![CDATA[
      K(T(x,y),z) * (y / z) = y / T(z,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,7678,a,b,8534,a)].">
      <j1 rule="hyper" parents="40 7678 8534"/>
    </justification>
  </clause>

  <clause id="8536">
    <literal><![CDATA[
      K(x,T(y,z)) * (z / y) = z / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(7790,a,8535,a)].">
      <j1 rule="hyper" parents="7790 8535"/>
    </justification>
  </clause>

  <clause id="8537">
    <literal><![CDATA[
      K(x,y) * (z / T(y,z)) = z / T(T(y,z),x)
    ]]></literal>
    <justification jstring="[para(7380(a,1),8535(a,1,1))].">
      <j1 rule="para" parents="7380 8535"/>
    </justification>
  </clause>

  <clause id="8538">
    <literal><![CDATA[
      K(x,y \ z) * (z / (z / y)) = z / T(z / y,x)
    ]]></literal>
    <justification jstring="[para(7643(a,1),8535(a,1,1))].">
      <j1 rule="para" parents="7643 8535"/>
    </justification>
  </clause>

  <clause id="8539">
    <literal><![CDATA[
      T(T(x,1),y) \ R(z,T(T(x,1),y) \ 1,T(T(x,1),y)) = T(z * (K(y,x) * (1 / T(x,1))),T(T(x,1),y))
    ]]></literal>
    <justification jstring="[para(8537(a,2),2269(a,2,1,2))].">
      <j1 rule="para" parents="8537 2269"/>
    </justification>
  </clause>

  <clause id="8540">
    <literal><![CDATA[
      x / T(x * (K(y,z) * (1 / T(z,1))),T(T(z,1),y)) = (x * (1 / T(T(z,1),y))) \ x
    ]]></literal>
    <justification jstring="[para(8537(a,2),6353(a,1,2,1,2))].">
      <j1 rule="para" parents="8537 6353"/>
    </justification>
  </clause>

  <clause id="8541">
    <literal><![CDATA[
      L(K(x,T(T(y,z * u),u)),u,z) = K((z * u) / (z * (x \ u)),y)
    ]]></literal>
    <justification jstring="[para(7097(a,1),7447(a,1,1))].">
      <j1 rule="para" parents="7097 7447"/>
    </justification>
  </clause>

  <clause id="8542">
    <literal><![CDATA[
      T(x,K(y,z)) / z = T(x / z,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7580,a,484,a(flip))].">
      <j1 rule="hyper" parents="7580 484"/>
    </justification>
  </clause>

  <clause id="8543">
    <literal><![CDATA[
      T(T(x,y) / z,K(y,z)) = T(x,T(y,z)) / z
    ]]></literal>
    <justification jstring="[para(6813(a,1),8542(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6813 8542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8544">
    <literal><![CDATA[
      K(x,R(T(y / z,u),z,y \ u)) = K(x,(z * (y \ u)) \ u)
    ]]></literal>
    <justification jstring="[para(27(a,2),7647(a,1,2))].">
      <j1 rule="para" parents="27 7647"/>
    </justification>
  </clause>

  <clause id="8545">
    <literal><![CDATA[
      K(L(x,y,L(x,z,u)),T(w,L(x,z,u) * y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(7745(a,1),7483(a,1))].">
      <j1 rule="para" parents="7745 7483"/>
    </justification>
  </clause>

  <clause id="8546">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(T(u * x,x) / u,z)
    ]]></literal>
    <justification jstring="[hyper(7756,a,7709,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="7756 7709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8547">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(8308,a,8546,a),flip(a)].">
      <j1 rule="hyper" parents="8308 8546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8548">
    <literal><![CDATA[
      K(T(x,y \ x) / y,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),8547(a,1,1,1,1))].">
      <j1 rule="para" parents="10 8547"/>
    </justification>
  </clause>

  <clause id="8549">
    <literal><![CDATA[
      K(T(x,y \ x) / y,z) = K(x / y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,7135,a,b,8548,a),flip(a)].">
      <j1 rule="hyper" parents="347 7135 8548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8550">
    <literal><![CDATA[
      K(T(x,y \ x) / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(8549(a,2),7481(a,1))].">
      <j1 rule="para" parents="8549 7481"/>
    </justification>
  </clause>

  <clause id="8551">
    <literal><![CDATA[
      x * K(y,(x \ 1) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(5412(a,1),7832(a,1,2))].">
      <j1 rule="para" parents="5412 7832"/>
    </justification>
  </clause>

  <clause id="8552">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,T(y,x)) * u = w
    ]]></literal>
    <justification jstring="[para(7260(a,1),8062(a,1,1))].">
      <j1 rule="para" parents="7260 8062"/>
    </justification>
  </clause>

  <clause id="8553">
    <literal><![CDATA[
      T(T(x,L(K(y,z),u,w)),L(K(y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(8063,a,4415,a),flip(a)].">
      <j1 rule="hyper" parents="8063 4415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8554">
    <literal><![CDATA[
      x * K(L(K(y,z),u,w),x) = T(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(5079,a,8553,a)].">
      <j1 rule="hyper" parents="5079 8553"/>
    </justification>
  </clause>

  <clause id="8555">
    <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(808,a,8553,a)].">
      <j1 rule="hyper" parents="808 8553"/>
    </justification>
  </clause>

  <clause id="8556">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(w,L(K(x,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(34,a,4929,a(flip),b,8554,a),flip(a)].">
      <j1 rule="hyper" parents="34 4929 8554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8557">
    <literal><![CDATA[
      K(x,R(T(K(x,y),z * u),z,u)) = K(x,a(K(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(744(a,1),8088(a,1,2))].">
      <j1 rule="para" parents="744 8088"/>
    </justification>
  </clause>

  <clause id="8558">
    <literal><![CDATA[
      K(x,a(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,5538,a(flip),b,8557,a),flip(a)].">
      <j1 rule="hyper" parents="63 5538 8557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8559">
    <literal><![CDATA[
      T(a(K(x,y),z,u),x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(5039,a,8558,a)].">
      <j1 rule="hyper" parents="5039 8558"/>
    </justification>
  </clause>

  <clause id="8561">
    <literal><![CDATA[
      T(x,a(K(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,8558,a)].">
      <j1 rule="hyper" parents="56 8558"/>
    </justification>
  </clause>

  <clause id="8562">
    <literal><![CDATA[
      K(x,y) * a(K(x,z),u,w) = a(K(x,z),u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8561(a,1),7076(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8561 7076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8563">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) * x = x * K(a(K(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(8559(a,1),7076(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8559 7076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8564">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(8172,a,6682,a),flip(a)].">
      <j1 rule="hyper" parents="8172 6682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8565">
    <literal><![CDATA[
      T(x,(y * (z * x)) \ u) = T(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(132,a,8564,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 8564 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8566">
    <literal><![CDATA[
      K(x,(y * (x * z)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8078,a(flip),b,8564,a)].">
      <j1 rule="hyper" parents="63 8078 8564"/>
    </justification>
  </clause>

  <clause id="8567">
    <literal><![CDATA[
      K(x,((1 / y) * y) \ (x \ z)) = K(x,L(x,y,y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2939(a,1),8564(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2939 8564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8568">
    <literal><![CDATA[
      (x * K(y,(z * u) \ (y \ w))) \ x = K((z * (u * y)) \ w,y)
    ]]></literal>
    <justification jstring="[para(8564(a,1),6123(a,1,1,2))].">
      <j1 rule="para" parents="8564 6123"/>
    </justification>
  </clause>

  <clause id="8569">
    <literal><![CDATA[
      L(T(x,(y * z) \ (x \ u)),w,v5) \ L(x,w,v5) = K((y * (z * x)) \ u,L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(8565(a,1),4936(a,1,1,1))].">
      <j1 rule="para" parents="8565 4936"/>
    </justification>
  </clause>

  <clause id="8570">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),8566(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 8566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8571">
    <literal><![CDATA[
      L(K(x,(y * z) \ (x \ u)),w * x,v5) = K(L(x,w,v5),(y * (x * z)) \ u)
    ]]></literal>
    <justification jstring="[para(8566(a,1),7039(a,1,1))].">
      <j1 rule="para" parents="8566 7039"/>
    </justification>
  </clause>

  <clause id="8572">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(8047,a,8570,a)].">
      <j1 rule="hyper" parents="8047 8570"/>
    </justification>
  </clause>

  <clause id="8573">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,8076,a,b,8572,a)].">
      <j1 rule="hyper" parents="63 8076 8572"/>
    </justification>
  </clause>

  <clause id="8574">
    <literal><![CDATA[
      K(x,(y * (x \ 1)) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(8(a,1),8572(a,2,2,1))].">
      <j1 rule="para" parents="8 8572"/>
    </justification>
  </clause>

  <clause id="8575">
    <literal><![CDATA[
      K(x,((y * K(x \ z,y)) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(4989(a,1),8572(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4989 8572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8576">
    <literal><![CDATA[
      L(K(x,(x \ 1) \ y),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[hyper(8438,a,8574,a)].">
      <j1 rule="hyper" parents="8438 8574"/>
    </justification>
  </clause>

  <clause id="8577">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,y) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,6794,a,b,8574,a)].">
      <j1 rule="hyper" parents="63 6794 8574"/>
    </justification>
  </clause>

  <clause id="8578">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * z) \ (u * x))) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(8573(a,1),5267(a,1,2,2))].">
      <j1 rule="para" parents="8573 5267"/>
    </justification>
  </clause>

  <clause id="8579">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[para(6766(a,1),8576(a,1,1))].">
      <j1 rule="para" parents="6766 8576"/>
    </justification>
  </clause>

  <clause id="8580">
    <literal><![CDATA[
      L(K(x,y * x),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[para(5297(a,2),8579(a,1,1))].">
      <j1 rule="para" parents="5297 8579"/>
    </justification>
  </clause>

  <clause id="8581">
    <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(327(a,1),8580(a,2,2))].">
      <j1 rule="para" parents="327 8580"/>
    </justification>
  </clause>

  <clause id="8582">
    <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(542(a,1),8304(a,2,2))].">
      <j1 rule="para" parents="542 8304"/>
    </justification>
  </clause>

  <clause id="8583">
    <literal><![CDATA[
      (x / (K(y,z) * L(K(z,u),w,v5))) * K(y,z) = x * L(K(u,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(1009,a,8316,a)].">
      <j1 rule="hyper" parents="1009 8316"/>
    </justification>
  </clause>

  <clause id="8584">
    <literal><![CDATA[
      K(x,L(y,z,T(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,6778,a,b,8424,a),flip(a)].">
      <j1 rule="hyper" parents="34 6778 8424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8585">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * (y * (z * K(u,y)))
    ]]></literal>
    <justification jstring="[para(6844(a,1),8424(a,2,2))].">
      <j1 rule="para" parents="6844 8424"/>
    </justification>
  </clause>

  <clause id="8586">
    <literal><![CDATA[
      K(x,T(L(y,z,T(x,u)),w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(25(a,1),8584(a,1,2))].">
      <j1 rule="para" parents="25 8584"/>
    </justification>
  </clause>

  <clause id="8587">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,u)) = K(x,T(z \ (y * x),u))
    ]]></literal>
    <justification jstring="[hyper(7017,a,8530,a)].">
      <j1 rule="hyper" parents="7017 8530"/>
    </justification>
  </clause>

  <clause id="8589">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,y)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,8231,a(flip),b,8587,a),flip(a)].">
      <j1 rule="hyper" parents="347 8231 8587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8590">
    <literal><![CDATA[
      T(x,T((y \ z) \ x,u)) = T(x,T(z \ (y * x),u))
    ]]></literal>
    <justification jstring="[hyper(132,a,8587,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 8587 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8591">
    <literal><![CDATA[
      K(x,((y * z) / y) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),8589(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 8589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8592">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,(z / (z / y)) \ x)
    ]]></literal>
    <justification jstring="[para(4339(a,1),8591(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4339 8591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8593">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,8237,a(flip),b,8592,a),flip(a)].">
      <j1 rule="hyper" parents="63 8237 8592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8594">
    <literal><![CDATA[
      K(x,T(y \ x,x * z)) = K(x,((x * z) / y) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8227,a(flip),b,8593,a),flip(a)].">
      <j1 rule="hyper" parents="63 8227 8593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8595">
    <literal><![CDATA[
      K(x,((x * y) / z) / y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ x,y)) = u
    ]]></literal>
    <justification jstring="[para(8594(a,1),7496(a,1))].">
      <j1 rule="para" parents="8594 7496"/>
    </justification>
  </clause>

  <clause id="8596">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(8271,a,8531,a),flip(a)].">
      <j1 rule="hyper" parents="8271 8531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8597">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ y,u)) = w
    ]]></literal>
    <justification jstring="[para(8531(a,1),401(a,1)),flip(b)].">
      <j1 rule="para" parents="8531 401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8598">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T((y \ z) \ 1,u)) = K(((y \ z) \ 1) * x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7971,a,b,8596,a)].">
      <j1 rule="hyper" parents="63 7971 8596"/>
    </justification>
  </clause>

  <clause id="8599">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T((x \ y) \ 1,u)) = K((x \ y) \ z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7813,a,b,8596,a)].">
      <j1 rule="hyper" parents="63 7813 8596"/>
    </justification>
  </clause>

  <clause id="8600">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(8596(a,2),7771(a,1))].">
      <j1 rule="para" parents="8596 7771"/>
    </justification>
  </clause>

  <clause id="8601">
    <literal><![CDATA[
      K(x,T(1 / (y \ z),y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(3894(a,2),8600(a,1))].">
      <j1 rule="para" parents="3894 8600"/>
    </justification>
  </clause>

  <clause id="8602">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(7818(a,1),8600(a,1))].">
      <j1 rule="para" parents="7818 8600"/>
    </justification>
  </clause>

  <clause id="8603">
    <literal><![CDATA[
      K(x,T(1 / y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / (z * y)) = u
    ]]></literal>
    <justification jstring="[para(9(a,1),8601(a,1,2,1,2))].">
      <j1 rule="para" parents="9 8601"/>
    </justification>
  </clause>

  <clause id="8604">
    <literal><![CDATA[
      K((x * y) / x,x / (x * z)) = K(y,1 / z)
    ]]></literal>
    <justification jstring="[hyper(8603,a,7138,a)].">
      <j1 rule="hyper" parents="8603 7138"/>
    </justification>
  </clause>

  <clause id="8605">
    <literal><![CDATA[
      K((x * y) / x,1 / ((x * z) / x)) = K(y,1 / z)
    ]]></literal>
    <justification jstring="[hyper(5626,a,8604,a)].">
      <j1 rule="hyper" parents="5626 8604"/>
    </justification>
  </clause>

  <clause id="8606">
    <literal><![CDATA[
      (((x * y) / x) \ z) * K(y,1 / y) = (1 / (1 / ((x * y) / x))) \ z
    ]]></literal>
    <justification jstring="[para(8605(a,1),3434(a,1,2))].">
      <j1 rule="para" parents="8605 3434"/>
    </justification>
  </clause>

  <clause id="8607">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u \ z,y)) = w
    ]]></literal>
    <justification jstring="[para(7729(a,1),8597(a,1))].">
      <j1 rule="para" parents="7729 8597"/>
    </justification>
  </clause>

  <clause id="8608">
    <literal><![CDATA[
      K(x,y \ (z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ 1,y)) = u
    ]]></literal>
    <justification jstring="[para(66(a,1),8607(a,1,2,2,1))].">
      <j1 rule="para" parents="66 8607"/>
    </justification>
  </clause>

  <clause id="8609">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(35,a,7373,a,b,8551,a(flip))].">
      <j1 rule="hyper" parents="35 7373 8551"/>
    </justification>
  </clause>

  <clause id="8610">
    <literal><![CDATA[
      K(x,L(x,y,y \ 1) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(184(a,1),8567(a,1,2)),flip(a)].">
      <j1 rule="para" parents="184 8567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8612">
    <literal><![CDATA[
      K((x \ 1) \ y,((x \ 1) \ y) \ z) = K((x \ 1) \ y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(2943(a,1),8610(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2943 8610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8613">
    <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(4849(a,2),8585(a,2,2))].">
      <j1 rule="para" parents="4849 8585"/>
    </justification>
  </clause>

  <clause id="8614">
    <literal><![CDATA[
      K((x \ 1) \ y,z \ (x * y)) = K(x * y,(x \ z) \ y)
    ]]></literal>
    <justification jstring="[para(66(a,1),7033(a,2,1))].">
      <j1 rule="para" parents="66 7033"/>
    </justification>
  </clause>

  <clause id="8615">
    <literal><![CDATA[
      K((R(x,y,z) \ (R(x,y,z) * (x \ u))) \ u,w \ (R(x,y,z) * u)) = K(T(x,R(x,y,z) * (x \ u)),(R(x,y,z) \ w) \ u)
    ]]></literal>
    <justification jstring="[para(1756(a,1),7033(a,2,1))].">
      <j1 rule="para" parents="1756 7033"/>
    </justification>
  </clause>

  <clause id="8617">
    <literal><![CDATA[
      K(x \ (y * z),z) * K(z,z \ T(z * ((y \ x) \ 1),z)) = (y \ x) * (T(z * ((y \ x) \ 1),z) / z)
    ]]></literal>
    <justification jstring="[para(7036(a,1),6071(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7036 6071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8618">
    <literal><![CDATA[
      K(L(x,y,z),R(z,u,w)) = K(x,R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,5546,a(flip),b,7046,a),flip(a)].">
      <j1 rule="hyper" parents="347 5546 7046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8619">
    <literal><![CDATA[
      K((x \ 1) \ y,R(x,z,u)) = K(x * y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(560(a,1),8618(a,1,1)),flip(a)].">
      <j1 rule="para" parents="560 8618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8620">
    <literal><![CDATA[
      K((x \ 1) * y,R(x \ 1,z,u)) = K(x \ y,R(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(3927,a,8619,a),flip(a)].">
      <j1 rule="hyper" parents="3927 8619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8622">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,z) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,6176,a(flip),b,7176,a),flip(a)].">
      <j1 rule="hyper" parents="63 6176 7176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8623">
    <literal><![CDATA[
      (1 / (x \ y)) * K(y / x,z) = K(y / x,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(7390(a,1),7458(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7390 7458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8624">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(8623(a,1),370(a,1))].">
      <j1 rule="para" parents="8623 370"/>
    </justification>
  </clause>

  <clause id="8625">
    <literal><![CDATA[
      1 / (x \ K(y,1 / x)) = x * K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(8624,a,5783,a),flip(a)].">
      <j1 rule="hyper" parents="8624 5783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8626">
    <literal><![CDATA[
      1 / ((x * (y \ 1)) / x) = y * K(1 / y,x)
    ]]></literal>
    <justification jstring="[para(5051(a,1),8625(a,1,2))].">
      <j1 rule="para" parents="5051 8625"/>
    </justification>
  </clause>

  <clause id="8627">
    <literal><![CDATA[
      1 / ((x * ((y / z) \ 1)) / x) = (y / z) * K(z / y,x)
    ]]></literal>
    <justification jstring="[para(5554(a,1),8626(a,2,2))].">
      <j1 rule="para" parents="5554 8626"/>
    </justification>
  </clause>

  <clause id="8628">
    <literal><![CDATA[
      x / (K(T(y,z),x) * K(x,z)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(7903(a,1),7466(a,1,2,2))].">
      <j1 rule="para" parents="7903 7466"/>
    </justification>
  </clause>

  <clause id="8629">
    <literal><![CDATA[
      T(x * K(y,x),z) \ x = K(T(z,y),x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(214,a,8628,a)].">
      <j1 rule="hyper" parents="214 8628"/>
    </justification>
  </clause>

  <clause id="8631">
    <literal><![CDATA[
      T((x * y) / x,z) \ y = K(T(z,x),y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(4942(a,2),8629(a,1,1,1))].">
      <j1 rule="para" parents="4942 8629"/>
    </justification>
  </clause>

  <clause id="8632">
    <literal><![CDATA[
      T((x * y) / x,z) \ y = K(y,x) * K(T(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,2556,a,b,8631,a),flip(a)].">
      <j1 rule="hyper" parents="347 2556 8631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8633">
    <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(1642(a,1),8632(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1642 8632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8634">
    <literal><![CDATA[
      T(K(x,y) * z,u) * T(K(y,x),T(w,T(K(x,y) * z,u))) = K(K(y,x),w) * (K(y,x) * T(z * K(x,y),u))
    ]]></literal>
    <justification jstring="[para(7529(a,1),7697(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7529 7697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8635">
    <literal><![CDATA[
      K(x,K(y,z)) * T(u,K(y,z)) = T(K(y,z),x) * (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(7292(a,1),7531(a,1,1))].">
      <j1 rule="para" parents="7292 7531"/>
    </justification>
  </clause>

  <clause id="8636">
    <literal><![CDATA[
      L(x,K(y,z) * (u * K(y,z)),w) = L(x,T(u,K(z,y)),w)
    ]]></literal>
    <justification jstring="[para(5173(a,1),7532(a,1,2,1))].">
      <j1 rule="para" parents="5173 7532"/>
    </justification>
  </clause>

  <clause id="8637">
    <literal><![CDATA[
      (x * K(y,z)) / T(z,u) = x / (K(z,y) * T(z,u))
    ]]></literal>
    <justification jstring="[para(7380(a,1),7545(a,1,1,2))].">
      <j1 rule="para" parents="7380 7545"/>
    </justification>
  </clause>

  <clause id="8638">
    <literal><![CDATA[
      (x * K(y,z)) / T(z,u) = (x / T(z,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7417,a(flip),b,8637,a),flip(a)].">
      <j1 rule="hyper" parents="347 7417 8637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8640">
    <literal><![CDATA[
      K(x,R(y,z * K(y,u),w)) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(8297,a,7546,a),flip(a)].">
      <j1 rule="hyper" parents="8297 7546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8641">
    <literal><![CDATA[
      K(x,R(y,T(z,y),u)) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(4915(a,1),8640(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4915 8640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8642">
    <literal><![CDATA[
      K(x,R(y,K(y,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(7104(a,1),8640(a,1,2,2))].">
      <j1 rule="para" parents="7104 8640"/>
    </justification>
  </clause>

  <clause id="8643">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6717,a,b,8641,a)].">
      <j1 rule="hyper" parents="63 6717 8641"/>
    </justification>
  </clause>

  <clause id="8644">
    <literal><![CDATA[
      K(R(x,y,z),y) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6508,a(flip),b,8643,a)].">
      <j1 rule="hyper" parents="63 6508 8643"/>
    </justification>
  </clause>

  <clause id="8645">
    <literal><![CDATA[
      R(K(x,y \ z),z,u) = K(x,R(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),8643(a,1,2))].">
      <j1 rule="para" parents="10 8643"/>
    </justification>
  </clause>

  <clause id="8646">
    <literal><![CDATA[
      R(K(x,y),z * T(y,u),w) = K(x,R(y,z * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(5914(a,1),8643(a,1,2))].">
      <j1 rule="para" parents="5914 8643"/>
    </justification>
  </clause>

  <clause id="8647">
    <literal><![CDATA[
      R(K(x,y),z * K(u,y),w) = K(x,R(y,z / T(y,u),w))
    ]]></literal>
    <justification jstring="[para(6107(a,1),8643(a,1,2))].">
      <j1 rule="para" parents="6107 8643"/>
    </justification>
  </clause>

  <clause id="8648">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = (v5 * K(w,R(x,z,u))) \ v5
    ]]></literal>
    <justification jstring="[para(8642(a,1),6123(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8642 6123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8649">
    <literal><![CDATA[
      R(K(x,y \ R(y,z,u)),R(y,z,u),z * u) = K(x,((y * z) * u) / (y * (z * u)))
    ]]></literal>
    <justification jstring="[para(3688(a,1),8645(a,2,2))].">
      <j1 rule="para" parents="3688 8645"/>
    </justification>
  </clause>

  <clause id="8650">
    <literal><![CDATA[
      R(K(x,y),z * T(y,u),w) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,8640,a(flip),b,8646,a),flip(a)].">
      <j1 rule="hyper" parents="347 8640 8646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8652">
    <literal><![CDATA[
      K(x,R(y,z / T(y,u),w)) = R(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),8650(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 8650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8653">
    <literal><![CDATA[
      R(K(x,y),z * K(u,y),w) = R(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,8652,a(flip),b,8647,a),flip(a)].">
      <j1 rule="hyper" parents="347 8652 8647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8654">
    <literal><![CDATA[
      R(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(601,a,8653,a),flip(a)].">
      <j1 rule="hyper" parents="601 8653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8656">
    <literal><![CDATA[
      R(K(x,y),y \ K(y,z),u) = R(K(x,y),y \ 1,u)
    ]]></literal>
    <justification jstring="[para(6130(a,1),8653(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6130 8653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8657">
    <literal><![CDATA[
      R(K(x,y),K(y,z) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7163(a,1),8653(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7163 8653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8658">
    <literal><![CDATA[
      R(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(601,a,8657,a),flip(a)].">
      <j1 rule="hyper" parents="601 8657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8659">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(x,y) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(133,a,8658,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 8658 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8660">
    <literal><![CDATA[
      R(K(x,y) * R(K(x,y) \ 1,z,u),K(y,w),v5) = K(x,y) * R(R(K(x,y),K(y,w),v5) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(8658(a,1),4685(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8658 4685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8661">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = ((((x \ 1) * (K(y,x) * u)) / ((x \ 1) * u)) * (x \ 1)) * u
    ]]></literal>
    <justification jstring="[para(8656(a,2),1743(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8656 1743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8662">
    <literal><![CDATA[
      x \ (K(y,z) * (K(z,u) * x)) = T(K(y,z) * K(z,u),x)
    ]]></literal>
    <justification jstring="[hyper(462,a,xx,b,8659,a),flip(a)].">
      <j1 rule="hyper" parents="462 8659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8663">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(2556(a,2),8659(a,1,1))].">
      <j1 rule="para" parents="2556 8659"/>
    </justification>
  </clause>

  <clause id="8664">
    <literal><![CDATA[
      K(x,y) * (K(y,x * y) * z) = (y \ L(y,x,y)) * z
    ]]></literal>
    <justification jstring="[para(5527(a,1),8659(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5527 8659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8665">
    <literal><![CDATA[
      K(x,y) * (K(y,T(x,z)) * u) = K(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[para(7247(a,1),8659(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7247 8659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8666">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(8337(a,1),8659(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8337 8659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8667">
    <literal><![CDATA[
      a(x,y,x) * (K(y,x) * z) = K(x * y,x) * z
    ]]></literal>
    <justification jstring="[para(5261(a,1),8666(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5261 8666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8668">
    <literal><![CDATA[
      K(x,y) * (K(y,y * x) * z) = a(y,x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(128,a,5261,a(flip),b,8667,a),flip(a)].">
      <j1 rule="hyper" parents="128 5261 8667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8669">
    <literal><![CDATA[
      K(x,y) * (K(y,x * y) * z) = a(y,x,y) \ z
    ]]></literal>
    <justification jstring="[para(5297(a,2),8668(a,1,2,1))].">
      <j1 rule="para" parents="5297 8668"/>
    </justification>
  </clause>

  <clause id="8670">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = (K(x,y) * K(z,x)) * ((K(z,x) * (K(x,y) * u)) / (K(x,y) * K(z,x)))
    ]]></literal>
    <justification jstring="[para(8663(a,1),4149(a,2,2,1))].">
      <j1 rule="para" parents="8663 4149"/>
    </justification>
  </clause>

  <clause id="8671">
    <literal><![CDATA[
      K(x,y) * (K(x,K(y,z)) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(5273,a,8665,a)].">
      <j1 rule="hyper" parents="5273 8665"/>
    </justification>
  </clause>

  <clause id="8672">
    <literal><![CDATA[
      T(K(x,y) \ T(K(x,T(y,z)) * u,w),K(x,y)) = K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w)
    ]]></literal>
    <justification jstring="[para(8671(a,1),4834(a,1,1,2,1))].">
      <j1 rule="para" parents="8671 4834"/>
    </justification>
  </clause>

  <clause id="8673">
    <literal><![CDATA[
      (x \ L(x,y,x)) * z = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,8669,a(flip),b,8664,a),flip(a)].">
      <j1 rule="hyper" parents="63 8669 8664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8674">
    <literal><![CDATA[
      a(x,y,x) \ 1 = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(130,a,8664,a(flip),b,8669,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="130 8664 8669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8675">
    <literal><![CDATA[
      (x \ L(x,y,x)) \ z = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(128,a,9,a(flip),b,8673,a)].">
      <j1 rule="hyper" parents="128 9 8673"/>
    </justification>
  </clause>

  <clause id="8676">
    <literal><![CDATA[
      (a(x,y,x) \ 1) \ z = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(8674(a,2),8675(a,1,1))].">
      <j1 rule="para" parents="8674 8675"/>
    </justification>
  </clause>

  <clause id="8677">
    <literal><![CDATA[
      L(x,y * (a(z,u,z) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y * (a(z,u,z) \ w),v5) = v6
    ]]></literal>
    <justification jstring="[para(8676(a,1),3617(a,1,2,2))].">
      <j1 rule="para" parents="8676 3617"/>
    </justification>
  </clause>

  <clause id="8678">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,6199,a(flip),b,8648,a),flip(a)].">
      <j1 rule="hyper" parents="347 6199 8648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8679">
    <literal><![CDATA[
      K(R(x,K(y,x) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(5261(a,1),8678(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5261 8678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8680">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,7775,a(flip),b,7670,a),flip(a)].">
      <j1 rule="hyper" parents="35 7775 7670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8681">
    <literal><![CDATA[
      K(x,y) \ T(x,T(z,y)) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(138,a,8680,a)].">
      <j1 rule="hyper" parents="138 8680"/>
    </justification>
  </clause>

  <clause id="8682">
    <literal><![CDATA[
      T(x,T(T(y / z,y),u)) = K(x,u) * T(x * K(u,x),z \ y)
    ]]></literal>
    <justification jstring="[para(7064(a,1),8680(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7064 8680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8683">
    <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(8681(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8681 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8684">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = (y / z) \ (x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(347,a,5604,a(flip),b,7743,a),flip(a)].">
      <j1 rule="hyper" parents="347 5604 7743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8685">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = K(x,y / z) * K(z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,8684,a(flip),b,4943,a)].">
      <j1 rule="hyper" parents="128 8684 4943"/>
    </justification>
  </clause>

  <clause id="8687">
    <literal><![CDATA[
      x * (K(y,z) * L(T(y,x),u,w)) = L(y,u,w) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6042,a,7863,a)].">
      <j1 rule="hyper" parents="6042 7863"/>
    </justification>
  </clause>

  <clause id="8688">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[hyper(5653,a,7923,a)].">
      <j1 rule="hyper" parents="5653 7923"/>
    </justification>
  </clause>

  <clause id="8689">
    <literal><![CDATA[
      K(x * ((T(y,y \ 1) * z) \ (((y \ 1) \ 1) \ (T(y,y \ 1) * z))),y \ 1) = K(x * (z / (T(y,y \ 1) * z)),y \ 1)
    ]]></literal>
    <justification jstring="[para(466(a,1),8039(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="466 8039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8690">
    <literal><![CDATA[
      K(L(x,y,z),(u * x) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z),u \ (x \ w)) = v5
    ]]></literal>
    <justification jstring="[para(8093(a,1),7808(a,1))].">
      <j1 rule="para" parents="8093 7808"/>
    </justification>
  </clause>

  <clause id="8691">
    <literal><![CDATA[
      T(K(x,y),T(z,u * x)) = T(K(x,y),T(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(7794,a,8111,a),flip(a)].">
      <j1 rule="hyper" parents="7794 8111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8692">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),T(y,x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y \ (z * x)),y) = u
    ]]></literal>
    <justification jstring="[para(8691(a,1),7799(a,1))].">
      <j1 rule="para" parents="8691 7799"/>
    </justification>
  </clause>

  <clause id="8693">
    <literal><![CDATA[
      R(x,K(y,T(z,u)),u * K(z,w)) = R(x,K(y,z),u * K(z,w))
    ]]></literal>
    <justification jstring="[para(7091(a,2),8176(a,1,2))].">
      <j1 rule="para" parents="7091 8176"/>
    </justification>
  </clause>

  <clause id="8694">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,u)),K(y,u)) = K(y,u) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(6109(a,1),8210(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6109 8210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8695">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * K(z,y)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(5256(a,1),8273(a,1,1,2))].">
      <j1 rule="para" parents="5256 8273"/>
    </justification>
  </clause>

  <clause id="8696">
    <literal><![CDATA[
      L(K(x,(y * z) \ ((u \ w) * x)),u \ w,u) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * (y * (z / x))) \ w) = v5
    ]]></literal>
    <justification jstring="[para(8573(a,1),8273(a,1,1))].">
      <j1 rule="para" parents="8573 8273"/>
    </justification>
  </clause>

  <clause id="8697">
    <literal><![CDATA[
      T(K(x,y) * z,x * y) = K(x,y) * T(z,x * y)
    ]]></literal>
    <justification jstring="[para(5143(a,1),8493(a,1,1,1))].">
      <j1 rule="para" parents="5143 8493"/>
    </justification>
  </clause>

  <clause id="8698">
    <literal><![CDATA[
      T(x * K(y,z),z * y) = T(x,z * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,5887,a(flip),b,8697,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 5887 8697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8699">
    <literal><![CDATA[
      (x * (y * z)) \ ((y * z) * T(x * K(z,y),y * z)) = L(K(z,y),T(x,y * z),y * z)
    ]]></literal>
    <justification jstring="[para(8698(a,2),262(a,1,2,2))].">
      <j1 rule="para" parents="8698 262"/>
    </justification>
  </clause>

  <clause id="8700">
    <literal><![CDATA[
      T(x * K(y,x),x * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(8698(a,2),5384(a,1))].">
      <j1 rule="para" parents="8698 5384"/>
    </justification>
  </clause>

  <clause id="8701">
    <literal><![CDATA[
      a(T(x,y),z,T(x,y)) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,8513,a(flip),b,8514,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 8513 8514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8703">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * y) \ (z \ u),z)
    ]]></literal>
    <justification jstring="[hyper(6141,a,8568,a),flip(a)].">
      <j1 rule="hyper" parents="6141 8568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8704">
    <literal><![CDATA[
      K((x * (y * z)) \ u,y) = K((x * z) \ (y \ u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8147,a(flip),b,8703,a)].">
      <j1 rule="hyper" parents="63 8147 8703"/>
    </justification>
  </clause>

  <clause id="8705">
    <literal><![CDATA[
      L(K(L(x,y,z),y * L(x,y,z)),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,7202,a(flip),b,8581,a),flip(a)].">
      <j1 rule="hyper" parents="347 7202 8581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8707">
    <literal><![CDATA[
      K((x / y) \ z,R((x / y) \ 1,x / y,y)) = K(((x / y) \ 1) * z,T(y / x,x / y))
    ]]></literal>
    <justification jstring="[para(868(a,1),8620(a,1,2)),flip(a)].">
      <j1 rule="para" parents="868 8620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8708">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,K(y,z)) = T(K(y,z),x) * (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7515,a,b,8635,a)].">
      <j1 rule="hyper" parents="63 7515 8635"/>
    </justification>
  </clause>

  <clause id="8709">
    <literal><![CDATA[
      T(x,T(T(y / z,y),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z \ y,u)) = w
    ]]></literal>
    <justification jstring="[para(8682(a,2),8683(a,1))].">
      <j1 rule="para" parents="8682 8683"/>
    </justification>
  </clause>

  <clause id="8710">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,8622,a(flip),b,8685,a),flip(a)].">
      <j1 rule="hyper" parents="347 8622 8685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8711">
    <literal><![CDATA[
      L(L(T(x,y),z,u),K(x,w),y) \ (L(x,z,u) * (y * K(x,w))) = T(y * K(x,w),L(L(T(x,y),z,u),K(x,w),y))
    ]]></literal>
    <justification jstring="[hyper(548,a,8687,a),flip(a)].">
      <j1 rule="hyper" parents="548 8687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8712">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (((x * y) \ x) \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3873,a(flip),b,8688,a),flip(a)].">
      <j1 rule="hyper" parents="347 3873 8688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8713">
    <literal><![CDATA[
      T(K(x,y) * T(z,K(y,u)),K(y,u)) = K(y,u) * (K(x,y) * (K(y,u) \ z))
    ]]></literal>
    <justification jstring="[para(6873(a,1),8694(a,1,1,2))].">
      <j1 rule="para" parents="6873 8694"/>
    </justification>
  </clause>

  <clause id="8714">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,K(y,z)) = K(y,T(z,x)) * (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(7814,a,8708,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="7814 8708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8715">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,K(x,y)) = K(x,T(y,z)) * (u * K(y,x))
    ]]></literal>
    <justification jstring="[para(7283(a,2),8714(a,1,1,1))].">
      <j1 rule="para" parents="7283 8714"/>
    </justification>
  </clause>

  <clause id="8716">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,(x \ 1) * L((x \ 1) \ 1,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(347,a,556,a(flip),b,7009,a),flip(a)].">
      <j1 rule="hyper" parents="347 556 7009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8718">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x \ L(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[para(1294(a,1),8716(a,1,2))].">
      <j1 rule="para" parents="1294 8716"/>
    </justification>
  </clause>

  <clause id="8719">
    <literal><![CDATA[
      T(x \ L(x,y,z),L(x,u,w) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(5039,a,8718,a)].">
      <j1 rule="hyper" parents="5039 8718"/>
    </justification>
  </clause>

  <clause id="8720">
    <literal><![CDATA[
      T(L(x,y,z) * (x \ 1),L(x,u,w) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1295(a,2),8719(a,1,1))].">
      <j1 rule="para" parents="1295 8719"/>
    </justification>
  </clause>

  <clause id="8721">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ (x \ 1) = (x \ 1) / (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(220,a,8720,a(flip),b,4235,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="220 8720 4235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8722">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,4616,a(flip),b,8721,a),flip(a)].">
      <j1 rule="hyper" parents="347 4616 8721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8723">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1295(a,1),8722(a,1,1))].">
      <j1 rule="para" parents="1295 8722"/>
    </justification>
  </clause>

  <clause id="8724">
    <literal><![CDATA[
      K(R(T(x,y),x \ z,z \ y),u) = K(((x \ z) * (z \ y)) \ y,u)
    ]]></literal>
    <justification jstring="[para(27(a,2),7073(a,1,1))].">
      <j1 rule="para" parents="27 7073"/>
    </justification>
  </clause>

  <clause id="8725">
    <literal><![CDATA[
      K(L(x,y,z),T(u,x \ w)) = K(L(x,y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(5117,a,7201,a),flip(a)].">
      <j1 rule="hyper" parents="5117 7201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8726">
    <literal><![CDATA[
      K(T(x,y \ z),L(y,u,w)) = 1 / K(L(y,u,w),T(x,z))
    ]]></literal>
    <justification jstring="[hyper(220,a,8725,a(flip),b,5173,a),flip(a)].">
      <j1 rule="hyper" parents="220 8725 5173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8727">
    <literal><![CDATA[
      K(T(x,y \ z),L(y,u,w)) = K(x,T(L(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(126,a,7126,a(flip),b,8726,a),flip(a)].">
      <j1 rule="hyper" parents="126 7126 8726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8728">
    <literal><![CDATA[
      K(T(x,y \ z),L(y,u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),8727(a,2,2))].">
      <j1 rule="para" parents="25 8727"/>
    </justification>
  </clause>

  <clause id="8729">
    <literal><![CDATA[
      K(x,L(T(y,y \ z),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,7133,a(flip),b,8728,a)].">
      <j1 rule="hyper" parents="63 7133 8728"/>
    </justification>
  </clause>

  <clause id="8730">
    <literal><![CDATA[
      K(x,L(T(y,y * z),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),8729(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8731">
    <literal><![CDATA[
      K(x,L(T(y,z * y),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(4323(a,2),8730(a,1,2,1))].">
      <j1 rule="para" parents="4323 8730"/>
    </justification>
  </clause>

  <clause id="8732">
    <literal><![CDATA[
      K(x,L(L(y,z,y * K(z,y)),u,w)) = K(x,L(T(y * K(z,y),z),u,w))
    ]]></literal>
    <justification jstring="[para(5081(a,1),8730(a,1,2,1))].">
      <j1 rule="para" parents="5081 8730"/>
    </justification>
  </clause>

  <clause id="8733">
    <literal><![CDATA[
      R(x * K(y,T(z,u)),K(z,T(y,u)),u) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(7126(a,1),7434(a,1,1))].">
      <j1 rule="para" parents="7126 7434"/>
    </justification>
  </clause>

  <clause id="8734">
    <literal><![CDATA[
      R(K(x,T(T(y,z),z * u)),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(7091(a,2),7438(a,1,1))].">
      <j1 rule="para" parents="7091 7438"/>
    </justification>
  </clause>

  <clause id="8735">
    <literal><![CDATA[
      R(K(x,y),z,u) \ K(w,R(K(y,x),z,u)) = R(T(K(y,x),w),z,u)
    ]]></literal>
    <justification jstring="[hyper(128,a,7527,a(flip),b,6703,a(flip))].">
      <j1 rule="hyper" parents="128 7527 6703"/>
    </justification>
  </clause>

  <clause id="8736">
    <literal><![CDATA[
      K(x,y / R(T(x,z),u,w)) = K(x,R(x,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(7758,a,7945,a)].">
      <j1 rule="hyper" parents="7758 7945"/>
    </justification>
  </clause>

  <clause id="8737">
    <literal><![CDATA[
      K(x,R(x,y,z) \ ((x * R(T(x,u),y,z)) / w)) = K(x,T(w \ x,R(T(x,u),y,z)))
    ]]></literal>
    <justification jstring="[hyper(8595,a,8736,a),flip(a)].">
      <j1 rule="hyper" parents="8595 8736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8738">
    <literal><![CDATA[
      K(x,R(T(y \ z,z * u),y,u)) = K(x,T((y * u) \ (z * u),y))
    ]]></literal>
    <justification jstring="[para(27(a,2),7770(a,1,2))].">
      <j1 rule="para" parents="27 7770"/>
    </justification>
  </clause>

  <clause id="8739">
    <literal><![CDATA[
      T(K(x,y) * L(y,z,u),x) = y * T(y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(7803,a,5218,a)].">
      <j1 rule="hyper" parents="7803 5218"/>
    </justification>
  </clause>

  <clause id="8740">
    <literal><![CDATA[
      T(K(x,y) * L(y,z,u),x) / (y * (y \ L(y,z,u))) = K(y \ L(y,z,u),T(x,y))
    ]]></literal>
    <justification jstring="[hyper(131,a,8739,a,b,7699,a)].">
      <j1 rule="hyper" parents="131 8739 7699"/>
    </justification>
  </clause>

  <clause id="8741">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K((K(z,u) * y) / x,z)
    ]]></literal>
    <justification jstring="[hyper(7859,a,8158,a),flip(a)].">
      <j1 rule="hyper" parents="7859 8158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8742">
    <literal><![CDATA[
      K((K(x,y) * z) / u,x) = K(z / u,x)
    ]]></literal>
    <justification jstring="[hyper(7492,a,8741,a),flip(a)].">
      <j1 rule="hyper" parents="7492 8741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8743">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = (w * K(z / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(8742(a,1),6123(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8742 6123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8744">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[hyper(347,a,6199,a(flip),b,8743,a),flip(a)].">
      <j1 rule="hyper" parents="347 6199 8743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8745">
    <literal><![CDATA[
      K(x,(T(y,x) * z) / u) = K(x,(y * z) / u)
    ]]></literal>
    <justification jstring="[para(4946(a,1),8744(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4946 8744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8746">
    <literal><![CDATA[
      K(x,(y * K(z,x)) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(7427(a,1),8744(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7427 8744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8747">
    <literal><![CDATA[
      K(x,(T(y / (z \ u),x) * K(z \ u,z)) / w) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[para(6125(a,1),8745(a,2,2,1))].">
      <j1 rule="para" parents="6125 8745"/>
    </justification>
  </clause>

  <clause id="8748">
    <literal><![CDATA[
      K(R(x,y,z),u * K(x,w)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,5548,a(flip),b,7913,a),flip(a)].">
      <j1 rule="hyper" parents="347 5548 7913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8749">
    <literal><![CDATA[
      K(R(x,y,z),u * K(w,x)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(6109(a,1),8748(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6109 8748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8750">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * y) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(347,a,8572,a(flip),b,8019,a),flip(a)].">
      <j1 rule="hyper" parents="347 8572 8019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8751">
    <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(1909(a,2),8024(a,2,2,1,2))].">
      <j1 rule="para" parents="1909 8024"/>
    </justification>
  </clause>

  <clause id="8752">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(8043,a,8020,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8043 8020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8753">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,7279,a,b,8752,a),flip(a)].">
      <j1 rule="hyper" parents="347 7279 8752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8754">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = K(x,K(y,z \ R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(1746(a,1),8752(a,1,2,2))].">
      <j1 rule="para" parents="1746 8752"/>
    </justification>
  </clause>

  <clause id="8755">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5096(a,1),8752(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5096 8752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8756">
    <literal><![CDATA[
      K(x,K(y,z \ (y * u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(8017(a,1),8752(a,1,2))].">
      <j1 rule="para" parents="8017 8752"/>
    </justification>
  </clause>

  <clause id="8757">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,7283,a,b,8755,a),flip(a)].">
      <j1 rule="hyper" parents="347 7283 8755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8758">
    <literal><![CDATA[
      T(x,K(y,y \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,8755,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 8755 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8759">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),8755(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8760">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5096(a,1),8755(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5096 8755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8761">
    <literal><![CDATA[
      K(x,K(y \ z,y)) = K(x,K(z / y,z))
    ]]></literal>
    <justification jstring="[para(5798(a,1),8755(a,1,2))].">
      <j1 rule="para" parents="5798 8755"/>
    </justification>
  </clause>

  <clause id="8763">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,x \ y) * u) = K(x,T(x \ y,z)) * u
    ]]></literal>
    <justification jstring="[para(8757(a,1),7446(a,1,1))].">
      <j1 rule="para" parents="8757 7446"/>
    </justification>
  </clause>

  <clause id="8764">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),8758(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8765">
    <literal><![CDATA[
      K(x \ y,x) * T(z,K(x,y)) = z * K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(8758(a,1),7344(a,1,2))].">
      <j1 rule="para" parents="8758 7344"/>
    </justification>
  </clause>

  <clause id="8767">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y * z,y) = K(y * z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(133,a,8759,a(flip),b,7105,a)].">
      <j1 rule="hyper" parents="133 8759 7105"/>
    </justification>
  </clause>

  <clause id="8768">
    <literal><![CDATA[
      K(x * y,x) * K(z,K(x,y)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[para(8759(a,1),7094(a,1,2))].">
      <j1 rule="para" parents="8759 7094"/>
    </justification>
  </clause>

  <clause id="8769">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(7278,a,8760,a)].">
      <j1 rule="hyper" parents="7278 8760"/>
    </justification>
  </clause>

  <clause id="8770">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7279,a,b,8760,a),flip(a)].">
      <j1 rule="hyper" parents="347 7279 8760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8771">
    <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(86(a,1),8760(a,1,2,2))].">
      <j1 rule="para" parents="86 8760"/>
    </justification>
  </clause>

  <clause id="8772">
    <literal><![CDATA[
      K(x,K(y,z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8760(a,2),7328(a,1))].">
      <j1 rule="para" parents="8760 7328"/>
    </justification>
  </clause>

  <clause id="8773">
    <literal><![CDATA[
      T(K(x * y,x) * z,K(x,y)) = z * K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(7353,a,8764,a),flip(a)].">
      <j1 rule="hyper" parents="7353 8764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8774">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,7330,a,b,8764,a),flip(a)].">
      <j1 rule="hyper" parents="347 7330 8764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8775">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7283,a,b,8769,a),flip(a)].">
      <j1 rule="hyper" parents="347 7283 8769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8776">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7260,a,b,8769,a),flip(a)].">
      <j1 rule="hyper" parents="347 7260 8769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8777">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7281,a,8770,a)].">
      <j1 rule="hyper" parents="7281 8770"/>
    </justification>
  </clause>

  <clause id="8778">
    <literal><![CDATA[
      T(x,K(y * z,y)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(7362,a,8774,a)].">
      <j1 rule="hyper" parents="7362 8774"/>
    </justification>
  </clause>

  <clause id="8779">
    <literal><![CDATA[
      T(x,K(y,z * y)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(5297(a,2),8774(a,1,2))].">
      <j1 rule="para" parents="5297 8774"/>
    </justification>
  </clause>

  <clause id="8780">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,T(z * y,z))
    ]]></literal>
    <justification jstring="[para(8774(a,1),7349(a,1,1))].">
      <j1 rule="para" parents="8774 7349"/>
    </justification>
  </clause>

  <clause id="8781">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(7314,a,8775,a)].">
      <j1 rule="hyper" parents="7314 8775"/>
    </justification>
  </clause>

  <clause id="8782">
    <literal><![CDATA[
      K(x,K(y * x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7281,a,8775,a)].">
      <j1 rule="hyper" parents="7281 8775"/>
    </justification>
  </clause>

  <clause id="8783">
    <literal><![CDATA[
      K(x * y,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8776(a,1),7509(a,1,2))].">
      <j1 rule="para" parents="8776 7509"/>
    </justification>
  </clause>

  <clause id="8784">
    <literal><![CDATA[
      T(x,K(y,z * x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,8777,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 8777 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8785">
    <literal><![CDATA[
      T(x,K(y \ z,y)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),8778(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 8778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8786">
    <literal><![CDATA[
      (x * y) \ T(z * (x * y),K(x,y)) = T(z,T(x * y,y))
    ]]></literal>
    <justification jstring="[hyper(128,a,8779,a(flip),b,7338,a(flip))].">
      <j1 rule="hyper" parents="128 8779 7338"/>
    </justification>
  </clause>

  <clause id="8789">
    <literal><![CDATA[
      T(x,K(y,z / x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),8784(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 8784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8790">
    <literal><![CDATA[
      T(x,K(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8785(a,2),7362(a,1))].">
      <j1 rule="para" parents="8785 7362"/>
    </justification>
  </clause>

  <clause id="8791">
    <literal><![CDATA[
      T(x,K(y,z / x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,7330,a,b,8789,a),flip(a)].">
      <j1 rule="hyper" parents="347 7330 8789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8792">
    <literal><![CDATA[
      T(x,K(y,z / x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8791(a,2),7362(a,1))].">
      <j1 rule="para" parents="8791 7362"/>
    </justification>
  </clause>

  <clause id="8793">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(x,K(z,z \ y))
    ]]></literal>
    <justification jstring="[hyper(7328,a,8761,a),flip(a)].">
      <j1 rule="hyper" parents="7328 8761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8794">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,8755,a(flip),b,8793,a),flip(a)].">
      <j1 rule="hyper" parents="347 8755 8793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8795">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(80(a,1),8794(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="80 8794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8796">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(7328,a,8795,a)].">
      <j1 rule="hyper" parents="7328 8795"/>
    </justification>
  </clause>

  <clause id="8797">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,7260,a,b,8795,a),flip(a)].">
      <j1 rule="hyper" parents="347 7260 8795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8798">
    <literal><![CDATA[
      K(x,K(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8797(a,2),7278(a,1))].">
      <j1 rule="para" parents="8797 7278"/>
    </justification>
  </clause>

  <clause id="8799">
    <literal><![CDATA[
      T(x * (y \ z),K(y,z)) = (y \ z) * T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(8790,a,7468,a)].">
      <j1 rule="hyper" parents="8790 7468"/>
    </justification>
  </clause>

  <clause id="8800">
    <literal><![CDATA[
      T(x,K(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7330(a,1),8790(a,1))].">
      <j1 rule="para" parents="7330 8790"/>
    </justification>
  </clause>

  <clause id="8801">
    <literal><![CDATA[
      K(x,K(y,z \ (u * x))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(7281,a,8753,a)].">
      <j1 rule="hyper" parents="7281 8753"/>
    </justification>
  </clause>

  <clause id="8802">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z \ u)) = w
    ]]></literal>
    <justification jstring="[para(8753(a,2),7281(a,1))].">
      <j1 rule="para" parents="8753 7281"/>
    </justification>
  </clause>

  <clause id="8803">
    <literal><![CDATA[
      K(x \ y,x) * z != u * K(x \ y,x)
    ]]></literal>
    <literal><![CDATA[
      T(u,K(x,y)) = z
    ]]></literal>
    <justification jstring="[para(8765(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="8765 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8804">
    <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(7309(a,2),8767(a,1,1))].">
      <j1 rule="para" parents="7309 8767"/>
    </justification>
  </clause>

  <clause id="8805">
    <literal><![CDATA[
      K(x * y,x) * K(x,K(y,z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7283(a,2),8768(a,1,2))].">
      <j1 rule="para" parents="7283 8768"/>
    </justification>
  </clause>

  <clause id="8806">
    <literal><![CDATA[
      K(x \ y,x) * (z * (y / x)) = T(z * (x \ y),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(5634,a,8799,a(flip))].">
      <j1 rule="hyper" parents="5634 8799"/>
    </justification>
  </clause>

  <clause id="8807">
    <literal><![CDATA[
      K(x,K(y,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),8802(a,1,2,2,2))].">
      <j1 rule="para" parents="7 8802"/>
    </justification>
  </clause>

  <clause id="8808">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8807,a,8796,a)].">
      <j1 rule="hyper" parents="8807 8796"/>
    </justification>
  </clause>

  <clause id="8809">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7328,a,8808,a)].">
      <j1 rule="hyper" parents="7328 8808"/>
    </justification>
  </clause>

  <clause id="8810">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7293,a,b,8808,a),flip(a)].">
      <j1 rule="hyper" parents="347 7293 8808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8811">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,7279,a,b,8808,a),flip(a)].">
      <j1 rule="hyper" parents="347 7279 8808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8812">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(132,a,8808,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 8808 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8813">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(3885(a,1),8808(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3885 8808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8814">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(3890(a,2),8808(a,1,2))].">
      <j1 rule="para" parents="3890 8808"/>
    </justification>
  </clause>

  <clause id="8815">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(6250(a,1),8808(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6250 8808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8816">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8808(a,2),7328(a,1))].">
      <j1 rule="para" parents="8808 7328"/>
    </justification>
  </clause>

  <clause id="8817">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,7283,a(flip),b,8809,a),flip(a)].">
      <j1 rule="hyper" parents="347 7283 8809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8818">
    <literal><![CDATA[
      K(x,y * ((z \ (y \ 1)) * z)) = K(x,K(y * z,z))
    ]]></literal>
    <justification jstring="[para(5682(a,2),8809(a,1,2))].">
      <j1 rule="para" parents="5682 8809"/>
    </justification>
  </clause>

  <clause id="8819">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(7295,a,8810,a)].">
      <j1 rule="hyper" parents="7295 8810"/>
    </justification>
  </clause>

  <clause id="8820">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,8810,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 8810 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8821">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8294,a,b,8810,a)].">
      <j1 rule="hyper" parents="63 8294 8810"/>
    </justification>
  </clause>

  <clause id="8822">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(83(a,1),8810(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="83 8810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8823">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[para(5621(a,1),8810(a,1,2))].">
      <j1 rule="para" parents="5621 8810"/>
    </justification>
  </clause>

  <clause id="8824">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(5623(a,2),8810(a,1,2))].">
      <j1 rule="para" parents="5623 8810"/>
    </justification>
  </clause>

  <clause id="8825">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6250(a,1),8810(a,1,2))].">
      <j1 rule="para" parents="6250 8810"/>
    </justification>
  </clause>

  <clause id="8826">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[para(8810(a,1),7266(a,1,2))].">
      <j1 rule="para" parents="8810 7266"/>
    </justification>
  </clause>

  <clause id="8827">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7295,a,8811,a)].">
      <j1 rule="hyper" parents="7295 8811"/>
    </justification>
  </clause>

  <clause id="8828">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(3890(a,2),8811(a,1,2))].">
      <j1 rule="para" parents="3890 8811"/>
    </justification>
  </clause>

  <clause id="8829">
    <literal><![CDATA[
      T(x,K(y \ z,u)) = T(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(6250(a,1),8812(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6250 8812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8830">
    <literal><![CDATA[
      K(x \ 1,y) * T(z,K(x,y)) = z * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(8812(a,1),7344(a,1,2))].">
      <j1 rule="para" parents="8812 7344"/>
    </justification>
  </clause>

  <clause id="8831">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ K(u,y)) = T(z \ K(u,y),K(x,y))
    ]]></literal>
    <justification jstring="[para(8813(a,1),8153(a,1,1))].">
      <j1 rule="para" parents="8813 8153"/>
    </justification>
  </clause>

  <clause id="8832">
    <literal><![CDATA[
      K(1 / x,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(7295,a,8814,a)].">
      <j1 rule="hyper" parents="7295 8814"/>
    </justification>
  </clause>

  <clause id="8833">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,(T(u,x) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(5695(a,1),8817(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5695 8817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8834">
    <literal><![CDATA[
      L(K(x \ 1,K(y,z)),u,w) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(8529,a,8819,a)].">
      <j1 rule="hyper" parents="8529 8819"/>
    </justification>
  </clause>

  <clause id="8835">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,7261,a,b,8819,a),flip(a)].">
      <j1 rule="hyper" parents="347 7261 8819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8836">
    <literal><![CDATA[
      K(x,y \ 1) * T(z,K(x,y)) = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,8820,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 8820 22"/>
    </justification>
  </clause>

  <clause id="8837">
    <literal><![CDATA[
      T(x,K(y,1 / z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(83(a,1),8820(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="83 8820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8838">
    <literal><![CDATA[
      T(x,K(y,x \ z)) / (z * T(z \ x,y)) = (x * (x / (z * T(z \ x,y)))) / x
    ]]></literal>
    <justification jstring="[para(8820(a,1),6330(a,1,1))].">
      <j1 rule="para" parents="8820 6330"/>
    </justification>
  </clause>

  <clause id="8839">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,y)) / w)) = K(x,K(y,1 / (z / w)))
    ]]></literal>
    <justification jstring="[para(8746(a,2),8822(a,2,2)),flip(a)].">
      <j1 rule="para" parents="8746 8822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8840">
    <literal><![CDATA[
      K(1 / x,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7213,a,8827,a),flip(a)].">
      <j1 rule="hyper" parents="7213 8827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8841">
    <literal><![CDATA[
      K(x,K(y,z)) / y != u
    ]]></literal>
    <literal><![CDATA[
      T(1 / y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8832(a,1),5229(a,1,1))].">
      <j1 rule="para" parents="8832 5229"/>
    </justification>
  </clause>

  <clause id="8842">
    <literal><![CDATA[
      K(1 / x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8832(a,2),7328(a,1))].">
      <j1 rule="para" parents="8832 7328"/>
    </justification>
  </clause>

  <clause id="8843">
    <literal><![CDATA[
      K(1 / x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8840(a,2),7281(a,1))].">
      <j1 rule="para" parents="8840 7281"/>
    </justification>
  </clause>

  <clause id="8844">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(8815(a,1),7328(a,1))].">
      <j1 rule="para" parents="8815 7328"/>
    </justification>
  </clause>

  <clause id="8845">
    <literal><![CDATA[
      K(x,K(y \ (z * u),u \ (z \ 1))) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(8614(a,1),8815(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8614 8815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8846">
    <literal><![CDATA[
      K(x,K(y,z \ (u * x))) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,8801,a,b,8825,a)].">
      <j1 rule="hyper" parents="347 8801 8825"/>
    </justification>
  </clause>

  <clause id="8847">
    <literal><![CDATA[
      T(x,K(y \ z,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,8758,a(flip),b,8829,a),flip(a)].">
      <j1 rule="hyper" parents="347 8758 8829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8848">
    <literal><![CDATA[
      T(x * K(y / z,x),z \ y) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7579,a,b,8847,a)].">
      <j1 rule="hyper" parents="63 7579 8847"/>
    </justification>
  </clause>

  <clause id="8849">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(5621(a,1),8816(a,1,2))].">
      <j1 rule="para" parents="5621 8816"/>
    </justification>
  </clause>

  <clause id="8850">
    <literal><![CDATA[
      (T(x * y,K(z,u)) / y) / x = K(z,K(u,(1 / y) / x))
    ]]></literal>
    <justification jstring="[hyper(8842,a,5577,a),flip(a)].">
      <j1 rule="hyper" parents="8842 5577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8851">
    <literal><![CDATA[
      T(K(x,y),z \ 1) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7509,a,8826,a),flip(a)].">
      <j1 rule="hyper" parents="7509 8826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8852">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7480,a,8851,a)].">
      <j1 rule="hyper" parents="7480 8851"/>
    </justification>
  </clause>

  <clause id="8853">
    <literal><![CDATA[
      K(x,T(T(y,z),z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7382,a,8851,a)].">
      <j1 rule="hyper" parents="7382 8851"/>
    </justification>
  </clause>

  <clause id="8854">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8851(a,1),7109(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8851 7109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8855">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ 1) = (z \ 1) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8851(a,1),7358(a,1,1))].">
      <j1 rule="para" parents="8851 7358"/>
    </justification>
  </clause>

  <clause id="8856">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(7605,a,8852,a),flip(a)].">
      <j1 rule="hyper" parents="7605 8852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8857">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,8852,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 8852 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8858">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,T(y * z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7657,a(flip),b,8852,a)].">
      <j1 rule="hyper" parents="63 7657 8852"/>
    </justification>
  </clause>

  <clause id="8859">
    <literal><![CDATA[
      K(x,T(y,z \ y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7652,a(flip),b,8852,a)].">
      <j1 rule="hyper" parents="63 7652 8852"/>
    </justification>
  </clause>

  <clause id="8860">
    <literal><![CDATA[
      K(x,T(y,1 / z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(83(a,1),8852(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="83 8852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8861">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),z)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),8852(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 8852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8862">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u / z))
    ]]></literal>
    <justification jstring="[para(4435(a,1),8852(a,1,2))].">
      <j1 rule="para" parents="4435 8852"/>
    </justification>
  </clause>

  <clause id="8864">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8853(a,1),7490(a,1))].">
      <j1 rule="para" parents="8853 7490"/>
    </justification>
  </clause>

  <clause id="8865">
    <literal><![CDATA[
      T(x * y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8857(a,1),7590(a,1))].">
      <j1 rule="para" parents="8857 7590"/>
    </justification>
  </clause>

  <clause id="8866">
    <literal><![CDATA[
      K((x \ y) \ z,T(y,x)) = K(z / (x \ y),y)
    ]]></literal>
    <justification jstring="[hyper(7485,a,8859,a),flip(a)].">
      <j1 rule="hyper" parents="7485 8859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8867">
    <literal><![CDATA[
      T(x,T(y,z \ y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,8859,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 8859 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8868">
    <literal><![CDATA[
      T(x,T(T(y,z \ y),u)) = K(x,u) * T(x * K(u,x),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,8867,a(flip),b,8681,a),flip(a)].">
      <j1 rule="hyper" parents="134 8867 8681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8869">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8854(a,2),4984(a,1))].">
      <j1 rule="para" parents="8854 4984"/>
    </justification>
  </clause>

  <clause id="8870">
    <literal><![CDATA[
      K(x * R(y,z,u),T(y,x)) = K(x * R(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(196(a,1),8856(a,1,2)),flip(a)].">
      <j1 rule="para" parents="196 8856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8871">
    <literal><![CDATA[
      K(x * L(y,z,u),T(y,x)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(197(a,1),8856(a,1,2)),flip(a)].">
      <j1 rule="para" parents="197 8856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8872">
    <literal><![CDATA[
      K(L(x,y,z) * u,T(x,u)) = K(L(x,y,z) * u,x)
    ]]></literal>
    <justification jstring="[para(197(a,1),8856(a,2,2))].">
      <j1 rule="para" parents="197 8856"/>
    </justification>
  </clause>

  <clause id="8873">
    <literal><![CDATA[
      K(x,T(y,x / z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7693,a(flip),b,8862,a),flip(a)].">
      <j1 rule="hyper" parents="347 7693 8862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8874">
    <literal><![CDATA[
      K(x,T(y,z \ x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(80(a,1),8873(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="80 8873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8875">
    <literal><![CDATA[
      (x / y) * K(x,T(z,y)) = K(x,z) * (x / y)
    ]]></literal>
    <justification jstring="[para(8873(a,1),7104(a,1,2))].">
      <j1 rule="para" parents="8873 7104"/>
    </justification>
  </clause>

  <clause id="8876">
    <literal><![CDATA[
      K(x,T(x \ y,z \ y)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7785,a,b,8874,a)].">
      <j1 rule="hyper" parents="63 7785 8874"/>
    </justification>
  </clause>

  <clause id="8877">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ x) = (z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,8874,a(flip),b,7378,a)].">
      <j1 rule="hyper" parents="133 8874 7378"/>
    </justification>
  </clause>

  <clause id="8878">
    <literal><![CDATA[
      (x \ y) * K(y,T(z,x)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(8874(a,1),7104(a,1,2))].">
      <j1 rule="para" parents="8874 7104"/>
    </justification>
  </clause>

  <clause id="8879">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(4435(a,1),8864(a,1,2))].">
      <j1 rule="para" parents="4435 8864"/>
    </justification>
  </clause>

  <clause id="8880">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(6258(a,1),8864(a,1,2))].">
      <j1 rule="para" parents="6258 8864"/>
    </justification>
  </clause>

  <clause id="8881">
    <literal><![CDATA[
      T(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(2966(a,1),8869(a,1,2))].">
      <j1 rule="para" parents="2966 8869"/>
    </justification>
  </clause>

  <clause id="8882">
    <literal><![CDATA[
      K(x,K(y,(z * x) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8825,a,b,8846,a)].">
      <j1 rule="hyper" parents="63 8825 8846"/>
    </justification>
  </clause>

  <clause id="8883">
    <literal><![CDATA[
      T(T(x,y / z),K(y,z)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4972(a,1),8848(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4972 8848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8884">
    <literal><![CDATA[
      T(x / (y / z),z \ y) = T((y / z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4990(a,1),8848(a,1,1))].">
      <j1 rule="para" parents="4990 8848"/>
    </justification>
  </clause>

  <clause id="8885">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(8848(a,1),5059(a,1,1))].">
      <j1 rule="para" parents="8848 5059"/>
    </justification>
  </clause>

  <clause id="8886">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(8848(a,1),5066(a,1,1))].">
      <j1 rule="para" parents="8848 5066"/>
    </justification>
  </clause>

  <clause id="8887">
    <literal><![CDATA[
      T(T(x,y \ z),K(y,z)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(6895,a,8883,a)].">
      <j1 rule="hyper" parents="6895 8883"/>
    </justification>
  </clause>

  <clause id="8888">
    <literal><![CDATA[
      T(T(x,y \ z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(8883(a,1),7538(a,1,1))].">
      <j1 rule="para" parents="8883 7538"/>
    </justification>
  </clause>

  <clause id="8889">
    <literal><![CDATA[
      T(T(x,K(y,z)),y \ z) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(6888(a,1),8885(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6888 8885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8892">
    <literal><![CDATA[
      T(T(x,K(y,z \ (y * u))),y \ ((y \ z) \ u)) = T(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(6767(a,1),8889(a,1,1,2))].">
      <j1 rule="para" parents="6767 8889"/>
    </justification>
  </clause>

  <clause id="8893">
    <literal><![CDATA[
      (x / (x * y)) * K(x,y) = K(x,y) * (x / (x * y))
    ]]></literal>
    <justification jstring="[para(7168(a,1),8875(a,1,2))].">
      <j1 rule="para" parents="7168 8875"/>
    </justification>
  </clause>

  <clause id="8894">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(12(a,1),8882(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 8882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8895">
    <literal><![CDATA[
      K(x,K(y,(x \ z) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7988,a(flip),b,8894,a)].">
      <j1 rule="hyper" parents="63 7988 8894"/>
    </justification>
  </clause>

  <clause id="8896">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(190(a,1),8895(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="190 8895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8897">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ u)) = K(x,T(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(8895(a,1),7267(a,1,2))].">
      <j1 rule="para" parents="8895 7267"/>
    </justification>
  </clause>

  <clause id="8898">
    <literal><![CDATA[
      T(x,K(y,x \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,8896,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 8896 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8899">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8825,a,b,8896,a)].">
      <j1 rule="hyper" parents="63 8825 8896"/>
    </justification>
  </clause>

  <clause id="8900">
    <literal><![CDATA[
      K(x,K(y,x * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),8896(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8901">
    <literal><![CDATA[
      K(x,K(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8896(a,2),7328(a,1))].">
      <j1 rule="para" parents="8896 7328"/>
    </justification>
  </clause>

  <clause id="8902">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,7283,a(flip),b,8899,a),flip(a)].">
      <j1 rule="hyper" parents="347 7283 8899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8903">
    <literal><![CDATA[
      T(x,K(y,z \ x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,8899,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 8899 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8904">
    <literal><![CDATA[
      K(x,K(y,x / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(83(a,1),8899(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="83 8899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8905">
    <literal><![CDATA[
      K(x,K(y,T(x,z) * u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7987,a,b,8900,a)].">
      <j1 rule="hyper" parents="63 7987 8900"/>
    </justification>
  </clause>

  <clause id="8906">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ y) = T(x \ y,K(y,z))
    ]]></literal>
    <justification jstring="[para(8902(a,1),7304(a,1,1))].">
      <j1 rule="para" parents="8902 7304"/>
    </justification>
  </clause>

  <clause id="8907">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z \ x) = K(y,z \ x) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,8903,a(flip),b,7355,a)].">
      <j1 rule="hyper" parents="133 8903 7355"/>
    </justification>
  </clause>

  <clause id="8908">
    <literal><![CDATA[
      T(x,K(y,x / z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(83(a,1),8903(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="83 8903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8909">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),K(z,(y * x) / u)) = (T(y * x,K(z,u)) / x) / y
    ]]></literal>
    <justification jstring="[para(8908(a,1),5577(a,2,1,1))].">
      <j1 rule="para" parents="8908 5577"/>
    </justification>
  </clause>

  <clause id="8910">
    <literal><![CDATA[
      K(x,K(y \ z,T(y,u))) = K(y,K(z,T(x,u)))
    ]]></literal>
    <justification jstring="[hyper(8901,a,7523,a),flip(a)].">
      <j1 rule="hyper" parents="8901 7523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8911">
    <literal><![CDATA[
      T(x \ y,K(y,z)) = T(x,K(y,z)) \ y
    ]]></literal>
    <justification jstring="[hyper(7327,a,8906,a),flip(a)].">
      <j1 rule="hyper" parents="7327 8906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8912">
    <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(8910(a,2),7475(a,1))].">
      <j1 rule="para" parents="8910 7475"/>
    </justification>
  </clause>

  <clause id="8913">
    <literal><![CDATA[
      1 / T(x,K(y,z)) = T(1 / x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8841,a,7312,a),flip(a)].">
      <j1 rule="hyper" parents="8841 7312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8914">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = 1 / (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(6121(a,1),8913(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6121 8913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8915">
    <literal><![CDATA[
      T(T(x,K(y,z)),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),8888(a,1))].">
      <j1 rule="para" parents="23 8888"/>
    </justification>
  </clause>

  <clause id="8916">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y \ z,z))
    ]]></literal>
    <justification jstring="[para(7787(a,1),8818(a,2,2))].">
      <j1 rule="para" parents="7787 8818"/>
    </justification>
  </clause>

  <clause id="8917">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(8810(a,1),8821(a,1,1))].">
      <j1 rule="para" parents="8810 8821"/>
    </justification>
  </clause>

  <clause id="8918">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,K(z,R(x,u,w)))
    ]]></literal>
    <justification jstring="[para(8811(a,1),8821(a,1,1))].">
      <j1 rule="para" parents="8811 8821"/>
    </justification>
  </clause>

  <clause id="8919">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(8819(a,1),8834(a,1,1))].">
      <j1 rule="para" parents="8819 8834"/>
    </justification>
  </clause>

  <clause id="8920">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(8827(a,1),8834(a,1,1))].">
      <j1 rule="para" parents="8827 8834"/>
    </justification>
  </clause>

  <clause id="8921">
    <literal><![CDATA[
      (x * y) * K(z,K(u,L(w,y,x))) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(134,a,8919,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 8919 18"/>
    </justification>
  </clause>

  <clause id="8922">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(z,K(x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8919,a(flip),b,8920,a),flip(a)].">
      <j1 rule="hyper" parents="63 8919 8920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8923">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(y,K(w,L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8134,a(flip),b,8920,a)].">
      <j1 rule="hyper" parents="63 8134 8920"/>
    </justification>
  </clause>

  <clause id="8924">
    <literal><![CDATA[
      (x * y) * K(z,K(u,L(w,y,x))) = x * (y * K(w,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(134,a,8920,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 8920 18"/>
    </justification>
  </clause>

  <clause id="8925">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,7279,a,b,8922,a)].">
      <j1 rule="hyper" parents="347 7279 8922"/>
    </justification>
  </clause>

  <clause id="8926">
    <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(8922(a,2),7281(a,1))].">
      <j1 rule="para" parents="8922 7281"/>
    </justification>
  </clause>

  <clause id="8927">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(w,K(y,L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,7279,a,b,8923,a),flip(a)].">
      <j1 rule="hyper" parents="347 7279 8923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8928">
    <literal><![CDATA[
      K(x,K(y,L(z,1 / u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(3189(a,1),8925(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3189 8925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8929">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8556,a(flip),b,8927,a)].">
      <j1 rule="hyper" parents="63 8556 8927"/>
    </justification>
  </clause>

  <clause id="8930">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,8925,a,b,8929,a),flip(a)].">
      <j1 rule="hyper" parents="347 8925 8929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8932">
    <literal><![CDATA[
      K(x,K(y / z,L(u,y,w))) = K(x,K(u,L(y / z,z,w)))
    ]]></literal>
    <justification jstring="[para(8425(a,1),8929(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8425 8929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8933">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w)) = T(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(132,a,8930,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 8930 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8935">
    <literal><![CDATA[
      T(x,y) * K(y * R(x,z,u),x) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(8870(a,1),5076(a,1,2))].">
      <j1 rule="para" parents="8870 5076"/>
    </justification>
  </clause>

  <clause id="8936">
    <literal><![CDATA[
      T(x,y) * K(y * L(x,z,u),x) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(8871(a,1),6586(a,1,2))].">
      <j1 rule="para" parents="8871 6586"/>
    </justification>
  </clause>

  <clause id="8937">
    <literal><![CDATA[
      K(T(L(x,y,z) * u,u),x) = K(L(x,y,z) * u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7093,a,b,8872,a)].">
      <j1 rule="hyper" parents="63 7093 8872"/>
    </justification>
  </clause>

  <clause id="8938">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z \ x) = x * K(y,x / z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7646,a(flip),b,8907,a),flip(a)].">
      <j1 rule="hyper" parents="347 7646 8907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8939">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z \ x) = K(y,x / z)
    ]]></literal>
    <justification jstring="[hyper(5168,a,8938,a)].">
      <j1 rule="hyper" parents="5168 8938"/>
    </justification>
  </clause>

  <clause id="8940">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z \ y) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(34,a,7288,a,b,8938,a(flip))].">
      <j1 rule="hyper" parents="34 7288 8938"/>
    </justification>
  </clause>

  <clause id="8941">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(7283(a,2),8939(a,1,1))].">
      <j1 rule="para" parents="7283 8939"/>
    </justification>
  </clause>

  <clause id="8942">
    <literal><![CDATA[
      K(x,y \ z) * K(x,K(z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(7586,a,8940,a)].">
      <j1 rule="hyper" parents="7586 8940"/>
    </justification>
  </clause>

  <clause id="8943">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(7322,a,8940,a)].">
      <j1 rule="hyper" parents="7322 8940"/>
    </justification>
  </clause>

  <clause id="8944">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(6900,a,8940,a)].">
      <j1 rule="hyper" parents="6900 8940"/>
    </justification>
  </clause>

  <clause id="8945">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) * K(x,((u * z) \ u) \ y) = K(x,y / ((u * z) \ u))
    ]]></literal>
    <justification jstring="[para(6259(a,1),8940(a,1,1,2))].">
      <j1 rule="para" parents="6259 8940"/>
    </justification>
  </clause>

  <clause id="8946">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,(u / (z * u)) \ y) = K(x,y / (u / (z * u)))
    ]]></literal>
    <justification jstring="[para(8824(a,1),8940(a,1,1))].">
      <j1 rule="para" parents="8824 8940"/>
    </justification>
  </clause>

  <clause id="8947">
    <literal><![CDATA[
      K(x,K(y,z \ (y * u))) * K(x,y \ ((y \ z) \ u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(6767(a,1),8941(a,1,1,2))].">
      <j1 rule="para" parents="6767 8941"/>
    </justification>
  </clause>

  <clause id="8948">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) * K(x,K(y,z \ (y * u))) = K(x,y / ((y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(6767(a,1),8942(a,1,2,2))].">
      <j1 rule="para" parents="6767 8942"/>
    </justification>
  </clause>

  <clause id="8949">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) * K(x,((y \ u) \ u) / z) = K(x,z \ ((y \ u) \ u))
    ]]></literal>
    <justification jstring="[para(7097(a,1),8943(a,1,1,2))].">
      <j1 rule="para" parents="7097 8943"/>
    </justification>
  </clause>

  <clause id="8950">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y / x) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[para(7260(a,1),8943(a,1,1))].">
      <j1 rule="para" parents="7260 8943"/>
    </justification>
  </clause>

  <clause id="8951">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(8944(a,1),7323(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8944 7323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8952">
    <literal><![CDATA[
      K(x,y \ z) * K(z / y,x) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(6138,a,8950,a)].">
      <j1 rule="hyper" parents="6138 8950"/>
    </justification>
  </clause>

  <clause id="8953">
    <literal><![CDATA[
      K(x \ y,z) * K(x,K(y,z)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(5273,a,8952,a)].">
      <j1 rule="hyper" parents="5273 8952"/>
    </justification>
  </clause>

  <clause id="8954">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ y,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[para(8952(a,1),6133(a,1,1))].">
      <j1 rule="para" parents="8952 6133"/>
    </justification>
  </clause>

  <clause id="8955">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ z,y) = K(z / x,y)
    ]]></literal>
    <justification jstring="[para(7293(a,1),8954(a,1,1))].">
      <j1 rule="para" parents="7293 8954"/>
    </justification>
  </clause>

  <clause id="8956">
    <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(7119(a,2),8912(a,1))].">
      <j1 rule="para" parents="7119 8912"/>
    </justification>
  </clause>

  <clause id="8957">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,L(w,z,u))) = v5
    ]]></literal>
    <justification jstring="[para(7293(a,1),8926(a,1))].">
      <j1 rule="para" parents="7293 8926"/>
    </justification>
  </clause>

  <clause id="8958">
    <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(8919(a,2),8926(a,1))].">
      <j1 rule="para" parents="8919 8926"/>
    </justification>
  </clause>

  <clause id="8959">
    <literal><![CDATA[
      K(x,y) * K(y * R(x,z,u),x) = x \ R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(128,a,8935,a(flip),b,4943,a),flip(a)].">
      <j1 rule="hyper" parents="128 8935 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8960">
    <literal><![CDATA[
      K(x,y) * K(y * L(x,z,u),x) = x \ R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(128,a,8936,a(flip),b,4943,a),flip(a)].">
      <j1 rule="hyper" parents="128 8936 4943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8962">
    <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(7279(a,1),8958(a,1,1))].">
      <j1 rule="para" parents="7279 8958"/>
    </justification>
  </clause>

  <clause id="8963">
    <literal><![CDATA[
      T(x \ K(y,z),K(u,z)) = T(x,K(u,z)) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(7275,a,8831,a),flip(a)].">
      <j1 rule="hyper" parents="7275 8831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8964">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,y)) / w)) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[hyper(347,a,8822,a(flip),b,8839,a),flip(a)].">
      <j1 rule="hyper" parents="347 8822 8839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8965">
    <literal><![CDATA[
      K(x,K(y,K(z,y) / u)) = K(x,K(y,1 / u))
    ]]></literal>
    <justification jstring="[para(7(a,1),8964(a,1,2,2,1))].">
      <j1 rule="para" parents="7 8964"/>
    </justification>
  </clause>

  <clause id="8966">
    <literal><![CDATA[
      (K(x,y) / z) * K(u,K(y,1 / z)) = T(K(x,y) / z,K(u,y))
    ]]></literal>
    <justification jstring="[para(8965(a,1),7290(a,1,2))].">
      <j1 rule="para" parents="8965 7290"/>
    </justification>
  </clause>

  <clause id="8967">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(7509,a,8897,a),flip(a)].">
      <j1 rule="hyper" parents="7509 8897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8968">
    <literal><![CDATA[
      K(x,T(y,z \ (x * u))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7595,a(flip),b,8967,a)].">
      <j1 rule="hyper" parents="63 7595 8967"/>
    </justification>
  </clause>

  <clause id="8969">
    <literal><![CDATA[
      K(x,T(x \ y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(8967(a,1),7665(a,1))].">
      <j1 rule="para" parents="8967 7665"/>
    </justification>
  </clause>

  <clause id="8970">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) = K(x,K(y / u,(z * y) \ K(z,1 / z)))
    ]]></literal>
    <justification jstring="[para(571(a,1),8932(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="571 8932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8973">
    <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(63,a,8328,a,b,8959,a)].">
      <j1 rule="hyper" parents="63 8328 8959"/>
    </justification>
  </clause>

  <clause id="8974">
    <literal><![CDATA[
      x \ R(x,y,R(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y * R(x,z,u),x) * K(x,y) = w
    ]]></literal>
    <justification jstring="[para(8959(a,1),2560(a,1))].">
      <j1 rule="para" parents="8959 2560"/>
    </justification>
  </clause>

  <clause id="8975">
    <literal><![CDATA[
      K(x,y) * (y \ R(y,x,L(y,z,u))) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(5273,a,8960,a)].">
      <j1 rule="hyper" parents="5273 8960"/>
    </justification>
  </clause>

  <clause id="8977">
    <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(63,a,8328,a,b,8960,a)].">
      <j1 rule="hyper" parents="63 8328 8960"/>
    </justification>
  </clause>

  <clause id="8978">
    <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(8960(a,1),2560(a,1))].">
      <j1 rule="para" parents="8960 2560"/>
    </justification>
  </clause>

  <clause id="8980">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) \ z)) = v5
    ]]></literal>
    <justification jstring="[para(8754(a,2),8844(a,1))].">
      <j1 rule="para" parents="8754 8844"/>
    </justification>
  </clause>

  <clause id="8981">
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) = T(x,x \ y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7713,a(flip),b,8763,a),flip(a)].">
      <j1 rule="hyper" parents="63 7713 8763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8982">
    <literal><![CDATA[
      T(x,T(T(y,z \ y),u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[hyper(347,a,8680,a(flip),b,8868,a),flip(a)].">
      <j1 rule="hyper" parents="347 8680 8868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8983">
    <literal><![CDATA[
      T(x,T(T(y * z,z),u)) = T(x,T(T(y * z,y),u))
    ]]></literal>
    <justification jstring="[para(9(a,1),8982(a,1,2,1,2))].">
      <j1 rule="para" parents="9 8982"/>
    </justification>
  </clause>

  <clause id="8984">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,8795,a(flip),b,8916,a),flip(a)].">
      <j1 rule="hyper" parents="347 8795 8916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8985">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(83(a,1),8984(a,1,2,2,1,2))].">
      <j1 rule="para" parents="83 8984"/>
    </justification>
  </clause>

  <clause id="8986">
    <literal><![CDATA[
      K(x,(y \ 1) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5412,a(flip),b,8985,a)].">
      <j1 rule="hyper" parents="63 5412 8985"/>
    </justification>
  </clause>

  <clause id="8987">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = T(K(x,y),1 / z) / z
    ]]></literal>
    <justification jstring="[hyper(63,a,7277,a(flip),b,8966,a),flip(a)].">
      <j1 rule="hyper" parents="63 7277 8966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8988">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = K(x,T(y,1 / z)) / z
    ]]></literal>
    <justification jstring="[para(7091(a,2),8987(a,2,1))].">
      <j1 rule="para" parents="7091 8987"/>
    </justification>
  </clause>

  <clause id="8989">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = K(x,T(y,z)) / z
    ]]></literal>
    <justification jstring="[para(8860(a,1),8988(a,2,1))].">
      <j1 rule="para" parents="8860 8988"/>
    </justification>
  </clause>

  <clause id="8990">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) * K(u,z) = K(x,T(y,z)) / T(z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,8989,a,b,6098,a)].">
      <j1 rule="hyper" parents="133 8989 6098"/>
    </justification>
  </clause>

  <clause id="8991">
    <literal><![CDATA[
      x / (x / R(K(y,z),u,w)) = (R(K(y,z),u,w) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(220,a,8164,a(flip),b,4320,a(flip))].">
      <j1 rule="hyper" parents="220 8164 4320"/>
    </justification>
  </clause>

  <clause id="8992">
    <literal><![CDATA[
      L(K(x,T(y,z)),z,L(y,u,w)) = K(x,T(y,L(y,u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7651,a(flip),b,8212,a),flip(a)].">
      <j1 rule="hyper" parents="347 7651 8212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8993">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6934,a(flip),b,8992,a),flip(a)].">
      <j1 rule="hyper" parents="63 6934 8992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8995">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),8993(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 8993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8996">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(7996(a,1),8993(a,1,2))].">
      <j1 rule="para" parents="7996 8993"/>
    </justification>
  </clause>

  <clause id="8997">
    <literal><![CDATA[
      K(x,T(y,z \ L(y,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8880,a,8995,a)].">
      <j1 rule="hyper" parents="8880 8995"/>
    </justification>
  </clause>

  <clause id="8998">
    <literal><![CDATA[
      T(x,T(y,z \ L(y,u,w))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,8997,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 8997 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8999">
    <literal><![CDATA[
      T(x / L(y,z,u),T(y,x)) = T(x / L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7802,a(flip),b,8998,a),flip(a)].">
      <j1 rule="hyper" parents="63 7802 8998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9000">
    <literal><![CDATA[
      K(x,T(y,z * (y * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(7867(a,1),8996(a,1,2))].">
      <j1 rule="para" parents="7867 8996"/>
    </justification>
  </clause>

  <clause id="9001">
    <literal><![CDATA[
      K(x * y,T(x,z * y)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(7710,a,9000,a),flip(a)].">
      <j1 rule="hyper" parents="7710 9000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9002">
    <literal><![CDATA[
      K(x,T(y,z * (y * x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7690,a(flip),b,9000,a),flip(a)].">
      <j1 rule="hyper" parents="347 7690 9000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9004">
    <literal><![CDATA[
      K(x * y,T(x,z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(9000(a,1),7710(a,1))].">
      <j1 rule="para" parents="9000 7710"/>
    </justification>
  </clause>

  <clause id="9005">
    <literal><![CDATA[
      K(x * y,T(y,z * x)) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7971,a,b,9001,a)].">
      <j1 rule="hyper" parents="63 7971 9001"/>
    </justification>
  </clause>

  <clause id="9006">
    <literal><![CDATA[
      K(x * (y \ z),T(x,z)) = K(x * (y \ z),T(x,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),9001(a,1,2,2))].">
      <j1 rule="para" parents="10 9001"/>
    </justification>
  </clause>

  <clause id="9007">
    <literal><![CDATA[
      K(T(x,y) * z,T(x,u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * z,T(x,u)) = w
    ]]></literal>
    <justification jstring="[para(7972(a,2),9004(a,1))].">
      <j1 rule="para" parents="7972 9004"/>
    </justification>
  </clause>

  <clause id="9008">
    <literal><![CDATA[
      L(T(K(x,y),z),z,K(x,u)) = T(K(x,y),K(x,u) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,6422,a(flip),b,8254,a),flip(a)].">
      <j1 rule="hyper" parents="347 6422 8254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9009">
    <literal><![CDATA[
      T(K(x,y),K(x,z) * u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6875,a(flip),b,9008,a),flip(a)].">
      <j1 rule="hyper" parents="63 6875 9008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9010">
    <literal><![CDATA[
      K(x,y) * ((K(x,y) \ z) * L(T(K(x,u),K(x,y) \ z),w,v5)) = z * L(T(K(x,u),K(x,y) * (K(x,y) \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(9008(a,1),839(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9008 839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9012">
    <literal><![CDATA[
      T(K(x,y),K(z,x) * u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[para(5261(a,1),9009(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5261 9009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9014">
    <literal><![CDATA[
      K(x,T(y,K(z,x) * u)) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(7480,a,9012,a)].">
      <j1 rule="hyper" parents="7480 9012"/>
    </justification>
  </clause>

  <clause id="9015">
    <literal><![CDATA[
      T(K(x,y),R(K(z,x),u,w) * v5) = T(K(x,y),v5)
    ]]></literal>
    <justification jstring="[para(5675(a,1),9012(a,1,2,1))].">
      <j1 rule="para" parents="5675 9012"/>
    </justification>
  </clause>

  <clause id="9016">
    <literal><![CDATA[
      K(x,T(y,K(z,x) * u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,7091,a,b,9014,a),flip(a)].">
      <j1 rule="hyper" parents="347 7091 9014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9017">
    <literal><![CDATA[
      K(x,T(y,z * K(x,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7432(a,1),9016(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7432 9016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9018">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,x)) * w)) = K(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(6565(a,1),9017(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6565 9017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9019">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,z * (x * u)))
    ]]></literal>
    <justification jstring="[para(6977(a,1),9017(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6977 9017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9020">
    <literal><![CDATA[
      K(x,T(y,T(z,K(u,x)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7262(a,1),9017(a,1,2,2))].">
      <j1 rule="para" parents="7262 9017"/>
    </justification>
  </clause>

  <clause id="9021">
    <literal><![CDATA[
      T(K(x,y),T(z,K(u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7793,a,9020,a)].">
      <j1 rule="hyper" parents="7793 9020"/>
    </justification>
  </clause>

  <clause id="9024">
    <literal><![CDATA[
      K(x,T(y,(z * x) * u)) = K(x,T(y,(x * z) * u))
    ]]></literal>
    <justification jstring="[para(91(a,1),9018(a,1,2,2,1))].">
      <j1 rule="para" parents="91 9018"/>
    </justification>
  </clause>

  <clause id="9025">
    <literal><![CDATA[
      T(x * R(x \ (x * y),z,u),x) = R(y * a(x,y,x),z,u) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,1719,a,b,8362,a)].">
      <j1 rule="hyper" parents="347 1719 8362"/>
    </justification>
  </clause>

  <clause id="9026">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z \ 1,y))) / x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T((z \ w) / w,x)) = u
    ]]></literal>
    <justification jstring="[para(5556(a,1),8526(a,1,2,1,2,2))].">
      <j1 rule="para" parents="5556 8526"/>
    </justification>
  </clause>

  <clause id="9027">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = K((u * z) / (u * (x \ z)),y)
    ]]></literal>
    <justification jstring="[para(23(a,1),8541(a,1,1,2))].">
      <j1 rule="para" parents="23 8541"/>
    </justification>
  </clause>

  <clause id="9028">
    <literal><![CDATA[
      T(L(K(x,y),z,u) \ w,K(x,L(y,z,u))) = w / L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8933,a(flip),b,8555,a)].">
      <j1 rule="hyper" parents="63 8933 8555"/>
    </justification>
  </clause>

  <clause id="9029">
    <literal><![CDATA[
      K(x,y) * K(L(x,z,u) * y,x) = L(x,y,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(8937(a,1),8633(a,1,2))].">
      <j1 rule="para" parents="8937 8633"/>
    </justification>
  </clause>

  <clause id="9030">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) * K(x,u) = L(x,u,L(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(2560,a,9029,a)].">
      <j1 rule="hyper" parents="2560 9029"/>
    </justification>
  </clause>

  <clause id="9031">
    <literal><![CDATA[
      K(R(T(x,y / (((x \ y) \ 1) \ 1)),x \ y,y \ (y / (((x \ y) \ 1) \ 1))),z) = K(((y \ (y / (x \ y))) * (x \ y)) \ (y / (((x \ y) \ 1) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(2325(a,1),8724(a,2,1,1))].">
      <j1 rule="para" parents="2325 8724"/>
    </justification>
  </clause>

  <clause id="9032">
    <literal><![CDATA[
      R(K(T(T(x,y),y * z),u),y,z) = ((y * z) \ ((y * K(u,x)) * z)) \ 1
    ]]></literal>
    <justification jstring="[para(8734(a,1),6701(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8734 6701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9033">
    <literal><![CDATA[
      R(x * a(y,x,y),z,u) * y = T(y * R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),9025(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 9025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9034">
    <literal><![CDATA[
      L(K(T(T(x,y),z * y),u),y,z) * w = K((z * y) / (z * (u \ y)),x) \ w
    ]]></literal>
    <justification jstring="[para(9027(a,1),8255(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9027 8255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9035">
    <literal><![CDATA[
      T(L(K(x,y),z,u) * w,K(y,L(x,z,u))) = w / L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(8255(a,1),9028(a,1,1))].">
      <j1 rule="para" parents="8255 9028"/>
    </justification>
  </clause>

  <clause id="9036">
    <literal><![CDATA[
      T(L(K(x,y),z,u) * w,K(y,L(x,z,u))) = w * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,8259,a(flip),b,9035,a),flip(a)].">
      <j1 rule="hyper" parents="347 8259 9035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9037">
    <literal><![CDATA[
      T(x * L(K(y,z),u,w),K(z,L(y,u,w))) = L(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[hyper(7352,a,9036,a)].">
      <j1 rule="hyper" parents="7352 9036"/>
    </justification>
  </clause>

  <clause id="9038">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) * (y / u) = T(y,K(x,z)) / u
    ]]></literal>
    <justification jstring="[para(7331(a,1),7303(a,1,1))].">
      <j1 rule="para" parents="7331 7303"/>
    </justification>
  </clause>

  <clause id="9039">
    <literal><![CDATA[
      K((T(x,y) / z) / (x / z),u) * (T(x,K(u,y)) / z) = x / z
    ]]></literal>
    <justification jstring="[hyper(5273,a,9038,a)].">
      <j1 rule="hyper" parents="5273 9038"/>
    </justification>
  </clause>

  <clause id="9040">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = ((T(y,K(x,z)) / u) * u) / y
    ]]></literal>
    <justification jstring="[para(9038(a,1),109(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9038 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9041">
    <literal><![CDATA[
      x * (T(y,K(z,u)) / w) != y / w
    ]]></literal>
    <literal><![CDATA[
      K((T(y,u) / w) / (y / w),z) = x
    ]]></literal>
    <justification jstring="[para(9039(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="9039 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9042">
    <literal><![CDATA[
      K(x \ y,T(z,(x \ y) \ T(y,x))) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7749,a(flip),b,7425,a),flip(a)].">
      <j1 rule="hyper" parents="347 7749 7425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9043">
    <literal><![CDATA[
      K(x \ y,T(z,T(y,x))) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(7495,a,9042,a)].">
      <j1 rule="hyper" parents="7495 9042"/>
    </justification>
  </clause>

  <clause id="9044">
    <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(4905(a,1),7694(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4905 7694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9045">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(34,a,7433,a(flip),b,7752,a)].">
      <j1 rule="hyper" parents="34 7433 7752"/>
    </justification>
  </clause>

  <clause id="9047">
    <literal><![CDATA[
      (x \ R(x,y,z)) * T(K(u,x),w) = T(x,T(u,w)) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7238,a(flip),b,7827,a),flip(a)].">
      <j1 rule="hyper" parents="347 7238 7827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9048">
    <literal><![CDATA[
      K(x * y,y) * K(x,K(y,z)) = T(y,T(x,z)) \ R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8163,a(flip),b,9047,a)].">
      <j1 rule="hyper" parents="63 8163 9047"/>
    </justification>
  </clause>

  <clause id="9049">
    <literal><![CDATA[
      T(x,T(y,z)) \ R(x,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(9048(a,1),8783(a,1))].">
      <j1 rule="para" parents="9048 8783"/>
    </justification>
  </clause>

  <clause id="9050">
    <literal><![CDATA[
      K(x,T(y,z)) * a(y,x,y) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(9049,a,8347,a),flip(a)].">
      <j1 rule="hyper" parents="9049 8347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9051">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (K(x,T(y,z)) * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(9050(a,1),8507(a,1,1))].">
      <j1 rule="para" parents="9050 8507"/>
    </justification>
  </clause>

  <clause id="9052">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (y * K(x,T(y,z))) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(3043(a,1),9051(a,1,2))].">
      <j1 rule="para" parents="3043 9051"/>
    </justification>
  </clause>

  <clause id="9053">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7151,a,9052,a)].">
      <j1 rule="hyper" parents="7151 9052"/>
    </justification>
  </clause>

  <clause id="9054">
    <literal><![CDATA[
      T(x,T(x * y,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4839(a,1),9053(a,1,1))].">
      <j1 rule="para" parents="4839 9053"/>
    </justification>
  </clause>

  <clause id="9055">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x,u) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[para(7851(a,1),7858(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7851 7858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9056">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,5308,a(flip),b,9055,a),flip(a)].">
      <j1 rule="hyper" parents="347 5308 9055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9058">
    <literal><![CDATA[
      T(x * K((K(x,y) * z) * R(x,u,w),x),z) = R(x,K(x,y) * z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5309,a(flip),b,9056,a),flip(a)].">
      <j1 rule="hyper" parents="63 5309 9056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9060">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * (z \ y)) \ u,z) = w
    ]]></literal>
    <justification jstring="[para(8165(a,1),5373(a,1))].">
      <j1 rule="para" parents="8165 5373"/>
    </justification>
  </clause>

  <clause id="9061">
    <literal><![CDATA[
      T(T(x,x * y) * R(x \ (x * y),z,u),x) = T(x * R(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,4305,a(flip),b,8180,a),flip(a)].">
      <j1 rule="hyper" parents="347 4305 8180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9062">
    <literal><![CDATA[
      T(T(x,y) * L(x \ y,z,u),x) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,4304,a(flip),b,8181,a),flip(a)].">
      <j1 rule="hyper" parents="347 4304 8181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9063">
    <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),9062(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 9062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9064">
    <literal><![CDATA[
      K(x \ ((y * z) * K(y,u)),T(y,w)) = K(x \ (z * T(y,u)),T(y,w))
    ]]></literal>
    <justification jstring="[para(6765(a,2),8193(a,1,1,2))].">
      <j1 rule="para" parents="6765 8193"/>
    </justification>
  </clause>

  <clause id="9065">
    <literal><![CDATA[
      (x * K(y,z)) * R(K(z,u),w,v5) = x * (R(K(z,u),w,v5) * K(y,z))
    ]]></literal>
    <justification jstring="[para(2559(a,2),8315(a,2,2))].">
      <j1 rule="para" parents="2559 8315"/>
    </justification>
  </clause>

  <clause id="9066">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * R(K(y,u),w,v5)) = x * R(K(y,u),w,v5)
    ]]></literal>
    <justification jstring="[para(6109(a,1),8315(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6109 8315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9067">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) * K(z,v5) = x * (K(z,v5) * L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(2562(a,1),8326(a,2,2))].">
      <j1 rule="para" parents="2562 8326"/>
    </justification>
  </clause>

  <clause id="9068">
    <literal><![CDATA[
      (K(x,K(y,z)) * T(y,K(u,w))) \ y = K(u,K(w,y)) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7283(a,1),8437(a,1,1,1))].">
      <j1 rule="para" parents="7283 8437"/>
    </justification>
  </clause>

  <clause id="9069">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(347,a,8449,a(flip),b,8450,a),flip(a)].">
      <j1 rule="hyper" parents="347 8449 8450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9070">
    <literal><![CDATA[
      K(x,R(x \ y,x,z / y)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,8451,a,b,9069,a)].">
      <j1 rule="hyper" parents="63 8451 9069"/>
    </justification>
  </clause>

  <clause id="9071">
    <literal><![CDATA[
      K(x,R(x \ (y / z),x,y / (y / z))) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(83(a,1),9070(a,2,2,2,1))].">
      <j1 rule="para" parents="83 9070"/>
    </justification>
  </clause>

  <clause id="9072">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z / ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),8479(a,1,2))].">
      <j1 rule="para" parents="9 8479"/>
    </justification>
  </clause>

  <clause id="9073">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) = K(x / ((y * z) \ y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8712,a(flip),b,9072,a)].">
      <j1 rule="hyper" parents="63 8712 9072"/>
    </justification>
  </clause>

  <clause id="9074">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(((y * z) \ y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(9073(a,2),7589(a,1))].">
      <j1 rule="para" parents="9073 7589"/>
    </justification>
  </clause>

  <clause id="9075">
    <literal><![CDATA[
      K(x,T(y,z * R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8532,a,8290,a),flip(a)].">
      <j1 rule="hyper" parents="8532 8290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9076">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),9075(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 9075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9077">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,8030,a(flip),b,9076,a)].">
      <j1 rule="hyper" parents="63 8030 9076"/>
    </justification>
  </clause>

  <clause id="9079">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),9077(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 9077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9080">
    <literal><![CDATA[
      K(x,T(y,(x * z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(209(a,1),9077(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="209 9077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9081">
    <literal><![CDATA[
      K(x,T(y \ (R(x,z,u) * w),w)) = K(x,(R(x,z,u) * w) / y)
    ]]></literal>
    <justification jstring="[hyper(7771,a,9079,a),flip(a)].">
      <j1 rule="hyper" parents="7771 9079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9082">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,y) * K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,7267,a,b,9079,a),flip(a)].">
      <j1 rule="hyper" parents="347 7267 9079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9083">
    <literal><![CDATA[
      K(x,T(y,(z * x) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9024,a,b,9080,a)].">
      <j1 rule="hyper" parents="63 9024 9080"/>
    </justification>
  </clause>

  <clause id="9084">
    <literal><![CDATA[
      K(x,T(y / ((z * x) * u),z * u)) = K(x,((z * x) * u) \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),9083(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 9083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9085">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(7521,a,9082,a)].">
      <j1 rule="hyper" parents="7521 9082"/>
    </justification>
  </clause>

  <clause id="9086">
    <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(9082(a,2),7509(a,1))].">
      <j1 rule="para" parents="9082 7509"/>
    </justification>
  </clause>

  <clause id="9087">
    <literal><![CDATA[
      K(x,K(y,(x * z) * u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(107(a,1),9085(a,1,2,2))].">
      <j1 rule="para" parents="107 9085"/>
    </justification>
  </clause>

  <clause id="9088">
    <literal><![CDATA[
      K(x,K(y,(y * z) * u)) = K(y,K(x,z * u))
    ]]></literal>
    <justification jstring="[hyper(7281,a,9087,a)].">
      <j1 rule="hyper" parents="7281 9087"/>
    </justification>
  </clause>

  <clause id="9089">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(y,x) = K(y,T(x,(x * z) * u))
    ]]></literal>
    <justification jstring="[para(9087(a,1),7301(a,1,1))].">
      <j1 rule="para" parents="9087 7301"/>
    </justification>
  </clause>

  <clause id="9090">
    <literal><![CDATA[
      K(x,T(y,(y * z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(7563,a,9089,a),flip(a)].">
      <j1 rule="hyper" parents="7563 9089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9091">
    <literal><![CDATA[
      K(x,T(y,(y \ z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),9090(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 9090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9092">
    <literal><![CDATA[
      K(x \ y,T(x,y * z)) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(7496,a,9091,a),flip(a)].">
      <j1 rule="hyper" parents="7496 9091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9093">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(x \ (y / z),T(x,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),9092(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 9092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9094">
    <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(9092(a,1),7445(a,1,1,1))].">
      <j1 rule="para" parents="9092 7445"/>
    </justification>
  </clause>

  <clause id="9095">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(7042(a,1),8545(a,1))].">
      <j1 rule="para" parents="7042 8545"/>
    </justification>
  </clause>

  <clause id="9096">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(9095,a,8243,a),flip(a)].">
      <j1 rule="hyper" parents="9095 8243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9098">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(8243(a,1),9095(a,1))].">
      <j1 rule="para" parents="8243 9095"/>
    </justification>
  </clause>

  <clause id="9099">
    <literal><![CDATA[
      K(x,T(y,z * (x * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9019,a(flip),b,9096,a)].">
      <j1 rule="hyper" parents="63 9019 9096"/>
    </justification>
  </clause>

  <clause id="9100">
    <literal><![CDATA[
      K(x,T(y,z * (u / x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(12(a,1),9096(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="12 9096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9101">
    <literal><![CDATA[
      K(x,T(y,z * (x \ u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),9099(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 9099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9102">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) = K(1 / x,T(y,z))
    ]]></literal>
    <justification jstring="[para(82(a,1),9099(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="82 9099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9103">
    <literal><![CDATA[
      K(x,T((y * (x \ z)) \ u,y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (y * (x \ z))) = w
    ]]></literal>
    <justification jstring="[para(9101(a,1),7491(a,1))].">
      <j1 rule="para" parents="9101 7491"/>
    </justification>
  </clause>

  <clause id="9104">
    <literal><![CDATA[
      K(1 / L(x,y,x),z) = K(1 / x,T(T(z,y),y))
    ]]></literal>
    <justification jstring="[hyper(63,a,8253,a(flip),b,9102,a)].">
      <j1 rule="hyper" parents="63 8253 9102"/>
    </justification>
  </clause>

  <clause id="9105">
    <literal><![CDATA[
      K(1 / L(x,y,x),z) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7379,a(flip),b,9104,a),flip(a)].">
      <j1 rule="hyper" parents="347 7379 9104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9107">
    <literal><![CDATA[
      (x * y) * K(1 / x,z) = x * (y * K(1 / x,z))
    ]]></literal>
    <justification jstring="[para(9105(a,1),6999(a,1,2))].">
      <j1 rule="para" parents="9105 6999"/>
    </justification>
  </clause>

  <clause id="9108">
    <literal><![CDATA[
      R(x,y,K(1 / x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(2387,a,9107,a)].">
      <j1 rule="hyper" parents="2387 9107"/>
    </justification>
  </clause>

  <clause id="9109">
    <literal><![CDATA[
      R(x \ 1,y,K(x,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(80(a,1),9108(a,1,3,1))].">
      <j1 rule="para" parents="80 9108"/>
    </justification>
  </clause>

  <clause id="9110">
    <literal><![CDATA[
      R(x,y,K(x \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(3403(a,1),9108(a,1,3))].">
      <j1 rule="para" parents="3403 9108"/>
    </justification>
  </clause>

  <clause id="9111">
    <literal><![CDATA[
      (x * y) * K(x \ 1,z) = x * (y * K(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,9110,a(flip),b,2253,a),flip(a)].">
      <j1 rule="hyper" parents="133 9110 2253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9112">
    <literal><![CDATA[
      R(T(x,y),z,K(x \ 1,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(9110(a,1),27(a,2,1))].">
      <j1 rule="para" parents="9110 27"/>
    </justification>
  </clause>

  <clause id="9113">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,z) = (x \ 1) * (y * K(x,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,9109,a(flip),b,2253,a),flip(a)].">
      <j1 rule="hyper" parents="133 9109 2253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9114">
    <literal><![CDATA[
      T(x,y * K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5742,a(flip),b,9112,a),flip(a)].">
      <j1 rule="hyper" parents="63 5742 9112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9116">
    <literal><![CDATA[
      x \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(x \ 1,u)) = z
    ]]></literal>
    <justification jstring="[para(9114(a,1),5006(a,1,2))].">
      <j1 rule="para" parents="9114 5006"/>
    </justification>
  </clause>

  <clause id="9118">
    <literal><![CDATA[
      T(x,K(x \ 1,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7104(a,1),9114(a,1,2))].">
      <j1 rule="para" parents="7104 9114"/>
    </justification>
  </clause>

  <clause id="9119">
    <literal><![CDATA[
      T(x,K(1 / x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(3403(a,2),9118(a,1,2,1))].">
      <j1 rule="para" parents="3403 9118"/>
    </justification>
  </clause>

  <clause id="9120">
    <literal><![CDATA[
      T(x \ 1,K(x,y) * z) = T(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(3407(a,1),9118(a,1,2,1))].">
      <j1 rule="para" parents="3407 9118"/>
    </justification>
  </clause>

  <clause id="9121">
    <literal><![CDATA[
      T(x,K(y,1 / x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5261(a,1),9119(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5261 9119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9122">
    <literal><![CDATA[
      x / T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(K(u,1 / x) * y,x) = z
    ]]></literal>
    <justification jstring="[para(9121(a,1),5013(a,1,2))].">
      <j1 rule="para" parents="9121 5013"/>
    </justification>
  </clause>

  <clause id="9123">
    <literal><![CDATA[
      T(x \ 1,y * x) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(4909(a,1),9120(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4909 9120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9124">
    <literal><![CDATA[
      T(x \ 1,(y / x) * z) = T(x \ 1,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(5479(a,1),9120(a,1,2))].">
      <j1 rule="para" parents="5479 9120"/>
    </justification>
  </clause>

  <clause id="9125">
    <literal><![CDATA[
      T(x \ 1,y * x) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,4416,a(flip),b,9123,a),flip(a)].">
      <j1 rule="hyper" parents="347 4416 9123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9126">
    <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(9123(a,1),2133(a,1,2,1,1))].">
      <j1 rule="para" parents="9123 2133"/>
    </justification>
  </clause>

  <clause id="9127">
    <literal><![CDATA[
      T(x \ 1,y * x) * L(T(x \ 1,x * y) \ 1,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,z,u),x * y) = w
    ]]></literal>
    <justification jstring="[para(9123(a,2),2138(a,1,1))].">
      <j1 rule="para" parents="9123 2138"/>
    </justification>
  </clause>

  <clause id="9128">
    <literal><![CDATA[
      T((x \ y) \ 1,y) = (((x \ y) \ 1) \ x) \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),9125(a,1,2))].">
      <j1 rule="para" parents="10 9125"/>
    </justification>
  </clause>

  <clause id="9129">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9116,a,4924,a(flip))].">
      <j1 rule="hyper" parents="9116 4924"/>
    </justification>
  </clause>

  <clause id="9130">
    <literal><![CDATA[
      K(x,y * K(z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6109(a,1),9129(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6109 9129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9131">
    <literal><![CDATA[
      K(x \ y,z * K(u,y \ x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(6250(a,1),9130(a,1,2,2))].">
      <j1 rule="para" parents="6250 9130"/>
    </justification>
  </clause>

  <clause id="9132">
    <literal><![CDATA[
      K(x \ y,z * (x / y)) = K(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[para(6075(a,1),9131(a,1,2))].">
      <j1 rule="para" parents="6075 9131"/>
    </justification>
  </clause>

  <clause id="9133">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(9122,a,4920,a(flip))].">
      <j1 rule="hyper" parents="9122 4920"/>
    </justification>
  </clause>

  <clause id="9134">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(3890(a,1),9133(a,1,1,1))].">
      <j1 rule="para" parents="3890 9133"/>
    </justification>
  </clause>

  <clause id="9137">
    <literal><![CDATA[
      K(K(x \ 1,y) \ z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(5256(a,2),9134(a,1,1))].">
      <j1 rule="para" parents="5256 9134"/>
    </justification>
  </clause>

  <clause id="9138">
    <literal><![CDATA[
      K(K(x,x \ y) * z,x / y) = K(z,x / y)
    ]]></literal>
    <justification jstring="[para(5313(a,1),9134(a,1,1,1))].">
      <j1 rule="para" parents="5313 9134"/>
    </justification>
  </clause>

  <clause id="9139">
    <literal><![CDATA[
      K(x \ T(y,z \ 1),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5570(a,1),9134(a,1,1))].">
      <j1 rule="para" parents="5570 9134"/>
    </justification>
  </clause>

  <clause id="9140">
    <literal><![CDATA[
      K(x * K(y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7372(a,1),9134(a,1,1))].">
      <j1 rule="para" parents="7372 9134"/>
    </justification>
  </clause>

  <clause id="9141">
    <literal><![CDATA[
      (K(x \ 1,y) \ z) * K(z,x) = T(K(x \ 1,y) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,9137,a(flip),b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 9137 4924"/>
    </justification>
  </clause>

  <clause id="9142">
    <literal><![CDATA[
      K(x * K(y,z \ u),u \ z) = K(x,u \ z)
    ]]></literal>
    <justification jstring="[para(6250(a,1),9140(a,1,1,2))].">
      <j1 rule="para" parents="6250 9140"/>
    </justification>
  </clause>

  <clause id="9143">
    <literal><![CDATA[
      K((x / y) \ z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[para(5603(a,1),9138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5603 9138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9144">
    <literal><![CDATA[
      K(x * (y / z),y \ z) = K(x * (z \ y),y \ z)
    ]]></literal>
    <justification jstring="[para(6075(a,1),9142(a,1,1))].">
      <j1 rule="para" parents="6075 9142"/>
    </justification>
  </clause>

  <clause id="9145">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(6483,a,9111,a),flip(a)].">
      <j1 rule="hyper" parents="6483 9111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9146">
    <literal><![CDATA[
      (x \ 1) \ ((x \ y) / T(y,x \ 1)) = x * (((x \ y) / y) * K(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6808,a,b,9111,a)].">
      <j1 rule="hyper" parents="63 6808 9111"/>
    </justification>
  </clause>

  <clause id="9147">
    <literal><![CDATA[
      K(x \ 1,y * x) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5748,a(flip),b,9145,a)].">
      <j1 rule="hyper" parents="63 5748 9145"/>
    </justification>
  </clause>

  <clause id="9148">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(9147(a,2),5559(a,2,2))].">
      <j1 rule="para" parents="9147 5559"/>
    </justification>
  </clause>

  <clause id="9149">
    <literal><![CDATA[
      x * (y * K(x \ 1,x * y)) = L(y / (x \ 1),x,x)
    ]]></literal>
    <justification jstring="[para(9147(a,1),5753(a,1,2,2))].">
      <j1 rule="para" parents="9147 5753"/>
    </justification>
  </clause>

  <clause id="9150">
    <literal><![CDATA[
      K(x,L(y,z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,8424,a,b,9113,a)].">
      <j1 rule="hyper" parents="34 8424 9113"/>
    </justification>
  </clause>

  <clause id="9151">
    <literal><![CDATA[
      ((x \ 1) * (y * K(x,z))) \ ((x \ 1) * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(9113(a,1),6141(a,1,1))].">
      <j1 rule="para" parents="9113 6141"/>
    </justification>
  </clause>

  <clause id="9152">
    <literal><![CDATA[
      K(R(x,x \ 1,y),L(z,u,x \ 1)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6510,a,b,9150,a)].">
      <j1 rule="hyper" parents="63 6510 9150"/>
    </justification>
  </clause>

  <clause id="9153">
    <literal><![CDATA[
      T(x \ y,z * (x / y)) = T(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(132,a,9132,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 9132 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9154">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (y / x),y \ x)
    ]]></literal>
    <justification jstring="[para(9144(a,2),6274(a,2,2))].">
      <j1 rule="para" parents="9144 6274"/>
    </justification>
  </clause>

  <clause id="9155">
    <literal><![CDATA[
      (K(x,y \ 1) * z) * K(z,y) = T(K(y \ 1,x) \ z,y)
    ]]></literal>
    <justification jstring="[para(5256(a,1),9141(a,1,1))].">
      <j1 rule="para" parents="5256 9141"/>
    </justification>
  </clause>

  <clause id="9156">
    <literal><![CDATA[
      T(K(x \ 1,y) \ z,x) = K(y,x \ 1) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(5973,a,9155,a),flip(a)].">
      <j1 rule="hyper" parents="5973 9155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9157">
    <literal><![CDATA[
      T(K(x,y \ 1) * z,y) = K(x,y \ 1) * T(z,y)
    ]]></literal>
    <justification jstring="[para(5256(a,1),9156(a,1,1))].">
      <j1 rule="para" parents="5256 9156"/>
    </justification>
  </clause>

  <clause id="9159">
    <literal><![CDATA[
      T(x * K(y \ 1,z),y) = T(x,y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,5887,a(flip),b,9157,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 5887 9157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9160">
    <literal><![CDATA[
      T(x,y) * K(y \ 1,x) = T(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5083,a(flip),b,9159,a),flip(a)].">
      <j1 rule="hyper" parents="63 5083 9159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9161">
    <literal><![CDATA[
      T(K(x,y),z) * K(K(x,y),z) = T(K(x,y),z * z)
    ]]></literal>
    <justification jstring="[para(8835(a,1),9160(a,1,2))].">
      <j1 rule="para" parents="8835 9160"/>
    </justification>
  </clause>

  <clause id="9162">
    <literal><![CDATA[
      T(T(K(x,y),z),z) = T(K(x,y),z * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5148,a(flip),b,9161,a)].">
      <j1 rule="hyper" parents="63 5148 9161"/>
    </justification>
  </clause>

  <clause id="9163">
    <literal><![CDATA[
      T(K(x,y),z * z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7369,a(flip),b,9162,a),flip(a)].">
      <j1 rule="hyper" parents="63 7369 9162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9164">
    <literal><![CDATA[
      K(x,T(y,z * z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7480,a,9163,a)].">
      <j1 rule="hyper" parents="7480 9163"/>
    </justification>
  </clause>

  <clause id="9166">
    <literal><![CDATA[
      K(x,K(y,z * z)) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,9163,a(flip),b,7265,a),flip(a)].">
      <j1 rule="hyper" parents="129 9163 7265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9167">
    <literal><![CDATA[
      T(x,K(y,z * z)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,9166,a)].">
      <j1 rule="hyper" parents="56 9166"/>
    </justification>
  </clause>

  <clause id="9168">
    <literal><![CDATA[
      T(x,T(y,z * z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(193,a,6816,a,b,9166,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="193 6816 9166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9169">
    <literal><![CDATA[
      T(x,K(y * y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(8790,a,9167,a)].">
      <j1 rule="hyper" parents="8790 9167"/>
    </justification>
  </clause>

  <clause id="9170">
    <literal><![CDATA[
      K(x * x,y) * z = z * K(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(7353,a,9167,a),flip(a)].">
      <j1 rule="hyper" parents="7353 9167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9171">
    <literal><![CDATA[
      T(x,y / (z * z)) = T(x,(z * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8883,a(flip),b,9167,a),flip(a)].">
      <j1 rule="hyper" parents="63 8883 9167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9172">
    <literal><![CDATA[
      T(x,T(y,z * z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(9167(a,1),6819(a,2))].">
      <j1 rule="para" parents="9167 6819"/>
    </justification>
  </clause>

  <clause id="9173">
    <literal><![CDATA[
      K(x,T(y,z * (u * u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(1305(a,1),9164(a,1,2))].">
      <j1 rule="para" parents="1305 9164"/>
    </justification>
  </clause>

  <clause id="9174">
    <literal><![CDATA[
      T(x,(y \ z) * (y * y)) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(816(a,1),9168(a,1,2))].">
      <j1 rule="para" parents="816 9168"/>
    </justification>
  </clause>

  <clause id="9175">
    <literal><![CDATA[
      T(x,T(y,z * (u * u))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(1305(a,1),9168(a,1,2))].">
      <j1 rule="para" parents="1305 9168"/>
    </justification>
  </clause>

  <clause id="9176">
    <literal><![CDATA[
      L(K(x,y),z,y \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9151,a,8264,a),flip(a)].">
      <j1 rule="hyper" parents="9151 8264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9177">
    <literal><![CDATA[
      K(L(x,y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(7808,a,9176,a)].">
      <j1 rule="hyper" parents="7808 9176"/>
    </justification>
  </clause>

  <clause id="9181">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (z * (x \ 1)),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7024,a(flip),b,9176,a)].">
      <j1 rule="hyper" parents="63 7024 9176"/>
    </justification>
  </clause>

  <clause id="9182">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,y)) = K(((x \ 1) \ z) / y,x)
    ]]></literal>
    <justification jstring="[hyper(7592,a,9177,a)].">
      <j1 rule="hyper" parents="7592 9177"/>
    </justification>
  </clause>

  <clause id="9183">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7032,a(flip),b,9181,a)].">
      <j1 rule="hyper" parents="63 7032 9181"/>
    </justification>
  </clause>

  <clause id="9184">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,9139,a(flip),b,9183,a),flip(a)].">
      <j1 rule="hyper" parents="347 9139 9183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9185">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(8029,a,9184,a)].">
      <j1 rule="hyper" parents="8029 9184"/>
    </justification>
  </clause>

  <clause id="9186">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K((x * y) \ (z * y),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8185,a(flip),b,9185,a)].">
      <j1 rule="hyper" parents="63 8185 9185"/>
    </justification>
  </clause>

  <clause id="9187">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,8100,a(flip),b,9186,a),flip(a)].">
      <j1 rule="hyper" parents="347 8100 9186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9188">
    <literal><![CDATA[
      T(x,y) \ T(x * K(z \ u,x),y) = K(L(z,x,x \ 1) \ u,T(x,y))
    ]]></literal>
    <justification jstring="[para(9187(a,1),5434(a,1,2,1,2))].">
      <j1 rule="para" parents="9187 5434"/>
    </justification>
  </clause>

  <clause id="9189">
    <literal><![CDATA[
      K(x,(((K(y,x \ z) / y) \ 1) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(5376(a,2),8575(a,1,2,1,1))].">
      <j1 rule="para" parents="5376 8575"/>
    </justification>
  </clause>

  <clause id="9190">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) = K((x * y) \ (u * z),z)
    ]]></literal>
    <justification jstring="[hyper(5373,a,8578,a),flip(a)].">
      <j1 rule="hyper" parents="5373 8578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9191">
    <literal><![CDATA[
      K((x * (y \ z)) \ u,y) = K((x * z) \ (u * y),y)
    ]]></literal>
    <justification jstring="[hyper(9060,a,9190,a)].">
      <j1 rule="hyper" parents="9060 9190"/>
    </justification>
  </clause>

  <clause id="9192">
    <literal><![CDATA[
      K((x * (y \ 1)) \ z,y) = K(x \ (z * y),y)
    ]]></literal>
    <justification jstring="[para(8(a,1),9191(a,2,1,1))].">
      <j1 rule="para" parents="8 9191"/>
    </justification>
  </clause>

  <clause id="9193">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(z \ ((z * y) * x),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7027,a,b,9192,a)].">
      <j1 rule="hyper" parents="63 7027 9192"/>
    </justification>
  </clause>

  <clause id="9194">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6598,a,b,9192,a)].">
      <j1 rule="hyper" parents="63 6598 9192"/>
    </justification>
  </clause>

  <clause id="9195">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(z \ (x * (z * y)),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,8008,a(flip),b,9193,a),flip(a)].">
      <j1 rule="hyper" parents="347 8008 9193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9196">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(z \ ((z * x) * y),y)
    ]]></literal>
    <justification jstring="[para(7899(a,2),9193(a,1,1))].">
      <j1 rule="para" parents="7899 9193"/>
    </justification>
  </clause>

  <clause id="9197">
    <literal><![CDATA[
      L(K(x * y,x) * K(z,K(x * y,x)),y,z) = K(z \ (x * (z * y)),x) * K(z,K(x * y,x))
    ]]></literal>
    <justification jstring="[para(9195(a,1),7621(a,2,1))].">
      <j1 rule="para" parents="9195 7621"/>
    </justification>
  </clause>

  <clause id="9198">
    <literal><![CDATA[
      (1 / (1 / ((x * y) / x))) \ K(x,y) = (y \ 1) * K(y,1 / y)
    ]]></literal>
    <justification jstring="[para(4980(a,1),8606(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4980 8606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9199">
    <literal><![CDATA[
      (1 / (1 / ((x * y) / x))) \ K(x,y) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(347,a,4949,a(flip),b,9198,a),flip(a)].">
      <j1 rule="hyper" parents="347 4949 9198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9200">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),(x * (x \ y)) \ z) = x \ T(y,((x \ 1) \ (x \ y)) \ z)
    ]]></literal>
    <justification jstring="[para(8612(a,1),6005(a,1,2))].">
      <j1 rule="para" parents="8612 6005"/>
    </justification>
  </clause>

  <clause id="9201">
    <literal><![CDATA[
      K(x \ (y * T(z,u)),T(z,w)) = K(x \ (z * y),T(z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,8162,a(flip),b,9064,a),flip(a)].">
      <j1 rule="hyper" parents="63 8162 9064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9203">
    <literal><![CDATA[
      L(K(x * T(y,z),T(y,z)),x,u) = K(u \ (y * (u * x)),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9196,a,b,9201,a)].">
      <j1 rule="hyper" parents="63 9196 9201"/>
    </justification>
  </clause>

  <clause id="9204">
    <literal><![CDATA[
      L(K(x * y,T(y,z)),x,u) = K(u \ (y * (u * x)),T(y,z))
    ]]></literal>
    <justification jstring="[para(7973(a,1),9203(a,1,1))].">
      <j1 rule="para" parents="7973 9203"/>
    </justification>
  </clause>

  <clause id="9206">
    <literal><![CDATA[
      K(x \ (y * (x * z)),T(y,u * z)) = L(K(y * z,T(y,u)),z,x)
    ]]></literal>
    <justification jstring="[para(9005(a,1),9204(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9005 9204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9207">
    <literal><![CDATA[
      L(K(x * y,T(x,z)),y,z) = K((z / (z * y)) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(7805,a,9206,a),flip(a)].">
      <j1 rule="hyper" parents="7805 9206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9208">
    <literal><![CDATA[
      x / (K(y,z) * R(K(z,u),w,v5)) = (x * R(K(u,z),w,v5)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,6715,a(flip),b,9066,a)].">
      <j1 rule="hyper" parents="131 6715 9066"/>
    </justification>
  </clause>

  <clause id="9209">
    <literal><![CDATA[
      (x * (K(y,z) * L(K(u,y),w,v5))) * K(z,y) = x * L(K(u,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(6138,a,9067,a)].">
      <j1 rule="hyper" parents="6138 9067"/>
    </justification>
  </clause>

  <clause id="9210">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) \ x = K(y,K(u,x)) * K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8477(a,1),9068(a,1,1))].">
      <j1 rule="para" parents="8477 9068"/>
    </justification>
  </clause>

  <clause id="9211">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) \ x = K(x,K(y,u)) * K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(7283(a,1),9210(a,2,1))].">
      <j1 rule="para" parents="7283 9210"/>
    </justification>
  </clause>

  <clause id="9212">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) \ x = K(x,K(y,u)) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7279(a,1),9211(a,2,2))].">
      <j1 rule="para" parents="7279 9211"/>
    </justification>
  </clause>

  <clause id="9213">
    <literal><![CDATA[
      L(x * K(y,T(x,z)),u,w) / L(x,u,w) = K(y,T(L(x,u,w),z))
    ]]></literal>
    <justification jstring="[para(7389(a,1),7450(a,1,1,1,2))].">
      <j1 rule="para" parents="7389 7450"/>
    </justification>
  </clause>

  <clause id="9214">
    <literal><![CDATA[
      L(x * K(y,T(x,z)),u,w) / L(x,u,w) = K(y,L(T(x,z),u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),9213(a,2,2))].">
      <j1 rule="para" parents="25 9213"/>
    </justification>
  </clause>

  <clause id="9215">
    <literal><![CDATA[
      L(x * K(y,T(x,z)),u,w) / L(x,u,w) = K(y,L(T(x,x * z),u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,8730,a,b,9214,a),flip(a)].">
      <j1 rule="hyper" parents="347 8730 9214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9216">
    <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(3688(a,2),7451(a,1,1))].">
      <j1 rule="para" parents="3688 7451"/>
    </justification>
  </clause>

  <clause id="9217">
    <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(347,a,7267,a,b,7461,a)].">
      <j1 rule="hyper" parents="347 7267 7461"/>
    </justification>
  </clause>

  <clause id="9218">
    <literal><![CDATA[
      K((x / y) \ z,L(y,u,w)) = K(x \ (z * y),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5114,a,8026,a),flip(a)].">
      <j1 rule="hyper" parents="5114 8026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9219">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * T(x,z),x)
    ]]></literal>
    <justification jstring="[para(7882(a,1),8028(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7882 8028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9221">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * x,x)
    ]]></literal>
    <justification jstring="[para(7904(a,1),9219(a,2,2))].">
      <j1 rule="para" parents="7904 9219"/>
    </justification>
  </clause>

  <clause id="9222">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,7910,a(flip),b,9221,a),flip(a)].">
      <j1 rule="hyper" parents="347 7910 9221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9224">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(8349,a,9222,a)].">
      <j1 rule="hyper" parents="8349 9222"/>
    </justification>
  </clause>

  <clause id="9225">
    <literal><![CDATA[
      a(x,y,T(x,z)) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(6929,a,9224,a)].">
      <j1 rule="hyper" parents="6929 9224"/>
    </justification>
  </clause>

  <clause id="9226">
    <literal><![CDATA[
      x * a(x,y,T(x,z)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,9225,a,b,xx)].">
      <j1 rule="hyper" parents="134 9225"/>
    </justification>
  </clause>

  <clause id="9227">
    <literal><![CDATA[
      a(x,y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9225(a,2),8349(a,1))].">
      <j1 rule="para" parents="9225 8349"/>
    </justification>
  </clause>

  <clause id="9228">
    <literal><![CDATA[
      x * (y * a(y,x,T(y,z))) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,9226,a,b,4374,a)].">
      <j1 rule="hyper" parents="134 9226 4374"/>
    </justification>
  </clause>

  <clause id="9229">
    <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(9228(a,1),1182(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9228 1182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9230">
    <literal><![CDATA[
      K(x,T(y / (x \ z),u)) = K(x,T((z / y) \ x,u))
    ]]></literal>
    <justification jstring="[hyper(8118,a,8234,a)].">
      <j1 rule="hyper" parents="8118 8234"/>
    </justification>
  </clause>

  <clause id="9231">
    <literal><![CDATA[
      x * K(x,T((y / z) \ x,u)) = T(x,T(z / (x \ y),u))
    ]]></literal>
    <justification jstring="[hyper(134,a,9230,a(flip),b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 9230 4924"/>
    </justification>
  </clause>

  <clause id="9232">
    <literal><![CDATA[
      T(x,T(y / (x \ z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T((z / y) \ x,u)) = w
    ]]></literal>
    <justification jstring="[para(9231(a,1),4984(a,1))].">
      <j1 rule="para" parents="9231 4984"/>
    </justification>
  </clause>

  <clause id="9233">
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,z)) = L(K(z,u),y,x) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(6143,a,8327,a)].">
      <j1 rule="hyper" parents="6143 8327"/>
    </justification>
  </clause>

  <clause id="9234">
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,z)) = K(u,z) * L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,2562,a(flip),b,9233,a),flip(a)].">
      <j1 rule="hyper" parents="347 2562 9233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9235">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z * K(x,y),u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6109(a,1),9234(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6109 9234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9236">
    <literal><![CDATA[
      T(x,a(y,z,K(x,u))) = x
    ]]></literal>
    <justification jstring="[para(9235(a,1),7856(a,1,2))].">
      <j1 rule="para" parents="9235 7856"/>
    </justification>
  </clause>

  <clause id="9237">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z,u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8266(a,1),9235(a,1,2))].">
      <j1 rule="para" parents="8266 9235"/>
    </justification>
  </clause>

  <clause id="9238">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,w)) = a(z,u,K(y,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9236(a,1),7104(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9236 7104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9239">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(K(z,u),y,x) = K(z,u)
    ]]></literal>
    <justification jstring="[hyper(8263,a,9237,a)].">
      <j1 rule="hyper" parents="8263 9237"/>
    </justification>
  </clause>

  <clause id="9240">
    <literal><![CDATA[
      K(x,y) \ L(K(x,y),z,u) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(5293,a,9237,a)].">
      <j1 rule="hyper" parents="5293 9237"/>
    </justification>
  </clause>

  <clause id="9241">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = L(K(x,y),u,z)
    ]]></literal>
    <justification jstring="[hyper(5273,a,9237,a)].">
      <j1 rule="hyper" parents="5273 9237"/>
    </justification>
  </clause>

  <clause id="9242">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(2564,a,9237,a)].">
      <j1 rule="hyper" parents="2564 9237"/>
    </justification>
  </clause>

  <clause id="9243">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,L(x,z,u) \ 1) = a(u,z,K(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(5656(a,1),9237(a,1,2))].">
      <j1 rule="para" parents="5656 9237"/>
    </justification>
  </clause>

  <clause id="9244">
    <literal><![CDATA[
      K(1 / x,y) * K(y,1 / L(x,z,u)) = a(u,z,K(1 / x,y))
    ]]></literal>
    <justification jstring="[para(5665(a,1),9237(a,1,2))].">
      <j1 rule="para" parents="5665 9237"/>
    </justification>
  </clause>

  <clause id="9245">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * w) = a(u,z,K(x,y)) * w
    ]]></literal>
    <justification jstring="[para(9237(a,1),6942(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9237 6942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9246">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z * y,K(x,y))
    ]]></literal>
    <justification jstring="[para(7039(a,1),9237(a,1,2))].">
      <j1 rule="para" parents="7039 9237"/>
    </justification>
  </clause>

  <clause id="9247">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,z * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(7610(a,1),9237(a,1,2))].">
      <j1 rule="para" parents="7610 9237"/>
    </justification>
  </clause>

  <clause id="9249">
    <literal><![CDATA[
      (x / a(y,z,K(u,w))) * K(u,w) = x * L(K(u,w),z,y)
    ]]></literal>
    <justification jstring="[para(9237(a,1),8583(a,1,1,2))].">
      <j1 rule="para" parents="9237 8583"/>
    </justification>
  </clause>

  <clause id="9250">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * K(w,u) = x * L(K(w,u),z,y)
    ]]></literal>
    <justification jstring="[para(9237(a,1),9209(a,1,1,2))].">
      <j1 rule="para" parents="9237 9209"/>
    </justification>
  </clause>

  <clause id="9251">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(3312,a,9239,a)].">
      <j1 rule="hyper" parents="3312 9239"/>
    </justification>
  </clause>

  <clause id="9252">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,u) * L(K(u,z),y,x) = w
    ]]></literal>
    <justification jstring="[para(9240(a,1),5286(a,1))].">
      <j1 rule="para" parents="9240 5286"/>
    </justification>
  </clause>

  <clause id="9253">
    <literal><![CDATA[
      x \ y != K(z,u) * L(K(u,z),w,v5)
    ]]></literal>
    <literal><![CDATA[
      x * a(v5,w,K(z,u)) = y
    ]]></literal>
    <justification jstring="[para(9241(a,1),5279(a,2,2))].">
      <j1 rule="para" parents="9241 5279"/>
    </justification>
  </clause>

  <clause id="9254">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,K(x,v5)))) = K(x,y * (z * L(K(v5,x),w,u)))
    ]]></literal>
    <justification jstring="[para(9241(a,1),8003(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9241 8003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9255">
    <literal><![CDATA[
      L(K(x,y),z,u) * a(u,z,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,8256,a,b,9242,a)].">
      <j1 rule="hyper" parents="34 8256 9242"/>
    </justification>
  </clause>

  <clause id="9256">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z * y,K(y,x))
    ]]></literal>
    <justification jstring="[para(7610(a,1),9242(a,1,1))].">
      <j1 rule="para" parents="7610 9242"/>
    </justification>
  </clause>

  <clause id="9257">
    <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(7028(a,1),9255(a,1,1))].">
      <j1 rule="para" parents="7028 9255"/>
    </justification>
  </clause>

  <clause id="9258">
    <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(134,a,9246,a(flip),b,5492,a),flip(a)].">
      <j1 rule="hyper" parents="134 9246 5492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9259">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (L(K(z,u),y,x) * w) = K(z,u) * w
    ]]></literal>
    <justification jstring="[para(8256(a,1),9245(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8256 9245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9260">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = x * a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,9249,a,b,9250,a)].">
      <j1 rule="hyper" parents="35 9249 9250"/>
    </justification>
  </clause>

  <clause id="9261">
    <literal><![CDATA[
      T(x * y,z) * a(x,y,K(z,x * y)) = x * (y * K(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(5010,a,9260,a),flip(a)].">
      <j1 rule="hyper" parents="5010 9260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9262">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) \ x = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(429,a,9260,a)].">
      <j1 rule="hyper" parents="429 9260"/>
    </justification>
  </clause>

  <clause id="9263">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) \ x != v5
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(w,u)) = v5
    ]]></literal>
    <justification jstring="[para(9260(a,1),359(a,1,1))].">
      <j1 rule="para" parents="9260 359"/>
    </justification>
  </clause>

  <clause id="9264">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * a(y,z,K(w,u)) = v5
    ]]></literal>
    <justification jstring="[para(9262(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9262 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9265">
    <literal><![CDATA[
      (T(x,x \ y) * a(z,u,K(w,v5))) \ ((x \ y) \ y) != v6
    ]]></literal>
    <literal><![CDATA[
      a(z,u,K(v5,w)) = v6
    ]]></literal>
    <justification jstring="[para(335(a,1),9263(a,1))].">
      <j1 rule="para" parents="335 9263"/>
    </justification>
  </clause>

  <clause id="9266">
    <literal><![CDATA[
      L(K(x,y),z,u) * (K(y,x) * w) = a(u,z,K(x,y)) \ w
    ]]></literal>
    <justification jstring="[hyper(128,a,5261,a(flip),b,9259,a),flip(a)].">
      <j1 rule="hyper" parents="128 5261 9259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9267">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,L(L(x \ 1,z,u),w,v5) \ 1) = a(v5,w,K(L(x \ 1,z,u) \ 1,y))
    ]]></literal>
    <justification jstring="[para(7006(a,1),9243(a,1,1))].">
      <j1 rule="para" parents="7006 9243"/>
    </justification>
  </clause>

  <clause id="9268">
    <literal><![CDATA[
      K(1 / x,K(y,z)) * K(y,K(z,1 / L(x,u,w))) = a(w,u,K(1 / x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(7261(a,1),9244(a,1,2))].">
      <j1 rule="para" parents="7261 9244"/>
    </justification>
  </clause>

  <clause id="9269">
    <literal><![CDATA[
      x \ y != L(K(z,u),w,v5) * K(u,z)
    ]]></literal>
    <literal><![CDATA[
      x * a(v5,w,K(u,z)) = y
    ]]></literal>
    <justification jstring="[para(2562(a,2),9253(a,2))].">
      <j1 rule="para" parents="2562 9253"/>
    </justification>
  </clause>

  <clause id="9270">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,K(x,v5)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,8000,a(flip),b,9254,a),flip(a)].">
      <j1 rule="hyper" parents="347 8000 9254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9272">
    <literal><![CDATA[
      K(x,y * (((z * u) / z) * w)) = K(x,y * (u * (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[para(6854(a,2),9270(a,1,2,2))].">
      <j1 rule="para" parents="6854 9270"/>
    </justification>
  </clause>

  <clause id="9273">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),T(y,z)) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(8692,a,8394,a),flip(a)].">
      <j1 rule="hyper" parents="8692 8394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9274">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ (z * x),T(y,z))) = u
    ]]></literal>
    <justification jstring="[para(9273(a,1),7480(a,1))].">
      <j1 rule="para" parents="9273 7480"/>
    </justification>
  </clause>

  <clause id="9275">
    <literal><![CDATA[
      K(x,(y / z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ (z * x),T(y,z))) = u
    ]]></literal>
    <justification jstring="[para(8230(a,1),9274(a,1))].">
      <j1 rule="para" parents="8230 9274"/>
    </justification>
  </clause>

  <clause id="9276">
    <literal><![CDATA[
      K(x,L(L(y,z,y * K(z,y)),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(5058(a,1),8732(a,2,2,1))].">
      <j1 rule="para" parents="5058 8732"/>
    </justification>
  </clause>

  <clause id="9277">
    <literal><![CDATA[
      K(x,L(L(y,z,y),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(7675(a,1),9276(a,1,2,1))].">
      <j1 rule="para" parents="7675 9276"/>
    </justification>
  </clause>

  <clause id="9278">
    <literal><![CDATA[
      K(x,L(R(y,z,y),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(4494(a,1),9277(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4494 9277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9280">
    <literal><![CDATA[
      R(K(T(x,y),T(z,y * u)),y,u) = ((y * u) \ ((y * K(z,x)) * u)) \ 1
    ]]></literal>
    <justification jstring="[para(7093(a,1),9032(a,1,1))].">
      <j1 rule="para" parents="7093 9032"/>
    </justification>
  </clause>

  <clause id="9281">
    <literal><![CDATA[
      (x * (K(y \ x,y) * z)) / (x * z) = L(K(y \ x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7371(a,1),9094(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7371 9094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9282">
    <literal><![CDATA[
      L(K(x \ y,x),z,y) * (y * z) = y * (K(x \ y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(148,a,9281,a)].">
      <j1 rule="hyper" parents="148 9281"/>
    </justification>
  </clause>

  <clause id="9284">
    <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),9282(a,1,1,1,1))].">
      <j1 rule="para" parents="9 9282"/>
    </justification>
  </clause>

  <clause id="9285">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,T(y,u)) = K(x \ z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(5579,a,9188,a),flip(a)].">
      <j1 rule="hyper" parents="5579 9188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9286">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[para(2938(a,1),9285(a,1,1,1))].">
      <j1 rule="para" parents="2938 9285"/>
    </justification>
  </clause>

  <clause id="9287">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(3930,a,9286,a)].">
      <j1 rule="hyper" parents="3930 9286"/>
    </justification>
  </clause>

  <clause id="9288">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,7031,a(flip),b,9287,a),flip(a)].">
      <j1 rule="hyper" parents="347 7031 9287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9289">
    <literal><![CDATA[
      K(x \ (y * z),T(y,x)) = K(((y \ 1) \ z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9182,a(flip),b,9288,a),flip(a)].">
      <j1 rule="hyper" parents="63 9182 9288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9290">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((x * y) / z,x)
    ]]></literal>
    <justification jstring="[hyper(7485,a,9289,a),flip(a)].">
      <j1 rule="hyper" parents="7485 9289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9291">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,6517,a(flip),b,9290,a),flip(a)].">
      <j1 rule="hyper" parents="347 6517 9290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9292">
    <literal><![CDATA[
      K((x / ((y \ 1) * z)) \ y,y) = K(z / x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),9291(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 9291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9293">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),z) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),9292(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 9292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9294">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),(z \ 1) \ 1) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(3921,a,9293,a)].">
      <j1 rule="hyper" parents="3921 9293"/>
    </justification>
  </clause>

  <clause id="9295">
    <literal><![CDATA[
      L(x * K(y,T(x,z)),u,w) / L(x,u,w) = K(y,L(T(x,x * (z \ 1)),u,w))
    ]]></literal>
    <justification jstring="[para(8852(a,1),9215(a,1,1,1,2))].">
      <j1 rule="para" parents="8852 9215"/>
    </justification>
  </clause>

  <clause id="9296">
    <literal><![CDATA[
      K(R(K(x,y) \ R(K(x,y),z,u),K(x,y),z * u),((z * u) \ K(y,x)) \ 1) = K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1)
    ]]></literal>
    <justification jstring="[para(5280(a,1),9216(a,2,2))].">
      <j1 rule="para" parents="5280 9216"/>
    </justification>
  </clause>

  <clause id="9297">
    <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(9216(a,1),8808(a,2,2))].">
      <j1 rule="para" parents="9216 8808"/>
    </justification>
  </clause>

  <clause id="9298">
    <literal><![CDATA[
      R(K(x,T(T(y,z),z * u)),z,u) = ((z * u) \ ((z * K(y,x)) * u)) \ 1
    ]]></literal>
    <justification jstring="[para(7131(a,1),9280(a,1,1))].">
      <j1 rule="para" parents="7131 9280"/>
    </justification>
  </clause>

  <clause id="9299">
    <literal><![CDATA[
      ((x * y) \ ((x * K(z,u)) * y)) \ 1 = (x * y) \ ((x * K(u,z)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8734,a(flip),b,9298,a),flip(a)].">
      <j1 rule="hyper" parents="63 8734 9298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9300">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) \ 1 = (x * z) \ ((x * K(u,y)) * z)
    ]]></literal>
    <justification jstring="[para(6568(a,2),9299(a,1,1))].">
      <j1 rule="para" parents="6568 9299"/>
    </justification>
  </clause>

  <clause id="9301">
    <literal><![CDATA[
      (x * y) \ ((x * K(z,u)) * y) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,((x / u) * y) \ (x * y)) = w
    ]]></literal>
    <justification jstring="[para(9300(a,1),5179(a,1))].">
      <j1 rule="para" parents="9300 5179"/>
    </justification>
  </clause>

  <clause id="9302">
    <literal><![CDATA[
      T(x * ((x \ y) * (y / x)),T(x,y)) = ((x \ y) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,495,a(flip),b,7085,a),flip(a)].">
      <j1 rule="hyper" parents="347 495 7085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9303">
    <literal><![CDATA[
      K(x,T(y,z)) * R(K(y,T(x,z)),u,w) = T(K(x,y) * R(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(7091(a,2),7121(a,1,2,1))].">
      <j1 rule="para" parents="7091 7121"/>
    </justification>
  </clause>

  <clause id="9304">
    <literal><![CDATA[
      K(x \ y,x) * L(T(x,x \ y),z,u) = y \ ((L(x,z,u) * (x \ y)) * x)
    ]]></literal>
    <justification jstring="[para(1368(a,1),7200(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1368 7200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9305">
    <literal><![CDATA[
      L(x \ 1,x,K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(7220,a,8137,a)].">
      <j1 rule="hyper" parents="7220 8137"/>
    </justification>
  </clause>

  <clause id="9306">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(7373(a,1),9305(a,1,3))].">
      <j1 rule="para" parents="7373 9305"/>
    </justification>
  </clause>

  <clause id="9307">
    <literal><![CDATA[
      L(x \ 1,T(x,y),z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6561,a(flip),b,9306,a)].">
      <j1 rule="hyper" parents="63 6561 9306"/>
    </justification>
  </clause>

  <clause id="9309">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),z) = T(x,z) * ((y * T(x,z)) \ y)
    ]]></literal>
    <justification jstring="[para(9307(a,1),2136(a,1,1,2))].">
      <j1 rule="para" parents="9307 2136"/>
    </justification>
  </clause>

  <clause id="9310">
    <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(9307(a,1),4629(a,1,1))].">
      <j1 rule="para" parents="9307 4629"/>
    </justification>
  </clause>

  <clause id="9311">
    <literal><![CDATA[
      L(x \ K(y,x),x,z) = (z * T(x,y)) \ z
    ]]></literal>
    <justification jstring="[hyper(5843,a,9309,a)].">
      <j1 rule="hyper" parents="5843 9309"/>
    </justification>
  </clause>

  <clause id="9312">
    <literal><![CDATA[
      T(x,y) * ((z * T(x,y)) \ z) = x * ((z * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6627,a(flip),b,9309,a),flip(a)].">
      <j1 rule="hyper" parents="63 6627 9309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9314">
    <literal><![CDATA[
      L(x \ K(x * y,x),x,y) = (L(x,y,x) * y) \ y
    ]]></literal>
    <justification jstring="[para(754(a,1),9311(a,2,1))].">
      <j1 rule="para" parents="754 9311"/>
    </justification>
  </clause>

  <clause id="9316">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ T(x,z) = 1 / ((y * T(x,z)) \ y)
    ]]></literal>
    <justification jstring="[para(9312(a,1),2062(a,1,1))].">
      <j1 rule="para" parents="9312 2062"/>
    </justification>
  </clause>

  <clause id="9317">
    <literal><![CDATA[
      L(T(x,x * y) \ 1,x,y) = (L(x,y,x) * y) \ y
    ]]></literal>
    <justification jstring="[para(4934(a,2),9314(a,1,1))].">
      <j1 rule="para" parents="4934 9314"/>
    </justification>
  </clause>

  <clause id="9318">
    <literal><![CDATA[
      ((x \ (L(y,x,y) * x)) \ 1) * (L(T(y,y * x) \ 1,y,x) \ (x \ (L(y,x,y) * x))) = 1 / ((L(y,x,y) * x) \ x)
    ]]></literal>
    <justification jstring="[para(9317(a,2),3661(a,1,2,1))].">
      <j1 rule="para" parents="9317 3661"/>
    </justification>
  </clause>

  <clause id="9319">
    <literal><![CDATA[
      (L(x,y * K(x,z),x) * (y * K(x,z))) \ (y * K(x,z)) = L(T(x,x * y) \ 1,x,y * K(x,z))
    ]]></literal>
    <justification jstring="[para(7979(a,1),9317(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7979 9317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9320">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ T(x,y) = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(111(a,1),9316(a,2,2,1))].">
      <j1 rule="para" parents="111 9316"/>
    </justification>
  </clause>

  <clause id="9321">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * (z * K(y,x)) = z * (R(K(x,y),u,w) * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,9065,a(flip),b,8065,a),flip(a)].">
      <j1 rule="hyper" parents="347 9065 8065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9322">
    <literal><![CDATA[
      K(L(x,y,z),(u * (w * x)) \ v5) = K(L(x,y,z),(u * (x * w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(7808,a,8166,a),flip(a)].">
      <j1 rule="hyper" parents="7808 8166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9323">
    <literal><![CDATA[
      K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(u,y * z,x),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,7045,a(flip),b,8188,a),flip(a)].">
      <j1 rule="hyper" parents="347 7045 8188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9325">
    <literal><![CDATA[
      K((x * y) \ (z \ (x * ((y * u) * z))),z) = K(L(u,z * y,x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8704,a(flip),b,9323,a)].">
      <j1 rule="hyper" parents="63 8704 9323"/>
    </justification>
  </clause>

  <clause id="9327">
    <literal><![CDATA[
      x / ((L(x,y,z) \ 1) * x) = (L(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(220,a,8211,a(flip),b,5340,a)].">
      <j1 rule="hyper" parents="220 8211 5340"/>
    </justification>
  </clause>

  <clause id="9328">
    <literal><![CDATA[
      x / ((L(x,y,z) \ 1) * x) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,4669,a,b,9327,a),flip(a)].">
      <j1 rule="hyper" parents="347 4669 9327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9329">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) \ x = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(214,a,9328,a)].">
      <j1 rule="hyper" parents="214 9328"/>
    </justification>
  </clause>

  <clause id="9330">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * (1 / x) = L(x \ 1,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(83(a,1),9329(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="83 9329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9331">
    <literal><![CDATA[
      L(T(x,x \ 1),y,z) \ x = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(112(a,2),9329(a,1,1,1))].">
      <j1 rule="para" parents="112 9329"/>
    </justification>
  </clause>

  <clause id="9332">
    <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(1624(a,1),8363(a,1,2,2))].">
      <j1 rule="para" parents="1624 8363"/>
    </justification>
  </clause>

  <clause id="9333">
    <literal><![CDATA[
      ((x * y) * a(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(8701(a,1),8510(a,1,1,2))].">
      <j1 rule="para" parents="8701 8510"/>
    </justification>
  </clause>

  <clause id="9335">
    <literal><![CDATA[
      K(L(x,y,z),(u * (x * w)) \ v5) = K(L(x,y,z),(u * w) \ (x \ v5))
    ]]></literal>
    <justification jstring="[hyper(7808,a,8571,a),flip(a)].">
      <j1 rule="hyper" parents="7808 8571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9336">
    <literal><![CDATA[
      K(L(x,y,z),(u * (w * x)) \ v5) = K(L(x,y,z),(u * w) \ (x \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,9322,a,b,9335,a)].">
      <j1 rule="hyper" parents="63 9322 9335"/>
    </justification>
  </clause>

  <clause id="9337">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) = K((x \ y) \ z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(8597,a,8599,a)].">
      <j1 rule="hyper" parents="8597 8599"/>
    </justification>
  </clause>

  <clause id="9338">
    <literal><![CDATA[
      (T(x * y,K(z,u)) / y) / x != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K((1 / y) / x,(x * y) / u)) = w
    ]]></literal>
    <justification jstring="[para(8909(a,1),8843(a,1))].">
      <j1 rule="para" parents="8909 8843"/>
    </justification>
  </clause>

  <clause id="9339">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,((u * z) \ u) \ y) = K(x,y / ((u * z) \ u))
    ]]></literal>
    <justification jstring="[para(8810(a,1),8945(a,1,1))].">
      <j1 rule="para" parents="8810 8945"/>
    </justification>
  </clause>

  <clause id="9341">
    <literal><![CDATA[
      T(T(x,x * y) * R(y,z,u),x) = T(x * R(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),9061(a,1,1,2,1))].">
      <j1 rule="para" parents="9 9061"/>
    </justification>
  </clause>

  <clause id="9342">
    <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),9063(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 9063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9343">
    <literal><![CDATA[
      (x \ 1) \ ((x \ y) / T(y,x \ 1)) = x * ((x \ y) / T(y,x \ 1))
    ]]></literal>
    <justification jstring="[para(6102(a,1),9146(a,2,2))].">
      <j1 rule="para" parents="6102 9146"/>
    </justification>
  </clause>

  <clause id="9344">
    <literal><![CDATA[
      (x \ 1) \ ((x \ y) / T(y,x \ 1)) = x * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(4221(a,1),9343(a,2,2))].">
      <j1 rule="para" parents="4221 9343"/>
    </justification>
  </clause>

  <clause id="9345">
    <literal><![CDATA[
      (x \ 1) \ (y \ (x \ y)) = x * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(4221(a,1),9344(a,1,2))].">
      <j1 rule="para" parents="4221 9344"/>
    </justification>
  </clause>

  <clause id="9346">
    <literal><![CDATA[
      ((1 / (x \ 1)) \ (x \ 1)) * (x * (y \ (x \ y))) = (1 / (x \ 1)) \ (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(9345(a,1),1127(a,1,2))].">
      <j1 rule="para" parents="9345 1127"/>
    </justification>
  </clause>

  <clause id="9347">
    <literal><![CDATA[
      K(x,((1 / (K(y,x \ z) / y)) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5425,a,b,9189,a)].">
      <j1 rule="hyper" parents="63 5425 9189"/>
    </justification>
  </clause>

  <clause id="9348">
    <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(7185,a,9258,a)].">
      <j1 rule="hyper" parents="7185 9258"/>
    </justification>
  </clause>

  <clause id="9349">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z * y,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(199(a,1),9348(a,1,2,2))].">
      <j1 rule="para" parents="199 9348"/>
    </justification>
  </clause>

  <clause id="9350">
    <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(7803,a,9304,a)].">
      <j1 rule="hyper" parents="7803 9304"/>
    </justification>
  </clause>

  <clause id="9351">
    <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(63,a,250,a(flip),b,9332,a),flip(a)].">
      <j1 rule="hyper" parents="63 250 9332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9352">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ ((L(y,z,u) * (y \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(7255,a,9350,a)].">
      <j1 rule="hyper" parents="7255 9350"/>
    </justification>
  </clause>

  <clause id="9353">
    <literal><![CDATA[
      K(x \ R(1 / y,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(7604,a,6993,a)].">
      <j1 rule="hyper" parents="7604 6993"/>
    </justification>
  </clause>

  <clause id="9354">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,3917,a(flip),b,9353,a)].">
      <j1 rule="hyper" parents="63 3917 9353"/>
    </justification>
  </clause>

  <clause id="9355">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (x / (z * x)),z \ 1)
    ]]></literal>
    <justification jstring="[para(247(a,1),9353(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="247 9353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9356">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ ((z * x) \ x),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,8160,a(flip),b,9355,a),flip(a)].">
      <j1 rule="hyper" parents="347 8160 9355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9357">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),(z \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x / ((z \ 1) * x)),z) = u
    ]]></literal>
    <justification jstring="[para(9355(a,2),3886(a,1))].">
      <j1 rule="para" parents="9355 3886"/>
    </justification>
  </clause>

  <clause id="9358">
    <literal><![CDATA[
      T(x * K(y * R(x,z,u),x),y) = R(x,T(y,T(x,w)),R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7199,a(flip),b,7975,a)].">
      <j1 rule="hyper" parents="63 7199 7975"/>
    </justification>
  </clause>

  <clause id="9360">
    <literal><![CDATA[
      R(x,T(y,T(x,z)),R(x,u,w)) = R(x,y,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5309,a(flip),b,9358,a),flip(a)].">
      <j1 rule="hyper" parents="63 5309 9358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9361">
    <literal><![CDATA[
      R(T(x,y),T(z,x),R(T(x,y),u,w)) = R(T(x,y),z,R(T(x,y),u,w))
    ]]></literal>
    <justification jstring="[para(7387(a,1),9360(a,1,2))].">
      <j1 rule="para" parents="7387 9360"/>
    </justification>
  </clause>

  <clause id="9362">
    <literal><![CDATA[
      K(L(x,y,z),u * (K(x,w) * v5)) = K(L(x,y,z),u * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,5545,a(flip),b,7993,a),flip(a)].">
      <j1 rule="hyper" parents="347 5545 7993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9363">
    <literal><![CDATA[
      K(x * (K(y,z) * u),R(y,w,v5)) = K(x * u,R(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,5546,a(flip),b,7994,a),flip(a)].">
      <j1 rule="hyper" parents="347 5546 7994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9364">
    <literal><![CDATA[
      K(x * y,R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(5030(a,1),9363(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5030 9363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9365">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(7336(a,1),8041(a,1,1,3))].">
      <j1 rule="para" parents="7336 8041"/>
    </justification>
  </clause>

  <clause id="9366">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5256(a,1),9365(a,2,2))].">
      <j1 rule="para" parents="5256 9365"/>
    </justification>
  </clause>

  <clause id="9367">
    <literal><![CDATA[
      K((x * y) \ z,L(y,u,w)) = K(x \ (y \ z),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5726,a,8102,a),flip(a)].">
      <j1 rule="hyper" parents="5726 8102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9368">
    <literal><![CDATA[
      K(L(x \ y,x,z),L(x,u,w)) = K(z \ (x \ (z * y)),L(x,u,w))
    ]]></literal>
    <justification jstring="[para(99(a,2),9367(a,1,1))].">
      <j1 rule="para" parents="99 9367"/>
    </justification>
  </clause>

  <clause id="9369">
    <literal><![CDATA[
      T((T(x,y) \ R(T(z,y),u,w)) * K(y,x \ R(z,u,w)),y) = T(x,y) \ R(T(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(7876(a,1),8139(a,1,1,2))].">
      <j1 rule="para" parents="7876 8139"/>
    </justification>
  </clause>

  <clause id="9370">
    <literal><![CDATA[
      K(x,(y \ (x * z)) \ (K(x * z,y) * x)) = K(x,R(y,y \ (x * z),y) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6463,a(flip),b,8233,a)].">
      <j1 rule="hyper" parents="63 6463 8233"/>
    </justification>
  </clause>

  <clause id="9371">
    <literal><![CDATA[
      K(x,T((y * R(x,z,u)) / w,w)) = K(x,(w / R(x,z,u)) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9076,a(flip),b,8291,a)].">
      <j1 rule="hyper" parents="63 9076 8291"/>
    </justification>
  </clause>

  <clause id="9373">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,y \ (w * R(x,z,u)))
    ]]></literal>
    <justification jstring="[para(113(a,1),9371(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 9371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9374">
    <literal><![CDATA[
      K(x,(R(x,y,z) \ u) \ w) = K(x,u \ (w * R(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7943,a(flip),b,9373,a)].">
      <j1 rule="hyper" parents="63 7943 9373"/>
    </justification>
  </clause>

  <clause id="9375">
    <literal><![CDATA[
      K(x,y \ (R(x,z,u) * w)) = K(x,y \ (w * R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6919,a(flip),b,9374,a)].">
      <j1 rule="hyper" parents="63 6919 9374"/>
    </justification>
  </clause>

  <clause id="9376">
    <literal><![CDATA[
      L(K(T(T(x,y),z * y),u),y,z) * w = K(x,(z * y) / (z * (u \ y))) * w
    ]]></literal>
    <justification jstring="[hyper(347,a,5256,a(flip),b,9034,a),flip(a)].">
      <j1 rule="hyper" parents="347 5256 9034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9377">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = T(y,K(x,z)) / y
    ]]></literal>
    <justification jstring="[hyper(347,a,171,a(flip),b,9040,a),flip(a)].">
      <j1 rule="hyper" parents="347 171 9040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9378">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,4969,a,b,9377,a),flip(a)].">
      <j1 rule="hyper" parents="347 4969 9377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9380">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7279,a,b,9378,a),flip(a)].">
      <j1 rule="hyper" parents="347 7279 9378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9381">
    <literal><![CDATA[
      T(x * K(y * R(x,z,u),x),y) = R(x,K(x,w) * y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(7940(a,1),9058(a,1,1,2))].">
      <j1 rule="para" parents="7940 9058"/>
    </justification>
  </clause>

  <clause id="9382">
    <literal><![CDATA[
      R(x,K(x,y) * z,R(x,u,w)) = R(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5309,a(flip),b,9381,a),flip(a)].">
      <j1 rule="hyper" parents="63 5309 9381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9384">
    <literal><![CDATA[
      ((x \ y) \ y) \ R((x \ y) \ y,K(x,z) * u,R(x,w,v5)) = x \ (y \ ((R(x,u,R(x,w,v5)) * (x \ y)) * x))
    ]]></literal>
    <justification jstring="[para(9382(a,1),6952(a,2,2,2,1,1))].">
      <j1 rule="para" parents="9382 6952"/>
    </justification>
  </clause>

  <clause id="9385">
    <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),9284(a,2,2,1,1))].">
      <j1 rule="para" parents="9 9284"/>
    </justification>
  </clause>

  <clause id="9386">
    <literal><![CDATA[
      ((x * y) * (K(y,x) * z)) / ((x * y) * z) = L(K(y,x),z,x * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,9385,a)].">
      <j1 rule="hyper" parents="145 9385"/>
    </justification>
  </clause>

  <clause id="9387">
    <literal><![CDATA[
      ((x * y) * (K(y,x) * z)) / (z * T(x * y,z)) = L(K(y,x),z,x * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,9385,a(flip),b,251,a)].">
      <j1 rule="hyper" parents="131 9385 251"/>
    </justification>
  </clause>

  <clause id="9388">
    <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(9385(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9385 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9390">
    <literal><![CDATA[
      ((K(x,y) * z) * T(y * x,z)) / (z * T(y * x,z)) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[para(8410(a,2),9387(a,1,1))].">
      <j1 rule="para" parents="8410 9387"/>
    </justification>
  </clause>

  <clause id="9391">
    <literal><![CDATA[
      K(x,L(T(y,y * (z \ 1)),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9214,a(flip),b,9295,a),flip(a)].">
      <j1 rule="hyper" parents="63 9214 9295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9392">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,8730,a(flip),b,9391,a)].">
      <j1 rule="hyper" parents="63 8730 9391"/>
    </justification>
  </clause>

  <clause id="9393">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = K(x,K(u,(1 / y) / z))
    ]]></literal>
    <justification jstring="[hyper(9338,a,8850,a)].">
      <j1 rule="hyper" parents="9338 8850"/>
    </justification>
  </clause>

  <clause id="9394">
    <literal><![CDATA[
      K(x,K((1 / (y \ z)) / u,R(u / y,y,y \ z))) = K(x,K(z,(1 / (y \ z)) / u))
    ]]></literal>
    <justification jstring="[para(606(a,2),9393(a,1,2,2))].">
      <j1 rule="para" parents="606 9393"/>
    </justification>
  </clause>

  <clause id="9395">
    <literal><![CDATA[
      L(K(T(x,y),T(z,u * y)),y,u) * w = K(x,(u * y) / (u * (z \ y))) * w
    ]]></literal>
    <justification jstring="[para(7093(a,1),9376(a,1,1,1))].">
      <j1 rule="para" parents="7093 9376"/>
    </justification>
  </clause>

  <clause id="9396">
    <literal><![CDATA[
      R(K(x,y),z,T(y * x,z)) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[hyper(595,a,9390,a)].">
      <j1 rule="hyper" parents="595 9390"/>
    </justification>
  </clause>

  <clause id="9397">
    <literal><![CDATA[
      L(K(x,T(T(y,z * u),u)),u,z) * w = K(x,(z * u) / (z * (y \ u))) * w
    ]]></literal>
    <justification jstring="[para(7093(a,1),9395(a,1,1,1))].">
      <j1 rule="para" parents="7093 9395"/>
    </justification>
  </clause>

  <clause id="9398">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) * w = K(z,(x * y) / (x * (u \ y))) * w
    ]]></literal>
    <justification jstring="[para(8541(a,1),9397(a,1,1))].">
      <j1 rule="para" parents="8541 9397"/>
    </justification>
  </clause>

  <clause id="9399">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = (x * y) / (x * (K(u,z) * y))
    ]]></literal>
    <justification jstring="[hyper(131,a,5885,a(flip),b,9398,a),flip(a)].">
      <j1 rule="hyper" parents="131 5885 9398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9400">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * z) = y * (K(x,u) * z)
    ]]></literal>
    <justification jstring="[hyper(5285,a,9399,a)].">
      <j1 rule="hyper" parents="5285 9399"/>
    </justification>
  </clause>

  <clause id="9401">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = (y * (K(x,u) * z)) / (y * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,9400,a),flip(a)].">
      <j1 rule="hyper" parents="145 9400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9402">
    <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(9401(a,2),9388(a,1))].">
      <j1 rule="para" parents="9401 9388"/>
    </justification>
  </clause>

  <clause id="9403">
    <literal><![CDATA[
      K(x,y) * (R(T(y,z),u,w) * (K(y,x) * v5)) = R(T(y,z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(7380(a,1),7411(a,1,2,2,1))].">
      <j1 rule="para" parents="7380 7411"/>
    </justification>
  </clause>

  <clause id="9405">
    <literal><![CDATA[
      x \ (((y * T(x,K(z,u))) / y) * w) = x * (T(T(x,K(z,u)),y) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,7736,a(flip),b,7739,a),flip(a)].">
      <j1 rule="hyper" parents="63 7736 7739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9406">
    <literal><![CDATA[
      x \ (T((y * x) / y,K(z,u)) * w) = x * (T(T(x,K(z,u)),y) \ w)
    ]]></literal>
    <justification jstring="[para(504(a,1),9405(a,1,2,1))].">
      <j1 rule="para" parents="504 9405"/>
    </justification>
  </clause>

  <clause id="9407">
    <literal><![CDATA[
      K(x,y) * (K(y,T(K(z,u),x)) * w) = y * (T(T(y,K(z,u)),x) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,7454,a(flip),b,9406,a)].">
      <j1 rule="hyper" parents="63 7454 9406"/>
    </justification>
  </clause>

  <clause id="9408">
    <literal><![CDATA[
      K(x,y) * (K(y,K(z,T(u,x))) * w) = y * (T(T(y,K(z,u)),x) \ w)
    ]]></literal>
    <justification jstring="[para(7091(a,2),9407(a,1,2,1,2))].">
      <j1 rule="para" parents="7091 9407"/>
    </justification>
  </clause>

  <clause id="9409">
    <literal><![CDATA[
      T(x * K(x * K(y,z),u),K(y,z)) = K(y,z) \ T(x / K(z,y),T(u,K(z,y)))
    ]]></literal>
    <justification jstring="[para(6117(a,1),7757(a,1,1,2,1))].">
      <j1 rule="para" parents="6117 7757"/>
    </justification>
  </clause>

  <clause id="9410">
    <literal><![CDATA[
      T(x * L(K(y,z),u,w),K(z,v5)) = T(x,K(z,v5)) * L(K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(7006(a,1),8476(a,1,1,2))].">
      <j1 rule="para" parents="7006 8476"/>
    </justification>
  </clause>

  <clause id="9411">
    <literal><![CDATA[
      T(L(K(x,y),z,u) \ w,K(y,v5)) = L(K(x,y),z,u) \ T(w,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(35,a,4830,a(flip),b,9410,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 4830 9410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9412">
    <literal><![CDATA[
      T(L(K(x,y),z,u) * w,K(x,v5)) = L(K(y,x),z,u) \ T(w,K(x,v5))
    ]]></literal>
    <justification jstring="[para(8255(a,1),9411(a,1,1))].">
      <j1 rule="para" parents="8255 9411"/>
    </justification>
  </clause>

  <clause id="9413">
    <literal><![CDATA[
      T(L(K(x,y),z,u) * w,K(x,v5)) = L(K(x,y),z,u) * T(w,K(x,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,8255,a(flip),b,9412,a),flip(a)].">
      <j1 rule="hyper" parents="347 8255 9412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9414">
    <literal><![CDATA[
      T(L(K(x,y),z,u) * T(w,L(K(x,y),z,u)),K(x,v5)) = T(w,K(x,v5)) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,266,a(flip),b,9413,a),flip(a)].">
      <j1 rule="hyper" parents="347 266 9413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9415">
    <literal><![CDATA[
      K(x,(T(y * z,z \ 1) / u) * w) = K(x,((((y * z) \ y) \ y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8038,a(flip),b,8478,a)].">
      <j1 rule="hyper" parents="63 8038 8478"/>
    </justification>
  </clause>

  <clause id="9416">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) = K(z * ((x \ y) \ 1),T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(8597,a,8598,a),flip(a)].">
      <j1 rule="hyper" parents="8597 8598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9417">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T(z \ y,u)) = K((y \ z) \ x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9337,a(flip),b,9416,a),flip(a)].">
      <j1 rule="hyper" parents="63 9337 9416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9418">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T(z \ y,z)) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7392,a(flip),b,9417,a),flip(a)].">
      <j1 rule="hyper" parents="347 7392 9417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9419">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),y / z) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(7491,a,9418,a)].">
      <j1 rule="hyper" parents="7491 9418"/>
    </justification>
  </clause>

  <clause id="9420">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K((x \ y) \ z,x / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8145,a,b,9419,a)].">
      <j1 rule="hyper" parents="63 8145 9419"/>
    </justification>
  </clause>

  <clause id="9421">
    <literal><![CDATA[
      T(x,K(y,z)) / (z * T(z \ x,y)) = (x * (x / (z * T(z \ x,y)))) / x
    ]]></literal>
    <justification jstring="[para(8898(a,1),8838(a,1,1))].">
      <j1 rule="para" parents="8898 8838"/>
    </justification>
  </clause>

  <clause id="9422">
    <literal><![CDATA[
      T(x,K(y,z)) / (z * T(z \ x,y)) = (x * K(y,(z / x) \ 1)) / x
    ]]></literal>
    <justification jstring="[para(5572(a,1),9421(a,2,1,2))].">
      <j1 rule="para" parents="5572 9421"/>
    </justification>
  </clause>

  <clause id="9423">
    <literal><![CDATA[
      T(x,K(y,z)) / (z * T(z \ x,y)) = K(y,T((z / x) \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,7378,a(flip),b,9422,a),flip(a)].">
      <j1 rule="hyper" parents="347 7378 9422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9424">
    <literal><![CDATA[
      T(x,K(y,z)) / (z * T(z \ x,y)) = K(y,(x \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,7235,a(flip),b,9423,a),flip(a)].">
      <j1 rule="hyper" parents="347 7235 9423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9425">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((y \ z) \ u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(8756(a,1),8947(a,1,1))].">
      <j1 rule="para" parents="8756 8947"/>
    </justification>
  </clause>

  <clause id="9426">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) * K(x,K(y,z \ u)) = K(x,y / ((y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(8756(a,1),8948(a,1,2))].">
      <j1 rule="para" parents="8756 8948"/>
    </justification>
  </clause>

  <clause id="9429">
    <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(1716(a,1),8973(a,1,2))].">
      <j1 rule="para" parents="1716 8973"/>
    </justification>
  </clause>

  <clause id="9430">
    <literal><![CDATA[
      x * a(x,y,R(x,z,u)) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(838,a,9429,a)].">
      <j1 rule="hyper" parents="838 9429"/>
    </justification>
  </clause>

  <clause id="9431">
    <literal><![CDATA[
      x \ R(x,y,R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(836,a,9429,a),flip(a)].">
      <j1 rule="hyper" parents="836 9429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9432">
    <literal><![CDATA[
      x \ R(x,y,R(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(9429(a,1),836(a,1))].">
      <j1 rule="para" parents="9429 836"/>
    </justification>
  </clause>

  <clause id="9433">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),T(z,x),R(T(x,y),u,w)) = a(T(x,y),z,R(T(x,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(128,a,9361,a,b,9430,a)].">
      <j1 rule="hyper" parents="128 9361 9430"/>
    </justification>
  </clause>

  <clause id="9434">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) != x * w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(9430(a,1),43(a,1))].">
      <j1 rule="para" parents="9430 43"/>
    </justification>
  </clause>

  <clause id="9435">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = a(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8974,a,9431,a)].">
      <j1 rule="hyper" parents="8974 9431"/>
    </justification>
  </clause>

  <clause id="9436">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) \ x = a(x,y,R(x,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(9431(a,1),4742(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9431 4742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9437">
    <literal><![CDATA[
      R(T(x,y),T(y,x),R(T(x,y),z,u)) \ T(x,y) = a(x,y,R(T(x,y),z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(4806(a,1),9436(a,2,1))].">
      <j1 rule="para" parents="4806 9436"/>
    </justification>
  </clause>

  <clause id="9438">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,T(x,R(y,w,v5))) = a(y,T(x,R(y,w,v5)),R(y,z,u))
    ]]></literal>
    <justification jstring="[para(7955(a,1),9435(a,1,1))].">
      <j1 rule="para" parents="7955 9435"/>
    </justification>
  </clause>

  <clause id="9439">
    <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(2019(a,1),8977(a,1,2))].">
      <j1 rule="para" parents="2019 8977"/>
    </justification>
  </clause>

  <clause id="9440">
    <literal><![CDATA[
      x \ R(x,y,L(x,z,u)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(836,a,9439,a),flip(a)].">
      <j1 rule="hyper" parents="836 9439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9441">
    <literal><![CDATA[
      K(x * L(y,z,u),y) * K(y,x) = a(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8978,a,9440,a)].">
      <j1 rule="hyper" parents="8978 9440"/>
    </justification>
  </clause>

  <clause id="9442">
    <literal><![CDATA[
      K(x,y) * K(y * L(x,z,u),x) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8960,a,b,9440,a)].">
      <j1 rule="hyper" parents="63 8960 9440"/>
    </justification>
  </clause>

  <clause id="9443">
    <literal><![CDATA[
      K(x,y) * a(y,x,L(y,z,u)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(9440(a,1),8975(a,1,2))].">
      <j1 rule="para" parents="9440 8975"/>
    </justification>
  </clause>

  <clause id="9444">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) * K(x,u) = a(x,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(7952(a,2),9441(a,1,1))].">
      <j1 rule="para" parents="7952 9441"/>
    </justification>
  </clause>

  <clause id="9446">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) \ x = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9030,a(flip),b,9444,a)].">
      <j1 rule="hyper" parents="63 9030 9444"/>
    </justification>
  </clause>

  <clause id="9447">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,K(z,1 / L(x,u,w))) = a(w,u,K(1 / x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(8840(a,1),9268(a,1,1))].">
      <j1 rule="para" parents="8840 9268"/>
    </justification>
  </clause>

  <clause id="9448">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,K(z,L(x,u,w))) = a(w,u,K(1 / x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(8822(a,1),9447(a,1,2))].">
      <j1 rule="para" parents="8822 9447"/>
    </justification>
  </clause>

  <clause id="9449">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,L(y,u,w))) = a(w,u,K(1 / y,K(x,z)))
    ]]></literal>
    <justification jstring="[para(7279(a,1),9448(a,1,1))].">
      <j1 rule="para" parents="7279 9448"/>
    </justification>
  </clause>

  <clause id="9450">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,L(y,u,w))) = a(w,u,K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(8832(a,1),9449(a,2,3))].">
      <j1 rule="para" parents="8832 9449"/>
    </justification>
  </clause>

  <clause id="9451">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z,K(w,L(u,y,x))) * K(z,K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(9450(a,1),7586(a,1))].">
      <j1 rule="para" parents="9450 7586"/>
    </justification>
  </clause>

  <clause id="9452">
    <literal><![CDATA[
      (x \ (x \ 1)) * (x * (y \ (x \ y))) = (1 / (x \ 1)) \ (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(80(a,1),9346(a,1,1,1))].">
      <j1 rule="para" parents="80 9346"/>
    </justification>
  </clause>

  <clause id="9453">
    <literal><![CDATA[
      (1 / (x \ 1)) \ (y \ (x \ y)) = (x * x) \ (x * (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(981,a,9452,a),flip(a)].">
      <j1 rule="hyper" parents="981 9452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9454">
    <literal><![CDATA[
      L(x \ (y \ (x \ y)),x,x) = (1 / (x \ 1)) \ (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(347,a,99,a,b,9453,a)].">
      <j1 rule="hyper" parents="347 99 9453"/>
    </justification>
  </clause>

  <clause id="9455">
    <literal><![CDATA[
      L(x \ (y \ (x \ y)),x,x) != z
    ]]></literal>
    <literal><![CDATA[
      x \ (y \ (x \ y)) = z
    ]]></literal>
    <justification jstring="[para(9454(a,2),646(a,1))].">
      <j1 rule="para" parents="9454 646"/>
    </justification>
  </clause>

  <clause id="9456">
    <literal><![CDATA[
      T(x * K(x * K(y,z),u),K(z,y)) = K(y,z) \ T(x / K(z,y),T(u,K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(7362,a,9409,a)].">
      <j1 rule="hyper" parents="7362 9409"/>
    </justification>
  </clause>

  <clause id="9457">
    <literal><![CDATA[
      a(T(x,y),T(z,x),R(T(x,y),u,w)) = a(T(x,y),z,R(T(x,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(9432,a,9433,a)].">
      <j1 rule="hyper" parents="9432 9433"/>
    </justification>
  </clause>

  <clause id="9458">
    <literal><![CDATA[
      a(T(x,y),T(y,x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4881,a(flip),b,9457,a),flip(a)].">
      <j1 rule="hyper" parents="63 4881 9457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9459">
    <literal><![CDATA[
      a(x,y,R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(4807,a,9458,a)].">
      <j1 rule="hyper" parents="4807 9458"/>
    </justification>
  </clause>

  <clause id="9460">
    <literal><![CDATA[
      R(T(x,y),y,R(T(x,y),z,u)) \ T(x,y) = a(x,y,R(T(x,y),z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(9361(a,1),9437(a,1,1))].">
      <j1 rule="para" parents="9361 9437"/>
    </justification>
  </clause>

  <clause id="9461">
    <literal><![CDATA[
      R(T(x,y),y,R(T(x,y),z,u)) \ T(x,y) = a(R(x,z,u),y,x) \ 1
    ]]></literal>
    <justification jstring="[para(9459(a,1),9460(a,2,1))].">
      <j1 rule="para" parents="9459 9460"/>
    </justification>
  </clause>

  <clause id="9462">
    <literal><![CDATA[
      a(T(x,y),y,R(T(x,y),z,u)) \ 1 = a(R(x,z,u),y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,9436,a(flip),b,9461,a)].">
      <j1 rule="hyper" parents="63 9436 9461"/>
    </justification>
  </clause>

  <clause id="9463">
    <literal><![CDATA[
      T(x * K(x * K(y,z),u),K(z,y)) = K(y,z) \ T(x * K(y,z),T(u,K(z,y)))
    ]]></literal>
    <justification jstring="[para(6117(a,1),9456(a,2,2,1))].">
      <j1 rule="para" parents="6117 9456"/>
    </justification>
  </clause>

  <clause id="9464">
    <literal><![CDATA[
      (x * K(T(y,z),u)) * (K(u,T(y,z)) * z) = R(x,K(y,T(u,z)),z * K(u,y)) * z
    ]]></literal>
    <justification jstring="[para(7093(a,1),7439(a,2,1,2))].">
      <j1 rule="para" parents="7093 7439"/>
    </justification>
  </clause>

  <clause id="9465">
    <literal><![CDATA[
      T(x,T((y \ 1) \ x,z)) * K(T(y \ 1,z) \ 1,x) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(4875(a,1),8097(a,1,1))].">
      <j1 rule="para" parents="4875 8097"/>
    </justification>
  </clause>

  <clause id="9466">
    <literal><![CDATA[
      T(T(x,y) / T(L(T(x,T(x,y)),z,u),w),L(x,z,u)) = T(L(x,z,u),w) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(25(a,2),8127(a,1,1,2,1))].">
      <j1 rule="para" parents="25 8127"/>
    </justification>
  </clause>

  <clause id="9467">
    <literal><![CDATA[
      K(x * R(T(y,z),u,w),T(T(y,v5),K(R(y,u,w),z))) = K(x * R(y,u,w),T(y,v5))
    ]]></literal>
    <justification jstring="[para(27(a,2),8416(a,1,1,2))].">
      <j1 rule="para" parents="27 8416"/>
    </justification>
  </clause>

  <clause id="9468">
    <literal><![CDATA[
      (x / T(y,x)) * L(z,K(x,y),y \ x) = (x / y) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(5600,a,8461,a),flip(a)].">
      <j1 rule="hyper" parents="5600 8461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9469">
    <literal><![CDATA[
      K((x * (y * z)) \ u,L(z,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ (z \ u),L(z,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(8569(a,1),5114(a,1))].">
      <j1 rule="para" parents="8569 5114"/>
    </justification>
  </clause>

  <clause id="9470">
    <literal><![CDATA[
      K(x,R(x,y,z) \ ((x * R(T(x,u),y,z)) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w \ x) = v5
    ]]></literal>
    <justification jstring="[para(8737(a,2),7486(a,1))].">
      <j1 rule="para" parents="8737 7486"/>
    </justification>
  </clause>

  <clause id="9471">
    <literal><![CDATA[
      T(K(x,y) * L(y,z,u),x) / L(y,z,u) = K(y \ L(y,z,u),T(x,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),8740(a,1,2))].">
      <j1 rule="para" parents="10 8740"/>
    </justification>
  </clause>

  <clause id="9472">
    <literal><![CDATA[
      K(x \ L(x,y,z),T(u,x)) = K(L(x,y,z),u) * K(u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8202,a(flip),b,9471,a),flip(a)].">
      <j1 rule="hyper" parents="63 8202 9471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9474">
    <literal><![CDATA[
      K(x,T((y \ z) / z,u)) = K(x,T(y \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(9026,a,8525,a)].">
      <j1 rule="hyper" parents="9026 8525"/>
    </justification>
  </clause>

  <clause id="9476">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,u)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(83(a,1),9474(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="83 9474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9477">
    <literal><![CDATA[
      K(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(9476(a,1),7726(a,1))].">
      <j1 rule="para" parents="9476 7726"/>
    </justification>
  </clause>

  <clause id="9478">
    <literal><![CDATA[
      K(x,R(x,y,z) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ R(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(7134(a,1),9477(a,1))].">
      <j1 rule="para" parents="7134 9477"/>
    </justification>
  </clause>

  <clause id="9479">
    <literal><![CDATA[
      K(x \ (y / ((z \ 1) * y)),z) = K(x \ z,z)
    ]]></literal>
    <justification jstring="[hyper(9357,a,9294,a)].">
      <j1 rule="hyper" parents="9357 9294"/>
    </justification>
  </clause>

  <clause id="9480">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[para(2267(a,2),9479(a,1,1,2))].">
      <j1 rule="para" parents="2267 9479"/>
    </justification>
  </clause>

  <clause id="9481">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (z \ 1),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,9354,a(flip),b,9480,a)].">
      <j1 rule="hyper" parents="63 9354 9480"/>
    </justification>
  </clause>

  <clause id="9483">
    <literal><![CDATA[
      K(x \ ((y * z) \ z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,9356,a(flip),b,9481,a)].">
      <j1 rule="hyper" parents="63 9356 9481"/>
    </justification>
  </clause>

  <clause id="9485">
    <literal><![CDATA[
      a(x,T(y,R(x,z,u)),R(x,w,v5)) = K(y * R(x,w,v5),x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7134(a,1),9438(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7134 9438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9486">
    <literal><![CDATA[
      a(x,T(y,R(x,z,u)),R(x,w,v5)) = a(x,y,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,9435,a(flip),b,9485,a),flip(a)].">
      <j1 rule="hyper" parents="347 9435 9485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9488">
    <literal><![CDATA[
      a(x,T(y,x),R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(586(a,1),9486(a,1,2,2))].">
      <j1 rule="para" parents="586 9486"/>
    </justification>
  </clause>

  <clause id="9489">
    <literal><![CDATA[
      (x * K(T(y,z),u)) * (K(u,T(y,z)) * z) = R(x,K(y,u),z * K(u,y)) * z
    ]]></literal>
    <justification jstring="[para(8693(a,1),9464(a,2,1))].">
      <j1 rule="para" parents="8693 9464"/>
    </justification>
  </clause>

  <clause id="9490">
    <literal><![CDATA[
      (x * K(T(y,z),u)) * (K(u,T(y,z)) * z) = (x * K(y,u)) * (K(u,y) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,9366,a(flip),b,9489,a),flip(a)].">
      <j1 rule="hyper" parents="347 9366 9489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9491">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * (K(z,T(y,u)) * u) = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(7093(a,1),9490(a,1,1,2))].">
      <j1 rule="para" parents="7093 9490"/>
    </justification>
  </clause>

  <clause id="9492">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * (u * K(z,y)) = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(7373(a,1),9491(a,1,2))].">
      <j1 rule="para" parents="7373 9491"/>
    </justification>
  </clause>

  <clause id="9493">
    <literal><![CDATA[
      (K(x,T(y,z)) * a(K(x,u),w,v5)) * (z * K(y,x)) = (a(K(x,u),w,v5) * K(x,y)) * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(8562(a,2),9492(a,1,1))].">
      <j1 rule="para" parents="8562 9492"/>
    </justification>
  </clause>

  <clause id="9494">
    <literal><![CDATA[
      T(x,T(1 \ (y * x),z)) * K(T(y \ 1,z) \ 1,x) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(8590(a,1),9465(a,1,1))].">
      <j1 rule="para" parents="8590 9465"/>
    </justification>
  </clause>

  <clause id="9495">
    <literal><![CDATA[
      T(T(x,y) / T(L(x,z,u),w),L(x,z,u)) = T(L(x,z,u),w) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(198(a,1),9466(a,1,1,2,1,1))].">
      <j1 rule="para" parents="198 9466"/>
    </justification>
  </clause>

  <clause id="9496">
    <literal><![CDATA[
      T(T(x,y) / L(T(x,z),u,w),L(x,u,w)) = T(L(x,u,w),z) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(25(a,2),9495(a,1,1,2))].">
      <j1 rule="para" parents="25 9495"/>
    </justification>
  </clause>

  <clause id="9497">
    <literal><![CDATA[
      T(x,y) / L(T(x,z),u,w) = T(L(x,u,w),z) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6937,a(flip),b,9496,a)].">
      <j1 rule="hyper" parents="63 6937 9496"/>
    </justification>
  </clause>

  <clause id="9498">
    <literal><![CDATA[
      T(x,y) / L(T(x,z),u,w) = L(T(x,z),u,w) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(25(a,2),9497(a,2,1))].">
      <j1 rule="para" parents="25 9497"/>
    </justification>
  </clause>

  <clause id="9499">
    <literal><![CDATA[
      K(x * R(T(y,z),u,w),T(T(y,v5),K(z,R(y,u,w)))) = K(x * R(y,u,w),T(y,v5))
    ]]></literal>
    <justification jstring="[para(7330(a,1),9467(a,1,2))].">
      <j1 rule="para" parents="7330 9467"/>
    </justification>
  </clause>

  <clause id="9500">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(T(y \ 1,z) \ 1,x) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(66(a,1),9494(a,1,1,2,1))].">
      <j1 rule="para" parents="66 9494"/>
    </justification>
  </clause>

  <clause id="9501">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K((y \ 1) \ 1,T(x,z)) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(7096(a,1),9500(a,1,2))].">
      <j1 rule="para" parents="7096 9500"/>
    </justification>
  </clause>

  <clause id="9502">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(y,T(x,z)) = L(x,T(1 / y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(3407(a,1),9501(a,1,2))].">
      <j1 rule="para" parents="3407 9501"/>
    </justification>
  </clause>

  <clause id="9503">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(y,T(x,z)) = L(x,T(y \ 1,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,4051,a(flip),b,9502,a),flip(a)].">
      <j1 rule="hyper" parents="347 4051 9502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9504">
    <literal><![CDATA[
      L(x,T(y \ 1,z) \ 1,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9053,a(flip),b,9503,a),flip(a)].">
      <j1 rule="hyper" parents="63 9053 9503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9506">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,x) = L(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,4052,a(flip),b,9504,a)].">
      <j1 rule="hyper" parents="63 4052 9504"/>
    </justification>
  </clause>

  <clause id="9507">
    <literal><![CDATA[
      L(x,(y / z) \ 1,x) = L(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(113(a,1),9506(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 9506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9508">
    <literal><![CDATA[
      K(x * R(T(y,z),u,w),T(y,v5)) = K(x * R(y,u,w),T(y,v5))
    ]]></literal>
    <justification jstring="[para(3046(a,1),9499(a,1,2))].">
      <j1 rule="para" parents="3046 9499"/>
    </justification>
  </clause>

  <clause id="9510">
    <literal><![CDATA[
      T(T(x,y) * K(z * R(x,u,w),T(x,y)),z) = R(T(x,y),z,R(T(x,y),u,w))
    ]]></literal>
    <justification jstring="[para(9508(a,1),5309(a,1,1,2))].">
      <j1 rule="para" parents="9508 5309"/>
    </justification>
  </clause>

  <clause id="9511">
    <literal><![CDATA[
      T(T(x * K(y * R(x,z,u),x),w),y) = R(T(x,w),y,R(T(x,w),z,u))
    ]]></literal>
    <justification jstring="[para(5308(a,1),9510(a,1,1))].">
      <j1 rule="para" parents="5308 9510"/>
    </justification>
  </clause>

  <clause id="9512">
    <literal><![CDATA[
      R(T(x,y),z,R(T(x,y),u,w)) = R(T(x,y),z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6742,a(flip),b,9511,a),flip(a)].">
      <j1 rule="hyper" parents="63 6742 9511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9513">
    <literal><![CDATA[
      ((x \ y) \ R(x \ y,z,x \ y)) * (y / x) = R((x \ y) * K(x,x \ y),z,x \ y)
    ]]></literal>
    <justification jstring="[para(3675(a,1),7767(a,1,1))].">
      <j1 rule="para" parents="3675 7767"/>
    </justification>
  </clause>

  <clause id="9514">
    <literal><![CDATA[
      1 * ((x \ R(x,y,z)) / K(u,R(x,w,v5))) = K(R(x,w,v5),u) * (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(225(a,1),7781(a,1,1))].">
      <j1 rule="para" parents="225 7781"/>
    </justification>
  </clause>

  <clause id="9516">
    <literal><![CDATA[
      1 * ((x \ R(x,y,z)) * K(R(x,u,w),v5)) = K(R(x,u,w),v5) * (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(6117(a,1),9514(a,1,2))].">
      <j1 rule="para" parents="6117 9514"/>
    </justification>
  </clause>

  <clause id="9517">
    <literal><![CDATA[
      K(R(x,y,z),u) * (x \ R(x,y,z)) = 1 * (x \ R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(6964(a,1),9516(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6964 9516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9518">
    <literal><![CDATA[
      K(R(x,y,z),u) * (x \ R(x,y,z)) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7,a(flip),b,9517,a),flip(a)].">
      <j1 rule="hyper" parents="347 7 9517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9519">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (y \ R(T(y,x),z,u)) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(5273,a,9518,a)].">
      <j1 rule="hyper" parents="5273 9518"/>
    </justification>
  </clause>

  <clause id="9520">
    <literal><![CDATA[
      K(x,y) * (x \ R(x,z,R(x,u,w))) = x \ R(T(x,y),z,R(x,u,w))
    ]]></literal>
    <justification jstring="[para(8290(a,1),9518(a,1,1))].">
      <j1 rule="para" parents="8290 9518"/>
    </justification>
  </clause>

  <clause id="9521">
    <literal><![CDATA[
      K(x * y,R(T(y,z),x,y)) * (T(y,z) \ T(T(y,z),x)) = T(y,z) \ R(T(y,z),x,y)
    ]]></literal>
    <justification jstring="[para(4504(a,1),9519(a,1,2,2))].">
      <j1 rule="para" parents="4504 9519"/>
    </justification>
  </clause>

  <clause id="9522">
    <literal><![CDATA[
      x \ R(T(x,y),z,R(x,u,w)) = K(x,y) * a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[para(9431(a,1),9520(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9431 9520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9523">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,R(x,u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(34,a,5159,a,b,9522,a(flip))].">
      <j1 rule="hyper" parents="34 5159 9522"/>
    </justification>
  </clause>

  <clause id="9524">
    <literal><![CDATA[
      ((x \ y) \ y) \ R((x \ y) \ y,z,R(x,u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,991,a(flip),b,9523,a)].">
      <j1 rule="hyper" parents="63 991 9523"/>
    </justification>
  </clause>

  <clause id="9525">
    <literal><![CDATA[
      K(T(x,y) * z,T(T(x,u),w)) = K(x * z,T(T(x,u),w))
    ]]></literal>
    <justification jstring="[hyper(347,a,5434,a(flip),b,8037,a),flip(a)].">
      <j1 rule="hyper" parents="347 5434 8037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9526">
    <literal><![CDATA[
      K(((x \ y) \ y) * z,T(T(x,u),w)) = K(x * z,T(T(x,u),w))
    ]]></literal>
    <justification jstring="[para(112(a,1),9525(a,1,1,1))].">
      <j1 rule="para" parents="112 9525"/>
    </justification>
  </clause>

  <clause id="9527">
    <literal><![CDATA[
      a(x,y,x) \ (x * L(x \ a(x,y,x),z,u)) = L(x,y,x) \ L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(8500(a,1),8504(a,2,2,1))].">
      <j1 rule="para" parents="8500 8504"/>
    </justification>
  </clause>

  <clause id="9528">
    <literal><![CDATA[
      a(x,y,x) \ (x * L(x \ a(x,y,x),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x \ L(x,z,u),y,x) = w
    ]]></literal>
    <justification jstring="[para(9527(a,2),4639(a,1))].">
      <j1 rule="para" parents="9527 4639"/>
    </justification>
  </clause>

  <clause id="9529">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ w) = K(x,(y * (z * u)) \ (w * x))
    ]]></literal>
    <justification jstring="[hyper(8696,a,8750,a)].">
      <j1 rule="hyper" parents="8696 8750"/>
    </justification>
  </clause>

  <clause id="9530">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (u \ (y * (z / x)))) = K(x,(u * (y * z)) \ ((y * (x \ z)) * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,8190,a(flip),b,9529,a)].">
      <j1 rule="hyper" parents="63 8190 9529"/>
    </justification>
  </clause>

  <clause id="9531">
    <literal><![CDATA[
      ((x \ y) \ R(x \ y,z,x \ y)) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(4990(a,1),9513(a,2,1))].">
      <j1 rule="para" parents="4990 9513"/>
    </justification>
  </clause>

  <clause id="9532">
    <literal><![CDATA[
      a(x \ y,z,x \ y) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(8336(a,1),9531(a,1,1))].">
      <j1 rule="para" parents="8336 9531"/>
    </justification>
  </clause>

  <clause id="9533">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(y \ x,z,y \ x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(347,a,6842,a,b,9532,a)].">
      <j1 rule="hyper" parents="347 6842 9532"/>
    </justification>
  </clause>

  <clause id="9534">
    <literal><![CDATA[
      a(x / y,z,x / y) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(35,a,8373,a(flip),b,9533,a(flip))].">
      <j1 rule="hyper" parents="35 8373 9533"/>
    </justification>
  </clause>

  <clause id="9535">
    <literal><![CDATA[
      K(x * y,T(y,z)) * (T(y,z) \ T(T(y,z),x)) = T(y,z) \ R(T(y,z),x,y)
    ]]></literal>
    <justification jstring="[para(7635(a,1),9521(a,1,1))].">
      <j1 rule="para" parents="7635 9521"/>
    </justification>
  </clause>

  <clause id="9536">
    <literal><![CDATA[
      K(x * y,T(y,z)) * K(T(y,z),x) = T(y,z) \ R(T(y,z),x,y)
    ]]></literal>
    <justification jstring="[para(4924(a,2),9535(a,1,2))].">
      <j1 rule="para" parents="4924 9535"/>
    </justification>
  </clause>

  <clause id="9538">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(T(x,z),y) = T(x,z) \ R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(7971(a,1),9536(a,1,1))].">
      <j1 rule="para" parents="7971 9536"/>
    </justification>
  </clause>

  <clause id="9539">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(T(x,z),y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,7215,a(flip),b,9538,a),flip(a)].">
      <j1 rule="hyper" parents="347 7215 9538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9540">
    <literal><![CDATA[
      K(T(x,y),z) * K(x * z,T(x,y)) = x \ R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(2558,a,9539,a)].">
      <j1 rule="hyper" parents="2558 9539"/>
    </justification>
  </clause>

  <clause id="9542">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * (u / x)))
    ]]></literal>
    <justification jstring="[hyper(8608,a,9530,a),flip(a)].">
      <j1 rule="hyper" parents="8608 9530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9543">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,9100,a(flip),b,9542,a),flip(a)].">
      <j1 rule="hyper" parents="347 9100 9542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9544">
    <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),9543(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 9543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9545">
    <literal><![CDATA[
      K(x,y \ ((z * (x \ u)) * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * u)) = w
    ]]></literal>
    <justification jstring="[para(9544(a,1),7726(a,1))].">
      <j1 rule="para" parents="9544 7726"/>
    </justification>
  </clause>

  <clause id="9546">
    <literal><![CDATA[
      K(x,y \ ((x \ y) * z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(9545,a,8018,a)].">
      <j1 rule="hyper" parents="9545 8018"/>
    </justification>
  </clause>

  <clause id="9547">
    <literal><![CDATA[
      K(x,x \ (y * z)) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(9545,a,5096,a)].">
      <j1 rule="hyper" parents="9545 5096"/>
    </justification>
  </clause>

  <clause id="9548">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x * z)) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),9545(a,1,2,2,1))].">
      <j1 rule="para" parents="10 9545"/>
    </justification>
  </clause>

  <clause id="9549">
    <literal><![CDATA[
      K(x,x \ ((x \ y) \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),9546(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 9546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9550">
    <literal><![CDATA[
      T(x,x \ (y * z)) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(132,a,9547,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 9547 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9551">
    <literal><![CDATA[
      K(x,x \ (y * (x * z))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9547(a,2,2,2))].">
      <j1 rule="para" parents="9 9547"/>
    </justification>
  </clause>

  <clause id="9552">
    <literal><![CDATA[
      (x * K(y,z * (y \ u))) \ x = K(y \ (z * u),y)
    ]]></literal>
    <justification jstring="[para(9547(a,1),6123(a,1,1,2))].">
      <j1 rule="para" parents="9547 6123"/>
    </justification>
  </clause>

  <clause id="9553">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(9(a,1),9549(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 9549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9555">
    <literal><![CDATA[
      K(x,x \ (y * (z * x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8178,a,b,9551,a)].">
      <j1 rule="hyper" parents="63 8178 9551"/>
    </justification>
  </clause>

  <clause id="9556">
    <literal><![CDATA[
      K(x,x \ (y \ (z * x))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(8057,a,9553,a),flip(a)].">
      <j1 rule="hyper" parents="8057 9553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9557">
    <literal><![CDATA[
      K(x,y \ (x \ z)) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(7209,a,9553,a)].">
      <j1 rule="hyper" parents="7209 9553"/>
    </justification>
  </clause>

  <clause id="9558">
    <literal><![CDATA[
      K(x,K(y,z * (u * y))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(9555(a,1),8755(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9555 8755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9559">
    <literal><![CDATA[
      x * (y * ((x \ 1) / y)) = K(y,y \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,6912,a,b,9557,a)].">
      <j1 rule="hyper" parents="63 6912 9557"/>
    </justification>
  </clause>

  <clause id="9560">
    <literal><![CDATA[
      x \ K(y,y \ (x \ 1)) = y * ((x \ 1) / y)
    ]]></literal>
    <justification jstring="[hyper(128,a,9557,a(flip),b,6912,a)].">
      <j1 rule="hyper" parents="128 9557 6912"/>
    </justification>
  </clause>

  <clause id="9561">
    <literal><![CDATA[
      K(x,x \ (y \ (x * z))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9557(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 9557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9562">
    <literal><![CDATA[
      K(x,y \ (x \ (y * z))) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9557(a,2,2,2))].">
      <j1 rule="para" parents="9 9557"/>
    </justification>
  </clause>

  <clause id="9563">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,5096,a(flip),b,9562,a),flip(a)].">
      <j1 rule="hyper" parents="347 5096 9562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9564">
    <literal><![CDATA[
      (x * y) * K(z,z \ y) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[para(9562(a,1),6910(a,1,2))].">
      <j1 rule="para" parents="9562 6910"/>
    </justification>
  </clause>

  <clause id="9565">
    <literal><![CDATA[
      K(x,L(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8246,a,9563,a)].">
      <j1 rule="hyper" parents="8246 9563"/>
    </justification>
  </clause>

  <clause id="9566">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8426,a,9565,a)].">
      <j1 rule="hyper" parents="8426 9565"/>
    </justification>
  </clause>

  <clause id="9569">
    <literal><![CDATA[
      T(x,L(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,9565,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 9565 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9570">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8420,a(flip),b,9565,a)].">
      <j1 rule="hyper" parents="63 8420 9565"/>
    </justification>
  </clause>

  <clause id="9571">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,9565,a(flip),b,6978,a)].">
      <j1 rule="hyper" parents="134 9565 6978"/>
    </justification>
  </clause>

  <clause id="9572">
    <literal><![CDATA[
      K(L(x,y,z),(z * (y * x)) \ ((z * y) * u)) = K(L(x,y,z),L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(573(a,1),9565(a,1,2))].">
      <j1 rule="para" parents="573 9565"/>
    </justification>
  </clause>

  <clause id="9573">
    <literal><![CDATA[
      K(L(x,y,z),L(u,x,w)) = L(K(x,u),y * x,z)
    ]]></literal>
    <justification jstring="[para(9565(a,1),7039(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9565 7039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9574">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(L(x,y,v5),L(y,u,w))
    ]]></literal>
    <justification jstring="[para(9565(a,1),8520(a,1,1))].">
      <j1 rule="para" parents="9565 8520"/>
    </justification>
  </clause>

  <clause id="9576">
    <literal><![CDATA[
      K(L(x,y,z),y) = (u * T(y,x)) \ (u * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,6161,a,b,9566,a),flip(a)].">
      <j1 rule="hyper" parents="347 6161 9566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9577">
    <literal><![CDATA[
      L(x,y,z) * K(x,y) = L(T(x,y),y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,9566,a(flip),b,4982,a)].">
      <j1 rule="hyper" parents="134 9566 4982"/>
    </justification>
  </clause>

  <clause id="9578">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(329(a,1),9566(a,1,1))].">
      <j1 rule="para" parents="329 9566"/>
    </justification>
  </clause>

  <clause id="9579">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(y \ (x * z),x \ y)
    ]]></literal>
    <justification jstring="[para(561(a,1),9566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="561 9566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9580">
    <literal><![CDATA[
      K((x * (y * z)) \ ((x * y) * u),L(z,y,x)) = K(L(z,y,x) \ u,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(573(a,1),9566(a,1,1))].">
      <j1 rule="para" parents="573 9566"/>
    </justification>
  </clause>

  <clause id="9583">
    <literal><![CDATA[
      L(x,y,z) = (z * T(y,x)) \ (z * (T(y,x) * x))
    ]]></literal>
    <justification jstring="[para(9569(a,1),6680(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9569 6680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9585">
    <literal><![CDATA[
      (x * y) * K(z \ y,z) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(134,a,9570,a(flip),b,510,a)].">
      <j1 rule="hyper" parents="134 9570 510"/>
    </justification>
  </clause>

  <clause id="9586">
    <literal><![CDATA[
      K(x,T(y,z * (y * x))) * (z * (y * x)) = z * (x * y)
    ]]></literal>
    <justification jstring="[hyper(7383,a,9571,a)].">
      <j1 rule="hyper" parents="7383 9571"/>
    </justification>
  </clause>

  <clause id="9587">
    <literal><![CDATA[
      (x * K(y,z)) / (y * z) = x / (z * y)
    ]]></literal>
    <justification jstring="[hyper(717,a,9571,a)].">
      <j1 rule="hyper" parents="717 9571"/>
    </justification>
  </clause>

  <clause id="9588">
    <literal><![CDATA[
      (x / (y * z)) * (z * y) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(353,a,9571,a),flip(a)].">
      <j1 rule="hyper" parents="353 9571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9589">
    <literal><![CDATA[
      K(x,y) = (1 / (y * x)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(233,a,9571,a)].">
      <j1 rule="hyper" parents="233 9571"/>
    </justification>
  </clause>

  <clause id="9590">
    <literal><![CDATA[
      T(x * (y * z),K(y,z)) = K(y,z) * (x * (z * y))
    ]]></literal>
    <justification jstring="[hyper(134,a,9571,a(flip),b,7345,a),flip(a)].">
      <j1 rule="hyper" parents="134 9571 7345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9591">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,596,a,b,9571,a(flip))].">
      <j1 rule="hyper" parents="35 596 9571"/>
    </justification>
  </clause>

  <clause id="9593">
    <literal><![CDATA[
      R(x,y,T(z,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(6674,a,9591,a)].">
      <j1 rule="hyper" parents="6674 9591"/>
    </justification>
  </clause>

  <clause id="9594">
    <literal><![CDATA[
      x * R(y,z,T(u,z)) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(134,a,9593,a,b,9,a)].">
      <j1 rule="hyper" parents="134 9593 9"/>
    </justification>
  </clause>

  <clause id="9595">
    <literal><![CDATA[
      R(x,y * K(z,y),z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6497,a,b,9593,a)].">
      <j1 rule="hyper" parents="63 6497 9593"/>
    </justification>
  </clause>

  <clause id="9596">
    <literal><![CDATA[
      R(x,T(y,z),z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6407,a,b,9593,a)].">
      <j1 rule="hyper" parents="63 6407 9593"/>
    </justification>
  </clause>

  <clause id="9597">
    <literal><![CDATA[
      R(x,y,z) = ((x * y) * T(z,y)) / (z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,265,a,b,9593,a),flip(a)].">
      <j1 rule="hyper" parents="63 265 9593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9598">
    <literal><![CDATA[
      R(x,y,z) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,9593,a(flip),b,265,a)].">
      <j1 rule="hyper" parents="133 9593 265"/>
    </justification>
  </clause>

  <clause id="9601">
    <literal><![CDATA[
      R(T(x,y),T(z,x),T(x,u)) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6793,a,b,9596,a)].">
      <j1 rule="hyper" parents="63 6793 9596"/>
    </justification>
  </clause>

  <clause id="9602">
    <literal><![CDATA[
      R(x,y / z,z) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[para(113(a,1),9596(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 9596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9604">
    <literal><![CDATA[
      R(x,(y \ z) \ z,y \ z) = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(112(a,1),9596(a,1,2))].">
      <j1 rule="para" parents="112 9596"/>
    </justification>
  </clause>

  <clause id="9605">
    <literal><![CDATA[
      K(x,y) = (x * y) * ((y * x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,4039,a(flip),b,9589,a),flip(a)].">
      <j1 rule="hyper" parents="347 4039 9589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9606">
    <literal><![CDATA[
      (x * y) \ K(x,y) = (y * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,9589,a,b,4039,a(flip))].">
      <j1 rule="hyper" parents="128 9589 4039"/>
    </justification>
  </clause>

  <clause id="9607">
    <literal><![CDATA[
      K(x,y) != 1
    ]]></literal>
    <literal><![CDATA[
      x * y = y * x
    ]]></literal>
    <justification jstring="[para(9589(a,2),140(a,1))].">
      <j1 rule="para" parents="9589 140"/>
    </justification>
  </clause>

  <clause id="9608">
    <literal><![CDATA[
      a(x,y * K(L(x,z,u),y),L(x,z,u)) = x \ R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(9595(a,1),9440(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9595 9440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9609">
    <literal><![CDATA[
      ((x * (y / z)) * z) / y = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,109,a,b,9602,a)].">
      <j1 rule="hyper" parents="63 109 9602"/>
    </justification>
  </clause>

  <clause id="9610">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),u \ z,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8228,a(flip),b,9602,a),flip(a)].">
      <j1 rule="hyper" parents="63 8228 9602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9611">
    <literal><![CDATA[
      R(K(x,(y / z) / u),z \ y,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6709,a(flip),b,9602,a),flip(a)].">
      <j1 rule="hyper" parents="63 6709 9602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9612">
    <literal><![CDATA[
      R(x / (y / z),z \ y,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,607,a(flip),b,9602,a),flip(a)].">
      <j1 rule="hyper" parents="63 607 9602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9613">
    <literal><![CDATA[
      R(x,y \ z,y) * z = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,9602,a(flip),b,109,a)].">
      <j1 rule="hyper" parents="133 9602 109"/>
    </justification>
  </clause>

  <clause id="9614">
    <literal><![CDATA[
      (x * (y \ z)) * T(y,y \ z) = R(x,y \ z,y) * z
    ]]></literal>
    <justification jstring="[para(9602(a,1),6371(a,2,1))].">
      <j1 rule="para" parents="9602 6371"/>
    </justification>
  </clause>

  <clause id="9615">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ K(x,K(y,z)) = (K(y \ 1,z) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,8809,a(flip),b,9605,a(flip))].">
      <j1 rule="hyper" parents="128 8809 9605"/>
    </justification>
  </clause>

  <clause id="9616">
    <literal><![CDATA[
      (x * ((x \ y) * z)) \ K(y,L(z,x \ y,x)) = (L(z,x \ y,x) * y) \ 1
    ]]></literal>
    <justification jstring="[para(476(a,1),9606(a,1,1))].">
      <j1 rule="para" parents="476 9606"/>
    </justification>
  </clause>

  <clause id="9617">
    <literal><![CDATA[
      L(x,y,z) * (K(x,y) * u) = L(T(x,y),y,z) * u
    ]]></literal>
    <justification jstring="[para(9577(a,1),5002(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9577 5002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9618">
    <literal><![CDATA[
      K(x \ (y \ z),y) = K(y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(8106,a,9578,a)].">
      <j1 rule="hyper" parents="8106 9578"/>
    </justification>
  </clause>

  <clause id="9619">
    <literal><![CDATA[
      K(x \ (y \ (z * x)),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(8103,a,9578,a),flip(a)].">
      <j1 rule="hyper" parents="8103 9578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9621">
    <literal><![CDATA[
      (x * T(y,z)) / (y * z) = (x * y) / (z * y)
    ]]></literal>
    <justification jstring="[para(5926(a,1),9587(a,1,1))].">
      <j1 rule="para" parents="5926 9587"/>
    </justification>
  </clause>

  <clause id="9622">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6863,a(flip),b,9618,a),flip(a)].">
      <j1 rule="hyper" parents="63 6863 9618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9623">
    <literal><![CDATA[
      K(L(x,y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(9576(a,2),6194(a,1))].">
      <j1 rule="para" parents="9576 6194"/>
    </justification>
  </clause>

  <clause id="9624">
    <literal><![CDATA[
      K(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8303(a,1),9623(a,1))].">
      <j1 rule="para" parents="8303 9623"/>
    </justification>
  </clause>

  <clause id="9627">
    <literal><![CDATA[
      (x * y) \ ((z * y) * T(x,y)) = R(T(z,x * y),y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,9598,a(flip),b,268,a)].">
      <j1 rule="hyper" parents="128 9598 268"/>
    </justification>
  </clause>

  <clause id="9629">
    <literal><![CDATA[
      K((x * y) * T(z,y),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      K((z * y) * R(x,y,z),z * y) = u
    ]]></literal>
    <justification jstring="[para(9598(a,1),7935(a,1,1))].">
      <j1 rule="para" parents="9598 7935"/>
    </justification>
  </clause>

  <clause id="9630">
    <literal><![CDATA[
      R(x,y \ z,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      (x * (z / y)) * y = u
    ]]></literal>
    <justification jstring="[para(9609(a,1),280(a,1,1))].">
      <j1 rule="para" parents="9609 280"/>
    </justification>
  </clause>

  <clause id="9631">
    <literal><![CDATA[
      x / y != R(z,u \ w,u) * w
    ]]></literal>
    <literal><![CDATA[
      ((z * (w / u)) * u) * y = x
    ]]></literal>
    <justification jstring="[para(9609(a,1),352(a,2,1))].">
      <j1 rule="para" parents="9609 352"/>
    </justification>
  </clause>

  <clause id="9632">
    <literal><![CDATA[
      R(x / (y / (y * K(z,u))),K(u,z),y * K(z,u)) = (x * (y * K(z,u))) / y
    ]]></literal>
    <justification jstring="[para(6123(a,1),9612(a,1,2))].">
      <j1 rule="para" parents="6123 9612"/>
    </justification>
  </clause>

  <clause id="9633">
    <literal><![CDATA[
      R((x / y) * K(y,z),z \ (z * y),z) = (x * z) / (z * y)
    ]]></literal>
    <justification jstring="[para(6126(a,1),9612(a,1,1))].">
      <j1 rule="para" parents="6126 9612"/>
    </justification>
  </clause>

  <clause id="9634">
    <literal><![CDATA[
      R(x * (y / (1 / z)),z,z) / z = R(x,(1 / z) \ y,1 / z) * y
    ]]></literal>
    <justification jstring="[hyper(347,a,2264,a,b,9613,a)].">
      <j1 rule="hyper" parents="347 2264 9613"/>
    </justification>
  </clause>

  <clause id="9635">
    <literal><![CDATA[
      R(x,(y \ 1) \ R(z,y,y),y \ 1) * R(z,y,y) = (x * (z * y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(788(a,1),9613(a,2,1,2))].">
      <j1 rule="para" parents="788 9613"/>
    </justification>
  </clause>

  <clause id="9636">
    <literal><![CDATA[
      K(x,K(y / z,u * z)) = K(x,K(y / z,u * y))
    ]]></literal>
    <justification jstring="[para(7999(a,1),9558(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7999 9558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9638">
    <literal><![CDATA[
      (x * (y * z)) * K(y,z) = x * ((z \ (y * z)) * z)
    ]]></literal>
    <justification jstring="[para(5143(a,1),9585(a,1,2))].">
      <j1 rule="para" parents="5143 9585"/>
    </justification>
  </clause>

  <clause id="9639">
    <literal><![CDATA[
      K(L(x,y,z),L(u,x,w)) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,7039,a(flip),b,9573,a),flip(a)].">
      <j1 rule="hyper" parents="347 7039 9573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9640">
    <literal><![CDATA[
      K(L(x,y,z),(u * x) \ (u * w)) = K(L(x,y,z),x \ w)
    ]]></literal>
    <justification jstring="[hyper(6472,a,9639,a)].">
      <j1 rule="hyper" parents="6472 9639"/>
    </justification>
  </clause>

  <clause id="9641">
    <literal><![CDATA[
      L(x,T(y,x),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,18,a,b,9583,a)].">
      <j1 rule="hyper" parents="347 18 9583"/>
    </justification>
  </clause>

  <clause id="9643">
    <literal><![CDATA[
      L(x,y / x,z) = L(x,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5474,a(flip),b,9641,a)].">
      <j1 rule="hyper" parents="63 5474 9641"/>
    </justification>
  </clause>

  <clause id="9644">
    <literal><![CDATA[
      L(x,x \ (y \ z),y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,624,a(flip),b,9643,a),flip(a)].">
      <j1 rule="hyper" parents="63 624 9643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9645">
    <literal><![CDATA[
      L(x,x \ y,z) = (z * (y / x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,100,a(flip),b,9643,a),flip(a)].">
      <j1 rule="hyper" parents="63 100 9643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9646">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(9643(a,1),8199(a,1,1))].">
      <j1 rule="para" parents="9643 8199"/>
    </justification>
  </clause>

  <clause id="9647">
    <literal><![CDATA[
      K(x \ (y * z),x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(6141,a,9552,a),flip(a)].">
      <j1 rule="hyper" parents="6141 9552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9648">
    <literal><![CDATA[
      K(x \ (y * z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * (x \ z),x) = u
    ]]></literal>
    <justification jstring="[para(9552(a,1),6141(a,1))].">
      <j1 rule="para" parents="9552 6141"/>
    </justification>
  </clause>

  <clause id="9649">
    <literal><![CDATA[
      K(x \ (y * z),x) = K(y * (z / x),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,7902,a,b,9647,a),flip(a)].">
      <j1 rule="hyper" parents="347 7902 9647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9650">
    <literal><![CDATA[
      K(x * (y \ (x \ z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),9647(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 9647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9651">
    <literal><![CDATA[
      K(x \ (y * (z * x)),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[para(11(a,1),9649(a,2,1,2))].">
      <j1 rule="para" parents="11 9649"/>
    </justification>
  </clause>

  <clause id="9652">
    <literal><![CDATA[
      K((x / y) \ z,y \ x) = K(x \ (y * z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(7951,a,9579,a)].">
      <j1 rule="hyper" parents="7951 9579"/>
    </justification>
  </clause>

  <clause id="9653">
    <literal><![CDATA[
      (x * (y * z)) * K(y,z) = x * (T(y,z) * z)
    ]]></literal>
    <justification jstring="[para(22(a,2),9638(a,2,2,1))].">
      <j1 rule="para" parents="22 9638"/>
    </justification>
  </clause>

  <clause id="9654">
    <literal><![CDATA[
      K(x \ (y * z),y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z / (x / y),y \ x) = u
    ]]></literal>
    <justification jstring="[para(9652(a,1),7600(a,1))].">
      <j1 rule="para" parents="9652 7600"/>
    </justification>
  </clause>

  <clause id="9655">
    <literal><![CDATA[
      K(L(x,y,z),L(y,u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,8518,a(flip),b,9574,a),flip(a)].">
      <j1 rule="hyper" parents="63 8518 9574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9656">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(9574(a,2),7204(a,1))].">
      <j1 rule="para" parents="9574 7204"/>
    </justification>
  </clause>

  <clause id="9658">
    <literal><![CDATA[
      K(x \ (y \ (x * z)),L(y,u,w)) = K(y \ z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9368,a(flip),b,9655,a)].">
      <j1 rule="hyper" parents="63 9368 9655"/>
    </justification>
  </clause>

  <clause id="9659">
    <literal><![CDATA[
      K(((x / y) \ z) / y,L(y,u,w)) = K((y * (x \ z)) / y,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(1082(a,1),9655(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1082 9655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9660">
    <literal><![CDATA[
      (x * (y \ z)) * T(y,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * (z / y)) * y = u
    ]]></literal>
    <justification jstring="[para(9614(a,2),9630(a,1))].">
      <j1 rule="para" parents="9614 9630"/>
    </justification>
  </clause>

  <clause id="9661">
    <literal><![CDATA[
      ((x * y) * T(z,y)) * K(z * y,R(T(x,z * y),y,z)) = (z * y) * (((x * y) * T(z,y)) / (z * y))
    ]]></literal>
    <justification jstring="[para(9627(a,1),5111(a,1,2,2))].">
      <j1 rule="para" parents="9627 5111"/>
    </justification>
  </clause>

  <clause id="9662">
    <literal><![CDATA[
      L(K(x,y),y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(110(a,1),9656(a,1,2,1))].">
      <j1 rule="para" parents="110 9656"/>
    </justification>
  </clause>

  <clause id="9663">
    <literal><![CDATA[
      L(K(x,y / z),y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = w
    ]]></literal>
    <justification jstring="[para(12(a,1),9662(a,1,2))].">
      <j1 rule="para" parents="12 9662"/>
    </justification>
  </clause>

  <clause id="9664">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * (y * x)) = z * (x * y)
    ]]></literal>
    <justification jstring="[para(9002(a,1),9586(a,1,1))].">
      <j1 rule="para" parents="9002 9586"/>
    </justification>
  </clause>

  <clause id="9665">
    <literal><![CDATA[
      K(L(x,y,z),u \ (x \ (u * w))) = K(L(x,y,z),x \ w)
    ]]></literal>
    <justification jstring="[hyper(8690,a,9640,a)].">
      <j1 rule="hyper" parents="8690 9640"/>
    </justification>
  </clause>

  <clause id="9667">
    <literal><![CDATA[
      R((x / y) * K(y,z),y,z) = (x * z) / (z * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),9633(a,1,2))].">
      <j1 rule="para" parents="9 9633"/>
    </justification>
  </clause>

  <clause id="9668">
    <literal><![CDATA[
      ((x * y) * z) / (z * y) = R(x * K(y,z),y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),9667(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 9667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9669">
    <literal><![CDATA[
      R(x * K(K(y,T(z,x)),u),K(y,T(z,x)),u) = ((K(y,z) * x) * u) / (u * K(y,T(z,x)))
    ]]></literal>
    <justification jstring="[para(7104(a,1),9668(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7104 9668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9670">
    <literal><![CDATA[
      a(x,y * K(L(x,z,u),y),L(x,z,u)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,9440,a(flip),b,9608,a),flip(a)].">
      <j1 rule="hyper" parents="347 9440 9608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9671">
    <literal><![CDATA[
      a(x,y,T(L(x,z,u),y)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6409,a(flip),b,9670,a)].">
      <j1 rule="hyper" parents="63 6409 9670"/>
    </justification>
  </clause>

  <clause id="9672">
    <literal><![CDATA[
      a(x,y,L(T(x,y),z,u)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),9671(a,1,3))].">
      <j1 rule="para" parents="25 9671"/>
    </justification>
  </clause>

  <clause id="9673">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (u * L(T(x,x \ u),y,z)) = a(x,x \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,2680,a(flip),b,9672,a)].">
      <j1 rule="hyper" parents="63 2680 9672"/>
    </justification>
  </clause>

  <clause id="9674">
    <literal><![CDATA[
      R(x * (y / (1 / z)),z,z) / z = R(x,(1 / z) \ y,z) * y
    ]]></literal>
    <justification jstring="[para(2191(a,1),9634(a,2,1))].">
      <j1 rule="para" parents="2191 9634"/>
    </justification>
  </clause>

  <clause id="9675">
    <literal><![CDATA[
      K(((x / y) \ z) / y,L(y,u,w)) = K(y \ (y * (x \ z)),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,7182,a(flip),b,9659,a),flip(a)].">
      <j1 rule="hyper" parents="347 7182 9659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9676">
    <literal><![CDATA[
      K(((x / y) \ z) / y,L(y,u,w)) = K(x \ z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,770,a(flip),b,9675,a),flip(a)].">
      <j1 rule="hyper" parents="347 770 9675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9677">
    <literal><![CDATA[
      K(x \ ((y / x) \ z),L(x,u,w)) = K(y \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(7596,a,9676,a)].">
      <j1 rule="hyper" parents="7596 9676"/>
    </justification>
  </clause>

  <clause id="9684">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(L(y,z,u),y \ x) = a(y,y \ x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8330,a(flip),b,9673,a)].">
      <j1 rule="hyper" parents="63 8330 9673"/>
    </justification>
  </clause>

  <clause id="9685">
    <literal><![CDATA[
      K(L(x,y,z),(z * y) \ (x \ ((z * y) * u))) = K(L(x,y,z),L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9336,a(flip),b,9572,a)].">
      <j1 rule="hyper" parents="63 9336 9572"/>
    </justification>
  </clause>

  <clause id="9686">
    <literal><![CDATA[
      K((x * y) \ (z \ ((x * y) * u)),L(z,y,x)) = K(L(z,y,x) \ u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(9469,a,9580,a)].">
      <j1 rule="hyper" parents="9469 9580"/>
    </justification>
  </clause>

  <clause id="9687">
    <literal><![CDATA[
      R(x / K(y,T(z,u)),K(y,z),u * K(z,y)) = (x * (u * K(z,y))) / u
    ]]></literal>
    <justification jstring="[para(7428(a,1),9632(a,1,1,2))].">
      <j1 rule="para" parents="7428 9632"/>
    </justification>
  </clause>

  <clause id="9688">
    <literal><![CDATA[
      R(x * K(y,T(z,u)),K(z,y),u * K(y,z)) = (x * (u * K(y,z))) / u
    ]]></literal>
    <justification jstring="[para(7126(a,1),9687(a,1,1))].">
      <j1 rule="para" parents="7126 9687"/>
    </justification>
  </clause>

  <clause id="9689">
    <literal><![CDATA[
      R(x,T(y * z,z \ 1),z \ 1) * R(y,z,z) = (x * (y * z)) * (z \ 1)
    ]]></literal>
    <justification jstring="[para(787(a,1),9635(a,1,1,2))].">
      <j1 rule="para" parents="787 9635"/>
    </justification>
  </clause>

  <clause id="9690">
    <literal><![CDATA[
      R(x,T(y * z,z \ 1),z) * R(y,z,z) = (x * (y * z)) * (z \ 1)
    ]]></literal>
    <justification jstring="[para(2190(a,1),9689(a,1,1))].">
      <j1 rule="para" parents="2190 9689"/>
    </justification>
  </clause>

  <clause id="9691">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) \ u) = K(L(x,y,z),x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9665,a(flip),b,9685,a),flip(a)].">
      <j1 rule="hyper" parents="63 9665 9685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9693">
    <literal><![CDATA[
      L(x,y,z) * K(L(x,y,z),L(x,y,z) \ u) = L(T(x,x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,9691,a,b,4982,a)].">
      <j1 rule="hyper" parents="134 9691 4982"/>
    </justification>
  </clause>

  <clause id="9694">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ u,L(x,y,z)) = K(u,L(x,y,z)) * K(L(x,y,z),x \ u)
    ]]></literal>
    <justification jstring="[para(9691(a,1),8341(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9691 8341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9695">
    <literal><![CDATA[
      x / L(T(y,y \ x),z,u) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(220,a,9693,a(flip),b,4973,a)].">
      <j1 rule="hyper" parents="220 9693 4973"/>
    </justification>
  </clause>

  <clause id="9697">
    <literal><![CDATA[
      x / L(y \ x,z,u) = L(x / y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(749(a,1),9695(a,1,2,1))].">
      <j1 rule="para" parents="749 9695"/>
    </justification>
  </clause>

  <clause id="9698">
    <literal><![CDATA[
      L(x / (x / y),z,u) \ x = x / L(y,z,u)
    ]]></literal>
    <justification jstring="[para(385(a,1),9695(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="385 9695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9700">
    <literal><![CDATA[
      (L(x / y,z,u) \ x) \ x = L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(214,a,9697,a)].">
      <j1 rule="hyper" parents="214 9697"/>
    </justification>
  </clause>

  <clause id="9701">
    <literal><![CDATA[
      L((x \ y) / z,z,x) \ (x \ y) = (x \ y) / ((x * z) \ y)
    ]]></literal>
    <justification jstring="[para(329(a,1),9697(a,1,2)),flip(a)].">
      <j1 rule="para" parents="329 9697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9702">
    <literal><![CDATA[
      L((x * y) / K(x,y),z,u) \ (x * y) = (x * y) / L(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(4907(a,1),9697(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4907 9697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9704">
    <literal><![CDATA[
      L(x / (x / y),y,x) = x / (x * (1 / y))
    ]]></literal>
    <justification jstring="[hyper(220,a,3282,a(flip),b,9698,a),flip(a)].">
      <j1 rule="hyper" parents="220 3282 9698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9705">
    <literal><![CDATA[
      L(x / (x / (y \ 1)),y,x) = x / (x * y)
    ]]></literal>
    <justification jstring="[hyper(220,a,412,a(flip),b,9698,a),flip(a)].">
      <j1 rule="hyper" parents="220 412 9698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9706">
    <literal><![CDATA[
      x \ T(x / y,y \ 1) = x / (x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6662,a(flip),b,9705,a)].">
      <j1 rule="hyper" parents="63 6662 9705"/>
    </justification>
  </clause>

  <clause id="9707">
    <literal><![CDATA[
      T(x / y,y \ 1) = x * (x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(134,a,9705,a(flip),b,6662,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 9705 6662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9708">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) = (L(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[para(80(a,1),9700(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="80 9700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9709">
    <literal><![CDATA[
      x / L(y \ x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x / y,z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(9700(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9700 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9710">
    <literal><![CDATA[
      (L(x,y,z) \ (x * u)) \ (x * u) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(340(a,2),9708(a,1,1)),flip(a)].">
      <j1 rule="para" parents="340 9708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9712">
    <literal><![CDATA[
      T(x,x * (L(x,y,z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(1801,a,9710,a(flip))].">
      <j1 rule="hyper" parents="1801 9710"/>
    </justification>
  </clause>

  <clause id="9713">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) \ (x * u) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(1407(a,1),9710(a,1,1))].">
      <j1 rule="para" parents="1407 9710"/>
    </justification>
  </clause>

  <clause id="9714">
    <literal><![CDATA[
      T(x,L(x,y,z) * u) = T(x,x * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),9712(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 9712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9715">
    <literal><![CDATA[
      T(x,L(x,y,z) * (x \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(75(a,1),9712(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 9712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9716">
    <literal><![CDATA[
      T(x,L(x,y,z) \ u) = T(x,x \ u)
    ]]></literal>
    <justification jstring="[para(1408(a,1),9712(a,1,2))].">
      <j1 rule="para" parents="1408 9712"/>
    </justification>
  </clause>

  <clause id="9717">
    <literal><![CDATA[
      T(x,L(x,y,z) * u) = x * K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,4929,a(flip),b,9714,a),flip(a)].">
      <j1 rule="hyper" parents="347 4929 9714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9718">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * T(x,L(x,w,v5) * (x \ u))) = x * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(9715(a,2),3553(a,1,2,2))].">
      <j1 rule="para" parents="9715 3553"/>
    </justification>
  </clause>

  <clause id="9721">
    <literal><![CDATA[
      x / L(T(y,L(y,z,u) \ x),w,v5) = L(y,w,v5) \ x
    ]]></literal>
    <justification jstring="[para(9716(a,2),9695(a,1,2,1))].">
      <j1 rule="para" parents="9716 9695"/>
    </justification>
  </clause>

  <clause id="9722">
    <literal><![CDATA[
      K(x,L(x,y,z) * u) = K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(5005,a,9717,a)].">
      <j1 rule="hyper" parents="5005 9717"/>
    </justification>
  </clause>

  <clause id="9723">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) \ (x * u) = L(u \ (x * u),y,z)
    ]]></literal>
    <justification jstring="[para(22(a,1),9713(a,2,1))].">
      <j1 rule="para" parents="22 9713"/>
    </justification>
  </clause>

  <clause id="9724">
    <literal><![CDATA[
      (L(x,y,z) * u) / L(T(x,u),w,v5) = L(x,w,v5) \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),9721(a,1,2,1,2))].">
      <j1 rule="para" parents="9 9721"/>
    </justification>
  </clause>

  <clause id="9725">
    <literal><![CDATA[
      R(x,x,x \ (y * x)) = y * (L(y,x,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(39,a,3235,a,b,9723,a)].">
      <j1 rule="hyper" parents="39 3235 9723"/>
    </justification>
  </clause>

  <clause id="9726">
    <literal><![CDATA[
      x * (L(x,y,y) \ y) = R(y,y,T(x,y))
    ]]></literal>
    <justification jstring="[para(22(a,2),9725(a,1,3)),flip(a)].">
      <j1 rule="para" parents="22 9725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9727">
    <literal><![CDATA[
      x * (L(x,y,y) \ y) = R(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,9593,a(flip),b,9726,a),flip(a)].">
      <j1 rule="hyper" parents="347 9593 9726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9728">
    <literal><![CDATA[
      L(x,y,y) \ y = x \ R(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,9593,a(flip),b,9726,a),flip(a)].">
      <j1 rule="hyper" parents="128 9593 9726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9729">
    <literal><![CDATA[
      L(x,y,y) * R(y,y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(134,a,9727,a(flip),b,1407,a)].">
      <j1 rule="hyper" parents="134 9727 1407"/>
    </justification>
  </clause>

  <clause id="9730">
    <literal><![CDATA[
      (x * y) / L(y * x,z,u) = L(y * x,z,u) \ (x * y)
    ]]></literal>
    <justification jstring="[para(211(a,1),9702(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="211 9702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9731">
    <literal><![CDATA[
      K(L(x,y,z) \ u,L(x,y,z)) = K(x \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9658,a(flip),b,9686,a),flip(a)].">
      <j1 rule="hyper" parents="63 9658 9686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9733">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ u,L(x,y,z)) = a(x,x \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,9684,a(flip),b,9694,a),flip(a)].">
      <j1 rule="hyper" parents="347 9684 9694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9734">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ (u * x),L(x,y,z)) = K(u * x,L(x,y,z)) * K(L(x,y,z),T(u,x))
    ]]></literal>
    <justification jstring="[para(22(a,2),9694(a,2,2,2))].">
      <j1 rule="para" parents="22 9694"/>
    </justification>
  </clause>

  <clause id="9735">
    <literal><![CDATA[
      x / (y * K(1 / z,z)) = K(z,1 / z) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(2221,a,6151,a),flip(a)].">
      <j1 rule="hyper" parents="2221 6151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9737">
    <literal><![CDATA[
      K(x,1 / x) * (y / L(x,z,u)) = y / (1 / (1 / L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(8196(a,1),9735(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8196 9735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9738">
    <literal><![CDATA[
      L(K(x,K(y,z)) \ u,K(T(x,y),K(y,z)),T(x,y)) = T(x,T(y,z)) \ (T(x,y) * u)
    ]]></literal>
    <justification jstring="[para(7142(a,1),6821(a,1,1,1))].">
      <j1 rule="para" parents="7142 6821"/>
    </justification>
  </clause>

  <clause id="9739">
    <literal><![CDATA[
      T(x,T(y,z)) \ (T(x,y) * u) = K(x,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(4994,a,9738,a),flip(a)].">
      <j1 rule="hyper" parents="4994 9738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9740">
    <literal><![CDATA[
      K(x,K(y,z)) \ (T(x,T(y,z)) * u) = T(x,y) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,6933,a(flip),b,9739,a),flip(a)].">
      <j1 rule="hyper" parents="63 6933 9739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9741">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) \ T(K(z,y) * x,x) = T(K(z,y),T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(7554(a,1),6923(a,1,2))].">
      <j1 rule="para" parents="7554 6923"/>
    </justification>
  </clause>

  <clause id="9742">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) \ T(K(z,y) * x,x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,9021,a(flip),b,9741,a),flip(a)].">
      <j1 rule="hyper" parents="347 9021 9741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9744">
    <literal><![CDATA[
      (x * y) \ (R(T(z * K(x,z),u),x,y) \ ((x * z) * y)) = K(u,(x * y) \ ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(27(a,2),7503(a,1,2,1))].">
      <j1 rule="para" parents="27 7503"/>
    </justification>
  </clause>

  <clause id="9745">
    <literal><![CDATA[
      R(T(x,y),T(K(x,z),T(x,y)),u) = (T(T(x,z),T(y,z)) * u) / (K(x,z) * u)
    ]]></literal>
    <justification jstring="[para(3583(a,1),7570(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3583 7570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9746">
    <literal><![CDATA[
      (T(T(x,y),T(z,y)) * u) / (K(x,y) * u) = R(T(x,z),K(x,y),u)
    ]]></literal>
    <justification jstring="[para(3583(a,1),9745(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3583 9745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9748">
    <literal><![CDATA[
      (K(x,y) * z) * R((K(x,y) * z) \ (T(T(x,y),T(u,y)) * z),w,v5) = R(R(T(x,u),K(x,y),z),w,v5) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9746(a,1),746(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9746 746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9750">
    <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(7488,a,8272,a),flip(a)].">
      <j1 rule="hyper" parents="7488 8272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9751">
    <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(8701(a,1),8358(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8701 8358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9752">
    <literal><![CDATA[
      a(x,y,x) * K(y,T(x,z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(9007,a,9751,a),flip(a)].">
      <j1 rule="hyper" parents="9007 9751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9754">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7153,a,9752,a)].">
      <j1 rule="hyper" parents="7153 9752"/>
    </justification>
  </clause>

  <clause id="9755">
    <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),9754(a,1,2,2))].">
      <j1 rule="para" parents="23 9754"/>
    </justification>
  </clause>

  <clause id="9756">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T((x \ y) \ 1,x)) * K((x \ y) \ 1,T(z,T(x,y))) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(7083(a,1),9754(a,1,1,2))].">
      <j1 rule="para" parents="7083 9754"/>
    </justification>
  </clause>

  <clause id="9757">
    <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(7666(a,1),9754(a,1,1))].">
      <j1 rule="para" parents="7666 9754"/>
    </justification>
  </clause>

  <clause id="9758">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,T(y / x,u)) * K((x / y) \ 1,T(z,u)) = a((x / y) \ 1,z,(x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(9476(a,1),9754(a,1,1))].">
      <j1 rule="para" parents="9476 9754"/>
    </justification>
  </clause>

  <clause id="9759">
    <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(9755(a,1),44(a,1))].">
      <j1 rule="para" parents="9755 44"/>
    </justification>
  </clause>

  <clause id="9760">
    <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),8582(a,1,2,1))].">
      <j1 rule="para" parents="9 8582"/>
    </justification>
  </clause>

  <clause id="9762">
    <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),9760(a,1,2))].">
      <j1 rule="para" parents="18 9760"/>
    </justification>
  </clause>

  <clause id="9763">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(L(z,y,x),x * y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7807,a(flip),b,9762,a)].">
      <j1 rule="hyper" parents="63 7807 9762"/>
    </justification>
  </clause>

  <clause id="9764">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(z,x * y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,7619,a(flip),b,9763,a),flip(a)].">
      <j1 rule="hyper" parents="347 7619 9763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9767">
    <literal><![CDATA[
      K(L(x,(x \ y) * z,u),z) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),9764(a,2,2,2))].">
      <j1 rule="para" parents="10 9764"/>
    </justification>
  </clause>

  <clause id="9768">
    <literal><![CDATA[
      K(x,L(y,x * (z / y),u)) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(12(a,1),9764(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 9764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9769">
    <literal><![CDATA[
      K(x,L(y * ((z * y) \ z),u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,6621,a(flip),b,9767,a),flip(a)].">
      <j1 rule="hyper" parents="63 6621 9767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9770">
    <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(4378(a,1),9767(a,1,1,2))].">
      <j1 rule="para" parents="4378 9767"/>
    </justification>
  </clause>

  <clause id="9771">
    <literal><![CDATA[
      a(x,y,K(z,L(y,u,w))) = 1
    ]]></literal>
    <justification jstring="[para(9767(a,1),6240(a,1,3))].">
      <j1 rule="para" parents="9767 6240"/>
    </justification>
  </clause>

  <clause id="9772">
    <literal><![CDATA[
      K(x,L(y,z,K(u,x))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7668(a,1),9767(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7668 9767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9773">
    <literal><![CDATA[
      T(x,L(y,z,K(u,x))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,9772,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 9772 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9774">
    <literal><![CDATA[
      K(x,L(L(y,z,K(u,x)),w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(30(a,1),9772(a,1,2))].">
      <j1 rule="para" parents="30 9772"/>
    </justification>
  </clause>

  <clause id="9775">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ (K(y,x) * u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(99(a,1),9773(a,1,2))].">
      <j1 rule="para" parents="99 9773"/>
    </justification>
  </clause>

  <clause id="9776">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(6581,a,9769,a)].">
      <j1 rule="hyper" parents="6581 9769"/>
    </justification>
  </clause>

  <clause id="9777">
    <literal><![CDATA[
      T(x,a(y,z,z \ 1) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,9776,a)].">
      <j1 rule="hyper" parents="56 9776"/>
    </justification>
  </clause>

  <clause id="9779">
    <literal><![CDATA[
      K(x,K(L(x,y,z),u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(9768(a,1),7870(a,1,2,1))].">
      <j1 rule="para" parents="9768 7870"/>
    </justification>
  </clause>

  <clause id="9780">
    <literal><![CDATA[
      K(x,L(x,y,z) * u) = K(x,u * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(4909(a,1),9779(a,1,2))].">
      <j1 rule="para" parents="4909 9779"/>
    </justification>
  </clause>

  <clause id="9783">
    <literal><![CDATA[
      K(x,y * L(x,z,u)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9722,a(flip),b,9780,a),flip(a)].">
      <j1 rule="hyper" parents="63 9722 9780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9785">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) * (y * x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(413(a,1),9783(a,1,2)),flip(a)].">
      <j1 rule="para" parents="413 9783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9786">
    <literal><![CDATA[
      L(K(x,x * y),z * x,u) = K(L(x,z,u),y * L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(9783(a,1),7039(a,1,1))].">
      <j1 rule="para" parents="9783 7039"/>
    </justification>
  </clause>

  <clause id="9787">
    <literal><![CDATA[
      K(x,(y * (K(z,x) * u)) \ (y * (u * w))) = K(x,L(w,K(z,x) * u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,8177,a(flip),b,9774,a)].">
      <j1 rule="hyper" parents="63 8177 9774"/>
    </justification>
  </clause>

  <clause id="9792">
    <literal><![CDATA[
      T(x,y \ (K(z,x) * u)) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8086,a(flip),b,9775,a)].">
      <j1 rule="hyper" parents="63 8086 9775"/>
    </justification>
  </clause>

  <clause id="9794">
    <literal><![CDATA[
      T(x,y \ K(x,z)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(5160(a,1),9792(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5160 9792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9795">
    <literal><![CDATA[
      T(x,y \ ((z / x) \ u)) = T(x,y \ ((x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(5441(a,1),9792(a,1,2,2))].">
      <j1 rule="para" parents="5441 9792"/>
    </justification>
  </clause>

  <clause id="9796">
    <literal><![CDATA[
      L(T(x,y \ ((x \ z) \ u)),w,v5) \ L(x,w,v5) = K(y \ ((z / x) \ u),L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(9795(a,1),4936(a,1,1,1))].">
      <j1 rule="para" parents="9795 4936"/>
    </justification>
  </clause>

  <clause id="9797">
    <literal><![CDATA[
      K(L(x,y,z),u * L(x,w,v5)) = K(L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(7808,a,9786,a),flip(a)].">
      <j1 rule="hyper" parents="7808 9786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9798">
    <literal><![CDATA[
      L(K(L(x,y,z),x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(9797(a,1),8705(a,1,1))].">
      <j1 rule="para" parents="9797 8705"/>
    </justification>
  </clause>

  <clause id="9799">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(8302(a,1),9798(a,1,1))].">
      <j1 rule="para" parents="8302 9798"/>
    </justification>
  </clause>

  <clause id="9801">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,T(x * y,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,7179,a,b,9799,a),flip(a)].">
      <j1 rule="hyper" parents="347 7179 9799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9802">
    <literal><![CDATA[
      1 / L(K(x,x * y),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(220,a,9799,a,b,5173,a)].">
      <j1 rule="hyper" parents="220 9799 5173"/>
    </justification>
  </clause>

  <clause id="9803">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8577,a(flip),b,9799,a)].">
      <j1 rule="hyper" parents="63 8577 9799"/>
    </justification>
  </clause>

  <clause id="9805">
    <literal><![CDATA[
      K(x,y \ (x * z)) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(9548,a,9803,a)].">
      <j1 rule="hyper" parents="9548 9803"/>
    </justification>
  </clause>

  <clause id="9806">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(7018,a,9803,a)].">
      <j1 rule="hyper" parents="7018 9803"/>
    </justification>
  </clause>

  <clause id="9808">
    <literal><![CDATA[
      T(x,y \ (z * x)) = T(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(132,a,9803,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 9803 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9809">
    <literal><![CDATA[
      K(x,x * (y \ (x \ z))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8025,a(flip),b,9803,a),flip(a)].">
      <j1 rule="hyper" parents="63 8025 9803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9810">
    <literal><![CDATA[
      K(x,(y \ 1) \ x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(66(a,1),9806(a,2,2,2))].">
      <j1 rule="para" parents="66 9806"/>
    </justification>
  </clause>

  <clause id="9811">
    <literal><![CDATA[
      K(x,(y / R(y,z,u)) \ x) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(3702(a,2),9806(a,1,2,1))].">
      <j1 rule="para" parents="3702 9806"/>
    </justification>
  </clause>

  <clause id="9812">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ x)) = T(x,x * (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(1407(a,1),9808(a,1,2))].">
      <j1 rule="para" parents="1407 9808"/>
    </justification>
  </clause>

  <clause id="9813">
    <literal><![CDATA[
      T(x,x * (y \ z)) * K(y \ z,x) = L(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(9808(a,1),6467(a,1,1))].">
      <j1 rule="para" parents="9808 6467"/>
    </justification>
  </clause>

  <clause id="9814">
    <literal><![CDATA[
      L(K(x,x * y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = u
    ]]></literal>
    <justification jstring="[para(9801(a,2),7180(a,1))].">
      <j1 rule="para" parents="9801 7180"/>
    </justification>
  </clause>

  <clause id="9815">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(7019,a,9802,a)].">
      <j1 rule="hyper" parents="7019 9802"/>
    </justification>
  </clause>

  <clause id="9816">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,7899,a,b,9815,a),flip(a)].">
      <j1 rule="hyper" parents="347 7899 9815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9817">
    <literal><![CDATA[
      K(x \ (y * z),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9194,a(flip),b,9815,a)].">
      <j1 rule="hyper" parents="63 9194 9815"/>
    </justification>
  </clause>

  <clause id="9818">
    <literal><![CDATA[
      K(x \ (y * (x * z)),y) = K(z * y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9195,a(flip),b,9816,a)].">
      <j1 rule="hyper" parents="63 9195 9816"/>
    </justification>
  </clause>

  <clause id="9819">
    <literal><![CDATA[
      L(K(x * y,x),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,x) = u
    ]]></literal>
    <justification jstring="[para(9816(a,2),7935(a,1))].">
      <j1 rule="para" parents="9816 7935"/>
    </justification>
  </clause>

  <clause id="9820">
    <literal><![CDATA[
      K(x * ((y * x) \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(8103,a,9817,a),flip(a)].">
      <j1 rule="hyper" parents="8103 9817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9821">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(z * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(7035,a,9817,a)].">
      <j1 rule="hyper" parents="7035 9817"/>
    </justification>
  </clause>

  <clause id="9824">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(8577(a,1),9814(a,1))].">
      <j1 rule="para" parents="8577 9814"/>
    </justification>
  </clause>

  <clause id="9825">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z * (x \ y),z) = u
    ]]></literal>
    <justification jstring="[para(9194(a,1),9819(a,1))].">
      <j1 rule="para" parents="9194 9819"/>
    </justification>
  </clause>

  <clause id="9826">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,x * (L(y,z,u) \ y)) = w
    ]]></literal>
    <justification jstring="[para(1407(a,1),9824(a,1,2))].">
      <j1 rule="para" parents="1407 9824"/>
    </justification>
  </clause>

  <clause id="9827">
    <literal><![CDATA[
      K((x \ y) \ z,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z * (y \ x),z) = u
    ]]></literal>
    <justification jstring="[para(7030(a,2),9825(a,1))].">
      <j1 rule="para" parents="7030 9825"/>
    </justification>
  </clause>

  <clause id="9828">
    <literal><![CDATA[
      K(x,T(y \ (R(y,z,u) * x),T(y,R(y,z,u)))) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(9275,a,9811,a)].">
      <j1 rule="hyper" parents="9275 9811"/>
    </justification>
  </clause>

  <clause id="9829">
    <literal><![CDATA[
      L(x,(y \ z) \ 1,x) = L(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(5384,a,9813,a),flip(a)].">
      <j1 rule="hyper" parents="5384 9813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9830">
    <literal><![CDATA[
      L(x,(y / z) \ 1,x) = L(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9507,a,b,9829,a)].">
      <j1 rule="hyper" parents="63 9507 9829"/>
    </justification>
  </clause>

  <clause id="9831">
    <literal><![CDATA[
      L(x,y * (y \ ((z / u) \ 1)),x) = L(x,z \ u,x)
    ]]></literal>
    <justification jstring="[para(10(a,2),9830(a,1,2))].">
      <j1 rule="para" parents="10 9830"/>
    </justification>
  </clause>

  <clause id="9833">
    <literal><![CDATA[
      K(x,L(y,K(z,x) * u,w)) = K(x,(w * u) \ (w * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8089,a(flip),b,9787,a),flip(a)].">
      <j1 rule="hyper" parents="63 8089 9787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9835">
    <literal><![CDATA[
      K(x,L(y,K(z,x) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(18(a,2),9833(a,2,2))].">
      <j1 rule="para" parents="18 9833"/>
    </justification>
  </clause>

  <clause id="9836">
    <literal><![CDATA[
      K(x,L(y,K(x,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(5261(a,1),9835(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5261 9835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9837">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = (y \ 1) / (y \ K(y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(9836(a,1),5267(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9836 5267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9838">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = K(L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,5267,a(flip),b,9837,a),flip(a)].">
      <j1 rule="hyper" parents="347 5267 9837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9839">
    <literal><![CDATA[
      K(L(x,T(y,z),u),z) = K(L(x,y,u),z)
    ]]></literal>
    <justification jstring="[para(4931(a,1),9838(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4931 9838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9840">
    <literal><![CDATA[
      K(x,T(R(y,z,u) * (y \ x),T(y,R(y,z,u)))) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(1746(a,1),9828(a,1,2,1))].">
      <j1 rule="para" parents="1746 9828"/>
    </justification>
  </clause>

  <clause id="9841">
    <literal><![CDATA[
      K(x,T(R(y,z,u) * (y \ x),y)) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(196(a,1),9840(a,1,2,2))].">
      <j1 rule="para" parents="196 9840"/>
    </justification>
  </clause>

  <clause id="9842">
    <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(63,a,7627,a(flip),b,9770,a)].">
      <j1 rule="hyper" parents="63 7627 9770"/>
    </justification>
  </clause>

  <clause id="9844">
    <literal><![CDATA[
      K(x,L(R(y,x \ z,y),z,u)) = K(L(x,y * (x \ z),u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9839,a(flip),b,9842,a),flip(a)].">
      <j1 rule="hyper" parents="63 9839 9842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9845">
    <literal><![CDATA[
      K(L(x,y * (x \ z),u),y) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9278,a(flip),b,9844,a),flip(a)].">
      <j1 rule="hyper" parents="63 9278 9844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9847">
    <literal><![CDATA[
      K(x \ ((y / z) \ u),L(z,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x \ ((z \ y) \ u),L(z,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(9796(a,1),5114(a,1))].">
      <j1 rule="para" parents="9796 5114"/>
    </justification>
  </clause>

  <clause id="9848">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),L(x,u,w)) = K(y \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(9847,a,9677,a)].">
      <j1 rule="hyper" parents="9847 9677"/>
    </justification>
  </clause>

  <clause id="9849">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * K(z,y)) * (y * z)) = L(K(z,y),T(x,y * z),y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,250,a(flip),b,8699,a)].">
      <j1 rule="hyper" parents="63 250 8699"/>
    </justification>
  </clause>

  <clause id="9850">
    <literal><![CDATA[
      K(x,((y / z) * (z * x)) \ (y * (z * x))) = L(K(x,z),T(y,z * x),z * x)
    ]]></literal>
    <justification jstring="[hyper(9301,a,9849,a)].">
      <j1 rule="hyper" parents="9301 9849"/>
    </justification>
  </clause>

  <clause id="9851">
    <literal><![CDATA[
      K(x,((y / z) * z) \ (x \ (y * (z * x)))) = L(K(x,z),T(y,z * x),z * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8564,a(flip),b,9850,a)].">
      <j1 rule="hyper" parents="63 8564 9850"/>
    </justification>
  </clause>

  <clause id="9852">
    <literal><![CDATA[
      L(K(x,y),T(z,y * x),y * x) = K(x,z \ (x \ (z * (y * x))))
    ]]></literal>
    <justification jstring="[para(12(a,1),9851(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 9851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9853">
    <literal><![CDATA[
      L(K(x,y),T(z,y * x),y * x) = K(x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,8245,a(flip),b,9852,a),flip(a)].">
      <j1 rule="hyper" parents="347 8245 9852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9854">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = (y * z) * T(x * K(z,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(134,a,9853,a(flip),b,8699,a)].">
      <j1 rule="hyper" parents="134 9853 8699"/>
    </justification>
  </clause>

  <clause id="9855">
    <literal><![CDATA[
      K(x,L(y,x,((y * x) * z) / (y * x))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[para(254(a,1),9853(a,1,2)),flip(a)].">
      <j1 rule="para" parents="254 9853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9856">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9624,a,9855,a),flip(a)].">
      <j1 rule="hyper" parents="9624 9855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9857">
    <literal><![CDATA[
      L(K(x,y),z,y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(9855(a,1),9624(a,1))].">
      <j1 rule="para" parents="9855 9624"/>
    </justification>
  </clause>

  <clause id="9860">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,9856,a(flip),b,9386,a)].">
      <j1 rule="hyper" parents="133 9856 9386"/>
    </justification>
  </clause>

  <clause id="9862">
    <literal><![CDATA[
      T(x * K(y,z),z * y) = (z * y) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(6979,a,9854,a),flip(a)].">
      <j1 rule="hyper" parents="6979 9854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9863">
    <literal><![CDATA[
      (x * K(y,z)) * (z * y) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(152,a,9862,a)].">
      <j1 rule="hyper" parents="152 9862"/>
    </justification>
  </clause>

  <clause id="9864">
    <literal><![CDATA[
      (x * K(y \ z,y)) * z = x * ((y \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(357,a,9863,a)].">
      <j1 rule="hyper" parents="357 9863"/>
    </justification>
  </clause>

  <clause id="9865">
    <literal><![CDATA[
      (x / (y * z)) * K(y,z) = x / (z * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,12,a(flip),b,9863,a),flip(a)].">
      <j1 rule="hyper" parents="131 12 9863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9866">
    <literal><![CDATA[
      ((x * K(y,z)) * z) \ (x * (y * z)) = L(y,z,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,9863,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="128 9863 97"/>
    </justification>
  </clause>

  <clause id="9867">
    <literal><![CDATA[
      (x * (y * z)) / (z * y) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(9863(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9863 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9868">
    <literal><![CDATA[
      (x / (y * z)) \ (x / (z * y)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,9865,a)].">
      <j1 rule="hyper" parents="138 9865"/>
    </justification>
  </clause>

  <clause id="9869">
    <literal><![CDATA[
      K(x,y) * (x / (x * y)) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8893,a(flip),b,9865,a)].">
      <j1 rule="hyper" parents="63 8893 9865"/>
    </justification>
  </clause>

  <clause id="9870">
    <literal><![CDATA[
      (x / (y * z)) * (z * K(y,z)) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,9865,a(flip),b,6233,a)].">
      <j1 rule="hyper" parents="133 9865 6233"/>
    </justification>
  </clause>

  <clause id="9871">
    <literal><![CDATA[
      (x / y) * K(z,z \ y) = x / ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),9865(a,1,1,2))].">
      <j1 rule="para" parents="10 9865"/>
    </justification>
  </clause>

  <clause id="9872">
    <literal><![CDATA[
      (x / y) * K(y / z,z) = x / (z * (y / z))
    ]]></literal>
    <justification jstring="[para(12(a,1),9865(a,1,1,2))].">
      <j1 rule="para" parents="12 9865"/>
    </justification>
  </clause>

  <clause id="9873">
    <literal><![CDATA[
      x / (y * z) != u * K(z,y)
    ]]></literal>
    <literal><![CDATA[
      x / (z * y) = u
    ]]></literal>
    <justification jstring="[para(9865(a,1),44(a,1))].">
      <j1 rule="para" parents="9865 44"/>
    </justification>
  </clause>

  <clause id="9874">
    <literal><![CDATA[
      (x / (y * z)) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z * y) = u
    ]]></literal>
    <justification jstring="[para(9865(a,1),6145(a,1,1))].">
      <j1 rule="para" parents="9865 6145"/>
    </justification>
  </clause>

  <clause id="9875">
    <literal><![CDATA[
      T(x,y) * (y / (x * y)) = x * (y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(134,a,9869,a(flip),b,5210,a)].">
      <j1 rule="hyper" parents="134 9869 5210"/>
    </justification>
  </clause>

  <clause id="9876">
    <literal><![CDATA[
      (x / (y \ z)) * ((y \ z) * y) = (x / (z / y)) * z
    ]]></literal>
    <justification jstring="[para(6125(a,1),9864(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6125 9864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9877">
    <literal><![CDATA[
      (x \ y) * K(z,z \ T(x,x \ y)) = y / ((z \ T(x,x \ y)) * z)
    ]]></literal>
    <justification jstring="[para(296(a,1),9871(a,1,1))].">
      <j1 rule="para" parents="296 9871"/>
    </justification>
  </clause>

  <clause id="9878">
    <literal><![CDATA[
      1 / ((x * ((x / y) \ 1)) / x) = x / (x * (y / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,8627,a,b,9872,a)].">
      <j1 rule="hyper" parents="63 8627 9872"/>
    </justification>
  </clause>

  <clause id="9879">
    <literal><![CDATA[
      (x / y) * K(z \ y,z) = x / (z * (y / z))
    ]]></literal>
    <justification jstring="[para(5138(a,1),9872(a,1,2))].">
      <j1 rule="para" parents="5138 9872"/>
    </justification>
  </clause>

  <clause id="9880">
    <literal><![CDATA[
      (x * K(y,z)) / (z * y) != u
    ]]></literal>
    <literal><![CDATA[
      (x / (z * y)) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(9588(a,1),9867(a,1,1))].">
      <j1 rule="para" parents="9588 9867"/>
    </justification>
  </clause>

  <clause id="9881">
    <literal><![CDATA[
      L(x,x \ y,(x \ y) \ 1) = (1 / (y / x)) * y
    ]]></literal>
    <justification jstring="[hyper(2953,a,9876,a)].">
      <j1 rule="hyper" parents="2953 9876"/>
    </justification>
  </clause>

  <clause id="9882">
    <literal><![CDATA[
      (x * ((x / y) \ 1)) / x = (x / (x * (y / x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(214,a,9878,a),flip(a)].">
      <j1 rule="hyper" parents="214 9878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9883">
    <literal><![CDATA[
      x / (x * (((y / x) \ 1) \ 1)) = ((x * ((x / y) \ 1)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(9882(a,2),2852(a,2,1))].">
      <j1 rule="para" parents="9882 2852"/>
    </justification>
  </clause>

  <clause id="9884">
    <literal><![CDATA[
      (x * (y * K(z,y))) \ (x * (z * y)) = L(z,y,x * K(z,y))
    ]]></literal>
    <justification jstring="[para(6051(a,1),9866(a,1,1))].">
      <j1 rule="para" parents="6051 9866"/>
    </justification>
  </clause>

  <clause id="9885">
    <literal><![CDATA[
      (x \ y) * K(z,z \ T(x,x \ y)) = y / T((z \ x) * z,x \ y)
    ]]></literal>
    <justification jstring="[para(4830(a,2),9877(a,2,2))].">
      <j1 rule="para" parents="4830 9877"/>
    </justification>
  </clause>

  <clause id="9886">
    <literal><![CDATA[
      (x \ y) * K(z,z \ T(x,x \ y)) = ((z \ x) * z) \ y
    ]]></literal>
    <justification jstring="[hyper(6615,a,9885,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="6615 9885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9887">
    <literal><![CDATA[
      K((x / y) \ z,R((x / y) \ 1,x / y,y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3893,a(flip),b,8707,a),flip(a)].">
      <j1 rule="hyper" parents="347 3893 8707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9888">
    <literal><![CDATA[
      K((x / y) \ z,T(y / x,x / y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[para(868(a,1),9887(a,1,2))].">
      <j1 rule="para" parents="868 9887"/>
    </justification>
  </clause>

  <clause id="9889">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((x / y) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(3905,a,9888,a),flip(a)].">
      <j1 rule="hyper" parents="3905 9888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9890">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(347,a,9143,a(flip),b,9889,a),flip(a)].">
      <j1 rule="hyper" parents="347 9143 9889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9891">
    <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(6700(a,1),9297(a,1,2))].">
      <j1 rule="para" parents="6700 9297"/>
    </justification>
  </clause>

  <clause id="9892">
    <literal><![CDATA[
      T(x * L(K(y,z),u,w),K(y,v5)) = T(x,K(y,v5)) * L(K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(111(a,1),9414(a,1,1))].">
      <j1 rule="para" parents="111 9414"/>
    </justification>
  </clause>

  <clause id="9893">
    <literal><![CDATA[
      R(x * K(y,K(T(z,x),u)),K(y,T(z,x)),u) = ((K(y,z) * x) * u) / (u * K(y,T(z,x)))
    ]]></literal>
    <justification jstring="[para(7261(a,1),9669(a,1,1,2))].">
      <j1 rule="para" parents="7261 9669"/>
    </justification>
  </clause>

  <clause id="9894">
    <literal><![CDATA[
      R(T(x * K(y,x),z),y,u) \ ((y * x) * u) = (y * u) * K(z,(y * u) \ ((y * x) * u))
    ]]></literal>
    <justification jstring="[hyper(150,a,9744,a),flip(a)].">
      <j1 rule="hyper" parents="150 9744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9895">
    <literal><![CDATA[
      (x * y) * K(z,(x * y) \ ((x * u) * y)) != w
    ]]></literal>
    <literal><![CDATA[
      R(T(u * K(x,u),z),x,y) \ ((x * u) * y) = w
    ]]></literal>
    <justification jstring="[para(9744(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9744 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9896">
    <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(347,a,8995,a(flip),b,9750,a),flip(a)].">
      <j1 rule="hyper" parents="347 8995 9750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9898">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((L(x,y,z) * w) / u,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,7390,a(flip),b,9896,a),flip(a)].">
      <j1 rule="hyper" parents="347 7390 9896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9899">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (y \ 1),1 / y)
    ]]></literal>
    <justification jstring="[para(6379(a,1),5775(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6379 5775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9900">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3874,a,b,9899,a),flip(a)].">
      <j1 rule="hyper" parents="347 3874 9899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9901">
    <literal><![CDATA[
      K((x / y) / (1 / y),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3874,a,b,9900,a)].">
      <j1 rule="hyper" parents="63 3874 9900"/>
    </justification>
  </clause>

  <clause id="9902">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[para(9901(a,1),4928(a,2,2))].">
      <j1 rule="para" parents="9901 4928"/>
    </justification>
  </clause>

  <clause id="9903">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) * y,1 / y)
    ]]></literal>
    <justification jstring="[para(5770(a,1),9902(a,2,2))].">
      <j1 rule="para" parents="5770 9902"/>
    </justification>
  </clause>

  <clause id="9904">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(5779(a,1),9903(a,2,2))].">
      <j1 rule="para" parents="5779 9903"/>
    </justification>
  </clause>

  <clause id="9905">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = K(x,1 / y) / y
    ]]></literal>
    <justification jstring="[hyper(347,a,2537,a(flip),b,9904,a),flip(a)].">
      <j1 rule="hyper" parents="347 2537 9904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9906">
    <literal><![CDATA[
      x / ((y / (x \ y)) / (1 / (x \ y))) = K(y,1 / (x \ y)) / (x \ y)
    ]]></literal>
    <justification jstring="[para(80(a,1),9905(a,1,1))].">
      <j1 rule="para" parents="80 9905"/>
    </justification>
  </clause>

  <clause id="9907">
    <literal><![CDATA[
      K(x,1 / (y \ x)) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(80(a,1),9906(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="80 9906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9908">
    <literal><![CDATA[
      K(x,y / x) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(6270(a,1),9907(a,1,1))].">
      <j1 rule="para" parents="6270 9907"/>
    </justification>
  </clause>

  <clause id="9909">
    <literal><![CDATA[
      ((x * ((K(y,x / y) / (x \ y)) \ 1)) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(9908(a,2),9883(a,2,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9908 9883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9910">
    <literal><![CDATA[
      (K(x,y) * (K(x,z) * u)) / (K(x,y) * u) = K((1 / x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(5693(a,1),6546(a,1,1,2))].">
      <j1 rule="para" parents="5693 6546"/>
    </justification>
  </clause>

  <clause id="9911">
    <literal><![CDATA[
      (K(x,y) * (K(x,z) * u)) / (K(x,y) * u) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,771,a(flip),b,9910,a),flip(a)].">
      <j1 rule="hyper" parents="347 771 9910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9914">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(133,a,7283,a,b,9911,a)].">
      <j1 rule="hyper" parents="133 7283 9911"/>
    </justification>
  </clause>

  <clause id="9915">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * (K(y,x) * u)) = K(y,z) * u
    ]]></literal>
    <justification jstring="[hyper(36,a,5259,a,b,9911,a)].">
      <j1 rule="hyper" parents="36 5259 9911"/>
    </justification>
  </clause>

  <clause id="9916">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * (K(x,y) * u) = w
    ]]></literal>
    <justification jstring="[para(9911(a,1),280(a,1,1))].">
      <j1 rule="para" parents="9911 280"/>
    </justification>
  </clause>

  <clause id="9917">
    <literal><![CDATA[
      a(x,y,x) * (K(x,x * y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,8666,a(flip),b,9915,a)].">
      <j1 rule="hyper" parents="63 8666 9915"/>
    </justification>
  </clause>

  <clause id="9918">
    <literal><![CDATA[
      (K(x,y) * z) / (K(x,u) * z) = K(u,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,9915,a(flip),b,8659,a)].">
      <j1 rule="hyper" parents="131 9915 8659"/>
    </justification>
  </clause>

  <clause id="9919">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(5261(a,1),9915(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5261 9915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9920">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (K(x,y) \ u)) = K(z,x) * u
    ]]></literal>
    <justification jstring="[para(5272(a,1),9915(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5272 9915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9921">
    <literal><![CDATA[
      a(x,x \ y,x) * (K(x,y) * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),9917(a,1,2,1,2))].">
      <j1 rule="para" parents="10 9917"/>
    </justification>
  </clause>

  <clause id="9922">
    <literal><![CDATA[
      x / (K(y \ x,z) * (y * (x / y))) = K(z,y \ x) * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4899(a,1),9918(a,1,1))].">
      <j1 rule="para" parents="4899 9918"/>
    </justification>
  </clause>

  <clause id="9923">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,8663,a,b,9919,a)].">
      <j1 rule="hyper" parents="347 8663 9919"/>
    </justification>
  </clause>

  <clause id="9924">
    <literal><![CDATA[
      T(x,y) \ (T(x,z) * u) = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,5350,a,b,9919,a)].">
      <j1 rule="hyper" parents="347 5350 9919"/>
    </justification>
  </clause>

  <clause id="9925">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,u)) * K(y,u) = K(x,y) * (K(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7351,a,b,9919,a)].">
      <j1 rule="hyper" parents="63 7351 9919"/>
    </justification>
  </clause>

  <clause id="9926">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (K(y,x) * u)) = K(z,x) * u
    ]]></literal>
    <justification jstring="[para(5261(a,1),9919(a,2,2))].">
      <j1 rule="para" parents="5261 9919"/>
    </justification>
  </clause>

  <clause id="9927">
    <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(7037(a,1),9919(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7037 9919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9928">
    <literal><![CDATA[
      T(T(K(x,y) * z,K(u,w)),K(u,w)) = K(y,v5) * (K(x,y) * (K(y,v5) \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7334,a,b,9920,a)].">
      <j1 rule="hyper" parents="347 7334 9920"/>
    </justification>
  </clause>

  <clause id="9929">
    <literal><![CDATA[
      L(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(544,a,9923,a)].">
      <j1 rule="hyper" parents="544 9923"/>
    </justification>
  </clause>

  <clause id="9930">
    <literal><![CDATA[
      L(x,K(y,z),K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(5182,a,9929,a)].">
      <j1 rule="hyper" parents="5182 9929"/>
    </justification>
  </clause>

  <clause id="9931">
    <literal><![CDATA[
      L(K(x,y) \ z,K(u,w),K(w,v5)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(347,a,5256,a(flip),b,9929,a),flip(a)].">
      <j1 rule="hyper" parents="347 5256 9929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9932">
    <literal><![CDATA[
      L(x,K(y,z),K(u,K(z,w))) = x
    ]]></literal>
    <justification jstring="[para(7279(a,1),9929(a,1,3))].">
      <j1 rule="para" parents="7279 9929"/>
    </justification>
  </clause>

  <clause id="9933">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,u) * K(x,y)) = T(z * K(x,y),K(y,u))
    ]]></literal>
    <justification jstring="[para(9929(a,1),8376(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9929 8376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9934">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) * u = K(x,y) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(1362,a,9930,a),flip(a)].">
      <j1 rule="hyper" parents="1362 9930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9935">
    <literal><![CDATA[
      (K(x,K(y,z)) * K(u,y)) * w = K(x,K(y,z)) * (K(u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(1362,a,9932,a),flip(a)].">
      <j1 rule="hyper" parents="1362 9932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9936">
    <literal><![CDATA[
      T(x,K(y,z) \ u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(9931(a,1),9773(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9931 9773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9937">
    <literal><![CDATA[
      T(x,K(y,z) * (y * u)) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(5187(a,1),9936(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5187 9936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9938">
    <literal><![CDATA[
      x \ (T(x,y) * (K(z,x) * u)) = T(x,z) \ (T(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,5157,a,b,9924,a)].">
      <j1 rule="hyper" parents="347 5157 9924"/>
    </justification>
  </clause>

  <clause id="9939">
    <literal><![CDATA[
      K(x,y) * (K(z,y) * u) = K(z,y) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5273,a,9926,a)].">
      <j1 rule="hyper" parents="5273 9926"/>
    </justification>
  </clause>

  <clause id="9940">
    <literal><![CDATA[
      (K(x,y) * K(x,y)) * z = y * (T(T(y,x),x) \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,5781,a(flip),b,9934,a),flip(a)].">
      <j1 rule="hyper" parents="347 5781 9934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9941">
    <literal><![CDATA[
      (x * y) * (K(y,z) * (K(y,z) * u)) = (x * T(T(y,z),z)) * u
    ]]></literal>
    <justification jstring="[para(9934(a,1),6954(a,1,2))].">
      <j1 rule="para" parents="9934 6954"/>
    </justification>
  </clause>

  <clause id="9942">
    <literal><![CDATA[
      (((K(x,y) * (K(z,y) * u)) / (K(z,y) * u)) * K(z,y)) * u = K(z,y) * (R(K(x,y),K(z,y),u) * u)
    ]]></literal>
    <justification jstring="[para(9939(a,1),1743(a,1,1,1,1))].">
      <j1 rule="para" parents="9939 1743"/>
    </justification>
  </clause>

  <clause id="9943">
    <literal><![CDATA[
      K(x,x \ y) * (K(y,x) * z) = a(x,x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(5261(a,1),9921(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5261 9921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9944">
    <literal><![CDATA[
      (x \ y) * (a(x,x \ y,x) * z) = (y / x) * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(134,a,9943,a(flip),b,5491,a)].">
      <j1 rule="hyper" parents="134 9943 5491"/>
    </justification>
  </clause>

  <clause id="9945">
    <literal><![CDATA[
      T(x,y) \ (T(x,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * (K(y,x) * u) = w
    ]]></literal>
    <justification jstring="[para(9938(a,1),5169(a,1))].">
      <j1 rule="para" parents="9938 5169"/>
    </justification>
  </clause>

  <clause id="9946">
    <literal><![CDATA[
      (x \ y) * (a(x,x \ y,x) * z) = (y / T(x,y)) * L(z,K(y,x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,9468,a,b,9944,a),flip(a)].">
      <j1 rule="hyper" parents="347 9468 9944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9947">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(7283(a,2),9914(a,2,2,1))].">
      <j1 rule="para" parents="7283 9914"/>
    </justification>
  </clause>

  <clause id="9948">
    <literal><![CDATA[
      (x * K(y * z,y)) * K(y,z) = K(y * z,y) * (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(8773(a,1),9925(a,1,1))].">
      <j1 rule="para" parents="8773 9925"/>
    </justification>
  </clause>

  <clause id="9949">
    <literal><![CDATA[
      K(x,y) * T(z,K(x,y) * K(y,u)) = T(z * K(x,y),K(y,u))
    ]]></literal>
    <justification jstring="[para(2556(a,1),9933(a,1,2,2))].">
      <j1 rule="para" parents="2556 9933"/>
    </justification>
  </clause>

  <clause id="9950">
    <literal><![CDATA[
      R(x,T(K(y,z),x),T(K(u,K(z,w)),K(y,z) * 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(9935(a,2),1029(a,1,2))].">
      <j1 rule="para" parents="9935 1029"/>
    </justification>
  </clause>

  <clause id="9951">
    <literal><![CDATA[
      K(x,y) * (K(z,K(u,x)) * (K(x,y) \ w)) = K(z,K(u,x)) * w
    ]]></literal>
    <justification jstring="[hyper(357,a,9947,a),flip(a)].">
      <j1 rule="hyper" parents="357 9947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9952">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = z * (K(x,y) * K(x * y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,8321,a(flip),b,9948,a),flip(a)].">
      <j1 rule="hyper" parents="63 8321 9948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9953">
    <literal><![CDATA[
      T((K(x,y) \ z) * K(x,y),K(y,u)) \ z = K(K(x,y) * K(y,u),K(x,y) \ z)
    ]]></literal>
    <justification jstring="[para(9949(a,1),6162(a,1,1))].">
      <j1 rule="para" parents="9949 6162"/>
    </justification>
  </clause>

  <clause id="9954">
    <literal><![CDATA[
      K(x,y) * (K(z,K(x,u)) * (K(x,y) \ w)) = K(u,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(7283(a,2),9951(a,1,2,1))].">
      <j1 rule="para" parents="7283 9951"/>
    </justification>
  </clause>

  <clause id="9955">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(8338(a,1),9952(a,2,2))].">
      <j1 rule="para" parents="8338 9952"/>
    </justification>
  </clause>

  <clause id="9956">
    <literal><![CDATA[
      K(x,x * y) * (z * a(x,y,x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(5273,a,9955,a)].">
      <j1 rule="hyper" parents="5273 9955"/>
    </justification>
  </clause>

  <clause id="9957">
    <literal><![CDATA[
      a(x,y,x) * z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8666,a(flip),b,9955,a)].">
      <j1 rule="hyper" parents="63 8666 9955"/>
    </justification>
  </clause>

  <clause id="9958">
    <literal><![CDATA[
      T(a(x,y,x),z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(269,a,8666,a(flip),b,9955,a(flip))].">
      <j1 rule="hyper" parents="269 8666 9955"/>
    </justification>
  </clause>

  <clause id="9959">
    <literal><![CDATA[
      T(x,a(y,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(269,a,9955,a(flip),b,8666,a(flip))].">
      <j1 rule="hyper" parents="269 9955 8666"/>
    </justification>
  </clause>

  <clause id="9960">
    <literal><![CDATA[
      a(x,y,x) \ (z * a(x,y,x)) = z
    ]]></literal>
    <justification jstring="[hyper(128,a,9955,a(flip),b,8666,a(flip))].">
      <j1 rule="hyper" parents="128 9955 8666"/>
    </justification>
  </clause>

  <clause id="9961">
    <literal><![CDATA[
      x / a(y,z,y) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(7761,a,9959,a),flip(a)].">
      <j1 rule="hyper" parents="7761 9959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9962">
    <literal><![CDATA[
      x * K(y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(6059,a,9959,a)].">
      <j1 rule="hyper" parents="6059 9959"/>
    </justification>
  </clause>

  <clause id="9963">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ z = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4352,a,9959,a)].">
      <j1 rule="hyper" parents="4352 9959"/>
    </justification>
  </clause>

  <clause id="9964">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(1847,a,9959,a)].">
      <j1 rule="hyper" parents="1847 9959"/>
    </justification>
  </clause>

  <clause id="9965">
    <literal><![CDATA[
      T(x,a(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(9959(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="9959 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9966">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) / (x * y) = L(a(z,u,z),y,x)
    ]]></literal>
    <justification jstring="[para(9962(a,1),5071(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9962 5071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9968">
    <literal><![CDATA[
      T(a(x,y,x),z) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,8336,a,b,9958,a),flip(a)].">
      <j1 rule="hyper" parents="347 8336 9958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9969">
    <literal><![CDATA[
      x * a(y,z,y) != u * x
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) = u
    ]]></literal>
    <justification jstring="[para(9958(a,1),271(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9958 271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9970">
    <literal><![CDATA[
      x * a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) * x = u
    ]]></literal>
    <justification jstring="[para(9958(a,1),315(a,1,2))].">
      <j1 rule="para" parents="9958 315"/>
    </justification>
  </clause>

  <clause id="9971">
    <literal><![CDATA[
      a(x,y,x) * (x \ z) = L(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(347,a,8511,a(flip),b,9957,a),flip(a)].">
      <j1 rule="hyper" parents="347 8511 9957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9972">
    <literal><![CDATA[
      a(x,y,x) * (z * L(x,y,x)) = z * x
    ]]></literal>
    <justification jstring="[hyper(347,a,8509,a(flip),b,9957,a),flip(a)].">
      <j1 rule="hyper" parents="347 8509 9957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9973">
    <literal><![CDATA[
      a(x,y,x) * (z / x) = z / L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,8496,a(flip),b,9957,a),flip(a)].">
      <j1 rule="hyper" parents="347 8496 9957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9974">
    <literal><![CDATA[
      a(x,y,x) \ (z * x) = z * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,8509,a(flip),b,9957,a)].">
      <j1 rule="hyper" parents="128 8509 9957"/>
    </justification>
  </clause>

  <clause id="9975">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (a(y,z,y) * (u * x)) = R(T(u,x * a(y,z,y)),x,a(y,z,y))
    ]]></literal>
    <justification jstring="[hyper(128,a,9957,a,b,743,a)].">
      <j1 rule="hyper" parents="128 9957 743"/>
    </justification>
  </clause>

  <clause id="9976">
    <literal><![CDATA[
      x * a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) \ u = x
    ]]></literal>
    <justification jstring="[para(9957(a,1),138(a,1))].">
      <j1 rule="para" parents="9957 138"/>
    </justification>
  </clause>

  <clause id="9977">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,z)) * y) = R(T(a(z,u,z),x * y),x,y)
    ]]></literal>
    <justification jstring="[para(9957(a,1),744(a,1,2,1))].">
      <j1 rule="para" parents="9957 744"/>
    </justification>
  </clause>

  <clause id="9978">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (a(y,z,y) * (u * x)) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(u,x),x,a(y,z,y)) = w
    ]]></literal>
    <justification jstring="[para(9957(a,1),881(a,1,1))].">
      <j1 rule="para" parents="9957 881"/>
    </justification>
  </clause>

  <clause id="9981">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,8512,a,b,9961,a)].">
      <j1 rule="hyper" parents="63 8512 9961"/>
    </justification>
  </clause>

  <clause id="9982">
    <literal><![CDATA[
      x * (a(x,y,x) \ z) = L(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(9961(a,1),8515(a,1,2))].">
      <j1 rule="para" parents="9961 8515"/>
    </justification>
  </clause>

  <clause id="9983">
    <literal><![CDATA[
      (x / y) \ (a(y,z,y) \ x) = L(y,z,y)
    ]]></literal>
    <justification jstring="[para(9961(a,1),8516(a,1,2))].">
      <j1 rule="para" parents="9961 8516"/>
    </justification>
  </clause>

  <clause id="9984">
    <literal><![CDATA[
      T(a(x / y,z,x / y),u) = (x / y) \ R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(6790(a,1),9968(a,2,2))].">
      <j1 rule="para" parents="6790 9968"/>
    </justification>
  </clause>

  <clause id="9986">
    <literal><![CDATA[
      a(x,y,x) \ y = x \ ((x * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(128,a,4361,a(flip),b,9971,a)].">
      <j1 rule="hyper" parents="128 4361 9971"/>
    </justification>
  </clause>

  <clause id="9987">
    <literal><![CDATA[
      a(x,y,x) \ (x * z) = L(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(620,a,9981,a),flip(a)].">
      <j1 rule="hyper" parents="620 9981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9988">
    <literal><![CDATA[
      a(x,y,x) * (L(x,y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(1052,a,9981,a(flip))].">
      <j1 rule="hyper" parents="1052 9981"/>
    </justification>
  </clause>

  <clause id="9989">
    <literal><![CDATA[
      a(x,y,x) \ K(x,z) = x \ L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,7051,a(flip),b,9982,a),flip(a)].">
      <j1 rule="hyper" parents="128 7051 9982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9990">
    <literal><![CDATA[
      x * (a(y,z,y) \ K(y,u)) = x * (y \ L(T(y,u),z,y))
    ]]></literal>
    <justification jstring="[hyper(134,a,9989,a,b,9,a)].">
      <j1 rule="hyper" parents="134 9989 9"/>
    </justification>
  </clause>

  <clause id="9991">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,z)) * y) = R(a(z,u,z),x,y)
    ]]></literal>
    <justification jstring="[para(9958(a,1),9977(a,2,1))].">
      <j1 rule="para" parents="9958 9977"/>
    </justification>
  </clause>

  <clause id="9993">
    <literal><![CDATA[
      (x * y) \ ((T(z * x,z) / z) * y) = R(a(z,x,z),x,y)
    ]]></literal>
    <justification jstring="[para(8346(a,2),9991(a,1,2,1))].">
      <j1 rule="para" parents="8346 9991"/>
    </justification>
  </clause>

  <clause id="9994">
    <literal><![CDATA[
      L(a(x,T(y,z),x),T(y,z),z) = R(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9351,a,b,9993,a)].">
      <j1 rule="hyper" parents="63 9351 9993"/>
    </justification>
  </clause>

  <clause id="9995">
    <literal><![CDATA[
      R(a(x,y * K(z,y),x),y * K(z,y),z) = L(a(x,y,x),T(y * K(z,y),z),z)
    ]]></literal>
    <justification jstring="[para(5058(a,1),9994(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5058 9994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9996">
    <literal><![CDATA[
      x / (K(((y \ 1) * x) \ x,z) * (((y \ 1) * x) * R(y,y \ 1,x))) = K(z,((y \ 1) * x) \ x) * K(((y \ 1) * x) \ x,(y \ 1) * x)
    ]]></literal>
    <justification jstring="[para(241(a,2),9922(a,1,2,2,2))].">
      <j1 rule="para" parents="241 9922"/>
    </justification>
  </clause>

  <clause id="9997">
    <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(7037(a,1),9927(a,1,1))].">
      <j1 rule="para" parents="7037 9927"/>
    </justification>
  </clause>

  <clause id="9998">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * w) = a(u,z,K(y,x)) \ w
    ]]></literal>
    <justification jstring="[hyper(63,a,9266,a(flip),b,9997,a),flip(a)].">
      <j1 rule="hyper" parents="63 9266 9997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9999">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(x,y,K(u,z)) * w
    ]]></literal>
    <justification jstring="[hyper(63,a,9245,a(flip),b,9998,a),flip(a)].">
      <j1 rule="hyper" parents="63 9245 9998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10000">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * x) = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(220,a,9245,a(flip),b,9998,a(flip))].">
      <j1 rule="hyper" parents="220 9245 9998"/>
    </justification>
  </clause>

  <clause id="10001">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ K(w,u) = K(w,u) * a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,9238,a,b,9999,a),flip(a)].">
      <j1 rule="hyper" parents="347 9238 9999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10002">
    <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(10001(a,2),43(a,1))].">
      <j1 rule="para" parents="10001 43"/>
    </justification>
  </clause>

  <clause id="10003">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,u)) = K(x,y) * T(z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(40,a,8713,a,b,9928,a),flip(a)].">
      <j1 rule="hyper" parents="40 8713 9928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10004">
    <literal><![CDATA[
      T(x * K(y,z),K(y,u)) = T(x,K(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,5887,a(flip),b,10003,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 5887 10003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10006">
    <literal><![CDATA[
      K(x,y) * (T(z,K(y,x)) * K(y,u)) = (z * K(y,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(10004(a,1),7344(a,1,2))].">
      <j1 rule="para" parents="10004 7344"/>
    </justification>
  </clause>

  <clause id="10007">
    <literal><![CDATA[
      K(x,y) * (T(z,K(y,x)) * K(y,u)) = z * (K(y,u) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,8375,a(flip),b,10006,a),flip(a)].">
      <j1 rule="hyper" parents="347 8375 10006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10008">
    <literal><![CDATA[
      ((x \ y) * a(x,x \ y,x)) \ ((y / T(x,y)) * L(z,K(y,x),x \ y)) = L(z,a(x,x \ y,x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(128,a,9946,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="128 9946 97"/>
    </justification>
  </clause>

  <clause id="10009">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),K(x,y) \ u) = T(T(u,K(x,y)),K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(6873(a,1),9953(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6873 9953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10010">
    <literal><![CDATA[
      R(a(x,y * K(z,y),x),y * K(z,y),z) = L(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[para(5058(a,1),9995(a,2,2))].">
      <j1 rule="para" parents="5058 9995"/>
    </justification>
  </clause>

  <clause id="10011">
    <literal><![CDATA[
      R(T(x,y * a(z,u,z)),y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(x,y),y,a(z,u,z)) = w
    ]]></literal>
    <justification jstring="[para(9975(a,1),9978(a,1))].">
      <j1 rule="para" parents="9975 9978"/>
    </justification>
  </clause>

  <clause id="10012">
    <literal><![CDATA[
      K(x,T(y / ((K(x,z) * u) * w),v5)) = K(x,T(y / (u * w),v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,8525,a(flip),b,8528,a),flip(a)].">
      <j1 rule="hyper" parents="347 8525 8528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10013">
    <literal><![CDATA[
      K(x,T(y / ((z * T(x,u)) * w),v5)) = K(x,T(y / ((z * x) * w),v5))
    ]]></literal>
    <justification jstring="[para(7699(a,1),10012(a,1,2,1,2,1))].">
      <j1 rule="para" parents="7699 10012"/>
    </justification>
  </clause>

  <clause id="10014">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),y \ z) = x \ T(y,((x \ 1) \ (x \ y)) \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),9200(a,1,2,2,1))].">
      <j1 rule="para" parents="10 9200"/>
    </justification>
  </clause>

  <clause id="10015">
    <literal><![CDATA[
      x \ T(y,((x \ 1) \ (x \ y)) \ z) = x \ T(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6005,a(flip),b,10014,a),flip(a)].">
      <j1 rule="hyper" parents="63 6005 10014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10017">
    <literal><![CDATA[
      K(x,y \ T(z,z \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10015(a,1),8407(a,1,2))].">
      <j1 rule="para" parents="10015 8407"/>
    </justification>
  </clause>

  <clause id="10018">
    <literal><![CDATA[
      T(x,y \ T(z,z \ x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(132,a,10017,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 10017 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10019">
    <literal><![CDATA[
      K(x,y \ ((z \ x) \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(112(a,1),10017(a,1,2,2))].">
      <j1 rule="para" parents="112 10017"/>
    </justification>
  </clause>

  <clause id="10020">
    <literal><![CDATA[
      T(x,y \ (x / z)) = T(x,y \ (z \ x))
    ]]></literal>
    <justification jstring="[para(749(a,1),10018(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="749 10018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10021">
    <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(6322,a,10019,a),flip(a)].">
      <j1 rule="hyper" parents="6322 10019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10022">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),x \ (K(y,z) * u),K(z,y)) = (K(z,y) * (x \ (K(y,z) * u))) \ u
    ]]></literal>
    <justification jstring="[para(9550(a,1),5292(a,1,1))].">
      <j1 rule="para" parents="9550 5292"/>
    </justification>
  </clause>

  <clause id="10023">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = L(T(K(x * y,x),z) \ 1,K(x * y,x),y)
    ]]></literal>
    <justification jstring="[para(7283(a,1),6224(a,1,2,2))].">
      <j1 rule="para" parents="7283 6224"/>
    </justification>
  </clause>

  <clause id="10025">
    <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(8490(a,1),8751(a,1,1))].">
      <j1 rule="para" parents="8490 8751"/>
    </justification>
  </clause>

  <clause id="10026">
    <literal><![CDATA[
      K(x,(y * ((((z \ x) / x) * z) * (1 / z))) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(8273,a,10025,a),flip(a)].">
      <j1 rule="hyper" parents="8273 10025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10027">
    <literal><![CDATA[
      K(x,(y * ((z \ x) / x)) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(1909(a,1),10026(a,1,2,1,2))].">
      <j1 rule="para" parents="1909 10026"/>
    </justification>
  </clause>

  <clause id="10028">
    <literal><![CDATA[
      K(x,(y * (z \ x)) \ (u * x)) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8573,a(flip),b,10027,a)].">
      <j1 rule="hyper" parents="63 8573 10027"/>
    </justification>
  </clause>

  <clause id="10029">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ 1)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,6741,a(flip),b,10028,a),flip(a)].">
      <j1 rule="hyper" parents="63 6741 10028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10030">
    <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(5550(a,1),10029(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5550 10029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10031">
    <literal><![CDATA[
      L(K(x * y,x) * K(z,K(x * y,x)),y,z) = K(z \ (x * (z * y)),x) * K(z,K(x,x * y))
    ]]></literal>
    <justification jstring="[para(7293(a,1),9197(a,2,2))].">
      <j1 rule="para" parents="7293 9197"/>
    </justification>
  </clause>

  <clause id="10032">
    <literal><![CDATA[
      L(K(x,y),z,u) * L(L(K(y,x),z,u),w,v5) = a(v5,w,K(L(x \ 1,z,u) \ 1,y))
    ]]></literal>
    <justification jstring="[para(5664(a,1),9267(a,1,2))].">
      <j1 rule="para" parents="5664 9267"/>
    </justification>
  </clause>

  <clause id="10033">
    <literal><![CDATA[
      L(K(x,y),z,u) * L(L(K(y,x),z,u),w,v5) = a(v5,w,L(K(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(7006(a,1),10032(a,2,3))].">
      <j1 rule="para" parents="7006 10032"/>
    </justification>
  </clause>

  <clause id="10034">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = L(K(x,T(x * y,z)),K(x * y,x),y)
    ]]></literal>
    <justification jstring="[para(7080(a,1),10023(a,2,1))].">
      <j1 rule="para" parents="7080 10023"/>
    </justification>
  </clause>

  <clause id="10035">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,8382,a(flip),b,10034,a),flip(a)].">
      <j1 rule="hyper" parents="347 8382 10034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10038">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) \ (K(x,z) * K(y,K(u,y * K(x,z)))) = K(y,T(y * K(x,z),u))
    ]]></literal>
    <justification jstring="[para(6558(a,2),10035(a,1,1))].">
      <j1 rule="para" parents="6558 10035"/>
    </justification>
  </clause>

  <clause id="10039">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) \ (K(x,z) * 1) = K(y,T(y * K(x,z),x))
    ]]></literal>
    <justification jstring="[para(7886(a,1),10038(a,1,2,2))].">
      <j1 rule="para" parents="7886 10038"/>
    </justification>
  </clause>

  <clause id="10040">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) \ K(x,z) = K(y,T(y * K(x,z),x))
    ]]></literal>
    <justification jstring="[hyper(363,a,10039,a)].">
      <j1 rule="hyper" parents="363 10039"/>
    </justification>
  </clause>

  <clause id="10041">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) * K(z,y) = K(x,T(x * K(z,y),z))
    ]]></literal>
    <justification jstring="[hyper(5286,a,10040,a)].">
      <j1 rule="hyper" parents="5286 10040"/>
    </justification>
  </clause>

  <clause id="10042">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,T(y * K(z,x),z))
    ]]></literal>
    <justification jstring="[para(6559(a,1),10041(a,1,1))].">
      <j1 rule="para" parents="6559 10041"/>
    </justification>
  </clause>

  <clause id="10043">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,7893,a(flip),b,10042,a),flip(a)].">
      <j1 rule="hyper" parents="347 7893 10042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10044">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(x,x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6688,a(flip),b,10043,a)].">
      <j1 rule="hyper" parents="63 6688 10043"/>
    </justification>
  </clause>

  <clause id="10045">
    <literal><![CDATA[
      T(T(x * K(x,x * K(y,z)),u),K(z,y)) = R(T(x,u),K(z,y),x)
    ]]></literal>
    <justification jstring="[para(10044(a,1),5789(a,1,1,1,2))].">
      <j1 rule="para" parents="10044 5789"/>
    </justification>
  </clause>

  <clause id="10046">
    <literal><![CDATA[
      T(T(T(x,x * K(y,z)),u),K(z,y)) = R(T(x,u),K(z,y),x)
    ]]></literal>
    <justification jstring="[para(4929(a,2),10045(a,1,1,1))].">
      <j1 rule="para" parents="4929 10045"/>
    </justification>
  </clause>

  <clause id="10047">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) = T(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7538,a,10046,a),flip(a)].">
      <j1 rule="hyper" parents="7538 10046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10048">
    <literal><![CDATA[
      T(x,x * K(y,z)) \ T(K(z,y) * x,x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(10047(a,1),9742(a,1,1))].">
      <j1 rule="para" parents="10047 9742"/>
    </justification>
  </clause>

  <clause id="10049">
    <literal><![CDATA[
      T(x,x * K((y * z) \ (u * w),w)) \ T(K(w,(y * (w \ z)) \ u) * x,x) = K(w,T((y * (w \ z)) \ u,x))
    ]]></literal>
    <justification jstring="[para(9191(a,1),10048(a,1,1,2,2))].">
      <j1 rule="para" parents="9191 10048"/>
    </justification>
  </clause>

  <clause id="10050">
    <literal><![CDATA[
      L(K(x * y,x) * K(z,K(x * y,x)),y,z) = K(z \ (x * (z * y)),x) * K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8759(a,1),10031(a,2,2))].">
      <j1 rule="para" parents="8759 10031"/>
    </justification>
  </clause>

  <clause id="10051">
    <literal><![CDATA[
      K(x \ (y * (x * z)),y) * K(x,K(y,z)) = L(K(y * z,T(y,x)),z,x)
    ]]></literal>
    <justification jstring="[para(7333(a,1),10050(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7333 10050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10052">
    <literal><![CDATA[
      K(x \ (y * (x * z)),y) * K(x,K(y,z)) = K((x / (x * z)) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,9207,a(flip),b,10051,a),flip(a)].">
      <j1 rule="hyper" parents="347 9207 10051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10053">
    <literal><![CDATA[
      K((x / (x * y)) \ z,z) = K(y * z,z) * K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(9818(a,1),10052(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9818 10052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10054">
    <literal><![CDATA[
      K((x / (x * y)) \ z,z) = K(z * y,z) * K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(7899(a,1),10053(a,2,1))].">
      <j1 rule="para" parents="7899 10053"/>
    </justification>
  </clause>

  <clause id="10056">
    <literal><![CDATA[
      K((x / (x * y)) \ z,z) = K(z * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,8768,a(flip),b,10054,a),flip(a)].">
      <j1 rule="hyper" parents="347 8768 10054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10057">
    <literal><![CDATA[
      K(x * (y \ z),T(x,y)) = K((y / z) \ x,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),10056(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 10056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10058">
    <literal><![CDATA[
      L((x * (1 / x)) / x,1 / (1 / x),y) = L(1 / x,1 / (1 / x),(1 / (1 / x)) \ y)
    ]]></literal>
    <justification jstring="[para(83(a,1),5509(a,1,1)),flip(a)].">
      <j1 rule="para" parents="83 5509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10059">
    <literal><![CDATA[
      L((x * (1 / x)) / x,1 / (1 / x),y) = L(1 / x,1 / (1 / x),((1 / x) \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3943,a(flip),b,10058,a),flip(a)].">
      <j1 rule="hyper" parents="347 3943 10058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10061">
    <literal><![CDATA[
      L((x * (1 / x)) / x,1 / (1 / x),y) = L(1 / x,1 / (1 / x),x \ y)
    ]]></literal>
    <justification jstring="[para(83(a,1),10059(a,2,3,1))].">
      <j1 rule="para" parents="83 10059"/>
    </justification>
  </clause>

  <clause id="10062">
    <literal><![CDATA[
      L((x * (1 / x)) / x,1 / (1 / x),y) = L(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3207,a(flip),b,10061,a),flip(a)].">
      <j1 rule="hyper" parents="347 3207 10061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10063">
    <literal><![CDATA[
      L(1 / L(x,x,x),1 / (1 / x),y) = L(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(3285(a,1),10062(a,1,1))].">
      <j1 rule="para" parents="3285 10062"/>
    </justification>
  </clause>

  <clause id="10064">
    <literal><![CDATA[
      L(1 / L(x,x,x),x,y) = L(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(3523,a,10063,a)].">
      <j1 rule="hyper" parents="3523 10063"/>
    </justification>
  </clause>

  <clause id="10065">
    <literal><![CDATA[
      L(1 / x,x,x \ 1) = 1 / L(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(402,a,10063,a),flip(a)].">
      <j1 rule="hyper" parents="402 10063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10066">
    <literal><![CDATA[
      R(x,y,K(y,z)) * (R(y,u,w) * K(y,z)) = (x * R(x \ (x * y),u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(5950(a,1),5965(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5950 5965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10067">
    <literal><![CDATA[
      R(x,y,K(y,z)) * (R(y,u,w) * K(y,z)) = (x * R(y,u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),10066(a,2,1,2,1))].">
      <j1 rule="para" parents="9 10066"/>
    </justification>
  </clause>

  <clause id="10068">
    <literal><![CDATA[
      (x * R(y,z,u)) * K(y,w) = x * (R(y,z,u) * K(y,w))
    ]]></literal>
    <justification jstring="[para(5950(a,1),10067(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5950 10067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10069">
    <literal><![CDATA[
      K(x,(y \ z) \ R(x,u,w)) = K(x,z \ (y * R(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(6481,a,10068,a),flip(a)].">
      <j1 rule="hyper" parents="6481 10068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10071">
    <literal><![CDATA[
      a(x,R(y,z,u),K(y,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(127,a,10068,a(flip),b,86,a),flip(a)].">
      <j1 rule="hyper" parents="127 10068 86"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10073">
    <literal><![CDATA[
      R(x,x \ 1,y \ R(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(6378,a,8207,a)].">
      <j1 rule="hyper" parents="6378 8207"/>
    </justification>
  </clause>

  <clause id="10074">
    <literal><![CDATA[
      R(x,x \ 1,a(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(8336(a,1),10073(a,1,3))].">
      <j1 rule="para" parents="8336 10073"/>
    </justification>
  </clause>

  <clause id="10075">
    <literal><![CDATA[
      (x \ 1) * a(y,x \ 1,y) = x \ a(y,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(10074(a,1),448(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10074 448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10076">
    <literal><![CDATA[
      x * (T(y * (x \ 1),y) / y) = a(y,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,8346,a,b,10075,a(flip))].">
      <j1 rule="hyper" parents="134 8346 10075"/>
    </justification>
  </clause>

  <clause id="10077">
    <literal><![CDATA[
      T(x \ a(y,x \ 1,y),y) = y \ T(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(10075(a,1),8361(a,1,1))].">
      <j1 rule="para" parents="10075 8361"/>
    </justification>
  </clause>

  <clause id="10078">
    <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(10077(a,1),2148(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10077 2148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10079">
    <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(347,a,8268,a(flip),b,6566,a),flip(a)].">
      <j1 rule="hyper" parents="347 8268 6566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10080">
    <literal><![CDATA[
      L(K(x,T(y,L(y,z,u))),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2005(a,1),10079(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2005 10079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10081">
    <literal><![CDATA[
      L(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(197(a,1),10080(a,1,1,2))].">
      <j1 rule="para" parents="197 10080"/>
    </justification>
  </clause>

  <clause id="10082">
    <literal><![CDATA[
      a(x,L(y,z,u),K(w,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,10081,a,b,9239,a),flip(a)].">
      <j1 rule="hyper" parents="129 10081 9239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10083">
    <literal><![CDATA[
      K((x \ 1) * L(y,z,u),y) = K(x \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7788,a(flip),b,10081,a)].">
      <j1 rule="hyper" parents="63 7788 10081"/>
    </justification>
  </clause>

  <clause id="10084">
    <literal><![CDATA[
      K((x \ y) \ L(z,u,w),z) = K(y \ (x * L(z,u,w)),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7022,a(flip),b,10081,a),flip(a)].">
      <j1 rule="hyper" parents="63 7022 10081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10086">
    <literal><![CDATA[
      L(K(x,y),L(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(189,a,9240,a,b,10082,a(flip))].">
      <j1 rule="hyper" parents="189 9240 10082"/>
    </justification>
  </clause>

  <clause id="10087">
    <literal><![CDATA[
      (x * L(y,z,u)) * K(y,w) = x * (L(y,z,u) * K(y,w))
    ]]></literal>
    <justification jstring="[hyper(134,a,10086,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 10086 18"/>
    </justification>
  </clause>

  <clause id="10088">
    <literal><![CDATA[
      R(T(K(x,y),R(K(y,x),z,u) * w),z,u) \ w = w / (R(K(y,x),z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(8735(a,1),6702(a,1,1))].">
      <j1 rule="para" parents="8735 6702"/>
    </justification>
  </clause>

  <clause id="10089">
    <literal><![CDATA[
      R(T(K(x,y),R(K(y,x),z,u) * w),z,u) \ w = w / R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(6701(a,1),10088(a,2,2))].">
      <j1 rule="para" parents="6701 10088"/>
    </justification>
  </clause>

  <clause id="10090">
    <literal><![CDATA[
      R(T(K(x,y),z),u,w) \ z = z / R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(9015(a,1),10089(a,1,1,1))].">
      <j1 rule="para" parents="9015 10089"/>
    </justification>
  </clause>

  <clause id="10091">
    <literal><![CDATA[
      x / (x / R(K(y,z),u,w)) = R(T(K(y,z),x),u,w)
    ]]></literal>
    <justification jstring="[hyper(222,a,10090,a)].">
      <j1 rule="hyper" parents="222 10090"/>
    </justification>
  </clause>

  <clause id="10093">
    <literal><![CDATA[
      (R(K(x,y),z,u) \ w) \ w = R(T(K(x,y),w),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8991,a(flip),b,10091,a)].">
      <j1 rule="hyper" parents="63 8991 10091"/>
    </justification>
  </clause>

  <clause id="10094">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(T(K(y,x),z * u),z,u)
    ]]></literal>
    <justification jstring="[para(6704(a,1),10093(a,1,1))].">
      <j1 rule="para" parents="6704 10093"/>
    </justification>
  </clause>

  <clause id="10095">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(K(y,T(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(7091(a,2),10094(a,2,1))].">
      <j1 rule="para" parents="7091 10094"/>
    </justification>
  </clause>

  <clause id="10096">
    <literal><![CDATA[
      ((K(x,T(y,z)) * L(x,u,w)) * z) \ (L(x,u,w) * z) = R(K(y,L(x,z,L(x,u,w))),L(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(7747(a,1),10095(a,2,1))].">
      <j1 rule="para" parents="7747 10095"/>
    </justification>
  </clause>

  <clause id="10097">
    <literal><![CDATA[
      T(T(x,y) * L(x \ (z / (x \ 1)),u,w),K(x,y)) = (L(z,u,w) / (x \ 1)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6665(a,1),6922(a,1,1))].">
      <j1 rule="para" parents="6665 6922"/>
    </justification>
  </clause>

  <clause id="10098">
    <literal><![CDATA[
      x * (L(x \ (y / (x \ 1)),z,u) * K(x,w)) = (L(y,z,u) / (x \ 1)) * K(x,w)
    ]]></literal>
    <justification jstring="[hyper(6870,a,10097,a)].">
      <j1 rule="hyper" parents="6870 10097"/>
    </justification>
  </clause>

  <clause id="10099">
    <literal><![CDATA[
      (L(x,y,z) / (u \ 1)) * K(u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L((x / (u \ 1)) / u,y,z) * T(u,w) = v5
    ]]></literal>
    <justification jstring="[para(10098(a,1),6776(a,1))].">
      <j1 rule="para" parents="10098 6776"/>
    </justification>
  </clause>

  <clause id="10100">
    <literal><![CDATA[
      L((x / (y \ 1)) / y,z,u) * T(y,w) = L(x,z,u) / (T(y,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(10099,a,6531,a)].">
      <j1 rule="hyper" parents="10099 6531"/>
    </justification>
  </clause>

  <clause id="10101">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[para(83(a,1),6985(a,2,2,2,1,1,2))].">
      <j1 rule="para" parents="83 6985"/>
    </justification>
  </clause>

  <clause id="10102">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * u = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(644,a,10101,a)].">
      <j1 rule="hyper" parents="644 10101"/>
    </justification>
  </clause>

  <clause id="10105">
    <literal><![CDATA[
      ((x * y) * (z * (((x * y) \ u) / z))) / u = K(z,u / ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(10102(a,1),6969(a,1,1))].">
      <j1 rule="para" parents="10102 6969"/>
    </justification>
  </clause>

  <clause id="10106">
    <literal><![CDATA[
      K(x,y / ((z * u) * x)) = K(x,y / ((z * x) * u))
    ]]></literal>
    <justification jstring="[hyper(6553,a,10105,a)].">
      <j1 rule="hyper" parents="6553 10105"/>
    </justification>
  </clause>

  <clause id="10107">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8442,a(flip),b,10106,a),flip(a)].">
      <j1 rule="hyper" parents="63 8442 10106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10108">
    <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(111(a,1),10106(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 10106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10109">
    <literal><![CDATA[
      K(x,R(y / (z * u),z * u,x)) = K(x,(y * x) / ((z * x) * u))
    ]]></literal>
    <justification jstring="[para(108(a,2),10106(a,1,2))].">
      <j1 rule="para" parents="108 10106"/>
    </justification>
  </clause>

  <clause id="10110">
    <literal><![CDATA[
      K(x,((y * x) * z) / (x * (y * (y \ z)))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[hyper(9402,a,10107,a),flip(a)].">
      <j1 rule="hyper" parents="9402 10107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10111">
    <literal><![CDATA[
      K(x,y / ((x * z) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8452,a(flip),b,10107,a)].">
      <j1 rule="hyper" parents="63 8452 10107"/>
    </justification>
  </clause>

  <clause id="10112">
    <literal><![CDATA[
      x * K(x,y / (x * (z * u))) = T(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[hyper(134,a,10111,a(flip),b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 10111 4924"/>
    </justification>
  </clause>

  <clause id="10113">
    <literal><![CDATA[
      K(x,(y * x) / ((z * x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7835,a(flip),b,10109,a),flip(a)].">
      <j1 rule="hyper" parents="63 7835 10109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10115">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,((y * x) * z) / (x * z))
    ]]></literal>
    <justification jstring="[para(10(a,1),10110(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 10110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10116">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[para(20(a,2),10115(a,2,2))].">
      <j1 rule="para" parents="20 10115"/>
    </justification>
  </clause>

  <clause id="10118">
    <literal><![CDATA[
      K(x,R(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9857,a,10116,a),flip(a)].">
      <j1 rule="hyper" parents="9857 10116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10119">
    <literal><![CDATA[
      R(K(x,y),z,T(y * x,z)) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9396,a,b,10116,a)].">
      <j1 rule="hyper" parents="63 9396 10116"/>
    </justification>
  </clause>

  <clause id="10120">
    <literal><![CDATA[
      K(x,R(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(10116(a,1),9857(a,1))].">
      <j1 rule="para" parents="10116 9857"/>
    </justification>
  </clause>

  <clause id="10122">
    <literal><![CDATA[
      T(x,R(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,10118,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 10118 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10123">
    <literal><![CDATA[
      K(R(x,y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8644,a,b,10118,a)].">
      <j1 rule="hyper" parents="63 8644 10118"/>
    </justification>
  </clause>

  <clause id="10124">
    <literal><![CDATA[
      R(K(x \ y,x),y,z) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6713,a(flip),b,10118,a)].">
      <j1 rule="hyper" parents="63 6713 10118"/>
    </justification>
  </clause>

  <clause id="10126">
    <literal><![CDATA[
      K(x,R(R(y,x,z),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(31(a,1),10118(a,1,2))].">
      <j1 rule="para" parents="31 10118"/>
    </justification>
  </clause>

  <clause id="10129">
    <literal><![CDATA[
      T(R(x,y,z),(u * (y * z)) / ((x * y) * z)) = T(R(x,y,z),u / R(x,y,z))
    ]]></literal>
    <justification jstring="[para(611(a,1),10122(a,1,2))].">
      <j1 rule="para" parents="611 10122"/>
    </justification>
  </clause>

  <clause id="10131">
    <literal><![CDATA[
      K(x,y) * ((x * y) * z) = (T(x,y) * y) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,10123,a(flip),b,5845,a)].">
      <j1 rule="hyper" parents="133 10123 5845"/>
    </justification>
  </clause>

  <clause id="10132">
    <literal><![CDATA[
      K(x,y) / R(x,y,y \ 1) = 1 / ((y * x) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(10123(a,1),5367(a,1,1))].">
      <j1 rule="para" parents="10123 5367"/>
    </justification>
  </clause>

  <clause id="10133">
    <literal><![CDATA[
      K(R(x,y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8644(a,2),10120(a,1))].">
      <j1 rule="para" parents="8644 10120"/>
    </justification>
  </clause>

  <clause id="10134">
    <literal><![CDATA[
      K(x,y / (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ (y / z)) = u
    ]]></literal>
    <justification jstring="[para(9071(a,1),10120(a,1))].">
      <j1 rule="para" parents="9071 10120"/>
    </justification>
  </clause>

  <clause id="10135">
    <literal><![CDATA[
      K(x / (y * z),y) = K(y \ (x / z),y)
    ]]></literal>
    <justification jstring="[hyper(5841,a,10124,a)].">
      <j1 rule="hyper" parents="5841 10124"/>
    </justification>
  </clause>

  <clause id="10136">
    <literal><![CDATA[
      K((x \ y) / z,x) = K(x \ (y / z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8131,a,b,10135,a)].">
      <j1 rule="hyper" parents="63 8131 10135"/>
    </justification>
  </clause>

  <clause id="10137">
    <literal><![CDATA[
      K(x \ (y / z),x) * z = z * K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(10136(a,1),7089(a,1,1))].">
      <j1 rule="para" parents="10136 7089"/>
    </justification>
  </clause>

  <clause id="10138">
    <literal><![CDATA[
      R(K(x,R(y,x,z)),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6718,a,b,10126,a)].">
      <j1 rule="hyper" parents="63 6718 10126"/>
    </justification>
  </clause>

  <clause id="10139">
    <literal><![CDATA[
      K(x,R(y,x,z)) * ((y * x) * z) = (K(x,y) * z) * T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,10119,a(flip),b,265,a)].">
      <j1 rule="hyper" parents="133 10119 265"/>
    </justification>
  </clause>

  <clause id="10140">
    <literal><![CDATA[
      ((x * y) / x) \ ((y * x) * z) = y \ ((T(y,x) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(128,a,10131,a(flip),b,4941,a),flip(a)].">
      <j1 rule="hyper" parents="128 10131 4941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10141">
    <literal><![CDATA[
      L(x,y * z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(34,a,5234,a,b,10131,a(flip))].">
      <j1 rule="hyper" parents="34 5234 10131"/>
    </justification>
  </clause>

  <clause id="10142">
    <literal><![CDATA[
      L(x,y,T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(6643,a,10141,a)].">
      <j1 rule="hyper" parents="6643 10141"/>
    </justification>
  </clause>

  <clause id="10143">
    <literal><![CDATA[
      (K(x,y) * (x * y)) \ z = (x * y) \ (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(5290,a,10141,a),flip(a)].">
      <j1 rule="hyper" parents="5290 10141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10144">
    <literal><![CDATA[
      L(x,y,K(z,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),10141(a,1,2))].">
      <j1 rule="para" parents="10 10141"/>
    </justification>
  </clause>

  <clause id="10145">
    <literal><![CDATA[
      K(x,x \ y) * (y * z) = (x * (y / x)) * z
    ]]></literal>
    <justification jstring="[hyper(134,a,10144,a(flip),b,5296,a),flip(a)].">
      <j1 rule="hyper" parents="134 10144 5296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10146">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(5096(a,1),10144(a,1,3))].">
      <j1 rule="para" parents="5096 10144"/>
    </justification>
  </clause>

  <clause id="10147">
    <literal><![CDATA[
      L(x,y,z / y) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6958,a(flip),b,10146,a)].">
      <j1 rule="hyper" parents="63 6958 10146"/>
    </justification>
  </clause>

  <clause id="10148">
    <literal><![CDATA[
      L(x,y,z) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,6957,a(flip),b,10146,a),flip(a)].">
      <j1 rule="hyper" parents="63 6957 10146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10149">
    <literal><![CDATA[
      (x * (T(y,x) * z)) / L(z,y,x) = y * x
    ]]></literal>
    <justification jstring="[hyper(220,a,10146,a(flip),b,6957,a(flip))].">
      <j1 rule="hyper" parents="220 10146 6957"/>
    </justification>
  </clause>

  <clause id="10150">
    <literal><![CDATA[
      (x * y) * L(z,x,y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(134,a,10146,a(flip),b,6957,a(flip))].">
      <j1 rule="hyper" parents="134 10146 6957"/>
    </justification>
  </clause>

  <clause id="10151">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) \ z) = L(x,y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(2111,a,10142,a)].">
      <j1 rule="hyper" parents="2111 10142"/>
    </justification>
  </clause>

  <clause id="10152">
    <literal><![CDATA[
      L(x,y,y \ (z * y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(22(a,1),10142(a,1,3))].">
      <j1 rule="para" parents="22 10142"/>
    </justification>
  </clause>

  <clause id="10154">
    <literal><![CDATA[
      L(x,x,x \ y) = (y * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,3299,a(flip),b,10147,a),flip(a)].">
      <j1 rule="hyper" parents="63 3299 10147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10155">
    <literal><![CDATA[
      L(T(x,y),y,y \ z) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,858,a(flip),b,10147,a),flip(a)].">
      <j1 rule="hyper" parents="63 858 10147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10156">
    <literal><![CDATA[
      L(x \ y,x,x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,565,a(flip),b,10147,a),flip(a)].">
      <j1 rule="hyper" parents="63 565 10147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10157">
    <literal><![CDATA[
      x * L(y,z,z \ x) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[para(10147(a,1),532(a,1,2))].">
      <j1 rule="para" parents="10147 532"/>
    </justification>
  </clause>

  <clause id="10159">
    <literal><![CDATA[
      x * L(y,z,z \ x) != u
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * y) = u
    ]]></literal>
    <justification jstring="[para(10147(a,1),928(a,1,2))].">
      <j1 rule="para" parents="10147 928"/>
    </justification>
  </clause>

  <clause id="10160">
    <literal><![CDATA[
      (x * T(y,(x / z) * z)) / a(x / z,z,T(y,(x / z) * z)) = L(y,z,z \ x) * ((x / z) * z)
    ]]></literal>
    <justification jstring="[para(10147(a,1),1075(a,2,1))].">
      <j1 rule="para" parents="10147 1075"/>
    </justification>
  </clause>

  <clause id="10161">
    <literal><![CDATA[
      L(1 / x,x,y * x) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5506,a(flip),b,10152,a)].">
      <j1 rule="hyper" parents="63 5506 10152"/>
    </justification>
  </clause>

  <clause id="10162">
    <literal><![CDATA[
      ((x * y) * (x \ 1)) \ (x * y) = L(x,x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),10154(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9 10154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10163">
    <literal><![CDATA[
      L(x * y,x * y,L(y \ 1,y,x)) = (x * ((x * y) \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(244(a,2),10154(a,1,3))].">
      <j1 rule="para" parents="244 10154"/>
    </justification>
  </clause>

  <clause id="10164">
    <literal><![CDATA[
      L(x,x,x \ y) \ y = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[para(10154(a,2),6305(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10154 6305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10165">
    <literal><![CDATA[
      L(x,T(y,z),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,262,a(flip),b,10148,a)].">
      <j1 rule="hyper" parents="347 262 10148"/>
    </justification>
  </clause>

  <clause id="10167">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,K(y,x),z) = z * (T(K(x,y),z) * u)
    ]]></literal>
    <justification jstring="[hyper(134,a,5181,a,b,10148,a(flip))].">
      <j1 rule="hyper" parents="134 5181 10148"/>
    </justification>
  </clause>

  <clause id="10168">
    <literal><![CDATA[
      (x * y) * L(L(z,x,y),u,w) = y * (T(x,y) * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(134,a,30,a,b,10148,a(flip))].">
      <j1 rule="hyper" parents="134 30 10148"/>
    </justification>
  </clause>

  <clause id="10169">
    <literal><![CDATA[
      L(T(x,y) \ z,x,y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),10148(a,2,2,2))].">
      <j1 rule="para" parents="10 10148"/>
    </justification>
  </clause>

  <clause id="10170">
    <literal><![CDATA[
      (x * y) * L(z,x,y) != u
    ]]></literal>
    <literal><![CDATA[
      y * (T(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(10148(a,2),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="10148 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10171">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * (T(y,z) * u))) = L(L(u,y,z),y * z,x)
    ]]></literal>
    <justification jstring="[para(10148(a,2),99(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10148 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10172">
    <literal><![CDATA[
      L(x,y,z) = (y * z) \ (z * (y * (K(y,z) * x)))
    ]]></literal>
    <justification jstring="[para(4943(a,2),10148(a,2,2,2))].">
      <j1 rule="para" parents="4943 10148"/>
    </justification>
  </clause>

  <clause id="10173">
    <literal><![CDATA[
      (x * y) \ (y * (x * z)) = L(K(y,x) * z,x,y)
    ]]></literal>
    <justification jstring="[para(5213(a,1),10148(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5213 10148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10174">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * (K(x,T(y,z)) * u)) = L(u,K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7091(a,2),10148(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7091 10148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10175">
    <literal><![CDATA[
      L(x,T(y,z),z) = L(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,10142,a,b,10165,a),flip(a)].">
      <j1 rule="hyper" parents="347 10142 10165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10176">
    <literal><![CDATA[
      (T(x,y) * (1 / y)) \ (x * z) = L((1 / T(y,x)) \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6589,a(flip),b,10165,a)].">
      <j1 rule="hyper" parents="63 6589 10165"/>
    </justification>
  </clause>

  <clause id="10177">
    <literal><![CDATA[
      L(x,y / z,z) = L(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5474,a(flip),b,10165,a)].">
      <j1 rule="hyper" parents="63 5474 10165"/>
    </justification>
  </clause>

  <clause id="10178">
    <literal><![CDATA[
      L(x,y \ (z * y),y) = L(x,z,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),10165(a,1,2))].">
      <j1 rule="para" parents="22 10165"/>
    </justification>
  </clause>

  <clause id="10179">
    <literal><![CDATA[
      L(x,(y \ z) \ z,y \ z) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(112(a,1),10165(a,1,2))].">
      <j1 rule="para" parents="112 10165"/>
    </justification>
  </clause>

  <clause id="10180">
    <literal><![CDATA[
      L(T(x,y) \ z,x,y) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) \ (y * z) = u
    ]]></literal>
    <justification jstring="[para(10165(a,1),909(a,1))].">
      <j1 rule="para" parents="10165 909"/>
    </justification>
  </clause>

  <clause id="10181">
    <literal><![CDATA[
      L(x,y \ z,T(y,y \ z)) = L(x,z / y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,5474,a(flip),b,10175,a),flip(a)].">
      <j1 rule="hyper" parents="63 5474 10175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10182">
    <literal><![CDATA[
      (x * (y / x)) * L(z,x \ y,x) = x * ((y / x) * z)
    ]]></literal>
    <justification jstring="[hyper(134,a,10177,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 10177 18"/>
    </justification>
  </clause>

  <clause id="10184">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ u,(y \ z) \ z) = L(x,u / T(y,y \ z),(y \ z) \ z)
    ]]></literal>
    <justification jstring="[para(394(a,1),10178(a,1,2,2))].">
      <j1 rule="para" parents="394 10178"/>
    </justification>
  </clause>

  <clause id="10185">
    <literal><![CDATA[
      (x * y) \ (y * (T(x,y) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,x,y) = u
    ]]></literal>
    <justification jstring="[para(10149(a,1),359(a,1,1))].">
      <j1 rule="para" parents="10149 359"/>
    </justification>
  </clause>

  <clause id="10186">
    <literal><![CDATA[
      ((x * y) / z) * L(z,x,y) != u
    ]]></literal>
    <literal><![CDATA[
      (y * (T(x,y) * z)) / z = u
    ]]></literal>
    <justification jstring="[para(10149(a,1),2017(a,1,1,1))].">
      <j1 rule="para" parents="10149 2017"/>
    </justification>
  </clause>

  <clause id="10187">
    <literal><![CDATA[
      x * (y * L(y \ (x \ z),x,y)) = y * (T(x,y) * ((x * y) \ z))
    ]]></literal>
    <justification jstring="[hyper(1196,a,10150,a)].">
      <j1 rule="hyper" parents="1196 10150"/>
    </justification>
  </clause>

  <clause id="10188">
    <literal><![CDATA[
      x * (T(y,x) * T(z,y * x)) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(436,a,10150,a),flip(a)].">
      <j1 rule="hyper" parents="436 10150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10189">
    <literal><![CDATA[
      R(x,y,(z * u) \ L(z * u,z,u)) = R(x,y,u * (T(z,u) * (z * u)))
    ]]></literal>
    <justification jstring="[para(10150(a,1),3975(a,2,3))].">
      <j1 rule="para" parents="10150 3975"/>
    </justification>
  </clause>

  <clause id="10190">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,x \ u) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,3965,a,b,10156,a),flip(a)].">
      <j1 rule="hyper" parents="347 3965 10156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10191">
    <literal><![CDATA[
      ((x \ y) * x) \ ((x \ y) * z) = y \ ((y / x) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,99,a(flip),b,10156,a)].">
      <j1 rule="hyper" parents="63 99 10156"/>
    </justification>
  </clause>

  <clause id="10192">
    <literal><![CDATA[
      x \ ((x / y) * (y * z)) = L(z,y,y \ x)
    ]]></literal>
    <justification jstring="[para(9(a,1),10156(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 10156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10193">
    <literal><![CDATA[
      (x * y) \ (((x * y) / x) * z) = L(x \ z,x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),10156(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9 10156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10194">
    <literal><![CDATA[
      L(L(x \ y,x,x \ (z \ 1)),z,z) = z * (((z \ 1) / x) * y)
    ]]></literal>
    <justification jstring="[para(10156(a,2),3192(a,1,1))].">
      <j1 rule="para" parents="10156 3192"/>
    </justification>
  </clause>

  <clause id="10195">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,x \ u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) = w
    ]]></literal>
    <justification jstring="[para(10156(a,2),3968(a,1))].">
      <j1 rule="para" parents="10156 3968"/>
    </justification>
  </clause>

  <clause id="10196">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),T(x,y) \ y) = y \ ((T(y,x) / x) * z)
    ]]></literal>
    <justification jstring="[para(4279(a,2),10156(a,2,2,1))].">
      <j1 rule="para" parents="4279 10156"/>
    </justification>
  </clause>

  <clause id="10197">
    <literal><![CDATA[
      L((x * K(y,z)) \ u,x * K(y,z),K(z,y)) = x \ ((x / (x * K(y,z))) * u)
    ]]></literal>
    <justification jstring="[para(6123(a,1),10156(a,1,3))].">
      <j1 rule="para" parents="6123 10156"/>
    </justification>
  </clause>

  <clause id="10198">
    <literal><![CDATA[
      (x / y) * L(y,z,z \ x) = ((x / z) * (z * y)) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,10157,a(flip),b,1999,a),flip(a)].">
      <j1 rule="hyper" parents="131 10157 1999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10199">
    <literal><![CDATA[
      ((x / y) * (y * x)) / x = L(x,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(131,a,10157,a(flip),b,274,a)].">
      <j1 rule="hyper" parents="131 10157 274"/>
    </justification>
  </clause>

  <clause id="10200">
    <literal><![CDATA[
      ((x * y) * (x \ 1)) \ (x * y) = L(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3188,a,b,10162,a),flip(a)].">
      <j1 rule="hyper" parents="347 3188 10162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10201">
    <literal><![CDATA[
      L(T(x,x \ 1),x,y) = L(x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(39,a,6391,a,b,10164,a)].">
      <j1 rule="hyper" parents="39 6391 10164"/>
    </justification>
  </clause>

  <clause id="10202">
    <literal><![CDATA[
      L(x,x,x \ y) \ x = (L(x,x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(10201(a,1),9331(a,1,1))].">
      <j1 rule="para" parents="10201 9331"/>
    </justification>
  </clause>

  <clause id="10203">
    <literal><![CDATA[
      1 / L(x,x,x \ y) = L(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(10201(a,1),9695(a,1,2))].">
      <j1 rule="para" parents="10201 9695"/>
    </justification>
  </clause>

  <clause id="10204">
    <literal><![CDATA[
      L(L(x,x,x),x,x \ y) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(4663,a,10203,a(flip))].">
      <j1 rule="hyper" parents="4663 10203"/>
    </justification>
  </clause>

  <clause id="10205">
    <literal><![CDATA[
      L(x,x,x * y) \ 1 = 1 / L(x,x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),10203(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="9 10203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10207">
    <literal><![CDATA[
      L(L(x,x,x),x,y) = L(x,x,x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),10204(a,1,3))].">
      <j1 rule="para" parents="9 10204"/>
    </justification>
  </clause>

  <clause id="10208">
    <literal><![CDATA[
      1 / (x * (L(x,1 / x,(1 / x) * y) \ x)) = L(L(1 / x,1 / x,1 / x),1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3646,a,b,10207,a)].">
      <j1 rule="hyper" parents="347 3646 10207"/>
    </justification>
  </clause>

  <clause id="10209">
    <literal><![CDATA[
      ((x * x) * y) \ (y * z) = T(x * x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(550,a,10169,a),flip(a)].">
      <j1 rule="hyper" parents="550 10169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10210">
    <literal><![CDATA[
      L(a(x,x,x \ (x \ T(y,z))),y,z) = (y * z) \ (z * ((x \ 1) \ (x \ T(y,z))))
    ]]></literal>
    <justification jstring="[para(1175(a,2),10169(a,1,1))].">
      <j1 rule="para" parents="1175 10169"/>
    </justification>
  </clause>

  <clause id="10211">
    <literal><![CDATA[
      (x * x) \ ((T(y,z) \ u) * L((T(y,z) \ u) \ (x * x),y,z)) = (T(y,z) \ u) \ ((y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[para(10169(a,1),4058(a,2,2))].">
      <j1 rule="para" parents="10169 4058"/>
    </justification>
  </clause>

  <clause id="10212">
    <literal><![CDATA[
      L(((x \ y) \ y) \ z,x,x \ y) = y \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(651,a,10179,a),flip(a)].">
      <j1 rule="hyper" parents="651 10179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10213">
    <literal><![CDATA[
      L(T(((x \ y) \ y) \ z,u),x,x \ y) = T(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,891,a(flip),b,10179,a),flip(a)].">
      <j1 rule="hyper" parents="63 891 10179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10214">
    <literal><![CDATA[
      T(x * x,y) \ T(z,y) = ((x * x) * y) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,250,a(flip),b,10209,a),flip(a)].">
      <j1 rule="hyper" parents="63 250 10209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10215">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(10134,a,10106,a),flip(a)].">
      <j1 rule="hyper" parents="10134 10106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10216">
    <literal><![CDATA[
      K(x,y / (x * z)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(10134,a,8442,a),flip(a)].">
      <j1 rule="hyper" parents="10134 8442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10217">
    <literal><![CDATA[
      K(x,x \ ((x * y) / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(10134,a,8218,a)].">
      <j1 rule="hyper" parents="10134 8218"/>
    </justification>
  </clause>

  <clause id="10218">
    <literal><![CDATA[
      x * K(x,x \ (y / (z * u))) = T(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(10216(a,1),10112(a,1,2))].">
      <j1 rule="para" parents="10216 10112"/>
    </justification>
  </clause>

  <clause id="10219">
    <literal><![CDATA[
      K(x,x \ ((y \ 1) \ (x * z))) = K(x,z / T(y \ 1,y * (x * z)))
    ]]></literal>
    <justification jstring="[para(4417(a,1),10217(a,1,2,2))].">
      <j1 rule="para" parents="4417 10217"/>
    </justification>
  </clause>

  <clause id="10220">
    <literal><![CDATA[
      ((x * y) \ y) * (x * x) = L(K(y,x) * x,x,y)
    ]]></literal>
    <justification jstring="[hyper(731,a,10173,a)].">
      <j1 rule="hyper" parents="731 10173"/>
    </justification>
  </clause>

  <clause id="10221">
    <literal><![CDATA[
      (x * (y * z)) / T(y * x,(y * x) \ (x * (y * z))) = L(K(x,y) * z,y,x)
    ]]></literal>
    <justification jstring="[hyper(658,a,10173,a)].">
      <j1 rule="hyper" parents="658 10173"/>
    </justification>
  </clause>

  <clause id="10222">
    <literal><![CDATA[
      L((x \ 1) \ 1,x \ 1,x * y) = L(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(443,a,10200,a)].">
      <j1 rule="hyper" parents="443 10200"/>
    </justification>
  </clause>

  <clause id="10223">
    <literal><![CDATA[
      ((x * y) \ y) * (x * x) = L(x * K(y,x),x,y)
    ]]></literal>
    <justification jstring="[para(3025(a,1),10220(a,2,1))].">
      <j1 rule="para" parents="3025 10220"/>
    </justification>
  </clause>

  <clause id="10224">
    <literal><![CDATA[
      L(x * K(x \ y,x),x,x \ y) = (y \ (x \ y)) * (x * x)
    ]]></literal>
    <justification jstring="[para(10(a,1),10223(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 10223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10225">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(7174,a,10137,a)].">
      <j1 rule="hyper" parents="7174 10137"/>
    </justification>
  </clause>

  <clause id="10226">
    <literal><![CDATA[
      K(x \ (y / z),T(x,y)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9093,a(flip),b,10225,a)].">
      <j1 rule="hyper" parents="63 9093 10225"/>
    </justification>
  </clause>

  <clause id="10227">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = (u * K(z \ (x \ y),x)) \ u
    ]]></literal>
    <justification jstring="[para(10226(a,1),6123(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10226 6123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10228">
    <literal><![CDATA[
      (x * y) \ (K(y,x) * z) = (T(x,y) * y) \ z
    ]]></literal>
    <justification jstring="[para(4974(a,1),10143(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4974 10143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10229">
    <literal><![CDATA[
      x * (y * L(z,x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      y * (T(x,y) * L(z,y,x)) = u
    ]]></literal>
    <justification jstring="[para(474(a,1),10170(a,1))].">
      <j1 rule="para" parents="474 10170"/>
    </justification>
  </clause>

  <clause id="10230">
    <literal><![CDATA[
      L(K(x,y) * (y \ z),y,x) != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(5209(a,2),10180(a,1,1))].">
      <j1 rule="para" parents="5209 10180"/>
    </justification>
  </clause>

  <clause id="10231">
    <literal><![CDATA[
      L(x,T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(262(a,1),10185(a,1))].">
      <j1 rule="para" parents="262 10185"/>
    </justification>
  </clause>

  <clause id="10232">
    <literal><![CDATA[
      L(x,y,z * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(6636(a,1),10185(a,1))].">
      <j1 rule="para" parents="6636 10185"/>
    </justification>
  </clause>

  <clause id="10233">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * (K(x,T(y,z)) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,K(x,y),z) = w
    ]]></literal>
    <justification jstring="[para(7091(a,2),10185(a,1,2,2,1))].">
      <j1 rule="para" parents="7091 10185"/>
    </justification>
  </clause>

  <clause id="10234">
    <literal><![CDATA[
      L(x,y \ (z * y),y) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,z,y) = u
    ]]></literal>
    <justification jstring="[para(22(a,1),10231(a,1,2))].">
      <j1 rule="para" parents="22 10231"/>
    </justification>
  </clause>

  <clause id="10235">
    <literal><![CDATA[
      L(x,T(y,z \ u),(u \ z) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(u \ z) \ 1) = w
    ]]></literal>
    <justification jstring="[para(6258(a,1),10231(a,1,2))].">
      <j1 rule="para" parents="6258 10231"/>
    </justification>
  </clause>

  <clause id="10236">
    <literal><![CDATA[
      L(x,y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(10175(a,1),10231(a,1))].">
      <j1 rule="para" parents="10175 10231"/>
    </justification>
  </clause>

  <clause id="10237">
    <literal><![CDATA[
      L(x,y,y \ (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(22(a,1),10236(a,1,3))].">
      <j1 rule="para" parents="22 10236"/>
    </justification>
  </clause>

  <clause id="10238">
    <literal><![CDATA[
      L(x,y,z \ K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(3056(a,1),10232(a,1,3))].">
      <j1 rule="para" parents="3056 10232"/>
    </justification>
  </clause>

  <clause id="10239">
    <literal><![CDATA[
      L(x,y,z / y) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,y \ z) = u
    ]]></literal>
    <justification jstring="[para(4990(a,1),10232(a,1,3))].">
      <j1 rule="para" parents="4990 10232"/>
    </justification>
  </clause>

  <clause id="10240">
    <literal><![CDATA[
      (x \ y) * ((y / x) \ (y * z)) = ((x \ y) * x) * z
    ]]></literal>
    <justification jstring="[hyper(134,a,74,a(flip),b,10191,a),flip(a)].">
      <j1 rule="hyper" parents="134 74 10191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10241">
    <literal><![CDATA[
      K(x,x \ (y / ((x \ z) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8453,a(flip),b,10215,a),flip(a)].">
      <j1 rule="hyper" parents="63 8453 10215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10242">
    <literal><![CDATA[
      L(x,x \ 1,x * y) \ 1 = 1 / L(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(220,a,10222,a(flip),b,9708,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="220 10222 9708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10243">
    <literal><![CDATA[
      (x \ y) \ (((x \ y) * x) * z) = (y / x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(138,a,10240,a)].">
      <j1 rule="hyper" parents="138 10240"/>
    </justification>
  </clause>

  <clause id="10244">
    <literal><![CDATA[
      K(x \ y,x) * (y * z) = ((x \ y) * x) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,5389,a(flip),b,10240,a)].">
      <j1 rule="hyper" parents="63 5389 10240"/>
    </justification>
  </clause>

  <clause id="10245">
    <literal><![CDATA[
      (x \ y) \ (((x \ y) * x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) \ (y * z) = u
    ]]></literal>
    <justification jstring="[para(10240(a,1),356(a,1,2))].">
      <j1 rule="para" parents="10240 356"/>
    </justification>
  </clause>

  <clause id="10246">
    <literal><![CDATA[
      (((x \ y) * x) * z) \ (K(x \ y,x) * (y * (z * u))) = L(L(u,z,y),y * z,K(x \ y,x))
    ]]></literal>
    <justification jstring="[para(10244(a,1),542(a,1,1))].">
      <j1 rule="para" parents="10244 542"/>
    </justification>
  </clause>

  <clause id="10247">
    <literal><![CDATA[
      K(x,(x * y) / (z * u)) = K(x,y / ((x \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10217,a(flip),b,10241,a),flip(a)].">
      <j1 rule="hyper" parents="63 10217 10241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10248">
    <literal><![CDATA[
      L(x,x \ 1,x * y) = y \ (y / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(39,a,3239,a,b,10242,a),flip(a)].">
      <j1 rule="hyper" parents="39 3239 10242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10249">
    <literal><![CDATA[
      L(x,x,x * y) = y \ (y / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(3524,a,10248,a)].">
      <j1 rule="hyper" parents="3524 10248"/>
    </justification>
  </clause>

  <clause id="10250">
    <literal><![CDATA[
      K(x,y / ((x \ z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z * u) / y) \ x) = w
    ]]></literal>
    <justification jstring="[para(10247(a,1),8241(a,1))].">
      <j1 rule="para" parents="10247 8241"/>
    </justification>
  </clause>

  <clause id="10251">
    <literal><![CDATA[
      1 / ((x * (L(x,y,z) \ 1)) * (x \ 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4612,a(flip),b,10132,a),flip(a)].">
      <j1 rule="hyper" parents="63 4612 10132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10253">
    <literal><![CDATA[
      1 / ((L(x,y,z) \ x) * (x \ 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1409(a,1),10251(a,1,2,1))].">
      <j1 rule="para" parents="1409 10251"/>
    </justification>
  </clause>

  <clause id="10254">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(214,a,10253,a),flip(a)].">
      <j1 rule="hyper" parents="214 10253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10255">
    <literal><![CDATA[
      (L(x,y,z) \ 1) / (x \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(145,a,10254,a)].">
      <j1 rule="hyper" parents="145 10254"/>
    </justification>
  </clause>

  <clause id="10256">
    <literal><![CDATA[
      (K(x,y) * (z / K(x,y))) * L(u,K(x,y) \ z,K(x,y)) = K(x,y) * ((z * K(y,x)) * u)
    ]]></literal>
    <justification jstring="[para(6117(a,1),10182(a,2,2,1))].">
      <j1 rule="para" parents="6117 10182"/>
    </justification>
  </clause>

  <clause id="10257">
    <literal><![CDATA[
      (L(x,y,z) * (y * z)) \ (x * (y * z)) = a(z,T(y,z),T(x,y * z))
    ]]></literal>
    <justification jstring="[para(10188(a,1),1174(a,1,1))].">
      <j1 rule="para" parents="10188 1174"/>
    </justification>
  </clause>

  <clause id="10258">
    <literal><![CDATA[
      (x / y) * L(y,K(z,u),K(u,z) * x) = ((x / K(z,u)) * (K(z,u) * y)) / y
    ]]></literal>
    <justification jstring="[para(5256(a,1),10198(a,1,2,3))].">
      <j1 rule="para" parents="5256 10198"/>
    </justification>
  </clause>

  <clause id="10259">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u * x) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(10237,a,10190,a),flip(a)].">
      <j1 rule="hyper" parents="10237 10190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10260">
    <literal><![CDATA[
      T(x,y / ((x * z) * u)) = T(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(4984,a,10218,a),flip(a)].">
      <j1 rule="hyper" parents="4984 10218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10261">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(347,a,6199,a(flip),b,10227,a),flip(a)].">
      <j1 rule="hyper" parents="347 6199 10227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10262">
    <literal><![CDATA[
      K(x,T(x \ (y / z),y)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(7488,a,10261,a)].">
      <j1 rule="hyper" parents="7488 10261"/>
    </justification>
  </clause>

  <clause id="10263">
    <literal><![CDATA[
      K(x,(y \ z) \ (x \ z)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(80(a,1),10262(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="80 10262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10264">
    <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(63,a,8105,a,b,10263,a)].">
      <j1 rule="hyper" parents="63 8105 10263"/>
    </justification>
  </clause>

  <clause id="10265">
    <literal><![CDATA[
      R(K(x,y),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[para(10118(a,1),10138(a,1,1))].">
      <j1 rule="para" parents="10118 10138"/>
    </justification>
  </clause>

  <clause id="10267">
    <literal><![CDATA[
      x * (T(y,x) * L(R(T(x,z),y,x),u,w)) = (y * x) * L(T(x,z),u,w)
    ]]></literal>
    <justification jstring="[para(4387(a,1),10168(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4387 10168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10268">
    <literal><![CDATA[
      L((1 / T(x,y)) \ (T(y,x) * (1 / x)),x,y) = T(y,T(y,x) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(360,a,10176,a),flip(a)].">
      <j1 rule="hyper" parents="360 10176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10269">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (y * (K(x,y) * x)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,6721,a(flip),b,10139,a),flip(a)].">
      <j1 rule="hyper" parents="63 6721 10139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10270">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(5030(a,1),10269(a,2,1))].">
      <j1 rule="para" parents="5030 10269"/>
    </justification>
  </clause>

  <clause id="10271">
    <literal><![CDATA[
      (x * y) * (K(y,x) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(8411,a,10270,a)].">
      <j1 rule="hyper" parents="8411 10270"/>
    </justification>
  </clause>

  <clause id="10272">
    <literal><![CDATA[
      (x * y) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(128,a,10270,a(flip),b,8410,a(flip))].">
      <j1 rule="hyper" parents="128 10270 8410"/>
    </justification>
  </clause>

  <clause id="10273">
    <literal><![CDATA[
      (x * y) * (T(x,y) \ z) = (y * x) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(5324,a,10271,a),flip(a)].">
      <j1 rule="hyper" parents="5324 10271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10274">
    <literal><![CDATA[
      K(x,y) * ((x * y) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(5282,a,10271,a),flip(a)].">
      <j1 rule="hyper" parents="5282 10271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10275">
    <literal><![CDATA[
      L(x,K(y,z),z * y) = x
    ]]></literal>
    <justification jstring="[hyper(937,a,10271,a)].">
      <j1 rule="hyper" parents="937 10271"/>
    </justification>
  </clause>

  <clause id="10276">
    <literal><![CDATA[
      K(x,y) \ ((y * x) \ z) = (x * y) \ z
    ]]></literal>
    <justification jstring="[hyper(675,a,10271,a),flip(a)].">
      <j1 rule="hyper" parents="675 10271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10277">
    <literal><![CDATA[
      x * (K(y \ x,y) * z) = ((y \ x) * y) * z
    ]]></literal>
    <justification jstring="[hyper(628,a,10271,a)].">
      <j1 rule="hyper" parents="628 10271"/>
    </justification>
  </clause>

  <clause id="10278">
    <literal><![CDATA[
      (x * y) \ T(y * x,z) = K(y,x) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,4929,a,b,10271,a)].">
      <j1 rule="hyper" parents="128 4929 10271"/>
    </justification>
  </clause>

  <clause id="10279">
    <literal><![CDATA[
      (x * y) \ (x * (T(y,x) * z)) = K(y,x) * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,10150,a(flip),b,10271,a)].">
      <j1 rule="hyper" parents="128 10150 10271"/>
    </justification>
  </clause>

  <clause id="10280">
    <literal><![CDATA[
      ((x \ y) * x) \ (y * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(128,a,165,a(flip),b,10271,a)].">
      <j1 rule="hyper" parents="128 165 10271"/>
    </justification>
  </clause>

  <clause id="10281">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,9860,a,b,10271,a)].">
      <j1 rule="hyper" parents="63 9860 10271"/>
    </justification>
  </clause>

  <clause id="10282">
    <literal><![CDATA[
      K(x,y) \ ((x * y) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(128,a,10271,a(flip),b,9860,a)].">
      <j1 rule="hyper" parents="128 10271 9860"/>
    </justification>
  </clause>

  <clause id="10284">
    <literal><![CDATA[
      (x * y) * (T(y,x) * z) = (y * x) * (y * z)
    ]]></literal>
    <justification jstring="[para(4946(a,1),10271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4946 10271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10285">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,T(x,z)) * u) = (z * K(x,y)) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(8070(a,1),10271(a,1,2))].">
      <j1 rule="para" parents="8070 10271"/>
    </justification>
  </clause>

  <clause id="10286">
    <literal><![CDATA[
      L(x,K(y,z),y * z) = x
    ]]></literal>
    <justification jstring="[hyper(5182,a,10275,a)].">
      <j1 rule="hyper" parents="5182 10275"/>
    </justification>
  </clause>

  <clause id="10287">
    <literal><![CDATA[
      L(L(x,y,z),K(u,w),w * u) = L(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,10165,a,b,10275,a),flip(a)].">
      <j1 rule="hyper" parents="347 10165 10275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10288">
    <literal><![CDATA[
      ((x * y) * K(x,y)) * z = (x * y) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(1362,a,10286,a),flip(a)].">
      <j1 rule="hyper" parents="1362 10286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10289">
    <literal><![CDATA[
      L(x,K(y,y \ z),z) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),10286(a,1,3))].">
      <j1 rule="para" parents="10 10286"/>
    </justification>
  </clause>

  <clause id="10290">
    <literal><![CDATA[
      (x * (y / x)) \ (y * z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,5896,a(flip),b,10289,a)].">
      <j1 rule="hyper" parents="63 5896 10289"/>
    </justification>
  </clause>

  <clause id="10291">
    <literal><![CDATA[
      x * (K(y,y \ x) * z) = (y * (x / y)) * z
    ]]></literal>
    <justification jstring="[hyper(134,a,10289,a(flip),b,5316,a),flip(a)].">
      <j1 rule="hyper" parents="134 10289 5316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10292">
    <literal><![CDATA[
      (x * y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) * z = u
    ]]></literal>
    <justification jstring="[para(10272(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="10272 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10293">
    <literal><![CDATA[
      ((x * y) \ z) / ((y * x) \ z) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,10274,a)].">
      <j1 rule="hyper" parents="145 10274"/>
    </justification>
  </clause>

  <clause id="10294">
    <literal><![CDATA[
      a(x,y,x) * (K(x,x * y) * ((x * y) \ z)) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,9917,a,b,10274,a)].">
      <j1 rule="hyper" parents="63 9917 10274"/>
    </justification>
  </clause>

  <clause id="10295">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) = x * ((y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(134,a,10274,a(flip),b,5210,a)].">
      <j1 rule="hyper" parents="134 10274 5210"/>
    </justification>
  </clause>

  <clause id="10296">
    <literal><![CDATA[
      K(x,x \ y) * (y \ z) = ((x \ y) * x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),10274(a,1,2,1))].">
      <j1 rule="para" parents="10 10274"/>
    </justification>
  </clause>

  <clause id="10297">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x * ((y * x) \ z) = u
    ]]></literal>
    <justification jstring="[para(10274(a,1),5355(a,1,2))].">
      <j1 rule="para" parents="10274 5355"/>
    </justification>
  </clause>

  <clause id="10298">
    <literal><![CDATA[
      T((x * y) \ z,K(y,x)) = ((y * x) \ z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(10274(a,1),6872(a,1,1))].">
      <j1 rule="para" parents="10274 6872"/>
    </justification>
  </clause>

  <clause id="10299">
    <literal><![CDATA[
      (x * y) \ (K(x,y) * z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(678,a,10281,a)].">
      <j1 rule="hyper" parents="678 10281"/>
    </justification>
  </clause>

  <clause id="10300">
    <literal><![CDATA[
      K(x,y) * (z * (y * x)) = (x * y) * T(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(639,a,10281,a)].">
      <j1 rule="hyper" parents="639 10281"/>
    </justification>
  </clause>

  <clause id="10301">
    <literal><![CDATA[
      (x * y) * ((y * x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(357,a,10281,a),flip(a)].">
      <j1 rule="hyper" parents="357 10281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10302">
    <literal><![CDATA[
      T(x,y) * ((y * x) * z) = x * ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(134,a,10281,a(flip),b,5210,a)].">
      <j1 rule="hyper" parents="134 10281 5210"/>
    </justification>
  </clause>

  <clause id="10303">
    <literal><![CDATA[
      ((x * y) * z) \ (K(x,y) * ((y * x) * (z * u))) = L(L(u,z,y * x),(y * x) * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10281(a,1),542(a,1,1))].">
      <j1 rule="para" parents="10281 542"/>
    </justification>
  </clause>

  <clause id="10304">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(10281(a,1),5274(a,1,2)),flip(b)].">
      <j1 rule="para" parents="10281 5274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10305">
    <literal><![CDATA[
      K(x \ ((y * z) * u),z) = K(x \ ((z * y) * u),z)
    ]]></literal>
    <justification jstring="[para(10281(a,1),8154(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10281 8154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10306">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,R(x,u,w))) * v5) = (R(x,z,R(x,u,w)) * y) * v5
    ]]></literal>
    <justification jstring="[para(8290(a,1),10281(a,1,1))].">
      <j1 rule="para" parents="8290 10281"/>
    </justification>
  </clause>

  <clause id="10307">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * z) = (y * x) \ (x * z)
    ]]></literal>
    <justification jstring="[para(4946(a,1),10299(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4946 10299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10308">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * R(T(z,x),u,w)) = (y * x) \ (R(z,u,w) * x)
    ]]></literal>
    <justification jstring="[para(5239(a,1),10299(a,1,2))].">
      <j1 rule="para" parents="5239 10299"/>
    </justification>
  </clause>

  <clause id="10309">
    <literal><![CDATA[
      x * ((y * (x / y)) \ z) = K(x / y,y) * z
    ]]></literal>
    <justification jstring="[hyper(353,a,10301,a)].">
      <j1 rule="hyper" parents="353 10301"/>
    </justification>
  </clause>

  <clause id="10310">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) * x) \ y = z
    ]]></literal>
    <justification jstring="[para(10301(a,1),232(a,1))].">
      <j1 rule="para" parents="10301 232"/>
    </justification>
  </clause>

  <clause id="10311">
    <literal><![CDATA[
      (x * y) \ (y * (x \ 1)) = T(x,y) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,784,a(flip),b,10273,a)].">
      <j1 rule="hyper" parents="128 784 10273"/>
    </justification>
  </clause>

  <clause id="10313">
    <literal><![CDATA[
      K(x \ y,x) * (y \ z) = (x * (y / x)) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),10290(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 10290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10314">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (T(x,z) * y) * (((x * (y * K(x,z))) * K(x,z)) \ u)
    ]]></literal>
    <justification jstring="[para(7354(a,1),10295(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7354 10295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10315">
    <literal><![CDATA[
      (x * (y / x)) \ (y / x) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(128,a,5027,a(flip),b,10309,a),flip(a)].">
      <j1 rule="hyper" parents="128 5027 10309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10316">
    <literal><![CDATA[
      x * ((y * (x / y)) \ z) = K(y \ x,y) * z
    ]]></literal>
    <justification jstring="[para(5138(a,1),10309(a,2,1))].">
      <j1 rule="para" parents="5138 10309"/>
    </justification>
  </clause>

  <clause id="10317">
    <literal><![CDATA[
      (x * y) \ (y * (x \ 1)) = x \ (T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,1243,a(flip),b,10311,a),flip(a)].">
      <j1 rule="hyper" parents="347 1243 10311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10318">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,u)) * x) != w
    ]]></literal>
    <literal><![CDATA[
      (x * y) * R(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(1704(a,2),10304(a,1,2))].">
      <j1 rule="para" parents="1704 10304"/>
    </justification>
  </clause>

  <clause id="10319">
    <literal><![CDATA[
      ((x \ 1) * x) \ y = y * (x * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(10310,a,2774,a)].">
      <j1 rule="hyper" parents="10310 2774"/>
    </justification>
  </clause>

  <clause id="10320">
    <literal><![CDATA[
      ((x \ 1) * x) \ y = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(347,a,2803,a,b,10319,a),flip(a)].">
      <j1 rule="hyper" parents="347 2803 10319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10321">
    <literal><![CDATA[
      (x * (1 / x)) \ (((x \ 1) * x) \ y) = y
    ]]></literal>
    <justification jstring="[hyper(128,a,10319,a,b,2803,a)].">
      <j1 rule="hyper" parents="128 10319 2803"/>
    </justification>
  </clause>

  <clause id="10322">
    <literal><![CDATA[
      (((x \ 1) * x) \ y) \ z = (x * (1 / x)) \ (y \ z)
    ]]></literal>
    <justification jstring="[para(10319(a,2),3243(a,1,1))].">
      <j1 rule="para" parents="10319 3243"/>
    </justification>
  </clause>

  <clause id="10323">
    <literal><![CDATA[
      (((x \ 1) * x) \ y) \ z = y \ ((x * (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[para(10320(a,2),3463(a,1,1))].">
      <j1 rule="para" parents="10320 3463"/>
    </justification>
  </clause>

  <clause id="10324">
    <literal><![CDATA[
      (x * (1 / x)) \ y != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) * x) \ z = y
    ]]></literal>
    <justification jstring="[para(10321(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="10321 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10325">
    <literal><![CDATA[
      (x * y) \ T(y * x,y) = a(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,8338,a(flip),b,10278,a),flip(a)].">
      <j1 rule="hyper" parents="347 8338 10278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10326">
    <literal><![CDATA[
      (x * y) * a(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,8338,a(flip),b,10278,a)].">
      <j1 rule="hyper" parents="134 8338 10278"/>
    </justification>
  </clause>

  <clause id="10327">
    <literal><![CDATA[
      a(x,y,x) * (y * x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,10325,a(flip),b,5842,a)].">
      <j1 rule="hyper" parents="133 10325 5842"/>
    </justification>
  </clause>

  <clause id="10328">
    <literal><![CDATA[
      R(T(x,T(x * y,x)),y * x,a(x,y,x)) = ((y * x) * a(x,y,x)) \ ((x * y) * x)
    ]]></literal>
    <justification jstring="[para(10326(a,1),1062(a,1,1,2))].">
      <j1 rule="para" parents="10326 1062"/>
    </justification>
  </clause>

  <clause id="10329">
    <literal><![CDATA[
      (x * y) * (K(x,y) * z) = (T(x,y) * y) * z
    ]]></literal>
    <justification jstring="[para(5147(a,1),10288(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5147 10288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10330">
    <literal><![CDATA[
      K(x,y) * ((y * x) \ z) = (T(y,x) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(5282,a,10329,a),flip(a)].">
      <j1 rule="hyper" parents="5282 10329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10331">
    <literal><![CDATA[
      (T(x,y) * (y * z)) \ ((T(x,y) * y) * z) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(10329(a,1),5581(a,1,2))].">
      <j1 rule="para" parents="10329 5581"/>
    </justification>
  </clause>

  <clause id="10332">
    <literal><![CDATA[
      (x * y) \ T(z * (x * y),K(x,y)) = T(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(128,a,9590,a,b,10300,a(flip))].">
      <j1 rule="hyper" parents="128 9590 10300"/>
    </justification>
  </clause>

  <clause id="10333">
    <literal><![CDATA[
      (x * (1 / x)) \ (y \ z) = y \ ((x * (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10322,a(flip),b,10323,a)].">
      <j1 rule="hyper" parents="63 10322 10323"/>
    </justification>
  </clause>

  <clause id="10334">
    <literal><![CDATA[
      T(x,T(y * z,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8786,a(flip),b,10332,a)].">
      <j1 rule="hyper" parents="63 8786 10332"/>
    </justification>
  </clause>

  <clause id="10335">
    <literal><![CDATA[
      T(x,(y * y) * z) = T(x,z * (y * y))
    ]]></literal>
    <justification jstring="[hyper(9172,a,10334,a),flip(a)].">
      <j1 rule="hyper" parents="9172 10334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10336">
    <literal><![CDATA[
      T(x,T(y * z,z \ 1)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(8881,a,10334,a)].">
      <j1 rule="hyper" parents="8881 10334"/>
    </justification>
  </clause>

  <clause id="10337">
    <literal><![CDATA[
      T(T(x,y * z),K(y * z,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(6824,a,10334,a)].">
      <j1 rule="hyper" parents="6824 10334"/>
    </justification>
  </clause>

  <clause id="10338">
    <literal><![CDATA[
      T(x,T(T(y * z,z),u)) = K(x,u) * T(x * K(u,x),z * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,10334,a(flip),b,8681,a),flip(a)].">
      <j1 rule="hyper" parents="134 10334 8681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10339">
    <literal><![CDATA[
      T(x,y * (z / y)) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),10334(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 10334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10340">
    <literal><![CDATA[
      K(x,y * z) * (z * x) = z * T(x,z * y)
    ]]></literal>
    <justification jstring="[para(10334(a,1),7697(a,2,2))].">
      <j1 rule="para" parents="10334 7697"/>
    </justification>
  </clause>

  <clause id="10341">
    <literal><![CDATA[
      T(x,(y * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (y * y)) = u
    ]]></literal>
    <justification jstring="[para(10334(a,1),9172(a,1))].">
      <j1 rule="para" parents="10334 9172"/>
    </justification>
  </clause>

  <clause id="10342">
    <literal><![CDATA[
      T(x / (y * (z / y)),T(z,y)) = (y * (z / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(386,a,10339,a),flip(a)].">
      <j1 rule="hyper" parents="386 10339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10343">
    <literal><![CDATA[
      T(T(x,y * y),z) = T(x,(y * y) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,1306,a,b,10335,a)].">
      <j1 rule="hyper" parents="347 1306 10335"/>
    </justification>
  </clause>

  <clause id="10344">
    <literal><![CDATA[
      T(K(x,y * z),y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(35,a,7705,a,b,10340,a)].">
      <j1 rule="hyper" parents="35 7705 10340"/>
    </justification>
  </clause>

  <clause id="10345">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(35,a,7699,a,b,10340,a)].">
      <j1 rule="hyper" parents="35 7699 10340"/>
    </justification>
  </clause>

  <clause id="10346">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(7382,a,10344,a)].">
      <j1 rule="hyper" parents="7382 10344"/>
    </justification>
  </clause>

  <clause id="10347">
    <literal><![CDATA[
      K(T(x,y),y * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7072,a,b,10344,a)].">
      <j1 rule="hyper" parents="63 7072 10344"/>
    </justification>
  </clause>

  <clause id="10348">
    <literal><![CDATA[
      K(x,T((y \ 1) * z,y)) = K(x,z * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,8851,a(flip),b,10344,a)].">
      <j1 rule="hyper" parents="63 8851 10344"/>
    </justification>
  </clause>

  <clause id="10349">
    <literal><![CDATA[
      K(x \ y,z * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,x * z) = u
    ]]></literal>
    <justification jstring="[para(10344(a,1),7479(a,1))].">
      <j1 rule="para" parents="10344 7479"/>
    </justification>
  </clause>

  <clause id="10350">
    <literal><![CDATA[
      T(x,T(y * z,y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(132,a,10345,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 10345 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10351">
    <literal><![CDATA[
      K(x,(y \ z) * y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),10345(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 10345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10352">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,T(y,z) * z)
    ]]></literal>
    <justification jstring="[para(111(a,1),10345(a,1,2,1))].">
      <j1 rule="para" parents="111 10345"/>
    </justification>
  </clause>

  <clause id="10353">
    <literal><![CDATA[
      K(x * K(y,x),z * u) = K(x,T(T(u * z,z),y))
    ]]></literal>
    <justification jstring="[hyper(7593,a,10346,a),flip(a)].">
      <j1 rule="hyper" parents="7593 10346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10354">
    <literal><![CDATA[
      K(x,y * (z / y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),10346(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 10346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10355">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8780,a,b,10350,a)].">
      <j1 rule="hyper" parents="63 8780 10350"/>
    </justification>
  </clause>

  <clause id="10356">
    <literal><![CDATA[
      T(x,(y \ z) * y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),10350(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 10350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10358">
    <literal><![CDATA[
      K(x,T(y * K(z,u),z)) = K(x,(z \ y) * T(z,u))
    ]]></literal>
    <justification jstring="[para(6759(a,1),10351(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6759 10351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10359">
    <literal><![CDATA[
      T(x,(y \ z) * y) = x / K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,7127,a,b,10356,a),flip(a)].">
      <j1 rule="hyper" parents="347 7127 10356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10360">
    <literal><![CDATA[
      K(x,T(y,z) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10346,a(flip),b,10352,a),flip(a)].">
      <j1 rule="hyper" parents="63 10346 10352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10361">
    <literal><![CDATA[
      T(x,T(y,z) * z) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(132,a,10360,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 10360 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10362">
    <literal><![CDATA[
      T(x,T(y,z) * z) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,10360,a(flip),b,4924,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 10360 4924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10363">
    <literal><![CDATA[
      K(T(x,y) * y,z) = z / T(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(220,a,10361,a(flip),b,4939,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="220 10361 4939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10364">
    <literal><![CDATA[
      T(x / (y * z),z * y) = T((y * z) \ x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(808,a,10355,a),flip(a)].">
      <j1 rule="hyper" parents="808 10355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10365">
    <literal><![CDATA[
      T(x,y * z) * K(z,y) = K(z,y) * T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,10355,a(flip),b,114,a),flip(a)].">
      <j1 rule="hyper" parents="134 10355 114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10366">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * z) = T(x,z * y)
    ]]></literal>
    <justification jstring="[para(7330(a,1),10355(a,1,1))].">
      <j1 rule="para" parents="7330 10355"/>
    </justification>
  </clause>

  <clause id="10367">
    <literal><![CDATA[
      T(T(x,y * z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(10355(a,1),7361(a,1,1))].">
      <j1 rule="para" parents="10355 7361"/>
    </justification>
  </clause>

  <clause id="10368">
    <literal><![CDATA[
      K((x \ y) * x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(4950,a,10359,a)].">
      <j1 rule="hyper" parents="4950 10359"/>
    </justification>
  </clause>

  <clause id="10369">
    <literal><![CDATA[
      K(x * y,T(z,x)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),10368(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 10368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10370">
    <literal><![CDATA[
      K(x * y,(z * x) \ x) = K(y * x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(7811,a,10369,a)].">
      <j1 rule="hyper" parents="7811 10369"/>
    </justification>
  </clause>

  <clause id="10371">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(7478,a,10369,a),flip(a)].">
      <j1 rule="hyper" parents="7478 10369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10373">
    <literal><![CDATA[
      K(x * y,z * x) = K(y * x,x * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10345,a(flip),b,10369,a)].">
      <j1 rule="hyper" parents="63 10345 10369"/>
    </justification>
  </clause>

  <clause id="10374">
    <literal><![CDATA[
      K(x * y,z) * y = y * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,10369,a(flip),b,7378,a)].">
      <j1 rule="hyper" parents="133 10369 7378"/>
    </justification>
  </clause>

  <clause id="10375">
    <literal><![CDATA[
      K(x * y,z) * x = x * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(10369(a,1),7104(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10369 7104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10376">
    <literal><![CDATA[
      K(x * y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(10369(a,1),7478(a,1))].">
      <j1 rule="para" parents="10369 7478"/>
    </justification>
  </clause>

  <clause id="10377">
    <literal><![CDATA[
      x * K(y * x,z) != u * x
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(10369(a,1),7110(a,1,2))].">
      <j1 rule="para" parents="10369 7110"/>
    </justification>
  </clause>

  <clause id="10378">
    <literal><![CDATA[
      K(x * y,z) * T(x,y) = T(x,y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(10369(a,1),8067(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10369 8067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10380">
    <literal><![CDATA[
      K(x * y,z) * K(y,K(z,x * y)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7094,a,b,10371,a)].">
      <j1 rule="hyper" parents="63 7094 10371"/>
    </justification>
  </clause>

  <clause id="10382">
    <literal><![CDATA[
      K(x * (y / x),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(12(a,1),10371(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 10371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10383">
    <literal><![CDATA[
      K(x * y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(10371(a,1),7478(a,1))].">
      <j1 rule="para" parents="10371 7478"/>
    </justification>
  </clause>

  <clause id="10384">
    <literal><![CDATA[
      K((x * y) / x,z) = K(x * (y / x),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7389,a,b,10382,a)].">
      <j1 rule="hyper" parents="347 7389 10382"/>
    </justification>
  </clause>

  <clause id="10385">
    <literal><![CDATA[
      K(x * K((x \ y) \ 1,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[para(5565(a,1),10382(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5565 10382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10386">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) * K(x \ (u * (y / u)),z) = K((u * (y / u)) / x,z)
    ]]></literal>
    <justification jstring="[para(10382(a,1),8954(a,1,1,2))].">
      <j1 rule="para" parents="10382 8954"/>
    </justification>
  </clause>

  <clause id="10387">
    <literal><![CDATA[
      T(x,T(y,z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(10362(a,2),4984(a,1))].">
      <j1 rule="para" parents="10362 4984"/>
    </justification>
  </clause>

  <clause id="10388">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,4920,a,b,10363,a),flip(a)].">
      <j1 rule="hyper" parents="347 4920 10363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10389">
    <literal><![CDATA[
      K(T(x,y) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(10363(a,2),5013(a,1))].">
      <j1 rule="para" parents="10363 5013"/>
    </justification>
  </clause>

  <clause id="10390">
    <literal><![CDATA[
      ((T(x,y) * y) \ z) * K(y * x,(T(x,y) * y) \ z) = z / (T(x,y) * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,10388,a(flip),b,5049,a)].">
      <j1 rule="hyper" parents="134 10388 5049"/>
    </justification>
  </clause>

  <clause id="10391">
    <literal><![CDATA[
      T(x / (y * z),z * y) = T((y * z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(808,a,10366,a),flip(a)].">
      <j1 rule="hyper" parents="808 10366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10392">
    <literal><![CDATA[
      K(x,(y \ (x * z)) \ (x * K(z * x,y))) = K(x,R(y,y \ (x * z),y) / z)
    ]]></literal>
    <justification jstring="[para(10375(a,1),9370(a,1,2,2))].">
      <j1 rule="para" parents="10375 9370"/>
    </justification>
  </clause>

  <clause id="10393">
    <literal><![CDATA[
      K(x * (y / x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(10384(a,1),7460(a,1))].">
      <j1 rule="para" parents="10384 7460"/>
    </justification>
  </clause>

  <clause id="10394">
    <literal><![CDATA[
      T(x,T(y \ z,u) * y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * T(z / y,u)) = w
    ]]></literal>
    <justification jstring="[para(277(a,1),10387(a,1,2,1))].">
      <j1 rule="para" parents="277 10387"/>
    </justification>
  </clause>

  <clause id="10395">
    <literal><![CDATA[
      T(x,y) * K(y * x,y \ 1) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(10370(a,1),6518(a,1,2))].">
      <j1 rule="para" parents="10370 6518"/>
    </justification>
  </clause>

  <clause id="10396">
    <literal><![CDATA[
      T(T(x,y * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (y * y)) = u
    ]]></literal>
    <justification jstring="[para(10343(a,2),10341(a,1))].">
      <j1 rule="para" parents="10343 10341"/>
    </justification>
  </clause>

  <clause id="10397">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),10367(a,1))].">
      <j1 rule="para" parents="23 10367"/>
    </justification>
  </clause>

  <clause id="10398">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(7339(a,2),10367(a,1))].">
      <j1 rule="para" parents="7339 10367"/>
    </justification>
  </clause>

  <clause id="10399">
    <literal><![CDATA[
      T(T(x,y * (z * z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      T(T(x,y),u * (z * z)) = w
    ]]></literal>
    <justification jstring="[para(1305(a,1),10396(a,1,1))].">
      <j1 rule="para" parents="1305 10396"/>
    </justification>
  </clause>

  <clause id="10400">
    <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(7379(a,1),10398(a,1,1,2))].">
      <j1 rule="para" parents="7379 10398"/>
    </justification>
  </clause>

  <clause id="10401">
    <literal><![CDATA[
      T(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(8780(a,1),10398(a,1))].">
      <j1 rule="para" parents="8780 10398"/>
    </justification>
  </clause>

  <clause id="10402">
    <literal><![CDATA[
      ((x \ 1) * x) \ (y \ ((x * (1 / x)) \ z)) = y \ z
    ]]></literal>
    <justification jstring="[hyper(10324,a,10333,a)].">
      <j1 rule="hyper" parents="10324 10333"/>
    </justification>
  </clause>

  <clause id="10403">
    <literal><![CDATA[
      K(x,T(T(y * z,z),u)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(7593,a,10353,a),flip(a)].">
      <j1 rule="hyper" parents="7593 10353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10404">
    <literal><![CDATA[
      T(x,T(T(y * z,z),u)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(132,a,10403,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 10403 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10405">
    <literal><![CDATA[
      K(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(10403(a,1),7478(a,1))].">
      <j1 rule="para" parents="10403 7478"/>
    </justification>
  </clause>

  <clause id="10406">
    <literal><![CDATA[
      K(x,T(y * z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(8858(a,2),10405(a,1))].">
      <j1 rule="para" parents="8858 10405"/>
    </justification>
  </clause>

  <clause id="10407">
    <literal><![CDATA[
      K(x,T(y * L(y \ z,u,w),y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * L(z / y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(740(a,1),10406(a,1,2,1))].">
      <j1 rule="para" parents="740 10406"/>
    </justification>
  </clause>

  <clause id="10408">
    <literal><![CDATA[
      K(x,T(y * (z \ x),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ x) * y) = u
    ]]></literal>
    <justification jstring="[para(8874(a,1),10406(a,1))].">
      <j1 rule="para" parents="8874 10406"/>
    </justification>
  </clause>

  <clause id="10409">
    <literal><![CDATA[
      K(x,T(y,z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(10352(a,1),10406(a,1))].">
      <j1 rule="para" parents="10352 10406"/>
    </justification>
  </clause>

  <clause id="10410">
    <literal><![CDATA[
      T(x,T(T(y * z,y),u)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8983,a(flip),b,10404,a)].">
      <j1 rule="hyper" parents="63 8983 10404"/>
    </justification>
  </clause>

  <clause id="10411">
    <literal><![CDATA[
      T(x,T(T(y * T(y \ z,u),y),w)) = T(x,T(y * T(z / y,u),w))
    ]]></literal>
    <justification jstring="[para(484(a,1),10404(a,1,2,1,1))].">
      <j1 rule="para" parents="484 10404"/>
    </justification>
  </clause>

  <clause id="10413">
    <literal><![CDATA[
      T(x,T(T(y * K(y / z,u),z),w)) = T(x,T(T(z \ y,T(u,z)) * z,w))
    ]]></literal>
    <justification jstring="[para(7456(a,1),10410(a,1,2,1,1))].">
      <j1 rule="para" parents="7456 10410"/>
    </justification>
  </clause>

  <clause id="10414">
    <literal><![CDATA[
      K(x,(y \ z) * T(y,z)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5058(a,1),10358(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5058 10358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10416">
    <literal><![CDATA[
      K(x * y,z) * K(y,K(x,z)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[para(8781(a,1),10380(a,1,2))].">
      <j1 rule="para" parents="8781 10380"/>
    </justification>
  </clause>

  <clause id="10417">
    <literal><![CDATA[
      K(x * y,z) * K(x,K(y,z)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,10416,a(flip),b,7315,a)].">
      <j1 rule="hyper" parents="133 10416 7315"/>
    </justification>
  </clause>

  <clause id="10418">
    <literal><![CDATA[
      K(x * y,z) * K(z,K(x,y)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[para(7260(a,1),10416(a,1,2))].">
      <j1 rule="para" parents="7260 10416"/>
    </justification>
  </clause>

  <clause id="10419">
    <literal><![CDATA[
      K(x * y,z) * K(z,y * x) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(34,a,5269,a,b,10417,a)].">
      <j1 rule="hyper" parents="34 5269 10417"/>
    </justification>
  </clause>

  <clause id="10420">
    <literal><![CDATA[
      K(x,y * z) \ K(x,K(y,z)) = K(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(5293,a,10418,a)].">
      <j1 rule="hyper" parents="5293 10418"/>
    </justification>
  </clause>

  <clause id="10421">
    <literal><![CDATA[
      K(x,y * z) * K(z,K(y,x)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(5273,a,10419,a)].">
      <j1 rule="hyper" parents="5273 10419"/>
    </justification>
  </clause>

  <clause id="10422">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(39,a,6123,a,b,10420,a)].">
      <j1 rule="hyper" parents="39 6123 10420"/>
    </justification>
  </clause>

  <clause id="10423">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z * x) = K(y,x * z)
    ]]></literal>
    <justification jstring="[para(7279(a,1),10422(a,1,1))].">
      <j1 rule="para" parents="7279 10422"/>
    </justification>
  </clause>

  <clause id="10424">
    <literal><![CDATA[
      T(((x * x) * y) \ (z * y),K(x * x,y)) = T(z / (x * x),y * (x * x))
    ]]></literal>
    <justification jstring="[para(465(a,1),10391(a,1,1)),flip(a)].">
      <j1 rule="para" parents="465 10391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10425">
    <literal><![CDATA[
      L(K(x,y) * z,x,y) = K(x,y) * L(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(5170,a,10279,a)].">
      <j1 rule="hyper" parents="5170 10279"/>
    </justification>
  </clause>

  <clause id="10426">
    <literal><![CDATA[
      x * L(K(x,y) * z,x,y) = T(x,y) * L(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,10425,a,b,5157,a)].">
      <j1 rule="hyper" parents="134 10425 5157"/>
    </justification>
  </clause>

  <clause id="10427">
    <literal><![CDATA[
      L(x,y,z) * L(K(x,y) * u,x,y) = L(T(x,y),y,z) * L(u,x,y)
    ]]></literal>
    <justification jstring="[para(10425(a,2),9617(a,1,2))].">
      <j1 rule="para" parents="10425 9617"/>
    </justification>
  </clause>

  <clause id="10428">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(10408,a,9841,a)].">
      <j1 rule="hyper" parents="10408 9841"/>
    </justification>
  </clause>

  <clause id="10429">
    <literal><![CDATA[
      a(x,y,x) * (T(x * y,x) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[para(5209(a,1),10294(a,1,2))].">
      <j1 rule="para" parents="5209 10294"/>
    </justification>
  </clause>

  <clause id="10430">
    <literal><![CDATA[
      T(x,T(T(y * z,z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z * y,u)) = w
    ]]></literal>
    <justification jstring="[para(10338(a,2),8683(a,1))].">
      <j1 rule="para" parents="10338 8683"/>
    </justification>
  </clause>

  <clause id="10431">
    <literal><![CDATA[
      T(x,T(T(y * T(y \ z,u),y),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),w)) = v5
    ]]></literal>
    <justification jstring="[para(484(a,1),10430(a,1,2,1,1))].">
      <j1 rule="para" parents="484 10430"/>
    </justification>
  </clause>

  <clause id="10432">
    <literal><![CDATA[
      T(x,T(T(y * z,y),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z * y,u)) = w
    ]]></literal>
    <justification jstring="[para(8983(a,1),10430(a,1))].">
      <j1 rule="para" parents="8983 10430"/>
    </justification>
  </clause>

  <clause id="10433">
    <literal><![CDATA[
      T(x,T(T(y * z,u),y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z * y,u)) = w
    ]]></literal>
    <justification jstring="[para(23(a,1),10432(a,1,2))].">
      <j1 rule="para" parents="23 10432"/>
    </justification>
  </clause>

  <clause id="10434">
    <literal><![CDATA[
      x * (y * L(y \ (x \ z),x,y)) = y * (x * ((y * x) \ z))
    ]]></literal>
    <justification jstring="[para(10295(a,1),10187(a,2,2))].">
      <j1 rule="para" parents="10295 10187"/>
    </justification>
  </clause>

  <clause id="10435">
    <literal><![CDATA[
      x * (y * L(y \ z,x,y)) = y * (x * ((y * x) \ (x * z)))
    ]]></literal>
    <justification jstring="[para(9(a,1),10434(a,1,2,2,1,2))].">
      <j1 rule="para" parents="9 10434"/>
    </justification>
  </clause>

  <clause id="10436">
    <literal><![CDATA[
      x * (y * ((x * y) \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ L(y * x,y,x) = z
    ]]></literal>
    <justification jstring="[para(10434(a,1),3402(a,1))].">
      <j1 rule="para" parents="10434 3402"/>
    </justification>
  </clause>

  <clause id="10437">
    <literal><![CDATA[
      L(L(((x \ y) \ y) \ 1,(x \ y) \ y,(x \ y) \ y),x,x \ y) = T(y \ ((x \ y) * 1),(x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(519(a,2),10213(a,1,1))].">
      <j1 rule="para" parents="519 10213"/>
    </justification>
  </clause>

  <clause id="10438">
    <literal><![CDATA[
      a(x,y,K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(T(x,y),y,z) = u
    ]]></literal>
    <justification jstring="[para(10331(a,1),836(a,1))].">
      <j1 rule="para" parents="10331 836"/>
    </justification>
  </clause>

  <clause id="10439">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9561,a(flip),b,10219,a),flip(a)].">
      <j1 rule="hyper" parents="63 9561 10219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10441">
    <literal><![CDATA[
      (x * y) \ (R(y,z,u) * T(x,y)) = (y * x) \ (R(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(4289(a,1),10308(a,1,2))].">
      <j1 rule="para" parents="4289 10308"/>
    </justification>
  </clause>

  <clause id="10442">
    <literal><![CDATA[
      ((x * y) * z) \ (R(z,x,y) * T(x * y,z)) = (z * (x * y)) \ ((z * x) * y)
    ]]></literal>
    <justification jstring="[para(107(a,1),10441(a,2,2))].">
      <j1 rule="para" parents="107 10441"/>
    </justification>
  </clause>

  <clause id="10443">
    <literal><![CDATA[
      (x * y) \ (R(y,y,x) * T(x,y)) = (y * x) \ (y \ ((y * y) * x))
    ]]></literal>
    <justification jstring="[para(1745(a,2),10441(a,2,2))].">
      <j1 rule="para" parents="1745 10441"/>
    </justification>
  </clause>

  <clause id="10444">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) * y,w)) = T(x,T(y * T(z / y,u),w))
    ]]></literal>
    <justification jstring="[hyper(10432,a,10411,a)].">
      <j1 rule="hyper" parents="10432 10411"/>
    </justification>
  </clause>

  <clause id="10445">
    <literal><![CDATA[
      T(x,T(x,y) * (1 / y)) = L(T(x,y \ 1),y,x)
    ]]></literal>
    <justification jstring="[para(8133(a,1),10268(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8133 10268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10446">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * w) * x = (x * w) * R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(10318,a,10306,a),flip(a)].">
      <j1 rule="hyper" parents="10318 10306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10447">
    <literal><![CDATA[
      ((x * y) * ((T(y,x) * x) \ z)) / (x * y) = z / (T(y,x) * x)
    ]]></literal>
    <justification jstring="[hyper(5091,a,10390,a)].">
      <j1 rule="hyper" parents="5091 10390"/>
    </justification>
  </clause>

  <clause id="10448">
    <literal><![CDATA[
      T(((x * x) * y) \ (z * y),K(x * x,y)) = T((x * x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,1308,a(flip),b,10424,a),flip(a)].">
      <j1 rule="hyper" parents="347 1308 10424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10449">
    <literal><![CDATA[
      T(T(x * x,y) \ T(z,y),K(x * x,y)) = T((x * x) \ z,y)
    ]]></literal>
    <justification jstring="[para(10214(a,2),10448(a,1,1))].">
      <j1 rule="para" parents="10214 10448"/>
    </justification>
  </clause>

  <clause id="10450">
    <literal><![CDATA[
      T(x * x,y) \ T(z,y) = T((x * x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9169,a(flip),b,10449,a)].">
      <j1 rule="hyper" parents="63 9169 10449"/>
    </justification>
  </clause>

  <clause id="10452">
    <literal><![CDATA[
      R(T(x,(y * (z * u)) / ((x * z) * u)),z,u) = T(R(x,z,u),y / R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(6366,a,10129,a)].">
      <j1 rule="hyper" parents="6366 10129"/>
    </justification>
  </clause>

  <clause id="10453">
    <literal><![CDATA[
      L((x * K(y,z)) \ u,x * K(y,z),K(z,y)) = x \ (K(z,T(y,x)) * u)
    ]]></literal>
    <justification jstring="[para(7428(a,1),10197(a,2,2,1))].">
      <j1 rule="para" parents="7428 10197"/>
    </justification>
  </clause>

  <clause id="10454">
    <literal><![CDATA[
      (x * (y * z)) / T(y * x,L(K(x,y) * z,y,x)) = L(K(x,y) * z,y,x)
    ]]></literal>
    <justification jstring="[para(10173(a,1),10221(a,1,2,2))].">
      <j1 rule="para" parents="10173 10221"/>
    </justification>
  </clause>

  <clause id="10455">
    <literal><![CDATA[
      (x / y) * L(y,K(z,u),K(u,z) * x) = ((x * K(u,z)) * (K(z,u) * y)) / y
    ]]></literal>
    <justification jstring="[para(6117(a,1),10258(a,2,1,1))].">
      <j1 rule="para" parents="6117 10258"/>
    </justification>
  </clause>

  <clause id="10456">
    <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(4001(a,1),10264(a,2,2))].">
      <j1 rule="para" parents="4001 10264"/>
    </justification>
  </clause>

  <clause id="10457">
    <literal><![CDATA[
      a(x,y,z) = ((y * z) * x) \ (R(x,y,z) * T(y * z,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,14,a,b,10442,a)].">
      <j1 rule="hyper" parents="347 14 10442"/>
    </justification>
  </clause>

  <clause id="10458">
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) = R(z,x,y) * T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,14,a,b,10442,a)].">
      <j1 rule="hyper" parents="134 14 10442"/>
    </justification>
  </clause>

  <clause id="10459">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,x) = ((y * z) * x) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,5947,a,b,10458,a)].">
      <j1 rule="hyper" parents="347 5947 10458"/>
    </justification>
  </clause>

  <clause id="10460">
    <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(347,a,4285,a(flip),b,10452,a),flip(a)].">
      <j1 rule="hyper" parents="347 4285 10452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10461">
    <literal><![CDATA[
      x * L(y,K(z,u),K(u,z) * x) = (x * K(u,z)) * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(2016,a,10455,a(flip))].">
      <j1 rule="hyper" parents="2016 10455"/>
    </justification>
  </clause>

  <clause id="10462">
    <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(347,a,8876,a(flip),b,10456,a),flip(a)].">
      <j1 rule="hyper" parents="347 8876 10456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10463">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,y \ ((1 / z) \ y))) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,8852,a(flip),b,10462,a),flip(a)].">
      <j1 rule="hyper" parents="347 8852 10462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10464">
    <literal><![CDATA[
      K(x,T(x \ y,z)) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(9624,a,10463,a),flip(a)].">
      <j1 rule="hyper" parents="9624 10463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10465">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,u)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,9565,a,b,10464,a)].">
      <j1 rule="hyper" parents="347 9565 10464"/>
    </justification>
  </clause>

  <clause id="10466">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,8480,a,b,10464,a)].">
      <j1 rule="hyper" parents="347 8480 10464"/>
    </justification>
  </clause>

  <clause id="10467">
    <literal><![CDATA[
      T(x,T(x \ y,z)) = T(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,10464,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 10464 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10468">
    <literal><![CDATA[
      K(x,T(T(x,y) \ z,u)) = K(x,x \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7965,a,b,10464,a)].">
      <j1 rule="hyper" parents="63 7965 10464"/>
    </justification>
  </clause>

  <clause id="10469">
    <literal><![CDATA[
      K(x,x \ T(x * y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),10464(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 10464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10470">
    <literal><![CDATA[
      K(x,x \ T(y,z)) \ 1 = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[para(10464(a,1),7122(a,1,1))].">
      <j1 rule="para" parents="10464 7122"/>
    </justification>
  </clause>

  <clause id="10471">
    <literal><![CDATA[
      T(x,y) / T(T(z,T(z \ x,y)),u) = T(z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(10467(a,2),7571(a,1,2,1))].">
      <j1 rule="para" parents="10467 7571"/>
    </justification>
  </clause>

  <clause id="10472">
    <literal><![CDATA[
      K(x,T(y,z) / x) = K(x,T(y / x,z))
    ]]></literal>
    <justification jstring="[para(4811(a,1),10469(a,1,2))].">
      <j1 rule="para" parents="4811 10469"/>
    </justification>
  </clause>

  <clause id="10473">
    <literal><![CDATA[
      K(x \ 1,T(R(y,x,1 / x),z) / (x \ 1)) = K(x \ 1,T(y * x,z))
    ]]></literal>
    <justification jstring="[para(2199(a,1),10472(a,2,2,1))].">
      <j1 rule="para" parents="2199 10472"/>
    </justification>
  </clause>

  <clause id="10474">
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) = T(K(y,z) * x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(133,a,10466,a(flip),b,4969,a(flip))].">
      <j1 rule="hyper" parents="133 10466 4969"/>
    </justification>
  </clause>

  <clause id="10475">
    <literal><![CDATA[
      K(x \ T(y,z),x) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(5179,a,10470,a)].">
      <j1 rule="hyper" parents="5179 10470"/>
    </justification>
  </clause>

  <clause id="10476">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,u)) = K(x,T(x \ y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(347,a,8852,a,b,10465,a),flip(a)].">
      <j1 rule="hyper" parents="347 8852 10465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10478">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = w
    ]]></literal>
    <justification jstring="[para(10476(a,2),8864(a,1))].">
      <j1 rule="para" parents="10476 8864"/>
    </justification>
  </clause>

  <clause id="10479">
    <literal><![CDATA[
      T(T(x,y),z) / T(T(x,T(K(x,y),z)),u) = T(x,u) \ T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(4924(a,2),10471(a,1,2,1,2,1))].">
      <j1 rule="para" parents="4924 10471"/>
    </justification>
  </clause>

  <clause id="10480">
    <literal><![CDATA[
      K(x,x \ T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(398(a,1),10478(a,1,2))].">
      <j1 rule="para" parents="398 10478"/>
    </justification>
  </clause>

  <clause id="10481">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,T(z \ x,y)) = u
    ]]></literal>
    <justification jstring="[para(8480(a,2),10480(a,1))].">
      <j1 rule="para" parents="8480 10480"/>
    </justification>
  </clause>

  <clause id="10482">
    <literal><![CDATA[
      T(K(x,y) * z,z \ x) = T(z,z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8981,a(flip),b,10474,a),flip(a)].">
      <j1 rule="hyper" parents="63 8981 10474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10483">
    <literal><![CDATA[
      (x \ y) * T(K(y,z) * x,x \ y) = (y / x) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(10482(a,2),4794(a,1,2))].">
      <j1 rule="para" parents="10482 4794"/>
    </justification>
  </clause>

  <clause id="10484">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ x) = (x / z) * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(315,a,10483,a)].">
      <j1 rule="hyper" parents="315 10483"/>
    </justification>
  </clause>

  <clause id="10485">
    <literal><![CDATA[
      T(T(x,y),z) / T(x,u) = T(x,u) \ T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(3587(a,1),10479(a,1,2,1))].">
      <j1 rule="para" parents="3587 10479"/>
    </justification>
  </clause>

  <clause id="10486">
    <literal><![CDATA[
      K(x \ 1,T(y * x,z)) = K(x \ 1,T(y,z) * x)
    ]]></literal>
    <justification jstring="[para(2208(a,1),10473(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2208 10473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10487">
    <literal><![CDATA[
      K(x \ 1,T(y * x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,x * T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(10486(a,2),10349(a,1))].">
      <j1 rule="para" parents="10486 10349"/>
    </justification>
  </clause>

  <clause id="10488">
    <literal><![CDATA[
      K(1 / x,T(y * x,z)) = K(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(10487,a,3403,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="10487 3403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10489">
    <literal><![CDATA[
      T(1 / x,T(y * x,z)) = T(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,10488,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 10488 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10490">
    <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(347,a,27,a,b,10460,a),flip(a)].">
      <j1 rule="hyper" parents="347 27 10460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10491">
    <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(10260(a,1),10490(a,1,1))].">
      <j1 rule="para" parents="10260 10490"/>
    </justification>
  </clause>

  <clause id="10492">
    <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),10491(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 10491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10493">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(683,a,10492,a),flip(a)].">
      <j1 rule="hyper" parents="683 10492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10495">
    <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(10492(a,1),5337(a,1,2,1))].">
      <j1 rule="para" parents="10492 5337"/>
    </justification>
  </clause>

  <clause id="10496">
    <literal><![CDATA[
      R((x \ y) \ y,z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,932,a(flip),b,10493,a)].">
      <j1 rule="hyper" parents="63 932 10493"/>
    </justification>
  </clause>

  <clause id="10497">
    <literal><![CDATA[
      (R(x,y,z) \ (x * u)) \ (x * u) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),10493(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 10493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10498">
    <literal><![CDATA[
      (R(x / y,z,u) \ x) \ x = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(749(a,1),10493(a,1,1)),flip(a)].">
      <j1 rule="para" parents="749 10493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10500">
    <literal><![CDATA[
      R(T(x,x \ y),x,y) = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(2257(a,1),10493(a,2,1))].">
      <j1 rule="para" parents="2257 10493"/>
    </justification>
  </clause>

  <clause id="10501">
    <literal><![CDATA[
      R(((x * K(y,x)) \ y) \ y,z,u) = (R(x,z,u) \ ((R(x,z,u) * y) / R(x,z,u))) \ y
    ]]></literal>
    <justification jstring="[para(5547(a,1),10496(a,2,1))].">
      <j1 rule="para" parents="5547 10496"/>
    </justification>
  </clause>

  <clause id="10502">
    <literal><![CDATA[
      K(x,R(x / y,z,u) \ w) = K(x,R(y \ x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(10498(a,1),8402(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10498 8402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10503">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = (x * u) \ (x * (R(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(1751(a,1),10497(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1751 10497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10504">
    <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(347,a,263,a(flip),b,10503,a),flip(a)].">
      <j1 rule="hyper" parents="347 263 10503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10505">
    <literal><![CDATA[
      T(x,R(x,y,z) * u) = T(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(1088,a,10504,a),flip(a)].">
      <j1 rule="hyper" parents="1088 10504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10506">
    <literal><![CDATA[
      T(x,x * (R(x,y,z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),10505(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 10505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10508">
    <literal><![CDATA[
      K(R(x,y,z) * u,R(x,w,v5)) = R(T(x,x * u),w,v5) \ R(x,w,v5)
    ]]></literal>
    <justification jstring="[para(10505(a,1),4937(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10505 4937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10509">
    <literal><![CDATA[
      T(x,x * (R(x,y,z) \ u)) = x * K(x,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,4929,a(flip),b,10506,a),flip(a)].">
      <j1 rule="hyper" parents="347 4929 10506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10510">
    <literal><![CDATA[
      K(x,x * (R(x,y,z) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(5005,a,10509,a)].">
      <j1 rule="hyper" parents="5005 10509"/>
    </justification>
  </clause>

  <clause id="10511">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9809,a(flip),b,10510,a)].">
      <j1 rule="hyper" parents="63 9809 10510"/>
    </justification>
  </clause>

  <clause id="10512">
    <literal><![CDATA[
      K(x,R(x,y,z) * u) = K(x,x * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),10510(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 10510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10513">
    <literal><![CDATA[
      K(x,R(x,y,z) * (x \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[para(75(a,1),10510(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 10510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10514">
    <literal><![CDATA[
      K(x,x \ (y * z)) = K(x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(578(a,1),10511(a,1,2)),flip(a)].">
      <j1 rule="para" parents="578 10511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10515">
    <literal><![CDATA[
      K(x,y * ((x * y) \ z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(581(a,1),10511(a,1,2))].">
      <j1 rule="para" parents="581 10511"/>
    </justification>
  </clause>

  <clause id="10516">
    <literal><![CDATA[
      K(x,x \ ((x * R(T(x,y),z,u)) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w \ x) = v5
    ]]></literal>
    <justification jstring="[para(10511(a,1),9470(a,1))].">
      <j1 rule="para" parents="10511 9470"/>
    </justification>
  </clause>

  <clause id="10518">
    <literal><![CDATA[
      K(x,y * R(x,z,u)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7942,a(flip),b,10512,a)].">
      <j1 rule="hyper" parents="63 7942 10512"/>
    </justification>
  </clause>

  <clause id="10522">
    <literal><![CDATA[
      K(x,(x \ y) * z) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9547,a(flip),b,10514,a),flip(a)].">
      <j1 rule="hyper" parents="63 9547 10514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10523">
    <literal><![CDATA[
      T(x,(x \ y) * z) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(132,a,10522,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 10522 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10524">
    <literal><![CDATA[
      K(x,R(x,y,z) * (x \ u)) = K(x,u * (x \ R(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,7942,a,b,10522,a)].">
      <j1 rule="hyper" parents="63 7942 10522"/>
    </justification>
  </clause>

  <clause id="10525">
    <literal><![CDATA[
      T(x,(y / x) * z) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(7931,a,10523,a)].">
      <j1 rule="hyper" parents="7931 10523"/>
    </justification>
  </clause>

  <clause id="10526">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * T(x,(x \ L(x,w,v5)) * u)) = x * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(10523(a,2),9718(a,1,2,2))].">
      <j1 rule="para" parents="10523 9718"/>
    </justification>
  </clause>

  <clause id="10527">
    <literal><![CDATA[
      K(x,y * (x \ R(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10513,a(flip),b,10524,a),flip(a)].">
      <j1 rule="hyper" parents="63 10513 10524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10529">
    <literal><![CDATA[
      K(x,y * (x \ R(x,z,u))) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,4913,a(flip),b,10527,a),flip(a)].">
      <j1 rule="hyper" parents="347 4913 10527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10530">
    <literal><![CDATA[
      x * K(x * (y \ R(y,z,u)),y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(6139,a,10529,a)].">
      <j1 rule="hyper" parents="6139 10529"/>
    </justification>
  </clause>

  <clause id="10531">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w \ x) = v5
    ]]></literal>
    <justification jstring="[para(10217(a,1),10516(a,1))].">
      <j1 rule="para" parents="10217 10516"/>
    </justification>
  </clause>

  <clause id="10533">
    <literal><![CDATA[
      K(R(x,y,z) * u,R(x,w,v5)) = K(x * u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,4937,a(flip),b,10508,a),flip(a)].">
      <j1 rule="hyper" parents="347 4937 10508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10534">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8050,a,10533,a)].">
      <j1 rule="hyper" parents="8050 10533"/>
    </justification>
  </clause>

  <clause id="10535">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(x * y,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,9364,a,b,10534,a),flip(a)].">
      <j1 rule="hyper" parents="347 9364 10534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10536">
    <literal><![CDATA[
      L(x,T(y,y \ z) \ 1,y) = L(x,((y \ z) \ z) \ 1,(y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,4805,a(flip),b,10184,a)].">
      <j1 rule="hyper" parents="347 4805 10184"/>
    </justification>
  </clause>

  <clause id="10538">
    <literal><![CDATA[
      K(R(x,y,z) \ u,R(x,y,z)) = K(x \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(5832,a,10495,a),flip(a)].">
      <j1 rule="hyper" parents="5832 10495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10539">
    <literal><![CDATA[
      T(R(x,y,z) * K(x \ u,R(x,y,z)),u) = L(R(x,y,z),R(x,y,z) \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(10538(a,1),4903(a,1,1,2))].">
      <j1 rule="para" parents="10538 4903"/>
    </justification>
  </clause>

  <clause id="10540">
    <literal><![CDATA[
      ((x * y) * a(y,x,y)) \ ((y * x) * y) = R(T(y,y * x),x * y,a(y,x,y))
    ]]></literal>
    <justification jstring="[para(4270(a,1),10328(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4270 10328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10541">
    <literal><![CDATA[
      L(x,y,x \ L(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(1020,a,10526,a)].">
      <j1 rule="hyper" parents="1020 10526"/>
    </justification>
  </clause>

  <clause id="10542">
    <literal><![CDATA[
      L(x,y,L(x,z,u) \ L(L(x,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(161,a,10541,a)].">
      <j1 rule="hyper" parents="161 10541"/>
    </justification>
  </clause>

  <clause id="10543">
    <literal><![CDATA[
      L(L(x,y,z),u,x \ L(x,w,v5)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(10541(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10541 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10544">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (u * x) = ((x \ L(x,y,z)) \ u) * x
    ]]></literal>
    <justification jstring="[para(10541(a,1),538(a,1,2,2))].">
      <j1 rule="para" parents="10541 538"/>
    </justification>
  </clause>

  <clause id="10545">
    <literal><![CDATA[
      L(x,y,L(x \ L(x,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(4638(a,1),10542(a,1,3))].">
      <j1 rule="para" parents="4638 10542"/>
    </justification>
  </clause>

  <clause id="10546">
    <literal><![CDATA[
      L(x,y,(z * u) \ ((z * (u * x)) / x)) = x
    ]]></literal>
    <justification jstring="[para(3970(a,1),10545(a,1,3))].">
      <j1 rule="para" parents="3970 10545"/>
    </justification>
  </clause>

  <clause id="10547">
    <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(347,a,7093,a(flip),b,10108,a),flip(a)].">
      <j1 rule="hyper" parents="347 7093 10108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10548">
    <literal><![CDATA[
      R(((x * K(y,x)) \ y) \ y,z,u) = (R(x,z,u) \ y) \ T(y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,7786,a(flip),b,10501,a),flip(a)].">
      <j1 rule="hyper" parents="347 7786 10501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10549">
    <literal><![CDATA[
      (R(x,y,z) \ u) \ T(u,R(x,y,z)) = R((x \ u) \ T(u,x),y,z)
    ]]></literal>
    <justification jstring="[para(7766(a,1),10548(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7766 10548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10551">
    <literal><![CDATA[
      T(R(x * K(x \ y,x),z,u),y) = L(R(x,z,u),R(x,z,u) \ y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(5438(a,1),10539(a,1,1))].">
      <j1 rule="para" parents="5438 10539"/>
    </justification>
  </clause>

  <clause id="10552">
    <literal><![CDATA[
      R(T(x * K(x \ y,x),y),z,u) = L(R(x,z,u),R(x,z,u) \ y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(6366,a,10551,a)].">
      <j1 rule="hyper" parents="6366 10551"/>
    </justification>
  </clause>

  <clause id="10553">
    <literal><![CDATA[
      L(R(x,y,z),R(x,y,z) \ u,R(x,y,z)) = R(L(x,x \ u,x),y,z)
    ]]></literal>
    <justification jstring="[para(4903(a,1),10552(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4903 10552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10554">
    <literal><![CDATA[
      L(R(x,y,z),R(x,y,z) \ u,R(x,y,z)) = L(R(x,y,z),x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,29,a(flip),b,10553,a),flip(a)].">
      <j1 rule="hyper" parents="347 29 10553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10555">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = (L(R(x,y,z),x \ u,x) * u) \ (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(10554(a,1),2128(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10554 2128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10556">
    <literal><![CDATA[
      K(T(x,y * z),u / ((y * T(x,y * z)) * z)) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,7716,a(flip),b,10547,a),flip(a)].">
      <j1 rule="hyper" parents="347 7716 10547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10557">
    <literal><![CDATA[
      K(x,T(y / ((z * T(x,z * u)) * u),z * u)) = K(x,(z * u) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(7488,a,10556,a)].">
      <j1 rule="hyper" parents="7488 10556"/>
    </justification>
  </clause>

  <clause id="10558">
    <literal><![CDATA[
      K(x,T(y / ((z * x) * u),z * u)) = K(x,(z * u) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10013,a(flip),b,10557,a)].">
      <j1 rule="hyper" parents="63 10013 10557"/>
    </justification>
  </clause>

  <clause id="10560">
    <literal><![CDATA[
      K(x,((y * x) * z) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9084,a(flip),b,10558,a)].">
      <j1 rule="hyper" parents="63 9084 10558"/>
    </justification>
  </clause>

  <clause id="10561">
    <literal><![CDATA[
      K(x,((x \ y) * z) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8485,a(flip),b,10560,a),flip(a)].">
      <j1 rule="hyper" parents="63 8485 10560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10562">
    <literal><![CDATA[
      K(x,((x \ y) * z) \ 1) = K(x,(y * z) \ x)
    ]]></literal>
    <justification jstring="[para(68(a,1),10561(a,1,2,2))].">
      <j1 rule="para" parents="68 10561"/>
    </justification>
  </clause>

  <clause id="10563">
    <literal><![CDATA[
      1 / (x * (L(x,1 / x,(1 / x) * y) \ x)) = L(L(1 / x,1 / x,x \ 1),1 / x,y)
    ]]></literal>
    <justification jstring="[para(3936(a,1),10208(a,2,1))].">
      <j1 rule="para" parents="3936 10208"/>
    </justification>
  </clause>

  <clause id="10564">
    <literal><![CDATA[
      T(x,K(y,z)) * L(u,K(y,z) \ x,K(y,z)) = K(y,z) * ((x * K(z,y)) * u)
    ]]></literal>
    <justification jstring="[para(7530(a,1),10256(a,1,1))].">
      <j1 rule="para" parents="7530 10256"/>
    </justification>
  </clause>

  <clause id="10565">
    <literal><![CDATA[
      T(x,K(y,z)) * L(u,K(z,y) * x,K(y,z)) = K(y,z) * ((x * K(z,y)) * u)
    ]]></literal>
    <justification jstring="[para(5256(a,1),10564(a,1,2,2))].">
      <j1 rule="para" parents="5256 10564"/>
    </justification>
  </clause>

  <clause id="10566">
    <literal><![CDATA[
      1 / (x * (L(x,1 / x,(1 / x) * y) \ x)) = L(L(1 / x,x,x \ 1),1 / x,y)
    ]]></literal>
    <justification jstring="[para(3189(a,1),10563(a,2,1))].">
      <j1 rule="para" parents="3189 10563"/>
    </justification>
  </clause>

  <clause id="10567">
    <literal><![CDATA[
      1 / (x * (L(x,1 / x,(1 / x) * y) \ x)) = L(1 / L(x,x,x),1 / x,y)
    ]]></literal>
    <justification jstring="[para(10065(a,1),10566(a,2,1))].">
      <j1 rule="para" parents="10065 10566"/>
    </justification>
  </clause>

  <clause id="10568">
    <literal><![CDATA[
      1 / (x * (L(x,1 / x,(1 / x) * y) \ x)) = L(1 / L(x,x,x),x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3189,a(flip),b,10567,a),flip(a)].">
      <j1 rule="hyper" parents="347 3189 10567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10569">
    <literal><![CDATA[
      1 / (x * (L(x,1 / x,(1 / x) * y) \ x)) = L(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,10064,a(flip),b,10568,a),flip(a)].">
      <j1 rule="hyper" parents="347 10064 10568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10570">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u \ z,u)) = (((u \ z) * u) * y) \ (((u \ z) * u) * (y * x))
    ]]></literal>
    <justification jstring="[para(10244(a,1),10246(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10244 10246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10571">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(u \ z) * u) = w
    ]]></literal>
    <justification jstring="[para(10570(a,2),545(a,1))].">
      <j1 rule="para" parents="10570 545"/>
    </justification>
  </clause>

  <clause id="10572">
    <literal><![CDATA[
      L(L(x,y,z * u),(z * u) * y,K(u,z)) = ((u * z) * y) \ ((u * z) * (y * x))
    ]]></literal>
    <justification jstring="[para(10281(a,1),10303(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10281 10303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10573">
    <literal><![CDATA[
      L(L(x,y,z * u),(z * u) * y,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(10572(a,2),545(a,1))].">
      <j1 rule="para" parents="10572 545"/>
    </justification>
  </clause>

  <clause id="10575">
    <literal><![CDATA[
      T(T(x * K(y,x \ z),u),T(z / x,y)) = T(T(x * K(y,x \ z),u),T(x \ z,y))
    ]]></literal>
    <justification jstring="[para(6104(a,1),7505(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6104 7505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10576">
    <literal><![CDATA[
      T(T(x * K(y,x \ z),u),T(z / x,y)) = T(T(K(y,x \ z) * x,x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,6843,a(flip),b,10575,a),flip(a)].">
      <j1 rule="hyper" parents="347 6843 10575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10577">
    <literal><![CDATA[
      T(T(x * K(y,x \ z),u),T(z / x,y)) = T(T(x \ z,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(7677(a,1),10576(a,2,1))].">
      <j1 rule="para" parents="7677 10576"/>
    </justification>
  </clause>

  <clause id="10578">
    <literal><![CDATA[
      T(x * K(y,x \ z),T(z / x,y)) = T(x \ z,y) \ z
    ]]></literal>
    <justification jstring="[hyper(156,a,10577,a)].">
      <j1 rule="hyper" parents="156 10577"/>
    </justification>
  </clause>

  <clause id="10579">
    <literal><![CDATA[
      T(x,T(y / T(y / z,u),w)) = T(x,T(T(z \ y,u) \ y,w))
    ]]></literal>
    <justification jstring="[para(10577(a,1),7751(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10577 7751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10580">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),K(z,T(y,x))) = (x * (z * y)) \ ((x * y) * T(z,y))
    ]]></literal>
    <justification jstring="[para(9664(a,1),8125(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9664 8125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10581">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),K(z,T(y,x))) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(10580(a,2),1106(a,1))].">
      <j1 rule="para" parents="10580 1106"/>
    </justification>
  </clause>

  <clause id="10582">
    <literal><![CDATA[
      (T(x,y) * (z * R(x,u,w))) \ ((T(x,y) * z) * R(x,u,w)) = a(x,K(x,y) * z,R(x,u,w))
    ]]></literal>
    <justification jstring="[para(4943(a,1),8287(a,1,1))].">
      <j1 rule="para" parents="4943 8287"/>
    </justification>
  </clause>

  <clause id="10583">
    <literal><![CDATA[
      a(x,K(x,y) * z,R(x,u,w)) = a(T(x,y),z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(836,a,10582,a),flip(a)].">
      <j1 rule="hyper" parents="836 10582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10584">
    <literal><![CDATA[
      a(x,K(x,y) * z,R(x,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(10582(a,1),836(a,1))].">
      <j1 rule="para" parents="10582 836"/>
    </justification>
  </clause>

  <clause id="10585">
    <literal><![CDATA[
      a(T(x,y),T(x,y) \ z,R(x,u,w)) = a(x,x \ z,R(x,u,w))
    ]]></literal>
    <justification jstring="[para(5159(a,1),10583(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5159 10583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10586">
    <literal><![CDATA[
      R(K(x,y) * R(K(x,y) \ 1,z,u),K(y,w),v5) = K(x,y) * R(K(x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(8658(a,1),8660(a,2,2,1,1))].">
      <j1 rule="para" parents="8658 8660"/>
    </justification>
  </clause>

  <clause id="10587">
    <literal><![CDATA[
      R(K(x,y) * R(K(x,y) \ 1,z,u),K(y,w),v5) = K(x,y) * R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5173(a,1),10586(a,2,2,1))].">
      <j1 rule="para" parents="5173 10586"/>
    </justification>
  </clause>

  <clause id="10589">
    <literal><![CDATA[
      R(K(x,y) * R(K(y,x),z,u),K(y,w),v5) = K(x,y) * R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5173(a,1),10587(a,1,1,2,1))].">
      <j1 rule="para" parents="5173 10587"/>
    </justification>
  </clause>

  <clause id="10590">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (K(x,y) * (z * u)) = K(y,x) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5283,a(flip),b,10589,a)].">
      <j1 rule="hyper" parents="63 5283 10589"/>
    </justification>
  </clause>

  <clause id="10591">
    <literal><![CDATA[
      L(x,K(y,z),R(K(u,y) * R(K(y,u),w,v5),K(y,z),x)) = ((K(u,y) * R(K(y,u),w,v5)) * K(y,z)) \ (((K(u,y) * R(K(y,u),w,v5)) * K(y,z)) * x)
    ]]></literal>
    <justification jstring="[para(10589(a,1),589(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10589 589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10592">
    <literal><![CDATA[
      R(K(x,y) * R(K(y,x),z,u),K(y,w),v5) * v6 = K(x,y) * (R(K(y,x),z,u) * v6)
    ]]></literal>
    <justification jstring="[para(10589(a,2),6940(a,1,1))].">
      <j1 rule="para" parents="10589 6940"/>
    </justification>
  </clause>

  <clause id="10594">
    <literal><![CDATA[
      R(K(x,K(y,z)) * R(K(y,K(z,x)),u,w),K(K(y,z),v5),v6) * v7 = K(x,K(y,z)) * (R(K(K(y,z),x),u,w) * v7)
    ]]></literal>
    <justification jstring="[para(7261(a,1),10592(a,1,1,1,2,1))].">
      <j1 rule="para" parents="7261 10592"/>
    </justification>
  </clause>

  <clause id="10595">
    <literal><![CDATA[
      K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w) = T(K(x,T(y,z)) * u,w) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7335,a(flip),b,8672,a),flip(a)].">
      <j1 rule="hyper" parents="63 7335 8672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10596">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ (u * x),L(x,y,z)) = K(u * x,L(x,y,z)) * K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(7139(a,1),9734(a,2,2))].">
      <j1 rule="para" parents="7139 9734"/>
    </justification>
  </clause>

  <clause id="10597">
    <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(347,a,5598,a(flip),b,10030,a),flip(a)].">
      <j1 rule="hyper" parents="347 5598 10030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10598">
    <literal><![CDATA[
      (L(x,y,z) * (K(x,T(u,w)) * w)) \ (L(x,y,z) * w) = R(K(u,L(x,w,L(x,y,z))),L(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(5737(a,1),10096(a,1,1))].">
      <j1 rule="para" parents="5737 10096"/>
    </justification>
  </clause>

  <clause id="10599">
    <literal><![CDATA[
      (x * T(y,(x / z) * z)) / a(x / z,z,T(y,(x / z) * z)) = L(y,z,z \ x) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,168,a(flip),b,10160,a),flip(a)].">
      <j1 rule="hyper" parents="347 168 10160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10601">
    <literal><![CDATA[
      (x * T(y,x)) / a(x / z,z,T(y,(x / z) * z)) = L(y,z,z \ x) * x
    ]]></literal>
    <justification jstring="[para(12(a,1),10599(a,1,1,2,2))].">
      <j1 rule="para" parents="12 10599"/>
    </justification>
  </clause>

  <clause id="10602">
    <literal><![CDATA[
      (x * y) / a(y / z,z,T(x,(y / z) * z)) = L(x,z,z \ y) * y
    ]]></literal>
    <justification jstring="[para(111(a,1),10601(a,1,1))].">
      <j1 rule="para" parents="111 10601"/>
    </justification>
  </clause>

  <clause id="10603">
    <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(80(a,1),10597(a,2,2,1,2))].">
      <j1 rule="para" parents="80 10597"/>
    </justification>
  </clause>

  <clause id="10605">
    <literal><![CDATA[
      K(x,((1 / (K(y,x \ z) / y)) * z) \ (u * x)) = K(x,(((z \ x) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(6250(a,1),10603(a,1,2,1,1,2,1))].">
      <j1 rule="para" parents="6250 10603"/>
    </justification>
  </clause>

  <clause id="10606">
    <literal><![CDATA[
      K(x,(((y \ x) \ 1) * z) \ u) = K(x,((x \ y) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9347,a(flip),b,10605,a),flip(a)].">
      <j1 rule="hyper" parents="63 9347 10605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10607">
    <literal><![CDATA[
      (L(x,y,z) * (u * K(x,w))) \ (L(x,y,z) * u) = R(K(w,L(x,u,L(x,y,z))),L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(7373(a,1),10598(a,1,1,2))].">
      <j1 rule="para" parents="7373 10598"/>
    </justification>
  </clause>

  <clause id="10608">
    <literal><![CDATA[
      R(K(x,L(y,z,L(y,u,w))),L(y,u,w),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6921,a,10607,a),flip(a)].">
      <j1 rule="hyper" parents="6921 10607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10609">
    <literal><![CDATA[
      R(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8269(a,1),10608(a,1,1))].">
      <j1 rule="para" parents="8269 10608"/>
    </justification>
  </clause>

  <clause id="10610">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K(L(x,y,z) / (w / u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6515,a(flip),b,10609,a)].">
      <j1 rule="hyper" parents="63 6515 10609"/>
    </justification>
  </clause>

  <clause id="10612">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K((w / u) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,6027,a(flip),b,10610,a),flip(a)].">
      <j1 rule="hyper" parents="347 6027 10610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10613">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((u / w) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9898,a,b,10612,a)].">
      <j1 rule="hyper" parents="63 9898 10612"/>
    </justification>
  </clause>

  <clause id="10614">
    <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(10613(a,1),7603(a,1))].">
      <j1 rule="para" parents="10613 7603"/>
    </justification>
  </clause>

  <clause id="10615">
    <literal><![CDATA[
      (R(x,y,y \ 1) \ (x * y)) * R(x,y,y \ 1) = (x * y) * K((y \ 1) \ 1,(x * y) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(585(a,1),5691(a,1,2))].">
      <j1 rule="para" parents="585 5691"/>
    </justification>
  </clause>

  <clause id="10616">
    <literal><![CDATA[
      (R(x,y,y \ 1) \ (x * y)) * R(x,y,y \ 1) = (x * y) * K((y \ 1) \ 1,R(x,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(585(a,1),10615(a,2,2,2))].">
      <j1 rule="para" parents="585 10615"/>
    </justification>
  </clause>

  <clause id="10617">
    <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(4944(a,1),6090(a,2,2))].">
      <j1 rule="para" parents="4944 6090"/>
    </justification>
  </clause>

  <clause id="10618">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),x \ y,T(x,x \ y)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,5975,a(flip),b,10617,a),flip(a)].">
      <j1 rule="hyper" parents="347 5975 10617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10620">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),y / x,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10181,a(flip),b,10618,a)].">
      <j1 rule="hyper" parents="63 10181 10618"/>
    </justification>
  </clause>

  <clause id="10621">
    <literal><![CDATA[
      K(R(x \ y,z,u),w \ (y / x)) = K(R(x \ y,z,u),w \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(6201,a,8186,a),flip(a)].">
      <j1 rule="hyper" parents="6201 8186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10622">
    <literal><![CDATA[
      K(R(x \ (x * y),z,u),R(y / w,w,K(x,y)) \ (x \ (x * y))) = K(R(x \ (x * y),z,u),w * K(x,y))
    ]]></literal>
    <justification jstring="[para(5062(a,1),10621(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5062 10621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10623">
    <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(2027(a,2),8364(a,1,2,2))].">
      <j1 rule="para" parents="2027 8364"/>
    </justification>
  </clause>

  <clause id="10624">
    <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(9526(a,1),9757(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9526 9757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10625">
    <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(7097(a,1),10624(a,2,2))].">
      <j1 rule="para" parents="7097 10624"/>
    </justification>
  </clause>

  <clause id="10627">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) * K((x / y) \ 1,T(z,y \ x)) = a((x / y) \ 1,z,(x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(3895(a,1),9758(a,1,1))].">
      <j1 rule="para" parents="3895 9758"/>
    </justification>
  </clause>

  <clause id="10628">
    <literal><![CDATA[
      K(x,y) * (R(K(z,y),K(x,y),u) * u) = (K(z,y) * K(x,y)) * u
    ]]></literal>
    <justification jstring="[para(11(a,1),9942(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 9942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10630">
    <literal><![CDATA[
      (K(x,y) * K(z,y)) * u = K(z,y) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(8654(a,1),10628(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8654 10628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10632">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = a(x,x \ u,T(R(x,y,z),u))
    ]]></literal>
    <justification jstring="[hyper(347,a,2128,a(flip),b,10555,a),flip(a)].">
      <j1 rule="hyper" parents="347 2128 10555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10633">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = a(x,x \ u,R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(27(a,2),10632(a,2,3))].">
      <j1 rule="para" parents="27 10632"/>
    </justification>
  </clause>

  <clause id="10634">
    <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(97(a,1),10623(a,1,2)),flip(a)].">
      <j1 rule="para" parents="97 10623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10635">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K((y / x) \ 1,T(z,x \ y)) = a((y / x) \ 1,z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(9890(a,1),10627(a,1,1))].">
      <j1 rule="para" parents="9890 10627"/>
    </justification>
  </clause>

  <clause id="10636">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,T(z,x \ y)) = a((y / x) \ 1,z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(5551(a,1),10635(a,1,2))].">
      <j1 rule="para" parents="5551 10635"/>
    </justification>
  </clause>

  <clause id="10637">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((y / x) \ 1,z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(7801(a,1),10636(a,1,2))].">
      <j1 rule="para" parents="7801 10636"/>
    </justification>
  </clause>

  <clause id="10638">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((z \ 1) * ((y * z) / y))) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(4980(a,1),6048(a,1,2,2,1))].">
      <j1 rule="para" parents="4980 6048"/>
    </justification>
  </clause>

  <clause id="10640">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((T(z,y) \ 1) * z)) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(6044(a,1),10638(a,1,2,2))].">
      <j1 rule="para" parents="6044 10638"/>
    </justification>
  </clause>

  <clause id="10641">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * ((T(y,x) \ 1) * y) = T(1 \ (1 / y),(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(185,a,10640,a)].">
      <j1 rule="hyper" parents="185 10640"/>
    </justification>
  </clause>

  <clause id="10642">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * ((T(y,x) \ 1) * y) = T(1 / y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(66(a,1),10641(a,2,1))].">
      <j1 rule="para" parents="66 10641"/>
    </justification>
  </clause>

  <clause id="10643">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ (y \ 1) = (T(y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(128,a,5307,a(flip),b,10642,a)].">
      <j1 rule="hyper" parents="128 5307 10642"/>
    </justification>
  </clause>

  <clause id="10644">
    <literal><![CDATA[
      R(R(x,y,z \ u),y * (z \ u),K(z,z \ u)) = ((x * y) * (u / z)) / (y * (u / z))
    ]]></literal>
    <justification jstring="[para(6075(a,1),6077(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6075 6077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10645">
    <literal><![CDATA[
      R(R(x,y,z \ u),y * (z \ u),K(z,z \ u)) = R(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(347,a,20,a,b,10644,a),flip(a)].">
      <j1 rule="hyper" parents="347 20 10644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10646">
    <literal><![CDATA[
      R(R(x,y,z \ u),y * (z \ u),K(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u / z) = w
    ]]></literal>
    <justification jstring="[para(10644(a,2),595(a,1))].">
      <j1 rule="para" parents="10644 595"/>
    </justification>
  </clause>

  <clause id="10647">
    <literal><![CDATA[
      K(R(x,K(y * z,x) * y,z),u \ x) = K(x,((y * z) * R(x,y,z)) / ((u * y) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8455,a(flip),b,6750,a),flip(a)].">
      <j1 rule="hyper" parents="63 8455 6750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10649">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = K(z,(1 / y) \ 1) * T(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(6259(a,1),7243(a,2,1))].">
      <j1 rule="para" parents="6259 7243"/>
    </justification>
  </clause>

  <clause id="10650">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = K(z,y) * T(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(83(a,1),10649(a,2,1,2))].">
      <j1 rule="para" parents="83 10649"/>
    </justification>
  </clause>

  <clause id="10652">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = T(K(z,y) * (x * (1 / y)),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,7515,a,b,10650,a),flip(a)].">
      <j1 rule="hyper" parents="347 7515 10650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10653">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = T(y,z) \ R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,7679,a(flip),b,10652,a),flip(a)].">
      <j1 rule="hyper" parents="347 7679 10652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10654">
    <literal><![CDATA[
      x / (T(y,z) \ R(x,y \ 1,y)) = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[para(10653(a,1),7507(a,1,2))].">
      <j1 rule="para" parents="10653 7507"/>
    </justification>
  </clause>

  <clause id="10655">
    <literal><![CDATA[
      K(x \ (y * z),z) * K(z,z \ T(z * ((y \ x) \ 1),z)) = a(z,(y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,10076,a(flip),b,8617,a),flip(a)].">
      <j1 rule="hyper" parents="347 10076 8617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10656">
    <literal><![CDATA[
      K(x \ (y * z),z) * K(z,(y \ x) \ 1) = a(z,(y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(7877(a,1),10655(a,1,2))].">
      <j1 rule="para" parents="7877 10655"/>
    </justification>
  </clause>

  <clause id="10657">
    <literal><![CDATA[
      K(x \ (y * z),z) * K(z,x \ y) = a(z,(y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(6250(a,1),10656(a,1,2))].">
      <j1 rule="para" parents="6250 10656"/>
    </justification>
  </clause>

  <clause id="10659">
    <literal><![CDATA[
      K(x * (y \ z),x) * K(x,y \ z) = a(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(9817(a,1),10657(a,1,1))].">
      <j1 rule="para" parents="9817 10657"/>
    </justification>
  </clause>

  <clause id="10660">
    <literal><![CDATA[
      a(x,(y \ z) \ 1,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,x) = u
    ]]></literal>
    <justification jstring="[para(10659(a,1),8366(a,1))].">
      <j1 rule="para" parents="10659 8366"/>
    </justification>
  </clause>

  <clause id="10661">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = (K(x,y) * K(z,x)) * ((K(z,x) * (K(x,y) * u)) * (K(x,z) * K(y,x)))
    ]]></literal>
    <justification jstring="[para(8385(a,1),8670(a,2,2))].">
      <j1 rule="para" parents="8385 8670"/>
    </justification>
  </clause>

  <clause id="10662">
    <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(1294(a,1),9126(a,2,1))].">
      <j1 rule="para" parents="1294 9126"/>
    </justification>
  </clause>

  <clause id="10663">
    <literal><![CDATA[
      (L(x,x \ y,x) \ y) \ ((y / T(x,y)) * L(z,K(y,x),x \ y)) = L(z,a(x,x \ y,x),x \ y)
    ]]></literal>
    <justification jstring="[para(8511(a,1),10008(a,1,1))].">
      <j1 rule="para" parents="8511 10008"/>
    </justification>
  </clause>

  <clause id="10664">
    <literal><![CDATA[
      (x / T(y,x)) \ ((x / T(y,x)) * L(z,K(x,y),y \ x)) = L(z,a(y,y \ x,y),y \ x)
    ]]></literal>
    <justification jstring="[para(4485(a,1),10663(a,1,1))].">
      <j1 rule="para" parents="4485 10663"/>
    </justification>
  </clause>

  <clause id="10665">
    <literal><![CDATA[
      L(x,a(y,y \ z,y),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,K(z,y),y \ z) = u
    ]]></literal>
    <justification jstring="[para(10664(a,1),356(a,1))].">
      <j1 rule="para" parents="10664 356"/>
    </justification>
  </clause>

  <clause id="10666">
    <literal><![CDATA[
      T(x \ ((y \ x) * 1),(y \ x) \ x) = L(L(((y \ x) \ x) \ 1,y,y),y,y \ x)
    ]]></literal>
    <justification jstring="[para(6961(a,1),10437(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6961 10437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10668">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = (K(x,y) * K(z,x)) * (T(K(x,y) * u,K(z,x)) * K(y,x))
    ]]></literal>
    <justification jstring="[para(8381(a,1),10661(a,2,2))].">
      <j1 rule="para" parents="8381 10661"/>
    </justification>
  </clause>

  <clause id="10669">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = (K(x,y) * K(z,x)) * (T(K(x,y) * u,K(x,z)) * K(y,x))
    ]]></literal>
    <justification jstring="[para(7330(a,1),10668(a,2,2,1))].">
      <j1 rule="para" parents="7330 10668"/>
    </justification>
  </clause>

  <clause id="10670">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = (K(x,y) * K(z,x)) * ((K(x,y) * T(u,K(x,z))) * K(y,x))
    ]]></literal>
    <justification jstring="[para(8475(a,1),10669(a,2,2,1))].">
      <j1 rule="para" parents="8475 10669"/>
    </justification>
  </clause>

  <clause id="10671">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = (K(x,y) * K(z,x)) * T(T(u,K(x,z)),K(x,y))
    ]]></literal>
    <justification jstring="[para(7340(a,1),10670(a,2,2))].">
      <j1 rule="para" parents="7340 10670"/>
    </justification>
  </clause>

  <clause id="10672">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = K(z,x) * (K(x,y) * T(T(u,K(x,z)),K(x,y)))
    ]]></literal>
    <justification jstring="[hyper(347,a,8663,a(flip),b,10671,a),flip(a)].">
      <j1 rule="hyper" parents="347 8663 10671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10673">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = K(z,x) * (T(u,K(x,z)) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,251,a(flip),b,10672,a),flip(a)].">
      <j1 rule="hyper" parents="347 251 10672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10674">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = u * (K(x,y) * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,10007,a(flip),b,10673,a),flip(a)].">
      <j1 rule="hyper" parents="347 10007 10673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10675">
    <literal><![CDATA[
      x * K(K(y,z) * K(u,y),x) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(269,a,10674,a(flip),b,4953,a),flip(a)].">
      <j1 rule="hyper" parents="269 10674 4953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10676">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(269,a,10674,a(flip),b,10671,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="269 10674 10671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10677">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(453,a,10676,a)].">
      <j1 rule="hyper" parents="453 10676"/>
    </justification>
  </clause>

  <clause id="10678">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) = T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(7330(a,1),10676(a,1,1))].">
      <j1 rule="para" parents="7330 10676"/>
    </justification>
  </clause>

  <clause id="10679">
    <literal><![CDATA[
      T(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10676,a(flip),b,10677,a)].">
      <j1 rule="hyper" parents="63 10676 10677"/>
    </justification>
  </clause>

  <clause id="10680">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(u,y) * K(y,z))
    ]]></literal>
    <justification jstring="[para(2556(a,1),10677(a,2,2))].">
      <j1 rule="para" parents="2556 10677"/>
    </justification>
  </clause>

  <clause id="10681">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),K(x,y) \ u) = T(u,K(y,z) * K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(10678(a,1),10009(a,2,1))].">
      <j1 rule="para" parents="10678 10009"/>
    </justification>
  </clause>

  <clause id="10682">
    <literal><![CDATA[
      x * K(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(5036,a,10679,a)].">
      <j1 rule="hyper" parents="5036 10679"/>
    </justification>
  </clause>

  <clause id="10683">
    <literal><![CDATA[
      T(x,K(y,z) * K(z,u)) \ x = K(x,K(z,y)) * K(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(10680(a,1),9212(a,1,1))].">
      <j1 rule="para" parents="10680 9212"/>
    </justification>
  </clause>

  <clause id="10684">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(x,y) * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(34,a,4929,a(flip),b,10675,a),flip(a)].">
      <j1 rule="hyper" parents="34 4929 10675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10685">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(x,z) * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(34,a,10675,a,b,10682,a)].">
      <j1 rule="hyper" parents="34 10675 10682"/>
    </justification>
  </clause>

  <clause id="10686">
    <literal><![CDATA[
      T(x,K(y,z) * K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u) * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(10682(a,1),4984(a,1))].">
      <j1 rule="para" parents="10682 4984"/>
    </justification>
  </clause>

  <clause id="10687">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),u) = K(u,K(y,x) * K(z,y))
    ]]></literal>
    <justification jstring="[para(2556(a,1),10685(a,1,1))].">
      <j1 rule="para" parents="2556 10685"/>
    </justification>
  </clause>

  <clause id="10688">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u) * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(10677(a,2),10686(a,1))].">
      <j1 rule="para" parents="10677 10686"/>
    </justification>
  </clause>

  <clause id="10689">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(z,y) * K(y,u),x)
    ]]></literal>
    <justification jstring="[hyper(4951,a,10683,a),flip(a)].">
      <j1 rule="hyper" parents="4951 10683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10690">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,10687,a(flip),b,10689,a),flip(a)].">
      <j1 rule="hyper" parents="347 10687 10689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10691">
    <literal><![CDATA[
      K(K(x,y) * K(y,(z * u) / ((w \ z) * u)),v5) = K(v5,K(y,x)) * K(v5,R(K(y,w),z,u))
    ]]></literal>
    <justification jstring="[para(6711(a,1),10689(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6711 10689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10692">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(y,z) * K(u,y),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,10684,a,b,10690,a),flip(a)].">
      <j1 rule="hyper" parents="347 10684 10690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10693">
    <literal><![CDATA[
      K(x,y) * (K(z,K(x,u)) * (K(x,y) \ K(u,K(z,w)))) = K(u,K(z,x) * K(w,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9954,a,b,10690,a)].">
      <j1 rule="hyper" parents="63 9954 10690"/>
    </justification>
  </clause>

  <clause id="10694">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x * K(y,u),K(y,w)) = K(x * K(y,u),K(y,z) * K(w,y))
    ]]></literal>
    <justification jstring="[para(8011(a,1),10690(a,1,1))].">
      <j1 rule="para" parents="8011 10690"/>
    </justification>
  </clause>

  <clause id="10695">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),K(x,y) \ u) = K(K(y,z) * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,4913,a,b,10681,a),flip(a)].">
      <j1 rule="hyper" parents="347 4913 10681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10696">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),K(y,x) * u) = K(K(y,z) * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(5256(a,1),10695(a,1,2))].">
      <j1 rule="para" parents="5256 10695"/>
    </justification>
  </clause>

  <clause id="10697">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),K(y,x) * u) = K(u,K(y,z) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,10684,a(flip),b,10696,a),flip(a)].">
      <j1 rule="hyper" parents="347 10684 10696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10698">
    <literal><![CDATA[
      K(x,y) * (K(z,K(x,u)) * (K(x,y) \ K(z,K(u,w)))) = K(u,K(z,x) * K(w,z))
    ]]></literal>
    <justification jstring="[para(7279(a,1),10693(a,1,2,2,2))].">
      <j1 rule="para" parents="7279 10693"/>
    </justification>
  </clause>

  <clause id="10699">
    <literal><![CDATA[
      K(x * K(y,z),K(y,u) * K(w,y)) = K(x,K(y,u)) * K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(8011(a,1),10694(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8011 10694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10700">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(10699(a,1),7898(a,1))].">
      <j1 rule="para" parents="10699 7898"/>
    </justification>
  </clause>

  <clause id="10702">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,K(y,x) * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(10689(a,1),10700(a,1))].">
      <j1 rule="para" parents="10689 10700"/>
    </justification>
  </clause>

  <clause id="10703">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(z,K(x,y) * K(u,x))
    ]]></literal>
    <justification jstring="[hyper(5471,a,10698,a)].">
      <j1 rule="hyper" parents="5471 10698"/>
    </justification>
  </clause>

  <clause id="10704">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,K(z,u)) = K(z,K(y,x) * K(u,y))
    ]]></literal>
    <justification jstring="[para(7279(a,1),10703(a,1,1))].">
      <j1 rule="para" parents="7279 10703"/>
    </justification>
  </clause>

  <clause id="10705">
    <literal><![CDATA[
      R(x,y,z) \ (R((x \ u) \ u,y,z) * w) = K(R((x \ u) \ u,y,z),x \ u) * w
    ]]></literal>
    <justification jstring="[hyper(371,a,5450,a)].">
      <j1 rule="hyper" parents="371 5450"/>
    </justification>
  </clause>

  <clause id="10707">
    <literal><![CDATA[
      (x / (y * K(z,y))) * R(y * K(z,y),z,L(y,u,w)) = (x * K(z * L(y,u,w),y)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,6234,a(flip),b,6587,a),flip(a)].">
      <j1 rule="hyper" parents="347 6234 6587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10708">
    <literal><![CDATA[
      (x / (y * K(z,y))) * R(y * K(z,y),z,L(y,u,w)) = x * (K(y,z) * K(z * L(y,u,w),y))
    ]]></literal>
    <justification jstring="[hyper(347,a,8321,a(flip),b,10707,a),flip(a)].">
      <j1 rule="hyper" parents="347 8321 10707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10709">
    <literal><![CDATA[
      (x / (y * K(z,y))) * R(y * K(z,y),z,L(y,u,w)) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(9442(a,1),10708(a,2,2))].">
      <j1 rule="para" parents="9442 10708"/>
    </justification>
  </clause>

  <clause id="10710">
    <literal><![CDATA[
      ((x / y) * K(y,z)) * R(y * K(z,y),z,L(y,u,w)) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(6217(a,1),10709(a,1,1))].">
      <j1 rule="para" parents="6217 10709"/>
    </justification>
  </clause>

  <clause id="10711">
    <literal><![CDATA[
      ((x / y) * K(y,z)) * (y * K(z * L(y,u,w),y)) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(6584(a,1),10710(a,1,2))].">
      <j1 rule="para" parents="6584 10710"/>
    </justification>
  </clause>

  <clause id="10712">
    <literal><![CDATA[
      (x / y) * (T(y,z) * K(z * L(y,u,w),y)) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6578,a(flip),b,10711,a)].">
      <j1 rule="hyper" parents="63 6578 10711"/>
    </justification>
  </clause>

  <clause id="10713">
    <literal><![CDATA[
      (x / y) * R(y,z,L(y,u,w)) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(8936(a,1),10712(a,1,2))].">
      <j1 rule="para" parents="8936 10712"/>
    </justification>
  </clause>

  <clause id="10714">
    <literal><![CDATA[
      T(x,y) \ R(z,T(T(x,1),y) \ 1,T(T(x,1),y)) = T(z * (K(y,x) * (1 / T(x,1))),T(T(x,1),y))
    ]]></literal>
    <justification jstring="[para(223(a,1),8539(a,1,1,1))].">
      <j1 rule="para" parents="223 8539"/>
    </justification>
  </clause>

  <clause id="10715">
    <literal><![CDATA[
      T(x * (K(y,z) * (1 / T(z,1))),T(T(z,1),y)) = T(z,y) \ R(x,T(z,y) \ 1,T(T(z,1),y))
    ]]></literal>
    <justification jstring="[para(223(a,1),10714(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="223 10714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10716">
    <literal><![CDATA[
      T(x * (K(y,z) * (1 / T(z,1))),T(T(z,1),y)) = T(z,y) \ R(x,T(z,y) \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[para(223(a,1),10715(a,2,2,3,1))].">
      <j1 rule="para" parents="223 10715"/>
    </justification>
  </clause>

  <clause id="10717">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = (K(y,x) * (x \ 1)) * u
    ]]></literal>
    <justification jstring="[para(5872(a,1),8661(a,2,1,1))].">
      <j1 rule="para" parents="5872 8661"/>
    </justification>
  </clause>

  <clause id="10718">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = (T(x,y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(5209(a,1),10717(a,2,1))].">
      <j1 rule="para" parents="5209 10717"/>
    </justification>
  </clause>

  <clause id="10720">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ 1,z) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(186(a,1),10718(a,1,2,1,2,2))].">
      <j1 rule="para" parents="186 10718"/>
    </justification>
  </clause>

  <clause id="10721">
    <literal><![CDATA[
      (x \ 1) * (K(y,x) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(5499(a,1),10720(a,1,2,1))].">
      <j1 rule="para" parents="5499 10720"/>
    </justification>
  </clause>

  <clause id="10723">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * z) = L(z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(10721(a,1),5875(a,1,2))].">
      <j1 rule="para" parents="10721 5875"/>
    </justification>
  </clause>

  <clause id="10724">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4801,a(flip),b,10723,a)].">
      <j1 rule="hyper" parents="63 4801 10723"/>
    </justification>
  </clause>

  <clause id="10726">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ 1,(y \ z) \ z) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10536,a(flip),b,10724,a)].">
      <j1 rule="hyper" parents="63 10536 10724"/>
    </justification>
  </clause>

  <clause id="10728">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z) \ z) = K(x,((((z \ x) \ x) \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(10726(a,1),10021(a,1,2,1))].">
      <j1 rule="para" parents="10726 10021"/>
    </justification>
  </clause>

  <clause id="10729">
    <literal><![CDATA[
      K(x,((((y \ x) \ x) \ 1) * z) \ 1) = K(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6322,a,10728,a),flip(a)].">
      <j1 rule="hyper" parents="6322 10728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10731">
    <literal><![CDATA[
      K(x,((x \ (y \ x)) * z) \ 1) = K(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,10606,a(flip),b,10729,a)].">
      <j1 rule="hyper" parents="63 10606 10729"/>
    </justification>
  </clause>

  <clause id="10732">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ 1) = K(x,((y \ x) * z) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10562,a(flip),b,10731,a),flip(a)].">
      <j1 rule="hyper" parents="63 10562 10731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10733">
    <literal><![CDATA[
      K(x,((y \ x) * (y / z)) \ x) = L(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,6394,a(flip),b,10732,a),flip(a)].">
      <j1 rule="hyper" parents="63 6394 10732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10734">
    <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(9307(a,1),9310(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9307 9310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10735">
    <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(347,a,4629,a(flip),b,10734,a),flip(a)].">
      <j1 rule="hyper" parents="347 4629 10734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10737">
    <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(1294(a,1),10735(a,2,1))].">
      <j1 rule="para" parents="1294 10735"/>
    </justification>
  </clause>

  <clause id="10738">
    <literal><![CDATA[
      L(x \ L(x,y,z),T(x,u),w) = L(x \ L(x,y,z),x,w)
    ]]></literal>
    <justification jstring="[para(1294(a,1),10737(a,1,1))].">
      <j1 rule="para" parents="1294 10737"/>
    </justification>
  </clause>

  <clause id="10740">
    <literal><![CDATA[
      K(R(x \ (x * y),z,u),R(y / w,w,K(x,y)) \ (x \ (x * y))) = K(R(y,z,u),w * K(x,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),10622(a,2,1,1))].">
      <j1 rule="para" parents="9 10622"/>
    </justification>
  </clause>

  <clause id="10741">
    <literal><![CDATA[
      K(R(x \ (x * y),z,u),R(y / w,w,K(x,y)) \ (x \ (x * y))) = K(R(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,8749,a(flip),b,10740,a),flip(a)].">
      <j1 rule="hyper" parents="347 8749 10740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10743">
    <literal><![CDATA[
      K(R(x,y,z),R(x / u,u,K(w,x)) \ (w \ (w * x))) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),10741(a,1,1,1))].">
      <j1 rule="para" parents="9 10741"/>
    </justification>
  </clause>

  <clause id="10744">
    <literal><![CDATA[
      K(R(x,y,z),R(x / u,u,K(w,x)) \ x) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),10743(a,1,2,2))].">
      <j1 rule="para" parents="9 10743"/>
    </justification>
  </clause>

  <clause id="10745">
    <literal><![CDATA[
      K(R(x,y,z),R(x / u,u,L(K(w,x),v5,v6)) \ x) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(7006(a,1),10744(a,1,2,1,3))].">
      <j1 rule="para" parents="7006 10744"/>
    </justification>
  </clause>

  <clause id="10746">
    <literal><![CDATA[
      ((T(x,(1 / y) \ z) * (z * y)) / T(x,(1 / y) \ z)) / y = z * K(x,(z \ (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,5666,a(flip),b,5436,a),flip(a)].">
      <j1 rule="hyper" parents="347 5666 5436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10747">
    <literal><![CDATA[
      ((x * y) * K(T(z,(1 / y) \ x),x * y)) / y = x * K(z,(x \ (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(4942(a,1),10746(a,1,1))].">
      <j1 rule="para" parents="4942 10746"/>
    </justification>
  </clause>

  <clause id="10748">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(x \ (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(7140(a,1),10747(a,1,1,2))].">
      <j1 rule="para" parents="7140 10747"/>
    </justification>
  </clause>

  <clause id="10749">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(1 / y) \ x)
    ]]></literal>
    <justification jstring="[para(6250(a,1),10748(a,2,2))].">
      <j1 rule="para" parents="6250 10748"/>
    </justification>
  </clause>

  <clause id="10750">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(5413(a,1),10749(a,2,2))].">
      <j1 rule="para" parents="5413 10749"/>
    </justification>
  </clause>

  <clause id="10751">
    <literal><![CDATA[
      (x * K(y,(z \ 1) \ x)) * z = (x * z) * K(y,x * z)
    ]]></literal>
    <justification jstring="[hyper(148,a,10750,a)].">
      <j1 rule="hyper" parents="148 10750"/>
    </justification>
  </clause>

  <clause id="10752">
    <literal><![CDATA[
      (x \ y) * K(z,(x \ 1) \ (x \ y)) = x \ (y * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,5668,a(flip),b,10751,a),flip(a)].">
      <j1 rule="hyper" parents="35 5668 10751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10753">
    <literal><![CDATA[
      (x \ y) \ (x \ (y * K(z,y))) = K(z,(x \ 1) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(138,a,10752,a)].">
      <j1 rule="hyper" parents="138 10752"/>
    </justification>
  </clause>

  <clause id="10754">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ K(y,T(z,u))) = K(u,(x \ 1) \ (x \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(7333(a,1),10753(a,1,2,2))].">
      <j1 rule="para" parents="7333 10753"/>
    </justification>
  </clause>

  <clause id="10755">
    <literal><![CDATA[
      T((1 / x) * R((1 / x) \ 1,y,z),R(x,u,w) \ x) = (1 / x) * R((1 / x) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(6733(a,1),6734(a,2,2,1,1))].">
      <j1 rule="para" parents="6733 6734"/>
    </justification>
  </clause>

  <clause id="10756">
    <literal><![CDATA[
      T((1 / x) * R((1 / x) \ 1,y,z),R(x,u,w) \ x) = (1 / x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),10755(a,2,2,1))].">
      <j1 rule="para" parents="83 10755"/>
    </justification>
  </clause>

  <clause id="10758">
    <literal><![CDATA[
      T((1 / x) * R((1 / x) \ 1,y,z),R(x,u,w) \ x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,3681,a(flip),b,10756,a),flip(a)].">
      <j1 rule="hyper" parents="347 3681 10756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10759">
    <literal><![CDATA[
      T((1 / x) * R(x,y,z),R(x,u,w) \ x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),10758(a,1,1,2,1))].">
      <j1 rule="para" parents="83 10758"/>
    </justification>
  </clause>

  <clause id="10760">
    <literal><![CDATA[
      T(x \ R(x,y,z),R(x,u,w) \ x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3681(a,1),10759(a,1,1))].">
      <j1 rule="para" parents="3681 10759"/>
    </justification>
  </clause>

  <clause id="10761">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) \ 1 = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2579,a(flip),b,10760,a)].">
      <j1 rule="hyper" parents="63 2579 10760"/>
    </justification>
  </clause>

  <clause id="10762">
    <literal><![CDATA[
      x / (x \ R(x,y,z)) = x * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(10760(a,1),3276(a,1,2))].">
      <j1 rule="para" parents="10760 3276"/>
    </justification>
  </clause>

  <clause id="10763">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ 1 = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(4742(a,1),10761(a,1,1))].">
      <j1 rule="para" parents="4742 10761"/>
    </justification>
  </clause>

  <clause id="10764">
    <literal><![CDATA[
      T(R(x \ R(x,y,z),x,y * z),x * (y * z)) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(10761(a,1),4729(a,1,1,1))].">
      <j1 rule="para" parents="10761 4729"/>
    </justification>
  </clause>

  <clause id="10765">
    <literal><![CDATA[
      (x \ L(x,y,x)) \ 1 = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(8387(a,1),10763(a,1,1))].">
      <j1 rule="para" parents="8387 10763"/>
    </justification>
  </clause>

  <clause id="10766">
    <literal><![CDATA[
      T((x * (y * z)) \ (R(x,y,z) * (y * z)),x) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(1039,a,10764,a)].">
      <j1 rule="hyper" parents="1039 10764"/>
    </justification>
  </clause>

  <clause id="10767">
    <literal><![CDATA[
      T((x * (y * z)) \ ((x * y) * z),x) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(107(a,1),10766(a,1,1,2))].">
      <j1 rule="para" parents="107 10766"/>
    </justification>
  </clause>

  <clause id="10768">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1 = T(a(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(14(a,2),10767(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14 10767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10769">
    <literal><![CDATA[
      T(K(x,y) * z,u) * T(K(y,x),T(w,T(K(x,y) * z,u))) = K(y,K(x,w)) * (K(y,x) * T(z * K(x,y),u))
    ]]></literal>
    <justification jstring="[para(7261(a,1),8634(a,2,1))].">
      <j1 rule="para" parents="7261 8634"/>
    </justification>
  </clause>

  <clause id="10770">
    <literal><![CDATA[
      a(x,K(x,y) * z,R(x,u,w)) = x \ (v5 \ ((R(x,z,R(x,u,w)) * (x \ v5)) * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,9524,a(flip),b,9384,a)].">
      <j1 rule="hyper" parents="63 9524 9384"/>
    </justification>
  </clause>

  <clause id="10771">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = x \ (v5 \ ((R(x,z,R(x,u,w)) * (x \ v5)) * x))
    ]]></literal>
    <justification jstring="[hyper(10584,a,10770,a)].">
      <j1 rule="hyper" parents="10584 10770"/>
    </justification>
  </clause>

  <clause id="10774">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = x \ (v5 \ ((x * (x \ v5)) * R(x,z,R(x,u,w))))
    ]]></literal>
    <justification jstring="[para(10446(a,1),10771(a,2,2,2))].">
      <j1 rule="para" parents="10446 10771"/>
    </justification>
  </clause>

  <clause id="10775">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = x \ (v5 \ (v5 * R(x,z,R(x,u,w))))
    ]]></literal>
    <justification jstring="[para(10(a,1),10774(a,2,2,2,1))].">
      <j1 rule="para" parents="10 10774"/>
    </justification>
  </clause>

  <clause id="10776">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = x \ R(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),10775(a,2,2))].">
      <j1 rule="para" parents="9 10775"/>
    </justification>
  </clause>

  <clause id="10778">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,9431,a(flip),b,10776,a),flip(a)].">
      <j1 rule="hyper" parents="347 9431 10776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10779">
    <literal><![CDATA[
      a(x,T(x,y) \ z,R(x,u,w)) = a(x,x \ z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,10585,a(flip),b,10778,a),flip(a)].">
      <j1 rule="hyper" parents="63 10585 10778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10781">
    <literal><![CDATA[
      T(x,x * K((y * z) \ (u * w),w)) \ T(K(w,(y * z) \ (u * w)) * x,x) = K(w,T((y * (w \ z)) \ u,x))
    ]]></literal>
    <justification jstring="[para(8572(a,1),10049(a,1,2,1,1))].">
      <j1 rule="para" parents="8572 10049"/>
    </justification>
  </clause>

  <clause id="10782">
    <literal><![CDATA[
      T(K(x,y) * z,u) * T(K(y,x),T(w,T(K(x,y) * z,u))) = K(y,T(x,w)) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,8061,a(flip),b,10769,a),flip(a)].">
      <j1 rule="hyper" parents="347 8061 10769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10783">
    <literal><![CDATA[
      K(x,T((y * (x \ z)) \ u,w)) = K(x,T((y * z) \ (u * x),w))
    ]]></literal>
    <justification jstring="[hyper(63,a,10048,a(flip),b,10781,a),flip(a)].">
      <j1 rule="hyper" parents="63 10048 10781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10784">
    <literal><![CDATA[
      K(x,T((y * z) \ (u * x),y * z)) = K(x,u / (y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(9103,a,10783,a),flip(a)].">
      <j1 rule="hyper" parents="9103 10783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10785">
    <literal><![CDATA[
      K(x,(y * x) / (z * u)) = K(x,y / (z * (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(7491,a,10784,a)].">
      <j1 rule="hyper" parents="7491 10784"/>
    </justification>
  </clause>

  <clause id="10786">
    <literal><![CDATA[
      K(x,y / (z * (x \ u))) = K(x,((z * u) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(8240,a,10785,a),flip(a)].">
      <j1 rule="hyper" parents="8240 10785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10787">
    <literal><![CDATA[
      R(K(x,((y * z) / (u / w)) \ x),w \ u,w) = K(x,u / ((y * (x \ z)) * w))
    ]]></literal>
    <justification jstring="[para(10786(a,1),9611(a,1,1))].">
      <j1 rule="para" parents="10786 9611"/>
    </justification>
  </clause>

  <clause id="10788">
    <literal><![CDATA[
      K(x,y / ((x \ (z * u)) * w)) = K(x,y / ((z * (x \ u)) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9610,a(flip),b,10787,a)].">
      <j1 rule="hyper" parents="63 9610 10787"/>
    </justification>
  </clause>

  <clause id="10789">
    <literal><![CDATA[
      K(x,y / ((z * (x \ u)) * w)) = K(x,(((z * u) * w) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(10250,a,10788,a),flip(a)].">
      <j1 rule="hyper" parents="10250 10788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10790">
    <literal><![CDATA[
      K(x,(((y * z) * u) / (z * u)) \ x) = R(K(x,y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6751,a(flip),b,10789,a),flip(a)].">
      <j1 rule="hyper" parents="63 6751 10789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10791">
    <literal><![CDATA[
      R(K(x,y \ x),z,u) = K(x,R(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(20(a,2),10790(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20 10790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10792">
    <literal><![CDATA[
      K(x,R(y \ x,z,u) \ x) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(6460(a,1),10791(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6460 10791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10793">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ x) = R(K(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(9810(a,1),10791(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9810 10791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10794">
    <literal><![CDATA[
      R(K(x,R(y \ x,z,u) \ x),w,v5) = K(x,R(R(x / y,z,u),w,v5) \ x)
    ]]></literal>
    <justification jstring="[para(10502(a,1),10791(a,1,1))].">
      <j1 rule="para" parents="10502 10791"/>
    </justification>
  </clause>

  <clause id="10795">
    <literal><![CDATA[
      K(x,R(R(x / y,z,u),w,v5) \ x) = R(R(K(x,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(10792(a,1),10794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10792 10794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10796">
    <literal><![CDATA[
      L(x \ (y * z),x,K(y * z,y)) = (K(y,T(y,y * z) * z) \ x) \ T(T(T(y,y * z) * z,y),y)
    ]]></literal>
    <justification jstring="[para(7916(a,1),5839(a,1,3))].">
      <j1 rule="para" parents="7916 5839"/>
    </justification>
  </clause>

  <clause id="10801">
    <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(5256(a,1),8613(a,1,1,2,2))].">
      <j1 rule="para" parents="5256 8613"/>
    </justification>
  </clause>

  <clause id="10802">
    <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(6041(a,1),8711(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6041 8711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10803">
    <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(347,a,5354,a(flip),b,10802,a),flip(a)].">
      <j1 rule="hyper" parents="347 5354 10802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10805">
    <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(347,a,4974,a(flip),b,10803,a),flip(a)].">
      <j1 rule="hyper" parents="347 4974 10803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10806">
    <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(6041(a,1),10805(a,1,2))].">
      <j1 rule="para" parents="6041 10805"/>
    </justification>
  </clause>

  <clause id="10809">
    <literal><![CDATA[
      T(x,L(y,z,u)) * K(y,w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x * K(y,w),L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(10806(a,1),7865(a,1))].">
      <j1 rule="para" parents="10806 7865"/>
    </justification>
  </clause>

  <clause id="10810">
    <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(9127,a,10662,a)].">
      <j1 rule="hyper" parents="9127 10662"/>
    </justification>
  </clause>

  <clause id="10811">
    <literal><![CDATA[
      T(x \ L(x,y,z),u * x) = T(x \ L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(1294(a,1),10810(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1294 10810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10812">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) * K((x \ y) \ 1,T(z,T(x,y))) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(7755(a,1),9756(a,1,1))].">
      <j1 rule="para" parents="7755 9756"/>
    </justification>
  </clause>

  <clause id="10813">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K((x \ y) \ 1,T(z,T(x,y))) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(9420(a,1),10812(a,1,1))].">
      <j1 rule="para" parents="9420 10812"/>
    </justification>
  </clause>

  <clause id="10814">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(y \ x,T(z,T(x,y))) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(5988(a,1),10813(a,1,2))].">
      <j1 rule="para" parents="5988 10813"/>
    </justification>
  </clause>

  <clause id="10815">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(9043(a,1),10814(a,1,2))].">
      <j1 rule="para" parents="9043 10814"/>
    </justification>
  </clause>

  <clause id="10816">
    <literal><![CDATA[
      R(K(x,K(y,z)) * K(y,K(z,R(x,u,w))),K(K(y,z),v5),v6) * v7 = K(x,K(y,z)) * (R(K(K(y,z),x),u,w) * v7)
    ]]></literal>
    <justification jstring="[para(8917(a,1),10594(a,1,1,1,2))].">
      <j1 rule="para" parents="8917 10594"/>
    </justification>
  </clause>

  <clause id="10817">
    <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(5191(a,1),10801(a,1,1,2))].">
      <j1 rule="para" parents="5191 10801"/>
    </justification>
  </clause>

  <clause id="10818">
    <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(5256(a,1),10817(a,1,2,2,2))].">
      <j1 rule="para" parents="5256 10817"/>
    </justification>
  </clause>

  <clause id="10819">
    <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(8433(a,1),10818(a,1,2))].">
      <j1 rule="para" parents="8433 10818"/>
    </justification>
  </clause>

  <clause id="10820">
    <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(8420(a,1),10819(a,1,2))].">
      <j1 rule="para" parents="8420 10819"/>
    </justification>
  </clause>

  <clause id="10823">
    <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(5256(a,1),10820(a,2,2,1,1))].">
      <j1 rule="para" parents="5256 10820"/>
    </justification>
  </clause>

  <clause id="10824">
    <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(7340(a,1),10823(a,2,2,1))].">
      <j1 rule="para" parents="7340 10823"/>
    </justification>
  </clause>

  <clause id="10825">
    <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(6835(a,2),10824(a,2,2))].">
      <j1 rule="para" parents="6835 10824"/>
    </justification>
  </clause>

  <clause id="10826">
    <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),10825(a,2,2,1))].">
      <j1 rule="para" parents="12 10825"/>
    </justification>
  </clause>

  <clause id="10827">
    <literal><![CDATA[
      ((x * (K(y,z) * u)) / (x * T(u,K(y,z)))) \ T(x * (K(y,z) * u),L(K(z,y),u,x)) = T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x)
    ]]></literal>
    <justification jstring="[para(10826(a,1),8031(a,1,1,2))].">
      <j1 rule="para" parents="10826 8031"/>
    </justification>
  </clause>

  <clause id="10828">
    <literal><![CDATA[
      R(K(x,K(y,z) * K(R(z,u,w),y)),K(K(y,x),v5),v6) * v7 = K(z,K(y,x)) * (R(K(K(y,x),z),u,w) * v7)
    ]]></literal>
    <justification jstring="[para(10704(a,1),10816(a,1,1,1))].">
      <j1 rule="para" parents="10704 10816"/>
    </justification>
  </clause>

  <clause id="10829">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) * T(y / R(y,z,y),R(y,z,y) / y) = R(x,(y / R(y,z,y)) \ 1,y / R(y,z,y))
    ]]></literal>
    <justification jstring="[para(10765(a,1),8390(a,1,1,2))].">
      <j1 rule="para" parents="10765 8390"/>
    </justification>
  </clause>

  <clause id="10830">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) * T(y \ L(y,z,y),R(y,z,y) / y) = R(x,(y / R(y,z,y)) \ 1,y / R(y,z,y))
    ]]></literal>
    <justification jstring="[para(8388(a,1),10829(a,1,2,1))].">
      <j1 rule="para" parents="8388 10829"/>
    </justification>
  </clause>

  <clause id="10831">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) * T(y \ L(y,z,y),y \ R(y,z,y)) = R(x,(y / R(y,z,y)) \ 1,y / R(y,z,y))
    ]]></literal>
    <justification jstring="[para(3675(a,1),10830(a,1,2,2))].">
      <j1 rule="para" parents="3675 10830"/>
    </justification>
  </clause>

  <clause id="10832">
    <literal><![CDATA[
      R(x,(y / R(y,z,y)) \ 1,y / R(y,z,y)) = (x * (y \ R(y,z,y))) * (y \ L(y,z,y))
    ]]></literal>
    <justification jstring="[para(4111(a,1),10831(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4111 10831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10834">
    <literal><![CDATA[
      R(x,(y \ L(y,z,y)) \ 1,y / R(y,z,y)) = (x * (y \ R(y,z,y))) * (y \ L(y,z,y))
    ]]></literal>
    <justification jstring="[para(8388(a,1),10832(a,1,2,1))].">
      <j1 rule="para" parents="8388 10832"/>
    </justification>
  </clause>

  <clause id="10835">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) * (y \ L(y,z,y)) = R(x,y \ R(y,z,y),y / R(y,z,y))
    ]]></literal>
    <justification jstring="[para(10765(a,1),10834(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10765 10834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10836">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) * (y \ L(y,z,y)) = R(x,y \ R(y,z,y),y \ L(y,z,y))
    ]]></literal>
    <justification jstring="[para(8388(a,1),10835(a,2,3))].">
      <j1 rule="para" parents="8388 10835"/>
    </justification>
  </clause>

  <clause id="10837">
    <literal><![CDATA[
      K(x,y) * ((K(x,y) \ z) * L(T(K(x,u),K(x,y) \ z),w,v5)) = z * L(T(K(x,u),z),w,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),9010(a,2,2,1,2))].">
      <j1 rule="para" parents="10 9010"/>
    </justification>
  </clause>

  <clause id="10838">
    <literal><![CDATA[
      K(x,y) * ((K(x,y) \ z) * L(T(K(x,u),K(x,y) \ z),w,v5)) = L(K(x,u),w,v5) * z
    ]]></literal>
    <justification jstring="[hyper(347,a,267,a(flip),b,10837,a),flip(a)].">
      <j1 rule="hyper" parents="347 267 10837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10839">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(x,y) \ v5)) = L(K(x,z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(267(a,1),10838(a,1,2))].">
      <j1 rule="para" parents="267 10838"/>
    </justification>
  </clause>

  <clause id="10840">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(y,x) * v5)) = L(K(x,z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(5256(a,1),10839(a,1,2,2))].">
      <j1 rule="para" parents="5256 10839"/>
    </justification>
  </clause>

  <clause id="10841">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(y,x) * L(L(K(x,z),u,w) \ 1,v5,v6))) = L(K(x,z) * L(K(x,z) \ 1,v5,v6),u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,4629,a(flip),b,10840,a),flip(a)].">
      <j1 rule="hyper" parents="347 4629 10840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10843">
    <literal><![CDATA[
      (T(L(x,y,x),y) \ 1) * (L(T(x,x * y) \ 1,x,y) \ (y \ (L(x,y,x) * y))) = 1 / ((L(x,y,x) * y) \ y)
    ]]></literal>
    <justification jstring="[para(22(a,2),9318(a,1,1,1))].">
      <j1 rule="para" parents="22 9318"/>
    </justification>
  </clause>

  <clause id="10844">
    <literal><![CDATA[
      (T(x,y * x) \ 1) * (L(T(x,x * y) \ 1,x,y) \ (y \ (L(x,y,x) * y))) = 1 / ((L(x,y,x) * y) \ y)
    ]]></literal>
    <justification jstring="[para(4327(a,1),10843(a,1,1,1))].">
      <j1 rule="para" parents="4327 10843"/>
    </justification>
  </clause>

  <clause id="10845">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (T(x,z) * y) * ((x * ((y * K(x,z)) * K(x,z))) \ u)
    ]]></literal>
    <justification jstring="[para(6765(a,1),10314(a,2,2,1))].">
      <j1 rule="para" parents="6765 10314"/>
    </justification>
  </clause>

  <clause id="10852">
    <literal><![CDATA[
      (x * (y * z)) * (1 / (1 / ((x * (y * z)) \ (x * y)))) = (x * y) * K(L(z,y,x),L(z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(212(a,1),2622(a,1,2,2,2,2))].">
      <j1 rule="para" parents="212 2622"/>
    </justification>
  </clause>

  <clause id="10853">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * ((y * z) * (1 / (1 / ((y * z) \ y))))
    ]]></literal>
    <justification jstring="[hyper(63,a,4679,a(flip),b,10852,a),flip(a)].">
      <j1 rule="hyper" parents="63 4679 10852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10855">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * (y * (z * (1 / (1 / (z \ (y \ y))))))
    ]]></literal>
    <justification jstring="[para(4674(a,1),10853(a,2,2))].">
      <j1 rule="para" parents="4674 10853"/>
    </justification>
  </clause>

  <clause id="10856">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * (y * (z * (1 / (1 / (z \ 1)))))
    ]]></literal>
    <justification jstring="[para(68(a,1),10855(a,2,2,2,2,2,2,2))].">
      <j1 rule="para" parents="68 10855"/>
    </justification>
  </clause>

  <clause id="10858">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * (y * (z * (1 / z)))
    ]]></literal>
    <justification jstring="[para(80(a,1),10856(a,2,2,2,2,2))].">
      <j1 rule="para" parents="80 10856"/>
    </justification>
  </clause>

  <clause id="10860">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * (y * K(z,z \ 1))
    ]]></literal>
    <justification jstring="[para(1924(a,2),10858(a,2,2,2))].">
      <j1 rule="para" parents="1924 10858"/>
    </justification>
  </clause>

  <clause id="10861">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,2226,a,b,10860,a),flip(a)].">
      <j1 rule="hyper" parents="34 2226 10860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10863">
    <literal><![CDATA[
      L(x,y,z) \ K(x,x \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,10861,a(flip),b,1924,a(flip))].">
      <j1 rule="hyper" parents="128 10861 1924"/>
    </justification>
  </clause>

  <clause id="10865">
    <literal><![CDATA[
      L(x,y,z) \ (1 / x) = x \ (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,10863,a(flip),b,1929,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 10863 1929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10866">
    <literal><![CDATA[
      L(x,y,z) \ K(x,L(x,u,w) \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5658(a,2),10863(a,1,2))].">
      <j1 rule="para" parents="5658 10863"/>
    </justification>
  </clause>

  <clause id="10867">
    <literal><![CDATA[
      K(L(x,y,z) \ ((x \ (1 / L(x,y,z))) \ u),L(x,y,z)) = K((1 / x) \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(10865(a,1),9622(a,1,1,2,1))].">
      <j1 rule="para" parents="10865 9622"/>
    </justification>
  </clause>

  <clause id="10868">
    <literal><![CDATA[
      (1 / x) * (L(x,y,z) \ x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5659,a(flip),b,10866,a)].">
      <j1 rule="hyper" parents="63 5659 10866"/>
    </justification>
  </clause>

  <clause id="10870">
    <literal><![CDATA[
      (1 / x) * ((L(x,y,z) \ 1) * x) = T(1 / L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(10868(a,1),1420(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10868 1420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10871">
    <literal><![CDATA[
      (x \ 1) \ T(1 / L(x,y,z),x) = (L(x,y,z) \ 1) * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,10870,a(flip),b,2955,a)].">
      <j1 rule="hyper" parents="128 10870 2955"/>
    </justification>
  </clause>

  <clause id="10872">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * T(x,x \ 1) = (x \ 1) \ (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(3316(a,1),10871(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3316 10871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10873">
    <literal><![CDATA[
      (x \ 1) \ (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,2994,a(flip),b,10872,a),flip(a)].">
      <j1 rule="hyper" parents="63 2994 10872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10874">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(134,a,2994,a(flip),b,10872,a(flip))].">
      <j1 rule="hyper" parents="134 2994 10872"/>
    </justification>
  </clause>

  <clause id="10875">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,3544,a,b,10873,a)].">
      <j1 rule="hyper" parents="63 3544 10873"/>
    </justification>
  </clause>

  <clause id="10876">
    <literal><![CDATA[
      x \ L(x * (L(x,y,z) \ 1),u,w) = (x \ 1) * L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(10873(a,1),1201(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10873 1201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10877">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = (x \ 1) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,8723,a,b,10874,a)].">
      <j1 rule="hyper" parents="347 8723 10874"/>
    </justification>
  </clause>

  <clause id="10878">
    <literal><![CDATA[
      T(L(x,y,z) \ x,x \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(269,a,10254,a,b,10874,a)].">
      <j1 rule="hyper" parents="269 10254 10874"/>
    </justification>
  </clause>

  <clause id="10879">
    <literal><![CDATA[
      (x \ 1) \ L(L(x,y,z) \ 1,u,w) = x * L(x \ (L(x,y,z) \ x),u,w)
    ]]></literal>
    <justification jstring="[para(10874(a,1),3172(a,1,2,1))].">
      <j1 rule="para" parents="10874 3172"/>
    </justification>
  </clause>

  <clause id="10880">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ 1) = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,3637,a,b,10875,a),flip(a)].">
      <j1 rule="hyper" parents="347 3637 10875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10881">
    <literal><![CDATA[
      L(x \ y,x \ y,x) \ (x \ y) = (y \ x) \ ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(408(a,1),10875(a,1,1)),flip(a)].">
      <j1 rule="para" parents="408 10875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10882">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(2528,a,10877,a)].">
      <j1 rule="hyper" parents="2528 10877"/>
    </justification>
  </clause>

  <clause id="10883">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (L(x,y,z) \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(150,a,10882,a)].">
      <j1 rule="hyper" parents="150 10882"/>
    </justification>
  </clause>

  <clause id="10884">
    <literal><![CDATA[
      1 / (x \ L(x,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,3734,a,b,10882,a)].">
      <j1 rule="hyper" parents="63 3734 10882"/>
    </justification>
  </clause>

  <clause id="10885">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x \ L(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,10882,a(flip),b,3734,a)].">
      <j1 rule="hyper" parents="133 10882 3734"/>
    </justification>
  </clause>

  <clause id="10886">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,w) = R(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(10882(a,1),2247(a,1,2))].">
      <j1 rule="para" parents="10882 2247"/>
    </justification>
  </clause>

  <clause id="10887">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) \ 1 = L(x \ y,z,u) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(3354(a,1),10882(a,1,1))].">
      <j1 rule="para" parents="3354 10882"/>
    </justification>
  </clause>

  <clause id="10888">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ 1 = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(10882(a,1),3733(a,1,1))].">
      <j1 rule="para" parents="10882 3733"/>
    </justification>
  </clause>

  <clause id="10889">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),y * L(y,z,u),x) = x / (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(10882(a,1),3615(a,2,2))].">
      <j1 rule="para" parents="10882 3615"/>
    </justification>
  </clause>

  <clause id="10890">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (L(x * L(x,y,z),u,w) \ (x * L(x,y,z))) = L(L(x,y,z) \ x,u,w) \ 1
    ]]></literal>
    <justification jstring="[para(10882(a,1),4093(a,2,1,1))].">
      <j1 rule="para" parents="10882 4093"/>
    </justification>
  </clause>

  <clause id="10891">
    <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(4638(a,1),10882(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4638 10882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10892">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((L(x,y,z) \ x) * u) = L(u,L(x,y,z) \ x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(193,a,212,a,b,10883,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="193 212 10883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10893">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(10883(a,1),356(a,1,2))].">
      <j1 rule="para" parents="10883 356"/>
    </justification>
  </clause>

  <clause id="10894">
    <literal><![CDATA[
      (L(x,y,z) \ x) * T(x \ L(x,y,z),u) = K(x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(133,a,10884,a(flip),b,4978,a)].">
      <j1 rule="hyper" parents="133 10884 4978"/>
    </justification>
  </clause>

  <clause id="10895">
    <literal><![CDATA[
      x * ((L(x,y,z) \ x) \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(10885(a,1),75(a,1,2,2))].">
      <j1 rule="para" parents="10885 75"/>
    </justification>
  </clause>

  <clause id="10896">
    <literal><![CDATA[
      (x \ (y \ z)) \ L(x \ (y \ z),x,y) = (((y * x) \ z) \ (x \ (y \ z))) \ 1
    ]]></literal>
    <justification jstring="[para(329(a,1),10888(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="329 10888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10897">
    <literal><![CDATA[
      x \ (L(x,y,z) * ((L(x,y,z) \ x) \ 1)) = (L(x,y,z) \ x) \ (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(10888(a,1),824(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10888 824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10898">
    <literal><![CDATA[
      ((((L(x,y,z) \ x) \ 1) \ 1) * (L(x,y,z) \ x)) * u = ((x \ L(x,y,z)) * ((L(x,y,z) \ x) \ 1)) \ u
    ]]></literal>
    <justification jstring="[para(10888(a,1),1132(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10888 1132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10899">
    <literal><![CDATA[
      a(x \ 1,x,y) \ 1 = y \ L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4026(a,1),10888(a,1,1))].">
      <j1 rule="para" parents="4026 10888"/>
    </justification>
  </clause>

  <clause id="10900">
    <literal><![CDATA[
      ((L(x,y,z) \ x) \ 1) \ 1 = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(10888(a,2),10882(a,1,1))].">
      <j1 rule="para" parents="10888 10882"/>
    </justification>
  </clause>

  <clause id="10901">
    <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(10895(a,1),783(a,1,1))].">
      <j1 rule="para" parents="10895 783"/>
    </justification>
  </clause>

  <clause id="10902">
    <literal><![CDATA[
      R(x,y * (z * (L(z,u,w) \ z)),v5) = R(x,y * L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(10895(a,1),2381(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10895 2381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10903">
    <literal><![CDATA[
      1 / (L(x,y,z) \ x) = (L(x,y,z) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(222,a,10900,a)].">
      <j1 rule="hyper" parents="222 10900"/>
    </justification>
  </clause>

  <clause id="10904">
    <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(4638(a,1),10893(a,1,1))].">
      <j1 rule="para" parents="4638 10893"/>
    </justification>
  </clause>

  <clause id="10905">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),w) = R(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(2366,a,10886,a),flip(a)].">
      <j1 rule="hyper" parents="2366 10886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10906">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(10880(a,2),3649(a,1))].">
      <j1 rule="para" parents="10880 3649"/>
    </justification>
  </clause>

  <clause id="10907">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((y \ x) \ 1) = (y \ x) \ ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,3659,a(flip),b,10881,a)].">
      <j1 rule="hyper" parents="63 3659 10881"/>
    </justification>
  </clause>

  <clause id="10908">
    <literal><![CDATA[
      L(x \ y,x \ y,x) \ (x \ y) = ((x \ y) * (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[para(538(a,1),10887(a,1,1)),flip(a)].">
      <j1 rule="para" parents="538 10887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10909">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ 1 = (y \ x) \ ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,10881,a(flip),b,10908,a),flip(a)].">
      <j1 rule="hyper" parents="63 10881 10908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10910">
    <literal><![CDATA[
      L(x,y,z) / L(L(x,u,w),y,z) = L(x \ L(x,u,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,3311,a,b,10891,a)].">
      <j1 rule="hyper" parents="63 3311 10891"/>
    </justification>
  </clause>

  <clause id="10911">
    <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(128,a,10891,a(flip),b,1409,a)].">
      <j1 rule="hyper" parents="128 10891 1409"/>
    </justification>
  </clause>

  <clause id="10912">
    <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(347,a,7293,a,b,10894,a),flip(a)].">
      <j1 rule="hyper" parents="347 7293 10894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10913">
    <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(10894(a,2),7328(a,1))].">
      <j1 rule="para" parents="10894 7328"/>
    </justification>
  </clause>

  <clause id="10914">
    <literal><![CDATA[
      (x \ 1) * L(L(x,y,z) \ x,u,w) = x \ L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(1409(a,1),10876(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1409 10876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10915">
    <literal><![CDATA[
      x \ L(L(x,y,z) \ x,L(x,y,z),z * y) = (x \ 1) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(1787(a,2),10914(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1787 10914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10916">
    <literal><![CDATA[
      (x \ 1) * a(y,z,x) = x \ a(y,z,x)
    ]]></literal>
    <justification jstring="[para(1787(a,2),10915(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1787 10915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10917">
    <literal><![CDATA[
      (x * x) * ((y \ (x * x)) \ a(z,u,y \ 1)) = ((y \ 1) \ 1) * a(z,u,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,778,a,b,10916,a)].">
      <j1 rule="hyper" parents="347 778 10916"/>
    </justification>
  </clause>

  <clause id="10918">
    <literal><![CDATA[
      R(x,x,a(y,z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(2268,a,10916,a(flip))].">
      <j1 rule="hyper" parents="2268 10916"/>
    </justification>
  </clause>

  <clause id="10919">
    <literal><![CDATA[
      (x * (y \ a(z,u,y))) \ ((x * (y \ 1)) * a(z,u,y)) = a(x,y \ 1,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(10916(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10916 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10920">
    <literal><![CDATA[
      (x \ 1) \ L(L(x,y,z) \ 1,u,w) = x * L(L(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(1415(a,1),10879(a,2,2,1))].">
      <j1 rule="para" parents="1415 10879"/>
    </justification>
  </clause>

  <clause id="10921">
    <literal><![CDATA[
      R(1 / x,x,L(L(x,y,z) \ 1,u,w)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(447,a,10920,a)].">
      <j1 rule="hyper" parents="447 10920"/>
    </justification>
  </clause>

  <clause id="10922">
    <literal><![CDATA[
      R(1 / x,x,L(L(x,y,z),u,w)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(3441,a,10921,a)].">
      <j1 rule="hyper" parents="3441 10921"/>
    </justification>
  </clause>

  <clause id="10923">
    <literal><![CDATA[
      (x \ 1) \ L(L(x,y,z),u,w) = x * L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(10922(a,1),420(a,1,1))].">
      <j1 rule="para" parents="10922 420"/>
    </justification>
  </clause>

  <clause id="10924">
    <literal><![CDATA[
      (x * (y \ 1)) * (y * L(L(y,z,u),w,v5)) = (x * y) * (y \ L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(10923(a,1),987(a,1,2))].">
      <j1 rule="para" parents="10923 987"/>
    </justification>
  </clause>

  <clause id="10925">
    <literal><![CDATA[
      R(x,y,z \ L(L(z,u,w),v5,v6)) = R(x,y,z * L(L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(10923(a,1),2241(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10923 2241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10926">
    <literal><![CDATA[
      L(x,y \ L(L(y,z,u),w,v5),v6) = L(x,y * L(L(y,z,u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(10923(a,1),3608(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10923 3608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10927">
    <literal><![CDATA[
      R(x,y,y * L(L(y,z,u),w,v5)) * L(L(y,z,u),w,v5) = (x * y) * (y \ L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(133,a,10925,a(flip),b,106,a)].">
      <j1 rule="hyper" parents="133 10925 106"/>
    </justification>
  </clause>

  <clause id="10928">
    <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(1429,a,10901,a),flip(a)].">
      <j1 rule="hyper" parents="1429 10901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10929">
    <literal><![CDATA[
      (((x * y) \ z) \ (y \ (x \ z))) \ 1 = (y \ (x \ z)) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(329(a,1),10896(a,1,2)),flip(a)].">
      <j1 rule="para" parents="329 10896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10930">
    <literal><![CDATA[
      (x \ (y \ ((y * x) * z))) \ ((y * x) \ ((y * x) * z)) = (z \ (x \ (y \ ((y * x) * z)))) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),10929(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 10929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10931">
    <literal><![CDATA[
      (x \ (y \ (y * z))) \ ((y * x) \ (y * z)) = (((y * x) \ (y * z)) \ (x \ z)) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),10929(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 10929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10932">
    <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(10888(a,1),10897(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10888 10897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10933">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (x \ L(x,y,z)) = L(x,y,z) * (x \ (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,1402,a(flip),b,10932,a),flip(a)].">
      <j1 rule="hyper" parents="347 1402 10932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10934">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (x \ L(x,y,z)) = L(x,y,z) * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(3344(a,1),10933(a,2,2))].">
      <j1 rule="para" parents="3344 10933"/>
    </justification>
  </clause>

  <clause id="10935">
    <literal><![CDATA[
      (((x * y) \ (x * z)) \ (y \ z)) \ 1 = (y \ z) \ ((x * y) \ (x * z))
    ]]></literal>
    <justification jstring="[para(9(a,1),10931(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 10931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10936">
    <literal><![CDATA[
      (x \ y) \ ((z * x) \ (z * y)) != u \ 1
    ]]></literal>
    <literal><![CDATA[
      ((z * x) \ (z * y)) \ (x \ y) = u
    ]]></literal>
    <justification jstring="[para(10935(a,1),48(a,1))].">
      <j1 rule="para" parents="10935 48"/>
    </justification>
  </clause>

  <clause id="10937">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ x = (L(x,y,z) \ x) * x
    ]]></literal>
    <justification jstring="[hyper(128,a,10541,a(flip),b,10892,a)].">
      <j1 rule="hyper" parents="128 10541 10892"/>
    </justification>
  </clause>

  <clause id="10938">
    <literal><![CDATA[
      K(x \ ((x \ (1 / L(x,y,z))) \ u),L(x,y,z)) = K((1 / x) \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9731,a(flip),b,10867,a)].">
      <j1 rule="hyper" parents="63 9731 10867"/>
    </justification>
  </clause>

  <clause id="10939">
    <literal><![CDATA[
      K((1 / L(x,y,z)) \ u,L(x,y,z)) = K((1 / x) \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9848,a(flip),b,10938,a)].">
      <j1 rule="hyper" parents="63 9848 10938"/>
    </justification>
  </clause>

  <clause id="10940">
    <literal><![CDATA[
      K(L(x,y,z) * u,L(x,y,z)) = K((1 / x) \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6225,a(flip),b,10939,a)].">
      <j1 rule="hyper" parents="63 6225 10939"/>
    </justification>
  </clause>

  <clause id="10941">
    <literal><![CDATA[
      K(x * L(y,z,u),L(y,z,u)) = K((1 / y) \ x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8050,a,10940,a)].">
      <j1 rule="hyper" parents="8050 10940"/>
    </justification>
  </clause>

  <clause id="10942">
    <literal><![CDATA[
      K(x * L(y,z,u),L(y,z,u)) = K(1 \ (x * y),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,9218,a(flip),b,10941,a),flip(a)].">
      <j1 rule="hyper" parents="347 9218 10941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10943">
    <literal><![CDATA[
      K(x * L(y,z,u),L(y,z,u)) = K(x * y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(66(a,1),10942(a,2,1))].">
      <j1 rule="para" parents="66 10942"/>
    </justification>
  </clause>

  <clause id="10944">
    <literal><![CDATA[
      T(L(x,y,z) * K(u * x,L(x,y,z)),u) = R(L(x,y,z),u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(10943(a,1),5070(a,1,1,2))].">
      <j1 rule="para" parents="10943 5070"/>
    </justification>
  </clause>

  <clause id="10945">
    <literal><![CDATA[
      K(x * y,L(y,z,u)) * K(L(y,z,u),L(y,z,u) \ (x * L(y,z,u))) = a(L(y,z,u),L(y,z,u) \ (x * L(y,z,u)),L(y,z,u))
    ]]></literal>
    <justification jstring="[para(10943(a,1),8341(a,1,1))].">
      <j1 rule="para" parents="10943 8341"/>
    </justification>
  </clause>

  <clause id="10946">
    <literal><![CDATA[
      T(L(x * K(y * x,x),z,u),y) = R(L(x,z,u),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(5437(a,1),10944(a,1,1))].">
      <j1 rule="para" parents="5437 10944"/>
    </justification>
  </clause>

  <clause id="10947">
    <literal><![CDATA[
      T(L(x * K(x * y,x),z,u),y) = R(L(x,z,u),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(7899(a,1),10946(a,1,1,1,2))].">
      <j1 rule="para" parents="7899 10946"/>
    </justification>
  </clause>

  <clause id="10948">
    <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="[hyper(347,a,4374,a,b,10947,a),flip(a)].">
      <j1 rule="hyper" parents="347 4374 10947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10949">
    <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(5652,a,10948,a)].">
      <j1 rule="hyper" parents="5652 10948"/>
    </justification>
  </clause>

  <clause id="10950">
    <literal><![CDATA[
      x \ T(L(y,z,u) * x,L(y,z,u)) = L(R(y,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5432(a,1),10949(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5432 10949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10951">
    <literal><![CDATA[
      R(L(x,y,z),u,L(x,y,z)) = L(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(4385,a,10950,a)].">
      <j1 rule="hyper" parents="4385 10950"/>
    </justification>
  </clause>

  <clause id="10952">
    <literal><![CDATA[
      R(x,y,L(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(160,a,10951,a)].">
      <j1 rule="hyper" parents="160 10951"/>
    </justification>
  </clause>

  <clause id="10953">
    <literal><![CDATA[
      R(L(T(x,y),z,u),T(w,x),L(T(x,y),z,u)) = L(R(T(x,y),w,x),z,u)
    ]]></literal>
    <justification jstring="[para(9601(a,1),10951(a,2,1))].">
      <j1 rule="para" parents="9601 10951"/>
    </justification>
  </clause>

  <clause id="10954">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,5070,a,b,10952,a)].">
      <j1 rule="hyper" parents="347 5070 10952"/>
    </justification>
  </clause>

  <clause id="10957">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(10952(a,1),10713(a,1,2))].">
      <j1 rule="para" parents="10952 10713"/>
    </justification>
  </clause>

  <clause id="10958">
    <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(10535(a,1),10954(a,1,1,2))].">
      <j1 rule="para" parents="10535 10954"/>
    </justification>
  </clause>

  <clause id="10959">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(398(a,1),10957(a,2,2,3))].">
      <j1 rule="para" parents="398 10957"/>
    </justification>
  </clause>

  <clause id="10961">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7071,a,b,10959,a)].">
      <j1 rule="hyper" parents="63 7071 10959"/>
    </justification>
  </clause>

  <clause id="10962">
    <literal><![CDATA[
      (x * a(y,z,y)) * y = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,10959,a(flip),b,1708,a)].">
      <j1 rule="hyper" parents="133 10959 1708"/>
    </justification>
  </clause>

  <clause id="10963">
    <literal><![CDATA[
      a(x,y,L(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,10957,a(flip),b,10959,a(flip))].">
      <j1 rule="hyper" parents="34 10957 10959"/>
    </justification>
  </clause>

  <clause id="10964">
    <literal><![CDATA[
      (x * y) * a(y,z,y) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),10959(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 10959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10965">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ T(z,y)) = x * a(y,y \ z,y)
    ]]></literal>
    <justification jstring="[para(4380(a,1),10959(a,1,2))].">
      <j1 rule="para" parents="4380 10959"/>
    </justification>
  </clause>

  <clause id="10966">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) \ x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9446,a,b,10963,a)].">
      <j1 rule="hyper" parents="63 9446 10963"/>
    </justification>
  </clause>

  <clause id="10967">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(x,y) * a(y,x,y)
    ]]></literal>
    <justification jstring="[para(10963(a,1),9443(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10963 9443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10969">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(39,a,8499,a,b,10966,a),flip(a)].">
      <j1 rule="hyper" parents="39 8499 10966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10970">
    <literal><![CDATA[
      L(L(x,y,z),u,L(x,w,v5)) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(10969(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10969 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10971">
    <literal><![CDATA[
      L(1 / x,y,L(x,z,u)) = 1 / (x * (L(x,y,x) \ x))
    ]]></literal>
    <justification jstring="[para(10969(a,1),3646(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10969 3646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10972">
    <literal><![CDATA[
      L(x,y,x) \ L(L(x,y,L(x,z,u)),w,v5) = L(x \ L(x,w,v5),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(10969(a,1),4638(a,1,1))].">
      <j1 rule="para" parents="10969 4638"/>
    </justification>
  </clause>

  <clause id="10973">
    <literal><![CDATA[
      (x * y) \ (R(x,z,x) * y) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(706,a,10961,a)].">
      <j1 rule="hyper" parents="706 10961"/>
    </justification>
  </clause>

  <clause id="10974">
    <literal><![CDATA[
      (x * y) * a(x,z,x) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(620,a,10961,a),flip(a)].">
      <j1 rule="hyper" parents="620 10961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10975">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(347,a,9957,a,b,10961,a),flip(a)].">
      <j1 rule="hyper" parents="347 9957 10961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10976">
    <literal><![CDATA[
      (R(x,y,x) \ z) * a(x,y,x) = x \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,1747,a(flip),b,10961,a),flip(a)].">
      <j1 rule="hyper" parents="63 1747 10961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10977">
    <literal><![CDATA[
      x * (y * a(x,z,x)) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,10961,a(flip),b,1746,a)].">
      <j1 rule="hyper" parents="134 10961 1746"/>
    </justification>
  </clause>

  <clause id="10979">
    <literal><![CDATA[
      (x / R(y,z,y)) * a(y,z,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(131,a,12,a(flip),b,10962,a),flip(a)].">
      <j1 rule="hyper" parents="131 12 10962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10980">
    <literal><![CDATA[
      a(x,y,x) * (z * x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9970,a,10964,a)].">
      <j1 rule="hyper" parents="9970 10964"/>
    </justification>
  </clause>

  <clause id="10981">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,y)) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(138,a,10964,a)].">
      <j1 rule="hyper" parents="138 10964"/>
    </justification>
  </clause>

  <clause id="10982">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,12,a(flip),b,10964,a),flip(a)].">
      <j1 rule="hyper" parents="131 12 10964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10983">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,10964,a(flip),b,9957,a)].">
      <j1 rule="hyper" parents="131 10964 9957"/>
    </justification>
  </clause>

  <clause id="10984">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(10964(a,1),9333(a,1,1))].">
      <j1 rule="para" parents="10964 9333"/>
    </justification>
  </clause>

  <clause id="10985">
    <literal><![CDATA[
      (x * (y * R(z,u,z))) / (x * (y * z)) = L(a(z,u,z),y * z,x)
    ]]></literal>
    <justification jstring="[para(10964(a,1),9966(a,1,1,2))].">
      <j1 rule="para" parents="10964 9966"/>
    </justification>
  </clause>

  <clause id="10986">
    <literal><![CDATA[
      a(x,y,x) * (x * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(9970,a,10974,a)].">
      <j1 rule="hyper" parents="9970 10974"/>
    </justification>
  </clause>

  <clause id="10988">
    <literal><![CDATA[
      a(x,y,x) * (R(x,y,x) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,1747,a(flip),b,10975,a),flip(a)].">
      <j1 rule="hyper" parents="63 1747 10975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10989">
    <literal><![CDATA[
      x * (a(x,y,x) * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(134,a,10975,a(flip),b,1746,a)].">
      <j1 rule="hyper" parents="134 10975 1746"/>
    </justification>
  </clause>

  <clause id="10990">
    <literal><![CDATA[
      a(x,y,x) \ (x \ z) = R(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(128,a,1747,a(flip),b,10975,a(flip))].">
      <j1 rule="hyper" parents="128 1747 10975"/>
    </justification>
  </clause>

  <clause id="10991">
    <literal><![CDATA[
      x * (R(x,y,x) \ z) = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(128,a,75,a(flip),b,10975,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 75 10975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10992">
    <literal><![CDATA[
      (x * y) \ (R(x,z,x) * y) = L(a(x,z,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,10977,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="128 10977 97"/>
    </justification>
  </clause>

  <clause id="10993">
    <literal><![CDATA[
      a(x,y,x) \ (z / x) = z / R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9976,a,10979,a)].">
      <j1 rule="hyper" parents="9976 10979"/>
    </justification>
  </clause>

  <clause id="10994">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,12,a(flip),b,10980,a),flip(a)].">
      <j1 rule="hyper" parents="128 12 10980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10995">
    <literal><![CDATA[
      (x * R(x \ y,z,x \ y)) / y = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(131,a,10980,a(flip),b,169,a(flip))].">
      <j1 rule="hyper" parents="131 10980 169"/>
    </justification>
  </clause>

  <clause id="10996">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8386,a(flip),b,10982,a)].">
      <j1 rule="hyper" parents="63 8386 10982"/>
    </justification>
  </clause>

  <clause id="10997">
    <literal><![CDATA[
      R(a(x,y,x),x,z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8348,a(flip),b,10983,a)].">
      <j1 rule="hyper" parents="63 8348 10983"/>
    </justification>
  </clause>

  <clause id="10998">
    <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(97(a,1),10983(a,1,2))].">
      <j1 rule="para" parents="97 10983"/>
    </justification>
  </clause>

  <clause id="11000">
    <literal><![CDATA[
      ((a(R(x,y,z),u,R(x,y,z)) * R(x,y,z)) * (y * z)) / ((x * y) * z) = a(R(x,y,z),u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,592,a,b,10997,a)].">
      <j1 rule="hyper" parents="63 592 10997"/>
    </justification>
  </clause>

  <clause id="11001">
    <literal><![CDATA[
      ((R(x,y,x) * z) * u) / ((x * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(a(x,y,x),x * z,u) = w
    ]]></literal>
    <justification jstring="[para(10986(a,1),595(a,1,1,1))].">
      <j1 rule="para" parents="10986 595"/>
    </justification>
  </clause>

  <clause id="11002">
    <literal><![CDATA[
      (R(x,y,x) * z) \ (a(x,y,x) * (x * (z * u))) = L(L(u,z,x),x * z,a(x,y,x))
    ]]></literal>
    <justification jstring="[para(10986(a,1),542(a,1,1))].">
      <j1 rule="para" parents="10986 542"/>
    </justification>
  </clause>

  <clause id="11003">
    <literal><![CDATA[
      a(x,x \ y,x) * y = T(x * (y / x),x)
    ]]></literal>
    <justification jstring="[hyper(269,a,9613,a(flip),b,10989,a),flip(a)].">
      <j1 rule="hyper" parents="269 9613 10989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11004">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,z * y) = a(z,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(6436,a,10994,a)].">
      <j1 rule="hyper" parents="6436 10994"/>
    </justification>
  </clause>

  <clause id="11005">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,8386,a(flip),b,10994,a)].">
      <j1 rule="hyper" parents="63 8386 10994"/>
    </justification>
  </clause>

  <clause id="11006">
    <literal><![CDATA[
      x * (a(y,z,y) \ 1) = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[para(8674(a,2),10996(a,1,2))].">
      <j1 rule="para" parents="8674 10996"/>
    </justification>
  </clause>

  <clause id="11007">
    <literal><![CDATA[
      x / (a(y,z,y) \ 1) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,11,a(flip),b,11006,a)].">
      <j1 rule="hyper" parents="131 11 11006"/>
    </justification>
  </clause>

  <clause id="11008">
    <literal><![CDATA[
      R(x,a(y,z,y),a(y,z,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(700,a,11007,a)].">
      <j1 rule="hyper" parents="700 11007"/>
    </justification>
  </clause>

  <clause id="11009">
    <literal><![CDATA[
      R(x,a(y,z,y),y \ L(y,z,y)) = x
    ]]></literal>
    <justification jstring="[para(8674(a,1),11008(a,1,3))].">
      <j1 rule="para" parents="8674 11008"/>
    </justification>
  </clause>

  <clause id="11010">
    <literal><![CDATA[
      R(x,y \ R(y,z,y),y \ L(y,z,y)) = x
    ]]></literal>
    <justification jstring="[para(8336(a,2),11009(a,1,2))].">
      <j1 rule="para" parents="8336 11009"/>
    </justification>
  </clause>

  <clause id="11011">
    <literal><![CDATA[
      (x * (y \ R(y,z,y))) * (y \ L(y,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,10836,a,b,11010,a)].">
      <j1 rule="hyper" parents="63 10836 11010"/>
    </justification>
  </clause>

  <clause id="11012">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,8354,a(flip),b,10967,a),flip(a)].">
      <j1 rule="hyper" parents="347 8354 10967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11014">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10083,a(flip),b,11012,a)].">
      <j1 rule="hyper" parents="63 10083 11012"/>
    </justification>
  </clause>

  <clause id="11015">
    <literal><![CDATA[
      K(x * (L(x,y,z) \ u),x) = K(u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8036,a(flip),b,11012,a),flip(a)].">
      <j1 rule="hyper" parents="63 8036 11012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11017">
    <literal><![CDATA[
      K(L(x,y,z) \ u,x) = K(x \ u,x)
    ]]></literal>
    <justification jstring="[para(1408(a,1),11015(a,1,1))].">
      <j1 rule="para" parents="1408 11015"/>
    </justification>
  </clause>

  <clause id="11018">
    <literal><![CDATA[
      K(x / L(y,z,u),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(7599,a,11017,a)].">
      <j1 rule="hyper" parents="7599 11017"/>
    </justification>
  </clause>

  <clause id="11019">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(11(a,1),11018(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 11018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11020">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9648,a,11019,a)].">
      <j1 rule="hyper" parents="9648 11019"/>
    </justification>
  </clause>

  <clause id="11021">
    <literal><![CDATA[
      T(x * L(y,z,u),K(x,y)) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(11019(a,1),4904(a,1,2))].">
      <j1 rule="para" parents="11019 4904"/>
    </justification>
  </clause>

  <clause id="11023">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,5986,a(flip),b,11014,a),flip(a)].">
      <j1 rule="hyper" parents="347 5986 11014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11024">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ w),y) = K((w / x) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(10614,a,11023,a)].">
      <j1 rule="hyper" parents="10614 11023"/>
    </justification>
  </clause>

  <clause id="11025">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K((y \ x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10084,a(flip),b,11023,a)].">
      <j1 rule="hyper" parents="63 10084 11023"/>
    </justification>
  </clause>

  <clause id="11026">
    <literal><![CDATA[
      (L(x,y,z) * K((u \ x) \ x,x)) * u = (x \ (L(x,y,z) * u)) * x
    ]]></literal>
    <justification jstring="[para(11023(a,1),8484(a,1,1,2))].">
      <j1 rule="para" parents="11023 8484"/>
    </justification>
  </clause>

  <clause id="11028">
    <literal><![CDATA[
      (x * (K(T(y,z),u) * K(y * u,T(y,z)))) * (y \ L(y,u,y)) = x
    ]]></literal>
    <justification jstring="[para(9540(a,2),11011(a,1,1,2))].">
      <j1 rule="para" parents="9540 11011"/>
    </justification>
  </clause>

  <clause id="11029">
    <literal><![CDATA[
      T(x * ((y * z) \ (y * u)),K(x,z \ u)) = x * L(z \ u,z,y)
    ]]></literal>
    <justification jstring="[para(99(a,1),11021(a,1,1,2))].">
      <j1 rule="para" parents="99 11021"/>
    </justification>
  </clause>

  <clause id="11030">
    <literal><![CDATA[
      L(L(x,y,x),z,u) \ L(x,z,u) = a(L(x,z,u),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(10970(a,1),8499(a,1,1))].">
      <j1 rule="para" parents="10970 8499"/>
    </justification>
  </clause>

  <clause id="11031">
    <literal><![CDATA[
      L(a(x,y,x),z,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10973,a(flip),b,10992,a),flip(a)].">
      <j1 rule="hyper" parents="63 10973 10992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11032">
    <literal><![CDATA[
      L(a(x,y,x),z,x) = (u * x) \ (u * R(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,10981,a,b,11031,a),flip(a)].">
      <j1 rule="hyper" parents="347 10981 11031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11035">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,9821,a(flip),b,11025,a),flip(a)].">
      <j1 rule="hyper" parents="347 9821 11025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11036">
    <literal><![CDATA[
      L(a(x \ y,z,x \ y),u,x \ y) = y \ (x * R(x \ y,z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(347,a,174,a(flip),b,11032,a),flip(a)].">
      <j1 rule="hyper" parents="347 174 11032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11038">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(u * (x \ (y * z)),u)
    ]]></literal>
    <justification jstring="[para(97(a,1),11035(a,1,1,2))].">
      <j1 rule="para" parents="97 11035"/>
    </justification>
  </clause>

  <clause id="11039">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(y * ((x * y) \ (z * u)),y)
    ]]></literal>
    <justification jstring="[hyper(8106,a,11038,a)].">
      <j1 rule="hyper" parents="8106 11038"/>
    </justification>
  </clause>

  <clause id="11040">
    <literal><![CDATA[
      (x / R(y,z,u)) * R((y \ w) \ T(w,y),z,u) = x * a(R(y,z,u),R(y,z,u) \ w,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(10549(a,1),10965(a,1,2))].">
      <j1 rule="para" parents="10549 10965"/>
    </justification>
  </clause>

  <clause id="11041">
    <literal><![CDATA[
      L(1 / x,y,L(x,z,u)) = L(1 / x,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3646,a(flip),b,10971,a),flip(a)].">
      <j1 rule="hyper" parents="347 3646 10971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11043">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(y,x),z,y) = u
    ]]></literal>
    <justification jstring="[para(10984(a,2),7257(a,1))].">
      <j1 rule="para" parents="10984 7257"/>
    </justification>
  </clause>

  <clause id="11045">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(x \ (z * u),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,9820,a(flip),b,11039,a),flip(a)].">
      <j1 rule="hyper" parents="347 9820 11039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11046">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K((u * z) \ (u * (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9325,a(flip),b,11045,a)].">
      <j1 rule="hyper" parents="63 9325 11045"/>
    </justification>
  </clause>

  <clause id="11047">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(18(a,2),11046(a,2,1))].">
      <j1 rule="para" parents="18 11046"/>
    </justification>
  </clause>

  <clause id="11048">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9845,a(flip),b,11047,a),flip(a)].">
      <j1 rule="hyper" parents="63 9845 11047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11049">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9646,a,11048,a)].">
      <j1 rule="hyper" parents="9646 11048"/>
    </justification>
  </clause>

  <clause id="11050">
    <literal><![CDATA[
      K(x,L(y,T(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6035(a,1),11048(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6035 11048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11051">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(11048(a,1),9646(a,1))].">
      <j1 rule="para" parents="11048 9646"/>
    </justification>
  </clause>

  <clause id="11052">
    <literal><![CDATA[
      K(x,(y * T(x,z)) \ u) = K(x,T(x,z) \ (y \ u))
    ]]></literal>
    <justification jstring="[para(329(a,1),11050(a,1,2))].">
      <j1 rule="para" parents="329 11050"/>
    </justification>
  </clause>

  <clause id="11053">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = K(x,L(y / z,y,u))
    ]]></literal>
    <justification jstring="[hyper(9663,a,11049,a)].">
      <j1 rule="hyper" parents="9663 11049"/>
    </justification>
  </clause>

  <clause id="11054">
    <literal><![CDATA[
      K(x,L(y,y * z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9662,a,11049,a),flip(a)].">
      <j1 rule="hyper" parents="9662 11049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11055">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = K(x,L(T(z,u),u,y))
    ]]></literal>
    <justification jstring="[hyper(7660,a,11049,a)].">
      <j1 rule="hyper" parents="7660 11049"/>
    </justification>
  </clause>

  <clause id="11056">
    <literal><![CDATA[
      K((x * y) \ (x * z),u) = K(y \ z,L(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(7007,a,11049,a)].">
      <j1 rule="hyper" parents="7007 11049"/>
    </justification>
  </clause>

  <clause id="11057">
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(6449,a,11049,a),flip(a)].">
      <j1 rule="hyper" parents="6449 11049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11058">
    <literal><![CDATA[
      K(x,L(y,z * z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(550,a,11049,a),flip(a)].">
      <j1 rule="hyper" parents="550 11049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11059">
    <literal><![CDATA[
      L(K(x,y \ z),y,u) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,6454,a(flip),b,11049,a),flip(a)].">
      <j1 rule="hyper" parents="347 6454 11049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11060">
    <literal><![CDATA[
      x * L(K(x,y),z,u) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,11049,a,b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 11049 4924"/>
    </justification>
  </clause>

  <clause id="11061">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9241,a,b,11049,a)].">
      <j1 rule="hyper" parents="63 9241 11049"/>
    </justification>
  </clause>

  <clause id="11062">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8420,a,b,11049,a)].">
      <j1 rule="hyper" parents="63 8420 11049"/>
    </justification>
  </clause>

  <clause id="11063">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) = K(u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,8264,a,b,11049,a)].">
      <j1 rule="hyper" parents="63 8264 11049"/>
    </justification>
  </clause>

  <clause id="11064">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7607,a,b,11049,a)].">
      <j1 rule="hyper" parents="63 7607 11049"/>
    </justification>
  </clause>

  <clause id="11065">
    <literal><![CDATA[
      K((x \ 1) \ (x \ y),L(z,y / x,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10620,a(flip),b,11049,a),flip(a)].">
      <j1 rule="hyper" parents="63 10620 11049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11066">
    <literal><![CDATA[
      K(x,L(y,K(z,u),u * z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10275,a(flip),b,11049,a),flip(a)].">
      <j1 rule="hyper" parents="63 10275 11049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11067">
    <literal><![CDATA[
      K(x \ y,L(z,y,y \ 1)) = K(((y \ 1) * x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,7020,a(flip),b,11049,a),flip(a)].">
      <j1 rule="hyper" parents="63 7020 11049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11068">
    <literal><![CDATA[
      K(x,L((y \ z) \ u,u,y)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,6450,a(flip),b,11049,a),flip(a)].">
      <j1 rule="hyper" parents="63 6450 11049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11069">
    <literal><![CDATA[
      x * K(y,L(z,u,u \ x)) = (x / u) * (u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,11049,a(flip),b,10192,a)].">
      <j1 rule="hyper" parents="134 11049 10192"/>
    </justification>
  </clause>

  <clause id="11070">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * K(z,L(T(y,u),u,x)) = x * u
    ]]></literal>
    <justification jstring="[hyper(134,a,11049,a(flip),b,8268,a)].">
      <j1 rule="hyper" parents="134 11049 8268"/>
    </justification>
  </clause>

  <clause id="11071">
    <literal><![CDATA[
      x * K(y,L(z,u \ x,u)) = u * ((u \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,11049,a(flip),b,98,a)].">
      <j1 rule="hyper" parents="134 11049 98"/>
    </justification>
  </clause>

  <clause id="11072">
    <literal><![CDATA[
      (x * y) * K(z,L(u,x,y)) = y * (T(x,y) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,11049,a(flip),b,10148,a(flip))].">
      <j1 rule="hyper" parents="134 11049 10148"/>
    </justification>
  </clause>

  <clause id="11073">
    <literal><![CDATA[
      (x * y) * K(z,L(u,y,x)) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,11049,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 11049 18"/>
    </justification>
  </clause>

  <clause id="11074">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),y,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(329(a,1),11049(a,2,2))].">
      <j1 rule="para" parents="329 11049"/>
    </justification>
  </clause>

  <clause id="11075">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),y \ z,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(561(a,1),11049(a,2,2))].">
      <j1 rule="para" parents="561 11049"/>
    </justification>
  </clause>

  <clause id="11076">
    <literal><![CDATA[
      (x * y) * K(z,L(u,y,x)) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(11049(a,1),322(a,1,2))].">
      <j1 rule="para" parents="11049 322"/>
    </justification>
  </clause>

  <clause id="11077">
    <literal><![CDATA[
      (x * y) * K(z,L(u,y,x)) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ (x * (y * K(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(11049(a,1),676(a,1,2))].">
      <j1 rule="para" parents="11049 676"/>
    </justification>
  </clause>

  <clause id="11078">
    <literal><![CDATA[
      K(x \ (y \ z),L(u,y \ z,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(11049(a,1),6595(a,1))].">
      <j1 rule="para" parents="11049 6595"/>
    </justification>
  </clause>

  <clause id="11079">
    <literal><![CDATA[
      K(x,L(y \ (z \ u),z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(11049(a,1),8273(a,1))].">
      <j1 rule="para" parents="11049 8273"/>
    </justification>
  </clause>

  <clause id="11080">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(11049(a,1),9237(a,1,2))].">
      <j1 rule="para" parents="11049 9237"/>
    </justification>
  </clause>

  <clause id="11081">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,L(u,y,x)) = K(z,u)
    ]]></literal>
    <justification jstring="[para(11049(a,1),9239(a,1,2))].">
      <j1 rule="para" parents="11049 9239"/>
    </justification>
  </clause>

  <clause id="11082">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(11049(a,1),9242(a,1,1))].">
      <j1 rule="para" parents="11049 9242"/>
    </justification>
  </clause>

  <clause id="11083">
    <literal><![CDATA[
      K(x,L(y,z,u)) \ K(x,y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(11049(a,1),9251(a,1,1))].">
      <j1 rule="para" parents="11049 9251"/>
    </justification>
  </clause>

  <clause id="11084">
    <literal><![CDATA[
      x \ y != K(z,L(u,w,v5)) * K(u,z)
    ]]></literal>
    <literal><![CDATA[
      x * a(v5,w,K(u,z)) = y
    ]]></literal>
    <justification jstring="[para(11049(a,1),9269(a,2,1))].">
      <j1 rule="para" parents="11049 9269"/>
    </justification>
  </clause>

  <clause id="11085">
    <literal><![CDATA[
      L(K(x,((y \ z) \ z) \ u),y,y \ z) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(10212(a,1),11049(a,2,2))].">
      <j1 rule="para" parents="10212 11049"/>
    </justification>
  </clause>

  <clause id="11086">
    <literal><![CDATA[
      K(x,L(y,T(z,u),u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(10287(a,1),11066(a,1,2))].">
      <j1 rule="para" parents="10287 11066"/>
    </justification>
  </clause>

  <clause id="11087">
    <literal><![CDATA[
      K(x,y) \ L(K(x,y),z,u) = T(y,x) \ T(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(11060(a,1),6519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11060 6519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11088">
    <literal><![CDATA[
      K(x,L(y,z / u,u)) = K(x,L(y,u \ z,u))
    ]]></literal>
    <justification jstring="[para(113(a,1),11086(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 11086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11089">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(u,z) = K(u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,9238,a(flip),b,11061,a)].">
      <j1 rule="hyper" parents="63 9238 11061"/>
    </justification>
  </clause>

  <clause id="11090">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(11061(a,1),5274(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11061 5274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11091">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9247,a(flip),b,11080,a)].">
      <j1 rule="hyper" parents="63 9247 11080"/>
    </justification>
  </clause>

  <clause id="11092">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,L(z,y,x)) * K(z,u) = w
    ]]></literal>
    <justification jstring="[para(11080(a,1),2558(a,1))].">
      <j1 rule="para" parents="11080 2558"/>
    </justification>
  </clause>

  <clause id="11093">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(11080(a,1),5274(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11080 5274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11094">
    <literal><![CDATA[
      K(L(x,y,z),u) * a(z,y,K(x,u)) = K(x,u)
    ]]></literal>
    <justification jstring="[para(11080(a,1),5269(a,1,2))].">
      <j1 rule="para" parents="11080 5269"/>
    </justification>
  </clause>

  <clause id="11095">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,z))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(7283(a,2),11091(a,1,3))].">
      <j1 rule="para" parents="7283 11091"/>
    </justification>
  </clause>

  <clause id="11096">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6138,a,11081,a)].">
      <j1 rule="hyper" parents="6138 11081"/>
    </justification>
  </clause>

  <clause id="11097">
    <literal><![CDATA[
      a(x,y,K(z,u * u)) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,8432,a,b,11081,a),flip(a)].">
      <j1 rule="hyper" parents="129 8432 11081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11098">
    <literal><![CDATA[
      K(L(x,y,z),u) * K(u,x) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(35,a,6131,a,b,11081,a)].">
      <j1 rule="hyper" parents="35 6131 11081"/>
    </justification>
  </clause>

  <clause id="11099">
    <literal><![CDATA[
      K(x,y) \ (a(z,u,K(x,y)) * L(y,u,z)) = T(L(y,u,z),x)
    ]]></literal>
    <justification jstring="[para(11081(a,1),6100(a,1,1))].">
      <j1 rule="para" parents="11081 6100"/>
    </justification>
  </clause>

  <clause id="11100">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(11081(a,1),6145(a,1,1))].">
      <j1 rule="para" parents="11081 6145"/>
    </justification>
  </clause>

  <clause id="11101">
    <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(10738(a,1),11081(a,1,2,2))].">
      <j1 rule="para" parents="10738 11081"/>
    </justification>
  </clause>

  <clause id="11102">
    <literal><![CDATA[
      T(x,L(y,z,u)) * K(y,x) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(134,a,11082,a(flip),b,5157,a),flip(a)].">
      <j1 rule="hyper" parents="134 11082 5157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11103">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,u) * K(u,L(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(11082(a,1),2560(a,1))].">
      <j1 rule="para" parents="11082 2560"/>
    </justification>
  </clause>

  <clause id="11104">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(35,a,9255,a,b,11094,a)].">
      <j1 rule="hyper" parents="35 9255 11094"/>
    </justification>
  </clause>

  <clause id="11106">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = K(L(x,u,y),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(7660,a,11104,a)].">
      <j1 rule="hyper" parents="7660 11104"/>
    </justification>
  </clause>

  <clause id="11108">
    <literal><![CDATA[
      K(L(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11049,a(flip),b,11104,a),flip(a)].">
      <j1 rule="hyper" parents="63 11049 11104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11109">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x),u) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,11104,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 11104 18"/>
    </justification>
  </clause>

  <clause id="11110">
    <literal><![CDATA[
      L(K((x \ 1) \ y,z),x \ 1,x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(560(a,1),11104(a,2,1))].">
      <j1 rule="para" parents="560 11104"/>
    </justification>
  </clause>

  <clause id="11111">
    <literal><![CDATA[
      K(x,L(y,x \ z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11048,a(flip),b,11108,a),flip(a)].">
      <j1 rule="hyper" parents="63 11048 11108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11112">
    <literal><![CDATA[
      L(x,y,z) * K(x,L(u,y,z)) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,11108,a(flip),b,4982,a)].">
      <j1 rule="hyper" parents="134 11108 4982"/>
    </justification>
  </clause>

  <clause id="11113">
    <literal><![CDATA[
      K(x \ (y \ z),L(u,x,y)) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(329(a,1),11108(a,1,1)),flip(a)].">
      <j1 rule="para" parents="329 11108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11114">
    <literal><![CDATA[
      K((x \ 1) \ y,L(z,x \ 1,x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(560(a,1),11108(a,1,1)),flip(a)].">
      <j1 rule="para" parents="560 11108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11115">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,x \ y,x)) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(561(a,1),11108(a,1,1)),flip(a)].">
      <j1 rule="para" parents="561 11108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11116">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (y \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(y,L(x,z,u)) \ w = v5
    ]]></literal>
    <justification jstring="[para(11108(a,1),5217(a,1,1))].">
      <j1 rule="para" parents="11108 5217"/>
    </justification>
  </clause>

  <clause id="11117">
    <literal><![CDATA[
      L(T(x,y),z,u) * (L(x,z,u) \ w) = K(x,L(y,z,u)) * w
    ]]></literal>
    <justification jstring="[para(11108(a,1),5199(a,2,1))].">
      <j1 rule="para" parents="11108 5199"/>
    </justification>
  </clause>

  <clause id="11118">
    <literal><![CDATA[
      x * (K(y,L(x,z,u)) * K(w,L(y,z,u))) = (L(y,z,u) * x) / T(L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(11108(a,1),6174(a,1,2,1))].">
      <j1 rule="para" parents="11108 6174"/>
    </justification>
  </clause>

  <clause id="11119">
    <literal><![CDATA[
      (L(x,y,z) * (u * K(x,L(w,y,z)))) / L(T(x,w),y,z) = (L(x,y,z) * u) / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(11108(a,1),6839(a,1,1,2,2))].">
      <j1 rule="para" parents="11108 6839"/>
    </justification>
  </clause>

  <clause id="11120">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,x,y)) = K((x * y) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(10169(a,1),11108(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10169 11108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11121">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(11108(a,2),11051(a,1))].">
      <j1 rule="para" parents="11108 11051"/>
    </justification>
  </clause>

  <clause id="11122">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(z,K(x,y)),u,w) = v5
    ]]></literal>
    <justification jstring="[para(7283(a,2),11121(a,1))].">
      <j1 rule="para" parents="7283 11121"/>
    </justification>
  </clause>

  <clause id="11123">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9246,a(flip),b,11096,a)].">
      <j1 rule="hyper" parents="63 9246 11096"/>
    </justification>
  </clause>

  <clause id="11124">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      (u * x) / T(u,L(x,z,y)) = w
    ]]></literal>
    <justification jstring="[para(11096(a,1),6314(a,1,2))].">
      <j1 rule="para" parents="11096 6314"/>
    </justification>
  </clause>

  <clause id="11125">
    <literal><![CDATA[
      a(x,y / z,K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),11123(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 11123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11126">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(11123(a,1),9349(a,2,2))].">
      <j1 rule="para" parents="11123 9349"/>
    </justification>
  </clause>

  <clause id="11127">
    <literal><![CDATA[
      K(x \ L(x,y,z),T(u,x)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,9472,a,b,11098,a)].">
      <j1 rule="hyper" parents="63 9472 11098"/>
    </justification>
  </clause>

  <clause id="11128">
    <literal><![CDATA[
      a(x,y,K(z,u)) != 1
    ]]></literal>
    <literal><![CDATA[
      K(z,L(u,y,x)) = K(z,u)
    ]]></literal>
    <justification jstring="[para(11098(a,1),5175(a,1))].">
      <j1 rule="para" parents="11098 5175"/>
    </justification>
  </clause>

  <clause id="11129">
    <literal><![CDATA[
      a(x,y,a(z,u,K(y,w))) = 1
    ]]></literal>
    <justification jstring="[para(11127(a,1),7156(a,1,3))].">
      <j1 rule="para" parents="11127 7156"/>
    </justification>
  </clause>

  <clause id="11131">
    <literal><![CDATA[
      a(x,T(y,z),a(u,w,K(y,v5))) = 1
    ]]></literal>
    <justification jstring="[para(7380(a,1),11129(a,1,3,3))].">
      <j1 rule="para" parents="7380 11129"/>
    </justification>
  </clause>

  <clause id="11132">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ ((y \ 1) * z),u) = K((y * x) \ z,L(u,z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,3920,a(flip),b,11056,a)].">
      <j1 rule="hyper" parents="63 3920 11056"/>
    </justification>
  </clause>

  <clause id="11133">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,u,z)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[para(111(a,1),11057(a,2,2,1))].">
      <j1 rule="para" parents="111 11057"/>
    </justification>
  </clause>

  <clause id="11134">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,R(1 / y,y,z))) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[para(420(a,1),11068(a,1,2,1,1))].">
      <j1 rule="para" parents="420 11068"/>
    </justification>
  </clause>

  <clause id="11135">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(u,L(w,L(x,y,z) \ 1,x)) = x * ((L(x,y,z) \ 1) * K(u,w))
    ]]></literal>
    <justification jstring="[para(1409(a,1),11073(a,1,1))].">
      <j1 rule="para" parents="1409 11073"/>
    </justification>
  </clause>

  <clause id="11136">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,z) = x * (K(y,z) * K(u,z))
    ]]></literal>
    <justification jstring="[para(6030(a,1),11073(a,1,2,2))].">
      <j1 rule="para" parents="6030 11073"/>
    </justification>
  </clause>

  <clause id="11137">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(u,y,x),z) = w
    ]]></literal>
    <justification jstring="[para(11073(a,1),6141(a,1,1))].">
      <j1 rule="para" parents="11073 6141"/>
    </justification>
  </clause>

  <clause id="11138">
    <literal><![CDATA[
      K(x,(T(y * z,x) * K(u,L(w,z,y))) / v5) = K(x,(y * (z * K(u,w))) / v5)
    ]]></literal>
    <justification jstring="[para(11073(a,1),8745(a,2,2,1))].">
      <j1 rule="para" parents="11073 8745"/>
    </justification>
  </clause>

  <clause id="11140">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,L(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(11109(a,1),6141(a,1,1))].">
      <j1 rule="para" parents="11109 6141"/>
    </justification>
  </clause>

  <clause id="11141">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(11109(a,1),5923(a,1,1))].">
      <j1 rule="para" parents="11109 5923"/>
    </justification>
  </clause>

  <clause id="11143">
    <literal><![CDATA[
      L(K((x \ 1) \ (y \ z),y),x \ 1,x) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,9647,a,b,11110,a),flip(a)].">
      <j1 rule="hyper" parents="347 9647 11110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11144">
    <literal><![CDATA[
      (x * L(y,z,u)) * K(y,L(w,z,u)) = x * L(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(11112(a,1),10087(a,2,2))].">
      <j1 rule="para" parents="11112 10087"/>
    </justification>
  </clause>

  <clause id="11145">
    <literal><![CDATA[
      K((x \ 1) \ y,x * z) = K(x * y,(x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(560(a,1),11114(a,1,2))].">
      <j1 rule="para" parents="560 11114"/>
    </justification>
  </clause>

  <clause id="11146">
    <literal><![CDATA[
      K(x,(y * T(x,z)) \ u) = K(x,x \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,7875,a(flip),b,11052,a),flip(a)].">
      <j1 rule="hyper" parents="347 7875 11052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11148">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(10809,a,11102,a)].">
      <j1 rule="hyper" parents="10809 11102"/>
    </justification>
  </clause>

  <clause id="11149">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x * K(u,x),L(u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(11102(a,1),10809(a,1))].">
      <j1 rule="para" parents="11102 10809"/>
    </justification>
  </clause>

  <clause id="11151">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (T(x,z) * y) * ((x * (y * (K(x,z) * K(x,z)))) \ u)
    ]]></literal>
    <justification jstring="[para(11136(a,1),10845(a,2,2,1,2))].">
      <j1 rule="para" parents="11136 10845"/>
    </justification>
  </clause>

  <clause id="11152">
    <literal><![CDATA[
      K(x * y,(x \ 1) \ (x \ z)) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),11145(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 11145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11153">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),u) = T(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(11148(a,1),5059(a,1,1))].">
      <j1 rule="para" parents="11148 5059"/>
    </justification>
  </clause>

  <clause id="11154">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(11148(a,1),5066(a,1,1))].">
      <j1 rule="para" parents="11148 5066"/>
    </justification>
  </clause>

  <clause id="11155">
    <literal><![CDATA[
      K((x \ 1) \ (x \ y),z) = K(y,(x \ 1) \ (x \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),11152(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 11152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11156">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ L(z,x / y,y))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11065,a(flip),b,11155,a),flip(a)].">
      <j1 rule="hyper" parents="63 11065 11155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11157">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),x / y,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(3538(a,2),11156(a,1,2))].">
      <j1 rule="para" parents="3538 11156"/>
    </justification>
  </clause>

  <clause id="11158">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),y \ x,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11088,a(flip),b,11157,a)].">
      <j1 rule="hyper" parents="63 11088 11157"/>
    </justification>
  </clause>

  <clause id="11159">
    <literal><![CDATA[
      K(x,((y \ 1) * T(z \ u,y)) \ ((T(y,z \ u) \ 1) * u)) = K(x,L(T(z,u),u,T(y,z \ u) \ 1))
    ]]></literal>
    <justification jstring="[para(5934(a,1),11055(a,1,2,1))].">
      <j1 rule="para" parents="5934 11055"/>
    </justification>
  </clause>

  <clause id="11160">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ L(z,y \ x,(y \ x) \ 1))) = K((((y \ x) \ 1) * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11155,a(flip),b,11067,a)].">
      <j1 rule="hyper" parents="63 11155 11067"/>
    </justification>
  </clause>

  <clause id="11161">
    <literal><![CDATA[
      x * K(y,L(T(z,u),u,u \ x)) = (x / u) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,7112,a(flip),b,11069,a),flip(a)].">
      <j1 rule="hyper" parents="347 7112 11069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11162">
    <literal><![CDATA[
      x * ((x \ y) * K(z,(x \ y) \ u)) = y * K(z,y \ (x * u))
    ]]></literal>
    <justification jstring="[para(561(a,1),11071(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="561 11071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11163">
    <literal><![CDATA[
      T(x * (T(y,x) * K(z,u)),K(z,L(u,y,x))) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,L(u,y,x)) * (y * x) = w
    ]]></literal>
    <justification jstring="[para(11072(a,1),7348(a,1,1))].">
      <j1 rule="para" parents="11072 7348"/>
    </justification>
  </clause>

  <clause id="11164">
    <literal><![CDATA[
      x \ (y * K(z,y \ (x * u))) = (x \ y) * K(z,(x \ y) \ u)
    ]]></literal>
    <justification jstring="[para(11075(a,1),538(a,1,2,2))].">
      <j1 rule="para" parents="11075 538"/>
    </justification>
  </clause>

  <clause id="11165">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(9247(a,1),11090(a,1))].">
      <j1 rule="para" parents="9247 11090"/>
    </justification>
  </clause>

  <clause id="11166">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(9241(a,1),11093(a,1))].">
      <j1 rule="para" parents="9241 11093"/>
    </justification>
  </clause>

  <clause id="11167">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) = w
    ]]></literal>
    <justification jstring="[para(6452(a,1),11166(a,1))].">
      <j1 rule="para" parents="6452 11166"/>
    </justification>
  </clause>

  <clause id="11168">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y * x,z)) = w
    ]]></literal>
    <justification jstring="[para(7039(a,1),11166(a,1))].">
      <j1 rule="para" parents="7039 11166"/>
    </justification>
  </clause>

  <clause id="11169">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(11104(a,1),11166(a,1))].">
      <j1 rule="para" parents="11104 11166"/>
    </justification>
  </clause>

  <clause id="11170">
    <literal><![CDATA[
      K(x,(y * z) \ (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z \ u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(11059(a,1),11166(a,1))].">
      <j1 rule="para" parents="11059 11166"/>
    </justification>
  </clause>

  <clause id="11171">
    <literal><![CDATA[
      K(x,L(y,z * x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(11168,a,11108,a)].">
      <j1 rule="hyper" parents="11168 11108"/>
    </justification>
  </clause>

  <clause id="11173">
    <literal><![CDATA[
      K(x,L(y,z / x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),11171(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 11171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11174">
    <literal><![CDATA[
      (x * (y / z)) * K(z,L(u,y,x)) = x * ((y / z) * K(z,u))
    ]]></literal>
    <justification jstring="[para(11173(a,1),11073(a,1,2))].">
      <j1 rule="para" parents="11173 11073"/>
    </justification>
  </clause>

  <clause id="11175">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(9246(a,1),11100(a,1))].">
      <j1 rule="para" parents="9246 11100"/>
    </justification>
  </clause>

  <clause id="11176">
    <literal><![CDATA[
      K(x,L(T(y \ 1,((y * z) \ z) \ z) \ u,u,((y * z) \ z) \ z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(4238(a,1),11133(a,2,2,1))].">
      <j1 rule="para" parents="4238 11133"/>
    </justification>
  </clause>

  <clause id="11177">
    <literal><![CDATA[
      L(x,y * K(x,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(5932,a,11141,a)].">
      <j1 rule="hyper" parents="5932 11141"/>
    </justification>
  </clause>

  <clause id="11178">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * K(x,y))) \ (z * (x * y))
    ]]></literal>
    <justification jstring="[para(111(a,1),11141(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 11141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11179">
    <literal><![CDATA[
      L(T(x,y),z * K(x,u),w) = L(T(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(7380(a,1),11177(a,1,2,2))].">
      <j1 rule="para" parents="7380 11177"/>
    </justification>
  </clause>

  <clause id="11180">
    <literal><![CDATA[
      L(x,T(y,x) \ z,u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(8122(a,1),11177(a,1,2))].">
      <j1 rule="para" parents="8122 11177"/>
    </justification>
  </clause>

  <clause id="11181">
    <literal><![CDATA[
      L(x,(y \ T(x,y \ x)) \ z,u) = L(x,(y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[para(4171(a,1),11180(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4171 11180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11182">
    <literal><![CDATA[
      L(T(x,y),z / x,u) = L(T(x,y),x \ z,u)
    ]]></literal>
    <justification jstring="[para(4949(a,1),11179(a,1,2))].">
      <j1 rule="para" parents="4949 11179"/>
    </justification>
  </clause>

  <clause id="11183">
    <literal><![CDATA[
      L(T(x,y),z \ T(u,x),w) = L(T(x,y),z \ u,w)
    ]]></literal>
    <justification jstring="[para(6127(a,1),11179(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6127 11179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11184">
    <literal><![CDATA[
      L(T(x,y),K(x,z) * u,w) = L(T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7104(a,1),11179(a,1,2))].">
      <j1 rule="para" parents="7104 11179"/>
    </justification>
  </clause>

  <clause id="11185">
    <literal><![CDATA[
      L(T(x,y),T(x,z) \ u,w) = L(T(x,y),x \ u,w)
    ]]></literal>
    <justification jstring="[para(5159(a,1),11184(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5159 11184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11186">
    <literal><![CDATA[
      L(x,y,z * K(x,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,9884,a(flip),b,11178,a)].">
      <j1 rule="hyper" parents="347 9884 11178"/>
    </justification>
  </clause>

  <clause id="11187">
    <literal><![CDATA[
      L(x,y,T((y * x) \ z,K(x,y))) = L(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(10298(a,2),11186(a,1,3))].">
      <j1 rule="para" parents="10298 11186"/>
    </justification>
  </clause>

  <clause id="11188">
    <literal><![CDATA[
      L(R(T(x,y),z,u),w \ T(v5,x),v6) = R(L(T(x,y),w \ v5,v6),z,u)
    ]]></literal>
    <justification jstring="[para(11183(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11183 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11189">
    <literal><![CDATA[
      K(x,L(T(y,z),y \ u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(11185(a,1),11062(a,1,2))].">
      <j1 rule="para" parents="11185 11062"/>
    </justification>
  </clause>

  <clause id="11190">
    <literal><![CDATA[
      K(x,L(T(y,z),u / y,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(11182(a,2),11189(a,1,2))].">
      <j1 rule="para" parents="11182 11189"/>
    </justification>
  </clause>

  <clause id="11191">
    <literal><![CDATA[
      K(x,L(T(y,z),u * y,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(11(a,1),11190(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 11190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11192">
    <literal><![CDATA[
      K(x,y) \ L(K(x,y),z,u) = K(y,L(x,z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5468,a,11087,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="5468 11087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11193">
    <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(11126(a,1),8710(a,2,2))].">
      <j1 rule="para" parents="11126 8710"/>
    </justification>
  </clause>

  <clause id="11194">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(11063(a,1),11137(a,1))].">
      <j1 rule="para" parents="11063 11137"/>
    </justification>
  </clause>

  <clause id="11196">
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) = w
    ]]></literal>
    <justification jstring="[para(11057(a,2),11170(a,1))].">
      <j1 rule="para" parents="11057 11170"/>
    </justification>
  </clause>

  <clause id="11197">
    <literal><![CDATA[
      K(x,y) \ K(x,L(y,z,u)) = K(y,L(x,z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(11049(a,1),11192(a,1,2))].">
      <j1 rule="para" parents="11049 11192"/>
    </justification>
  </clause>

  <clause id="11198">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(x,y)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,11082,a(flip),b,11197,a)].">
      <j1 rule="hyper" parents="134 11082 11197"/>
    </justification>
  </clause>

  <clause id="11199">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(11198(a,1),5274(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11198 5274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11200">
    <literal><![CDATA[
      L(T(x,y),z,u) \ T(x,L(y,z,u)) = L(x,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,4977,a,b,11117,a)].">
      <j1 rule="hyper" parents="128 4977 11117"/>
    </justification>
  </clause>

  <clause id="11201">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(T(x,u),y,z) = T(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,11200,a(flip),b,9498,a)].">
      <j1 rule="hyper" parents="133 11200 9498"/>
    </justification>
  </clause>

  <clause id="11202">
    <literal><![CDATA[
      L(x * K(y,x),z,u) \ (x * K(y,x)) = L(x,z,u) \ T(x * K(y,x),L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5058(a,1),11200(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5058 11200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11203">
    <literal><![CDATA[
      T(x,L(y,z,u)) / (L(T(x,y),z,u) * K(w,L(x,z,u) \ x)) = T(L(x,z,u) \ x,T(w,L(T(x,y),z,u)))
    ]]></literal>
    <justification jstring="[para(11201(a,1),7429(a,1,1))].">
      <j1 rule="para" parents="11201 7429"/>
    </justification>
  </clause>

  <clause id="11204">
    <literal><![CDATA[
      L(K((x \ y) \ z,y),x \ 1,x) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[para(8248(a,1),11143(a,1,1))].">
      <j1 rule="para" parents="8248 11143"/>
    </justification>
  </clause>

  <clause id="11206">
    <literal><![CDATA[
      L(x,y,z) * (x \ ((L(x,y,z) \ x) * K(u,(L(x,y,z) \ x) \ w))) = K(u,x \ (L(x,y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(1425,a,11162,a)].">
      <j1 rule="hyper" parents="1425 11162"/>
    </justification>
  </clause>

  <clause id="11207">
    <literal><![CDATA[
      K(x,T(y,z)) * K(T(y,z),y * x) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(8384,a,11028,a)].">
      <j1 rule="hyper" parents="8384 11028"/>
    </justification>
  </clause>

  <clause id="11208">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,T(y * x,z)) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(7791,a,11207,a)].">
      <j1 rule="hyper" parents="7791 11207"/>
    </justification>
  </clause>

  <clause id="11209">
    <literal><![CDATA[
      K(x,T(y,z)) * T(y,T(y * x,z)) = (y \ L(y,x,y)) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,11208,a(flip),b,5919,a),flip(a)].">
      <j1 rule="hyper" parents="133 11208 5919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11210">
    <literal><![CDATA[
      K(x,T(y,z)) * T(y,T(y * x,z)) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3163,a(flip),b,11209,a),flip(a)].">
      <j1 rule="hyper" parents="347 3163 11209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11211">
    <literal><![CDATA[
      K(x * y,z) * T(z,T(z * (y * x),y)) = L(z,y * x,z)
    ]]></literal>
    <justification jstring="[para(10369(a,1),11210(a,1,1))].">
      <j1 rule="para" parents="10369 11210"/>
    </justification>
  </clause>

  <clause id="11212">
    <literal><![CDATA[
      K((x / y) \ 1,z) * T(z,T(z * ((y / x) * ((y / x) \ ((x / y) \ 1))),y / x)) = L(z,(y / x) * ((y / x) \ ((x / y) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(4562(a,1),11211(a,1,1,1))].">
      <j1 rule="para" parents="4562 11211"/>
    </justification>
  </clause>

  <clause id="11217">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = (L(x,y,z) * K(u,x)) * u
    ]]></literal>
    <justification jstring="[para(5983(a,1),11026(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5983 11026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11218">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,5914,a(flip),b,11217,a),flip(a)].">
      <j1 rule="hyper" parents="347 5914 11217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11219">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[para(1402(a,1),11218(a,1,1))].">
      <j1 rule="para" parents="1402 11218"/>
    </justification>
  </clause>

  <clause id="11220">
    <literal><![CDATA[
      (L(x,y,z) * T(u,x)) / x = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(145,a,11219,a)].">
      <j1 rule="hyper" parents="145 11219"/>
    </justification>
  </clause>

  <clause id="11221">
    <literal><![CDATA[
      L(x,y,z) * T(x * u,x) = (L(x,y,z) * u) * x
    ]]></literal>
    <justification jstring="[para(9(a,1),11219(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 11219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11222">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ (L(y,z,u) * T(x,y))
    ]]></literal>
    <justification jstring="[para(11219(a,1),9352(a,2,2))].">
      <j1 rule="para" parents="11219 9352"/>
    </justification>
  </clause>

  <clause id="11223">
    <literal><![CDATA[
      (L(x,y,z) * L(x,u,w)) / x = L(x,y,z) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[para(199(a,1),11220(a,1,1,2))].">
      <j1 rule="para" parents="199 11220"/>
    </justification>
  </clause>

  <clause id="11224">
    <literal><![CDATA[
      L(x,y,z) * (x \ u) != w
    ]]></literal>
    <literal><![CDATA[
      (L(x,y,z) * u) / T(x,u) = w
    ]]></literal>
    <justification jstring="[para(11220(a,1),6315(a,1))].">
      <j1 rule="para" parents="11220 6315"/>
    </justification>
  </clause>

  <clause id="11225">
    <literal><![CDATA[
      T(x * (L(x,y,z) \ u),x) = L(x,y,z) \ (u * x)
    ]]></literal>
    <justification jstring="[hyper(128,a,165,a(flip),b,11221,a),flip(a)].">
      <j1 rule="hyper" parents="128 165 11221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11226">
    <literal><![CDATA[
      T(x,y) != L(y,z,u) \ (w * y)
    ]]></literal>
    <literal><![CDATA[
      y * (L(y,z,u) \ w) = x
    ]]></literal>
    <justification jstring="[para(11225(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="11225 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11227">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * x)) != w
    ]]></literal>
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * x = w
    ]]></literal>
    <justification jstring="[para(11225(a,1),315(a,1,2))].">
      <j1 rule="para" parents="11225 315"/>
    </justification>
  </clause>

  <clause id="11228">
    <literal><![CDATA[
      L(x,y,z) \ ((x \ u) * x) = T(L(x,y,z) \ u,x)
    ]]></literal>
    <justification jstring="[para(1408(a,1),11225(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1408 11225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11229">
    <literal><![CDATA[
      T(T(x * (L(x,y,z) \ u),w),T(x,x * (L(x,y,z) \ u))) = T(L(x,y,z) \ (u * x),w)
    ]]></literal>
    <justification jstring="[para(11225(a,1),4282(a,2,1))].">
      <j1 rule="para" parents="11225 4282"/>
    </justification>
  </clause>

  <clause id="11230">
    <literal><![CDATA[
      T((x / y) * (L(x / y,z,u) \ y),x / y) = L(x / y,z,u) \ (x * K(y,y \ x))
    ]]></literal>
    <justification jstring="[para(5111(a,2),11225(a,2,2))].">
      <j1 rule="para" parents="5111 11225"/>
    </justification>
  </clause>

  <clause id="11231">
    <literal><![CDATA[
      L(x,y,z) * T(L(x,y,z) \ u,x) != w
    ]]></literal>
    <literal><![CDATA[
      (x \ u) * x = w
    ]]></literal>
    <justification jstring="[para(11228(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11228 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11232">
    <literal><![CDATA[
      (x \ (y * L(x,z,u))) * x = T(y,x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(11231,a,481,a)].">
      <j1 rule="hyper" parents="11231 481"/>
    </justification>
  </clause>

  <clause id="11233">
    <literal><![CDATA[
      (T(x,y) / y) * L(y,z,u) = y \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,1999,a,b,11232,a)].">
      <j1 rule="hyper" parents="35 1999 11232"/>
    </justification>
  </clause>

  <clause id="11234">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = T(L(y,z,u) * K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,5916,a,b,11222,a),flip(a)].">
      <j1 rule="hyper" parents="347 5916 11222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11235">
    <literal><![CDATA[
      (L(x,y,z) / x) * L(x,u,w) = L(x,y,z) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(2014,a,11223,a)].">
      <j1 rule="hyper" parents="2014 11223"/>
    </justification>
  </clause>

  <clause id="11236">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(x,u,w) = L(x,y,z) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[para(3161(a,1),11235(a,1,1))].">
      <j1 rule="para" parents="3161 11235"/>
    </justification>
  </clause>

  <clause id="11237">
    <literal><![CDATA[
      L(R(T(x,y),z,u),w \ T(v5,x),v6) = L(R(T(x,y),z,u),w \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,29,a(flip),b,11188,a),flip(a)].">
      <j1 rule="hyper" parents="347 29 11188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11238">
    <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(748(a,1),11036(a,2,2))].">
      <j1 rule="para" parents="748 11036"/>
    </justification>
  </clause>

  <clause id="11239">
    <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(10969(a,1),10972(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10969 10972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11240">
    <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(347,a,4638,a(flip),b,11239,a),flip(a)].">
      <j1 rule="hyper" parents="347 4638 11239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11242">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,R(y \ 1,y,z))) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[para(3948(a,1),11134(a,1,2))].">
      <j1 rule="para" parents="3948 11134"/>
    </justification>
  </clause>

  <clause id="11243">
    <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(5438(a,1),10958(a,1,1))].">
      <j1 rule="para" parents="5438 10958"/>
    </justification>
  </clause>

  <clause id="11244">
    <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(7899(a,1),11243(a,1,1,1,2))].">
      <j1 rule="para" parents="7899 11243"/>
    </justification>
  </clause>

  <clause id="11245">
    <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(6366,a,11244,a)].">
      <j1 rule="hyper" parents="6366 11244"/>
    </justification>
  </clause>

  <clause id="11246">
    <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(5432(a,1),11245(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5432 11245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11247">
    <literal><![CDATA[
      R(R(x,y,z),u,R(x,y,z)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10952,a(flip),b,11246,a)].">
      <j1 rule="hyper" parents="63 10952 11246"/>
    </justification>
  </clause>

  <clause id="11248">
    <literal><![CDATA[
      (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(R(y,z,u),w,L(R(y,z,u),v5,v6))
    ]]></literal>
    <justification jstring="[para(11246(a,1),10713(a,1,2))].">
      <j1 rule="para" parents="11246 10713"/>
    </justification>
  </clause>

  <clause id="11249">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(163,a,11247,a)].">
      <j1 rule="hyper" parents="163 11247"/>
    </justification>
  </clause>

  <clause id="11250">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) = x * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,8339,a,b,11249,a),flip(a)].">
      <j1 rule="hyper" parents="347 8339 11249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11252">
    <literal><![CDATA[
      K(x,R(y,z,R(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11249(a,2),7627(a,1,2))].">
      <j1 rule="para" parents="11249 7627"/>
    </justification>
  </clause>

  <clause id="11253">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,R(z,u,R(T(z,y),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(7484,a,11252,a),flip(a)].">
      <j1 rule="hyper" parents="7484 11252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11254">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9434,a,11250,a)].">
      <j1 rule="hyper" parents="9434 11250"/>
    </justification>
  </clause>

  <clause id="11255">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = a(x,y,L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,10963,a,b,11254,a),flip(a)].">
      <j1 rule="hyper" parents="347 10963 11254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11257">
    <literal><![CDATA[
      a(x,T(y,x),L(x,z,u)) = a(x,y,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,9488,a(flip),b,11255,a),flip(a)].">
      <j1 rule="hyper" parents="63 9488 11255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11259">
    <literal><![CDATA[
      a(x,x \ (y * x),L(x,z,u)) = a(x,y,R(x,w,v5))
    ]]></literal>
    <justification jstring="[para(22(a,1),11257(a,1,2))].">
      <j1 rule="para" parents="22 11257"/>
    </justification>
  </clause>

  <clause id="11260">
    <literal><![CDATA[
      K(x,R(y,z,R(T(y,u),w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7477,a,11253,a),flip(a)].">
      <j1 rule="hyper" parents="7477 11253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11262">
    <literal><![CDATA[
      K(x,y) * (y \ R(T(y,x),z,R(T(y,u),w,v5))) = y \ R(y,z,R(T(y,u),w,v5))
    ]]></literal>
    <justification jstring="[para(11260(a,1),9519(a,1,1))].">
      <j1 rule="para" parents="11260 9519"/>
    </justification>
  </clause>

  <clause id="11263">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ (u * x),L(x,y,z)) = a(x,u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,9733,a,b,11259,a)].">
      <j1 rule="hyper" parents="63 9733 11259"/>
    </justification>
  </clause>

  <clause id="11264">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = K(y * x,L(x,w,v5)) * K(L(x,w,v5),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10596,a(flip),b,11263,a),flip(a)].">
      <j1 rule="hyper" parents="63 10596 11263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11266">
    <literal><![CDATA[
      x * (K(y,L(x,z,u)) * K(w,L(y,z,u))) = (L(y,z,u) * x) / L(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),11118(a,2,2))].">
      <j1 rule="para" parents="25 11118"/>
    </justification>
  </clause>

  <clause id="11267">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,R(T(x,u),w,v5)) = x \ R(x,z,R(T(x,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(5217,a,11262,a)].">
      <j1 rule="hyper" parents="5217 11262"/>
    </justification>
  </clause>

  <clause id="11268">
    <literal><![CDATA[
      K(x,y) * (y \ R(T(y,x),z,R(y,u,w))) = y \ R(y,z,R(T(y,x),u,w))
    ]]></literal>
    <justification jstring="[para(9512(a,1),11262(a,1,2,2))].">
      <j1 rule="para" parents="9512 11262"/>
    </justification>
  </clause>

  <clause id="11269">
    <literal><![CDATA[
      x \ R(x,y,R(T(x,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(T(x,z),y,R(T(x,z),u,w)) = v5
    ]]></literal>
    <justification jstring="[para(11267(a,1),9432(a,1))].">
      <j1 rule="para" parents="11267 9432"/>
    </justification>
  </clause>

  <clause id="11270">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * a(y,z,R(y,u,w))) = y \ R(y,z,R(T(y,x),u,w))
    ]]></literal>
    <justification jstring="[para(9522(a,1),11268(a,1,2))].">
      <j1 rule="para" parents="9522 11268"/>
    </justification>
  </clause>

  <clause id="11271">
    <literal><![CDATA[
      x \ R(x,y,R(T(x,z),u,w)) = a(x,y,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(5275,a,11270,a),flip(a)].">
      <j1 rule="hyper" parents="5275 11270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11272">
    <literal><![CDATA[
      a(T(x,y),z,R(T(x,y),u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(11269,a,11271,a)].">
      <j1 rule="hyper" parents="11269 11271"/>
    </justification>
  </clause>

  <clause id="11274">
    <literal><![CDATA[
      a(R(x,y,z),u,x) \ 1 = a(x,u,R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(11272(a,1),9462(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11272 9462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11275">
    <literal><![CDATA[
      a(R(x,y,z),u,x) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(313,a,11274,a),flip(a)].">
      <j1 rule="hyper" parents="313 11274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11277">
    <literal><![CDATA[
      (x * L(R(T(y,x),z,u),y \ T(x,y),y)) \ (x * R(T(y,x),z,u)) = a(R(T(y,x),z,u),T(y,x) \ x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,4877,a,b,11275,a)].">
      <j1 rule="hyper" parents="347 4877 11275"/>
    </justification>
  </clause>

  <clause id="11279">
    <literal><![CDATA[
      (R(x,y,x) * z) \ (R(x,y,x) * (z * u)) = L(L(u,z,x),x * z,a(x,y,x))
    ]]></literal>
    <justification jstring="[para(10986(a,1),11002(a,1,2))].">
      <j1 rule="para" parents="10986 11002"/>
    </justification>
  </clause>

  <clause id="11280">
    <literal><![CDATA[
      L(L(x,y,z),z * y,a(z,u,z)) = L(x,y,R(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(545,a,11279,a),flip(a)].">
      <j1 rule="hyper" parents="545 11279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11281">
    <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(11234(a,1),11193(a,1,2))].">
      <j1 rule="para" parents="11234 11193"/>
    </justification>
  </clause>

  <clause id="11282">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(L(x,z,y),u) * K(u,x)
    ]]></literal>
    <justification jstring="[hyper(7561,a,11281,a),flip(a)].">
      <j1 rule="hyper" parents="7561 11281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11283">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,11098,a(flip),b,11282,a),flip(a)].">
      <j1 rule="hyper" parents="347 11098 11282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11284">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(358,a,11283,a),flip(a)].">
      <j1 rule="hyper" parents="358 11283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11285">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(11283(a,1),356(a,1))].">
      <j1 rule="para" parents="11283 356"/>
    </justification>
  </clause>

  <clause id="11287">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),11284(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="9 11284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11288">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(x,y,K(z \ u,u))
    ]]></literal>
    <justification jstring="[para(5529(a,1),11284(a,1,3))].">
      <j1 rule="para" parents="5529 11284"/>
    </justification>
  </clause>

  <clause id="11289">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u * z)) = a(x,y,K(u,u * z))
    ]]></literal>
    <justification jstring="[para(5996(a,1),11284(a,1,3))].">
      <j1 rule="para" parents="5996 11284"/>
    </justification>
  </clause>

  <clause id="11290">
    <literal><![CDATA[
      a(x,y,K(z \ (u * w),w)) = a(x,y,K(z \ u,w))
    ]]></literal>
    <justification jstring="[para(9619(a,1),11284(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9619 11284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11291">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,z,K(y * x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,11080,a,b,11287,a)].">
      <j1 rule="hyper" parents="347 11080 11287"/>
    </justification>
  </clause>

  <clause id="11292">
    <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(11287(a,2),10001(a,1,1))].">
      <j1 rule="para" parents="11287 10001"/>
    </justification>
  </clause>

  <clause id="11293">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(11199,a,11291,a),flip(a)].">
      <j1 rule="hyper" parents="11199 11291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11294">
    <literal><![CDATA[
      a(x,y,K(z,z * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(10002,a,11292,a)].">
      <j1 rule="hyper" parents="10002 11292"/>
    </justification>
  </clause>

  <clause id="11295">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u * z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11289,a,b,11294,a)].">
      <j1 rule="hyper" parents="63 11289 11294"/>
    </justification>
  </clause>

  <clause id="11296">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),11294(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10 11294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11297">
    <literal><![CDATA[
      a(x,y,K(z,u * z)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5297(a,2),11294(a,1,3))].">
      <j1 rule="para" parents="5297 11294"/>
    </justification>
  </clause>

  <clause id="11298">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u * z)) = a(x,y,K(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(9785(a,1),11294(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9785 11294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11299">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11295,a(flip),b,11298,a),flip(a)].">
      <j1 rule="hyper" parents="63 11295 11298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11300">
    <literal><![CDATA[
      a(x,y,K(y \ 1,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(347,a,6240,a(flip),b,11299,a),flip(a)].">
      <j1 rule="hyper" parents="347 6240 11299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11301">
    <literal><![CDATA[
      a(x,y,K(z \ u,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11288,a(flip),b,11299,a)].">
      <j1 rule="hyper" parents="63 11288 11299"/>
    </justification>
  </clause>

  <clause id="11302">
    <literal><![CDATA[
      a(x,y,K(z \ u,w)) = a(x,y,K(w,u \ z))
    ]]></literal>
    <justification jstring="[para(5988(a,1),11299(a,1,3))].">
      <j1 rule="para" parents="5988 11299"/>
    </justification>
  </clause>

  <clause id="11303">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(5983(a,1),11301(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5983 11301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11304">
    <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(475(a,1),10998(a,1,1))].">
      <j1 rule="para" parents="475 10998"/>
    </justification>
  </clause>

  <clause id="11305">
    <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(10952(a,1),11304(a,1,1,2,2))].">
      <j1 rule="para" parents="10952 11304"/>
    </justification>
  </clause>

  <clause id="11306">
    <literal><![CDATA[
      L(a(x,y,x),z * x,u) = a(L(x,z,u),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10985,a(flip),b,11305,a)].">
      <j1 rule="hyper" parents="63 10985 11305"/>
    </justification>
  </clause>

  <clause id="11308">
    <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),11306(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 11306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11309">
    <literal><![CDATA[
      L(x / y,z,u) \ (x * K(y,y \ x)) = T(L(x / y,z,u) \ x,x / y)
    ]]></literal>
    <justification jstring="[para(1427(a,1),11230(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1427 11230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11310">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),y \ x,(y \ x) \ 1)) = K((((y \ x) \ 1) * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(3538(a,2),11160(a,1,2))].">
      <j1 rule="para" parents="3538 11160"/>
    </justification>
  </clause>

  <clause id="11311">
    <literal><![CDATA[
      T(T(x * (L(x,y,z) \ u),w),T(x,u)) = T(L(x,y,z) \ (u * x),w)
    ]]></literal>
    <justification jstring="[para(9712(a,1),11229(a,1,2))].">
      <j1 rule="para" parents="9712 11229"/>
    </justification>
  </clause>

  <clause id="11313">
    <literal><![CDATA[
      (x \ (y \ (z \ ((z * y) * x)))) \ 1 = (y \ (z \ ((z * y) * x))) \ x
    ]]></literal>
    <justification jstring="[para(9(a,1),10930(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 10930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11314">
    <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(6791(a,1),11238(a,2,2,1))].">
      <j1 rule="para" parents="6791 11238"/>
    </justification>
  </clause>

  <clause id="11316">
    <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(10961(a,1),11314(a,2,2))].">
      <j1 rule="para" parents="10961 11314"/>
    </justification>
  </clause>

  <clause id="11317">
    <literal><![CDATA[
      a((x \ y) \ y,z,(x \ y) \ y) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(41,a,552,a,b,11316,a),flip(a)].">
      <j1 rule="hyper" parents="41 552 11316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11318">
    <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(63,a,10625,a(flip),b,11317,a)].">
      <j1 rule="hyper" parents="63 10625 11317"/>
    </justification>
  </clause>

  <clause id="11320">
    <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),11318(a,1,1,2))].">
      <j1 rule="para" parents="23 11318"/>
    </justification>
  </clause>

  <clause id="11321">
    <literal><![CDATA[
      x * a(R(y,z,u),R(y,z,u) \ (w * y),R(y,z,u)) = (x / R(y,z,u)) * R(R(y,w,y),z,u)
    ]]></literal>
    <justification jstring="[para(4411(a,1),11040(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4411 11040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11322">
    <literal><![CDATA[
      L(x,y,z) * (x \ ((L(x,y,z) \ x) * K(u,(L(x,y,z) \ x) \ w))) = K(u,L(x,y,z) * (x \ w))
    ]]></literal>
    <justification jstring="[para(1402(a,1),11206(a,2,2))].">
      <j1 rule="para" parents="1402 11206"/>
    </justification>
  </clause>

  <clause id="11323">
    <literal><![CDATA[
      (R(R(x,y,z),u,R(x,y,z)) * (y * z)) / ((x * y) * z) = a(R(x,y,z),u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(8342(a,1),11000(a,1,1,1))].">
      <j1 rule="para" parents="8342 11000"/>
    </justification>
  </clause>

  <clause id="11324">
    <literal><![CDATA[
      ((R(x,y,R(x,z,u)) * z) * u) / ((x * z) * u) = a(R(x,z,u),y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(469(a,1),11323(a,1,1))].">
      <j1 rule="para" parents="469 11323"/>
    </justification>
  </clause>

  <clause id="11325">
    <literal><![CDATA[
      ((R(x,y,x) * z) * u) / ((x * z) * u) = a(R(x,z,u),y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(11249(a,1),11324(a,1,1,1,1))].">
      <j1 rule="para" parents="11249 11324"/>
    </justification>
  </clause>

  <clause id="11326">
    <literal><![CDATA[
      a(R(x,y,z),u,R(x,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      R(a(x,u,x),x * y,z) = w
    ]]></literal>
    <justification jstring="[para(11325(a,1),11001(a,1))].">
      <j1 rule="para" parents="11325 11001"/>
    </justification>
  </clause>

  <clause id="11346">
    <literal><![CDATA[
      ((((L(x,y,z) \ x) \ 1) \ 1) * (L(x,y,z) \ x)) * u = ((x \ L(x,y,z)) * (x \ L(x,y,z))) \ u
    ]]></literal>
    <justification jstring="[para(10888(a,1),10898(a,2,1,2))].">
      <j1 rule="para" parents="10888 10898"/>
    </justification>
  </clause>

  <clause id="11347">
    <literal><![CDATA[
      (x * L(R(T(y,x),z,u),y \ x,y)) \ (x * R(T(y,x),z,u)) = a(R(T(y,x),z,u),T(y,x) \ x,T(y,x))
    ]]></literal>
    <justification jstring="[para(11237(a,1),11277(a,1,1,2))].">
      <j1 rule="para" parents="11237 11277"/>
    </justification>
  </clause>

  <clause id="11348">
    <literal><![CDATA[
      (L(R(x,y,z),x \ u,x) * u) \ (u * R(T(x,u),y,z)) = a(R(T(x,u),y,z),T(x,u) \ u,T(x,u))
    ]]></literal>
    <justification jstring="[para(739(a,1),11347(a,1,1))].">
      <j1 rule="para" parents="739 11347"/>
    </justification>
  </clause>

  <clause id="11349">
    <literal><![CDATA[
      a(R(T(x,y),z,u),T(x,y) \ y,T(x,y)) = (L(R(x,z,u),x \ y,x) * y) \ (R(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(268(a,1),11348(a,1,2)),flip(a)].">
      <j1 rule="para" parents="268 11348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11350">
    <literal><![CDATA[
      a(R(T(x,y),z,u),T(x,y) \ y,T(x,y)) = a(x,x \ y,T(R(x,z,u),y))
    ]]></literal>
    <justification jstring="[hyper(347,a,2128,a(flip),b,11349,a),flip(a)].">
      <j1 rule="hyper" parents="347 2128 11349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11351">
    <literal><![CDATA[
      a(R(T(x,y),z,u),T(x,y) \ y,T(x,y)) = a(x,x \ y,R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(27(a,2),11350(a,2,3))].">
      <j1 rule="para" parents="27 11350"/>
    </justification>
  </clause>

  <clause id="11352">
    <literal><![CDATA[
      a(T(x,y),T(x,y) \ y,R(T(x,y),z,u)) = a(x,x \ y,R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11275,a(flip),b,11351,a)].">
      <j1 rule="hyper" parents="63 11275 11351"/>
    </justification>
  </clause>

  <clause id="11353">
    <literal><![CDATA[
      a(x,T(x,y) \ y,R(x,z,u)) = a(x,x \ y,R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11272,a(flip),b,11352,a)].">
      <j1 rule="hyper" parents="63 11272 11352"/>
    </justification>
  </clause>

  <clause id="11355">
    <literal><![CDATA[
      a(x,x \ y,R(T(x,y),z,u)) = a(x,x \ y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10779,a(flip),b,11353,a),flip(a)].">
      <j1 rule="hyper" parents="63 10779 11353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11357">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = a(x,x \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10633,a,b,11355,a)].">
      <j1 rule="hyper" parents="63 10633 11355"/>
    </justification>
  </clause>

  <clause id="11358">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z) \ u,R(x,y,z)) = a(x,x \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(9227,a,11357,a)].">
      <j1 rule="hyper" parents="9227 11357"/>
    </justification>
  </clause>

  <clause id="11359">
    <literal><![CDATA[
      (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(y,y \ (w * y),R(y,z,u))
    ]]></literal>
    <justification jstring="[para(11358(a,1),11321(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11358 11321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11360">
    <literal><![CDATA[
      (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(y,T(w,y),R(y,z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),11359(a,2,2,2))].">
      <j1 rule="para" parents="22 11359"/>
    </justification>
  </clause>

  <clause id="11361">
    <literal><![CDATA[
      (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(y,w,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(9488(a,1),11360(a,2,2))].">
      <j1 rule="para" parents="9488 11360"/>
    </justification>
  </clause>

  <clause id="11362">
    <literal><![CDATA[
      x * a(R(y,z,u),w,L(R(y,z,u),v5,v6)) = x * a(y,w,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11248,a(flip),b,11361,a)].">
      <j1 rule="hyper" parents="63 11248 11361"/>
    </justification>
  </clause>

  <clause id="11363">
    <literal><![CDATA[
      x * a(R(y,z,u),w,R(y,z,u)) = x * a(y,w,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(398(a,1),11362(a,1,2,3))].">
      <j1 rule="para" parents="398 11362"/>
    </justification>
  </clause>

  <clause id="11364">
    <literal><![CDATA[
      a(R(x,y,z),u,R(x,y,z)) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(9969,a,11363,a)].">
      <j1 rule="hyper" parents="9969 11363"/>
    </justification>
  </clause>

  <clause id="11365">
    <literal><![CDATA[
      R(a(x,y,x),x * z,u) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(11326,a,11364,a)].">
      <j1 rule="hyper" parents="11326 11364"/>
    </justification>
  </clause>

  <clause id="11366">
    <literal><![CDATA[
      a(x,y,R(x,x \ z,u)) = R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11365(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 11365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11367">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11254,a(flip),b,11366,a),flip(a)].">
      <j1 rule="hyper" parents="63 11254 11366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11371">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = L(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10010,a(flip),b,11367,a),flip(a)].">
      <j1 rule="hyper" parents="63 10010 11367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11372">
    <literal><![CDATA[
      (a(x,y,x) * z) * u = a(x,y,x) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(133,a,11367,a(flip),b,6210,a),flip(a)].">
      <j1 rule="hyper" parents="133 11367 6210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11373">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) * u) = z * u
    ]]></literal>
    <justification jstring="[hyper(133,a,11367,a(flip),b,104,a(flip))].">
      <j1 rule="hyper" parents="133 11367 104"/>
    </justification>
  </clause>

  <clause id="11374">
    <literal><![CDATA[
      a(x,y,x) \ (z * u) = (a(x,y,x) \ z) * u
    ]]></literal>
    <justification jstring="[para(11367(a,1),578(a,1,1))].">
      <j1 rule="para" parents="11367 578"/>
    </justification>
  </clause>

  <clause id="11376">
    <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(5437(a,1),11371(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5437 11371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11377">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(3558,a,11372,a)].">
      <j1 rule="hyper" parents="3558 11372"/>
    </justification>
  </clause>

  <clause id="11378">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = a(x,y,x) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(131,a,168,a(flip),b,11372,a)].">
      <j1 rule="hyper" parents="131 168 11372"/>
    </justification>
  </clause>

  <clause id="11379">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(128,a,76,a(flip),b,11372,a)].">
      <j1 rule="hyper" parents="128 76 11372"/>
    </justification>
  </clause>

  <clause id="11380">
    <literal><![CDATA[
      (a(x,y,x) * (z * u)) \ ((a(x,y,x) * z) * (u * w)) = L(w,u,a(x,y,x) * z)
    ]]></literal>
    <justification jstring="[para(11372(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11372 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11381">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      z * u = w
    ]]></literal>
    <justification jstring="[para(11372(a,1),628(a,1))].">
      <j1 rule="para" parents="11372 628"/>
    </justification>
  </clause>

  <clause id="11382">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) \ (x * (a(y,z,y) * (u * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(w,a(y,z,y) * u,x) = v5
    ]]></literal>
    <justification jstring="[para(11372(a,1),545(a,1,2,2))].">
      <j1 rule="para" parents="11372 545"/>
    </justification>
  </clause>

  <clause id="11383">
    <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(11372(a,1),836(a,1,1,2))].">
      <j1 rule="para" parents="11372 836"/>
    </justification>
  </clause>

  <clause id="11384">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = a(y,z,y) * (x * u)
    ]]></literal>
    <justification jstring="[para(9957(a,1),11372(a,1,1))].">
      <j1 rule="para" parents="9957 11372"/>
    </justification>
  </clause>

  <clause id="11385">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ u = z \ (a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(651,a,11377,a),flip(a)].">
      <j1 rule="hyper" parents="651 11377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11386">
    <literal><![CDATA[
      L(x,y,R(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11280,a(flip),b,11377,a)].">
      <j1 rule="hyper" parents="63 11280 11377"/>
    </justification>
  </clause>

  <clause id="11387">
    <literal><![CDATA[
      a(x,y,x) \ (a(x,y,x) / z) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(63,a,3264,a(flip),b,11377,a)].">
      <j1 rule="hyper" parents="63 3264 11377"/>
    </justification>
  </clause>

  <clause id="11388">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(11377(a,1),50(a,2))].">
      <j1 rule="para" parents="11377 50"/>
    </justification>
  </clause>

  <clause id="11389">
    <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(11377(a,1),543(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11377 543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11390">
    <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(11377(a,1),540(a,1,1,2,1))].">
      <j1 rule="para" parents="11377 540"/>
    </justification>
  </clause>

  <clause id="11393">
    <literal><![CDATA[
      L(x,y,T(z,z \ u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(4426(a,1),11386(a,1,3))].">
      <j1 rule="para" parents="4426 11386"/>
    </justification>
  </clause>

  <clause id="11395">
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(6798(a,1),11386(a,1,3))].">
      <j1 rule="para" parents="6798 11386"/>
    </justification>
  </clause>

  <clause id="11396">
    <literal><![CDATA[
      L(x,y,R(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(11280(a,1),11388(a,1))].">
      <j1 rule="para" parents="11280 11388"/>
    </justification>
  </clause>

  <clause id="11397">
    <literal><![CDATA[
      L(x,y,T(z * u,u \ 1)) = L(x,y,T(z * u,z))
    ]]></literal>
    <justification jstring="[para(6276(a,1),11393(a,1,3))].">
      <j1 rule="para" parents="6276 11393"/>
    </justification>
  </clause>

  <clause id="11398">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),w)) = L(x,y,T(T(z,w),u))
    ]]></literal>
    <justification jstring="[para(7573(a,2),11395(a,1,3))].">
      <j1 rule="para" parents="7573 11395"/>
    </justification>
  </clause>

  <clause id="11399">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(795(a,1),11396(a,1,3))].">
      <j1 rule="para" parents="795 11396"/>
    </justification>
  </clause>

  <clause id="11400">
    <literal><![CDATA[
      (a(x,y,x) \ z) / u = a(x,y,x) \ (z / u)
    ]]></literal>
    <justification jstring="[hyper(649,a,11378,a),flip(a)].">
      <j1 rule="hyper" parents="649 11378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11401">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = (z / u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,9957,a(flip),b,11378,a),flip(a)].">
      <j1 rule="hyper" parents="347 9957 11378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11402">
    <literal><![CDATA[
      (a(x,y,x) * z) \ x = z \ L(x,y,x)
    ]]></literal>
    <justification jstring="[para(8500(a,1),11379(a,2,2))].">
      <j1 rule="para" parents="8500 11379"/>
    </justification>
  </clause>

  <clause id="11403">
    <literal><![CDATA[
      (x * y) \ L(y,x,y) = T(y * x,y) \ y
    ]]></literal>
    <justification jstring="[para(10327(a,1),11402(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10327 11402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11404">
    <literal><![CDATA[
      ((x * (y * z)) / x) \ L(z,z \ ((x * (z * y)) / x),z) = T(z * (z \ ((x * (z * y)) / x)),z) \ z
    ]]></literal>
    <justification jstring="[para(4866(a,1),11403(a,1,1))].">
      <j1 rule="para" parents="4866 11403"/>
    </justification>
  </clause>

  <clause id="11405">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (a(y,z,y) * u) = x \ u
    ]]></literal>
    <justification jstring="[hyper(128,a,169,a(flip),b,11384,a)].">
      <j1 rule="hyper" parents="128 169 11384"/>
    </justification>
  </clause>

  <clause id="11406">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ x = z \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(8342(a,1),11385(a,2,2))].">
      <j1 rule="para" parents="8342 11385"/>
    </justification>
  </clause>

  <clause id="11407">
    <literal><![CDATA[
      (L(x,y,x) * z) \ x = (x * z) \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(9987(a,1),11406(a,1,1))].">
      <j1 rule="para" parents="9987 11406"/>
    </justification>
  </clause>

  <clause id="11408">
    <literal><![CDATA[
      (R(x,y,x) \ z) \ x = (x \ z) \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(10990(a,1),11406(a,1,1))].">
      <j1 rule="para" parents="10990 11406"/>
    </justification>
  </clause>

  <clause id="11409">
    <literal><![CDATA[
      a(x,y,x) \ (x / z) = L(x,y,x) / z
    ]]></literal>
    <justification jstring="[para(8500(a,1),11400(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8500 11400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11410">
    <literal><![CDATA[
      L(x,y,x) \ (L(x,y,x) / z) = x \ (x / z)
    ]]></literal>
    <justification jstring="[hyper(128,a,11409,a(flip),b,9981,a)].">
      <j1 rule="hyper" parents="128 11409 9981"/>
    </justification>
  </clause>

  <clause id="11411">
    <literal><![CDATA[
      (x / y) * a(x,z,x) = R(x,z,x) / y
    ]]></literal>
    <justification jstring="[para(8342(a,1),11401(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8342 11401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11412">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),w)) = L(x,y,T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(23(a,1),11398(a,2,3))].">
      <j1 rule="para" parents="23 11398"/>
    </justification>
  </clause>

  <clause id="11413">
    <literal><![CDATA[
      a(x,y,x) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (z * a(x,y,x)) * u = w
    ]]></literal>
    <justification jstring="[para(9960(a,1),11381(a,1,2,1))].">
      <j1 rule="para" parents="9960 11381"/>
    </justification>
  </clause>

  <clause id="11414">
    <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(63,a,10634,a(flip),b,11376,a)].">
      <j1 rule="hyper" parents="63 10634 11376"/>
    </justification>
  </clause>

  <clause id="11415">
    <literal><![CDATA[
      (a(x,y,x) * (z * u)) \ (a(x,y,x) * (z * (u * w))) = L(w,u,a(x,y,x) * z)
    ]]></literal>
    <justification jstring="[para(11372(a,1),11380(a,1,2))].">
      <j1 rule="para" parents="11372 11380"/>
    </justification>
  </clause>

  <clause id="11416">
    <literal><![CDATA[
      L(L(x,y,z),z * y,a(u,w,u)) = L(x,y,a(u,w,u) * z)
    ]]></literal>
    <justification jstring="[hyper(942,a,11415,a)].">
      <j1 rule="hyper" parents="942 11415"/>
    </justification>
  </clause>

  <clause id="11417">
    <literal><![CDATA[
      L(x,y,a(z,u,z) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(11388,a,11416,a),flip(a)].">
      <j1 rule="hyper" parents="11388 11416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11419">
    <literal><![CDATA[
      L(x,y,a(z,u,z) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(11416(a,1),11388(a,1))].">
      <j1 rule="para" parents="11416 11388"/>
    </justification>
  </clause>

  <clause id="11421">
    <literal><![CDATA[
      L(x,y,a(z,u,z) \ w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),11417(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 11417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11422">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(8352(a,1),11417(a,1,3))].">
      <j1 rule="para" parents="8352 11417"/>
    </justification>
  </clause>

  <clause id="11423">
    <literal><![CDATA[
      L(x,y,K(z,z * u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(8355(a,1),11417(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8355 11417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11424">
    <literal><![CDATA[
      L(x,y,K(z,z \ u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(8370(a,1),11417(a,1,3))].">
      <j1 rule="para" parents="8370 11417"/>
    </justification>
  </clause>

  <clause id="11425">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8497(a,1),11417(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8497 11417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11426">
    <literal><![CDATA[
      L(x,y,z * a(u,w,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(9957(a,1),11417(a,1,3))].">
      <j1 rule="para" parents="9957 11417"/>
    </justification>
  </clause>

  <clause id="11427">
    <literal><![CDATA[
      L(x,y,T(z * u,z)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(10327(a,1),11417(a,1,3))].">
      <j1 rule="para" parents="10327 11417"/>
    </justification>
  </clause>

  <clause id="11428">
    <literal><![CDATA[
      L(x,y,z * R(u,w,u)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(10980(a,1),11417(a,1,3))].">
      <j1 rule="para" parents="10980 11417"/>
    </justification>
  </clause>

  <clause id="11429">
    <literal><![CDATA[
      L(x,y,R(z,u,z) \ w) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(10988(a,1),11417(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10988 11417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11430">
    <literal><![CDATA[
      L(x,y,R(z,u,z)) = L(x,y,L(z,w,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,11386,a,b,11425,a)].">
      <j1 rule="hyper" parents="347 11386 11425"/>
    </justification>
  </clause>

  <clause id="11431">
    <literal><![CDATA[
      L(x,y,K(z \ u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(8333(a,1),11421(a,1,3))].">
      <j1 rule="para" parents="8333 11421"/>
    </justification>
  </clause>

  <clause id="11432">
    <literal><![CDATA[
      L(x,y,z / R(u,w,u)) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(10993(a,1),11421(a,1,3))].">
      <j1 rule="para" parents="10993 11421"/>
    </justification>
  </clause>

  <clause id="11433">
    <literal><![CDATA[
      L(x,y,K(z * y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,4250,a(flip),b,11422,a),flip(a)].">
      <j1 rule="hyper" parents="347 4250 11422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11434">
    <literal><![CDATA[
      L(x \ (y * z),x,K(z,y)) = (K(y,T(y,y * z) * z) \ x) \ T(T(T(y,y * z) * z,y),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10796,a(flip),b,11422,a),flip(a)].">
      <j1 rule="hyper" parents="63 10796 11422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11435">
    <literal><![CDATA[
      L(x,y / z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(7909(a,1),11433(a,1,3))].">
      <j1 rule="para" parents="7909 11433"/>
    </justification>
  </clause>

  <clause id="11436">
    <literal><![CDATA[
      (K(x,y) * (x / y)) \ z = (x / y) \ (K(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(623,a,11435,a),flip(a)].">
      <j1 rule="hyper" parents="623 11435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11437">
    <literal><![CDATA[
      K(x,y) * ((x / y) * z) = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(11435(a,1),5375(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11435 5375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11439">
    <literal><![CDATA[
      L(x,y,K(z,u * z)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5297(a,2),11423(a,1,3))].">
      <j1 rule="para" parents="5297 11423"/>
    </justification>
  </clause>

  <clause id="11440">
    <literal><![CDATA[
      L(x,y,K(z * u,(z * u) * (u \ 1))) = L(x,y,K(u * z,u \ 1))
    ]]></literal>
    <justification jstring="[para(5777(a,1),11423(a,2,3))].">
      <j1 rule="para" parents="5777 11423"/>
    </justification>
  </clause>

  <clause id="11441">
    <literal><![CDATA[
      L(x \ y,z,K(x,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(7681,a,11424,a)].">
      <j1 rule="hyper" parents="7681 11424"/>
    </justification>
  </clause>

  <clause id="11442">
    <literal><![CDATA[
      L(x,y \ z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(5496,a,11424,a),flip(a)].">
      <j1 rule="hyper" parents="5496 11424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11444">
    <literal><![CDATA[
      L(L(x,y,z \ u),(z \ u) * y,K(z,u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6958,a(flip),b,11424,a),flip(a)].">
      <j1 rule="hyper" parents="63 6958 11424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11445">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) * z = K(x,y) * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(1362,a,11442,a),flip(a)].">
      <j1 rule="hyper" parents="1362 11442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11446">
    <literal><![CDATA[
      (K(x,y) * z) / (x \ y) = K(x,y) * (z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(220,a,11441,a(flip),b,9645,a(flip))].">
      <j1 rule="hyper" parents="220 11441 9645"/>
    </justification>
  </clause>

  <clause id="11447">
    <literal><![CDATA[
      L(x,y,z * y) = L(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(10236,a,11427,a),flip(a)].">
      <j1 rule="hyper" parents="10236 11427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11448">
    <literal><![CDATA[
      L(x,y,T(z * u,u \ 1)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11397,a,b,11427,a)].">
      <j1 rule="hyper" parents="63 11397 11427"/>
    </justification>
  </clause>

  <clause id="11449">
    <literal><![CDATA[
      L(x,y,(z \ u) * z) = L(x,y,T(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),11427(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 11427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11450">
    <literal><![CDATA[
      L(x,y,T((z \ u) * z,z \ u)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11427(a,2,3))].">
      <j1 rule="para" parents="10 11427"/>
    </justification>
  </clause>

  <clause id="11451">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(11430(a,1),11396(a,1))].">
      <j1 rule="para" parents="11430 11396"/>
    </justification>
  </clause>

  <clause id="11452">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(z,u)) = L(x,y,(u \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(10571,a,11431,a),flip(a)].">
      <j1 rule="hyper" parents="10571 11431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11453">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(u,z \ 1))
    ]]></literal>
    <justification jstring="[para(4459(a,1),11431(a,1,3))].">
      <j1 rule="para" parents="4459 11431"/>
    </justification>
  </clause>

  <clause id="11454">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,y,K(u,u \ z))
    ]]></literal>
    <justification jstring="[para(5144(a,1),11431(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5144 11431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11455">
    <literal><![CDATA[
      L(x,y,(z \ T(u * K(z,u),w)) * z) = L(x,y,T(u,w))
    ]]></literal>
    <justification jstring="[para(5059(a,1),11449(a,2,3))].">
      <j1 rule="para" parents="5059 11449"/>
    </justification>
  </clause>

  <clause id="11456">
    <literal><![CDATA[
      L(x,y,T(z / u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(4398(a,1),11451(a,1,3))].">
      <j1 rule="para" parents="4398 11451"/>
    </justification>
  </clause>

  <clause id="11457">
    <literal><![CDATA[
      L(x,y,z * T(u,u \ w)) = L(x,y,z * T(u,w))
    ]]></literal>
    <justification jstring="[para(4426(a,1),11428(a,1,3,2))].">
      <j1 rule="para" parents="4426 11428"/>
    </justification>
  </clause>

  <clause id="11458">
    <literal><![CDATA[
      L(x,y,(z \ T(u,z \ u)) \ w) = L(x,y,(u / z) \ w)
    ]]></literal>
    <justification jstring="[para(4404(a,1),11429(a,1,3,1))].">
      <j1 rule="para" parents="4404 11429"/>
    </justification>
  </clause>

  <clause id="11459">
    <literal><![CDATA[
      L(x,y,K(z,u) * (z \ u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(7249(a,1),11432(a,1,3))].">
      <j1 rule="para" parents="7249 11432"/>
    </justification>
  </clause>

  <clause id="11460">
    <literal><![CDATA[
      L(x,y,K(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(8370(a,1),11419(a,1,3))].">
      <j1 rule="para" parents="8370 11419"/>
    </justification>
  </clause>

  <clause id="11461">
    <literal><![CDATA[
      L(x,y,z * a(u,w,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(9957(a,1),11419(a,1,3))].">
      <j1 rule="para" parents="9957 11419"/>
    </justification>
  </clause>

  <clause id="11462">
    <literal><![CDATA[
      K(x,T(y,y \ x)) * ((y \ x) * z) = (x / T(T(y,y \ x),x)) * z
    ]]></literal>
    <justification jstring="[para(296(a,1),11437(a,1,2,1))].">
      <j1 rule="para" parents="296 11437"/>
    </justification>
  </clause>

  <clause id="11463">
    <literal><![CDATA[
      K(x,y) * ((y \ x) * ((x / y) * z)) = (x / T(y,x)) * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[para(1313(a,1),11437(a,1,2))].">
      <j1 rule="para" parents="1313 11437"/>
    </justification>
  </clause>

  <clause id="11464">
    <literal><![CDATA[
      K(x * K(y,z),z) * (((x * K(y,z)) / z) * u) = ((x * K(y,z)) / T(z,x)) * u
    ]]></literal>
    <justification jstring="[para(7854(a,1),11437(a,2,1,2))].">
      <j1 rule="para" parents="7854 11437"/>
    </justification>
  </clause>

  <clause id="11465">
    <literal><![CDATA[
      L(x,y,((z * u) / z) \ z) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(5161(a,2),11459(a,1,3))].">
      <j1 rule="para" parents="5161 11459"/>
    </justification>
  </clause>

  <clause id="11466">
    <literal><![CDATA[
      L(x,y,z / T(u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(255(a,1),11465(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="255 11465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11467">
    <literal><![CDATA[
      L(x,T(y,z),T(y,z) \ z) = L(x,T(y,z),y \ z)
    ]]></literal>
    <justification jstring="[hyper(10239,a,11466,a)].">
      <j1 rule="hyper" parents="10239 11466"/>
    </justification>
  </clause>

  <clause id="11468">
    <literal><![CDATA[
      L(x,y,y / z) = L(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(11456,a,10142,a),flip(a)].">
      <j1 rule="hyper" parents="11456 10142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11469">
    <literal><![CDATA[
      L(x,y * z,(y * z) / y) = L(x,y * z,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),11468(a,2,3))].">
      <j1 rule="para" parents="9 11468"/>
    </justification>
  </clause>

  <clause id="11470">
    <literal><![CDATA[
      L(x,y * z,z * K(y,z)) = L(x,y * z,z)
    ]]></literal>
    <justification jstring="[para(4942(a,1),11469(a,1,3))].">
      <j1 rule="para" parents="4942 11469"/>
    </justification>
  </clause>

  <clause id="11471">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(11454(a,2),11460(a,1))].">
      <j1 rule="para" parents="11454 11460"/>
    </justification>
  </clause>

  <clause id="11472">
    <literal><![CDATA[
      (x / y) \ (K(x,y) \ z) = (T(x,y) / y) \ z
    ]]></literal>
    <justification jstring="[para(5362(a,1),11436(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5362 11436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11473">
    <literal><![CDATA[
      (x / y) \ (K(y,x) * z) = (T(x,y) / y) \ z
    ]]></literal>
    <justification jstring="[para(5256(a,1),11472(a,1,2))].">
      <j1 rule="para" parents="5256 11472"/>
    </justification>
  </clause>

  <clause id="11474">
    <literal><![CDATA[
      (((x \ y) * T(x,y)) / x) \ (K(x,(x \ y) * T(x,y)) * z) = (((x \ y) * x) / x) \ z
    ]]></literal>
    <justification jstring="[para(4371(a,1),11473(a,2,1,1))].">
      <j1 rule="para" parents="4371 11473"/>
    </justification>
  </clause>

  <clause id="11475">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2384,a,11445,a)].">
      <j1 rule="hyper" parents="2384 11445"/>
    </justification>
  </clause>

  <clause id="11476">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),11475(a,1,2))].">
      <j1 rule="para" parents="9 11475"/>
    </justification>
  </clause>

  <clause id="11477">
    <literal><![CDATA[
      K(x,R(y \ 1,y,z) \ x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10793,a,b,11476,a)].">
      <j1 rule="hyper" parents="63 10793 11476"/>
    </justification>
  </clause>

  <clause id="11478">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(132,a,11477,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 11477 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11479">
    <literal><![CDATA[
      T(x,(y / (z * y)) \ x) = T(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4010,a(flip),b,11478,a)].">
      <j1 rule="hyper" parents="63 4010 11478"/>
    </justification>
  </clause>

  <clause id="11480">
    <literal><![CDATA[
      T(x,(y / z) \ x) = T(x,x * (z / y))
    ]]></literal>
    <justification jstring="[para(12(a,1),11479(a,1,2,1,2))].">
      <j1 rule="para" parents="12 11479"/>
    </justification>
  </clause>

  <clause id="11481">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8232,a,b,11480,a)].">
      <j1 rule="hyper" parents="63 8232 11480"/>
    </justification>
  </clause>

  <clause id="11482">
    <literal><![CDATA[
      x * K(x,x * (y / z)) = T(x,(y * x) / z)
    ]]></literal>
    <justification jstring="[hyper(347,a,4929,a(flip),b,11481,a)].">
      <j1 rule="hyper" parents="347 4929 11481"/>
    </justification>
  </clause>

  <clause id="11483">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(34,a,4929,a(flip),b,11482,a)].">
      <j1 rule="hyper" parents="34 4929 11482"/>
    </justification>
  </clause>

  <clause id="11484">
    <literal><![CDATA[
      K(x,(y / z) \ x) = K(x,x * (z / y))
    ]]></literal>
    <justification jstring="[hyper(8240,a,11483,a)].">
      <j1 rule="hyper" parents="8240 11483"/>
    </justification>
  </clause>

  <clause id="11485">
    <literal><![CDATA[
      K(x,x * (y / ((z * x) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10113,a(flip),b,11483,a),flip(a)].">
      <j1 rule="hyper" parents="63 10113 11483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11486">
    <literal><![CDATA[
      (x * K(y,y * (z / u))) / (y \ x) = T(y,T((z * y) / u,x))
    ]]></literal>
    <justification jstring="[para(11483(a,1),7435(a,1,1,2))].">
      <j1 rule="para" parents="11483 7435"/>
    </justification>
  </clause>

  <clause id="11487">
    <literal><![CDATA[
      (x * K(y,y * (z / u))) \ x = K((u / z) \ y,y)
    ]]></literal>
    <justification jstring="[para(11484(a,1),6123(a,1,1,2))].">
      <j1 rule="para" parents="11484 6123"/>
    </justification>
  </clause>

  <clause id="11488">
    <literal><![CDATA[
      L(x,y,(z / u) * T(u,w)) = L(x,y,z * K(u,u \ w))
    ]]></literal>
    <justification jstring="[para(5925(a,1),11457(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5925 11457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11489">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),x \ y) = y \ ((T(y,x) / x) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10196,a(flip),b,11467,a),flip(a)].">
      <j1 rule="hyper" parents="63 10196 11467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11490">
    <literal><![CDATA[
      K((x / y) \ z,z) = K(z * (y / x),z)
    ]]></literal>
    <justification jstring="[hyper(6141,a,11487,a),flip(a)].">
      <j1 rule="hyper" parents="6141 11487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11491">
    <literal><![CDATA[
      K(x * (y \ z),T(x,y)) = K(x * (z / y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10057,a,b,11490,a)].">
      <j1 rule="hyper" parents="63 10057 11490"/>
    </justification>
  </clause>

  <clause id="11492">
    <literal><![CDATA[
      K(x * (y \ z),T(x,z)) = K(x * (z / y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9006,a,b,11491,a)].">
      <j1 rule="hyper" parents="63 9006 11491"/>
    </justification>
  </clause>

  <clause id="11493">
    <literal><![CDATA[
      K(x * (y / z),x) * K(x,T(z \ y,y)) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(11492(a,1),9754(a,1,1))].">
      <j1 rule="para" parents="11492 9754"/>
    </justification>
  </clause>

  <clause id="11494">
    <literal><![CDATA[
      L(x,y,T((z \ (u * K(z,u))) * z,w)) = L(x,y,T(u,w))
    ]]></literal>
    <justification jstring="[para(4830(a,2),11455(a,1,3))].">
      <j1 rule="para" parents="4830 11455"/>
    </justification>
  </clause>

  <clause id="11495">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ w)) = L(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(5925(a,1),11488(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5925 11488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11496">
    <literal><![CDATA[
      L(x,y,z / ((u \ w) * u)) = L(x,y,(z / w) * K(u,w))
    ]]></literal>
    <justification jstring="[para(9871(a,1),11495(a,1,3))].">
      <j1 rule="para" parents="9871 11495"/>
    </justification>
  </clause>

  <clause id="11497">
    <literal><![CDATA[
      L(x,y,T((z \ u) * z,w)) = L(x,y,T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(4972(a,1),11494(a,1,3,1,1,2))].">
      <j1 rule="para" parents="4972 11494"/>
    </justification>
  </clause>

  <clause id="11498">
    <literal><![CDATA[
      L(x,y,T(T(z,u),u \ z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11450,a(flip),b,11497,a),flip(a)].">
      <j1 rule="hyper" parents="63 11450 11497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11499">
    <literal><![CDATA[
      L(x,y,z / ((u \ w) * u)) = L(x,y,z / T(w,u))
    ]]></literal>
    <justification jstring="[para(6102(a,1),11496(a,2,3))].">
      <j1 rule="para" parents="6102 11496"/>
    </justification>
  </clause>

  <clause id="11500">
    <literal><![CDATA[
      L(x,y,T(z,z \ u) / u) = L(x,y,z / T(u,z))
    ]]></literal>
    <justification jstring="[para(4348(a,2),11499(a,1,3))].">
      <j1 rule="para" parents="4348 11499"/>
    </justification>
  </clause>

  <clause id="11501">
    <literal><![CDATA[
      L(x,y,T(z,z \ u) / u) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,11466,a(flip),b,11500,a),flip(a)].">
      <j1 rule="hyper" parents="347 11466 11500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11502">
    <literal><![CDATA[
      L(x,y,z \ (z / (z / u))) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(385(a,1),11501(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="385 11501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11503">
    <literal><![CDATA[
      L(x,y,(z * (u / z)) \ z) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(5139(a,2),11502(a,1,3))].">
      <j1 rule="para" parents="5139 11502"/>
    </justification>
  </clause>

  <clause id="11504">
    <literal><![CDATA[
      L(x,y,z / (u * z)) = L(x,y,(z * u) \ z)
    ]]></literal>
    <justification jstring="[para(11(a,1),11503(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="11 11503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11505">
    <literal><![CDATA[
      L(x,y,((z * (1 / u)) * (z / (z * (1 / u)))) \ (z * (1 / u))) = L(x,y,K(z,u \ 1) / u)
    ]]></literal>
    <justification jstring="[para(5019(a,2),11503(a,2,3))].">
      <j1 rule="para" parents="5019 11503"/>
    </justification>
  </clause>

  <clause id="11506">
    <literal><![CDATA[
      K(x * (y / z),x) * K(x,y / z) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(7663(a,1),11493(a,1,2))].">
      <j1 rule="para" parents="7663 11493"/>
    </justification>
  </clause>

  <clause id="11507">
    <literal><![CDATA[
      a(x,y / z,x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(8366,a,11506,a)].">
      <j1 rule="hyper" parents="8366 11506"/>
    </justification>
  </clause>

  <clause id="11508">
    <literal><![CDATA[
      a(x,y \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z / y,x) = u
    ]]></literal>
    <justification jstring="[para(11506(a,1),8366(a,1))].">
      <j1 rule="para" parents="11506 8366"/>
    </justification>
  </clause>

  <clause id="11510">
    <literal><![CDATA[
      T(x,T((y * x) / z,u)) = T(x,T(x * (y / z),u))
    ]]></literal>
    <justification jstring="[hyper(63,a,7435,a(flip),b,11486,a),flip(a)].">
      <j1 rule="hyper" parents="63 7435 11486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11511">
    <literal><![CDATA[
      T(x,T(y / (x \ z),u)) = T(x,T(x * (y / z),u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8184,a(flip),b,11510,a)].">
      <j1 rule="hyper" parents="63 8184 11510"/>
    </justification>
  </clause>

  <clause id="11512">
    <literal><![CDATA[
      T(x,T((y / z) \ x,u)) = T(x,T(x * (z / y),u))
    ]]></literal>
    <justification jstring="[hyper(9232,a,11511,a)].">
      <j1 rule="hyper" parents="9232 11511"/>
    </justification>
  </clause>

  <clause id="11513">
    <literal><![CDATA[
      L(x,y,K(z * u,R(z,u,u \ 1))) = L(x,y,K(u * z,u \ 1))
    ]]></literal>
    <justification jstring="[para(585(a,1),11440(a,1,3,2))].">
      <j1 rule="para" parents="585 11440"/>
    </justification>
  </clause>

  <clause id="11514">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(u * z,u))
    ]]></literal>
    <justification jstring="[para(6720(a,1),11513(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6720 11513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11515">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,11422,a(flip),b,11514,a),flip(a)].">
      <j1 rule="hyper" parents="347 11422 11514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11517">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11453,a(flip),b,11515,a)].">
      <j1 rule="hyper" parents="63 11453 11515"/>
    </justification>
  </clause>

  <clause id="11518">
    <literal><![CDATA[
      L(x,y,K(z \ 1,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(3885(a,1),11517(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3885 11517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11519">
    <literal><![CDATA[
      (x / T(T(y,y \ x),x)) * z = K(x,y) * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[para(6466(a,1),11462(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6466 11462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11520">
    <literal><![CDATA[
      K(x,y) * ((y \ x) * z) = (T(y,x) \ x) * z
    ]]></literal>
    <justification jstring="[para(7571(a,1),11519(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7571 11519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11521">
    <literal><![CDATA[
      (x \ y) \ (K(y,x) \ z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(675,a,11520,a),flip(a)].">
      <j1 rule="hyper" parents="675 11520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11522">
    <literal><![CDATA[
      (x \ y) \ (K(x,y) * z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[para(5256(a,1),11521(a,1,2))].">
      <j1 rule="para" parents="5256 11521"/>
    </justification>
  </clause>

  <clause id="11523">
    <literal><![CDATA[
      (x / T(y,x)) * ((y \ x) * z) = (T(y,x) \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11520,a(flip),b,11463,a),flip(a)].">
      <j1 rule="hyper" parents="63 11520 11463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11526">
    <literal><![CDATA[
      K(x,y) * (((x * K(z,y)) / y) * u) = ((x * K(z,y)) / T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(7897(a,1),11464(a,1,1))].">
      <j1 rule="para" parents="7897 11464"/>
    </justification>
  </clause>

  <clause id="11527">
    <literal><![CDATA[
      ((x * K(y,z)) / T(z,x)) * u = K(x,z) * ((x / T(z,y)) * u)
    ]]></literal>
    <justification jstring="[para(6135(a,1),11526(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6135 11526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11529">
    <literal><![CDATA[
      ((x / T(y,x)) * K(z,y)) * u = K(x,y) * ((x / T(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(8638(a,1),11527(a,1,1))].">
      <j1 rule="para" parents="8638 11527"/>
    </justification>
  </clause>

  <clause id="11530">
    <literal><![CDATA[
      K(x,y) * ((x / T(y,z)) * u) = (T(x,y) / T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(6101(a,1),11529(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6101 11529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11531">
    <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(11372(a,1),11389(a,2,1))].">
      <j1 rule="para" parents="11372 11389"/>
    </justification>
  </clause>

  <clause id="11532">
    <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(347,a,11378,a(flip),b,11531,a),flip(a)].">
      <j1 rule="hyper" parents="347 11378 11531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11533">
    <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),11532(a,2,2))].">
      <j1 rule="para" parents="20 11532"/>
    </justification>
  </clause>

  <clause id="11534">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) = a(x,y,x) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(11377(a,1),11533(a,1,2))].">
      <j1 rule="para" parents="11377 11533"/>
    </justification>
  </clause>

  <clause id="11535">
    <literal><![CDATA[
      a(x,y,x) * R(a(x,y,x) \ z,u,w) = R(z,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),11534(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 11534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11536">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) * v5 = a(x,y,x) * (R(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(11534(a,2),11372(a,1,1))].">
      <j1 rule="para" parents="11534 11372"/>
    </justification>
  </clause>

  <clause id="11537">
    <literal><![CDATA[
      R(a(x,y,x) \ z,u,w) = a(x,y,x) \ R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(138,a,11535,a),flip(a)].">
      <j1 rule="hyper" parents="138 11535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11538">
    <literal><![CDATA[
      R(x * a(y,z,y),u,w) * v5 = a(y,z,y) * (R(x,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(9957(a,1),11536(a,1,1,1))].">
      <j1 rule="para" parents="9957 11536"/>
    </justification>
  </clause>

  <clause id="11539">
    <literal><![CDATA[
      a(x,y,x) * (R(y,z,u) * x) = T(x * R(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9033,a(flip),b,11538,a),flip(a)].">
      <j1 rule="hyper" parents="63 9033 11538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11540">
    <literal><![CDATA[
      a(x,R(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,10327,a,b,11539,a)].">
      <j1 rule="hyper" parents="35 10327 11539"/>
    </justification>
  </clause>

  <clause id="11541">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,R(y,w,v5),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,11367,a,b,11540,a)].">
      <j1 rule="hyper" parents="347 11367 11540"/>
    </justification>
  </clause>

  <clause id="11542">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = a(x,z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(11540(a,1),8372(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11540 8372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11543">
    <literal><![CDATA[
      a(x,R(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(11541(a,1),406(a,1)),flip(b)].">
      <j1 rule="para" parents="11541 406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11544">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,8372,a(flip),b,11542,a),flip(a)].">
      <j1 rule="hyper" parents="347 8372 11542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11545">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = a(u,(x * (y * z)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(5071(a,1),11414(a,2,2))].">
      <j1 rule="para" parents="5071 11414"/>
    </justification>
  </clause>

  <clause id="11546">
    <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(8365,a,11545,a)].">
      <j1 rule="hyper" parents="8365 11545"/>
    </justification>
  </clause>

  <clause id="11547">
    <literal><![CDATA[
      ((x \ y) * K(x,y)) \ (K(x,(x \ y) * T(x,y)) * z) = (((x \ y) * x) / x) \ z
    ]]></literal>
    <justification jstring="[para(5919(a,1),11474(a,1,1))].">
      <j1 rule="para" parents="5919 11474"/>
    </justification>
  </clause>

  <clause id="11548">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ (K(x,(x \ y) * T(x,y)) * z) = (((x \ y) * x) / x) \ z
    ]]></literal>
    <justification jstring="[para(6832(a,2),11547(a,1,1))].">
      <j1 rule="para" parents="6832 11547"/>
    </justification>
  </clause>

  <clause id="11549">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ (K(x,y) * z) = (((x \ y) * x) / x) \ z
    ]]></literal>
    <justification jstring="[para(10414(a,1),11548(a,1,2,1))].">
      <j1 rule="para" parents="10414 11548"/>
    </justification>
  </clause>

  <clause id="11552">
    <literal><![CDATA[
      L(x,y,((z \ u) * z) \ (u * (1 / z))) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[para(5879(a,1),11505(a,1,3,1))].">
      <j1 rule="para" parents="5879 11505"/>
    </justification>
  </clause>

  <clause id="11553">
    <literal><![CDATA[
      L(x,y,K(z,z \ u) * (1 / z)) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[para(10280(a,1),11552(a,1,3))].">
      <j1 rule="para" parents="10280 11552"/>
    </justification>
  </clause>

  <clause id="11554">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1) / u) = L(x,y,K(u,u \ z) / u)
    ]]></literal>
    <justification jstring="[para(4249(a,1),11553(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4249 11553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11555">
    <literal><![CDATA[
      (K(x,T(x,x * y) * y) \ z) \ T(T(T(x,x * y) * y,x),x) = (K(x,y) \ z) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5735,a(flip),b,11434,a),flip(a)].">
      <j1 rule="hyper" parents="63 5735 11434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11556">
    <literal><![CDATA[
      (K(x,x * y) \ z) \ T(T(T(x,x * y) * y,x),x) = (K(x,y) \ z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(7873(a,1),11555(a,1,1,1))].">
      <j1 rule="para" parents="7873 11555"/>
    </justification>
  </clause>

  <clause id="11557">
    <literal><![CDATA[
      (K(x,x * y) \ z) \ T(x * y,x) = (K(x,y) \ z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(4189(a,1),11556(a,1,2,1))].">
      <j1 rule="para" parents="4189 11556"/>
    </justification>
  </clause>

  <clause id="11559">
    <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(11372(a,1),11390(a,1,1))].">
      <j1 rule="para" parents="11372 11390"/>
    </justification>
  </clause>

  <clause id="11560">
    <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(11372(a,1),11559(a,1,2))].">
      <j1 rule="para" parents="11372 11559"/>
    </justification>
  </clause>

  <clause id="11561">
    <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(944,a,11560,a)].">
      <j1 rule="hyper" parents="944 11560"/>
    </justification>
  </clause>

  <clause id="11562">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),a(u,w,u)) = a(a(u,w,u) * x,y,z)
    ]]></literal>
    <justification jstring="[para(11377(a,1),11561(a,2,2))].">
      <j1 rule="para" parents="11377 11561"/>
    </justification>
  </clause>

  <clause id="11563">
    <literal><![CDATA[
      a(a(x,y,x) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(11388,a,11562,a),flip(a)].">
      <j1 rule="hyper" parents="11388 11562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11564">
    <literal><![CDATA[
      a(a(x,y,x) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(11562(a,1),11388(a,1))].">
      <j1 rule="para" parents="11562 11388"/>
    </justification>
  </clause>

  <clause id="11566">
    <literal><![CDATA[
      a(K(x * y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(8352(a,1),11563(a,1,1))].">
      <j1 rule="para" parents="8352 11563"/>
    </justification>
  </clause>

  <clause id="11567">
    <literal><![CDATA[
      a(K(x * y,y),z,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8367(a,1),11563(a,1,1))].">
      <j1 rule="para" parents="8367 11563"/>
    </justification>
  </clause>

  <clause id="11568">
    <literal><![CDATA[
      a(K(x,x \ y),z,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8370(a,1),11563(a,1,1))].">
      <j1 rule="para" parents="8370 11563"/>
    </justification>
  </clause>

  <clause id="11569">
    <literal><![CDATA[
      a(L(x,y,x),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(8497(a,1),11563(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8497 11563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11570">
    <literal><![CDATA[
      a(K(x * y,x) * z,u,w) = a(K(y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(8667(a,1),11563(a,1,1))].">
      <j1 rule="para" parents="8667 11563"/>
    </justification>
  </clause>

  <clause id="11571">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(9957(a,1),11563(a,1,1))].">
      <j1 rule="para" parents="9957 11563"/>
    </justification>
  </clause>

  <clause id="11572">
    <literal><![CDATA[
      a(R(x,y,x) \ z,u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(10988(a,1),11563(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10988 11563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11573">
    <literal><![CDATA[
      a(T(x * (y / x),x),z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(11003(a,1),11563(a,1,1))].">
      <j1 rule="para" parents="11003 11563"/>
    </justification>
  </clause>

  <clause id="11574">
    <literal><![CDATA[
      a(T(x / y,x),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(4398(a,1),11569(a,1,1))].">
      <j1 rule="para" parents="4398 11569"/>
    </justification>
  </clause>

  <clause id="11575">
    <literal><![CDATA[
      a(x / R(y,z,y),u,w) = a(x / y,u,w)
    ]]></literal>
    <justification jstring="[para(10979(a,1),11571(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10979 11571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11576">
    <literal><![CDATA[
      a(K(x \ y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11566(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 11566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11577">
    <literal><![CDATA[
      a(K(x * T(y,z),y),u,w) = a(K(x * y,(x * y) \ y),u,w)
    ]]></literal>
    <justification jstring="[para(7904(a,2),11568(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7904 11568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11578">
    <literal><![CDATA[
      a(x * (y / x),x,z) = a(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(4809,a,11573,a)].">
      <j1 rule="hyper" parents="4809 11573"/>
    </justification>
  </clause>

  <clause id="11579">
    <literal><![CDATA[
      a(K(x * y,y \ 1),z,u) = a(K(x,y \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(5768(a,1),11576(a,1,1))].">
      <j1 rule="para" parents="5768 11576"/>
    </justification>
  </clause>

  <clause id="11580">
    <literal><![CDATA[
      a(L(x \ 1,y,x),z,u) = a(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(8391(a,2),11572(a,1,1))].">
      <j1 rule="para" parents="8391 11572"/>
    </justification>
  </clause>

  <clause id="11581">
    <literal><![CDATA[
      a(K(x,y) * (x \ y),z,u) = a(y / x,z,u)
    ]]></literal>
    <justification jstring="[para(7249(a,1),11575(a,1,1))].">
      <j1 rule="para" parents="7249 11575"/>
    </justification>
  </clause>

  <clause id="11582">
    <literal><![CDATA[
      a(K(x,x \ 1) * y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(8351(a,2),11564(a,1,1,1))].">
      <j1 rule="para" parents="8351 11564"/>
    </justification>
  </clause>

  <clause id="11583">
    <literal><![CDATA[
      a(L(x,y,x) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x \ z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(9971(a,1),11564(a,1,1))].">
      <j1 rule="para" parents="9971 11564"/>
    </justification>
  </clause>

  <clause id="11584">
    <literal><![CDATA[
      a(T(x * y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y * x,z,u) = w
    ]]></literal>
    <justification jstring="[para(10327(a,1),11564(a,1,1))].">
      <j1 rule="para" parents="10327 11564"/>
    </justification>
  </clause>

  <clause id="11585">
    <literal><![CDATA[
      a(T(x * (y / x),x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(11003(a,1),11564(a,1,1))].">
      <j1 rule="para" parents="11003 11564"/>
    </justification>
  </clause>

  <clause id="11586">
    <literal><![CDATA[
      a((x \ 1) \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1905(a,1),11582(a,1,1))].">
      <j1 rule="para" parents="1905 11582"/>
    </justification>
  </clause>

  <clause id="11587">
    <literal><![CDATA[
      a(1 / x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x \ 1,y,z) = u
    ]]></literal>
    <justification jstring="[para(1907(a,1),11582(a,1,1))].">
      <j1 rule="para" parents="1907 11582"/>
    </justification>
  </clause>

  <clause id="11588">
    <literal><![CDATA[
      a(R(x / y,y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a((y * (x \ 1)) \ 1,z,u) = w
    ]]></literal>
    <justification jstring="[para(2194(a,2),11587(a,1,1))].">
      <j1 rule="para" parents="2194 11587"/>
    </justification>
  </clause>

  <clause id="11589">
    <literal><![CDATA[
      a(K(x \ y,x) * z,u,w) = a(K(y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),11570(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 11570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11590">
    <literal><![CDATA[
      a(K(x,y) * ((y \ x) \ z),u,w) = a((x / y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(5441(a,1),11589(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5441 11589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11591">
    <literal><![CDATA[
      a(K(x * T(y,z),y),u,w) = a(K(y * x,x \ 1),u,w)
    ]]></literal>
    <justification jstring="[para(5898(a,1),11577(a,2,1))].">
      <j1 rule="para" parents="5898 11577"/>
    </justification>
  </clause>

  <clause id="11592">
    <literal><![CDATA[
      a(K(x * T(y,z),y),u,w) = a(K(y,x \ 1),u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,11579,a(flip),b,11591,a),flip(a)].">
      <j1 rule="hyper" parents="347 11579 11591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11593">
    <literal><![CDATA[
      a(K(x * y,y),z,u) = a(K(y,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(110(a,1),11592(a,1,1,1,2))].">
      <j1 rule="para" parents="110 11592"/>
    </justification>
  </clause>

  <clause id="11594">
    <literal><![CDATA[
      a(K(x,y \ 1),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11567,a(flip),b,11593,a),flip(a)].">
      <j1 rule="hyper" parents="63 11567 11593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11595">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(3885(a,1),11594(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3885 11594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11596">
    <literal><![CDATA[
      a(R(K(x,y),(y * x) * z,u),w,v5) = a(K(R(y,x * z,u) \ 1,x),w,v5)
    ]]></literal>
    <justification jstring="[para(10265(a,2),11595(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10265 11595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11597">
    <literal><![CDATA[
      a(R(K(x,y),(y * x) * z,u),w,v5) = a(K(y \ 1,R(x,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(6719(a,1),11596(a,2,1))].">
      <j1 rule="para" parents="6719 11596"/>
    </justification>
  </clause>

  <clause id="11598">
    <literal><![CDATA[
      a(R(K(x,y),(y * x) * z,u),w,v5) = a(K(R(x,z,u),y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,11595,a(flip),b,11597,a),flip(a)].">
      <j1 rule="hyper" parents="347 11595 11597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11599">
    <literal><![CDATA[
      a(K(x,R(y,x * z,u)),w,v5) = a(K(R(x,z,u),y),w,v5)
    ]]></literal>
    <justification jstring="[para(10265(a,1),11598(a,1,1))].">
      <j1 rule="para" parents="10265 11598"/>
    </justification>
  </clause>

  <clause id="11604">
    <literal><![CDATA[
      (R(x,y,z) / (x * x)) \ K(T(x \ (x \ R(x,y,z)),x),x * x) = (((x * x) * (x \ (x \ R(x,y,z)))) / (x * x)) \ 1
    ]]></literal>
    <justification jstring="[para(1777(a,1),5696(a,2,1,1,2))].">
      <j1 rule="para" parents="1777 5696"/>
    </justification>
  </clause>

  <clause id="11605">
    <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(8244(a,1),8116(a,1,1,1))].">
      <j1 rule="para" parents="8244 8116"/>
    </justification>
  </clause>

  <clause id="11606">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,x * (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(4280(a,1),11605(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4280 11605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11607">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,6805,a(flip),b,11606,a),flip(a)].">
      <j1 rule="hyper" parents="347 6805 11606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11609">
    <literal><![CDATA[
      (K(x,y) * z) * R((K(x,y) * z) \ (T(T(x,y),T(u,y)) * z),w,v5) = (R(T(x,u),w,v5) * K(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(347,a,469,a(flip),b,9748,a),flip(a)].">
      <j1 rule="hyper" parents="347 469 9748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11610">
    <literal><![CDATA[
      (K(x,y) * R(K(x,y) \ T(T(x,y),T(z,y)),u,w)) * v5 = (R(T(x,z),u,w) * K(x,y)) * v5
    ]]></literal>
    <justification jstring="[hyper(63,a,1683,a(flip),b,11609,a)].">
      <j1 rule="hyper" parents="63 1683 11609"/>
    </justification>
  </clause>

  <clause id="11611">
    <literal><![CDATA[
      (K(x,y) * R(T(T(x,y),T(z,y)) * K(y,x),u,w)) * v5 = (R(T(x,z),u,w) * K(x,y)) * v5
    ]]></literal>
    <justification jstring="[para(5266(a,1),11610(a,1,1,2,1))].">
      <j1 rule="para" parents="5266 11610"/>
    </justification>
  </clause>

  <clause id="11612">
    <literal><![CDATA[
      (K(x,y) * R(x * K(T(x,y),T(z,y)),u,w)) * v5 = (R(T(x,z),u,w) * K(x,y)) * v5
    ]]></literal>
    <justification jstring="[para(5576(a,1),11611(a,1,1,2,1))].">
      <j1 rule="para" parents="5576 11611"/>
    </justification>
  </clause>

  <clause id="11613">
    <literal><![CDATA[
      (R(T(x,y),z,u) * K(x,w)) * v5 = (K(x,w) * R(T(x,y),z,u)) * v5
    ]]></literal>
    <justification jstring="[para(7396(a,1),11612(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7396 11612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11614">
    <literal><![CDATA[
      (K(x,y) * R(T(x,z),u,w)) * v5 = R(T(x,z),u,w) * (K(x,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,5116,a(flip),b,11613,a),flip(a)].">
      <j1 rule="hyper" parents="63 5116 11613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11616">
    <literal><![CDATA[
      (K(x,y) \ (R(T(x,z),u,w) * (K(x,y) * v5))) / (K(x,y) \ (R(T(x,z),u,w) * v5)) = R(K(x,y),R(T(x,z),u,w),v5)
    ]]></literal>
    <justification jstring="[para(11614(a,1),1770(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11614 1770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11617">
    <literal><![CDATA[
      (K(x,y) * (R(T(y,z),u,w) * (K(y,x) * v5))) / (K(y,x) \ (R(T(y,z),u,w) * v5)) = R(K(y,x),R(T(y,z),u,w),v5)
    ]]></literal>
    <justification jstring="[para(5256(a,1),11616(a,1,1))].">
      <j1 rule="para" parents="5256 11616"/>
    </justification>
  </clause>

  <clause id="11618">
    <literal><![CDATA[
      (R(T(x,y),z,u) * w) / (K(x,v5) \ (R(T(x,y),z,u) * w)) = R(K(x,v5),R(T(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(9403(a,1),11617(a,1,1))].">
      <j1 rule="para" parents="9403 11617"/>
    </justification>
  </clause>

  <clause id="11619">
    <literal><![CDATA[
      R(K(x,y),R(T(x,z),u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,11618,a),flip(a)].">
      <j1 rule="hyper" parents="320 11618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11622">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) * (w \ 1)) = K(x,R(T(x,y),z,u) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,6707,a(flip),b,11619,a)].">
      <j1 rule="hyper" parents="63 6707 11619"/>
    </justification>
  </clause>

  <clause id="11623">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) * (w \ 1)) = K(x,w \ R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,7662,a(flip),b,11622,a),flip(a)].">
      <j1 rule="hyper" parents="347 7662 11622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11624">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,R(x,u,w) * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,7944,a(flip),b,11623,a),flip(a)].">
      <j1 rule="hyper" parents="63 7944 11623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11626">
    <literal><![CDATA[
      K(x,R(x,y,z) * (u \ 1)) = K(x,u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7892,a(flip),b,11624,a),flip(a)].">
      <j1 rule="hyper" parents="63 7892 11624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11627">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,y \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,11624,a,b,11626,a)].">
      <j1 rule="hyper" parents="63 11624 11626"/>
    </justification>
  </clause>

  <clause id="11628">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(7759,a,11627,a)].">
      <j1 rule="hyper" parents="7759 11627"/>
    </justification>
  </clause>

  <clause id="11629">
    <literal><![CDATA[
      K(x,y \ R(x,z,u)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(10531,a,11628,a),flip(a)].">
      <j1 rule="hyper" parents="10531 11628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11631">
    <literal><![CDATA[
      K(x,y \ (z * R(x,u,w))) = K(x,(z \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10069,a(flip),b,11629,a)].">
      <j1 rule="hyper" parents="63 10069 11629"/>
    </justification>
  </clause>

  <clause id="11633">
    <literal><![CDATA[
      K(x,y \ (z * R(x,u,w))) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,9806,a(flip),b,11631,a),flip(a)].">
      <j1 rule="hyper" parents="347 9806 11631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11634">
    <literal><![CDATA[
      K(x,y \ (R(x,z,u) * w)) = K(x,x * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9375,a,b,11633,a)].">
      <j1 rule="hyper" parents="63 9375 11633"/>
    </justification>
  </clause>

  <clause id="11635">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,x * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9373,a,b,11633,a)].">
      <j1 rule="hyper" parents="63 9373 11633"/>
    </justification>
  </clause>

  <clause id="11637">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * u))) = K(x,x * (y \ (x \ (z * u))))
    ]]></literal>
    <justification jstring="[para(1762(a,1),11634(a,1,2,2))].">
      <j1 rule="para" parents="1762 11634"/>
    </justification>
  </clause>

  <clause id="11639">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * u))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,9809,a(flip),b,11637,a),flip(a)].">
      <j1 rule="hyper" parents="347 9809 11637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11640">
    <literal><![CDATA[
      K(x,y \ (x \ (z * u))) = K(x,y \ ((x \ z) * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),11639(a,1,2,2,2,1))].">
      <j1 rule="para" parents="10 11639"/>
    </justification>
  </clause>

  <clause id="11641">
    <literal><![CDATA[
      K(x,y \ (x \ (z * y))) = K(x,T(x \ z,y))
    ]]></literal>
    <justification jstring="[para(22(a,2),11640(a,2,2))].">
      <j1 rule="para" parents="22 11640"/>
    </justification>
  </clause>

  <clause id="11642">
    <literal><![CDATA[
      K(x,T(x \ y,y \ (x * z))) = K(x,(y \ (x * z)) \ z)
    ]]></literal>
    <justification jstring="[para(74(a,1),11641(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="74 11641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11643">
    <literal><![CDATA[
      K(x,T(x \ y,y \ z)) = K(x,(y \ (x * z)) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,8968,a(flip),b,11642,a)].">
      <j1 rule="hyper" parents="63 8968 11642"/>
    </justification>
  </clause>

  <clause id="11644">
    <literal><![CDATA[
      K(x,(y \ (x * z)) \ z) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(8969,a,11643,a),flip(a)].">
      <j1 rule="hyper" parents="8969 11643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11645">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(y,x) * L(L(K(x,z),u,w) \ 1,v5,v6))) = L(K(x,z) * L(K(z,x),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(5173(a,1),10841(a,2,1,2,1))].">
      <j1 rule="para" parents="5173 10841"/>
    </justification>
  </clause>

  <clause id="11646">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(y,x) * L(L(K(x,z),u,w) \ 1,v5,v6))) = L(a(v6,v5,K(x,z)),u,w)
    ]]></literal>
    <justification jstring="[para(9237(a,1),11645(a,2,1))].">
      <j1 rule="para" parents="9237 11645"/>
    </justification>
  </clause>

  <clause id="11647">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(y,x) * L(L(K(z,x),u,w),v5,v6))) = L(a(v6,v5,K(x,z)),u,w)
    ]]></literal>
    <justification jstring="[para(7015(a,1),11646(a,1,2,2,2,1))].">
      <j1 rule="para" parents="7015 11646"/>
    </justification>
  </clause>

  <clause id="11648">
    <literal><![CDATA[
      L(K(x,y),z,u) * L(L(K(y,x),z,u),w,v5) = L(a(v5,w,K(x,y)),z,u)
    ]]></literal>
    <justification jstring="[hyper(2860,a,11647,a)].">
      <j1 rule="hyper" parents="2860 11647"/>
    </justification>
  </clause>

  <clause id="11649">
    <literal><![CDATA[
      a(x,y,L(K(z,u),w,v5)) = L(a(x,y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,10033,a(flip),b,11648,a)].">
      <j1 rule="hyper" parents="63 10033 11648"/>
    </justification>
  </clause>

  <clause id="11650">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = L(a(x,y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(11049(a,1),11649(a,1,3))].">
      <j1 rule="para" parents="11049 11649"/>
    </justification>
  </clause>

  <clause id="11651">
    <literal><![CDATA[
      (R(x,y,z) / (x * x)) \ K(T(x \ (x \ R(x,y,z)),x),x * x) = (((x \ 1) \ (x \ R(x,y,z))) / (x * x)) \ 1
    ]]></literal>
    <justification jstring="[para(495(a,1),11604(a,2,1,1))].">
      <j1 rule="para" parents="495 11604"/>
    </justification>
  </clause>

  <clause id="11652">
    <literal><![CDATA[
      (R(x,y,z) / (x * x)) \ K(T(x \ (x \ R(x,y,z)),x),x * x) = (R(T(x,x \ 1),y,z) / (x * x)) \ 1
    ]]></literal>
    <justification jstring="[para(1468(a,1),11651(a,2,1,1))].">
      <j1 rule="para" parents="1468 11651"/>
    </justification>
  </clause>

  <clause id="11653">
    <literal><![CDATA[
      (x \ y) * (((x \ y) * (x \ y)) \ (x \ (y * (x \ y)))) = (x \ y) \ (x \ (y * (x \ y)))
    ]]></literal>
    <justification jstring="[para(10918(a,1),1633(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10918 1633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11654">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,x \ y) = (x \ y) \ (x \ (y * (x \ y)))
    ]]></literal>
    <justification jstring="[para(1007(a,1),11653(a,1,2))].">
      <j1 rule="para" parents="1007 11653"/>
    </justification>
  </clause>

  <clause id="11656">
    <literal><![CDATA[
      ((x / y) \ K(y,y \ x)) * R(((x / y) \ K(y,y \ x)) \ z,u,w) = (y \ x) \ R((y \ x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(5430(a,1),5611(a,2,2,1))].">
      <j1 rule="para" parents="5430 5611"/>
    </justification>
  </clause>

  <clause id="11657">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) * (R(K(y,z),w,v5) * K(z,u)) = (x * R(x \ (x * K(y,z)),w,v5)) * K(z,u)
    ]]></literal>
    <justification jstring="[para(8318(a,1),8323(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="8318 8323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11658">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) * (R(K(y,z),w,v5) * K(z,u)) = (x * R(K(y,z),w,v5)) * K(z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),11657(a,2,1,2,1))].">
      <j1 rule="para" parents="9 11657"/>
    </justification>
  </clause>

  <clause id="11660">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) * K(z,v5) = x * (R(K(y,z),u,w) * K(z,v5))
    ]]></literal>
    <justification jstring="[para(8318(a,1),11658(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8318 11658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11661">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) * K(z,v5) = x * (K(z,v5) * R(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(2563(a,1),11660(a,2,2))].">
      <j1 rule="para" parents="2563 11660"/>
    </justification>
  </clause>

  <clause id="11662">
    <literal><![CDATA[
      x / (K(y,z) * R(K(z,u),w,v5)) = x * (K(z,y) * R(K(u,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,9208,a,b,11661,a)].">
      <j1 rule="hyper" parents="63 9208 11661"/>
    </justification>
  </clause>

  <clause id="11663">
    <literal><![CDATA[
      (x * (K(y,z) * R(K(z,u),w,v5))) * (K(z,y) * R(K(u,z),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(283,a,11662,a),flip(a)].">
      <j1 rule="hyper" parents="283 11662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11664">
    <literal><![CDATA[
      K(x * ((T(y,y \ 1) * z) \ (((y \ 1) \ 1) \ (T(y,y \ 1) * z))),y \ 1) = K(x * R(y \ 1,y,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(2298(a,1),8689(a,2,1,2))].">
      <j1 rule="para" parents="2298 8689"/>
    </justification>
  </clause>

  <clause id="11665">
    <literal><![CDATA[
      K(x * ((T(y,y \ 1) * z) \ z),y \ 1) = K(x * R(y \ 1,y,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(466(a,1),11664(a,1,1,2,2))].">
      <j1 rule="para" parents="466 11664"/>
    </justification>
  </clause>

  <clause id="11666">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),y \ 1) = K(x * R(y \ 1,y,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(2993(a,1),11665(a,1,1,2))].">
      <j1 rule="para" parents="2993 11665"/>
    </justification>
  </clause>

  <clause id="11667">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,3908,a(flip),b,11666,a),flip(a)].">
      <j1 rule="hyper" parents="63 3908 11666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11668">
    <literal><![CDATA[
      K(T(x,R(x,y,z) * (x \ u)),(R(x,y,z) \ w) \ u) = K((x \ u) \ u,w \ (R(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(9(a,1),8615(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 8615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11669">
    <literal><![CDATA[
      K(T(x,R(x,y,z) * (x \ u)),(R(x,y,z) \ w) \ u) = K(x,T(w \ (R(x,y,z) * u),u))
    ]]></literal>
    <justification jstring="[hyper(347,a,7097,a(flip),b,11668,a),flip(a)].">
      <j1 rule="hyper" parents="347 7097 11668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11671">
    <literal><![CDATA[
      K(T(x,R(x,y,z) * (x \ u)),(R(x,y,z) \ w) \ u) = K(x,(R(x,y,z) * u) / w)
    ]]></literal>
    <justification jstring="[hyper(347,a,9081,a(flip),b,11669,a),flip(a)].">
      <j1 rule="hyper" parents="347 9081 11669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11672">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,R(x,y,z) * (x \ w))) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(7488,a,11671,a)].">
      <j1 rule="hyper" parents="7488 11671"/>
    </justification>
  </clause>

  <clause id="11673">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,R(x,y,z) * w)) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9101,a(flip),b,11672,a)].">
      <j1 rule="hyper" parents="63 9101 11672"/>
    </justification>
  </clause>

  <clause id="11674">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,w)) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(9086,a,11673,a)].">
      <j1 rule="hyper" parents="9086 11673"/>
    </justification>
  </clause>

  <clause id="11676">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (R(x,y,z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(11674(a,1),7771(a,1))].">
      <j1 rule="para" parents="11674 7771"/>
    </justification>
  </clause>

  <clause id="11677">
    <literal><![CDATA[
      K(x,R(x,y,z) / (u / w)) = K(x,w / (R(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(11676,a,6968,a),flip(a)].">
      <j1 rule="hyper" parents="11676 6968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11678">
    <literal><![CDATA[
      K(x,y / (R(x,z,u) \ w)) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(9478,a,11677,a),flip(a)].">
      <j1 rule="hyper" parents="9478 11677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11679">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8494,a,b,11678,a)].">
      <j1 rule="hyper" parents="63 8494 11678"/>
    </justification>
  </clause>

  <clause id="11680">
    <literal><![CDATA[
      K(R(x,K(y * z,x) * y,z),u \ x) = K(x,(((u * y) * z) / (y * z)) \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10647,a,b,11679,a)].">
      <j1 rule="hyper" parents="63 10647 11679"/>
    </justification>
  </clause>

  <clause id="11681">
    <literal><![CDATA[
      K(R(x,K(y * z,x) * y,z),u \ x) = K(x,R(u,y,z) \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(20(a,2),11680(a,2,2,1))].">
      <j1 rule="para" parents="20 11680"/>
    </justification>
  </clause>

  <clause id="11682">
    <literal><![CDATA[
      K(x,R(y,z,u) \ R(x,z,u)) = K(R(x,z,u),y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8679,a(flip),b,11681,a),flip(a)].">
      <j1 rule="hyper" parents="63 8679 11681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11684">
    <literal><![CDATA[
      K(R(x,y,z),u \ x) = K(x,R(u,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11629,a(flip),b,11682,a),flip(a)].">
      <j1 rule="hyper" parents="63 11629 11682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11686">
    <literal><![CDATA[
      K(x,R(R(x / y,y,L(K(z,x),u,w)),v5,v6) \ x) = K(R(x,v5,v6),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10745,a(flip),b,11684,a),flip(a)].">
      <j1 rule="hyper" parents="63 10745 11684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11687">
    <literal><![CDATA[
      R(R(K(x,y),y,L(K(z,x),u,w)),v5,v6) = K(R(x,v5,v6),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10795,a(flip),b,11686,a)].">
      <j1 rule="hyper" parents="63 10795 11686"/>
    </justification>
  </clause>

  <clause id="11688">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(5493(a,1),11687(a,1,1))].">
      <j1 rule="para" parents="5493 11687"/>
    </justification>
  </clause>

  <clause id="11689">
    <literal><![CDATA[
      K(R(R(x,y,z),u,w),w) = R(K(x,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7637,a,b,11688,a)].">
      <j1 rule="hyper" parents="347 7637 11688"/>
    </justification>
  </clause>

  <clause id="11690">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 = K(y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(11688(a,2),5173(a,1,1))].">
      <j1 rule="para" parents="11688 5173"/>
    </justification>
  </clause>

  <clause id="11692">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[para(11688(a,2),7293(a,1,2))].">
      <j1 rule="para" parents="11688 7293"/>
    </justification>
  </clause>

  <clause id="11693">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,R(x,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(11688(a,2),7314(a,1))].">
      <j1 rule="para" parents="11688 7314"/>
    </justification>
  </clause>

  <clause id="11694">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,R(y,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(11688(a,2),7328(a,1,2))].">
      <j1 rule="para" parents="11688 7328"/>
    </justification>
  </clause>

  <clause id="11695">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w)) * K(v5,y)) = T(x,K(y,v5) * R(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(11688(a,2),10679(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11688 10679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11696">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(6705,a,11690,a)].">
      <j1 rule="hyper" parents="6705 11690"/>
    </justification>
  </clause>

  <clause id="11697">
    <literal><![CDATA[
      K(x,R(y,z,u)) * 1 = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,8,a,b,11696,a)].">
      <j1 rule="hyper" parents="347 8 11696"/>
    </justification>
  </clause>

  <clause id="11698">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,R(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11688,a(flip),b,11696,a)].">
      <j1 rule="hyper" parents="63 11688 11696"/>
    </justification>
  </clause>

  <clause id="11699">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(133,a,11696,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="133 11696 20"/>
    </justification>
  </clause>

  <clause id="11700">
    <literal><![CDATA[
      K(x,(y * z) * (z \ 1)) = R(K(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(585(a,2),11696(a,2,2)),flip(a)].">
      <j1 rule="para" parents="585 11696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11701">
    <literal><![CDATA[
      K(K(x,y) * K(y,(z * u) / ((w \ z) * u)),v5) = K(v5,K(y,x)) * K(v5,K(y,R(w,z,u)))
    ]]></literal>
    <justification jstring="[para(11696(a,1),10691(a,2,2,2))].">
      <j1 rule="para" parents="11696 10691"/>
    </justification>
  </clause>

  <clause id="11702">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w))) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[para(11698(a,1),7330(a,1,2))].">
      <j1 rule="para" parents="11698 7330"/>
    </justification>
  </clause>

  <clause id="11703">
    <literal><![CDATA[
      x * K(x,K(y,z) * K(u,R(y,w,v5))) = T(x,K(y,R(u,w,v5)) * K(z,y))
    ]]></literal>
    <justification jstring="[para(11698(a,1),10682(a,1,2,2,2))].">
      <j1 rule="para" parents="11698 10682"/>
    </justification>
  </clause>

  <clause id="11704">
    <literal><![CDATA[
      a(K(x,R(y,z,u) \ 1),w,v5) = a(K(y,R(x,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(11698(a,1),11594(a,2,1))].">
      <j1 rule="para" parents="11698 11594"/>
    </justification>
  </clause>

  <clause id="11705">
    <literal><![CDATA[
      a(K(x,R(y,x * z,u)),w,v5) = a(K(x,R(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(11698(a,1),11599(a,2,1))].">
      <j1 rule="para" parents="11698 11599"/>
    </justification>
  </clause>

  <clause id="11706">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(11697(a,1),141(a,1)),flip(b)].">
      <j1 rule="para" parents="11697 141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11707">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(R(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(11689(a,1),10133(a,1))].">
      <j1 rule="para" parents="11689 10133"/>
    </justification>
  </clause>

  <clause id="11708">
    <literal><![CDATA[
      K(x,K(R(y,z,u) \ y,R(w,y,z * u))) = K(x,K(a(y,z,u),T(w,y * (z * u))))
    ]]></literal>
    <justification jstring="[hyper(63,a,9891,a(flip),b,11692,a),flip(a)].">
      <j1 rule="hyper" parents="63 9891 11692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11709">
    <literal><![CDATA[
      K(x,K(R(y,z,u) \ y,R(w,y,v5))) = K(x,K(w,(y * v5) / (R(y,z,u) * v5)))
    ]]></literal>
    <justification jstring="[para(6712(a,1),11692(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6712 11692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11710">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) * (K(z,y) \ R(T(K(z,y),x),u,w)) = K(z,y) \ R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(11692(a,1),9519(a,1,1))].">
      <j1 rule="para" parents="11692 9519"/>
    </justification>
  </clause>

  <clause id="11711">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,R(u,w,v5))) = K(x,y) * T(z,K(u,R(x,w,v5)))
    ]]></literal>
    <justification jstring="[para(11702(a,1),8475(a,2,2))].">
      <j1 rule="para" parents="11702 8475"/>
    </justification>
  </clause>

  <clause id="11712">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) * ((y \ z) * u) = (T(y,x) \ z) * u
    ]]></literal>
    <justification jstring="[para(5209(a,1),11699(a,2,1))].">
      <j1 rule="para" parents="5209 11699"/>
    </justification>
  </clause>

  <clause id="11713">
    <literal><![CDATA[
      ((x * y) * z) / ((K(u,x) * y) * z) = T(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(11699(a,1),5357(a,1,2))].">
      <j1 rule="para" parents="11699 5357"/>
    </justification>
  </clause>

  <clause id="11714">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = R(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,10348,a,b,11700,a)].">
      <j1 rule="hyper" parents="63 10348 11700"/>
    </justification>
  </clause>

  <clause id="11715">
    <literal><![CDATA[
      K(x,K(y,(z * u) / (R(z,w,v5) * u))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(R(z,w,v5) \ z,R(y,z,u))) = v6
    ]]></literal>
    <justification jstring="[para(6712(a,1),11694(a,1,2))].">
      <j1 rule="para" parents="6712 11694"/>
    </justification>
  </clause>

  <clause id="11716">
    <literal><![CDATA[
      ((x * y) * z) / (T(y,x) * z) = T(R(x,y,z),y)
    ]]></literal>
    <justification jstring="[para(4977(a,2),11713(a,1,2,1))].">
      <j1 rule="para" parents="4977 11713"/>
    </justification>
  </clause>

  <clause id="11717">
    <literal><![CDATA[
      R(T(x,y),T(y,x),z) = T(R(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(4316,a,11716,a)].">
      <j1 rule="hyper" parents="4316 11716"/>
    </justification>
  </clause>

  <clause id="11718">
    <literal><![CDATA[
      R(x,T(y,x),z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,27,a(flip),b,11717,a(flip))].">
      <j1 rule="hyper" parents="40 27 11717"/>
    </justification>
  </clause>

  <clause id="11722">
    <literal><![CDATA[
      R(x,y,z) * (T(y,x) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,11718,a(flip),b,264,a)].">
      <j1 rule="hyper" parents="133 11718 264"/>
    </justification>
  </clause>

  <clause id="11726">
    <literal><![CDATA[
      R(x,y,z) \ ((y * x) * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[para(11718(a,1),577(a,1,1))].">
      <j1 rule="para" parents="11718 577"/>
    </justification>
  </clause>

  <clause id="11727">
    <literal><![CDATA[
      R(x,y,(y * x) \ z) \ z = T(y,x) * ((y * x) \ z)
    ]]></literal>
    <justification jstring="[para(11718(a,1),910(a,1,1))].">
      <j1 rule="para" parents="11718 910"/>
    </justification>
  </clause>

  <clause id="11728">
    <literal><![CDATA[
      ((x * y) * z) / (T(y,x) * (K(x,y) * z)) = R(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(131,a,10271,a(flip),b,11722,a)].">
      <j1 rule="hyper" parents="131 10271 11722"/>
    </justification>
  </clause>

  <clause id="11729">
    <literal><![CDATA[
      K(x,(((y * x) * z) / R(x,y,z)) \ u) = K(x,(T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(11726(a,1),7943(a,2,2,1))].">
      <j1 rule="para" parents="11726 7943"/>
    </justification>
  </clause>

  <clause id="11730">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,8609,a(flip),b,11714,a),flip(a)].">
      <j1 rule="hyper" parents="63 8609 11714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11731">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(11706,a,11730,a)].">
      <j1 rule="hyper" parents="11706 11730"/>
    </justification>
  </clause>

  <clause id="11732">
    <literal><![CDATA[
      K(x,L(y,1 / z,(1 / z) \ 1)) = R(K(x,y),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,2304,a(flip),b,11730,a),flip(a)].">
      <j1 rule="hyper" parents="63 2304 11730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11733">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(11730(a,1),11706(a,1))].">
      <j1 rule="para" parents="11730 11706"/>
    </justification>
  </clause>

  <clause id="11734">
    <literal><![CDATA[
      K(x,L(y / z,z,z \ 1)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(691(a,1),11731(a,1,2)),flip(a)].">
      <j1 rule="para" parents="691 11731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11735">
    <literal><![CDATA[
      (R(x,y,y \ 1) \ (x * y)) * R(x,y,y \ 1) = (x * y) * K((y \ 1) \ 1,L(x,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(11731(a,1),10616(a,2,2))].">
      <j1 rule="para" parents="11731 10616"/>
    </justification>
  </clause>

  <clause id="11736">
    <literal><![CDATA[
      R(x,y,(y * x) \ z) \ z = y * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,10295,a(flip),b,11727,a),flip(a)].">
      <j1 rule="hyper" parents="347 10295 11727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11737">
    <literal><![CDATA[
      R(x,y,L(x \ 1,x,y)) \ y = y * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(244(a,2),11736(a,1,1,3))].">
      <j1 rule="para" parents="244 11736"/>
    </justification>
  </clause>

  <clause id="11738">
    <literal><![CDATA[
      R(x,y,L(x,x,y)) \ y = y * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(3328(a,1),11737(a,1,1))].">
      <j1 rule="para" parents="3328 11737"/>
    </justification>
  </clause>

  <clause id="11739">
    <literal><![CDATA[
      R(x,y,x) \ y = y * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(10952(a,1),11738(a,1,1))].">
      <j1 rule="para" parents="10952 11738"/>
    </justification>
  </clause>

  <clause id="11742">
    <literal><![CDATA[
      R(K(x,y),z \ 1,z) = K(x,L(y,z \ 1,z))
    ]]></literal>
    <justification jstring="[para(2988(a,1),11732(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2988 11732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11743">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) / z = K(x,y) * (1 / z)
    ]]></literal>
    <justification jstring="[hyper(131,a,11742,a(flip),b,2270,a)].">
      <j1 rule="hyper" parents="131 11742 2270"/>
    </justification>
  </clause>

  <clause id="11744">
    <literal><![CDATA[
      R(x,y,K(x,y) * z) = ((x * y) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(5213(a,1),11728(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5213 11728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11745">
    <literal><![CDATA[
      R(x,y,K(x,y) * z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,20,a,b,11744,a),flip(a)].">
      <j1 rule="hyper" parents="347 20 11744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11747">
    <literal><![CDATA[
      K(x,(((y * x) * z) / R(x,y,z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(11729(a,2),8168(a,1))].">
      <j1 rule="para" parents="11729 8168"/>
    </justification>
  </clause>

  <clause id="11748">
    <literal><![CDATA[
      K(x,x * (((y * x) * z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(11635(a,1),11747(a,1))].">
      <j1 rule="para" parents="11635 11747"/>
    </justification>
  </clause>

  <clause id="11750">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w)) * K(v5,y)) = K(x,K(y,v5) * K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(34,a,4929,a(flip),b,11703,a)].">
      <j1 rule="hyper" parents="34 4929 11703"/>
    </justification>
  </clause>

  <clause id="11751">
    <literal><![CDATA[
      K(x,K(R(y,z,u),R(z,w,v5) \ z)) = K(x,K(y,(z * u) / (R(z,w,v5) * u)))
    ]]></literal>
    <justification jstring="[hyper(7328,a,11709,a)].">
      <j1 rule="hyper" parents="7328 11709"/>
    </justification>
  </clause>

  <clause id="11752">
    <literal><![CDATA[
      K(K(x,y) * K(y,(z * u) / ((w \ z) * u)),v5) = K(K(x,y) * K(y,R(w,z,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,10689,a(flip),b,11701,a),flip(a)].">
      <j1 rule="hyper" parents="347 10689 11701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11753">
    <literal><![CDATA[
      K(K(x,y) * R(K(y,z),u,w),v5) = K(K(x,y) * K(y,R(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(6711(a,1),11752(a,1,1,2))].">
      <j1 rule="para" parents="6711 11752"/>
    </justification>
  </clause>

  <clause id="11754">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) * (K(z,y) \ R(K(z,T(y,x)),u,w)) = K(z,y) \ R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(7091(a,2),11710(a,1,2,2,1))].">
      <j1 rule="para" parents="7091 11710"/>
    </justification>
  </clause>

  <clause id="11755">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) * (K(y,z) * R(K(z,T(y,x)),u,w)) = K(z,y) \ R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(5256(a,1),11754(a,1,2))].">
      <j1 rule="para" parents="5256 11754"/>
    </justification>
  </clause>

  <clause id="11756">
    <literal><![CDATA[
      x * (K(y,z) * R(K(z,T(y,u)),w,v5)) != K(z,y) \ R(K(z,y),w,v5)
    ]]></literal>
    <literal><![CDATA[
      K(u,K(y,R(z,w,v5))) = x
    ]]></literal>
    <justification jstring="[para(11755(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="11755 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11757">
    <literal><![CDATA[
      (R(x,y,y \ 1) \ (x * y)) * R(x,y,y \ 1) = (x * y) * K(y,L(x,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(3407(a,1),11735(a,2,2))].">
      <j1 rule="para" parents="3407 11735"/>
    </justification>
  </clause>

  <clause id="11758">
    <literal><![CDATA[
      (R(x,y,y \ 1) \ (x * y)) * R(x,y,y \ 1) = (x * y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(9150(a,1),11757(a,2,2))].">
      <j1 rule="para" parents="9150 11757"/>
    </justification>
  </clause>

  <clause id="11759">
    <literal><![CDATA[
      (R(x,y,y \ 1) \ (x * y)) * R(x,y,y \ 1) = y * x
    ]]></literal>
    <justification jstring="[hyper(347,a,91,a(flip),b,11758,a),flip(a)].">
      <j1 rule="hyper" parents="347 91 11758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11762">
    <literal><![CDATA[
      (R(x,y,y) \ (x * y)) * R(x,y,y \ 1) = y * x
    ]]></literal>
    <justification jstring="[para(2190(a,1),11759(a,1,1,1))].">
      <j1 rule="para" parents="2190 11759"/>
    </justification>
  </clause>

  <clause id="11763">
    <literal><![CDATA[
      (R(x,y,y) \ (x * y)) * R(x,y,y) = y * x
    ]]></literal>
    <justification jstring="[para(2190(a,1),11762(a,1,2))].">
      <j1 rule="para" parents="2190 11762"/>
    </justification>
  </clause>

  <clause id="11764">
    <literal><![CDATA[
      L(x,x,y) * R(y,x,x) = x * y
    ]]></literal>
    <justification jstring="[para(3296(a,1),11763(a,1,1))].">
      <j1 rule="para" parents="3296 11763"/>
    </justification>
  </clause>

  <clause id="11765">
    <literal><![CDATA[
      K(R(K(x,y) * R(K(y,x),z,u),K(y,x),z * u),((z * u) \ K(x,y)) \ 1) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(5256(a,1),9296(a,1,1,1))].">
      <j1 rule="para" parents="5256 9296"/>
    </justification>
  </clause>

  <clause id="11766">
    <literal><![CDATA[
      K(x,L(T(y \ 1,T(y * z,z)) \ u,u,((y * z) \ z) \ z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(7070(a,1),11176(a,1,2,1,1))].">
      <j1 rule="para" parents="7070 11176"/>
    </justification>
  </clause>

  <clause id="11767">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z * y) \ u,u,((y * z) \ z) \ z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(10334(a,1),11766(a,1,2,1,1))].">
      <j1 rule="para" parents="10334 11766"/>
    </justification>
  </clause>

  <clause id="11768">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z * y) \ u,u,T(y * z,z))) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(11395(a,1),11767(a,1,2))].">
      <j1 rule="para" parents="11395 11767"/>
    </justification>
  </clause>

  <clause id="11769">
    <literal><![CDATA[
      K(K(x,y) * R(K(y,x),z,u),((z * u) \ K(x,y)) \ 1) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(10589(a,1),11765(a,1,1))].">
      <j1 rule="para" parents="10589 11765"/>
    </justification>
  </clause>

  <clause id="11770">
    <literal><![CDATA[
      K(K(x,y) * R(K(y,x),z,u),K(y,x) * (z * u)) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6326,a,11769,a)].">
      <j1 rule="hyper" parents="6326 11769"/>
    </justification>
  </clause>

  <clause id="11772">
    <literal><![CDATA[
      K(K(x,y) * K(y,R(x,z,u)),K(y,x) * (z * u)) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,11753,a(flip),b,11770,a)].">
      <j1 rule="hyper" parents="63 11753 11770"/>
    </justification>
  </clause>

  <clause id="11773">
    <literal><![CDATA[
      K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = K(z * u,K(x,R(y,z,u)) * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,10697,a(flip),b,11772,a),flip(a)].">
      <j1 rule="hyper" parents="63 10697 11772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11774">
    <literal><![CDATA[
      K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = K(z * u,K(x,y) * K(y,R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,11750,a(flip),b,11773,a),flip(a)].">
      <j1 rule="hyper" parents="347 11750 11773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11775">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ T(1 / y,1 / (1 / ((x * y) / x))) = (1 / y) * (1 / (1 / ((x * y) / x)))
    ]]></literal>
    <justification jstring="[para(9199(a,1),6050(a,2,1))].">
      <j1 rule="para" parents="9199 6050"/>
    </justification>
  </clause>

  <clause id="11776">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ T(1 / y,(x * y) / x) = (1 / y) * (1 / (1 / ((x * y) / x)))
    ]]></literal>
    <justification jstring="[para(2967(a,1),11775(a,1,2))].">
      <j1 rule="para" parents="2967 11775"/>
    </justification>
  </clause>

  <clause id="11777">
    <literal><![CDATA[
      (1 / x) * (1 / (1 / ((y * x) / y))) = (1 / ((y * x) / y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(5307(a,1),11776(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5307 11776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11778">
    <literal><![CDATA[
      (1 / x) * (1 / (1 / ((y * x) / y))) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,10643,a(flip),b,11777,a),flip(a)].">
      <j1 rule="hyper" parents="347 10643 11777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11780">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * ((L(z,y,x) \ z) * ((x * y) \ (x * (y * z))))) = T(a(x,y,z),(x * y) \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(18(a,2),2110(a,1,2,2,1,1))].">
      <j1 rule="para" parents="18 2110"/>
    </justification>
  </clause>

  <clause id="11781">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * ((L(z,y,x) \ z) * L(z,y,x))) = T(a(x,y,z),(x * y) \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(18(a,2),11780(a,1,2,2,2))].">
      <j1 rule="para" parents="18 11780"/>
    </justification>
  </clause>

  <clause id="11782">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * ((L(z,y,x) \ z) * L(z,y,x))) = T(a(x,y,z),L(z,y,x))
    ]]></literal>
    <justification jstring="[para(18(a,2),11781(a,2,2))].">
      <j1 rule="para" parents="18 11781"/>
    </justification>
  </clause>

  <clause id="11783">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = T(a(x,y,z),L(z,y,x))
    ]]></literal>
    <justification jstring="[para(3302(a,1),11782(a,1,2,2))].">
      <j1 rule="para" parents="3302 11782"/>
    </justification>
  </clause>

  <clause id="11784">
    <literal><![CDATA[
      T(a(x,y,z),L(z,y,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(836,a,11783,a),flip(a)].">
      <j1 rule="hyper" parents="836 11783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11785">
    <literal><![CDATA[
      K(L(x,y,z),a(z,y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(4952,a,11784,a)].">
      <j1 rule="hyper" parents="4952 11784"/>
    </justification>
  </clause>

  <clause id="11786">
    <literal><![CDATA[
      L(T(x,a(y,z,x)),z,y) = L(x,z,y)
    ]]></literal>
    <justification jstring="[hyper(189,a,4982,a,b,11785,a(flip))].">
      <j1 rule="hyper" parents="189 4982 11785"/>
    </justification>
  </clause>

  <clause id="11787">
    <literal><![CDATA[
      T(x,a(y,z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(50,a,11786,a)].">
      <j1 rule="hyper" parents="50 11786"/>
    </justification>
  </clause>

  <clause id="11788">
    <literal><![CDATA[
      a(x,y,z) * z = z * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1068,a,11787,a),flip(a)].">
      <j1 rule="hyper" parents="1068 11787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11789">
    <literal><![CDATA[
      T(a(x,y,z),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,11787,a)].">
      <j1 rule="hyper" parents="54 11787"/>
    </justification>
  </clause>

  <clause id="11790">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,x) = a(u,w,x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(11787(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11787 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11791">
    <literal><![CDATA[
      x * a(y,z,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,x) * x = u
    ]]></literal>
    <justification jstring="[para(11789(a,1),315(a,1,2))].">
      <j1 rule="para" parents="11789 315"/>
    </justification>
  </clause>

  <clause id="11795">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) * R(R(x * T(x \ 1,u),y,z) \ 1,w,v5) = R((x * T(x \ 1,u)) * R(K(u,x \ 1),w,v5),y,z)
    ]]></literal>
    <justification jstring="[para(5121(a,1),5388(a,1,1))].">
      <j1 rule="para" parents="5121 5388"/>
    </justification>
  </clause>

  <clause id="11796">
    <literal><![CDATA[
      R((x * T(x \ 1,y)) * R(K(y,x \ 1),z,u),w,v5) = K(R(x,w,v5) \ 1,y) * R(K(R(x,w,v5) \ 1,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(5121(a,1),11795(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5121 11795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11797">
    <literal><![CDATA[
      R((x * T(x \ 1,y)) * R(K(y,x \ 1),z,u),w,v5) = K(R(x,w,v5) \ 1,y) * R(K(y,R(x,w,v5) \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(5173(a,1),11796(a,2,2,1))].">
      <j1 rule="para" parents="5173 11796"/>
    </justification>
  </clause>

  <clause id="11798">
    <literal><![CDATA[
      R((x * T(x \ 1,y)) * R(K(y,x \ 1),z,u),w,v5) = K(R(x,w,v5) \ 1,y) * K(y,R(R(x,w,v5),z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(6694(a,1),11797(a,2,2))].">
      <j1 rule="para" parents="6694 11797"/>
    </justification>
  </clause>

  <clause id="11799">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) * K(u,R(R(x,y,z),w,v5) \ 1) = R(K(x \ 1,u) * R(K(u,x \ 1),w,v5),y,z)
    ]]></literal>
    <justification jstring="[para(4925(a,1),11798(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4925 11798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11800">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) * K(u,R(R(x,y,z),w,v5) \ 1) = R(K(x \ 1,u) * K(u,R(x,w,v5) \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(6694(a,1),11799(a,2,1,2))].">
      <j1 rule="para" parents="6694 11799"/>
    </justification>
  </clause>

  <clause id="11801">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ (u * L(x,y,z)),L(x,y,z)) = K(u * x,L(x,y,z)) * K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5096(a,1),10945(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5096 10945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11802">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ (u * L(x,y,z)),L(x,y,z)) = a(x,u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,11264,a,b,11801,a),flip(a)].">
      <j1 rule="hyper" parents="347 11264 11801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11804">
    <literal><![CDATA[
      a(L(x,y,z),T(u,L(x,y,z)),L(x,y,z)) = a(x,u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[para(22(a,2),11802(a,1,2))].">
      <j1 rule="para" parents="22 11802"/>
    </justification>
  </clause>

  <clause id="11805">
    <literal><![CDATA[
      K(x / y,z) * T(z,T(z * ((x / y) * ((x / y) \ ((y / x) \ 1))),x / y)) = L(z,(x / y) * ((x / y) \ ((y / x) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(5551(a,1),11212(a,1,1))].">
      <j1 rule="para" parents="5551 11212"/>
    </justification>
  </clause>

  <clause id="11806">
    <literal><![CDATA[
      K(x / y,z) * T(z,T(z * ((y / x) \ 1),x / y)) = L(z,(x / y) * ((x / y) \ ((y / x) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(10(a,1),11805(a,1,2,2,1,2))].">
      <j1 rule="para" parents="10 11805"/>
    </justification>
  </clause>

  <clause id="11808">
    <literal><![CDATA[
      K(x / y,z) * T(z,T((y / x) \ z,x / y)) = L(z,(x / y) * ((x / y) \ ((y / x) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(8414(a,1),11806(a,1,2))].">
      <j1 rule="para" parents="8414 11806"/>
    </justification>
  </clause>

  <clause id="11809">
    <literal><![CDATA[
      K(x / y,z) * T(z,T(z * (x / y),x / y)) = L(z,(x / y) * ((x / y) \ ((y / x) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(11512(a,1),11808(a,1,2))].">
      <j1 rule="para" parents="11512 11808"/>
    </justification>
  </clause>

  <clause id="11810">
    <literal><![CDATA[
      L(x,(y / z) * ((y / z) \ ((z / y) \ 1)),x) = K(y / z,x) * T(x,x * (y / z))
    ]]></literal>
    <justification jstring="[para(6904(a,1),11809(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6904 11809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11811">
    <literal><![CDATA[
      L(x,(y / z) * ((y / z) \ ((z / y) \ 1)),x) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y / z,x) = u
    ]]></literal>
    <justification jstring="[para(11810(a,2),5582(a,1))].">
      <j1 rule="para" parents="11810 5582"/>
    </justification>
  </clause>

  <clause id="11812">
    <literal><![CDATA[
      L(x,y / z,x) = L(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(11811,a,9831,a)].">
      <j1 rule="hyper" parents="11811 9831"/>
    </justification>
  </clause>

  <clause id="11813">
    <literal><![CDATA[
      L(x,(y \ z) \ z,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(80(a,1),11812(a,1,2)),flip(a)].">
      <j1 rule="para" parents="80 11812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11814">
    <literal><![CDATA[
      L(x,R(y \ R(y,z,u),y,z * u),x) = L(x,(y * (z * u)) \ ((y * z) * u),x)
    ]]></literal>
    <justification jstring="[para(3688(a,2),11812(a,1,2))].">
      <j1 rule="para" parents="3688 11812"/>
    </justification>
  </clause>

  <clause id="11815">
    <literal><![CDATA[
      L(x,R(y * K(z,y),z,u),x) = L(x,(z * u) \ ((z * y) * u),x)
    ]]></literal>
    <justification jstring="[para(5061(a,2),11812(a,1,2))].">
      <j1 rule="para" parents="5061 11812"/>
    </justification>
  </clause>

  <clause id="11816">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(340(a,2),11813(a,1,2))].">
      <j1 rule="para" parents="340 11813"/>
    </justification>
  </clause>

  <clause id="11817">
    <literal><![CDATA[
      L(x,T(y,z),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(347,a,8500,a,b,11816,a),flip(a)].">
      <j1 rule="hyper" parents="347 8500 11816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11818">
    <literal><![CDATA[
      L(x,R(y * K(z,y),u,w),x) = L(x,R(y,u,w),x)
    ]]></literal>
    <justification jstring="[para(5078(a,1),11816(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5078 11816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11819">
    <literal><![CDATA[
      a(x,T(y,z),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(8501,a,11817,a)].">
      <j1 rule="hyper" parents="8501 11817"/>
    </justification>
  </clause>

  <clause id="11820">
    <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(347,a,11320,a,b,11819,a),flip(a)].">
      <j1 rule="hyper" parents="347 11320 11819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11821">
    <literal><![CDATA[
      a(x,T(y / z,u),x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,11507,a(flip),b,11819,a),flip(a)].">
      <j1 rule="hyper" parents="347 11507 11819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11823">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,11804,a(flip),b,11819,a),flip(a)].">
      <j1 rule="hyper" parents="63 11804 11819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11824">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(5058(a,1),11819(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5058 11819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11825">
    <literal><![CDATA[
      L(a(x,y,x),y,z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11371,a(flip),b,11824,a)].">
      <j1 rule="hyper" parents="63 11371 11824"/>
    </justification>
  </clause>

  <clause id="11827">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * (z * y)) / (u * z),x)
    ]]></literal>
    <justification jstring="[para(11825(a,1),11546(a,1,1))].">
      <j1 rule="para" parents="11825 11546"/>
    </justification>
  </clause>

  <clause id="11828">
    <literal><![CDATA[
      a(x,R(y \ z,y,u),x) = a(x,(y * u) \ (z * u),x)
    ]]></literal>
    <justification jstring="[para(1033(a,1),11821(a,1,2))].">
      <j1 rule="para" parents="1033 11821"/>
    </justification>
  </clause>

  <clause id="11829">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,11254,a(flip),b,11823,a),flip(a)].">
      <j1 rule="hyper" parents="347 11254 11823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11831">
    <literal><![CDATA[
      L(L(x,y,x),z,u) \ L(x,z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11030,a,b,11829,a)].">
      <j1 rule="hyper" parents="63 11030 11829"/>
    </justification>
  </clause>

  <clause id="11832">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11308,a(flip),b,11829,a)].">
      <j1 rule="hyper" parents="63 11308 11829"/>
    </justification>
  </clause>

  <clause id="11839">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = w \ (w * a(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,9,a,b,11832,a),flip(a)].">
      <j1 rule="hyper" parents="347 9 11832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11840">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,11832,a(flip),b,4782,a)].">
      <j1 rule="hyper" parents="134 11832 4782"/>
    </justification>
  </clause>

  <clause id="11841">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (u * a(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(133,a,11832,a(flip),b,9966,a)].">
      <j1 rule="hyper" parents="133 11832 9966"/>
    </justification>
  </clause>

  <clause id="11842">
    <literal><![CDATA[
      (x \ 1) * a(y,z,y) = x \ a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,11832,a(flip),b,3197,a),flip(a)].">
      <j1 rule="hyper" parents="128 11832 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11843">
    <literal><![CDATA[
      x \ (y * a(z,u,z)) = (x \ y) * a(z,u,z)
    ]]></literal>
    <justification jstring="[para(11832(a,1),538(a,1,2,2))].">
      <j1 rule="para" parents="11832 538"/>
    </justification>
  </clause>

  <clause id="11845">
    <literal><![CDATA[
      a(x,y,x) \ (z \ a(x,y,x)) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(9976,a,11842,a)].">
      <j1 rule="hyper" parents="9976 11842"/>
    </justification>
  </clause>

  <clause id="11846">
    <literal><![CDATA[
      a(x,y,x) * (z \ 1) = z \ a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9970,a,11842,a)].">
      <j1 rule="hyper" parents="9970 11842"/>
    </justification>
  </clause>

  <clause id="11848">
    <literal><![CDATA[
      L(x,y,z \ a(u,w,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = v5
    ]]></literal>
    <justification jstring="[para(11842(a,1),11461(a,1,3))].">
      <j1 rule="para" parents="11842 11461"/>
    </justification>
  </clause>

  <clause id="11849">
    <literal><![CDATA[
      (a(x,y,x) / z) \ 1 = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[para(83(a,1),11845(a,1,2)),flip(a)].">
      <j1 rule="para" parents="83 11845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11850">
    <literal><![CDATA[
      (x \ 1) \ (a(y,z,y) \ u) = (x \ a(y,z,y)) \ u
    ]]></literal>
    <justification jstring="[para(11846(a,1),11379(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11846 11379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11851">
    <literal><![CDATA[
      1 / L(a(x,y,x) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(1 / (a(x,y,x) / z),u,w) \ 1 = v5
    ]]></literal>
    <justification jstring="[para(11849(a,1),9709(a,1,2,1))].">
      <j1 rule="para" parents="11849 9709"/>
    </justification>
  </clause>

  <clause id="11852">
    <literal><![CDATA[
      L(a(x,y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(11839(a,2),356(a,1))].">
      <j1 rule="para" parents="11839 356"/>
    </justification>
  </clause>

  <clause id="11855">
    <literal><![CDATA[
      a(x,y,x) \ L(x,z,u) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(39,a,9963,a,b,11831,a)].">
      <j1 rule="hyper" parents="39 9963 11831"/>
    </justification>
  </clause>

  <clause id="11856">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(2387,a,11840,a)].">
      <j1 rule="hyper" parents="2387 11840"/>
    </justification>
  </clause>

  <clause id="11857">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (a(z,u,z) * y)
    ]]></literal>
    <justification jstring="[para(9957(a,2),11840(a,2,2))].">
      <j1 rule="para" parents="9957 11840"/>
    </justification>
  </clause>

  <clause id="11858">
    <literal><![CDATA[
      L(T(x,y),y,a(z,u,z)) = T(x,y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(10011,a,11856,a)].">
      <j1 rule="hyper" parents="10011 11856"/>
    </justification>
  </clause>

  <clause id="11860">
    <literal><![CDATA[
      (((x * y) * z) * a(u,w,u)) / ((y * z) * a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(994,a,11856,a)].">
      <j1 rule="hyper" parents="994 11856"/>
    </justification>
  </clause>

  <clause id="11861">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(11856(a,1),51(a,2))].">
      <j1 rule="para" parents="11856 51"/>
    </justification>
  </clause>

  <clause id="11863">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) = (x \ u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(678,a,11841,a)].">
      <j1 rule="hyper" parents="678 11841"/>
    </justification>
  </clause>

  <clause id="11864">
    <literal><![CDATA[
      (x \ (a(y,z,y) \ u)) * a(y,z,y) = x \ u
    ]]></literal>
    <justification jstring="[hyper(675,a,11841,a),flip(a)].">
      <j1 rule="hyper" parents="675 11841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11865">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[para(9957(a,2),11841(a,2,2))].">
      <j1 rule="para" parents="9957 11841"/>
    </justification>
  </clause>

  <clause id="11866">
    <literal><![CDATA[
      a(x,y,x) * (z * (a(x,y,x) \ u)) = z * u
    ]]></literal>
    <justification jstring="[para(9964(a,1),11841(a,2,2))].">
      <j1 rule="para" parents="9964 11841"/>
    </justification>
  </clause>

  <clause id="11867">
    <literal><![CDATA[
      x \ (y * a(z,u,z)) = a(z,u,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,9957,a,b,11843,a),flip(a)].">
      <j1 rule="hyper" parents="347 9957 11843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11868">
    <literal><![CDATA[
      (x \ K(y,z)) * a(y,y \ z,y) = x \ K(y,y \ z)
    ]]></literal>
    <justification jstring="[para(8369(a,1),11843(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8369 11843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11869">
    <literal><![CDATA[
      x \ (y * (z * a(u,w,u))) = (x \ (y * z)) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(11840(a,1),11843(a,1,2))].">
      <j1 rule="para" parents="11840 11843"/>
    </justification>
  </clause>

  <clause id="11870">
    <literal><![CDATA[
      a(x,y,x) * L(L(x,y,x),z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(150,a,11855,a)].">
      <j1 rule="hyper" parents="150 11855"/>
    </justification>
  </clause>

  <clause id="11871">
    <literal><![CDATA[
      a(x,y,x) * L(L(x,y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(11855(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11855 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11873">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) = a(y,z,y) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,9957,a,b,11863,a),flip(a)].">
      <j1 rule="hyper" parents="347 9957 11863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11874">
    <literal><![CDATA[
      a(x,y,x) \ (z \ (a(x,y,x) * u)) = z \ u
    ]]></literal>
    <justification jstring="[hyper(128,a,11863,a,b,9957,a)].">
      <j1 rule="hyper" parents="128 11863 9957"/>
    </justification>
  </clause>

  <clause id="11875">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ u = (z \ u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11385,a,b,11863,a)].">
      <j1 rule="hyper" parents="63 11385 11863"/>
    </justification>
  </clause>

  <clause id="11876">
    <literal><![CDATA[
      a(x,y,x) \ (z \ u) = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(9976,a,11864,a)].">
      <j1 rule="hyper" parents="9976 11864"/>
    </justification>
  </clause>

  <clause id="11878">
    <literal><![CDATA[
      a(x,y,x) * ((z \ (a(x,y,x) \ u)) * w) = (z \ u) * w
    ]]></literal>
    <justification jstring="[para(11864(a,1),11384(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11864 11384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11879">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = x * (a(y,z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(11413,a,11865,a)].">
      <j1 rule="hyper" parents="11413 11865"/>
    </justification>
  </clause>

  <clause id="11880">
    <literal><![CDATA[
      (a(x,y,x) \ z) * (a(x,y,x) * u) = z * u
    ]]></literal>
    <justification jstring="[hyper(11381,a,11865,a),flip(a)].">
      <j1 rule="hyper" parents="11381 11865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11881">
    <literal><![CDATA[
      a(x,y,x) \ (z * u) = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(128,a,169,a(flip),b,11865,a)].">
      <j1 rule="hyper" parents="128 169 11865"/>
    </justification>
  </clause>

  <clause id="11883">
    <literal><![CDATA[
      (a(x,y,x) \ z) * u = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(11381,a,11866,a),flip(a)].">
      <j1 rule="hyper" parents="11381 11866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11884">
    <literal><![CDATA[
      x \ (y * (a(z,u,z) \ x)) = T(a(z,u,z) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(462,a,11373,a(flip),b,11866,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="462 11373 11866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11885">
    <literal><![CDATA[
      (a(x,y,x) \ z) * u != w
    ]]></literal>
    <literal><![CDATA[
      z * (a(x,y,x) \ u) = w
    ]]></literal>
    <justification jstring="[para(11866(a,1),11381(a,1))].">
      <j1 rule="para" parents="11866 11381"/>
    </justification>
  </clause>

  <clause id="11886">
    <literal><![CDATA[
      a(x,y,x) * (z \ x) = z \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(8339(a,1),11867(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8339 11867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11888">
    <literal><![CDATA[
      x \ (y * (z * a(u,w,u))) = a(u,w,u) * (x \ (y * z))
    ]]></literal>
    <justification jstring="[para(11840(a,1),11867(a,1,2))].">
      <j1 rule="para" parents="11840 11867"/>
    </justification>
  </clause>

  <clause id="11889">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ u = a(x,y,x) * (z \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11385,a,b,11873,a)].">
      <j1 rule="hyper" parents="63 11385 11873"/>
    </justification>
  </clause>

  <clause id="11890">
    <literal><![CDATA[
      (x * a(y,z,y)) \ u = a(y,z,y) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(128,a,11405,a(flip),b,11873,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 11405 11873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11891">
    <literal><![CDATA[
      a(x,y,x) \ (z \ x) = z \ L(x,y,x)
    ]]></literal>
    <justification jstring="[para(8497(a,1),11874(a,1,2,2))].">
      <j1 rule="para" parents="8497 11874"/>
    </justification>
  </clause>

  <clause id="11892">
    <literal><![CDATA[
      a(x,y,x) \ (z \ T(x * y,x)) = z \ (y * x)
    ]]></literal>
    <justification jstring="[para(10327(a,1),11874(a,1,2,2))].">
      <j1 rule="para" parents="10327 11874"/>
    </justification>
  </clause>

  <clause id="11893">
    <literal><![CDATA[
      ((x \ y) * K(z,y)) * K(y,y * z) = x \ L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,11004,a,b,11891,a)].">
      <j1 rule="hyper" parents="63 11004 11891"/>
    </justification>
  </clause>

  <clause id="11894">
    <literal><![CDATA[
      x / (y * a(z,u,z)) = a(z,u,z) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(220,a,218,a(flip),b,11875,a)].">
      <j1 rule="hyper" parents="220 218 11875"/>
    </justification>
  </clause>

  <clause id="11895">
    <literal><![CDATA[
      ((x \ y) \ z) * a(x,u,x) = (R(x,u,x) \ y) \ z
    ]]></literal>
    <justification jstring="[para(10990(a,1),11875(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10990 11875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11896">
    <literal><![CDATA[
      ((a(x,y,x) / z) \ u) * a(x,y,x) = (1 / z) \ u
    ]]></literal>
    <justification jstring="[para(11387(a,1),11875(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11387 11875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11898">
    <literal><![CDATA[
      L(x,a(y,z,y),u) = x
    ]]></literal>
    <justification jstring="[hyper(544,a,11879,a)].">
      <j1 rule="hyper" parents="544 11879"/>
    </justification>
  </clause>

  <clause id="11900">
    <literal><![CDATA[
      L(x,K(y,z),z \ y) = x
    ]]></literal>
    <justification jstring="[hyper(10665,a,11898,a)].">
      <j1 rule="hyper" parents="10665 11898"/>
    </justification>
  </clause>

  <clause id="11902">
    <literal><![CDATA[
      x / (a(y,z,y) \ u) = (x / u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(220,a,11898,a(flip),b,566,a(flip))].">
      <j1 rule="hyper" parents="220 11898 566"/>
    </justification>
  </clause>

  <clause id="11903">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) \ ((x * a(y,z,y)) * (u * w)) = L(w,L(u,a(y,z,y),x),x * a(y,z,y))
    ]]></literal>
    <justification jstring="[para(11898(a,1),541(a,1,2,2,1))].">
      <j1 rule="para" parents="11898 541"/>
    </justification>
  </clause>

  <clause id="11904">
    <literal><![CDATA[
      ((x * a(y,z,y)) * (u * w)) \ ((x * (a(y,z,y) * u)) * w) = a(x * a(y,z,y),L(u,a(y,z,y),x),w)
    ]]></literal>
    <justification jstring="[para(11898(a,1),540(a,1,1,2,1))].">
      <j1 rule="para" parents="11898 540"/>
    </justification>
  </clause>

  <clause id="11905">
    <literal><![CDATA[
      L(x,K(y,z),y \ z) = x
    ]]></literal>
    <justification jstring="[hyper(5182,a,11900,a)].">
      <j1 rule="hyper" parents="5182 11900"/>
    </justification>
  </clause>

  <clause id="11906">
    <literal><![CDATA[
      ((x \ y) * K(x,y)) \ z = K(x,y) \ ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(623,a,11905,a),flip(a)].">
      <j1 rule="hyper" parents="623 11905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11907">
    <literal><![CDATA[
      x * (a(x,y,x) \ L(x \ a(x,y,x),z,u)) = L(x \ L(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(9528,a,11881,a),flip(a)].">
      <j1 rule="hyper" parents="9528 11881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11908">
    <literal><![CDATA[
      x * (y * (a(x,z,x) \ u)) = L(x,z,x) * (y * u)
    ]]></literal>
    <justification jstring="[para(11881(a,1),9982(a,1,2))].">
      <j1 rule="para" parents="11881 9982"/>
    </justification>
  </clause>

  <clause id="11909">
    <literal><![CDATA[
      (x * (a(y,z,y) \ u)) / w = a(y,z,y) \ ((x * u) / w)
    ]]></literal>
    <justification jstring="[para(11881(a,1),11400(a,1,1))].">
      <j1 rule="para" parents="11881 11400"/>
    </justification>
  </clause>

  <clause id="11910">
    <literal><![CDATA[
      ((x * (a(y,z,y) \ u)) * w) / (u * (a(y,z,y) \ w)) = R(x,a(y,z,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(220,a,11883,a(flip),b,209,a)].">
      <j1 rule="hyper" parents="220 11883 209"/>
    </justification>
  </clause>

  <clause id="11911">
    <literal><![CDATA[
      (x * (y * (a(z,u,z) \ w))) \ ((x * (a(z,u,z) \ y)) * w) = a(x,a(z,u,z) \ y,w)
    ]]></literal>
    <justification jstring="[para(11883(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11883 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11912">
    <literal><![CDATA[
      (x * y) * (a(x,z,x) \ u) = (L(x,z,x) * y) * u
    ]]></literal>
    <justification jstring="[para(9987(a,1),11883(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9987 11883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11913">
    <literal><![CDATA[
      (x \ y) * (a(x,z,x) \ u) = (R(x,z,x) \ y) * u
    ]]></literal>
    <justification jstring="[para(10990(a,1),11883(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10990 11883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11914">
    <literal><![CDATA[
      (a(x,y,x) / z) * (a(x,y,x) \ u) = (1 / z) * u
    ]]></literal>
    <justification jstring="[para(11387(a,1),11883(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11387 11883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11915">
    <literal><![CDATA[
      (x * (a(y,z,y) \ u)) * w = (x * u) * (a(y,z,y) \ w)
    ]]></literal>
    <justification jstring="[para(11881(a,1),11883(a,1,1))].">
      <j1 rule="para" parents="11881 11883"/>
    </justification>
  </clause>

  <clause id="11916">
    <literal><![CDATA[
      a(x,y,x) * ((x * z) \ u) = (L(x,y,x) * z) \ u
    ]]></literal>
    <justification jstring="[para(9987(a,1),11889(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9987 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11917">
    <literal><![CDATA[
      (x \ (a(y,z,y) \ u)) \ w = a(y,z,y) * ((x \ u) \ w)
    ]]></literal>
    <justification jstring="[para(11876(a,1),11889(a,1,1))].">
      <j1 rule="para" parents="11876 11889"/>
    </justification>
  </clause>

  <clause id="11918">
    <literal><![CDATA[
      (x * (a(y,z,y) \ u)) \ w = a(y,z,y) * ((x * u) \ w)
    ]]></literal>
    <justification jstring="[para(11881(a,1),11889(a,1,1))].">
      <j1 rule="para" parents="11881 11889"/>
    </justification>
  </clause>

  <clause id="11919">
    <literal><![CDATA[
      a(x,y,x) \ (z / (u \ 1)) = z / (u \ a(x,y,x))
    ]]></literal>
    <justification jstring="[para(11842(a,1),11894(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11842 11894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11920">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(11388,a,11858,a),flip(a)].">
      <j1 rule="hyper" parents="11388 11858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11921">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(11858(a,1),11388(a,1))].">
      <j1 rule="para" parents="11858 11388"/>
    </justification>
  </clause>

  <clause id="11923">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = u / T(u,x)
    ]]></literal>
    <justification jstring="[hyper(220,a,11920,a(flip),b,4939,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="220 11920 4939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11924">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,11920,a(flip),b,4929,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 11920 4929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11925">
    <literal><![CDATA[
      T(x,T(y,z) / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(8360(a,1),11920(a,1,2))].">
      <j1 rule="para" parents="8360 11920"/>
    </justification>
  </clause>

  <clause id="11926">
    <literal><![CDATA[
      T(x,a(y,z,y) \ u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(9964(a,1),11920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9964 11920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11927">
    <literal><![CDATA[
      T(x,y * R(z,u,z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(10964(a,1),11920(a,1,2))].">
      <j1 rule="para" parents="10964 11920"/>
    </justification>
  </clause>

  <clause id="11928">
    <literal><![CDATA[
      T(x,y / R(z,u,z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(10979(a,1),11920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10979 11920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11929">
    <literal><![CDATA[
      T(x,y * (a(z,u,z) \ w)) = T(x,y * w)
    ]]></literal>
    <justification jstring="[para(11881(a,1),11926(a,1,2))].">
      <j1 rule="para" parents="11881 11926"/>
    </justification>
  </clause>

  <clause id="11932">
    <literal><![CDATA[
      T(x,y / T(z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4279(a,1),11925(a,1,2))].">
      <j1 rule="para" parents="4279 11925"/>
    </justification>
  </clause>

  <clause id="11933">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) = T(x,y / T(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,8885,a,b,11932,a)].">
      <j1 rule="hyper" parents="347 8885 11932"/>
    </justification>
  </clause>

  <clause id="11934">
    <literal><![CDATA[
      T(x,y / T(T(z,y),u)) = T(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[para(23(a,1),11932(a,1,2,2))].">
      <j1 rule="para" parents="23 11932"/>
    </justification>
  </clause>

  <clause id="11935">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,4920,a,b,11923,a),flip(a)].">
      <j1 rule="hyper" parents="347 4920 11923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11936">
    <literal><![CDATA[
      K(x * a(y,z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(11923(a,2),5013(a,1))].">
      <j1 rule="para" parents="11923 5013"/>
    </justification>
  </clause>

  <clause id="11937">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(8360(a,1),11935(a,1,1))].">
      <j1 rule="para" parents="8360 11935"/>
    </justification>
  </clause>

  <clause id="11938">
    <literal><![CDATA[
      K(x / L(y,z,y),u) = K(x / y,u)
    ]]></literal>
    <justification jstring="[para(8496(a,1),11935(a,1,1))].">
      <j1 rule="para" parents="8496 11935"/>
    </justification>
  </clause>

  <clause id="11939">
    <literal><![CDATA[
      K(a(x,y,x) * z,u) = K(z,u)
    ]]></literal>
    <justification jstring="[para(9957(a,2),11935(a,1,1))].">
      <j1 rule="para" parents="9957 11935"/>
    </justification>
  </clause>

  <clause id="11941">
    <literal><![CDATA[
      K(x \ (a(y,z,y) * u),w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(11863(a,2),11935(a,1,1))].">
      <j1 rule="para" parents="11863 11935"/>
    </justification>
  </clause>

  <clause id="11942">
    <literal><![CDATA[
      K(L(x,y,x) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(9988(a,1),11939(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9988 11939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11943">
    <literal><![CDATA[
      K(T(x * y,x) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(10429(a,1),11939(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10429 11939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11944">
    <literal><![CDATA[
      K(x / T(y,x),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9045,a(flip),b,11937,a)].">
      <j1 rule="hyper" parents="63 9045 11937"/>
    </justification>
  </clause>

  <clause id="11945">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,4924,a,b,11924,a),flip(a)].">
      <j1 rule="hyper" parents="347 4924 11924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11946">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(11924(a,2),5006(a,1))].">
      <j1 rule="para" parents="11924 5006"/>
    </justification>
  </clause>

  <clause id="11947">
    <literal><![CDATA[
      K(x,T(y,z) / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(8360(a,1),11945(a,1,2))].">
      <j1 rule="para" parents="8360 11945"/>
    </justification>
  </clause>

  <clause id="11948">
    <literal><![CDATA[
      K(x,y / L(z,u,z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(8496(a,1),11945(a,1,2))].">
      <j1 rule="para" parents="8496 11945"/>
    </justification>
  </clause>

  <clause id="11949">
    <literal><![CDATA[
      K(x,L(y,z,y) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(8511(a,1),11945(a,1,2))].">
      <j1 rule="para" parents="8511 11945"/>
    </justification>
  </clause>

  <clause id="11950">
    <literal><![CDATA[
      K(x,a(y,z,y) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(9957(a,2),11945(a,1,2))].">
      <j1 rule="para" parents="9957 11945"/>
    </justification>
  </clause>

  <clause id="11951">
    <literal><![CDATA[
      K(x,a(y,z,y) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(9964(a,1),11945(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9964 11945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11952">
    <literal><![CDATA[
      K(x,y * R(z,u,z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(10964(a,1),11945(a,1,2))].">
      <j1 rule="para" parents="10964 11945"/>
    </justification>
  </clause>

  <clause id="11953">
    <literal><![CDATA[
      K(x,R(y,z,y) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(10974(a,1),11945(a,1,2))].">
      <j1 rule="para" parents="10974 11945"/>
    </justification>
  </clause>

  <clause id="11954">
    <literal><![CDATA[
      K(x,R(y,z,y) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(10976(a,1),11945(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10976 11945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11955">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) / w) = K(x,u / w)
    ]]></literal>
    <justification jstring="[para(11401(a,2),11945(a,1,2))].">
      <j1 rule="para" parents="11401 11945"/>
    </justification>
  </clause>

  <clause id="11956">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(11840(a,1),11945(a,1,2))].">
      <j1 rule="para" parents="11840 11945"/>
    </justification>
  </clause>

  <clause id="11957">
    <literal><![CDATA[
      K(x,y \ (z * a(u,w,u))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(11843(a,2),11945(a,1,2))].">
      <j1 rule="para" parents="11843 11945"/>
    </justification>
  </clause>

  <clause id="11958">
    <literal><![CDATA[
      K(x,y * (a(z,u,z) * w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(11857(a,1),11945(a,1,2))].">
      <j1 rule="para" parents="11857 11945"/>
    </justification>
  </clause>

  <clause id="11959">
    <literal><![CDATA[
      K(x,y \ (a(z,u,z) \ w)) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(11864(a,1),11945(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11864 11945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11960">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(9921(a,1),11950(a,1,2))].">
      <j1 rule="para" parents="9921 11950"/>
    </justification>
  </clause>

  <clause id="11961">
    <literal><![CDATA[
      K(x,T(y * z,y) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(10429(a,1),11950(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10429 11950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11962">
    <literal><![CDATA[
      K(x,(a(y,z,y) \ u) * w) = K(x,u * w)
    ]]></literal>
    <justification jstring="[para(11373(a,1),11950(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11373 11950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11963">
    <literal><![CDATA[
      K(x,(y * a(z,u,z)) * w) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(11384(a,2),11950(a,1,2))].">
      <j1 rule="para" parents="11384 11950"/>
    </justification>
  </clause>

  <clause id="11964">
    <literal><![CDATA[
      K(x,y * (a(z,u,z) \ w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(11866(a,1),11950(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11866 11950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11965">
    <literal><![CDATA[
      K(x,(y * a(z,u,z)) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(11890(a,2),11951(a,1,2))].">
      <j1 rule="para" parents="11890 11951"/>
    </justification>
  </clause>

  <clause id="11966">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w) / z) = K(x,z \ L(y,u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),11947(a,1,2,1))].">
      <j1 rule="para" parents="25 11947"/>
    </justification>
  </clause>

  <clause id="11967">
    <literal><![CDATA[
      K(x,y / T(z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4279(a,1),11947(a,1,2))].">
      <j1 rule="para" parents="4279 11947"/>
    </justification>
  </clause>

  <clause id="11968">
    <literal><![CDATA[
      K(x,y / T(z,y)) = K(x,T(y / z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,7626,a,b,11967,a),flip(a)].">
      <j1 rule="hyper" parents="347 7626 11967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11969">
    <literal><![CDATA[
      T(x,y / ((z \ u) \ u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(6798(a,1),11928(a,1,2,2))].">
      <j1 rule="para" parents="6798 11928"/>
    </justification>
  </clause>

  <clause id="11971">
    <literal><![CDATA[
      K(T(x / y,x) * z,u) = K((y \ x) * z,u)
    ]]></literal>
    <justification jstring="[para(4398(a,1),11942(a,1,1,1))].">
      <j1 rule="para" parents="4398 11942"/>
    </justification>
  </clause>

  <clause id="11972">
    <literal><![CDATA[
      K(x,y / T(z / u,z)) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[para(4398(a,1),11948(a,1,2,2))].">
      <j1 rule="para" parents="4398 11948"/>
    </justification>
  </clause>

  <clause id="11973">
    <literal><![CDATA[
      K(x,T(y / z,y) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4398(a,1),11949(a,1,2,1))].">
      <j1 rule="para" parents="4398 11949"/>
    </justification>
  </clause>

  <clause id="11974">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(11607(a,1),11949(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11607 11949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11975">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(6800(a,1),11952(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6800 11952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11976">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(6798(a,1),11952(a,1,2,2))].">
      <j1 rule="para" parents="6798 11952"/>
    </justification>
  </clause>

  <clause id="11978">
    <literal><![CDATA[
      K(x,T(y,y \ z) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(4426(a,1),11953(a,1,2,1))].">
      <j1 rule="para" parents="4426 11953"/>
    </justification>
  </clause>

  <clause id="11979">
    <literal><![CDATA[
      K(x,T(y,y * z) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(6800(a,1),11953(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6800 11953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11980">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4426(a,1),11954(a,1,2,1))].">
      <j1 rule="para" parents="4426 11954"/>
    </justification>
  </clause>

  <clause id="11981">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,T(y * z,y) \ u)
    ]]></literal>
    <justification jstring="[para(11954(a,1),6470(a,1,1))].">
      <j1 rule="para" parents="11954 6470"/>
    </justification>
  </clause>

  <clause id="11982">
    <literal><![CDATA[
      T(x,L(y,z,y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(8511(a,1),11921(a,1,2))].">
      <j1 rule="para" parents="8511 11921"/>
    </justification>
  </clause>

  <clause id="11983">
    <literal><![CDATA[
      T(x,a(y,z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(9957(a,2),11921(a,1,2))].">
      <j1 rule="para" parents="9957 11921"/>
    </justification>
  </clause>

  <clause id="11985">
    <literal><![CDATA[
      K(x,T(y,z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(8360(a,1),11946(a,1,2))].">
      <j1 rule="para" parents="8360 11946"/>
    </justification>
  </clause>

  <clause id="11986">
    <literal><![CDATA[
      K(x,a(y,z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(9957(a,2),11946(a,1,2))].">
      <j1 rule="para" parents="9957 11946"/>
    </justification>
  </clause>

  <clause id="11987">
    <literal><![CDATA[
      K(x,R(y,z,y) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / u) = w
    ]]></literal>
    <justification jstring="[para(11411(a,1),11946(a,1,2))].">
      <j1 rule="para" parents="11411 11946"/>
    </justification>
  </clause>

  <clause id="11988">
    <literal><![CDATA[
      K(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(11968(a,2),9477(a,1))].">
      <j1 rule="para" parents="11968 9477"/>
    </justification>
  </clause>

  <clause id="11989">
    <literal><![CDATA[
      T(x,K(y \ 1,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(2796(a,1),11983(a,1,2,1))].">
      <j1 rule="para" parents="2796 11983"/>
    </justification>
  </clause>

  <clause id="11990">
    <literal><![CDATA[
      T(x,K(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(9921(a,1),11983(a,1,2))].">
      <j1 rule="para" parents="9921 11983"/>
    </justification>
  </clause>

  <clause id="11991">
    <literal><![CDATA[
      K(x,K(y \ 1,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(2796(a,1),11986(a,1,2,1))].">
      <j1 rule="para" parents="2796 11986"/>
    </justification>
  </clause>

  <clause id="11992">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(8351(a,2),11986(a,1,2,1))].">
      <j1 rule="para" parents="8351 11986"/>
    </justification>
  </clause>

  <clause id="11993">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(9921(a,1),11986(a,1,2))].">
      <j1 rule="para" parents="9921 11986"/>
    </justification>
  </clause>

  <clause id="11994">
    <literal><![CDATA[
      T(x,y * (L(z,u,z) * w)) = T(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(9987(a,1),11929(a,1,2,2))].">
      <j1 rule="para" parents="9987 11929"/>
    </justification>
  </clause>

  <clause id="11995">
    <literal><![CDATA[
      T(x,y * (R(z,u,z) \ w)) = T(x,y * (z \ w))
    ]]></literal>
    <justification jstring="[para(10990(a,1),11929(a,1,2,2))].">
      <j1 rule="para" parents="10990 11929"/>
    </justification>
  </clause>

  <clause id="11996">
    <literal><![CDATA[
      K(x \ L(y,z,y),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(8497(a,1),11941(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8497 11941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11997">
    <literal><![CDATA[
      K(x \ T(y * z,y),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(10327(a,1),11941(a,1,1,2))].">
      <j1 rule="para" parents="10327 11941"/>
    </justification>
  </clause>

  <clause id="11998">
    <literal><![CDATA[
      K(x \ T(y,y * z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4797(a,1),11996(a,1,1,2))].">
      <j1 rule="para" parents="4797 11996"/>
    </justification>
  </clause>

  <clause id="11999">
    <literal><![CDATA[
      K(x \ ((y \ z) \ z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(11607(a,1),11996(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11607 11996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12000">
    <literal><![CDATA[
      K(x,(y * L(z,u,z)) / w) = K(x,(y * z) / w)
    ]]></literal>
    <justification jstring="[para(9972(a,1),11955(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9972 11955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12001">
    <literal><![CDATA[
      K(x,T(y * z,y) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(10327(a,1),11955(a,1,2,1))].">
      <j1 rule="para" parents="10327 11955"/>
    </justification>
  </clause>

  <clause id="12002">
    <literal><![CDATA[
      K(x,y * (z * L(u,w,u))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(8509(a,1),11956(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8509 11956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12003">
    <literal><![CDATA[
      K(x,y * T(z * u,z)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(10326(a,1),11956(a,1,2,2))].">
      <j1 rule="para" parents="10326 11956"/>
    </justification>
  </clause>

  <clause id="12004">
    <literal><![CDATA[
      K(x,y * (z * (u * a(w,v5,w)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(11840(a,1),11956(a,1,2,2))].">
      <j1 rule="para" parents="11840 11956"/>
    </justification>
  </clause>

  <clause id="12005">
    <literal><![CDATA[
      K(x,y \ ((z * u) * z)) = K(x,y \ (z * (u * z)))
    ]]></literal>
    <justification jstring="[para(86(a,1),11957(a,1,2,2))].">
      <j1 rule="para" parents="86 11957"/>
    </justification>
  </clause>

  <clause id="12006">
    <literal><![CDATA[
      K(x,y \ (T(z,u) / u)) = K(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[para(8360(a,1),11957(a,1,2,2))].">
      <j1 rule="para" parents="8360 11957"/>
    </justification>
  </clause>

  <clause id="12007">
    <literal><![CDATA[
      K(x,y \ T(z * u,z)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(10326(a,1),11957(a,1,2,2))].">
      <j1 rule="para" parents="10326 11957"/>
    </justification>
  </clause>

  <clause id="12008">
    <literal><![CDATA[
      K(x,y \ (z * R(u,w,u))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(10964(a,1),11957(a,1,2,2))].">
      <j1 rule="para" parents="10964 11957"/>
    </justification>
  </clause>

  <clause id="12009">
    <literal><![CDATA[
      K(x,y \ (R(z,u,z) * w)) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(10974(a,1),11957(a,1,2,2))].">
      <j1 rule="para" parents="10974 11957"/>
    </justification>
  </clause>

  <clause id="12010">
    <literal><![CDATA[
      K(x,y * (K(z,z \ u) * w)) = K(x,y * (K(z,u) * w))
    ]]></literal>
    <justification jstring="[para(9921(a,1),11958(a,1,2,2))].">
      <j1 rule="para" parents="9921 11958"/>
    </justification>
  </clause>

  <clause id="12011">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(z \ u,u))
    ]]></literal>
    <justification jstring="[para(8359(a,1),11959(a,1,2,2))].">
      <j1 rule="para" parents="8359 11959"/>
    </justification>
  </clause>

  <clause id="12012">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) \ w) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(11379(a,2),11959(a,1,2))].">
      <j1 rule="para" parents="11379 11959"/>
    </justification>
  </clause>

  <clause id="12013">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(8333(a,1),11962(a,1,2,1))].">
      <j1 rule="para" parents="8333 11962"/>
    </justification>
  </clause>

  <clause id="12014">
    <literal><![CDATA[
      K(x,(R(y,z,y) \ u) * w) = K(x,(y \ u) * w)
    ]]></literal>
    <justification jstring="[para(10990(a,1),11962(a,1,2,1))].">
      <j1 rule="para" parents="10990 11962"/>
    </justification>
  </clause>

  <clause id="12015">
    <literal><![CDATA[
      K(x,(T(y,z) / z) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(8360(a,1),11963(a,1,2,1))].">
      <j1 rule="para" parents="8360 11963"/>
    </justification>
  </clause>

  <clause id="12016">
    <literal><![CDATA[
      K(x,T(y * z,y) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(10326(a,1),11963(a,1,2,1))].">
      <j1 rule="para" parents="10326 11963"/>
    </justification>
  </clause>

  <clause id="12017">
    <literal><![CDATA[
      K(x,K(y * z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(8354(a,1),11965(a,1,2,1))].">
      <j1 rule="para" parents="8354 11965"/>
    </justification>
  </clause>

  <clause id="12018">
    <literal><![CDATA[
      K(x,(T(y,z) / z) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(8360(a,1),11965(a,1,2,1))].">
      <j1 rule="para" parents="8360 11965"/>
    </justification>
  </clause>

  <clause id="12020">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(2868(a,1),11989(a,1,2))].">
      <j1 rule="para" parents="2868 11989"/>
    </justification>
  </clause>

  <clause id="12021">
    <literal><![CDATA[
      T(x,T((y \ 1) \ 1,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(3121(a,1),11989(a,1,2))].">
      <j1 rule="para" parents="3121 11989"/>
    </justification>
  </clause>

  <clause id="12022">
    <literal><![CDATA[
      T(x,T(y,y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(3115(a,1),11989(a,1,2))].">
      <j1 rule="para" parents="3115 11989"/>
    </justification>
  </clause>

  <clause id="12023">
    <literal><![CDATA[
      T(x,(((y \ 1) \ 1) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(y \ z) * u) = w
    ]]></literal>
    <justification jstring="[para(3484(a,1),11989(a,1,2))].">
      <j1 rule="para" parents="3484 11989"/>
    </justification>
  </clause>

  <clause id="12024">
    <literal><![CDATA[
      T(x,(y * ((z \ 1) \ 1)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(3509(a,1),11989(a,1,2))].">
      <j1 rule="para" parents="3509 11989"/>
    </justification>
  </clause>

  <clause id="12025">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(2868(a,1),11991(a,1,2))].">
      <j1 rule="para" parents="2868 11991"/>
    </justification>
  </clause>

  <clause id="12026">
    <literal><![CDATA[
      K(x,(y / (1 / z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / (z \ 1)) * u) = w
    ]]></literal>
    <justification jstring="[para(3483(a,1),11991(a,1,2))].">
      <j1 rule="para" parents="3483 11991"/>
    </justification>
  </clause>

  <clause id="12027">
    <literal><![CDATA[
      K(x,y * (z * K(u,u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = w
    ]]></literal>
    <justification jstring="[para(2769(a,1),11992(a,1,2))].">
      <j1 rule="para" parents="2769 11992"/>
    </justification>
  </clause>

  <clause id="12028">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(1 / y) \ z) = u
    ]]></literal>
    <justification jstring="[para(2958(a,1),11992(a,1,2))].">
      <j1 rule="para" parents="2958 11992"/>
    </justification>
  </clause>

  <clause id="12029">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(1 / y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(3632(a,1),11992(a,1,2))].">
      <j1 rule="para" parents="3632 11992"/>
    </justification>
  </clause>

  <clause id="12030">
    <literal><![CDATA[
      K(x,(y \ R(z,u,z)) \ w) = K(x,(y \ z) \ w)
    ]]></literal>
    <justification jstring="[para(11886(a,1),12012(a,1,2,1))].">
      <j1 rule="para" parents="11886 12012"/>
    </justification>
  </clause>

  <clause id="12031">
    <literal><![CDATA[
      T(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(11933(a,1),8886(a,1))].">
      <j1 rule="para" parents="11933 8886"/>
    </justification>
  </clause>

  <clause id="12032">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11943(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 11943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12033">
    <literal><![CDATA[
      T(x,T(y * z,y) \ u) = (w * K((z * y) \ u,x)) \ (w * x)
    ]]></literal>
    <justification jstring="[para(11943(a,1),6100(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11943 6100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12034">
    <literal><![CDATA[
      K(x,K(y,z) * ((y \ z) * u)) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(5479(a,1),11960(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5479 11960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12035">
    <literal><![CDATA[
      K(x,K(y * (z \ u),(y * (z \ u)) \ u) * w) = K(x,K(y * (u / z),u) * w)
    ]]></literal>
    <justification jstring="[para(8412(a,2),11960(a,2,2,1))].">
      <j1 rule="para" parents="8412 11960"/>
    </justification>
  </clause>

  <clause id="12036">
    <literal><![CDATA[
      T(x,T(y * z,y) \ u) = T(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(132,a,11961,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 11961 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12037">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11961(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 11961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12038">
    <literal><![CDATA[
      T(x,y / T((z \ u) \ u,w)) = T(x,y / T(T(z,w),u))
    ]]></literal>
    <justification jstring="[para(7558(a,2),11969(a,1,2,2))].">
      <j1 rule="para" parents="7558 11969"/>
    </justification>
  </clause>

  <clause id="12039">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) = (w * K(u,(y \ x) \ z)) \ w
    ]]></literal>
    <justification jstring="[para(11973(a,1),6123(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11973 6123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12040">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = (w * K(T(y,z) \ u,x)) \ w
    ]]></literal>
    <justification jstring="[hyper(347,a,6123,a,b,11974,a),flip(a)].">
      <j1 rule="hyper" parents="347 6123 11974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12041">
    <literal><![CDATA[
      K(x,T(((y / z) \ 1) * y,y) \ u) = K(x,(((z \ y) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(6542(a,1),11974(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6542 11974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12042">
    <literal><![CDATA[
      L(K(x,T(y,z) \ u),y,y \ z) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(11974(a,1),11085(a,1,1))].">
      <j1 rule="para" parents="11974 11085"/>
    </justification>
  </clause>

  <clause id="12043">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) = x \ T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,4924,a(flip),b,11975,a),flip(a)].">
      <j1 rule="hyper" parents="347 4924 11975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12044">
    <literal><![CDATA[
      K(x,y * T(z,u * z)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4323(a,2),11975(a,1,2,2))].">
      <j1 rule="para" parents="4323 11975"/>
    </justification>
  </clause>

  <clause id="12045">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) = w / (K(y * T(z,u),x) * w)
    ]]></literal>
    <justification jstring="[hyper(347,a,5259,a,b,11976,a),flip(a)].">
      <j1 rule="hyper" parents="347 5259 11976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12046">
    <literal><![CDATA[
      T(x,T(y,y \ z) * u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(132,a,11978,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 11978 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12047">
    <literal><![CDATA[
      K(x,T(y \ z,z) * u) = K(x,T(y \ z,y) * u)
    ]]></literal>
    <justification jstring="[para(4286(a,1),11978(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4286 11978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12048">
    <literal><![CDATA[
      K(x,L(T(y,y * z) * u,w,v5)) = K(L(x,w,v5),T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(11169,a,11979,a)].">
      <j1 rule="hyper" parents="11169 11979"/>
    </justification>
  </clause>

  <clause id="12049">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,K(z,y) * (y \ u))
    ]]></literal>
    <justification jstring="[para(5209(a,2),11980(a,2,2))].">
      <j1 rule="para" parents="5209 11980"/>
    </justification>
  </clause>

  <clause id="12050">
    <literal><![CDATA[
      K(x,((y \ z) \ z) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) / u) = w
    ]]></literal>
    <justification jstring="[para(6798(a,1),11987(a,1,2,1))].">
      <j1 rule="para" parents="6798 11987"/>
    </justification>
  </clause>

  <clause id="12051">
    <literal><![CDATA[
      K((x * y) / z,T(u,x * y)) = K(z \ T(y * x,y),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,7165,a,b,11997,a)].">
      <j1 rule="hyper" parents="347 7165 11997"/>
    </justification>
  </clause>

  <clause id="12052">
    <literal><![CDATA[
      K((x \ y) \ (z * u),L(w,x \ y,x)) = K(y \ (x * T(u * z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11115,a(flip),b,11997,a),flip(a)].">
      <j1 rule="hyper" parents="63 11115 11997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12053">
    <literal><![CDATA[
      T(x,y \ T(z,z * u)) = (w * K(y \ T(z,u),x)) \ (w * x)
    ]]></literal>
    <justification jstring="[para(11998(a,1),6100(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11998 6100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12054">
    <literal><![CDATA[
      K(x \ T(y * z,z \ 1),u) = K(x \ T(y * z,y),u)
    ]]></literal>
    <justification jstring="[para(6289(a,2),11999(a,1,1,2))].">
      <j1 rule="para" parents="6289 11999"/>
    </justification>
  </clause>

  <clause id="12055">
    <literal><![CDATA[
      K(x,((y \ z) * y) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12001(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 12001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12056">
    <literal><![CDATA[
      K(T(x * y,x) / z,u) = (w * K(u,(y * x) / z)) \ w
    ]]></literal>
    <justification jstring="[para(12001(a,1),6123(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12001 6123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12057">
    <literal><![CDATA[
      T(x,y * T(z * u,z)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(132,a,12003,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 12003 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12058">
    <literal><![CDATA[
      K(x,y * ((z \ u) * z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),12003(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 12003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12059">
    <literal><![CDATA[
      K(x,y \ (z / T(u,z))) = K(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[para(4279(a,1),12006(a,1,2,2))].">
      <j1 rule="para" parents="4279 12006"/>
    </justification>
  </clause>

  <clause id="12060">
    <literal><![CDATA[
      K(x,y \ ((z \ u) * z)) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),12007(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 12007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12061">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) = x \ T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,4924,a(flip),b,12013,a),flip(a)].">
      <j1 rule="hyper" parents="347 4924 12013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12062">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(132,a,12013,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 12013 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12063">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ y) \ u)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(5441(a,1),12013(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5441 12013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12064">
    <literal><![CDATA[
      K(x,(y / T(z,y)) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(4279(a,1),12015(a,1,2,1))].">
      <j1 rule="para" parents="4279 12015"/>
    </justification>
  </clause>

  <clause id="12065">
    <literal><![CDATA[
      K(x,((y \ z) * y) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12016(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 12016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12066">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12017(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 12017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12067">
    <literal><![CDATA[
      T(x,(T(y,z) / z) \ u) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(132,a,12018,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 12018 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12068">
    <literal><![CDATA[
      K(x,(y / T(z,y)) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4279(a,1),12018(a,1,2,1))].">
      <j1 rule="para" parents="4279 12018"/>
    </justification>
  </clause>

  <clause id="12069">
    <literal><![CDATA[
      T(x,((y \ z) * y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12036(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 12036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12070">
    <literal><![CDATA[
      K(x,T(y,z) \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(8602,a,12037,a),flip(a)].">
      <j1 rule="hyper" parents="8602 12037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12071">
    <literal><![CDATA[
      K(x,T(y,z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(12037(a,1),8602(a,1))].">
      <j1 rule="para" parents="12037 8602"/>
    </justification>
  </clause>

  <clause id="12072">
    <literal><![CDATA[
      T(x,T(y,z) \ z) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(132,a,12070,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 12070 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12073">
    <literal><![CDATA[
      K(x,y \ T(z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(4281(a,1),12070(a,1,2))].">
      <j1 rule="para" parents="4281 12070"/>
    </justification>
  </clause>

  <clause id="12074">
    <literal><![CDATA[
      T(x,y \ T(z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(4281(a,1),12072(a,1,2))].">
      <j1 rule="para" parents="4281 12072"/>
    </justification>
  </clause>

  <clause id="12075">
    <literal><![CDATA[
      K(x,y \ (T(z,u / w) / (T(w,u) \ u))) = K(x,y \ ((T(w,u) \ u) \ z))
    ]]></literal>
    <justification jstring="[para(12072(a,1),12006(a,1,2,2,1))].">
      <j1 rule="para" parents="12072 12006"/>
    </justification>
  </clause>

  <clause id="12076">
    <literal><![CDATA[
      T(x,y / z) \ (T(z \ T(y,z),x) \ u) = x \ ((z \ T(y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(12074(a,1),4784(a,1,1))].">
      <j1 rule="para" parents="12074 4784"/>
    </justification>
  </clause>

  <clause id="12077">
    <literal><![CDATA[
      K(x,y \ T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(4281(a,1),12071(a,1,2))].">
      <j1 rule="para" parents="4281 12071"/>
    </justification>
  </clause>

  <clause id="12078">
    <literal><![CDATA[
      K(x,((y \ z) \ 1) \ T(u,z \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / ((y \ z) \ 1)) = w
    ]]></literal>
    <justification jstring="[para(6258(a,1),12077(a,1,2,2))].">
      <j1 rule="para" parents="6258 12077"/>
    </justification>
  </clause>

  <clause id="12079">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) \ T(u,z / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (T(y,z) \ z)) = w
    ]]></literal>
    <justification jstring="[para(12072(a,1),12077(a,1,2,2))].">
      <j1 rule="para" parents="12072 12077"/>
    </justification>
  </clause>

  <clause id="12080">
    <literal><![CDATA[
      T(x,((y \ z) \ z) * u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(112(a,1),12046(a,1,2,1))].">
      <j1 rule="para" parents="112 12046"/>
    </justification>
  </clause>

  <clause id="12081">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(z * u) * y) = T(x,y * T(u * z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,10355,a,b,12057,a)].">
      <j1 rule="hyper" parents="347 10355 12057"/>
    </justification>
  </clause>

  <clause id="12082">
    <literal><![CDATA[
      T(x,y * ((z \ u) * z)) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),12057(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 12057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12083">
    <literal><![CDATA[
      T(x,y * T(z * u,u)) = T(x,y * (T(z,u) * u))
    ]]></literal>
    <justification jstring="[para(111(a,1),12057(a,1,2,2,1))].">
      <j1 rule="para" parents="111 12057"/>
    </justification>
  </clause>

  <clause id="12084">
    <literal><![CDATA[
      K(x,y * T((z \ 1) \ u,z)) = K(x,y * ((z \ K(z,u)) \ u))
    ]]></literal>
    <justification jstring="[para(7722(a,2),12058(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7722 12058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12085">
    <literal><![CDATA[
      T(x,y \ (z / T(u,z))) = T(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(132,a,12059,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 12059 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12086">
    <literal><![CDATA[
      K(x,y \ ((z \ x) * z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,8087,a(flip),b,12060,a),flip(a)].">
      <j1 rule="hyper" parents="347 8087 12060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12087">
    <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(12086(a,1),7806(a,1))].">
      <j1 rule="para" parents="12086 7806"/>
    </justification>
  </clause>

  <clause id="12088">
    <literal><![CDATA[
      T(x,K(y * z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),12062(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 12062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12089">
    <literal><![CDATA[
      T(x,K(y * z,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(5143(a,1),12062(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5143 12062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12090">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w) \ (K(u \ z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(u \ z,u) * w) / y) = v5
    ]]></literal>
    <justification jstring="[para(12062(a,1),12071(a,1,2,1))].">
      <j1 rule="para" parents="12062 12071"/>
    </justification>
  </clause>

  <clause id="12091">
    <literal><![CDATA[
      T(x,((y \ z) * y) * u) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(132,a,12065,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 12065 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12092">
    <literal><![CDATA[
      K(x,((L(y,z,y) * z) \ y) \ u) = K(x,(y / (z * y)) \ u)
    ]]></literal>
    <justification jstring="[para(4368(a,1),12068(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4368 12068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12093">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(6324,a,12069,a),flip(a)].">
      <j1 rule="hyper" parents="6324 12069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12094">
    <literal><![CDATA[
      L(x,y,T(T(z,u),u \ 1)) = L(x,y,T(T(z,u),u \ z))
    ]]></literal>
    <justification jstring="[para(12093(a,1),11393(a,1,3))].">
      <j1 rule="para" parents="12093 11393"/>
    </justification>
  </clause>

  <clause id="12095">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) = x \ T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(128,a,12080,a(flip),b,4929,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 12080 4929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12096">
    <literal><![CDATA[
      T(x,y \ (z / T(T(u,u \ z),z))) = T(x,y \ T(u \ z,u))
    ]]></literal>
    <justification jstring="[para(4301(a,1),12085(a,2,2,2))].">
      <j1 rule="para" parents="4301 12085"/>
    </justification>
  </clause>

  <clause id="12097">
    <literal><![CDATA[
      K(x,y * (z \ T(u * w,u))) = K(x,y * (z \ (w * u)))
    ]]></literal>
    <justification jstring="[para(11892(a,1),11964(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11892 11964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12098">
    <literal><![CDATA[
      T(x,y * (T(z / u,z) * w)) = T(x,y * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(4398(a,1),11994(a,1,2,2,1))].">
      <j1 rule="para" parents="4398 11994"/>
    </justification>
  </clause>

  <clause id="12099">
    <literal><![CDATA[
      K(x,(y * ((z \ u) \ u)) / w) = K(x,(y * T(z,u)) / w)
    ]]></literal>
    <justification jstring="[para(11607(a,1),12000(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11607 12000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12100">
    <literal><![CDATA[
      K(x,y * (z * T(u / w,u))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(4398(a,1),12002(a,1,2,2,2))].">
      <j1 rule="para" parents="4398 12002"/>
    </justification>
  </clause>

  <clause id="12101">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) \ w))) = K(x,y \ (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(6798(a,1),12008(a,1,2,2,2))].">
      <j1 rule="para" parents="6798 12008"/>
    </justification>
  </clause>

  <clause id="12102">
    <literal><![CDATA[
      K(x,y \ (((z \ u) \ u) * w)) = K(x,y \ (T(z,u) * w))
    ]]></literal>
    <justification jstring="[para(6798(a,1),12009(a,1,2,2,1))].">
      <j1 rule="para" parents="6798 12009"/>
    </justification>
  </clause>

  <clause id="12103">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) \ u) * w) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(6798(a,1),12014(a,1,2,1,1))].">
      <j1 rule="para" parents="6798 12014"/>
    </justification>
  </clause>

  <clause id="12105">
    <literal><![CDATA[
      T(x,(y \ (y / ((z \ 1) \ 1))) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(y \ (y / z)) \ u) = w
    ]]></literal>
    <justification jstring="[para(2599(a,1),12020(a,1,2,1))].">
      <j1 rule="para" parents="2599 12020"/>
    </justification>
  </clause>

  <clause id="12106">
    <literal><![CDATA[
      T(x,((((y \ 1) \ 1) \ z) / z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,((y \ z) / z) \ u) = w
    ]]></literal>
    <justification jstring="[para(2866(a,2),12020(a,1,2,1))].">
      <j1 rule="para" parents="2866 12020"/>
    </justification>
  </clause>

  <clause id="12107">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(112(a,1),12022(a,1,2,1))].">
      <j1 rule="para" parents="112 12022"/>
    </justification>
  </clause>

  <clause id="12108">
    <literal><![CDATA[
      T(x,L((y \ 1) \ 1,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(4669(a,2),12107(a,1,2,1))].">
      <j1 rule="para" parents="4669 12107"/>
    </justification>
  </clause>

  <clause id="12109">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ z = K(x,y) \ ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(6832(a,2),11906(a,1,1))].">
      <j1 rule="para" parents="6832 11906"/>
    </justification>
  </clause>

  <clause id="12110">
    <literal><![CDATA[
      (x * x) * (a(x,x,x) \ y) = ((1 / x) \ x) * y
    ]]></literal>
    <justification jstring="[para(5712(a,1),11912(a,2,1))].">
      <j1 rule="para" parents="5712 11912"/>
    </justification>
  </clause>

  <clause id="12111">
    <literal><![CDATA[
      L(x,y,x) * ((x \ z) * u) = x * ((R(x,y,x) \ z) * u)
    ]]></literal>
    <justification jstring="[para(11913(a,1),11908(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11913 11908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12112">
    <literal><![CDATA[
      (1 / x) * (y * a(z,u,z)) = (a(z,u,z) / x) * y
    ]]></literal>
    <justification jstring="[para(9960(a,1),11914(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9960 11914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12113">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * u) \ w) = v5
    ]]></literal>
    <justification jstring="[para(11916(a,1),11986(a,1,2))].">
      <j1 rule="para" parents="11916 11986"/>
    </justification>
  </clause>

  <clause id="12114">
    <literal><![CDATA[
      K(x,L(y / (z * y),u,w) / (z \ 1)) = K(x,(z \ 1) \ L(y / (z * y),u,w))
    ]]></literal>
    <justification jstring="[para(4436(a,1),11966(a,1,2,1,1))].">
      <j1 rule="para" parents="4436 11966"/>
    </justification>
  </clause>

  <clause id="12115">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(12043(a,2),5006(a,1))].">
      <j1 rule="para" parents="12043 5006"/>
    </justification>
  </clause>

  <clause id="12116">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(12061(a,2),5006(a,1))].">
      <j1 rule="para" parents="12061 5006"/>
    </justification>
  </clause>

  <clause id="12117">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(12095(a,2),5006(a,1))].">
      <j1 rule="para" parents="12095 5006"/>
    </justification>
  </clause>

  <clause id="12118">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * ((x \ y) \ z) = u
    ]]></literal>
    <justification jstring="[para(12109(a,2),5286(a,1))].">
      <j1 rule="para" parents="12109 5286"/>
    </justification>
  </clause>

  <clause id="12119">
    <literal><![CDATA[
      a(x,(y * z) \ (u * z),x) = a(x,y \ u,x)
    ]]></literal>
    <justification jstring="[hyper(11543,a,11828,a),flip(a)].">
      <j1 rule="hyper" parents="11543 11828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12121">
    <literal><![CDATA[
      a(x,(y * z) \ z,x) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),12119(a,1,2,2))].">
      <j1 rule="para" parents="7 12119"/>
    </justification>
  </clause>

  <clause id="12122">
    <literal><![CDATA[
      a(x,y * (z \ 1),x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(183(a,1),12119(a,1,2))].">
      <j1 rule="para" parents="183 12119"/>
    </justification>
  </clause>

  <clause id="12123">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) = (w / x) \ (a(x,y \ u,x) \ w)
    ]]></literal>
    <justification jstring="[para(12119(a,1),9983(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12119 9983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12124">
    <literal><![CDATA[
      a(x,y / (z * y),x) = a(x,z \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(11508,a,12121,a)].">
      <j1 rule="hyper" parents="11508 12121"/>
    </justification>
  </clause>

  <clause id="12125">
    <literal><![CDATA[
      a(x,((y * (z * (u * K(w,w \ 1)))) \ ((y * z) * u)) \ 1,x) = a(x,K(w,w \ 1) / a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(4130(a,1),12124(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4130 12124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12126">
    <literal><![CDATA[
      L(x,y,z \ K(u,u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(11868(a,1),11461(a,1,3))].">
      <j1 rule="para" parents="11868 11461"/>
    </justification>
  </clause>

  <clause id="12127">
    <literal><![CDATA[
      K(x,y \ K(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(11868(a,1),11946(a,1,2))].">
      <j1 rule="para" parents="11868 11946"/>
    </justification>
  </clause>

  <clause id="12128">
    <literal><![CDATA[
      K(x,y * (z \ K(u,u \ w))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(11868(a,1),11956(a,1,2,2))].">
      <j1 rule="para" parents="11868 11956"/>
    </justification>
  </clause>

  <clause id="12129">
    <literal><![CDATA[
      (x \ y) * (K(z,y) * K(y,y * z)) = x \ L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(8314,a,11893,a)].">
      <j1 rule="hyper" parents="8314 11893"/>
    </justification>
  </clause>

  <clause id="12130">
    <literal><![CDATA[
      K(x,y * (z * (L(u,w,u) \ v5))) = K(x,y * (z * (u \ v5)))
    ]]></literal>
    <justification jstring="[para(8511(a,1),12004(a,1,2,2,2))].">
      <j1 rule="para" parents="8511 12004"/>
    </justification>
  </clause>

  <clause id="12131">
    <literal><![CDATA[
      K(x,y * (z * (u \ K(w,w \ v5)))) = K(x,y * (z * (u \ K(w,v5))))
    ]]></literal>
    <justification jstring="[para(11868(a,1),12004(a,1,2,2,2))].">
      <j1 rule="para" parents="11868 12004"/>
    </justification>
  </clause>

  <clause id="12132">
    <literal><![CDATA[
      K(x,y * (z * ((u \ 1) \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * u)) = w
    ]]></literal>
    <justification jstring="[para(2340(a,1),12027(a,1,2,2))].">
      <j1 rule="para" parents="2340 12027"/>
    </justification>
  </clause>

  <clause id="12133">
    <literal><![CDATA[
      K(x,((y \ z) \ z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(12050,a,xx),flip(a)].">
      <j1 rule="hyper" parents="12050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12134">
    <literal><![CDATA[
      T(x,((y \ z) \ z) / u) = T(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(132,a,12133,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 12133 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12135">
    <literal><![CDATA[
      K(x,T(y / z,y) / u) = K(x,(z \ y) / u)
    ]]></literal>
    <justification jstring="[para(83(a,1),12133(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="83 12133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12137">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,T(y * (1 / z),y) / u)
    ]]></literal>
    <justification jstring="[para(6308(a,2),12133(a,1,2,1))].">
      <j1 rule="para" parents="6308 12133"/>
    </justification>
  </clause>

  <clause id="12138">
    <literal><![CDATA[
      K(x,T(y,T(z,u) / w) * (((z \ u) \ u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(((z \ u) \ u) / w) * y) = v5
    ]]></literal>
    <justification jstring="[para(12134(a,1),10409(a,1,2,1))].">
      <j1 rule="para" parents="12134 10409"/>
    </justification>
  </clause>

  <clause id="12139">
    <literal><![CDATA[
      K(x,T(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(112(a,2),12117(a,1,2,1))].">
      <j1 rule="para" parents="112 12117"/>
    </justification>
  </clause>

  <clause id="12140">
    <literal><![CDATA[
      K(x,T(y,z * (y \ u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u) * w) = v5
    ]]></literal>
    <justification jstring="[para(9550(a,1),12139(a,1,2,1))].">
      <j1 rule="para" parents="9550 12139"/>
    </justification>
  </clause>

  <clause id="12142">
    <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),11869(a,2,1))].">
      <j1 rule="para" parents="18 11869"/>
    </justification>
  </clause>

  <clause id="12143">
    <literal><![CDATA[
      a(x,y,x) * ((z \ (u \ 1)) * w) = (z \ (u \ a(x,y,x))) * w
    ]]></literal>
    <justification jstring="[para(11845(a,1),11878(a,1,2,1,2))].">
      <j1 rule="para" parents="11845 11878"/>
    </justification>
  </clause>

  <clause id="12144">
    <literal><![CDATA[
      (x * (y * (a(z,u,z) \ w))) * v5 = (x * (y * w)) * (a(z,u,z) \ v5)
    ]]></literal>
    <justification jstring="[para(11881(a,1),11915(a,1,1,2))].">
      <j1 rule="para" parents="11881 11915"/>
    </justification>
  </clause>

  <clause id="12145">
    <literal><![CDATA[
      a((x \ (a(y,z,y) \ u)) \ w,v5,v6) = a((x \ u) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(11917(a,2),11563(a,1,1))].">
      <j1 rule="para" parents="11917 11563"/>
    </justification>
  </clause>

  <clause id="12146">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,6199,a(flip),b,12039,a),flip(a)].">
      <j1 rule="hyper" parents="347 6199 12039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12147">
    <literal><![CDATA[
      K(((x \ y) \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(80(a,1),12146(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="80 12146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12148">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,z)) = K(z / ((x \ y) \ y),u)
    ]]></literal>
    <justification jstring="[hyper(7492,a,12147,a),flip(a)].">
      <j1 rule="hyper" parents="7492 12147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12149">
    <literal><![CDATA[
      K(T(x \ y,y) \ z,u) = K(T(x \ y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(4320(a,2),12147(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4320 12147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12150">
    <literal><![CDATA[
      K(x / ((y \ z) \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x / T(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(12148(a,1),7492(a,1))].">
      <j1 rule="para" parents="12148 7492"/>
    </justification>
  </clause>

  <clause id="12151">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(12040(a,2),6141(a,1))].">
      <j1 rule="para" parents="12040 6141"/>
    </justification>
  </clause>

  <clause id="12152">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(112(a,2),12151(a,1,2,1))].">
      <j1 rule="para" parents="112 12151"/>
    </justification>
  </clause>

  <clause id="12153">
    <literal><![CDATA[
      K(x,K(y,z) * (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(12049(a,1),12152(a,1))].">
      <j1 rule="para" parents="12049 12152"/>
    </justification>
  </clause>

  <clause id="12154">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(12045(a,2),5276(a,1))].">
      <j1 rule="para" parents="12045 5276"/>
    </justification>
  </clause>

  <clause id="12155">
    <literal><![CDATA[
      K(x,y * T(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(112(a,2),12154(a,1,2,2))].">
      <j1 rule="para" parents="112 12154"/>
    </justification>
  </clause>

  <clause id="12156">
    <literal><![CDATA[
      K(x \ T(y * z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ (z * y),u) = w
    ]]></literal>
    <justification jstring="[para(12051(a,1),7493(a,1))].">
      <j1 rule="para" parents="12051 7493"/>
    </justification>
  </clause>

  <clause id="12157">
    <literal><![CDATA[
      K(x \ (y * z),T(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ (z * y),x) = u
    ]]></literal>
    <justification jstring="[para(10475(a,1),12156(a,1))].">
      <j1 rule="para" parents="10475 12156"/>
    </justification>
  </clause>

  <clause id="12158">
    <literal><![CDATA[
      K(T(x * y,x) / z,u) = K((y * x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,6199,a(flip),b,12056,a),flip(a)].">
      <j1 rule="hyper" parents="347 6199 12056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12159">
    <literal><![CDATA[
      K(((x \ y) * x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12158(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 12158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12160">
    <literal><![CDATA[
      K(x \ T(y,z),T(u,T(y,z))) = K(((z \ y) * z) / x,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,7388,a,b,12159,a)].">
      <j1 rule="hyper" parents="347 7388 12159"/>
    </justification>
  </clause>

  <clause id="12161">
    <literal><![CDATA[
      L(x,y,T(T(z,u),u \ 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,11498,a(flip),b,12094,a),flip(a)].">
      <j1 rule="hyper" parents="347 11498 12094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12163">
    <literal><![CDATA[
      K(x,y \ (T(z / u,z) * w)) = K(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(83(a,1),12102(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="83 12102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12164">
    <literal><![CDATA[
      K(((x \ y) * x) / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y,x) / z,u) = w
    ]]></literal>
    <justification jstring="[para(12160(a,1),7492(a,1))].">
      <j1 rule="para" parents="12160 7492"/>
    </justification>
  </clause>

  <clause id="12165">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * z) \ (u * (z * y)),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,11507,a(flip),b,11827,a),flip(a)].">
      <j1 rule="hyper" parents="347 11507 11827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12168">
    <literal><![CDATA[
      K(x,T(y * z,y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(11981(a,1),8273(a,1))].">
      <j1 rule="para" parents="11981 8273"/>
    </justification>
  </clause>

  <clause id="12170">
    <literal><![CDATA[
      K(x,T((1 / y) * z,y \ 1) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * (1 / y)) \ u) = w
    ]]></literal>
    <justification jstring="[para(2962(a,1),12168(a,1,2,1))].">
      <j1 rule="para" parents="2962 12168"/>
    </justification>
  </clause>

  <clause id="12171">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,y,y \ z)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(11166,a,12042,a)].">
      <j1 rule="hyper" parents="11166 12042"/>
    </justification>
  </clause>

  <clause id="12172">
    <literal><![CDATA[
      K(x,((y * z) \ R(y,z,y)) \ u) = K(x,(y / (z * y)) \ u)
    ]]></literal>
    <justification jstring="[para(11407(a,1),12092(a,1,2,1))].">
      <j1 rule="para" parents="11407 12092"/>
    </justification>
  </clause>

  <clause id="12173">
    <literal><![CDATA[
      K(x,y) * ((y \ x) \ (K(y,x) * z)) = (((y \ x) * y) / y) \ z
    ]]></literal>
    <justification jstring="[hyper(12118,a,11549,a)].">
      <j1 rule="hyper" parents="12118 11549"/>
    </justification>
  </clause>

  <clause id="12174">
    <literal><![CDATA[
      K(x,y * (z * (u / T(w,u)))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(4485(a,1),12130(a,1,2,2,2))].">
      <j1 rule="para" parents="4485 12130"/>
    </justification>
  </clause>

  <clause id="12175">
    <literal><![CDATA[
      T(x,y * (z * (u / T(w,u)))) = T(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(132,a,12174,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 12174 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12176">
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * (1 / u))) = w
    ]]></literal>
    <justification jstring="[para(83(a,1),12132(a,1,2,2,2,1))].">
      <j1 rule="para" parents="83 12132"/>
    </justification>
  </clause>

  <clause id="12177">
    <literal><![CDATA[
      a(((x \ a(y,z,y)) \ u) \ w,v5,v6) = a(((x \ 1) \ u) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(11850(a,1),12145(a,1,1,1))].">
      <j1 rule="para" parents="11850 12145"/>
    </justification>
  </clause>

  <clause id="12178">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(18(a,2),12165(a,2,2))].">
      <j1 rule="para" parents="18 12165"/>
    </justification>
  </clause>

  <clause id="12179">
    <literal><![CDATA[
      a(x,L(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(11852,a,12178,a),flip(a)].">
      <j1 rule="hyper" parents="11852 12178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12180">
    <literal><![CDATA[
      a(x,L(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(12178(a,1),11852(a,1))].">
      <j1 rule="para" parents="12178 11852"/>
    </justification>
  </clause>

  <clause id="12182">
    <literal><![CDATA[
      a(x,L(y,z,u),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,8336,a,b,12179,a),flip(a)].">
      <j1 rule="hyper" parents="347 8336 12179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12183">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = x * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,12179,a(flip),b,8336,a),flip(a)].">
      <j1 rule="hyper" parents="134 12179 8336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12184">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(12179(a,1),8500(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12179 8500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12185">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(8343,a,12182,a)].">
      <j1 rule="hyper" parents="8343 12182"/>
    </justification>
  </clause>

  <clause id="12186">
    <literal><![CDATA[
      R(x,L(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(12183(a,2),8344(a,1))].">
      <j1 rule="para" parents="12183 8344"/>
    </justification>
  </clause>

  <clause id="12187">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,8500,a(flip),b,12184,a),flip(a)].">
      <j1 rule="hyper" parents="347 8500 12184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12188">
    <literal><![CDATA[
      L(x,L(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(12184(a,2),8502(a,1))].">
      <j1 rule="para" parents="12184 8502"/>
    </justification>
  </clause>

  <clause id="12189">
    <literal><![CDATA[
      L(x,y \ z,x) = L(x,y * z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3613,a(flip),b,12187,a),flip(a)].">
      <j1 rule="hyper" parents="63 3613 12187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12190">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,x) = L(x,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(1787(a,2),12187(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1787 12187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12191">
    <literal><![CDATA[
      L(T(x,y),z,T(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(x,y),L(z,w,v5),x) = u
    ]]></literal>
    <justification jstring="[para(12187(a,1),7257(a,1))].">
      <j1 rule="para" parents="12187 7257"/>
    </justification>
  </clause>

  <clause id="12192">
    <literal><![CDATA[
      L(x,y \ (y \ z),x) = L(x,z,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),12189(a,2,2))].">
      <j1 rule="para" parents="10 12189"/>
    </justification>
  </clause>

  <clause id="12193">
    <literal><![CDATA[
      L(x,x * y,x) \ y = y / T(x,y)
    ]]></literal>
    <justification jstring="[para(12189(a,1),4485(a,1,1))].">
      <j1 rule="para" parents="12189 4485"/>
    </justification>
  </clause>

  <clause id="12194">
    <literal><![CDATA[
      ((x \ y) * z) * K(z,(x \ y) * z) = L(z,x * y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(12189(a,1),5056(a,2,1))].">
      <j1 rule="para" parents="12189 5056"/>
    </justification>
  </clause>

  <clause id="12195">
    <literal><![CDATA[
      T(L(x,y,x) * (z \ (z \ y)),x) = (z \ (z \ y)) * x
    ]]></literal>
    <justification jstring="[para(12192(a,1),4368(a,1,1,1))].">
      <j1 rule="para" parents="12192 4368"/>
    </justification>
  </clause>

  <clause id="12196">
    <literal><![CDATA[
      a(x,(y * z) \ u,x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ (y \ u),x) = w
    ]]></literal>
    <justification jstring="[para(329(a,1),12180(a,1,2))].">
      <j1 rule="para" parents="329 12180"/>
    </justification>
  </clause>

  <clause id="12197">
    <literal><![CDATA[
      L(x,y \ (z * u),x) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,(z \ y) \ u,x) = w
    ]]></literal>
    <justification jstring="[para(561(a,1),12188(a,1,2))].">
      <j1 rule="para" parents="561 12188"/>
    </justification>
  </clause>

  <clause id="12198">
    <literal><![CDATA[
      T(a(x,y,x) \ (x \ y),x) = (x \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[para(9981(a,1),12195(a,1,1))].">
      <j1 rule="para" parents="9981 12195"/>
    </justification>
  </clause>

  <clause id="12199">
    <literal><![CDATA[
      T(R(x,y,x) \ y,x) = (x \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[para(10990(a,1),12198(a,1,1))].">
      <j1 rule="para" parents="10990 12198"/>
    </justification>
  </clause>

  <clause id="12200">
    <literal><![CDATA[
      R(x,y,x) \ y = (x \ (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(4852,a,12199,a),flip(a)].">
      <j1 rule="hyper" parents="4852 12199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12201">
    <literal><![CDATA[
      L(x,(y \ z) \ u,x) = L(x,z * (y * u),x)
    ]]></literal>
    <justification jstring="[hyper(12197,a,12189,a)].">
      <j1 rule="hyper" parents="12197 12189"/>
    </justification>
  </clause>

  <clause id="12202">
    <literal><![CDATA[
      L(x,(y \ z) * u,x) = L(x,z * (y * u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12189,a(flip),b,12201,a)].">
      <j1 rule="hyper" parents="63 12189 12201"/>
    </justification>
  </clause>

  <clause id="12203">
    <literal><![CDATA[
      L(T(x,y),L(z,u,w),x) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(12191,a,7230,a)].">
      <j1 rule="hyper" parents="12191 7230"/>
    </justification>
  </clause>

  <clause id="12204">
    <literal><![CDATA[
      L(T(x,y),z \ u,x) = L(T(x,y),z * u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3613,a(flip),b,12203,a),flip(a)].">
      <j1 rule="hyper" parents="63 3613 12203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12205">
    <literal><![CDATA[
      K(x,(y / (z * y)) \ u) = K(x,((y * z) \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12030,a(flip),b,12172,a),flip(a)].">
      <j1 rule="hyper" parents="63 12030 12172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12207">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,((u * z) \ u) \ y) = K(x,y / (u / (z * u)))
    ]]></literal>
    <justification jstring="[para(12205(a,1),8946(a,1,2))].">
      <j1 rule="para" parents="12205 8946"/>
    </justification>
  </clause>

  <clause id="12208">
    <literal><![CDATA[
      T(x,T(y * z,y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(12033(a,2),6114(a,1))].">
      <j1 rule="para" parents="12033 6114"/>
    </justification>
  </clause>

  <clause id="12209">
    <literal><![CDATA[
      K(x,L(T(y,y * z) * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(12048(a,2),11169(a,1))].">
      <j1 rule="para" parents="12048 11169"/>
    </justification>
  </clause>

  <clause id="12210">
    <literal><![CDATA[
      T(x,y \ T(z,z * u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,6100,a(flip),b,12053,a),flip(a)].">
      <j1 rule="hyper" parents="347 6100 12053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12211">
    <literal><![CDATA[
      T(x,y \ T(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(12053(a,2),6114(a,1))].">
      <j1 rule="para" parents="12053 6114"/>
    </justification>
  </clause>

  <clause id="12212">
    <literal><![CDATA[
      T(x,y \ T(z,z \ u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),12210(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 12210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12213">
    <literal><![CDATA[
      T(x,y \ ((z \ u) \ u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(112(a,1),12212(a,1,2,2))].">
      <j1 rule="para" parents="112 12212"/>
    </justification>
  </clause>

  <clause id="12214">
    <literal><![CDATA[
      T(x,y \ T(z,z * u)) = T(x,y \ ((z \ u) \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,12210,a,b,12213,a)].">
      <j1 rule="hyper" parents="347 12210 12213"/>
    </justification>
  </clause>

  <clause id="12215">
    <literal><![CDATA[
      T(x \ T(y,y \ z),x \ T(y,z)) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,762,a(flip),b,12213,a),flip(a)].">
      <j1 rule="hyper" parents="63 762 12213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12216">
    <literal><![CDATA[
      T(x,y \ ((z \ u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(12214(a,1),12211(a,1))].">
      <j1 rule="para" parents="12214 12211"/>
    </justification>
  </clause>

  <clause id="12217">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),z \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(T(z,u),w)) = v5
    ]]></literal>
    <justification jstring="[para(7574(a,2),12216(a,1,2,2))].">
      <j1 rule="para" parents="7574 12216"/>
    </justification>
  </clause>

  <clause id="12218">
    <literal><![CDATA[
      T(x,y * T(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u * z)) = w
    ]]></literal>
    <justification jstring="[para(12081(a,1),10398(a,1))].">
      <j1 rule="para" parents="12081 10398"/>
    </justification>
  </clause>

  <clause id="12219">
    <literal><![CDATA[
      L(K(x,y),z,z \ 1) = L(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(12087,a,10733,a),flip(a)].">
      <j1 rule="hyper" parents="12087 10733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12220">
    <literal><![CDATA[
      L(K(x,y),z,z \ x) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(11166,a,12219,a),flip(a)].">
      <j1 rule="hyper" parents="11166 12219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12221">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) = K(x,L(y,z,z \ x))
    ]]></literal>
    <justification jstring="[hyper(11166,a,12220,a),flip(a)].">
      <j1 rule="hyper" parents="11166 12220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12222">
    <literal><![CDATA[
      K(x,L(y,z \ x,(z \ x) \ 1)) = K(x,L(y,z \ x,z))
    ]]></literal>
    <justification jstring="[para(10151(a,1),12221(a,2,2))].">
      <j1 rule="para" parents="10151 12221"/>
    </justification>
  </clause>

  <clause id="12223">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),y \ x,y)) = K((((y \ x) \ 1) * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11310,a(flip),b,12222,a),flip(a)].">
      <j1 rule="hyper" parents="63 11310 12222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12224">
    <literal><![CDATA[
      T(x,y \ T(z \ u,z)) = T(x,y \ (T(z,u) \ u))
    ]]></literal>
    <justification jstring="[para(7571(a,1),12096(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7571 12096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12225">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) = L(x,y \ u,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,9983,a(flip),b,12123,a),flip(a)].">
      <j1 rule="hyper" parents="347 9983 12123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12226">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,((1 / z) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(347,a,12001,a(flip),b,12137,a),flip(a)].">
      <j1 rule="hyper" parents="347 12001 12137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12227">
    <literal><![CDATA[
      K(x,((1 / y) * (y * z)) / u) = K(x,((z * y) * (1 / y)) / u)
    ]]></literal>
    <justification jstring="[para(2519(a,1),12226(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2519 12226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12228">
    <literal><![CDATA[
      L(x,y,(z \ (u \ a(w,v5,w))) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z \ (u \ 1)) * v6) = v7
    ]]></literal>
    <justification jstring="[para(12143(a,1),11419(a,1,3))].">
      <j1 rule="para" parents="12143 11419"/>
    </justification>
  </clause>

  <clause id="12229">
    <literal><![CDATA[
      (((x \ y) * x) / x) \ z = K(y,x) * ((T(x,y) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(11522(a,1),12173(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11522 12173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12230">
    <literal><![CDATA[
      K(x,y) * ((T(y,x) \ x) \ z) = (y \ x) \ z
    ]]></literal>
    <justification jstring="[hyper(371,a,12229,a),flip(a)].">
      <j1 rule="hyper" parents="371 12229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12232">
    <literal><![CDATA[
      K(x,((y * z) * (1 / z)) / u) = K(x,L(y,z,z \ 1) / u)
    ]]></literal>
    <justification jstring="[para(2939(a,1),12227(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2939 12227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12233">
    <literal><![CDATA[
      K(x,((y * z) * (z \ 1)) / u) = K(x,L(y,z,z \ 1) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5593,a(flip),b,12232,a)].">
      <j1 rule="hyper" parents="63 5593 12232"/>
    </justification>
  </clause>

  <clause id="12234">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * u) * z),x) = L(x,R(u,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11818,a(flip),b,11815,a),flip(a)].">
      <j1 rule="hyper" parents="63 11818 11815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12236">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,z \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12225,a(flip),b,12234,a),flip(a)].">
      <j1 rule="hyper" parents="63 12225 12234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12238">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),12236(a,2,2))].">
      <j1 rule="para" parents="9 12236"/>
    </justification>
  </clause>

  <clause id="12239">
    <literal><![CDATA[
      K(x * T(y,z),T(x,u)) = K(x * y,T(T(x,u),z))
    ]]></literal>
    <justification jstring="[hyper(9759,a,11820,a)].">
      <j1 rule="hyper" parents="9759 11820"/>
    </justification>
  </clause>

  <clause id="12240">
    <literal><![CDATA[
      K(x * T(y,z),T(x,u)) = T(K(x * y,T(x,u)),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7091,a(flip),b,12239,a),flip(a)].">
      <j1 rule="hyper" parents="347 7091 12239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12242">
    <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(8805(a,2),12240(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8805 12240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12243">
    <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(7899(a,2),12242(a,1,1,1))].">
      <j1 rule="para" parents="7899 12242"/>
    </justification>
  </clause>

  <clause id="12244">
    <literal><![CDATA[
      ((x * y) * (z * a(u,w,u))) / ((y * z) * a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(11840(a,1),11860(a,1,1))].">
      <j1 rule="para" parents="11840 11860"/>
    </justification>
  </clause>

  <clause id="12245">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * a(u,w,u)))) = L(z,y,x) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(11840(a,1),12142(a,1,2,2))].">
      <j1 rule="para" parents="11840 12142"/>
    </justification>
  </clause>

  <clause id="12246">
    <literal><![CDATA[
      ((x \ y) * x) * K(x,(x \ y) * x) = a(x,x * y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,9981,a(flip),b,12194,a),flip(a)].">
      <j1 rule="hyper" parents="347 9981 12194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12247">
    <literal><![CDATA[
      ((x \ y) * x) * K(x,x * (x \ y)) = a(x,x * y,x) \ y
    ]]></literal>
    <justification jstring="[para(5297(a,1),12246(a,1,2))].">
      <j1 rule="para" parents="5297 12246"/>
    </justification>
  </clause>

  <clause id="12248">
    <literal><![CDATA[
      ((x \ y) * x) * K(x,y) = a(x,x * y,x) \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),12247(a,1,2,2))].">
      <j1 rule="para" parents="10 12247"/>
    </justification>
  </clause>

  <clause id="12249">
    <literal><![CDATA[
      a(x,x * y,x) \ y = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(5973,a,12248,a),flip(a)].">
      <j1 rule="hyper" parents="5973 12248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12250">
    <literal><![CDATA[
      ((x * y) * (z * a(u,w,u))) / (y * (z * a(u,w,u))) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(11840(a,1),12244(a,1,2))].">
      <j1 rule="para" parents="11840 12244"/>
    </justification>
  </clause>

  <clause id="12251">
    <literal><![CDATA[
      L(x * a(y,z,y),u,w) = L(x,u,w) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(545,a,12245,a)].">
      <j1 rule="hyper" parents="545 12245"/>
    </justification>
  </clause>

  <clause id="12252">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) = a(x,y,x) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(3303,a,12251,a),flip(a)].">
      <j1 rule="hyper" parents="3303 12251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12253">
    <literal><![CDATA[
      L(a(x,y,x) * z,u,w) = a(x,y,x) * L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(35,a,3376,a(flip),b,12251,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 3376 12251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12254">
    <literal><![CDATA[
      1 / L(a(x,y,x) \ z,u,w) = a(x,y,x) / L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(220,a,12252,a,b,11849,a)].">
      <j1 rule="hyper" parents="220 12252 11849"/>
    </justification>
  </clause>

  <clause id="12255">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) * v5 = L(z,u,w) * (a(x,y,x) \ v5)
    ]]></literal>
    <justification jstring="[para(12252(a,2),11883(a,1,1))].">
      <j1 rule="para" parents="12252 11883"/>
    </justification>
  </clause>

  <clause id="12256">
    <literal><![CDATA[
      (x * x) * L(a(x,x,x) \ y,z,u) = ((1 / x) \ x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(12252(a,2),12110(a,1,2))].">
      <j1 rule="para" parents="12252 12110"/>
    </justification>
  </clause>

  <clause id="12257">
    <literal><![CDATA[
      x * L(a(x,y,x) * z,u,w) = R(x,y,x) * L(z,u,w)
    ]]></literal>
    <justification jstring="[para(12253(a,2),10989(a,1,2))].">
      <j1 rule="para" parents="12253 10989"/>
    </justification>
  </clause>

  <clause id="12258">
    <literal><![CDATA[
      R(x,y,x) * L(R(x,y,x) \ z,u,w) = x * L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(10988(a,1),12257(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10988 12257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12259">
    <literal><![CDATA[
      L(x \ a(y,z,y),u,w) * (a(y,z,y) \ v5) = L(x \ 1,u,w) * v5
    ]]></literal>
    <justification jstring="[para(11845(a,1),12255(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11845 12255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12260">
    <literal><![CDATA[
      L(x \ y,z,u) * (a(y,w,y) \ v5) = L(x \ L(y,w,y),z,u) * v5
    ]]></literal>
    <justification jstring="[para(11891(a,1),12255(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11891 12255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12261">
    <literal><![CDATA[
      R(x,y,z * a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(595,a,12250,a)].">
      <j1 rule="hyper" parents="595 12250"/>
    </justification>
  </clause>

  <clause id="12262">
    <literal><![CDATA[
      R(R(x,y,z),u,a(w,v5,w)) = R(x,y,z * a(v6,v7,v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,11856,a,b,12261,a)].">
      <j1 rule="hyper" parents="347 11856 12261"/>
    </justification>
  </clause>

  <clause id="12263">
    <literal><![CDATA[
      R(x,y,a(z,u,z) \ w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[para(9964(a,1),12261(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9964 12261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12264">
    <literal><![CDATA[
      R(x,y,z \ a(u,w,u)) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(11842(a,1),12261(a,1,3))].">
      <j1 rule="para" parents="11842 12261"/>
    </justification>
  </clause>

  <clause id="12265">
    <literal><![CDATA[
      R(x,y,z \ L(u,w,u)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(11891(a,1),12263(a,1,3))].">
      <j1 rule="para" parents="11891 12263"/>
    </justification>
  </clause>

  <clause id="12266">
    <literal><![CDATA[
      R(x,y,z \ a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,2190,a(flip),b,12264,a),flip(a)].">
      <j1 rule="hyper" parents="347 2190 12264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12267">
    <literal><![CDATA[
      R(x,y,z \ ((u \ w) \ w)) = R(x,y,z \ T(u,w))
    ]]></literal>
    <justification jstring="[para(11607(a,1),12265(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="11607 12265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12268">
    <literal><![CDATA[
      R(x,y,z * a(u,w,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(12262(a,1),601(a,1))].">
      <j1 rule="para" parents="12262 601"/>
    </justification>
  </clause>

  <clause id="12269">
    <literal><![CDATA[
      R(x,y,T(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(10326(a,1),12268(a,1,3))].">
      <j1 rule="para" parents="10326 12268"/>
    </justification>
  </clause>

  <clause id="12270">
    <literal><![CDATA[
      L((x * x) * (a(x,x,x) \ y),z,u) = ((1 / x) \ x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(3182,a,12256,a)].">
      <j1 rule="hyper" parents="3182 12256"/>
    </justification>
  </clause>

  <clause id="12271">
    <literal><![CDATA[
      L(((1 / x) \ x) * y,z,u) = ((1 / x) \ x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(12110(a,1),12270(a,1,1))].">
      <j1 rule="para" parents="12110 12270"/>
    </justification>
  </clause>

  <clause id="12272">
    <literal><![CDATA[
      L((1 / x) \ x,y,z) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(35,a,1393,a,b,12271,a(flip))].">
      <j1 rule="hyper" parents="35 1393 12271"/>
    </justification>
  </clause>

  <clause id="12273">
    <literal><![CDATA[
      (x \ 1) * ((1 / y) \ y) = x \ ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[hyper(128,a,12272,a(flip),b,3197,a),flip(a)].">
      <j1 rule="hyper" parents="128 12272 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12274">
    <literal><![CDATA[
      T(x,y / z) \ (T(z \ T(y,z),x) \ u) = x \ ((T(z,y) \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4281(a,2),12076(a,2,2,1))].">
      <j1 rule="para" parents="4281 12076"/>
    </justification>
  </clause>

  <clause id="12275">
    <literal><![CDATA[
      K(x,y / (z / (u * z))) = K(x,y / ((z * u) \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9339,a(flip),b,12207,a),flip(a)].">
      <j1 rule="hyper" parents="63 9339 12207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12276">
    <literal><![CDATA[
      R(a(x,y,x) / L(z \ a(x,y,x),u,w),L(z \ a(x,y,x),u,w),a(x,y,x)) = 1 / (L(z \ 1,u,w) * 1)
    ]]></literal>
    <justification jstring="[hyper(220,a,12259,a(flip),b,2196,a),flip(a)].">
      <j1 rule="hyper" parents="220 12259 2196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12277">
    <literal><![CDATA[
      x \ ((T(y,z) \ z) \ u) = x \ ((y \ T(z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12076,a(flip),b,12274,a),flip(a)].">
      <j1 rule="hyper" parents="63 12076 12274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12278">
    <literal><![CDATA[
      x * L(a(x,y,x) \ (x \ a(x,y,x)),z,u) = L(x \ L(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(12252(a,2),11907(a,1,2))].">
      <j1 rule="para" parents="12252 11907"/>
    </justification>
  </clause>

  <clause id="12279">
    <literal><![CDATA[
      K(x \ (y * T(z * u,z)),w) = K(x \ (y * (u * z)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11115,a(flip),b,12052,a),flip(a)].">
      <j1 rule="hyper" parents="63 11115 12052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12280">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,x) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(11845(a,1),12278(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11845 12278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12281">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,3343,a(flip),b,12280,a),flip(a)].">
      <j1 rule="hyper" parents="347 3343 12280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12283">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,L(x,w,v5)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11240,a,b,12281,a)].">
      <j1 rule="hyper" parents="63 11240 12281"/>
    </justification>
  </clause>

  <clause id="12284">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ L(x \ L(x,y,z),u,w) = x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,3654,a(flip),b,12281,a),flip(a)].">
      <j1 rule="hyper" parents="63 3654 12281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12285">
    <literal><![CDATA[
      a(x,y,x \ L(x,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,12281,a)].">
      <j1 rule="hyper" parents="53 12281"/>
    </justification>
  </clause>

  <clause id="12286">
    <literal><![CDATA[
      x * ((x \ y) * (x \ L(x,z,u))) = y * (x \ L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,12281,a(flip),b,98,a),flip(a)].">
      <j1 rule="hyper" parents="134 12281 98"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12287">
    <literal><![CDATA[
      (x * y) * (x \ L(x,z,u)) = x * (y * (x \ L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(134,a,12281,a(flip),b,4048,a(flip))].">
      <j1 rule="hyper" parents="134 12281 4048"/>
    </justification>
  </clause>

  <clause id="12288">
    <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(12281(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12281 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12289">
    <literal><![CDATA[
      (x * y) * (x \ L(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * (x \ L(x,z,u))) = w
    ]]></literal>
    <justification jstring="[para(12281(a,1),322(a,1,2))].">
      <j1 rule="para" parents="12281 322"/>
    </justification>
  </clause>

  <clause id="12290">
    <literal><![CDATA[
      R(x,y,z \ L(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z * L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(12281(a,1),2290(a,1,3))].">
      <j1 rule="para" parents="12281 2290"/>
    </justification>
  </clause>

  <clause id="12291">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ 1,u,x) = ((x \ L(x,y,z)) \ 1) * ((x \ L(x,y,z)) \ (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(12281(a,1),3347(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12281 3347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12292">
    <literal><![CDATA[
      a(x \ y,z,(1 / (y \ x)) \ (x \ y)) = 1
    ]]></literal>
    <justification jstring="[para(3533(a,1),12285(a,1,3))].">
      <j1 rule="para" parents="3533 12285"/>
    </justification>
  </clause>

  <clause id="12293">
    <literal><![CDATA[
      a(x \ y,z,(x \ y) * (y \ x)) = 1
    ]]></literal>
    <justification jstring="[para(1636(a,1),12292(a,1,3))].">
      <j1 rule="para" parents="1636 12292"/>
    </justification>
  </clause>

  <clause id="12295">
    <literal><![CDATA[
      (L(x,y,z) * u) / (x \ L(x,w,v5)) = L(x,y,z) * (u / (x \ L(x,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(220,a,12283,a(flip),b,9645,a(flip))].">
      <j1 rule="hyper" parents="220 12283 9645"/>
    </justification>
  </clause>

  <clause id="12296">
    <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(34,a,3358,a,b,12286,a),flip(a)].">
      <j1 rule="hyper" parents="34 3358 12286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12297">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (x \ L(x,y,z))) \ (x \ u) = (L(x,y,z) * (x \ L(x,y,z))) \ u
    ]]></literal>
    <justification jstring="[para(12286(a,1),459(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12286 459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12298">
    <literal><![CDATA[
      L(x,y * (L(z,u,w) * (z \ L(z,u,w))),v5) = L(x,y * z,v5)
    ]]></literal>
    <justification jstring="[para(12286(a,1),3187(a,1,2,2))].">
      <j1 rule="para" parents="12286 3187"/>
    </justification>
  </clause>

  <clause id="12299">
    <literal><![CDATA[
      R(x,y,x \ L(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(2387,a,12287,a)].">
      <j1 rule="hyper" parents="2387 12287"/>
    </justification>
  </clause>

  <clause id="12300">
    <literal><![CDATA[
      R(x * y,z,y * (T(x,y) * (x * y))) = x * y
    ]]></literal>
    <justification jstring="[hyper(63,a,10189,a(flip),b,12299,a)].">
      <j1 rule="hyper" parents="63 10189 12299"/>
    </justification>
  </clause>

  <clause id="12301">
    <literal><![CDATA[
      L((x * y) \ ((x * (y * z)) / z),u,z) = L(z \ L(z,y,x),z,x * y)
    ]]></literal>
    <justification jstring="[para(3970(a,1),12288(a,1,1))].">
      <j1 rule="para" parents="3970 12288"/>
    </justification>
  </clause>

  <clause id="12302">
    <literal><![CDATA[
      R(x,y,(1 / z) * (u \ (u / z))) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z * L(z,z,u)) = w
    ]]></literal>
    <justification jstring="[para(3982(a,1),12290(a,1))].">
      <j1 rule="para" parents="3982 12290"/>
    </justification>
  </clause>

  <clause id="12303">
    <literal><![CDATA[
      x * (y / ((z \ L(z,u,w)) * (z \ L(z,u,w)))) = (x * y) / (L(z,u,w) * L(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(12296(a,1),464(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12296 464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12304">
    <literal><![CDATA[
      T(x,L(y,z,u) * L(y \ 1,z,u)) * (((y \ L(y,z,u)) * (y \ L(y,z,u))) \ w) = (((y \ L(y,z,u)) * (y \ L(y,z,u))) \ x) * w
    ]]></literal>
    <justification jstring="[para(12296(a,1),829(a,1,1,2))].">
      <j1 rule="para" parents="12296 829"/>
    </justification>
  </clause>

  <clause id="12305">
    <literal><![CDATA[
      ((((L(x,y,z) \ x) \ 1) \ 1) * (L(x,y,z) \ x)) * u = (L(x,y,z) * L(x \ 1,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(12296(a,1),11346(a,2,1))].">
      <j1 rule="para" parents="12296 11346"/>
    </justification>
  </clause>

  <clause id="12306">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,z * y) != u
    ]]></literal>
    <literal><![CDATA[
      (z * y) \ ((z * (y * x)) / x) = u
    ]]></literal>
    <justification jstring="[para(12301(a,1),550(a,1))].">
      <j1 rule="para" parents="12301 550"/>
    </justification>
  </clause>

  <clause id="12307">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) / z) = u
    ]]></literal>
    <justification jstring="[para(574(a,1),12306(a,1))].">
      <j1 rule="para" parents="574 12306"/>
    </justification>
  </clause>

  <clause id="12308">
    <literal><![CDATA[
      T(L(x,y,z) * (u / (x \ L(x,w,v5))),x \ L(x,w,v5)) = (x \ L(x,w,v5)) \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(12295(a,1),113(a,1,1))].">
      <j1 rule="para" parents="12295 113"/>
    </justification>
  </clause>

  <clause id="12309">
    <literal><![CDATA[
      L(1 / (a(x,y,x) / z),u,w) \ 1 = a(x,y,x) / L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(11851,a,12254,a)].">
      <j1 rule="hyper" parents="11851 12254"/>
    </justification>
  </clause>

  <clause id="12311">
    <literal><![CDATA[
      K((((x \ y) \ 1) * (x \ 1)) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11158,a(flip),b,12223,a),flip(a)].">
      <j1 rule="hyper" parents="63 11158 12223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12312">
    <literal><![CDATA[
      K(((((x \ 1) \ y) \ 1) * x) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(3929,a,12311,a)].">
      <j1 rule="hyper" parents="3929 12311"/>
    </justification>
  </clause>

  <clause id="12314">
    <literal><![CDATA[
      K(x,y) / (z \ T(x,y)) = 1 / (z \ x)
    ]]></literal>
    <justification jstring="[para(12311(a,1),8198(a,1,1))].">
      <j1 rule="para" parents="12311 8198"/>
    </justification>
  </clause>

  <clause id="12315">
    <literal><![CDATA[
      (1 / (x \ y)) \ K(y,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(214,a,12314,a)].">
      <j1 rule="hyper" parents="214 12314"/>
    </justification>
  </clause>

  <clause id="12316">
    <literal><![CDATA[
      (1 / (x \ y)) * (x \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(148,a,12314,a)].">
      <j1 rule="hyper" parents="148 12314"/>
    </justification>
  </clause>

  <clause id="12317">
    <literal><![CDATA[
      (1 / (x \ y)) \ K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(12314(a,1),359(a,1,1))].">
      <j1 rule="para" parents="12314 359"/>
    </justification>
  </clause>

  <clause id="12319">
    <literal><![CDATA[
      (1 / x) \ K(y,z) = (y / x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),12315(a,1,1,2))].">
      <j1 rule="para" parents="83 12315"/>
    </justification>
  </clause>

  <clause id="12320">
    <literal><![CDATA[
      (1 / x) * ((y / x) \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),12316(a,1,1,2))].">
      <j1 rule="para" parents="83 12316"/>
    </justification>
  </clause>

  <clause id="12321">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = K(x,y) / z
    ]]></literal>
    <justification jstring="[para(12312(a,1),6689(a,2,1))].">
      <j1 rule="para" parents="12312 6689"/>
    </justification>
  </clause>

  <clause id="12322">
    <literal><![CDATA[
      (K(x,y) / z) \ T(x,y) = (1 / z) \ x
    ]]></literal>
    <justification jstring="[hyper(214,a,12321,a)].">
      <j1 rule="hyper" parents="214 12321"/>
    </justification>
  </clause>

  <clause id="12324">
    <literal><![CDATA[
      (1 / (x \ K(y,z))) \ y = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(646,a,12322,a),flip(a)].">
      <j1 rule="hyper" parents="646 12322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12326">
    <literal><![CDATA[
      L(x,R(y \ R(y,z,u),y,z * u),x) = L(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(14(a,2),11814(a,2,2))].">
      <j1 rule="para" parents="14 11814"/>
    </justification>
  </clause>

  <clause id="12327">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),x) = L(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12238,a(flip),b,12326,a)].">
      <j1 rule="hyper" parents="63 12238 12326"/>
    </justification>
  </clause>

  <clause id="12329">
    <literal><![CDATA[
      ((x * y) * (a(z,u,z) \ w)) / (y * (a(z,u,z) \ w)) = R(x,a(z,u,z) \ y,w)
    ]]></literal>
    <justification jstring="[para(11915(a,1),11910(a,1,1))].">
      <j1 rule="para" parents="11915 11910"/>
    </justification>
  </clause>

  <clause id="12330">
    <literal><![CDATA[
      R(x,a(y,z,y) \ u,w) = R(x,u,a(y,z,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(595,a,12329,a),flip(a)].">
      <j1 rule="hyper" parents="595 12329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12331">
    <literal><![CDATA[
      R(x,a(y,z,y) \ u,w) = R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,12263,a(flip),b,12330,a),flip(a)].">
      <j1 rule="hyper" parents="347 12263 12330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12333">
    <literal><![CDATA[
      R(x,a(y,z,y) * u,w) = R(x,u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),12331(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 12331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12334">
    <literal><![CDATA[
      R(x,y * a(z,u,z),w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[para(9960(a,1),12331(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9960 12331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12335">
    <literal><![CDATA[
      R(x,y,z) * ((a(u,w,u) * y) * z) = (x * (a(u,w,u) * y)) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,12333,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="133 12333 20"/>
    </justification>
  </clause>

  <clause id="12336">
    <literal><![CDATA[
      R(x,T(y * z,y),u) = R(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(10327(a,1),12333(a,1,2))].">
      <j1 rule="para" parents="10327 12333"/>
    </justification>
  </clause>

  <clause id="12337">
    <literal><![CDATA[
      R(x,(R(y,z,y) \ u) \ w,v5) = R(x,(y \ u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(11895(a,1),12334(a,1,2))].">
      <j1 rule="para" parents="11895 12334"/>
    </justification>
  </clause>

  <clause id="12338">
    <literal><![CDATA[
      R(x,(y \ z) * y,u) = R(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12336(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 12336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12339">
    <literal><![CDATA[
      R(x,(y * ((z * y) \ y)) \ u,w) = R(x,(z \ y) \ u,w)
    ]]></literal>
    <justification jstring="[para(11739(a,1),12337(a,1,2,1))].">
      <j1 rule="para" parents="11739 12337"/>
    </justification>
  </clause>

  <clause id="12340">
    <literal><![CDATA[
      R(x,(((y \ z) / z) * ((y \ R(y,y,z)) \ ((y \ z) / z))) \ u,w) = R(x,(y \ ((y \ z) / z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(2377(a,2),12339(a,1,2,1,2,1))].">
      <j1 rule="para" parents="2377 12339"/>
    </justification>
  </clause>

  <clause id="12341">
    <literal><![CDATA[
      R(x,((y \ (y / z)) * (z \ 1)) \ u,w) = R(x,(z \ (y \ (y / z))) \ u,w)
    ]]></literal>
    <justification jstring="[para(6628(a,1),12339(a,1,2,1,2))].">
      <j1 rule="para" parents="6628 12339"/>
    </justification>
  </clause>

  <clause id="12342">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) * w != v5 * ((a(y,z,y) * u) * w)
    ]]></literal>
    <literal><![CDATA[
      R(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(12335(a,1),44(a,1))].">
      <j1 rule="para" parents="12335 44"/>
    </justification>
  </clause>

  <clause id="12343">
    <literal><![CDATA[
      (x * (y * (a(z,u,z) \ w))) \ ((x * y) * (a(z,u,z) \ w)) = a(x,a(z,u,z) \ y,w)
    ]]></literal>
    <justification jstring="[para(11915(a,1),11911(a,1,2))].">
      <j1 rule="para" parents="11915 11911"/>
    </justification>
  </clause>

  <clause id="12344">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) \ (x \ u) = (L(x,y,z) * (x \ L(x,y,z))) \ u
    ]]></literal>
    <justification jstring="[para(12296(a,1),12297(a,1,1))].">
      <j1 rule="para" parents="12296 12297"/>
    </justification>
  </clause>

  <clause id="12345">
    <literal><![CDATA[
      a(x,a(y,z,y) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,a(y,z,y) \ w) = v5
    ]]></literal>
    <justification jstring="[para(12343(a,1),836(a,1))].">
      <j1 rule="para" parents="12343 836"/>
    </justification>
  </clause>

  <clause id="12346">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * ((x \ L(x,y,z)) \ 1) = x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(1301,a,12284,a)].">
      <j1 rule="hyper" parents="1301 12284"/>
    </justification>
  </clause>

  <clause id="12347">
    <literal><![CDATA[
      (x * y) / (L(z,u,w) * L(z \ 1,u,w)) = x * (y / (L(z,u,w) * L(z \ 1,u,w)))
    ]]></literal>
    <justification jstring="[para(12296(a,1),12303(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12296 12303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12348">
    <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(10900(a,1),12305(a,1,1,1))].">
      <j1 rule="para" parents="10900 12305"/>
    </justification>
  </clause>

  <clause id="12349">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) \ u != w * u
    ]]></literal>
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x,y,z) \ x) = w
    ]]></literal>
    <justification jstring="[para(12348(a,1),44(a,1))].">
      <j1 rule="para" parents="12348 44"/>
    </justification>
  </clause>

  <clause id="12350">
    <literal><![CDATA[
      (x * (L(x,y,z) \ (L(x,y,z) \ x))) * u = (L(x,y,z) * L(x \ 1,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(10928(a,1),12348(a,1,1))].">
      <j1 rule="para" parents="10928 12348"/>
    </justification>
  </clause>

  <clause id="12351">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ 1,u,x) = (L(x,y,z) \ x) * ((x \ L(x,y,z)) \ (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(10882(a,1),12291(a,2,1))].">
      <j1 rule="para" parents="10882 12291"/>
    </justification>
  </clause>

  <clause id="12352">
    <literal><![CDATA[
      L((x \ L(x,y,z)) \ 1,u,x) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(347,a,188,a(flip),b,12351,a),flip(a)].">
      <j1 rule="hyper" parents="347 188 12351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12354">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,x) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(10882(a,1),12352(a,1,1))].">
      <j1 rule="para" parents="10882 12352"/>
    </justification>
  </clause>

  <clause id="12356">
    <literal><![CDATA[
      L(L(x,y,z) \ x,L(x,y,z),z * y) = L((z * (y * x)) \ ((z * y) * x),u,x)
    ]]></literal>
    <justification jstring="[para(12354(a,1),1188(a,1,1))].">
      <j1 rule="para" parents="12354 1188"/>
    </justification>
  </clause>

  <clause id="12358">
    <literal><![CDATA[
      L((x * (y * z)) \ ((x * y) * z),u,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1788,a,12356,a),flip(a)].">
      <j1 rule="hyper" parents="1788 12356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12359">
    <literal><![CDATA[
      L(a(x,y,z),u,z) = L(L(z,y,x) \ z,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(14(a,2),12356(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14 12356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12360">
    <literal><![CDATA[
      L(a(x,y,z),u,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(14(a,2),12358(a,1,1))].">
      <j1 rule="para" parents="14 12358"/>
    </justification>
  </clause>

  <clause id="12361">
    <literal><![CDATA[
      a(x,y,a(z,u,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,12360,a)].">
      <j1 rule="hyper" parents="53 12360"/>
    </justification>
  </clause>

  <clause id="12362">
    <literal><![CDATA[
      (x * y) * a(z,u,x) = x * (y * a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(134,a,12360,a(flip),b,4048,a(flip))].">
      <j1 rule="hyper" parents="134 12360 4048"/>
    </justification>
  </clause>

  <clause id="12363">
    <literal><![CDATA[
      x \ (y * a(z,u,x)) = (x \ y) * a(z,u,x)
    ]]></literal>
    <justification jstring="[para(12360(a,1),538(a,1,2,2))].">
      <j1 rule="para" parents="12360 538"/>
    </justification>
  </clause>

  <clause id="12364">
    <literal><![CDATA[
      R(x,y,a(z,u,x)) = x
    ]]></literal>
    <justification jstring="[hyper(12342,a,12362,a)].">
      <j1 rule="hyper" parents="12342 12362"/>
    </justification>
  </clause>

  <clause id="12365">
    <literal><![CDATA[
      (L(x,y,z) * u) * a(w,v5,x) = L(x,y,z) * (u * a(w,v5,x))
    ]]></literal>
    <justification jstring="[para(12364(a,1),471(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12364 471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12367">
    <literal><![CDATA[
      x \ y != (x \ z) * a(u,w,x)
    ]]></literal>
    <literal><![CDATA[
      z * a(u,w,x) = y
    ]]></literal>
    <justification jstring="[para(12363(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="12363 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12368">
    <literal><![CDATA[
      L(a(x,y,z),u,z) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(12359(a,2),1788(a,1))].">
      <j1 rule="para" parents="12359 1788"/>
    </justification>
  </clause>

  <clause id="12369">
    <literal><![CDATA[
      L(a(x,y,z),u,L(z,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3558,a,12365,a)].">
      <j1 rule="hyper" parents="3558 12365"/>
    </justification>
  </clause>

  <clause id="12370">
    <literal><![CDATA[
      L(x,y,z) \ (u * a(w,v5,x)) = (L(x,y,z) \ u) * a(w,v5,x)
    ]]></literal>
    <justification jstring="[hyper(705,a,12365,a)].">
      <j1 rule="hyper" parents="705 12365"/>
    </justification>
  </clause>

  <clause id="12372">
    <literal><![CDATA[
      (L(x,y,z) \ x) * a(u,w,x) = x * (L(x,y,z) \ a(u,w,x))
    ]]></literal>
    <justification jstring="[hyper(1429,a,12370,a),flip(a)].">
      <j1 rule="hyper" parents="1429 12370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12373">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) \ (x * (a(y,z,y) * (u * w))) = L(w,L(u,a(y,z,y),x),x * a(y,z,y))
    ]]></literal>
    <justification jstring="[para(11879(a,1),11903(a,1,2))].">
      <j1 rule="para" parents="11879 11903"/>
    </justification>
  </clause>

  <clause id="12374">
    <literal><![CDATA[
      L(x,L(y,a(z,u,z),w),w * a(z,u,z)) = L(x,a(z,u,z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(11382,a,12373,a),flip(a)].">
      <j1 rule="hyper" parents="11382 12373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12375">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = L(x,u,w * a(y,z,y))
    ]]></literal>
    <justification jstring="[para(11898(a,1),12374(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11898 12374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12376">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,11426,a(flip),b,12375,a),flip(a)].">
      <j1 rule="hyper" parents="347 11426 12375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12377">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(12375(a,2),11461(a,1))].">
      <j1 rule="para" parents="12375 11461"/>
    </justification>
  </clause>

  <clause id="12379">
    <literal><![CDATA[
      L(x,R(y,z,y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(8342(a,1),12376(a,1,2))].">
      <j1 rule="para" parents="8342 12376"/>
    </justification>
  </clause>

  <clause id="12380">
    <literal><![CDATA[
      L(x,L(y,z,y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(8497(a,1),12376(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8497 12376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12381">
    <literal><![CDATA[
      L(x,y / L(z,u,z),w) = L(x,y / z,w)
    ]]></literal>
    <justification jstring="[para(9973(a,1),12376(a,1,2))].">
      <j1 rule="para" parents="9973 12376"/>
    </justification>
  </clause>

  <clause id="12382">
    <literal><![CDATA[
      L(x,T(y * z,y),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(10327(a,1),12376(a,1,2))].">
      <j1 rule="para" parents="10327 12376"/>
    </justification>
  </clause>

  <clause id="12383">
    <literal><![CDATA[
      L(x,R(y,z,y) \ u,w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(10988(a,1),12376(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10988 12376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12384">
    <literal><![CDATA[
      L(x,T(y * (z / y),y),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(11003(a,1),12376(a,1,2))].">
      <j1 rule="para" parents="11003 12376"/>
    </justification>
  </clause>

  <clause id="12385">
    <literal><![CDATA[
      L(x,T(y,y \ z),u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4426(a,1),12379(a,1,2))].">
      <j1 rule="para" parents="4426 12379"/>
    </justification>
  </clause>

  <clause id="12386">
    <literal><![CDATA[
      L(x,(y \ z) \ z,u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(6798(a,1),12379(a,1,2))].">
      <j1 rule="para" parents="6798 12379"/>
    </justification>
  </clause>

  <clause id="12387">
    <literal><![CDATA[
      (x * L(y,z,y)) * L(u,y,x) = x * (L(y,z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(134,a,12380,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 12380 18"/>
    </justification>
  </clause>

  <clause id="12388">
    <literal><![CDATA[
      L(x,y \ (y * z),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(552(a,1),12380(a,1,2))].">
      <j1 rule="para" parents="552 12380"/>
    </justification>
  </clause>

  <clause id="12390">
    <literal><![CDATA[
      L(x,y * z,z) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(10231,a,12382,a),flip(a)].">
      <j1 rule="hyper" parents="10231 12382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12391">
    <literal><![CDATA[
      L(x,y * (z / T(y,z)),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(4297(a,1),12384(a,1,2))].">
      <j1 rule="para" parents="4297 12384"/>
    </justification>
  </clause>

  <clause id="12392">
    <literal><![CDATA[
      L(x,T(y,z),T((y / z) \ 1,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(y / z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(12385(a,1),4799(a,1))].">
      <j1 rule="para" parents="12385 4799"/>
    </justification>
  </clause>

  <clause id="12393">
    <literal><![CDATA[
      L(x,T(y,z),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,y \ z) = u
    ]]></literal>
    <justification jstring="[para(12385(a,1),10231(a,1))].">
      <j1 rule="para" parents="12385 10231"/>
    </justification>
  </clause>

  <clause id="12394">
    <literal><![CDATA[
      L(x,T(y,z),(z \ y) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z \ y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(12385(a,1),10235(a,1))].">
      <j1 rule="para" parents="12385 10235"/>
    </justification>
  </clause>

  <clause id="12395">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ 1),u) = L(x,T(T(y,z),z \ y),u)
    ]]></literal>
    <justification jstring="[para(12093(a,1),12385(a,1,2))].">
      <j1 rule="para" parents="12093 12385"/>
    </justification>
  </clause>

  <clause id="12396">
    <literal><![CDATA[
      L(x,T(y \ z,z),u) = L(x,z / y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5490,a(flip),b,12386,a),flip(a)].">
      <j1 rule="hyper" parents="63 5490 12386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12397">
    <literal><![CDATA[
      L(x,T((y / T(z,y)) * z,y / T(z,y)),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12382,a,b,12391,a)].">
      <j1 rule="hyper" parents="63 12382 12391"/>
    </justification>
  </clause>

  <clause id="12398">
    <literal><![CDATA[
      L(x,y / z,y) = L(x,z \ y,y)
    ]]></literal>
    <justification jstring="[hyper(10231,a,12396,a),flip(a)].">
      <j1 rule="hyper" parents="10231 12396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12399">
    <literal><![CDATA[
      L(x,(y * z) / y,u) = L(x,y * (z / y),u)
    ]]></literal>
    <justification jstring="[para(530(a,1),12381(a,1,2)),flip(a)].">
      <j1 rule="para" parents="530 12381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12400">
    <literal><![CDATA[
      L(x,(y \ T(z,y \ z)) \ u,w) = L(x,(z / y) \ u,w)
    ]]></literal>
    <justification jstring="[para(4404(a,1),12383(a,1,2,1))].">
      <j1 rule="para" parents="4404 12383"/>
    </justification>
  </clause>

  <clause id="12401">
    <literal><![CDATA[
      L(x,y * ((z * y) \ y),u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(11739(a,1),12383(a,1,2))].">
      <j1 rule="para" parents="11739 12383"/>
    </justification>
  </clause>

  <clause id="12402">
    <literal><![CDATA[
      L(x,K(y,y \ z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,K(y,z) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(9921(a,1),12377(a,1,2))].">
      <j1 rule="para" parents="9921 12377"/>
    </justification>
  </clause>

  <clause id="12403">
    <literal><![CDATA[
      L(x,T(y * z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z * y,u) = w
    ]]></literal>
    <justification jstring="[para(10327(a,1),12377(a,1,2))].">
      <j1 rule="para" parents="10327 12377"/>
    </justification>
  </clause>

  <clause id="12404">
    <literal><![CDATA[
      L(T(x,y) \ z,x,x \ y) = y \ ((T(y,x) / x) * z)
    ]]></literal>
    <justification jstring="[hyper(12393,a,11489,a)].">
      <j1 rule="hyper" parents="12393 11489"/>
    </justification>
  </clause>

  <clause id="12405">
    <literal><![CDATA[
      L(x,T(y,z \ y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z * (y / z),u) = w
    ]]></literal>
    <justification jstring="[para(4412(a,1),12403(a,1,2))].">
      <j1 rule="para" parents="4412 12403"/>
    </justification>
  </clause>

  <clause id="12406">
    <literal><![CDATA[
      (x * L(y,z,y)) * u != x * (L(y,z,y) * w)
    ]]></literal>
    <literal><![CDATA[
      L(w,y,x) = u
    ]]></literal>
    <justification jstring="[para(12387(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="12387 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12407">
    <literal><![CDATA[
      L(x,T(T(y,z),y / T(z,y)),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(4275(a,1),12397(a,1,2,1))].">
      <j1 rule="para" parents="4275 12397"/>
    </justification>
  </clause>

  <clause id="12408">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(11932(a,1),12407(a,1,2))].">
      <j1 rule="para" parents="11932 12407"/>
    </justification>
  </clause>

  <clause id="12409">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ 1),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12395,a,b,12408,a)].">
      <j1 rule="hyper" parents="63 12395 12408"/>
    </justification>
  </clause>

  <clause id="12410">
    <literal><![CDATA[
      L(x,T(y,z),z \ 1) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(10231,a,12409,a)].">
      <j1 rule="hyper" parents="10231 12409"/>
    </justification>
  </clause>

  <clause id="12412">
    <literal><![CDATA[
      L(x,y * (z / y),(y \ z) \ 1) = L(x,z,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(12405,a,12410,a)].">
      <j1 rule="hyper" parents="12405 12410"/>
    </justification>
  </clause>

  <clause id="12413">
    <literal><![CDATA[
      L(x,(x / y) \ z,u) = L(x,(y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11181,a(flip),b,12400,a),flip(a)].">
      <j1 rule="hyper" parents="63 11181 12400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12414">
    <literal><![CDATA[
      a(x,((y * z) * u) \ (y * (z * (u * K(w,w \ 1)))),x) = a(x,K(w,w \ 1) / a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(10660,a,12125,a)].">
      <j1 rule="hyper" parents="10660 12125"/>
    </justification>
  </clause>

  <clause id="12415">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ (z * (u * (y * K(w,w \ 1))))),x) = a(x,K(w,w \ 1) / a(z,u,y),x)
    ]]></literal>
    <justification jstring="[hyper(12196,a,12414,a)].">
      <j1 rule="hyper" parents="12196 12414"/>
    </justification>
  </clause>

  <clause id="12416">
    <literal><![CDATA[
      a(x,y \ L(y * K(z,z \ 1),u,w),x) = a(x,K(z,z \ 1) / a(w,u,y),x)
    ]]></literal>
    <justification jstring="[para(18(a,2),12415(a,1,2,2))].">
      <j1 rule="para" parents="18 12415"/>
    </justification>
  </clause>

  <clause id="12417">
    <literal><![CDATA[
      a(x,(y \ L(y,z,u)) * K(w,w \ 1),x) = a(x,K(w,w \ 1) / a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(2703(a,1),12416(a,1,2))].">
      <j1 rule="para" parents="2703 12416"/>
    </justification>
  </clause>

  <clause id="12418">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),x) = a(x,K(w,w \ 1) / a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(5849,a,12417,a)].">
      <j1 rule="hyper" parents="5849 12417"/>
    </justification>
  </clause>

  <clause id="12419">
    <literal><![CDATA[
      a(x,a(y,z,u) \ K(w,w \ 1),x) = a(x,u \ L(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,11507,a(flip),b,12418,a)].">
      <j1 rule="hyper" parents="347 11507 12418"/>
    </justification>
  </clause>

  <clause id="12420">
    <literal><![CDATA[
      a(x,a(y,z,u) \ 1,x) = a(x,u \ L(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(227(a,1),12419(a,1,2,2))].">
      <j1 rule="para" parents="227 12419"/>
    </justification>
  </clause>

  <clause id="12421">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) * u) * a(u,z \ L(z,y,x),u)) \ ((u * (a(x,y,z) \ 1)) * u) = R(T(u,u * (a(x,y,z) \ 1)),(a(x,y,z) \ 1) * u,a(u,a(x,y,z) \ 1,u))
    ]]></literal>
    <justification jstring="[para(12420(a,1),10540(a,1,1,2))].">
      <j1 rule="para" parents="12420 10540"/>
    </justification>
  </clause>

  <clause id="12422">
    <literal><![CDATA[
      R(x,(((y \ z) / z) * (y \ 1)) \ u,w) = R(x,(y \ ((y \ z) / z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(3720(a,1),12340(a,1,2,1,2))].">
      <j1 rule="para" parents="3720 12340"/>
    </justification>
  </clause>

  <clause id="12424">
    <literal><![CDATA[
      (x * (a(y,z,y) * (u * w))) \ ((x * (a(y,z,y) * u)) * w) = a(x * a(y,z,y),L(u,a(y,z,y),x),w)
    ]]></literal>
    <justification jstring="[para(11879(a,1),11904(a,1,1))].">
      <j1 rule="para" parents="11879 11904"/>
    </justification>
  </clause>

  <clause id="12425">
    <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(11898(a,1),12424(a,2,2))].">
      <j1 rule="para" parents="11898 12424"/>
    </justification>
  </clause>

  <clause id="12426">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,a(y,z,y) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(12425(a,1),11383(a,1))].">
      <j1 rule="para" parents="12425 11383"/>
    </justification>
  </clause>

  <clause id="12427">
    <literal><![CDATA[
      a(x,a(y,z,y) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(12426,a,11571,a)].">
      <j1 rule="hyper" parents="12426 11571"/>
    </justification>
  </clause>

  <clause id="12428">
    <literal><![CDATA[
      a(a(x,y,x) * z,u,w) = a(z,a(v5,v6,v5) * u,w)
    ]]></literal>
    <justification jstring="[hyper(11564,a,12427,a),flip(a)].">
      <j1 rule="hyper" parents="11564 12427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12429">
    <literal><![CDATA[
      a(x,a(y,z,y) \ u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),12427(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 12427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12430">
    <literal><![CDATA[
      a(x,L(y,z,y),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(8497(a,1),12427(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8497 12427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12431">
    <literal><![CDATA[
      a(x,L(L(y,z,y),u,w),v5) = a(x,L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(11870(a,1),12427(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11870 12427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12432">
    <literal><![CDATA[
      a(x,L(a(y,z,y) * u,w,v5),v6) = a(x,L(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(12253(a,2),12427(a,1,2))].">
      <j1 rule="para" parents="12253 12427"/>
    </justification>
  </clause>

  <clause id="12433">
    <literal><![CDATA[
      a(x,y \ (y * z),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(552(a,1),12430(a,1,2))].">
      <j1 rule="para" parents="552 12430"/>
    </justification>
  </clause>

  <clause id="12434">
    <literal><![CDATA[
      a(x,y,a(z,u,z) \ w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(12345,a,12429,a)].">
      <j1 rule="hyper" parents="12345 12429"/>
    </justification>
  </clause>

  <clause id="12435">
    <literal><![CDATA[
      a(x,((y \ 1) * y) \ z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(2795(a,1),12429(a,1,2,1))].">
      <j1 rule="para" parents="2795 12429"/>
    </justification>
  </clause>

  <clause id="12437">
    <literal><![CDATA[
      a(x,y,a(z,u,z) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),12434(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9 12434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12438">
    <literal><![CDATA[
      a(x,y,L(z,u,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(8500(a,1),12434(a,1,3))].">
      <j1 rule="para" parents="8500 12434"/>
    </justification>
  </clause>

  <clause id="12439">
    <literal><![CDATA[
      a(x,y,z * L(u,w,u)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(9974(a,1),12434(a,1,3))].">
      <j1 rule="para" parents="9974 12434"/>
    </justification>
  </clause>

  <clause id="12440">
    <literal><![CDATA[
      a(x,y,R(a(z,u,z) \ w,v5,v6)) = a(x,y,R(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(11537(a,2),12434(a,1,3))].">
      <j1 rule="para" parents="11537 12434"/>
    </justification>
  </clause>

  <clause id="12441">
    <literal><![CDATA[
      a(x,y,L(L(z,u,z),w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(11855(a,1),12434(a,1,3))].">
      <j1 rule="para" parents="11855 12434"/>
    </justification>
  </clause>

  <clause id="12442">
    <literal><![CDATA[
      a(x,y,z \ (a(u,w,u) \ v5)) = a(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(11876(a,1),12434(a,1,3))].">
      <j1 rule="para" parents="11876 12434"/>
    </justification>
  </clause>

  <clause id="12443">
    <literal><![CDATA[
      a(x,y,z \ (z * u)) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(552(a,1),12438(a,1,3))].">
      <j1 rule="para" parents="552 12438"/>
    </justification>
  </clause>

  <clause id="12444">
    <literal><![CDATA[
      a(x,y,T(z * u,z)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(10327(a,1),12437(a,1,3))].">
      <j1 rule="para" parents="10327 12437"/>
    </justification>
  </clause>

  <clause id="12445">
    <literal><![CDATA[
      a(x,y \ ((z * (1 / z)) \ u),w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(10402(a,1),12435(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10402 12435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12448">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),v5,z)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),12441(a,1,3))].">
      <j1 rule="para" parents="30 12441"/>
    </justification>
  </clause>

  <clause id="12449">
    <literal><![CDATA[
      a(x,y,L(z,z,z \ u)) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[para(10204(a,1),12441(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10204 12441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12450">
    <literal><![CDATA[
      a(x,y,L(z,z,z * u)) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[para(10207(a,1),12441(a,1,3))].">
      <j1 rule="para" parents="10207 12441"/>
    </justification>
  </clause>

  <clause id="12451">
    <literal><![CDATA[
      a(x,y,L(L(L(z,u,z),w,v5),v6,v7)) = a(x,y,L(L(z,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(10970(a,1),12441(a,1,3,1))].">
      <j1 rule="para" parents="10970 12441"/>
    </justification>
  </clause>

  <clause id="12452">
    <literal><![CDATA[
      a(x,y,L((a(z,u,z) \ w) * v5,(a(z,u,z) \ w) * v5,L(v5 \ 1,v5,a(z,u,z) \ w))) = a(x,y,((a(z,u,z) \ w) * (((a(z,u,z) \ w) * v5) \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(10163(a,2),12442(a,1,3))].">
      <j1 rule="para" parents="10163 12442"/>
    </justification>
  </clause>

  <clause id="12453">
    <literal><![CDATA[
      a(x,a(y,z,y) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(12428(a,1),11564(a,1))].">
      <j1 rule="para" parents="12428 11564"/>
    </justification>
  </clause>

  <clause id="12454">
    <literal><![CDATA[
      a(x,y,L(L(z,z,z \ u),w,v5)) = a(x,y,L(L(z,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(10204(a,1),12451(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10204 12451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12455">
    <literal><![CDATA[
      R(L(a(x,y,x) / z,u,w) \ a(x,y,x),L(z \ a(x,y,x),u,w),a(x,y,x)) = 1 / (L(z \ 1,u,w) * 1)
    ]]></literal>
    <justification jstring="[para(9697(a,1),12276(a,1,1))].">
      <j1 rule="para" parents="9697 12276"/>
    </justification>
  </clause>

  <clause id="12456">
    <literal><![CDATA[
      L(a(x,y,x) / z,u,w) \ a(x,y,x) = 1 / (L(z \ 1,u,w) * 1)
    ]]></literal>
    <justification jstring="[hyper(11861,a,12455,a)].">
      <j1 rule="hyper" parents="11861 12455"/>
    </justification>
  </clause>

  <clause id="12458">
    <literal><![CDATA[
      L(a(x,y,x) / z,u,w) \ a(x,y,x) = 1 / L(z \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(8(a,1),12456(a,2,2))].">
      <j1 rule="para" parents="8 12456"/>
    </justification>
  </clause>

  <clause id="12459">
    <literal><![CDATA[
      L(a(x,y,x) / z,u,w) \ a(x,y,x) = L(1 / z,u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,9697,a(flip),b,12458,a),flip(a)].">
      <j1 rule="hyper" parents="347 9697 12458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12462">
    <literal><![CDATA[
      T(x,L(y,z,u) * L(y \ 1,z,u)) * ((L(y,z,u) * L(y \ 1,z,u)) \ w) = (((y \ L(y,z,u)) * (y \ L(y,z,u))) \ x) * w
    ]]></literal>
    <justification jstring="[para(12296(a,1),12304(a,1,2,1))].">
      <j1 rule="para" parents="12296 12304"/>
    </justification>
  </clause>

  <clause id="12463">
    <literal><![CDATA[
      T(x,L(y,z,u) * L(y \ 1,z,u)) * ((L(y,z,u) * L(y \ 1,z,u)) \ w) = ((L(y,z,u) * L(y \ 1,z,u)) \ x) * w
    ]]></literal>
    <justification jstring="[para(12296(a,1),12462(a,2,1,1))].">
      <j1 rule="para" parents="12296 12462"/>
    </justification>
  </clause>

  <clause id="12464">
    <literal><![CDATA[
      a(1 / ((x * y) \ x),z,1 / ((x * y) \ x)) * K(T(z,y),1 / ((x * y) \ x)) = K(z * (1 / ((x * y) \ x)),1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(11819(a,1),8368(a,1,1))].">
      <j1 rule="para" parents="11819 8368"/>
    </justification>
  </clause>

  <clause id="12465">
    <literal><![CDATA[
      a(((x * y) \ x) \ 1,z,((x * y) \ x) \ 1) * K(T(z,y),1 / ((x * y) \ x)) = K(z * (1 / ((x * y) \ x)),1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(9534(a,1),12464(a,1,1))].">
      <j1 rule="para" parents="9534 12464"/>
    </justification>
  </clause>

  <clause id="12467">
    <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(9228(a,1),9229(a,2,2,1,1))].">
      <j1 rule="para" parents="9228 9229"/>
    </justification>
  </clause>

  <clause id="12468">
    <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(9226(a,1),12467(a,1,2,1))].">
      <j1 rule="para" parents="9226 12467"/>
    </justification>
  </clause>

  <clause id="12470">
    <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(9226(a,1),12468(a,1,2,2,1,1))].">
      <j1 rule="para" parents="9226 12468"/>
    </justification>
  </clause>

  <clause id="12472">
    <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(12258(a,1),12470(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12258 12470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12473">
    <literal><![CDATA[
      T((x * y) * L((x * y) \ x,z,u),x) = y * (x * L(x \ (y \ x),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,2131,a(flip),b,12472,a)].">
      <j1 rule="hyper" parents="63 2131 12472"/>
    </justification>
  </clause>

  <clause id="12475">
    <literal><![CDATA[
      T(x * (y * L(y \ 1,z,u)),x) = y * (x * L(x \ (y \ x),z,u))
    ]]></literal>
    <justification jstring="[para(1015(a,1),12473(a,1,1))].">
      <j1 rule="para" parents="1015 12473"/>
    </justification>
  </clause>

  <clause id="12476">
    <literal><![CDATA[
      T(x * (y * L(y \ 1,z,u)),x) = (y * L(y \ 1,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,2028,a(flip),b,12475,a),flip(a)].">
      <j1 rule="hyper" parents="347 2028 12475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12477">
    <literal><![CDATA[
      T(x * ((1 / y) * L(y,z,u)),x) = ((1 / y) * L((1 / y) \ 1,z,u)) * x
    ]]></literal>
    <justification jstring="[para(83(a,1),12476(a,1,1,2,2,1))].">
      <j1 rule="para" parents="83 12476"/>
    </justification>
  </clause>

  <clause id="12478">
    <literal><![CDATA[
      T(x * (y \ L(y,z,u)),x) = ((1 / y) * L((1 / y) \ 1,z,u)) * x
    ]]></literal>
    <justification jstring="[para(3162(a,1),12477(a,1,1,2))].">
      <j1 rule="para" parents="3162 12477"/>
    </justification>
  </clause>

  <clause id="12479">
    <literal><![CDATA[
      T(x * (y \ L(y,z,u)),x) = ((1 / y) * L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(83(a,1),12478(a,2,1,2,1))].">
      <j1 rule="para" parents="83 12478"/>
    </justification>
  </clause>

  <clause id="12480">
    <literal><![CDATA[
      T(x * (y \ L(y,z,u)),x) = (y \ L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(3162(a,1),12479(a,2,1))].">
      <j1 rule="para" parents="3162 12479"/>
    </justification>
  </clause>

  <clause id="12481">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,12480,a(flip),b,10327,a),flip(a)].">
      <j1 rule="hyper" parents="129 12480 10327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12482">
    <literal><![CDATA[
      R(x,T(K(y,z),x),T(K(z,K(u,w)),K(y,z) * 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(7279(a,1),9950(a,1,1,3,1))].">
      <j1 rule="para" parents="7279 9950"/>
    </justification>
  </clause>

  <clause id="12483">
    <literal><![CDATA[
      x / (T(K(y,z),x) * (((y \ 1) * x) * R(y,y \ 1,x))) = K(z,((y \ 1) * x) \ x) * K(((y \ 1) * x) \ x,(y \ 1) * x)
    ]]></literal>
    <justification jstring="[para(6426(a,1),9996(a,1,2,1))].">
      <j1 rule="para" parents="6426 9996"/>
    </justification>
  </clause>

  <clause id="12484">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ z) * K(((y \ 1) * z) \ z,(y \ 1) * z) = z / (T(K(y,x),z) * ((y \ z) * y))
    ]]></literal>
    <justification jstring="[para(3850(a,1),12483(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3850 12483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12485">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ z) * K(((y \ 1) * z) \ z,(y \ 1) * z) = z / ((y \ z) * T(y,x))
    ]]></literal>
    <justification jstring="[para(7706(a,1),12484(a,2,2))].">
      <j1 rule="para" parents="7706 12484"/>
    </justification>
  </clause>

  <clause id="12486">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) \ (y * z)) * K(((y \ 1) * (y * z)) \ (y * z),(y \ 1) * (y * z)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),12485(a,2,2,1))].">
      <j1 rule="para" parents="9 12485"/>
    </justification>
  </clause>

  <clause id="12487">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,z * y)) * K(((y \ 1) * (y * z)) \ (y * z),(y \ 1) * (y * z)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(4749(a,1),12486(a,1,1,2))].">
      <j1 rule="para" parents="4749 12486"/>
    </justification>
  </clause>

  <clause id="12488">
    <literal><![CDATA[
      T(K(x,y),z) * K(((y \ 1) * (y * z)) \ (y * z),(y \ 1) * (y * z)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(8192(a,1),12487(a,1,1))].">
      <j1 rule="para" parents="8192 12487"/>
    </justification>
  </clause>

  <clause id="12489">
    <literal><![CDATA[
      T(K(x,y),z) * K(R(T(y,z),y \ 1,z * y),(y \ 1) * (y * z)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(4749(a,1),12488(a,1,2,1))].">
      <j1 rule="para" parents="4749 12488"/>
    </justification>
  </clause>

  <clause id="12491">
    <literal><![CDATA[
      T(K(x,y),z) * K(R(T(y,z),y \ 1,z * y),L(z,y,y \ 1)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(5411(a,1),12489(a,1,2))].">
      <j1 rule="para" parents="5411 12489"/>
    </justification>
  </clause>

  <clause id="12492">
    <literal><![CDATA[
      T(K(x,y),z) * K(R(y,y \ 1,z * y),L(z,y,y \ 1)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(7748(a,1),12491(a,1,2))].">
      <j1 rule="para" parents="7748 12491"/>
    </justification>
  </clause>

  <clause id="12493">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x),y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9152(a,1),12492(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9152 12492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12494">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x) * K(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,7253,a,b,12493,a),flip(a)].">
      <j1 rule="hyper" parents="347 7253 12493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12496">
    <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(9012(a,1),12482(a,1,1,3))].">
      <j1 rule="para" parents="9012 12482"/>
    </justification>
  </clause>

  <clause id="12497">
    <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(7123(a,2),12496(a,1,1,3))].">
      <j1 rule="para" parents="7123 12496"/>
    </justification>
  </clause>

  <clause id="12499">
    <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(7279(a,1),12497(a,1,2,1,1))].">
      <j1 rule="para" parents="7279 12497"/>
    </justification>
  </clause>

  <clause id="12500">
    <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(8663(a,1),12499(a,1,2))].">
      <j1 rule="para" parents="8663 12499"/>
    </justification>
  </clause>

  <clause id="12501">
    <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(7279(a,1),12500(a,2,2,1))].">
      <j1 rule="para" parents="7279 12500"/>
    </justification>
  </clause>

  <clause id="12502">
    <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(9012(a,1),12501(a,2,2))].">
      <j1 rule="para" parents="9012 12501"/>
    </justification>
  </clause>

  <clause id="12503">
    <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(7123(a,2),12502(a,2,2))].">
      <j1 rule="para" parents="7123 12502"/>
    </justification>
  </clause>

  <clause id="12505">
    <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(8322(a,1),12503(a,1,1))].">
      <j1 rule="para" parents="8322 12503"/>
    </justification>
  </clause>

  <clause id="12506">
    <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(63,a,8662,a(flip),b,12505,a),flip(a)].">
      <j1 rule="hyper" parents="63 8662 12505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12507">
    <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(63,a,2561,a(flip),b,12506,a)].">
      <j1 rule="hyper" parents="63 2561 12506"/>
    </justification>
  </clause>

  <clause id="12508">
    <literal><![CDATA[
      T(K(x,y) * K(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,T(u,w))) * K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(12507(a,1),7815(a,1))].">
      <j1 rule="para" parents="12507 7815"/>
    </justification>
  </clause>

  <clause id="12509">
    <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(12508,a,12243,a)].">
      <j1 rule="hyper" parents="12508 12243"/>
    </justification>
  </clause>

  <clause id="12510">
    <literal><![CDATA[
      K(x * T(y,z),x) = K(y * x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(34,a,8804,a,b,12509,a)].">
      <j1 rule="hyper" parents="34 8804 12509"/>
    </justification>
  </clause>

  <clause id="12511">
    <literal><![CDATA[
      1 / (x \ K(y * x,T(x,z))) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[para(12510(a,1),5044(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="12510 5044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12512">
    <literal><![CDATA[
      T(x,T(y * x,z)) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7148,a,12511,a)].">
      <j1 rule="hyper" parents="7148 12511"/>
    </justification>
  </clause>

  <clause id="12513">
    <literal><![CDATA[
      T(x,T(x * y,z)) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4839,a(flip),b,12512,a)].">
      <j1 rule="hyper" parents="63 4839 12512"/>
    </justification>
  </clause>

  <clause id="12514">
    <literal><![CDATA[
      T(x,T(x * (x \ y),z)) = T(x,y * K(x \ y,z))
    ]]></literal>
    <justification jstring="[para(5941(a,1),12513(a,2,2))].">
      <j1 rule="para" parents="5941 12513"/>
    </justification>
  </clause>

  <clause id="12515">
    <literal><![CDATA[
      T(x,y * K(x \ y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),12514(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 12514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12516">
    <literal><![CDATA[
      T(x \ y,y * K(x,T(z,y))) = T(x \ y,T(y,z))
    ]]></literal>
    <justification jstring="[para(7097(a,1),12515(a,1,2,2))].">
      <j1 rule="para" parents="7097 12515"/>
    </justification>
  </clause>

  <clause id="12517">
    <literal><![CDATA[
      T(x \ y,K(x,z) * y) = T(x \ y,T(y,z))
    ]]></literal>
    <justification jstring="[para(7104(a,1),12516(a,1,2))].">
      <j1 rule="para" parents="7104 12516"/>
    </justification>
  </clause>

  <clause id="12518">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / T(T(y \ u,T(u,z)),w)) = T(x,T(y \ u,w) \ (K(y,z) * u))
    ]]></literal>
    <justification jstring="[para(12517(a,1),11934(a,1,2,2,1))].">
      <j1 rule="para" parents="12517 11934"/>
    </justification>
  </clause>

  <clause id="12519">
    <literal><![CDATA[
      R(x,y,z) * T(R(u,R(x,y,z),u),R(u,R(x,y,z),u) * x) = K(u,u * x) * T(u * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(8472(a,1),5877(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8472 5877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12520">
    <literal><![CDATA[
      R(x,y,z) * T(R(u,R(x,y,z),u),R(u,R(x,y,z),u) * x) = T(K(u,u * x) * (u * R(x,y,z)),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,7218,a,b,12519,a),flip(a)].">
      <j1 rule="hyper" parents="347 7218 12519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12522">
    <literal><![CDATA[
      R(x,y,z) * T(R(u,R(x,y,z),u),R(u,R(x,y,z),u) * x) = T(T(u,u * x) * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(4974(a,1),12520(a,2,1))].">
      <j1 rule="para" parents="4974 12520"/>
    </justification>
  </clause>

  <clause id="12523">
    <literal><![CDATA[
      R(x,y,z) * T(R(u,R(x,y,z),u),R(u,R(x,y,z),u) * x) = T(u * R(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,9341,a(flip),b,12522,a),flip(a)].">
      <j1 rule="hyper" parents="347 9341 12522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12524">
    <literal><![CDATA[
      R(x,y,z) * R(T(u,x * R(u,R(x,y,z),u)),R(x,y,z),u) = T(u * R(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[para(4329(a,2),12523(a,1,2))].">
      <j1 rule="para" parents="4329 12523"/>
    </justification>
  </clause>

  <clause id="12526">
    <literal><![CDATA[
      R(x,y,z) * R(T(u,x * u),R(x,y,z),u) = T(u * R(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[para(11927(a,1),12524(a,1,2,1))].">
      <j1 rule="para" parents="11927 12524"/>
    </justification>
  </clause>

  <clause id="12528">
    <literal><![CDATA[
      R(x,y,z) * R(T(u,x * u),x,u) = T(u * R(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[para(11544(a,1),12526(a,1,2))].">
      <j1 rule="para" parents="11544 12526"/>
    </justification>
  </clause>

  <clause id="12529">
    <literal><![CDATA[
      T(x * R(y,z,u),x * y) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(1042(a,1),12528(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1042 12528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12531">
    <literal><![CDATA[
      (x * R(y,z,u)) / (R(y,z,u) * T(x,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * y,x * R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(12529(a,1),5013(a,1,2))].">
      <j1 rule="para" parents="12529 5013"/>
    </justification>
  </clause>

  <clause id="12532">
    <literal><![CDATA[
      T(K(x,y) * K(y,R(x,z,u)),R(x,z,u)) = K(y * x,y * R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(12531,a,12494,a),flip(a)].">
      <j1 rule="hyper" parents="12531 12494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12533">
    <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(8472(a,1),5901(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8472 5901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12534">
    <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(347,a,7218,a,b,12533,a),flip(a)].">
      <j1 rule="hyper" parents="347 7218 12533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12536">
    <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(4974(a,1),12534(a,2,1))].">
      <j1 rule="para" parents="4974 12534"/>
    </justification>
  </clause>

  <clause id="12537">
    <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(12185(a,1),12536(a,1,2,1))].">
      <j1 rule="para" parents="12185 12536"/>
    </justification>
  </clause>

  <clause id="12538">
    <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(12185(a,1),12537(a,1,2,2,1))].">
      <j1 rule="para" parents="12185 12537"/>
    </justification>
  </clause>

  <clause id="12540">
    <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(4323(a,2),12538(a,1,2))].">
      <j1 rule="para" parents="4323 12538"/>
    </justification>
  </clause>

  <clause id="12542">
    <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(11927(a,1),12540(a,1,2))].">
      <j1 rule="para" parents="11927 12540"/>
    </justification>
  </clause>

  <clause id="12543">
    <literal><![CDATA[
      T(T(x,x * y) * L(y,z,u),x) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(1041(a,1),12542(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1041 12542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12545">
    <literal><![CDATA[
      T(x * L(y,z,u),x * y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9342,a(flip),b,12543,a)].">
      <j1 rule="hyper" parents="63 9342 12543"/>
    </justification>
  </clause>

  <clause id="12546">
    <literal><![CDATA[
      (x * L(y,z,u)) \ (L(y,z,u) * T(x,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = w
    ]]></literal>
    <justification jstring="[para(12545(a,1),5006(a,1,2))].">
      <j1 rule="para" parents="12545 5006"/>
    </justification>
  </clause>

  <clause id="12547">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = K(x,y) * K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(12546,a,8328,a)].">
      <j1 rule="hyper" parents="12546 8328"/>
    </justification>
  </clause>

  <clause id="12548">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,11096,a(flip),b,12547,a),flip(a)].">
      <j1 rule="hyper" parents="347 11096 12547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12549">
    <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),12548(a,1,1))].">
      <j1 rule="para" parents="12 12548"/>
    </justification>
  </clause>

  <clause id="12550">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x / L(y,z,u),y))
    ]]></literal>
    <justification jstring="[hyper(63,a,8527,a(flip),b,12549,a)].">
      <j1 rule="hyper" parents="63 8527 12549"/>
    </justification>
  </clause>

  <clause id="12551">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(11018(a,1),12550(a,2,3))].">
      <j1 rule="para" parents="11018 12550"/>
    </justification>
  </clause>

  <clause id="12552">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,11284,a(flip),b,12551,a),flip(a)].">
      <j1 rule="hyper" parents="347 11284 12551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12554">
    <literal><![CDATA[
      K(x,x * (L(y,z,u) \ y)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(9826,a,12552,a)].">
      <j1 rule="hyper" parents="9826 12552"/>
    </justification>
  </clause>

  <clause id="12555">
    <literal><![CDATA[
      (x * K(L(y,z,u) \ y,x)) \ L(x,L(y,z,u) \ y,x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6063,a,b,12554,a)].">
      <j1 rule="hyper" parents="63 6063 12554"/>
    </justification>
  </clause>

  <clause id="12556">
    <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),12554(a,1,2))].">
      <j1 rule="para" parents="12 12554"/>
    </justification>
  </clause>

  <clause id="12557">
    <literal><![CDATA[
      K(x * (L(y,z,u) \ y),x) = w / (a(u,z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(12554(a,1),5259(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12554 5259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12558">
    <literal><![CDATA[
      K(x * (L(y,z,u) \ y),x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,10000,a(flip),b,12557,a),flip(a)].">
      <j1 rule="hyper" parents="347 10000 12557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12559">
    <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(12558(a,1),11287(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12558 11287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12560">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(u,w,v5))) = a(x,y,a(v5,w,K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,11302,a(flip),b,12559,a)].">
      <j1 rule="hyper" parents="63 11302 12559"/>
    </justification>
  </clause>

  <clause id="12561">
    <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(12559(a,1),9257(a,1,2))].">
      <j1 rule="para" parents="12559 9257"/>
    </justification>
  </clause>

  <clause id="12562">
    <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(12560(a,1),11101(a,1,1))].">
      <j1 rule="para" parents="12560 11101"/>
    </justification>
  </clause>

  <clause id="12563">
    <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(7587,a,12556,a)].">
      <j1 rule="hyper" parents="7587 12556"/>
    </justification>
  </clause>

  <clause id="12564">
    <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(9827,a,12563,a)].">
      <j1 rule="hyper" parents="9827 12563"/>
    </justification>
  </clause>

  <clause id="12565">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K((y / x) \ y,y))
    ]]></literal>
    <justification jstring="[para(11024(a,1),12564(a,2,3))].">
      <j1 rule="para" parents="11024 12564"/>
    </justification>
  </clause>

  <clause id="12566">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(83(a,1),12565(a,2,3,1))].">
      <j1 rule="para" parents="83 12565"/>
    </justification>
  </clause>

  <clause id="12569">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = w / (a(u,z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(12566(a,1),5259(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12566 5259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12570">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,10000,a(flip),b,12569,a),flip(a)].">
      <j1 rule="hyper" parents="347 10000 12569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12571">
    <literal><![CDATA[
      T(x,x * (y \ L(y,z,u))) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(134,a,12570,a(flip),b,4924,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 12570 4924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12572">
    <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(12190(a,1),12555(a,1,2))].">
      <j1 rule="para" parents="12190 12555"/>
    </justification>
  </clause>

  <clause id="12573">
    <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(5723,a,12572,a)].">
      <j1 rule="hyper" parents="5723 12572"/>
    </justification>
  </clause>

  <clause id="12574">
    <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(7725,a,12573,a)].">
      <j1 rule="hyper" parents="7725 12573"/>
    </justification>
  </clause>

  <clause id="12575">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u) * 1
    ]]></literal>
    <justification jstring="[para(11129(a,1),12561(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11129 12561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12576">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,8,a(flip),b,12575,a),flip(a)].">
      <j1 rule="hyper" parents="347 8 12575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12578">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = w / (K(a(u,z,y),x) * w)
    ]]></literal>
    <justification jstring="[para(12576(a,1),5259(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12576 5259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12579">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = K(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,5487,a(flip),b,12578,a),flip(a)].">
      <j1 rule="hyper" parents="347 5487 12578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12580">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(132,a,12579,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 12579 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12582">
    <literal><![CDATA[
      K(x,K(y,z \ L(z,u,w))) = K(x,K(y,a(w,u,z)))
    ]]></literal>
    <justification jstring="[para(12579(a,1),8825(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12579 8825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12583">
    <literal><![CDATA[
      T(x \ L(x,y,z),a(z,y,x)) = ((x \ L(x,y,z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,2579,a(flip),b,12580,a),flip(a)].">
      <j1 rule="hyper" parents="63 2579 12580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12584">
    <literal><![CDATA[
      x \ L(T(x,a(y,z,u)),a(y,z,u),x) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(12580(a,1),12574(a,1,2,1))].">
      <j1 rule="para" parents="12580 12574"/>
    </justification>
  </clause>

  <clause id="12585">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(5118,a,12584,a)].">
      <j1 rule="hyper" parents="5118 12584"/>
    </justification>
  </clause>

  <clause id="12587">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (((x \ L(x,y,z)) \ 1) \ 1) = K(x \ L(x,y,z),a(z,y,x))
    ]]></literal>
    <justification jstring="[para(12583(a,1),10894(a,1,2))].">
      <j1 rule="para" parents="12583 10894"/>
    </justification>
  </clause>

  <clause id="12588">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (L(x,y,z) \ x) = K(x \ L(x,y,z),a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,2590,a(flip),b,12587,a)].">
      <j1 rule="hyper" parents="63 2590 12587"/>
    </justification>
  </clause>

  <clause id="12589">
    <literal><![CDATA[
      K(x \ L(x,y,z),a(z,y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,10883,a(flip),b,12588,a),flip(a)].">
      <j1 rule="hyper" parents="63 10883 12588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12591">
    <literal><![CDATA[
      K(a(x,y,z),z \ L(z,y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,12589,a,b,5160,a),flip(a)].">
      <j1 rule="hyper" parents="129 12589 5160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12592">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ 1 = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(189,a,4999,a(flip),b,12591,a(flip))].">
      <j1 rule="hyper" parents="189 4999 12591"/>
    </justification>
  </clause>

  <clause id="12593">
    <literal><![CDATA[
      1 / a(x,y,z) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(222,a,12592,a)].">
      <j1 rule="hyper" parents="222 12592"/>
    </justification>
  </clause>

  <clause id="12594">
    <literal><![CDATA[
      a(x,y,z) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(14(a,1),12592(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14 12592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12595">
    <literal><![CDATA[
      a(x,y,z) \ R(u,a(x,y,z),a(x,y,z)) = T(u * (a(x,y,z) \ 1),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(12592(a,1),2981(a,1,1))].">
      <j1 rule="para" parents="12592 2981"/>
    </justification>
  </clause>

  <clause id="12596">
    <literal><![CDATA[
      L(R(x,a(y,z,u) \ 1,a(y,z,u) \ 1),a(y,z,u) \ 1,x) = T(((a(y,z,u) \ 1) * x) * a(y,z,u),(a(y,z,u) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(12592(a,1),4460(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12592 4460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12597">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(12593(a,1),359(a,1,1))].">
      <j1 rule="para" parents="12593 359"/>
    </justification>
  </clause>

  <clause id="12598">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * (u * (a(x,y,z) \ (1 / a(x,y,z)))) = T(u,a(x,y,z) \ (a(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(12593(a,2),978(a,1,2,2,2))].">
      <j1 rule="para" parents="12593 978"/>
    </justification>
  </clause>

  <clause id="12599">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z),u,w) \ a(x,y,z)) = L(a(x,y,z) \ 1,u,w) \ 1
    ]]></literal>
    <justification jstring="[para(12593(a,1),3638(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12593 3638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12600">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(14(a,1),12597(a,1,1,1))].">
      <j1 rule="para" parents="14 12597"/>
    </justification>
  </clause>

  <clause id="12601">
    <literal><![CDATA[
      a(x,y,z) = T(R(x \ R(x,y,z),x,y * z),x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,10764,a,b,12594,a),flip(a)].">
      <j1 rule="hyper" parents="347 10764 12594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12602">
    <literal><![CDATA[
      T(a(x,y,z),x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,10768,a(flip),b,12594,a)].">
      <j1 rule="hyper" parents="347 10768 12594"/>
    </justification>
  </clause>

  <clause id="12603">
    <literal><![CDATA[
      a(x,y,z) * x = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1068,a,12602,a)].">
      <j1 rule="hyper" parents="1068 12602"/>
    </justification>
  </clause>

  <clause id="12605">
    <literal><![CDATA[
      a(x,R(y \ R(y,z,u),y,z * u),x) = a(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(12601(a,2),11819(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12601 11819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12606">
    <literal><![CDATA[
      a(x,y \ R(y,z,u),x) = a(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(11543,a,12605,a)].">
      <j1 rule="hyper" parents="11543 12605"/>
    </justification>
  </clause>

  <clause id="12608">
    <literal><![CDATA[
      T(a(x,y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(10768(a,1),12600(a,1))].">
      <j1 rule="para" parents="10768 12600"/>
    </justification>
  </clause>

  <clause id="12609">
    <literal><![CDATA[
      T(a(1 / x,y,z),x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      a(x \ 1,y,z) = u
    ]]></literal>
    <justification jstring="[para(4024(a,2),12608(a,1,1))].">
      <j1 rule="para" parents="4024 12608"/>
    </justification>
  </clause>

  <clause id="12610">
    <literal><![CDATA[
      1 * K(x,L(y \ L(y,z,u),y,w)) = K(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11131(a,1),12562(a,1,1))].">
      <j1 rule="para" parents="11131 12562"/>
    </justification>
  </clause>

  <clause id="12611">
    <literal><![CDATA[
      K(x,L(y \ L(y,z,u),y,w)) = K(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(135,a,12610,a)].">
      <j1 rule="hyper" parents="135 12610"/>
    </justification>
  </clause>

  <clause id="12613">
    <literal><![CDATA[
      K(x,a(y,z,u) \ 1) = K(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(6562,a,12611,a)].">
      <j1 rule="hyper" parents="6562 12611"/>
    </justification>
  </clause>

  <clause id="12614">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = T(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(132,a,12613,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 12613 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12615">
    <literal><![CDATA[
      x * K(x,y \ L(y,z,u)) = T(x,a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,12613,a(flip),b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 12613 4924"/>
    </justification>
  </clause>

  <clause id="12616">
    <literal><![CDATA[
      L(T(x,a(y,z,u) \ 1),u \ L(u,z,y),x) = T(x,x * (u \ L(u,z,y)))
    ]]></literal>
    <justification jstring="[para(12614(a,2),750(a,1,1))].">
      <j1 rule="para" parents="12614 750"/>
    </justification>
  </clause>

  <clause id="12617">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ L(u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(12615(a,1),4984(a,1))].">
      <j1 rule="para" parents="12615 4984"/>
    </justification>
  </clause>

  <clause id="12618">
    <literal><![CDATA[
      L(T(x,a(y,z,u) \ 1),u \ L(u,z,y),x) = x * a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,12571,a(flip),b,12616,a),flip(a)].">
      <j1 rule="hyper" parents="347 12571 12616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12619">
    <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(10077(a,1),10078(a,2,2,1,1))].">
      <j1 rule="para" parents="10077 10078"/>
    </justification>
  </clause>

  <clause id="12620">
    <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(347,a,1668,a(flip),b,12619,a),flip(a)].">
      <j1 rule="hyper" parents="347 1668 12619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12621">
    <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(2144(a,1),12620(a,2,2))].">
      <j1 rule="para" parents="2144 12620"/>
    </justification>
  </clause>

  <clause id="12622">
    <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(1184(a,1),12621(a,2,2,1))].">
      <j1 rule="para" parents="1184 12621"/>
    </justification>
  </clause>

  <clause id="12623">
    <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(1462(a,1),12622(a,2,2,1,2))].">
      <j1 rule="para" parents="1462 12622"/>
    </justification>
  </clause>

  <clause id="12624">
    <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(1668(a,1),12623(a,1,1))].">
      <j1 rule="para" parents="1668 12623"/>
    </justification>
  </clause>

  <clause id="12625">
    <literal><![CDATA[
      x \ T(x * (y \ R(y,z,u)),x) = T(y \ R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(11535(a,1),12624(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11535 12624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12626">
    <literal><![CDATA[
      R(x,y \ R(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(1775,a,12625,a)].">
      <j1 rule="hyper" parents="1775 12625"/>
    </justification>
  </clause>

  <clause id="12628">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(4377,a,12626,a)].">
      <j1 rule="hyper" parents="4377 12626"/>
    </justification>
  </clause>

  <clause id="12630">
    <literal><![CDATA[
      L(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,12327,a(flip),b,12628,a)].">
      <j1 rule="hyper" parents="63 12327 12628"/>
    </justification>
  </clause>

  <clause id="12631">
    <literal><![CDATA[
      R(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(4505,a,12630,a)].">
      <j1 rule="hyper" parents="4505 12630"/>
    </justification>
  </clause>

  <clause id="12633">
    <literal><![CDATA[
      a(x,a(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,12630,a,b,8497,a),flip(a)].">
      <j1 rule="hyper" parents="129 12630 8497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12634">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,x) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,12190,a,b,12630,a)].">
      <j1 rule="hyper" parents="63 12190 12630"/>
    </justification>
  </clause>

  <clause id="12635">
    <literal><![CDATA[
      (x * a(y,z,u)) * x = x * (a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(134,a,12630,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 12630 18"/>
    </justification>
  </clause>

  <clause id="12636">
    <literal><![CDATA[
      L(R(x,y,z),a(u,w,v5),x) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(12630(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12630 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12637">
    <literal><![CDATA[
      T(x * a(y,z,u),x) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(12630(a,1),4368(a,1,1,1))].">
      <j1 rule="para" parents="12630 4368"/>
    </justification>
  </clause>

  <clause id="12638">
    <literal><![CDATA[
      L(x,a(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(12631(a,1),4461(a,1,1))].">
      <j1 rule="para" parents="12631 4461"/>
    </justification>
  </clause>

  <clause id="12639">
    <literal><![CDATA[
      a(x,y,z) * ((u * a(x,y,z)) \ a(x,y,z)) = u \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(12631(a,1),11739(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12631 11739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12640">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(193,a,8356,a,b,12633,a(flip))].">
      <j1 rule="hyper" parents="193 8356 12633"/>
    </justification>
  </clause>

  <clause id="12641">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ w = w
    ]]></literal>
    <justification jstring="[hyper(193,a,80,a,b,12633,a(flip))].">
      <j1 rule="hyper" parents="193 80 12633"/>
    </justification>
  </clause>

  <clause id="12644">
    <literal><![CDATA[
      T(x,x * (L(y,z,u) \ y)) = T(x,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(12634(a,1),752(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12634 752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12645">
    <literal><![CDATA[
      x * (y \ L(y,a(z,u,w),y)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,11005,a,b,12641,a)].">
      <j1 rule="hyper" parents="63 11005 12641"/>
    </justification>
  </clause>

  <clause id="12646">
    <literal><![CDATA[
      a(x,a(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      1 = w
    ]]></literal>
    <justification jstring="[para(12641(a,1),236(a,1))].">
      <j1 rule="para" parents="12641 236"/>
    </justification>
  </clause>

  <clause id="12647">
    <literal><![CDATA[
      L(T(x,y),a(z,u,w),x) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(7230(a,1),12638(a,1)),flip(b)].">
      <j1 rule="para" parents="7230 12638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12648">
    <literal><![CDATA[
      a(x,y \ R(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      1 = w
    ]]></literal>
    <justification jstring="[para(12606(a,2),12646(a,1))].">
      <j1 rule="para" parents="12606 12646"/>
    </justification>
  </clause>

  <clause id="12649">
    <literal><![CDATA[
      x \ T((x / a(y,z,u)) * a(y,z,u),x / a(y,z,u)) = K(a(y,z,u),a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(128,a,12637,a,b,5111,a)].">
      <j1 rule="hyper" parents="128 12637 5111"/>
    </justification>
  </clause>

  <clause id="12650">
    <literal><![CDATA[
      T((x * y) * z,x * (y * z)) = a(x,y,z) * (x * (y * z))
    ]]></literal>
    <justification jstring="[para(86(a,1),12637(a,1,1))].">
      <j1 rule="para" parents="86 12637"/>
    </justification>
  </clause>

  <clause id="12651">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12585,a(flip),b,12640,a)].">
      <j1 rule="hyper" parents="63 12585 12640"/>
    </justification>
  </clause>

  <clause id="12652">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = K(y,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(11092,a,12651,a)].">
      <j1 rule="hyper" parents="11092 12651"/>
    </justification>
  </clause>

  <clause id="12653">
    <literal><![CDATA[
      x \ T(x,a(y,z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,4924,a(flip),b,12651,a)].">
      <j1 rule="hyper" parents="347 4924 12651"/>
    </justification>
  </clause>

  <clause id="12654">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) = x * T(y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(134,a,12651,a,b,5956,a)].">
      <j1 rule="hyper" parents="134 12651 5956"/>
    </justification>
  </clause>

  <clause id="12655">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,12651,a,b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 12651 4924"/>
    </justification>
  </clause>

  <clause id="12656">
    <literal><![CDATA[
      a(x,y,K(z,u)) * z = T(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(133,a,12651,a,b,4969,a(flip))].">
      <j1 rule="hyper" parents="133 12651 4969"/>
    </justification>
  </clause>

  <clause id="12657">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = K(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,11096,a,b,12651,a)].">
      <j1 rule="hyper" parents="63 11096 12651"/>
    </justification>
  </clause>

  <clause id="12658">
    <literal><![CDATA[
      K(x,a(y,z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,6240,a(flip),b,12651,a),flip(a)].">
      <j1 rule="hyper" parents="63 6240 12651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12659">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(12651(a,2),4984(a,1,2))].">
      <j1 rule="para" parents="12651 4984"/>
    </justification>
  </clause>

  <clause id="12660">
    <literal><![CDATA[
      a(x,y,K(z,u)) * z != w
    ]]></literal>
    <literal><![CDATA[
      T(z,a(x,y,u)) = w
    ]]></literal>
    <justification jstring="[para(12651(a,2),4987(a,1,1))].">
      <j1 rule="para" parents="12651 4987"/>
    </justification>
  </clause>

  <clause id="12661">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (z * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(z,a(x,y,u)) * w = v5
    ]]></literal>
    <justification jstring="[para(12651(a,2),5200(a,1,1))].">
      <j1 rule="para" parents="12651 5200"/>
    </justification>
  </clause>

  <clause id="12662">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * T(y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(12651(a,2),5973(a,1,2))].">
      <j1 rule="para" parents="12651 5973"/>
    </justification>
  </clause>

  <clause id="12664">
    <literal><![CDATA[
      T(a(x,y,y),z) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(5039,a,12658,a)].">
      <j1 rule="hyper" parents="5039 12658"/>
    </justification>
  </clause>

  <clause id="12665">
    <literal><![CDATA[
      T(x,a(y,z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(56,a,12658,a)].">
      <j1 rule="hyper" parents="56 12658"/>
    </justification>
  </clause>

  <clause id="12666">
    <literal><![CDATA[
      x / a(y,z,z) = a(y,z,z) \ x
    ]]></literal>
    <justification jstring="[hyper(193,a,5250,a,b,12658,a(flip))].">
      <j1 rule="hyper" parents="193 5250 12658"/>
    </justification>
  </clause>

  <clause id="12667">
    <literal><![CDATA[
      T(x,a(y,z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(12665(a,1),49(a,2))].">
      <j1 rule="para" parents="12665 49"/>
    </justification>
  </clause>

  <clause id="12668">
    <literal><![CDATA[
      T(x,a(y,z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(189,a,12653,a,b,6253,a(flip))].">
      <j1 rule="hyper" parents="189 12653 6253"/>
    </justification>
  </clause>

  <clause id="12669">
    <literal><![CDATA[
      T(x,a(y,x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(189,a,12653,a,b,5967,a(flip))].">
      <j1 rule="hyper" parents="189 12653 5967"/>
    </justification>
  </clause>

  <clause id="12670">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,x)) = T(x * y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(134,a,11287,a(flip),b,12653,a)].">
      <j1 rule="hyper" parents="134 11287 12653"/>
    </justification>
  </clause>

  <clause id="12671">
    <literal><![CDATA[
      T(x,a(y,z / u,u)) = x * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,11125,a(flip),b,12653,a),flip(a)].">
      <j1 rule="hyper" parents="134 11125 12653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12672">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,a(x,y,u)) = w
    ]]></literal>
    <justification jstring="[para(12653(a,1),5006(a,1))].">
      <j1 rule="para" parents="12653 5006"/>
    </justification>
  </clause>

  <clause id="12674">
    <literal><![CDATA[
      a(x,y,z) * y = y * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1068,a,12669,a),flip(a)].">
      <j1 rule="hyper" parents="1068 12669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12675">
    <literal><![CDATA[
      T(a(x,y,z),y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,12669,a)].">
      <j1 rule="hyper" parents="54 12669"/>
    </justification>
  </clause>

  <clause id="12676">
    <literal><![CDATA[
      (x * a(y,x,z)) / x = a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(220,a,12669,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="220 12669 22"/>
    </justification>
  </clause>

  <clause id="12677">
    <literal><![CDATA[
      T(a(x,y \ 1,y),z) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,12668,a)].">
      <j1 rule="hyper" parents="54 12668"/>
    </justification>
  </clause>

  <clause id="12678">
    <literal><![CDATA[
      T(x,a(y,z,L(u,w,x))) = x * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(7612(a,1),12655(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="7612 12655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12679">
    <literal><![CDATA[
      T(x,a(y,z,u)) \ x = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[para(12655(a,1),9262(a,1,1))].">
      <j1 rule="para" parents="12655 9262"/>
    </justification>
  </clause>

  <clause id="12680">
    <literal><![CDATA[
      T(a(x,y \ 1,y),z) = x \ R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3466,a,b,12677,a),flip(a)].">
      <j1 rule="hyper" parents="347 3466 12677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12681">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(4951,a,12679,a),flip(a)].">
      <j1 rule="hyper" parents="4951 12679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12682">
    <literal><![CDATA[
      T(x,a(y,z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(189,a,12679,a,b,11300,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="189 12679 11300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12683">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(a(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(12679(a,1),4951(a,1))].">
      <j1 rule="para" parents="12679 4951"/>
    </justification>
  </clause>

  <clause id="12684">
    <literal><![CDATA[
      T(a(x,y,y \ 1),z) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(54,a,12682,a)].">
      <j1 rule="hyper" parents="54 12682"/>
    </justification>
  </clause>

  <clause id="12685">
    <literal><![CDATA[
      T(x,y \ (z * ((y \ z) \ 1))) = x
    ]]></literal>
    <justification jstring="[para(852(a,1),12682(a,1,2))].">
      <j1 rule="para" parents="852 12682"/>
    </justification>
  </clause>

  <clause id="12686">
    <literal><![CDATA[
      a(x,y,K(z,a(x,y,z) \ u)) * u = a(x,y,z) * (u / a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,12681,a,b,5197,a)].">
      <j1 rule="hyper" parents="133 12681 5197"/>
    </justification>
  </clause>

  <clause id="12687">
    <literal><![CDATA[
      a(x,y,K(z,u)) * a(x,y,z) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(133,a,12681,a,b,4969,a(flip))].">
      <j1 rule="hyper" parents="133 12681 4969"/>
    </justification>
  </clause>

  <clause id="12688">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[para(12681(a,2),5058(a,1,1,2))].">
      <j1 rule="para" parents="12681 5058"/>
    </justification>
  </clause>

  <clause id="12689">
    <literal><![CDATA[
      a(x,y,K(z,u)) * a(x,y,z) != w
    ]]></literal>
    <literal><![CDATA[
      T(a(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(12681(a,2),4987(a,1,1))].">
      <j1 rule="para" parents="12681 4987"/>
    </justification>
  </clause>

  <clause id="12690">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u \ w) = T(u,a(x,y,z)) \ w
    ]]></literal>
    <justification jstring="[para(12681(a,2),5209(a,1,1))].">
      <j1 rule="para" parents="12681 5209"/>
    </justification>
  </clause>

  <clause id="12691">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,u) * x) / a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(12681(a,2),5091(a,1,2))].">
      <j1 rule="para" parents="12681 5091"/>
    </justification>
  </clause>

  <clause id="12692">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(u,a(x,y,z)) \ w = v5
    ]]></literal>
    <justification jstring="[para(12681(a,2),5217(a,1,1))].">
      <j1 rule="para" parents="12681 5217"/>
    </justification>
  </clause>

  <clause id="12693">
    <literal><![CDATA[
      (x * ((y \ x) \ 1)) / y = y \ (x * ((y \ x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(220,a,12685,a(flip),b,112,a(flip))].">
      <j1 rule="hyper" parents="220 12685 112"/>
    </justification>
  </clause>

  <clause id="12694">
    <literal><![CDATA[
      T((x * x) \ (x * (a(y,z,u) * x)),x) = R(T(a(y,z,u),x * x),x,x)
    ]]></literal>
    <justification jstring="[para(12635(a,1),1211(a,1,1,2))].">
      <j1 rule="para" parents="12635 1211"/>
    </justification>
  </clause>

  <clause id="12695">
    <literal><![CDATA[
      K(x,a(y,z,u)) != w \ v5
    ]]></literal>
    <literal><![CDATA[
      w * a(y,z,K(x,u)) = v5
    ]]></literal>
    <justification jstring="[para(12652(a,1),11084(a,2)),flip(a)].">
      <j1 rule="para" parents="12652 11084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12696">
    <literal><![CDATA[
      K(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(x,u)) = w
    ]]></literal>
    <justification jstring="[para(12657(a,1),11100(a,1))].">
      <j1 rule="para" parents="12657 11100"/>
    </justification>
  </clause>

  <clause id="12697">
    <literal><![CDATA[
      T(x,a(y,z / u,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,12655,a(flip),b,12671,a),flip(a)].">
      <j1 rule="hyper" parents="347 12655 12671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12698">
    <literal><![CDATA[
      T(x,a(y,z * u,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),12697(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 12697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12699">
    <literal><![CDATA[
      T(x * y,a(z,x,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(63,a,12669,a(flip),b,12698,a),flip(a)].">
      <j1 rule="hyper" parents="63 12669 12698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12700">
    <literal><![CDATA[
      a(x,y,z) * (y * z) = (y * z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1068,a,12699,a),flip(a)].">
      <j1 rule="hyper" parents="1068 12699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12701">
    <literal><![CDATA[
      T(K(x,y) * R(K(y,x),z \ 1,z),u) = K(y,x) \ R(K(y,x),z \ 1,z)
    ]]></literal>
    <justification jstring="[para(5271(a,2),12680(a,1,1))].">
      <j1 rule="para" parents="5271 12680"/>
    </justification>
  </clause>

  <clause id="12702">
    <literal><![CDATA[
      (x \ 1) * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x \ 1,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(11299(a,1),12659(a,1,2))].">
      <j1 rule="para" parents="11299 12659"/>
    </justification>
  </clause>

  <clause id="12703">
    <literal><![CDATA[
      T(x,a(y,z,L(u,w,x))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(12678(a,2),12659(a,1))].">
      <j1 rule="para" parents="12678 12659"/>
    </justification>
  </clause>

  <clause id="12704">
    <literal><![CDATA[
      a(x,y,K(z,u)) * a(x,y,z) = T(a(x,y,z),z \ u)
    ]]></literal>
    <justification jstring="[para(11296(a,1),12687(a,1,1))].">
      <j1 rule="para" parents="11296 12687"/>
    </justification>
  </clause>

  <clause id="12705">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ x)) = T(x,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9812,a,b,12644,a)].">
      <j1 rule="hyper" parents="63 9812 12644"/>
    </justification>
  </clause>

  <clause id="12706">
    <literal><![CDATA[
      T(x * y,a(z,u,x)) = x * T(y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,12654,a(flip),b,12670,a),flip(a)].">
      <j1 rule="hyper" parents="63 12654 12670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12707">
    <literal><![CDATA[
      T(a(x,y,z),z \ u) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12687,a(flip),b,12704,a),flip(a)].">
      <j1 rule="hyper" parents="63 12687 12704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12708">
    <literal><![CDATA[
      T(a(x,y,z),z * u) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),12707(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 12707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12709">
    <literal><![CDATA[
      L(a(x,y,z),u,z) * (z * u) = z * (u * T(a(x,y,z),u))
    ]]></literal>
    <justification jstring="[para(12708(a,1),734(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12708 734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12710">
    <literal><![CDATA[
      1 * a(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(a(x,y,z),w * w) = u
    ]]></literal>
    <justification jstring="[para(11097(a,1),12689(a,1,1))].">
      <j1 rule="para" parents="11097 12689"/>
    </justification>
  </clause>

  <clause id="12711">
    <literal><![CDATA[
      T(a(x,y,z),u * u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(12710,a,7,a)].">
      <j1 rule="hyper" parents="12710 7"/>
    </justification>
  </clause>

  <clause id="12712">
    <literal><![CDATA[
      L(a(x,y,z),u,z) * (z * u) = z * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,251,a(flip),b,12709,a),flip(a)].">
      <j1 rule="hyper" parents="347 251 12709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12713">
    <literal><![CDATA[
      a(x,y,z) * (z * u) = z * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(12360(a,1),12712(a,1,1))].">
      <j1 rule="para" parents="12360 12712"/>
    </justification>
  </clause>

  <clause id="12714">
    <literal><![CDATA[
      x \ (a(y,z,x) * u) = a(y,z,x) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(678,a,12713,a)].">
      <j1 rule="hyper" parents="678 12713"/>
    </justification>
  </clause>

  <clause id="12715">
    <literal><![CDATA[
      x * (a(y,z,x) * (x \ u)) = a(y,z,x) * u
    ]]></literal>
    <justification jstring="[hyper(357,a,12713,a),flip(a)].">
      <j1 rule="hyper" parents="357 12713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12716">
    <literal><![CDATA[
      a(x,y,z) \ (z * u) = z * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(128,a,169,a(flip),b,12713,a)].">
      <j1 rule="hyper" parents="128 169 12713"/>
    </justification>
  </clause>

  <clause id="12717">
    <literal><![CDATA[
      x * (a(y,z,x) \ 1) = a(y,z,x) \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,73,a(flip),b,12713,a),flip(a)].">
      <j1 rule="hyper" parents="128 73 12713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12720">
    <literal><![CDATA[
      x \ (a(y,z,x) \ x) = a(y,z,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(138,a,12717,a)].">
      <j1 rule="hyper" parents="138 12717"/>
    </justification>
  </clause>

  <clause id="12721">
    <literal><![CDATA[
      (x * a(y,z,u)) \ a(y,z,u) = a(y,z,u) \ (x \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(138,a,12639,a),flip(a)].">
      <j1 rule="hyper" parents="138 12639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12722">
    <literal><![CDATA[
      (x \ (y * a(z,u,w))) * (a(z,u,w) \ (a(z,u,w) \ a(z,u,w))) = (x \ (y * (a(z,u,w) \ 1))) * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(12721(a,1),1104(a,1,2))].">
      <j1 rule="para" parents="12721 1104"/>
    </justification>
  </clause>

  <clause id="12723">
    <literal><![CDATA[
      R(T(a(x,y,z),u * u),u,u) = T(L(T(a(x,y,z),u),u,u),u)
    ]]></literal>
    <justification jstring="[para(263(a,1),12694(a,1,1)),flip(a)].">
      <j1 rule="para" parents="263 12694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12724">
    <literal><![CDATA[
      R(T(a(x,y,z),u * u),u,u) = L(T(T(a(x,y,z),u),u),u,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,25,a,b,12723,a),flip(a)].">
      <j1 rule="hyper" parents="347 25 12723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12725">
    <literal><![CDATA[
      K(x,T(y,z)) * R(K(y,T(x,z)),u \ 1,u) = K(y,x) \ R(K(y,x),u \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9303,a,b,12701,a)].">
      <j1 rule="hyper" parents="63 9303 12701"/>
    </justification>
  </clause>

  <clause id="12726">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * R(K(y,T(z,x)),u \ 1,u)) = K(y,z) \ R(K(y,z),u \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8070,a,b,12725,a)].">
      <j1 rule="hyper" parents="63 8070 12725"/>
    </justification>
  </clause>

  <clause id="12727">
    <literal><![CDATA[
      K(a(x,y,z),a(x,y,z) \ u) = u \ T(u,a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4412(a,1),12649(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4412 12649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12728">
    <literal><![CDATA[
      K(a(x,y,z),a(x,y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,a(x,y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(12727(a,2),5006(a,1))].">
      <j1 rule="para" parents="12727 5006"/>
    </justification>
  </clause>

  <clause id="12729">
    <literal><![CDATA[
      K(x,a(y,z,u) \ x) = a(y,z,K(u,a(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(12728,a,12681,a(flip))].">
      <j1 rule="hyper" parents="12728 12681"/>
    </justification>
  </clause>

  <clause id="12730">
    <literal><![CDATA[
      K(x,K(y,R(z,u \ 1,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(11756,a,12726,a)].">
      <j1 rule="hyper" parents="11756 12726"/>
    </justification>
  </clause>

  <clause id="12731">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(9604(a,1),12730(a,1,2,2))].">
      <j1 rule="para" parents="9604 12730"/>
    </justification>
  </clause>

  <clause id="12732">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7293,a,b,12731,a),flip(a)].">
      <j1 rule="hyper" parents="347 7293 12731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12733">
    <literal><![CDATA[
      K(x,K(y,z * (u \ 1))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(691(a,1),12732(a,1,2,2))].">
      <j1 rule="para" parents="691 12732"/>
    </justification>
  </clause>

  <clause id="12734">
    <literal><![CDATA[
      T(x,K(y,z * (u \ 1))) = T(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(132,a,12733,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 12733 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12735">
    <literal><![CDATA[
      K(x,K(y,z * (1 / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(5404(a,2),12733(a,1,2))].">
      <j1 rule="para" parents="5404 12733"/>
    </justification>
  </clause>

  <clause id="12736">
    <literal><![CDATA[
      K(x,K(y,z / (u \ 1))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(5405(a,1),12733(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5405 12733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12737">
    <literal><![CDATA[
      T(x,K(y,z / (u \ 1))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(5405(a,1),12734(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5405 12734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12738">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8849,a,12736,a)].">
      <j1 rule="hyper" parents="8849 12736"/>
    </justification>
  </clause>

  <clause id="12739">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(7328,a,12736,a)].">
      <j1 rule="hyper" parents="7328 12736"/>
    </justification>
  </clause>

  <clause id="12740">
    <literal><![CDATA[
      K(x,K(T(y,z),z * u)) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(7643(a,1),12736(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7643 12736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12741">
    <literal><![CDATA[
      T(x \ 1,K(y,z * x)) = T(x \ 1,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8792,a,12737,a),flip(a)].">
      <j1 rule="hyper" parents="8792 12737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12742">
    <literal><![CDATA[
      T(x,K(y,(z * (u \ 1)) * u)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(11(a,1),12737(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 12737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12743">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),12738(a,2,2,2))].">
      <j1 rule="para" parents="12 12738"/>
    </justification>
  </clause>

  <clause id="12744">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[para(5414(a,2),12738(a,1,2))].">
      <j1 rule="para" parents="5414 12738"/>
    </justification>
  </clause>

  <clause id="12745">
    <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(12741(a,1),5046(a,1,1))].">
      <j1 rule="para" parents="12741 5046"/>
    </justification>
  </clause>

  <clause id="12746">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(7281,a,12743,a)].">
      <j1 rule="hyper" parents="7281 12743"/>
    </justification>
  </clause>

  <clause id="12747">
    <literal><![CDATA[
      a(x,y * ((1 / z) / u),K(w,K(v5,u * z))) = a(x,y,K((1 / z) / u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(12744(a,1),11095(a,1,3))].">
      <j1 rule="para" parents="12744 11095"/>
    </justification>
  </clause>

  <clause id="12748">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,8833,a(flip),b,12746,a)].">
      <j1 rule="hyper" parents="63 8833 12746"/>
    </justification>
  </clause>

  <clause id="12750">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / u) = T(z,K(x,y)) / u
    ]]></literal>
    <justification jstring="[para(12748(a,1),9038(a,1,1))].">
      <j1 rule="para" parents="12748 9038"/>
    </justification>
  </clause>

  <clause id="12751">
    <literal><![CDATA[
      R(K(x,K(y,z)),z / u,u) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(12748(a,1),9380(a,1,1))].">
      <j1 rule="para" parents="12748 9380"/>
    </justification>
  </clause>

  <clause id="12752">
    <literal><![CDATA[
      R(K(x,K(y,z)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7293(a,1),12751(a,1,1))].">
      <j1 rule="para" parents="7293 12751"/>
    </justification>
  </clause>

  <clause id="12754">
    <literal><![CDATA[
      K(x,K(y,R(z,x / u,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(11693,a,12752,a)].">
      <j1 rule="hyper" parents="11693 12752"/>
    </justification>
  </clause>

  <clause id="12755">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(80(a,1),12754(a,1,2,2,2))].">
      <j1 rule="para" parents="80 12754"/>
    </justification>
  </clause>

  <clause id="12756">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,K(x,y)) / u) = z / u
    ]]></literal>
    <justification jstring="[hyper(7322,a,12750,a)].">
      <j1 rule="hyper" parents="7322 12750"/>
    </justification>
  </clause>

  <clause id="12757">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(y,K(z,x)) * u
    ]]></literal>
    <justification jstring="[hyper(643,a,12750,a),flip(a)].">
      <j1 rule="hyper" parents="643 12750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12759">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,K(z,y)) / u) = x / u
    ]]></literal>
    <justification jstring="[para(7260(a,1),12756(a,1,1))].">
      <j1 rule="para" parents="7260 12756"/>
    </justification>
  </clause>

  <clause id="12760">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(7283(a,1),12757(a,2,1))].">
      <j1 rule="para" parents="7283 12757"/>
    </justification>
  </clause>

  <clause id="12761">
    <literal><![CDATA[
      K((T(x,y) / z) / (x / z),u) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(9041,a,12759,a)].">
      <j1 rule="hyper" parents="9041 12759"/>
    </justification>
  </clause>

  <clause id="12762">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ T(x,K(y,z)) = u \ x
    ]]></literal>
    <justification jstring="[hyper(214,a,12760,a)].">
      <j1 rule="hyper" parents="214 12760"/>
    </justification>
  </clause>

  <clause id="12763">
    <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(10811(a,1),12761(a,1,1,1,1))].">
      <j1 rule="para" parents="10811 12761"/>
    </justification>
  </clause>

  <clause id="12765">
    <literal><![CDATA[
      L(x \ y,x,K(y,K(z,u))) = x \ y
    ]]></literal>
    <justification jstring="[hyper(5035,a,12762,a)].">
      <j1 rule="hyper" parents="5035 12762"/>
    </justification>
  </clause>

  <clause id="12766">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,u \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,12765,a)].">
      <j1 rule="hyper" parents="53 12765"/>
    </justification>
  </clause>

  <clause id="12767">
    <literal><![CDATA[
      a(K(x * y,K(z,u)),x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,12443,a(flip),b,12766,a)].">
      <j1 rule="hyper" parents="63 12443 12766"/>
    </justification>
  </clause>

  <clause id="12768">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = 1
    ]]></literal>
    <justification jstring="[para(6897(a,2),12766(a,1,1))].">
      <j1 rule="para" parents="6897 12766"/>
    </justification>
  </clause>

  <clause id="12769">
    <literal><![CDATA[
      a(K(x,K(y,z * u)),z,u) = 1
    ]]></literal>
    <justification jstring="[para(7260(a,1),12767(a,1,1))].">
      <j1 rule="para" parents="7260 12767"/>
    </justification>
  </clause>

  <clause id="12770">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = K(w,K(v5,v6)) * K(w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,7298,a,b,12768,a),flip(a)].">
      <j1 rule="hyper" parents="347 7298 12768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12771">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(10347(a,1),12740(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10347 12740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12772">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ 1))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8844,a,12771,a)].">
      <j1 rule="hyper" parents="8844 12771"/>
    </justification>
  </clause>

  <clause id="12773">
    <literal><![CDATA[
      K(x,K(y,((z / u) \ 1) \ u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),12771(a,2,2,2))].">
      <j1 rule="para" parents="12 12771"/>
    </justification>
  </clause>

  <clause id="12774">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,x * y))
    ]]></literal>
    <justification jstring="[para(12771(a,1),7299(a,2,2))].">
      <j1 rule="para" parents="12771 7299"/>
    </justification>
  </clause>

  <clause id="12776">
    <literal><![CDATA[
      T(x,K(y,z \ (u \ 1))) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(132,a,12772,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 12772 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12777">
    <literal><![CDATA[
      K(x,K(y \ (z * u),z * u)) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8845,a(flip),b,12772,a),flip(a)].">
      <j1 rule="hyper" parents="63 8845 12772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12778">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(u,x))
    ]]></literal>
    <justification jstring="[para(12773(a,1),8295(a,2,2))].">
      <j1 rule="para" parents="12773 8295"/>
    </justification>
  </clause>

  <clause id="12779">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (u \ (z \ 1))) = T(x,(u \ (z \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(12776(a,1),10366(a,1,1))].">
      <j1 rule="para" parents="12776 10366"/>
    </justification>
  </clause>

  <clause id="12780">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (u \ (z \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(u \ (z \ 1)) * y) = w
    ]]></literal>
    <justification jstring="[para(12776(a,1),10397(a,1,1))].">
      <j1 rule="para" parents="12776 10397"/>
    </justification>
  </clause>

  <clause id="12781">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(7283(a,1),12778(a,2,2))].">
      <j1 rule="para" parents="7283 12778"/>
    </justification>
  </clause>

  <clause id="12783">
    <literal><![CDATA[
      (x \ y) * K(y,K(z,u)) = x \ T(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(646,a,12781,a),flip(a)].">
      <j1 rule="hyper" parents="646 12781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12784">
    <literal><![CDATA[
      (T(x,K(y,z)) / u) \ x = u * K(T(x,K(y,z)),K(y,z))
    ]]></literal>
    <justification jstring="[para(7334(a,1),12781(a,1,2))].">
      <j1 rule="para" parents="7334 12781"/>
    </justification>
  </clause>

  <clause id="12787">
    <literal><![CDATA[
      (T(x,K(y,z)) / u) \ x = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5146(a,1),12784(a,2,2))].">
      <j1 rule="para" parents="5146 12784"/>
    </justification>
  </clause>

  <clause id="12788">
    <literal><![CDATA[
      T(x,K(y,z)) / (u * x) = x / (u * T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(220,a,5926,a(flip),b,12787,a),flip(a)].">
      <j1 rule="hyper" parents="220 5926 12787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12789">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = K(w,K(v5,R(v6,v7,v7 \ w))) * K(v6,K(w,v5))
    ]]></literal>
    <justification jstring="[para(12755(a,1),12770(a,2,2))].">
      <j1 rule="para" parents="12755 12770"/>
    </justification>
  </clause>

  <clause id="12792">
    <literal><![CDATA[
      K(x,K(y * z,(y \ u) \ z)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8798,a,12777,a),flip(a)].">
      <j1 rule="hyper" parents="8798 12777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12793">
    <literal><![CDATA[
      K(x,K(y * z,z \ (y \ u))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8844,a,12792,a)].">
      <j1 rule="hyper" parents="8844 12792"/>
    </justification>
  </clause>

  <clause id="12794">
    <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(5299(a,2),12793(a,2,2))].">
      <j1 rule="para" parents="5299 12793"/>
    </justification>
  </clause>

  <clause id="12795">
    <literal><![CDATA[
      T(T(x,K(y,z * R(u,z \ 1,u))),y * (R(u,z \ 1,u) \ (z \ 1))) = T(x,((z \ 1) * ((u * (z \ 1)) \ (z \ 1))) * y)
    ]]></literal>
    <justification jstring="[para(11739(a,1),12779(a,2,2,1))].">
      <j1 rule="para" parents="11739 12779"/>
    </justification>
  </clause>

  <clause id="12796">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = K(w,K(v5,R(v6,v7,v7 \ w))) * K(w,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(7283(a,2),12789(a,2,2))].">
      <j1 rule="para" parents="7283 12789"/>
    </justification>
  </clause>

  <clause id="12797">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,u \ x) = K(w,K(v5,R(v6,v7,v7 \ w))) * K(w,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(6897(a,1),12796(a,1,1))].">
      <j1 rule="para" parents="6897 12796"/>
    </justification>
  </clause>

  <clause id="12798">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x)) * K(z,y)) = a(K(w,K(v5,v6)),v7,v7 \ w)
    ]]></literal>
    <justification jstring="[hyper(347,a,10690,a(flip),b,12797,a)].">
      <j1 rule="hyper" parents="347 10690 12797"/>
    </justification>
  </clause>

  <clause id="12799">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x)) * K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(347,a,12769,a(flip),b,12798,a),flip(a)].">
      <j1 rule="hyper" parents="347 12769 12798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12800">
    <literal><![CDATA[
      K(x,K(y,z) * K(z,R(y,u,u \ x))) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,11750,a(flip),b,12799,a)].">
      <j1 rule="hyper" parents="63 11750 12799"/>
    </justification>
  </clause>

  <clause id="12801">
    <literal><![CDATA[
      K(x * y,K(z,u) * K(u,R(z,x,y))) = 1
    ]]></literal>
    <justification jstring="[para(9(a,1),12800(a,1,2,2,2,3))].">
      <j1 rule="para" parents="9 12800"/>
    </justification>
  </clause>

  <clause id="12802">
    <literal><![CDATA[
      K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,11774,a,b,12801,a)].">
      <j1 rule="hyper" parents="63 11774 12801"/>
    </justification>
  </clause>

  <clause id="12803">
    <literal><![CDATA[
      K(a(K(x,y),z,u),K(x,y) * (z * u)) = 1
    ]]></literal>
    <justification jstring="[hyper(6326,a,12802,a)].">
      <j1 rule="hyper" parents="6326 12802"/>
    </justification>
  </clause>

  <clause id="12805">
    <literal><![CDATA[
      1 * (((K(x,y) * z) * u) / (K(x,y) * (z * u))) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(12803(a,1),6639(a,1,1))].">
      <j1 rule="para" parents="12803 6639"/>
    </justification>
  </clause>

  <clause id="12806">
    <literal><![CDATA[
      1 * (K(x,y) * R(K(y,x),z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(10590(a,1),12805(a,1,2))].">
      <j1 rule="para" parents="10590 12805"/>
    </justification>
  </clause>

  <clause id="12807">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(135,a,12806,a)].">
      <j1 rule="hyper" parents="135 12806"/>
    </justification>
  </clause>

  <clause id="12808">
    <literal><![CDATA[
      1 * (K(x,K(y,z)) * R(K(x,K(y,z)),u,w)) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(7292(a,1),12806(a,1,2,1))].">
      <j1 rule="para" parents="7292 12806"/>
    </justification>
  </clause>

  <clause id="12809">
    <literal><![CDATA[
      K(x,y) \ R(K(x,y),z,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(5293,a,12807,a)].">
      <j1 rule="hyper" parents="5293 12807"/>
    </justification>
  </clause>

  <clause id="12810">
    <literal><![CDATA[
      K(x,y) * a(K(x,y),z,u) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(5273,a,12807,a)].">
      <j1 rule="hyper" parents="5273 12807"/>
    </justification>
  </clause>

  <clause id="12811">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(2565,a,12807,a)].">
      <j1 rule="hyper" parents="2565 12807"/>
    </justification>
  </clause>

  <clause id="12812">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(y,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(6694(a,1),12807(a,1,2))].">
      <j1 rule="para" parents="6694 12807"/>
    </justification>
  </clause>

  <clause id="12813">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z * x,u)
    ]]></literal>
    <justification jstring="[para(8643(a,1),12807(a,1,2))].">
      <j1 rule="para" parents="8643 12807"/>
    </justification>
  </clause>

  <clause id="12814">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * (K(y,z) * R(K(z,y),u,w)) = x
    ]]></literal>
    <justification jstring="[para(12807(a,1),11663(a,1,1,2))].">
      <j1 rule="para" parents="12807 11663"/>
    </justification>
  </clause>

  <clause id="12815">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(11696(a,1),12807(a,1,2))].">
      <j1 rule="para" parents="11696 12807"/>
    </justification>
  </clause>

  <clause id="12816">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w)) * K(z,y)) = T(x,a(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(12807(a,1),11695(a,2,2))].">
      <j1 rule="para" parents="12807 11695"/>
    </justification>
  </clause>

  <clause id="12817">
    <literal><![CDATA[
      (a(K(x,T(y,z)),u,w) * K(x,y)) * (K(y,x) * z) = R(K(x,T(y,z)),u,w) * (z * K(y,x))
    ]]></literal>
    <justification jstring="[para(12810(a,1),9493(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12810 9493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12818">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * (z * K(y,x)) = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(12811(a,1),9321(a,2,2))].">
      <j1 rule="para" parents="12811 9321"/>
    </justification>
  </clause>

  <clause id="12819">
    <literal><![CDATA[
      K(x,K(y,z) * K(R(z,u,w),y)) = K(a(K(y,z),u,w),x)
    ]]></literal>
    <justification jstring="[para(12815(a,1),10687(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12815 10687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12820">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(w,K(x,y) * K(R(y,z,u),x)) = v5
    ]]></literal>
    <justification jstring="[para(12815(a,1),10702(a,1,1))].">
      <j1 rule="para" parents="12815 10702"/>
    </justification>
  </clause>

  <clause id="12822">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12815,a(flip),b,12813,a),flip(a)].">
      <j1 rule="hyper" parents="63 12815 12813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12823">
    <literal><![CDATA[
      T(a(K(x,y),z * y,u),R(y,z,u)) = K(x * y,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(12813(a,1),12532(a,1,1))].">
      <j1 rule="para" parents="12813 12532"/>
    </justification>
  </clause>

  <clause id="12824">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * a(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[para(12807(a,1),12814(a,1,2))].">
      <j1 rule="para" parents="12807 12814"/>
    </justification>
  </clause>

  <clause id="12825">
    <literal><![CDATA[
      (T(x,x \ y) * a(K(z,u),w,v5)) \ ((x \ y) \ y) = a(K(u,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(128,a,112,a(flip),b,12824,a)].">
      <j1 rule="hyper" parents="128 112 12824"/>
    </justification>
  </clause>

  <clause id="12826">
    <literal><![CDATA[
      R(K(a(K(x,y),z,u),w),K(K(x,w),v5),v6) * v7 = K(y,K(x,w)) * (R(K(K(x,w),y),z,u) * v7)
    ]]></literal>
    <justification jstring="[para(12819(a,1),10828(a,1,1,1))].">
      <j1 rule="para" parents="12819 10828"/>
    </justification>
  </clause>

  <clause id="12827">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,11594,a(flip),b,12812,a),flip(a)].">
      <j1 rule="hyper" parents="347 11594 12812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12828">
    <literal><![CDATA[
      R(K(x \ 1,y) * K(y,R(x,z,u) \ 1),w,v5) = a(K(y,R(x,w,v5) \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11800,a(flip),b,12812,a)].">
      <j1 rule="hyper" parents="63 11800 12812"/>
    </justification>
  </clause>

  <clause id="12829">
    <literal><![CDATA[
      1 * (K(x,K(y,z)) * K(y,K(z,R(x,u,w)))) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(8918(a,1),12808(a,1,2,2))].">
      <j1 rule="para" parents="8918 12808"/>
    </justification>
  </clause>

  <clause id="12830">
    <literal><![CDATA[
      1 * K(x,K(y,z) * K(R(z,u,w),y)) = a(K(z,K(y,x)),u,w)
    ]]></literal>
    <justification jstring="[para(10704(a,1),12829(a,1,2))].">
      <j1 rule="para" parents="10704 12829"/>
    </justification>
  </clause>

  <clause id="12831">
    <literal><![CDATA[
      R(K(x \ 1,y) * K(y,R(x,z,u) \ 1),w,v5) = a(K(x,R(y,w,v5)),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,11704,a(flip),b,12828,a),flip(a)].">
      <j1 rule="hyper" parents="347 11704 12828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12832">
    <literal><![CDATA[
      a(K(x,R(y,z,u)),w,v5) = R(a(K(x,y),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(12827(a,1),12831(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12827 12831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12835">
    <literal><![CDATA[
      (a(K(x,T(y,z)),u,w) * K(x,y)) * (K(y,x) * z) = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,12818,a(flip),b,12817,a),flip(a)].">
      <j1 rule="hyper" parents="347 12818 12817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12836">
    <literal><![CDATA[
      K(x,K(y,z)) * (R(K(K(y,z),x),u,w) * v5) = K(a(K(y,x),u,w),z) * v5
    ]]></literal>
    <justification jstring="[para(586(a,1),12826(a,1,1)),flip(a)].">
      <j1 rule="para" parents="586 12826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12837">
    <literal><![CDATA[
      K(x,K(y,z)) * (R(K(K(y,z),x),u,w) * y) = y * K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,8563,a(flip),b,12836,a),flip(a)].">
      <j1 rule="hyper" parents="347 8563 12836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12838">
    <literal><![CDATA[
      K(x,K(y,z)) * (R(K(y,K(z,x)),u,w) * y) = y * K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(7261(a,1),12837(a,1,2,1,1))].">
      <j1 rule="para" parents="7261 12837"/>
    </justification>
  </clause>

  <clause id="12839">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(y,K(z,R(x,u,w))) * y) = y * K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(8917(a,1),12838(a,1,2,1))].">
      <j1 rule="para" parents="8917 12838"/>
    </justification>
  </clause>

  <clause id="12840">
    <literal><![CDATA[
      K(x,K(y,z)) * T(y,K(z,R(x,u,w))) = y * K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(4977(a,2),12839(a,1,2))].">
      <j1 rule="para" parents="4977 12839"/>
    </justification>
  </clause>

  <clause id="12841">
    <literal><![CDATA[
      T(K(x,K(y,z)) * y,K(x,R(z,u,w))) = y * K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11711,a,b,12840,a)].">
      <j1 rule="hyper" parents="63 11711 12840"/>
    </justification>
  </clause>

  <clause id="12842">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,R(z,u,w))) = x * K(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(7285(a,1),12841(a,1,1))].">
      <j1 rule="para" parents="7285 12841"/>
    </justification>
  </clause>

  <clause id="12843">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w)) * K(z,y)) = x * K(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(10688,a,12842,a)].">
      <j1 rule="hyper" parents="10688 12842"/>
    </justification>
  </clause>

  <clause id="12844">
    <literal><![CDATA[
      x * K(a(K(x,y),z,u),w) = T(x,a(K(w,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12816,a(flip),b,12843,a),flip(a)].">
      <j1 rule="hyper" parents="63 12816 12843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12845">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) = K(x,a(K(w,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(34,a,4929,a(flip),b,12844,a),flip(a)].">
      <j1 rule="hyper" parents="34 4929 12844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12846">
    <literal><![CDATA[
      K(x,K(y,z) * K(R(z,u,w),y)) = K(y,a(K(x,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(12820,a,12845,a)].">
      <j1 rule="hyper" parents="12820 12845"/>
    </justification>
  </clause>

  <clause id="12847">
    <literal><![CDATA[
      1 * K(x,a(K(y,z),u,w)) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(12846(a,1),12830(a,1,2))].">
      <j1 rule="para" parents="12846 12830"/>
    </justification>
  </clause>

  <clause id="12848">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(y,a(K(z,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(135,a,12847,a),flip(a)].">
      <j1 rule="hyper" parents="135 12847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12849">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,12845,a,b,12848,a),flip(a)].">
      <j1 rule="hyper" parents="347 12845 12848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12850">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(x,a(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(7279(a,1),12848(a,1,1))].">
      <j1 rule="para" parents="7279 12848"/>
    </justification>
  </clause>

  <clause id="12851">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(7279(a,1),12849(a,1,1))].">
      <j1 rule="para" parents="7279 12849"/>
    </justification>
  </clause>

  <clause id="12852">
    <literal><![CDATA[
      K(a(K(x,y),z * y,u),w) = a(K(y,K(x,w)),z,u)
    ]]></literal>
    <justification jstring="[para(12822(a,2),12849(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12822 12849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12853">
    <literal><![CDATA[
      a(K(x,K(y,z)),u * y,w) = a(K(y,K(x,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,12851,a,b,12852,a)].">
      <j1 rule="hyper" parents="63 12851 12852"/>
    </justification>
  </clause>

  <clause id="12854">
    <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(5214(a,2),12763(a,1,1))].">
      <j1 rule="para" parents="5214 12763"/>
    </justification>
  </clause>

  <clause id="12855">
    <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(7472,a,12854,a)].">
      <j1 rule="hyper" parents="7472 12854"/>
    </justification>
  </clause>

  <clause id="12856">
    <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(63,a,12739,a(flip),b,12855,a)].">
      <j1 rule="hyper" parents="63 12739 12855"/>
    </justification>
  </clause>

  <clause id="12857">
    <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),12856(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 12856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12858">
    <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(12857(a,1),7278(a,1))].">
      <j1 rule="para" parents="12857 7278"/>
    </justification>
  </clause>

  <clause id="12859">
    <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),12794(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="18 12794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12860">
    <literal><![CDATA[
      (x \ (y * (a(z,u,w) \ 1))) * a(z,u,w) = (x \ (y * a(z,u,w))) * (a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(68(a,1),12722(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="68 12722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12862">
    <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(7261(a,1),12745(a,1,2,1,2))].">
      <j1 rule="para" parents="7261 12745"/>
    </justification>
  </clause>

  <clause id="12863">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (R(u,z \ 1,u) \ (z \ 1))) = T(x,((z \ 1) * ((u * (z \ 1)) \ (z \ 1))) * y)
    ]]></literal>
    <justification jstring="[para(11952(a,1),12795(a,1,1,2))].">
      <j1 rule="para" parents="11952 12795"/>
    </justification>
  </clause>

  <clause id="12864">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (u \ (z \ 1))) = T(x,((z \ 1) * ((u * (z \ 1)) \ (z \ 1))) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,11995,a(flip),b,12863,a)].">
      <j1 rule="hyper" parents="63 11995 12863"/>
    </justification>
  </clause>

  <clause id="12866">
    <literal><![CDATA[
      T(x,((y \ 1) * ((z * (y \ 1)) \ (y \ 1))) * u) = T(x,(z \ (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(12780,a,12864,a),flip(a)].">
      <j1 rule="hyper" parents="12780 12864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12868">
    <literal><![CDATA[
      T(x,(y * ((z * y) \ (y \ 1))) * u) = T(x,(z \ (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(974(a,1),12866(a,1,2,1))].">
      <j1 rule="para" parents="974 12866"/>
    </justification>
  </clause>

  <clause id="12869">
    <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(8808(a,1),12862(a,1,2,1,2))].">
      <j1 rule="para" parents="8808 12862"/>
    </justification>
  </clause>

  <clause id="12870">
    <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(8770(a,1),12869(a,1,2,1,2))].">
      <j1 rule="para" parents="8770 12869"/>
    </justification>
  </clause>

  <clause id="12871">
    <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(4959(a,2),12870(a,1,2,1))].">
      <j1 rule="para" parents="4959 12870"/>
    </justification>
  </clause>

  <clause id="12872">
    <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(5647,a,12871,a)].">
      <j1 rule="hyper" parents="5647 12871"/>
    </justification>
  </clause>

  <clause id="12873">
    <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(8827(a,1),12872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8827 12872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12874">
    <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(1447(a,1),12873(a,2,2))].">
      <j1 rule="para" parents="1447 12873"/>
    </justification>
  </clause>

  <clause id="12875">
    <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(347,a,7321,a(flip),b,12874,a),flip(a)].">
      <j1 rule="hyper" parents="347 7321 12874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12876">
    <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(347,a,3530,a(flip),b,12875,a),flip(a)].">
      <j1 rule="hyper" parents="347 3530 12875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12877">
    <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(1294(a,1),12876(a,1,1))].">
      <j1 rule="para" parents="1294 12876"/>
    </justification>
  </clause>

  <clause id="12878">
    <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(12877(a,1),10912(a,1,2))].">
      <j1 rule="para" parents="12877 10912"/>
    </justification>
  </clause>

  <clause id="12879">
    <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(10913,a,12878,a),flip(a)].">
      <j1 rule="hyper" parents="10913 12878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12880">
    <literal><![CDATA[
      K(x \ L(x,y,z),K(u * x,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,K(w,x \ L(x,y,z))) = v5
    ]]></literal>
    <justification jstring="[para(12879(a,2),7314(a,1))].">
      <j1 rule="para" parents="12879 7314"/>
    </justification>
  </clause>

  <clause id="12881">
    <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(12880,a,12857,a),flip(a)].">
      <j1 rule="hyper" parents="12880 12857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12882">
    <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(347,a,7279,a,b,12881,a),flip(a)].">
      <j1 rule="hyper" parents="347 7279 12881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12883">
    <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(12858,a,12882,a)].">
      <j1 rule="hyper" parents="12858 12882"/>
    </justification>
  </clause>

  <clause id="12884">
    <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(63,a,12859,a,b,12883,a)].">
      <j1 rule="hyper" parents="63 12859 12883"/>
    </justification>
  </clause>

  <clause id="12885">
    <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(347,a,12582,a(flip),b,12884,a),flip(a)].">
      <j1 rule="hyper" parents="347 12582 12884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12886">
    <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(8772,a,12885,a)].">
      <j1 rule="hyper" parents="8772 12885"/>
    </justification>
  </clause>

  <clause id="12887">
    <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(12885(a,1),8772(a,1))].">
      <j1 rule="para" parents="12885 8772"/>
    </justification>
  </clause>

  <clause id="12888">
    <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(63,a,8771,a,b,12886,a)].">
      <j1 rule="hyper" parents="63 8771 12886"/>
    </justification>
  </clause>

  <clause id="12898">
    <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(347,a,8986,a(flip),b,9044,a),flip(a)].">
      <j1 rule="hyper" parents="347 8986 9044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12899">
    <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(347,a,7283,a(flip),b,12898,a),flip(a)].">
      <j1 rule="hyper" parents="347 7283 12898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12900">
    <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(347,a,12888,a(flip),b,12899,a),flip(a)].">
      <j1 rule="hyper" parents="347 12888 12899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12901">
    <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(8956,a,12900,a)].">
      <j1 rule="hyper" parents="8956 12900"/>
    </justification>
  </clause>

  <clause id="12902">
    <literal><![CDATA[
      K(R(T(x,y * (((y \ x) \ 1) \ 1)),x \ y,y \ (y / (((x \ y) \ 1) \ 1))),z) = K(((y \ (y / (x \ y))) * (x \ y)) \ (y / (((x \ y) \ 1) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(2606(a,1),9031(a,1,1,1,2))].">
      <j1 rule="para" parents="2606 9031"/>
    </justification>
  </clause>

  <clause id="12903">
    <literal><![CDATA[
      L(x,K(y,z),R(K(u,y) * R(K(y,u),w,v5),K(y,z),x)) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,9,a(flip),b,10591,a),flip(a)].">
      <j1 rule="hyper" parents="347 9 10591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12905">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y) * R(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(10589(a,1),12903(a,1,3))].">
      <j1 rule="para" parents="10589 12903"/>
    </justification>
  </clause>

  <clause id="12907">
    <literal><![CDATA[
      L(x,K(y,z),a(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(12807(a,1),12905(a,1,3))].">
      <j1 rule="para" parents="12807 12905"/>
    </justification>
  </clause>

  <clause id="12908">
    <literal><![CDATA[
      (a(K(x,y),z,u) * K(x,w)) * v5 = a(K(x,y),z,u) * (K(x,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(1362,a,12907,a),flip(a)].">
      <j1 rule="hyper" parents="1362 12907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12909">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) * (K(x,y) * (K(y,x) * z)) = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,12835,a(flip),b,12908,a),flip(a)].">
      <j1 rule="hyper" parents="63 12835 12908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12910">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) * z = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(5261(a,1),12909(a,1,2))].">
      <j1 rule="para" parents="5261 12909"/>
    </justification>
  </clause>

  <clause id="12911">
    <literal><![CDATA[
      x * a(K(y,T(z,x)),u,w) = a(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(7379(a,1),12910(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7379 12910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12912">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) = T(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(270,a,12911,a),flip(a)].">
      <j1 rule="hyper" parents="270 12911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12913">
    <literal><![CDATA[
      K(x * y,x * R(y,z,u)) = a(K(x,T(y,R(y,z,u))),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,12823,a(flip),b,12912,a)].">
      <j1 rule="hyper" parents="347 12823 12912"/>
    </justification>
  </clause>

  <clause id="12914">
    <literal><![CDATA[
      K(x * y,x * R(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(196(a,1),12913(a,2,1,2))].">
      <j1 rule="para" parents="196 12913"/>
    </justification>
  </clause>

  <clause id="12915">
    <literal><![CDATA[
      R(K(x * y,x * R(y,z,u)),x * R(y,z,u),w) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(5501,a,12914,a)].">
      <j1 rule="hyper" parents="5501 12914"/>
    </justification>
  </clause>

  <clause id="12916">
    <literal><![CDATA[
      K(x,(x / y) * R(y,z,u)) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),12914(a,1,1))].">
      <j1 rule="para" parents="12 12914"/>
    </justification>
  </clause>

  <clause id="12917">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8403,a(flip),b,12916,a)].">
      <j1 rule="hyper" parents="63 8403 12916"/>
    </justification>
  </clause>

  <clause id="12918">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10428,a(flip),b,12917,a)].">
      <j1 rule="hyper" parents="63 10428 12917"/>
    </justification>
  </clause>

  <clause id="12919">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(y \ x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(5138(a,1),12918(a,2,1))].">
      <j1 rule="para" parents="5138 12918"/>
    </justification>
  </clause>

  <clause id="12920">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,11576,a(flip),b,12919,a),flip(a)].">
      <j1 rule="hyper" parents="347 11576 12919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12921">
    <literal><![CDATA[
      (x * K(y \ R(y,z,u),x)) \ L(x,y \ R(y,z,u),x) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6063,a,b,12920,a)].">
      <j1 rule="hyper" parents="63 6063 12920"/>
    </justification>
  </clause>

  <clause id="12922">
    <literal><![CDATA[
      R(a(K(x,y),z * y,u),x * R(y,z,u),w) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(12914(a,1),12915(a,1,1))].">
      <j1 rule="para" parents="12914 12915"/>
    </justification>
  </clause>

  <clause id="12923">
    <literal><![CDATA[
      a(K(x,R(y,x * R(y,z,u),w)),z * y,u) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12832,a,b,12922,a)].">
      <j1 rule="hyper" parents="63 12832 12922"/>
    </justification>
  </clause>

  <clause id="12924">
    <literal><![CDATA[
      a(K(x,R(y,R(y,z,u),w)),z * y,u) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11705,a(flip),b,12923,a)].">
      <j1 rule="hyper" parents="63 11705 12923"/>
    </justification>
  </clause>

  <clause id="12925">
    <literal><![CDATA[
      (x * K(y \ R(y,z,u),x)) \ L(x,a(y,z,u),x) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(12327(a,1),12921(a,1,2))].">
      <j1 rule="para" parents="12327 12921"/>
    </justification>
  </clause>

  <clause id="12926">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) * (x \ L(x,a(y,z,u),x)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(5723,a,12925,a)].">
      <j1 rule="hyper" parents="5723 12925"/>
    </justification>
  </clause>

  <clause id="12927">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12645,a(flip),b,12926,a),flip(a)].">
      <j1 rule="hyper" parents="63 12645 12926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12929">
    <literal><![CDATA[
      a(K(x,K(y,z)),u * y,w) = K(x,K(z,y \ R(y,u,w)))
    ]]></literal>
    <justification jstring="[para(12927(a,1),12850(a,2,2))].">
      <j1 rule="para" parents="12927 12850"/>
    </justification>
  </clause>

  <clause id="12930">
    <literal><![CDATA[
      K(x,K(y,z \ R(z,u,w))) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,12853,a(flip),b,12929,a),flip(a)].">
      <j1 rule="hyper" parents="63 12853 12929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12931">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8754,a,b,12930,a)].">
      <j1 rule="hyper" parents="63 8754 12930"/>
    </justification>
  </clause>

  <clause id="12932">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(7283(a,2),12931(a,2,1))].">
      <j1 rule="para" parents="7283 12931"/>
    </justification>
  </clause>

  <clause id="12933">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) \ z)) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(8980,a,12932,a)].">
      <j1 rule="hyper" parents="8980 12932"/>
    </justification>
  </clause>

  <clause id="12934">
    <literal><![CDATA[
      K(x,K(y,(z * u) / (R(z,w,v5) * u))) = a(K(x,K(R(y,z,u),z)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,11751,a(flip),b,12933,a)].">
      <j1 rule="hyper" parents="63 11751 12933"/>
    </justification>
  </clause>

  <clause id="12935">
    <literal><![CDATA[
      K(x,K(y,(z * u) / (R(z,w,v5) * u))) = a(K(x,K(z,R(y,z,u))),w,v5)
    ]]></literal>
    <justification jstring="[para(7293(a,1),12934(a,2,1))].">
      <j1 rule="para" parents="7293 12934"/>
    </justification>
  </clause>

  <clause id="12936">
    <literal><![CDATA[
      K(x,K(y,(z * u) / (R(z,w,v5) * u))) = a(K(x,K(z,y)),w,v5)
    ]]></literal>
    <justification jstring="[para(10118(a,1),12935(a,2,1,2))].">
      <j1 rule="para" parents="10118 12935"/>
    </justification>
  </clause>

  <clause id="12937">
    <literal><![CDATA[
      K(x,K(R(y,z,u) \ y,R(w,y,v5))) = a(K(x,K(y,w)),z,u)
    ]]></literal>
    <justification jstring="[hyper(11715,a,12936,a)].">
      <j1 rule="hyper" parents="11715 12936"/>
    </justification>
  </clause>

  <clause id="12940">
    <literal><![CDATA[
      K(x,K(a(y,z,u),T(w,y * (z * u)))) = a(K(x,K(y,w)),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11708,a(flip),b,12937,a)].">
      <j1 rule="hyper" parents="63 11708 12937"/>
    </justification>
  </clause>

  <clause id="12942">
    <literal><![CDATA[
      a(K(x,K(y,(y * z) * u)),z,u) = K(x,K(y * z,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12901,a(flip),b,12940,a),flip(a)].">
      <j1 rule="hyper" parents="63 12901 12940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12943">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = a(K(y,K(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(9088(a,1),12942(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9088 12942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12944">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(347,a,12769,a(flip),b,12943,a),flip(a)].">
      <j1 rule="hyper" parents="347 12769 12943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12945">
    <literal><![CDATA[
      K(x,K(a(y,z,u),y * (z * u))) = 1
    ]]></literal>
    <justification jstring="[hyper(12887,a,12944,a)].">
      <j1 rule="hyper" parents="12887 12944"/>
    </justification>
  </clause>

  <clause id="12948">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u)) * 1
    ]]></literal>
    <justification jstring="[para(12945(a,1),9217(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12945 9217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12949">
    <literal><![CDATA[
      R(K(x,y \ R(y,z,u)),R(y,z,u),z * u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(130,a,12948,a(flip),b,8649,a),flip(a)].">
      <j1 rule="hyper" parents="130 12948 8649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12951">
    <literal><![CDATA[
      R(a(K(x,y),z * y,u),R(y,z,u),z * u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(12927(a,2),12949(a,1,1))].">
      <j1 rule="para" parents="12927 12949"/>
    </justification>
  </clause>

  <clause id="12952">
    <literal><![CDATA[
      a(K(x,R(y,R(y,z,u),z * u)),z * y,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12832,a,b,12951,a)].">
      <j1 rule="hyper" parents="63 12832 12951"/>
    </justification>
  </clause>

  <clause id="12953">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12924,a(flip),b,12952,a)].">
      <j1 rule="hyper" parents="63 12924 12952"/>
    </justification>
  </clause>

  <clause id="12955">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12927,a(flip),b,12953,a)].">
      <j1 rule="hyper" parents="63 12927 12953"/>
    </justification>
  </clause>

  <clause id="12956">
    <literal><![CDATA[
      a(K(x,y),z,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12822,a(flip),b,12953,a)].">
      <j1 rule="hyper" parents="63 12822 12953"/>
    </justification>
  </clause>

  <clause id="12957">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,12651,a,b,12956,a),flip(a)].">
      <j1 rule="hyper" parents="347 12651 12956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12958">
    <literal><![CDATA[
      a(x,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(5503,a,12957,a),flip(a)].">
      <j1 rule="hyper" parents="5503 12957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12959">
    <literal><![CDATA[
      (T(x,x \ y) * a(z,u,K(w,v5))) \ ((x \ y) \ y) = a(K(z,w),u,v5)
    ]]></literal>
    <justification jstring="[para(12957(a,1),12825(a,1,1,2))].">
      <j1 rule="para" parents="12957 12825"/>
    </justification>
  </clause>

  <clause id="12960">
    <literal><![CDATA[
      K(a(x,x,y),z) = 1
    ]]></literal>
    <justification jstring="[hyper(12683,a,12958,a)].">
      <j1 rule="hyper" parents="12683 12958"/>
    </justification>
  </clause>

  <clause id="12962">
    <literal><![CDATA[
      L(K(x,y),z,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(52,a,12958,a)].">
      <j1 rule="hyper" parents="52 12958"/>
    </justification>
  </clause>

  <clause id="12963">
    <literal><![CDATA[
      T(x,a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(189,a,12679,a,b,12958,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="189 12679 12958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12964">
    <literal><![CDATA[
      a(x,x,y) * z = z * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(9607,a,12960,a)].">
      <j1 rule="hyper" parents="9607 12960"/>
    </justification>
  </clause>

  <clause id="12965">
    <literal><![CDATA[
      T(a(x,x,y),z) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(56,a,12960,a)].">
      <j1 rule="hyper" parents="56 12960"/>
    </justification>
  </clause>

  <clause id="12966">
    <literal><![CDATA[
      x / a(y,y,z) = a(y,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(193,a,5104,a,b,12960,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="193 5104 12960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12967">
    <literal><![CDATA[
      T(x * (a(y,z,x) \ u),a(w,w,v5)) = a(y,z,x) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,12716,a,b,12963,a),flip(a)].">
      <j1 rule="hyper" parents="347 12716 12963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12968">
    <literal><![CDATA[
      T(x,a(y * z,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,12698,a(flip),b,12963,a)].">
      <j1 rule="hyper" parents="63 12698 12963"/>
    </justification>
  </clause>

  <clause id="12970">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3519,a,12962,a)].">
      <j1 rule="hyper" parents="3519 12962"/>
    </justification>
  </clause>

  <clause id="12971">
    <literal><![CDATA[
      K(L(x,y,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11104,a(flip),b,12962,a)].">
      <j1 rule="hyper" parents="63 11104 12962"/>
    </justification>
  </clause>

  <clause id="12972">
    <literal><![CDATA[
      K(x,(y * y) \ z) = K(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11074,a(flip),b,12962,a)].">
      <j1 rule="hyper" parents="63 11074 12962"/>
    </justification>
  </clause>

  <clause id="12973">
    <literal><![CDATA[
      (x \ 1) * K(y,z) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,12962,a(flip),b,3197,a),flip(a)].">
      <j1 rule="hyper" parents="128 12962 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12974">
    <literal><![CDATA[
      T(x,L(y,z,z)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[para(12962(a,1),11060(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12962 11060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12975">
    <literal><![CDATA[
      K((x \ 1) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(3192(a,1),12971(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3192 12971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12976">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11166,a,12970,a)].">
      <j1 rule="hyper" parents="11166 12970"/>
    </justification>
  </clause>

  <clause id="12977">
    <literal><![CDATA[
      K(x,(y * z) \ 1) = K(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(8273,a,12970,a)].">
      <j1 rule="hyper" parents="8273 12970"/>
    </justification>
  </clause>

  <clause id="12979">
    <literal><![CDATA[
      a(x,x \ 1,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,12970,a,b,9239,a),flip(a)].">
      <j1 rule="hyper" parents="129 12970 9239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12980">
    <literal><![CDATA[
      K((x \ y) \ z,y) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,11204,a(flip),b,12970,a),flip(a)].">
      <j1 rule="hyper" parents="63 11204 12970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12981">
    <literal><![CDATA[
      a(1 / x,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[para(83(a,1),12979(a,1,2))].">
      <j1 rule="para" parents="83 12979"/>
    </justification>
  </clause>

  <clause id="12982">
    <literal><![CDATA[
      (1 / x) * (x * K(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(189,a,246,a,b,12981,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="189 246 12981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12983">
    <literal><![CDATA[
      T(x,L(y,z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(12974(a,2),4984(a,1))].">
      <j1 rule="para" parents="12974 4984"/>
    </justification>
  </clause>

  <clause id="12984">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(560(a,1),12976(a,1,2)),flip(a)].">
      <j1 rule="para" parents="560 12976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12985">
    <literal><![CDATA[
      K(x,T((y \ 1) \ z,u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(688(a,1),12976(a,1,2)),flip(a)].">
      <j1 rule="para" parents="688 12976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12986">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = K(x,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[para(689(a,1),12976(a,1,2)),flip(a)].">
      <j1 rule="para" parents="689 12976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12987">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3193(a,1),12976(a,1,2))].">
      <j1 rule="para" parents="3193 12976"/>
    </justification>
  </clause>

  <clause id="12988">
    <literal><![CDATA[
      K(x,y) * (1 / z) = K(x,y) / z
    ]]></literal>
    <justification jstring="[para(12976(a,1),11743(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12976 11743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12989">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11733,a,12987,a)].">
      <j1 rule="hyper" parents="11733 12987"/>
    </justification>
  </clause>

  <clause id="12990">
    <literal><![CDATA[
      K(x,L(y,z \ x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,12222,a(flip),b,12987,a)].">
      <j1 rule="hyper" parents="63 12222 12987"/>
    </justification>
  </clause>

  <clause id="12991">
    <literal><![CDATA[
      K(x,L(y,z,z \ x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,12221,a(flip),b,12987,a)].">
      <j1 rule="hyper" parents="63 12221 12987"/>
    </justification>
  </clause>

  <clause id="12992">
    <literal><![CDATA[
      K(x,y * (z \ 1)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11734,a(flip),b,12987,a)].">
      <j1 rule="hyper" parents="63 11734 12987"/>
    </justification>
  </clause>

  <clause id="12993">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2938(a,1),12987(a,1,2))].">
      <j1 rule="para" parents="2938 12987"/>
    </justification>
  </clause>

  <clause id="12995">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,L(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(347,a,12987,a,b,12989,a),flip(a)].">
      <j1 rule="hyper" parents="347 12987 12989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12996">
    <literal><![CDATA[
      K(x,R(y,z,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2190(a,1),12989(a,1,2))].">
      <j1 rule="para" parents="2190 12989"/>
    </justification>
  </clause>

  <clause id="13000">
    <literal><![CDATA[
      K(x,(y * z) \ x) = K(x,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(11079,a,12990,a)].">
      <j1 rule="hyper" parents="11079 12990"/>
    </justification>
  </clause>

  <clause id="13002">
    <literal><![CDATA[
      T(x,L(y,z \ x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,12990,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 12990 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13003">
    <literal><![CDATA[
      (x * ((x \ y) * z)) \ K(y,z) = (L(z,x \ y,x) * y) \ 1
    ]]></literal>
    <justification jstring="[para(12990(a,1),9616(a,1,2))].">
      <j1 rule="para" parents="12990 9616"/>
    </justification>
  </clause>

  <clause id="13004">
    <literal><![CDATA[
      K(x * y,L(z,x,y)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(10178(a,1),12990(a,1,2))].">
      <j1 rule="para" parents="10178 12990"/>
    </justification>
  </clause>

  <clause id="13006">
    <literal><![CDATA[
      K(x,x \ ((x / y) * z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10156(a,1),12991(a,1,2))].">
      <j1 rule="para" parents="10156 12991"/>
    </justification>
  </clause>

  <clause id="13007">
    <literal><![CDATA[
      T(x,(y \ x) \ z) = T(x,x \ (y * z))
    ]]></literal>
    <justification jstring="[para(561(a,1),13002(a,1,2)),flip(a)].">
      <j1 rule="para" parents="561 13002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13008">
    <literal><![CDATA[
      T(x * y,L(z,x,y)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(10178(a,1),13002(a,1,2))].">
      <j1 rule="para" parents="10178 13002"/>
    </justification>
  </clause>

  <clause id="13009">
    <literal><![CDATA[
      (x \ K(y,z)) * K(z,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(6138,a,12973,a)].">
      <j1 rule="hyper" parents="6138 12973"/>
    </justification>
  </clause>

  <clause id="13010">
    <literal><![CDATA[
      x \ K(y \ (x \ 1),z) = y * T(y \ (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(5948,a,12973,a),flip(a)].">
      <j1 rule="hyper" parents="5948 12973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13011">
    <literal><![CDATA[
      (1 / x) \ K(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(708,a,12973,a),flip(a)].">
      <j1 rule="hyper" parents="708 12973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13012">
    <literal><![CDATA[
      K(x,y) * (z \ K(y,x)) = T(z \ 1,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(269,a,12973,a,b,5261,a),flip(a)].">
      <j1 rule="hyper" parents="269 12973 5261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13013">
    <literal><![CDATA[
      (x \ 1) \ (x \ K(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(138,a,12973,a)].">
      <j1 rule="hyper" parents="138 12973"/>
    </justification>
  </clause>

  <clause id="13014">
    <literal><![CDATA[
      x * ((y \ 1) * K(z,u)) = x * (y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,12973,a,b,9,a)].">
      <j1 rule="hyper" parents="134 12973 9"/>
    </justification>
  </clause>

  <clause id="13015">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ 1) = z \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8855,a,b,12973,a)].">
      <j1 rule="hyper" parents="63 8855 12973"/>
    </justification>
  </clause>

  <clause id="13017">
    <literal><![CDATA[
      (x \ 1) * (y * K(z,y)) = (x \ K(z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,12973,a(flip),b,6046,a),flip(a)].">
      <j1 rule="hyper" parents="133 12973 6046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13019">
    <literal><![CDATA[
      (1 / x) \ K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(12973(a,1),708(a,1))].">
      <j1 rule="para" parents="12973 708"/>
    </justification>
  </clause>

  <clause id="13020">
    <literal><![CDATA[
      (x * K(y,z)) / a(x / (u \ 1),u \ 1,K(y,z)) = (x / (u \ 1)) * (u \ K(y,z))
    ]]></literal>
    <justification jstring="[para(12973(a,1),832(a,2,2))].">
      <j1 rule="para" parents="12973 832"/>
    </justification>
  </clause>

  <clause id="13022">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ 1) = K(z,y)
    ]]></literal>
    <justification jstring="[para(12973(a,1),6123(a,1,1))].">
      <j1 rule="para" parents="12973 6123"/>
    </justification>
  </clause>

  <clause id="13023">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(12973(a,1),6141(a,1,1))].">
      <j1 rule="para" parents="12973 6141"/>
    </justification>
  </clause>

  <clause id="13024">
    <literal><![CDATA[
      T(x \ K(y,z),K(z,y)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(12973(a,1),6121(a,1,1))].">
      <j1 rule="para" parents="12973 6121"/>
    </justification>
  </clause>

  <clause id="13025">
    <literal><![CDATA[
      T(x \ K(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(12973(a,1),6211(a,1,1))].">
      <j1 rule="para" parents="12973 6211"/>
    </justification>
  </clause>

  <clause id="13026">
    <literal><![CDATA[
      T(x \ K(y,z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(12973(a,1),7348(a,1,1))].">
      <j1 rule="para" parents="12973 7348"/>
    </justification>
  </clause>

  <clause id="13027">
    <literal><![CDATA[
      K(x / (y \ 1),z) = K(y * x,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(7492,a,12975,a)].">
      <j1 rule="hyper" parents="7492 12975"/>
    </justification>
  </clause>

  <clause id="13028">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(3932,a,12975,a)].">
      <j1 rule="hyper" parents="3932 12975"/>
    </justification>
  </clause>

  <clause id="13029">
    <literal><![CDATA[
      K((x \ 1) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(3927,a,12975,a),flip(a)].">
      <j1 rule="hyper" parents="3927 12975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13032">
    <literal><![CDATA[
      K((x \ 1) \ (y \ 1),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,9483,a(flip),b,12975,a)].">
      <j1 rule="hyper" parents="63 9483 12975"/>
    </justification>
  </clause>

  <clause id="13033">
    <literal><![CDATA[
      K((x \ y) \ z,y) = K(x * (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8248,a(flip),b,12975,a)].">
      <j1 rule="hyper" parents="63 8248 12975"/>
    </justification>
  </clause>

  <clause id="13034">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,12975,a(flip),b,5991,a),flip(a)].">
      <j1 rule="hyper" parents="134 12975 5991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13036">
    <literal><![CDATA[
      K((x \ 1) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(12975(a,1),3927(a,1))].">
      <j1 rule="para" parents="12975 3927"/>
    </justification>
  </clause>

  <clause id="13037">
    <literal><![CDATA[
      (x * K(y * x,z)) / (y \ 1) = T(x / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(12975(a,1),6002(a,1,1,2))].">
      <j1 rule="para" parents="12975 6002"/>
    </justification>
  </clause>

  <clause id="13038">
    <literal><![CDATA[
      x * (y * K(x * y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(12975(a,1),6020(a,1,2,2))].">
      <j1 rule="para" parents="12975 6020"/>
    </justification>
  </clause>

  <clause id="13039">
    <literal><![CDATA[
      (x * K(y * x,z)) * y = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(12975(a,1),6022(a,1,1,2))].">
      <j1 rule="para" parents="12975 6022"/>
    </justification>
  </clause>

  <clause id="13040">
    <literal><![CDATA[
      T(x * K(y * x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(12975(a,1),6068(a,1,1,2))].">
      <j1 rule="para" parents="12975 6068"/>
    </justification>
  </clause>

  <clause id="13043">
    <literal><![CDATA[
      (x * K(y * (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(12975(a,1),8170(a,1,1,2))].">
      <j1 rule="para" parents="12975 8170"/>
    </justification>
  </clause>

  <clause id="13044">
    <literal><![CDATA[
      (x / y) \ T(x,z) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,12320,a,b,12982,a)].">
      <j1 rule="hyper" parents="34 12320 12982"/>
    </justification>
  </clause>

  <clause id="13045">
    <literal><![CDATA[
      (x \ y) * K(y,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,12316,a,b,12982,a),flip(a)].">
      <j1 rule="hyper" parents="34 12316 12982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13046">
    <literal><![CDATA[
      K(x \ 1,x) * K(y,z) = (x \ 1) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,12982,a(flip),b,2927,a)].">
      <j1 rule="hyper" parents="134 12982 2927"/>
    </justification>
  </clause>

  <clause id="13047">
    <literal><![CDATA[
      T(x,(y * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(329(a,1),12983(a,1,2))].">
      <j1 rule="para" parents="329 12983"/>
    </justification>
  </clause>

  <clause id="13048">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,z \ y)) = K(x,u / ((y \ z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(12078,a,12984,a),flip(a)].">
      <j1 rule="hyper" parents="12078 12984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13049">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(12028,a,12984,a)].">
      <j1 rule="hyper" parents="12028 12984"/>
    </justification>
  </clause>

  <clause id="13050">
    <literal><![CDATA[
      K(x,(y \ 1) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(12025,a,12984,a),flip(a)].">
      <j1 rule="hyper" parents="12025 12984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13051">
    <literal><![CDATA[
      K(x * x,x \ y) = K(x * x,x * y)
    ]]></literal>
    <justification jstring="[hyper(6738,a,12984,a)].">
      <j1 rule="hyper" parents="6738 12984"/>
    </justification>
  </clause>

  <clause id="13053">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,10345,a,b,12984,a)].">
      <j1 rule="hyper" parents="347 10345 12984"/>
    </justification>
  </clause>

  <clause id="13054">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(132,a,12984,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 12984 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13055">
    <literal><![CDATA[
      K(x,L(y / (z * y),u,w) / (z \ 1)) = K(x,z * L(y / (z * y),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12114,a,b,12984,a)].">
      <j1 rule="hyper" parents="63 12114 12984"/>
    </justification>
  </clause>

  <clause id="13056">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y = K(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,6163,a,b,12984,a)].">
      <j1 rule="hyper" parents="63 6163 12984"/>
    </justification>
  </clause>

  <clause id="13060">
    <literal><![CDATA[
      (x * y) * K(z,x * y) = x * (y * K(z,x * y))
    ]]></literal>
    <justification jstring="[para(12984(a,1),6482(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12984 6482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13061">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(12984(a,1),11049(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12984 11049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13062">
    <literal><![CDATA[
      K(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(12984(a,1),12025(a,1))].">
      <j1 rule="para" parents="12984 12025"/>
    </justification>
  </clause>

  <clause id="13063">
    <literal><![CDATA[
      K(x,y) * (K(y,x) / z) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(5273,a,12988,a)].">
      <j1 rule="hyper" parents="5273 12988"/>
    </justification>
  </clause>

  <clause id="13064">
    <literal><![CDATA[
      K(x,y) / (z \ 1) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(643,a,12988,a),flip(a)].">
      <j1 rule="hyper" parents="643 12988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13065">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(12988(a,1),6872(a,1,1))].">
      <j1 rule="para" parents="12988 6872"/>
    </justification>
  </clause>

  <clause id="13066">
    <literal><![CDATA[
      K(x,y * (((z * (u / z)) / z) * (w \ 1))) = K(x,y * ((u / z) * (K(z,z \ u) / w)))
    ]]></literal>
    <justification jstring="[para(12988(a,1),5793(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="12988 5793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13069">
    <literal><![CDATA[
      T(x,y * (z \ 1)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(132,a,12992,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 12992 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13070">
    <literal><![CDATA[
      K(x,(y \ 1) \ (z \ 1)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12984,a,b,12992,a)].">
      <j1 rule="hyper" parents="63 12984 12992"/>
    </justification>
  </clause>

  <clause id="13071">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5404,a,b,12992,a)].">
      <j1 rule="hyper" parents="63 5404 12992"/>
    </justification>
  </clause>

  <clause id="13072">
    <literal><![CDATA[
      K(x,y / (z \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,5405,a(flip),b,12992,a),flip(a)].">
      <j1 rule="hyper" parents="63 5405 12992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13073">
    <literal><![CDATA[
      (K(x,y) / z) \ 1 = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(708,a,13009,a),flip(a)].">
      <j1 rule="hyper" parents="708 13009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13074">
    <literal><![CDATA[
      1 / (x * K(y,z)) = K(z,y) / x
    ]]></literal>
    <justification jstring="[hyper(220,a,218,a(flip),b,13009,a(flip))].">
      <j1 rule="hyper" parents="220 218 13009"/>
    </justification>
  </clause>

  <clause id="13077">
    <literal><![CDATA[
      (x \ 1) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ K(y,z) = u
    ]]></literal>
    <justification jstring="[para(13009(a,1),6145(a,1,1))].">
      <j1 rule="para" parents="13009 6145"/>
    </justification>
  </clause>

  <clause id="13081">
    <literal><![CDATA[
      (x / y) * (y * K(x,z)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,13011,a(flip),b,12319,a(flip))].">
      <j1 rule="hyper" parents="134 13011 12319"/>
    </justification>
  </clause>

  <clause id="13082">
    <literal><![CDATA[
      (x \ y) \ (x \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,12315,a(flip),b,13011,a(flip))].">
      <j1 rule="hyper" parents="128 12315 13011"/>
    </justification>
  </clause>

  <clause id="13083">
    <literal><![CDATA[
      (x \ y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(13011(a,1),12317(a,1))].">
      <j1 rule="para" parents="13011 12317"/>
    </justification>
  </clause>

  <clause id="13084">
    <literal><![CDATA[
      x * ((y \ 1) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y \ K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13013(a,1),357(a,1,2,2))].">
      <j1 rule="para" parents="13013 357"/>
    </justification>
  </clause>

  <clause id="13085">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ K(z,u))) = K(z,K(u,x))
    ]]></literal>
    <justification jstring="[para(13013(a,2),7283(a,2,2)),flip(a)].">
      <j1 rule="para" parents="13013 7283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13086">
    <literal><![CDATA[
      (x \ K(y,z)) \ x = K(z,y) * (x * x)
    ]]></literal>
    <justification jstring="[hyper(133,a,13022,a(flip),b,820,a),flip(a)].">
      <j1 rule="hyper" parents="133 13022 820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13087">
    <literal><![CDATA[
      (x \ K(y,z * (y \ u))) \ (x \ 1) = K((y \ z) * u,y)
    ]]></literal>
    <justification jstring="[para(10522(a,1),13022(a,1,1,2))].">
      <j1 rule="para" parents="10522 13022"/>
    </justification>
  </clause>

  <clause id="13088">
    <literal><![CDATA[
      T(x,((y * K(z * y,u)) / (z \ 1)) * w) = T(x,T(y / (1 / z),u) * w)
    ]]></literal>
    <justification jstring="[para(13028(a,1),6026(a,1,2,1,1,2))].">
      <j1 rule="para" parents="13028 6026"/>
    </justification>
  </clause>

  <clause id="13089">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z) = K(y,T(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(10393,a,13029,a),flip(a)].">
      <j1 rule="hyper" parents="10393 13029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13093">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),13029(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13094">
    <literal><![CDATA[
      (x / (y / z)) * (y / T(z,x)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(6168,a,13044,a)].">
      <j1 rule="hyper" parents="6168 13044"/>
    </justification>
  </clause>

  <clause id="13098">
    <literal><![CDATA[
      x / (y * K(z,x)) = T(x,z) / y
    ]]></literal>
    <justification jstring="[hyper(220,a,6109,a(flip),b,13044,a),flip(a)].">
      <j1 rule="hyper" parents="220 6109 13044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13099">
    <literal><![CDATA[
      T(x,y) / (z * T(x,y)) = x / (z * x)
    ]]></literal>
    <justification jstring="[hyper(220,a,5926,a(flip),b,13044,a)].">
      <j1 rule="hyper" parents="220 5926 13044"/>
    </justification>
  </clause>

  <clause id="13100">
    <literal><![CDATA[
      T(x,y) * K(x * y,z) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(213(a,1),13044(a,1,1)),flip(a)].">
      <j1 rule="para" parents="213 13044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13101">
    <literal><![CDATA[
      T(x,y) \ T(x * y,z) = T(y,x) * K(x * y,z)
    ]]></literal>
    <justification jstring="[para(4295(a,1),13044(a,1,1))].">
      <j1 rule="para" parents="4295 13044"/>
    </justification>
  </clause>

  <clause id="13102">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(6138,a,13045,a)].">
      <j1 rule="hyper" parents="6138 13045"/>
    </justification>
  </clause>

  <clause id="13103">
    <literal><![CDATA[
      x \ ((y \ z) \ z) = (x \ y) * K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,335,a(flip),b,13045,a)].">
      <j1 rule="hyper" parents="347 335 13045"/>
    </justification>
  </clause>

  <clause id="13104">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ x) = z \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8877,a,b,13045,a)].">
      <j1 rule="hyper" parents="63 8877 13045"/>
    </justification>
  </clause>

  <clause id="13106">
    <literal><![CDATA[
      x \ T(y,T(z,x)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8878,a(flip),b,13045,a),flip(a)].">
      <j1 rule="hyper" parents="63 8878 13045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13108">
    <literal><![CDATA[
      (x \ T(y,z)) * y = (x \ y) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,13045,a(flip),b,5919,a)].">
      <j1 rule="hyper" parents="133 13045 5919"/>
    </justification>
  </clause>

  <clause id="13109">
    <literal><![CDATA[
      (x \ T(y,z)) * L(u,K(y,z),x \ y) = (x \ y) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(133,a,13045,a(flip),b,212,a)].">
      <j1 rule="hyper" parents="133 13045 212"/>
    </justification>
  </clause>

  <clause id="13110">
    <literal><![CDATA[
      (x \ T(y,z)) / T(y,z) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,13045,a(flip),b,5925,a)].">
      <j1 rule="hyper" parents="131 13045 5925"/>
    </justification>
  </clause>

  <clause id="13113">
    <literal><![CDATA[
      (x \ (y / z)) * K(y / z,z) = x \ (z \ y)
    ]]></literal>
    <justification jstring="[para(113(a,1),13045(a,2,2))].">
      <j1 rule="para" parents="113 13045"/>
    </justification>
  </clause>

  <clause id="13114">
    <literal><![CDATA[
      T(x,x \ y) \ T(y,z) = T(x \ y,x) * K(y,z)
    ]]></literal>
    <justification jstring="[para(4301(a,1),13045(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4301 13045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13115">
    <literal><![CDATA[
      (x \ T(y,z)) \ (x \ y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(13045(a,1),6123(a,1,1))].">
      <j1 rule="para" parents="13045 6123"/>
    </justification>
  </clause>

  <clause id="13116">
    <literal><![CDATA[
      T(x \ T(y,z),K(z,y)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(13045(a,1),6121(a,1,1))].">
      <j1 rule="para" parents="13045 6121"/>
    </justification>
  </clause>

  <clause id="13117">
    <literal><![CDATA[
      K(x * (y \ T(z,u)),z) = K(x * (y \ z),z)
    ]]></literal>
    <justification jstring="[para(13045(a,1),7938(a,1,1,2))].">
      <j1 rule="para" parents="13045 7938"/>
    </justification>
  </clause>

  <clause id="13118">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(K(x,y),z \ x) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(13045(a,1),9606(a,2,1))].">
      <j1 rule="para" parents="13045 9606"/>
    </justification>
  </clause>

  <clause id="13119">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(132,a,13049,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 13049 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13120">
    <literal><![CDATA[
      K(x,L((1 / y) \ z,u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(13049(a,1),11049(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13049 11049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13121">
    <literal><![CDATA[
      K(x,y \ (T(z / u,z) * w)) = K(x,(y \ 1) * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,12163,a,b,13050,a)].">
      <j1 rule="hyper" parents="347 12163 13050"/>
    </justification>
  </clause>

  <clause id="13122">
    <literal><![CDATA[
      T(x,(y \ 1) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(132,a,13050,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 13050 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13123">
    <literal><![CDATA[
      T(x,(y \ z) * (y * y)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,9174,a,b,13054,a)].">
      <j1 rule="hyper" parents="63 9174 13054"/>
    </justification>
  </clause>

  <clause id="13124">
    <literal><![CDATA[
      T(x,y * ((y \ 1) * z)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),13054(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 13054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13125">
    <literal><![CDATA[
      T(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(13054(a,1),12020(a,1))].">
      <j1 rule="para" parents="13054 12020"/>
    </justification>
  </clause>

  <clause id="13126">
    <literal><![CDATA[
      1 / (x \ K(y,z)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(643,a,13063,a),flip(a)].">
      <j1 rule="hyper" parents="643 13063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13127">
    <literal><![CDATA[
      K(x,y) * (1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(13063(a,1),5274(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13063 5274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13128">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x) / z,u,w) \ K(y,x)) = 1 / L(z \ K(y,x),u,w)
    ]]></literal>
    <justification jstring="[para(9697(a,1),13063(a,1,2))].">
      <j1 rule="para" parents="9697 13063"/>
    </justification>
  </clause>

  <clause id="13129">
    <literal><![CDATA[
      (K(x,y) \ z) \ 1 = z \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,13064,a),flip(a)].">
      <j1 rule="hyper" parents="373 13064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13130">
    <literal><![CDATA[
      (K(x,y) * z) \ K(x,y) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(214,a,13064,a)].">
      <j1 rule="hyper" parents="214 13064"/>
    </justification>
  </clause>

  <clause id="13131">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3994,a,b,13069,a)].">
      <j1 rule="hyper" parents="63 3994 13069"/>
    </justification>
  </clause>

  <clause id="13132">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(83(a,1),13069(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="83 13069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13133">
    <literal><![CDATA[
      L(x,y \ 1,z) * (z * (y \ 1)) = z * ((y \ 1) * T(x,z / y))
    ]]></literal>
    <justification jstring="[para(13069(a,1),734(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13069 734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13134">
    <literal><![CDATA[
      K(x / (x / y),z / u) = K(y,T(z * (1 / u),x))
    ]]></literal>
    <justification jstring="[hyper(7449,a,13071,a),flip(a)].">
      <j1 rule="hyper" parents="7449 13071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13135">
    <literal><![CDATA[
      K(x,y * ((z \ (z / u)) \ 1)) = K(x,y / ((z * u) \ z))
    ]]></literal>
    <justification jstring="[para(3259(a,1),13071(a,1,2,2))].">
      <j1 rule="para" parents="3259 13071"/>
    </justification>
  </clause>

  <clause id="13136">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * K(u,y / z)) = K(x,T(y * (1 / z),u))
    ]]></literal>
    <justification jstring="[para(13071(a,1),7394(a,1,2,2))].">
      <j1 rule="para" parents="13071 7394"/>
    </justification>
  </clause>

  <clause id="13137">
    <literal><![CDATA[
      K(x,y / T((z \ 1) \ 1,u)) = K(x,y * (T(z,u) \ 1))
    ]]></literal>
    <justification jstring="[para(7555(a,1),13071(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7555 13071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13138">
    <literal><![CDATA[
      K(x,y / (z \ 1)) = x \ T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,4924,a(flip),b,13072,a),flip(a)].">
      <j1 rule="hyper" parents="347 4924 13072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13139">
    <literal><![CDATA[
      T(x,y / (z \ 1)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(132,a,13072,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 13072 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13140">
    <literal><![CDATA[
      K(x,y * z) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[para(13072(a,1),5260(a,1,1))].">
      <j1 rule="para" parents="13072 5260"/>
    </justification>
  </clause>

  <clause id="13141">
    <literal><![CDATA[
      K(x,L(y / (z \ 1),u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(13072(a,1),11049(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13072 11049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13142">
    <literal><![CDATA[
      1 / T(x * K(y,z),y) = K(z,y) / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(220,a,7510,a,b,13073,a)].">
      <j1 rule="hyper" parents="220 7510 13073"/>
    </justification>
  </clause>

  <clause id="13143">
    <literal><![CDATA[
      1 / (x * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) / x = u
    ]]></literal>
    <justification jstring="[para(13073(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13073 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13144">
    <literal><![CDATA[
      K(x,y * (z / ((u * K(w,v5)) \ 1))) = K(x,y * (z / (K(v5,w) / u)))
    ]]></literal>
    <justification jstring="[para(13073(a,1),5419(a,1,2,2,2,1))].">
      <j1 rule="para" parents="13073 5419"/>
    </justification>
  </clause>

  <clause id="13145">
    <literal><![CDATA[
      ((x * ((x \ y) * K(x / y,y))) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(13073(a,1),9909(a,1,1,1,2))].">
      <j1 rule="para" parents="13073 9909"/>
    </justification>
  </clause>

  <clause id="13146">
    <literal><![CDATA[
      K(x,y / (K(z,u) / w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(13073(a,1),12992(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13073 12992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13147">
    <literal><![CDATA[
      1 / (L(x \ K(y,z),u,w) * K(z,y)) = L(K(y,z) / x,u,w) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,9697,a(flip),b,13074,a),flip(a)].">
      <j1 rule="hyper" parents="347 9697 13074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13148">
    <literal><![CDATA[
      T(K(x,y) / z,z * K(y,x)) = (z * K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(13074(a,1),113(a,1,1))].">
      <j1 rule="para" parents="13074 113"/>
    </justification>
  </clause>

  <clause id="13151">
    <literal><![CDATA[
      K(x,(y / (1 / (K(z,u) / w))) * v5) = K(x,(y / (w * K(u,z))) * v5)
    ]]></literal>
    <justification jstring="[para(13074(a,1),6403(a,1,2,1,2,2))].">
      <j1 rule="para" parents="13074 6403"/>
    </justification>
  </clause>

  <clause id="13152">
    <literal><![CDATA[
      x / (y * K(x * K(z,x),z)) = (x * K(z,x)) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,5058,a(flip),b,13081,a)].">
      <j1 rule="hyper" parents="131 5058 13081"/>
    </justification>
  </clause>

  <clause id="13153">
    <literal><![CDATA[
      T(x,y) / (z \ x) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(131,a,13081,a(flip),b,10484,a)].">
      <j1 rule="hyper" parents="131 13081 10484"/>
    </justification>
  </clause>

  <clause id="13154">
    <literal><![CDATA[
      (K(x,y) * z) \ T(x,y) = z \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,13081,a(flip),b,10484,a)].">
      <j1 rule="hyper" parents="128 13081 10484"/>
    </justification>
  </clause>

  <clause id="13159">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(K(u,u \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,3878,a,b,13093,a),flip(a)].">
      <j1 rule="hyper" parents="347 3878 13093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13163">
    <literal><![CDATA[
      L(R(x,a(y,z,u) \ 1,a(y,z,u) \ 1),a(y,z,u) \ 1,x) = T(((a(y,z,u) \ 1) * x) * a(y,z,u),a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12596,a,b,13122,a)].">
      <j1 rule="hyper" parents="63 12596 13122"/>
    </justification>
  </clause>

  <clause id="13164">
    <literal><![CDATA[
      T(x,T(y * (z \ 1),y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10350,a,b,13122,a)].">
      <j1 rule="hyper" parents="63 10350 13122"/>
    </justification>
  </clause>

  <clause id="13166">
    <literal><![CDATA[
      T(x,(y \ 1) / z) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,13069,a(flip),b,13122,a)].">
      <j1 rule="hyper" parents="63 13069 13122"/>
    </justification>
  </clause>

  <clause id="13167">
    <literal><![CDATA[
      T(((x \ 1) * y) * a(z,u,w),x \ y) = a(z,u,w) * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,12637,a(flip),b,13122,a),flip(a)].">
      <j1 rule="hyper" parents="63 12637 13122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13169">
    <literal><![CDATA[
      ((x \ 1) * y) * T(z,x \ y) = z * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,13122,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 13122 22"/>
    </justification>
  </clause>

  <clause id="13170">
    <literal><![CDATA[
      ((x \ 1) * y) * T(z,x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x \ 1) * y) = u
    ]]></literal>
    <justification jstring="[para(13122(a,1),315(a,1,2))].">
      <j1 rule="para" parents="13122 315"/>
    </justification>
  </clause>

  <clause id="13171">
    <literal><![CDATA[
      T(x,y \ ((z * (y \ 1)) \ u)) = T(x,y * ((z * y) \ u))
    ]]></literal>
    <justification jstring="[para(974(a,1),13122(a,1,2)),flip(a)].">
      <j1 rule="para" parents="974 13122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13172">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ u,y \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / ((y \ 1) * z)) = w
    ]]></literal>
    <justification jstring="[para(13122(a,1),7491(a,1,2))].">
      <j1 rule="para" parents="13122 7491"/>
    </justification>
  </clause>

  <clause id="13173">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(13122(a,1),12107(a,1))].">
      <j1 rule="para" parents="13122 12107"/>
    </justification>
  </clause>

  <clause id="13174">
    <literal><![CDATA[
      (K(x,y) * z) \ 1 = z \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(214,a,13126,a)].">
      <j1 rule="hyper" parents="214 13126"/>
    </justification>
  </clause>

  <clause id="13175">
    <literal><![CDATA[
      (K(x,y) * z) \ y = z \ T(y,x)
    ]]></literal>
    <justification jstring="[para(13126(a,1),12324(a,1,1))].">
      <j1 rule="para" parents="13126 12324"/>
    </justification>
  </clause>

  <clause id="13176">
    <literal><![CDATA[
      (T(x,y) \ z) \ 1 = (x \ z) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5153(a,1),13129(a,1,1))].">
      <j1 rule="para" parents="5153 13129"/>
    </justification>
  </clause>

  <clause id="13177">
    <literal><![CDATA[
      ((x / y) * z) \ K(y,y \ x) = ((y \ x) * z) \ 1
    ]]></literal>
    <justification jstring="[para(5430(a,1),13129(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5430 13129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13178">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ 1 = u \ K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7318(a,1),13129(a,1,1))].">
      <j1 rule="para" parents="7318 13129"/>
    </justification>
  </clause>

  <clause id="13179">
    <literal><![CDATA[
      K(K(x,y) * z,(K(x,y) * z) \ K(x,y)) = (z \ 1) \ (K(x,y) / (K(x,y) * z))
    ]]></literal>
    <justification jstring="[para(13130(a,1),5049(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13130 5049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13180">
    <literal><![CDATA[
      T(x,K(y,z)) \ K(y,z) = (x / K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(7530(a,1),13130(a,1,1))].">
      <j1 rule="para" parents="7530 13130"/>
    </justification>
  </clause>

  <clause id="13181">
    <literal><![CDATA[
      T(x,T(y \ z,y)) = T(x,z * (1 / y))
    ]]></literal>
    <justification jstring="[hyper(347,a,7419,a,b,13131,a)].">
      <j1 rule="hyper" parents="347 7419 13131"/>
    </justification>
  </clause>

  <clause id="13182">
    <literal><![CDATA[
      L(T(x,y \ 1),y,x) = T(x,T(x,y) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10445,a(flip),b,13131,a)].">
      <j1 rule="hyper" parents="63 10445 13131"/>
    </justification>
  </clause>

  <clause id="13185">
    <literal><![CDATA[
      T(x,y / (z \ K(u,w))) = T(x,y * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[para(13126(a,1),13131(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13126 13131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13188">
    <literal><![CDATA[
      T(x,y / (K(z,u) * w)) = T(x,y * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(13126(a,1),13132(a,1,2,2))].">
      <j1 rule="para" parents="13126 13132"/>
    </justification>
  </clause>

  <clause id="13189">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[para(13139(a,1),8862(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13139 8862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13191">
    <literal><![CDATA[
      (T(x,y) \ z) * ((x \ z) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,5209,a(flip),b,13153,a)].">
      <j1 rule="hyper" parents="133 5209 13153"/>
    </justification>
  </clause>

  <clause id="13192">
    <literal><![CDATA[
      K(x,y) * (x / z) = T(x,y) / z
    ]]></literal>
    <justification jstring="[para(83(a,1),13153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="83 13153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13194">
    <literal><![CDATA[
      (T(x,y) * z) \ y = (x * z) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4946(a,1),13154(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4946 13154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13195">
    <literal><![CDATA[
      (T(x,y) * z) \ T(x,y) = (x * z) \ x
    ]]></literal>
    <justification jstring="[para(4974(a,1),13154(a,1,1))].">
      <j1 rule="para" parents="4974 13154"/>
    </justification>
  </clause>

  <clause id="13196">
    <literal><![CDATA[
      ((x / T(y,x)) * z) \ T(x,y) = ((x / y) * z) \ x
    ]]></literal>
    <justification jstring="[para(11437(a,1),13154(a,1,1))].">
      <j1 rule="para" parents="11437 13154"/>
    </justification>
  </clause>

  <clause id="13197">
    <literal><![CDATA[
      R(x,y,z \ T(K(u,w) * v5,T(u,w))) = R(x,y,z \ ((v5 \ u) \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(13154(a,1),12267(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="13154 12267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13198">
    <literal><![CDATA[
      L(x,y,z / (1 / (K(u,w) * v5))) = L(x,y,z / (v5 \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(13174(a,1),3939(a,2,3,2))].">
      <j1 rule="para" parents="13174 3939"/>
    </justification>
  </clause>

  <clause id="13199">
    <literal><![CDATA[
      L(x,y,(1 / (K(z,u) * w)) \ v5) = L(x,y,(w \ K(u,z)) \ v5)
    ]]></literal>
    <justification jstring="[para(13174(a,1),3943(a,2,3,1))].">
      <j1 rule="para" parents="13174 3943"/>
    </justification>
  </clause>

  <clause id="13200">
    <literal><![CDATA[
      T(x \ T(y,z),(K(z,y) * x) \ y) = (K(z,y) * x) \ y
    ]]></literal>
    <justification jstring="[hyper(468,a,xx,b,13175,a)].">
      <j1 rule="hyper" parents="468 13175"/>
    </justification>
  </clause>

  <clause id="13201">
    <literal><![CDATA[
      x / (y * K(x,z)) = K(z,x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(220,a,13044,a(flip),b,13175,a)].">
      <j1 rule="hyper" parents="220 13044 13175"/>
    </justification>
  </clause>

  <clause id="13202">
    <literal><![CDATA[
      K(x,y) * (T(y,x) / z) = y / z
    ]]></literal>
    <justification jstring="[hyper(220,a,83,a(flip),b,13175,a),flip(a)].">
      <j1 rule="hyper" parents="220 83 13175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13203">
    <literal><![CDATA[
      (K(x,y) \ z) \ T(y,x) != u \ w
    ]]></literal>
    <literal><![CDATA[
      w / (z \ y) = u
    ]]></literal>
    <justification jstring="[para(13175(a,1),660(a,1))].">
      <j1 rule="para" parents="13175 660"/>
    </justification>
  </clause>

  <clause id="13204">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = (T(K(x,y),z) * z) \ y
    ]]></literal>
    <justification jstring="[para(4149(a,2),13175(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4149 13175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13206">
    <literal><![CDATA[
      ((x \ y) \ y) / z = K(x,x \ y) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(347,a,337,a(flip),b,13192,a)].">
      <j1 rule="hyper" parents="347 337 13192"/>
    </justification>
  </clause>

  <clause id="13208">
    <literal><![CDATA[
      T(T(x,y) / z,K(x,y)) = (x / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(13192(a,1),6872(a,1,1))].">
      <j1 rule="para" parents="13192 6872"/>
    </justification>
  </clause>

  <clause id="13209">
    <literal><![CDATA[
      (T(x,y) / z) \ K(K(x,y),x / z) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(13192(a,1),9606(a,1,1))].">
      <j1 rule="para" parents="13192 9606"/>
    </justification>
  </clause>

  <clause id="13210">
    <literal><![CDATA[
      K(x \ y,x) * (((x \ y) \ y) / z) = x / z
    ]]></literal>
    <justification jstring="[para(112(a,1),13202(a,1,2,1))].">
      <j1 rule="para" parents="112 13202"/>
    </justification>
  </clause>

  <clause id="13211">
    <literal><![CDATA[
      K(x,y) * (x / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(13202(a,1),5274(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13202 5274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13212">
    <literal><![CDATA[
      L(x,y,z) * T(y * z,x) = (y * z) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,13008,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 13008 22"/>
    </justification>
  </clause>

  <clause id="13213">
    <literal><![CDATA[
      (x * (y * z)) / T(y * x,K(x,y) * z) = L(K(x,y) * z,y,x)
    ]]></literal>
    <justification jstring="[para(13008(a,1),10454(a,1,2))].">
      <j1 rule="para" parents="13008 10454"/>
    </justification>
  </clause>

  <clause id="13214">
    <literal><![CDATA[
      T(x,(y * z) \ 1) = T(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(132,a,12977,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 12977 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13216">
    <literal><![CDATA[
      K(x \ ((y \ x) * z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ z,x) = u
    ]]></literal>
    <justification jstring="[para(12980(a,1),8283(a,1))].">
      <j1 rule="para" parents="12980 8283"/>
    </justification>
  </clause>

  <clause id="13217">
    <literal><![CDATA[
      T(x,(y * z) \ x) = T(x,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(132,a,13000,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 13000 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13219">
    <literal><![CDATA[
      K(x,y \ T(z,x / y)) = K(x,x \ (z * (x / y)))
    ]]></literal>
    <justification jstring="[para(111(a,1),13006(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 13006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13220">
    <literal><![CDATA[
      T(T(x,x \ (y * z)),u) \ T(x,u) = K((y \ x) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[para(13007(a,1),4923(a,1,1,1))].">
      <j1 rule="para" parents="13007 4923"/>
    </justification>
  </clause>

  <clause id="13221">
    <literal><![CDATA[
      K(x / (y \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,10371,a(flip),b,13027,a),flip(a)].">
      <j1 rule="hyper" parents="347 10371 13027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13222">
    <literal><![CDATA[
      K(x / (y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(13027(a,2),10376(a,1))].">
      <j1 rule="para" parents="13027 10376"/>
    </justification>
  </clause>

  <clause id="13223">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3874,a,b,13221,a)].">
      <j1 rule="hyper" parents="63 3874 13221"/>
    </justification>
  </clause>

  <clause id="13224">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),13221(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="83 13221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13225">
    <literal><![CDATA[
      K(x / (y \ K(z,u)),w) = K(x * (K(u,z) * y),w)
    ]]></literal>
    <justification jstring="[para(13174(a,1),13221(a,1,1,2))].">
      <j1 rule="para" parents="13174 13221"/>
    </justification>
  </clause>

  <clause id="13226">
    <literal><![CDATA[
      K(x * (y \ 1),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(80(a,1),13223(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="80 13223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13227">
    <literal><![CDATA[
      K(x / (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(13224(a,1),3926(a,1))].">
      <j1 rule="para" parents="13224 3926"/>
    </justification>
  </clause>

  <clause id="13228">
    <literal><![CDATA[
      K(L(x / y,z,z),u) = K(x * (y \ 1),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,12971,a,b,13226,a)].">
      <j1 rule="hyper" parents="347 12971 13226"/>
    </justification>
  </clause>

  <clause id="13229">
    <literal><![CDATA[
      T(T(x,y * (z \ 1)),K(y / z,u)) = T(x,T(y * (z \ 1),u))
    ]]></literal>
    <justification jstring="[para(13226(a,1),6813(a,1,2))].">
      <j1 rule="para" parents="13226 6813"/>
    </justification>
  </clause>

  <clause id="13230">
    <literal><![CDATA[
      x \ ((y \ (x * z)) * y) = z * K(x * (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(134,a,13033,a(flip),b,5992,a),flip(a)].">
      <j1 rule="hyper" parents="134 13033 5992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13231">
    <literal><![CDATA[
      x \ (y \ T(y * x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(13034(a,2),356(a,1,2))].">
      <j1 rule="para" parents="13034 356"/>
    </justification>
  </clause>

  <clause id="13232">
    <literal><![CDATA[
      L(x * K(y * x,z),y,z) = (z * y) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(13034(a,1),480(a,1,1))].">
      <j1 rule="para" parents="13034 480"/>
    </justification>
  </clause>

  <clause id="13234">
    <literal><![CDATA[
      R(K(x * y,z) * K(y,K(x * y,z)),y,u) = ((x \ T(x * y,z)) * u) / (y * u)
    ]]></literal>
    <justification jstring="[para(13034(a,2),5061(a,2,1,1))].">
      <j1 rule="para" parents="13034 5061"/>
    </justification>
  </clause>

  <clause id="13235">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x * y) = u
    ]]></literal>
    <justification jstring="[para(13034(a,2),6141(a,1,1))].">
      <j1 rule="para" parents="13034 6141"/>
    </justification>
  </clause>

  <clause id="13236">
    <literal><![CDATA[
      a(x,y,K(z,x * y)) = 1
    ]]></literal>
    <justification jstring="[hyper(127,a,13038,a(flip),b,9261,a),flip(a)].">
      <j1 rule="hyper" parents="127 13038 9261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13237">
    <literal><![CDATA[
      a(x,y,K(z,x * (y * z))) = 1
    ]]></literal>
    <justification jstring="[hyper(11165,a,13236,a)].">
      <j1 rule="hyper" parents="11165 13236"/>
    </justification>
  </clause>

  <clause id="13238">
    <literal><![CDATA[
      K(a(x,y,z),x * (y * z)) = 1
    ]]></literal>
    <justification jstring="[hyper(12683,a,13237,a)].">
      <j1 rule="hyper" parents="12683 13237"/>
    </justification>
  </clause>

  <clause id="13239">
    <literal><![CDATA[
      K(x * (y * z),a(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,13238,a,b,5160,a),flip(a)].">
      <j1 rule="hyper" parents="129 13238 5160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13240">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * z)) = a(x,y,z) * 1
    ]]></literal>
    <justification jstring="[para(13239(a,1),5065(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13239 5065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13241">
    <literal><![CDATA[
      (x * K(y,z)) * (y / x) = T(x * (y / x),z)
    ]]></literal>
    <justification jstring="[para(12(a,1),13039(a,1,1,2,1))].">
      <j1 rule="para" parents="12 13039"/>
    </justification>
  </clause>

  <clause id="13242">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(13053(a,1),10405(a,1))].">
      <j1 rule="para" parents="13053 10405"/>
    </justification>
  </clause>

  <clause id="13244">
    <literal><![CDATA[
      T((x * K(y,z)) / (u / K(z,y)),u / T(K(z,y),x * K(y,z))) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(462,a,6121,a(flip),b,13094,a)].">
      <j1 rule="hyper" parents="462 6121 13094"/>
    </justification>
  </clause>

  <clause id="13245">
    <literal><![CDATA[
      K(x,y) * (y / (z * y)) = y / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(13099(a,1),13202(a,1,2))].">
      <j1 rule="para" parents="13099 13202"/>
    </justification>
  </clause>

  <clause id="13246">
    <literal><![CDATA[
      (x \ y) / (x \ T(y,z)) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(220,a,13104,a(flip),b,7129,a)].">
      <j1 rule="hyper" parents="220 13104 7129"/>
    </justification>
  </clause>

  <clause id="13247">
    <literal><![CDATA[
      K(x,y) * (z \ T(y,T(x,z))) = z \ y
    ]]></literal>
    <justification jstring="[hyper(134,a,13106,a,b,5256,a)].">
      <j1 rule="hyper" parents="134 13106 5256"/>
    </justification>
  </clause>

  <clause id="13248">
    <literal><![CDATA[
      T(x,T(K(y,z) * (u \ y),w) * u) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u * T(T(y,T(z,u)) / u,w)) = v5
    ]]></literal>
    <justification jstring="[para(13106(a,1),10394(a,1,2,1,1))].">
      <j1 rule="para" parents="13106 10394"/>
    </justification>
  </clause>

  <clause id="13249">
    <literal><![CDATA[
      R(x,x,x * y) = ((x \ 1) \ T(y,z)) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,3389,a,b,13110,a)].">
      <j1 rule="hyper" parents="347 3389 13110"/>
    </justification>
  </clause>

  <clause id="13250">
    <literal><![CDATA[
      L(T(x,x \ y),x,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1309,a(flip),b,13123,a)].">
      <j1 rule="hyper" parents="63 1309 13123"/>
    </justification>
  </clause>

  <clause id="13251">
    <literal><![CDATA[
      T(x,y * (z * z)) = T(x,z * (z * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),13123(a,1,2,1))].">
      <j1 rule="para" parents="9 13123"/>
    </justification>
  </clause>

  <clause id="13252">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(13123(a,1),9173(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13123 9173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13253">
    <literal><![CDATA[
      T(x,T(y,z \ u)) = T(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(13123(a,1),9175(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13123 9175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13254">
    <literal><![CDATA[
      R(T(x,x * y),x,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(41,a,4387,a,b,13250,a)].">
      <j1 rule="hyper" parents="41 4387 13250"/>
    </justification>
  </clause>

  <clause id="13255">
    <literal><![CDATA[
      T((x \ 1) \ 1,x * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,797,a,b,13254,a)].">
      <j1 rule="hyper" parents="63 797 13254"/>
    </justification>
  </clause>

  <clause id="13256">
    <literal><![CDATA[
      T(x,x \ (x \ y)) = R(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),13254(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 13254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13257">
    <literal><![CDATA[
      R(T(x,y),x,x) \ y = (x \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[para(13256(a,1),4788(a,1,1))].">
      <j1 rule="para" parents="13256 4788"/>
    </justification>
  </clause>

  <clause id="13258">
    <literal><![CDATA[
      K(x,y / (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(13138(a,2),5006(a,1))].">
      <j1 rule="para" parents="13138 5006"/>
    </justification>
  </clause>

  <clause id="13259">
    <literal><![CDATA[
      T(K(x,(y * K(z,z \ u)) * w),w \ T(w * (y * K(z,z \ u)),x)) = (w \ T(w * (y * K(z,z \ u)),x)) \ ((y / z) * ((z \ u) \ u))
    ]]></literal>
    <justification jstring="[hyper(462,a,5942,a,b,13140,a)].">
      <j1 rule="hyper" parents="462 5942 13140"/>
    </justification>
  </clause>

  <clause id="13260">
    <literal><![CDATA[
      T(K(x,K(y \ (z * (u \ 1)),w) * v5),v5 \ T(v5 * K(y \ (z * (u \ 1)),w),x)) = (v5 \ T(v5 * K(y \ (z * (u \ 1)),w),x)) \ K(y \ (z * (1 / u)),w)
    ]]></literal>
    <justification jstring="[hyper(462,a,3915,a,b,13140,a)].">
      <j1 rule="hyper" parents="462 3915 13140"/>
    </justification>
  </clause>

  <clause id="13261">
    <literal><![CDATA[
      T(x,y * (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(13181(a,1),7683(a,1))].">
      <j1 rule="para" parents="13181 7683"/>
    </justification>
  </clause>

  <clause id="13262">
    <literal><![CDATA[
      (T(L(x,y,z) \ x,u) \ x) * (L(x,y,z) \ u) = T(u,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(3309(a,1),13191(a,1,2,1))].">
      <j1 rule="para" parents="3309 13191"/>
    </justification>
  </clause>

  <clause id="13264">
    <literal><![CDATA[
      (x * ((x * y) / x)) \ y = (x * y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4149(a,1),13194(a,1,1))].">
      <j1 rule="para" parents="4149 13194"/>
    </justification>
  </clause>

  <clause id="13265">
    <literal><![CDATA[
      T(x,y) / L(z \ 1,z,x) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(220,a,244,a,b,13195,a)].">
      <j1 rule="hyper" parents="220 244 13195"/>
    </justification>
  </clause>

  <clause id="13266">
    <literal><![CDATA[
      K(x,y) * (y / (z / x)) = y / (z / T(x,y))
    ]]></literal>
    <justification jstring="[para(6102(a,1),13201(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6102 13201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13267">
    <literal><![CDATA[
      T(x,a(y * z,(y * z) \ y,z)) = T(x,z \ (((y * z) \ y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,6291,a,b,13214,a)].">
      <j1 rule="hyper" parents="63 6291 13214"/>
    </justification>
  </clause>

  <clause id="13268">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (y \ T(R(y,z,u),T(x,y))) = R(y,z,u) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,1463,a,b,13247,a),flip(a)].">
      <j1 rule="hyper" parents="347 1463 13247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13269">
    <literal><![CDATA[
      T(T(x,y),z * z) = T(x,z * (z * y))
    ]]></literal>
    <justification jstring="[hyper(1307,a,13251,a)].">
      <j1 rule="hyper" parents="1307 13251"/>
    </justification>
  </clause>

  <clause id="13270">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8880,a,13252,a)].">
      <j1 rule="hyper" parents="8880 13252"/>
    </justification>
  </clause>

  <clause id="13271">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z * u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(13252(a,1),7297(a,1,2))].">
      <j1 rule="para" parents="13252 7297"/>
    </justification>
  </clause>

  <clause id="13272">
    <literal><![CDATA[
      1 / T(x,x \ y) = T(x,x * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(220,a,13255,a(flip),b,7558,a(flip))].">
      <j1 rule="hyper" parents="220 13255 7558"/>
    </justification>
  </clause>

  <clause id="13273">
    <literal><![CDATA[
      T(x,(y \ 1) * ((y \ 1) * z)) = T(T(x,z),y \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,13122,a(flip),b,13269,a),flip(a)].">
      <j1 rule="hyper" parents="63 13122 13269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13274">
    <literal><![CDATA[
      K(x,T(y,z * u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13252,a(flip),b,13270,a)].">
      <j1 rule="hyper" parents="63 13252 13270"/>
    </justification>
  </clause>

  <clause id="13275">
    <literal><![CDATA[
      K((x \ y) * z,T(u,y * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * (x \ y),u) = w
    ]]></literal>
    <justification jstring="[para(13270(a,1),10383(a,1))].">
      <j1 rule="para" parents="13270 10383"/>
    </justification>
  </clause>

  <clause id="13276">
    <literal><![CDATA[
      K(x,T((y \ z) * u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (y \ z)) = w
    ]]></literal>
    <justification jstring="[para(13270(a,1),10405(a,1))].">
      <j1 rule="para" parents="13270 10405"/>
    </justification>
  </clause>

  <clause id="13277">
    <literal><![CDATA[
      K(x,T(y * (z \ u),u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ u) * y) = w
    ]]></literal>
    <justification jstring="[para(13270(a,1),10406(a,1))].">
      <j1 rule="para" parents="13270 10406"/>
    </justification>
  </clause>

  <clause id="13278">
    <literal><![CDATA[
      L(1 / T(x,x \ y),x,y) = (L(x,y,x) * y) \ y
    ]]></literal>
    <justification jstring="[para(13272(a,2),9317(a,1,1))].">
      <j1 rule="para" parents="13272 9317"/>
    </justification>
  </clause>

  <clause id="13279">
    <literal><![CDATA[
      K(x * (y * z),T(u,z * y)) = K((y * z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(10376,a,13274,a),flip(a)].">
      <j1 rule="hyper" parents="10376 13274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13280">
    <literal><![CDATA[
      K(x,T(y \ (z * u),u * z)) = K(x,(z * u) / y)
    ]]></literal>
    <justification jstring="[hyper(7771,a,13274,a),flip(a)].">
      <j1 rule="hyper" parents="7771 13274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13281">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z * y)) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(7491,a,13274,a),flip(a)].">
      <j1 rule="hyper" parents="7491 13274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13282">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,9096,a,b,13274,a)].">
      <j1 rule="hyper" parents="347 9096 13274"/>
    </justification>
  </clause>

  <clause id="13283">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,8996,a,b,13274,a)].">
      <j1 rule="hyper" parents="347 8996 13274"/>
    </justification>
  </clause>

  <clause id="13285">
    <literal><![CDATA[
      K(x,T(y,z * u)) * (u * z) = (u * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,13274,a,b,7378,a)].">
      <j1 rule="hyper" parents="133 13274 7378"/>
    </justification>
  </clause>

  <clause id="13289">
    <literal><![CDATA[
      (K(x,y) * z) \ K(u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      (z \ K(y,x)) * K(u,w) = v5
    ]]></literal>
    <justification jstring="[para(13126(a,1),13019(a,1,1))].">
      <j1 rule="para" parents="13126 13019"/>
    </justification>
  </clause>

  <clause id="13290">
    <literal><![CDATA[
      K((1 / x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3881(a,2),13036(a,1))].">
      <j1 rule="para" parents="3881 13036"/>
    </justification>
  </clause>

  <clause id="13291">
    <literal><![CDATA[
      K(x,(1 / y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(5412(a,2),13062(a,1))].">
      <j1 rule="para" parents="5412 13062"/>
    </justification>
  </clause>

  <clause id="13292">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(u,z) / y) \ w) = v5
    ]]></literal>
    <justification jstring="[para(13073(a,1),13062(a,1,2,1))].">
      <j1 rule="para" parents="13073 13062"/>
    </justification>
  </clause>

  <clause id="13293">
    <literal><![CDATA[
      L(T(x,y),z,u) * K(x * y,w) != v5
    ]]></literal>
    <literal><![CDATA[
      (x * (L(x,z,u) \ y)) \ T(x * y,w) = v5
    ]]></literal>
    <justification jstring="[para(9713(a,1),13083(a,1,1))].">
      <j1 rule="para" parents="9713 13083"/>
    </justification>
  </clause>

  <clause id="13294">
    <literal><![CDATA[
      T(x,(y \ 1) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(13069(a,1),13125(a,1))].">
      <j1 rule="para" parents="13069 13125"/>
    </justification>
  </clause>

  <clause id="13295">
    <literal><![CDATA[
      K(x,y) * (K(z,u) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / T(u,z) = w
    ]]></literal>
    <justification jstring="[para(4932(a,2),13127(a,1,2))].">
      <j1 rule="para" parents="4932 13127"/>
    </justification>
  </clause>

  <clause id="13296">
    <literal><![CDATA[
      1 / x != y
    ]]></literal>
    <literal><![CDATA[
      K(z,u) / (x * K(z,u)) = y
    ]]></literal>
    <justification jstring="[para(6109(a,1),13143(a,1,2))].">
      <j1 rule="para" parents="6109 13143"/>
    </justification>
  </clause>

  <clause id="13298">
    <literal><![CDATA[
      L(T(x,y \ 1),y,x) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,11925,a(flip),b,13182,a),flip(a)].">
      <j1 rule="hyper" parents="347 11925 13182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13299">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = w
    ]]></literal>
    <justification jstring="[para(13298(a,1),12647(a,1))].">
      <j1 rule="para" parents="13298 12647"/>
    </justification>
  </clause>

  <clause id="13300">
    <literal><![CDATA[
      K(x * y,z) * T(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,z) / T(y,x) = u
    ]]></literal>
    <justification jstring="[para(4295(a,1),13211(a,1,2))].">
      <j1 rule="para" parents="4295 13211"/>
    </justification>
  </clause>

  <clause id="13301">
    <literal><![CDATA[
      K(x / (y \ K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * (K(u,z) * y),w) = v5
    ]]></literal>
    <justification jstring="[para(13174(a,1),13222(a,1,1,2))].">
      <j1 rule="para" parents="13174 13222"/>
    </justification>
  </clause>

  <clause id="13302">
    <literal><![CDATA[
      K(x * (y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / y,z) = u
    ]]></literal>
    <justification jstring="[para(13228(a,1),7204(a,1))].">
      <j1 rule="para" parents="13228 7204"/>
    </justification>
  </clause>

  <clause id="13303">
    <literal><![CDATA[
      K(x,(1 / y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(5413(a,2),13242(a,1))].">
      <j1 rule="para" parents="5413 13242"/>
    </justification>
  </clause>

  <clause id="13304">
    <literal><![CDATA[
      K(x,(y \ x) \ (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(8491(a,2),13242(a,1))].">
      <j1 rule="para" parents="8491 13242"/>
    </justification>
  </clause>

  <clause id="13305">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(8861(a,2),13242(a,1))].">
      <j1 rule="para" parents="8861 13242"/>
    </justification>
  </clause>

  <clause id="13306">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(10439(a,2),13242(a,1))].">
      <j1 rule="para" parents="10439 13242"/>
    </justification>
  </clause>

  <clause id="13307">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ y) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = v5
    ]]></literal>
    <justification jstring="[para(10882(a,1),13242(a,1,2,1))].">
      <j1 rule="para" parents="10882 13242"/>
    </justification>
  </clause>

  <clause id="13308">
    <literal><![CDATA[
      K(x,(y \ 1) \ ((T(z,u) \ u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((z \ T(u,z)) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(12277(a,2),13242(a,1,2))].">
      <j1 rule="para" parents="12277 13242"/>
    </justification>
  </clause>

  <clause id="13309">
    <literal><![CDATA[
      K(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(13070(a,1),13242(a,1))].">
      <j1 rule="para" parents="13070 13242"/>
    </justification>
  </clause>

  <clause id="13310">
    <literal><![CDATA[
      K(x,y / (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(5406(a,2),13258(a,1))].">
      <j1 rule="para" parents="5406 13258"/>
    </justification>
  </clause>

  <clause id="13311">
    <literal><![CDATA[
      T(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(3994(a,1),13261(a,1))].">
      <j1 rule="para" parents="3994 13261"/>
    </justification>
  </clause>

  <clause id="13312">
    <literal><![CDATA[
      L(x \ 1,x,T(y,z)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(442,a,13265,a)].">
      <j1 rule="hyper" parents="442 13265"/>
    </justification>
  </clause>

  <clause id="13313">
    <literal><![CDATA[
      L(x \ 1,x,y / z) = L(x \ 1,x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(11456,a,13312,a),flip(a)].">
      <j1 rule="hyper" parents="11456 13312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13314">
    <literal><![CDATA[
      K(x \ (y \ ((1 / x) \ z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(13290,a,9650,a)].">
      <j1 rule="hyper" parents="13290 9650"/>
    </justification>
  </clause>

  <clause id="13315">
    <literal><![CDATA[
      K((K(x,y) / z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((z * K(y,x)) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(13074(a,1),13290(a,1,1,1))].">
      <j1 rule="para" parents="13074 13290"/>
    </justification>
  </clause>

  <clause id="13316">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u \ K(z,y)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(13126(a,1),13291(a,1,2,1))].">
      <j1 rule="para" parents="13126 13291"/>
    </justification>
  </clause>

  <clause id="13317">
    <literal><![CDATA[
      K(x,y) / ((L(z,u,w) \ z) * K(x,y)) = (L(z,u,w) \ z) \ 1
    ]]></literal>
    <justification jstring="[hyper(13296,a,10903,a)].">
      <j1 rule="hyper" parents="13296 10903"/>
    </justification>
  </clause>

  <clause id="13318">
    <literal><![CDATA[
      K(x,L((y * z) \ y,u,w) * z) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,z * L((y * z) \ y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(1810(a,1),13303(a,1,2))].">
      <j1 rule="para" parents="1810 13303"/>
    </justification>
  </clause>

  <clause id="13319">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (w \ K(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(13126(a,1),13310(a,1,2,2))].">
      <j1 rule="para" parents="13126 13310"/>
    </justification>
  </clause>

  <clause id="13320">
    <literal><![CDATA[
      x * (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      T(x * (y \ 1),x / y) = z
    ]]></literal>
    <justification jstring="[para(110(a,1),13311(a,1))].">
      <j1 rule="para" parents="110 13311"/>
    </justification>
  </clause>

  <clause id="13321">
    <literal><![CDATA[
      T(x,T((y \ 1) \ z,u)) = T(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(132,a,12985,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 12985 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13323">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(12995(a,2),7618(a,1))].">
      <j1 rule="para" parents="12995 7618"/>
    </justification>
  </clause>

  <clause id="13324">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(12995(a,1),10120(a,1))].">
      <j1 rule="para" parents="12995 10120"/>
    </justification>
  </clause>

  <clause id="13327">
    <literal><![CDATA[
      K(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(691(a,1),13323(a,1,2))].">
      <j1 rule="para" parents="691 13323"/>
    </justification>
  </clause>

  <clause id="13328">
    <literal><![CDATA[
      K(x,T(y * (z \ 1),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(721(a,1),13323(a,1,2))].">
      <j1 rule="para" parents="721 13323"/>
    </justification>
  </clause>

  <clause id="13329">
    <literal><![CDATA[
      L(K(x,y),z,z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(11049(a,2),13324(a,1))].">
      <j1 rule="para" parents="11049 13324"/>
    </justification>
  </clause>

  <clause id="13330">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2988(a,1),13329(a,1))].">
      <j1 rule="para" parents="2988 13329"/>
    </justification>
  </clause>

  <clause id="13331">
    <literal><![CDATA[
      K(L(x,y \ 1,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(11104(a,1),13330(a,1))].">
      <j1 rule="para" parents="11104 13330"/>
    </justification>
  </clause>

  <clause id="13332">
    <literal><![CDATA[
      K(K(x,y \ 1) * (y * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y \ 1,x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(6640(a,1),13331(a,1,1))].">
      <j1 rule="para" parents="6640 13331"/>
    </justification>
  </clause>

  <clause id="13333">
    <literal><![CDATA[
      K(x,y * (z \ K(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(4934(a,1),13327(a,1,2,2))].">
      <j1 rule="para" parents="4934 13327"/>
    </justification>
  </clause>

  <clause id="13334">
    <literal><![CDATA[
      K(x,y * (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(5404(a,2),13327(a,1))].">
      <j1 rule="para" parents="5404 13327"/>
    </justification>
  </clause>

  <clause id="13335">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ K(z,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (T(z,w) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(13176(a,1),13327(a,1,2,2))].">
      <j1 rule="para" parents="13176 13327"/>
    </justification>
  </clause>

  <clause id="13336">
    <literal><![CDATA[
      (x \ K(x \ y,y)) * y = T((x \ 1) * y,y)
    ]]></literal>
    <justification jstring="[hyper(6368,a,13017,a),flip(a)].">
      <j1 rule="hyper" parents="6368 13017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13337">
    <literal><![CDATA[
      T(T(x,y * x) * K(L(x,y,x) * y,z),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(4331(a,1),13040(a,1,1,2,1))].">
      <j1 rule="para" parents="4331 13040"/>
    </justification>
  </clause>

  <clause id="13338">
    <literal><![CDATA[
      T(K(x * y,z) * x,y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(10375(a,2),13040(a,1,1))].">
      <j1 rule="para" parents="10375 13040"/>
    </justification>
  </clause>

  <clause id="13339">
    <literal><![CDATA[
      K(x,T(y,z)) / z = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,8989,a(flip),b,13065,a)].">
      <j1 rule="hyper" parents="63 8989 13065"/>
    </justification>
  </clause>

  <clause id="13340">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(y,T(z,x)) / T(x,u)
    ]]></literal>
    <justification jstring="[para(13065(a,1),8990(a,1,1))].">
      <j1 rule="para" parents="13065 8990"/>
    </justification>
  </clause>

  <clause id="13341">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = (1 / x) * K(z,y)
    ]]></literal>
    <justification jstring="[para(13074(a,2),13065(a,1,1))].">
      <j1 rule="para" parents="13074 13065"/>
    </justification>
  </clause>

  <clause id="13342">
    <literal><![CDATA[
      (1 / x) * K(y,z / x) = K(y,x \ z) / x
    ]]></literal>
    <justification jstring="[para(113(a,1),13339(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="113 13339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13343">
    <literal><![CDATA[
      (x * K(y,z)) / a(x / (1 / u),1 / u,K(y,z)) = (x / (1 / u)) * (K(y,T(z,u)) / u)
    ]]></literal>
    <justification jstring="[para(13339(a,2),832(a,2,2))].">
      <j1 rule="para" parents="13339 832"/>
    </justification>
  </clause>

  <clause id="13344">
    <literal><![CDATA[
      (x \ K(y,z)) * K(y,K(z,u)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,13085,a(flip),b,10754,a)].">
      <j1 rule="hyper" parents="134 13085 10754"/>
    </justification>
  </clause>

  <clause id="13345">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(13089(a,2),8864(a,1))].">
      <j1 rule="para" parents="13089 8864"/>
    </justification>
  </clause>

  <clause id="13346">
    <literal><![CDATA[
      (x \ (y / z)) * K(z \ y,z) = x \ (z \ y)
    ]]></literal>
    <justification jstring="[para(5138(a,1),13113(a,1,2))].">
      <j1 rule="para" parents="5138 13113"/>
    </justification>
  </clause>

  <clause id="13347">
    <literal><![CDATA[
      T(x \ K(y,z),K(y,z)) = (x / K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,8963,a,b,13180,a)].">
      <j1 rule="hyper" parents="63 8963 13180"/>
    </justification>
  </clause>

  <clause id="13348">
    <literal><![CDATA[
      (x \ y) * (((x \ y) \ y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * (x / z) = u
    ]]></literal>
    <justification jstring="[para(13206(a,2),5619(a,1,2))].">
      <j1 rule="para" parents="13206 5619"/>
    </justification>
  </clause>

  <clause id="13349">
    <literal><![CDATA[
      K(x,y) * (y / L((x * z) / x,u,w)) = y / ((x * L(z,u,w)) / T(x,y))
    ]]></literal>
    <justification jstring="[para(949(a,2),13266(a,1,2,2))].">
      <j1 rule="para" parents="949 13266"/>
    </justification>
  </clause>

  <clause id="13350">
    <literal><![CDATA[
      K(x,T(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(13282(a,1),9098(a,1))].">
      <j1 rule="para" parents="13282 9098"/>
    </justification>
  </clause>

  <clause id="13351">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,u * (x * z)))
    ]]></literal>
    <justification jstring="[para(13283(a,1),7959(a,1,1,2))].">
      <j1 rule="para" parents="13283 7959"/>
    </justification>
  </clause>

  <clause id="13352">
    <literal><![CDATA[
      L(L(x \ 1,x,T(x,y) \ z) \ u,(z * K(y,x)) \ (z / T(x,y)),(z / T(x,y)) * x) = (z / T(x,y)) \ (((z / T(x,y)) * x) * u)
    ]]></literal>
    <justification jstring="[para(13313(a,1),6187(a,1,1,1))].">
      <j1 rule="para" parents="13313 6187"/>
    </justification>
  </clause>

  <clause id="13353">
    <literal><![CDATA[
      T(x,T((y \ 1) * z,u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4874,a(flip),b,13321,a),flip(a)].">
      <j1 rule="hyper" parents="63 4874 13321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13354">
    <literal><![CDATA[
      (x \ (y \ z)) * K(y,y \ z) = x \ (z / y)
    ]]></literal>
    <justification jstring="[hyper(6138,a,13346,a)].">
      <j1 rule="hyper" parents="6138 13346"/>
    </justification>
  </clause>

  <clause id="13355">
    <literal><![CDATA[
      (x \ y) / (z * K(x \ y,x)) = (y / x) / z
    ]]></literal>
    <justification jstring="[hyper(220,a,218,a(flip),b,13346,a(flip))].">
      <j1 rule="hyper" parents="220 218 13346"/>
    </justification>
  </clause>

  <clause id="13356">
    <literal><![CDATA[
      (x \ (y \ z)) * ((y \ z) \ z) = (x \ (z / y)) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,13346,a(flip),b,6108,a)].">
      <j1 rule="hyper" parents="133 13346 6108"/>
    </justification>
  </clause>

  <clause id="13357">
    <literal><![CDATA[
      (x \ (y \ z)) * T(y,y \ z) = (x \ (z / y)) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,13346,a(flip),b,6099,a)].">
      <j1 rule="hyper" parents="133 13346 6099"/>
    </justification>
  </clause>

  <clause id="13358">
    <literal><![CDATA[
      ((x \ y) / z) \ (y / x) = z * K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(708,a,13354,a),flip(a)].">
      <j1 rule="hyper" parents="708 13354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13359">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ 1) * (x \ 1) = L(x \ 1,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2910,a(flip),b,13354,a)].">
      <j1 rule="hyper" parents="63 2910 13354"/>
    </justification>
  </clause>

  <clause id="13360">
    <literal><![CDATA[
      L(x,y,z * (u \ (1 / w))) = L(x,y,z * (u \ (w \ 1)))
    ]]></literal>
    <justification jstring="[para(13354(a,1),3947(a,1,3,2))].">
      <j1 rule="para" parents="13354 3947"/>
    </justification>
  </clause>

  <clause id="13361">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) / z) = (y / x) / z
    ]]></literal>
    <justification jstring="[hyper(63,a,13201,a(flip),b,13355,a)].">
      <j1 rule="hyper" parents="63 13201 13355"/>
    </justification>
  </clause>

  <clause id="13362">
    <literal><![CDATA[
      (x / y) \ ((x / y) / z) = (y \ x) \ ((y \ x) / z)
    ]]></literal>
    <justification jstring="[hyper(128,a,13361,a(flip),b,5477,a)].">
      <j1 rule="hyper" parents="128 13361 5477"/>
    </justification>
  </clause>

  <clause id="13363">
    <literal><![CDATA[
      T(x,T((y \ 1) / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ (z \ y))) = u
    ]]></literal>
    <justification jstring="[para(7825(a,2),13047(a,1))].">
      <j1 rule="para" parents="7825 13047"/>
    </justification>
  </clause>

  <clause id="13364">
    <literal><![CDATA[
      T(x,y / (z * z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (z \ y)) = u
    ]]></literal>
    <justification jstring="[para(9171(a,2),13047(a,1))].">
      <j1 rule="para" parents="9171 13047"/>
    </justification>
  </clause>

  <clause id="13365">
    <literal><![CDATA[
      K(x \ (y * z),z) = K((x \ z) * y,z)
    ]]></literal>
    <justification jstring="[hyper(13216,a,9651,a)].">
      <j1 rule="hyper" parents="13216 9651"/>
    </justification>
  </clause>

  <clause id="13366">
    <literal><![CDATA[
      K((x \ y) * z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(9825,a,13365,a),flip(a)].">
      <j1 rule="hyper" parents="9825 13365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13367">
    <literal><![CDATA[
      K((x / y) * z,x) = K(x * (y \ z),x)
    ]]></literal>
    <justification jstring="[hyper(8284,a,13366,a)].">
      <j1 rule="hyper" parents="8284 13366"/>
    </justification>
  </clause>

  <clause id="13368">
    <literal><![CDATA[
      K((x * y) * (T(x,y) \ z),x * y) = K(y * z,x * y)
    ]]></literal>
    <justification jstring="[para(213(a,1),13367(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="213 13367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13369">
    <literal><![CDATA[
      K((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(5991(a,1),13231(a,1))].">
      <j1 rule="para" parents="5991 13231"/>
    </justification>
  </clause>

  <clause id="13370">
    <literal><![CDATA[
      K(((x \ 1) \ 1) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(13029(a,2),13369(a,1))].">
      <j1 rule="para" parents="13029 13369"/>
    </justification>
  </clause>

  <clause id="13371">
    <literal><![CDATA[
      a(x,y,z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,8,a(flip),b,13240,a)].">
      <j1 rule="hyper" parents="347 8 13240"/>
    </justification>
  </clause>

  <clause id="13372">
    <literal><![CDATA[
      a(x,y,z) * (x * (y * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(281,a,13240,a)].">
      <j1 rule="hyper" parents="281 13240"/>
    </justification>
  </clause>

  <clause id="13373">
    <literal><![CDATA[
      a(x,y,z) = R(x \ R(x,y,z),x,y * z)
    ]]></literal>
    <justification jstring="[hyper(130,a,13240,a(flip),b,3688,a)].">
      <j1 rule="hyper" parents="130 13240 3688"/>
    </justification>
  </clause>

  <clause id="13374">
    <literal><![CDATA[
      a(x,y,z) = R(R(x,y,z) / x,x,y * z)
    ]]></literal>
    <justification jstring="[hyper(130,a,13240,a(flip),b,610,a)].">
      <j1 rule="hyper" parents="130 13240 610"/>
    </justification>
  </clause>

  <clause id="13375">
    <literal><![CDATA[
      ((x * y) * z) / ((x * (y * (z * (u * u)))) / (u * u)) = a(x,y,z * (u * u))
    ]]></literal>
    <justification jstring="[hyper(130,a,13240,a(flip),b,907,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="130 13240 907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13376">
    <literal><![CDATA[
      ((x * y) * z) / (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(13240(a,2),141(a,1)),flip(b)].">
      <j1 rule="para" parents="13240 141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13378">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,x) = a(x,y,z) * ((y * z) * x)
    ]]></literal>
    <justification jstring="[hyper(133,a,13371,a,b,9587,a),flip(a)].">
      <j1 rule="hyper" parents="133 13371 9587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13379">
    <literal><![CDATA[
      a(x,y,z) \ ((x * y) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(132,a,13371,a,b,172,a)].">
      <j1 rule="hyper" parents="132 13371 172"/>
    </justification>
  </clause>

  <clause id="13380">
    <literal><![CDATA[
      a(x * (y / x),x,z) * (y * (T(x,y) * z)) = (y * T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,11578,a,b,13371,a(flip))].">
      <j1 rule="hyper" parents="133 11578 13371"/>
    </justification>
  </clause>

  <clause id="13381">
    <literal><![CDATA[
      K(x,a(y,z,u)) * (K(x,y) * (z * u)) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(133,a,12956,a(flip),b,13371,a(flip))].">
      <j1 rule="hyper" parents="133 12956 13371"/>
    </justification>
  </clause>

  <clause id="13382">
    <literal><![CDATA[
      (x * y) / (z * ((z \ x) * y)) = a(z,z \ x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),13371(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13383">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / (x * z) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),13371(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 13371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13384">
    <literal><![CDATA[
      (x * (y * z)) / (y * (z * T(x,y * z))) = a(y,z,T(x,y * z))
    ]]></literal>
    <justification jstring="[para(111(a,1),13371(a,2,1)),flip(a)].">
      <j1 rule="para" parents="111 13371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13385">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / (x * (z * y)) = a(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[para(111(a,1),13371(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="111 13371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13386">
    <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(274(a,1),13371(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="274 13371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13387">
    <literal><![CDATA[
      (x * (y * (x * y))) / ((x * y) * (x * y)) = a(x,y,x * y) \ 1
    ]]></literal>
    <justification jstring="[para(13371(a,2),515(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13371 515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13388">
    <literal><![CDATA[
      (L(x,y,z) * u) / ((x \ L(x,y,z)) * (x * u)) = a(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(3163(a,1),13371(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3163 13371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13389">
    <literal><![CDATA[
      ((x * (y \ (x \ 1))) * y) / K(y \ (x \ 1),y) = a(x,y \ (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(5387(a,1),13371(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5387 13371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13391">
    <literal><![CDATA[
      a(x,x \ y,z) \ (y * z) = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(128,a,165,a(flip),b,13372,a)].">
      <j1 rule="hyper" parents="128 165 13372"/>
    </justification>
  </clause>

  <clause id="13392">
    <literal><![CDATA[
      a(x / y,y,z) \ (x * z) = (x / y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(128,a,164,a(flip),b,13372,a)].">
      <j1 rule="hyper" parents="128 164 13372"/>
    </justification>
  </clause>

  <clause id="13393">
    <literal><![CDATA[
      T((x * y) * z,x * (y * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,12650,a,b,13372,a)].">
      <j1 rule="hyper" parents="63 12650 13372"/>
    </justification>
  </clause>

  <clause id="13394">
    <literal><![CDATA[
      ((x * y) * z) / L(y * z,x,a(x,y,z)) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(131,a,13372,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="131 13372 97"/>
    </justification>
  </clause>

  <clause id="13395">
    <literal><![CDATA[
      a(x,y,y \ z) * (x * z) = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),13372(a,1,2,2))].">
      <j1 rule="para" parents="10 13372"/>
    </justification>
  </clause>

  <clause id="13396">
    <literal><![CDATA[
      a(x,y / z,z) * (x * y) = (x * (y / z)) * z
    ]]></literal>
    <justification jstring="[para(12(a,1),13372(a,1,2,2))].">
      <j1 rule="para" parents="12 13372"/>
    </justification>
  </clause>

  <clause id="13398">
    <literal><![CDATA[
      x \ R(x,y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,586,a(flip),b,13373,a)].">
      <j1 rule="hyper" parents="347 586 13373"/>
    </justification>
  </clause>

  <clause id="13399">
    <literal><![CDATA[
      x * a(x,y,y) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,13373,a,b,586,a(flip))].">
      <j1 rule="hyper" parents="134 13373 586"/>
    </justification>
  </clause>

  <clause id="13400">
    <literal><![CDATA[
      x \ R(x * R(x \ 1,y,z),x \ 1,y * z) = (x \ 1) * a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(13373(a,2),1461(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13373 1461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13401">
    <literal><![CDATA[
      (R(x,y,y) \ x) \ 1 = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10763,a,b,13398,a)].">
      <j1 rule="hyper" parents="63 10763 13398"/>
    </justification>
  </clause>

  <clause id="13402">
    <literal><![CDATA[
      R(x,y,y) / x = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3675,a,b,13398,a)].">
      <j1 rule="hyper" parents="63 3675 13398"/>
    </justification>
  </clause>

  <clause id="13403">
    <literal><![CDATA[
      a(x,y,y) * x = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,13398,a(flip),b,3675,a)].">
      <j1 rule="hyper" parents="133 13398 3675"/>
    </justification>
  </clause>

  <clause id="13404">
    <literal><![CDATA[
      R(x,y,L(a(z,u,u),z,z)) = R(x,y,z * R(z,u,u))
    ]]></literal>
    <justification jstring="[para(13398(a,1),2242(a,1,3,1))].">
      <j1 rule="para" parents="13398 2242"/>
    </justification>
  </clause>

  <clause id="13405">
    <literal><![CDATA[
      R(x,y,y) \ x = a(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[para(13398(a,1),4742(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13398 4742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13407">
    <literal><![CDATA[
      a(x,y,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,y) = z
    ]]></literal>
    <justification jstring="[para(13402(a,1),280(a,1,1))].">
      <j1 rule="para" parents="13402 280"/>
    </justification>
  </clause>

  <clause id="13408">
    <literal><![CDATA[
      R(x,y,y) * L(z,x,a(x,y,y)) = a(x,y,y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,13403,a(flip),b,212,a)].">
      <j1 rule="hyper" parents="133 13403 212"/>
    </justification>
  </clause>

  <clause id="13409">
    <literal><![CDATA[
      R(R(x \ 1,y,z) / (x \ 1),x,y * z) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,2247,a(flip),b,13374,a)].">
      <j1 rule="hyper" parents="347 2247 13374"/>
    </justification>
  </clause>

  <clause id="13410">
    <literal><![CDATA[
      R(R(x,y,z) * (x \ 1),x,y * z) = R(a(x,y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(13374(a,2),722(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13374 722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13411">
    <literal><![CDATA[
      ((x * y) * z) * (x * (y * z)) = (x * (y * z)) * ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(1068,a,13393,a)].">
      <j1 rule="hyper" parents="1068 13393"/>
    </justification>
  </clause>

  <clause id="13412">
    <literal><![CDATA[
      K(x,x * ((y \ x) \ z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(13304,a,9805,a),flip(a)].">
      <j1 rule="hyper" parents="13304 9805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13413">
    <literal><![CDATA[
      K(x,(x / y) * z) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[para(83(a,1),13412(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="83 13412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13415">
    <literal><![CDATA[
      K(x,(y \ x) * z) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8403,a(flip),b,13413,a)].">
      <j1 rule="hyper" parents="63 8403 13413"/>
    </justification>
  </clause>

  <clause id="13416">
    <literal><![CDATA[
      K(x,K(y,(z \ y) * u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(13415(a,2),8759(a,1,2))].">
      <j1 rule="para" parents="13415 8759"/>
    </justification>
  </clause>

  <clause id="13417">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ z) * K(x,K(z,y \ u)) = K(x,z / ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(13416(a,1),8942(a,1,2))].">
      <j1 rule="para" parents="13416 8942"/>
    </justification>
  </clause>

  <clause id="13418">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((z \ y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z \ y) * u) / y) = w
    ]]></literal>
    <justification jstring="[para(13416(a,1),8951(a,1,1))].">
      <j1 rule="para" parents="13416 8951"/>
    </justification>
  </clause>

  <clause id="13419">
    <literal><![CDATA[
      K(x,T(y,z / (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(13132(a,2),13350(a,1,2))].">
      <j1 rule="para" parents="13132 13350"/>
    </justification>
  </clause>

  <clause id="13420">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(13252(a,2),13350(a,1))].">
      <j1 rule="para" parents="13252 13350"/>
    </justification>
  </clause>

  <clause id="13421">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(13270(a,2),13350(a,1))].">
      <j1 rule="para" parents="13270 13350"/>
    </justification>
  </clause>

  <clause id="13422">
    <literal><![CDATA[
      T(x * x,y) * (y / T(x * x,y)) = T(y,x \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(13364,a,4522,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="13364 4522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13423">
    <literal><![CDATA[
      T(x,y * (z / (u * u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ (u \ (y * z))) = w
    ]]></literal>
    <justification jstring="[para(464(a,1),13364(a,1,2))].">
      <j1 rule="para" parents="464 13364"/>
    </justification>
  </clause>

  <clause id="13424">
    <literal><![CDATA[
      (x * y) / (z * ((z \ x) * y)) = (z * ((z \ x) * y)) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,88,a,b,13382,a),flip(a)].">
      <j1 rule="hyper" parents="347 88 13382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13425">
    <literal><![CDATA[
      a(x,x \ (y / z),z) != u
    ]]></literal>
    <literal><![CDATA[
      y / (x * ((x \ (y / z)) * z)) = u
    ]]></literal>
    <justification jstring="[para(13382(a,1),438(a,1))].">
      <j1 rule="para" parents="13382 438"/>
    </justification>
  </clause>

  <clause id="13426">
    <literal><![CDATA[
      (x * y) / (z * ((z \ x) * y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(z,z \ x,y) = u
    ]]></literal>
    <justification jstring="[para(13391(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13391 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13427">
    <literal><![CDATA[
      a(x \ y,(x \ y) \ 1,(y \ x) \ (x \ y)) \ (1 * ((y \ x) \ (x \ y))) = (x \ y) * (1 / (y \ x))
    ]]></literal>
    <justification jstring="[para(3661(a,1),13391(a,2,2))].">
      <j1 rule="para" parents="3661 13391"/>
    </justification>
  </clause>

  <clause id="13428">
    <literal><![CDATA[
      L(x,(y * z) * (z \ y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,z \ y),u) = w
    ]]></literal>
    <justification jstring="[para(13395(a,1),3518(a,1,2))].">
      <j1 rule="para" parents="13395 3518"/>
    </justification>
  </clause>

  <clause id="13429">
    <literal><![CDATA[
      K(x,L(T(1 / (1 / y),z) * u,w,v5)) = K(x,L((1 / T(y,z)) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(2726(a,1),12986(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2726 12986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13430">
    <literal><![CDATA[
      x * T(x \ (x \ 1),y) = x \ K(y,x * x)
    ]]></literal>
    <justification jstring="[para(6653(a,1),13010(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6653 13010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13431">
    <literal><![CDATA[
      (x * x) * K(y,x \ (x \ 1)) = (x \ K(y,x * x)) \ x
    ]]></literal>
    <justification jstring="[para(13430(a,1),6477(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13430 6477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13432">
    <literal><![CDATA[
      (x \ (y * z)) * K(x * (y \ (x \ (y * z))),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(35,a,4880,a(flip),b,13043,a),flip(a)].">
      <j1 rule="hyper" parents="35 4880 13043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13433">
    <literal><![CDATA[
      (x * ((x \ (y \ 1)) * (y * K(z,u)))) \ (K(y \ 1,y) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,x \ (y \ 1),y * K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13046(a,2),1105(a,1,2))].">
      <j1 rule="para" parents="13046 1105"/>
    </justification>
  </clause>

  <clause id="13435">
    <literal><![CDATA[
      K(L(x,y,z),z * y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(34,a,11109,a,b,13060,a)].">
      <j1 rule="hyper" parents="34 11109 13060"/>
    </justification>
  </clause>

  <clause id="13436">
    <literal><![CDATA[
      T(x * (y * K(z,x * y)),z) = x * y
    ]]></literal>
    <justification jstring="[para(13060(a,1),5058(a,1,1))].">
      <j1 rule="para" parents="13060 5058"/>
    </justification>
  </clause>

  <clause id="13437">
    <literal><![CDATA[
      K(x,y * (z * K(u,y * z))) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(13060(a,1),7394(a,1,2))].">
      <j1 rule="para" parents="13060 7394"/>
    </justification>
  </clause>

  <clause id="13438">
    <literal><![CDATA[
      K((x * y) \ z,x * y) = K(y \ (x \ z),x * y)
    ]]></literal>
    <justification jstring="[para(329(a,1),13435(a,1,1))].">
      <j1 rule="para" parents="329 13435"/>
    </justification>
  </clause>

  <clause id="13439">
    <literal><![CDATA[
      (x * (y * z)) * K(z,x * y) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(13435(a,1),537(a,1,2))].">
      <j1 rule="para" parents="13435 537"/>
    </justification>
  </clause>

  <clause id="13440">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(13061(a,2),11166(a,1))].">
      <j1 rule="para" parents="13061 11166"/>
    </justification>
  </clause>

  <clause id="13441">
    <literal><![CDATA[
      K(x,L((1 / y) \ z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(13120(a,2),11166(a,1))].">
      <j1 rule="para" parents="13120 11166"/>
    </justification>
  </clause>

  <clause id="13442">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(13134(a,1),7449(a,1))].">
      <j1 rule="para" parents="13134 7449"/>
    </justification>
  </clause>

  <clause id="13443">
    <literal><![CDATA[
      K(x,L(y / (z \ 1),u,w)) = K(x,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,11049,a(flip),b,13141,a),flip(a)].">
      <j1 rule="hyper" parents="347 11049 13141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13444">
    <literal><![CDATA[
      K(x,L(y / (z \ 1),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(13141(a,2),11166(a,1))].">
      <j1 rule="para" parents="13141 11166"/>
    </justification>
  </clause>

  <clause id="13445">
    <literal><![CDATA[
      (x * K(y,x)) / z = x / (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(7903(a,1),13152(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7903 13152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13446">
    <literal><![CDATA[
      (x * K(y,x)) / z = K(y,x) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(347,a,13201,a(flip),b,13445,a),flip(a)].">
      <j1 rule="hyper" parents="347 13201 13445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13448">
    <literal><![CDATA[
      L(x * K(y,x),z,u) \ (x * K(y,x)) = K(y,x) * (x / L((y * x) / y,z,u))
    ]]></literal>
    <justification jstring="[hyper(5620,a,13446,a)].">
      <j1 rule="hyper" parents="5620 13446"/>
    </justification>
  </clause>

  <clause id="13449">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,207,a(flip),b,13446,a)].">
      <j1 rule="hyper" parents="133 207 13446"/>
    </justification>
  </clause>

  <clause id="13450">
    <literal><![CDATA[
      L(x,y / x,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,3049,a,b,13446,a)].">
      <j1 rule="hyper" parents="36 3049 13446"/>
    </justification>
  </clause>

  <clause id="13451">
    <literal><![CDATA[
      ((x * y) / x) / z = K(x,y) * (y / z)
    ]]></literal>
    <justification jstring="[para(4942(a,2),13446(a,1,1))].">
      <j1 rule="para" parents="4942 13446"/>
    </justification>
  </clause>

  <clause id="13452">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,9643,a(flip),b,13450,a)].">
      <j1 rule="hyper" parents="63 9643 13450"/>
    </justification>
  </clause>

  <clause id="13453">
    <literal><![CDATA[
      (1 / x) * ((K(y,z) / x) \ y) = y * K(z,y)
    ]]></literal>
    <justification jstring="[para(13063(a,1),13449(a,1,1))].">
      <j1 rule="para" parents="13063 13449"/>
    </justification>
  </clause>

  <clause id="13454">
    <literal><![CDATA[
      ((x * y) / x) / (z * y) = y / (z * T(y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,13245,a(flip),b,13451,a),flip(a)].">
      <j1 rule="hyper" parents="347 13245 13451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13455">
    <literal><![CDATA[
      K(x,L(T(1 / y,(K(z,u) / y) \ z) \ w,w,(K(z,u) / y) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(13453(a,1),11133(a,2,2,1))].">
      <j1 rule="para" parents="13453 11133"/>
    </justification>
  </clause>

  <clause id="13456">
    <literal><![CDATA[
      R(K(x,y) / z,z,y) = y / (z * T(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,5106,a,b,13454,a)].">
      <j1 rule="hyper" parents="63 5106 13454"/>
    </justification>
  </clause>

  <clause id="13457">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(13159(a,2),8049(a,1))].">
      <j1 rule="para" parents="13159 8049"/>
    </justification>
  </clause>

  <clause id="13458">
    <literal><![CDATA[
      K(x \ T((x \ 1) \ y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y * K((x \ 1) \ y,z),u) = w
    ]]></literal>
    <justification jstring="[para(5946(a,1),13457(a,1,1,2))].">
      <j1 rule="para" parents="5946 13457"/>
    </justification>
  </clause>

  <clause id="13459">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * T(w,(x \ L(x,y,z)) \ u) = w * (((x \ L(x,y,z)) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(10882(a,1),13169(a,1,1,1))].">
      <j1 rule="para" parents="10882 13169"/>
    </justification>
  </clause>

  <clause id="13460">
    <literal><![CDATA[
      K(x,((y / (K(z,u) * w)) / T(v5,y * (w \ K(u,z)))) * v6) = K(x,(v5 \ (y / (K(z,u) * w))) * v6)
    ]]></literal>
    <justification jstring="[para(13188(a,1),12064(a,1,2,1,2))].">
      <j1 rule="para" parents="13188 12064"/>
    </justification>
  </clause>

  <clause id="13461">
    <literal><![CDATA[
      L(x \ y,x,z / T(y,z)) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(4296,a,13196,a)].">
      <j1 rule="hyper" parents="4296 13196"/>
    </justification>
  </clause>

  <clause id="13462">
    <literal><![CDATA[
      L(x \ y,x,y \ z) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,11466,a(flip),b,13461,a)].">
      <j1 rule="hyper" parents="63 11466 13461"/>
    </justification>
  </clause>

  <clause id="13463">
    <literal><![CDATA[
      x / L(y \ z,y,z \ x) = (x / z) * y
    ]]></literal>
    <justification jstring="[hyper(220,a,11466,a(flip),b,13461,a(flip))].">
      <j1 rule="hyper" parents="220 11466 13461"/>
    </justification>
  </clause>

  <clause id="13464">
    <literal><![CDATA[
      ((x \ y) * z) \ ((x \ y) * x) = ((y / x) * z) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,99,a(flip),b,13462,a)].">
      <j1 rule="hyper" parents="63 99 13462"/>
    </justification>
  </clause>

  <clause id="13465">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) = ((z / (y * x)) * y) \ z
    ]]></literal>
    <justification jstring="[para(9(a,1),13462(a,1,1))].">
      <j1 rule="para" parents="9 13462"/>
    </justification>
  </clause>

  <clause id="13467">
    <literal><![CDATA[
      K(x / ((1 / y) * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * L(z \ y,z,y \ 1),u) = w
    ]]></literal>
    <justification jstring="[para(13463(a,1),13227(a,1,1,2))].">
      <j1 rule="para" parents="13463 13227"/>
    </justification>
  </clause>

  <clause id="13468">
    <literal><![CDATA[
      L(x,y,z) * T(y * z,x) = z * (T(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,10150,a(flip),b,13212,a),flip(a)].">
      <j1 rule="hyper" parents="347 10150 13212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13469">
    <literal><![CDATA[
      K(x / ((y * a(z,u,z)) \ K(z * u,z)),w) = K(x * (K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[para(9956(a,1),13225(a,2,1,2))].">
      <j1 rule="para" parents="9956 13225"/>
    </justification>
  </clause>

  <clause id="13470">
    <literal><![CDATA[
      R(x,y,z) \ ((x \ (R(x,y,z) * u)) * x) = u * K((x \ u) * R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(7954(a,1),13230(a,2,2))].">
      <j1 rule="para" parents="7954 13230"/>
    </justification>
  </clause>

  <clause id="13471">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(7474,a,13271,a),flip(a)].">
      <j1 rule="hyper" parents="7474 13271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13472">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(13271(a,1),7474(a,1))].">
      <j1 rule="para" parents="13271 7474"/>
    </justification>
  </clause>

  <clause id="13473">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8844,a,13471,a)].">
      <j1 rule="hyper" parents="8844 13471"/>
    </justification>
  </clause>

  <clause id="13474">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(132,a,13471,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 13471 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13475">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(132,a,13473,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 13473 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13476">
    <literal><![CDATA[
      K(x,K(y,z * u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13471,a(flip),b,13473,a)].">
      <j1 rule="hyper" parents="63 13471 13473"/>
    </justification>
  </clause>

  <clause id="13477">
    <literal><![CDATA[
      K(x,K(y,z * u)) * ((u \ z) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(u \ z,K(x,y)) \ w = v5
    ]]></literal>
    <justification jstring="[para(13473(a,1),7275(a,1,1))].">
      <j1 rule="para" parents="13473 7275"/>
    </justification>
  </clause>

  <clause id="13478">
    <literal><![CDATA[
      T(x,K(y,z * (u \ 1))) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12776,a(flip),b,13474,a),flip(a)].">
      <j1 rule="hyper" parents="63 12776 13474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13479">
    <literal><![CDATA[
      T(x,K(y,z * (z * u))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),13474(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 13474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13480">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y / (z \ u)) = T(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[para(13474(a,1),8885(a,1,1))].">
      <j1 rule="para" parents="13474 8885"/>
    </justification>
  </clause>

  <clause id="13481">
    <literal><![CDATA[
      T(T(x,K(y,z * (y * u))),y \ ((y \ z) \ u)) = T(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(13474(a,1),8892(a,1,1))].">
      <j1 rule="para" parents="13474 8892"/>
    </justification>
  </clause>

  <clause id="13482">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ u) * y) = w
    ]]></literal>
    <justification jstring="[para(13474(a,1),10397(a,1,1))].">
      <j1 rule="para" parents="13474 10397"/>
    </justification>
  </clause>

  <clause id="13483">
    <literal><![CDATA[
      T(x,K(y,z * u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13474,a(flip),b,13475,a)].">
      <j1 rule="hyper" parents="63 13474 13475"/>
    </justification>
  </clause>

  <clause id="13484">
    <literal><![CDATA[
      T(x,K(y,z * (z / u))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(83(a,1),13475(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="83 13475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13485">
    <literal><![CDATA[
      K(x,K(y * z,u)) = K(x,K(u,z * y))
    ]]></literal>
    <justification jstring="[hyper(7328,a,13476,a)].">
      <j1 rule="hyper" parents="7328 13476"/>
    </justification>
  </clause>

  <clause id="13488">
    <literal><![CDATA[
      K(x,K(y,z * u)) * y = T(y,K(x,u * z))
    ]]></literal>
    <justification jstring="[para(13476(a,1),7285(a,1,1))].">
      <j1 rule="para" parents="13476 7285"/>
    </justification>
  </clause>

  <clause id="13489">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,u * z)) = w
    ]]></literal>
    <justification jstring="[para(13476(a,1),7281(a,1))].">
      <j1 rule="para" parents="13476 7281"/>
    </justification>
  </clause>

  <clause id="13490">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u * z,y)) = w
    ]]></literal>
    <justification jstring="[para(13476(a,1),7328(a,1))].">
      <j1 rule="para" parents="13476 7328"/>
    </justification>
  </clause>

  <clause id="13491">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,y * x))
    ]]></literal>
    <justification jstring="[para(13476(a,1),12774(a,2,2))].">
      <j1 rule="para" parents="13476 12774"/>
    </justification>
  </clause>

  <clause id="13493">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (u * (u * z))) = T(x,(u * (u * z)) * y)
    ]]></literal>
    <justification jstring="[para(13479(a,1),10366(a,1,1))].">
      <j1 rule="para" parents="13479 10366"/>
    </justification>
  </clause>

  <clause id="13494">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (u * (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(u * (u * z)) * y) = w
    ]]></literal>
    <justification jstring="[para(13479(a,1),10397(a,1,1))].">
      <j1 rule="para" parents="13479 10397"/>
    </justification>
  </clause>

  <clause id="13495">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (u * z)) = T(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[para(13483(a,1),10366(a,1,1))].">
      <j1 rule="para" parents="13483 10366"/>
    </justification>
  </clause>

  <clause id="13497">
    <literal><![CDATA[
      K(x,K(y,(z \ u) * z)) = K(x,K(u,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),13485(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 13485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13498">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(13485(a,1),7328(a,1))].">
      <j1 rule="para" parents="13485 7328"/>
    </justification>
  </clause>

  <clause id="13499">
    <literal><![CDATA[
      K(x,K(y * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z * y,u)) = w
    ]]></literal>
    <justification jstring="[para(13485(a,2),7328(a,1))].">
      <j1 rule="para" parents="13485 7328"/>
    </justification>
  </clause>

  <clause id="13500">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,y / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9636,a(flip),b,13497,a)].">
      <j1 rule="hyper" parents="63 9636 13497"/>
    </justification>
  </clause>

  <clause id="13501">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(10351(a,1),13497(a,1,2))].">
      <j1 rule="para" parents="10351 13497"/>
    </justification>
  </clause>

  <clause id="13502">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7774,a,13501,a)].">
      <j1 rule="hyper" parents="7774 13501"/>
    </justification>
  </clause>

  <clause id="13503">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(7473,a,13501,a)].">
      <j1 rule="hyper" parents="7473 13501"/>
    </justification>
  </clause>

  <clause id="13504">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(7328,a,13501,a)].">
      <j1 rule="hyper" parents="7328 13501"/>
    </justification>
  </clause>

  <clause id="13505">
    <literal><![CDATA[
      K(x,T(K(y,z),u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7332,a(flip),b,13501,a)].">
      <j1 rule="hyper" parents="63 7332 13501"/>
    </justification>
  </clause>

  <clause id="13506">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z / y))
    ]]></literal>
    <justification jstring="[para(7135(a,1),13501(a,1,2))].">
      <j1 rule="para" parents="7135 13501"/>
    </justification>
  </clause>

  <clause id="13507">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(13501(a,2),7328(a,1))].">
      <j1 rule="para" parents="13501 7328"/>
    </justification>
  </clause>

  <clause id="13508">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,T(y,u) / z) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[para(13501(a,1),8944(a,1,1))].">
      <j1 rule="para" parents="13501 8944"/>
    </justification>
  </clause>

  <clause id="13509">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ T(y,u),z) = K(T(y,u) / x,z)
    ]]></literal>
    <justification jstring="[para(13501(a,1),8955(a,1,1))].">
      <j1 rule="para" parents="13501 8955"/>
    </justification>
  </clause>

  <clause id="13511">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,13502,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 13502 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13512">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(113(a,1),13502(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 13502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13514">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(13502(a,1),7177(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13502 7177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13516">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * u) \ (w * z)))
    ]]></literal>
    <justification jstring="[para(7463(a,1),13502(a,1,2))].">
      <j1 rule="para" parents="7463 13502"/>
    </justification>
  </clause>

  <clause id="13517">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,((y \ u) \ u) / z) = K(x,z \ ((y \ u) \ u))
    ]]></literal>
    <justification jstring="[para(13502(a,1),8949(a,1,1))].">
      <j1 rule="para" parents="13502 8949"/>
    </justification>
  </clause>

  <clause id="13518">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ (u * (y / u)),z) = K((u * (y / u)) / x,z)
    ]]></literal>
    <justification jstring="[para(13502(a,1),10386(a,1,1))].">
      <j1 rule="para" parents="13502 10386"/>
    </justification>
  </clause>

  <clause id="13520">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(13503(a,1),7177(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13503 7177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13521">
    <literal><![CDATA[
      K(x,y) * (K(z,K(y,u)) * w) = y * (T(T(y,K(z,u)),x) \ w)
    ]]></literal>
    <justification jstring="[para(13503(a,1),9408(a,1,2,1))].">
      <j1 rule="para" parents="13503 9408"/>
    </justification>
  </clause>

  <clause id="13523">
    <literal><![CDATA[
      T(x,K(T(y,z),u)) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(132,a,13504,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 13504 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13525">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(x,T(y,z))) = R(z * K(x,K(y,u)),K(x,T(y,z)),u)
    ]]></literal>
    <justification jstring="[para(13504(a,1),9893(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13504 9893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13529">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * x) = u * T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,13505,a(flip),b,7700,a)].">
      <j1 rule="hyper" parents="133 13505 7700"/>
    </justification>
  </clause>

  <clause id="13530">
    <literal><![CDATA[
      x * (y * K(x,K(z,u))) = T(x,K(z,u)) * y
    ]]></literal>
    <justification jstring="[para(13505(a,1),7169(a,1,2,2))].">
      <j1 rule="para" parents="13505 7169"/>
    </justification>
  </clause>

  <clause id="13531">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,u)) * x = w
    ]]></literal>
    <justification jstring="[para(13505(a,1),7111(a,1,2))].">
      <j1 rule="para" parents="13505 7111"/>
    </justification>
  </clause>

  <clause id="13532">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(13505(a,1),7442(a,1,1))].">
      <j1 rule="para" parents="13505 7442"/>
    </justification>
  </clause>

  <clause id="13533">
    <literal><![CDATA[
      x * (K(y,K(z,u)) * w) = x * (w * K(y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(13505(a,1),7112(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13505 7112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13534">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ 1) = u \ K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(13505(a,1),13015(a,1,1))].">
      <j1 rule="para" parents="13505 13015"/>
    </justification>
  </clause>

  <clause id="13535">
    <literal><![CDATA[
      (1 / x) * K(y,K(z,u)) = K(y,K(z,u)) / x
    ]]></literal>
    <justification jstring="[para(13505(a,1),13339(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13505 13339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13536">
    <literal><![CDATA[
      K(x,T(y,z)) * (u * K(y,T(x,z))) = T(u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,7533,a,b,13511,a)].">
      <j1 rule="hyper" parents="63 7533 13511"/>
    </justification>
  </clause>

  <clause id="13537">
    <literal><![CDATA[
      T(x,y) * T(z,T(T(x,y),u)) = T(z * T(x,y),K(x,u))
    ]]></literal>
    <justification jstring="[hyper(6061,a,13523,a)].">
      <j1 rule="hyper" parents="6061 13523"/>
    </justification>
  </clause>

  <clause id="13538">
    <literal><![CDATA[
      T(x,y) * T(z,T(T(x,y),u)) = T(z,K(x,u)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(13523(a,1),6811(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13523 6811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13539">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,u) \ z) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z / T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(13523(a,1),8915(a,1,1))].">
      <j1 rule="para" parents="13523 8915"/>
    </justification>
  </clause>

  <clause id="13540">
    <literal><![CDATA[
      K(x,K(y \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z / y,u)) = w
    ]]></literal>
    <justification jstring="[para(13506(a,2),7328(a,1))].">
      <j1 rule="para" parents="13506 7328"/>
    </justification>
  </clause>

  <clause id="13541">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(w,u / (z * y)))
    ]]></literal>
    <justification jstring="[para(11113(a,2),13506(a,1,2))].">
      <j1 rule="para" parents="11113 13506"/>
    </justification>
  </clause>

  <clause id="13542">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) = K(x,K(y / u,K(z,1 / z) / (z * y)))
    ]]></literal>
    <justification jstring="[hyper(347,a,8970,a,b,13512,a)].">
      <j1 rule="hyper" parents="347 8970 13512"/>
    </justification>
  </clause>

  <clause id="13543">
    <literal><![CDATA[
      T(x,K(K(y,z),u)) = x
    ]]></literal>
    <justification jstring="[hyper(8803,a,13514,a)].">
      <j1 rule="hyper" parents="8803 13514"/>
    </justification>
  </clause>

  <clause id="13544">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,K(y,u)) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[hyper(8062,a,13514,a),flip(a)].">
      <j1 rule="hyper" parents="8062 13514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13545">
    <literal><![CDATA[
      T(x,K(y,K(z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(7359,a,13514,a)].">
      <j1 rule="hyper" parents="7359 13514"/>
    </justification>
  </clause>

  <clause id="13546">
    <literal><![CDATA[
      (x \ y) * K(x,K(z,u)) = T(x,K(z,u)) \ y
    ]]></literal>
    <justification jstring="[hyper(7327,a,13514,a),flip(a)].">
      <j1 rule="hyper" parents="7327 13514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13547">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7326,a,13514,a)].">
      <j1 rule="hyper" parents="7326 13514"/>
    </justification>
  </clause>

  <clause id="13548">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(7324,a,13514,a),flip(a)].">
      <j1 rule="hyper" parents="7324 13514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13549">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,K(y,z))) = u
    ]]></literal>
    <justification jstring="[hyper(7322,a,13514,a)].">
      <j1 rule="hyper" parents="7322 13514"/>
    </justification>
  </clause>

  <clause id="13550">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) * (w * u) = w * (u * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,8921,a(flip),b,13514,a),flip(a)].">
      <j1 rule="hyper" parents="347 8921 13514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13551">
    <literal><![CDATA[
      K(x,K(y,z)) * (u / x) = u / T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7316,a(flip),b,13514,a),flip(a)].">
      <j1 rule="hyper" parents="347 7316 13514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13552">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) = u * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7269,a(flip),b,13514,a),flip(a)].">
      <j1 rule="hyper" parents="347 7269 13514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13554">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,6815,a,b,13514,a)].">
      <j1 rule="hyper" parents="34 6815 13514"/>
    </justification>
  </clause>

  <clause id="13555">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(34,a,10365,a(flip),b,13514,a),flip(a)].">
      <j1 rule="hyper" parents="34 10365 13514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13557">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(x,K(y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(13514(a,1),7324(a,1))].">
      <j1 rule="para" parents="13514 7324"/>
    </justification>
  </clause>

  <clause id="13558">
    <literal><![CDATA[
      K(x,y) * (z * K(x,K(y,u))) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[para(13514(a,1),8671(a,1,2))].">
      <j1 rule="para" parents="13514 8671"/>
    </justification>
  </clause>

  <clause id="13560">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8213,a,13543,a)].">
      <j1 rule="hyper" parents="8213 13543"/>
    </justification>
  </clause>

  <clause id="13561">
    <literal><![CDATA[
      T(x,K(y,z) / u) = T(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8883,a(flip),b,13543,a),flip(a)].">
      <j1 rule="hyper" parents="63 8883 13543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13562">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(13543(a,1),7796(a,1,1))].">
      <j1 rule="para" parents="13543 7796"/>
    </justification>
  </clause>

  <clause id="13563">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(13543(a,1),10367(a,1))].">
      <j1 rule="para" parents="13543 10367"/>
    </justification>
  </clause>

  <clause id="13564">
    <literal><![CDATA[
      T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(13543(a,1),10398(a,1,1))].">
      <j1 rule="para" parents="13543 10398"/>
    </justification>
  </clause>

  <clause id="13565">
    <literal><![CDATA[
      T(x,T(T(y,K(z,u)),w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,6818,a(flip),b,13545,a)].">
      <j1 rule="hyper" parents="63 6818 13545"/>
    </justification>
  </clause>

  <clause id="13566">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,T(u * K(y,z),w))
    ]]></literal>
    <justification jstring="[hyper(10433,a,13554,a),flip(a)].">
      <j1 rule="hyper" parents="10433 13554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13567">
    <literal><![CDATA[
      T(x * K(y,z),T(u,x)) = T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(8865,a,13554,a)].">
      <j1 rule="hyper" parents="8865 13554"/>
    </justification>
  </clause>

  <clause id="13569">
    <literal><![CDATA[
      (K(x,y) \ z) * K(z / K(x,y),u) = T(K(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,7426,a,b,13554,a)].">
      <j1 rule="hyper" parents="63 7426 13554"/>
    </justification>
  </clause>

  <clause id="13570">
    <literal><![CDATA[
      T(x / T(y,K(z,u)),y) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,K(z,u)) \ x = w
    ]]></literal>
    <justification jstring="[para(13554(a,1),386(a,1))].">
      <j1 rule="para" parents="13554 386"/>
    </justification>
  </clause>

  <clause id="13571">
    <literal><![CDATA[
      T(x,K(y,z) * (u * y)) = T(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(6191(a,1),13554(a,1,2))].">
      <j1 rule="para" parents="6191 13554"/>
    </justification>
  </clause>

  <clause id="13572">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6813(a,1),13554(a,1,2))].">
      <j1 rule="para" parents="6813 13554"/>
    </justification>
  </clause>

  <clause id="13573">
    <literal><![CDATA[
      (x * K(y,z)) * K(x,u) = T(x,u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(13554(a,1),7414(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13554 7414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13576">
    <literal><![CDATA[
      T(x * K(x * K(y,z),u),K(z,y)) = K(y,z) \ T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[para(13554(a,1),9463(a,2,2))].">
      <j1 rule="para" parents="13554 9463"/>
    </justification>
  </clause>

  <clause id="13578">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(u * K(y,z),w)) = v5
    ]]></literal>
    <justification jstring="[para(13554(a,1),10433(a,1))].">
      <j1 rule="para" parents="13554 10433"/>
    </justification>
  </clause>

  <clause id="13579">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(10406,a,13560,a)].">
      <j1 rule="hyper" parents="10406 13560"/>
    </justification>
  </clause>

  <clause id="13580">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(10383,a,13560,a),flip(a)].">
      <j1 rule="hyper" parents="10383 13560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13581">
    <literal><![CDATA[
      K(x,K(y,z) / u) = K(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(9477,a,13560,a),flip(a)].">
      <j1 rule="hyper" parents="9477 13560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13583">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(7477,a,13560,a),flip(a)].">
      <j1 rule="hyper" parents="7477 13560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13585">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ K(z,u) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7090,a,b,13560,a)].">
      <j1 rule="hyper" parents="63 7090 13560"/>
    </justification>
  </clause>

  <clause id="13586">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)),w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,7391,a(flip),b,13560,a),flip(a)].">
      <j1 rule="hyper" parents="63 7391 13560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13587">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(z,u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,13560,a(flip),b,7099,a),flip(a)].">
      <j1 rule="hyper" parents="134 13560 7099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13590">
    <literal><![CDATA[
      K(x,y) * K(z,u) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,13560,a(flip),b,7378,a)].">
      <j1 rule="hyper" parents="133 13560 7378"/>
    </justification>
  </clause>

  <clause id="13591">
    <literal><![CDATA[
      K(x,K(y,z) * (u / z)) = K(x,u / T(z,y))
    ]]></literal>
    <justification jstring="[para(5938(a,1),13560(a,1,2))].">
      <j1 rule="para" parents="5938 13560"/>
    </justification>
  </clause>

  <clause id="13592">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6116(a,1),13560(a,1,2))].">
      <j1 rule="para" parents="6116 13560"/>
    </justification>
  </clause>

  <clause id="13593">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) = K(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(6191(a,1),13560(a,1,2))].">
      <j1 rule="para" parents="6191 13560"/>
    </justification>
  </clause>

  <clause id="13594">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6813(a,1),13560(a,1,2))].">
      <j1 rule="para" parents="6813 13560"/>
    </justification>
  </clause>

  <clause id="13596">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(13560(a,1),7443(a,1,1))].">
      <j1 rule="para" parents="13560 7443"/>
    </justification>
  </clause>

  <clause id="13597">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(13560(a,1),7477(a,1))].">
      <j1 rule="para" parents="13560 7477"/>
    </justification>
  </clause>

  <clause id="13598">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(13560(a,1),7478(a,1))].">
      <j1 rule="para" parents="13560 7478"/>
    </justification>
  </clause>

  <clause id="13600">
    <literal><![CDATA[
      x * (K(y,z) * K(u,w)) = x * (K(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[para(13560(a,1),7112(a,1,2,2))].">
      <j1 rule="para" parents="13560 7112"/>
    </justification>
  </clause>

  <clause id="13601">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(7363(a,1),13560(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7363 13560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13602">
    <literal><![CDATA[
      K(x,T(T(y,K(z,u)),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(13560(a,1),7490(a,1))].">
      <j1 rule="para" parents="13560 7490"/>
    </justification>
  </clause>

  <clause id="13603">
    <literal><![CDATA[
      L(K(x,y),x,z) = (x * K(u,w)) \ (T(x,y) * K(u,w))
    ]]></literal>
    <justification jstring="[para(13560(a,1),7498(a,1,1))].">
      <j1 rule="para" parents="13560 7498"/>
    </justification>
  </clause>

  <clause id="13606">
    <literal><![CDATA[
      K(K(x,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * K(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(13560(a,1),10383(a,1))].">
      <j1 rule="para" parents="13560 10383"/>
    </justification>
  </clause>

  <clause id="13607">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(13560(a,1),10405(a,1))].">
      <j1 rule="para" parents="13560 10405"/>
    </justification>
  </clause>

  <clause id="13608">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(13560(a,1),10406(a,1))].">
      <j1 rule="para" parents="13560 10406"/>
    </justification>
  </clause>

  <clause id="13610">
    <literal><![CDATA[
      K(T(x / y,K(z,u)),w) = K(x / L(y,v5,y),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,11938,a,b,13583,a),flip(a)].">
      <j1 rule="hyper" parents="347 11938 13583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13612">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,y)) = T(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7683,a,13572,a),flip(a)].">
      <j1 rule="hyper" parents="7683 13572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13613">
    <literal><![CDATA[
      T(x,T(T(y,z) / u,y)) = T(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7081,a,13572,a),flip(a)].">
      <j1 rule="hyper" parents="7081 13572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13614">
    <literal><![CDATA[
      T(x * (L(x,y,z) \ T(u,w)),T(x,u)) = L(x,y,z) \ (T(u,w) * x)
    ]]></literal>
    <justification jstring="[hyper(40,a,11311,a,b,13572,a)].">
      <j1 rule="hyper" parents="40 11311 13572"/>
    </justification>
  </clause>

  <clause id="13615">
    <literal><![CDATA[
      T(x / y,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,K(y,T(z,w))) = u
    ]]></literal>
    <justification jstring="[para(13572(a,1),6825(a,1))].">
      <j1 rule="para" parents="13572 6825"/>
    </justification>
  </clause>

  <clause id="13616">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = y * T(y \ T(x,y),T(z,x))
    ]]></literal>
    <justification jstring="[para(13572(a,1),7752(a,2,2))].">
      <j1 rule="para" parents="13572 7752"/>
    </justification>
  </clause>

  <clause id="13617">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7793,a,13594,a)].">
      <j1 rule="hyper" parents="7793 13594"/>
    </justification>
  </clause>

  <clause id="13623">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,u) * T(x,y) = w
    ]]></literal>
    <justification jstring="[para(13594(a,1),7111(a,1,2))].">
      <j1 rule="para" parents="13594 7111"/>
    </justification>
  </clause>

  <clause id="13625">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * T(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(13594(a,1),10383(a,1))].">
      <j1 rule="para" parents="13594 10383"/>
    </justification>
  </clause>

  <clause id="13630">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,T(x,w)) = K(y,T(x,w)) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(13617(a,1),10782(a,1,2))].">
      <j1 rule="para" parents="13617 10782"/>
    </justification>
  </clause>

  <clause id="13631">
    <literal><![CDATA[
      T(x,K(y,z) * (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(5938(a,1),13562(a,1,2))].">
      <j1 rule="para" parents="5938 13562"/>
    </justification>
  </clause>

  <clause id="13632">
    <literal><![CDATA[
      T(x,K(y,z) * (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(6191(a,1),13562(a,1,2))].">
      <j1 rule="para" parents="6191 13562"/>
    </justification>
  </clause>

  <clause id="13633">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(6813(a,1),13562(a,1,2))].">
      <j1 rule="para" parents="6813 13562"/>
    </justification>
  </clause>

  <clause id="13634">
    <literal><![CDATA[
      T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) \ y) = w
    ]]></literal>
    <justification jstring="[para(6879(a,1),13562(a,1,2))].">
      <j1 rule="para" parents="6879 13562"/>
    </justification>
  </clause>

  <clause id="13635">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(13116(a,1),13562(a,1,2))].">
      <j1 rule="para" parents="13116 13562"/>
    </justification>
  </clause>

  <clause id="13636">
    <literal><![CDATA[
      K((x \ y) * K(z,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z) \ y,u) = w
    ]]></literal>
    <justification jstring="[para(7528(a,1),13597(a,1,1))].">
      <j1 rule="para" parents="7528 13597"/>
    </justification>
  </clause>

  <clause id="13637">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(6191(a,1),13598(a,1,2))].">
      <j1 rule="para" parents="6191 13598"/>
    </justification>
  </clause>

  <clause id="13638">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(6813(a,1),13598(a,1,2))].">
      <j1 rule="para" parents="6813 13598"/>
    </justification>
  </clause>

  <clause id="13639">
    <literal><![CDATA[
      K(x,y * (z * K(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) * z) = w
    ]]></literal>
    <justification jstring="[para(6866(a,1),13598(a,1,2))].">
      <j1 rule="para" parents="6866 13598"/>
    </justification>
  </clause>

  <clause id="13640">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) \ y) = w
    ]]></literal>
    <justification jstring="[para(6879(a,1),13598(a,1,2))].">
      <j1 rule="para" parents="6879 13598"/>
    </justification>
  </clause>

  <clause id="13641">
    <literal><![CDATA[
      K(x,T(y,z) \ (u / T(z,y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (u / z)) = w
    ]]></literal>
    <justification jstring="[para(6807(a,1),13598(a,1,2))].">
      <j1 rule="para" parents="6807 13598"/>
    </justification>
  </clause>

  <clause id="13643">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ K(z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = w
    ]]></literal>
    <justification jstring="[para(7090(a,2),13598(a,1))].">
      <j1 rule="para" parents="7090 13598"/>
    </justification>
  </clause>

  <clause id="13644">
    <literal><![CDATA[
      K(L((x \ y) / K(z,u),K(z,u),x),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((x * K(z,u)) \ y,w) = v5
    ]]></literal>
    <justification jstring="[para(7452(a,2),13598(a,1))].">
      <j1 rule="para" parents="7452 13598"/>
    </justification>
  </clause>

  <clause id="13645">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(8887(a,1),13598(a,1,2))].">
      <j1 rule="para" parents="8887 13598"/>
    </justification>
  </clause>

  <clause id="13646">
    <literal><![CDATA[
      K(x,y * L(z \ u,z,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((w * z) \ (w * u))) = v5
    ]]></literal>
    <justification jstring="[para(11029(a,1),13598(a,1,2))].">
      <j1 rule="para" parents="11029 13598"/>
    </justification>
  </clause>

  <clause id="13647">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(13116(a,1),13598(a,1,2))].">
      <j1 rule="para" parents="13116 13598"/>
    </justification>
  </clause>

  <clause id="13648">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,x) = x \ (u * T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,7559,a,b,13547,a),flip(a)].">
      <j1 rule="hyper" parents="347 7559 13547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13649">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) * K(y,K(z,x)) = x \ u
    ]]></literal>
    <justification jstring="[para(7274(a,1),13548(a,1,1))].">
      <j1 rule="para" parents="7274 13548"/>
    </justification>
  </clause>

  <clause id="13650">
    <literal><![CDATA[
      T(x,y * K(z \ u,z)) = T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,12062,a(flip),b,13555,a),flip(a)].">
      <j1 rule="hyper" parents="63 12062 13555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13651">
    <literal><![CDATA[
      x / T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,u) * y,x) = w
    ]]></literal>
    <justification jstring="[para(13555(a,1),5013(a,1,2))].">
      <j1 rule="para" parents="13555 5013"/>
    </justification>
  </clause>

  <clause id="13652">
    <literal><![CDATA[
      T(x,T(T(y,T(z,u)) * u,w)) = T(x,T(T(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(7566(a,1),13565(a,1,2,1))].">
      <j1 rule="para" parents="7566 13565"/>
    </justification>
  </clause>

  <clause id="13653">
    <literal><![CDATA[
      K(x * K(y,z),x \ y) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(10481,a,13580,a),flip(a)].">
      <j1 rule="hyper" parents="10481 13580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13654">
    <literal><![CDATA[
      K(x * K(y,z),y * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(8282,a,13580,a),flip(a)].">
      <j1 rule="hyper" parents="8282 13580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13655">
    <literal><![CDATA[
      K(x * K(y \ z,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(8277,a,13580,a),flip(a)].">
      <j1 rule="hyper" parents="8277 13580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13656">
    <literal><![CDATA[
      K(x / ((y \ z) \ z),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(6175(a,2),13655(a,1,1))].">
      <j1 rule="para" parents="6175 13655"/>
    </justification>
  </clause>

  <clause id="13657">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(u,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,5256,a,b,13587,a)].">
      <j1 rule="hyper" parents="347 5256 13587"/>
    </justification>
  </clause>

  <clause id="13659">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ (u * (y \ z))) = K(x,u * (z / y))
    ]]></literal>
    <justification jstring="[para(6075(a,1),13592(a,2,2))].">
      <j1 rule="para" parents="6075 13592"/>
    </justification>
  </clause>

  <clause id="13660">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) = K(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[para(6102(a,1),13592(a,2,2))].">
      <j1 rule="para" parents="6102 13592"/>
    </justification>
  </clause>

  <clause id="13661">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / z)) = K(x,u / ((y * z) / y))
    ]]></literal>
    <justification jstring="[para(6126(a,2),13592(a,2,2))].">
      <j1 rule="para" parents="6126 13592"/>
    </justification>
  </clause>

  <clause id="13662">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ (u * z)) = K(x,u * (y * (z / y)))
    ]]></literal>
    <justification jstring="[para(9564(a,1),13592(a,2,2))].">
      <j1 rule="para" parents="9564 13592"/>
    </justification>
  </clause>

  <clause id="13663">
    <literal><![CDATA[
      K(x,K(y,y \ z) \ (u / z)) = K(x,u / (y * (z / y)))
    ]]></literal>
    <justification jstring="[para(9879(a,1),13592(a,2,2))].">
      <j1 rule="para" parents="9879 13592"/>
    </justification>
  </clause>

  <clause id="13664">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,13252,a(flip),b,13601,a),flip(a)].">
      <j1 rule="hyper" parents="347 13252 13601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13665">
    <literal><![CDATA[
      K(x,T(y,z \ K(u,z))) = K(x,T(y,1 / T(z,u)))
    ]]></literal>
    <justification jstring="[para(4932(a,1),13601(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4932 13601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13666">
    <literal><![CDATA[
      K((x / y) \ z,T(u,y \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z / (x / y),u) = w
    ]]></literal>
    <justification jstring="[para(13601(a,1),7485(a,1))].">
      <j1 rule="para" parents="13601 7485"/>
    </justification>
  </clause>

  <clause id="13667">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(13601(a,2),13420(a,1))].">
      <j1 rule="para" parents="13601 13420"/>
    </justification>
  </clause>

  <clause id="13668">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(13601(a,2),13421(a,1))].">
      <j1 rule="para" parents="13601 13421"/>
    </justification>
  </clause>

  <clause id="13669">
    <literal><![CDATA[
      K((x * y) * K(y,z),y * z) = K(y * x,z * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,10373,a,b,13654,a),flip(a)].">
      <j1 rule="hyper" parents="347 10373 13654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13670">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(w,v5) = K(v5,w) \ K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(11049(a,2),13657(a,1,1))].">
      <j1 rule="para" parents="11049 13657"/>
    </justification>
  </clause>

  <clause id="13671">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(113(a,1),13507(a,1,2,2))].">
      <j1 rule="para" parents="113 13507"/>
    </justification>
  </clause>

  <clause id="13672">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(7093(a,2),13507(a,1,2))].">
      <j1 rule="para" parents="7093 13507"/>
    </justification>
  </clause>

  <clause id="13673">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(10356(a,2),13638(a,1,2))].">
      <j1 rule="para" parents="10356 13638"/>
    </justification>
  </clause>

  <clause id="13675">
    <literal><![CDATA[
      T(x,K(y,z / u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12734,a(flip),b,13478,a)].">
      <j1 rule="hyper" parents="63 12734 13478"/>
    </justification>
  </clause>

  <clause id="13676">
    <literal><![CDATA[
      T(x,K(y,z * (u * z))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),13675(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 13675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13677">
    <literal><![CDATA[
      T(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(13488(a,1),7287(a,1))].">
      <j1 rule="para" parents="13488 7287"/>
    </justification>
  </clause>

  <clause id="13678">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u * x) = x \ (u * T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(13529(a,1),7320(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13529 7320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13680">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / T(x,K(y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      u / x = w
    ]]></literal>
    <justification jstring="[para(13551(a,1),356(a,1,2))].">
      <j1 rule="para" parents="13551 356"/>
    </justification>
  </clause>

  <clause id="13681">
    <literal><![CDATA[
      T(x * K(y,z),K(x,u)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6902,a,13567,a)].">
      <j1 rule="hyper" parents="6902 13567"/>
    </justification>
  </clause>

  <clause id="13685">
    <literal><![CDATA[
      T((x * K(y,z)) * u,K(x,u)) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(13681(a,1),7535(a,2,1))].">
      <j1 rule="para" parents="13681 7535"/>
    </justification>
  </clause>

  <clause id="13686">
    <literal><![CDATA[
      K(x,L(T(y,T(z,u)),w,v5)) = K(x,L(T(y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(6813(a,1),13586(a,1,2,1))].">
      <j1 rule="para" parents="6813 13586"/>
    </justification>
  </clause>

  <clause id="13687">
    <literal><![CDATA[
      K(x,K(y / (z / u),u \ z) * (w * (y / (z / u)))) = K(x,w * T((z / u) \ y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(8884(a,1),13593(a,2,2,2))].">
      <j1 rule="para" parents="8884 13593"/>
    </justification>
  </clause>

  <clause id="13688">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(y,w)) = T(x,T(y,w) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(7733(a,1),13612(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7733 13612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13689">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,(u * w) * R(z,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(107(a,1),13498(a,1,2,2))].">
      <j1 rule="para" parents="107 13498"/>
    </justification>
  </clause>

  <clause id="13691">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(7283(a,1),13532(a,1,1))].">
      <j1 rule="para" parents="7283 13532"/>
    </justification>
  </clause>

  <clause id="13692">
    <literal><![CDATA[
      K(x,T(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * u) * K(y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(8069(a,1),13532(a,1))].">
      <j1 rule="para" parents="8069 13532"/>
    </justification>
  </clause>

  <clause id="13693">
    <literal><![CDATA[
      T(x,K(y,z) * T(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,((w \ u) * w) * K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(12082(a,1),13563(a,1))].">
      <j1 rule="para" parents="12082 13563"/>
    </justification>
  </clause>

  <clause id="13694">
    <literal><![CDATA[
      K(T(x / (y \ z),K(u,w)),v5) = K(x / L(y \ z,v6,z / y),v5)
    ]]></literal>
    <justification jstring="[para(7674(a,2),13610(a,2,1,2))].">
      <j1 rule="para" parents="7674 13610"/>
    </justification>
  </clause>

  <clause id="13695">
    <literal><![CDATA[
      K((x / y) * z,T(u,x * y)) = K(z * (x / y),u)
    ]]></literal>
    <justification jstring="[hyper(13667,a,10369,a)].">
      <j1 rule="hyper" parents="13667 10369"/>
    </justification>
  </clause>

  <clause id="13696">
    <literal><![CDATA[
      K(x,K(y,(1 / z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(12993(a,2),13671(a,1,2))].">
      <j1 rule="para" parents="12993 13671"/>
    </justification>
  </clause>

  <clause id="13697">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / u)) = w
    ]]></literal>
    <justification jstring="[para(13473(a,1),13671(a,1))].">
      <j1 rule="para" parents="13473 13671"/>
    </justification>
  </clause>

  <clause id="13698">
    <literal><![CDATA[
      K(x,K(y,T(x,z) / u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(13697,a,8905,a)].">
      <j1 rule="hyper" parents="13697 8905"/>
    </justification>
  </clause>

  <clause id="13699">
    <literal><![CDATA[
      (T(x,y) / z) * K(x,K(u,z)) = T(T(x,y) / z,K(u,x))
    ]]></literal>
    <justification jstring="[para(13698(a,1),7262(a,1,2))].">
      <j1 rule="para" parents="13698 7262"/>
    </justification>
  </clause>

  <clause id="13700">
    <literal><![CDATA[
      K((x * y) * T(z,y),T(u,y * z)) = K((z * y) * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(9598(a,1),13279(a,1,1))].">
      <j1 rule="para" parents="9598 13279"/>
    </justification>
  </clause>

  <clause id="13701">
    <literal><![CDATA[
      K(x,T(L(y \ z,y,y \ u),z * (u / y))) = K(x,((u / y) * z) / u)
    ]]></literal>
    <justification jstring="[para(10156(a,2),13280(a,1,2,1))].">
      <j1 rule="para" parents="10156 13280"/>
    </justification>
  </clause>

  <clause id="13702">
    <literal><![CDATA[
      K(x,T(L(y \ z,y,z \ u),y * (u / z))) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[para(13462(a,2),13281(a,1,2,1))].">
      <j1 rule="para" parents="13462 13281"/>
    </justification>
  </clause>

  <clause id="13703">
    <literal><![CDATA[
      1 / (K(x,y) * z) = (1 / z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,8914,a(flip),b,13341,a)].">
      <j1 rule="hyper" parents="63 8914 13341"/>
    </justification>
  </clause>

  <clause id="13704">
    <literal><![CDATA[
      K(x,y) * ((1 / z) * K(u,w)) = K(x,y) / (K(w,u) * z)
    ]]></literal>
    <justification jstring="[para(13703(a,1),12988(a,1,2))].">
      <j1 rule="para" parents="13703 12988"/>
    </justification>
  </clause>

  <clause id="13705">
    <literal><![CDATA[
      K(x,y) * ((1 / z) * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / (K(w,u) * z) = v5
    ]]></literal>
    <justification jstring="[para(13703(a,1),13127(a,1,2))].">
      <j1 rule="para" parents="13703 13127"/>
    </justification>
  </clause>

  <clause id="13706">
    <literal><![CDATA[
      (x \ K(y,z)) * K(z,K(y,u)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[para(7279(a,1),13344(a,1,2))].">
      <j1 rule="para" parents="7279 13344"/>
    </justification>
  </clause>

  <clause id="13707">
    <literal><![CDATA[
      (x \ K(y,z)) * K(y,K(u,z)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[para(7293(a,1),13344(a,1,2))].">
      <j1 rule="para" parents="7293 13344"/>
    </justification>
  </clause>

  <clause id="13709">
    <literal><![CDATA[
      L(x,y \ (x \ z),y) * (x \ z) = y * ((y \ (z / x)) * x)
    ]]></literal>
    <justification jstring="[hyper(134,a,13357,a(flip),b,874,a),flip(a)].">
      <j1 rule="hyper" parents="134 13357 874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13710">
    <literal><![CDATA[
      (x / y) * L(z,z,y \ x) = (x / y) / (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,2007,a,b,13362,a)].">
      <j1 rule="hyper" parents="134 2007 13362"/>
    </justification>
  </clause>

  <clause id="13711">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3688(a,2),13376(a,1))].">
      <j1 rule="para" parents="3688 13376"/>
    </justification>
  </clause>

  <clause id="13713">
    <literal><![CDATA[
      K(x,y * (((z * y) \ u) * K(z,z \ u))) = K(x,T(y * ((z * y) \ u),z))
    ]]></literal>
    <justification jstring="[para(10515(a,1),13437(a,1,2,2,2))].">
      <j1 rule="para" parents="10515 13437"/>
    </justification>
  </clause>

  <clause id="13714">
    <literal><![CDATA[
      x * K(y \ (z \ x),z * y) = ((z * y) \ x) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,13438,a(flip),b,92,a)].">
      <j1 rule="hyper" parents="134 13438 92"/>
    </justification>
  </clause>

  <clause id="13715">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) \ x = K(u,L(z,y,y \ x))
    ]]></literal>
    <justification jstring="[hyper(11140,a,13464,a),flip(a)].">
      <j1 rule="hyper" parents="11140 13464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13718">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) * K(y,T(x,z)) = T(u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6859,a,b,13536,a)].">
      <j1 rule="hyper" parents="63 6859 13536"/>
    </justification>
  </clause>

  <clause id="13719">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * T(u,K(x,y))) = L(u * K(y,T(x,z)),K(x,y),z)
    ]]></literal>
    <justification jstring="[para(13536(a,1),10174(a,1,2,2))].">
      <j1 rule="para" parents="13536 10174"/>
    </justification>
  </clause>

  <clause id="13720">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7103,a,b,13552,a),flip(a)].">
      <j1 rule="hyper" parents="347 7103 13552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13721">
    <literal><![CDATA[
      T(x,T(y * K(y * z,u),z)) = T(x,z \ T(y * z,u))
    ]]></literal>
    <justification jstring="[para(13338(a,1),13566(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13338 13566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13722">
    <literal><![CDATA[
      K(x / K(y,z),K(y,z)) \ T(u,x / K(y,z)) = (x / K(y,z)) \ (u * (K(y,z) \ x))
    ]]></literal>
    <justification jstring="[para(113(a,1),13648(a,2,2,2))].">
      <j1 rule="para" parents="113 13648"/>
    </justification>
  </clause>

  <clause id="13723">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,z) = z \ (u * T(z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(7283(a,2),13648(a,1,1))].">
      <j1 rule="para" parents="7283 13648"/>
    </justification>
  </clause>

  <clause id="13724">
    <literal><![CDATA[
      K(x,T(y,K(z,u) / u)) = K(x,T(y,1 / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13601,a,b,13665,a)].">
      <j1 rule="hyper" parents="63 13601 13665"/>
    </justification>
  </clause>

  <clause id="13725">
    <literal><![CDATA[
      K(x * T(y,z),y * z) = K(y * x,z * y)
    ]]></literal>
    <justification jstring="[para(5926(a,1),13669(a,1,1))].">
      <j1 rule="para" parents="5926 13669"/>
    </justification>
  </clause>

  <clause id="13726">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),x * y) = K(x * (z * y),y * x)
    ]]></literal>
    <justification jstring="[hyper(9629,a,13725,a)].">
      <j1 rule="hyper" parents="9629 13725"/>
    </justification>
  </clause>

  <clause id="13727">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * T(K(x,y) \ z,K(x,y))) = (z * K(y,x)) \ (u * (K(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(7335(a,1),13678(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7335 13678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13728">
    <literal><![CDATA[
      T(K(x,((y * K(z,u)) * w) * v5),v5 \ T(v5 * ((y * K(z,u)) * w),x)) = (v5 \ T(v5 * ((y * K(z,u)) * w),x)) \ T((y * K(z,u)) * w,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(462,a,13685,a,b,13140,a)].">
      <j1 rule="hyper" parents="462 13685 13140"/>
    </justification>
  </clause>

  <clause id="13729">
    <literal><![CDATA[
      T(x,y) * K(z,L(T(u,x),w,v5)) = K(z,L(u,w,v5)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(13686(a,1),7173(a,1,2))].">
      <j1 rule="para" parents="13686 7173"/>
    </justification>
  </clause>

  <clause id="13730">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ K(y,z)) = u \ K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,13520,a,b,13707,a)].">
      <j1 rule="hyper" parents="63 13520 13707"/>
    </justification>
  </clause>

  <clause id="13731">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) != u * w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(13720(a,2),43(a,1))].">
      <j1 rule="para" parents="13720 43"/>
    </justification>
  </clause>

  <clause id="13732">
    <literal><![CDATA[
      K(x,T(y,T(1 / z,u))) = K(x,T(y,K(u,z) / z))
    ]]></literal>
    <justification jstring="[para(8293(a,1),13724(a,2,2)),flip(a)].">
      <j1 rule="para" parents="8293 13724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13733">
    <literal><![CDATA[
      K(x,T(y,K(z,u) / u)) = K(x,T(y,1 / u))
    ]]></literal>
    <justification jstring="[hyper(13638,a,13732,a),flip(a)].">
      <j1 rule="hyper" parents="13638 13732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13735">
    <literal><![CDATA[
      K(x,T(y,K(z,u) / u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,8860,a(flip),b,13733,a),flip(a)].">
      <j1 rule="hyper" parents="347 8860 13733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13736">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(u,z) / z) = (K(u,z) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,13735,a(flip),b,7378,a)].">
      <j1 rule="hyper" parents="133 13735 7378"/>
    </justification>
  </clause>

  <clause id="13737">
    <literal><![CDATA[
      (x / K(y,z)) \ 1 = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(13026,a,13347,a),flip(a)].">
      <j1 rule="hyper" parents="13026 13347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13738">
    <literal><![CDATA[
      (x * K(y,z)) \ 1 = K(z,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(6117(a,1),13737(a,1,1))].">
      <j1 rule="para" parents="6117 13737"/>
    </justification>
  </clause>

  <clause id="13739">
    <literal><![CDATA[
      T(x \ K(y,z),K(z,y)) = (x * K(z,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,13024,a,b,13738,a)].">
      <j1 rule="hyper" parents="347 13024 13738"/>
    </justification>
  </clause>

  <clause id="13740">
    <literal><![CDATA[
      T(K(x,y) / z,z * K(y,x)) = K(x,y) * (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,13148,a,b,13738,a)].">
      <j1 rule="hyper" parents="63 13148 13738"/>
    </justification>
  </clause>

  <clause id="13741">
    <literal><![CDATA[
      ((x * K(y,z)) \ 1) \ 1 = (x \ 1) \ K(y,z)
    ]]></literal>
    <justification jstring="[para(13738(a,2),13174(a,1,1))].">
      <j1 rule="para" parents="13738 13174"/>
    </justification>
  </clause>

  <clause id="13742">
    <literal><![CDATA[
      (x * K(y,z)) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(13739(a,1),13025(a,1))].">
      <j1 rule="para" parents="13739 13025"/>
    </justification>
  </clause>

  <clause id="13743">
    <literal><![CDATA[
      L(x,(y \ 1) \ K(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * K(z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(13741(a,1),3526(a,1,2))].">
      <j1 rule="para" parents="13741 3526"/>
    </justification>
  </clause>

  <clause id="13744">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((x * K(y,z)) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(13741(a,1),13370(a,1,1,1))].">
      <j1 rule="para" parents="13741 13370"/>
    </justification>
  </clause>

  <clause id="13745">
    <literal><![CDATA[
      (x * y) / (z \ (y * x)) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(13203,a,11557,a)].">
      <j1 rule="hyper" parents="13203 11557"/>
    </justification>
  </clause>

  <clause id="13746">
    <literal><![CDATA[
      (x * y) / (z \ (y * x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(347,a,5256,a(flip),b,13745,a),flip(a)].">
      <j1 rule="hyper" parents="347 5256 13745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13747">
    <literal><![CDATA[
      (K(x,y) * z) \ (x * y) = z \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(214,a,13746,a)].">
      <j1 rule="hyper" parents="214 13746"/>
    </justification>
  </clause>

  <clause id="13748">
    <literal><![CDATA[
      K(x,y) * ((y * x) / z) = (x * y) / z
    ]]></literal>
    <justification jstring="[para(83(a,1),13746(a,1,2)),flip(a)].">
      <j1 rule="para" parents="83 13746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13749">
    <literal><![CDATA[
      K(x,y) * ((y / z) * (z * x)) = (x * y) / a(y / z,z,x)
    ]]></literal>
    <justification jstring="[para(90(a,1),13746(a,1,2)),flip(a)].">
      <j1 rule="para" parents="90 13746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13750">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * (y * x)) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(39,a,4569,a(flip),b,13747,a),flip(a)].">
      <j1 rule="hyper" parents="39 4569 13747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13751">
    <literal><![CDATA[
      (x * (T(y,x) * z)) \ (y * x) = (x * (y * z)) \ (x * y)
    ]]></literal>
    <justification jstring="[para(5231(a,1),13747(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5231 13747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13752">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) \ (z * K(x,y)) = (K(x,y) * u) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7446(a,1),13747(a,1,1))].">
      <j1 rule="para" parents="7446 13747"/>
    </justification>
  </clause>

  <clause id="13753">
    <literal><![CDATA[
      K(x * y,R(z,x,y)) * (((z * x) * y) / u) = ((x * y) * R(z,x,y)) / u
    ]]></literal>
    <justification jstring="[para(107(a,1),13748(a,1,2,1))].">
      <j1 rule="para" parents="107 13748"/>
    </justification>
  </clause>

  <clause id="13754">
    <literal><![CDATA[
      ((x * y) / z) \ K(x,y) = ((y * x) / z) \ 1
    ]]></literal>
    <justification jstring="[para(13748(a,1),13130(a,1,1))].">
      <j1 rule="para" parents="13748 13130"/>
    </justification>
  </clause>

  <clause id="13755">
    <literal><![CDATA[
      ((x * y) / z) \ T(x,y) = ((y * x) / z) \ x
    ]]></literal>
    <justification jstring="[para(13748(a,1),13154(a,1,1))].">
      <j1 rule="para" parents="13748 13154"/>
    </justification>
  </clause>

  <clause id="13756">
    <literal><![CDATA[
      ((x * T(y,x)) / z) \ T(x,T(y,x)) = ((y * ((y * x) / y)) / z) \ x
    ]]></literal>
    <justification jstring="[para(4149(a,1),13755(a,2,1,1))].">
      <j1 rule="para" parents="4149 13755"/>
    </justification>
  </clause>

  <clause id="13757">
    <literal><![CDATA[
      (K(x,y) / x) * (y * x) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,6493,a(flip),b,13750,a)].">
      <j1 rule="hyper" parents="63 6493 13750"/>
    </justification>
  </clause>

  <clause id="13758">
    <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(10388(a,1),13232(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10388 13232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13759">
    <literal><![CDATA[
      L(x,y,z) * T(z * y,x) = z * (y * x)
    ]]></literal>
    <justification jstring="[hyper(6193,a,13439,a)].">
      <j1 rule="hyper" parents="6193 13439"/>
    </justification>
  </clause>

  <clause id="13760">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * x)) / T(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(6183,a,13439,a),flip(a)].">
      <j1 rule="hyper" parents="6183 13439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13762">
    <literal><![CDATA[
      L(x,y,z) \ (z * (y * x)) = T(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(138,a,13759,a)].">
      <j1 rule="hyper" parents="138 13759"/>
    </justification>
  </clause>

  <clause id="13763">
    <literal><![CDATA[
      L(x \ y,x,z) \ (z * y) = T(z * x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(128,a,169,a(flip),b,13759,a)].">
      <j1 rule="hyper" parents="128 169 13759"/>
    </justification>
  </clause>

  <clause id="13764">
    <literal><![CDATA[
      L(x,y / x,z) \ (z * y) = T(z * (y / x),x)
    ]]></literal>
    <justification jstring="[hyper(128,a,168,a(flip),b,13759,a)].">
      <j1 rule="hyper" parents="128 168 13759"/>
    </justification>
  </clause>

  <clause id="13765">
    <literal><![CDATA[
      L(x,y,z) * (x \ (z * y)) = (z * (y * x)) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,13759,a(flip),b,11219,a),flip(a)].">
      <j1 rule="hyper" parents="131 13759 11219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13767">
    <literal><![CDATA[
      L(x,y \ z,y) * T(z,x) = y * ((y \ z) * x)
    ]]></literal>
    <justification jstring="[para(10(a,1),13759(a,1,2,1))].">
      <j1 rule="para" parents="10 13759"/>
    </justification>
  </clause>

  <clause id="13768">
    <literal><![CDATA[
      (x * (y * z)) / T(x * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(13759(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="13759 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13769">
    <literal><![CDATA[
      L(K(x,y),z / y,u) * T(u * (z / y),K(x,y)) = u * (z / T(y,x))
    ]]></literal>
    <justification jstring="[para(6102(a,1),13759(a,2,2))].">
      <j1 rule="para" parents="6102 13759"/>
    </justification>
  </clause>

  <clause id="13770">
    <literal><![CDATA[
      L(x,y,y \ z) * T((z / y) * y,x) = (z / y) * (y * x)
    ]]></literal>
    <justification jstring="[para(10147(a,1),13759(a,1,1))].">
      <j1 rule="para" parents="10147 13759"/>
    </justification>
  </clause>

  <clause id="13771">
    <literal><![CDATA[
      (x * (L(1 / y,y,x) * z)) / T(x / y,z) = L(z,L(1 / y,y,x),x)
    ]]></literal>
    <justification jstring="[para(3266(a,1),13760(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3266 13760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13773">
    <literal><![CDATA[
      T(x * y,y \ z) = ((x * y) \ (x * z)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,564,a(flip),b,13763,a),flip(a)].">
      <j1 rule="hyper" parents="63 564 13763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13774">
    <literal><![CDATA[
      L(x \ y,x,z / y) \ z = T((z / y) * x,x \ y)
    ]]></literal>
    <justification jstring="[para(12(a,1),13763(a,1,2))].">
      <j1 rule="para" parents="12 13763"/>
    </justification>
  </clause>

  <clause id="13775">
    <literal><![CDATA[
      L(x,y,z) * (z * y) = x * ((z * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(134,a,13765,a(flip),b,1402,a),flip(a)].">
      <j1 rule="hyper" parents="134 13765 1402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13776">
    <literal><![CDATA[
      L(x,y,T(x,T(z,y))) * (x \ (T(x,T(z,y)) * y)) = (x * (y * T(x,z))) / x
    ]]></literal>
    <justification jstring="[para(7702(a,1),13765(a,2,1))].">
      <j1 rule="para" parents="7702 13765"/>
    </justification>
  </clause>

  <clause id="13777">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * K(z,T(u,y)),y) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,K(z,T(u,y)),x) = w
    ]]></literal>
    <justification jstring="[para(7373(a,1),13768(a,1,1,2))].">
      <j1 rule="para" parents="7373 13768"/>
    </justification>
  </clause>

  <clause id="13778">
    <literal><![CDATA[
      ((x * y) * ((K(y,x) * z) * u)) / T((y * x) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,K(y,x) * z,x * y) = w
    ]]></literal>
    <justification jstring="[para(10271(a,1),13768(a,1,2,1))].">
      <j1 rule="para" parents="10271 13768"/>
    </justification>
  </clause>

  <clause id="13779">
    <literal><![CDATA[
      L(K(x,y * K(z,u)),x,w) = (x * K(v5,v6)) \ (T(x,K(z,u) * y) * K(v5,v6))
    ]]></literal>
    <justification jstring="[para(13555(a,2),13603(a,2,2,1))].">
      <j1 rule="para" parents="13555 13603"/>
    </justification>
  </clause>

  <clause id="13780">
    <literal><![CDATA[
      T(x / ((y \ 1) * z),T(y \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(((y \ 1) * z) \ x,K((y \ 1) * z,T(u,v5))) = w
    ]]></literal>
    <justification jstring="[para(13353(a,1),13615(a,1))].">
      <j1 rule="para" parents="13353 13615"/>
    </justification>
  </clause>

  <clause id="13781">
    <literal><![CDATA[
      T(x,y) * K(z \ x,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x / z,u) * T(x,y) = w
    ]]></literal>
    <justification jstring="[para(7165(a,1),13623(a,1,2))].">
      <j1 rule="para" parents="7165 13623"/>
    </justification>
  </clause>

  <clause id="13782">
    <literal><![CDATA[
      K(T(x,y) * z,T(T(u,x),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z * T(x,y),T(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(23(a,1),13625(a,1,2))].">
      <j1 rule="para" parents="23 13625"/>
    </justification>
  </clause>

  <clause id="13783">
    <literal><![CDATA[
      T(x,K(y / z,u) * T(z * (y / z),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * K(y,w)) * T(y / z,u)) = v5
    ]]></literal>
    <justification jstring="[para(13241(a,1),13632(a,1,2,2))].">
      <j1 rule="para" parents="13241 13632"/>
    </justification>
  </clause>

  <clause id="13784">
    <literal><![CDATA[
      K(x,K(y / z,u) * (w * ((z / y) \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * T((z / y) \ 1,u)) = v5
    ]]></literal>
    <justification jstring="[para(5551(a,1),13637(a,1,2,1))].">
      <j1 rule="para" parents="5551 13637"/>
    </justification>
  </clause>

  <clause id="13785">
    <literal><![CDATA[
      K(x,K(y,z * (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / u)) = w
    ]]></literal>
    <justification jstring="[para(13476(a,1),13696(a,1))].">
      <j1 rule="para" parents="13476 13696"/>
    </justification>
  </clause>

  <clause id="13786">
    <literal><![CDATA[
      x / K(y,L(z,u,u \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      (x / u) * (u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(13715(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13715 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13787">
    <literal><![CDATA[
      T((x / y) * z,z \ y) = (((x / y) * z) \ x) \ x
    ]]></literal>
    <justification jstring="[para(566(a,1),13774(a,1,1)),flip(a)].">
      <j1 rule="para" parents="566 13774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13788">
    <literal><![CDATA[
      L(x \ y,x,y \ z) \ z = T((z / y) * x,x \ y)
    ]]></literal>
    <justification jstring="[para(13462(a,2),13787(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13462 13787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13789">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,z \ y)) = K(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,13072,a(flip),b,13048,a),flip(a)].">
      <j1 rule="hyper" parents="347 13072 13048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13790">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) * (z \ y)) = K(x,(z \ y) * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(199(a,1),13789(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="199 13789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13791">
    <literal><![CDATA[
      K((x \ y) * z,x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(13023,a,13087,a),flip(a)].">
      <j1 rule="hyper" parents="13023 13087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13792">
    <literal><![CDATA[
      K(x \ (y * z),x) = K((x \ y) * z,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,9647,a,b,13791,a)].">
      <j1 rule="hyper" parents="347 9647 13791"/>
    </justification>
  </clause>

  <clause id="13793">
    <literal><![CDATA[
      K(x \ ((x * y) * z),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),13792(a,2,1,1))].">
      <j1 rule="para" parents="9 13792"/>
    </justification>
  </clause>

  <clause id="13794">
    <literal><![CDATA[
      K(x \ ((y * x) * z),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10305,a,b,13793,a)].">
      <j1 rule="hyper" parents="63 10305 13793"/>
    </justification>
  </clause>

  <clause id="13795">
    <literal><![CDATA[
      K(x * y,z) * (((z * x) * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      z \ ((z * x) * y) = u
    ]]></literal>
    <justification jstring="[para(13793(a,1),5370(a,1,1))].">
      <j1 rule="para" parents="13793 5370"/>
    </justification>
  </clause>

  <clause id="13796">
    <literal><![CDATA[
      K((x \ y) \ (y * z),x \ y) = K(x * z,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),13794(a,1,1,2,1))].">
      <j1 rule="para" parents="10 13794"/>
    </justification>
  </clause>

  <clause id="13797">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(x * (y \ z),x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),13796(a,1,1,2))].">
      <j1 rule="para" parents="10 13796"/>
    </justification>
  </clause>

  <clause id="13798">
    <literal><![CDATA[
      K(x \ (y * z),y \ x) = K(y * (x \ z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9579,a(flip),b,13797,a)].">
      <j1 rule="hyper" parents="63 9579 13797"/>
    </justification>
  </clause>

  <clause id="13799">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),z \ u)) = a(x,y,K(w,z \ u))
    ]]></literal>
    <justification jstring="[para(13797(a,1),11284(a,1,3))].">
      <j1 rule="para" parents="13797 11284"/>
    </justification>
  </clause>

  <clause id="13800">
    <literal><![CDATA[
      K(x / (y / z),z \ y) = K(z * (y \ x),z \ y)
    ]]></literal>
    <justification jstring="[hyper(9654,a,13798,a)].">
      <j1 rule="hyper" parents="9654 13798"/>
    </justification>
  </clause>

  <clause id="13801">
    <literal><![CDATA[
      K(x,y / ((z * u) \ z)) = K(x,y / (z \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(13327,a,13135,a),flip(a)].">
      <j1 rule="hyper" parents="13327 13135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13802">
    <literal><![CDATA[
      K(x,y / (z / (u * z))) = K(x,y / (z \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12275,a,b,13801,a)].">
      <j1 rule="hyper" parents="63 12275 13801"/>
    </justification>
  </clause>

  <clause id="13803">
    <literal><![CDATA[
      K(x,y / (z \ (z / u))) \ 1 = K(y / (z / (u * z)),x)
    ]]></literal>
    <justification jstring="[para(13802(a,1),5173(a,1,1))].">
      <j1 rule="para" parents="13802 5173"/>
    </justification>
  </clause>

  <clause id="13804">
    <literal><![CDATA[
      K(x,y / T((z \ 1) \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13137(a,2),13327(a,1))].">
      <j1 rule="para" parents="13137 13327"/>
    </justification>
  </clause>

  <clause id="13805">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),T(x * y,K(y,z)) \ y) = (K(z,y) * (x * T(y,z))) \ y
    ]]></literal>
    <justification jstring="[para(5955(a,1),13200(a,1,2,1))].">
      <j1 rule="para" parents="5955 13200"/>
    </justification>
  </clause>

  <clause id="13806">
    <literal><![CDATA[
      T(T(x,y),z \ (z \ 1)) = T(x,z \ ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(13125,a,13273,a),flip(a)].">
      <j1 rule="hyper" parents="13125 13273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13807">
    <literal><![CDATA[
      T(T(x,y),z \ (z \ 1)) = T(x,(z * z) \ y)
    ]]></literal>
    <justification jstring="[para(499(a,1),13806(a,2,2))].">
      <j1 rule="para" parents="499 13806"/>
    </justification>
  </clause>

  <clause id="13808">
    <literal><![CDATA[
      T(T(x,y),z \ (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (z \ y)) = u
    ]]></literal>
    <justification jstring="[para(13807(a,2),13047(a,1))].">
      <j1 rule="para" parents="13807 13047"/>
    </justification>
  </clause>

  <clause id="13809">
    <literal><![CDATA[
      T(T(x,y \ (y \ 1)),z) = T(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(13808,a,23,a),flip(a)].">
      <j1 rule="hyper" parents="13808 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13810">
    <literal><![CDATA[
      T(T(x,y \ (y \ 1)),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),13808(a,1))].">
      <j1 rule="para" parents="23 13808"/>
    </justification>
  </clause>

  <clause id="13811">
    <literal><![CDATA[
      T(T(T(x,y),z),u \ (u \ 1)) = T(T(x,u \ (u \ y)),z)
    ]]></literal>
    <justification jstring="[para(13809(a,1),115(a,2,1))].">
      <j1 rule="para" parents="13809 115"/>
    </justification>
  </clause>

  <clause id="13812">
    <literal><![CDATA[
      T(x,y \ (y \ x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ 1)) = z
    ]]></literal>
    <justification jstring="[para(13809(a,1),918(a,1))].">
      <j1 rule="para" parents="13809 918"/>
    </justification>
  </clause>

  <clause id="13813">
    <literal><![CDATA[
      T(x \ 1,x \ (x \ y)) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(3240(a,1),13809(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3240 13809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13814">
    <literal><![CDATA[
      T(1 / x,x * y) = T(x \ 1,x \ y)
    ]]></literal>
    <justification jstring="[para(9(a,1),13813(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 13813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13815">
    <literal><![CDATA[
      R(T(x \ 1,x \ y),x,y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[para(13814(a,1),865(a,1,1))].">
      <j1 rule="para" parents="13814 865"/>
    </justification>
  </clause>

  <clause id="13816">
    <literal><![CDATA[
      R(T(x \ 1,x \ ((y \ 1) \ z)),x,y \ z) = (x * ((y \ 1) \ z)) \ ((y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(2379,a,13815,a)].">
      <j1 rule="hyper" parents="2379 13815"/>
    </justification>
  </clause>

  <clause id="13817">
    <literal><![CDATA[
      T(x,K(y,z * (x * u))) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(7764,a,13351,a),flip(a)].">
      <j1 rule="hyper" parents="7764 13351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13818">
    <literal><![CDATA[
      L(x,y,z * (u \ (1 / u))) = L(x,y,z / (u * u))
    ]]></literal>
    <justification jstring="[para(667(a,1),13360(a,2,3))].">
      <j1 rule="para" parents="667 13360"/>
    </justification>
  </clause>

  <clause id="13819">
    <literal><![CDATA[
      T(x * x,y) * ((x * x) \ y) = T(y,x \ (x \ y))
    ]]></literal>
    <justification jstring="[para(1108(a,1),13422(a,1,2))].">
      <j1 rule="para" parents="1108 13422"/>
    </justification>
  </clause>

  <clause id="13820">
    <literal><![CDATA[
      T(x,y \ (y \ x)) = x * K(y * y,x)
    ]]></literal>
    <justification jstring="[hyper(5202,a,13819,a),flip(a)].">
      <j1 rule="hyper" parents="5202 13819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13821">
    <literal><![CDATA[
      T(x \ y,x \ (x \ (x \ y))) = (x \ y) * K(x * x,x * y)
    ]]></literal>
    <justification jstring="[para(13051(a,1),13820(a,2,2))].">
      <j1 rule="para" parents="13051 13820"/>
    </justification>
  </clause>

  <clause id="13822">
    <literal><![CDATA[
      (x * x) * K(y,x \ (x \ 1)) = K(x * x,y) * (x * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,13086,a(flip),b,13431,a),flip(a)].">
      <j1 rule="hyper" parents="347 13086 13431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13823">
    <literal><![CDATA[
      T(T(x,K(y,z * (z / (u \ 1)))),y / (z \ (z / (u \ 1)))) = T(x,L(u,u,z) \ y)
    ]]></literal>
    <justification jstring="[para(2007(a,2),13480(a,2,2,1))].">
      <j1 rule="para" parents="2007 13480"/>
    </justification>
  </clause>

  <clause id="13824">
    <literal><![CDATA[
      T(T(x,K(y,(z * u) * (u \ 1))),y * T((u \ 1) * (u * z),u)) = T(x,((u \ 1) * (z * u)) * y)
    ]]></literal>
    <justification jstring="[para(1846(a,2),13495(a,1,2,2))].">
      <j1 rule="para" parents="1846 13495"/>
    </justification>
  </clause>

  <clause id="13825">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (u * (z * (u \ 1)))) = T(x,(u * (z * (u \ 1))) * y)
    ]]></literal>
    <justification jstring="[para(12742(a,1),13495(a,1,1))].">
      <j1 rule="para" parents="12742 13495"/>
    </justification>
  </clause>

  <clause id="13826">
    <literal><![CDATA[
      K(x,y \ ((z \ u) * z)) = K(x,K(u,y)) * K(x,T(u,z) / y)
    ]]></literal>
    <justification jstring="[hyper(347,a,12060,a,b,13508,a)].">
      <j1 rule="hyper" parents="347 12060 13508"/>
    </justification>
  </clause>

  <clause id="13827">
    <literal><![CDATA[
      T(x * T(y,z),K(y,u)) = T(x,K(y,u)) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13537,a(flip),b,13538,a)].">
      <j1 rule="hyper" parents="63 13537 13538"/>
    </justification>
  </clause>

  <clause id="13828">
    <literal><![CDATA[
      T(T(x,y) \ z,K(x,u)) = T(x,y) \ T(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,4830,a(flip),b,13827,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 4830 13827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13829">
    <literal><![CDATA[
      T(T(K(x,y) * z,K(x,y)) \ u,K(K(x,y) * z,w)) = (z * K(x,y)) \ T(u,K(K(x,y) * z,w))
    ]]></literal>
    <justification jstring="[para(6872(a,1),13828(a,2,1))].">
      <j1 rule="para" parents="6872 13828"/>
    </justification>
  </clause>

  <clause id="13830">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(u / K(x,K(y,z)),w) = T(K(x,K(y,z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(7318(a,1),13569(a,1,1))].">
      <j1 rule="para" parents="7318 13569"/>
    </justification>
  </clause>

  <clause id="13831">
    <literal><![CDATA[
      T(x,T(T(y * K(y / z,u),z),w)) = T(x,T(T(z \ y,u) * z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,10413,a,b,13652,a)].">
      <j1 rule="hyper" parents="63 10413 13652"/>
    </justification>
  </clause>

  <clause id="13832">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * y)) = K(x,u * (z * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12066,a(flip),b,13662,a)].">
      <j1 rule="hyper" parents="63 12066 13662"/>
    </justification>
  </clause>

  <clause id="13833">
    <literal><![CDATA[
      T(x,y) / T(z,K(x,u)) = T(T(x,y) / z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(7276,a,13699,a)].">
      <j1 rule="hyper" parents="7276 13699"/>
    </justification>
  </clause>

  <clause id="13834">
    <literal><![CDATA[
      T(x,y) / T(z,K(x,u)) = T(T(x,y) / z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,7330,a,b,13833,a),flip(a)].">
      <j1 rule="hyper" parents="347 7330 13833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13835">
    <literal><![CDATA[
      T(T(K(x,y) * z,K(x,y)) / u,K(K(x,y) * z,w)) = (z * K(x,y)) / T(u,K(K(x,y) * z,w))
    ]]></literal>
    <justification jstring="[para(6872(a,1),13834(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6872 13834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13836">
    <literal><![CDATA[
      K(x,y) / (K(x,y) * z) = T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(7476,a,13704,a),flip(a)].">
      <j1 rule="hyper" parents="7476 13704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13837">
    <literal><![CDATA[
      x / T(y * z,z \ (y \ x)) = (y * z) \ x
    ]]></literal>
    <justification jstring="[hyper(6183,a,13714,a)].">
      <j1 rule="hyper" parents="6183 13714"/>
    </justification>
  </clause>

  <clause id="13838">
    <literal><![CDATA[
      T(x * y,(x * y) \ z) = T(x * y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(36,a,296,a,b,13837,a)].">
      <j1 rule="hyper" parents="36 296 13837"/>
    </justification>
  </clause>

  <clause id="13839">
    <literal><![CDATA[
      T(x * y,y \ (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      ((x * y) \ z) \ z = u
    ]]></literal>
    <justification jstring="[para(13838(a,1),440(a,1))].">
      <j1 rule="para" parents="13838 440"/>
    </justification>
  </clause>

  <clause id="13840">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),(x \ y) * (L(x \ y,z,u) \ (x * L(x \ y,z,u)))) = ((x * L(x \ y,z,u)) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(13839,a,12705,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="13839 12705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13841">
    <literal><![CDATA[
      K(x,T(y,z)) / T(z,u) = (K(u,z) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13295,a,13736,a)].">
      <j1 rule="hyper" parents="13295 13736"/>
    </justification>
  </clause>

  <clause id="13842">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = (K(u,x) / x) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13340,a,b,13841,a)].">
      <j1 rule="hyper" parents="63 13340 13841"/>
    </justification>
  </clause>

  <clause id="13843">
    <literal><![CDATA[
      ((x \ y) * (T(K(z,x),x \ y) * u)) \ (T(x,z) \ y) = ((x \ y) * (K(z,x) * u)) \ ((x \ y) * K(z,x))
    ]]></literal>
    <justification jstring="[para(5209(a,1),13751(a,1,2))].">
      <j1 rule="para" parents="5209 13751"/>
    </justification>
  </clause>

  <clause id="13844">
    <literal><![CDATA[
      K(x / (y / (z * y)),u) = K(x / (y \ (y / z)),u)
    ]]></literal>
    <justification jstring="[hyper(5179,a,13803,a),flip(a)].">
      <j1 rule="hyper" parents="5179 13803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13845">
    <literal><![CDATA[
      K(x / (y \ (y / z)),T(u,x)) = K((y / (z * y)) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(7493,a,13844,a),flip(a)].">
      <j1 rule="hyper" parents="7493 13844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13846">
    <literal><![CDATA[
      T(T(x,y \ (y \ z)),u) = T(T(x,z),y \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(13808,a,13811,a),flip(a)].">
      <j1 rule="hyper" parents="13808 13811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13847">
    <literal><![CDATA[
      T(T(x,y * z),y \ (y \ u)) = T(T(x,y \ z),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),13846(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 13846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13848">
    <literal><![CDATA[
      T(T(x,y * z),y \ T(u,y)) = T(T(x,y \ z),u * y)
    ]]></literal>
    <justification jstring="[para(22(a,2),13847(a,1,2,2))].">
      <j1 rule="para" parents="22 13847"/>
    </justification>
  </clause>

  <clause id="13849">
    <literal><![CDATA[
      (x * x) * K(y,x \ (x \ 1)) = T(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,4977,a,b,13822,a),flip(a)].">
      <j1 rule="hyper" parents="347 4977 13822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13850">
    <literal><![CDATA[
      x * T(y \ (y \ 1),z) = x / T(y * y,z)
    ]]></literal>
    <justification jstring="[hyper(220,a,13849,a(flip),b,6477,a),flip(a)].">
      <j1 rule="hyper" parents="220 13849 6477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13851">
    <literal><![CDATA[
      K((x / (y * x)) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x \ (x / y)) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(13845(a,1),7493(a,1))].">
      <j1 rule="para" parents="13845 7493"/>
    </justification>
  </clause>

  <clause id="13852">
    <literal><![CDATA[
      T(T(x,y \ z),u * y) = T(T(x,y * z),u / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,12074,a(flip),b,13848,a),flip(a)].">
      <j1 rule="hyper" parents="63 12074 13848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13853">
    <literal><![CDATA[
      a(x,y,z) \ (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      z * (a(x,y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(12967(a,1),9965(a,1)),flip(b)].">
      <j1 rule="para" parents="12967 9965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13855">
    <literal><![CDATA[
      K(x,y * (z \ K(x,u))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(13319,a,8445,a)].">
      <j1 rule="hyper" parents="13319 8445"/>
    </justification>
  </clause>

  <clause id="13856">
    <literal><![CDATA[
      K(x,y / T(z / u,z)) = K(x,y * ((u \ z) \ K(x,w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,11972,a,b,13855,a)].">
      <j1 rule="hyper" parents="347 11972 13855"/>
    </justification>
  </clause>

  <clause id="13857">
    <literal><![CDATA[
      ((x * y) * z) / L(y * z,x,a(x,y,z)) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,12603,a(flip),b,13394,a),flip(a)].">
      <j1 rule="hyper" parents="347 12603 13394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13858">
    <literal><![CDATA[
      R(x * R(x \ 1,y,z),x,y * z) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1292(a,1),13409(a,1,1))].">
      <j1 rule="para" parents="1292 13409"/>
    </justification>
  </clause>

  <clause id="13859">
    <literal><![CDATA[
      K(x,L(y / T((z \ u) \ 1,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * (z \ T(u,u \ z)),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(6611(a,1),13444(a,1,2,1,2))].">
      <j1 rule="para" parents="6611 13444"/>
    </justification>
  </clause>

  <clause id="13860">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * z) / (w * u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,13512,a,b,13516,a),flip(a)].">
      <j1 rule="hyper" parents="347 13512 13516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13861">
    <literal><![CDATA[
      K(x,K((y \ z) / u,L(w,u,y))) = K(x,K(w,z / (y * u)))
    ]]></literal>
    <justification jstring="[hyper(13540,a,13541,a)].">
      <j1 rule="hyper" parents="13540 13541"/>
    </justification>
  </clause>

  <clause id="13862">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) * K(y,K(x,z)) = z \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(13692,a,13104,a)].">
      <j1 rule="hyper" parents="13692 13104"/>
    </justification>
  </clause>

  <clause id="13863">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(z,y) = K(z,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(35,a,13649,a,b,13862,a)].">
      <j1 rule="hyper" parents="35 13649 13862"/>
    </justification>
  </clause>

  <clause id="13864">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = K(y,x) * (z \ y)
    ]]></literal>
    <justification jstring="[para(7355(a,2),13863(a,1,1))].">
      <j1 rule="para" parents="7355 13863"/>
    </justification>
  </clause>

  <clause id="13865">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(y,z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = w
    ]]></literal>
    <justification jstring="[para(7283(a,1),13731(a,1,1))].">
      <j1 rule="para" parents="7283 13731"/>
    </justification>
  </clause>

  <clause id="13866">
    <literal><![CDATA[
      L(x,y,y \ z) * T(z,x) = (z / y) * (y * x)
    ]]></literal>
    <justification jstring="[para(12(a,1),13770(a,1,2,1))].">
      <j1 rule="para" parents="12 13770"/>
    </justification>
  </clause>

  <clause id="13867">
    <literal><![CDATA[
      ((x / y) * (y * z)) / T(x,z) = L(z,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,13866,a)].">
      <j1 rule="hyper" parents="145 13866"/>
    </justification>
  </clause>

  <clause id="13868">
    <literal><![CDATA[
      L(x,y,y \ z) * (x \ z) = ((z / y) * (y * x)) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,13866,a(flip),b,11219,a),flip(a)].">
      <j1 rule="hyper" parents="131 13866 11219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13869">
    <literal><![CDATA[
      L(x,y,y \ (z / x)) * (x \ z) = ((z / x) / y) * (y * x)
    ]]></literal>
    <justification jstring="[para(113(a,1),13866(a,1,2))].">
      <j1 rule="para" parents="113 13866"/>
    </justification>
  </clause>

  <clause id="13870">
    <literal><![CDATA[
      L(x,y,y \ z) * z = x * (((z / y) * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(134,a,13868,a(flip),b,1402,a),flip(a)].">
      <j1 rule="hyper" parents="134 13868 1402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13871">
    <literal><![CDATA[
      K((x / ((y * (y * x)) / y)) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x \ (x / T(y,y * x))) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(4156(a,2),13851(a,1,1,1,2))].">
      <j1 rule="para" parents="4156 13851"/>
    </justification>
  </clause>

  <clause id="13872">
    <literal><![CDATA[
      K(x,K(y,(z * (u * w)) / (z * w))) = K(x,K(y,L(u,w,z)))
    ]]></literal>
    <justification jstring="[para(11(a,1),13860(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="11 13860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13873">
    <literal><![CDATA[
      K(x,K(T(y,z) / u,L(w,u,z))) = K(x,K(w,(y * z) / (z * u)))
    ]]></literal>
    <justification jstring="[para(22(a,2),13861(a,1,2,1,1))].">
      <j1 rule="para" parents="22 13861"/>
    </justification>
  </clause>

  <clause id="13874">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(x * (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(13369,a,13032,a),flip(a)].">
      <j1 rule="hyper" parents="13369 13032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13875">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,7908,a(flip),b,13874,a),flip(a)].">
      <j1 rule="hyper" parents="347 7908 13874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13876">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,11667,a,b,13875,a)].">
      <j1 rule="hyper" parents="63 11667 13875"/>
    </justification>
  </clause>

  <clause id="13878">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,z / (x * z))
    ]]></literal>
    <justification jstring="[para(13876(a,1),6946(a,1,1,1))].">
      <j1 rule="para" parents="13876 6946"/>
    </justification>
  </clause>

  <clause id="13879">
    <literal><![CDATA[
      R(1 / x,y,z / (x * z)) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,8034,a(flip),b,13878,a),flip(a)].">
      <j1 rule="hyper" parents="63 8034 13878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13881">
    <literal><![CDATA[
      R(1 / (x / y),z,(x / y) \ 1) = R(1 / (x / y),z,y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),13879(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="12 13879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13882">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(x,K(y,z \ x)) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(7261(a,1),13118(a,1,2))].">
      <j1 rule="para" parents="7261 13118"/>
    </justification>
  </clause>

  <clause id="13883">
    <literal><![CDATA[
      K(x,y \ (T(z / u,z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((u \ z) * w)) = v5
    ]]></literal>
    <justification jstring="[para(13121(a,2),13062(a,1))].">
      <j1 rule="para" parents="13121 13062"/>
    </justification>
  </clause>

  <clause id="13884">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * K(u,y / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(13136(a,2),13442(a,1))].">
      <j1 rule="para" parents="13136 13442"/>
    </justification>
  </clause>

  <clause id="13885">
    <literal><![CDATA[
      L(x,y,z / ((1 / u) * K(w,v5))) = L(x,y,z / (u \ K(w,v5)))
    ]]></literal>
    <justification jstring="[para(13703(a,1),13198(a,1,3,2))].">
      <j1 rule="para" parents="13703 13198"/>
    </justification>
  </clause>

  <clause id="13886">
    <literal><![CDATA[
      L(x,y,((1 / z) * K(u,w)) \ v5) = L(x,y,(z \ K(u,w)) \ v5)
    ]]></literal>
    <justification jstring="[para(13703(a,1),13199(a,1,3,1))].">
      <j1 rule="para" parents="13703 13199"/>
    </justification>
  </clause>

  <clause id="13887">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = (z * K(x,y)) \ y
    ]]></literal>
    <justification jstring="[para(7358(a,1),13204(a,2,1))].">
      <j1 rule="para" parents="7358 13204"/>
    </justification>
  </clause>

  <clause id="13888">
    <literal><![CDATA[
      (x * K(y,z)) \ z = K(z,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13864,a(flip),b,13887,a),flip(a)].">
      <j1 rule="hyper" parents="63 13864 13887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13889">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,x / z)) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(7261(a,1),13209(a,1,2))].">
      <j1 rule="para" parents="7261 13209"/>
    </justification>
  </clause>

  <clause id="13890">
    <literal><![CDATA[
      K((x \ y) \ z,T(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x * z),T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(13220(a,1),5113(a,1))].">
      <j1 rule="para" parents="13220 5113"/>
    </justification>
  </clause>

  <clause id="13891">
    <literal><![CDATA[
      K(x \ (y * z),T(x,y)) = K(z / (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(13890,a,8866,a)].">
      <j1 rule="hyper" parents="13890 8866"/>
    </justification>
  </clause>

  <clause id="13892">
    <literal><![CDATA[
      K(x / (y \ z),z) = K(z \ (x * y),z)
    ]]></literal>
    <justification jstring="[hyper(12157,a,13891,a),flip(a)].">
      <j1 rule="hyper" parents="12157 13891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13893">
    <literal><![CDATA[
      K(x \ (y * (z \ x)),x) = K(y / z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13656,a(flip),b,13892,a),flip(a)].">
      <j1 rule="hyper" parents="63 13656 13892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13894">
    <literal><![CDATA[
      K(x \ (y * (x / z)),x) = K(y / z,x)
    ]]></literal>
    <justification jstring="[para(83(a,1),13892(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="83 13892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13895">
    <literal><![CDATA[
      K(x,K(y / z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y * (z \ u),u) * w) = v5
    ]]></literal>
    <justification jstring="[para(13893(a,1),12116(a,1,2,1))].">
      <j1 rule="para" parents="13893 12116"/>
    </justification>
  </clause>

  <clause id="13896">
    <literal><![CDATA[
      T(T(x,y / z),K(y / z,u)) = T(x,T(y * (z \ 1),u))
    ]]></literal>
    <justification jstring="[para(13069(a,1),13229(a,1,1))].">
      <j1 rule="para" parents="13069 13229"/>
    </justification>
  </clause>

  <clause id="13897">
    <literal><![CDATA[
      T(x,T(y * (z \ 1),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(13896(a,1),7539(a,1))].">
      <j1 rule="para" parents="13896 7539"/>
    </justification>
  </clause>

  <clause id="13898">
    <literal><![CDATA[
      T(x,T((y \ 1) / z,u)) = T(x,T(y \ (z \ 1),u))
    ]]></literal>
    <justification jstring="[hyper(13897,a,13353,a)].">
      <j1 rule="hyper" parents="13897 13353"/>
    </justification>
  </clause>

  <clause id="13899">
    <literal><![CDATA[
      T(x,T(y \ (z \ 1),y)) = T(x,y \ (y \ (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(13363,a,13898,a),flip(a)].">
      <j1 rule="hyper" parents="13363 13898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13900">
    <literal><![CDATA[
      T(x,y \ (y \ (z \ y))) = T(x,(z \ 1) / y)
    ]]></literal>
    <justification jstring="[hyper(7683,a,13899,a),flip(a)].">
      <j1 rule="hyper" parents="7683 13899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13901">
    <literal><![CDATA[
      T(x,y \ (y \ (z \ y))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ 1)) = u
    ]]></literal>
    <justification jstring="[para(13900(a,2),13294(a,1))].">
      <j1 rule="para" parents="13900 13294"/>
    </justification>
  </clause>

  <clause id="13902">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) = R(a(x,y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1463(a,1),13410(a,1,1))].">
      <j1 rule="para" parents="1463 13410"/>
    </justification>
  </clause>

  <clause id="13903">
    <literal><![CDATA[
      R(a(x,y,z),x,x \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13711,a,13902,a),flip(a)].">
      <j1 rule="hyper" parents="13711 13902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13904">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,a(x,z,u) * x) = a(x,z,u) \ ((a(x,z,u) * x) * y)
    ]]></literal>
    <justification jstring="[para(13903(a,1),699(a,2,1))].">
      <j1 rule="para" parents="13903 699"/>
    </justification>
  </clause>

  <clause id="13905">
    <literal><![CDATA[
      (x \ (y * z)) * K(y \ (y * z),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(9650(a,1),13432(a,1,2))].">
      <j1 rule="para" parents="9650 13432"/>
    </justification>
  </clause>

  <clause id="13906">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),13905(a,1,2,1))].">
      <j1 rule="para" parents="9 13905"/>
    </justification>
  </clause>

  <clause id="13908">
    <literal><![CDATA[
      ((x * y) / z) \ (y * x) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(708,a,13906,a),flip(a)].">
      <j1 rule="hyper" parents="708 13906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13909">
    <literal><![CDATA[
      T(x \ (y * z),K(z,y)) = K(y,z) * (x \ (z * y))
    ]]></literal>
    <justification jstring="[hyper(269,a,13906,a,b,5261,a)].">
      <j1 rule="hyper" parents="269 13906 5261"/>
    </justification>
  </clause>

  <clause id="13911">
    <literal><![CDATA[
      (x * (y * z)) / (L(x,z,y) * (y * z)) = ((y * z) * x) / (y * (z * x))
    ]]></literal>
    <justification jstring="[hyper(220,a,13439,a(flip),b,13908,a)].">
      <j1 rule="hyper" parents="220 13439 13908"/>
    </justification>
  </clause>

  <clause id="13912">
    <literal><![CDATA[
      (x * y) / (z * T(x,y)) = (y * x) / (z * x)
    ]]></literal>
    <justification jstring="[hyper(220,a,6111,a(flip),b,13908,a),flip(a)].">
      <j1 rule="hyper" parents="220 6111 13908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13913">
    <literal><![CDATA[
      (x * y) / (z * K(y,x)) = K(x,y) * ((x * y) / z)
    ]]></literal>
    <justification jstring="[hyper(220,a,13908,a(flip),b,13747,a)].">
      <j1 rule="hyper" parents="220 13908 13747"/>
    </justification>
  </clause>

  <clause id="13914">
    <literal><![CDATA[
      (x * y) / (z * K(y,T(x,y))) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[hyper(220,a,13908,a(flip),b,250,a(flip))].">
      <j1 rule="hyper" parents="220 13908 250"/>
    </justification>
  </clause>

  <clause id="13915">
    <literal><![CDATA[
      x / (y * K(x / z,z)) = (z * (x / z)) / y
    ]]></literal>
    <justification jstring="[para(13908(a,1),351(a,1,2))].">
      <j1 rule="para" parents="13908 351"/>
    </justification>
  </clause>

  <clause id="13916">
    <literal><![CDATA[
      (x * R(y,z,u)) / (y * T(x,R(y,z,u))) = R(y \ R(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3686,a,b,13912,a),flip(a)].">
      <j1 rule="hyper" parents="347 3686 13912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13917">
    <literal><![CDATA[
      R(x,y,z) = (z * (x * y)) / (y * T(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,20,a,b,13912,a)].">
      <j1 rule="hyper" parents="347 20 13912"/>
    </justification>
  </clause>

  <clause id="13918">
    <literal><![CDATA[
      x / (y * K(z \ x,z)) = (z * (x / z)) / y
    ]]></literal>
    <justification jstring="[para(5138(a,1),13915(a,1,2,2))].">
      <j1 rule="para" parents="5138 13915"/>
    </justification>
  </clause>

  <clause id="13919">
    <literal><![CDATA[
      (x * (y / x)) / (z * (y / x)) = y / (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(5927(a,1),13915(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5927 13915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13920">
    <literal><![CDATA[
      R(x,y,z) \ (z * (x * y)) = y * T(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(132,a,13917,a,b,172,a)].">
      <j1 rule="hyper" parents="132 13917 172"/>
    </justification>
  </clause>

  <clause id="13921">
    <literal><![CDATA[
      R(K(x,y),T(x,y) \ z,u) \ (u * (x \ z)) = (T(x,y) \ z) * T(u,K(x,y) * (T(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(5159(a,1),13920(a,1,2,2))].">
      <j1 rule="para" parents="5159 13920"/>
    </justification>
  </clause>

  <clause id="13922">
    <literal><![CDATA[
      (x * y) / (z * K(y,x)) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[para(5095(a,1),13914(a,1,2,2))].">
      <j1 rule="para" parents="5095 13914"/>
    </justification>
  </clause>

  <clause id="13923">
    <literal><![CDATA[
      K(x,y) * ((x * y) / z) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[hyper(63,a,13913,a(flip),b,13922,a)].">
      <j1 rule="hyper" parents="63 13913 13922"/>
    </justification>
  </clause>

  <clause id="13924">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u * u))),y * (L(z,u,u) * (u * u))) = T(x,(u * (u * T(z,u * u))) * y)
    ]]></literal>
    <justification jstring="[para(734(a,1),13493(a,1,2,2))].">
      <j1 rule="para" parents="734 13493"/>
    </justification>
  </clause>

  <clause id="13926">
    <literal><![CDATA[
      T(x * T(x \ y,T(z,y)),x) = T(y,x) * K(y / T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,1588,a,b,13616,a)].">
      <j1 rule="hyper" parents="347 1588 13616"/>
    </justification>
  </clause>

  <clause id="13928">
    <literal><![CDATA[
      (T(x,K(y,L(z,u,w)) * v5) * K(y,L(T(z,x),u,w))) / (K(y,L(z,u,w)) * x) = K(x,v5 * K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(131,a,13729,a,b,10340,a)].">
      <j1 rule="hyper" parents="131 13729 10340"/>
    </justification>
  </clause>

  <clause id="13929">
    <literal><![CDATA[
      T(x \ (x \ y),x \ (x \ (x \ (x \ y)))) = (x \ (x \ y)) * K(x * x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),13821(a,2,2,2))].">
      <j1 rule="para" parents="10 13821"/>
    </justification>
  </clause>

  <clause id="13930">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (1 / (x / y)) \ R(1 / (x / y),z,y / x)
    ]]></literal>
    <justification jstring="[para(13881(a,1),9984(a,2,2))].">
      <j1 rule="para" parents="13881 9984"/>
    </justification>
  </clause>

  <clause id="13931">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(x,K(y,z)) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8899(a,1),13882(a,1,2))].">
      <j1 rule="para" parents="8899 13882"/>
    </justification>
  </clause>

  <clause id="13932">
    <literal><![CDATA[
      ((x \ y) \ K(z,y)) * K(y,K(z,x)) = (x \ T(y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(13289,a,13931,a)].">
      <j1 rule="hyper" parents="13289 13931"/>
    </justification>
  </clause>

  <clause id="13933">
    <literal><![CDATA[
      (x \ y) \ K(z,T(y,x)) = (x \ T(y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,13706,a(flip),b,13932,a)].">
      <j1 rule="hyper" parents="63 13706 13932"/>
    </justification>
  </clause>

  <clause id="13934">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8904(a,1),13889(a,1,2))].">
      <j1 rule="para" parents="8904 13889"/>
    </justification>
  </clause>

  <clause id="13935">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * ((x / z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(13934(a,2),13742(a,1))].">
      <j1 rule="para" parents="13934 13742"/>
    </justification>
  </clause>

  <clause id="13936">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = T(x * K(x / y,z),y)
    ]]></literal>
    <justification jstring="[para(7433(a,1),13926(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7433 13926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13937">
    <literal><![CDATA[
      T(x * K(x / y,z),y) = T(x,y) * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(11944(a,1),13936(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11944 13936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13938">
    <literal><![CDATA[
      T(x * K(x / y,z),y) = K(x / y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(13781,a,13937,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="13781 13937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13939">
    <literal><![CDATA[
      (x * (y * z)) / T(y * x,z) = L(K(x,y) * z,y,x)
    ]]></literal>
    <justification jstring="[para(8408(a,1),13213(a,1,2))].">
      <j1 rule="para" parents="8408 13213"/>
    </justification>
  </clause>

  <clause id="13940">
    <literal><![CDATA[
      L(K(x,y) * (y \ z),y,x) = (x * z) / T(y * x,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),13939(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 13939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13941">
    <literal><![CDATA[
      (x * y) / T(z * x,z \ y) = (z * x) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(10230,a,13940,a),flip(a)].">
      <j1 rule="hyper" parents="10230 13940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13942">
    <literal><![CDATA[
      a(x * (y / x),x,z) * (y * (T(x,y) * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(347,a,252,a(flip),b,13380,a),flip(a)].">
      <j1 rule="hyper" parents="347 252 13380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13943">
    <literal><![CDATA[
      (x * (y * z)) / (L(x,z,y) * (y * z)) = a(y,z,T(x,y * z))
    ]]></literal>
    <justification jstring="[para(734(a,1),13384(a,1,2))].">
      <j1 rule="para" parents="734 13384"/>
    </justification>
  </clause>

  <clause id="13944">
    <literal><![CDATA[
      x * (y * ((x * y) \ 1)) = a(x,y,x * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,792,a(flip),b,13387,a)].">
      <j1 rule="hyper" parents="63 792 13387"/>
    </justification>
  </clause>

  <clause id="13945">
    <literal><![CDATA[
      (x * y) \ L(x * y,x,y) = a(y,x,y * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(10436,a,13944,a)].">
      <j1 rule="hyper" parents="10436 13944"/>
    </justification>
  </clause>

  <clause id="13946">
    <literal><![CDATA[
      (x * y) \ L(x * y,y,x) = a(x,y,x * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(3401,a,13944,a)].">
      <j1 rule="hyper" parents="3401 13944"/>
    </justification>
  </clause>

  <clause id="13947">
    <literal><![CDATA[
      R(x,y,z * (T(u,z) * (u * z))) = R(x,y,a(z,u,z * u) \ 1)
    ]]></literal>
    <justification jstring="[para(13945(a,1),10189(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13945 10189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13948">
    <literal><![CDATA[
      (x * y) \ L(x * y,y,x) != z \ 1
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x * y) = z
    ]]></literal>
    <justification jstring="[para(13946(a,2),48(a,1))].">
      <j1 rule="para" parents="13946 48"/>
    </justification>
  </clause>

  <clause id="13949">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (u \ (u / z))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(u \ (u / z)) * y) = w
    ]]></literal>
    <justification jstring="[para(13484(a,1),13482(a,1,1))].">
      <j1 rule="para" parents="13484 13482"/>
    </justification>
  </clause>

  <clause id="13950">
    <literal><![CDATA[
      L(K(x \ y,z),u,x / y) = K(T(1 / (y \ x),K(w,v5)),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7002,a(flip),b,13694,a)].">
      <j1 rule="hyper" parents="347 7002 13694"/>
    </justification>
  </clause>

  <clause id="13951">
    <literal><![CDATA[
      L(K(x,y),z,u / (u * x)) = K(T(1 / ((u * x) \ u),K(w,v5)),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),13950(a,1,1,1))].">
      <j1 rule="para" parents="9 13950"/>
    </justification>
  </clause>

  <clause id="13952">
    <literal><![CDATA[
      K(x,y \ ((1 / z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * u)) = w
    ]]></literal>
    <justification jstring="[para(223(a,1),13883(a,1,2,2,1))].">
      <j1 rule="para" parents="223 13883"/>
    </justification>
  </clause>

  <clause id="13953">
    <literal><![CDATA[
      R(x,y,z * (T(u,z) * (u * z))) = R(x,y,a(z,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,2190,a(flip),b,13947,a),flip(a)].">
      <j1 rule="hyper" parents="347 2190 13947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13954">
    <literal><![CDATA[
      R(x * y,z,a(y,x,y * x)) = x * y
    ]]></literal>
    <justification jstring="[hyper(63,a,12300,a(flip),b,13953,a),flip(a)].">
      <j1 rule="hyper" parents="63 12300 13953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13955">
    <literal><![CDATA[
      L(K(x,y),z,u / (u * x)) = K(1 / ((u * x) \ u),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,13583,a(flip),b,13951,a),flip(a)].">
      <j1 rule="hyper" parents="347 13583 13951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13956">
    <literal><![CDATA[
      L(K(x,y),z,u / (u * x)) = K(u \ (u * x),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,5994,a(flip),b,13955,a),flip(a)].">
      <j1 rule="hyper" parents="347 5994 13955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13957">
    <literal><![CDATA[
      L(K(x,y),z,u / (u * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(13956(a,2),7205(a,1))].">
      <j1 rule="para" parents="13956 7205"/>
    </justification>
  </clause>

  <clause id="13958">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(9265,a,12959,a),flip(a)].">
      <j1 rule="hyper" parents="9265 12959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13959">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12957,a(flip),b,13958,a),flip(a)].">
      <j1 rule="hyper" parents="63 12957 13958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13960">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12956,a(flip),b,13958,a),flip(a)].">
      <j1 rule="hyper" parents="63 12956 13958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13961">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / a(x,z,K(u,y)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(220,a,13958,a(flip),b,14,a(flip))].">
      <j1 rule="hyper" parents="220 13958 14"/>
    </justification>
  </clause>

  <clause id="13962">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(134,a,13958,a(flip),b,12809,a)].">
      <j1 rule="hyper" parents="134 13958 12809"/>
    </justification>
  </clause>

  <clause id="13963">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / a(x,z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (z * u) = w
    ]]></literal>
    <justification jstring="[para(13958(a,1),325(a,1,2))].">
      <j1 rule="para" parents="13958 325"/>
    </justification>
  </clause>

  <clause id="13964">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) = a(T(x,z),u,K(w,y))
    ]]></literal>
    <justification jstring="[para(7093(a,1),13958(a,1,1))].">
      <j1 rule="para" parents="7093 13958"/>
    </justification>
  </clause>

  <clause id="13965">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,x))) = a(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(7612(a,1),13958(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7612 13958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13966">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(12672,a,13959,a),flip(a)].">
      <j1 rule="hyper" parents="12672 13959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13967">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(11285,a,13959,a)].">
      <j1 rule="hyper" parents="11285 13959"/>
    </justification>
  </clause>

  <clause id="13968">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(11103,a,13959,a)].">
      <j1 rule="hyper" parents="11103 13959"/>
    </justification>
  </clause>

  <clause id="13969">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(11092,a,13959,a)].">
      <j1 rule="hyper" parents="11092 13959"/>
    </justification>
  </clause>

  <clause id="13970">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z,u) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(9252,a,13959,a)].">
      <j1 rule="hyper" parents="9252 13959"/>
    </justification>
  </clause>

  <clause id="13971">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,13958,a,b,13959,a)].">
      <j1 rule="hyper" parents="347 13958 13959"/>
    </justification>
  </clause>

  <clause id="13972">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,11296,a,b,13959,a)].">
      <j1 rule="hyper" parents="347 11296 13959"/>
    </justification>
  </clause>

  <clause id="13973">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * x) = a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,10000,a,b,13959,a)].">
      <j1 rule="hyper" parents="347 10000 13959"/>
    </justification>
  </clause>

  <clause id="13974">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(w,z,K(u,y \ x))
    ]]></literal>
    <justification jstring="[hyper(347,a,11302,a(flip),b,13959,a),flip(a)].">
      <j1 rule="hyper" parents="347 11302 13959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13975">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = x * a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(220,a,13959,a,b,9262,a)].">
      <j1 rule="hyper" parents="220 13959 9262"/>
    </justification>
  </clause>

  <clause id="13976">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,13959,a,b,12653,a)].">
      <j1 rule="hyper" parents="134 13959 12653"/>
    </justification>
  </clause>

  <clause id="13977">
    <literal><![CDATA[
      K(x,L(y,z,u)) * a(x,z,K(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,13959,a,b,11083,a)].">
      <j1 rule="hyper" parents="134 13959 11083"/>
    </justification>
  </clause>

  <clause id="13978">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) = x * a(w,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,13959,a,b,9,a)].">
      <j1 rule="hyper" parents="134 13959 9"/>
    </justification>
  </clause>

  <clause id="13979">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11303,a,b,13959,a)].">
      <j1 rule="hyper" parents="63 11303 13959"/>
    </justification>
  </clause>

  <clause id="13980">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(u,z,K(y \ x,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,11302,a,b,13959,a),flip(a)].">
      <j1 rule="hyper" parents="63 11302 13959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13981">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,11296,a,b,13959,a)].">
      <j1 rule="hyper" parents="63 11296 13959"/>
    </justification>
  </clause>

  <clause id="13982">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11287,a,b,13959,a)].">
      <j1 rule="hyper" parents="63 11287 13959"/>
    </justification>
  </clause>

  <clause id="13983">
    <literal><![CDATA[
      a(x,L(x,y,z),K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,10082,a(flip),b,13959,a),flip(a)].">
      <j1 rule="hyper" parents="63 10082 13959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13984">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(134,a,13959,a(flip),b,12653,a)].">
      <j1 rule="hyper" parents="134 13959 12653"/>
    </justification>
  </clause>

  <clause id="13985">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(x,K(w,z)))
    ]]></literal>
    <justification jstring="[para(7280(a,1),13959(a,1,3))].">
      <j1 rule="para" parents="7280 13959"/>
    </justification>
  </clause>

  <clause id="13986">
    <literal><![CDATA[
      a(x,y,K(z * (u / T(w,x)),v5)) = a(v5,y,K(x,z * (u / w)))
    ]]></literal>
    <justification jstring="[para(7982(a,1),13959(a,2,3))].">
      <j1 rule="para" parents="7982 13959"/>
    </justification>
  </clause>

  <clause id="13987">
    <literal><![CDATA[
      a(x,y,K(z * (T(u,x) \ w),v5)) = a(v5,y,K(x,z * (u \ w)))
    ]]></literal>
    <justification jstring="[para(8002(a,1),13959(a,2,3))].">
      <j1 rule="para" parents="8002 13959"/>
    </justification>
  </clause>

  <clause id="13988">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * w) = a(y,z,K(u,x)) * w
    ]]></literal>
    <justification jstring="[para(13959(a,1),9245(a,2,1))].">
      <j1 rule="para" parents="13959 9245"/>
    </justification>
  </clause>

  <clause id="13989">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(u,y,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(13959(a,2),9999(a,1,1))].">
      <j1 rule="para" parents="13959 9999"/>
    </justification>
  </clause>

  <clause id="13990">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13959(a,1),11061(a,1,2))].">
      <j1 rule="para" parents="13959 11061"/>
    </justification>
  </clause>

  <clause id="13991">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13959(a,2),11061(a,1,2))].">
      <j1 rule="para" parents="13959 11061"/>
    </justification>
  </clause>

  <clause id="13992">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,L(z,y,u)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(13959(a,2),11081(a,1,1))].">
      <j1 rule="para" parents="13959 11081"/>
    </justification>
  </clause>

  <clause id="13993">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[para(13959(a,1),11089(a,1,1))].">
      <j1 rule="para" parents="13959 11089"/>
    </justification>
  </clause>

  <clause id="13994">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,x) = K(z,L(x,y,u))
    ]]></literal>
    <justification jstring="[para(13959(a,2),11089(a,1,1))].">
      <j1 rule="para" parents="13959 11089"/>
    </justification>
  </clause>

  <clause id="13995">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(13959(a,1),11093(a,1,2))].">
      <j1 rule="para" parents="13959 11093"/>
    </justification>
  </clause>

  <clause id="13996">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(13959(a,2),11093(a,1,2))].">
      <j1 rule="para" parents="13959 11093"/>
    </justification>
  </clause>

  <clause id="13997">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(u,x)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13959(a,1),11198(a,1,2))].">
      <j1 rule="para" parents="13959 11198"/>
    </justification>
  </clause>

  <clause id="13998">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13959(a,2),11198(a,1,2))].">
      <j1 rule="para" parents="13959 11198"/>
    </justification>
  </clause>

  <clause id="13999">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(13959(a,1),12656(a,1,1))].">
      <j1 rule="para" parents="13959 12656"/>
    </justification>
  </clause>

  <clause id="14000">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(13959(a,2),12656(a,1,1))].">
      <j1 rule="para" parents="13959 12656"/>
    </justification>
  </clause>

  <clause id="14001">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(13959(a,1),12659(a,1,2))].">
      <j1 rule="para" parents="13959 12659"/>
    </justification>
  </clause>

  <clause id="14002">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(13959(a,2),12659(a,1,2))].">
      <j1 rule="para" parents="13959 12659"/>
    </justification>
  </clause>

  <clause id="14003">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u != w
    ]]></literal>
    <literal><![CDATA[
      T(u,a(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(13959(a,1),12660(a,1,1))].">
      <j1 rule="para" parents="13959 12660"/>
    </justification>
  </clause>

  <clause id="14004">
    <literal><![CDATA[
      (x * y) * a(z,u,K(w,y)) = x * T(y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(13959(a,1),12654(a,1,2))].">
      <j1 rule="para" parents="13959 12654"/>
    </justification>
  </clause>

  <clause id="14005">
    <literal><![CDATA[
      (x * y) * a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * T(y,a(w,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(13959(a,2),12662(a,1,2))].">
      <j1 rule="para" parents="13959 12662"/>
    </justification>
  </clause>

  <clause id="14006">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11128,a,13983,a)].">
      <j1 rule="hyper" parents="11128 13983"/>
    </justification>
  </clause>

  <clause id="14007">
    <literal><![CDATA[
      K(a(x,y,z),u) = K(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(12683,a,13960,a)].">
      <j1 rule="hyper" parents="12683 13960"/>
    </justification>
  </clause>

  <clause id="14008">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,12955,a,b,13960,a)].">
      <j1 rule="hyper" parents="347 12955 13960"/>
    </justification>
  </clause>

  <clause id="14009">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,12579,a,b,13960,a)].">
      <j1 rule="hyper" parents="347 12579 13960"/>
    </justification>
  </clause>

  <clause id="14010">
    <literal><![CDATA[
      (x \ y) * a(y,z,K(u,w)) = x \ T(y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,13960,a,b,13082,a)].">
      <j1 rule="hyper" parents="134 13960 13082"/>
    </justification>
  </clause>

  <clause id="14011">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) / x = T(1 / x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,13960,a,b,5015,a)].">
      <j1 rule="hyper" parents="131 13960 5015"/>
    </justification>
  </clause>

  <clause id="14012">
    <literal><![CDATA[
      L(x,y,a(y,z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[para(13960(a,2),4250(a,1,3))].">
      <j1 rule="para" parents="13960 4250"/>
    </justification>
  </clause>

  <clause id="14013">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * x) = T(x,a(u,y,z)) * T(w,x)
    ]]></literal>
    <justification jstring="[para(13960(a,2),5162(a,1,1))].">
      <j1 rule="para" parents="13960 5162"/>
    </justification>
  </clause>

  <clause id="14015">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(z,K(x,a(w,y,u)))
    ]]></literal>
    <justification jstring="[para(13960(a,1),12651(a,2,2))].">
      <j1 rule="para" parents="13960 12651"/>
    </justification>
  </clause>

  <clause id="14016">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(13960(a,2),12696(a,1))].">
      <j1 rule="para" parents="13960 12696"/>
    </justification>
  </clause>

  <clause id="14018">
    <literal><![CDATA[
      ((x * y) * K(z,u)) / (y * K(z,u)) = x * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(14012(a,1),13857(a,1,2))].">
      <j1 rule="para" parents="14012 13857"/>
    </justification>
  </clause>

  <clause id="14019">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(13966(a,2),12696(a,1))].">
      <j1 rule="para" parents="13966 12696"/>
    </justification>
  </clause>

  <clause id="14020">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w \ v5
    ]]></literal>
    <literal><![CDATA[
      w * a(z,y,K(u,x)) = v5
    ]]></literal>
    <justification jstring="[para(13966(a,2),12695(a,1))].">
      <j1 rule="para" parents="13966 12695"/>
    </justification>
  </clause>

  <clause id="14021">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u / w) = T(u,a(z,y,x)) / w
    ]]></literal>
    <justification jstring="[para(13966(a,2),13192(a,1,1))].">
      <j1 rule="para" parents="13966 13192"/>
    </justification>
  </clause>

  <clause id="14022">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,y) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,9251,a,b,13971,a)].">
      <j1 rule="hyper" parents="347 9251 13971"/>
    </justification>
  </clause>

  <clause id="14023">
    <literal><![CDATA[
      a(K(x,y),z,u) = K(a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,12681,a(flip),b,13971,a),flip(a)].">
      <j1 rule="hyper" parents="347 12681 13971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14024">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w) \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3188(a,2),14006(a,1,2))].">
      <j1 rule="para" parents="3188 14006"/>
    </justification>
  </clause>

  <clause id="14025">
    <literal><![CDATA[
      a(x,y,K(z \ (u * x),w)) = a(w,y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[para(9556(a,1),13972(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9556 13972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14026">
    <literal><![CDATA[
      T(x,a(y * z,u,y)) = x * a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[para(11294(a,1),13976(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11294 13976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14027">
    <literal><![CDATA[
      x * a(x,y,a(z,u,K(w,v5))) = T(x,a(v5,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(12681(a,2),13976(a,1,2,3))].">
      <j1 rule="para" parents="12681 13976"/>
    </justification>
  </clause>

  <clause id="14028">
    <literal><![CDATA[
      a(x \ y,z,K(u,x)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,13959,a(flip),b,13981,a)].">
      <j1 rule="hyper" parents="63 13959 13981"/>
    </justification>
  </clause>

  <clause id="14029">
    <literal><![CDATA[
      a(x,y,K(z,x * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13959,a(flip),b,13982,a)].">
      <j1 rule="hyper" parents="63 13959 13982"/>
    </justification>
  </clause>

  <clause id="14030">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11293,a(flip),b,13982,a)].">
      <j1 rule="hyper" parents="63 11293 13982"/>
    </justification>
  </clause>

  <clause id="14031">
    <literal><![CDATA[
      (a(x,y,z) * u) / a(x,y,z) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(12691,a,13984,a)].">
      <j1 rule="hyper" parents="12691 13984"/>
    </justification>
  </clause>

  <clause id="14032">
    <literal><![CDATA[
      (x * y) / T(x,L(y,z,u)) = T(y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(11124,a,13984,a)].">
      <j1 rule="hyper" parents="11124 13984"/>
    </justification>
  </clause>

  <clause id="14033">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),y) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13984(a,1),11153(a,1,1))].">
      <j1 rule="para" parents="13984 11153"/>
    </justification>
  </clause>

  <clause id="14034">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),a(u,z,y)) = x
    ]]></literal>
    <justification jstring="[para(13984(a,1),12688(a,1,1))].">
      <j1 rule="para" parents="13984 12688"/>
    </justification>
  </clause>

  <clause id="14035">
    <literal><![CDATA[
      T(a(x,y,z) \ u,a(z,y,x)) = u / a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(808,a,14034,a)].">
      <j1 rule="hyper" parents="808 14034"/>
    </justification>
  </clause>

  <clause id="14036">
    <literal><![CDATA[
      T(x,a(y,z,u)) * a(u,z,y) = a(u,z,y) * x
    ]]></literal>
    <justification jstring="[hyper(134,a,14034,a(flip),b,114,a),flip(a)].">
      <j1 rule="hyper" parents="134 14034 114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14037">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(w,a(u,z,y)) = x
    ]]></literal>
    <justification jstring="[para(14034(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="14034 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14038">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = a(y,z,K(u,x)) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,12580,a,b,13999,a)].">
      <j1 rule="hyper" parents="347 12580 13999"/>
    </justification>
  </clause>

  <clause id="14039">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ x = T(x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9999,a,b,14000,a)].">
      <j1 rule="hyper" parents="63 9999 14000"/>
    </justification>
  </clause>

  <clause id="14040">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ R(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(14008(a,1),4984(a,1,2))].">
      <j1 rule="para" parents="14008 4984"/>
    </justification>
  </clause>

  <clause id="14041">
    <literal><![CDATA[
      (x \ R(x,y,z)) * a(u,y,K(z,x)) != w
    ]]></literal>
    <literal><![CDATA[
      (u * (x \ R(x,y,z))) / u = w
    ]]></literal>
    <justification jstring="[para(14008(a,1),5091(a,1,2))].">
      <j1 rule="para" parents="14008 5091"/>
    </justification>
  </clause>

  <clause id="14042">
    <literal><![CDATA[
      T((T(x,y) \ R(T(x,y),z,u)) * a(y,z,K(u,x)),y) = T(x,y) \ R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(14008(a,1),9369(a,1,1,2))].">
      <j1 rule="para" parents="14008 9369"/>
    </justification>
  </clause>

  <clause id="14043">
    <literal><![CDATA[
      x * ((L(x,y,z) \ 1) * K(u,w)) = (L(x,y,z) \ x) * K(u,w)
    ]]></literal>
    <justification jstring="[para(14024(a,1),11135(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14024 11135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14044">
    <literal><![CDATA[
      a(x * y,z,K(u,x)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),14028(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 14028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14045">
    <literal><![CDATA[
      a(L(x,y,z) \ u,w,K(z,x)) = a(u,w,K(z,L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(7612(a,1),14028(a,1,3))].">
      <j1 rule="para" parents="7612 14028"/>
    </justification>
  </clause>

  <clause id="14046">
    <literal><![CDATA[
      T(T(x,y),a(y,z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(453,a,14033,a)].">
      <j1 rule="hyper" parents="453 14033"/>
    </justification>
  </clause>

  <clause id="14047">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),L(u,z,y)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(14034(a,1),14033(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14034 14033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14048">
    <literal><![CDATA[
      (x * y) * a(y,z,K(u,x)) = T(x * y,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(14044(a,1),13976(a,1,2))].">
      <j1 rule="para" parents="14044 13976"/>
    </justification>
  </clause>

  <clause id="14049">
    <literal><![CDATA[
      T(x,L(y,z,u)) != T(w,y)
    ]]></literal>
    <literal><![CDATA[
      T(w,a(u,z,y)) = x
    ]]></literal>
    <justification jstring="[para(14047(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="14047 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14050">
    <literal><![CDATA[
      K(L(x,y,z) * T(u,a(z,y,x)),w) = K(T(u,x) * L(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(14047(a,1),10388(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14047 10388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14051">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,x))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,13958,a(flip),b,13965,a),flip(a)].">
      <j1 rule="hyper" parents="347 13958 13965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14052">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(11080(a,2),14016(a,1))].">
      <j1 rule="para" parents="11080 14016"/>
    </justification>
  </clause>

  <clause id="14053">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(11082(a,2),14016(a,1))].">
      <j1 rule="para" parents="11082 14016"/>
    </justification>
  </clause>

  <clause id="14054">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(12566(a,2),14016(a,1))].">
      <j1 rule="para" parents="12566 14016"/>
    </justification>
  </clause>

  <clause id="14055">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(12957(a,2),14016(a,1))].">
      <j1 rule="para" parents="12957 14016"/>
    </justification>
  </clause>

  <clause id="14056">
    <literal><![CDATA[
      a(x,y,K(z / u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,y,K(x,w \ (z * (w / u)))) = v5
    ]]></literal>
    <justification jstring="[para(13894(a,1),14016(a,1,3))].">
      <j1 rule="para" parents="13894 14016"/>
    </justification>
  </clause>

  <clause id="14057">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u \ 1,y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(11299(a,1),14019(a,1))].">
      <j1 rule="para" parents="11299 14019"/>
    </justification>
  </clause>

  <clause id="14058">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(13967(a,2),14019(a,1))].">
      <j1 rule="para" parents="13967 14019"/>
    </justification>
  </clause>

  <clause id="14059">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(u,w,x) = T(L(u,w,x),a(z,y,x))
    ]]></literal>
    <justification jstring="[para(14051(a,1),13999(a,1,1))].">
      <j1 rule="para" parents="14051 13999"/>
    </justification>
  </clause>

  <clause id="14060">
    <literal><![CDATA[
      a(T(x,y),z,K(u,w)) = a(x,z,K(u,T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13958,a(flip),b,13964,a),flip(a)].">
      <j1 rule="hyper" parents="63 13958 13964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14061">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) / K(x,L(x,y,z) \ u) = u / a(L(x,y,z) \ u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(13968(a,1),13918(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13968 13918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14062">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) * K(y,x) = a(x,z / y,K(u,y))
    ]]></literal>
    <justification jstring="[para(9643(a,1),13969(a,1,1,2))].">
      <j1 rule="para" parents="9643 13969"/>
    </justification>
  </clause>

  <clause id="14063">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(x,x \ z,K(u,y))
    ]]></literal>
    <justification jstring="[para(11111(a,1),13969(a,1,1))].">
      <j1 rule="para" parents="11111 13969"/>
    </justification>
  </clause>

  <clause id="14064">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ 1 = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,2597,a(flip),b,13973,a)].">
      <j1 rule="hyper" parents="63 2597 13973"/>
    </justification>
  </clause>

  <clause id="14065">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,x)) * w = v5
    ]]></literal>
    <justification jstring="[para(13973(a,1),359(a,1,1))].">
      <j1 rule="para" parents="13973 359"/>
    </justification>
  </clause>

  <clause id="14066">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = a(y,z,K(u,x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,14008,a,b,14064,a)].">
      <j1 rule="hyper" parents="347 14008 14064"/>
    </justification>
  </clause>

  <clause id="14067">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) = x * a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14030(a,1),13978(a,1,2))].">
      <j1 rule="para" parents="14030 13978"/>
    </justification>
  </clause>

  <clause id="14068">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(w,y,K(z,K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14030,a,b,13985,a),flip(a)].">
      <j1 rule="hyper" parents="63 14030 13985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14069">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(z,K(x,w)))
    ]]></literal>
    <justification jstring="[para(7283(a,1),13985(a,2,3))].">
      <j1 rule="para" parents="7283 13985"/>
    </justification>
  </clause>

  <clause id="14070">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,x) = L(K(z,x),y,u)
    ]]></literal>
    <justification jstring="[hyper(134,a,9239,a(flip),b,13989,a)].">
      <j1 rule="hyper" parents="134 9239 13989"/>
    </justification>
  </clause>

  <clause id="14071">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * T(a(w,z,K(u,y)) * x,v5)) = K(v5,x / a(y,z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(13989(a,1),5258(a,1,2,2,1))].">
      <j1 rule="para" parents="13989 5258"/>
    </justification>
  </clause>

  <clause id="14072">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13962,a(flip),b,13990,a)].">
      <j1 rule="hyper" parents="63 13962 13990"/>
    </justification>
  </clause>

  <clause id="14073">
    <literal><![CDATA[
      K(x,L(y,R(z,u,w),z)) = K(x,y) * 1
    ]]></literal>
    <justification jstring="[para(10071(a,1),13990(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10071 13990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14074">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y \ (u / w),y)) = K(x,L(y,z,u / (y * w)))
    ]]></literal>
    <justification jstring="[para(10135(a,1),13990(a,1,2,3))].">
      <j1 rule="para" parents="10135 13990"/>
    </justification>
  </clause>

  <clause id="14076">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[para(11299(a,1),13990(a,1,2))].">
      <j1 rule="para" parents="11299 13990"/>
    </justification>
  </clause>

  <clause id="14077">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u \ y))
    ]]></literal>
    <justification jstring="[para(11301(a,1),13990(a,1,2))].">
      <j1 rule="para" parents="11301 13990"/>
    </justification>
  </clause>

  <clause id="14078">
    <literal><![CDATA[
      K(x,y) * K(a(x,z,u),y) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12681(a,1),13990(a,1,2))].">
      <j1 rule="para" parents="12681 13990"/>
    </justification>
  </clause>

  <clause id="14079">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ T(y,v5)))) = K(x,y) * a(x,z,K(u * (w \ y),y))
    ]]></literal>
    <justification jstring="[para(13117(a,1),13990(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="13117 13990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14080">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(11707,a,14072,a)].">
      <j1 rule="hyper" parents="11707 14072"/>
    </justification>
  </clause>

  <clause id="14081">
    <literal><![CDATA[
      K(x,R(y,z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(11706,a,14072,a)].">
      <j1 rule="hyper" parents="11706 14072"/>
    </justification>
  </clause>

  <clause id="14082">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(6724,a,14072,a)].">
      <j1 rule="hyper" parents="6724 14072"/>
    </justification>
  </clause>

  <clause id="14083">
    <literal><![CDATA[
      K(x,L(y / z,y,u)) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(6708,a,14072,a),flip(a)].">
      <j1 rule="hyper" parents="6708 14072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14084">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) = K(x \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(5679,a,14072,a)].">
      <j1 rule="hyper" parents="5679 14072"/>
    </justification>
  </clause>

  <clause id="14085">
    <literal><![CDATA[
      K(x,L(y,z,u * u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(598,a,14072,a),flip(a)].">
      <j1 rule="hyper" parents="598 14072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14086">
    <literal><![CDATA[
      R(K(x,y),z,u) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,11049,a,b,14072,a),flip(a)].">
      <j1 rule="hyper" parents="347 11049 14072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14087">
    <literal><![CDATA[
      K(x,L((y / z) / u,z \ y,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9611,a(flip),b,14072,a),flip(a)].">
      <j1 rule="hyper" parents="63 9611 14072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14088">
    <literal><![CDATA[
      K(x,L(y / (z / u),y,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6710,a(flip),b,14072,a),flip(a)].">
      <j1 rule="hyper" parents="63 6710 14072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14090">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) * u = (K(x,y) * (u / z)) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,14072,a(flip),b,9609,a)].">
      <j1 rule="hyper" parents="133 14072 9609"/>
    </justification>
  </clause>

  <clause id="14091">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (u * z) = (K(x,y) * z) * T(u,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,14072,a(flip),b,9597,a(flip))].">
      <j1 rule="hyper" parents="133 14072 9597"/>
    </justification>
  </clause>

  <clause id="14092">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(133,a,14072,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="133 14072 20"/>
    </justification>
  </clause>

  <clause id="14093">
    <literal><![CDATA[
      K(x,L(y,z,u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(14072(a,1),598(a,1))].">
      <j1 rule="para" parents="14072 598"/>
    </justification>
  </clause>

  <clause id="14094">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * z) * u = w
    ]]></literal>
    <justification jstring="[para(14072(a,1),314(a,1,1))].">
      <j1 rule="para" parents="14072 314"/>
    </justification>
  </clause>

  <clause id="14095">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) * u != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * z) * (z \ u) = w
    ]]></literal>
    <justification jstring="[para(14072(a,1),847(a,1,1))].">
      <j1 rule="para" parents="14072 847"/>
    </justification>
  </clause>

  <clause id="14098">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,11108,a,b,14080,a),flip(a)].">
      <j1 rule="hyper" parents="347 11108 14080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14099">
    <literal><![CDATA[
      x * (K(y,L(x,z,u)) * K(w,R(y,z,u))) = (R(y,z,u) * x) / R(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(14080(a,1),6332(a,1,2,1))].">
      <j1 rule="para" parents="14080 6332"/>
    </justification>
  </clause>

  <clause id="14100">
    <literal><![CDATA[
      K(x / y,L(T(z,y * u),y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * u) \ (x * u),z) = w
    ]]></literal>
    <justification jstring="[para(14080(a,1),7597(a,1))].">
      <j1 rule="para" parents="14080 7597"/>
    </justification>
  </clause>

  <clause id="14101">
    <literal><![CDATA[
      (R(x,y,z) * (u * K(x,L(w,y,z)))) / R(T(x,w),y,z) = (R(x,y,z) * u) / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(14080(a,1),6840(a,1,1,2,2))].">
      <j1 rule="para" parents="14080 6840"/>
    </justification>
  </clause>

  <clause id="14102">
    <literal><![CDATA[
      K(x * y,R(z,x,y)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,13004,a(flip),b,14081,a),flip(a)].">
      <j1 rule="hyper" parents="347 13004 14081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14103">
    <literal><![CDATA[
      K(x,R(y \ z,y,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,6454,a(flip),b,14081,a),flip(a)].">
      <j1 rule="hyper" parents="347 6454 14081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14104">
    <literal><![CDATA[
      T(x,R(y,z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(132,a,14081,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 14081 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14105">
    <literal><![CDATA[
      ((x * y) * z) / ((T(x,u) * y) * z) = K(u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5847,a,b,14081,a)].">
      <j1 rule="hyper" parents="63 5847 14081"/>
    </justification>
  </clause>

  <clause id="14106">
    <literal><![CDATA[
      K(x,L(T(y \ z,z * u),y,u)) = K(x,T((y * u) \ (z * u),y))
    ]]></literal>
    <justification jstring="[hyper(63,a,8738,a(flip),b,14081,a),flip(a)].">
      <j1 rule="hyper" parents="63 8738 14081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14107">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[para(108(a,1),14081(a,1,2)),flip(a)].">
      <j1 rule="para" parents="108 14081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14108">
    <literal><![CDATA[
      K(x,L((y / z) / u,u,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(605(a,1),14081(a,1,2)),flip(a)].">
      <j1 rule="para" parents="605 14081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14109">
    <literal><![CDATA[
      K(x,K((1 / (y \ z)) / u,L(u / y,y,y \ z))) = K(x,K(z,(1 / (y \ z)) / u))
    ]]></literal>
    <justification jstring="[para(14081(a,1),9394(a,1,2))].">
      <j1 rule="para" parents="14081 9394"/>
    </justification>
  </clause>

  <clause id="14111">
    <literal><![CDATA[
      L(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6515,a(flip),b,14086,a),flip(a)].">
      <j1 rule="hyper" parents="63 6515 14086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14113">
    <literal><![CDATA[
      L(K(x,y),z,u) \ ((K(x,y) * z) * u) = z * u
    ]]></literal>
    <justification jstring="[para(14086(a,1),209(a,1,1))].">
      <j1 rule="para" parents="14086 209"/>
    </justification>
  </clause>

  <clause id="14114">
    <literal><![CDATA[
      L(L(K(x,y),z,u),w,v5) * (z * u) = (L(K(x,y),w,v5) * z) * u
    ]]></literal>
    <justification jstring="[para(14086(a,1),471(a,1,1,1))].">
      <j1 rule="para" parents="14086 471"/>
    </justification>
  </clause>

  <clause id="14116">
    <literal><![CDATA[
      (K(x,T(y,z * u)) * z) * u = (z * u) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(14086(a,1),7385(a,2,2))].">
      <j1 rule="para" parents="14086 7385"/>
    </justification>
  </clause>

  <clause id="14117">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(14086(a,2),11166(a,1))].">
      <j1 rule="para" parents="14086 11166"/>
    </justification>
  </clause>

  <clause id="14118">
    <literal><![CDATA[
      L(K(x,y),z,u) \ (u * (K(x,y) * z)) = z * T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(14086(a,1),13920(a,1,1))].">
      <j1 rule="para" parents="14086 13920"/>
    </justification>
  </clause>

  <clause id="14119">
    <literal><![CDATA[
      K(L(x,y,z),u) * R(x,y,z) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,14098,a(flip),b,5022,a)].">
      <j1 rule="hyper" parents="133 14098 5022"/>
    </justification>
  </clause>

  <clause id="14120">
    <literal><![CDATA[
      K(L(x / y,y,z),u) = K((x * z) / (y * z),u)
    ]]></literal>
    <justification jstring="[para(108(a,1),14098(a,1,1)),flip(a)].">
      <j1 rule="para" parents="108 14098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14122">
    <literal><![CDATA[
      R(x,y,z) * T(u,L(x,y,z)) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,14104,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 14104 22"/>
    </justification>
  </clause>

  <clause id="14123">
    <literal><![CDATA[
      R(x,y,z) * T(u,L(x,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      u * R(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(14104(a,1),315(a,1,2))].">
      <j1 rule="para" parents="14104 315"/>
    </justification>
  </clause>

  <clause id="14124">
    <literal><![CDATA[
      T(x,L((y / z) / u,u,z)) = T(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(605(a,1),14104(a,1,2)),flip(a)].">
      <j1 rule="para" parents="605 14104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14125">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,14102,a(flip),b,590,a)].">
      <j1 rule="hyper" parents="134 14102 590"/>
    </justification>
  </clause>

  <clause id="14126">
    <literal><![CDATA[
      K(x * y,z) * ((z * x) * y) = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[para(14102(a,1),4910(a,1,1))].">
      <j1 rule="para" parents="14102 4910"/>
    </justification>
  </clause>

  <clause id="14127">
    <literal><![CDATA[
      K(x,L(y,R(z,u,w),z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14073(a,2),141(a,1)),flip(b)].">
      <j1 rule="para" parents="14073 141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14128">
    <literal><![CDATA[
      K(x,L(y,T(z,u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(10287(a,1),14093(a,1,2))].">
      <j1 rule="para" parents="10287 14093"/>
    </justification>
  </clause>

  <clause id="14129">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(6711(a,2),14117(a,1))].">
      <j1 rule="para" parents="6711 14117"/>
    </justification>
  </clause>

  <clause id="14130">
    <literal><![CDATA[
      K(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(11696(a,1),14117(a,1))].">
      <j1 rule="para" parents="11696 14117"/>
    </justification>
  </clause>

  <clause id="14131">
    <literal><![CDATA[
      K(x,(y * z) / (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / u,u,z)) = w
    ]]></literal>
    <justification jstring="[para(108(a,1),14130(a,1,2))].">
      <j1 rule="para" parents="108 14130"/>
    </justification>
  </clause>

  <clause id="14132">
    <literal><![CDATA[
      K(x,T((y * z) / u,u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L((u / z) \ y,u / z,z)) = w
    ]]></literal>
    <justification jstring="[para(1038(a,1),14130(a,1,2))].">
      <j1 rule="para" parents="1038 14130"/>
    </justification>
  </clause>

  <clause id="14133">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u / (w * v5))) = K(x,L(y,z,u / (T(w,x) * v5)))
    ]]></literal>
    <justification jstring="[para(8443(a,1),13991(a,1,2,3))].">
      <j1 rule="para" parents="8443 13991"/>
    </justification>
  </clause>

  <clause id="14134">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) = K(x,y) * 1
    ]]></literal>
    <justification jstring="[para(9771(a,1),13991(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9771 13991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14135">
    <literal><![CDATA[
      K(x,L(y,z,(u * T(x,w)) \ v5)) = K(x,y) * a(y,z,K(x,x \ (u \ v5)))
    ]]></literal>
    <justification jstring="[para(11146(a,1),13991(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="11146 13991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14136">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u * (w * K(v5,v6)))) = K(x,L(y,z,u / (K(v6,v5) / w)))
    ]]></literal>
    <justification jstring="[para(13146(a,1),13991(a,1,2,3))].">
      <j1 rule="para" parents="13146 13991"/>
    </justification>
  </clause>

  <clause id="14137">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,L(u,w,v5))) = K(x,L(y,z,R(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(14081(a,1),13991(a,1,2,3))].">
      <j1 rule="para" parents="14081 13991"/>
    </justification>
  </clause>

  <clause id="14138">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14134(a,2),141(a,1)),flip(b)].">
      <j1 rule="para" parents="14134 141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14139">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(1620(a,2),14138(a,1,2))].">
      <j1 rule="para" parents="1620 14138"/>
    </justification>
  </clause>

  <clause id="14140">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,11049,a,b,13993,a),flip(a)].">
      <j1 rule="hyper" parents="347 11049 13993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14141">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(x,u)) = w
    ]]></literal>
    <justification jstring="[para(13994(a,1),44(a,1))].">
      <j1 rule="para" parents="13994 44"/>
    </justification>
  </clause>

  <clause id="14142">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(u,K(x,a(w,y,z)))
    ]]></literal>
    <justification jstring="[para(7279(a,1),14015(a,1,3))].">
      <j1 rule="para" parents="7279 14015"/>
    </justification>
  </clause>

  <clause id="14143">
    <literal><![CDATA[
      K(x,y) \ K(L(x,z,u),y) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13670,a(flip),b,14022,a)].">
      <j1 rule="hyper" parents="63 13670 14022"/>
    </justification>
  </clause>

  <clause id="14144">
    <literal><![CDATA[
      T(x,a(y * z,u,y)) = T(x,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,13976,a(flip),b,14026,a),flip(a)].">
      <j1 rule="hyper" parents="347 13976 14026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14145">
    <literal><![CDATA[
      T(x,a(y \ z,u,y)) = T(x,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),14144(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 14144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14146">
    <literal><![CDATA[
      K(x \ R(x,y,z),u) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(5177,a,14066,a)].">
      <j1 rule="hyper" parents="5177 14066"/>
    </justification>
  </clause>

  <clause id="14147">
    <literal><![CDATA[
      (x \ R(x,y,z)) * a(x,y,K(z,u)) = T(x \ R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(134,a,14146,a(flip),b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 14146 4924"/>
    </justification>
  </clause>

  <clause id="14148">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(14067(a,1),11093(a,1))].">
      <j1 rule="para" parents="14067 11093"/>
    </justification>
  </clause>

  <clause id="14149">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) = x * K(a(w,z,u),y)
    ]]></literal>
    <justification jstring="[para(12681(a,1),14067(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12681 14067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14150">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) * K(x,K(z,y)) = a(z,u,K(x,K(w,y)))
    ]]></literal>
    <justification jstring="[hyper(9451,a,14069,a)].">
      <j1 rule="hyper" parents="9451 14069"/>
    </justification>
  </clause>

  <clause id="14151">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,x) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,L(x,y,u)) = w
    ]]></literal>
    <justification jstring="[para(14070(a,2),11166(a,1))].">
      <j1 rule="para" parents="14070 11166"/>
    </justification>
  </clause>

  <clause id="14152">
    <literal><![CDATA[
      K(a(x,y,z),u) * (K(x,u) * w) = K(x,L(u,y,z)) * w
    ]]></literal>
    <justification jstring="[para(14078(a,1),10630(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14078 10630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14153">
    <literal><![CDATA[
      K(x \ 1,L(T(y,z),u,(x * u) \ z)) = K(z \ (u * ((x * u) \ z)),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,7245,a(flip),b,14084,a),flip(a)].">
      <j1 rule="hyper" parents="63 7245 14084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14154">
    <literal><![CDATA[
      K(T(x / y,z) \ 1,L(u,y,y \ z)) = K((z \ (x * (y \ z))) \ 1,u)
    ]]></literal>
    <justification jstring="[para(1077(a,1),14084(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1077 14084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14155">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) * K(x,K(u,w)) = K(u,K(w,L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,8920,a(flip),b,14140,a),flip(a)].">
      <j1 rule="hyper" parents="347 8920 14140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14156">
    <literal><![CDATA[
      L(K(x,y),z,u) != w * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(14140(a,1),44(a,1))].">
      <j1 rule="para" parents="14140 44"/>
    </justification>
  </clause>

  <clause id="14157">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) * K(x,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,K(w,L(x,y,z))) = v5
    ]]></literal>
    <justification jstring="[para(14140(a,2),8962(a,1))].">
      <j1 rule="para" parents="14140 8962"/>
    </justification>
  </clause>

  <clause id="14158">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(x,K(z,a(u,y,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13985,a(flip),b,14142,a)].">
      <j1 rule="hyper" parents="63 13985 14142"/>
    </justification>
  </clause>

  <clause id="14159">
    <literal><![CDATA[
      K(x,y) * K(a(z,u,y),x) = K(L(x,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(134,a,14023,a(flip),b,14143,a)].">
      <j1 rule="hyper" parents="134 14023 14143"/>
    </justification>
  </clause>

  <clause id="14160">
    <literal><![CDATA[
      x * K(a(y,z,u),w) = x * K(w,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(13960(a,1),14149(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13960 14149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14161">
    <literal><![CDATA[
      T(x,y) / T(x,a(z,u,y)) = K(L(x,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(6313,a,14159,a)].">
      <j1 rule="hyper" parents="6313 14159"/>
    </justification>
  </clause>

  <clause id="14162">
    <literal><![CDATA[
      (x * a(y,z,u)) / T(a(y,z,u),w) = x * K(a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,6099,a,b,14160,a)].">
      <j1 rule="hyper" parents="347 6099 14160"/>
    </justification>
  </clause>

  <clause id="14163">
    <literal><![CDATA[
      T(x,y) / (a(x,z,K(u,y)) \ x) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(14039(a,2),14161(a,1,2))].">
      <j1 rule="para" parents="14039 14161"/>
    </justification>
  </clause>

  <clause id="14164">
    <literal><![CDATA[
      x * a(x,y,a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,a(a(v5,u,w),y,z)) = v6
    ]]></literal>
    <justification jstring="[para(13960(a,2),14002(a,1,2,3))].">
      <j1 rule="para" parents="13960 14002"/>
    </justification>
  </clause>

  <clause id="14165">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(14057,a,13959,a)].">
      <j1 rule="hyper" parents="14057 13959"/>
    </justification>
  </clause>

  <clause id="14166">
    <literal><![CDATA[
      a(K(x,y) / z,u,K(w,v5)) = a(z * K(y,x),u,K(v5,w))
    ]]></literal>
    <justification jstring="[para(13073(a,1),14165(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13073 14165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14167">
    <literal><![CDATA[
      a(x,y,K(z \ (u \ w),u)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z \ w,u)) = v5
    ]]></literal>
    <justification jstring="[para(9618(a,2),14058(a,1,3))].">
      <j1 rule="para" parents="9618 14058"/>
    </justification>
  </clause>

  <clause id="14168">
    <literal><![CDATA[
      a(x,y,K(z,x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(13959(a,1),14058(a,1))].">
      <j1 rule="para" parents="13959 14058"/>
    </justification>
  </clause>

  <clause id="14169">
    <literal><![CDATA[
      K(x,L(y * z,y,u)) = K(x,(y * u) / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(13444,a,14083,a)].">
      <j1 rule="hyper" parents="13444 14083"/>
    </justification>
  </clause>

  <clause id="14170">
    <literal><![CDATA[
      a(x,y,K(z,y / (u / z))) \ K(x,(y * z) / u) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(128,a,14088,a(flip),b,13993,a)].">
      <j1 rule="hyper" parents="128 14088 13993"/>
    </justification>
  </clause>

  <clause id="14171">
    <literal><![CDATA[
      (K(x,y) * z) * u != w * (z * u)
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(14092(a,1),44(a,1))].">
      <j1 rule="para" parents="14092 44"/>
    </justification>
  </clause>

  <clause id="14172">
    <literal><![CDATA[
      K(L(x,y,z),u) * (y * z) = (K(x,u) * y) * z
    ]]></literal>
    <justification jstring="[para(11108(a,2),14092(a,1,1))].">
      <j1 rule="para" parents="11108 14092"/>
    </justification>
  </clause>

  <clause id="14173">
    <literal><![CDATA[
      K(x,T(y / (z * u),z)) = K(x,(u * z) \ (u * (y / u)))
    ]]></literal>
    <justification jstring="[para(1037(a,1),14103(a,1,2))].">
      <j1 rule="para" parents="1037 14103"/>
    </justification>
  </clause>

  <clause id="14174">
    <literal><![CDATA[
      K(x * y,L(z / x,x,y)) = K(x * y,(x * y) \ (z * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,5098,a(flip),b,14107,a),flip(a)].">
      <j1 rule="hyper" parents="347 5098 14107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14175">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) * (z * u) = (z * u) * K(x,(z * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(14107(a,2),7175(a,1,1))].">
      <j1 rule="para" parents="14107 7175"/>
    </justification>
  </clause>

  <clause id="14176">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,y / z,z))) = K(x,K(w,y / (u * z)))
    ]]></literal>
    <justification jstring="[para(14108(a,1),8932(a,2,2))].">
      <j1 rule="para" parents="14108 8932"/>
    </justification>
  </clause>

  <clause id="14177">
    <literal><![CDATA[
      x \ (y * (K((y \ x) / (z / y),u) * (y \ x))) = K(((y \ x) * y) / z,T(u,y \ x))
    ]]></literal>
    <justification jstring="[hyper(7117,a,14111,a)].">
      <j1 rule="hyper" parents="7117 14111"/>
    </justification>
  </clause>

  <clause id="14179">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(((x \ z) * x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(7592,a,14120,a)].">
      <j1 rule="hyper" parents="7592 14120"/>
    </justification>
  </clause>

  <clause id="14180">
    <literal><![CDATA[
      R(x,x,y) * T(z,x) = z * R(x,x,y)
    ]]></literal>
    <justification jstring="[para(7624(a,1),14122(a,1,2))].">
      <j1 rule="para" parents="7624 14122"/>
    </justification>
  </clause>

  <clause id="14181">
    <literal><![CDATA[
      (x * y) \ (x \ ((x * x) * y)) = (y * x) \ (y * R(x,x,y))
    ]]></literal>
    <justification jstring="[para(14180(a,1),10443(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14180 10443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14182">
    <literal><![CDATA[
      K(x,L(y,z / u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(5474(a,1),14128(a,1,2))].">
      <j1 rule="para" parents="5474 14128"/>
    </justification>
  </clause>

  <clause id="14183">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) / u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(11053(a,2),14128(a,1))].">
      <j1 rule="para" parents="11053 14128"/>
    </justification>
  </clause>

  <clause id="14184">
    <literal><![CDATA[
      T(1 / x,a(y,z,u)) = a(x,z,K(y,u)) / x
    ]]></literal>
    <justification jstring="[para(14165(a,1),14011(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14165 14011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14185">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13969,a(flip),b,14063,a),flip(a)].">
      <j1 rule="hyper" parents="63 13969 14063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14186">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,y) * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(14185(a,1),11061(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14185 11061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14187">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = w
    ]]></literal>
    <justification jstring="[para(14185(a,1),11093(a,1,2))].">
      <j1 rule="para" parents="14185 11093"/>
    </justification>
  </clause>

  <clause id="14188">
    <literal><![CDATA[
      T(x,a(y,x \ z,u)) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14185(a,1),13976(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14185 13976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14189">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y \ z,y)) = w
    ]]></literal>
    <justification jstring="[para(14185(a,1),14001(a,1,2))].">
      <j1 rule="para" parents="14185 14001"/>
    </justification>
  </clause>

  <clause id="14190">
    <literal><![CDATA[
      T(x,a(y,x \ z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,13976,a(flip),b,14188,a),flip(a)].">
      <j1 rule="hyper" parents="347 13976 14188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14191">
    <literal><![CDATA[
      T(x * K(y,z),a(u,K(z,y),w)) = T(x * K(y,z),a(u,x,w))
    ]]></literal>
    <justification jstring="[para(6123(a,1),14190(a,1,2,2))].">
      <j1 rule="para" parents="6123 14190"/>
    </justification>
  </clause>

  <clause id="14193">
    <literal><![CDATA[
      K(x,L(y,z,u)) * a(x,w,K(y,u)) = K(x,L(L(y,z,u),w,u \ 1))
    ]]></literal>
    <justification jstring="[para(7043(a,1),14076(a,1,2,3))].">
      <j1 rule="para" parents="7043 14076"/>
    </justification>
  </clause>

  <clause id="14194">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,z,u \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14076,a(flip),b,14077,a)].">
      <j1 rule="hyper" parents="63 14076 14077"/>
    </justification>
  </clause>

  <clause id="14195">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,(w \ u) \ y))
    ]]></literal>
    <justification jstring="[para(11302(a,2),14077(a,1,2))].">
      <j1 rule="para" parents="11302 14077"/>
    </justification>
  </clause>

  <clause id="14196">
    <literal><![CDATA[
      T(x,y) / (a(K(x,y),z,u) \ x) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(13958(a,2),14163(a,1,2,1))].">
      <j1 rule="para" parents="13958 14163"/>
    </justification>
  </clause>

  <clause id="14197">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,11061,a(flip),b,14186,a),flip(a)].">
      <j1 rule="hyper" parents="347 11061 14186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14198">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(14186(a,2),11093(a,1))].">
      <j1 rule="para" parents="14186 11093"/>
    </justification>
  </clause>

  <clause id="14199">
    <literal><![CDATA[
      K(x,L(y \ (z \ u),u,z)) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(11079,a,14197,a),flip(a)].">
      <j1 rule="hyper" parents="11079 14197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14200">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,y,x)) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11115,a(flip),b,14197,a),flip(a)].">
      <j1 rule="hyper" parents="63 11115 14197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14201">
    <literal><![CDATA[
      K(x,L(y,z * u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),14197(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 14197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14202">
    <literal><![CDATA[
      K(x,L(y,T(z,u),u)) = K(x,L(y,z * u,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),14197(a,1,2,2))].">
      <j1 rule="para" parents="22 14197"/>
    </justification>
  </clause>

  <clause id="14203">
    <literal><![CDATA[
      K(x,L(y,a(z,u,u \ 1),z)) = K(x,L(y,R(z,u,u \ 1),z))
    ]]></literal>
    <justification jstring="[para(853(a,1),14197(a,1,2,2))].">
      <j1 rule="para" parents="853 14197"/>
    </justification>
  </clause>

  <clause id="14204">
    <literal><![CDATA[
      K(x,L((y \ z) \ u,z,y)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(561(a,1),14197(a,1,2)),flip(a)].">
      <j1 rule="para" parents="561 14197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14205">
    <literal><![CDATA[
      K(x,L(y,z * u,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(10178(a,1),14197(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10178 14197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14206">
    <literal><![CDATA[
      K(x,L(y,z,u \ z)) = K(x,L(y,u,u \ z))
    ]]></literal>
    <justification jstring="[para(10179(a,1),14197(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10179 14197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14207">
    <literal><![CDATA[
      x * K(y,L(z,x,u)) = u * ((u \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[para(14197(a,1),11071(a,1,2))].">
      <j1 rule="para" parents="14197 11071"/>
    </justification>
  </clause>

  <clause id="14208">
    <literal><![CDATA[
      K(x \ (y \ z),L(u,z,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(14197(a,1),11078(a,1))].">
      <j1 rule="para" parents="14197 11078"/>
    </justification>
  </clause>

  <clause id="14209">
    <literal><![CDATA[
      K(x,L(y,z * u,z \ 1)) = K(x,L(y,u,z \ 1))
    ]]></literal>
    <justification jstring="[para(3599(a,1),14201(a,1,2))].">
      <j1 rule="para" parents="3599 14201"/>
    </justification>
  </clause>

  <clause id="14210">
    <literal><![CDATA[
      K(x,L(y,z * u,u \ 1)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[para(3229(a,1),14205(a,1,2))].">
      <j1 rule="para" parents="3229 14205"/>
    </justification>
  </clause>

  <clause id="14211">
    <literal><![CDATA[
      K(x,L(y,z * u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(14202(a,1),14128(a,1))].">
      <j1 rule="para" parents="14202 14128"/>
    </justification>
  </clause>

  <clause id="14212">
    <literal><![CDATA[
      K(x,L(y \ z,u,y \ u)) = K(x,u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[para(10156(a,1),14206(a,2,2))].">
      <j1 rule="para" parents="10156 14206"/>
    </justification>
  </clause>

  <clause id="14213">
    <literal><![CDATA[
      (x / y) * (y * K(z,u)) = x * K(z,L(u,x,y \ x))
    ]]></literal>
    <justification jstring="[para(14206(a,2),11069(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14206 11069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14214">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u \ x)) = (x / u) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(14206(a,2),11161(a,1,2))].">
      <j1 rule="para" parents="14206 11161"/>
    </justification>
  </clause>

  <clause id="14215">
    <literal><![CDATA[
      K(x,L(y,(z \ u) / w,((z \ u) / w) \ (u / z))) = K(x,L(y,u / z,w * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(13358(a,1),14206(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="13358 14206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14216">
    <literal><![CDATA[
      K(x,L(y,z \ u,z \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z \ 1)) = w
    ]]></literal>
    <justification jstring="[para(3608(a,1),14198(a,1,2))].">
      <j1 rule="para" parents="3608 14198"/>
    </justification>
  </clause>

  <clause id="14217">
    <literal><![CDATA[
      K(x,(y * z) \ L(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ (y \ L(y,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(14199(a,1),14139(a,1))].">
      <j1 rule="para" parents="14199 14139"/>
    </justification>
  </clause>

  <clause id="14218">
    <literal><![CDATA[
      K(x,(y \ R(y,z,u)) \ w) = K(x,R(y,z,u) \ (y * w))
    ]]></literal>
    <justification jstring="[hyper(14127,a,14204,a)].">
      <j1 rule="hyper" parents="14127 14204"/>
    </justification>
  </clause>

  <clause id="14219">
    <literal><![CDATA[
      K(x,L((a(y \ 1,y,z) \ 1) \ u,L(z,y,y \ 1),z)) = K(x,L(z,y,y \ 1) \ (z * u))
    ]]></literal>
    <justification jstring="[para(10899(a,2),14204(a,1,2,1,1))].">
      <j1 rule="para" parents="10899 14204"/>
    </justification>
  </clause>

  <clause id="14220">
    <literal><![CDATA[
      x \ (K(y,L(z,u,x)) * u) = (x \ u) * K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(7831,a,14207,a)].">
      <j1 rule="hyper" parents="7831 14207"/>
    </justification>
  </clause>

  <clause id="14221">
    <literal><![CDATA[
      x \ (y * K(z,L(u,y,x))) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(613,a,14207,a)].">
      <j1 rule="hyper" parents="613 14207"/>
    </justification>
  </clause>

  <clause id="14222">
    <literal><![CDATA[
      x \ (y * K(z,y)) = (x \ y) * K(z,y)
    ]]></literal>
    <justification jstring="[para(7613(a,1),14221(a,1,2,2))].">
      <j1 rule="para" parents="7613 14221"/>
    </justification>
  </clause>

  <clause id="14224">
    <literal><![CDATA[
      x \ ((y * z) / y) = (x \ z) * K(y,z)
    ]]></literal>
    <justification jstring="[para(4942(a,2),14222(a,1,2))].">
      <j1 rule="para" parents="4942 14222"/>
    </justification>
  </clause>

  <clause id="14225">
    <literal><![CDATA[
      K(x,L(y,z,u)) * T(y,x) = a(K(y,x),z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(36,a,5259,a,b,14196,a)].">
      <j1 rule="hyper" parents="36 5259 14196"/>
    </justification>
  </clause>

  <clause id="14226">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = w
    ]]></literal>
    <justification jstring="[para(14209(a,1),11167(a,1))].">
      <j1 rule="para" parents="14209 11167"/>
    </justification>
  </clause>

  <clause id="14227">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,((y * z) * (z \ 1)) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14083,a(flip),b,14210,a),flip(a)].">
      <j1 rule="hyper" parents="63 14083 14210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14228">
    <literal><![CDATA[
      T(K(x,L(y,z,u)) * y,x) = a(K(y,x),z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(7511,a,14225,a)].">
      <j1 rule="hyper" parents="7511 14225"/>
    </justification>
  </clause>

  <clause id="14229">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = a(K(x,y),z,u) \ x
    ]]></literal>
    <justification jstring="[para(3047(a,1),14228(a,1,1))].">
      <j1 rule="para" parents="3047 14228"/>
    </justification>
  </clause>

  <clause id="14230">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = a(x,z,K(u,y)) \ x
    ]]></literal>
    <justification jstring="[para(13958(a,1),14229(a,2,1))].">
      <j1 rule="para" parents="13958 14229"/>
    </justification>
  </clause>

  <clause id="14231">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,14039,a(flip),b,14230,a),flip(a)].">
      <j1 rule="hyper" parents="347 14039 14230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14232">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) != w \ v5
    ]]></literal>
    <literal><![CDATA[
      w * a(y,z,K(x,u)) = v5
    ]]></literal>
    <justification jstring="[para(12570(a,2),14020(a,1))].">
      <j1 rule="para" parents="12570 14020"/>
    </justification>
  </clause>

  <clause id="14233">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(13976(a,1),14040(a,1))].">
      <j1 rule="para" parents="13976 14040"/>
    </justification>
  </clause>

  <clause id="14234">
    <literal><![CDATA[
      K(x * L(T(y,x),z,u),y * x) = a(T(y,x),z,K(u,y * x))
    ]]></literal>
    <justification jstring="[hyper(14054,a,13368,a),flip(a)].">
      <j1 rule="hyper" parents="14054 13368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14236">
    <literal><![CDATA[
      K(x,L((y / z) / u,y,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(14198,a,14087,a)].">
      <j1 rule="hyper" parents="14198 14087"/>
    </justification>
  </clause>

  <clause id="14237">
    <literal><![CDATA[
      K(x,L(y / z,u,y \ u)) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[para(80(a,1),14236(a,1,2,1,1))].">
      <j1 rule="para" parents="80 14236"/>
    </justification>
  </clause>

  <clause id="14238">
    <literal><![CDATA[
      K(x,L(y,z,u)) * z = (K(x,y) * (z / u)) * u
    ]]></literal>
    <justification jstring="[para(14197(a,1),14090(a,1,1))].">
      <j1 rule="para" parents="14197 14090"/>
    </justification>
  </clause>

  <clause id="14239">
    <literal><![CDATA[
      (x * K(y,L(z,x,u))) / u = K(y,T(z,x)) * (x / u)
    ]]></literal>
    <justification jstring="[hyper(8201,a,14238,a)].">
      <j1 rule="hyper" parents="8201 14238"/>
    </justification>
  </clause>

  <clause id="14240">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * z) / u = K(x,y) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(652,a,14238,a)].">
      <j1 rule="hyper" parents="652 14238"/>
    </justification>
  </clause>

  <clause id="14241">
    <literal><![CDATA[
      (K(x,L(y,z,K(u,w) * K(v5,v6))) * z) / (K(v5,v6) * K(u,w)) = K(x,y) * (z / (K(u,w) * K(v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(131,a,14238,a,b,13600,a)].">
      <j1 rule="hyper" parents="131 14238 13600"/>
    </justification>
  </clause>

  <clause id="14242">
    <literal><![CDATA[
      T(L(x,y,K(z,L(u,y * x,x))),x \ (K(z,L(u,y * x,x)) * y)) = (x \ (K(z,L(u,y * x,x)) * y)) \ (K(z,u) * ((y * x) / x))
    ]]></literal>
    <justification jstring="[hyper(462,a,14240,a(flip),b,13765,a)].">
      <j1 rule="hyper" parents="462 14240 13765"/>
    </justification>
  </clause>

  <clause id="14243">
    <literal><![CDATA[
      K(x,L(y,z,(T(y,x) * z) \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(14105(a,1),350(a,1,1))].">
      <j1 rule="para" parents="14105 350"/>
    </justification>
  </clause>

  <clause id="14244">
    <literal><![CDATA[
      a(x,y,z) * ((y * z) * x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13378,a(flip),b,14125,a)].">
      <j1 rule="hyper" parents="63 13378 14125"/>
    </justification>
  </clause>

  <clause id="14245">
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10459,a(flip),b,14125,a)].">
      <j1 rule="hyper" parents="63 10459 14125"/>
    </justification>
  </clause>

  <clause id="14246">
    <literal><![CDATA[
      a(x,y,z) = ((y * z) * x) \ ((y * z) * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,14125,a(flip),b,10459,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 14125 10459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14247">
    <literal><![CDATA[
      a(x,y,T(z,y)) * ((y * T(z,y)) * x) = (y * T(z,y)) * (((x * y) * T(z,y)) / (z * y))
    ]]></literal>
    <justification jstring="[para(265(a,2),14244(a,2,2))].">
      <j1 rule="para" parents="265 14244"/>
    </justification>
  </clause>

  <clause id="14248">
    <literal><![CDATA[
      ((x * y) * z) \ ((x * y) * R(z,x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(z,x,y) = u
    ]]></literal>
    <justification jstring="[para(14245(a,1),356(a,1,2))].">
      <j1 rule="para" parents="14245 356"/>
    </justification>
  </clause>

  <clause id="14249">
    <literal><![CDATA[
      (x * ((y * z) * u)) \ (x * ((y * z) * R(u,y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      L(a(u,y,z),(y * z) * u,x) = w
    ]]></literal>
    <justification jstring="[para(14245(a,1),545(a,1,2,2))].">
      <j1 rule="para" parents="14245 545"/>
    </justification>
  </clause>

  <clause id="14250">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,y * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,99,a,b,14246,a),flip(a)].">
      <j1 rule="hyper" parents="347 99 14246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14251">
    <literal><![CDATA[
      a(x,y,z) = (y * z) \ (((y * z) / x) * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,4070,a(flip),b,14246,a),flip(a)].">
      <j1 rule="hyper" parents="347 4070 14246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14252">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * R(L(z,y,x),x,y)) = a(L(z,y,x),x,y)
    ]]></literal>
    <justification jstring="[para(97(a,1),14246(a,2,1)),flip(a)].">
      <j1 rule="para" parents="97 14246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14253">
    <literal><![CDATA[
      L(x,y,z * u) != a(y,z,u)
    ]]></literal>
    <literal><![CDATA[
      y \ R(y,z,u) = x
    ]]></literal>
    <justification jstring="[para(14246(a,2),569(a,2))].">
      <j1 rule="para" parents="14246 569"/>
    </justification>
  </clause>

  <clause id="14254">
    <literal><![CDATA[
      (K(x,y) * ((y * z) * x)) \ ((y * (K(x,y) * z)) * R(x,y,K(x,y) * z)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7221(a,1),14246(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7221 14246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14257">
    <literal><![CDATA[
      K(x \ L(x,y,z),u) * ((u * x) * L(x \ 1,y,z)) = (x * L(x \ 1,y,z)) * R(u,x,L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(3343(a,1),14126(a,1,1,1))].">
      <j1 rule="para" parents="3343 14126"/>
    </justification>
  </clause>

  <clause id="14258">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,T(y,z),1 / z)) = K(x,(y * (1 / T(z,y))) / ((u \ 1) * (1 / z)))
    ]]></literal>
    <justification jstring="[para(5356(a,1),14169(a,2,2,1))].">
      <j1 rule="para" parents="5356 14169"/>
    </justification>
  </clause>

  <clause id="14259">
    <literal><![CDATA[
      a(x,y,K(y * z,u)) * K(x,(y * u) / ((z \ 1) * u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(14169(a,1),13992(a,1,2))].">
      <j1 rule="para" parents="14169 13992"/>
    </justification>
  </clause>

  <clause id="14260">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(14189,a,13984,a)].">
      <j1 rule="hyper" parents="14189 13984"/>
    </justification>
  </clause>

  <clause id="14261">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) / u,z \ y,T(y,z \ 1) \ (z \ y))) = K(x,(z \ y) / (u * T(y \ (z \ y),y)))
    ]]></literal>
    <justification jstring="[para(4350(a,2),14237(a,2,2,2,2))].">
      <j1 rule="para" parents="4350 14237"/>
    </justification>
  </clause>

  <clause id="14262">
    <literal><![CDATA[
      T(x,a(y,z,a(u,w,v5))) != x * v6
    ]]></literal>
    <literal><![CDATA[
      a(x,z,a(u,w,K(v5,y))) = v6
    ]]></literal>
    <justification jstring="[para(14027(a,1),43(a,1))].">
      <j1 rule="para" parents="14027 43"/>
    </justification>
  </clause>

  <clause id="14263">
    <literal><![CDATA[
      a(L(x,y,z) \ u,w,K(z,x)) = a(u,w,K(z,x))
    ]]></literal>
    <justification jstring="[para(7612(a,1),14045(a,2,3))].">
      <j1 rule="para" parents="7612 14045"/>
    </justification>
  </clause>

  <clause id="14265">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(u,w,x) = L(T(u,a(z,y,x)),w,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,25,a,b,14059,a),flip(a)].">
      <j1 rule="hyper" parents="347 25 14059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14266">
    <literal><![CDATA[
      a(x,y / z,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(14062(a,1),14053(a,1))].">
      <j1 rule="para" parents="14062 14053"/>
    </justification>
  </clause>

  <clause id="14267">
    <literal><![CDATA[
      a(x,y \ z,K(u,y)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(14266,a,11125,a)].">
      <j1 rule="hyper" parents="14266 11125"/>
    </justification>
  </clause>

  <clause id="14268">
    <literal><![CDATA[
      a(x,y \ z,K(u,y)) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,13959,a,b,14267,a),flip(a)].">
      <j1 rule="hyper" parents="347 13959 14267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14269">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(14019,a,14268,a)].">
      <j1 rule="hyper" parents="14019 14268"/>
    </justification>
  </clause>

  <clause id="14270">
    <literal><![CDATA[
      a(x,y \ z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(14268(a,2),14016(a,1))].">
      <j1 rule="para" parents="14268 14016"/>
    </justification>
  </clause>

  <clause id="14271">
    <literal><![CDATA[
      a(x,y * z,K(y,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12433,a(flip),b,14269,a),flip(a)].">
      <j1 rule="hyper" parents="63 12433 14269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14272">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(y,K(u,w)))
    ]]></literal>
    <justification jstring="[para(7283(a,2),14271(a,1,3))].">
      <j1 rule="para" parents="7283 14271"/>
    </justification>
  </clause>

  <clause id="14273">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(u,K(w,y)))
    ]]></literal>
    <justification jstring="[para(7283(a,2),14272(a,2,3))].">
      <j1 rule="para" parents="7283 14272"/>
    </justification>
  </clause>

  <clause id="14274">
    <literal><![CDATA[
      K(x,(y * z) / (z * T(z \ u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / T(u / z,w),T(u / z,w),z)) = v5
    ]]></literal>
    <justification jstring="[para(484(a,1),14131(a,1,2,2))].">
      <j1 rule="para" parents="484 14131"/>
    </justification>
  </clause>

  <clause id="14275">
    <literal><![CDATA[
      K(x,a(y,z,u)) * (K(x,y) * w) = K(x,L(y,z,u)) * w
    ]]></literal>
    <justification jstring="[para(14007(a,1),14152(a,1,1))].">
      <j1 rule="para" parents="14007 14152"/>
    </justification>
  </clause>

  <clause id="14276">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),z \ u)) = K(x,u \ (z * (y / z)))
    ]]></literal>
    <justification jstring="[para(10(a,1),14173(a,2,2,1))].">
      <j1 rule="para" parents="10 14173"/>
    </justification>
  </clause>

  <clause id="14277">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,(z * y) \ K(z,1 / z))
    ]]></literal>
    <justification jstring="[para(292(a,2),14173(a,2,2,2))].">
      <j1 rule="para" parents="292 14173"/>
    </justification>
  </clause>

  <clause id="14278">
    <literal><![CDATA[
      K((x \ T(y,x \ 1)) \ z,T(u,(x \ y) / y)) = K(((y \ z) * y) / (((x \ y) / y) * y),u)
    ]]></literal>
    <justification jstring="[para(3837(a,2),14179(a,1,1,1))].">
      <j1 rule="para" parents="3837 14179"/>
    </justification>
  </clause>

  <clause id="14279">
    <literal><![CDATA[
      1 / K(((x \ y) * x) / (z * x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(u,z),(x * z) \ y) = w
    ]]></literal>
    <justification jstring="[para(14179(a,1),5178(a,1,2))].">
      <j1 rule="para" parents="14179 5178"/>
    </justification>
  </clause>

  <clause id="14280">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(z,x) / (y * x),u) = w
    ]]></literal>
    <justification jstring="[para(14179(a,2),12164(a,1))].">
      <j1 rule="para" parents="14179 12164"/>
    </justification>
  </clause>

  <clause id="14281">
    <literal><![CDATA[
      K(x,R(y,z,z) \ (y * u)) = K(x,a(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[para(13398(a,1),14218(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13398 14218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14282">
    <literal><![CDATA[
      K(x,y) \ L(T(y,a(x,z,u)),z,u) = T(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(14265(a,1),11099(a,1,2))].">
      <j1 rule="para" parents="14265 11099"/>
    </justification>
  </clause>

  <clause id="14283">
    <literal><![CDATA[
      K(x,y) * L(T(x,a(y,z,u)),z,u) = T(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(5286,a,14282,a)].">
      <j1 rule="hyper" parents="5286 14282"/>
    </justification>
  </clause>

  <clause id="14284">
    <literal><![CDATA[
      K(x,y) * L(T(x,a(y,z,u)),z,u) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,25,a,b,14283,a),flip(a)].">
      <j1 rule="hyper" parents="347 25 14283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14285">
    <literal><![CDATA[
      K(x,y) * (K(x,a(y,z,u)) * w) = K(x,L(y,z,u)) * w
    ]]></literal>
    <justification jstring="[hyper(9916,a,14275,a)].">
      <j1 rule="hyper" parents="9916 14275"/>
    </justification>
  </clause>

  <clause id="14286">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,K(z,1 / z) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,13581,a,b,14277,a),flip(a)].">
      <j1 rule="hyper" parents="347 13581 14277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14287">
    <literal><![CDATA[
      K(x,a(y,z,u)) * T(x,y) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(34,a,5454,a,b,14285,a),flip(a)].">
      <j1 rule="hyper" parents="34 5454 14285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14288">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,5427,a(flip),b,14286,a),flip(a)].">
      <j1 rule="hyper" parents="347 5427 14286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14289">
    <literal><![CDATA[
      K(x,y / (y * (y * z))) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(8603,a,14288,a)].">
      <j1 rule="hyper" parents="8603 14288"/>
    </justification>
  </clause>

  <clause id="14291">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(x,z,K(y,u)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(9264,a,13961,a)].">
      <j1 rule="hyper" parents="9264 13961"/>
    </justification>
  </clause>

  <clause id="14292">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(x,z,K(u,L(y,z,u))) = (K(x,L(y,z,u)) * z) * u
    ]]></literal>
    <justification jstring="[hyper(133,a,14092,a(flip),b,13961,a)].">
      <j1 rule="hyper" parents="133 14092 13961"/>
    </justification>
  </clause>

  <clause id="14293">
    <literal><![CDATA[
      T(x * y,a(x,z,u)) = x * T(y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(14005,a,14048,a),flip(a)].">
      <j1 rule="hyper" parents="14005 14048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14294">
    <literal><![CDATA[
      T(x,a(y,z,u)) / y = T(x / y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(34,a,4812,a(flip),b,14293,a(flip))].">
      <j1 rule="hyper" parents="34 4812 14293"/>
    </justification>
  </clause>

  <clause id="14296">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = R(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(595,a,14018,a),flip(a)].">
      <j1 rule="hyper" parents="595 14018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14297">
    <literal><![CDATA[
      T(x,a(y,z,u)) * (z * K(u,y)) = (x * z) * K(u,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,13976,a(flip),b,14018,a)].">
      <j1 rule="hyper" parents="133 13976 14018"/>
    </justification>
  </clause>

  <clause id="14298">
    <literal><![CDATA[
      ((x * y) * K(z,u)) / L(y * K(z,u),w,a(w,v5,K(v6,v7))) = x * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(14012(a,2),14018(a,1,2))].">
      <j1 rule="para" parents="14012 14018"/>
    </justification>
  </clause>

  <clause id="14299">
    <literal><![CDATA[
      R(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(14002,a,14296,a),flip(a)].">
      <j1 rule="hyper" parents="14002 14296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14300">
    <literal><![CDATA[
      T(K(x,T(y,z * u)) * z,u) = T(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(269,a,14116,a,b,10150,a(flip))].">
      <j1 rule="hyper" parents="269 14116 10150"/>
    </justification>
  </clause>

  <clause id="14301">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x * y)) = T(K(z,u) * x,y)
    ]]></literal>
    <justification jstring="[para(7379(a,1),14300(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7379 14300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14302">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,w) = T(u,w) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(13505(a,1),14300(a,1,1,1))].">
      <j1 rule="para" parents="13505 14300"/>
    </justification>
  </clause>

  <clause id="14305">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,w) = K(x,K(y,z)) * T(u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,13514,a,b,14302,a),flip(a)].">
      <j1 rule="hyper" parents="347 13514 14302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14306">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) = T(x,w) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(13514(a,1),14302(a,1,1))].">
      <j1 rule="para" parents="13514 14302"/>
    </justification>
  </clause>

  <clause id="14309">
    <literal><![CDATA[
      T(K(x,K(y,z)) \ u,w) = K(x,K(y,z)) * T(u,w)
    ]]></literal>
    <justification jstring="[para(7318(a,2),14305(a,1,1))].">
      <j1 rule="para" parents="7318 14305"/>
    </justification>
  </clause>

  <clause id="14311">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) / K(y,z) = T(x,w) / T(K(y,z),u)
    ]]></literal>
    <justification jstring="[para(14306(a,2),7308(a,1,1))].">
      <j1 rule="para" parents="14306 7308"/>
    </justification>
  </clause>

  <clause id="14313">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(u,w) = T(K(x,K(y,z)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,5926,a,b,14309,a)].">
      <j1 rule="hyper" parents="347 5926 14309"/>
    </justification>
  </clause>

  <clause id="14314">
    <literal><![CDATA[
      T(K(x,K(y,z)) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,w) = v5
    ]]></literal>
    <justification jstring="[para(14309(a,2),7326(a,1))].">
      <j1 rule="para" parents="14309 7326"/>
    </justification>
  </clause>

  <clause id="14316">
    <literal><![CDATA[
      (x * a(y,z,u)) / x = T(a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(6231,a,14162,a)].">
      <j1 rule="hyper" parents="6231 14162"/>
    </justification>
  </clause>

  <clause id="14317">
    <literal><![CDATA[
      T(T(a(x,y,z),u),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(14316(a,1),254(a,1,1))].">
      <j1 rule="para" parents="14316 254"/>
    </justification>
  </clause>

  <clause id="14318">
    <literal><![CDATA[
      R(T(a(x,y,z),u * u),u,u) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[para(14317(a,1),12724(a,2,1))].">
      <j1 rule="para" parents="14317 12724"/>
    </justification>
  </clause>

  <clause id="14319">
    <literal><![CDATA[
      R(a(x,y,z),u,u) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[para(12711(a,1),14318(a,1,1))].">
      <j1 rule="para" parents="12711 14318"/>
    </justification>
  </clause>

  <clause id="14321">
    <literal><![CDATA[
      L(a(x,y,z),1 / u,1 / u) = R(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(2266,a,14319,a),flip(a)].">
      <j1 rule="hyper" parents="2266 14319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14323">
    <literal><![CDATA[
      L(a(x,y,z),1 / u,1 / u) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,14319,a(flip),b,14321,a),flip(a)].">
      <j1 rule="hyper" parents="347 14319 14321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14324">
    <literal><![CDATA[
      L(a(x,y,z),u,u \ 1) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(3945,a,14323,a)].">
      <j1 rule="hyper" parents="3945 14323"/>
    </justification>
  </clause>

  <clause id="14325">
    <literal><![CDATA[
      (1 / x) \ L(a(y,z,u),x,x) = x * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(128,a,14324,a(flip),b,2939,a)].">
      <j1 rule="hyper" parents="128 14324 2939"/>
    </justification>
  </clause>

  <clause id="14326">
    <literal><![CDATA[
      (1 / x) \ a(y,z,x) = x * a(y,z,x)
    ]]></literal>
    <justification jstring="[para(12360(a,1),14325(a,1,2))].">
      <j1 rule="para" parents="12360 14325"/>
    </justification>
  </clause>

  <clause id="14327">
    <literal><![CDATA[
      x \ a(y,z,u) != u * a(y,z,u)
    ]]></literal>
    <literal><![CDATA[
      1 / u = x
    ]]></literal>
    <justification jstring="[para(14326(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="14326 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14328">
    <literal><![CDATA[
      K(x * y,(x * y) \ (z * y)) = K(x * y,z / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13004,a(flip),b,14174,a),flip(a)].">
      <j1 rule="hyper" parents="63 13004 14174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14329">
    <literal><![CDATA[
      T(x * y,(x * y) \ (z * y)) = T(x * y,z / x)
    ]]></literal>
    <justification jstring="[hyper(132,a,14328,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 14328 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14330">
    <literal><![CDATA[
      K(x * (y \ z),(x * (y \ z)) \ z) = K(x * (y \ z),y / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),14328(a,1,2,2))].">
      <j1 rule="para" parents="10 14328"/>
    </justification>
  </clause>

  <clause id="14332">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(11061(a,1),14187(a,1))].">
      <j1 rule="para" parents="11061 14187"/>
    </justification>
  </clause>

  <clause id="14333">
    <literal><![CDATA[
      x * K(y,L(T(z,K(z,y) / u),x,(K(z,y) / u) \ x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(13063(a,1),14214(a,2,2))].">
      <j1 rule="para" parents="13063 14214"/>
    </justification>
  </clause>

  <clause id="14334">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(99(a,2),14248(a,1))].">
      <j1 rule="para" parents="99 14248"/>
    </justification>
  </clause>

  <clause id="14335">
    <literal><![CDATA[
      K((x * ((y \ 1) / z)) \ u,T(w,z * y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(u,x) / (((y \ 1) / z) * x),w) = v5
    ]]></literal>
    <justification jstring="[para(13189(a,1),14280(a,1))].">
      <j1 rule="para" parents="13189 14280"/>
    </justification>
  </clause>

  <clause id="14336">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,y) * (z * u)) = T(u,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(128,a,14291,a(flip),b,14004,a(flip))].">
      <j1 rule="hyper" parents="128 14291 14004"/>
    </justification>
  </clause>

  <clause id="14337">
    <literal><![CDATA[
      L(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(545,a,14336,a)].">
      <j1 rule="hyper" parents="545 14336"/>
    </justification>
  </clause>

  <clause id="14338">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(14336(a,1),545(a,1))].">
      <j1 rule="para" parents="14336 545"/>
    </justification>
  </clause>

  <clause id="14339">
    <literal><![CDATA[
      R(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,14299,a,b,14337,a)].">
      <j1 rule="hyper" parents="347 14299 14337"/>
    </justification>
  </clause>

  <clause id="14340">
    <literal><![CDATA[
      (a(x,y,z) * u) / a(x,y,z) = L(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,14031,a,b,14337,a)].">
      <j1 rule="hyper" parents="347 14031 14337"/>
    </justification>
  </clause>

  <clause id="14341">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u = L(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,13999,a,b,14337,a)].">
      <j1 rule="hyper" parents="347 13999 14337"/>
    </justification>
  </clause>

  <clause id="14342">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,13984,a,b,14337,a)].">
      <j1 rule="hyper" parents="347 13984 14337"/>
    </justification>
  </clause>

  <clause id="14343">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,13976,a,b,14337,a)].">
      <j1 rule="hyper" parents="347 13976 14337"/>
    </justification>
  </clause>

  <clause id="14344">
    <literal><![CDATA[
      a(x,y,z) \ R(u,a(x,y,z),a(x,y,z)) = L(u * (a(x,y,z) \ 1),y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,12595,a,b,14337,a)].">
      <j1 rule="hyper" parents="347 12595 14337"/>
    </justification>
  </clause>

  <clause id="14345">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,12580,a,b,14337,a)].">
      <j1 rule="hyper" parents="347 12580 14337"/>
    </justification>
  </clause>

  <clause id="14346">
    <literal><![CDATA[
      L(x,y \ z,K(y,u)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,14260,a(flip),b,14337,a),flip(a)].">
      <j1 rule="hyper" parents="347 14260 14337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14347">
    <literal><![CDATA[
      L(1 / x,y,K(z,u)) = a(x,y,K(u,z)) / x
    ]]></literal>
    <justification jstring="[hyper(347,a,14184,a(flip),b,14337,a),flip(a)].">
      <j1 rule="hyper" parents="347 14184 14337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14348">
    <literal><![CDATA[
      L(T(x,y),z,K(u,y)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,14046,a(flip),b,14337,a),flip(a)].">
      <j1 rule="hyper" parents="347 14046 14337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14349">
    <literal><![CDATA[
      L(a(x,x,y),z,K(u,w)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,12965,a(flip),b,14337,a),flip(a)].">
      <j1 rule="hyper" parents="347 12965 14337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14350">
    <literal><![CDATA[
      L(x,y * z,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,12698,a(flip),b,14337,a),flip(a)].">
      <j1 rule="hyper" parents="347 12698 14337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14351">
    <literal><![CDATA[
      L(a(x,y,y \ 1),z,K(u,w)) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,12684,a(flip),b,14337,a),flip(a)].">
      <j1 rule="hyper" parents="347 12684 14337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14352">
    <literal><![CDATA[
      L(x / a(y,z,u),z,K(u,y)) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(347,a,113,a(flip),b,14337,a),flip(a)].">
      <j1 rule="hyper" parents="347 113 14337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14353">
    <literal><![CDATA[
      (x / y) * L(y,z,K(u,w)) = x * K(y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,14337,a,b,5936,a)].">
      <j1 rule="hyper" parents="134 14337 5936"/>
    </justification>
  </clause>

  <clause id="14354">
    <literal><![CDATA[
      L(x,y,K(z,u)) * a(z,y,u) = a(z,y,u) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,14337,a,b,14031,a)].">
      <j1 rule="hyper" parents="133 14337 14031"/>
    </justification>
  </clause>

  <clause id="14355">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,14337,a,b,12655,a)].">
      <j1 rule="hyper" parents="128 14337 12655"/>
    </justification>
  </clause>

  <clause id="14356">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),a(z,y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,14034,a(flip),b,14337,a),flip(a)].">
      <j1 rule="hyper" parents="41 14034 14337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14357">
    <literal><![CDATA[
      T(x,y \ R(y,z,u)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(14233,a,14337,a(flip))].">
      <j1 rule="hyper" parents="14233 14337"/>
    </justification>
  </clause>

  <clause id="14358">
    <literal><![CDATA[
      L(x,y,K(L(z,u,x),w)) = T(x,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(12703,a,14337,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="12703 14337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14359">
    <literal><![CDATA[
      L(x / a(y,z,u),z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(14337(a,2),386(a,1))].">
      <j1 rule="para" parents="14337 386"/>
    </justification>
  </clause>

  <clause id="14360">
    <literal><![CDATA[
      x * (L(x,y,K(z,u)) \ w) = K(a(u,y,z),x) * w
    ]]></literal>
    <justification jstring="[para(14337(a,2),4947(a,1,2,1))].">
      <j1 rule="para" parents="14337 4947"/>
    </justification>
  </clause>

  <clause id="14361">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ x = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(14337(a,2),12679(a,1,1))].">
      <j1 rule="para" parents="14337 12679"/>
    </justification>
  </clause>

  <clause id="14362">
    <literal><![CDATA[
      T(x * y,a(z,u,x)) = x * L(y,u,K(x,z))
    ]]></literal>
    <justification jstring="[para(14337(a,2),12706(a,2,2))].">
      <j1 rule="para" parents="14337 12706"/>
    </justification>
  </clause>

  <clause id="14363">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u \ w) = L(u,y,K(z,x)) \ w
    ]]></literal>
    <justification jstring="[para(14337(a,2),12690(a,2,1))].">
      <j1 rule="para" parents="14337 12690"/>
    </justification>
  </clause>

  <clause id="14364">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),u) = T(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[para(14337(a,2),14033(a,1,1))].">
      <j1 rule="para" parents="14337 14033"/>
    </justification>
  </clause>

  <clause id="14365">
    <literal><![CDATA[
      (x \ y) * a(y,z,K(u,w)) = x \ L(y,z,K(u,w))
    ]]></literal>
    <justification jstring="[para(14337(a,2),14010(a,2,2))].">
      <j1 rule="para" parents="14337 14010"/>
    </justification>
  </clause>

  <clause id="14366">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u / w) = L(u,y,K(x,z)) / w
    ]]></literal>
    <justification jstring="[para(14337(a,2),14021(a,2,1))].">
      <j1 rule="para" parents="14337 14021"/>
    </justification>
  </clause>

  <clause id="14367">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * x) = L(x,y,K(z,u)) * T(w,x)
    ]]></literal>
    <justification jstring="[para(14337(a,2),14013(a,2,1))].">
      <j1 rule="para" parents="14337 14013"/>
    </justification>
  </clause>

  <clause id="14368">
    <literal><![CDATA[
      K(x,y) * L(L(x,z,K(u,y)),z,u) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(14337(a,2),14284(a,1,2,1))].">
      <j1 rule="para" parents="14337 14284"/>
    </justification>
  </clause>

  <clause id="14369">
    <literal><![CDATA[
      L(x,y,K(z,u)) / u = T(x / u,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(14337(a,2),14294(a,1,1))].">
      <j1 rule="para" parents="14337 14294"/>
    </justification>
  </clause>

  <clause id="14370">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (y * K(z,u)) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14337(a,2),14297(a,1,1))].">
      <j1 rule="para" parents="14337 14297"/>
    </justification>
  </clause>

  <clause id="14371">
    <literal><![CDATA[
      L(R(x,y,z),y * z,K(z,u)) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(6674,a,14339,a),flip(a)].">
      <j1 rule="hyper" parents="6674 14339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14372">
    <literal><![CDATA[
      L((x * K(y,z)) / u,u,K(z,y)) = x / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6148,a,14339,a),flip(a)].">
      <j1 rule="hyper" parents="6148 14339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14373">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) = (y * K(z,u)) / ((x \ y) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(995,a,14339,a),flip(a)].">
      <j1 rule="hyper" parents="995 14339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14375">
    <literal><![CDATA[
      L(R(x / y,y,z),y * z,K(y,u)) = ((x * z) * K(y,u)) / (y * (z * K(y,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6773,a(flip),b,14339,a),flip(a)].">
      <j1 rule="hyper" parents="63 6773 14339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14376">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) \ (y * K(z,u)) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14339(a,1),578(a,1,1))].">
      <j1 rule="para" parents="14339 578"/>
    </justification>
  </clause>

  <clause id="14377">
    <literal><![CDATA[
      L(x,x \ y,K(z,z \ y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(14339(a,1),5318(a,1,1))].">
      <j1 rule="para" parents="14339 5318"/>
    </justification>
  </clause>

  <clause id="14378">
    <literal><![CDATA[
      L(R(x,y,z),y * z,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14339(a,1),6674(a,1))].">
      <j1 rule="para" parents="14339 6674"/>
    </justification>
  </clause>

  <clause id="14379">
    <literal><![CDATA[
      R(x,y,a(z,u,K(w,v5))) = L(x,y,K(a(z,u,w),v5))
    ]]></literal>
    <justification jstring="[para(12681(a,2),14339(a,1,3))].">
      <j1 rule="para" parents="12681 14339"/>
    </justification>
  </clause>

  <clause id="14380">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,K(u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,14337,a,b,14356,a)].">
      <j1 rule="hyper" parents="63 14337 14356"/>
    </justification>
  </clause>

  <clause id="14382">
    <literal><![CDATA[
      K(x,y) * (z * L(u,z,K(y,x))) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(134,a,14356,a(flip),b,14336,a),flip(a)].">
      <j1 rule="hyper" parents="134 14356 14336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14383">
    <literal><![CDATA[
      T((K(x,y) * z) \ u,a(x,z,y)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(5277(a,1),14356(a,1,1))].">
      <j1 rule="para" parents="5277 14356"/>
    </justification>
  </clause>

  <clause id="14384">
    <literal><![CDATA[
      L(x,y,T(z,a(u,w,v5) \ 1)) = L(x,y,L(z,w,K(u,v5)))
    ]]></literal>
    <justification jstring="[para(14356(a,1),12161(a,1,3,1))].">
      <j1 rule="para" parents="14356 12161"/>
    </justification>
  </clause>

  <clause id="14385">
    <literal><![CDATA[
      L((K(x,y) * z) \ u,z,K(y,x)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(5290,a,14380,a),flip(a)].">
      <j1 rule="hyper" parents="5290 14380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14386">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(14341(a,1),14003(a,1))].">
      <j1 rule="para" parents="14341 14003"/>
    </justification>
  </clause>

  <clause id="14387">
    <literal><![CDATA[
      L(x,y * z,K(u,y)) = a(u,z,K(y,x)) * x
    ]]></literal>
    <justification jstring="[para(14271(a,1),14341(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14271 14341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14388">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(11149,a,14342,a)].">
      <j1 rule="hyper" parents="11149 14342"/>
    </justification>
  </clause>

  <clause id="14389">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),w) = L(T(x,w),z,K(y,u))
    ]]></literal>
    <justification jstring="[para(14342(a,2),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14342 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14390">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14030(a,1),14342(a,1,2))].">
      <j1 rule="para" parents="14030 14342"/>
    </justification>
  </clause>

  <clause id="14391">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14343(a,1),356(a,1,2))].">
      <j1 rule="para" parents="14343 356"/>
    </justification>
  </clause>

  <clause id="14392">
    <literal><![CDATA[
      L(x * L(x \ y,z,u),z,K(x \ y,u)) = ((x * L(x \ y,z,u)) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(13839,a,14345,a),flip(a)].">
      <j1 rule="hyper" parents="13839 14345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14393">
    <literal><![CDATA[
      L(x \ y,z,K(u,x)) = T(y / x,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(113(a,1),14348(a,1,1))].">
      <j1 rule="para" parents="113 14348"/>
    </justification>
  </clause>

  <clause id="14394">
    <literal><![CDATA[
      L(x,y,K(z,u)) * u = u * T(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[para(14348(a,1),267(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14348 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14395">
    <literal><![CDATA[
      L(x,y * z,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,14337,a,b,14350,a),flip(a)].">
      <j1 rule="hyper" parents="347 14337 14350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14396">
    <literal><![CDATA[
      L(x,y,K(x * z,u)) = x * a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,11294,a(flip),b,14355,a),flip(a)].">
      <j1 rule="hyper" parents="134 11294 14355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14397">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(14355(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14355 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14398">
    <literal><![CDATA[
      (x * R(y,z,u)) / L(x * y,z,K(u,y)) = (x * y) \ (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(220,a,14357,a(flip),b,13773,a(flip))].">
      <j1 rule="hyper" parents="220 14357 13773"/>
    </justification>
  </clause>

  <clause id="14399">
    <literal><![CDATA[
      L(x,y,K(z,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14342,a(flip),b,14390,a)].">
      <j1 rule="hyper" parents="63 14342 14390"/>
    </justification>
  </clause>

  <clause id="14400">
    <literal><![CDATA[
      (x * T(y,T(z,x))) \ (K(y,z) * u) = L((x * y) \ u,x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,7698,a(flip),b,14395,a)].">
      <j1 rule="hyper" parents="63 7698 14395"/>
    </justification>
  </clause>

  <clause id="14402">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(13984(a,2),14338(a,1))].">
      <j1 rule="para" parents="13984 14338"/>
    </justification>
  </clause>

  <clause id="14403">
    <literal><![CDATA[
      L(x,y \ z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(14346(a,2),14338(a,1))].">
      <j1 rule="para" parents="14346 14338"/>
    </justification>
  </clause>

  <clause id="14404">
    <literal><![CDATA[
      L(x,y,K(z,L(u,w,x))) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(9767(a,1),14358(a,1,3))].">
      <j1 rule="para" parents="9767 14358"/>
    </justification>
  </clause>

  <clause id="14405">
    <literal><![CDATA[
      L(x,y,K(z,L(u,w,x))) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,14337,a,b,14404,a),flip(a)].">
      <j1 rule="hyper" parents="347 14337 14404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14406">
    <literal><![CDATA[
      L(x * y,z,K(x,u)) = x * L(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(14338,a,14362,a)].">
      <j1 rule="hyper" parents="14338 14362"/>
    </justification>
  </clause>

  <clause id="14407">
    <literal><![CDATA[
      L(x / y,z,K(u,y)) = L(x,z,K(u,y)) / y
    ]]></literal>
    <justification jstring="[hyper(347,a,14337,a,b,14369,a)].">
      <j1 rule="hyper" parents="347 14337 14369"/>
    </justification>
  </clause>

  <clause id="14408">
    <literal><![CDATA[
      L(x,y * z,K(u,y)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,14341,a(flip),b,14387,a),flip(a)].">
      <j1 rule="hyper" parents="347 14341 14387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14409">
    <literal><![CDATA[
      T(x,a(y,y * z,u)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(14386,a,14408,a)].">
      <j1 rule="hyper" parents="14386 14408"/>
    </justification>
  </clause>

  <clause id="14410">
    <literal><![CDATA[
      T(x,a(y,y * z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,14337,a(flip),b,14409,a),flip(a)].">
      <j1 rule="hyper" parents="347 14337 14409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14411">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = T(x,a(z \ y,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14145,a(flip),b,14410,a)].">
      <j1 rule="hyper" parents="63 14145 14410"/>
    </justification>
  </clause>

  <clause id="14412">
    <literal><![CDATA[
      T(x,a(y,y \ z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),14410(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 14410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14413">
    <literal><![CDATA[
      T(x,y \ (((z * y) \ z) \ 1)) = T(x,a(z * y,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,13267,a(flip),b,14412,a)].">
      <j1 rule="hyper" parents="63 13267 14412"/>
    </justification>
  </clause>

  <clause id="14414">
    <literal><![CDATA[
      L(x * K(y,x),z,u) \ (x * K(y,x)) = L(x,z,u) \ L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14388(a,1),11202(a,2,2))].">
      <j1 rule="para" parents="14388 11202"/>
    </justification>
  </clause>

  <clause id="14415">
    <literal><![CDATA[
      R(x,y,z) * L(x \ u,y,K(z,x)) = (u / x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(14393(a,2),14122(a,1,2))].">
      <j1 rule="para" parents="14393 14122"/>
    </justification>
  </clause>

  <clause id="14416">
    <literal><![CDATA[
      R(x,y,z) * L(x \ u,y,K(z,x)) != w
    ]]></literal>
    <literal><![CDATA[
      (u / x) * R(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(14393(a,2),14123(a,1,2))].">
      <j1 rule="para" parents="14393 14123"/>
    </justification>
  </clause>

  <clause id="14417">
    <literal><![CDATA[
      L(x * y,z,K(u,x)) = x * L(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(37,a,949,a(flip),b,14407,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="37 949 14407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14418">
    <literal><![CDATA[
      L(x * y,z,K(u,y)) = L(x,z,K(u,y)) * y
    ]]></literal>
    <justification jstring="[hyper(34,a,3374,a(flip),b,14417,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 3374 14417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14420">
    <literal><![CDATA[
      L(x * y,z,K(u,y)) = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,14394,a(flip),b,14418,a),flip(a)].">
      <j1 rule="hyper" parents="347 14394 14418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14421">
    <literal><![CDATA[
      a(x,y,z) * (x \ 1) = (x \ 1) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,8136,a(flip),b,14340,a),flip(a)].">
      <j1 rule="hyper" parents="133 8136 14340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14422">
    <literal><![CDATA[
      L(T(x,a(y,z,u)),z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(14340(a,1),318(a,1))].">
      <j1 rule="para" parents="14340 318"/>
    </justification>
  </clause>

  <clause id="14423">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),a(z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(14340(a,1),362(a,1,1))].">
      <j1 rule="para" parents="14340 362"/>
    </justification>
  </clause>

  <clause id="14424">
    <literal><![CDATA[
      (x / y) * K(y,a(z,u,w)) = x / L(y,u,K(z,w))
    ]]></literal>
    <justification jstring="[para(14340(a,1),6126(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14340 6126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14425">
    <literal><![CDATA[
      L(a(x,y,y),z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y) = v5
    ]]></literal>
    <justification jstring="[para(12664(a,1),14422(a,1,1)),flip(b)].">
      <j1 rule="para" parents="12664 14422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14426">
    <literal><![CDATA[
      K(x,y) \ L((z * K(x,L(y,z,a(u,w,v5)))) / a(u,w,v5),w,K(v5,u)) = T(a(u,w,v5) \ z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(462,a,14352,a,b,14221,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="462 14352 14221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14427">
    <literal><![CDATA[
      L(x,y,K(x * z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(14397,a,14396,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14397 14396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14428">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(14030(a,1),14397(a,1,2))].">
      <j1 rule="para" parents="14030 14397"/>
    </justification>
  </clause>

  <clause id="14430">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(14390(a,1),14402(a,1))].">
      <j1 rule="para" parents="14390 14402"/>
    </justification>
  </clause>

  <clause id="14431">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(14337(a,1),14430(a,1))].">
      <j1 rule="para" parents="14337 14430"/>
    </justification>
  </clause>

  <clause id="14432">
    <literal><![CDATA[
      L(a(x,y,z) \ u,y,K(z,x)) = u / a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(14431,a,14035,a)].">
      <j1 rule="hyper" parents="14431 14035"/>
    </justification>
  </clause>

  <clause id="14433">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(14431,a,14231,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14431 14231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14434">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(14231(a,2),14431(a,1))].">
      <j1 rule="para" parents="14231 14431"/>
    </justification>
  </clause>

  <clause id="14435">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = L(x,x * z,K(u,y))
    ]]></literal>
    <justification jstring="[para(11054(a,1),14433(a,1,1,2))].">
      <j1 rule="para" parents="11054 14433"/>
    </justification>
  </clause>

  <clause id="14436">
    <literal><![CDATA[
      L(x,y * z,K(y,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(14403,a,12388,a)].">
      <j1 rule="hyper" parents="14403 12388"/>
    </justification>
  </clause>

  <clause id="14437">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z * y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(9(a,1),14403(a,1,2))].">
      <j1 rule="para" parents="9 14403"/>
    </justification>
  </clause>

  <clause id="14438">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(6643,a,14436,a),flip(a)].">
      <j1 rule="hyper" parents="6643 14436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14439">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,z) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(14436(a,1),6644(a,1,1))].">
      <j1 rule="para" parents="14436 6644"/>
    </justification>
  </clause>

  <clause id="14440">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14436(a,1),6643(a,1))].">
      <j1 rule="para" parents="14436 6643"/>
    </justification>
  </clause>

  <clause id="14441">
    <literal><![CDATA[
      L(x,T(y,z),T(u,y)) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(7188,a,14438,a),flip(a)].">
      <j1 rule="hyper" parents="7188 14438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14443">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) * (L(x,y,z) \ w) = L(x,y,z) \ (L(x,y,T(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(14438(a,1),1402(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14438 1402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14444">
    <literal><![CDATA[
      L(x,y,T(z,u)) \ L(x,y,z) = a(u,y,K(z,L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(14438(a,1),14361(a,1,1))].">
      <j1 rule="para" parents="14438 14361"/>
    </justification>
  </clause>

  <clause id="14445">
    <literal><![CDATA[
      L(x,T(y,z),(y / z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(y / z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(14441(a,1),12392(a,1))].">
      <j1 rule="para" parents="14441 12392"/>
    </justification>
  </clause>

  <clause id="14446">
    <literal><![CDATA[
      L(L(x,y,K(z * u,u \ 1)),y,z * u) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,11448,a(flip),b,14439,a),flip(a)].">
      <j1 rule="hyper" parents="347 11448 14439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14447">
    <literal><![CDATA[
      (x / y) * L(y,z,K(u,w)) = x * a(y,z,K(u,w))
    ]]></literal>
    <justification jstring="[para(13960(a,2),14353(a,2,2))].">
      <j1 rule="para" parents="13960 14353"/>
    </justification>
  </clause>

  <clause id="14448">
    <literal><![CDATA[
      x * (L(x,y,K(z,u)) \ w) = a(u,y,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(12681(a,2),14360(a,2,1))].">
      <j1 rule="para" parents="12681 14360"/>
    </justification>
  </clause>

  <clause id="14449">
    <literal><![CDATA[
      R(x,y,a(z,u,K(w,v5))) = L(x,y,a(z,u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(12681(a,2),14379(a,2,3))].">
      <j1 rule="para" parents="12681 14379"/>
    </justification>
  </clause>

  <clause id="14450">
    <literal><![CDATA[
      L(T(x,y),z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(14389(a,1),11154(a,1))].">
      <j1 rule="para" parents="14389 11154"/>
    </justification>
  </clause>

  <clause id="14451">
    <literal><![CDATA[
      T(T(x,y),a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(14337(a,1),14450(a,1))].">
      <j1 rule="para" parents="14337 14450"/>
    </justification>
  </clause>

  <clause id="14452">
    <literal><![CDATA[
      L(T(x,y),z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(14399(a,1),14450(a,1))].">
      <j1 rule="para" parents="14399 14450"/>
    </justification>
  </clause>

  <clause id="14453">
    <literal><![CDATA[
      T(x,a(a(y,x,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,L(a(y,x,z),u,w)) = v5
    ]]></literal>
    <justification jstring="[para(12669(a,1),14451(a,1,1))].">
      <j1 rule="para" parents="12669 14451"/>
    </justification>
  </clause>

  <clause id="14454">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,14145,a(flip),b,14411,a),flip(a)].">
      <j1 rule="hyper" parents="347 14145 14411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14455">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,14337,a,b,14454,a),flip(a)].">
      <j1 rule="hyper" parents="347 14337 14454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14456">
    <literal><![CDATA[
      L(x,(y \ z) * u,K(y,z)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(14338,a,14455,a)].">
      <j1 rule="hyper" parents="14338 14455"/>
    </justification>
  </clause>

  <clause id="14457">
    <literal><![CDATA[
      L(L(x,y,z \ u),y,K(z,u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11444,a(flip),b,14456,a),flip(a)].">
      <j1 rule="hyper" parents="63 11444 14456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14458">
    <literal><![CDATA[
      (x / y) * a(y,z,K(u,w)) = x / L(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[para(13960(a,2),14424(a,1,2))].">
      <j1 rule="para" parents="13960 14424"/>
    </justification>
  </clause>

  <clause id="14459">
    <literal><![CDATA[
      L(x,x * y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14433,a(flip),b,14435,a),flip(a)].">
      <j1 rule="hyper" parents="63 14433 14435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14460">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),14459(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14461">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) = T(L(x,z,K(u,w)),y)
    ]]></literal>
    <justification jstring="[para(14460(a,1),25(a,2,1))].">
      <j1 rule="para" parents="14460 25"/>
    </justification>
  </clause>

  <clause id="14462">
    <literal><![CDATA[
      L(x,x \ y,a(z,u,K(w,v5))) = L(x,y,K(a(z,u,w),v5))
    ]]></literal>
    <justification jstring="[para(12681(a,2),14460(a,1,3))].">
      <j1 rule="para" parents="12681 14460"/>
    </justification>
  </clause>

  <clause id="14463">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ L(x,y,K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(14447(a,1),433(a,1))].">
      <j1 rule="para" parents="14447 433"/>
    </justification>
  </clause>

  <clause id="14464">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(u,y,K(z,x)) \ w = v5
    ]]></literal>
    <justification jstring="[para(14448(a,1),1424(a,1))].">
      <j1 rule="para" parents="14448 1424"/>
    </justification>
  </clause>

  <clause id="14465">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(T(x,y),z,K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(14461(a,2),5652(a,1))].">
      <j1 rule="para" parents="14461 5652"/>
    </justification>
  </clause>

  <clause id="14466">
    <literal><![CDATA[
      K(x,y) * L(x,z,T(u,y)) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(14439(a,1),14368(a,1,2))].">
      <j1 rule="para" parents="14439 14368"/>
    </justification>
  </clause>

  <clause id="14467">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,u) = x \ L(x,z,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(128,a,14466,a(flip),b,4944,a)].">
      <j1 rule="hyper" parents="128 14466 4944"/>
    </justification>
  </clause>

  <clause id="14468">
    <literal><![CDATA[
      L(T(x,y),z,u) \ T(x,y) = L(x,z,T(u,y)) \ x
    ]]></literal>
    <justification jstring="[para(14466(a,1),13154(a,1,1))].">
      <j1 rule="para" parents="14466 13154"/>
    </justification>
  </clause>

  <clause id="14469">
    <literal><![CDATA[
      x * T(x \ L(x,y,z),u) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(3551,a,14467,a)].">
      <j1 rule="hyper" parents="3551 14467"/>
    </justification>
  </clause>

  <clause id="14470">
    <literal><![CDATA[
      T(L(T(x,y),z,u) \ T(x,y),w) \ T(x,y) = L(T(x,y),z,u) * K(w,L(x,z,T(u,y)) \ x)
    ]]></literal>
    <justification jstring="[para(14468(a,1),7500(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14468 7500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14471">
    <literal><![CDATA[
      L(x,1 / T(y,z),K(y,u)) * (K(y,u) / T(y,z)) = (x * (1 / T(y,z))) * K(y,u)
    ]]></literal>
    <justification jstring="[para(6577(a,1),14370(a,1,2))].">
      <j1 rule="para" parents="6577 14370"/>
    </justification>
  </clause>

  <clause id="14472">
    <literal><![CDATA[
      L(T(x,y) / z,z,K(y,x)) = x / (z * K(y,x))
    ]]></literal>
    <justification jstring="[para(4929(a,2),14372(a,1,1,1))].">
      <j1 rule="para" parents="4929 14372"/>
    </justification>
  </clause>

  <clause id="14473">
    <literal><![CDATA[
      K(x,y) * ((K(y,x) * z) * u) = z * L(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(5273,a,14382,a)].">
      <j1 rule="hyper" parents="5273 14382"/>
    </justification>
  </clause>

  <clause id="14474">
    <literal><![CDATA[
      (x * y) * (z * L(u,z,K(y,x))) = (y * x) * ((K(x,y) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(134,a,14382,a(flip),b,10272,a),flip(a)].">
      <j1 rule="hyper" parents="134 14382 10272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14475">
    <literal><![CDATA[
      x \ (K(y,z) * R(K(z,y) * x,u,u \ 1)) = L(a(K(z,y) * x,u,u \ 1),x,K(y,z))
    ]]></literal>
    <justification jstring="[para(853(a,1),14385(a,1,1)),flip(a)].">
      <j1 rule="para" parents="853 14385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14476">
    <literal><![CDATA[
      T(x,y \ (((z * y) \ z) \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,12968,a(flip),b,14413,a),flip(a)].">
      <j1 rule="hyper" parents="347 12968 14413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14478">
    <literal><![CDATA[
      T(x,(y \ z) \ ((z \ y) \ 1)) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),14476(a,1,2,2,1,1))].">
      <j1 rule="para" parents="10 14476"/>
    </justification>
  </clause>

  <clause id="14479">
    <literal><![CDATA[
      T(x,(y \ (y / z)) \ (z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(83(a,1),14478(a,1,2,2,1))].">
      <j1 rule="para" parents="83 14478"/>
    </justification>
  </clause>

  <clause id="14480">
    <literal><![CDATA[
      T(T(x,(y \ (y / z)) * (z \ 1)),u / (y \ (y / z))) = T(x,u * (y \ (y / z)))
    ]]></literal>
    <justification jstring="[para(14479(a,1),13852(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14479 13852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14481">
    <literal><![CDATA[
      T((x / y) * L(y,x,K(z,u)),y) = y \ (K(z,u) * ((K(u,z) * x) * y))
    ]]></literal>
    <justification jstring="[hyper(462,a,14473,a,b,1999,a)].">
      <j1 rule="hyper" parents="462 14473 1999"/>
    </justification>
  </clause>

  <clause id="14482">
    <literal><![CDATA[
      L(R(x,y,z),y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14395(a,1),14378(a,1))].">
      <j1 rule="para" parents="14395 14378"/>
    </justification>
  </clause>

  <clause id="14485">
    <literal><![CDATA[
      L(x,y,T(z,u)) \ L(x,y,z) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(7612(a,1),14444(a,2,3))].">
      <j1 rule="para" parents="7612 14444"/>
    </justification>
  </clause>

  <clause id="14486">
    <literal><![CDATA[
      L(a(x,y,K(z,u)) \ w,L(u,y,T(z,x)) \ L(u,y,z),L(u,y,T(z,x))) = L(u,y,z) \ (L(u,y,T(z,x)) * w)
    ]]></literal>
    <justification jstring="[para(14485(a,1),561(a,1,1,1))].">
      <j1 rule="para" parents="14485 561"/>
    </justification>
  </clause>

  <clause id="14488">
    <literal><![CDATA[
      L(x,x \ y,a(z,u,K(w,v5))) = L(x,y,a(z,u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(12681(a,2),14462(a,2,3))].">
      <j1 rule="para" parents="12681 14462"/>
    </justification>
  </clause>

  <clause id="14489">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) \ (y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * K(z,u) = w
    ]]></literal>
    <justification jstring="[para(14373(a,2),359(a,1,1))].">
      <j1 rule="para" parents="14373 359"/>
    </justification>
  </clause>

  <clause id="14490">
    <literal><![CDATA[
      L(L(x,y,K(z,u * z)),y,u * z) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(11517(a,1),14446(a,1,1))].">
      <j1 rule="para" parents="11517 14446"/>
    </justification>
  </clause>

  <clause id="14491">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,u * z) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(11439(a,1),14490(a,1,1))].">
      <j1 rule="para" parents="11439 14490"/>
    </justification>
  </clause>

  <clause id="14492">
    <literal><![CDATA[
      L(L(x,y,z * u),y,K(u,z)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(1094,a,14491,a)].">
      <j1 rule="hyper" parents="1094 14491"/>
    </justification>
  </clause>

  <clause id="14493">
    <literal><![CDATA[
      ((x * y) * (z * L(u,z,K(y,x)))) / T((x * y) * z,L(u,z,K(y,x))) = L(u,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13760,a(flip),b,14491,a)].">
      <j1 rule="hyper" parents="63 13760 14491"/>
    </justification>
  </clause>

  <clause id="14494">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ L(x,y,K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(12603(a,2),14463(a,1))].">
      <j1 rule="para" parents="12603 14463"/>
    </justification>
  </clause>

  <clause id="14495">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(u,w) = x * (L(x,y,z) \ K(u,w))
    ]]></literal>
    <justification jstring="[hyper(13084,a,14043,a),flip(a)].">
      <j1 rule="hyper" parents="13084 14043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14497">
    <literal><![CDATA[
      L(x,y,z) * (x \ (x * (L(x,y,z) \ K(u,(L(x,y,z) \ x) \ w)))) = K(u,L(x,y,z) * (x \ w))
    ]]></literal>
    <justification jstring="[para(14495(a,1),11322(a,1,2,2))].">
      <j1 rule="para" parents="14495 11322"/>
    </justification>
  </clause>

  <clause id="14498">
    <literal><![CDATA[
      K(x,y) / (z * (L(z,u,w) \ K(x,y))) = (L(z,u,w) \ z) \ 1
    ]]></literal>
    <justification jstring="[para(14495(a,1),13317(a,1,2))].">
      <j1 rule="para" parents="14495 13317"/>
    </justification>
  </clause>

  <clause id="14499">
    <literal><![CDATA[
      K(x,L(y,z,R(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,v5))) = v6
    ]]></literal>
    <justification jstring="[para(14137(a,1),13996(a,1))].">
      <j1 rule="para" parents="14137 13996"/>
    </justification>
  </clause>

  <clause id="14500">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,L(y \ 1,y,z))) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(14499,a,11242,a)].">
      <j1 rule="hyper" parents="14499 11242"/>
    </justification>
  </clause>

  <clause id="14501">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) * K(x,K(y,z)) = a(z,u,K(x,K(w,y)))
    ]]></literal>
    <justification jstring="[para(7293(a,1),14150(a,1,2))].">
      <j1 rule="para" parents="7293 14150"/>
    </justification>
  </clause>

  <clause id="14502">
    <literal><![CDATA[
      K(x,K(y,z \ (u * ((u \ z) * w)))) = a(w,u \ z,K(u,K(x,y))) * K(w,K(x,y))
    ]]></literal>
    <justification jstring="[para(98(a,2),14155(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="98 14155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14503">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ y)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(13995,a,14195,a),flip(a)].">
      <j1 rule="hyper" parents="13995 14195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14504">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(14195(a,1),13995(a,1))].">
      <j1 rule="para" parents="14195 13995"/>
    </justification>
  </clause>

  <clause id="14505">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ 1)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14194,a,b,14503,a)].">
      <j1 rule="hyper" parents="63 14194 14503"/>
    </justification>
  </clause>

  <clause id="14506">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ u)) = K(x,L(y,z,w \ 1))
    ]]></literal>
    <justification jstring="[para(9(a,1),14505(a,1,2,3,1)),flip(a)].">
      <j1 rule="para" parents="9 14505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14507">
    <literal><![CDATA[
      K(x,L(y,z * u,(w * u) \ w)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(347,a,14210,a(flip),b,14506,a),flip(a)].">
      <j1 rule="hyper" parents="347 14210 14506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14508">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,y / (u * ((y * z) \ y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14237,a(flip),b,14506,a),flip(a)].">
      <j1 rule="hyper" parents="63 14237 14506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14509">
    <literal><![CDATA[
      K(x,L(y,z,L(u \ 1,u,w))) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[para(244(a,2),14506(a,1,2,3))].">
      <j1 rule="para" parents="244 14506"/>
    </justification>
  </clause>

  <clause id="14510">
    <literal><![CDATA[
      K(x,L(y \ (((z * u) \ z) \ w),y,u \ 1)) = K(x,(((z * u) \ z) * y) \ w)
    ]]></literal>
    <justification jstring="[para(329(a,1),14506(a,1,2)),flip(a)].">
      <j1 rule="para" parents="329 14506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14511">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ 1)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(14194(a,2),14504(a,1))].">
      <j1 rule="para" parents="14194 14504"/>
    </justification>
  </clause>

  <clause id="14512">
    <literal><![CDATA[
      K(x,L(y,a(z,u,u \ 1),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,14073,a(flip),b,14203,a),flip(a)].">
      <j1 rule="hyper" parents="130 14073 14203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14513">
    <literal><![CDATA[
      K(x,L(y \ a(z,u,u \ 1),y,z)) = K(x,y \ a(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(11196,a,14512,a)].">
      <j1 rule="hyper" parents="11196 14512"/>
    </justification>
  </clause>

  <clause id="14514">
    <literal><![CDATA[
      a(T(x,y),z,K(u,x * y)) = K(L(x,z,u) * y,x * y)
    ]]></literal>
    <justification jstring="[para(267(a,1),14234(a,1,1)),flip(a)].">
      <j1 rule="para" parents="267 14234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14515">
    <literal><![CDATA[
      T(K(x,T(y,z)) * u,w) / K(x,y) = T(K(x,y) * u,w) / T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(13544(a,1),14311(a,1,1,1))].">
      <j1 rule="para" parents="13544 14311"/>
    </justification>
  </clause>

  <clause id="14516">
    <literal><![CDATA[
      K(x,K(y * (z \ u),z / y) * w) = K(x,K(y * (u / z),u) * w)
    ]]></literal>
    <justification jstring="[para(14330(a,1),12035(a,1,2,1))].">
      <j1 rule="para" parents="14330 12035"/>
    </justification>
  </clause>

  <clause id="14517">
    <literal><![CDATA[
      K(K(x,L(y,z,u)) * K(y,x),w) = a(y,z,K(w,K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,10692,a(flip),b,14501,a)].">
      <j1 rule="hyper" parents="63 10692 14501"/>
    </justification>
  </clause>

  <clause id="14518">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(9256(a,1),14517(a,1,1))].">
      <j1 rule="para" parents="9256 14517"/>
    </justification>
  </clause>

  <clause id="14519">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(u,x)))
    ]]></literal>
    <justification jstring="[para(7293(a,1),14518(a,2,3))].">
      <j1 rule="para" parents="7293 14518"/>
    </justification>
  </clause>

  <clause id="14520">
    <literal><![CDATA[
      L(K(x,y),z,u) * (u * (K(y,x) * z)) = z * T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(8257,a,14118,a)].">
      <j1 rule="hyper" parents="8257 14118"/>
    </justification>
  </clause>

  <clause id="14521">
    <literal><![CDATA[
      T(x,a(a(y,z,u),w,v5)) = T(x,a(y,w,a(v5,z,u)))
    ]]></literal>
    <justification jstring="[hyper(14164,a,14027,a)].">
      <j1 rule="hyper" parents="14164 14027"/>
    </justification>
  </clause>

  <clause id="14522">
    <literal><![CDATA[
      T(x,a(y,z,a(u,x,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,L(a(y,x,w),z,u)) = v5
    ]]></literal>
    <justification jstring="[para(14521(a,1),14453(a,1))].">
      <j1 rule="para" parents="14521 14453"/>
    </justification>
  </clause>

  <clause id="14523">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,y / z,z))) = K(x,K(w,y / ((1 / u) * z)))
    ]]></literal>
    <justification jstring="[para(13223(a,1),14176(a,1,2))].">
      <j1 rule="para" parents="13223 14176"/>
    </justification>
  </clause>

  <clause id="14524">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),x) * a(y,z,K(x,u)) = K(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(14232,a,8357,a(flip))].">
      <j1 rule="hyper" parents="14232 8357"/>
    </justification>
  </clause>

  <clause id="14525">
    <literal><![CDATA[
      K(x,(y * z) \ R(y,u,u \ 1)) = K(x,z \ a(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[para(855(a,1),14513(a,1,2))].">
      <j1 rule="para" parents="855 14513"/>
    </justification>
  </clause>

  <clause id="14526">
    <literal><![CDATA[
      T((x * (K(y,z) * u)) * L(K(z,y),u,x),K(y,L(z,u,x))) = u * T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,9037,a,b,14520,a)].">
      <j1 rule="hyper" parents="63 9037 14520"/>
    </justification>
  </clause>

  <clause id="14527">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) * (v5 \ 1)))) = K(x,y * (z / (K(u,w) / v5)))
    ]]></literal>
    <justification jstring="[para(13738(a,1),13144(a,1,2,2,2))].">
      <j1 rule="para" parents="13738 13144"/>
    </justification>
  </clause>

  <clause id="14528">
    <literal><![CDATA[
      T(((a(x,y,z) \ 1) * u) * a(x,y,z),a(x,y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,a(x,y,z),a(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(13167(a,2),3226(a,1))].">
      <j1 rule="para" parents="13167 3226"/>
    </justification>
  </clause>

  <clause id="14529">
    <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(1993(a,1),13386(a,1,1))].">
      <j1 rule="para" parents="1993 13386"/>
    </justification>
  </clause>

  <clause id="14530">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ u)) = K(x,K(z,y)) * K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[para(12133(a,1),13517(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12133 13517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14533">
    <literal><![CDATA[
      T(x * K(x * K(y,z),u),K(z,y)) = K(z,y) * T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,5256,a(flip),b,13576,a),flip(a)].">
      <j1 rule="hyper" parents="347 5256 13576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14535">
    <literal><![CDATA[
      ((x * ((x * y) / x)) / z) \ y = ((x * y) / z) \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(111(a,1),13756(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="111 13756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14536">
    <literal><![CDATA[
      ((x * ((x * y) / x)) / z) \ y = ((x * y) / z) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4270(a,1),14535(a,2,2))].">
      <j1 rule="para" parents="4270 14535"/>
    </justification>
  </clause>

  <clause id="14537">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) * (1 \ T(1 / (y / z),y))) = K(x,(1 \ T(1 / (y / z),y)) * L(T(1 / (y / z),y) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(5869(a,1),13790(a,1,2,1,1))].">
      <j1 rule="para" parents="5869 13790"/>
    </justification>
  </clause>

  <clause id="14538">
    <literal><![CDATA[
      K(x,L(((y * (z * y)) / y) \ y,u,w) * (a(y,z,y) \ z)) = K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w))
    ]]></literal>
    <justification jstring="[para(9986(a,2),13790(a,1,2,2))].">
      <j1 rule="para" parents="9986 13790"/>
    </justification>
  </clause>

  <clause id="14539">
    <literal><![CDATA[
      T(x,T(T(y * K(y / z,u),z),w)) = T(x,T(z * T(y / z,u),w))
    ]]></literal>
    <justification jstring="[hyper(347,a,10444,a(flip),b,13831,a),flip(a)].">
      <j1 rule="hyper" parents="347 10444 13831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14540">
    <literal><![CDATA[
      (x * R(y,z,u)) / (y * T(x,L(y,z,u))) = R(y \ R(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(14104(a,1),13916(a,1,2,2))].">
      <j1 rule="para" parents="14104 13916"/>
    </justification>
  </clause>

  <clause id="14541">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (z * u) = w
    ]]></literal>
    <justification jstring="[para(13975(a,1),13963(a,1))].">
      <j1 rule="para" parents="13975 13963"/>
    </justification>
  </clause>

  <clause id="14542">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u / w,y)) = K(x,L(y,z,u / (y * w)))
    ]]></literal>
    <justification jstring="[para(11284(a,1),14074(a,1,2))].">
      <j1 rule="para" parents="11284 14074"/>
    </justification>
  </clause>

  <clause id="14543">
    <literal><![CDATA[
      K(x,L(L(y,z,u),z,u \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13977,a(flip),b,14193,a),flip(a)].">
      <j1 rule="hyper" parents="63 13977 14193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14544">
    <literal><![CDATA[
      K(x,L(L(y,z,u \ 1),z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(30(a,1),14543(a,1,2))].">
      <j1 rule="para" parents="30 14543"/>
    </justification>
  </clause>

  <clause id="14545">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y \ 1)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(329(a,1),14543(a,1,2,1))].">
      <j1 rule="para" parents="329 14543"/>
    </justification>
  </clause>

  <clause id="14546">
    <literal><![CDATA[
      K((x * y) \ z,L(u,z,x \ 1)) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(14208,a,14544,a)].">
      <j1 rule="hyper" parents="14208 14544"/>
    </justification>
  </clause>

  <clause id="14547">
    <literal><![CDATA[
      x * (y * K(z,L(u,y,x \ 1))) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14544(a,1),11073(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14544 11073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14548">
    <literal><![CDATA[
      (K(x,L(y,z,u \ 1)) * z) * u = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(14544(a,1),14092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14544 14092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14549">
    <literal><![CDATA[
      (x \ y) * K(z,L(u,y,x \ 1)) = x \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(14544(a,1),14221(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14544 14221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14550">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) * (z / u) = (K(x,y) * z) / u
    ]]></literal>
    <justification jstring="[para(14544(a,1),14240(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14544 14240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14551">
    <literal><![CDATA[
      K(x,L(T(y,z * u),u,z \ 1)) = K(x,u \ (z \ (y * (z * u))))
    ]]></literal>
    <justification jstring="[para(22(a,2),14545(a,1,2,1))].">
      <j1 rule="para" parents="22 14545"/>
    </justification>
  </clause>

  <clause id="14553">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ ((y \ 1) * z),u) = K(x \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11132,a,b,14546,a)].">
      <j1 rule="hyper" parents="63 11132 14546"/>
    </justification>
  </clause>

  <clause id="14554">
    <literal><![CDATA[
      x * K(y,L(T(z,u * x),x,u \ 1)) = u \ (K(y,z) * (u * x))
    ]]></literal>
    <justification jstring="[hyper(128,a,7104,a(flip),b,14547,a),flip(a)].">
      <j1 rule="hyper" parents="128 7104 14547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14556">
    <literal><![CDATA[
      x * (y * K(z,L(u,y,x \ u))) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14194(a,1),14547(a,1,2,2))].">
      <j1 rule="para" parents="14194 14547"/>
    </justification>
  </clause>

  <clause id="14563">
    <literal><![CDATA[
      (K(x,L(y,z * u,(z \ K(u,z)) \ 1)) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(6540(a,1),14548(a,2,2))].">
      <j1 rule="para" parents="6540 14548"/>
    </justification>
  </clause>

  <clause id="14564">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(34,a,11164,a(flip),b,14549,a),flip(a)].">
      <j1 rule="hyper" parents="34 11164 14549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14565">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,(K(x,y) / x) \ u))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(13757(a,1),14556(a,2,1))].">
      <j1 rule="para" parents="13757 14556"/>
    </justification>
  </clause>

  <clause id="14566">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ ((z \ 1) * u)) = w / (K(y \ (z \ u),x) * w)
    ]]></literal>
    <justification jstring="[para(14553(a,1),5259(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14553 5259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14567">
    <literal><![CDATA[
      x * K(y,x \ (z \ (u * (z * x)))) = z \ (K(y,u) * (z * x))
    ]]></literal>
    <justification jstring="[para(14551(a,1),14554(a,1,2))].">
      <j1 rule="para" parents="14551 14554"/>
    </justification>
  </clause>

  <clause id="14568">
    <literal><![CDATA[
      x \ (K(y,R(z,x,u)) * (x * u)) = u * K(y,u \ (x \ ((z * x) * u)))
    ]]></literal>
    <justification jstring="[para(107(a,1),14567(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="107 14567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14569">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * R(z,x,y))) = a(L(z,y,x),x,y)
    ]]></literal>
    <justification jstring="[para(475(a,1),14252(a,1,2))].">
      <j1 rule="para" parents="475 14252"/>
    </justification>
  </clause>

  <clause id="14570">
    <literal><![CDATA[
      (x * (y * z)) * a(L(z,y,x),x,y) = x * (y * R(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(150,a,14569,a)].">
      <j1 rule="hyper" parents="150 14569"/>
    </justification>
  </clause>

  <clause id="14571">
    <literal><![CDATA[
      x \ (y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(13452(a,1),14489(a,1,1))].">
      <j1 rule="para" parents="13452 14489"/>
    </justification>
  </clause>

  <clause id="14572">
    <literal><![CDATA[
      K(x,y \ L(y,z,u)) = 1 * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(12481(a,1),14524(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12481 14524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14574">
    <literal><![CDATA[
      a(x,L(y,z,u),y) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(13376,a,14529,a),flip(a)].">
      <j1 rule="hyper" parents="13376 14529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14575">
    <literal><![CDATA[
      T(x * K(x * K(y,z),u),K(y,z)) = K(z,y) * T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(7362,a,14533,a)].">
      <j1 rule="hyper" parents="7362 14533"/>
    </justification>
  </clause>

  <clause id="14576">
    <literal><![CDATA[
      (x * R(y,z,u)) / L(x * y,z,K(u,y)) = R(y \ R(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(14420(a,2),14540(a,1,2))].">
      <j1 rule="para" parents="14420 14540"/>
    </justification>
  </clause>

  <clause id="14577">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / ((y \ 1) * z)) = w
    ]]></literal>
    <justification jstring="[para(13270(a,1),13172(a,1))].">
      <j1 rule="para" parents="13270 13172"/>
    </justification>
  </clause>

  <clause id="14578">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (y \ T(R(y,z,u),T(x,y))) = R(y,z,u) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(14081(a,1),13268(a,1,1))].">
      <j1 rule="para" parents="14081 13268"/>
    </justification>
  </clause>

  <clause id="14579">
    <literal><![CDATA[
      (x * (y \ (x \ 1))) * T(y,y \ (x \ 1)) = a(x,y \ (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(6155,a,13389,a)].">
      <j1 rule="hyper" parents="6155 13389"/>
    </justification>
  </clause>

  <clause id="14580">
    <literal><![CDATA[
      (x * ((x \ 1) / y)) * y = a(x,y \ (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(9660,a,14579,a)].">
      <j1 rule="hyper" parents="9660 14579"/>
    </justification>
  </clause>

  <clause id="14581">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),T(x,z)) = K(y * K((x \ 1) \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(13458,a,10475,a),flip(a)].">
      <j1 rule="hyper" parents="13458 10475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14582">
    <literal><![CDATA[
      K(x * K((y \ 1) \ x,z),y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(13457,a,14581,a),flip(a)].">
      <j1 rule="hyper" parents="13457 14581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14584">
    <literal><![CDATA[
      K(x * K(y * x,z),y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(12975(a,1),14582(a,1,1,2))].">
      <j1 rule="para" parents="12975 14582"/>
    </justification>
  </clause>

  <clause id="14585">
    <literal><![CDATA[
      T(x,x * (y * K(x * y,z))) * K(y,T(x,z)) = L(x,y * K(x * y,z),x)
    ]]></literal>
    <justification jstring="[hyper(134,a,14584,a(flip),b,5380,a(flip))].">
      <j1 rule="hyper" parents="134 14584 5380"/>
    </justification>
  </clause>

  <clause id="14586">
    <literal><![CDATA[
      K(x / (a(y,z,y) \ (u \ K(y * z,y))),w) = K(x * (K(y,z) * u),w)
    ]]></literal>
    <justification jstring="[para(11890(a,1),13469(a,1,1,2))].">
      <j1 rule="para" parents="11890 13469"/>
    </justification>
  </clause>

  <clause id="14587">
    <literal><![CDATA[
      K(x,L(T(y \ z,z * (u / y)),y,y \ u)) = K(x,((u / y) * z) / u)
    ]]></literal>
    <justification jstring="[para(25(a,2),13701(a,1,2))].">
      <j1 rule="para" parents="25 13701"/>
    </justification>
  </clause>

  <clause id="14588">
    <literal><![CDATA[
      K(x,L(T(y \ z,y * (u / z)),y,z \ u)) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[para(25(a,2),13702(a,1,2))].">
      <j1 rule="para" parents="25 13702"/>
    </justification>
  </clause>

  <clause id="14589">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) * T(u * (z / y),K(x,y)) = u * (z / T(y,x))
    ]]></literal>
    <justification jstring="[para(11049(a,1),13769(a,1,1))].">
      <j1 rule="para" parents="11049 13769"/>
    </justification>
  </clause>

  <clause id="14590">
    <literal><![CDATA[
      (x * (L(1 / y,y,x) * z)) / T(x / y,z) = L(z,L(y,y,x),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3370,a(flip),b,13771,a),flip(a)].">
      <j1 rule="hyper" parents="347 3370 13771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14591">
    <literal><![CDATA[
      a(x,y,z) = (z * (x * y)) / (L(z,y,x) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,13371,a,b,13911,a)].">
      <j1 rule="hyper" parents="347 13371 13911"/>
    </justification>
  </clause>

  <clause id="14592">
    <literal><![CDATA[
      a(x,y,z) * (L(z,y,x) * (x * y)) = z * (x * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,13371,a,b,13911,a)].">
      <j1 rule="hyper" parents="133 13371 13911"/>
    </justification>
  </clause>

  <clause id="14593">
    <literal><![CDATA[
      a(x,y,T(z,x * y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,13943,a(flip),b,14591,a)].">
      <j1 rule="hyper" parents="347 13943 14591"/>
    </justification>
  </clause>

  <clause id="14594">
    <literal><![CDATA[
      a(x,y,z) \ (z * (x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(132,a,14591,a,b,172,a)].">
      <j1 rule="hyper" parents="132 14591 172"/>
    </justification>
  </clause>

  <clause id="14595">
    <literal><![CDATA[
      a(x,y,z) = (L(z,y,x) * (x * y)) \ (z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1629,a,b,14593,a),flip(a)].">
      <j1 rule="hyper" parents="63 1629 14593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14596">
    <literal><![CDATA[
      a(x,T(y,x),T(z,y * x)) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(111(a,1),14593(a,1,3,2))].">
      <j1 rule="para" parents="111 14593"/>
    </justification>
  </clause>

  <clause id="14597">
    <literal><![CDATA[
      (x * y) / a(y / z,z,x) = L(x,z,z \ y) * y
    ]]></literal>
    <justification jstring="[para(14593(a,1),10602(a,1,2))].">
      <j1 rule="para" parents="14593 10602"/>
    </justification>
  </clause>

  <clause id="14598">
    <literal><![CDATA[
      (L(x,y,z) * (y * z)) \ (x * (y * z)) = a(z,T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10257,a,b,14596,a)].">
      <j1 rule="hyper" parents="63 10257 14596"/>
    </justification>
  </clause>

  <clause id="14599">
    <literal><![CDATA[
      a(x,x,y) * L(y,x,x) = y
    ]]></literal>
    <justification jstring="[hyper(146,a,14592,a)].">
      <j1 rule="hyper" parents="146 14592"/>
    </justification>
  </clause>

  <clause id="14600">
    <literal><![CDATA[
      L(x,y,y) \ x = a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(3312,a,14599,a)].">
      <j1 rule="hyper" parents="3312 14599"/>
    </justification>
  </clause>

  <clause id="14601">
    <literal><![CDATA[
      a(x,x,y) \ y = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(138,a,14599,a)].">
      <j1 rule="hyper" parents="138 14599"/>
    </justification>
  </clause>

  <clause id="14602">
    <literal><![CDATA[
      L(x,y,y) * a(y,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,11790,a,b,14599,a)].">
      <j1 rule="hyper" parents="63 11790 14599"/>
    </justification>
  </clause>

  <clause id="14603">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,u) \ 1 = a(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,10891,a(flip),b,14600,a)].">
      <j1 rule="hyper" parents="63 10891 14600"/>
    </justification>
  </clause>

  <clause id="14604">
    <literal><![CDATA[
      T(L(x,y,y),z) * a(y,y,x) = K(L(x,y,y),z) * x
    ]]></literal>
    <justification jstring="[hyper(134,a,14600,a(flip),b,5189,a)].">
      <j1 rule="hyper" parents="134 14600 5189"/>
    </justification>
  </clause>

  <clause id="14605">
    <literal><![CDATA[
      a(x,x,y) * (y \ 1) = L(y,x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,14600,a(flip),b,10255,a)].">
      <j1 rule="hyper" parents="133 14600 10255"/>
    </justification>
  </clause>

  <clause id="14606">
    <literal><![CDATA[
      R(x,y,z * L(z,u,u)) = R(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(14600(a,1),2213(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14600 2213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14607">
    <literal><![CDATA[
      a((x \ 1) \ y,(x \ 1) \ y,z) = L(z,x \ y,(x \ 1) \ y) \ z
    ]]></literal>
    <justification jstring="[para(3608(a,1),14600(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3608 14600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14608">
    <literal><![CDATA[
      (x * a(y,y,x)) \ 1 = L(x \ 1,y,y)
    ]]></literal>
    <justification jstring="[para(14600(a,1),4670(a,1,1,2))].">
      <j1 rule="para" parents="14600 4670"/>
    </justification>
  </clause>

  <clause id="14609">
    <literal><![CDATA[
      L(a(x,x,K(y,z) * u),L(K(y,z) * u,x,x),K(z,y)) = (K(z,y) * L(K(y,z) * u,x,x)) \ u
    ]]></literal>
    <justification jstring="[para(14600(a,1),5277(a,1,1))].">
      <j1 rule="para" parents="14600 5277"/>
    </justification>
  </clause>

  <clause id="14610">
    <literal><![CDATA[
      a(x,x,y) \ 1 = y \ L(y,x,x)
    ]]></literal>
    <justification jstring="[para(14600(a,1),10888(a,1,1))].">
      <j1 rule="para" parents="14600 10888"/>
    </justification>
  </clause>

  <clause id="14611">
    <literal><![CDATA[
      x * (a(y,y,x) \ 1) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(14600(a,1),10895(a,1,2,1))].">
      <j1 rule="para" parents="14600 10895"/>
    </justification>
  </clause>

  <clause id="14612">
    <literal><![CDATA[
      R(x,y * (z * a(u,u,z)),w) = R(x,y * L(z,u,u),w)
    ]]></literal>
    <justification jstring="[para(14600(a,1),10902(a,1,2,2,2))].">
      <j1 rule="para" parents="14600 10902"/>
    </justification>
  </clause>

  <clause id="14613">
    <literal><![CDATA[
      (x * y) / L(y * x,z,z) = K(x,y) * a(z,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(220,a,14601,a(flip),b,13747,a)].">
      <j1 rule="hyper" parents="220 14601 13747"/>
    </justification>
  </clause>

  <clause id="14614">
    <literal><![CDATA[
      L(x,y,y) * z != x
    ]]></literal>
    <literal><![CDATA[
      a(y,y,x) = z
    ]]></literal>
    <justification jstring="[para(14602(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="14602 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14615">
    <literal><![CDATA[
      L(x,y,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      a(y,y,x) = z
    ]]></literal>
    <justification jstring="[para(14602(a,1),356(a,1,2))].">
      <j1 rule="para" parents="14602 356"/>
    </justification>
  </clause>

  <clause id="14616">
    <literal><![CDATA[
      x \ (y * L(y \ x,z,z)) = a(z,z,x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,3354,a(flip),b,14610,a)].">
      <j1 rule="hyper" parents="347 3354 14610"/>
    </justification>
  </clause>

  <clause id="14617">
    <literal><![CDATA[
      R(x,y,(z \ L(z,u,u)) \ w) = R(x,y,a(u,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(14610(a,1),2241(a,1,3,1))].">
      <j1 rule="para" parents="14610 2241"/>
    </justification>
  </clause>

  <clause id="14618">
    <literal><![CDATA[
      L(x \ y,x,a(z,z,y) \ 1) = ((L(y,z,z) / y) * x) \ L(y,z,z)
    ]]></literal>
    <justification jstring="[para(14610(a,2),13462(a,1,3))].">
      <j1 rule="para" parents="14610 13462"/>
    </justification>
  </clause>

  <clause id="14619">
    <literal><![CDATA[
      R(x,y,z * a(u,u,z)) = R(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[para(14611(a,1),2204(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14611 2204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14620">
    <literal><![CDATA[
      R(x,y * a(z,z,y),u) = R(x,L(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(14611(a,1),2284(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14611 2284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14621">
    <literal><![CDATA[
      L(x,y * a(z,z,y),u) = L(x,L(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(14611(a,1),3229(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14611 3229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14622">
    <literal><![CDATA[
      T(x,(L(y \ 1,z,z) \ 1) \ u) = T(x,(y * a(z,z,y)) \ u)
    ]]></literal>
    <justification jstring="[para(14608(a,1),3998(a,1,2,1,1))].">
      <j1 rule="para" parents="14608 3998"/>
    </justification>
  </clause>

  <clause id="14623">
    <literal><![CDATA[
      x * (a(y,z,x) \ (y * z)) = L(x,z,y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(13853,a,14594,a)].">
      <j1 rule="hyper" parents="13853 14594"/>
    </justification>
  </clause>

  <clause id="14624">
    <literal><![CDATA[
      (L(L(T(x \ 1,x),y,z),u,w) * (x * x)) \ (L(L(x \ 1,y,z),u,w) * (x * x)) = a(x,x,L(L(x \ 1,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(1213(a,1),14595(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="1213 14595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14625">
    <literal><![CDATA[
      (L(x,y,y \ z) * z) \ (x * z) = a(z / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(214,a,14597,a)].">
      <j1 rule="hyper" parents="214 14597"/>
    </justification>
  </clause>

  <clause id="14626">
    <literal><![CDATA[
      K(x,y) * ((y / z) * (z * x)) = L(x,z,z \ y) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,13749,a,b,14597,a)].">
      <j1 rule="hyper" parents="63 13749 14597"/>
    </justification>
  </clause>

  <clause id="14627">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) \ 1 = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14610(a,2),14603(a,1,1,1))].">
      <j1 rule="para" parents="14610 14603"/>
    </justification>
  </clause>

  <clause id="14628">
    <literal><![CDATA[
      a(x,y,z) \ (x * y) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(34,a,13775,a(flip),b,14623,a),flip(a)].">
      <j1 rule="hyper" parents="34 13775 14623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14629">
    <literal><![CDATA[
      (a(x,y,z) \ (x * y)) * z = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,14628,a,b,xx)].">
      <j1 rule="hyper" parents="133 14628"/>
    </justification>
  </clause>

  <clause id="14630">
    <literal><![CDATA[
      (a(x,y,z) \ (x * y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(14628(a,2),280(a,1,1))].">
      <j1 rule="para" parents="14628 280"/>
    </justification>
  </clause>

  <clause id="14631">
    <literal><![CDATA[
      (a(x,x \ y,z) \ y) * z = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14629(a,1,1,2))].">
      <j1 rule="para" parents="10 14629"/>
    </justification>
  </clause>

  <clause id="14632">
    <literal><![CDATA[
      (a(x,T(y,x),z) \ (y * x)) * z = x * ((x \ (y * x)) * z)
    ]]></literal>
    <justification jstring="[para(22(a,2),14631(a,1,1,1,2))].">
      <j1 rule="para" parents="22 14631"/>
    </justification>
  </clause>

  <clause id="14633">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) = a(x,x,L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(39,a,12592,a,b,14627,a),flip(a)].">
      <j1 rule="hyper" parents="39 12592 14627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14634">
    <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(128,a,14627,a(flip),b,12599,a),flip(a)].">
      <j1 rule="hyper" parents="128 14627 12599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14635">
    <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(14633(a,2),48(a,1))].">
      <j1 rule="para" parents="14633 48"/>
    </justification>
  </clause>

  <clause id="14636">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      a(x,x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(14633(a,2),12597(a,1,1))].">
      <j1 rule="para" parents="14633 12597"/>
    </justification>
  </clause>

  <clause id="14637">
    <literal><![CDATA[
      T(L(x,y,y),z) * a(y,y,x) = K(x,z) * x
    ]]></literal>
    <justification jstring="[para(12971(a,1),14604(a,2,1))].">
      <j1 rule="para" parents="12971 14604"/>
    </justification>
  </clause>

  <clause id="14638">
    <literal><![CDATA[
      T(L(x,y,y),z) * a(y,y,x) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,4977,a,b,14637,a),flip(a)].">
      <j1 rule="hyper" parents="347 4977 14637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14640">
    <literal><![CDATA[
      L(T(x,y),z,z) * a(z,z,x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(25(a,2),14638(a,1,1))].">
      <j1 rule="para" parents="25 14638"/>
    </justification>
  </clause>

  <clause id="14641">
    <literal><![CDATA[
      a(x,x,T(y,z)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(14614,a,14640,a)].">
      <j1 rule="hyper" parents="14614 14640"/>
    </justification>
  </clause>

  <clause id="14642">
    <literal><![CDATA[
      a(x,x,y * z) = a(x,x,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,12444,a(flip),b,14641,a)].">
      <j1 rule="hyper" parents="63 12444 14641"/>
    </justification>
  </clause>

  <clause id="14643">
    <literal><![CDATA[
      (x * y) \ L(x * y,z,z) = a(z,z,y * x) \ 1
    ]]></literal>
    <justification jstring="[para(14642(a,1),14610(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14642 14610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14644">
    <literal><![CDATA[
      L(x * y,z,z) \ (y * x) = K(y,x) * a(z,z,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9730,a(flip),b,14613,a)].">
      <j1 rule="hyper" parents="63 9730 14613"/>
    </justification>
  </clause>

  <clause id="14645">
    <literal><![CDATA[
      R(x,y,(z * L(z,u,u)) \ w) = R(x,y,a(u,u,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3730,a(flip),b,14617,a)].">
      <j1 rule="hyper" parents="63 3730 14617"/>
    </justification>
  </clause>

  <clause id="14646">
    <literal><![CDATA[
      T(x,(y * a(z,z,y)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y \ 1,z,z) * u) = w
    ]]></literal>
    <justification jstring="[para(14622(a,1),13173(a,1))].">
      <j1 rule="para" parents="14622 13173"/>
    </justification>
  </clause>

  <clause id="14647">
    <literal><![CDATA[
      L(x \ y,x,a(z,z,y) \ 1) = ((y \ L(y,z,z)) * x) \ L(y,z,z)
    ]]></literal>
    <justification jstring="[para(3161(a,1),14618(a,2,1,1))].">
      <j1 rule="para" parents="3161 14618"/>
    </justification>
  </clause>

  <clause id="14648">
    <literal><![CDATA[
      K(T(x / y,z) \ 1,L(u,y,y \ z)) = K((x * (y \ z)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,5988,a(flip),b,14154,a),flip(a)].">
      <j1 rule="hyper" parents="347 5988 14154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14649">
    <literal><![CDATA[
      K((x / y) \ 1,T(L(z,y,y \ u),u)) = K((x * (y \ u)) \ u,z)
    ]]></literal>
    <justification jstring="[hyper(7494,a,14648,a)].">
      <j1 rule="hyper" parents="7494 14648"/>
    </justification>
  </clause>

  <clause id="14650">
    <literal><![CDATA[
      K((x / y) \ 1,L(T(z,u),y,y \ u)) = K((x * (y \ u)) \ u,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),14649(a,1,2))].">
      <j1 rule="para" parents="25 14649"/>
    </justification>
  </clause>

  <clause id="14651">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) * K(x,K(z,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z,K(w,L(x,y,u))) = v5
    ]]></literal>
    <justification jstring="[para(7279(a,1),14157(a,1,1,3))].">
      <j1 rule="para" parents="7279 14157"/>
    </justification>
  </clause>

  <clause id="14652">
    <literal><![CDATA[
      a(x,y,K(z,(u / y) \ z)) \ K(x,(y * z) / u) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(8226(a,1),14170(a,1,1,3))].">
      <j1 rule="para" parents="8226 14170"/>
    </justification>
  </clause>

  <clause id="14653">
    <literal><![CDATA[
      (x * y) * K(z,(x * y) \ (u * y)) = (K(z,u / x) * x) * y
    ]]></literal>
    <justification jstring="[hyper(14094,a,14175,a),flip(a)].">
      <j1 rule="hyper" parents="14094 14175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14654">
    <literal><![CDATA[
      (x * y) * K(z,(x * y) \ (u * y)) = (x * K(z,x \ u)) * y
    ]]></literal>
    <justification jstring="[para(7175(a,1),14653(a,2,1))].">
      <j1 rule="para" parents="7175 14653"/>
    </justification>
  </clause>

  <clause id="14655">
    <literal><![CDATA[
      R(T(x * K(y,x),z),y,u) \ ((y * x) * u) = (y * K(z,y \ (y * x))) * u
    ]]></literal>
    <justification jstring="[hyper(9895,a,14654,a)].">
      <j1 rule="hyper" parents="9895 14654"/>
    </justification>
  </clause>

  <clause id="14656">
    <literal><![CDATA[
      K(T(x,y),(z * y) \ u) = K(x,((z \ u) * z) / (y * z))
    ]]></literal>
    <justification jstring="[hyper(14279,a,5172,a)].">
      <j1 rule="hyper" parents="14279 5172"/>
    </justification>
  </clause>

  <clause id="14657">
    <literal><![CDATA[
      K(x,((y \ z) * y) / (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T((y * u) \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(14656(a,1),7488(a,1))].">
      <j1 rule="para" parents="14656 7488"/>
    </justification>
  </clause>

  <clause id="14658">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z)) = K(x,T(u,y) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(14657,a,12055,a)].">
      <j1 rule="hyper" parents="14657 12055"/>
    </justification>
  </clause>

  <clause id="14659">
    <literal><![CDATA[
      K(x,T(y,z) / (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T((z * u) \ y,u)) = w
    ]]></literal>
    <justification jstring="[para(12055(a,1),14657(a,1))].">
      <j1 rule="para" parents="12055 14657"/>
    </justification>
  </clause>

  <clause id="14660">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ u) / (T(u * z,z \ 1) * ((z * u) \ u))) = K(x,T(T(u,z) \ y,T(u * z,z \ 1)))
    ]]></literal>
    <justification jstring="[para(6351(a,1),14658(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6351 14658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14661">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u) / (z \ K(u,u \ (z \ 1)))) = K(x,T((((z \ 1) / u) * u) \ y,u))
    ]]></literal>
    <justification jstring="[para(9560(a,2),14658(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9560 14658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14663">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(11424(a,1),14377(a,1,1))].">
      <j1 rule="para" parents="11424 14377"/>
    </justification>
  </clause>

  <clause id="14664">
    <literal><![CDATA[
      (x \ y) * K(z,z \ y) = x \ (z * (y / z))
    ]]></literal>
    <justification jstring="[para(13452(a,1),14663(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13452 14663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14665">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,u) = (u * x) \ (u * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14576,a(flip),b,14398,a)].">
      <j1 rule="hyper" parents="63 14576 14398"/>
    </justification>
  </clause>

  <clause id="14666">
    <literal><![CDATA[
      (x * y) \ (x \ ((x * x) * y)) = R(x \ R(x,x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,14181,a,b,14665,a)].">
      <j1 rule="hyper" parents="347 14181 14665"/>
    </justification>
  </clause>

  <clause id="14667">
    <literal><![CDATA[
      ((x * y) \ (x * R(y,z,u))) * (y * x) = R(y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,14665,a(flip),b,3686,a(flip))].">
      <j1 rule="hyper" parents="133 14665 3686"/>
    </justification>
  </clause>

  <clause id="14668">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,u) * (x * u) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,563,a,b,14667,a)].">
      <j1 rule="hyper" parents="63 563 14667"/>
    </justification>
  </clause>

  <clause id="14669">
    <literal><![CDATA[
      L(x,y,z) \ L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (L(x * K(u,x),y,z) \ x) * K(u,x) = w
    ]]></literal>
    <justification jstring="[para(14414(a,1),14571(a,1))].">
      <j1 rule="para" parents="14414 14571"/>
    </justification>
  </clause>

  <clause id="14670">
    <literal><![CDATA[
      T(x * a(y,x,K(z,u)),y) = y \ (K(z,u) * ((K(u,z) * x) * y))
    ]]></literal>
    <justification jstring="[para(14447(a,1),14481(a,1,1))].">
      <j1 rule="para" parents="14447 14481"/>
    </justification>
  </clause>

  <clause id="14671">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) * u)) / u = z * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(279,a,14670,a)].">
      <j1 rule="hyper" parents="279 14670"/>
    </justification>
  </clause>

  <clause id="14672">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) * (u \ 1))) / (u \ 1) = z * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(14165(a,1),14671(a,2,2))].">
      <j1 rule="para" parents="14165 14671"/>
    </justification>
  </clause>

  <clause id="14673">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ ((z \ 1) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z \ u)) = w
    ]]></literal>
    <justification jstring="[para(14566(a,2),5276(a,1))].">
      <j1 rule="para" parents="14566 5276"/>
    </justification>
  </clause>

  <clause id="14674">
    <literal><![CDATA[
      x * K(y,x \ (z \ ((u * z) * x))) = z \ ((K(y,u) * z) * x)
    ]]></literal>
    <justification jstring="[para(11699(a,1),14568(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11699 14568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14675">
    <literal><![CDATA[
      T(x,K(y,x \ (z \ ((u * z) * x)))) \ (z \ ((K(y,u) * z) * x)) = T(K(y,x \ (z \ ((u * z) * x))),x)
    ]]></literal>
    <justification jstring="[hyper(128,a,14674,a(flip),b,4292,a)].">
      <j1 rule="hyper" parents="128 14674 4292"/>
    </justification>
  </clause>

  <clause id="14676">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (y \ R(T(y,T(x,y)),z,u)) = R(y,z,u) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(27(a,2),14578(a,1,2,2))].">
      <j1 rule="para" parents="27 14578"/>
    </justification>
  </clause>

  <clause id="14677">
    <literal><![CDATA[
      K((x / (y \ K(z * u,z))) * a(z,u,z),w) = K(x * (K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[para(11902(a,1),14586(a,1,1))].">
      <j1 rule="para" parents="11902 14586"/>
    </justification>
  </clause>

  <clause id="14678">
    <literal><![CDATA[
      K(x,L(y,z,u)) * T(u * (z / y),K(x,y)) = u * (z / T(y,x))
    ]]></literal>
    <justification jstring="[para(11064(a,1),14589(a,1,1))].">
      <j1 rule="para" parents="11064 14589"/>
    </justification>
  </clause>

  <clause id="14679">
    <literal><![CDATA[
      a(x,y,K(z,u / y)) \ K(z,(y * x) / u) = K(z,y / (u / x))
    ]]></literal>
    <justification jstring="[para(13979(a,1),14652(a,1,1))].">
      <j1 rule="para" parents="13979 14652"/>
    </justification>
  </clause>

  <clause id="14680">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (y \ R(T(y,x),z,u)) = R(y,z,u) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(4270(a,1),14676(a,1,2,2,1))].">
      <j1 rule="para" parents="4270 14676"/>
    </justification>
  </clause>

  <clause id="14681">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,L(w,y,z)) \ R(T(x,w),y,z) = u
    ]]></literal>
    <justification jstring="[para(14680(a,1),11116(a,1))].">
      <j1 rule="para" parents="14680 11116"/>
    </justification>
  </clause>

  <clause id="14682">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ R(T(x,y),z,u) = x \ R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(14681,a,1463,a)].">
      <j1 rule="hyper" parents="14681 1463"/>
    </justification>
  </clause>

  <clause id="14683">
    <literal><![CDATA[
      K(x / (y \ K(z * u,z)),w) = K(x * (K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[hyper(11936,a,14677,a)].">
      <j1 rule="hyper" parents="11936 14677"/>
    </justification>
  </clause>

  <clause id="14684">
    <literal><![CDATA[
      K(x * (K(y,y * z) * u),w) = K(x * (K(y,z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(13301,a,14683,a)].">
      <j1 rule="hyper" parents="13301 14683"/>
    </justification>
  </clause>

  <clause id="14686">
    <literal><![CDATA[
      K(x,y * L(z / (y * z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z / (y * z),u,w) * y) = v5
    ]]></literal>
    <justification jstring="[para(13055(a,1),13258(a,1))].">
      <j1 rule="para" parents="13055 13258"/>
    </justification>
  </clause>

  <clause id="14687">
    <literal><![CDATA[
      T(x,T(y / (1 / z),u) * w) = T(x,T(y / (z \ 1),u) * w)
    ]]></literal>
    <justification jstring="[para(13037(a,1),13088(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13037 13088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14688">
    <literal><![CDATA[
      T(x,T(y / (1 / z),z \ 1) * u) = T(x,((z \ 1) \ y) * u)
    ]]></literal>
    <justification jstring="[para(113(a,1),14687(a,2,2,1))].">
      <j1 rule="para" parents="113 14687"/>
    </justification>
  </clause>

  <clause id="14689">
    <literal><![CDATA[
      T(x,((1 / y) \ z) * u) = T(x,((y \ 1) \ z) * u)
    ]]></literal>
    <justification jstring="[para(2963(a,1),14688(a,1,2,1))].">
      <j1 rule="para" parents="2963 14688"/>
    </justification>
  </clause>

  <clause id="14690">
    <literal><![CDATA[
      R(x,y,z \ T(u * K(w,v5),w)) = R(x,y,z \ ((u \ w) \ T(w,v5)))
    ]]></literal>
    <justification jstring="[para(6882(a,1),13197(a,1,3,2))].">
      <j1 rule="para" parents="6882 13197"/>
    </justification>
  </clause>

  <clause id="14691">
    <literal><![CDATA[
      (L(x,y,z) * u) / (x * ((x \ L(x,y,z)) * u)) = a(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(3552(a,1),13388(a,1,2))].">
      <j1 rule="para" parents="3552 13388"/>
    </justification>
  </clause>

  <clause id="14692">
    <literal><![CDATA[
      K(x,L(T(1 / (1 / y),z) * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(13429(a,2),13441(a,1))].">
      <j1 rule="para" parents="13429 13441"/>
    </justification>
  </clause>

  <clause id="14694">
    <literal><![CDATA[
      K(L((x \ y) * K(z,u),K(u,z),x),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((x * K(u,z)) \ y,w) = v5
    ]]></literal>
    <justification jstring="[para(6117(a,1),13644(a,1,1,1))].">
      <j1 rule="para" parents="6117 13644"/>
    </justification>
  </clause>

  <clause id="14695">
    <literal><![CDATA[
      K(x,y * ((z * y) \ (z * (u / z)))) = K(x,T(y * ((z * y) \ u),z))
    ]]></literal>
    <justification jstring="[para(14664(a,1),13713(a,1,2,2))].">
      <j1 rule="para" parents="14664 13713"/>
    </justification>
  </clause>

  <clause id="14696">
    <literal><![CDATA[
      K(x * y,z) * (((z * x) * y) / u) = ((x * y) * R(z,x,y)) / u
    ]]></literal>
    <justification jstring="[para(14102(a,1),13753(a,1,1))].">
      <j1 rule="para" parents="14102 13753"/>
    </justification>
  </clause>

  <clause id="14697">
    <literal><![CDATA[
      ((x * y) * R(z,x,y)) / z = z \ ((z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(13795,a,14696,a),flip(a)].">
      <j1 rule="hyper" parents="13795 14696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14698">
    <literal><![CDATA[
      ((x * y) / z) * R(z,x,y) = z \ ((z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(1713,a,14697,a)].">
      <j1 rule="hyper" parents="1713 14697"/>
    </justification>
  </clause>

  <clause id="14699">
    <literal><![CDATA[
      a(x,y,z) = (y * z) \ (x \ ((x * y) * z))
    ]]></literal>
    <justification jstring="[para(14698(a,1),14251(a,2,2))].">
      <j1 rule="para" parents="14698 14251"/>
    </justification>
  </clause>

  <clause id="14700">
    <literal><![CDATA[
      R(x \ R(x,x,y),x,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,14666,a(flip),b,14699,a)].">
      <j1 rule="hyper" parents="347 14666 14699"/>
    </justification>
  </clause>

  <clause id="14701">
    <literal><![CDATA[
      x \ (y \ ((y * z) * (z \ x))) = a(y,z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,174,a(flip),b,14699,a)].">
      <j1 rule="hyper" parents="347 174 14699"/>
    </justification>
  </clause>

  <clause id="14702">
    <literal><![CDATA[
      x \ ((x * y) * z) = (y * z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,14699,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="134 14699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14703">
    <literal><![CDATA[
      (x * y) \ (z \ ((z * y) * T(x,y))) = a(z,y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(650,a,14699,a(flip))].">
      <j1 rule="hyper" parents="650 14699"/>
    </justification>
  </clause>

  <clause id="14704">
    <literal><![CDATA[
      ((x \ y) * z) \ (x \ (y * z)) = a(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14699(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 14699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14705">
    <literal><![CDATA[
      (x * ((y * x) \ z)) \ (y \ z) = a(y,x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14699(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 14699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14706">
    <literal><![CDATA[
      x * ((y * z) * a(x,y,z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(14699(a,2),76(a,1,2,2))].">
      <j1 rule="para" parents="14699 76"/>
    </justification>
  </clause>

  <clause id="14707">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) = (y * L(z,y,x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(327(a,1),14699(a,2,2))].">
      <j1 rule="para" parents="327 14699"/>
    </justification>
  </clause>

  <clause id="14708">
    <literal><![CDATA[
      (x * y) \ ((z / x) \ (z * y)) = a(x \ z,x,y)
    ]]></literal>
    <justification jstring="[para(10243(a,1),14699(a,2,2)),flip(a)].">
      <j1 rule="para" parents="10243 14699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14709">
    <literal><![CDATA[
      R(x * ((x \ y) / y),x,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[para(2377(a,1),14700(a,1,1))].">
      <j1 rule="para" parents="2377 14700"/>
    </justification>
  </clause>

  <clause id="14710">
    <literal><![CDATA[
      (x \ y) / ((x \ 1) * y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,2254,a(flip),b,14709,a)].">
      <j1 rule="hyper" parents="63 2254 14709"/>
    </justification>
  </clause>

  <clause id="14711">
    <literal><![CDATA[
      a(x,x,y) * ((x \ 1) * y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(133,a,14709,a(flip),b,2254,a(flip))].">
      <j1 rule="hyper" parents="133 14709 2254"/>
    </justification>
  </clause>

  <clause id="14712">
    <literal><![CDATA[
      a(x,x,y) * (y \ ((x \ 1) * y)) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(128,a,14711,a(flip),b,12715,a),flip(a)].">
      <j1 rule="hyper" parents="128 14711 12715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14713">
    <literal><![CDATA[
      ((x \ 1) * y) \ (x \ y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,14711,a(flip),b,12964,a(flip))].">
      <j1 rule="hyper" parents="128 14711 12964"/>
    </justification>
  </clause>

  <clause id="14716">
    <literal><![CDATA[
      K(x \ 1,y) * a(x,x,y) = (y * (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(134,a,14713,a(flip),b,10276,a)].">
      <j1 rule="hyper" parents="134 14713 10276"/>
    </justification>
  </clause>

  <clause id="14718">
    <literal><![CDATA[
      ((x \ 1) * y) \ ((x \ y) * L((x \ y) \ ((x \ 1) * y),z,u)) = a(x,x,y) \ L(((x \ 1) * y) \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[para(14713(a,1),3354(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14713 3354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14719">
    <literal><![CDATA[
      (x / y) \ (x * z) = (y * z) * a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(10245,a,14702,a)].">
      <j1 rule="hyper" parents="10245 14702"/>
    </justification>
  </clause>

  <clause id="14720">
    <literal><![CDATA[
      (x * L(y,x,z)) * a(z,x,L(y,x,z)) = x * y
    ]]></literal>
    <justification jstring="[hyper(546,a,14702,a),flip(a)].">
      <j1 rule="hyper" parents="546 14702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14721">
    <literal><![CDATA[
      x \ ((x * y) * z) = a(x,y,z) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,12700,a,b,14702,a),flip(a)].">
      <j1 rule="hyper" parents="347 12700 14702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14722">
    <literal><![CDATA[
      x * (a(x,y,z) * (y * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(134,a,12700,a,b,14702,a)].">
      <j1 rule="hyper" parents="134 12700 14702"/>
    </justification>
  </clause>

  <clause id="14723">
    <literal><![CDATA[
      a(x,y,z) = (x \ ((x * y) * z)) / (y * z)
    ]]></literal>
    <justification jstring="[hyper(131,a,14702,a,b,12700,a),flip(a)].">
      <j1 rule="hyper" parents="131 14702 12700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14724">
    <literal><![CDATA[
      x \ (y \ ((y * x) * x)) = x * a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,14702,a,b,12362,a(flip))].">
      <j1 rule="hyper" parents="128 14702 12362"/>
    </justification>
  </clause>

  <clause id="14725">
    <literal><![CDATA[
      ((x \ y) * z) * a(x,x \ y,z) = x \ (y * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14702(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 14702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14726">
    <literal><![CDATA[
      (x / y) \ (x * z) = (y * z) * a(x / y,y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),14702(a,1,2,1))].">
      <j1 rule="para" parents="12 14702"/>
    </justification>
  </clause>

  <clause id="14727">
    <literal><![CDATA[
      (x * y) \ (z \ ((z * x) * y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(z,x,y) = u
    ]]></literal>
    <justification jstring="[para(14702(a,2),356(a,1,2))].">
      <j1 rule="para" parents="14702 356"/>
    </justification>
  </clause>

  <clause id="14728">
    <literal><![CDATA[
      (x * L(y,z,x)) * a(z,x,L(y,z,x)) = z \ (x * (T(z,x) * y))
    ]]></literal>
    <justification jstring="[para(10150(a,1),14702(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10150 14702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14729">
    <literal><![CDATA[
      x \ ((x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * z) * a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(14706(a,1),356(a,1,2))].">
      <j1 rule="para" parents="14706 356"/>
    </justification>
  </clause>

  <clause id="14730">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) * (y * L(z,y,x)) = y * z
    ]]></literal>
    <justification jstring="[hyper(546,a,14721,a),flip(a)].">
      <j1 rule="hyper" parents="546 14721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14731">
    <literal><![CDATA[
      (x \ ((x * y) * z)) * L(u,y * z,a(x,y,z)) = a(x,y,z) * ((y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(133,a,14721,a,b,212,a)].">
      <j1 rule="hyper" parents="133 14721 212"/>
    </justification>
  </clause>

  <clause id="14733">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) \ (y * z) = y * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,327,a(flip),b,14721,a(flip))].">
      <j1 rule="hyper" parents="128 327 14721"/>
    </justification>
  </clause>

  <clause id="14734">
    <literal><![CDATA[
      a(x,x \ y,z) * ((x \ y) * z) = x \ (y * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14721(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 14721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14735">
    <literal><![CDATA[
      a(x \ y,x,z) * (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) \ (y * z) = u
    ]]></literal>
    <justification jstring="[para(14721(a,1),10245(a,1))].">
      <j1 rule="para" parents="14721 10245"/>
    </justification>
  </clause>

  <clause id="14736">
    <literal><![CDATA[
      (x * y) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) * (y * z) = u
    ]]></literal>
    <justification jstring="[para(14722(a,1),43(a,1))].">
      <j1 rule="para" parents="14722 43"/>
    </justification>
  </clause>

  <clause id="14737">
    <literal><![CDATA[
      a(x,y,z) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ ((x * y) * z) = u
    ]]></literal>
    <justification jstring="[para(14723(a,2),280(a,1,1))].">
      <j1 rule="para" parents="14723 280"/>
    </justification>
  </clause>

  <clause id="14738">
    <literal><![CDATA[
      L(x * a(y,x,x),x,y) = x
    ]]></literal>
    <justification jstring="[para(14724(a,1),536(a,1,1))].">
      <j1 rule="para" parents="14724 536"/>
    </justification>
  </clause>

  <clause id="14739">
    <literal><![CDATA[
      x * T(x * a(y,x,x),y * x) = y \ (x * (y * x))
    ]]></literal>
    <justification jstring="[para(14738(a,1),735(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14738 735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14740">
    <literal><![CDATA[
      K(x \ y,z) * a(x,x \ y,z) = (z * (x \ y)) \ (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(134,a,14704,a(flip),b,10276,a)].">
      <j1 rule="hyper" parents="134 14704 10276"/>
    </justification>
  </clause>

  <clause id="14743">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(x,y \ z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14704(a,2),13960(a,2,2)),flip(a)].">
      <j1 rule="para" parents="14704 13960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14745">
    <literal><![CDATA[
      (x * (y \ z)) \ ((y / x) \ z) = a(x \ y,x,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14708(a,1,2,2))].">
      <j1 rule="para" parents="10 14708"/>
    </justification>
  </clause>

  <clause id="14746">
    <literal><![CDATA[
      a(x,x,y) * T(x \ 1,y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(707,a,14712,a)].">
      <j1 rule="hyper" parents="707 14712"/>
    </justification>
  </clause>

  <clause id="14748">
    <literal><![CDATA[
      a(x / y,y,z) = a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,14719,a(flip),b,14726,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 14719 14726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14749">
    <literal><![CDATA[
      (L(x,y,y \ z) * z) \ (x * z) = a(y \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,14625,a,b,14748,a)].">
      <j1 rule="hyper" parents="63 14625 14748"/>
    </justification>
  </clause>

  <clause id="14750">
    <literal><![CDATA[
      a(x \ y,x,z) \ (y * z) = (y / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(14748(a,1),13392(a,1,1))].">
      <j1 rule="para" parents="14748 13392"/>
    </justification>
  </clause>

  <clause id="14752">
    <literal><![CDATA[
      a(x * y,(x * y) \ x,z) * (((x * y) \ x) * z) = L(y \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,99,a,b,14734,a),flip(a)].">
      <j1 rule="hyper" parents="347 99 14734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14753">
    <literal><![CDATA[
      a(x,x \ y,z) * K(x \ y,z) = (x \ (y * z)) / (z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(131,a,14734,a(flip),b,9863,a),flip(a)].">
      <j1 rule="hyper" parents="131 14734 9863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14754">
    <literal><![CDATA[
      a(x \ y,(x \ y) \ y,x) * (x * ((x \ y) \ y)) = (x \ y) \ (y * x)
    ]]></literal>
    <justification jstring="[para(346(a,1),14734(a,1,2))].">
      <j1 rule="para" parents="346 14734"/>
    </justification>
  </clause>

  <clause id="14755">
    <literal><![CDATA[
      a(x \ y,x,z) \ (y * z) != u * w
    ]]></literal>
    <literal><![CDATA[
      ((y / x) * (x * z)) / w = u
    ]]></literal>
    <justification jstring="[para(14750(a,2),652(a,1))].">
      <j1 rule="para" parents="14750 652"/>
    </justification>
  </clause>

  <clause id="14757">
    <literal><![CDATA[
      (L(x,y,y \ (x \ z)) * (x \ z)) \ z = a(y \ (x \ z),y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),14749(a,1,2))].">
      <j1 rule="para" parents="10 14749"/>
    </justification>
  </clause>

  <clause id="14758">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) * a(x,x,(x \ 1) \ y) = K(x \ 1,(x \ 1) \ y) * (y \ (x \ ((x \ 1) \ y)))
    ]]></literal>
    <justification jstring="[hyper(347,a,10296,a,b,14716,a),flip(a)].">
      <j1 rule="hyper" parents="347 10296 14716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14759">
    <literal><![CDATA[
      K(x \ 1,x * (y / x)) * a(x,x,x * (y / x)) = ((x * (y * (x \ 1))) / x) \ (x \ (x * (y / x)))
    ]]></literal>
    <justification jstring="[para(1085(a,2),14716(a,2,1))].">
      <j1 rule="para" parents="1085 14716"/>
    </justification>
  </clause>

  <clause id="14760">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,14267,a(flip),b,14743,a),flip(a)].">
      <j1 rule="hyper" parents="347 14267 14743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14761">
    <literal><![CDATA[
      K(x,(y / (y / ((z \ u) * y))) \ (z \ (u * ((((z \ u) * y) \ y) * ((z \ u) * y))))) = a(x,u,K((((z \ u) * y) \ y) * ((z \ u) * y),z))
    ]]></literal>
    <justification jstring="[para(5716(a,1),14760(a,1,2,1))].">
      <j1 rule="para" parents="5716 14760"/>
    </justification>
  </clause>

  <clause id="14762">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(u * K(K(y,z),x),w) = T(K(x,K(y,z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(6117(a,1),13830(a,1,2,1))].">
      <j1 rule="para" parents="6117 13830"/>
    </justification>
  </clause>

  <clause id="14763">
    <literal><![CDATA[
      T(x \ (x \ y),x \ (x \ (x \ (x \ y)))) = K(x * x,y) * (x \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(347,a,9170,a,b,13929,a),flip(a)].">
      <j1 rule="hyper" parents="347 9170 13929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14764">
    <literal><![CDATA[
      K(x,L((y / z) \ u,y / z,z)) = K(x,T((u * z) / y,z \ y))
    ]]></literal>
    <justification jstring="[hyper(14132,a,13601,a)].">
      <j1 rule="hyper" parents="14132 13601"/>
    </justification>
  </clause>

  <clause id="14765">
    <literal><![CDATA[
      K(x,L((y / z) \ K(u,T(T(w,z),v5)),y / z,z)) = K(x,T((z * K(u,T(w,v5))) / y,z \ y))
    ]]></literal>
    <justification jstring="[para(7431(a,1),14764(a,2,2,1,1))].">
      <j1 rule="para" parents="7431 14764"/>
    </justification>
  </clause>

  <clause id="14766">
    <literal><![CDATA[
      K(x,L(y,z,(u * T(x,w)) \ v5)) = K(x,y) * a(u \ v5,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(13981(a,1),14135(a,2,2))].">
      <j1 rule="para" parents="13981 14135"/>
    </justification>
  </clause>

  <clause id="14767">
    <literal><![CDATA[
      K(x,L(y,z,(u * T(x,w)) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(14766(a,2),11093(a,1))].">
      <j1 rule="para" parents="14766 11093"/>
    </justification>
  </clause>

  <clause id="14768">
    <literal><![CDATA[
      K(x,L(y,z,(u * x) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ w)) = v5
    ]]></literal>
    <justification jstring="[para(110(a,1),14767(a,1,2,3,1,2))].">
      <j1 rule="para" parents="110 14767"/>
    </justification>
  </clause>

  <clause id="14769">
    <literal><![CDATA[
      K(x,L(y,z,(u * x) \ w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(14768,a,xx),flip(a)].">
      <j1 rule="hyper" parents="14768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14770">
    <literal><![CDATA[
      K(x \ 1,L(y,z,x \ u)) = K(x \ 1,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(183(a,1),14769(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="183 14769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14771">
    <literal><![CDATA[
      T(K(x,y) * z,u) / T(K(x,y),w) = T(K(x,T(y,w)) * z,u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(6140,a,14515,a),flip(a)].">
      <j1 rule="hyper" parents="6140 14515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14772">
    <literal><![CDATA[
      a(x \ L(x,y,z),x,u) = a(x,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(13426,a,14691,a),flip(a)].">
      <j1 rule="hyper" parents="13426 14691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14773">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(u * K(y,K(z,x)),w) = T(K(x,K(y,z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(7261(a,1),14762(a,1,2,1,2))].">
      <j1 rule="para" parents="7261 14762"/>
    </justification>
  </clause>

  <clause id="14774">
    <literal><![CDATA[
      T(x \ (x \ y),x \ (x \ 1)) = K(x * x,y) * (x \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(13812,a,14763,a)].">
      <j1 rule="hyper" parents="13812 14763"/>
    </justification>
  </clause>

  <clause id="14775">
    <literal><![CDATA[
      K(x * x,y) * (x \ (x \ y)) = T((x \ y) / x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(4885,a,14774,a),flip(a)].">
      <j1 rule="hyper" parents="4885 14774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14776">
    <literal><![CDATA[
      T(K(x,y) * z,u) / K(x,T(y,w)) = T(K(x,T(y,w)) * z,u) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7091(a,2),14771(a,1,2))].">
      <j1 rule="para" parents="7091 14771"/>
    </justification>
  </clause>

  <clause id="14777">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(34,a,14313,a,b,14773,a),flip(a)].">
      <j1 rule="hyper" parents="34 14313 14773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14778">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = w / T(w,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,4920,a(flip),b,14777,a),flip(a)].">
      <j1 rule="hyper" parents="347 4920 14777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14779">
    <literal><![CDATA[
      K(x * (K(y,z) * u),w) = K(x * (u * K(y,z)),w)
    ]]></literal>
    <justification jstring="[para(8013(a,1),14777(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8013 14777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14781">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4954,a,14778,a)].">
      <j1 rule="hyper" parents="4954 14778"/>
    </justification>
  </clause>

  <clause id="14782">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(14778(a,2),5013(a,1))].">
      <j1 rule="para" parents="14778 5013"/>
    </justification>
  </clause>

  <clause id="14783">
    <literal><![CDATA[
      T(x,K(y,K(z,u)) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(13564,a,14781,a)].">
      <j1 rule="hyper" parents="13564 14781"/>
    </justification>
  </clause>

  <clause id="14784">
    <literal><![CDATA[
      T(x,y \ K(z,K(u,w))) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(13125,a,14781,a)].">
      <j1 rule="hyper" parents="13125 14781"/>
    </justification>
  </clause>

  <clause id="14786">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w))) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(5922(a,1),14781(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5922 14781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14787">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[para(7163(a,1),14781(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7163 14781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14788">
    <literal><![CDATA[
      T(x,y * (K(z,u) * w)) = T(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(8013(a,1),14781(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8013 14781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14789">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) \ w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[para(13546(a,1),14781(a,1,2))].">
      <j1 rule="para" parents="13546 14781"/>
    </justification>
  </clause>

  <clause id="14790">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) = T(x,K(y,z) * w)
    ]]></literal>
    <justification jstring="[para(13544(a,1),14781(a,1,2))].">
      <j1 rule="para" parents="13544 14781"/>
    </justification>
  </clause>

  <clause id="14791">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = x \ T(x,w)
    ]]></literal>
    <justification jstring="[hyper(128,a,14783,a(flip),b,4929,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 14783 4929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14792">
    <literal><![CDATA[
      T(x,y / T(z,T(u,w))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(6813(a,1),14786(a,1,2,2))].">
      <j1 rule="para" parents="6813 14786"/>
    </justification>
  </clause>

  <clause id="14793">
    <literal><![CDATA[
      T(x,y / T(T(z,T(u,w)),v5)) = T(x,y / T(T(z,u),v5))
    ]]></literal>
    <justification jstring="[para(6817(a,1),14786(a,1,2,2))].">
      <j1 rule="para" parents="6817 14786"/>
    </justification>
  </clause>

  <clause id="14794">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) \ w) = T(x,T(y,z) \ w)
    ]]></literal>
    <justification jstring="[para(6813(a,1),14789(a,1,2,1))].">
      <j1 rule="para" parents="6813 14789"/>
    </justification>
  </clause>

  <clause id="14795">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,4924,a,b,14791,a),flip(a)].">
      <j1 rule="hyper" parents="347 4924 14791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14796">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(14791(a,2),5006(a,1))].">
      <j1 rule="para" parents="14791 5006"/>
    </justification>
  </clause>

  <clause id="14797">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(13647,a,14795,a)].">
      <j1 rule="hyper" parents="13647 14795"/>
    </justification>
  </clause>

  <clause id="14798">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(13637,a,14795,a)].">
      <j1 rule="hyper" parents="13637 14795"/>
    </justification>
  </clause>

  <clause id="14799">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) \ w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),14795(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14800">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(5159(a,1),14795(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5159 14795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14801">
    <literal><![CDATA[
      K(x,(T(y,K(z,u)) * w) * v5) = K(x,(y * w) * v5)
    ]]></literal>
    <justification jstring="[para(5846(a,1),14795(a,1,2))].">
      <j1 rule="para" parents="5846 14795"/>
    </justification>
  </clause>

  <clause id="14802">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) = K(x,K(y,z) * w)
    ]]></literal>
    <justification jstring="[para(7446(a,1),14795(a,1,2))].">
      <j1 rule="para" parents="7446 14795"/>
    </justification>
  </clause>

  <clause id="14803">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * w) = K(x,T(y,z) * w)
    ]]></literal>
    <justification jstring="[para(8415(a,1),14795(a,1,2))].">
      <j1 rule="para" parents="8415 14795"/>
    </justification>
  </clause>

  <clause id="14804">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(10274(a,1),14795(a,1,2))].">
      <j1 rule="para" parents="10274 14795"/>
    </justification>
  </clause>

  <clause id="14805">
    <literal><![CDATA[
      K(x,(K(y,z) * (u / K(y,z))) \ w) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(10313(a,1),14795(a,1,2))].">
      <j1 rule="para" parents="10313 14795"/>
    </justification>
  </clause>

  <clause id="14806">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(13551(a,1),14795(a,1,2))].">
      <j1 rule="para" parents="13551 14795"/>
    </justification>
  </clause>

  <clause id="14807">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * (w * K(v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,K(v5,v6) * w) = v7
    ]]></literal>
    <justification jstring="[para(14795(a,2),13608(a,1))].">
      <j1 rule="para" parents="14795 13608"/>
    </justification>
  </clause>

  <clause id="14808">
    <literal><![CDATA[
      K(x,y * (z * K(u,K(w,v5)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(13550(a,1),14795(a,1,2))].">
      <j1 rule="para" parents="13550 14795"/>
    </justification>
  </clause>

  <clause id="14809">
    <literal><![CDATA[
      K(x,y \ T(z,u / w)) = K(x,y \ T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(7363(a,1),14797(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7363 14797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14810">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12003,a(flip),b,14798,a),flip(a)].">
      <j1 rule="hyper" parents="63 12003 14798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14811">
    <literal><![CDATA[
      K(x,y * ((z * u) * K(z,w))) = K(x,y * (T(z,w) * u))
    ]]></literal>
    <justification jstring="[para(6867(a,1),14798(a,1,2,2))].">
      <j1 rule="para" parents="6867 14798"/>
    </justification>
  </clause>

  <clause id="14812">
    <literal><![CDATA[
      K(x,y * T(z,u * w)) = K(x,y * T(z,w * u))
    ]]></literal>
    <justification jstring="[para(10337(a,1),14798(a,1,2,2))].">
      <j1 rule="para" parents="10337 14798"/>
    </justification>
  </clause>

  <clause id="14813">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)) \ w,v5,v6)) = L(K(x,y \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(14800(a,1),11049(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14800 11049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14814">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * K(y,z)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(14800(a,1),12168(a,1))].">
      <j1 rule="para" parents="14800 12168"/>
    </justification>
  </clause>

  <clause id="14815">
    <literal><![CDATA[
      K(x,y \ T(z,y)) = K(x,z / T(y,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,12073,a,b,14806,a)].">
      <j1 rule="hyper" parents="347 12073 14806"/>
    </justification>
  </clause>

  <clause id="14816">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,y / (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(6121(a,1),14806(a,1,2,2))].">
      <j1 rule="para" parents="6121 14806"/>
    </justification>
  </clause>

  <clause id="14817">
    <literal><![CDATA[
      K(x,y / T(z,u / w)) = K(x,y / T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(7363(a,1),14806(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7363 14806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14818">
    <literal><![CDATA[
      K(T(x,K(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * u,w) = v5
    ]]></literal>
    <justification jstring="[para(5564(a,1),14782(a,1,1))].">
      <j1 rule="para" parents="5564 14782"/>
    </justification>
  </clause>

  <clause id="14819">
    <literal><![CDATA[
      K(x * (y * K(z,K(u,w))),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * y,v5) = v6
    ]]></literal>
    <justification jstring="[para(8921(a,1),14782(a,1,1))].">
      <j1 rule="para" parents="8921 14782"/>
    </justification>
  </clause>

  <clause id="14820">
    <literal><![CDATA[
      K(T(x,K(y,z)) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(13546(a,1),14782(a,1,1))].">
      <j1 rule="para" parents="13546 14782"/>
    </justification>
  </clause>

  <clause id="14821">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * w) = v5
    ]]></literal>
    <justification jstring="[para(4974(a,1),14796(a,1,2))].">
      <j1 rule="para" parents="4974 14796"/>
    </justification>
  </clause>

  <clause id="14822">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v5
    ]]></literal>
    <justification jstring="[para(5573(a,1),14796(a,1,2))].">
      <j1 rule="para" parents="5573 14796"/>
    </justification>
  </clause>

  <clause id="14823">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / w) = v5
    ]]></literal>
    <justification jstring="[para(5569(a,1),14796(a,1,2))].">
      <j1 rule="para" parents="5569 14796"/>
    </justification>
  </clause>

  <clause id="14824">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = v5
    ]]></literal>
    <justification jstring="[para(5570(a,1),14796(a,1,2))].">
      <j1 rule="para" parents="5570 14796"/>
    </justification>
  </clause>

  <clause id="14825">
    <literal><![CDATA[
      K(x,K(K(y,z),u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(6897(a,2),14796(a,1,2,1))].">
      <j1 rule="para" parents="6897 14796"/>
    </justification>
  </clause>

  <clause id="14826">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(7372(a,1),14796(a,1,2))].">
      <j1 rule="para" parents="7372 14796"/>
    </justification>
  </clause>

  <clause id="14827">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(7318(a,2),14796(a,1,2))].">
      <j1 rule="para" parents="7318 14796"/>
    </justification>
  </clause>

  <clause id="14828">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ w) = v5
    ]]></literal>
    <justification jstring="[para(7274(a,1),14796(a,1,2))].">
      <j1 rule="para" parents="7274 14796"/>
    </justification>
  </clause>

  <clause id="14829">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = v5
    ]]></literal>
    <justification jstring="[para(13551(a,1),14796(a,1,2))].">
      <j1 rule="para" parents="13551 14796"/>
    </justification>
  </clause>

  <clause id="14830">
    <literal><![CDATA[
      K(x,y \ K(z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(13730(a,1),14796(a,1,2))].">
      <j1 rule="para" parents="13730 14796"/>
    </justification>
  </clause>

  <clause id="14831">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(z,u) * y) / w) = v5
    ]]></literal>
    <justification jstring="[para(13748(a,1),14796(a,1,2))].">
      <j1 rule="para" parents="13748 14796"/>
    </justification>
  </clause>

  <clause id="14832">
    <literal><![CDATA[
      K(x,y * (z * K(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(13550(a,1),14796(a,1,2))].">
      <j1 rule="para" parents="13550 14796"/>
    </justification>
  </clause>

  <clause id="14833">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * K(y,z)) * w) = v5
    ]]></literal>
    <justification jstring="[para(10281(a,1),14825(a,1,2))].">
      <j1 rule="para" parents="10281 14825"/>
    </justification>
  </clause>

  <clause id="14834">
    <literal><![CDATA[
      K(x,y * (z * T(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * u)) = v6
    ]]></literal>
    <justification jstring="[para(6975(a,1),14826(a,1,2))].">
      <j1 rule="para" parents="6975 14826"/>
    </justification>
  </clause>

  <clause id="14835">
    <literal><![CDATA[
      K(x,y * (z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (K(u,w) * z)) = v5
    ]]></literal>
    <justification jstring="[para(8013(a,1),14826(a,1,2))].">
      <j1 rule="para" parents="8013 14826"/>
    </justification>
  </clause>

  <clause id="14836">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (K(u,w) * z)) = v5
    ]]></literal>
    <justification jstring="[para(13432(a,1),14826(a,1,2))].">
      <j1 rule="para" parents="13432 14826"/>
    </justification>
  </clause>

  <clause id="14837">
    <literal><![CDATA[
      T(x,T(y,z) / T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(14792(a,1),12031(a,1))].">
      <j1 rule="para" parents="14792 12031"/>
    </justification>
  </clause>

  <clause id="14838">
    <literal><![CDATA[
      K(x,K(y / z,u) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[para(7135(a,1),14802(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7135 14802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14839">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,10360,a(flip),b,14803,a),flip(a)].">
      <j1 rule="hyper" parents="347 10360 14803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14840">
    <literal><![CDATA[
      K(x,T(y,z \ u) * (u / z)) = K(x,(u / z) * y)
    ]]></literal>
    <justification jstring="[para(113(a,1),14839(a,1,2,1,2))].">
      <j1 rule="para" parents="113 14839"/>
    </justification>
  </clause>

  <clause id="14841">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * z)) = K(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[para(10334(a,1),14839(a,1,2,1))].">
      <j1 rule="para" parents="10334 14839"/>
    </justification>
  </clause>

  <clause id="14842">
    <literal><![CDATA[
      K(x,T(y,z \ u) * (u * (z \ 1))) = K(x,(u * (z \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(13164(a,1),14839(a,1,2,1))].">
      <j1 rule="para" parents="13164 14839"/>
    </justification>
  </clause>

  <clause id="14843">
    <literal><![CDATA[
      K(x,y * (z \ T(u,K(w,v5)))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(1438(a,1),14808(a,1,2,2))].">
      <j1 rule="para" parents="1438 14808"/>
    </justification>
  </clause>

  <clause id="14844">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w)) / v5)) = K(x,y * (z / v5))
    ]]></literal>
    <justification jstring="[para(1439(a,1),14808(a,1,2,2))].">
      <j1 rule="para" parents="1439 14808"/>
    </justification>
  </clause>

  <clause id="14845">
    <literal><![CDATA[
      K((K(x,y) / z) * u,w) = K((z \ K(x,y)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(14818,a,11971,a)].">
      <j1 rule="hyper" parents="14818 11971"/>
    </justification>
  </clause>

  <clause id="14846">
    <literal><![CDATA[
      K((x * K(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((K(y,z) * x) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(6872(a,1),14818(a,1,1,1))].">
      <j1 rule="para" parents="6872 14818"/>
    </justification>
  </clause>

  <clause id="14847">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((z * K(x,y)) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(6121(a,1),14820(a,1,1,1))].">
      <j1 rule="para" parents="6121 14820"/>
    </justification>
  </clause>

  <clause id="14848">
    <literal><![CDATA[
      K(x,y * (z * (u * K(z,w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(z,w) * u)) = v5
    ]]></literal>
    <justification jstring="[para(6866(a,1),14822(a,1,2,2))].">
      <j1 rule="para" parents="6866 14822"/>
    </justification>
  </clause>

  <clause id="14849">
    <literal><![CDATA[
      K(x,y * T(z,u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(8887(a,1),14822(a,1,2,2))].">
      <j1 rule="para" parents="8887 14822"/>
    </justification>
  </clause>

  <clause id="14850">
    <literal><![CDATA[
      K(x,y * T(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,w * u)) = v5
    ]]></literal>
    <justification jstring="[para(10337(a,1),14822(a,1,2,2))].">
      <j1 rule="para" parents="10337 14822"/>
    </justification>
  </clause>

  <clause id="14851">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(z,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(z,w) / u)) = v5
    ]]></literal>
    <justification jstring="[para(13208(a,1),14822(a,1,2,2))].">
      <j1 rule="para" parents="13208 14822"/>
    </justification>
  </clause>

  <clause id="14852">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) / w) = v5
    ]]></literal>
    <justification jstring="[para(6813(a,1),14823(a,1,2,1))].">
      <j1 rule="para" parents="6813 14823"/>
    </justification>
  </clause>

  <clause id="14853">
    <literal><![CDATA[
      K(x,T(y,z / u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z) / w) = v5
    ]]></literal>
    <justification jstring="[para(8887(a,1),14823(a,1,2,1))].">
      <j1 rule="para" parents="8887 14823"/>
    </justification>
  </clause>

  <clause id="14854">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (w * K(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(6121(a,1),14824(a,1,2,2))].">
      <j1 rule="para" parents="6121 14824"/>
    </justification>
  </clause>

  <clause id="14855">
    <literal><![CDATA[
      K(x,y \ T(z,u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(8887(a,1),14824(a,1,2,2))].">
      <j1 rule="para" parents="8887 14824"/>
    </justification>
  </clause>

  <clause id="14856">
    <literal><![CDATA[
      K(x,y \ T(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,w * u)) = v5
    ]]></literal>
    <justification jstring="[para(10337(a,1),14824(a,1,2,2))].">
      <j1 rule="para" parents="10337 14824"/>
    </justification>
  </clause>

  <clause id="14857">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (K(u,w) * z)) = v5
    ]]></literal>
    <justification jstring="[para(6872(a,1),14829(a,1,2,2))].">
      <j1 rule="para" parents="6872 14829"/>
    </justification>
  </clause>

  <clause id="14858">
    <literal><![CDATA[
      K(x,y / (K(z,u) * (w \ z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (w \ T(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(13116(a,1),14829(a,1,2,2))].">
      <j1 rule="para" parents="13116 14829"/>
    </justification>
  </clause>

  <clause id="14859">
    <literal><![CDATA[
      K(x,((y / K(z,u)) * w) * v5) = K(x,((K(u,z) * y) * w) * v5)
    ]]></literal>
    <justification jstring="[para(6877(a,1),14801(a,1,2,1,1))].">
      <j1 rule="para" parents="6877 14801"/>
    </justification>
  </clause>

  <clause id="14860">
    <literal><![CDATA[
      K(x,y \ T(z,y \ x)) = K(x,x \ (z * (x / y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13219,a(flip),b,14809,a),flip(a)].">
      <j1 rule="hyper" parents="63 13219 14809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14861">
    <literal><![CDATA[
      K(x,y * (z * K(u,u \ w))) = K(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12010,a(flip),b,14810,a),flip(a)].">
      <j1 rule="hyper" parents="63 12010 14810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14862">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(13319,a,14816,a),flip(a)].">
      <j1 rule="hyper" parents="13319 14816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14863">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ K(w,u))) = v5
    ]]></literal>
    <justification jstring="[para(14816(a,1),13319(a,1))].">
      <j1 rule="para" parents="14816 13319"/>
    </justification>
  </clause>

  <clause id="14864">
    <literal><![CDATA[
      K(x,(y / z) / T(u,z \ y)) = K(x,u \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(11988,a,14817,a),flip(a)].">
      <j1 rule="hyper" parents="11988 14817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14865">
    <literal><![CDATA[
      K(x,(y / z) / T(u,z \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (y / z)) = w
    ]]></literal>
    <justification jstring="[para(14817(a,1),11988(a,1))].">
      <j1 rule="para" parents="14817 11988"/>
    </justification>
  </clause>

  <clause id="14866">
    <literal><![CDATA[
      K(x,K(y * (z \ u),u) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(13895,a,14838,a)].">
      <j1 rule="hyper" parents="13895 14838"/>
    </justification>
  </clause>

  <clause id="14867">
    <literal><![CDATA[
      K(x,T(y,(z / y) * u) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(9613(a,2),14841(a,2,2))].">
      <j1 rule="para" parents="9613 14841"/>
    </justification>
  </clause>

  <clause id="14868">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) / v5)) = K(x,y * (T(z,w \ u) / v5))
    ]]></literal>
    <justification jstring="[para(7363(a,1),14844(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7363 14844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14869">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K((x \ K(z,y)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(13315,a,14845,a)].">
      <j1 rule="hyper" parents="13315 14845"/>
    </justification>
  </clause>

  <clause id="14870">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(w,u))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(5926(a,1),14862(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5926 14862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14871">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(u,w))) = K(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(6102(a,1),14862(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6102 14862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14872">
    <literal><![CDATA[
      K(x,y / (z * (u * K(w,u)))) = K(x,y * ((z * u) \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(6227(a,1),14862(a,1,2,2))].">
      <j1 rule="para" parents="6227 14862"/>
    </justification>
  </clause>

  <clause id="14873">
    <literal><![CDATA[
      K(x,y * (z \ K(y,u))) = K(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[para(13098(a,1),14862(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13098 14862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14874">
    <literal><![CDATA[
      T(x,y * (z \ K(y,u))) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[hyper(132,a,14873,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 14873 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14875">
    <literal><![CDATA[
      K(x * (K(y,K(z,u)) * w),v5) = K(x * w,v5)
    ]]></literal>
    <justification jstring="[hyper(14819,a,14779,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14819 14779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14876">
    <literal><![CDATA[
      K(x * (K(y,T(z,u)) * w),v5) = K(x * (K(y,z) * w),v5)
    ]]></literal>
    <justification jstring="[para(7446(a,1),14875(a,1,1,2))].">
      <j1 rule="para" parents="7446 14875"/>
    </justification>
  </clause>

  <clause id="14877">
    <literal><![CDATA[
      K(x,(y \ (z * (u \ y))) \ K(z,u \ z)) = K(x,z \ ((y \ (z * (u \ y))) \ z))
    ]]></literal>
    <justification jstring="[hyper(14830,a,8239,a)].">
      <j1 rule="hyper" parents="14830 8239"/>
    </justification>
  </clause>

  <clause id="14878">
    <literal><![CDATA[
      K(x,y \ K(z,u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(7392(a,1),14830(a,1,2,2))].">
      <j1 rule="para" parents="7392 14830"/>
    </justification>
  </clause>

  <clause id="14879">
    <literal><![CDATA[
      K(x,y * (K(z,K(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * v5) = v6
    ]]></literal>
    <justification jstring="[para(7076(a,1),14832(a,1,2,2))].">
      <j1 rule="para" parents="7076 14832"/>
    </justification>
  </clause>

  <clause id="14880">
    <literal><![CDATA[
      K(x,y * (z / T(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z / u)) = v6
    ]]></literal>
    <justification jstring="[para(7316(a,1),14832(a,1,2,2))].">
      <j1 rule="para" parents="7316 14832"/>
    </justification>
  </clause>

  <clause id="14881">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,K(v5,v6))))) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * u)) = v7
    ]]></literal>
    <justification jstring="[para(8921(a,1),14832(a,1,2,2))].">
      <j1 rule="para" parents="8921 14832"/>
    </justification>
  </clause>

  <clause id="14882">
    <literal><![CDATA[
      K(x,y * K(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(z,w * u)) = v5
    ]]></literal>
    <justification jstring="[para(10421(a,1),14832(a,1,2,2))].">
      <j1 rule="para" parents="10421 14832"/>
    </justification>
  </clause>

  <clause id="14883">
    <literal><![CDATA[
      K(x,y * (z \ K(u,T(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ K(u,w))) = v6
    ]]></literal>
    <justification jstring="[para(13344(a,1),14832(a,1,2,2))].">
      <j1 rule="para" parents="13344 14832"/>
    </justification>
  </clause>

  <clause id="14884">
    <literal><![CDATA[
      K(x,y * T(z * K(u,K(w,v5)),v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,v6)) = v7
    ]]></literal>
    <justification jstring="[para(14306(a,2),14832(a,1,2,2))].">
      <j1 rule="para" parents="14306 14832"/>
    </justification>
  </clause>

  <clause id="14885">
    <literal><![CDATA[
      K(x,T(T(y,z) / u,y) / w) = K(x,(u \ T(y,z)) / w)
    ]]></literal>
    <justification jstring="[hyper(14852,a,12135,a)].">
      <j1 rule="hyper" parents="14852 12135"/>
    </justification>
  </clause>

  <clause id="14886">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(z,u) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(8415(a,1),14879(a,1,2,2))].">
      <j1 rule="para" parents="8415 14879"/>
    </justification>
  </clause>

  <clause id="14887">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / T(T(y \ u,u),w)) = T(x,T(y \ u,w) \ (K(y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12518,a(flip),b,14793,a),flip(a)].">
      <j1 rule="hyper" parents="63 12518 14793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14888">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)) \ w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(14813(a,2),11166(a,1))].">
      <j1 rule="para" parents="14813 11166"/>
    </justification>
  </clause>

  <clause id="14889">
    <literal><![CDATA[
      (x \ T(x * (y * K(z,z \ u)),w)) \ (y * K(z,z \ u)) = K(w,x * (K(z,u) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,13056,a,b,14861,a)].">
      <j1 rule="hyper" parents="63 13056 14861"/>
    </justification>
  </clause>

  <clause id="14890">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * u))) = K(x,y * (w * (z * (u / z))))
    ]]></literal>
    <justification jstring="[para(9564(a,1),14861(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9564 14861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14891">
    <literal><![CDATA[
      K(x,T(y * ((y / z) / y),y) / u) = K(x,(z \ T(y,z \ 1)) / u)
    ]]></literal>
    <justification jstring="[para(3805(a,1),14885(a,1,2,1,1))].">
      <j1 rule="para" parents="3805 14885"/>
    </justification>
  </clause>

  <clause id="14892">
    <literal><![CDATA[
      K(x,y * (z * (K(u,w) / v5))) = K(x,y * (z * (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(14834,a,12100,a)].">
      <j1 rule="hyper" parents="14834 12100"/>
    </justification>
  </clause>

  <clause id="14893">
    <literal><![CDATA[
      K(x,y * (z * T(u,w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * T(u,v5 / w))) = v6
    ]]></literal>
    <justification jstring="[para(7363(a,1),14834(a,1,2,2,2))].">
      <j1 rule="para" parents="7363 14834"/>
    </justification>
  </clause>

  <clause id="14894">
    <literal><![CDATA[
      K(x,T(y,z / u) / w) = K(x,T(y,u \ z) / w)
    ]]></literal>
    <justification jstring="[hyper(14853,a,xx),flip(a)].">
      <j1 rule="hyper" parents="14853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14895">
    <literal><![CDATA[
      K(x,T(y,z \ 1) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,v5 \ (z \ v5)) / u) = w
    ]]></literal>
    <justification jstring="[para(4431(a,1),14853(a,1,2,1))].">
      <j1 rule="para" parents="4431 14853"/>
    </justification>
  </clause>

  <clause id="14896">
    <literal><![CDATA[
      K(x,T(y,z \ u) / (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u / z) \ y) = w
    ]]></literal>
    <justification jstring="[para(14894(a,1),11985(a,1))].">
      <j1 rule="para" parents="14894 11985"/>
    </justification>
  </clause>

  <clause id="14897">
    <literal><![CDATA[
      K(x,(y / T(z,T(u,w))) / T(v5,T(z,u) \ y)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5 \ (y / T(z,T(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(14794(a,1),14865(a,1,2,2))].">
      <j1 rule="para" parents="14794 14865"/>
    </justification>
  </clause>

  <clause id="14898">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) * (v5 \ 1)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z / (v5 \ K(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(13024(a,1),14880(a,1,2,2,2))].">
      <j1 rule="para" parents="13024 14880"/>
    </justification>
  </clause>

  <clause id="14899">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * (T(w,v5) * v6)) = K(x,K(w,v5) * (w * v6))
    ]]></literal>
    <justification jstring="[hyper(14807,a,14811,a),flip(a)].">
      <j1 rule="hyper" parents="14807 14811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14900">
    <literal><![CDATA[
      K(x,K(y,z) * (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(14899(a,1),7871(a,1))].">
      <j1 rule="para" parents="14899 7871"/>
    </justification>
  </clause>

  <clause id="14901">
    <literal><![CDATA[
      K(x,y * (z * K(u,w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * K(u,v5 / w))) = v6
    ]]></literal>
    <justification jstring="[para(7642(a,1),14881(a,1,2,2,2))].">
      <j1 rule="para" parents="7642 14881"/>
    </justification>
  </clause>

  <clause id="14902">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * v5)) = K(x,y * (T(z,u) * v5))
    ]]></literal>
    <justification jstring="[hyper(14886,a,xx),flip(a)].">
      <j1 rule="hyper" parents="14886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14903">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) * v5)) = K(x,y * (T(z,w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(113(a,1),14902(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="113 14902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14904">
    <literal><![CDATA[
      K(x,L(T(y,T(z,u)) \ w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) \ w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(6813(a,1),14888(a,1,2,1,1))].">
      <j1 rule="para" parents="6813 14888"/>
    </justification>
  </clause>

  <clause id="14905">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) / u) = K(x,(((z / y) / z) * z) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12001,a(flip),b,14891,a),flip(a)].">
      <j1 rule="hyper" parents="63 12001 14891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14906">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) / u) = K(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[para(12(a,1),14905(a,2,2,1))].">
      <j1 rule="para" parents="12 14905"/>
    </justification>
  </clause>

  <clause id="14908">
    <literal><![CDATA[
      K(x,(y * ((z \ y) / y)) / u) = K(x,(y / z) / u)
    ]]></literal>
    <justification jstring="[para(3837(a,1),14906(a,1,2,1))].">
      <j1 rule="para" parents="3837 14906"/>
    </justification>
  </clause>

  <clause id="14909">
    <literal><![CDATA[
      K(x,T(y,z * (y \ u)) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(10525(a,1),14867(a,1,2,1))].">
      <j1 rule="para" parents="10525 14867"/>
    </justification>
  </clause>

  <clause id="14910">
    <literal><![CDATA[
      K(x,y * (z * T(u,w / v5))) = K(x,y * (z * T(u,v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(14893,a,xx)].">
      <j1 rule="hyper" parents="14893"/>
    </justification>
  </clause>

  <clause id="14911">
    <literal><![CDATA[
      T(x,y * (z * T(u,w / v5))) = T(x,y * (z * T(u,v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(132,a,14910,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 14910 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14912">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[hyper(12140,a,14909,a)].">
      <j1 rule="hyper" parents="12140 14909"/>
    </justification>
  </clause>

  <clause id="14913">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * (z / y))) = K(x,(u * (z / y)) * y)
    ]]></literal>
    <justification jstring="[para(9613(a,1),14912(a,2,2))].">
      <j1 rule="para" parents="9613 14912"/>
    </justification>
  </clause>

  <clause id="14914">
    <literal><![CDATA[
      T(K(x,T(y,z)) * u,w) * K(y,x) = T(K(x,y) * u,w) * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(7154,a,14776,a),flip(a)].">
      <j1 rule="hyper" parents="7154 14776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14915">
    <literal><![CDATA[
      K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w) = T(K(x,y) * u,w) * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,10595,a,b,14914,a)].">
      <j1 rule="hyper" parents="63 10595 14914"/>
    </justification>
  </clause>

  <clause id="14916">
    <literal><![CDATA[
      T(T(x,x * y) * K(L(x,y,x) * y,z),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(4323(a,1),13337(a,1,1,1))].">
      <j1 rule="para" parents="4323 13337"/>
    </justification>
  </clause>

  <clause id="14917">
    <literal><![CDATA[
      a(x,y,z * (u * u)) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(1388(a,1),13375(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1388 13375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14918">
    <literal><![CDATA[
      a(x,y,z * (u * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,13371,a,b,14917,a),flip(a)].">
      <j1 rule="hyper" parents="347 13371 14917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14920">
    <literal><![CDATA[
      a(x,y,z * (u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(14917(a,2),13376(a,1))].">
      <j1 rule="para" parents="14917 13376"/>
    </justification>
  </clause>

  <clause id="14921">
    <literal><![CDATA[
      a(x,y,z * (u * (w * w))) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(33(a,1),14918(a,1,3))].">
      <j1 rule="para" parents="33 14918"/>
    </justification>
  </clause>

  <clause id="14922">
    <literal><![CDATA[
      a(x,y,z \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(240(a,1),14918(a,1,3)),flip(a)].">
      <j1 rule="para" parents="240 14918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14923">
    <literal><![CDATA[
      a(x,y,1 / z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(245(a,1),14918(a,1,3))].">
      <j1 rule="para" parents="245 14918"/>
    </justification>
  </clause>

  <clause id="14924">
    <literal><![CDATA[
      a(x,y,z \ (u * u)) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(460(a,1),14918(a,1,3))].">
      <j1 rule="para" parents="460 14918"/>
    </justification>
  </clause>

  <clause id="14925">
    <literal><![CDATA[
      a(x,y,z * (1 / u)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(479(a,1),14918(a,1,3))].">
      <j1 rule="para" parents="479 14918"/>
    </justification>
  </clause>

  <clause id="14926">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * w))) = a(x,y,z \ (u \ 1))
    ]]></literal>
    <justification jstring="[para(727(a,1),14918(a,1,3))].">
      <j1 rule="para" parents="727 14918"/>
    </justification>
  </clause>

  <clause id="14927">
    <literal><![CDATA[
      a(x,y,L(z * (u * u),w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(1390(a,2),14918(a,1,3))].">
      <j1 rule="para" parents="1390 14918"/>
    </justification>
  </clause>

  <clause id="14928">
    <literal><![CDATA[
      a(x,y,((z * u) * z) * u) = a(x,y,a(z * u,z,u))
    ]]></literal>
    <justification jstring="[para(13372(a,1),14918(a,1,3))].">
      <j1 rule="para" parents="13372 14918"/>
    </justification>
  </clause>

  <clause id="14929">
    <literal><![CDATA[
      a(x,y,(z * z) \ u) = a(x,y,u \ (z * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4128,a(flip),b,14922,a),flip(a)].">
      <j1 rule="hyper" parents="63 4128 14922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14930">
    <literal><![CDATA[
      R(x,y,(z * ((u * u) * (w * (v5 \ 1)))) \ ((z * ((u * u) * w)) * v5)) = R(x,y,a(z * (u * u),w,v5))
    ]]></literal>
    <justification jstring="[para(14922(a,1),2389(a,2,3))].">
      <j1 rule="para" parents="14922 2389"/>
    </justification>
  </clause>

  <clause id="14931">
    <literal><![CDATA[
      a(x,y,z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(14922(a,1),6430(a,1))].">
      <j1 rule="para" parents="14922 6430"/>
    </justification>
  </clause>

  <clause id="14932">
    <literal><![CDATA[
      T(x,a(y,z,z) \ 1) = x
    ]]></literal>
    <justification jstring="[para(14922(a,1),9777(a,1,2,1))].">
      <j1 rule="para" parents="14922 9777"/>
    </justification>
  </clause>

  <clause id="14933">
    <literal><![CDATA[
      (x * x) * ((y \ (x * x)) \ a(z,u,y \ 1)) = ((y \ 1) \ 1) * a(z,u,y)
    ]]></literal>
    <justification jstring="[para(14922(a,1),10917(a,2,2))].">
      <j1 rule="para" parents="14922 10917"/>
    </justification>
  </clause>

  <clause id="14934">
    <literal><![CDATA[
      a(x,y,z) \ ((x * y) * (z \ 1)) = x * (y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(14922(a,1),13379(a,1,1))].">
      <j1 rule="para" parents="14922 13379"/>
    </justification>
  </clause>

  <clause id="14935">
    <literal><![CDATA[
      x / (a(y,z,z) \ 1) = (a(y,z,z) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(7761,a,14932,a),flip(a)].">
      <j1 rule="hyper" parents="7761 14932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14936">
    <literal><![CDATA[
      a(x,y,z \ (u * u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,14922,a(flip),b,14924,a),flip(a)].">
      <j1 rule="hyper" parents="347 14922 14924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14937">
    <literal><![CDATA[
      a(x,y,z \ (u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(14924(a,2),14931(a,1))].">
      <j1 rule="para" parents="14924 14931"/>
    </justification>
  </clause>

  <clause id="14938">
    <literal><![CDATA[
      a(x,y,z * (u \ 1)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(80(a,1),14925(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="80 14925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14939">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ z) = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1409(a,1),14938(a,1,3))].">
      <j1 rule="para" parents="1409 14938"/>
    </justification>
  </clause>

  <clause id="14940">
    <literal><![CDATA[
      a(x,y,z * (u * (w * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * u) = v5
    ]]></literal>
    <justification jstring="[para(33(a,1),14920(a,1,3))].">
      <j1 rule="para" parents="33 14920"/>
    </justification>
  </clause>

  <clause id="14941">
    <literal><![CDATA[
      a(x,y,z * (1 / u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * u) = w
    ]]></literal>
    <justification jstring="[para(479(a,1),14920(a,1,3))].">
      <j1 rule="para" parents="479 14920"/>
    </justification>
  </clause>

  <clause id="14942">
    <literal><![CDATA[
      a(x,y,L(z * (u * u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(1390(a,2),14920(a,1,3))].">
      <j1 rule="para" parents="1390 14920"/>
    </justification>
  </clause>

  <clause id="14943">
    <literal><![CDATA[
      a(x,y,(z * u) * (u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(13395(a,1),14920(a,1,3))].">
      <j1 rule="para" parents="13395 14920"/>
    </justification>
  </clause>

  <clause id="14944">
    <literal><![CDATA[
      a(x,y,z * (u * (z * u))) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,z * u)) = w
    ]]></literal>
    <justification jstring="[para(13379(a,1),14937(a,1,3))].">
      <j1 rule="para" parents="13379 14937"/>
    </justification>
  </clause>

  <clause id="14945">
    <literal><![CDATA[
      a(x,y,z * (u * (w * (v5 * v5)))) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(33(a,1),14921(a,1,3,2))].">
      <j1 rule="para" parents="33 14921"/>
    </justification>
  </clause>

  <clause id="14947">
    <literal><![CDATA[
      a(x,y,z * ((u \ L(u,w,v5)) * L(u,w,v5))) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(3537(a,1),14921(a,1,3,2))].">
      <j1 rule="para" parents="3537 14921"/>
    </justification>
  </clause>

  <clause id="14948">
    <literal><![CDATA[
      a(x,y,(z * z) \ u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,14936,a(flip),b,14929,a),flip(a)].">
      <j1 rule="hyper" parents="347 14936 14929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14949">
    <literal><![CDATA[
      a(x,y,(z * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(14929(a,2),14937(a,1))].">
      <j1 rule="para" parents="14929 14937"/>
    </justification>
  </clause>

  <clause id="14950">
    <literal><![CDATA[
      a(x,y \ 1,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1786,a,14948,a)].">
      <j1 rule="hyper" parents="1786 14948"/>
    </justification>
  </clause>

  <clause id="14951">
    <literal><![CDATA[
      a(x,y,(z * z) \ (u * w)) = a(x,y,u * (w \ 1))
    ]]></literal>
    <justification jstring="[hyper(347,a,14938,a,b,14948,a),flip(a)].">
      <j1 rule="hyper" parents="347 14938 14948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14953">
    <literal><![CDATA[
      a(x,y / (z * z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2104,a,b,14948,a)].">
      <j1 rule="hyper" parents="63 2104 14948"/>
    </justification>
  </clause>

  <clause id="14954">
    <literal><![CDATA[
      a(x,y,(z * z) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12443,a(flip),b,14948,a),flip(a)].">
      <j1 rule="hyper" parents="63 12443 14948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14955">
    <literal><![CDATA[
      a(x,y * (z * z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2101,a(flip),b,14948,a),flip(a)].">
      <j1 rule="hyper" parents="63 2101 14948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14956">
    <literal><![CDATA[
      a(x,y,z * (z * u)) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(18(a,2),14948(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18 14948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14957">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ u) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(500(a,1),14948(a,1,3)),flip(a)].">
      <j1 rule="para" parents="500 14948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14958">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,z)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(99(a,2),14948(a,1,3))].">
      <j1 rule="para" parents="99 14948"/>
    </justification>
  </clause>

  <clause id="14959">
    <literal><![CDATA[
      a(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(14948(a,1),1786(a,1))].">
      <j1 rule="para" parents="14948 1786"/>
    </justification>
  </clause>

  <clause id="14960">
    <literal><![CDATA[
      a(x,y,L((z * z) * u,w,v5)) = a(x,y,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(3174(a,1),14948(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3174 14948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14961">
    <literal><![CDATA[
      a(x,y,L((z \ 1) \ u,w,v5)) = a(x,y,L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(3183(a,1),14948(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3183 14948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14962">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * (z \ L(z,u,w))) \ v5) = a(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(12297(a,1),14948(a,1,3))].">
      <j1 rule="para" parents="12297 14948"/>
    </justification>
  </clause>

  <clause id="14963">
    <literal><![CDATA[
      (x * (y \ a(z,u,y))) \ ((x * (y \ 1)) * a(z,u,y)) = a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10919,a,b,14950,a)].">
      <j1 rule="hyper" parents="63 10919 14950"/>
    </justification>
  </clause>

  <clause id="14964">
    <literal><![CDATA[
      a(x,1 / y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,4044,a,b,14950,a)].">
      <j1 rule="hyper" parents="63 4044 14950"/>
    </justification>
  </clause>

  <clause id="14965">
    <literal><![CDATA[
      a(x,y \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(14950(a,1),5850(a,1))].">
      <j1 rule="para" parents="14950 5850"/>
    </justification>
  </clause>

  <clause id="14966">
    <literal><![CDATA[
      a(x,L(y \ 1,z,z),u) = a(x,y * a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(14608(a,1),14950(a,1,2))].">
      <j1 rule="para" parents="14608 14950"/>
    </justification>
  </clause>

  <clause id="14967">
    <literal><![CDATA[
      a(x,y \ 1,z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(14950(a,2),14931(a,1))].">
      <j1 rule="para" parents="14950 14931"/>
    </justification>
  </clause>

  <clause id="14970">
    <literal><![CDATA[
      a(x,y * (z \ 1),u) = a(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(780(a,1),14953(a,1,2))].">
      <j1 rule="para" parents="780 14953"/>
    </justification>
  </clause>

  <clause id="14971">
    <literal><![CDATA[
      a(x,y \ (z \ 1),u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(820(a,1),14953(a,1,2))].">
      <j1 rule="para" parents="820 14953"/>
    </justification>
  </clause>

  <clause id="14972">
    <literal><![CDATA[
      a(x,L(y \ 1,z,u),w) = a(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(3322(a,1),14953(a,1,2))].">
      <j1 rule="para" parents="3322 14953"/>
    </justification>
  </clause>

  <clause id="14973">
    <literal><![CDATA[
      a(x,(y \ 1) \ 1,z) = a(x,y,(u * u) * z)
    ]]></literal>
    <justification jstring="[hyper(5850,a,14954,a),flip(a)].">
      <j1 rule="hyper" parents="5850 14954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14974">
    <literal><![CDATA[
      a(x,y * (z * (u * u)),w) = a(x,y * z,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,2102,a,b,14954,a)].">
      <j1 rule="hyper" parents="63 2102 14954"/>
    </justification>
  </clause>

  <clause id="14975">
    <literal><![CDATA[
      a(x,L(y \ z,y \ z,y),u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2103,a(flip),b,14954,a)].">
      <j1 rule="hyper" parents="63 2103 14954"/>
    </justification>
  </clause>

  <clause id="14976">
    <literal><![CDATA[
      a(x,y,(1 / z) \ u) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(521(a,1),14954(a,1,3)),flip(a)].">
      <j1 rule="para" parents="521 14954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14977">
    <literal><![CDATA[
      a(x,y,z \ L(z,u,w)) = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(3972(a,1),14954(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3972 14954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14978">
    <literal><![CDATA[
      R(x,y,((z * z) * u) * L((z * z) * u,w,w)) = R(x,y,a(w,w,u))
    ]]></literal>
    <justification jstring="[para(14954(a,1),14606(a,2,3))].">
      <j1 rule="para" parents="14954 14606"/>
    </justification>
  </clause>

  <clause id="14981">
    <literal><![CDATA[
      a(x,y \ (z * z),u) = a(x,y \ 1,u)
    ]]></literal>
    <justification jstring="[para(460(a,1),14955(a,1,2))].">
      <j1 rule="para" parents="460 14955"/>
    </justification>
  </clause>

  <clause id="14983">
    <literal><![CDATA[
      a(x,K(y,z) * T(y,z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(5448(a,1),14955(a,1,2))].">
      <j1 rule="para" parents="5448 14955"/>
    </justification>
  </clause>

  <clause id="14985">
    <literal><![CDATA[
      a(x,1 / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4044(a,2),14965(a,1))].">
      <j1 rule="para" parents="4044 14965"/>
    </justification>
  </clause>

  <clause id="14986">
    <literal><![CDATA[
      a(x,y,z \ L(L(z,u,w),v5,v6)) = a(x,y,z * L(L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(10923(a,1),14957(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10923 14957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14987">
    <literal><![CDATA[
      a(x,y \ z,x) = a(x,z * y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12122,a(flip),b,14970,a)].">
      <j1 rule="hyper" parents="63 12122 14970"/>
    </justification>
  </clause>

  <clause id="14988">
    <literal><![CDATA[
      a(x,L(y,z,u) \ y,w) = a(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(1409(a,1),14970(a,1,2))].">
      <j1 rule="para" parents="1409 14970"/>
    </justification>
  </clause>

  <clause id="14989">
    <literal><![CDATA[
      (x * ((x \ 1) / y)) * y = a(x,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14580,a,b,14971,a)].">
      <j1 rule="hyper" parents="63 14580 14971"/>
    </justification>
  </clause>

  <clause id="14990">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (u \ z)) = a(x,y,(u \ z) * (z \ u))
    ]]></literal>
    <justification jstring="[para(1636(a,1),14976(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1636 14976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14991">
    <literal><![CDATA[
      a(x,y,z \ a(u,w,z)) = a(x,y,z * a(u,w,z))
    ]]></literal>
    <justification jstring="[para(14326(a,1),14976(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14326 14976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14992">
    <literal><![CDATA[
      a(x,y \ (z * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(14981(a,2),14965(a,1))].">
      <j1 rule="para" parents="14981 14965"/>
    </justification>
  </clause>

  <clause id="14993">
    <literal><![CDATA[
      a(x,y,L(z,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u * (u * z)) = w
    ]]></literal>
    <justification jstring="[para(18(a,2),14949(a,1,3))].">
      <j1 rule="para" parents="18 14949"/>
    </justification>
  </clause>

  <clause id="14994">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * u) = w
    ]]></literal>
    <justification jstring="[para(99(a,2),14949(a,1,3))].">
      <j1 rule="para" parents="99 14949"/>
    </justification>
  </clause>

  <clause id="14995">
    <literal><![CDATA[
      a(x,y,L((z * z) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(3181(a,2),14949(a,1,3))].">
      <j1 rule="para" parents="3181 14949"/>
    </justification>
  </clause>

  <clause id="14996">
    <literal><![CDATA[
      a(x,y,L(L(z \ u,w,v5),z,z)) = a(x,y,L(z * u,w,v5))
    ]]></literal>
    <justification jstring="[para(3336(a,1),14956(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3336 14956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14997">
    <literal><![CDATA[
      x \ a(y,x \ y,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y * ((y \ 1) / x),x) = z
    ]]></literal>
    <justification jstring="[para(14989(a,1),360(a,1,2))].">
      <j1 rule="para" parents="14989 360"/>
    </justification>
  </clause>

  <clause id="14998">
    <literal><![CDATA[
      a(x,L(y \ z,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z * y,u) = w
    ]]></literal>
    <justification jstring="[para(99(a,2),14992(a,1,2))].">
      <j1 rule="para" parents="99 14992"/>
    </justification>
  </clause>

  <clause id="14999">
    <literal><![CDATA[
      a(x,T(y,y \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,(y \ z) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(466(a,1),14992(a,1,2))].">
      <j1 rule="para" parents="466 14992"/>
    </justification>
  </clause>

  <clause id="15000">
    <literal><![CDATA[
      a(x,K(y,z) * T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(5157(a,1),14992(a,1,2))].">
      <j1 rule="para" parents="5157 14992"/>
    </justification>
  </clause>

  <clause id="15001">
    <literal><![CDATA[
      a(x,L(y \ 1,z,u),w) = a(x,L(y,z,u) \ 1,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,14950,a,b,14972,a),flip(a)].">
      <j1 rule="hyper" parents="347 14950 14972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15002">
    <literal><![CDATA[
      a(x,y,(z * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(14973(a,1),5850(a,1))].">
      <j1 rule="para" parents="14973 5850"/>
    </justification>
  </clause>

  <clause id="15003">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ u) = w
    ]]></literal>
    <justification jstring="[para(495(a,1),15002(a,1,3))].">
      <j1 rule="para" parents="495 15002"/>
    </justification>
  </clause>

  <clause id="15004">
    <literal><![CDATA[
      a(x,y,(z * (u \ 1)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * u) \ w) = v5
    ]]></literal>
    <justification jstring="[para(819(a,1),15002(a,1,3))].">
      <j1 rule="para" parents="819 15002"/>
    </justification>
  </clause>

  <clause id="15005">
    <literal><![CDATA[
      a(x,y * (z * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(2100(a,2),15002(a,1))].">
      <j1 rule="para" parents="2100 15002"/>
    </justification>
  </clause>

  <clause id="15006">
    <literal><![CDATA[
      a(x,L(y \ z,y \ z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,u) = w
    ]]></literal>
    <justification jstring="[para(2103(a,1),15002(a,1))].">
      <j1 rule="para" parents="2103 15002"/>
    </justification>
  </clause>

  <clause id="15007">
    <literal><![CDATA[
      a(x,y,L((z * z) * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(3176(a,2),15002(a,1,3))].">
      <j1 rule="para" parents="3176 15002"/>
    </justification>
  </clause>

  <clause id="15008">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(3325(a,1),15002(a,1,3))].">
      <j1 rule="para" parents="3325 15002"/>
    </justification>
  </clause>

  <clause id="15011">
    <literal><![CDATA[
      a(x,y,z \ (u \ 1)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),14926(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="9 14926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15012">
    <literal><![CDATA[
      a(x,y,y \ x) / (y \ (x \ 1)) = x * y
    ]]></literal>
    <justification jstring="[hyper(131,a,15011,a(flip),b,851,a)].">
      <j1 rule="hyper" parents="131 15011 851"/>
    </justification>
  </clause>

  <clause id="15013">
    <literal><![CDATA[
      a(x,y,L((z \ 1) * u,(z \ 1) * u,L(u \ 1,u,z \ 1))) = a(x,y,((z \ 1) * (((z \ 1) * u) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(10163(a,2),15011(a,1,3))].">
      <j1 rule="para" parents="10163 15011"/>
    </justification>
  </clause>

  <clause id="15014">
    <literal><![CDATA[
      R(x * y,y \ (x \ 1),a(x,y,y \ x)) \ 1 = (y \ (x \ 1)) * (a(x,y,y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(15012(a,1),2196(a,1,1,1))].">
      <j1 rule="para" parents="15012 2196"/>
    </justification>
  </clause>

  <clause id="15015">
    <literal><![CDATA[
      a(x,y,L(z / (u * u),w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(12(a,1),14927(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="12 14927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15016">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(240(a,1),14927(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="240 14927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15017">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w)) = a(x,y,L(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,14922,a,b,15016,a),flip(a)].">
      <j1 rule="hyper" parents="347 14922 15016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15018">
    <literal><![CDATA[
      a(x,y,L(R(z / u,u,z),w,v5)) = a(x,y,L(u * (z \ 1),w,v5))
    ]]></literal>
    <justification jstring="[para(2196(a,1),15016(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="2196 15016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15019">
    <literal><![CDATA[
      a(x,y,L(1 / z,z,u) \ (1 / z)) = a(x,y,(1 / z) * ((u * (1 / (1 / z))) \ u))
    ]]></literal>
    <justification jstring="[para(3284(a,1),14939(a,2,3,2))].">
      <j1 rule="para" parents="3284 14939"/>
    </justification>
  </clause>

  <clause id="15020">
    <literal><![CDATA[
      a(x,y,z * L(z,u,u)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(14600(a,1),14939(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14600 14939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15021">
    <literal><![CDATA[
      a(x,y,z * (u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * u) = w
    ]]></literal>
    <justification jstring="[para(14951(a,1),14949(a,1))].">
      <j1 rule="para" parents="14951 14949"/>
    </justification>
  </clause>

  <clause id="15022">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ z) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(1409(a,1),15021(a,1,3))].">
      <j1 rule="para" parents="1409 15021"/>
    </justification>
  </clause>

  <clause id="15023">
    <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(97(a,1),14960(a,1,3,1))].">
      <j1 rule="para" parents="97 14960"/>
    </justification>
  </clause>

  <clause id="15024">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * L((z \ 1) \ u,z,z)) = a(x,y,((z \ 1) \ u) \ (z * u))
    ]]></literal>
    <justification jstring="[para(3192(a,1),14977(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3192 14977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15026">
    <literal><![CDATA[
      a(x,y * L(y,z,z),u) = a(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(14600(a,1),14988(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14600 14988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15027">
    <literal><![CDATA[
      a(x,y,z \ L(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(12281(a,1),14994(a,1,3))].">
      <j1 rule="para" parents="12281 14994"/>
    </justification>
  </clause>

  <clause id="15028">
    <literal><![CDATA[
      a(x,L(y,z,u) \ y,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y * L(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(12354(a,1),14998(a,1,2))].">
      <j1 rule="para" parents="12354 14998"/>
    </justification>
  </clause>

  <clause id="15029">
    <literal><![CDATA[
      a(x,L(y \ 1,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,L(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(15001(a,2),14965(a,1))].">
      <j1 rule="para" parents="15001 14965"/>
    </justification>
  </clause>

  <clause id="15030">
    <literal><![CDATA[
      a(x,y,L(z * (u \ 1),w,v5)) = a(x,y,L(z * u,w,v5))
    ]]></literal>
    <justification jstring="[para(780(a,1),15015(a,1,3,1))].">
      <j1 rule="para" parents="780 15015"/>
    </justification>
  </clause>

  <clause id="15031">
    <literal><![CDATA[
      a(x,y,L(L(z \ 1,u,w),v5,v6)) = a(x,y,L(L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(3322(a,1),15015(a,1,3,1))].">
      <j1 rule="para" parents="3322 15015"/>
    </justification>
  </clause>

  <clause id="15032">
    <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(15017(a,2),14931(a,1))].">
      <j1 rule="para" parents="15017 14931"/>
    </justification>
  </clause>

  <clause id="15033">
    <literal><![CDATA[
      1 \ ((x * y) * (a(z,u,x) \ 1)) = x * (y * (a(z,u,x) \ 1))
    ]]></literal>
    <justification jstring="[para(12361(a,1),14934(a,1,1))].">
      <j1 rule="para" parents="12361 14934"/>
    </justification>
  </clause>

  <clause id="15034">
    <literal><![CDATA[
      a(x,y * a(z,z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,L(y,z,z),u) = w
    ]]></literal>
    <justification jstring="[para(14966(a,1),15029(a,1))].">
      <j1 rule="para" parents="14966 15029"/>
    </justification>
  </clause>

  <clause id="15035">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ 1))) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(240(a,1),14945(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="240 14945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15036">
    <literal><![CDATA[
      a(x,y,z * (L(u,w,v5) \ u)) = a(x,y,z * (u * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(1409(a,1),15035(a,1,3,2))].">
      <j1 rule="para" parents="1409 15035"/>
    </justification>
  </clause>

  <clause id="15037">
    <literal><![CDATA[
      a(x,y,L((z \ 1) \ R(z,u,u),w,v5)) = a(x,y,L(a(z,u,u),w,v5))
    ]]></literal>
    <justification jstring="[para(13398(a,1),14961(a,2,3,1))].">
      <j1 rule="para" parents="13398 14961"/>
    </justification>
  </clause>

  <clause id="15038">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((u \ z) \ 1)) = a(x,y,(u \ z) \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,14938,a,b,14990,a)].">
      <j1 rule="hyper" parents="347 14938 14990"/>
    </justification>
  </clause>

  <clause id="15039">
    <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(1409(a,1),15030(a,1,3,1))].">
      <j1 rule="para" parents="1409 15030"/>
    </justification>
  </clause>

  <clause id="15040">
    <literal><![CDATA[
      a(x,y,L(L(z \ u,w,v5),z,z)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(568(a,2),14995(a,1,3))].">
      <j1 rule="para" parents="568 14995"/>
    </justification>
  </clause>

  <clause id="15041">
    <literal><![CDATA[
      a(x,y,L(L((z \ 1) \ u,w,v5),z,z \ 1)) = a(x,y,L((z \ 1) * u,w,v5))
    ]]></literal>
    <justification jstring="[para(3188(a,1),14996(a,1,3))].">
      <j1 rule="para" parents="3188 14996"/>
    </justification>
  </clause>

  <clause id="15043">
    <literal><![CDATA[
      a(x,y,L((z * z) * L(u,w,v5),v6,v7)) = a(x,y,L(L(u \ 1,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(347,a,14960,a,b,15031,a)].">
      <j1 rule="hyper" parents="347 14960 15031"/>
    </justification>
  </clause>

  <clause id="15044">
    <literal><![CDATA[
      (x * y) * (a(z,u,x) \ 1) = x * (y * (a(z,u,x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(185,a,15033,a)].">
      <j1 rule="hyper" parents="185 15033"/>
    </justification>
  </clause>

  <clause id="15045">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,z) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(12406,a,15044,a)].">
      <j1 rule="hyper" parents="12406 15044"/>
    </justification>
  </clause>

  <clause id="15046">
    <literal><![CDATA[
      a(x,y,z) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      L(a(x,y,z) \ 1,w,z) = u
    ]]></literal>
    <justification jstring="[para(15045(a,1),3518(a,1))].">
      <j1 rule="para" parents="15045 3518"/>
    </justification>
  </clause>

  <clause id="15047">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u \ z) * (z \ u)) = w
    ]]></literal>
    <justification jstring="[para(15038(a,1),15021(a,1))].">
      <j1 rule="para" parents="15038 15021"/>
    </justification>
  </clause>

  <clause id="15048">
    <literal><![CDATA[
      R(x,y,((z * z) * u) * (z * (z * u))) = R(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(3180(a,1),14978(a,1,3,2))].">
      <j1 rule="para" parents="3180 14978"/>
    </justification>
  </clause>

  <clause id="15049">
    <literal><![CDATA[
      R(x,y,(z * (z * u)) * ((z * z) * u)) = R(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(13411(a,1),15048(a,1,3))].">
      <j1 rule="para" parents="13411 15048"/>
    </justification>
  </clause>

  <clause id="15050">
    <literal><![CDATA[
      a(x,y,L(z \ L(z,u,w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(12288(a,1),15040(a,1,3))].">
      <j1 rule="para" parents="12288 15040"/>
    </justification>
  </clause>

  <clause id="15051">
    <literal><![CDATA[
      (x * x) * ((y \ (x * x)) \ a(z,u,y)) = ((y \ 1) \ 1) * a(z,u,y)
    ]]></literal>
    <justification jstring="[para(14922(a,1),14933(a,1,2,2))].">
      <j1 rule="para" parents="14922 14933"/>
    </justification>
  </clause>

  <clause id="15052">
    <literal><![CDATA[
      ((x \ 1) \ 1) * a(y,z,x) = (x \ 1) \ a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(965,a,15051,a),flip(a)].">
      <j1 rule="hyper" parents="965 15051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15053">
    <literal><![CDATA[
      a(x,y,L(L(z \ 1,u,w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(15043(a,1),15007(a,1))].">
      <j1 rule="para" parents="15043 15007"/>
    </justification>
  </clause>

  <clause id="15054">
    <literal><![CDATA[
      x \ R(x * R(x \ 1,y,z),x,y * z) = (x \ 1) * a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2247(a,1),13400(a,1,2))].">
      <j1 rule="para" parents="2247 13400"/>
    </justification>
  </clause>

  <clause id="15055">
    <literal><![CDATA[
      (x \ 1) * a(x \ 1,y,z) = x \ a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(13858(a,1),15054(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13858 15054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15056">
    <literal><![CDATA[
      T((1 / x) \ a((1 / x) \ 1,y,z),x * a((1 / x) \ 1,y,z)) = x * a((1 / x) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(468,a,15055,a(flip),b,218,a(flip))].">
      <j1 rule="hyper" parents="468 15055 218"/>
    </justification>
  </clause>

  <clause id="15057">
    <literal><![CDATA[
      R(x,y,z) \ ((R(x,y,z) * (x \ u)) * x) = u * K((x \ u) * R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(1746(a,1),13470(a,1,2,1))].">
      <j1 rule="para" parents="1746 13470"/>
    </justification>
  </clause>

  <clause id="15058">
    <literal><![CDATA[
      L(x,y,x) * (x \ (T(x,T(z,y)) * y)) = (x * (y * T(x,z))) / x
    ]]></literal>
    <justification jstring="[para(7224(a,1),13776(a,1,1))].">
      <j1 rule="para" parents="7224 13776"/>
    </justification>
  </clause>

  <clause id="15059">
    <literal><![CDATA[
      L(x,y,x) * (K(x,T(z,y)) * y) = (x * (y * T(x,z))) / x
    ]]></literal>
    <justification jstring="[para(5157(a,1),15058(a,1,2))].">
      <j1 rule="para" parents="5157 15058"/>
    </justification>
  </clause>

  <clause id="15061">
    <literal><![CDATA[
      L(x,y,x) * (y * K(x,z)) = (x * (y * T(x,z))) / x
    ]]></literal>
    <justification jstring="[para(7373(a,1),15059(a,1,2))].">
      <j1 rule="para" parents="7373 15059"/>
    </justification>
  </clause>

  <clause id="15062">
    <literal><![CDATA[
      L(x,y * z,x) * ((y \ z) * K(x,u)) = (x * ((y \ z) * T(x,u))) / x
    ]]></literal>
    <justification jstring="[para(12189(a,1),15061(a,1,1))].">
      <j1 rule="para" parents="12189 15061"/>
    </justification>
  </clause>

  <clause id="15063">
    <literal><![CDATA[
      x * ((R(x,x * y,x) \ y) * K(x,z)) = (x * ((x \ y) * T(x,z))) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,12111,a(flip),b,15062,a)].">
      <j1 rule="hyper" parents="63 12111 15062"/>
    </justification>
  </clause>

  <clause id="15064">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(14226,a,14545,a)].">
      <j1 rule="hyper" parents="14226 14545"/>
    </justification>
  </clause>

  <clause id="15065">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,L(y,z,z \ 1) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(347,a,12233,a(flip),b,14227,a),flip(a)].">
      <j1 rule="hyper" parents="347 12233 14227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15066">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(x,z,K(u,y)) = (K(x,L(y,z,u)) * z) * u
    ]]></literal>
    <justification jstring="[para(7612(a,1),14292(a,1,2,3))].">
      <j1 rule="para" parents="7612 14292"/>
    </justification>
  </clause>

  <clause id="15067">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(y,z,K(u,x)) = (K(x,L(y,z,u)) * z) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,14067,a,b,15066,a)].">
      <j1 rule="hyper" parents="63 14067 15066"/>
    </justification>
  </clause>

  <clause id="15069">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * z) * u = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(14541,a,15067,a),flip(a)].">
      <j1 rule="hyper" parents="14541 15067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15070">
    <literal><![CDATA[
      K(x,L(L(y,z,u),z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14171,a,15069,a)].">
      <j1 rule="hyper" parents="14171 15069"/>
    </justification>
  </clause>

  <clause id="15071">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * (z * u)) * u = K(x,y) * ((z * u) * u)
    ]]></literal>
    <justification jstring="[para(14205(a,1),15069(a,1,1,1))].">
      <j1 rule="para" parents="14205 15069"/>
    </justification>
  </clause>

  <clause id="15073">
    <literal><![CDATA[
      K(x,L(L(y,z,u),z,u)) = K(x,L(y,w,v5 * v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,14085,a,b,15070,a),flip(a)].">
      <j1 rule="hyper" parents="347 14085 15070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15074">
    <literal><![CDATA[
      K(x \ (y * z),L(u,x,y)) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14200,a(flip),b,15070,a)].">
      <j1 rule="hyper" parents="63 14200 15070"/>
    </justification>
  </clause>

  <clause id="15075">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(329(a,1),15070(a,1,2,1))].">
      <j1 rule="para" parents="329 15070"/>
    </justification>
  </clause>

  <clause id="15076">
    <literal><![CDATA[
      K(x,L(y \ (z * u),z \ y,z)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(561(a,1),15070(a,1,2,1))].">
      <j1 rule="para" parents="561 15070"/>
    </justification>
  </clause>

  <clause id="15077">
    <literal><![CDATA[
      K(x,L(L(y,z,u),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(15073(a,2),7618(a,1))].">
      <j1 rule="para" parents="15073 7618"/>
    </justification>
  </clause>

  <clause id="15078">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(329(a,1),15077(a,1,2,1))].">
      <j1 rule="para" parents="329 15077"/>
    </justification>
  </clause>

  <clause id="15079">
    <literal><![CDATA[
      K((x * y) \ z,L(u,y,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ z),u) = w
    ]]></literal>
    <justification jstring="[para(11113(a,1),15077(a,1))].">
      <j1 rule="para" parents="11113 15077"/>
    </justification>
  </clause>

  <clause id="15080">
    <literal><![CDATA[
      K(x \ (y * z),L(u,x,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(14200(a,1),15077(a,1))].">
      <j1 rule="para" parents="14200 15077"/>
    </justification>
  </clause>

  <clause id="15081">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,y,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x * z),u) = w
    ]]></literal>
    <justification jstring="[para(15074(a,1),15077(a,1))].">
      <j1 rule="para" parents="15074 15077"/>
    </justification>
  </clause>

  <clause id="15082">
    <literal><![CDATA[
      K(x,L((y * z) \ u,T(y,z),z)) = K(x,T(y,z) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(111(a,1),15075(a,1,2,1,1))].">
      <j1 rule="para" parents="111 15075"/>
    </justification>
  </clause>

  <clause id="15083">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(14198,a,15076,a)].">
      <j1 rule="hyper" parents="14198 15076"/>
    </justification>
  </clause>

  <clause id="15084">
    <literal><![CDATA[
      T(x,L(y \ (z * u),y,z)) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(132,a,15083,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 15083 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15085">
    <literal><![CDATA[
      T(x,L(y \ (z * u),y,z)) = x * K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(134,a,15083,a(flip),b,4924,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 15083 4924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15086">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,z \ 1),y,z)) = K(x,(z \ y) \ (((z \ 1) \ u) * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(1139(a,1),15083(a,1,2,1,2))].">
      <j1 rule="para" parents="1139 15083"/>
    </justification>
  </clause>

  <clause id="15087">
    <literal><![CDATA[
      T(x,(y \ (y \ z)) \ u) = T(x,z \ (y * (y * u)))
    ]]></literal>
    <justification jstring="[para(561(a,1),15084(a,1,2)),flip(a)].">
      <j1 rule="para" parents="561 15084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15088">
    <literal><![CDATA[
      T(x,L((y \ z) \ ((y \ 1) * u),y \ z,y \ 1)) = T(x,((y \ z) / T(y \ 1,z)) \ u)
    ]]></literal>
    <justification jstring="[para(4420(a,2),15084(a,2,2,1))].">
      <j1 rule="para" parents="4420 15084"/>
    </justification>
  </clause>

  <clause id="15089">
    <literal><![CDATA[
      T(x,L(y \ (z * u),y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15085(a,2),4984(a,1))].">
      <j1 rule="para" parents="15085 4984"/>
    </justification>
  </clause>

  <clause id="15090">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,y,x \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ ((x \ y) * z),u) = w
    ]]></literal>
    <justification jstring="[para(12147(a,1),15081(a,1))].">
      <j1 rule="para" parents="12147 15081"/>
    </justification>
  </clause>

  <clause id="15091">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * u = K(x,y) * ((z * u) * u)
    ]]></literal>
    <justification jstring="[para(14092(a,1),15071(a,1,1))].">
      <j1 rule="para" parents="14092 15071"/>
    </justification>
  </clause>

  <clause id="15092">
    <literal><![CDATA[
      (x * x) \ ((K(y,z) * u) \ (K(y,z) * ((u * x) * x))) = a(K(y,z) * u,x,x)
    ]]></literal>
    <justification jstring="[para(15091(a,1),14699(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="15091 14699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15093">
    <literal><![CDATA[
      K(x,L((y * z) \ u,y,z)) = K(x,T(y,z) \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(14128,a,15082,a)].">
      <j1 rule="hyper" parents="14128 15082"/>
    </justification>
  </clause>

  <clause id="15094">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14509,a(flip),b,14500,a)].">
      <j1 rule="hyper" parents="63 14509 14500"/>
    </justification>
  </clause>

  <clause id="15096">
    <literal><![CDATA[
      K(x,y \ (R(1 / z,z,y) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15064,a(flip),b,15094,a),flip(a)].">
      <j1 rule="hyper" parents="63 15064 15094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15097">
    <literal><![CDATA[
      K(x,y \ ((y / (z * y)) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(247(a,1),15096(a,1,2,2,1))].">
      <j1 rule="para" parents="247 15096"/>
    </justification>
  </clause>

  <clause id="15098">
    <literal><![CDATA[
      K(x,y \ ((z / y) \ u)) = K(x,y \ ((y / z) * u))
    ]]></literal>
    <justification jstring="[para(422(a,1),15096(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="422 15096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15099">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z \ ((z / u) * w)) = K(y,T(z \ ((u / z) \ w),x))
    ]]></literal>
    <justification jstring="[hyper(13345,a,15098,a),flip(a)].">
      <j1 rule="hyper" parents="13345 15098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15100">
    <literal><![CDATA[
      K(x,T(y \ ((z / y) \ u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),w)) = v5
    ]]></literal>
    <justification jstring="[para(15099(a,1),13345(a,1))].">
      <j1 rule="para" parents="15099 13345"/>
    </justification>
  </clause>

  <clause id="15101">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * u) \ y) = K(x,((z \ 1) * u) \ R(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,6469,a(flip),b,14510,a),flip(a)].">
      <j1 rule="hyper" parents="63 6469 14510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15102">
    <literal><![CDATA[
      T(x,T(x * y,z)) * K(y,T(x,z)) = L(x,y * K(x * y,z),x)
    ]]></literal>
    <justification jstring="[para(13038(a,1),14585(a,1,1,2))].">
      <j1 rule="para" parents="13038 14585"/>
    </justification>
  </clause>

  <clause id="15103">
    <literal><![CDATA[
      L(x,y * K(x * y,z),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9054,a(flip),b,15102,a),flip(a)].">
      <j1 rule="hyper" parents="63 9054 15102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15105">
    <literal><![CDATA[
      L(x,x \ T(x * y,z),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(13034(a,2),15103(a,1,2))].">
      <j1 rule="para" parents="13034 15103"/>
    </justification>
  </clause>

  <clause id="15106">
    <literal><![CDATA[
      L(x,x \ T(y,z),x) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),15105(a,1,2,2,1))].">
      <j1 rule="para" parents="10 15105"/>
    </justification>
  </clause>

  <clause id="15107">
    <literal><![CDATA[
      L(x,x \ (y / z),x) = L(x,x \ (z \ y),x)
    ]]></literal>
    <justification jstring="[para(113(a,1),15106(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 15106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15108">
    <literal><![CDATA[
      ((x * (y * z)) / x) \ L(z,z \ (x \ (x * (z * y))),z) = T(z * (z \ ((x * (z * y)) / x)),z) \ z
    ]]></literal>
    <justification jstring="[para(15107(a,1),11404(a,1,2))].">
      <j1 rule="para" parents="15107 11404"/>
    </justification>
  </clause>

  <clause id="15109">
    <literal><![CDATA[
      R(T(x * K(y,x),z),y,u) \ ((y * x) * u) = (y * K(z,x)) * u
    ]]></literal>
    <justification jstring="[para(9(a,1),14655(a,2,1,2,2))].">
      <j1 rule="para" parents="9 14655"/>
    </justification>
  </clause>

  <clause id="15110">
    <literal><![CDATA[
      K(x,(y * z) \ ((y * u) * z)) = (y * z) \ ((y * K(x,u)) * z)
    ]]></literal>
    <justification jstring="[hyper(128,a,15109,a(flip),b,9894,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 15109 9894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15111">
    <literal><![CDATA[
      K(x,(y * z) \ ((y * (u / y)) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      R(T(K(x,y \ u),y * z),y,z) = w
    ]]></literal>
    <justification jstring="[para(15110(a,2),7547(a,1))].">
      <j1 rule="para" parents="15110 7547"/>
    </justification>
  </clause>

  <clause id="15116">
    <literal><![CDATA[
      (R(x,x,y) * y) * L(z,x * y,a(x,x,y)) = a(x,x,y) * ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(1745(a,1),14731(a,1,1))].">
      <j1 rule="para" parents="1745 14731"/>
    </justification>
  </clause>

  <clause id="15117">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) / v5))) = K(x,y * (z / (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(14898,a,14527,a),flip(a)].">
      <j1 rule="hyper" parents="14898 14527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15118">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ L(T(K(y,z) / u,(K(y,z) / u) \ 1),w,v5)) = K(x,L(K(y,z) / u,w,v5) * (1 / (u \ K(y,z))))
    ]]></literal>
    <justification jstring="[para(3442(a,2),15117(a,1,2))].">
      <j1 rule="para" parents="3442 15117"/>
    </justification>
  </clause>

  <clause id="15119">
    <literal><![CDATA[
      T(T(x,x * y) * K(x * y,z),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(11942(a,1),14916(a,1,1,2))].">
      <j1 rule="para" parents="11942 14916"/>
    </justification>
  </clause>

  <clause id="15120">
    <literal><![CDATA[
      T(T(x * K(x * y,z),x * y),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(7510(a,2),15119(a,1,1))].">
      <j1 rule="para" parents="7510 15119"/>
    </justification>
  </clause>

  <clause id="15122">
    <literal><![CDATA[
      T(T(x * K(x * y,z),y),x * y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[hyper(453,a,15120,a)].">
      <j1 rule="hyper" parents="453 15120"/>
    </justification>
  </clause>

  <clause id="15123">
    <literal><![CDATA[
      T(T(x * K(x * y,z),y),x * y) = y \ T(T(x,x * y) * y,z)
    ]]></literal>
    <justification jstring="[para(4323(a,1),15122(a,2,2,1,1))].">
      <j1 rule="para" parents="4323 15122"/>
    </justification>
  </clause>

  <clause id="15124">
    <literal><![CDATA[
      R(x,y,z) \ ((R(x,y,z) * (x \ u)) * x) = u * K(u * (x \ R(x,y,z)),x)
    ]]></literal>
    <justification jstring="[para(13791(a,1),15057(a,2,2))].">
      <j1 rule="para" parents="13791 15057"/>
    </justification>
  </clause>

  <clause id="15125">
    <literal><![CDATA[
      L(a(x,y,y),x,K(z,u)) = a(K(z,u) * x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3184,a(flip),b,15092,a)].">
      <j1 rule="hyper" parents="63 3184 15092"/>
    </justification>
  </clause>

  <clause id="15126">
    <literal><![CDATA[
      a(K(x,y) * z,u,u) = a(z,u,u)
    ]]></literal>
    <justification jstring="[hyper(14425,a,15125,a),flip(a)].">
      <j1 rule="hyper" parents="14425 15125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15127">
    <literal><![CDATA[
      a(T(x,y),z,z) = a(x,z,z)
    ]]></literal>
    <justification jstring="[para(1324(a,2),15126(a,1,1))].">
      <j1 rule="para" parents="1324 15126"/>
    </justification>
  </clause>

  <clause id="15128">
    <literal><![CDATA[
      a(x \ T(y,z),u,u) = a(x \ y,u,u)
    ]]></literal>
    <justification jstring="[para(5456(a,1),15126(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5456 15126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15129">
    <literal><![CDATA[
      (R(x,y,z) * (x \ u)) * x = R(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,10530,a(flip),b,15124,a),flip(a)].">
      <j1 rule="hyper" parents="134 10530 15124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15130">
    <literal><![CDATA[
      K(K(x,y) * z,(K(x,y) * z) \ K(x,y)) = (z \ 1) \ T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(13836(a,1),13179(a,2,2))].">
      <j1 rule="para" parents="13836 13179"/>
    </justification>
  </clause>

  <clause id="15131">
    <literal><![CDATA[
      K(K(x,y) * z,(K(x,y) * z) \ K(x,y)) = z * T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,4499,a(flip),b,15130,a),flip(a)].">
      <j1 rule="hyper" parents="347 4499 15130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15132">
    <literal><![CDATA[
      K(K(x,y) * z,z \ 1) = z * T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6321,a,15131,a)].">
      <j1 rule="hyper" parents="6321 15131"/>
    </justification>
  </clause>

  <clause id="15134">
    <literal><![CDATA[
      K(x,y) * (y / L((x * y) / x,z,u)) = (L(y * K(x,y),z,u) \ y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14571,a,13448,a),flip(a)].">
      <j1 rule="hyper" parents="14571 13448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15135">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) * x) * u) != w
    ]]></literal>
    <literal><![CDATA[
      L((x \ 1) \ u,x,a(x,y,z) * x) = w
    ]]></literal>
    <justification jstring="[para(13904(a,1),3524(a,1))].">
      <j1 rule="para" parents="13904 3524"/>
    </justification>
  </clause>

  <clause id="15136">
    <literal><![CDATA[
      x * (K(y,L(x,z,u)) * K(w,L(y,z,u))) = (R(y,z,u) * x) / R(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(14081(a,1),14099(a,1,2,2))].">
      <j1 rule="para" parents="14081 14099"/>
    </justification>
  </clause>

  <clause id="15138">
    <literal><![CDATA[
      (L(x * K(y,x),z,u) \ x) * K(y,x) = x / ((y * L(x,z,u)) / T(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,13349,a(flip),b,15134,a),flip(a)].">
      <j1 rule="hyper" parents="63 13349 15134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15139">
    <literal><![CDATA[
      (R(x,y,z) * u) / R(T(x,w),y,z) = (L(x,y,z) * u) / L(T(x,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11266,a(flip),b,15136,a),flip(a)].">
      <j1 rule="hyper" parents="63 11266 15136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15140">
    <literal><![CDATA[
      (x * K(y,z)) / a((u \ 1) \ x,u \ 1,K(y,z)) = (x / (u \ 1)) * (u \ K(y,z))
    ]]></literal>
    <justification jstring="[para(14748(a,1),13020(a,1,2))].">
      <j1 rule="para" parents="14748 13020"/>
    </justification>
  </clause>

  <clause id="15141">
    <literal><![CDATA[
      R(K(x * y,z) * K(y,K(x,z)),y,u) = ((x \ T(x * y,z)) * u) / (y * u)
    ]]></literal>
    <justification jstring="[para(8782(a,1),13234(a,1,1,2))].">
      <j1 rule="para" parents="8782 13234"/>
    </justification>
  </clause>

  <clause id="15142">
    <literal><![CDATA[
      ((x \ T(x * y,z)) * u) / (y * u) = R(K(y * x,z),y,u)
    ]]></literal>
    <justification jstring="[para(10416(a,1),15141(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10416 15141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15143">
    <literal><![CDATA[
      ((x \ T(x * y,z)) * u) / (y * u) = K(y * x,L(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,14072,a(flip),b,15142,a),flip(a)].">
      <j1 rule="hyper" parents="347 14072 15142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15144">
    <literal><![CDATA[
      K((x / y) * z,L(u,x / y,y)) = ((z \ T(z * (x / y),u)) * y) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),15143(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 15143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15145">
    <literal><![CDATA[
      K((x / y) * z,L(u,y \ x,y)) = ((z \ T(z * (x / y),u)) * y) / x
    ]]></literal>
    <justification jstring="[hyper(14182,a,15144,a)].">
      <j1 rule="hyper" parents="14182 15144"/>
    </justification>
  </clause>

  <clause id="15146">
    <literal><![CDATA[
      ((x \ T(x * (y / z),u)) * z) / y = K((y / z) * x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(14198,a,15145,a),flip(a)].">
      <j1 rule="hyper" parents="14198 15145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15147">
    <literal><![CDATA[
      K((x / y) * z,L(u,x,y)) = K(x / ((1 / z) * y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6637,a(flip),b,15146,a),flip(a)].">
      <j1 rule="hyper" parents="63 6637 15146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15149">
    <literal><![CDATA[
      K(x,K(y \ z,u) * (w * ((y / z) \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * T((y / z) \ 1,u)) = v5
    ]]></literal>
    <justification jstring="[para(14838(a,1),13784(a,1))].">
      <j1 rule="para" parents="14838 13784"/>
    </justification>
  </clause>

  <clause id="15150">
    <literal><![CDATA[
      x / L(y * K(z,u),w,a(w,v5,K(v6,v7))) != v8 * a(v8,y,K(z,u))
    ]]></literal>
    <literal><![CDATA[
      (v8 * y) * K(z,u) = x
    ]]></literal>
    <justification jstring="[para(14298(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="14298 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15151">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,y,T(z,u)) * w) = L(x,y,T(z,u)) * (L(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(14438(a,1),14443(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14438 14443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15152">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,K(y,u)) * (K(y,u) / T(y,z)) = (x * (1 / T(y,z))) * K(y,u)
    ]]></literal>
    <justification jstring="[para(3206(a,1),14471(a,1,1))].">
      <j1 rule="para" parents="3206 14471"/>
    </justification>
  </clause>

  <clause id="15153">
    <literal><![CDATA[
      K(x,K(y,z \ (u * ((u \ z) * w)))) = a(w,z,K(u,K(x,y))) * K(w,K(x,y))
    ]]></literal>
    <justification jstring="[para(14269(a,1),14502(a,2,1))].">
      <j1 rule="para" parents="14269 14502"/>
    </justification>
  </clause>

  <clause id="15154">
    <literal><![CDATA[
      K(x,K(y,z \ (u * ((u \ z) * w)))) = K(x,K(y,L(w,z,u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,14155,a(flip),b,15153,a),flip(a)].">
      <j1 rule="hyper" parents="347 14155 15153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15155">
    <literal><![CDATA[
      K(x,K(y,L(z,u \ w,u))) = K(x,K(y,L(z,w,u)))
    ]]></literal>
    <justification jstring="[para(98(a,1),15154(a,1,2,2))].">
      <j1 rule="para" parents="98 15154"/>
    </justification>
  </clause>

  <clause id="15156">
    <literal><![CDATA[
      K(x,K(y,L(z,u / w,w))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(10177(a,2),15155(a,1,2,2))].">
      <j1 rule="para" parents="10177 15155"/>
    </justification>
  </clause>

  <clause id="15157">
    <literal><![CDATA[
      a(x,y,L(z \ 1,z,u) \ (z \ 1)) = a(x,y,(1 / z) * ((u * (1 / (1 / z))) \ u))
    ]]></literal>
    <justification jstring="[para(3504(a,1),15019(a,1,3))].">
      <j1 rule="para" parents="3504 15019"/>
    </justification>
  </clause>

  <clause id="15158">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) \ (z * u)) = a(x,y,(z * u) * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(3210(a,1),15024(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3210 15024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15159">
    <literal><![CDATA[
      (x * (1 / T(y,z))) * K(y,u) = x * (K(y,u) / T(y,z))
    ]]></literal>
    <justification jstring="[para(7407(a,1),15152(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7407 15152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15160">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = x * (K(y,z) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6506,a,b,15159,a)].">
      <j1 rule="hyper" parents="63 6506 15159"/>
    </justification>
  </clause>

  <clause id="15161">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(4978(a,1),15160(a,2,2))].">
      <j1 rule="para" parents="4978 15160"/>
    </justification>
  </clause>

  <clause id="15162">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2281,a,15161,a),flip(a)].">
      <j1 rule="hyper" parents="2281 15161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15164">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,T(y,z)) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(6507,a,15162,a)].">
      <j1 rule="hyper" parents="6507 15162"/>
    </justification>
  </clause>

  <clause id="15165">
    <literal><![CDATA[
      T(x * (K(y,z) * (1 / T(z,1))),T(T(z,1),y)) = T(z,y) \ R(x,z \ 1,z)
    ]]></literal>
    <justification jstring="[para(15164(a,1),10716(a,2,2))].">
      <j1 rule="para" parents="15164 10716"/>
    </justification>
  </clause>

  <clause id="15166">
    <literal><![CDATA[
      x / (T(y,z) \ R(x,y \ 1,y)) = (x * (1 / T(T(y,1),z))) \ x
    ]]></literal>
    <justification jstring="[para(15165(a,1),8540(a,1,2))].">
      <j1 rule="para" parents="15165 8540"/>
    </justification>
  </clause>

  <clause id="15168">
    <literal><![CDATA[
      (x * (1 / T(T(y,1),z))) \ x = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10654,a(flip),b,15166,a),flip(a)].">
      <j1 rule="hyper" parents="63 10654 15166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15169">
    <literal><![CDATA[
      T((x * (1 / y)) \ x,z) = (x * (1 / T(y,z))) \ x
    ]]></literal>
    <justification jstring="[para(223(a,1),15168(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="223 15168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15170">
    <literal><![CDATA[
      a(x,y,L(z,z,u) \ z) = a(x,y,(1 / z) * ((u * (1 / (1 / z))) \ u))
    ]]></literal>
    <justification jstring="[para(10875(a,1),15157(a,1,3))].">
      <j1 rule="para" parents="10875 15157"/>
    </justification>
  </clause>

  <clause id="15171">
    <literal><![CDATA[
      a(x,y,(1 / z) * ((u * (1 / (1 / z))) \ u)) = a(x,y,z * L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(15022,a,15170,a),flip(a)].">
      <j1 rule="hyper" parents="15022 15170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15172">
    <literal><![CDATA[
      K(x,y * (((z * (u / z)) / z) * (w \ 1))) = K(x,y * ((u / z) * (w \ K(z,z \ u))))
    ]]></literal>
    <justification jstring="[hyper(347,a,14892,a(flip),b,13066,a),flip(a)].">
      <j1 rule="hyper" parents="347 14892 13066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15173">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * (z * K(y,x))) = (z * K(y,x)) \ (u * (K(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(7335(a,1),13727(a,1,2,2))].">
      <j1 rule="para" parents="7335 13727"/>
    </justification>
  </clause>

  <clause id="15174">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = (K(z,y) * (x * T(y,z))) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,14789,a(flip),b,13805,a)].">
      <j1 rule="hyper" parents="63 14789 13805"/>
    </justification>
  </clause>

  <clause id="15176">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = T(x * y,K(y,z)) \ y
    ]]></literal>
    <justification jstring="[para(5955(a,1),15174(a,2,1))].">
      <j1 rule="para" parents="5955 15174"/>
    </justification>
  </clause>

  <clause id="15177">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = T((x * y) \ y,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,8911,a,b,15176,a),flip(a)].">
      <j1 rule="hyper" parents="347 8911 15176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15178">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x / y) * R((x / y) \ 1,z,y / x)
    ]]></literal>
    <justification jstring="[hyper(347,a,1471,a(flip),b,13930,a),flip(a)].">
      <j1 rule="hyper" parents="347 1471 13930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15179">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,y / x)) / y
    ]]></literal>
    <justification jstring="[hyper(347,a,2117,a(flip),b,15178,a),flip(a)].">
      <j1 rule="hyper" parents="347 2117 15178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15180">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,x \ y)) / y
    ]]></literal>
    <justification jstring="[para(6795(a,1),15179(a,2,1,2))].">
      <j1 rule="para" parents="6795 15179"/>
    </justification>
  </clause>

  <clause id="15181">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,10995,a(flip),b,15180,a),flip(a)].">
      <j1 rule="hyper" parents="347 10995 15180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15182">
    <literal><![CDATA[
      T(a(1 / (x / y),z,(x / y) \ 1),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(4122(a,1),15181(a,1,1))].">
      <j1 rule="para" parents="4122 15181"/>
    </justification>
  </clause>

  <clause id="15183">
    <literal><![CDATA[
      a((x / y) \ 1,z,(x / y) \ 1) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(12609,a,15182,a)].">
      <j1 rule="hyper" parents="12609 15182"/>
    </justification>
  </clause>

  <clause id="15184">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10637,a,b,15183,a)].">
      <j1 rule="hyper" parents="63 10637 15183"/>
    </justification>
  </clause>

  <clause id="15185">
    <literal><![CDATA[
      a((x \ y) \ 1,z,(x \ y) \ 1) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10815,a(flip),b,15184,a)].">
      <j1 rule="hyper" parents="63 10815 15184"/>
    </justification>
  </clause>

  <clause id="15186">
    <literal><![CDATA[
      a(x \ (x * y),z,x \ (x * y)) * K(T(z,y),1 / ((x * y) \ x)) = K(z * (1 / ((x * y) \ x)),1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(15185(a,1),12465(a,1,1))].">
      <j1 rule="para" parents="15185 12465"/>
    </justification>
  </clause>

  <clause id="15187">
    <literal><![CDATA[
      x \ (y * (K((y \ x) / (z / y),u) * (y \ x))) = K(((y \ x) * y) / z,T(u,x / y))
    ]]></literal>
    <justification jstring="[hyper(347,a,13601,a,b,14177,a),flip(a)].">
      <j1 rule="hyper" parents="347 13601 14177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15188">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(z,L(u,y,x))) = y * T(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(10826(a,1),14526(a,1,1))].">
      <j1 rule="para" parents="10826 14526"/>
    </justification>
  </clause>

  <clause id="15189">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(u,L(z,y,x))) = y * T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(7330(a,1),15188(a,1,1,2))].">
      <j1 rule="para" parents="7330 15188"/>
    </justification>
  </clause>

  <clause id="15191">
    <literal><![CDATA[
      (x \ T(x * (y * K(z,z \ u)),w)) \ ((y / z) * ((z \ u) \ u)) = K(w,x * (K(z,u) * y))
    ]]></literal>
    <justification jstring="[para(5942(a,2),14889(a,1,2))].">
      <j1 rule="para" parents="5942 14889"/>
    </justification>
  </clause>

  <clause id="15192">
    <literal><![CDATA[
      K(x,y) \ T(K(x,K(y,z)) * (u * K(x,y)),w) = T(K(x,y) * u,w) * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(6781(a,1),14915(a,1,2,1))].">
      <j1 rule="para" parents="6781 14915"/>
    </justification>
  </clause>

  <clause id="15193">
    <literal><![CDATA[
      K(x,y * (((z * (u / z)) / z) * (w \ 1))) = K(x,y * ((u / z) * (w \ K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(347,a,12131,a(flip),b,15172,a),flip(a)].">
      <j1 rule="hyper" parents="347 12131 15172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15194">
    <literal><![CDATA[
      x \ (y * ((y \ x) * K((z / y) \ (y \ x),u))) = K(((y \ x) * y) / z,T(u,x / y))
    ]]></literal>
    <justification jstring="[para(6017(a,1),15187(a,1,2,2))].">
      <j1 rule="para" parents="6017 15187"/>
    </justification>
  </clause>

  <clause id="15196">
    <literal><![CDATA[
      K(x,y) \ T(z * K(x,T(y,u)),w) = T(K(x,y) * z,w) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[para(13720(a,1),15192(a,1,2,1))].">
      <j1 rule="para" parents="13720 15192"/>
    </justification>
  </clause>

  <clause id="15197">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,T(x,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * T(z * K(x,T(y,w)),u) = v5
    ]]></literal>
    <justification jstring="[para(15196(a,1),5286(a,1))].">
      <j1 rule="para" parents="15196 5286"/>
    </justification>
  </clause>

  <clause id="15198">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u * K(y,x),w) = K(x,y) * T(u * K(y,T(x,z)),w)
    ]]></literal>
    <justification jstring="[hyper(15197,a,13630,a),flip(a)].">
      <j1 rule="hyper" parents="15197 13630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15199">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = y \ (y * K((x * (z / x)) \ y,u))
    ]]></literal>
    <justification jstring="[para(6597(a,1),15194(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6597 15194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15200">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = K((x * (z / x)) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,9,a(flip),b,15199,a),flip(a)].">
      <j1 rule="hyper" parents="347 9 15199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15201">
    <literal><![CDATA[
      K((x * ((y * ((x \ z) * x)) / x)) \ z,u) = K(1 / y,T(u,z / x))
    ]]></literal>
    <justification jstring="[hyper(5558,a,15200,a),flip(a)].">
      <j1 rule="hyper" parents="5558 15200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15203">
    <literal><![CDATA[
      (x * K(y,z)) / a(x / (1 / u),u \ 1,K(y,z)) = (x / (1 / u)) * (K(y,T(z,u)) / u)
    ]]></literal>
    <justification jstring="[para(4044(a,1),13343(a,1,2))].">
      <j1 rule="para" parents="4044 13343"/>
    </justification>
  </clause>

  <clause id="15204">
    <literal><![CDATA[
      (L(x,y,z) * (u * K(x,L(w,y,z)))) / L(T(x,w),y,z) = (R(x,y,z) * u) / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,15139,a(flip),b,14101,a)].">
      <j1 rule="hyper" parents="63 15139 14101"/>
    </justification>
  </clause>

  <clause id="15205">
    <literal><![CDATA[
      a(x,y,T(z,y)) * ((z * y) * x) = (y * T(z,y)) * (((x * y) * T(z,y)) / (z * y))
    ]]></literal>
    <justification jstring="[para(111(a,1),14247(a,1,2,1))].">
      <j1 rule="para" parents="111 14247"/>
    </justification>
  </clause>

  <clause id="15206">
    <literal><![CDATA[
      a(x,y,T(z,y)) * ((z * y) * x) = (z * y) * (((x * y) * T(z,y)) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,252,a(flip),b,15205,a),flip(a)].">
      <j1 rule="hyper" parents="347 252 15205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15207">
    <literal><![CDATA[
      a(x,y,T(z,y)) * ((z * y) * x) = (z * y) * R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[para(265(a,1),15206(a,2,2))].">
      <j1 rule="para" parents="265 15206"/>
    </justification>
  </clause>

  <clause id="15208">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,T(y,z),z \ 1)) = K(x,(y * (1 / T(z,y))) / ((u \ 1) * (1 / z)))
    ]]></literal>
    <justification jstring="[para(3936(a,1),14258(a,1,2))].">
      <j1 rule="para" parents="3936 14258"/>
    </justification>
  </clause>

  <clause id="15209">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ K(z,y)),x,(K(z,y) / u) \ x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(13561(a,1),14333(a,1,2,2,1))].">
      <j1 rule="para" parents="13561 14333"/>
    </justification>
  </clause>

  <clause id="15210">
    <literal><![CDATA[
      x \ (K(y,z) * R(K(z,y) * x,u,u \ 1)) = a(K(z,y) * x,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,14351,a(flip),b,14475,a),flip(a)].">
      <j1 rule="hyper" parents="347 14351 14475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15212">
    <literal><![CDATA[
      ((x * y) * ((K(y,x) * z) * u)) / T((y * x) * z,L(u,z,K(x,y))) = L(u,z,x * y)
    ]]></literal>
    <justification jstring="[para(14474(a,1),14493(a,1,1))].">
      <j1 rule="para" parents="14474 14493"/>
    </justification>
  </clause>

  <clause id="15213">
    <literal><![CDATA[
      (R(x,y,z) * u) / R(x,y,z) = (L(x,y,z) * u) / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11119,a(flip),b,15204,a),flip(a)].">
      <j1 rule="hyper" parents="63 11119 15204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15214">
    <literal><![CDATA[
      K(x,(y * (1 / T(z,y))) / ((u \ 1) * (1 / z))) = K(x,L(T(y,z) * u,y,z \ 1))
    ]]></literal>
    <justification jstring="[para(12410(a,1),15208(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12410 15208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15215">
    <literal><![CDATA[
      K(x,(y * (1 / T(z,y))) / ((u \ 1) * (z \ 1))) = K(x,L(T(y,z) * u,y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,5596,a(flip),b,15214,a)].">
      <j1 rule="hyper" parents="63 5596 15214"/>
    </justification>
  </clause>

  <clause id="15216">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ 1),x,(K(z,y) / u) \ x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(9794(a,1),15209(a,1,2,2,1))].">
      <j1 rule="para" parents="9794 15209"/>
    </justification>
  </clause>

  <clause id="15218">
    <literal><![CDATA[
      ((x * ((y * (x / y)) \ y)) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(8112(a,1),13145(a,1,1,1,2))].">
      <j1 rule="para" parents="8112 13145"/>
    </justification>
  </clause>

  <clause id="15219">
    <literal><![CDATA[
      x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(5439(a,1),15218(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5439 15218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15220">
    <literal><![CDATA[
      x / (x * ((1 / ((x / ((x \ y) \ 1)) / x)) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(2865(a,2),15219(a,1,2,2,1))].">
      <j1 rule="para" parents="2865 15219"/>
    </justification>
  </clause>

  <clause id="15221">
    <literal><![CDATA[
      x / (x * ((x / ((x \ y) \ 1)) / x)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(83(a,1),15220(a,1,2,2))].">
      <j1 rule="para" parents="83 15220"/>
    </justification>
  </clause>

  <clause id="15223">
    <literal><![CDATA[
      x / (x / ((y / x) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(8132(a,1),15221(a,1,2))].">
      <j1 rule="para" parents="8132 15221"/>
    </justification>
  </clause>

  <clause id="15224">
    <literal><![CDATA[
      1 / (x / (x / ((y / x) \ 1))) = (x / (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(220,a,15223,a,b,xx)].">
      <j1 rule="hyper" parents="220 15223"/>
    </justification>
  </clause>

  <clause id="15225">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * (w * (u / (z / y)))) = K(x,w * T((z / y) \ u,K(z,y)))
    ]]></literal>
    <justification jstring="[para(13800(a,1),13687(a,1,2,1))].">
      <j1 rule="para" parents="13800 13687"/>
    </justification>
  </clause>

  <clause id="15226">
    <literal><![CDATA[
      K(x,L(y,(z \ u) / w,((z \ u) / w) \ (u / z))) = K(x,L(y,u / z,w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(11495(a,1),14215(a,2,2))].">
      <j1 rule="para" parents="11495 14215"/>
    </justification>
  </clause>

  <clause id="15227">
    <literal><![CDATA[
      K(x,L(y,(z \ u) / w,w * K(z,z \ u))) = K(x,L(y,u / z,w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(13358(a,1),15226(a,1,2,3))].">
      <j1 rule="para" parents="13358 15226"/>
    </justification>
  </clause>

  <clause id="15228">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ (y * u)) = K(x,(a(z \ 1,z,y) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(14139,a,14219,a),flip(a)].">
      <j1 rule="hyper" parents="14139 14219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15230">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ (y * u)) = K(x,a(z \ 1,z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,12984,a(flip),b,15228,a),flip(a)].">
      <j1 rule="hyper" parents="347 12984 15228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15231">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,a(z \ 1,z,y) * u)
    ]]></literal>
    <justification jstring="[para(1407(a,1),15230(a,1,2))].">
      <j1 rule="para" parents="1407 15230"/>
    </justification>
  </clause>

  <clause id="15232">
    <literal><![CDATA[
      K(x,L(y / T(z / K(u,w),v5),T(z / K(u,w),v5),K(u,w))) = K(x,(y * K(u,w)) / (T(K(u,w) \ z,v5) * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(14274,a,14816,a)].">
      <j1 rule="hyper" parents="14274 14816"/>
    </justification>
  </clause>

  <clause id="15233">
    <literal><![CDATA[
      K((x \ T(y,x \ 1)) \ z,T(u,x \ 1)) = K(((y \ z) * y) / (((x \ y) / y) * y),u)
    ]]></literal>
    <justification jstring="[para(4431(a,1),14278(a,1,2))].">
      <j1 rule="para" parents="4431 14278"/>
    </justification>
  </clause>

  <clause id="15234">
    <literal><![CDATA[
      K((x \ T(y,x \ 1)) \ z,T(u,x)) = K(((y \ z) * y) / (((x \ y) / y) * y),u)
    ]]></literal>
    <justification jstring="[hyper(8864,a,15233,a)].">
      <j1 rule="hyper" parents="8864 15233"/>
    </justification>
  </clause>

  <clause id="15236">
    <literal><![CDATA[
      K((x \ T(y,x \ 1)) \ z,T(u,x)) = K(((y \ z) * y) / (x \ y),u)
    ]]></literal>
    <justification jstring="[para(12(a,1),15234(a,2,1,2))].">
      <j1 rule="para" parents="12 15234"/>
    </justification>
  </clause>

  <clause id="15238">
    <literal><![CDATA[
      K((x \ T(y,x \ 1)) \ z,T(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(z,y) / (x \ y),u) = w
    ]]></literal>
    <justification jstring="[para(15236(a,2),12164(a,1))].">
      <j1 rule="para" parents="15236 12164"/>
    </justification>
  </clause>

  <clause id="15239">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u) / (z \ K(u,u \ (z \ 1)))) = K(x,T((z \ 1) \ y,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),14661(a,2,2,1,1))].">
      <j1 rule="para" parents="12 14661"/>
    </justification>
  </clause>

  <clause id="15240">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u) / (z \ K(u,u \ (z \ 1)))) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,12985,a(flip),b,15239,a),flip(a)].">
      <j1 rule="hyper" parents="347 12985 15239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15242">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) / (z \ K(u,u \ (z \ 1)))) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(13166(a,1),15240(a,1,2,1))].">
      <j1 rule="para" parents="13166 15240"/>
    </justification>
  </clause>

  <clause id="15243">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) / (u * ((z \ 1) / u))) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(9560(a,1),15242(a,1,2,2))].">
      <j1 rule="para" parents="9560 15242"/>
    </justification>
  </clause>

  <clause id="15244">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K((x \ 1) * y,T(x,u))) = T(z / ((x \ 1) * y),y / x)
    ]]></literal>
    <justification jstring="[hyper(13780,a,7419,a)].">
      <j1 rule="hyper" parents="13780 7419"/>
    </justification>
  </clause>

  <clause id="15245">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K(y * (x \ 1),x)) = T(z / ((x \ 1) * y),y / x)
    ]]></literal>
    <justification jstring="[para(10369(a,1),15244(a,1,2))].">
      <j1 rule="para" parents="10369 15244"/>
    </justification>
  </clause>

  <clause id="15246">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K(x \ y,x)) = T(z / ((x \ 1) * y),y / x)
    ]]></literal>
    <justification jstring="[para(5763(a,1),15245(a,1,2))].">
      <j1 rule="para" parents="5763 15245"/>
    </justification>
  </clause>

  <clause id="15247">
    <literal><![CDATA[
      T(x / ((y \ 1) * z),z / y) = T(((y \ 1) * z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8790,a,15246,a),flip(a)].">
      <j1 rule="hyper" parents="8790 15246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15248">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (L(z,u,u) * (u * u))) = T(x,(u * (u * T(z,u * u))) * y)
    ]]></literal>
    <justification jstring="[para(9164(a,1),13924(a,1,1,2))].">
      <j1 rule="para" parents="9164 13924"/>
    </justification>
  </clause>

  <clause id="15249">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * L(z * (u * u),u,u)) = T(x,(u * (u * T(z,u * u))) * y)
    ]]></literal>
    <justification jstring="[para(1390(a,2),15248(a,1,2,2))].">
      <j1 rule="para" parents="1390 15248"/>
    </justification>
  </clause>

  <clause id="15252">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) / K(x,L(x,y,z) \ u) = u / a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(14263(a,1),14061(a,2,2))].">
      <j1 rule="para" parents="14263 14061"/>
    </justification>
  </clause>

  <clause id="15255">
    <literal><![CDATA[
      L(T(x,y),z,u) * K(w,L(x,z,T(u,y)) \ x) = T(L(x,z,T(u,y)) \ x,w) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(14468(a,1),14470(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14468 14470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15256">
    <literal><![CDATA[
      T((1 / x) \ a((1 / x) \ 1,y,z),x * a((1 / x) \ 1,y,z)) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),15056(a,2,2,1))].">
      <j1 rule="para" parents="83 15056"/>
    </justification>
  </clause>

  <clause id="15257">
    <literal><![CDATA[
      T((1 / x) \ a(x,y,z),x * a((1 / x) \ 1,y,z)) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),15256(a,1,1,2,1))].">
      <j1 rule="para" parents="83 15256"/>
    </justification>
  </clause>

  <clause id="15258">
    <literal><![CDATA[
      T((1 / x) \ a(x,y,z),x * a(x,y,z)) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(83(a,1),15257(a,1,2,2,1))].">
      <j1 rule="para" parents="83 15257"/>
    </justification>
  </clause>

  <clause id="15259">
    <literal><![CDATA[
      (1 / x) \ a(x,y,z) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(201,a,15258,a),flip(a)].">
      <j1 rule="hyper" parents="201 15258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15261">
    <literal><![CDATA[
      (1 / x) \ a(x,y,z) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,12603,a,b,15259,a),flip(a)].">
      <j1 rule="hyper" parents="347 12603 15259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15262">
    <literal><![CDATA[
      L(a(x,y,z),x,x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(38,a,14325,a,b,15259,a)].">
      <j1 rule="hyper" parents="38 14325 15259"/>
    </justification>
  </clause>

  <clause id="15264">
    <literal><![CDATA[
      (x \ 1) * a(x,y,z) = x \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,15262,a(flip),b,3197,a),flip(a)].">
      <j1 rule="hyper" parents="128 15262 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15265">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (a(x,y,z) \ a(x,y,z)) = L(a(x,y,z) \ 1,x,x)
    ]]></literal>
    <justification jstring="[para(15262(a,1),3347(a,1,2,2))].">
      <j1 rule="para" parents="15262 3347"/>
    </justification>
  </clause>

  <clause id="15266">
    <literal><![CDATA[
      R(x,y,z * R(z,u,u)) = R(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[para(15262(a,1),13404(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15262 13404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15268">
    <literal><![CDATA[
      a(x,y,z) * (x \ 1) = x \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14421,a,b,15264,a)].">
      <j1 rule="hyper" parents="63 14421 15264"/>
    </justification>
  </clause>

  <clause id="15269">
    <literal><![CDATA[
      (x \ a(x,y,z)) * L(u,a(x,y,z),x \ 1) = (x \ 1) * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(133,a,15264,a(flip),b,212,a)].">
      <j1 rule="hyper" parents="133 15264 212"/>
    </justification>
  </clause>

  <clause id="15271">
    <literal><![CDATA[
      L(x,y \ a(y,z,u),w) = L(x,y * a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(15264(a,1),3599(a,1,2))].">
      <j1 rule="para" parents="15264 3599"/>
    </justification>
  </clause>

  <clause id="15273">
    <literal><![CDATA[
      a(x,y,z) \ ((x \ a(x,y,z)) * u) = a(a(x,y,z),x \ 1,u) * ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(15268(a,1),14721(a,1,2,1))].">
      <j1 rule="para" parents="15268 14721"/>
    </justification>
  </clause>

  <clause id="15276">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,x) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(230,a,15265,a),flip(a)].">
      <j1 rule="hyper" parents="230 15265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15277">
    <literal><![CDATA[
      a(x,x,L(y,x,x)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(14635,a,15276,a)].">
      <j1 rule="hyper" parents="14635 15276"/>
    </justification>
  </clause>

  <clause id="15279">
    <literal><![CDATA[
      a(x,x,x \ y) = a(x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(14994,a,15277,a),flip(a)].">
      <j1 rule="hyper" parents="14994 15277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15280">
    <literal><![CDATA[
      a(x,x,(x \ 1) \ y) = a(x,x,x * y)
    ]]></literal>
    <justification jstring="[para(3192(a,1),15277(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3192 15277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15281">
    <literal><![CDATA[
      (x * y) * a(x,x,x * y) = (x * x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(134,a,15279,a(flip),b,87,a)].">
      <j1 rule="hyper" parents="134 15279 87"/>
    </justification>
  </clause>

  <clause id="15282">
    <literal><![CDATA[
      (x * y) * a(x,x,x * y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,495,a(flip),b,15281,a),flip(a)].">
      <j1 rule="hyper" parents="347 495 15281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15283">
    <literal><![CDATA[
      L((x * y) \ 1,x,x) = ((x \ 1) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(15282(a,1),14608(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15282 14608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15284">
    <literal><![CDATA[
      R(x,L(y * z,y,y),u) = R(x,(y \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(15282(a,1),14620(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15282 14620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15285">
    <literal><![CDATA[
      ((x \ 1) \ (x \ y)) \ 1 = L(y \ 1,x,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),15283(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 15283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15286">
    <literal><![CDATA[
      (x \ 1) \ (x \ y) = y * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,14608,a,b,15285,a),flip(a)].">
      <j1 rule="hyper" parents="39 14608 15285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15287">
    <literal><![CDATA[
      L(1 / x,y,y) \ 1 = (y \ 1) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(39,a,9700,a,b,15285,a)].">
      <j1 rule="hyper" parents="39 9700 15285"/>
    </justification>
  </clause>

  <clause id="15288">
    <literal><![CDATA[
      (x \ 1) \ (x \ (y \ 1)) = L(y,x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(39,a,9708,a(flip),b,15285,a),flip(a)].">
      <j1 rule="hyper" parents="39 9708 15285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15289">
    <literal><![CDATA[
      x \ ((y \ 1) \ (y \ x)) = a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(630,a,15286,a)].">
      <j1 rule="hyper" parents="630 15286"/>
    </justification>
  </clause>

  <clause id="15290">
    <literal><![CDATA[
      (x \ 1) \ (x \ y) = a(x,x,y) * y
    ]]></literal>
    <justification jstring="[hyper(347,a,12964,a,b,15286,a),flip(a)].">
      <j1 rule="hyper" parents="347 12964 15286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15291">
    <literal><![CDATA[
      (x \ 1) * (y * a(x,x,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(150,a,15286,a)].">
      <j1 rule="hyper" parents="150 15286"/>
    </justification>
  </clause>

  <clause id="15292">
    <literal><![CDATA[
      (x * x) * (x \ (x \ y)) = y * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,495,a,b,15286,a)].">
      <j1 rule="hyper" parents="63 495 15286"/>
    </justification>
  </clause>

  <clause id="15293">
    <literal><![CDATA[
      T(x * (a(y,y,x) \ 1),a(y,y,x) * a(y,y,x)) = (a(y,y,x) * a(y,y,x)) \ ((y \ 1) \ (y \ x))
    ]]></literal>
    <justification jstring="[para(15286(a,2),791(a,2,2))].">
      <j1 rule="para" parents="15286 791"/>
    </justification>
  </clause>

  <clause id="15294">
    <literal><![CDATA[
      L(x,y * a(z,z,y),u) = L(x,z \ (z \ y),u)
    ]]></literal>
    <justification jstring="[para(15286(a,1),3608(a,1,2))].">
      <j1 rule="para" parents="15286 3608"/>
    </justification>
  </clause>

  <clause id="15295">
    <literal><![CDATA[
      (x \ 1) \ (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,x,y) * y = z
    ]]></literal>
    <justification jstring="[para(15286(a,2),11791(a,1))].">
      <j1 rule="para" parents="15286 11791"/>
    </justification>
  </clause>

  <clause id="15296">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ (z \ u)) = R(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(15286(a,2),14619(a,1,3))].">
      <j1 rule="para" parents="15286 14619"/>
    </justification>
  </clause>

  <clause id="15297">
    <literal><![CDATA[
      R(x,(y \ 1) \ (y \ z),u) = R(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(15286(a,2),14620(a,1,2))].">
      <j1 rule="para" parents="15286 14620"/>
    </justification>
  </clause>

  <clause id="15298">
    <literal><![CDATA[
      R(x,y * ((z \ 1) \ (z \ u)),w) = R(x,y * L(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(15286(a,2),14612(a,1,2,2))].">
      <j1 rule="para" parents="15286 14612"/>
    </justification>
  </clause>

  <clause id="15299">
    <literal><![CDATA[
      a(L(x,y,z) \ x,L(x,y,z) \ x,u) * u = (x \ L(x,y,z)) \ ((L(x,y,z) \ x) \ u)
    ]]></literal>
    <justification jstring="[para(10888(a,1),15290(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10888 15290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15300">
    <literal><![CDATA[
      L(x * a(y,y,x),y,y) = x
    ]]></literal>
    <justification jstring="[hyper(3225,a,15291,a(flip))].">
      <j1 rule="hyper" parents="3225 15291"/>
    </justification>
  </clause>

  <clause id="15301">
    <literal><![CDATA[
      L(a(x,x,y) * y,x,x) = y
    ]]></literal>
    <justification jstring="[para(11788(a,2),15300(a,1,1))].">
      <j1 rule="para" parents="11788 15300"/>
    </justification>
  </clause>

  <clause id="15302">
    <literal><![CDATA[
      (x \ 1) * (L(y,x,x) \ 1) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(150,a,15288,a)].">
      <j1 rule="hyper" parents="150 15288"/>
    </justification>
  </clause>

  <clause id="15303">
    <literal><![CDATA[
      L(x,y \ (y \ z),u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14621,a(flip),b,15294,a),flip(a)].">
      <j1 rule="hyper" parents="63 14621 15294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15304">
    <literal><![CDATA[
      L(x,L(y * z,y,y),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),15303(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 15303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15305">
    <literal><![CDATA[
      R(x,y,z \ (z \ u)) = R(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(2379,a,15296,a)].">
      <j1 rule="hyper" parents="2379 15296"/>
    </justification>
  </clause>

  <clause id="15306">
    <literal><![CDATA[
      R(x,y,L(z * u,z,z)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),15305(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="9 15305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15307">
    <literal><![CDATA[
      R(T(x \ 1,x \ L(y * z,y,y)),x,y \ z) = (x * L(y * z,y,y)) \ L(y * z,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13815,a(flip),b,15306,a),flip(a)].">
      <j1 rule="hyper" parents="63 13815 15306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15308">
    <literal><![CDATA[
      a(x,y,z) \ ((x \ a(x,y,z)) * u) = a(a(x,y,z),x,u) * ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(14950(a,1),15273(a,2,1))].">
      <j1 rule="para" parents="14950 15273"/>
    </justification>
  </clause>

  <clause id="15309">
    <literal><![CDATA[
      a(L(x,y,z) \ x,x * L(x,y,z),u) * u = (x \ L(x,y,z)) \ ((L(x,y,z) \ x) \ u)
    ]]></literal>
    <justification jstring="[para(14988(a,1),15299(a,1,1))].">
      <j1 rule="para" parents="14988 15299"/>
    </justification>
  </clause>

  <clause id="15310">
    <literal><![CDATA[
      T(T(x,K(y,R(z,u,u))),y * T((u \ 1) * (u * z),u)) = T(x,((u \ 1) * (z * u)) * y)
    ]]></literal>
    <justification jstring="[para(786(a,1),13824(a,1,1,2,2))].">
      <j1 rule="para" parents="786 13824"/>
    </justification>
  </clause>

  <clause id="15311">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T((u \ 1) * (u * z),u)) = T(x,((u \ 1) * (z * u)) * y)
    ]]></literal>
    <justification jstring="[para(12996(a,1),15310(a,1,1,2))].">
      <j1 rule="para" parents="12996 15310"/>
    </justification>
  </clause>

  <clause id="15312">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * ((u \ 1) * (z * u))) = T(x,((u \ 1) * (z * u)) * y)
    ]]></literal>
    <justification jstring="[para(1846(a,1),15311(a,1,2,2))].">
      <j1 rule="para" parents="1846 15311"/>
    </justification>
  </clause>

  <clause id="15314">
    <literal><![CDATA[
      T(T(K(x,y) * z,K(x,y)) \ u,K(K(x,y) * z,w)) = (z * K(x,y)) \ T(u,K(w,K(x,y) * z))
    ]]></literal>
    <justification jstring="[para(7330(a,1),13829(a,2,2))].">
      <j1 rule="para" parents="7330 13829"/>
    </justification>
  </clause>

  <clause id="15315">
    <literal><![CDATA[
      T(T(K(x,y) * z,K(x,y)) / u,K(K(x,y) * z,w)) = (z * K(x,y)) / T(u,K(w,K(x,y) * z))
    ]]></literal>
    <justification jstring="[para(7330(a,1),13835(a,2,2))].">
      <j1 rule="para" parents="7330 13835"/>
    </justification>
  </clause>

  <clause id="15316">
    <literal><![CDATA[
      (K(x,y) * ((y * z) * x)) \ ((y * (K(x,y) * z)) * R(x,y,z)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(11745(a,1),14254(a,1,2,2))].">
      <j1 rule="para" parents="11745 14254"/>
    </justification>
  </clause>

  <clause id="15317">
    <literal><![CDATA[
      (K(x,y) * ((y * z) * x)) \ (K(x,y) * ((y * z) * R(x,y,z))) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(8286(a,1),15316(a,1,2))].">
      <j1 rule="para" parents="8286 15316"/>
    </justification>
  </clause>

  <clause id="15318">
    <literal><![CDATA[
      L(a(x,y,z),(y * z) * x,K(x,y)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(14249,a,15317,a)].">
      <j1 rule="hyper" parents="14249 15317"/>
    </justification>
  </clause>

  <clause id="15319">
    <literal><![CDATA[
      L(a(x,y,z),y * z,K(x,y)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14395,a(flip),b,15318,a)].">
      <j1 rule="hyper" parents="63 14395 15318"/>
    </justification>
  </clause>

  <clause id="15320">
    <literal><![CDATA[
      L(a(x,y,z),z,K(x,y)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14408,a(flip),b,15319,a)].">
      <j1 rule="hyper" parents="63 14408 15319"/>
    </justification>
  </clause>

  <clause id="15321">
    <literal><![CDATA[
      L(a(x,y,z),z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(T(x,y),y,z) = u
    ]]></literal>
    <justification jstring="[para(15320(a,2),10438(a,1))].">
      <j1 rule="para" parents="15320 10438"/>
    </justification>
  </clause>

  <clause id="15322">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ y) \ w) = K(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(324,a,14497,a)].">
      <j1 rule="hyper" parents="324 14497"/>
    </justification>
  </clause>

  <clause id="15323">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = K(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(13307,a,15322,a)].">
      <j1 rule="hyper" parents="13307 15322"/>
    </justification>
  </clause>

  <clause id="15325">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * (y \ u)) = K(x,a(z \ 1,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(4026(a,1),15322(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4026 15322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15326">
    <literal><![CDATA[
      K(x,L(y,z,z) * (y \ u)) = K(x,a(z,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(14600(a,1),15322(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14600 15322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15327">
    <literal><![CDATA[
      (K(x,L(y,z * u,T(T(z,z \ 1),u))) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(5047(a,2),14563(a,1,1,1,2,3))].">
      <j1 rule="para" parents="5047 14563"/>
    </justification>
  </clause>

  <clause id="15328">
    <literal><![CDATA[
      (K(x,y) * L(K(y,x) * z,u,u)) \ z = a(u,u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14349,a(flip),b,14609,a),flip(a)].">
      <j1 rule="hyper" parents="63 14349 14609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15330">
    <literal><![CDATA[
      (K(x,L(y,z * u,T(T(z,1),u))) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(11412(a,1),15327(a,1,1,1,2))].">
      <j1 rule="para" parents="11412 15327"/>
    </justification>
  </clause>

  <clause id="15331">
    <literal><![CDATA[
      (K(x,L(y,z * u,T(z,u))) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(223(a,1),15330(a,1,1,1,2,3,1))].">
      <j1 rule="para" parents="223 15330"/>
    </justification>
  </clause>

  <clause id="15332">
    <literal><![CDATA[
      a(x \ y,(x \ y) \ 1,(x \ y) * (y \ x)) \ (1 * ((y \ x) \ (x \ y))) = (x \ y) * (1 / (y \ x))
    ]]></literal>
    <justification jstring="[para(14990(a,1),13427(a,1,1))].">
      <j1 rule="para" parents="14990 13427"/>
    </justification>
  </clause>

  <clause id="15333">
    <literal><![CDATA[
      K(x,y) \ L(K(x,T(y,z)) * (z / a(u,w,v5)),w,K(v5,u)) = T(a(u,w,v5) \ z,K(x,y))
    ]]></literal>
    <justification jstring="[para(14239(a,1),14426(a,1,2,1))].">
      <j1 rule="para" parents="14239 14426"/>
    </justification>
  </clause>

  <clause id="15334">
    <literal><![CDATA[
      K(x,y) * L(K(y,T(x,z)) * (z / a(u,w,v5)),w,K(v5,u)) = T(a(u,w,v5) \ z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(5286,a,15333,a)].">
      <j1 rule="hyper" parents="5286 15333"/>
    </justification>
  </clause>

  <clause id="15335">
    <literal><![CDATA[
      ((x * (y * (x \ 1))) / x) \ (x \ (x * (y / x))) = K(x \ 1,T(y,x)) * a(x,x,x * (y / x))
    ]]></literal>
    <justification jstring="[para(10354(a,1),14759(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10354 14759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15336">
    <literal><![CDATA[
      ((x * (y * (x \ 1))) / x) \ (x \ (x * (y / x))) = K(x \ 1,y) * a(x,x,x * (y / x))
    ]]></literal>
    <justification jstring="[para(7102(a,1),15335(a,2,1))].">
      <j1 rule="para" parents="7102 15335"/>
    </justification>
  </clause>

  <clause id="15337">
    <literal><![CDATA[
      T(x * (x \ ((y * (x * z)) / y)),x) \ x = ((y * (z * x)) / y) \ L(x,z,x)
    ]]></literal>
    <justification jstring="[para(69(a,1),15108(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="69 15108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15338">
    <literal><![CDATA[
      ((x * (y * z)) / x) \ L(z,y,z) = T((x * (z * y)) / x,z) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),15337(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 15337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15340">
    <literal><![CDATA[
      (a(x,x,y) * a(x,x,y)) \ ((x \ 1) \ (x \ y)) = T(L(y,x,x),a(x,x,y) * a(x,x,y))
    ]]></literal>
    <justification jstring="[para(14611(a,1),15293(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14611 15293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15341">
    <literal><![CDATA[
      1 \ (1 * ((x \ y) \ (y \ x))) = (y \ x) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(12293(a,1),15332(a,1,1))].">
      <j1 rule="para" parents="12293 15332"/>
    </justification>
  </clause>

  <clause id="15342">
    <literal><![CDATA[
      (x \ y) * (1 / (y \ x)) != z
    ]]></literal>
    <literal><![CDATA[
      (y \ x) \ (x \ y) = z
    ]]></literal>
    <justification jstring="[para(15341(a,1),356(a,1))].">
      <j1 rule="para" parents="15341 356"/>
    </justification>
  </clause>

  <clause id="15344">
    <literal><![CDATA[
      (x \ (x / y)) \ ((x / y) \ x) = y * (1 / (x \ (x / y)))
    ]]></literal>
    <justification jstring="[hyper(15342,a,218,a)].">
      <j1 rule="hyper" parents="15342 218"/>
    </justification>
  </clause>

  <clause id="15345">
    <literal><![CDATA[
      x * (1 / (y \ (y / x))) = (y \ (y / x)) \ x
    ]]></literal>
    <justification jstring="[para(83(a,1),15344(a,1,2)),flip(a)].">
      <j1 rule="para" parents="83 15344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15346">
    <literal><![CDATA[
      (x \ (x / (x \ y))) \ ((x / (x \ y)) \ x) = (x \ y) * (1 / (1 / (1 / (y \ x))))
    ]]></literal>
    <justification jstring="[para(3396(a,1),15344(a,2,2,2))].">
      <j1 rule="para" parents="3396 15344"/>
    </justification>
  </clause>

  <clause id="15347">
    <literal><![CDATA[
      x \ ((y \ (y / x)) \ x) = 1 / (y \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(138,a,15345,a)].">
      <j1 rule="hyper" parents="138 15345"/>
    </justification>
  </clause>

  <clause id="15348">
    <literal><![CDATA[
      (x \ (x / (x \ y))) \ ((x / (x \ y)) \ x) = (x \ y) / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3750,a(flip),b,15346,a),flip(a)].">
      <j1 rule="hyper" parents="347 3750 15346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15349">
    <literal><![CDATA[
      (x \ (x / (x \ y))) \ (x \ y) = (x \ y) / (y \ x)
    ]]></literal>
    <justification jstring="[para(83(a,1),15348(a,1,2))].">
      <j1 rule="para" parents="83 15348"/>
    </justification>
  </clause>

  <clause id="15351">
    <literal><![CDATA[
      ((x \ y) * (K(z,T(x,x \ y)) * u)) \ (T(x,z) \ y) = ((x \ y) * (K(z,x) * u)) \ ((x \ y) * K(z,x))
    ]]></literal>
    <justification jstring="[para(7091(a,2),13843(a,1,1,2,1))].">
      <j1 rule="para" parents="7091 13843"/>
    </justification>
  </clause>

  <clause id="15352">
    <literal><![CDATA[
      ((x \ y) * (K(z,T(x,y)) * u)) \ (T(x,z) \ y) = ((x \ y) * (K(z,x) * u)) \ ((x \ y) * K(z,x))
    ]]></literal>
    <justification jstring="[para(7633(a,1),15351(a,1,1,2,1))].">
      <j1 rule="para" parents="7633 15351"/>
    </justification>
  </clause>

  <clause id="15353">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) * (y \ (x \ ((x \ 1) \ y))) = K(x \ 1,x * y) * a(x,x,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(9145(a,1),14758(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9145 14758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15354">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) * (y \ (x \ ((x \ 1) \ y))) = K(x \ 1,x * y) * a(x,x,x * y)
    ]]></literal>
    <justification jstring="[para(15280(a,1),15353(a,2,2))].">
      <j1 rule="para" parents="15280 15353"/>
    </justification>
  </clause>

  <clause id="15355">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) * (y \ (x \ ((x \ 1) \ y))) = ((x * y) * (x \ 1)) \ (x \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,14716,a(flip),b,15354,a),flip(a)].">
      <j1 rule="hyper" parents="347 14716 15354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15356">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) * (y \ (x \ ((x \ 1) \ y))) = ((x * y) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(9(a,1),15355(a,2,2))].">
      <j1 rule="para" parents="9 15355"/>
    </justification>
  </clause>

  <clause id="15357">
    <literal><![CDATA[
      K(x \ 1,x * y) * (y \ (x \ ((x \ 1) \ y))) = ((x * y) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(9145(a,1),15356(a,1,1))].">
      <j1 rule="para" parents="9145 15356"/>
    </justification>
  </clause>

  <clause id="15358">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ u) / (T(u * z,z \ 1) * ((z * u) \ u))) = K(x,T(T(u,z) \ y,z * u))
    ]]></literal>
    <justification jstring="[para(10336(a,1),14660(a,2,2))].">
      <j1 rule="para" parents="10336 14660"/>
    </justification>
  </clause>

  <clause id="15359">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / (T(z * u,u \ 1) * ((u * z) \ z))) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(7820(a,1),15358(a,1,2,1))].">
      <j1 rule="para" parents="7820 15358"/>
    </justification>
  </clause>

  <clause id="15360">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / (K(z * u,u \ 1) * T(z,u))) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(6349(a,1),15359(a,1,2,2))].">
      <j1 rule="para" parents="6349 15359"/>
    </justification>
  </clause>

  <clause id="15361">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / T(K(z * u,u \ 1) * z,u)) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(9157(a,2),15360(a,1,2,2))].">
      <j1 rule="para" parents="9157 15360"/>
    </justification>
  </clause>

  <clause id="15362">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / (u \ T(z * u,u \ 1))) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(13338(a,1),15361(a,1,2,2))].">
      <j1 rule="para" parents="13338 15361"/>
    </justification>
  </clause>

  <clause id="15363">
    <literal><![CDATA[
      L(a(x,y,K(z,u)) * w,L(x,y,T(z,u)) \ L(x,y,z),L(x,y,T(z,u))) = L(x,y,z) \ (L(x,y,T(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(13989(a,1),14486(a,1,1))].">
      <j1 rule="para" parents="13989 14486"/>
    </justification>
  </clause>

  <clause id="15364">
    <literal><![CDATA[
      ((x \ 1) * y) \ ((x \ y) * L((x \ y) \ ((x \ 1) * y),z,u)) = a(x,x,y) \ L(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(14713(a,1),14718(a,2,2,1))].">
      <j1 rule="para" parents="14713 14718"/>
    </justification>
  </clause>

  <clause id="15365">
    <literal><![CDATA[
      L(a(x,y,K(z,u)) * w,a(u,y,K(z,x)),L(x,y,T(z,u))) = L(x,y,z) \ (L(x,y,T(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(14485(a,1),15363(a,1,2))].">
      <j1 rule="para" parents="14485 15363"/>
    </justification>
  </clause>

  <clause id="15366">
    <literal><![CDATA[
      T((x * K(y,z)) / (u * K(y,z)),u / T(K(z,y),x * K(y,z))) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(6117(a,1),13244(a,1,1,2))].">
      <j1 rule="para" parents="6117 13244"/>
    </justification>
  </clause>

  <clause id="15367">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),(x \ y) * T(x,L(x \ y,z,u))) = ((x * L(x \ y,z,u)) \ y) \ y
    ]]></literal>
    <justification jstring="[para(22(a,2),13840(a,1,2,2))].">
      <j1 rule="para" parents="22 13840"/>
    </justification>
  </clause>

  <clause id="15368">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),L(x * (x \ y),z,K(u,x \ y))) = ((x * L(x \ y,z,u)) \ y) \ y
    ]]></literal>
    <justification jstring="[para(14420(a,2),15367(a,1,2))].">
      <j1 rule="para" parents="14420 15367"/>
    </justification>
  </clause>

  <clause id="15369">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),L(y,z,K(u,x \ y))) = ((x * L(x \ y,z,u)) \ y) \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),15368(a,1,2,1))].">
      <j1 rule="para" parents="10 15368"/>
    </justification>
  </clause>

  <clause id="15370">
    <literal><![CDATA[
      L(L(T(x \ 1,x),y,z) * (x * x),u,w) \ (L(L(x \ 1,y,z),u,w) * (x * x)) = a(x,x,L(L(x \ 1,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(1390(a,2),14624(a,1,1))].">
      <j1 rule="para" parents="1390 14624"/>
    </justification>
  </clause>

  <clause id="15371">
    <literal><![CDATA[
      a(x,y,z \ (z * x)) * K(T(y,x),1 / ((z * x) \ z)) = K(y * (1 / ((z * x) \ z)),1 / ((z * x) \ z))
    ]]></literal>
    <justification jstring="[para(9(a,1),15186(a,1,1,1))].">
      <j1 rule="para" parents="9 15186"/>
    </justification>
  </clause>

  <clause id="15372">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(T(x,z),1 / ((y * z) \ y))
    ]]></literal>
    <justification jstring="[para(9(a,1),15371(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="9 15371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15373">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(T(x,z),y \ (y * z))
    ]]></literal>
    <justification jstring="[para(6257(a,1),15372(a,2,2))].">
      <j1 rule="para" parents="6257 15372"/>
    </justification>
  </clause>

  <clause id="15375">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(T(x,z),z)
    ]]></literal>
    <justification jstring="[para(9(a,1),15373(a,2,2,2))].">
      <j1 rule="para" parents="9 15373"/>
    </justification>
  </clause>

  <clause id="15376">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(x,z)
    ]]></literal>
    <justification jstring="[para(5146(a,1),15375(a,2,2))].">
      <j1 rule="para" parents="5146 15375"/>
    </justification>
  </clause>

  <clause id="15377">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,8352,a(flip),b,15376,a),flip(a)].">
      <j1 rule="hyper" parents="347 8352 15376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15378">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),y \ (y * z)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(6317,a,15377,a)].">
      <j1 rule="hyper" parents="6317 15377"/>
    </justification>
  </clause>

  <clause id="15379">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),15378(a,1,2))].">
      <j1 rule="para" parents="9 15378"/>
    </justification>
  </clause>

  <clause id="15380">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(3931,a,15379,a)].">
      <j1 rule="hyper" parents="3931 15379"/>
    </justification>
  </clause>

  <clause id="15381">
    <literal><![CDATA[
      K(((x * y) \ x) \ z,y) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(9074,a,15380,a)].">
      <j1 rule="hyper" parents="9074 15380"/>
    </justification>
  </clause>

  <clause id="15382">
    <literal><![CDATA[
      K(((x * y) \ x) \ (y \ z),y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),15381(a,2,1))].">
      <j1 rule="para" parents="10 15381"/>
    </justification>
  </clause>

  <clause id="15383">
    <literal><![CDATA[
      K((1 / ((x * y) \ x)) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13314,a(flip),b,15382,a),flip(a)].">
      <j1 rule="hyper" parents="63 13314 15382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15384">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(3928,a,15383,a)].">
      <j1 rule="hyper" parents="3928 15383"/>
    </justification>
  </clause>

  <clause id="15385">
    <literal><![CDATA[
      K(x * ((y * z) \ y),z) = K(z \ x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6676,a(flip),b,15384,a)].">
      <j1 rule="hyper" parents="63 6676 15384"/>
    </justification>
  </clause>

  <clause id="15387">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (y \ x),x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),15385(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 15385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15388">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (x / y),x \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,9144,a,b,15387,a),flip(a)].">
      <j1 rule="hyper" parents="347 9144 15387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15389">
    <literal><![CDATA[
      x * K(x * (y / z),y \ z) = ((y \ z) \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(134,a,15388,a(flip),b,92,a)].">
      <j1 rule="hyper" parents="134 15388 92"/>
    </justification>
  </clause>

  <clause id="15390">
    <literal><![CDATA[
      (K(x \ y,z) * ((x \ y) \ u)) \ (K(x \ y,z) * u) = (x * K(u * (x / y),x \ y)) \ y
    ]]></literal>
    <justification jstring="[para(15388(a,1),8058(a,2,1,2))].">
      <j1 rule="para" parents="15388 8058"/>
    </justification>
  </clause>

  <clause id="15391">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,9154,a,b,15389,a)].">
      <j1 rule="hyper" parents="63 9154 15389"/>
    </justification>
  </clause>

  <clause id="15392">
    <literal><![CDATA[
      (((x \ y) \ 1) \ z) * ((x \ y) \ 1) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,2960,a(flip),b,15391,a)].">
      <j1 rule="hyper" parents="63 2960 15391"/>
    </justification>
  </clause>

  <clause id="15393">
    <literal><![CDATA[
      K(((1 / (x \ y)) * ((z * (((y \ x) \ u) * (y \ x))) / (1 / (x \ y)))) \ u,w) = K(1 / z,T(w,u / (1 / (x \ y))))
    ]]></literal>
    <justification jstring="[para(15391(a,1),15201(a,1,1,1,2,1,2))].">
      <j1 rule="para" parents="15391 15201"/>
    </justification>
  </clause>

  <clause id="15394">
    <literal><![CDATA[
      ((x \ y) * z) * (z / ((x \ y) * z)) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3847,a(flip),b,15392,a)].">
      <j1 rule="hyper" parents="63 3847 15392"/>
    </justification>
  </clause>

  <clause id="15395">
    <literal><![CDATA[
      (K(x \ y,z) * ((x \ y) \ u)) \ (K(x \ y,z) * u) = T(x \ y,u * (x / y))
    ]]></literal>
    <justification jstring="[hyper(347,a,6104,a(flip),b,15390,a),flip(a)].">
      <j1 rule="hyper" parents="347 6104 15390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15396">
    <literal><![CDATA[
      T(x \ y,z * (x / y)) = ((x \ y) \ z) \ z
    ]]></literal>
    <justification jstring="[hyper(3456,a,15395,a),flip(a)].">
      <j1 rule="hyper" parents="3456 15395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15397">
    <literal><![CDATA[
      T(x \ y,z * (y \ x)) = ((x \ y) \ z) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,9153,a(flip),b,15396,a)].">
      <j1 rule="hyper" parents="63 9153 15396"/>
    </justification>
  </clause>

  <clause id="15398">
    <literal><![CDATA[
      T(x \ y,z / (x \ y)) = T(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(347,a,4306,a,b,15397,a)].">
      <j1 rule="hyper" parents="347 4306 15397"/>
    </justification>
  </clause>

  <clause id="15399">
    <literal><![CDATA[
      K(x \ y,z * (y \ x)) * (x \ y) = T(x \ y,z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(347,a,4977,a(flip),b,15398,a)].">
      <j1 rule="hyper" parents="347 4977 15398"/>
    </justification>
  </clause>

  <clause id="15400">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ z) = K(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(35,a,5025,a,b,15399,a)].">
      <j1 rule="hyper" parents="35 5025 15399"/>
    </justification>
  </clause>

  <clause id="15401">
    <literal><![CDATA[
      x * K(y \ z,x * (z \ y)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[hyper(134,a,15400,a(flip),b,5110,a)].">
      <j1 rule="hyper" parents="134 15400 5110"/>
    </justification>
  </clause>

  <clause id="15402">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = (y \ x) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,6004,a,b,15401,a)].">
      <j1 rule="hyper" parents="63 6004 15401"/>
    </justification>
  </clause>

  <clause id="15403">
    <literal><![CDATA[
      x * K((y \ z) \ 1,x * (y \ z)) = (z \ y) * (x / (z \ y))
    ]]></literal>
    <justification jstring="[para(5988(a,2),15401(a,1,2))].">
      <j1 rule="para" parents="5988 15401"/>
    </justification>
  </clause>

  <clause id="15404">
    <literal><![CDATA[
      (((x \ y) * z) \ z) * ((x \ y) * z) = (y \ x) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,9148,a,b,15403,a)].">
      <j1 rule="hyper" parents="63 9148 15403"/>
    </justification>
  </clause>

  <clause id="15405">
    <literal><![CDATA[
      K(((x \ y) * ((z * (((x \ y) \ u) * (x \ y))) / (x \ y))) \ u,w) = K(1 / z,T(w,u / (1 / (y \ x))))
    ]]></literal>
    <justification jstring="[para(15402(a,1),15393(a,1,1,1))].">
      <j1 rule="para" parents="15402 15393"/>
    </justification>
  </clause>

  <clause id="15406">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15201,a(flip),b,15405,a),flip(a)].">
      <j1 rule="hyper" parents="63 15201 15405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15407">
    <literal><![CDATA[
      K(x,L(y / T(z * K(u,K(w,v5)),v6),T(z / K(u,K(w,v5)),v6),K(u,K(w,v5)))) = K(x,(y * K(u,K(w,v5))) / (T(K(u,K(w,v5)) \ z,v6) * K(u,K(w,v5))))
    ]]></literal>
    <justification jstring="[para(7315(a,1),15232(a,1,2,1,2,1))].">
      <j1 rule="para" parents="7315 15232"/>
    </justification>
  </clause>

  <clause id="15408">
    <literal><![CDATA[
      L(L(T(x \ 1,x) * (x * x),y,z),u,w) \ (L(L(x \ 1,y,z),u,w) * (x * x)) = a(x,x,L(L(x \ 1,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(1390(a,2),15370(a,1,1,1))].">
      <j1 rule="para" parents="1390 15370"/>
    </justification>
  </clause>

  <clause id="15409">
    <literal><![CDATA[
      L(L(x * K(x \ 1,x),y,z),u,w) \ (L(L(x \ 1,y,z),u,w) * (x * x)) = a(x,x,L(L(x \ 1,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(5728(a,1),15408(a,1,1,1,1))].">
      <j1 rule="para" parents="5728 15408"/>
    </justification>
  </clause>

  <clause id="15410">
    <literal><![CDATA[
      L(L(1 / (1 / x),y,z),u,w) \ (L(L(x \ 1,y,z),u,w) * (x * x)) = a(x,x,L(L(x \ 1,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(1902(a,1),15409(a,1,1,1,1))].">
      <j1 rule="para" parents="1902 15409"/>
    </justification>
  </clause>

  <clause id="15411">
    <literal><![CDATA[
      L(L(1 / (1 / x),y,z),u,w) \ L(L(x \ 1,y,z) * (x * x),u,w) = a(x,x,L(L(x \ 1,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(1390(a,2),15410(a,1,2))].">
      <j1 rule="para" parents="1390 15410"/>
    </justification>
  </clause>

  <clause id="15412">
    <literal><![CDATA[
      L(L(1 / (1 / x),y,z),u,w) \ L(L((x \ 1) * (x * x),y,z),u,w) = a(x,x,L(L(x \ 1,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(1390(a,2),15411(a,1,2,1))].">
      <j1 rule="para" parents="1390 15411"/>
    </justification>
  </clause>

  <clause id="15413">
    <literal><![CDATA[
      a(x,x,L(L(x \ 1,y,z),u,w)) = L(L(1 / (1 / x),y,z),u,w) \ L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(240(a,1),15412(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="240 15412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15414">
    <literal><![CDATA[
      L(R(x,a(y,z,u) \ 1,a(y,z,u) \ 1),a(y,z,u) \ 1,x) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(14528,a,13163,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14528 13163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15415">
    <literal><![CDATA[
      L(R(x,a(y,z,u),a(y,z,u)),a(y,z,u) \ 1,x) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(2252(a,1),15414(a,1,1))].">
      <j1 rule="para" parents="2252 15414"/>
    </justification>
  </clause>

  <clause id="15416">
    <literal><![CDATA[
      L(R(x,a(y,z,u),a(y,z,u)),a(y,z,u),x) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(3524,a,15415,a)].">
      <j1 rule="hyper" parents="3524 15415"/>
    </justification>
  </clause>

  <clause id="15417">
    <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(63,a,12636,a(flip),b,15416,a)].">
      <j1 rule="hyper" parents="63 12636 15416"/>
    </justification>
  </clause>

  <clause id="15418">
    <literal><![CDATA[
      (x * a(y,z,u)) * (a(y,z,u) \ 1) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(825,a,15417,a)].">
      <j1 rule="hyper" parents="825 15417"/>
    </justification>
  </clause>

  <clause id="15420">
    <literal><![CDATA[
      a(x,y,z) \ L(u,a(x,y,z),a(x,y,z)) = L(u * (a(x,y,z) \ 1),y,K(z,x))
    ]]></literal>
    <justification jstring="[para(15417(a,1),14344(a,1,2))].">
      <j1 rule="para" parents="15417 14344"/>
    </justification>
  </clause>

  <clause id="15421">
    <literal><![CDATA[
      L(x * (a(y,z,u) \ 1),z,K(u,y)) = (a(y,z,u) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(3220,a,15420,a),flip(a)].">
      <j1 rule="hyper" parents="3220 15420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15422">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ L(T(K(y,z) / u,u * K(z,y)),w,v5)) = K(x,L(K(y,z) / u,w,v5) * (1 / (u \ K(y,z))))
    ]]></literal>
    <justification jstring="[para(13073(a,1),15118(a,1,2,2,1,2))].">
      <j1 rule="para" parents="13073 15118"/>
    </justification>
  </clause>

  <clause id="15423">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ L(K(y,z) * (u \ 1),w,v5)) = K(x,L(K(y,z) / u,w,v5) * (1 / (u \ K(y,z))))
    ]]></literal>
    <justification jstring="[para(13740(a,1),15422(a,1,2,2,1))].">
      <j1 rule="para" parents="13740 15422"/>
    </justification>
  </clause>

  <clause id="15424">
    <literal><![CDATA[
      K(x,L(((y * (z * y)) / y) \ L(y,z,y),u,w) * z) = K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w))
    ]]></literal>
    <justification jstring="[para(12260(a,1),14538(a,1,2))].">
      <j1 rule="para" parents="12260 14538"/>
    </justification>
  </clause>

  <clause id="15425">
    <literal><![CDATA[
      K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w)) = K(x,L(T((y * (y * z)) / y,y) \ y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(15338(a,1),15424(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="15338 15424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15426">
    <literal><![CDATA[
      K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w)) = K(x,L((y * z) \ y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(254(a,1),15425(a,2,2,1,1,1))].">
      <j1 rule="para" parents="254 15425"/>
    </justification>
  </clause>

  <clause id="15428">
    <literal><![CDATA[
      K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,z * L((y * z) \ y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(15426(a,2),13318(a,1))].">
      <j1 rule="para" parents="15426 13318"/>
    </justification>
  </clause>

  <clause id="15429">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = T(L(x,u,K(y,z)),x \ (K(y,L(z,u * x,x)) * u))
    ]]></literal>
    <justification jstring="[para(14405(a,1),14242(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14405 14242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15430">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = T(L(x,u,K(y,z)),x \ (K(y,L(z,u,x)) * u))
    ]]></literal>
    <justification jstring="[para(14205(a,1),15429(a,2,2,2,1))].">
      <j1 rule="para" parents="14205 15429"/>
    </justification>
  </clause>

  <clause id="15432">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = T(L(x,u,K(y,z)),(x \ u) * K(y,T(z,u)))
    ]]></literal>
    <justification jstring="[para(14220(a,1),15430(a,2,2))].">
      <j1 rule="para" parents="14220 15430"/>
    </justification>
  </clause>

  <clause id="15433">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) * T(1 / (y / z),y)) = K(x,(1 \ T(1 / (y / z),y)) * L(T(1 / (y / z),y) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(66(a,1),14537(a,1,2,2))].">
      <j1 rule="para" parents="66 14537"/>
    </justification>
  </clause>

  <clause id="15434">
    <literal><![CDATA[
      K(x,(y / (y / ((z \ u) * y))) \ (z \ (u * ((u \ z) * (y / (u \ z)))))) = a(x,u,K((((z \ u) * y) \ y) * ((z \ u) * y),z))
    ]]></literal>
    <justification jstring="[para(15404(a,1),14761(a,1,2,2,2,2))].">
      <j1 rule="para" parents="15404 14761"/>
    </justification>
  </clause>

  <clause id="15435">
    <literal><![CDATA[
      K(x,(y / (y / ((z \ u) * y))) \ L(y / (u \ z),u \ z,u)) = a(x,u,K((((z \ u) * y) \ y) * ((z \ u) * y),z))
    ]]></literal>
    <justification jstring="[para(98(a,1),15434(a,1,2,2))].">
      <j1 rule="para" parents="98 15434"/>
    </justification>
  </clause>

  <clause id="15436">
    <literal><![CDATA[
      ((x * (K(y,z) * u)) / (x * T(u,K(y,z)))) \ T(x * (K(y,z) * u),K(z,L(y,u,x))) = T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x)
    ]]></literal>
    <justification jstring="[para(8933(a,1),10827(a,1,2))].">
      <j1 rule="para" parents="8933 10827"/>
    </justification>
  </clause>

  <clause id="15437">
    <literal><![CDATA[
      K(R(T(x,x),x \ y,y \ (y / (((x \ y) \ 1) \ 1))),z) = K(((y \ (y / (x \ y))) * (x \ y)) \ (y / (((x \ y) \ 1) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(4005(a,1),12902(a,1,1,1))].">
      <j1 rule="para" parents="4005 12902"/>
    </justification>
  </clause>

  <clause id="15438">
    <literal><![CDATA[
      K(((x \ (x / (y \ x))) * (y \ x)) \ (x / (((y \ x) \ 1) \ 1)),z) = K(R(y,y \ x,x \ (x / (((y \ x) \ 1) \ 1))),z)
    ]]></literal>
    <justification jstring="[para(110(a,1),15437(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="110 15437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15440">
    <literal><![CDATA[
      K(((x \ (x / (y \ x))) * (y \ x)) \ (x / (((y \ x) \ 1) \ 1)),z) = K(R(y,y \ x,x \ (x * (((x \ y) \ 1) \ 1))),z)
    ]]></literal>
    <justification jstring="[para(2606(a,1),15438(a,2,1,3,2))].">
      <j1 rule="para" parents="2606 15438"/>
    </justification>
  </clause>

  <clause id="15441">
    <literal><![CDATA[
      K(((x \ (x / (y \ x))) * (y \ x)) \ (x / (((y \ x) \ 1) \ 1)),z) = K(R(y,y \ x,((x \ y) \ 1) \ 1),z)
    ]]></literal>
    <justification jstring="[para(9(a,1),15440(a,2,1,3))].">
      <j1 rule="para" parents="9 15440"/>
    </justification>
  </clause>

  <clause id="15443">
    <literal><![CDATA[
      K(((x \ (x / (y \ x))) * (y \ x)) \ (x / (((y \ x) \ 1) \ 1)),z) = K(R(y,y \ x,x \ y),z)
    ]]></literal>
    <justification jstring="[para(2195(a,1),15441(a,2,1))].">
      <j1 rule="para" parents="2195 15441"/>
    </justification>
  </clause>

  <clause id="15444">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ (x / (((y \ x) \ 1) \ 1)),z) = K(R(y,y \ x,x \ y),z)
    ]]></literal>
    <justification jstring="[para(80(a,1),15443(a,1,1,1,1,2))].">
      <j1 rule="para" parents="80 15443"/>
    </justification>
  </clause>

  <clause id="15445">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ (x * (((x \ y) \ 1) \ 1)),z) = K(R(y,y \ x,x \ y),z)
    ]]></literal>
    <justification jstring="[para(2606(a,1),15444(a,1,1,2))].">
      <j1 rule="para" parents="2606 15444"/>
    </justification>
  </clause>

  <clause id="15446">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ y,z) = K(R(y,y \ x,x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3919,a(flip),b,15445,a)].">
      <j1 rule="hyper" parents="63 3919 15445"/>
    </justification>
  </clause>

  <clause id="15448">
    <literal><![CDATA[
      K(R(x * y,(x * y) \ y,y \ (x * y)),z) = K((T(x,y) * ((x * y) \ y)) \ (x * y),z)
    ]]></literal>
    <justification jstring="[para(22(a,2),15446(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="22 15446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15449">
    <literal><![CDATA[
      K(R(x * y,(x * y) \ y,y \ (x * y)),z) = K((x * ((y * x) \ y)) \ (x * y),z)
    ]]></literal>
    <justification jstring="[para(10295(a,1),15448(a,2,1,1))].">
      <j1 rule="para" parents="10295 15448"/>
    </justification>
  </clause>

  <clause id="15450">
    <literal><![CDATA[
      K(R(x * y,(x * y) \ y,y \ (x * y)),z) = L(K(T(y * x,y),z),y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,7075,a(flip),b,15449,a),flip(a)].">
      <j1 rule="hyper" parents="347 7075 15449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15451">
    <literal><![CDATA[
      K(R(x * y,(x * y) \ y,T(x,y)),z) = L(K(T(y * x,y),z),y,x)
    ]]></literal>
    <justification jstring="[para(22(a,2),15450(a,1,1,3))].">
      <j1 rule="para" parents="22 15450"/>
    </justification>
  </clause>

  <clause id="15452">
    <literal><![CDATA[
      K(R(x * y,(x * y) \ y,T(x,y)),z) = L(K(y * x,T(z,y)),y,x)
    ]]></literal>
    <justification jstring="[para(7093(a,1),15451(a,2,1))].">
      <j1 rule="para" parents="7093 15451"/>
    </justification>
  </clause>

  <clause id="15453">
    <literal><![CDATA[
      R(K(x * y,z),y,T(x,y)) = L(K(y * x,T(z,y)),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,6509,a(flip),b,15452,a)].">
      <j1 rule="hyper" parents="63 6509 15452"/>
    </justification>
  </clause>

  <clause id="15454">
    <literal><![CDATA[
      K(x,T(y,K(y * T(x,y),z))) * ((K(y * T(x,y),z) * y) * x) = (x * y) * L(K(y * x,T(z,y)),y,x)
    ]]></literal>
    <justification jstring="[para(15453(a,1),8124(a,2,2))].">
      <j1 rule="para" parents="15453 8124"/>
    </justification>
  </clause>

  <clause id="15455">
    <literal><![CDATA[
      K(x,T(y,K(y * T(x,y),z))) * ((K(y * T(x,y),z) * y) * x) = x * (y * K(y * x,T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(347,a,97,a(flip),b,15454,a),flip(a)].">
      <j1 rule="hyper" parents="347 97 15454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15456">
    <literal><![CDATA[
      K(x,T(y,K(y * T(x,y),z))) * ((K(y * T(x,y),z) * y) * x) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,7112,a(flip),b,15455,a),flip(a)].">
      <j1 rule="hyper" parents="347 7112 15455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15458">
    <literal><![CDATA[
      K(x,y) * ((K(y * T(x,y),z) * y) * x) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[para(13560(a,1),15456(a,1,1))].">
      <j1 rule="para" parents="13560 15456"/>
    </justification>
  </clause>

  <clause id="15459">
    <literal><![CDATA[
      K(x,y) * ((K(x * y,z) * y) * x) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[para(111(a,1),15458(a,1,2,1,1,1))].">
      <j1 rule="para" parents="111 15458"/>
    </justification>
  </clause>

  <clause id="15462">
    <literal><![CDATA[
      L(T(K(x * y,z) * y,x),x,K(x,y)) = T(x,y) \ (x * (K(y * x,z) * y))
    ]]></literal>
    <justification jstring="[para(15459(a,1),5033(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15459 5033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15463">
    <literal><![CDATA[
      L(T(K(x * y,z) * y,x),x,K(x,y)) = K(y,x) * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,5210,a(flip),b,15462,a),flip(a)].">
      <j1 rule="hyper" parents="347 5210 15462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15464">
    <literal><![CDATA[
      K(x,y) * (K(x * y,z) * x) = T(K(y * x,z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(4252,a,15463,a),flip(a)].">
      <j1 rule="hyper" parents="4252 15463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15466">
    <literal><![CDATA[
      T(K(x * y,z) * y,x) = K(y * x,z) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,7782,a(flip),b,15464,a),flip(a)].">
      <j1 rule="hyper" parents="63 7782 15464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15467">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(10374(a,1),15466(a,1,1))].">
      <j1 rule="para" parents="10374 15466"/>
    </justification>
  </clause>

  <clause id="15468">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = T(x,y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,10378,a(flip),b,15467,a),flip(a)].">
      <j1 rule="hyper" parents="347 10378 15467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15469">
    <literal><![CDATA[
      T(x * y,z) / T(y,x) = T(x * K(x * y,z),y)
    ]]></literal>
    <justification jstring="[hyper(13300,a,15467,a(flip))].">
      <j1 rule="hyper" parents="13300 15467"/>
    </justification>
  </clause>

  <clause id="15470">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = T(y,x) \ T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,13101,a,b,15468,a),flip(a)].">
      <j1 rule="hyper" parents="347 13101 15468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15471">
    <literal><![CDATA[
      T(x * K(x * y,y \ 1),y) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[hyper(347,a,10395,a(flip),b,15468,a),flip(a)].">
      <j1 rule="hyper" parents="347 10395 15468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15472">
    <literal><![CDATA[
      (x * y) / (K(z * K(z * u,w),T(x,u)) * y) = T(x,T(z * u,w) / T(u,z))
    ]]></literal>
    <justification jstring="[para(15469(a,2),7147(a,2,2))].">
      <j1 rule="para" parents="15469 7147"/>
    </justification>
  </clause>

  <clause id="15473">
    <literal><![CDATA[
      T(x,T(T(y * K(y * z,u),z),y * z)) = T(x,T(z,y) \ T(y * z,u))
    ]]></literal>
    <justification jstring="[para(15469(a,1),13613(a,1,2,1))].">
      <j1 rule="para" parents="15469 13613"/>
    </justification>
  </clause>

  <clause id="15474">
    <literal><![CDATA[
      x \ T(y * x,x \ 1) = (y * x) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,6370,a(flip),b,15471,a)].">
      <j1 rule="hyper" parents="63 6370 15471"/>
    </justification>
  </clause>

  <clause id="15475">
    <literal><![CDATA[
      K(x,L((y * z) / u,y * z,y / (z * y))) = K(x,(z \ T(y * z,z \ 1)) / (u * (y / (z * y))))
    ]]></literal>
    <justification jstring="[para(15474(a,2),14083(a,2,2,1))].">
      <j1 rule="para" parents="15474 14083"/>
    </justification>
  </clause>

  <clause id="15476">
    <literal><![CDATA[
      T(x,y \ T(T(z,z * y) * y,u)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(15123(a,1),15473(a,1,2))].">
      <j1 rule="para" parents="15123 15473"/>
    </justification>
  </clause>

  <clause id="15477">
    <literal><![CDATA[
      K(x,L((y * z) / u,y * z,(y * z) \ y)) = K(x,(z \ T(y * z,z \ 1)) / (u * (y / (z * y))))
    ]]></literal>
    <justification jstring="[para(11504(a,1),15475(a,1,2))].">
      <j1 rule="para" parents="11504 15475"/>
    </justification>
  </clause>

  <clause id="15478">
    <literal><![CDATA[
      K(x,(y \ T(z * y,y \ 1)) / (u * (z / (y * z)))) = K(x,L((z * y) / u,z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,14507,a(flip),b,15477,a),flip(a)].">
      <j1 rule="hyper" parents="63 14507 15477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15480">
    <literal><![CDATA[
      K(x,((y * z) / z) / (u * (y / (z * y)))) = K(x,L((y * z) / u,y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,14906,a(flip),b,15478,a)].">
      <j1 rule="hyper" parents="63 14906 15478"/>
    </justification>
  </clause>

  <clause id="15481">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,y / (u * (y / (z * y))))
    ]]></literal>
    <justification jstring="[para(11(a,1),15480(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 15480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15482">
    <literal><![CDATA[
      (x * T(y,K(z,u))) * K(u,K(L(z,y,x),x * (K(z,u) * y))) = T(x * (K(z,u) * y),L(K(u,z),y,x)) * L(K(u,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,12778,a(flip),b,15436,a)].">
      <j1 rule="hyper" parents="63 12778 15436"/>
    </justification>
  </clause>

  <clause id="15483">
    <literal><![CDATA[
      T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(z,K(L(y,u,x),x * u))
    ]]></literal>
    <justification jstring="[para(9362(a,1),15482(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9362 15482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15486">
    <literal><![CDATA[
      T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(z,K(y,x * u))
    ]]></literal>
    <justification jstring="[para(13435(a,1),15483(a,2,2,2))].">
      <j1 rule="para" parents="13435 15483"/>
    </justification>
  </clause>

  <clause id="15487">
    <literal><![CDATA[
      T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(y,K(z,x * u))
    ]]></literal>
    <justification jstring="[para(7279(a,1),15486(a,2,2))].">
      <j1 rule="para" parents="7279 15486"/>
    </justification>
  </clause>

  <clause id="15488">
    <literal><![CDATA[
      T(x * (K(y,z) * u),K(z,L(y,u,x))) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(y,K(z,x * u))
    ]]></literal>
    <justification jstring="[para(8933(a,1),15487(a,1,1))].">
      <j1 rule="para" parents="8933 15487"/>
    </justification>
  </clause>

  <clause id="15489">
    <literal><![CDATA[
      T((x * (K(y,z) * u)) * L(K(z,y),u,x),K(z,L(y,u,x))) = (x * T(u,K(y,z))) * K(y,K(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,9892,a,b,15488,a)].">
      <j1 rule="hyper" parents="63 9892 15488"/>
    </justification>
  </clause>

  <clause id="15490">
    <literal><![CDATA[
      (x * T(y,K(z,u))) * K(z,K(u,x * y)) = T(x * T(y,K(z,u)),K(u,L(z,y,x)))
    ]]></literal>
    <justification jstring="[para(10826(a,1),15489(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10826 15489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15491">
    <literal><![CDATA[
      x \ ((y * T(x,K(z,u))) * K(z,K(u,y * x))) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[hyper(128,a,15490,a,b,15189,a(flip))].">
      <j1 rule="hyper" parents="128 15490 15189"/>
    </justification>
  </clause>

  <clause id="15493">
    <literal><![CDATA[
      x \ ((y * T(x,K(z,u))) * (K(u,T(z,y * x)) * K(z,u))) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(7522(a,2),15491(a,1,2,2))].">
      <j1 rule="para" parents="7522 15491"/>
    </justification>
  </clause>

  <clause id="15494">
    <literal><![CDATA[
      x \ (((y * T(x,K(z,u))) * K(z,u)) * K(u,T(z,y * x))) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(8321(a,2),15493(a,1,2))].">
      <j1 rule="para" parents="8321 15493"/>
    </justification>
  </clause>

  <clause id="15495">
    <literal><![CDATA[
      x \ (((y * T(x,K(z,u))) * K(z,u)) * K(u,T(z,y * T(x,K(z,w))))) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(7998(a,2),15494(a,1,2,2,2))].">
      <j1 rule="para" parents="7998 15494"/>
    </justification>
  </clause>

  <clause id="15496">
    <literal><![CDATA[
      x \ (((y * T(x,K(z,u))) * K(z,u)) * ((K(z,u) * (y * T(x,K(z,w)))) \ (y * T(x,K(z,w))))) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(7090(a,2),15495(a,1,2,2))].">
      <j1 rule="para" parents="7090 15495"/>
    </justification>
  </clause>

  <clause id="15497">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(6348(a,2),15496(a,1,2))].">
      <j1 rule="para" parents="6348 15496"/>
    </justification>
  </clause>

  <clause id="15498">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,x * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,13555,a(flip),b,15497,a),flip(a)].">
      <j1 rule="hyper" parents="347 13555 15497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15499">
    <literal><![CDATA[
      T(x * T(1 / x,K(y,z)),K(y,z)) = K(x,K(z,y) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(38,a,4981,a(flip),b,15497,a),flip(a)].">
      <j1 rule="hyper" parents="38 4981 15497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15500">
    <literal><![CDATA[
      (x * K(K(y,z),x)) \ T(u * x,K(y,z)) = T(u,K(z,y) * (x * K(K(y,z),x)))
    ]]></literal>
    <justification jstring="[para(5058(a,1),15497(a,1,2,1,2))].">
      <j1 rule="para" parents="5058 15497"/>
    </justification>
  </clause>

  <clause id="15501">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(u,z)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(7330(a,1),15497(a,1,2,1,2))].">
      <j1 rule="para" parents="7330 15497"/>
    </justification>
  </clause>

  <clause id="15502">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,1 / u)) = T(y,K(1 / u,z) * x)
    ]]></literal>
    <justification jstring="[para(8837(a,1),15497(a,1,2,1,2))].">
      <j1 rule="para" parents="8837 15497"/>
    </justification>
  </clause>

  <clause id="15503">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u * w)),K(z,u \ w)) = T(y,K(u \ w,z) * x)
    ]]></literal>
    <justification jstring="[para(13474(a,1),15497(a,1,2,1,2))].">
      <j1 rule="para" parents="13474 15497"/>
    </justification>
  </clause>

  <clause id="15504">
    <literal><![CDATA[
      K(x,y * (z \ (u * T(z,K(w,v5))))) = K(x,y * T(u,K(v5,w) * z))
    ]]></literal>
    <justification jstring="[para(15497(a,1),14843(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15497 14843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15505">
    <literal><![CDATA[
      T(x / T(y,K(z,u)),y * K(u,z)) = y \ T(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),15498(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 15498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15506">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,K(u,z) * x) = w
    ]]></literal>
    <justification jstring="[para(15498(a,2),13564(a,1))].">
      <j1 rule="para" parents="15498 13564"/>
    </justification>
  </clause>

  <clause id="15507">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(7330(a,1),15501(a,1,2))].">
      <j1 rule="para" parents="7330 15501"/>
    </justification>
  </clause>

  <clause id="15508">
    <literal><![CDATA[
      T(x / T(y,K(z,u)),K(z,u) \ y) = y \ T(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(13634,a,15505,a)].">
      <j1 rule="hyper" parents="13634 15505"/>
    </justification>
  </clause>

  <clause id="15509">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(z,u)) = y * T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,13555,a(flip),b,15507,a),flip(a)].">
      <j1 rule="hyper" parents="134 13555 15507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15510">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15498,a(flip),b,15507,a),flip(a)].">
      <j1 rule="hyper" parents="63 15498 15507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15511">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15497,a(flip),b,15507,a)].">
      <j1 rule="hyper" parents="63 15497 15507"/>
    </justification>
  </clause>

  <clause id="15512">
    <literal><![CDATA[
      x * T(y,K(z,u) * x) != w
    ]]></literal>
    <literal><![CDATA[
      T(y * T(x,K(z,u)),K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15507(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="15507 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15513">
    <literal><![CDATA[
      T(x,(y / z) * K(z,u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(13631,a,15510,a),flip(a)].">
      <j1 rule="hyper" parents="13631 15510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15514">
    <literal><![CDATA[
      T(x,y * K(z,u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(13563,a,15510,a)].">
      <j1 rule="hyper" parents="13563 15510"/>
    </justification>
  </clause>

  <clause id="15515">
    <literal><![CDATA[
      x \ T(y,K(z,u) * w) = x \ T(y,w * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,15510,a,b,10,a)].">
      <j1 rule="hyper" parents="128 15510 10"/>
    </justification>
  </clause>

  <clause id="15516">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),z * K(u,w)) = T(x,T(K(w,u) * z,y))
    ]]></literal>
    <justification jstring="[hyper(134,a,15510,a(flip),b,8681,a)].">
      <j1 rule="hyper" parents="134 15510 8681"/>
    </justification>
  </clause>

  <clause id="15517">
    <literal><![CDATA[
      T(x / (y * K(z,u)),K(u,z) * y) != w
    ]]></literal>
    <literal><![CDATA[
      (y * K(z,u)) \ x = w
    ]]></literal>
    <justification jstring="[para(15510(a,2),386(a,1))].">
      <j1 rule="para" parents="15510 386"/>
    </justification>
  </clause>

  <clause id="15518">
    <literal><![CDATA[
      T(x,(y \ z) * K(y,u)) = T(x,T(y,u) \ z)
    ]]></literal>
    <justification jstring="[para(5209(a,1),15510(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5209 15510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15519">
    <literal><![CDATA[
      T(x,K(y \ K(z,u),w) * K(u,z)) = T(x,y * T(y \ K(z,u),w))
    ]]></literal>
    <justification jstring="[para(5941(a,2),15510(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5941 15510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15520">
    <literal><![CDATA[
      T(x,(y / z) * K(u,y)) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[para(13192(a,1),15510(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13192 15510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15521">
    <literal><![CDATA[
      T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15510(a,1),13563(a,1))].">
      <j1 rule="para" parents="15510 13563"/>
    </justification>
  </clause>

  <clause id="15522">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15510(a,2),13564(a,1))].">
      <j1 rule="para" parents="15510 13564"/>
    </justification>
  </clause>

  <clause id="15523">
    <literal><![CDATA[
      T(x,(y \ z) * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15510(a,1),13635(a,1))].">
      <j1 rule="para" parents="15510 13635"/>
    </justification>
  </clause>

  <clause id="15525">
    <literal><![CDATA[
      T(x,K(y,z) * (z * u)) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,9937,a(flip),b,15511,a),flip(a)].">
      <j1 rule="hyper" parents="347 9937 15511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15526">
    <literal><![CDATA[
      x \ T(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(128,a,15511,a,b,4929,a(flip))].">
      <j1 rule="hyper" parents="128 15511 4929"/>
    </justification>
  </clause>

  <clause id="15527">
    <literal><![CDATA[
      T(x,K(y,z) * T(u,K(z,y))) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(111(a,1),15511(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 15511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15528">
    <literal><![CDATA[
      T(x,K(y,z) * (K(y,z) * u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(5261(a,1),15511(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5261 15511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15529">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5209(a,1),15511(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5209 15511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15530">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(15511(a,1),13563(a,1))].">
      <j1 rule="para" parents="15511 13563"/>
    </justification>
  </clause>

  <clause id="15531">
    <literal><![CDATA[
      x / T(x,y * K(z,u)) = K(y * K(u,z),x)
    ]]></literal>
    <justification jstring="[hyper(220,a,15514,a,b,4939,a(flip))].">
      <j1 rule="hyper" parents="220 15514 4939"/>
    </justification>
  </clause>

  <clause id="15532">
    <literal><![CDATA[
      T(x,K(y,z) * K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,13269,a(flip),b,15528,a),flip(a)].">
      <j1 rule="hyper" parents="40 13269 15528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15533">
    <literal><![CDATA[
      T(x,y * (T(T(y,z),z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(5781(a,1),15528(a,1,2))].">
      <j1 rule="para" parents="5781 15528"/>
    </justification>
  </clause>

  <clause id="15534">
    <literal><![CDATA[
      T(x,K(y,z) * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(15532(a,1),49(a,2))].">
      <j1 rule="para" parents="15532 49"/>
    </justification>
  </clause>

  <clause id="15535">
    <literal><![CDATA[
      (K(x,y) * K(x,y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * (K(x,y) * K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(15532(a,1),315(a,1,2))].">
      <j1 rule="para" parents="15532 315"/>
    </justification>
  </clause>

  <clause id="15536">
    <literal><![CDATA[
      T(x,y * (K(z,u) * K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(1305(a,1),15534(a,1))].">
      <j1 rule="para" parents="1305 15534"/>
    </justification>
  </clause>

  <clause id="15537">
    <literal><![CDATA[
      T(x,K(y,z) * (K(y,z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(13269(a,1),15534(a,1))].">
      <j1 rule="para" parents="13269 15534"/>
    </justification>
  </clause>

  <clause id="15538">
    <literal><![CDATA[
      T(x,y * (T(T(y,z),z) \ u)) = x * K(x,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,4929,a(flip),b,15533,a),flip(a)].">
      <j1 rule="hyper" parents="347 4929 15533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15539">
    <literal><![CDATA[
      T(x,T(T(y,z),z) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),15533(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 15533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15540">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * T(T(z,u),u))
    ]]></literal>
    <justification jstring="[hyper(10400,a,15539,a),flip(a)].">
      <j1 rule="hyper" parents="10400 15539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15541">
    <literal><![CDATA[
      T(x,T(y / (y / z),u) * K(y / z,w)) = T(x,(y * K(z,u)) / T(y / z,w))
    ]]></literal>
    <justification jstring="[para(5944(a,1),15513(a,1,2,1))].">
      <j1 rule="para" parents="5944 15513"/>
    </justification>
  </clause>

  <clause id="15542">
    <literal><![CDATA[
      T(x,y / ((z * u) / z)) = T(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(6126(a,2),15513(a,1,2))].">
      <j1 rule="para" parents="6126 15513"/>
    </justification>
  </clause>

  <clause id="15543">
    <literal><![CDATA[
      K(x,T(y,z / T(u,w)) \ ((z / u) * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,((z / u) * K(u,w)) / y) = v5
    ]]></literal>
    <justification jstring="[para(15513(a,1),12071(a,1,2,1))].">
      <j1 rule="para" parents="15513 12071"/>
    </justification>
  </clause>

  <clause id="15544">
    <literal><![CDATA[
      T(x,((y * z) / T(y,u)) * K(w,y * (z * K(u,y)))) = T(x,T(y * (z * K(u,y)),w) / y)
    ]]></literal>
    <justification jstring="[para(6841(a,1),15520(a,1,2,1))].">
      <j1 rule="para" parents="6841 15520"/>
    </justification>
  </clause>

  <clause id="15545">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5006,a,15526,a)].">
      <j1 rule="hyper" parents="5006 15526"/>
    </justification>
  </clause>

  <clause id="15546">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15526(a,1),5006(a,1))].">
      <j1 rule="para" parents="15526 5006"/>
    </justification>
  </clause>

  <clause id="15547">
    <literal><![CDATA[
      K(x,K(y,z) * (u * z)) = K(x,u * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(13637,a,15545,a),flip(a)].">
      <j1 rule="hyper" parents="13637 15545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15548">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(13607,a,15545,a),flip(a)].">
      <j1 rule="hyper" parents="13607 15545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15549">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ u)) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(12153,a,15545,a),flip(a)].">
      <j1 rule="hyper" parents="12153 15545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15551">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(5256(a,2),15545(a,1,2))].">
      <j1 rule="para" parents="5256 15545"/>
    </justification>
  </clause>

  <clause id="15552">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15545(a,1),12116(a,1))].">
      <j1 rule="para" parents="15545 12116"/>
    </justification>
  </clause>

  <clause id="15553">
    <literal><![CDATA[
      K(x,K(y,z) * (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(15545(a,1),13637(a,1))].">
      <j1 rule="para" parents="15545 13637"/>
    </justification>
  </clause>

  <clause id="15554">
    <literal><![CDATA[
      K(x,K(y,z) * (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15545(a,1),14900(a,1))].">
      <j1 rule="para" parents="15545 14900"/>
    </justification>
  </clause>

  <clause id="15555">
    <literal><![CDATA[
      K(x,(y * z) * K(u,y)) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(14900,a,15548,a),flip(a)].">
      <j1 rule="hyper" parents="14900 15548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15556">
    <literal><![CDATA[
      K(x,(y \ z) * K(u,z)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(13647,a,15548,a),flip(a)].">
      <j1 rule="hyper" parents="13647 15548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15558">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13591,a(flip),b,15548,a),flip(a)].">
      <j1 rule="hyper" parents="63 13591 15548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15559">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[para(5256(a,2),15548(a,1,2))].">
      <j1 rule="para" parents="5256 15548"/>
    </justification>
  </clause>

  <clause id="15560">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15548(a,1),13607(a,1))].">
      <j1 rule="para" parents="15548 13607"/>
    </justification>
  </clause>

  <clause id="15561">
    <literal><![CDATA[
      K(x,(y \ z) * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15548(a,1),13647(a,1))].">
      <j1 rule="para" parents="15548 13647"/>
    </justification>
  </clause>

  <clause id="15562">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15551(a,2),13637(a,1))].">
      <j1 rule="para" parents="15551 13637"/>
    </justification>
  </clause>

  <clause id="15563">
    <literal><![CDATA[
      K(x,K(y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15559(a,2),13640(a,1))].">
      <j1 rule="para" parents="15559 13640"/>
    </justification>
  </clause>

  <clause id="15564">
    <literal><![CDATA[
      T(x,((y * z) / y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5161(a,2),15529(a,1,2))].">
      <j1 rule="para" parents="5161 15529"/>
    </justification>
  </clause>

  <clause id="15565">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = T(x,y \ (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[para(5321(a,1),15529(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5321 15529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15566">
    <literal><![CDATA[
      T(x,T(y \ z,y) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(5441(a,1),15529(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5441 15529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15567">
    <literal><![CDATA[
      T(x,(y \ K(z,y \ 1)) \ u) = T(x,T(y \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[para(5445(a,1),15529(a,1,2))].">
      <j1 rule="para" parents="5445 15529"/>
    </justification>
  </clause>

  <clause id="15568">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(13651,a,15531,a)].">
      <j1 rule="hyper" parents="13651 15531"/>
    </justification>
  </clause>

  <clause id="15569">
    <literal><![CDATA[
      K(x * K(y,z),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(5013,a,15531,a)].">
      <j1 rule="hyper" parents="5013 15531"/>
    </justification>
  </clause>

  <clause id="15570">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,13580,a,b,15568,a)].">
      <j1 rule="hyper" parents="347 13580 15568"/>
    </justification>
  </clause>

  <clause id="15571">
    <literal><![CDATA[
      K(K(x,y) * (x \ z),u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(13636,a,15568,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="13636 15568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15572">
    <literal><![CDATA[
      K(K(x,y) * (z \ y),u) = K(z \ T(y,x),u)
    ]]></literal>
    <justification jstring="[para(13045(a,1),15568(a,2,1))].">
      <j1 rule="para" parents="13045 15568"/>
    </justification>
  </clause>

  <clause id="15573">
    <literal><![CDATA[
      K((x / y) * K(z,x),u) = K(T(x,z) / y,u)
    ]]></literal>
    <justification jstring="[para(13192(a,1),15568(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13192 15568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15574">
    <literal><![CDATA[
      K(K(x,y) * (x \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(15568(a,2),13636(a,1))].">
      <j1 rule="para" parents="15568 13636"/>
    </justification>
  </clause>

  <clause id="15575">
    <literal><![CDATA[
      K((x * K(y,z)) * K(y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(6109(a,1),15569(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6109 15569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15576">
    <literal><![CDATA[
      K(K(x,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * K(y,x),u) = w
    ]]></literal>
    <justification jstring="[para(15570(a,1),13606(a,1))].">
      <j1 rule="para" parents="15570 13606"/>
    </justification>
  </clause>

  <clause id="15577">
    <literal><![CDATA[
      K(x * (K(y,z) * K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(11136(a,1),15575(a,1,1))].">
      <j1 rule="para" parents="11136 15575"/>
    </justification>
  </clause>

  <clause id="15578">
    <literal><![CDATA[
      K(x,y) * (x * (K(z,u) * K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x * (K(z,u) * K(z,u)),y) = w
    ]]></literal>
    <justification jstring="[para(15577(a,1),4987(a,1,1))].">
      <j1 rule="para" parents="15577 4987"/>
    </justification>
  </clause>

  <clause id="15579">
    <literal><![CDATA[
      K(x \ T(T(y,z),z),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(5780(a,1),15577(a,1,1))].">
      <j1 rule="para" parents="5780 15577"/>
    </justification>
  </clause>

  <clause id="15580">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = 1 / K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(220,a,15579,a(flip),b,5173,a),flip(a)].">
      <j1 rule="hyper" parents="220 15579 5173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15581">
    <literal><![CDATA[
      K(x \ ((y * z) / y),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(254(a,1),15579(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="254 15579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15583">
    <literal><![CDATA[
      K(x,y * (T(T(y,z),z) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(5005,a,15538,a)].">
      <j1 rule="hyper" parents="5005 15538"/>
    </justification>
  </clause>

  <clause id="15584">
    <literal><![CDATA[
      K(x,T(T(y,z),z) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),15583(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 15583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15585">
    <literal><![CDATA[
      K(x,T(y \ z,y) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(113(a,1),15584(a,1,2,1,1))].">
      <j1 rule="para" parents="113 15584"/>
    </justification>
  </clause>

  <clause id="15586">
    <literal><![CDATA[
      K(x,T(T(R(y,z,u),w),w) * (z * u)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(107(a,1),15584(a,2,2))].">
      <j1 rule="para" parents="107 15584"/>
    </justification>
  </clause>

  <clause id="15587">
    <literal><![CDATA[
      K(x,T(L(y \ z,u,w),y) * v5) = K(x,L(z / y,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(278(a,1),15584(a,1,2,1,1))].">
      <j1 rule="para" parents="278 15584"/>
    </justification>
  </clause>

  <clause id="15588">
    <literal><![CDATA[
      T(x,y / T(T(z,u),u)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(255(a,1),15542(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="255 15542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15589">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,w),z)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(490(a,1),15542(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="490 15542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15590">
    <literal><![CDATA[
      T(x,y / T(T(z,u),u)) = x / K(y / z,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,4914,a(flip),b,15588,a),flip(a)].">
      <j1 rule="hyper" parents="347 4914 15588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15591">
    <literal><![CDATA[
      K(x,K(y,L(y \ z,u,w)) * (v5 * L(z / y,u,w))) = K(x,v5 * T(L(z / y,u,w),y))
    ]]></literal>
    <justification jstring="[para(5101(a,1),15547(a,1,2,1))].">
      <j1 rule="para" parents="5101 15547"/>
    </justification>
  </clause>

  <clause id="15592">
    <literal><![CDATA[
      K(x,((y * z) / y) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5161(a,2),15549(a,1,2))].">
      <j1 rule="para" parents="5161 15549"/>
    </justification>
  </clause>

  <clause id="15593">
    <literal><![CDATA[
      K(x,T(y \ z,y) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(5441(a,1),15549(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5441 15549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15594">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,(z / (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(5443(a,2),15549(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5443 15549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15596">
    <literal><![CDATA[
      K(x,y * (z * K(u,y))) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[para(6844(a,1),15555(a,1,2))].">
      <j1 rule="para" parents="6844 15555"/>
    </justification>
  </clause>

  <clause id="15597">
    <literal><![CDATA[
      K(x,y \ T(z \ u,z)) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[para(13354(a,1),15556(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13354 15556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15598">
    <literal><![CDATA[
      K(x,y \ ((z * u) / z)) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(14224(a,2),15556(a,1,2))].">
      <j1 rule="para" parents="14224 15556"/>
    </justification>
  </clause>

  <clause id="15599">
    <literal><![CDATA[
      K(x,y / ((z * u) / z)) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(6126(a,2),15558(a,1,2))].">
      <j1 rule="para" parents="6126 15558"/>
    </justification>
  </clause>

  <clause id="15600">
    <literal><![CDATA[
      K(x,y / T(z \ u,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(6125(a,1),15558(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6125 15558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15602">
    <literal><![CDATA[
      T(x,T(((y \ z) \ z) / u,K(y \ z,y)) \ w) = T(x,((y / u) / K(y \ z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(13210(a,1),15564(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="13210 15564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15603">
    <literal><![CDATA[
      T(x,T((y / (z \ 1)) / y,y) \ u) = T(x,((y / (z \ K(z,y))) / y) \ u)
    ]]></literal>
    <justification jstring="[para(7720(a,1),15566(a,1,2,1,1))].">
      <j1 rule="para" parents="7720 15566"/>
    </justification>
  </clause>

  <clause id="15604">
    <literal><![CDATA[
      K(T(x \ y,x) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[para(5441(a,1),15571(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5441 15571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15605">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,5172,a(flip),b,15580,a),flip(a)].">
      <j1 rule="hyper" parents="347 5172 15580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15606">
    <literal><![CDATA[
      K(x,y \ T(z * (u / T(z,u)),z)) = K(x,y \ (z * (u / z)))
    ]]></literal>
    <justification jstring="[para(4297(a,1),15605(a,1,2,2,1))].">
      <j1 rule="para" parents="4297 15605"/>
    </justification>
  </clause>

  <clause id="15608">
    <literal><![CDATA[
      T(x,K(y \ ((z * u) / z),w)) = K(x,K(w,y \ T(u,z))) * x
    ]]></literal>
    <justification jstring="[para(15581(a,2),7329(a,2,2)),flip(a)].">
      <j1 rule="para" parents="15581 7329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15610">
    <literal><![CDATA[
      K(x,T(y \ z,y) / u) = K(x,(z / y) * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(13327,a,15585,a)].">
      <j1 rule="hyper" parents="13327 15585"/>
    </justification>
  </clause>

  <clause id="15611">
    <literal><![CDATA[
      K(x,T(y,z / u) * (z / u)) = K(x,T(u \ z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,10360,a,b,15585,a)].">
      <j1 rule="hyper" parents="347 10360 15585"/>
    </justification>
  </clause>

  <clause id="15612">
    <literal><![CDATA[
      K(x,T(y \ z,z) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12047,a,b,15585,a)].">
      <j1 rule="hyper" parents="63 12047 15585"/>
    </justification>
  </clause>

  <clause id="15613">
    <literal><![CDATA[
      K(T(x \ y,x) * z,u) = (w * K(u,(y / x) * z)) \ w
    ]]></literal>
    <justification jstring="[para(15585(a,1),6123(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="15585 6123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15614">
    <literal><![CDATA[
      K(x,T((y * z) \ u,y * z) * (z * K(y,z))) = K(x,(u / (z * y)) * z)
    ]]></literal>
    <justification jstring="[para(9870(a,1),15585(a,2,2))].">
      <j1 rule="para" parents="9870 15585"/>
    </justification>
  </clause>

  <clause id="15615">
    <literal><![CDATA[
      K(x / T(T(y,z),z),u) = K(x / y,u)
    ]]></literal>
    <justification jstring="[hyper(4950,a,15590,a)].">
      <j1 rule="hyper" parents="4950 15590"/>
    </justification>
  </clause>

  <clause id="15616">
    <literal><![CDATA[
      K(x / T(y \ z,y),u) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[para(113(a,1),15615(a,1,1,2,1))].">
      <j1 rule="para" parents="113 15615"/>
    </justification>
  </clause>

  <clause id="15618">
    <literal><![CDATA[
      K(x,T(T(y,z),z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(255(a,1),15592(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="255 15592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15619">
    <literal><![CDATA[
      K(x,((L(y,z,z \ 1) * z) / z) \ u) = K(x,T((1 / z) * (y * z),z) \ u)
    ]]></literal>
    <justification jstring="[para(2945(a,1),15592(a,1,2,1,1))].">
      <j1 rule="para" parents="2945 15592"/>
    </justification>
  </clause>

  <clause id="15620">
    <literal><![CDATA[
      K(x,(L(y,z,y) * z) \ u) = K(x,T(z * y,y) \ u)
    ]]></literal>
    <justification jstring="[para(4358(a,1),15592(a,1,2,1))].">
      <j1 rule="para" parents="4358 15592"/>
    </justification>
  </clause>

  <clause id="15621">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y) \ u) = K(x,((y \ 1) * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(1846(a,1),15618(a,1,2,1,1))].">
      <j1 rule="para" parents="1846 15618"/>
    </justification>
  </clause>

  <clause id="15622">
    <literal><![CDATA[
      K(x,T(((y * z) \ z) \ 1,z) \ u) = K(x,(((z * y) \ z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(6613(a,1),15618(a,1,2,1,1))].">
      <j1 rule="para" parents="6613 15618"/>
    </justification>
  </clause>

  <clause id="15623">
    <literal><![CDATA[
      K(x,y \ T(z * K(u,z \ w),T(w / z,u))) = K(x,y \ (w / T(w / z,u)))
    ]]></literal>
    <justification jstring="[para(7239(a,1),15597(a,1,2,2,1))].">
      <j1 rule="para" parents="7239 15597"/>
    </justification>
  </clause>

  <clause id="15624">
    <literal><![CDATA[
      K(x,y \ ((z * u) / z)) = K(x,K(u,y)) * K(x,T(u,z) / y)
    ]]></literal>
    <justification jstring="[hyper(347,a,13508,a,b,15598,a),flip(a)].">
      <j1 rule="hyper" parents="347 13508 15598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15625">
    <literal><![CDATA[
      T(x,y \ ((z * u) / z)) = T(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,15598,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 15598 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15626">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,T(y,z))) = K(x,u / ((z * y) / z))
    ]]></literal>
    <justification jstring="[hyper(347,a,12073,a,b,15599,a)].">
      <j1 rule="hyper" parents="347 12073 15599"/>
    </justification>
  </clause>

  <clause id="15628">
    <literal><![CDATA[
      K(T(x \ y,y) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12149,a,b,15604,a)].">
      <j1 rule="hyper" parents="63 12149 15604"/>
    </justification>
  </clause>

  <clause id="15629">
    <literal><![CDATA[
      T(x,T(y \ z,z) * u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(132,a,15612,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 15612 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15630">
    <literal><![CDATA[
      K(x / (((y \ z) \ z) \ z),u) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[para(4320(a,1),15616(a,1,1,2))].">
      <j1 rule="para" parents="4320 15616"/>
    </justification>
  </clause>

  <clause id="15632">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * w) = v5
    ]]></literal>
    <justification jstring="[para(14790(a,2),15522(a,1))].">
      <j1 rule="para" parents="14790 15522"/>
    </justification>
  </clause>

  <clause id="15633">
    <literal><![CDATA[
      T(x,y * (z * (K(u,w) * K(u,w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = v5
    ]]></literal>
    <justification jstring="[para(33(a,1),15536(a,1,2))].">
      <j1 rule="para" parents="33 15536"/>
    </justification>
  </clause>

  <clause id="15634">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = w
    ]]></literal>
    <justification jstring="[para(5780(a,1),15536(a,1,2))].">
      <j1 rule="para" parents="5780 15536"/>
    </justification>
  </clause>

  <clause id="15635">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w) = v5
    ]]></literal>
    <justification jstring="[para(14787(a,1),15537(a,1))].">
      <j1 rule="para" parents="14787 15537"/>
    </justification>
  </clause>

  <clause id="15636">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ w) = v5
    ]]></literal>
    <justification jstring="[para(5209(a,1),15635(a,1,2))].">
      <j1 rule="para" parents="5209 15635"/>
    </justification>
  </clause>

  <clause id="15637">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(15510(a,1),15635(a,1))].">
      <j1 rule="para" parents="15510 15635"/>
    </justification>
  </clause>

  <clause id="15638">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * w) = v5
    ]]></literal>
    <justification jstring="[para(15525(a,1),15635(a,1))].">
      <j1 rule="para" parents="15525 15635"/>
    </justification>
  </clause>

  <clause id="15639">
    <literal><![CDATA[
      T(x,y * (z * K(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(8921(a,1),15637(a,1,2))].">
      <j1 rule="para" parents="8921 15637"/>
    </justification>
  </clause>

  <clause id="15640">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(13579(a,1),15546(a,1))].">
      <j1 rule="para" parents="13579 15546"/>
    </justification>
  </clause>

  <clause id="15641">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * w) = v5
    ]]></literal>
    <justification jstring="[para(14802(a,2),15546(a,1))].">
      <j1 rule="para" parents="14802 15546"/>
    </justification>
  </clause>

  <clause id="15642">
    <literal><![CDATA[
      K(x,K(y,y \ z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(15563,a,12066,a)].">
      <j1 rule="hyper" parents="15563 12066"/>
    </justification>
  </clause>

  <clause id="15643">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) = K(x,u / (z * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13663,a(flip),b,15642,a),flip(a)].">
      <j1 rule="hyper" parents="63 13663 15642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15644">
    <literal><![CDATA[
      T(x,y \ T(z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (u / z)) = w
    ]]></literal>
    <justification jstring="[para(113(a,1),15634(a,1,2,2,1))].">
      <j1 rule="para" parents="113 15634"/>
    </justification>
  </clause>

  <clause id="15646">
    <literal><![CDATA[
      T(x,T(y * K(z,u),w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,T(K(z,u) * y,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(6878(a,1),15638(a,1,2,1))].">
      <j1 rule="para" parents="6878 15638"/>
    </justification>
  </clause>

  <clause id="15647">
    <literal><![CDATA[
      K(x,(y \ T(T(z,K(u,w) * v5),x)) * v6) = K(x,(y \ T(z,v5 * K(w,u))) * v6)
    ]]></literal>
    <justification jstring="[para(15515(a,1),7977(a,2,2,1))].">
      <j1 rule="para" parents="15515 7977"/>
    </justification>
  </clause>

  <clause id="15648">
    <literal><![CDATA[
      T(x,K(y,z) * (u * K(K(z,y),u))) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(7296(a,2),15527(a,1,2,2))].">
      <j1 rule="para" parents="7296 15527"/>
    </justification>
  </clause>

  <clause id="15649">
    <literal><![CDATA[
      T(x,y * T(T(z,u),u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(10398,a,15540,a),flip(a)].">
      <j1 rule="hyper" parents="10398 15540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15650">
    <literal><![CDATA[
      T(x,y * ((z * u) / z)) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(254(a,1),15649(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="254 15649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15651">
    <literal><![CDATA[
      T(x,y * (z * K(u,z))) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(5058(a,1),15649(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5058 15649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15652">
    <literal><![CDATA[
      x / T(x,y * T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y * ((u * z) / u),x) = w
    ]]></literal>
    <justification jstring="[para(15650(a,1),5013(a,1,2))].">
      <j1 rule="para" parents="15650 5013"/>
    </justification>
  </clause>

  <clause id="15653">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,z)),w) / T(v5,y * T(z,u))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5 \ T(y * (z * K(u,z)),w)) = v6
    ]]></literal>
    <justification jstring="[para(15651(a,1),14837(a,1,2,2))].">
      <j1 rule="para" parents="15651 14837"/>
    </justification>
  </clause>

  <clause id="15654">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(12152,a,15594,a),flip(a)].">
      <j1 rule="hyper" parents="12152 15594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15656">
    <literal><![CDATA[
      K(x,T((y \ z) * u,u) \ L(u / (z \ y),z \ y,z)) = a(x,z,K((((y \ z) * u) \ u) * ((y \ z) * u),y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15435,a(flip),b,15654,a),flip(a)].">
      <j1 rule="hyper" parents="63 15435 15654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15657">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(80(a,1),15654(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="80 15654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15658">
    <literal><![CDATA[
      K(x,T(y \ z,y) / u) = K(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[hyper(347,a,12992,a(flip),b,15610,a),flip(a)].">
      <j1 rule="hyper" parents="347 12992 15610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15659">
    <literal><![CDATA[
      K(x,((y * z) / y) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(9(a,1),15658(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 15658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15660">
    <literal><![CDATA[
      (x * K(y,(z / u) / w)) \ x != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(u \ z,u) / w,y) = v5
    ]]></literal>
    <justification jstring="[para(15658(a,1),6141(a,1,1,2))].">
      <j1 rule="para" parents="15658 6141"/>
    </justification>
  </clause>

  <clause id="15661">
    <literal><![CDATA[
      K(x,T((T(y,z) \ z) \ u,y \ z) / w) = K(x,((K(y,z) * u) / (y \ z)) / w)
    ]]></literal>
    <justification jstring="[para(11522(a,1),15658(a,1,2,1,1))].">
      <j1 rule="para" parents="11522 15658"/>
    </justification>
  </clause>

  <clause id="15662">
    <literal><![CDATA[
      K(x,T((T(y,z) \ z) \ u,z / y) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[para(12072(a,1),15658(a,1,2,1))].">
      <j1 rule="para" parents="12072 15658"/>
    </justification>
  </clause>

  <clause id="15663">
    <literal><![CDATA[
      K(x,T(y * K(z,u),z / y) / w) = K(x,(T(z,u) / (z / y)) / w)
    ]]></literal>
    <justification jstring="[para(13044(a,1),15658(a,1,2,1,1))].">
      <j1 rule="para" parents="13044 15658"/>
    </justification>
  </clause>

  <clause id="15664">
    <literal><![CDATA[
      K(x,T(T(y,z),z) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(255(a,1),15659(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="255 15659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15665">
    <literal><![CDATA[
      K(x,((y * z) / T(y,u)) / w) = K(x,T(z * K(u,y),y) / w)
    ]]></literal>
    <justification jstring="[para(6841(a,1),15659(a,1,2,1))].">
      <j1 rule="para" parents="6841 15659"/>
    </justification>
  </clause>

  <clause id="15666">
    <literal><![CDATA[
      K(x,(((y * z) / y) * K(y,u)) / w) = K(x,T(z * K(y,u),y) / w)
    ]]></literal>
    <justification jstring="[para(6775(a,1),15659(a,1,2,1))].">
      <j1 rule="para" parents="6775 15659"/>
    </justification>
  </clause>

  <clause id="15667">
    <literal><![CDATA[
      K(x,T(T(y,T(z,u)),u) / w) = K(x,(T(y,z) * K(u,y)) / w)
    ]]></literal>
    <justification jstring="[para(7696(a,1),15664(a,1,2,1,1))].">
      <j1 rule="para" parents="7696 15664"/>
    </justification>
  </clause>

  <clause id="15668">
    <literal><![CDATA[
      K(x / T(y \ z,z),u) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(12150,a,15630,a)].">
      <j1 rule="hyper" parents="12150 15630"/>
    </justification>
  </clause>

  <clause id="15669">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) = (w * K(y / (u / z),x)) \ w
    ]]></literal>
    <justification jstring="[para(15668(a,1),6123(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="15668 6123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15670">
    <literal><![CDATA[
      K(x,y / (z * (u / z))) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13660,a(flip),b,15643,a),flip(a)].">
      <j1 rule="hyper" parents="63 13660 15643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15671">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) / T(z \ 1,u)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15243,a(flip),b,15670,a),flip(a)].">
      <j1 rule="hyper" parents="63 15243 15670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15672">
    <literal><![CDATA[
      K(x,y / T(z * u,u)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(11(a,1),15670(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 15670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15673">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) = K(x,y / (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(3837(a,2),15670(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3837 15670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15674">
    <literal><![CDATA[
      K(x,y * (K(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(5353(a,1),15554(a,1,2))].">
      <j1 rule="para" parents="5353 15554"/>
    </justification>
  </clause>

  <clause id="15675">
    <literal><![CDATA[
      K(x,(y \ z) * K(u \ (w * (v5 \ 1)),z)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = v6
    ]]></literal>
    <justification jstring="[para(3915(a,1),15561(a,1,2,2))].">
      <j1 rule="para" parents="3915 15561"/>
    </justification>
  </clause>

  <clause id="15676">
    <literal><![CDATA[
      K(x,y \ ((z * u) / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(14224(a,2),15561(a,1,2))].">
      <j1 rule="para" parents="14224 15561"/>
    </justification>
  </clause>

  <clause id="15677">
    <literal><![CDATA[
      K(x,y * (z * (u / z))) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(15562,a,13832,a),flip(a)].">
      <j1 rule="hyper" parents="15562 13832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15678">
    <literal><![CDATA[
      K(x,y * T(z \ u,z)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(15562,a,13659,a)].">
      <j1 rule="hyper" parents="15562 13659"/>
    </justification>
  </clause>

  <clause id="15679">
    <literal><![CDATA[
      K(x,y * (z * ((z * u) / z))) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,12003,a(flip),b,15677,a),flip(a)].">
      <j1 rule="hyper" parents="347 12003 15677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15680">
    <literal><![CDATA[
      T(x,y * (z * (u / z))) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,15677,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 15677 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15681">
    <literal><![CDATA[
      K(x,y * T(z * u,u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(11(a,1),15677(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 15677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15682">
    <literal><![CDATA[
      K(x,y * (z * (T(u,w) / z))) = K(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(23(a,1),15677(a,2,2,2))].">
      <j1 rule="para" parents="23 15677"/>
    </justification>
  </clause>

  <clause id="15683">
    <literal><![CDATA[
      (x * K(y,z * T(u,w))) \ x != v5
    ]]></literal>
    <literal><![CDATA[
      K(z * (w * (u / w)),y) = v5
    ]]></literal>
    <justification jstring="[para(15677(a,1),6141(a,1,1,2))].">
      <j1 rule="para" parents="15677 6141"/>
    </justification>
  </clause>

  <clause id="15684">
    <literal><![CDATA[
      K(x,y * ((z * u) / z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),15678(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 15678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15685">
    <literal><![CDATA[
      T(x,y * T(z * u,u)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(11(a,1),15680(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 15680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15686">
    <literal><![CDATA[
      T(x,y * T(R(z,u,u),u \ 1)) = T(x,y * ((u \ 1) * (z * u)))
    ]]></literal>
    <justification jstring="[para(788(a,1),15680(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="788 15680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15687">
    <literal><![CDATA[
      T(x,y * T(z * u,z)) = T(x,y * (T(z,u) * u))
    ]]></literal>
    <justification jstring="[para(4149(a,2),15680(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4149 15680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15688">
    <literal><![CDATA[
      T(x,y * (z * ((u \ ((z * w) / z)) * u))) = T(x,y * T(z * ((u \ w) * u),z))
    ]]></literal>
    <justification jstring="[para(4865(a,1),15680(a,1,2,2,2))].">
      <j1 rule="para" parents="4865 15680"/>
    </justification>
  </clause>

  <clause id="15689">
    <literal><![CDATA[
      K(x,y * T(T(z,u),u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(255(a,1),15684(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="255 15684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15690">
    <literal><![CDATA[
      K(x,y * T(z,z \ u)) = K(x,y * (u / (u / z)))
    ]]></literal>
    <justification jstring="[para(4339(a,1),15684(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4339 15684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15691">
    <literal><![CDATA[
      K(x,y * (z * K(u,z))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4942(a,1),15684(a,1,2,2))].">
      <j1 rule="para" parents="4942 15684"/>
    </justification>
  </clause>

  <clause id="15692">
    <literal><![CDATA[
      K(x,y * T(((z \ u) \ u) / w,K(z \ u,z))) = K(x,y * ((z / w) / K(z \ u,z)))
    ]]></literal>
    <justification jstring="[para(13210(a,1),15684(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="13210 15684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15693">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,z * u)))) = K(x,y * T(z * u,w))
    ]]></literal>
    <justification jstring="[para(13436(a,1),15689(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="13436 15689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15694">
    <literal><![CDATA[
      T(x,y * (T(z,u) * u)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12083,a(flip),b,15685,a)].">
      <j1 rule="hyper" parents="63 12083 15685"/>
    </justification>
  </clause>

  <clause id="15695">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * (((1 / z) * u) * K(z,(1 / z) * u)))
    ]]></literal>
    <justification jstring="[para(4239(a,1),15691(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4239 15691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15696">
    <literal><![CDATA[
      T(x,y * (T(z,u / T(w,u)) * (u / T(w,u)))) = T(x,y * (K(u,w) * ((u / w) * z)))
    ]]></literal>
    <justification jstring="[para(11437(a,2),15694(a,2,2,2))].">
      <j1 rule="para" parents="11437 15694"/>
    </justification>
  </clause>

  <clause id="15697">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(255(a,1),15679(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="255 15679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15698">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(u,w))) = K(x,y * (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(14886,a,15697,a)].">
      <j1 rule="hyper" parents="14886 15697"/>
    </justification>
  </clause>

  <clause id="15699">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * u)) = K(x,(y \ 1) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(13062,a,15697,a)].">
      <j1 rule="hyper" parents="13062 15697"/>
    </justification>
  </clause>

  <clause id="15700">
    <literal><![CDATA[
      K(x,T((y * z) * u,y * z)) = K(x,u * (T(z,y) * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,10345,a,b,15697,a)].">
      <j1 rule="hyper" parents="347 10345 15697"/>
    </justification>
  </clause>

  <clause id="15701">
    <literal><![CDATA[
      T(x,y * (T(z,u) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u * z)) = w
    ]]></literal>
    <justification jstring="[para(15687(a,1),12218(a,1))].">
      <j1 rule="para" parents="15687 12218"/>
    </justification>
  </clause>

  <clause id="15702">
    <literal><![CDATA[
      K(x,y * (z / (z / u))) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(12155,a,15690,a),flip(a)].">
      <j1 rule="hyper" parents="12155 15690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15703">
    <literal><![CDATA[
      K(x,y * T(z \ u,u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(80(a,1),15702(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="80 15702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15704">
    <literal><![CDATA[
      K(x,L(y * T(z \ u,u),w,v5)) = K(L(x,w,v5),y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(11169,a,15703,a)].">
      <j1 rule="hyper" parents="11169 15703"/>
    </justification>
  </clause>

  <clause id="15705">
    <literal><![CDATA[
      K(x,y * (K(z,u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (w \ K(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(15703(a,1),14822(a,1))].">
      <j1 rule="para" parents="15703 14822"/>
    </justification>
  </clause>

  <clause id="15706">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,13050,a(flip),b,15699,a),flip(a)].">
      <j1 rule="hyper" parents="347 13050 15699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15707">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(15699(a,2),13062(a,1))].">
      <j1 rule="para" parents="15699 13062"/>
    </justification>
  </clause>

  <clause id="15708">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((1 / u) \ w))) = K(x,y \ (((1 / u) \ w) * z))
    ]]></literal>
    <justification jstring="[para(13119(a,1),15706(a,1,2,2,1))].">
      <j1 rule="para" parents="13119 15706"/>
    </justification>
  </clause>

  <clause id="15709">
    <literal><![CDATA[
      K(K(x \ 1,y) * ((z / (x * z)) \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(z / (x * z),y) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(5555(a,1),15574(a,1,1,1))].">
      <j1 rule="para" parents="5555 15574"/>
    </justification>
  </clause>

  <clause id="15710">
    <literal><![CDATA[
      K(x \ (T(y,x) \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y) \ (y \ z),u) = w
    ]]></literal>
    <justification jstring="[para(5321(a,1),15574(a,1,1))].">
      <j1 rule="para" parents="5321 15574"/>
    </justification>
  </clause>

  <clause id="15711">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(12113,a,15620,a),flip(a)].">
      <j1 rule="hyper" parents="12113 15620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15712">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15620(a,1),12113(a,1))].">
      <j1 rule="para" parents="15620 12113"/>
    </justification>
  </clause>

  <clause id="15713">
    <literal><![CDATA[
      T(x,T(y * z,z) \ u) = T(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(132,a,15711,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 15711 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15714">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),15711(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 15711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15715">
    <literal><![CDATA[
      T(x,T(y * z,z) \ u) = T(x,T(y * z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,12036,a,b,15713,a),flip(a)].">
      <j1 rule="hyper" parents="347 12036 15713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15716">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,w,v5)) = K(L(x,w,v5),T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(11169,a,15714,a)].">
      <j1 rule="hyper" parents="11169 15714"/>
    </justification>
  </clause>

  <clause id="15717">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,(y * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,12037,a,b,15714,a)].">
      <j1 rule="hyper" parents="347 12037 15714"/>
    </justification>
  </clause>

  <clause id="15718">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ u) = K(x,(y \ T(z,y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(3837(a,2),15714(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3837 15714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15719">
    <literal><![CDATA[
      T(x,T(y * z,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15715(a,2),12208(a,1))].">
      <j1 rule="para" parents="15715 12208"/>
    </justification>
  </clause>

  <clause id="15720">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) \ 1 = K(((y \ z) * y) \ u,x)
    ]]></literal>
    <justification jstring="[para(15717(a,1),5173(a,1,1))].">
      <j1 rule="para" parents="15717 5173"/>
    </justification>
  </clause>

  <clause id="15721">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) = T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(15632,a,13555,a),flip(a)].">
      <j1 rule="hyper" parents="15632 13555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15722">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) * y) = v5
    ]]></literal>
    <justification jstring="[para(13555(a,1),15632(a,1))].">
      <j1 rule="para" parents="13555 15632"/>
    </justification>
  </clause>

  <clause id="15723">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = T(L(x,u,K(y,z)),K(z,y) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15432,a,b,15721,a)].">
      <j1 rule="hyper" parents="63 15432 15721"/>
    </justification>
  </clause>

  <clause id="15724">
    <literal><![CDATA[
      L((x \ (y * (x * K(z,T(u,w))))) / K(z,T(u,w)),K(z,T(u,w)),x) = T((K(z,T(u,w)) * y) / K(z,T(u,w)),K(u,z) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,1372,a,b,15721,a)].">
      <j1 rule="hyper" parents="63 1372 15721"/>
    </justification>
  </clause>

  <clause id="15725">
    <literal><![CDATA[
      L(K(x,y * K(z,T(u,w))),x,v5) = (x * K(v6,v7)) \ (T(x,K(u,z) * y) * K(v6,v7))
    ]]></literal>
    <justification jstring="[para(15721(a,1),13603(a,2,2,1))].">
      <j1 rule="para" parents="15721 13603"/>
    </justification>
  </clause>

  <clause id="15726">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ T(y,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(T(y,w),z)) = v5
    ]]></literal>
    <justification jstring="[para(15721(a,1),15523(a,1))].">
      <j1 rule="para" parents="15721 15523"/>
    </justification>
  </clause>

  <clause id="15727">
    <literal><![CDATA[
      T(x,y * K(z / u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * K(u \ z,w)) = v5
    ]]></literal>
    <justification jstring="[para(8953(a,1),15639(a,1,2,2))].">
      <j1 rule="para" parents="8953 15639"/>
    </justification>
  </clause>

  <clause id="15728">
    <literal><![CDATA[
      T(x,y \ (T(z,u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (u / z)) = w
    ]]></literal>
    <justification jstring="[para(12224(a,1),15644(a,1))].">
      <j1 rule="para" parents="12224 15644"/>
    </justification>
  </clause>

  <clause id="15729">
    <literal><![CDATA[
      T(x,y * (T(z \ u,w) * z)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (z * T(u / z,w))) = v5
    ]]></literal>
    <justification jstring="[para(277(a,1),15701(a,1,2,2,1))].">
      <j1 rule="para" parents="277 15701"/>
    </justification>
  </clause>

  <clause id="15730">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * T(w * u,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (T(w * u,u) * z)) = v5
    ]]></literal>
    <justification jstring="[para(10334(a,1),15707(a,1,2,2,1))].">
      <j1 rule="para" parents="10334 15707"/>
    </justification>
  </clause>

  <clause id="15731">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((u \ 1) \ w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (((u \ 1) \ w) * z)) = v5
    ]]></literal>
    <justification jstring="[para(13054(a,1),15707(a,1,2,2,1))].">
      <j1 rule="para" parents="13054 15707"/>
    </justification>
  </clause>

  <clause id="15732">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * ((z / y) \ 1)) \ u) = w
    ]]></literal>
    <justification jstring="[para(12041(a,1),15712(a,1))].">
      <j1 rule="para" parents="12041 15712"/>
    </justification>
  </clause>

  <clause id="15733">
    <literal><![CDATA[
      T(x,y \ (z \ T(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (u / z)) = w
    ]]></literal>
    <justification jstring="[para(4281(a,1),15728(a,1,2,2))].">
      <j1 rule="para" parents="4281 15728"/>
    </justification>
  </clause>

  <clause id="15734">
    <literal><![CDATA[
      T(x,y \ (z \ T(u,z))) = T(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[hyper(15733,a,xx),flip(a)].">
      <j1 rule="hyper" parents="15733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15735">
    <literal><![CDATA[
      T(R(x * K(K(y,z),u),K(w,v5),w),K(y,z) \ u) = u \ T(x * u,K(y,z))
    ]]></literal>
    <justification jstring="[para(6169(a,2),15508(a,1,1))].">
      <j1 rule="para" parents="6169 15508"/>
    </justification>
  </clause>

  <clause id="15736">
    <literal><![CDATA[
      T(x * T(y,x * K(z,u)),K(z,u)) = y * T(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(7352,a,15509,a)].">
      <j1 rule="hyper" parents="7352 15509"/>
    </justification>
  </clause>

  <clause id="15737">
    <literal><![CDATA[
      T(x,((y \ z) \ K(u,z \ y)) \ w) = T(x,T((y \ z) \ 1,u) \ w)
    ]]></literal>
    <justification jstring="[para(6250(a,1),15567(a,1,2,1,2))].">
      <j1 rule="para" parents="6250 15567"/>
    </justification>
  </clause>

  <clause id="15738">
    <literal><![CDATA[
      T(x,y / T(((z \ u) \ u) \ u,w)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(4351(a,1),15589(a,1,2,2))].">
      <j1 rule="para" parents="4351 15589"/>
    </justification>
  </clause>

  <clause id="15740">
    <literal><![CDATA[
      K(x,T(y \ z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) * u) = w
    ]]></literal>
    <justification jstring="[para(15611(a,1),10409(a,1))].">
      <j1 rule="para" parents="15611 10409"/>
    </justification>
  </clause>

  <clause id="15741">
    <literal><![CDATA[
      K(x,T(y \ z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) * u) = w
    ]]></literal>
    <justification jstring="[para(12047(a,2),15740(a,1))].">
      <j1 rule="para" parents="12047 15740"/>
    </justification>
  </clause>

  <clause id="15742">
    <literal><![CDATA[
      K(T(x \ y,x) * z,u) = K((y / x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,13585,a(flip),b,15613,a),flip(a)].">
      <j1 rule="hyper" parents="347 13585 15613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15743">
    <literal><![CDATA[
      K(T(x \ y,x) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((y / x) * z,u) = w
    ]]></literal>
    <justification jstring="[para(15613(a,2),6141(a,1))].">
      <j1 rule="para" parents="15613 6141"/>
    </justification>
  </clause>

  <clause id="15744">
    <literal><![CDATA[
      K(((x * y) / x) * z,u) = K(T(y,x) * z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),15742(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 15742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15745">
    <literal><![CDATA[
      K(x * (K(y,x) * z),u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5449(a,1),15744(a,1,1))].">
      <j1 rule="para" parents="5449 15744"/>
    </justification>
  </clause>

  <clause id="15746">
    <literal><![CDATA[
      K(((T(T(x,y),y) \ z) / K(y,x)) * u,w) = K(T(T(x,y) \ z,K(y,x)) * u,w)
    ]]></literal>
    <justification jstring="[para(5349(a,1),15744(a,1,1,1,1))].">
      <j1 rule="para" parents="5349 15744"/>
    </justification>
  </clause>

  <clause id="15747">
    <literal><![CDATA[
      K(x,y / ((z * u) / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15626(a,1),12077(a,1))].">
      <j1 rule="para" parents="15626 12077"/>
    </justification>
  </clause>

  <clause id="15748">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(6126(a,1),15747(a,1,2))].">
      <j1 rule="para" parents="6126 15747"/>
    </justification>
  </clause>

  <clause id="15749">
    <literal><![CDATA[
      K(x,K(y,z) * (u / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(13579(a,2),15748(a,1))].">
      <j1 rule="para" parents="13579 15748"/>
    </justification>
  </clause>

  <clause id="15750">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(15669(a,2),6141(a,1))].">
      <j1 rule="para" parents="15669 6141"/>
    </justification>
  </clause>

  <clause id="15751">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(15673(a,1),15750(a,1))].">
      <j1 rule="para" parents="15673 15750"/>
    </justification>
  </clause>

  <clause id="15752">
    <literal><![CDATA[
      K(x,y * T(z * (u / z),w)) = K(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(4812(a,2),15682(a,1,2,2))].">
      <j1 rule="para" parents="4812 15682"/>
    </justification>
  </clause>

  <clause id="15753">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (u * z)) = w
    ]]></literal>
    <justification jstring="[para(15700(a,1),10405(a,1))].">
      <j1 rule="para" parents="15700 10405"/>
    </justification>
  </clause>

  <clause id="15754">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w * v5)) * T(u,w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(u,w \ v5) * z)) = v6
    ]]></literal>
    <justification jstring="[para(13253(a,1),15753(a,1,2,2,1))].">
      <j1 rule="para" parents="13253 15753"/>
    </justification>
  </clause>

  <clause id="15755">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(u,w) * z)) = v5
    ]]></literal>
    <justification jstring="[para(14902(a,1),15753(a,1))].">
      <j1 rule="para" parents="14902 15753"/>
    </justification>
  </clause>

  <clause id="15756">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) * (w / u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((w / u) * z)) = v5
    ]]></literal>
    <justification jstring="[para(14903(a,1),15753(a,1))].">
      <j1 rule="para" parents="14903 15753"/>
    </justification>
  </clause>

  <clause id="15757">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15657,a(flip),b,15718,a),flip(a)].">
      <j1 rule="hyper" parents="63 15657 15718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15758">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,u) = K((x * (y / x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(5179,a,15720,a),flip(a)].">
      <j1 rule="hyper" parents="5179 15720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15759">
    <literal><![CDATA[
      K((x * (y / x)) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12032,a(flip),b,15758,a),flip(a)].">
      <j1 rule="hyper" parents="63 12032 15758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15760">
    <literal><![CDATA[
      K(T(x \ y,y) \ z,u) = K((x \ T(y,x \ 1)) \ z,u)
    ]]></literal>
    <justification jstring="[para(3837(a,2),15759(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3837 15759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15761">
    <literal><![CDATA[
      K(T(x * y,x) \ z,u) = K((T(x,y) * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(4149(a,2),15759(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4149 15759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15762">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,T(u,y * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(z,y) / (((x \ 1) / y) * y),u) = w
    ]]></literal>
    <justification jstring="[para(15759(a,1),14335(a,1))].">
      <j1 rule="para" parents="15759 14335"/>
    </justification>
  </clause>

  <clause id="15763">
    <literal><![CDATA[
      K((T(x,y) * y) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11943,a(flip),b,15761,a),flip(a)].">
      <j1 rule="hyper" parents="63 11943 15761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15764">
    <literal><![CDATA[
      K(T(x,(y * z) \ x) / (y * z),u) = K((T(z,y) * y) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,8548,a,b,15763,a)].">
      <j1 rule="hyper" parents="347 8548 15763"/>
    </justification>
  </clause>

  <clause id="15765">
    <literal><![CDATA[
      T(x,y * T(z * (u / z),w)) = T(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(132,a,15752,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 15752 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15766">
    <literal><![CDATA[
      K((x \ T(y,x \ 1)) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15628,a(flip),b,15760,a),flip(a)].">
      <j1 rule="hyper" parents="63 15628 15760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15767">
    <literal><![CDATA[
      K((x / y) \ z,T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(z,x) / (y \ x),u) = w
    ]]></literal>
    <justification jstring="[para(15766(a,1),15238(a,1))].">
      <j1 rule="para" parents="15766 15238"/>
    </justification>
  </clause>

  <clause id="15768">
    <literal><![CDATA[
      T(x,K(y / z,u) * T(T(y,z),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * K(y,w)) * T(y / z,u)) = v5
    ]]></literal>
    <justification jstring="[para(15765(a,1),13783(a,1))].">
      <j1 rule="para" parents="15765 13783"/>
    </justification>
  </clause>

  <clause id="15769">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * z) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(15535,a,10630,a),flip(a)].">
      <j1 rule="hyper" parents="15535 10630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15770">
    <literal><![CDATA[
      x * (T(T(x,y),y) \ z) = z * (K(y,x) * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(15535,a,9940,a),flip(a)].">
      <j1 rule="hyper" parents="15535 9940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15771">
    <literal><![CDATA[
      (x * y) * ((y * x) \ (K(x,y) * z)) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10301,a,b,15769,a)].">
      <j1 rule="hyper" parents="63 10301 15769"/>
    </justification>
  </clause>

  <clause id="15772">
    <literal><![CDATA[
      x * (y * (K(x,z) * K(x,z))) = T(x,z) * (K(x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,15769,a(flip),b,5157,a)].">
      <j1 rule="hyper" parents="134 15769 5157"/>
    </justification>
  </clause>

  <clause id="15773">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) * u = z * ((K(y,x) * K(y,x)) * u)
    ]]></literal>
    <justification jstring="[para(15770(a,2),32(a,1,1))].">
      <j1 rule="para" parents="15770 32"/>
    </justification>
  </clause>

  <clause id="15774">
    <literal><![CDATA[
      x * (y * (K(x,z) * K(x,z))) = T(T(x,z),z) * y
    ]]></literal>
    <justification jstring="[hyper(347,a,5171,a(flip),b,15772,a),flip(a)].">
      <j1 rule="hyper" parents="347 5171 15772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15775">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (T(x,z) * y) * ((T(T(x,z),z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(15774(a,1),11151(a,2,2,1))].">
      <j1 rule="para" parents="15774 11151"/>
    </justification>
  </clause>

  <clause id="15776">
    <literal><![CDATA[
      K(x,R(T(T(y,z),z),u,w) * (u * w)) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(1198(a,2),15586(a,1,2,1))].">
      <j1 rule="para" parents="1198 15586"/>
    </justification>
  </clause>

  <clause id="15777">
    <literal><![CDATA[
      T(x,y * (z * (u * (K(w,v5) * K(w,v5))))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (z * u)) = v6
    ]]></literal>
    <justification jstring="[para(33(a,1),15633(a,1,2,2))].">
      <j1 rule="para" parents="33 15633"/>
    </justification>
  </clause>

  <clause id="15778">
    <literal><![CDATA[
      T(x,y * (z * (T(T(z,u),u) \ w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * w) = v5
    ]]></literal>
    <justification jstring="[para(15770(a,2),15633(a,1,2,2))].">
      <j1 rule="para" parents="15770 15633"/>
    </justification>
  </clause>

  <clause id="15779">
    <literal><![CDATA[
      T(x,T(T(y,z),z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * u) = w
    ]]></literal>
    <justification jstring="[para(15774(a,1),15633(a,1,2))].">
      <j1 rule="para" parents="15774 15633"/>
    </justification>
  </clause>

  <clause id="15780">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(15652,a,4920,a(flip))].">
      <j1 rule="hyper" parents="15652 4920"/>
    </justification>
  </clause>

  <clause id="15781">
    <literal><![CDATA[
      K((x \ y) * ((z * ((x \ y) \ (x \ u))) / z),w) = K(x \ (y * T(y \ u,z)),w)
    ]]></literal>
    <justification jstring="[para(1436(a,1),15780(a,2,1))].">
      <j1 rule="para" parents="1436 15780"/>
    </justification>
  </clause>

  <clause id="15782">
    <literal><![CDATA[
      K(x * (y * K(z,y)),u) = K(x * T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4942(a,1),15780(a,1,1,2))].">
      <j1 rule="para" parents="4942 15780"/>
    </justification>
  </clause>

  <clause id="15783">
    <literal><![CDATA[
      T(x,(y * (z * K(u,z))) * (w \ K(y * T(z,u),v5))) = T(x,T(y * (z * K(u,z)),v5) / w)
    ]]></literal>
    <justification jstring="[para(15782(a,1),14874(a,1,2,2,2))].">
      <j1 rule="para" parents="15782 14874"/>
    </justification>
  </clause>

  <clause id="15784">
    <literal><![CDATA[
      T(x,((y / z) \ u) * K(z \ y,w)) = T(x,T(y / z,w) \ u)
    ]]></literal>
    <justification jstring="[hyper(15727,a,15518,a)].">
      <j1 rule="hyper" parents="15727 15518"/>
    </justification>
  </clause>

  <clause id="15785">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / ((z * u) / u)) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[hyper(15751,a,15362,a)].">
      <j1 rule="hyper" parents="15751 15362"/>
    </justification>
  </clause>

  <clause id="15786">
    <literal><![CDATA[
      K(x,(T(T(y,z),z) * u) * w) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(107(a,1),15776(a,1,2))].">
      <j1 rule="para" parents="107 15776"/>
    </justification>
  </clause>

  <clause id="15787">
    <literal><![CDATA[
      K(x,(((y * z) / y) * u) * w) = K(x,(T(z,y) * u) * w)
    ]]></literal>
    <justification jstring="[para(254(a,1),15786(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="254 15786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15788">
    <literal><![CDATA[
      K(x,(T(y,z) * z) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(12(a,1),15787(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 15787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15789">
    <literal><![CDATA[
      K(x,((y \ z) * y) * u) = K(x,(y * (z / y)) * u)
    ]]></literal>
    <justification jstring="[para(113(a,1),15788(a,1,2,1,1))].">
      <j1 rule="para" parents="113 15788"/>
    </justification>
  </clause>

  <clause id="15790">
    <literal><![CDATA[
      K(x,(y * (z / y)) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12065,a(flip),b,15789,a),flip(a)].">
      <j1 rule="hyper" parents="63 12065 15789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15791">
    <literal><![CDATA[
      K(x,T(y * z,z) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(11(a,1),15790(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 15790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15792">
    <literal><![CDATA[
      T(x * T(1 / x,K(y,z)),K(y,z)) = K(x,x \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,5756,a(flip),b,15499,a),flip(a)].">
      <j1 rule="hyper" parents="347 5756 15499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15793">
    <literal><![CDATA[
      T(K(K(x,y) * z,z \ 1),K(x,y)) = K(z,z \ K(y,x))
    ]]></literal>
    <justification jstring="[para(15132(a,2),15792(a,1,1))].">
      <j1 rule="para" parents="15132 15792"/>
    </justification>
  </clause>

  <clause id="15794">
    <literal><![CDATA[
      K(K(x,y) * z,z \ 1) = K(z,z \ K(y,x))
    ]]></literal>
    <justification jstring="[hyper(13596,a,15793,a)].">
      <j1 rule="hyper" parents="13596 15793"/>
    </justification>
  </clause>

  <clause id="15795">
    <literal><![CDATA[
      T((L(K(x,x \ K(y,z)),u,w) \ K(x,x \ K(y,z))) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(468,a,3302,a,b,15794,a)].">
      <j1 rule="hyper" parents="468 3302 15794"/>
    </justification>
  </clause>

  <clause id="15796">
    <literal><![CDATA[
      K(x,y \ ((z / T(u,z)) * u)) = K(x,y \ (u * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12007,a(flip),b,15606,a)].">
      <j1 rule="hyper" parents="63 12007 15606"/>
    </justification>
  </clause>

  <clause id="15797">
    <literal><![CDATA[
      K(x,y \ (z * (u / z))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(4275(a,1),15796(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4275 15796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15798">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),z \ u)) = K(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14276,a,b,15797,a)].">
      <j1 rule="hyper" parents="63 14276 15797"/>
    </justification>
  </clause>

  <clause id="15799">
    <literal><![CDATA[
      K(x,y \ T(z * u,u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(11(a,1),15797(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 15797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15800">
    <literal><![CDATA[
      K(x,y \ T(z \ u,u)) = K(x,y \ (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(3837(a,2),15797(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3837 15797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15801">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),u * z)) = K(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(13420,a,15798,a)].">
      <j1 rule="hyper" parents="13420 15798"/>
    </justification>
  </clause>

  <clause id="15802">
    <literal><![CDATA[
      T(x,K(y \ ((z * u) / z),w)) = K(x,K(w,y * T(u,z))) * x
    ]]></literal>
    <justification jstring="[para(13471(a,1),15608(a,2,1))].">
      <j1 rule="para" parents="13471 15608"/>
    </justification>
  </clause>

  <clause id="15803">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,T(y,u) / z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(15624(a,1),15676(a,1))].">
      <j1 rule="para" parents="15624 15676"/>
    </justification>
  </clause>

  <clause id="15804">
    <literal><![CDATA[
      K(x,T(T(y,z),T(u,z)) / w) = K(x,(T(y,u) * K(z,y)) / w)
    ]]></literal>
    <justification jstring="[para(23(a,1),15667(a,1,2,1))].">
      <j1 rule="para" parents="23 15667"/>
    </justification>
  </clause>

  <clause id="15805">
    <literal><![CDATA[
      K(x,y * L(z / (u \ 1),u,u)) = K(x,y * T(u * z,u \ 1))
    ]]></literal>
    <justification jstring="[para(9149(a,1),15693(a,1,2,2))].">
      <j1 rule="para" parents="9149 15693"/>
    </justification>
  </clause>

  <clause id="15806">
    <literal><![CDATA[
      K(x,L(y * T(z \ u,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * (u / z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(15704(a,2),11169(a,1))].">
      <j1 rule="para" parents="15704 11169"/>
    </justification>
  </clause>

  <clause id="15807">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(z,y) \ u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(15716(a,2),11169(a,1))].">
      <j1 rule="para" parents="15716 11169"/>
    </justification>
  </clause>

  <clause id="15808">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,w),u)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12038,a(flip),b,15738,a)].">
      <j1 rule="hyper" parents="63 12038 15738"/>
    </justification>
  </clause>

  <clause id="15809">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,u),w)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(23(a,1),15808(a,1,2,2))].">
      <j1 rule="para" parents="23 15808"/>
    </justification>
  </clause>

  <clause id="15810">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / T(u / y,w)) = T(x,T(y \ u,w) \ (K(y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14887,a(flip),b,15809,a),flip(a)].">
      <j1 rule="hyper" parents="63 14887 15809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15811">
    <literal><![CDATA[
      K((T(x,y) * y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(15764(a,1),8550(a,1))].">
      <j1 rule="para" parents="15764 8550"/>
    </justification>
  </clause>

  <clause id="15812">
    <literal><![CDATA[
      (x * y) * ((T(y,x) * x) \ z) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(10228(a,1),15771(a,1,2))].">
      <j1 rule="para" parents="10228 15771"/>
    </justification>
  </clause>

  <clause id="15813">
    <literal><![CDATA[
      (x * (K(y,z) * K(y,z))) / (y * z) = x / (T(z,y) * y)
    ]]></literal>
    <justification jstring="[para(15812(a,1),10447(a,1,1))].">
      <j1 rule="para" parents="15812 10447"/>
    </justification>
  </clause>

  <clause id="15814">
    <literal><![CDATA[
      (x * (T(T(x,y),y) \ z)) * u = z * (x * (T(T(x,y),y) \ u))
    ]]></literal>
    <justification jstring="[para(9940(a,1),15773(a,2,2))].">
      <j1 rule="para" parents="9940 15773"/>
    </justification>
  </clause>

  <clause id="15815">
    <literal><![CDATA[
      K(x,(T(y,z) * K(u,y)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(T(y,u),z) / w) = v5
    ]]></literal>
    <justification jstring="[para(15804(a,1),14852(a,1))].">
      <j1 rule="para" parents="15804 14852"/>
    </justification>
  </clause>

  <clause id="15816">
    <literal><![CDATA[
      K(T(x \ y,x) / z,u) = K((y / x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(15660,a,13585,a)].">
      <j1 rule="hyper" parents="15660 13585"/>
    </justification>
  </clause>

  <clause id="15817">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),15816(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 15816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15818">
    <literal><![CDATA[
      K(T(T(x,y),y) / z,u) = K(x / z,u)
    ]]></literal>
    <justification jstring="[para(255(a,1),15817(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="255 15817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15819">
    <literal><![CDATA[
      K(x * (y * (z / y)),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(15683,a,13585,a)].">
      <j1 rule="hyper" parents="15683 13585"/>
    </justification>
  </clause>

  <clause id="15820">
    <literal><![CDATA[
      K(x * T(y * z,z),u) = K(x * (z * y),u)
    ]]></literal>
    <justification jstring="[para(11(a,1),15819(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 15819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15821">
    <literal><![CDATA[
      T(x,y * R(T(z,u \ 1),u,u)) = T(x,y * ((u \ 1) * (z * u)))
    ]]></literal>
    <justification jstring="[para(27(a,2),15686(a,1,2,2))].">
      <j1 rule="para" parents="27 15686"/>
    </justification>
  </clause>

  <clause id="15822">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(u,w / v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(u,T(v5 \ w,v5)) * z)) = v6
    ]]></literal>
    <justification jstring="[para(7419(a,1),15755(a,1,2,2,2))].">
      <j1 rule="para" parents="7419 15755"/>
    </justification>
  </clause>

  <clause id="15824">
    <literal><![CDATA[
      K(x,y \ ((z \ u) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(13826(a,2),15803(a,1))].">
      <j1 rule="para" parents="13826 15803"/>
    </justification>
  </clause>

  <clause id="15825">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14530(a,2),15803(a,1))].">
      <j1 rule="para" parents="14530 15803"/>
    </justification>
  </clause>

  <clause id="15826">
    <literal><![CDATA[
      K(x,y \ (T((z * (1 / u)) \ z,w) \ z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z * (1 / T(u,w)),z)) = v5
    ]]></literal>
    <justification jstring="[para(15169(a,2),15825(a,1,2,2,1))].">
      <j1 rule="para" parents="15169 15825"/>
    </justification>
  </clause>

  <clause id="15827">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(1 / u,z) * x)
    ]]></literal>
    <justification jstring="[para(8837(a,1),15502(a,1,2))].">
      <j1 rule="para" parents="8837 15502"/>
    </justification>
  </clause>

  <clause id="15828">
    <literal><![CDATA[
      T(x,K(1 / y,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(15506,a,15827,a),flip(a)].">
      <j1 rule="hyper" parents="15506 15827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15829">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(80(a,1),15828(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="80 15828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15830">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = x \ T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(128,a,15829,a(flip),b,4929,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 15829 4929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15831">
    <literal><![CDATA[
      T(x,K(y,z) * T(u,K(y,z))) = T(x,u * K(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(8830(a,1),15829(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8830 15829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15832">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,4924,a,b,15830,a),flip(a)].">
      <j1 rule="hyper" parents="347 4924 15830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15833">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(15546,a,15832,a)].">
      <j1 rule="hyper" parents="15546 15832"/>
    </justification>
  </clause>

  <clause id="15834">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(u,z \ y) * w)
    ]]></literal>
    <justification jstring="[para(6250(a,1),15833(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6250 15833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15835">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(K(y \ K(y,u),z) * u) \ w)
    ]]></literal>
    <justification jstring="[para(15833(a,1),6501(a,1,1))].">
      <j1 rule="para" parents="15833 6501"/>
    </justification>
  </clause>

  <clause id="15836">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,K(z,y))) = K(x,u * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(8836(a,1),15833(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8836 15833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15837">
    <literal><![CDATA[
      K(x,K(y \ (z \ 1),u) * w) = K(x,K(u,z * y) * w)
    ]]></literal>
    <justification jstring="[para(12984(a,1),15834(a,2,2,1))].">
      <j1 rule="para" parents="12984 15834"/>
    </justification>
  </clause>

  <clause id="15838">
    <literal><![CDATA[
      K(x,K(y \ z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15834(a,2),15552(a,1))].">
      <j1 rule="para" parents="15834 15552"/>
    </justification>
  </clause>

  <clause id="15839">
    <literal><![CDATA[
      T(x,y * K(z \ 1,u)) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(111(a,1),15831(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 15831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15840">
    <literal><![CDATA[
      T(x,y \ T(z,u \ 1)) = T(x,(y \ z) * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(15523,a,15839,a)].">
      <j1 rule="hyper" parents="15523 15839"/>
    </justification>
  </clause>

  <clause id="15841">
    <literal><![CDATA[
      T(x,y \ T(z,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15840(a,2),15523(a,1))].">
      <j1 rule="para" parents="15840 15523"/>
    </justification>
  </clause>

  <clause id="15842">
    <literal><![CDATA[
      K(x,y * K(z,u \ 1)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(7344(a,1),15836(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7344 15836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15843">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = 1 / K(u,x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(220,a,15842,a(flip),b,5173,a),flip(a)].">
      <j1 rule="hyper" parents="220 15842 5173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15844">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,5172,a(flip),b,15843,a),flip(a)].">
      <j1 rule="hyper" parents="347 5172 15843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15845">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) = K(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15569,a,b,15844,a)].">
      <j1 rule="hyper" parents="63 15569 15844"/>
    </justification>
  </clause>

  <clause id="15846">
    <literal><![CDATA[
      K(x * K(x \ y,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10385,a(flip),b,15845,a),flip(a)].">
      <j1 rule="hyper" parents="63 10385 15845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15847">
    <literal><![CDATA[
      K(x,y * T(z * K(u,K(w,v5)),u)) = K(x,y * T(z,K(v5,w) * u))
    ]]></literal>
    <justification jstring="[para(5916(a,2),15504(a,1,2,2))].">
      <j1 rule="para" parents="5916 15504"/>
    </justification>
  </clause>

  <clause id="15848">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,T(u * K(z,y),w))
    ]]></literal>
    <justification jstring="[hyper(8683,a,15516,a),flip(a)].">
      <j1 rule="hyper" parents="8683 15516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15849">
    <literal><![CDATA[
      K(x,T(y * K(z,u),y \ z) / w) = K(x,(T(z,u) / (z / y)) / w)
    ]]></literal>
    <justification jstring="[hyper(14853,a,15663,a)].">
      <j1 rule="hyper" parents="14853 15663"/>
    </justification>
  </clause>

  <clause id="15850">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(15847(a,1),14884(a,1))].">
      <j1 rule="para" parents="15847 14884"/>
    </justification>
  </clause>

  <clause id="15851">
    <literal><![CDATA[
      K(x,y * T(z,u * T(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u * w)) = v6
    ]]></literal>
    <justification jstring="[para(5573(a,1),15850(a,1,2,2,2))].">
      <j1 rule="para" parents="5573 15850"/>
    </justification>
  </clause>

  <clause id="15852">
    <literal><![CDATA[
      K(x,y * T(z,u * K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = v6
    ]]></literal>
    <justification jstring="[para(7372(a,1),15850(a,1,2,2,2))].">
      <j1 rule="para" parents="7372 15850"/>
    </justification>
  </clause>

  <clause id="15853">
    <literal><![CDATA[
      K(x,y * T(z,u \ (w / v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u \ (v5 \ w))) = v6
    ]]></literal>
    <justification jstring="[para(13354(a,1),15852(a,1,2,2,2))].">
      <j1 rule="para" parents="13354 15852"/>
    </justification>
  </clause>

  <clause id="15854">
    <literal><![CDATA[
      T(x,y * (z * (u * (K(w,v5) * K(w,v5))))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(15777,a,xx),flip(a)].">
      <j1 rule="hyper" parents="15777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15855">
    <literal><![CDATA[
      T(x,y * (z * (u * K(w,u)))) = T(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(5213(a,1),15854(a,1,2,2,2))].">
      <j1 rule="para" parents="5213 15854"/>
    </justification>
  </clause>

  <clause id="15856">
    <literal><![CDATA[
      T(x,y * (T(T(z,u),u) * w)) = T(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(15774(a,1),15854(a,1,2,2))].">
      <j1 rule="para" parents="15774 15854"/>
    </justification>
  </clause>

  <clause id="15857">
    <literal><![CDATA[
      T(x,y * (T(z \ u,z) * w)) = T(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(113(a,1),15856(a,1,2,2,1,1))].">
      <j1 rule="para" parents="113 15856"/>
    </justification>
  </clause>

  <clause id="15859">
    <literal><![CDATA[
      T(x,y * (z * T((u * w) / u,v5))) = T(x,y * (z * T(T(w,v5),u)))
    ]]></literal>
    <justification jstring="[para(5050(a,2),15855(a,1,2,2,2))].">
      <j1 rule="para" parents="5050 15855"/>
    </justification>
  </clause>

  <clause id="15860">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u * w)),K(z,u * w)) = T(y,K(u \ w,z) * x)
    ]]></literal>
    <justification jstring="[para(13474(a,1),15503(a,1,2))].">
      <j1 rule="para" parents="13474 15503"/>
    </justification>
  </clause>

  <clause id="15861">
    <literal><![CDATA[
      T(x,((y / (z \ K(z,y))) / y) \ u) = T(x,(y \ (y / (z \ 1))) \ u)
    ]]></literal>
    <justification jstring="[para(113(a,1),15603(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 15603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15862">
    <literal><![CDATA[
      K(x,T((y * z) \ u,y * z) * T(z,y)) = K(x,(u / (z * y)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,15691,a(flip),b,15614,a)].">
      <j1 rule="hyper" parents="63 15691 15614"/>
    </justification>
  </clause>

  <clause id="15863">
    <literal><![CDATA[
      K(x,T((T(y,z) \ z) \ u,y \ z) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[hyper(14853,a,15662,a)].">
      <j1 rule="hyper" parents="14853 15662"/>
    </justification>
  </clause>

  <clause id="15864">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((u \ 1) \ w))) = K(x,y \ (((1 / u) \ w) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,5590,a(flip),b,15708,a)].">
      <j1 rule="hyper" parents="63 5590 15708"/>
    </justification>
  </clause>

  <clause id="15865">
    <literal><![CDATA[
      K(x,T(T(y,z) \ u,z * y)) = K(x,T(u,y \ (z \ y)) / y)
    ]]></literal>
    <justification jstring="[para(11(a,1),15785(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 15785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15866">
    <literal><![CDATA[
      T(x,K(y \ z,u) * w) = T(x,K(y * z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(15506,a,15860,a),flip(a)].">
      <j1 rule="hyper" parents="15506 15860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15867">
    <literal><![CDATA[
      T(x,K(y \ z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y * z,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(15860(a,1),15506(a,1))].">
      <j1 rule="para" parents="15860 15506"/>
    </justification>
  </clause>

  <clause id="15868">
    <literal><![CDATA[
      T(x,K(y * z,T(u,w)) * v5) = T(x,K(u,y \ z) * v5)
    ]]></literal>
    <justification jstring="[hyper(15632,a,15866,a),flip(a)].">
      <j1 rule="hyper" parents="15632 15866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15869">
    <literal><![CDATA[
      T(x,K(y \ z,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,12089,a(flip),b,15866,a),flip(a)].">
      <j1 rule="hyper" parents="347 12089 15866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15870">
    <literal><![CDATA[
      x / T(x,K(y * z,u) * w) = K(K(y \ z,u) * w,x)
    ]]></literal>
    <justification jstring="[hyper(220,a,15866,a(flip),b,4939,a(flip))].">
      <j1 rule="hyper" parents="220 15866 4939"/>
    </justification>
  </clause>

  <clause id="15871">
    <literal><![CDATA[
      x \ T(x,K(y * z,u) * w) = K(x,K(y \ z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(128,a,15866,a(flip),b,4929,a(flip))].">
      <j1 rule="hyper" parents="128 15866 4929"/>
    </justification>
  </clause>

  <clause id="15872">
    <literal><![CDATA[
      T(x,K(y * z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w * K(y \ z,u)) = v5
    ]]></literal>
    <justification jstring="[para(15866(a,1),13563(a,1))].">
      <j1 rule="para" parents="15866 13563"/>
    </justification>
  </clause>

  <clause id="15873">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w) \ (K(z \ u,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(z \ u,u) * w) / y) = v5
    ]]></literal>
    <justification jstring="[para(15869(a,1),12071(a,1,2,1))].">
      <j1 rule="para" parents="15869 12071"/>
    </justification>
  </clause>

  <clause id="15874">
    <literal><![CDATA[
      T(x,K(y,z \ u) * w) = T(x,K(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(15632,a,15868,a),flip(a)].">
      <j1 rule="hyper" parents="15632 15868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15875">
    <literal><![CDATA[
      x / T(x,K(y,z * u) * w) = K(K(y,z \ u) * w,x)
    ]]></literal>
    <justification jstring="[hyper(220,a,15874,a(flip),b,4939,a(flip))].">
      <j1 rule="hyper" parents="220 15874 4939"/>
    </justification>
  </clause>

  <clause id="15876">
    <literal><![CDATA[
      T(x,K(y,z * u) * T(w,K(y,z \ u))) = T(x,w * K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(111(a,1),15874(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 15874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15877">
    <literal><![CDATA[
      K(K(x \ y,z) * u,w) = K(K(x * y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(5013,a,15870,a),flip(a)].">
      <j1 rule="hyper" parents="5013 15870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15878">
    <literal><![CDATA[
      K(K(x * y,z) * (u \ z),w) = K(u \ T(z,x \ y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15572,a(flip),b,15877,a),flip(a)].">
      <j1 rule="hyper" parents="63 15572 15877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15879">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(y * z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(5006,a,15871,a),flip(a)].">
      <j1 rule="hyper" parents="5006 15871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15880">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y * z,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(15871(a,1),5006(a,1))].">
      <j1 rule="para" parents="15871 5006"/>
    </justification>
  </clause>

  <clause id="15881">
    <literal><![CDATA[
      K(x,K(y * z,u) * w) = K(x,K(u,y \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(15546,a,15879,a),flip(a)].">
      <j1 rule="hyper" parents="15546 15879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15882">
    <literal><![CDATA[
      K(x,K(y * z,u) * (u \ w)) = K(x,T(u,y \ z) \ w)
    ]]></literal>
    <justification jstring="[hyper(12153,a,15879,a),flip(a)].">
      <j1 rule="hyper" parents="12153 15879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15883">
    <literal><![CDATA[
      K(x,K(y * z,u) * T(w,K(u,y \ z))) = K(x,w * K(y \ z,u))
    ]]></literal>
    <justification jstring="[para(7344(a,1),15879(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7344 15879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15884">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(347,a,15834,a,b,15881,a)].">
      <j1 rule="hyper" parents="347 15834 15881"/>
    </justification>
  </clause>

  <clause id="15885">
    <literal><![CDATA[
      K(K(x,y \ z) * u,w) = K(K(x,y * z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(5013,a,15875,a),flip(a)].">
      <j1 rule="hyper" parents="5013 15875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15886">
    <literal><![CDATA[
      K(K(x,y * z) * u,w) = K(u * K(y \ z,x),w)
    ]]></literal>
    <justification jstring="[hyper(15576,a,15885,a),flip(a)].">
      <j1 rule="hyper" parents="15576 15885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15887">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(8(a,1),15885(a,2,1,1,2))].">
      <j1 rule="para" parents="8 15885"/>
    </justification>
  </clause>

  <clause id="15888">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(K(y,x) * (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(13332,a,15887,a)].">
      <j1 rule="hyper" parents="13332 15887"/>
    </justification>
  </clause>

  <clause id="15889">
    <literal><![CDATA[
      K(x * K(y \ z,u),w) = K(x * K(y * z,u),w)
    ]]></literal>
    <justification jstring="[hyper(15576,a,15886,a),flip(a)].">
      <j1 rule="hyper" parents="15576 15886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15890">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(x * (K(y,x) * z),u)
    ]]></literal>
    <justification jstring="[para(5353(a,1),15888(a,2,1))].">
      <j1 rule="para" parents="5353 15888"/>
    </justification>
  </clause>

  <clause id="15891">
    <literal><![CDATA[
      K(x * K(x * y,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15846,a(flip),b,15889,a),flip(a)].">
      <j1 rule="hyper" parents="63 15846 15889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15892">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,15745,a(flip),b,15890,a),flip(a)].">
      <j1 rule="hyper" parents="347 15745 15890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15893">
    <literal><![CDATA[
      K(T(1 / x,y) \ z,u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3884,a,b,15892,a)].">
      <j1 rule="hyper" parents="63 3884 15892"/>
    </justification>
  </clause>

  <clause id="15894">
    <literal><![CDATA[
      K(T(x \ 1,y) * z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(80(a,1),15893(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="80 15893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15895">
    <literal><![CDATA[
      K(T(x \ 1,y) * z,u) = u / T(u,T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,4920,a(flip),b,15894,a),flip(a)].">
      <j1 rule="hyper" parents="347 4920 15894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15896">
    <literal><![CDATA[
      T(x,T(y \ 1,z) * u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(4954,a,15895,a)].">
      <j1 rule="hyper" parents="4954 15895"/>
    </justification>
  </clause>

  <clause id="15897">
    <literal><![CDATA[
      T(x,T(1 / y,z) \ u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(83(a,1),15896(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="83 15896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15898">
    <literal><![CDATA[
      T(x,T(K(y,z) / u,w) \ v5) = T(x,T(u * K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[para(13073(a,1),15896(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="13073 15896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15899">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w) \ v5) = T(x,T(u \ K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[para(13174(a,1),15896(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="13174 15896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15900">
    <literal><![CDATA[
      T(x,T(y \ 1,z) \ u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4006,a(flip),b,15897,a)].">
      <j1 rule="hyper" parents="63 4006 15897"/>
    </justification>
  </clause>

  <clause id="15901">
    <literal><![CDATA[
      T(x,T(y \ 1,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(15900(a,1),12021(a,1))].">
      <j1 rule="para" parents="15900 12021"/>
    </justification>
  </clause>

  <clause id="15902">
    <literal><![CDATA[
      T(x,T((y \ z) \ K(y,u),w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,T(T(y,u) \ z,w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(13176(a,1),15901(a,1,2,1,1))].">
      <j1 rule="para" parents="13176 15901"/>
    </justification>
  </clause>

  <clause id="15903">
    <literal><![CDATA[
      K(x \ T(y,z \ u),w) = K(x \ T(y,z * u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15572,a(flip),b,15878,a),flip(a)].">
      <j1 rule="hyper" parents="63 15572 15878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15904">
    <literal><![CDATA[
      K((x * y) \ T(z,u * w),L(v5,y,x)) = K(y \ (x \ T(z,u \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(15079,a,15903,a),flip(a)].">
      <j1 rule="hyper" parents="15079 15903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15905">
    <literal><![CDATA[
      K(x \ T(y,z \ 1),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(8(a,1),15903(a,2,1,2,2))].">
      <j1 rule="para" parents="8 15903"/>
    </justification>
  </clause>

  <clause id="15906">
    <literal><![CDATA[
      (x * K(y \ T(z,u * w),v5)) \ x = K(v5,y \ T(z,u \ w))
    ]]></literal>
    <justification jstring="[para(15903(a,1),6123(a,1,1,2))].">
      <j1 rule="para" parents="15903 6123"/>
    </justification>
  </clause>

  <clause id="15907">
    <literal><![CDATA[
      K(x \ T(y * z,z),u) = K(x \ T(y * z,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12054,a(flip),b,15905,a),flip(a)].">
      <j1 rule="hyper" parents="63 12054 15905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15908">
    <literal><![CDATA[
      K(x,y \ T(z,u \ 1)) * a(w,v5,K(y \ T(z,u),x)) = K(x,L(y \ T(z,u \ 1),v5,w))
    ]]></literal>
    <justification jstring="[para(15905(a,1),11061(a,1,2,3))].">
      <j1 rule="para" parents="15905 11061"/>
    </justification>
  </clause>

  <clause id="15909">
    <literal><![CDATA[
      K(x \ T(y * z,z),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,11997,a(flip),b,15907,a),flip(a)].">
      <j1 rule="hyper" parents="347 11997 15907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15910">
    <literal><![CDATA[
      K(x \ (y * (z / y)),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(12(a,1),15909(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 15909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15911">
    <literal><![CDATA[
      K(x \ T(y * z,y),u) = K(x \ (T(y,z) * z),u)
    ]]></literal>
    <justification jstring="[para(4149(a,2),15910(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4149 15910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15912">
    <literal><![CDATA[
      K((x * (y / x)) / z,u) = K(z,K(y,u)) * K(z \ T(y,x),u)
    ]]></literal>
    <justification jstring="[para(15910(a,1),13518(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15910 13518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15913">
    <literal><![CDATA[
      K(x \ (T(y,z) * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ (z * y),u) = w
    ]]></literal>
    <justification jstring="[para(15911(a,1),12156(a,1))].">
      <j1 rule="para" parents="15911 12156"/>
    </justification>
  </clause>

  <clause id="15914">
    <literal><![CDATA[
      K(x,T(y,z \ u) \ w) = K(x,T(y,z * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(12153,a,15882,a),flip(a)].">
      <j1 rule="hyper" parents="12153 15882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15915">
    <literal><![CDATA[
      K(x,T(y,z \ 1) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(8(a,1),15914(a,2,2,1,2))].">
      <j1 rule="para" parents="8 15914"/>
    </justification>
  </clause>

  <clause id="15916">
    <literal><![CDATA[
      K(x,T((1 / y) * z,y) \ u) = K(x,(z * (1 / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(12170,a,15915,a),flip(a)].">
      <j1 rule="hyper" parents="12170 15915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15917">
    <literal><![CDATA[
      K(x,T((y \ 1) * z,y) \ u) = K(x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(12168,a,15915,a),flip(a)].">
      <j1 rule="hyper" parents="12168 15915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15918">
    <literal><![CDATA[
      T(x,T(y,z \ 1) \ u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(132,a,15915,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 15915 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15919">
    <literal><![CDATA[
      T(x,T(y * (z \ 1),z) \ u) = T(x,((z \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(15719,a,15918,a),flip(a)].">
      <j1 rule="hyper" parents="15719 15918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15920">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(z,y)) = (x * w) / (K(z * T(y / z,u),x) * w)
    ]]></literal>
    <justification jstring="[para(15891(a,1),15472(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15891 15472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15921">
    <literal><![CDATA[
      K(x,T((1 / y) * z,y) \ u) = K(x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,5591,a(flip),b,15916,a),flip(a)].">
      <j1 rule="hyper" parents="347 5591 15916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15922">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) \ u) = K(x,((z * y) * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15621,a(flip),b,15917,a)].">
      <j1 rule="hyper" parents="63 15621 15917"/>
    </justification>
  </clause>

  <clause id="15923">
    <literal><![CDATA[
      K(x,y \ T(z,u \ w)) = K(x,y \ T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(13643,a,15906,a),flip(a)].">
      <j1 rule="hyper" parents="13643 15906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15924">
    <literal><![CDATA[
      K(x,y \ T(z,u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u * w)) = v5
    ]]></literal>
    <justification jstring="[para(15906(a,1),6141(a,1))].">
      <j1 rule="para" parents="15906 6141"/>
    </justification>
  </clause>

  <clause id="15925">
    <literal><![CDATA[
      K(x,(y \ 1) \ T(z,u * w)) = K(x,y * T(z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(13242,a,15923,a),flip(a)].">
      <j1 rule="hyper" parents="13242 15923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15926">
    <literal><![CDATA[
      K(x,y \ T(z,u \ 1)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),15923(a,2,2,2,2))].">
      <j1 rule="para" parents="8 15923"/>
    </justification>
  </clause>

  <clause id="15927">
    <literal><![CDATA[
      K(x,y \ T(z * (u \ 1),u)) = K(x,y \ ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15799,a(flip),b,15926,a),flip(a)].">
      <j1 rule="hyper" parents="63 15799 15926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15928">
    <literal><![CDATA[
      K(x,y \ T(((1 / z) * u) * z,z)) = K(x,y \ R(u,z,z))
    ]]></literal>
    <justification jstring="[para(2984(a,1),15926(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2984 15926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15929">
    <literal><![CDATA[
      K(x,y * T(z,u \ w)) = K(x,y * T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(13242,a,15925,a),flip(a)].">
      <j1 rule="hyper" parents="13242 15925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15930">
    <literal><![CDATA[
      K(x,y * T(z,u \ w)) = K(x,y * T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,14812,a,b,15929,a),flip(a)].">
      <j1 rule="hyper" parents="347 14812 15929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15931">
    <literal><![CDATA[
      K(x,y * T(z,u \ 1)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),15929(a,2,2,2,2))].">
      <j1 rule="para" parents="8 15929"/>
    </justification>
  </clause>

  <clause id="15932">
    <literal><![CDATA[
      K(x,y * T(z,u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,w * u)) = v5
    ]]></literal>
    <justification jstring="[para(15929(a,2),14850(a,1))].">
      <j1 rule="para" parents="15929 14850"/>
    </justification>
  </clause>

  <clause id="15933">
    <literal><![CDATA[
      T(x,y * T(z,u \ 1)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(132,a,15931,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 15931 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15934">
    <literal><![CDATA[
      K(x,y * L(z / (u \ 1),u,u)) = K(x,y * T(u * z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15805,a,b,15931,a)].">
      <j1 rule="hyper" parents="63 15805 15931"/>
    </justification>
  </clause>

  <clause id="15935">
    <literal><![CDATA[
      K(x,y * T((z \ 1) \ u,z)) = K(x,y * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15678,a(flip),b,15931,a),flip(a)].">
      <j1 rule="hyper" parents="63 15678 15931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15936">
    <literal><![CDATA[
      T(x,(y * ((z \ 1) * K(u,z \ 1))) * u) = T(x,(y * (z \ 1)) * T(u,z))
    ]]></literal>
    <justification jstring="[para(6239(a,2),15933(a,1,2))].">
      <j1 rule="para" parents="6239 15933"/>
    </justification>
  </clause>

  <clause id="15937">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * (z * u))) = K(x,y \ R(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(1059(a,1),15927(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1059 15927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15938">
    <literal><![CDATA[
      K(x,y * ((z \ K(z,u)) \ u)) = K(x,y * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12084,a(flip),b,15935,a)].">
      <j1 rule="hyper" parents="63 12084 15935"/>
    </justification>
  </clause>

  <clause id="15939">
    <literal><![CDATA[
      K(x,y \ (z * ((1 / z) * u))) = K(x,y \ R(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15799,a(flip),b,15928,a)].">
      <j1 rule="hyper" parents="63 15799 15928"/>
    </justification>
  </clause>

  <clause id="15940">
    <literal><![CDATA[
      K(x,y \ R(z,u,u)) = K(x,y \ L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5855,a(flip),b,15939,a),flip(a)].">
      <j1 rule="hyper" parents="63 5855 15939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15941">
    <literal><![CDATA[
      K(x,(1 / y) \ L(z,u,u)) = K(x,y * R(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(13303,a,15940,a),flip(a)].">
      <j1 rule="hyper" parents="13303 15940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15942">
    <literal><![CDATA[
      K(x,y * R(z,u,u)) = K(x,y * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(13303,a,15941,a),flip(a)].">
      <j1 rule="hyper" parents="13303 15941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15943">
    <literal><![CDATA[
      x * K(x,y * L(z,u,u)) = T(x,y * R(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,15942,a(flip),b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 15942 4924"/>
    </justification>
  </clause>

  <clause id="15944">
    <literal><![CDATA[
      T(x,y * R(z,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * L(z,u,u)) = w
    ]]></literal>
    <justification jstring="[para(15943(a,1),4984(a,1))].">
      <j1 rule="para" parents="15943 4984"/>
    </justification>
  </clause>

  <clause id="15945">
    <literal><![CDATA[
      T(x,y * L(T(z,u \ 1),u,u)) = T(x,y * ((u \ 1) * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(15944,a,15821,a)].">
      <j1 rule="hyper" parents="15944 15821"/>
    </justification>
  </clause>

  <clause id="15946">
    <literal><![CDATA[
      K(x,y * L(z / (u \ 1),u,u)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,12003,a(flip),b,15934,a),flip(a)].">
      <j1 rule="hyper" parents="347 12003 15934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15947">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,((z \ 1) * y) \ R(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(11170,a,15937,a)].">
      <j1 rule="hyper" parents="11170 15937"/>
    </justification>
  </clause>

  <clause id="15948">
    <literal><![CDATA[
      K(x,y \ R(z,u,u \ 1)) = K(x,y \ L(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,5708,a(flip),b,15937,a),flip(a)].">
      <j1 rule="hyper" parents="63 5708 15937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15949">
    <literal><![CDATA[
      K(x,(y * z) \ L(y,u,u \ 1)) = K(x,z \ a(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,14525,a(flip),b,15948,a),flip(a)].">
      <j1 rule="hyper" parents="63 14525 15948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15950">
    <literal><![CDATA[
      K(x,y \ L(z / u,u,u \ 1)) = K(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(691(a,1),15948(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="691 15948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15951">
    <literal><![CDATA[
      K((x * (y / x)) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,13509,a(flip),b,15912,a),flip(a)].">
      <j1 rule="hyper" parents="347 13509 15912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15952">
    <literal><![CDATA[
      K(T(x * y,y) / z,u) = K((y * x) / z,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),15951(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 15951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15953">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) = (w * K((z * y) / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(15952(a,1),6123(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="15952 6123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15954">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(347,a,13585,a(flip),b,15953,a),flip(a)].">
      <j1 rule="hyper" parents="347 13585 15953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15955">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) / u) = w
    ]]></literal>
    <justification jstring="[para(15953(a,2),6141(a,1))].">
      <j1 rule="para" parents="15953 6141"/>
    </justification>
  </clause>

  <clause id="15956">
    <literal><![CDATA[
      K(x,(y * (z / y)) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(12(a,1),15954(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 15954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15957">
    <literal><![CDATA[
      K(x,(y * ((y * z) / y)) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(347,a,12001,a(flip),b,15956,a),flip(a)].">
      <j1 rule="hyper" parents="347 12001 15956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15958">
    <literal><![CDATA[
      K(x,T(y \ z,z) / u) = K(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14908,a(flip),b,15956,a),flip(a)].">
      <j1 rule="hyper" parents="63 14908 15956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15959">
    <literal><![CDATA[
      K(x,T(y,y / z) / u) = K(x,((z \ y) * z) / u)
    ]]></literal>
    <justification jstring="[para(4213(a,1),15956(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4213 15956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15960">
    <literal><![CDATA[
      K(x,T(y,z) / (u * (y / z))) = K(x,y / (u * (z \ y)))
    ]]></literal>
    <justification jstring="[para(13919(a,1),15956(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13919 15956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15961">
    <literal><![CDATA[
      K(x,(y / (y / z)) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(83(a,1),15958(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="83 15958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15962">
    <literal><![CDATA[
      K(x,T(y * T(z,u),T(z,u)) / w) = K(x,(T(z,u) / (z / (y * z))) / w)
    ]]></literal>
    <justification jstring="[para(13099(a,1),15961(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="13099 15961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15963">
    <literal><![CDATA[
      K(x,(T(y,z) * z) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(255(a,1),15957(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="255 15957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15964">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,u,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(14131,a,15963,a)].">
      <j1 rule="hyper" parents="14131 15963"/>
    </justification>
  </clause>

  <clause id="15965">
    <literal><![CDATA[
      K(x,T(y,y / z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(347,a,12055,a(flip),b,15959,a),flip(a)].">
      <j1 rule="hyper" parents="347 12055 15959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15966">
    <literal><![CDATA[
      K(x,T(y,z \ y) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(14853,a,15965,a)].">
      <j1 rule="hyper" parents="14853 15965"/>
    </justification>
  </clause>

  <clause id="15967">
    <literal><![CDATA[
      K(x,T(y,z) / (u * (y / z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,u)) = w
    ]]></literal>
    <justification jstring="[para(15965(a,1),14659(a,1))].">
      <j1 rule="para" parents="15965 14659"/>
    </justification>
  </clause>

  <clause id="15968">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ y)) / w) = K(x,T(y,u * z) / w)
    ]]></literal>
    <justification jstring="[para(13217(a,1),15966(a,1,2,1))].">
      <j1 rule="para" parents="13217 15966"/>
    </justification>
  </clause>

  <clause id="15969">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,y,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(14183,a,15964,a)].">
      <j1 rule="hyper" parents="14183 15964"/>
    </justification>
  </clause>

  <clause id="15970">
    <literal><![CDATA[
      K(x,T(y,z \ (y / u)) / w) = K(x,T(y,u * z) / w)
    ]]></literal>
    <justification jstring="[para(10020(a,2),15968(a,1,2,1))].">
      <j1 rule="para" parents="10020 15968"/>
    </justification>
  </clause>

  <clause id="15971">
    <literal><![CDATA[
      K(x,T(y,z * u) / ((y / z) / u)) = K(x,((y / z) / u) \ y)
    ]]></literal>
    <justification jstring="[hyper(14896,a,15970,a),flip(a)].">
      <j1 rule="hyper" parents="14896 15970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15972">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) \ u) = K(x,R(z,y,y) \ u)
    ]]></literal>
    <justification jstring="[para(786(a,1),15922(a,2,2,1))].">
      <j1 rule="para" parents="786 15922"/>
    </justification>
  </clause>

  <clause id="15973">
    <literal><![CDATA[
      K(x,R(y * z,K(u,L(w,y,z)),K(u,L(w,y,z))) \ v5) = K(x,((K(u,L(w,y,z)) \ 1) * ((K(u,w) * y) * z)) \ v5)
    ]]></literal>
    <justification jstring="[para(14092(a,1),15972(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="14092 15972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15974">
    <literal><![CDATA[
      K(x,y \ (z \ L(z,u,u \ 1))) = K(x,y \ a(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(14217,a,15949,a)].">
      <j1 rule="hyper" parents="14217 15949"/>
    </justification>
  </clause>

  <clause id="15975">
    <literal><![CDATA[
      K(x,(y \ 1) \ a(z,u,u \ 1)) = K(x,y * (z \ L(z,u,u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(13242,a,15974,a),flip(a)].">
      <j1 rule="hyper" parents="13242 15974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15976">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * (u * z))) = T(x,y * (z * (u * (z \ 1))))
    ]]></literal>
    <justification jstring="[para(3211(a,1),15945(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3211 15945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15977">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (u * (z * (u \ 1)))) = T(x,((u \ 1) * (z * u)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,15312,a(flip),b,15976,a),flip(a)].">
      <j1 rule="hyper" parents="63 15312 15976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15978">
    <literal><![CDATA[
      T(x,K(y,z * u) * T(w,K(y,z * u))) = T(x,w * K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(13474(a,1),15876(a,1,2,2))].">
      <j1 rule="para" parents="13474 15876"/>
    </justification>
  </clause>

  <clause id="15979">
    <literal><![CDATA[
      K(x,K(y * z,u) * T(w,K(u,y * z))) = K(x,w * K(y \ z,u))
    ]]></literal>
    <justification jstring="[para(13474(a,1),15883(a,1,2,2))].">
      <j1 rule="para" parents="13474 15883"/>
    </justification>
  </clause>

  <clause id="15980">
    <literal><![CDATA[
      K(x,y * (z \ L(z,u,u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * a(z,u,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(15975(a,1),13242(a,1))].">
      <j1 rule="para" parents="15975 13242"/>
    </justification>
  </clause>

  <clause id="15981">
    <literal><![CDATA[
      T(x,y * K(z,u \ w)) = T(x,y * K(z,u * w))
    ]]></literal>
    <justification jstring="[para(111(a,1),15978(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 15978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15982">
    <literal><![CDATA[
      x \ T(x,y * K(z,u * w)) = K(x,y * K(z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(128,a,15981,a(flip),b,4929,a(flip))].">
      <j1 rule="hyper" parents="128 15981 4929"/>
    </justification>
  </clause>

  <clause id="15983">
    <literal><![CDATA[
      K(x,y * K(z,u \ w)) = K(x,y * K(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(5006,a,15982,a),flip(a)].">
      <j1 rule="hyper" parents="5006 15982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15984">
    <literal><![CDATA[
      K(x,y * K(z,u \ w)) = K(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(14882,a,15983,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14882 15983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15985">
    <literal><![CDATA[
      K(x,(y * (z * u)) * K(L(u,z,y),w * v5)) = K(x,y * (z * T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[para(6975(a,1),15983(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6975 15983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15986">
    <literal><![CDATA[
      K(x,y * K(z \ u,w)) = K(x,y * K(z * u,w))
    ]]></literal>
    <justification jstring="[para(7344(a,1),15979(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7344 15979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15987">
    <literal><![CDATA[
      K(x,(y * z) * K(u * w,L(v5,z,y))) = K(x,y * (z * K(u \ w,v5)))
    ]]></literal>
    <justification jstring="[para(11073(a,1),15986(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11073 15986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15988">
    <literal><![CDATA[
      K(x \ (y \ T(z,u \ w)),v5) = K(x \ (y \ T(z,u * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(15079,a,15904,a),flip(a)].">
      <j1 rule="hyper" parents="15079 15904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15989">
    <literal><![CDATA[
      K((x \ 1) \ (y \ T(z,u * w)),v5) = K(x * (y \ T(z,u \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(13369,a,15988,a),flip(a)].">
      <j1 rule="hyper" parents="13369 15988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15990">
    <literal><![CDATA[
      K((x \ K(x * (y \ T(z,u \ w)),x \ 1)) \ (y \ T(z,u * w)),v5) = K((y \ T(z,u \ w)) / (x \ 1),v5)
    ]]></literal>
    <justification jstring="[para(5655(a,1),15988(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5655 15988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15991">
    <literal><![CDATA[
      K(x * (y \ T(z,u \ w)),v5) = K(x * (y \ T(z,u * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(13369,a,15989,a),flip(a)].">
      <j1 rule="hyper" parents="13369 15989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15992">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,u)) = K(x,y / (u * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(15967,a,15960,a)].">
      <j1 rule="hyper" parents="15967 15960"/>
    </justification>
  </clause>

  <clause id="15993">
    <literal><![CDATA[
      K(x,y * (z * K(u \ w,v5))) = K(x,y * (z * K(u * w,v5)))
    ]]></literal>
    <justification jstring="[para(11073(a,1),15987(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11073 15987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15994">
    <literal><![CDATA[
      T(x,y * (z * K(u \ w,v5))) = T(x,y * (z * K(u * w,v5)))
    ]]></literal>
    <justification jstring="[hyper(132,a,15993,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 15993 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15995">
    <literal><![CDATA[
      K(x,y * (z * K(u \ 1,w))) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(8(a,1),15993(a,2,2,2,2,1))].">
      <j1 rule="para" parents="8 15993"/>
    </justification>
  </clause>

  <clause id="15996">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,6664,a,b,15995,a)].">
      <j1 rule="hyper" parents="63 6664 15995"/>
    </justification>
  </clause>

  <clause id="15997">
    <literal><![CDATA[
      T(x,y * ((z * u) * K(w * u,w))) = T(x,y * (z * ((w \ u) * w)))
    ]]></literal>
    <justification jstring="[para(9585(a,1),15994(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9585 15994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15998">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(4929(a,2),15996(a,2,2,2))].">
      <j1 rule="para" parents="4929 15996"/>
    </justification>
  </clause>

  <clause id="15999">
    <literal><![CDATA[
      K(x,y / ((z * (u \ 1)) / z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(13327,a,15998,a)].">
      <j1 rule="hyper" parents="13327 15998"/>
    </justification>
  </clause>

  <clause id="16000">
    <literal><![CDATA[
      K(x,y / T(z \ 1,u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(15747,a,15999,a)].">
      <j1 rule="hyper" parents="15747 15999"/>
    </justification>
  </clause>

  <clause id="16001">
    <literal><![CDATA[
      K(x,y * T(z,z * (x * y))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(13306,a,16000,a),flip(a)].">
      <j1 rule="hyper" parents="13306 16000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16002">
    <literal><![CDATA[
      K(x,L(y / T(z \ 1,u),w,v5)) = K(L(x,w,v5),y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(11169,a,16000,a)].">
      <j1 rule="hyper" parents="11169 16000"/>
    </justification>
  </clause>

  <clause id="16003">
    <literal><![CDATA[
      K(x,y / T(z \ 1,u)) = K(x,K(u,z) * (y * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,15547,a,b,16000,a),flip(a)].">
      <j1 rule="hyper" parents="347 15547 16000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16004">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) * T(z,u)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15671,a(flip),b,16000,a),flip(a)].">
      <j1 rule="hyper" parents="63 15671 16000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16005">
    <literal><![CDATA[
      K(x,y * T(1 / z,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(83(a,1),16000(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="83 16000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16006">
    <literal><![CDATA[
      K(x,y * T(z \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(16000(a,1),13804(a,1))].">
      <j1 rule="para" parents="16000 13804"/>
    </justification>
  </clause>

  <clause id="16007">
    <literal><![CDATA[
      K(x,y * T(z,x * y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(12115,a,16001,a)].">
      <j1 rule="hyper" parents="12115 16001"/>
    </justification>
  </clause>

  <clause id="16008">
    <literal><![CDATA[
      K(x,y * T(z,y * x)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(14850,a,16007,a)].">
      <j1 rule="hyper" parents="14850 16007"/>
    </justification>
  </clause>

  <clause id="16009">
    <literal><![CDATA[
      T(x,y * T(z,x * y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(132,a,16007,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 16007 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16010">
    <literal><![CDATA[
      K(T(x,y),z * T(u,z * x)) = K(T(x,y),u * z)
    ]]></literal>
    <justification jstring="[hyper(15851,a,16008,a)].">
      <j1 rule="hyper" parents="15851 16008"/>
    </justification>
  </clause>

  <clause id="16011">
    <literal><![CDATA[
      T(x,y * K(z,u)) \ T(y * T(T(x,y * K(z,u)),K(z,u)),K(u,z)) = T(y,x * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15501,a,b,16009,a)].">
      <j1 rule="hyper" parents="63 15501 16009"/>
    </justification>
  </clause>

  <clause id="16012">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / T(y / z,y)) = K(x,(1 \ T(1 / (y / z),y)) * L(T(1 / (y / z),y) \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15433,a(flip),b,16005,a),flip(a)].">
      <j1 rule="hyper" parents="63 15433 16005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16013">
    <literal><![CDATA[
      K(x,y / T(z \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(16003(a,2),15553(a,1))].">
      <j1 rule="para" parents="16003 15553"/>
    </justification>
  </clause>

  <clause id="16014">
    <literal><![CDATA[
      K(x,L(y / T(z \ 1,u),w,v5)) = K(x,L(y * T(z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,11108,a(flip),b,16002,a),flip(a)].">
      <j1 rule="hyper" parents="347 11108 16002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16015">
    <literal><![CDATA[
      K(x,L(y * (z \ T(u,u \ z)),w,v5)) = K(x,L(y * T(z \ u,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(13859,a,16014,a)].">
      <j1 rule="hyper" parents="13859 16014"/>
    </justification>
  </clause>

  <clause id="16016">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(z,y)) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,5212,a(flip),b,15920,a),flip(a)].">
      <j1 rule="hyper" parents="347 5212 15920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16017">
    <literal><![CDATA[
      T(x,T(y * K(y * z,u),z)) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[para(15469(a,1),16016(a,1,2))].">
      <j1 rule="para" parents="15469 16016"/>
    </justification>
  </clause>

  <clause id="16018">
    <literal><![CDATA[
      T(x,y \ T(z * y,u)) = T(x,y * T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13721,a(flip),b,16017,a)].">
      <j1 rule="hyper" parents="63 13721 16017"/>
    </justification>
  </clause>

  <clause id="16019">
    <literal><![CDATA[
      T(x,y * T(T(z,z * y) / y,u)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15476,a(flip),b,16018,a),flip(a)].">
      <j1 rule="hyper" parents="63 15476 16018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16020">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,(y * (z \ 1)) * T(u,z))
    ]]></literal>
    <justification jstring="[para(3056(a,1),15936(a,1,2,1,2))].">
      <j1 rule="para" parents="3056 15936"/>
    </justification>
  </clause>

  <clause id="16021">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ R(u,y,y \ 1)) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14564,a(flip),b,15947,a),flip(a)].">
      <j1 rule="hyper" parents="63 14564 15947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16022">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * u) \ y) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,15101,a,b,16021,a)].">
      <j1 rule="hyper" parents="63 15101 16021"/>
    </justification>
  </clause>

  <clause id="16023">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ L(u,y,y \ 1)) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15948,a(flip),b,16021,a)].">
      <j1 rule="hyper" parents="63 15948 16021"/>
    </justification>
  </clause>

  <clause id="16024">
    <literal><![CDATA[
      K(x,T(y \ z,K(u,w)) \ v5) = K(x,(((v5 * y) \ v5) * z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,14800,a,b,16022,a)].">
      <j1 rule="hyper" parents="347 14800 16022"/>
    </justification>
  </clause>

  <clause id="16025">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * T(u,z \ 1)) \ y) = K(x,(u / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,15757,a(flip),b,16022,a),flip(a)].">
      <j1 rule="hyper" parents="347 15757 16022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16026">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) = K(x,((z \ y) * u) \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),16022(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 16022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16027">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * (u * K(w,L(v5,u,z)))) \ y) = K(x,((z \ u) * K(w,v5)) \ y)
    ]]></literal>
    <justification jstring="[para(14221(a,1),16022(a,2,2,1))].">
      <j1 rule="para" parents="14221 16022"/>
    </justification>
  </clause>

  <clause id="16028">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ z) * K(x,K(z,y \ u)) = K(x,z / ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(16026(a,1),9426(a,1,1))].">
      <j1 rule="para" parents="16026 9426"/>
    </justification>
  </clause>

  <clause id="16029">
    <literal><![CDATA[
      K(x,(y * ((z * u) \ z)) \ z) = K(x,(y / u) \ z)
    ]]></literal>
    <justification jstring="[para(6290(a,1),16025(a,1,2,1))].">
      <j1 rule="para" parents="6290 16025"/>
    </justification>
  </clause>

  <clause id="16030">
    <literal><![CDATA[
      T(x,((y \ 1) * (z * y)) * u) = T(x,(y * (z * (y \ 1))) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13825,a(flip),b,15977,a),flip(a)].">
      <j1 rule="hyper" parents="63 13825 15977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16031">
    <literal><![CDATA[
      K(x,L(y * (z \ T(u,u \ z)),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * (u / z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(16015(a,2),15806(a,1))].">
      <j1 rule="para" parents="16015 15806"/>
    </justification>
  </clause>

  <clause id="16032">
    <literal><![CDATA[
      K(x,y / ((y \ z) \ u)) = K(x,y / ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13417,a(flip),b,16028,a),flip(a)].">
      <j1 rule="hyper" parents="63 13417 16028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16033">
    <literal><![CDATA[
      T(x * (K(y,z) * K(y,z)),u) = T(x,u) * (K(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(15578,a,4974,a)].">
      <j1 rule="hyper" parents="15578 4974"/>
    </justification>
  </clause>

  <clause id="16034">
    <literal><![CDATA[
      K(x,T((1 / y) * (z * y),y) \ u) = K(x,L(z,y,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(11(a,1),15619(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 15619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16035">
    <literal><![CDATA[
      K(x,((y * z) * (z \ 1)) \ u) = K(x,L(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15921,a(flip),b,16034,a)].">
      <j1 rule="hyper" parents="63 15921 16034"/>
    </justification>
  </clause>

  <clause id="16037">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ u) = K(x,L(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(585(a,1),16035(a,1,2,1))].">
      <j1 rule="para" parents="585 16035"/>
    </justification>
  </clause>

  <clause id="16038">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ u) = K(x,R(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[para(786(a,1),16035(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="786 16035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16039">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,R(y,z,z) \ (y * u))
    ]]></literal>
    <justification jstring="[para(1407(a,1),16038(a,1,2))].">
      <j1 rule="para" parents="1407 16038"/>
    </justification>
  </clause>

  <clause id="16040">
    <literal><![CDATA[
      K(x,R(y,1 / z,1 / z) \ u) = K(x,L(y,z \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[para(2988(a,1),16038(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2988 16038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16041">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ ((z \ 1) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(14673,a,16037,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14673 16037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16042">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((z \ 1) * u)) = K(x,(y / z) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(691(a,1),16041(a,1,2,1))].">
      <j1 rule="para" parents="691 16041"/>
    </justification>
  </clause>

  <clause id="16043">
    <literal><![CDATA[
      K(x,R(y,1 / z,1 / z) \ u) = K(x,L(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[para(3188(a,1),16040(a,2,2,1))].">
      <j1 rule="para" parents="3188 16040"/>
    </justification>
  </clause>

  <clause id="16044">
    <literal><![CDATA[
      K(x,R(y,z,z) \ u) = K(x,L(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[para(2261(a,1),16043(a,1,2,1))].">
      <j1 rule="para" parents="2261 16043"/>
    </justification>
  </clause>

  <clause id="16045">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,L(y,z,z) \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16039,a,b,16044,a)].">
      <j1 rule="hyper" parents="63 16039 16044"/>
    </justification>
  </clause>

  <clause id="16046">
    <literal><![CDATA[
      K(x,L(y,z,z) \ (y * u)) = K(x,a(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14281,a(flip),b,16044,a),flip(a)].">
      <j1 rule="hyper" parents="63 14281 16044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16047">
    <literal><![CDATA[
      K(x,y * (L(y,z,z) \ u)) = K(x,a(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[para(1407(a,1),16046(a,1,2))].">
      <j1 rule="para" parents="1407 16046"/>
    </justification>
  </clause>

  <clause id="16048">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((z \ 1) * (z * u))) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),16042(a,2,2,2))].">
      <j1 rule="para" parents="9 16042"/>
    </justification>
  </clause>

  <clause id="16049">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,y * (L(y,z,z) \ u))
    ]]></literal>
    <justification jstring="[para(1407(a,1),16045(a,2,2))].">
      <j1 rule="para" parents="1407 16045"/>
    </justification>
  </clause>

  <clause id="16050">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ L(u,z,z \ 1)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5708,a(flip),b,16048,a)].">
      <j1 rule="hyper" parents="63 5708 16048"/>
    </justification>
  </clause>

  <clause id="16051">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) * u) = K(x,z * (L(z,y,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15231,a(flip),b,16049,a)].">
      <j1 rule="hyper" parents="63 15231 16049"/>
    </justification>
  </clause>

  <clause id="16052">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) * u) = K(x,a(z,y,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,16047,a(flip),b,16051,a),flip(a)].">
      <j1 rule="hyper" parents="347 16047 16051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16053">
    <literal><![CDATA[
      K(x,a(y,1 / z,1 / z) \ u) = K(x,a(z,1 / z,y) * u)
    ]]></literal>
    <justification jstring="[para(83(a,1),16052(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="83 16052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16054">
    <literal><![CDATA[
      K(x,a(y,1 / z,1 / z) \ u) = K(x,a(z,z,y) * u)
    ]]></literal>
    <justification jstring="[para(14964(a,1),16053(a,2,2,1))].">
      <j1 rule="para" parents="14964 16053"/>
    </justification>
  </clause>

  <clause id="16055">
    <literal><![CDATA[
      K(x,a(y,1 / z,z) \ u) = K(x,a(z,z,y) * u)
    ]]></literal>
    <justification jstring="[para(14923(a,1),16054(a,1,2,1))].">
      <j1 rule="para" parents="14923 16054"/>
    </justification>
  </clause>

  <clause id="16056">
    <literal><![CDATA[
      K(x,a(y,z,z) \ u) = K(x,a(z,z,y) * u)
    ]]></literal>
    <justification jstring="[para(14964(a,1),16055(a,1,2,1))].">
      <j1 rule="para" parents="14964 16055"/>
    </justification>
  </clause>

  <clause id="16057">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) * u) = K(x,a(y,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16052,a,b,16056,a)].">
      <j1 rule="hyper" parents="63 16052 16056"/>
    </justification>
  </clause>

  <clause id="16058">
    <literal><![CDATA[
      T(x,a(y \ 1,y,z) * u) = T(x,a(y,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(132,a,16057,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 16057 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16059">
    <literal><![CDATA[
      (x \ T(y,a(z,z,u) * w)) \ (x \ y) = K(a(z \ 1,z,u) * w,y)
    ]]></literal>
    <justification jstring="[para(16058(a,1),13115(a,1,1,2))].">
      <j1 rule="para" parents="16058 13115"/>
    </justification>
  </clause>

  <clause id="16060">
    <literal><![CDATA[
      K(a(x \ 1,x,y) * z,u) = K(a(x,x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13115,a(flip),b,16059,a),flip(a)].">
      <j1 rule="hyper" parents="63 13115 16059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16061">
    <literal><![CDATA[
      T(R(x * K(y,K(z,u)),K(w,v5),w),K(y,z) \ u) = u \ T(x * u,K(y,z))
    ]]></literal>
    <justification jstring="[para(7261(a,1),15735(a,1,1,1,2))].">
      <j1 rule="para" parents="7261 15735"/>
    </justification>
  </clause>

  <clause id="16062">
    <literal><![CDATA[
      K(x,(K(y \ K(y,z),u) * z) \ w) = K(x,(z * K(u,y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(8695,a,15835,a),flip(a)].">
      <j1 rule="hyper" parents="8695 15835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16063">
    <literal><![CDATA[
      K(x,(y * K(z \ 1,u)) \ w) = K(x,(y * K(u,z)) \ w)
    ]]></literal>
    <justification jstring="[para(6428(a,1),16062(a,1,2,1))].">
      <j1 rule="para" parents="6428 16062"/>
    </justification>
  </clause>

  <clause id="16064">
    <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(7289(a,1),16063(a,2,2))].">
      <j1 rule="para" parents="7289 16063"/>
    </justification>
  </clause>

  <clause id="16065">
    <literal><![CDATA[
      K(x,y * (z * T(u,w \ v5))) = K(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[para(6975(a,1),15985(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6975 15985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16066">
    <literal><![CDATA[
      T(R(K(x,K(y,z)) \ u,K(w,v5),w),K(x,y) \ z) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(13547(a,2),16061(a,1,1,1))].">
      <j1 rule="para" parents="13547 16061"/>
    </justification>
  </clause>

  <clause id="16067">
    <literal><![CDATA[
      T(K(x,K(y,z)) \ u,K(x,y) \ z) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(586(a,1),16066(a,1,1))].">
      <j1 rule="para" parents="586 16066"/>
    </justification>
  </clause>

  <clause id="16068">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,K(x,y) \ z) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(14314,a,16067,a)].">
      <j1 rule="hyper" parents="14314 16067"/>
    </justification>
  </clause>

  <clause id="16069">
    <literal><![CDATA[
      T(x,K(y,z) * (u * K(K(z,y),u))) = T(u,K(z,y)) \ T(x * u,K(z,y))
    ]]></literal>
    <justification jstring="[para(7296(a,1),15500(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7296 15500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16070">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * x,K(y,z)) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15648,a(flip),b,16069,a),flip(a)].">
      <j1 rule="hyper" parents="63 15648 16069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16071">
    <literal><![CDATA[
      x \ T(y * x,K(z,u * u)) = T(y,x * K(z,u * u))
    ]]></literal>
    <justification jstring="[para(9167(a,1),16070(a,1,1))].">
      <j1 rule="para" parents="9167 16070"/>
    </justification>
  </clause>

  <clause id="16072">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ T(w * y,K(z,u))) = K(x,T(w,K(z,u) \ y))
    ]]></literal>
    <justification jstring="[para(16070(a,2),13270(a,2,2)),flip(a)].">
      <j1 rule="para" parents="16070 13270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16073">
    <literal><![CDATA[
      T(x,y * K(z,u * u)) = y \ (x * y)
    ]]></literal>
    <justification jstring="[para(9167(a,1),16071(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9167 16071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16074">
    <literal><![CDATA[
      T(x,y * K(z,u * u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,22,a,b,16073,a),flip(a)].">
      <j1 rule="hyper" parents="347 22 16073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16076">
    <literal><![CDATA[
      T(x,y * K(z * z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(15521,a,16074,a)].">
      <j1 rule="hyper" parents="15521 16074"/>
    </justification>
  </clause>

  <clause id="16077">
    <literal><![CDATA[
      T(x,K(y,z * z) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(13564,a,16074,a)].">
      <j1 rule="hyper" parents="13564 16074"/>
    </justification>
  </clause>

  <clause id="16078">
    <literal><![CDATA[
      T(x,y * (z / (u * u))) = T(x,y * ((u * u) \ z))
    ]]></literal>
    <justification jstring="[para(5927(a,1),16074(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5927 16074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16080">
    <literal><![CDATA[
      T(x,y * (z * K(u,w * w))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(11109(a,1),16074(a,1,2))].">
      <j1 rule="para" parents="11109 16074"/>
    </justification>
  </clause>

  <clause id="16081">
    <literal><![CDATA[
      K(x,y * K(z * z,u)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,16076,a(flip),b,4929,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 16076 4929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16082">
    <literal><![CDATA[
      T(x,K(y,z * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(16077(a,1),15537(a,1))].">
      <j1 rule="para" parents="16077 15537"/>
    </justification>
  </clause>

  <clause id="16083">
    <literal><![CDATA[
      K(x,y * K(z * z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,4924,a,b,16081,a),flip(a)].">
      <j1 rule="hyper" parents="347 4924 16081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16084">
    <literal><![CDATA[
      K(x,y * K(z * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(16081(a,2),5006(a,1))].">
      <j1 rule="para" parents="16081 5006"/>
    </justification>
  </clause>

  <clause id="16085">
    <literal><![CDATA[
      K(x,y * K(z,u * u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15560,a,16083,a)].">
      <j1 rule="hyper" parents="15560 16083"/>
    </justification>
  </clause>

  <clause id="16086">
    <literal><![CDATA[
      K(x,T(y,z * z) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15555,a(flip),b,16083,a)].">
      <j1 rule="hyper" parents="63 15555 16083"/>
    </justification>
  </clause>

  <clause id="16087">
    <literal><![CDATA[
      K(x,T(y,z * z) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(1439(a,1),16085(a,1,2))].">
      <j1 rule="para" parents="1439 16085"/>
    </justification>
  </clause>

  <clause id="16088">
    <literal><![CDATA[
      K(x,T(y,z \ 1) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(1310(a,1),16086(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1310 16086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16089">
    <literal><![CDATA[
      K(x,T(y,z * (z * u)) * w) = K(x,T(y,u) * w)
    ]]></literal>
    <justification jstring="[para(13269(a,1),16086(a,1,2,1))].">
      <j1 rule="para" parents="13269 16086"/>
    </justification>
  </clause>

  <clause id="16090">
    <literal><![CDATA[
      K(x,T(y,z \ 1) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(1310(a,1),16087(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1310 16087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16091">
    <literal><![CDATA[
      T(x,T(y,z * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * u) = w
    ]]></literal>
    <justification jstring="[para(4974(a,1),16082(a,1,2))].">
      <j1 rule="para" parents="4974 16082"/>
    </justification>
  </clause>

  <clause id="16092">
    <literal><![CDATA[
      K(x,y \ T(z,u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = w
    ]]></literal>
    <justification jstring="[para(15556(a,1),16084(a,1))].">
      <j1 rule="para" parents="15556 16084"/>
    </justification>
  </clause>

  <clause id="16093">
    <literal><![CDATA[
      T(x,y * (z * (u / (w * w)))) = T(x,y * (z * ((w * w) \ u)))
    ]]></literal>
    <justification jstring="[para(5927(a,1),16080(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5927 16080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16094">
    <literal><![CDATA[
      T(x,y * (z * (u * T(w,v5 * v5)))) = T(x,y * (z * (u * w)))
    ]]></literal>
    <justification jstring="[para(6975(a,1),16080(a,1,2,2))].">
      <j1 rule="para" parents="6975 16080"/>
    </justification>
  </clause>

  <clause id="16095">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) * w) = K(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[para(13214(a,1),16088(a,1,2,1))].">
      <j1 rule="para" parents="13214 16088"/>
    </justification>
  </clause>

  <clause id="16096">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / w) = K(x,T(y,u) / w)
    ]]></literal>
    <justification jstring="[hyper(14895,a,16090,a)].">
      <j1 rule="hyper" parents="14895 16090"/>
    </justification>
  </clause>

  <clause id="16097">
    <literal><![CDATA[
      T(x,T(y,z * (u * u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) * w) = v5
    ]]></literal>
    <justification jstring="[para(1305(a,1),16091(a,1,2,1))].">
      <j1 rule="para" parents="1305 16091"/>
    </justification>
  </clause>

  <clause id="16098">
    <literal><![CDATA[
      K(x,y \ T(z,u * (u * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,w)) = v5
    ]]></literal>
    <justification jstring="[para(13269(a,1),16092(a,1,2,2))].">
      <j1 rule="para" parents="13269 16092"/>
    </justification>
  </clause>

  <clause id="16099">
    <literal><![CDATA[
      T(x,y \ (y \ (z * u))) = T(x,z * ((y * y) \ u))
    ]]></literal>
    <justification jstring="[hyper(13423,a,16078,a)].">
      <j1 rule="hyper" parents="13423 16078"/>
    </justification>
  </clause>

  <clause id="16100">
    <literal><![CDATA[
      T(x,y * ((z * z) \ (u * w))) = T(x,y * (u * (w / (z * z))))
    ]]></literal>
    <justification jstring="[para(464(a,1),16078(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="464 16078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16101">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,T(u,w * (w * v5)) * v6)),K(T(u,w * (w * v5)) * v6,z)) = T(y,K(z,T(u,v5) * v6) * x)
    ]]></literal>
    <justification jstring="[para(16089(a,1),15501(a,2,2,1))].">
      <j1 rule="para" parents="16089 15501"/>
    </justification>
  </clause>

  <clause id="16102">
    <literal><![CDATA[
      K(x,T(T(y,z) \ u,z * y)) = K(x,T(u,z) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,15865,a,b,16096,a)].">
      <j1 rule="hyper" parents="63 15865 16096"/>
    </justification>
  </clause>

  <clause id="16103">
    <literal><![CDATA[
      T(T(x,y * ((z * z) \ u)),w) = T(T(x,y * u),z \ (z \ w))
    ]]></literal>
    <justification jstring="[para(16099(a,1),13846(a,1,1))].">
      <j1 rule="para" parents="16099 13846"/>
    </justification>
  </clause>

  <clause id="16105">
    <literal><![CDATA[
      K(x,T(y \ ((z / y) \ u),(y \ z) * y)) = K(x,T((y \ z) \ u,y \ z) / y)
    ]]></literal>
    <justification jstring="[para(5605(a,1),16102(a,1,2,1))].">
      <j1 rule="para" parents="5605 16102"/>
    </justification>
  </clause>

  <clause id="16106">
    <literal><![CDATA[
      K(x,T(y,z * u) * T(u,z)) = K(x,T(u * y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16004,a(flip),b,16095,a),flip(a)].">
      <j1 rule="hyper" parents="63 16004 16095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16107">
    <literal><![CDATA[
      K(x,T(y * ((z * y) \ u),z)) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,15862,a(flip),b,16106,a),flip(a)].">
      <j1 rule="hyper" parents="63 15862 16106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16108">
    <literal><![CDATA[
      K(x,((((y \ (z * u)) \ 1) \ y) \ y) * T(u,z)) = K(x,T(u * ((y \ (z * u)) \ 1),z))
    ]]></literal>
    <justification jstring="[para(9128(a,1),16106(a,1,2,1))].">
      <j1 rule="para" parents="9128 16106"/>
    </justification>
  </clause>

  <clause id="16109">
    <literal><![CDATA[
      T(x,T(y,z \ 1) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(13124(a,1),16097(a,1,2,1))].">
      <j1 rule="para" parents="13124 16097"/>
    </justification>
  </clause>

  <clause id="16110">
    <literal><![CDATA[
      K(x,y \ T(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u \ w)) = v5
    ]]></literal>
    <justification jstring="[para(10(a,1),16098(a,1,2,2,2,2))].">
      <j1 rule="para" parents="10 16098"/>
    </justification>
  </clause>

  <clause id="16111">
    <literal><![CDATA[
      T(x,y * (z * ((u \ 1) * (w * (u * u))))) = T(x,y * (z * (u * w)))
    ]]></literal>
    <justification jstring="[para(496(a,2),16094(a,1,2,2,2))].">
      <j1 rule="para" parents="496 16094"/>
    </justification>
  </clause>

  <clause id="16112">
    <literal><![CDATA[
      T(x,y * ((z * z) \ (u * w))) = T(x,y * (u * ((z * z) \ w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,16093,a(flip),b,16100,a),flip(a)].">
      <j1 rule="hyper" parents="347 16093 16100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16113">
    <literal><![CDATA[
      T(T(x,y * (z * ((u * u) \ w))),v5) = T(T(x,y * (z * w)),u \ (u \ v5))
    ]]></literal>
    <justification jstring="[para(16112(a,1),16103(a,1,1))].">
      <j1 rule="para" parents="16112 16103"/>
    </justification>
  </clause>

  <clause id="16114">
    <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(5256(a,1),16072(a,2,2,2))].">
      <j1 rule="para" parents="5256 16072"/>
    </justification>
  </clause>

  <clause id="16115">
    <literal><![CDATA[
      T(x,y * L(z * (u * u),u,u)) = T(x,y * (u * (u * z)))
    ]]></literal>
    <justification jstring="[para(3197(a,1),16111(a,1,2,2))].">
      <j1 rule="para" parents="3197 16111"/>
    </justification>
  </clause>

  <clause id="16116">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (u * (u * z))) = T(x,(u * (u * T(z,u * u))) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,15249,a(flip),b,16115,a),flip(a)].">
      <j1 rule="hyper" parents="63 15249 16115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16117">
    <literal><![CDATA[
      T(x,y * (K(z,u) * (K(z,u) * w))) = T(x,y * (w * (K(z,u) * K(z,u))))
    ]]></literal>
    <justification jstring="[para(9930(a,1),16115(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9930 16115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16118">
    <literal><![CDATA[
      K(x,y \ T(z * y,K(u,w))) = K(x,T(z,K(w,u) * y))
    ]]></literal>
    <justification jstring="[hyper(14828,a,16114,a)].">
      <j1 rule="hyper" parents="14828 16114"/>
    </justification>
  </clause>

  <clause id="16119">
    <literal><![CDATA[
      K(x,T(y * z,K(u,w)) / y) = K(x,T(z,K(w,u) * y))
    ]]></literal>
    <justification jstring="[hyper(7602,a,16118,a)].">
      <j1 rule="hyper" parents="7602 16118"/>
    </justification>
  </clause>

  <clause id="16121">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = K(x,(w * y) / w)
    ]]></literal>
    <justification jstring="[hyper(14823,a,16119,a),flip(a)].">
      <j1 rule="hyper" parents="14823 16119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16122">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,7393,a(flip),b,16121,a),flip(a)].">
      <j1 rule="hyper" parents="347 7393 16121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16123">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(13350,a,16122,a)].">
      <j1 rule="hyper" parents="13350 16122"/>
    </justification>
  </clause>

  <clause id="16126">
    <literal><![CDATA[
      T(x,T(y,K(z,u) * w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(132,a,16122,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 16122 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16129">
    <literal><![CDATA[
      K(x,T(y,z * (u * w))) = K(x,T(y,z * (w * u)))
    ]]></literal>
    <justification jstring="[para(9586(a,1),16122(a,1,2,2))].">
      <j1 rule="para" parents="9586 16122"/>
    </justification>
  </clause>

  <clause id="16132">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = (z * K(u,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(16122(a,1),13285(a,1,1))].">
      <j1 rule="para" parents="16122 13285"/>
    </justification>
  </clause>

  <clause id="16133">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7793,a,16123,a)].">
      <j1 rule="hyper" parents="7793 16123"/>
    </justification>
  </clause>

  <clause id="16137">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(6047(a,1),16123(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6047 16123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16138">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,w)) * v5)) = K(x,T(y,z * v5))
    ]]></literal>
    <justification jstring="[para(6565(a,1),16123(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6565 16123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16140">
    <literal><![CDATA[
      K(x,T(y,K(z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16123(a,1),13673(a,1))].">
      <j1 rule="para" parents="16123 13673"/>
    </justification>
  </clause>

  <clause id="16141">
    <literal><![CDATA[
      T(x,T(y,T(z,u) * w)) = T(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(4946(a,1),16126(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4946 16126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16142">
    <literal><![CDATA[
      T(x,T(y,(T(z,u) * w) * v5)) = T(x,T(y,(z * w) * v5))
    ]]></literal>
    <justification jstring="[para(5846(a,1),16126(a,1,2,2))].">
      <j1 rule="para" parents="5846 16126"/>
    </justification>
  </clause>

  <clause id="16143">
    <literal><![CDATA[
      T(x,T(y,(z * u) * w)) = T(x,T(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(10281(a,1),16126(a,1,2,2))].">
      <j1 rule="para" parents="10281 16126"/>
    </justification>
  </clause>

  <clause id="16144">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7091,a(flip),b,16133,a),flip(a)].">
      <j1 rule="hyper" parents="347 7091 16133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16146">
    <literal><![CDATA[
      T((x * K(y,z)) / (u * K(y,z)),u / K(z,T(y,x))) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(16133(a,1),15366(a,1,2,2))].">
      <j1 rule="para" parents="16133 15366"/>
    </justification>
  </clause>

  <clause id="16148">
    <literal><![CDATA[
      T(K(x,y),K(z,u) \ w) = T(K(x,y),w)
    ]]></literal>
    <justification jstring="[hyper(13634,a,16144,a)].">
      <j1 rule="hyper" parents="13634 16144"/>
    </justification>
  </clause>

  <clause id="16154">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(16144(a,2),7480(a,1))].">
      <j1 rule="para" parents="16144 7480"/>
    </justification>
  </clause>

  <clause id="16157">
    <literal><![CDATA[
      T(K(x,y),K(z,u) \ w) = K(x,y) * K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,7266,a,b,16148,a),flip(a)].">
      <j1 rule="hyper" parents="347 7266 16148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16158">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(7398(a,1),16140(a,1,2,2))].">
      <j1 rule="para" parents="7398 16140"/>
    </justification>
  </clause>

  <clause id="16160">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z \ u)) = v5
    ]]></literal>
    <justification jstring="[para(1438(a,1),16158(a,1,2,2))].">
      <j1 rule="para" parents="1438 16158"/>
    </justification>
  </clause>

  <clause id="16161">
    <literal><![CDATA[
      K(x,T(y,z * (u / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * (w \ u))) = v5
    ]]></literal>
    <justification jstring="[para(6075(a,1),16158(a,1,2,2))].">
      <j1 rule="para" parents="6075 16158"/>
    </justification>
  </clause>

  <clause id="16162">
    <literal><![CDATA[
      K(x,T(y,z * (u * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * (w * u))) = v5
    ]]></literal>
    <justification jstring="[para(6977(a,1),16158(a,1,2,2))].">
      <j1 rule="para" parents="6977 16158"/>
    </justification>
  </clause>

  <clause id="16163">
    <literal><![CDATA[
      T(x * K(y,T(x,z * (u * w))),y) = T(x,K(y,z * (w * u)))
    ]]></literal>
    <justification jstring="[para(16129(a,1),7564(a,1,1,2))].">
      <j1 rule="para" parents="16129 7564"/>
    </justification>
  </clause>

  <clause id="16164">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(7804,a,16137,a)].">
      <j1 rule="hyper" parents="7804 16137"/>
    </justification>
  </clause>

  <clause id="16165">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,15406,a,b,16137,a)].">
      <j1 rule="hyper" parents="347 15406 16137"/>
    </justification>
  </clause>

  <clause id="16166">
    <literal><![CDATA[
      K(x,K(y,K(z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(7520,a,16157,a)].">
      <j1 rule="hyper" parents="7520 16157"/>
    </justification>
  </clause>

  <clause id="16167">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(13472,a,16166,a)].">
      <j1 rule="hyper" parents="13472 16166"/>
    </justification>
  </clause>

  <clause id="16168">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13473,a(flip),b,16166,a)].">
      <j1 rule="hyper" parents="63 13473 16166"/>
    </justification>
  </clause>

  <clause id="16170">
    <literal><![CDATA[
      K(x,K(y,((z * u) / z) * w)) = K(x,K(y,u * w))
    ]]></literal>
    <justification jstring="[para(5000(a,1),16166(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5000 16166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16171">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(y,1 / w))
    ]]></literal>
    <justification jstring="[para(6273(a,1),16166(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6273 16166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16172">
    <literal><![CDATA[
      K(x,K(y,z * T(u,w))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(7701(a,1),16166(a,1,2,2))].">
      <j1 rule="para" parents="7701 16166"/>
    </justification>
  </clause>

  <clause id="16173">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) = K(x,K(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(10282(a,1),16166(a,1,2,2))].">
      <j1 rule="para" parents="10282 16166"/>
    </justification>
  </clause>

  <clause id="16174">
    <literal><![CDATA[
      K(x,K(y,z / T(u,w))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(13660(a,1),16166(a,1,2))].">
      <j1 rule="para" parents="13660 16166"/>
    </justification>
  </clause>

  <clause id="16175">
    <literal><![CDATA[
      K(x,K(y,z / ((u * w) / u))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(13661(a,1),16166(a,1,2))].">
      <j1 rule="para" parents="13661 16166"/>
    </justification>
  </clause>

  <clause id="16176">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * T(K(x,y) \ z,K(w,v5))) = K(w,K(v5,z)) \ T(u,K(x,y) \ z)
    ]]></literal>
    <justification jstring="[para(16166(a,1),13723(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16166 13723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16180">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = T(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(132,a,16167,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 16167 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16183">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,(K(u,w) * z) * x) = K(y,x * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[para(16167(a,1),10423(a,1,1))].">
      <j1 rule="para" parents="16167 10423"/>
    </justification>
  </clause>

  <clause id="16184">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[para(13748(a,1),16167(a,1,2,2))].">
      <j1 rule="para" parents="13748 16167"/>
    </justification>
  </clause>

  <clause id="16185">
    <literal><![CDATA[
      K(x,K(y,(K(z,u) * w) / v5)) = K(x,K(y,w / v5))
    ]]></literal>
    <justification jstring="[para(14550(a,1),16167(a,1,2,2))].">
      <j1 rule="para" parents="14550 16167"/>
    </justification>
  </clause>

  <clause id="16186">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,7293,a,b,16168,a),flip(a)].">
      <j1 rule="hyper" parents="347 7293 16168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16187">
    <literal><![CDATA[
      T(x,K(y,z * K(u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,16168,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 16168 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16188">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(6047(a,1),16168(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6047 16168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16189">
    <literal><![CDATA[
      K(x,K(y,z / (u / (u / w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(6215(a,2),16168(a,1,2,2))].">
      <j1 rule="para" parents="6215 16168"/>
    </justification>
  </clause>

  <clause id="16190">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) * v5)) = K(x,K(y,z * v5))
    ]]></literal>
    <justification jstring="[para(6565(a,1),16168(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6565 16168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16191">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(u,w)) = T(z * K(u,w),K(x,y))
    ]]></literal>
    <justification jstring="[para(16168(a,1),7304(a,1,1))].">
      <j1 rule="para" parents="16168 7304"/>
    </justification>
  </clause>

  <clause id="16192">
    <literal><![CDATA[
      K(x,K(y,z / (u * w))) = K(x,K(y,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(9865(a,1),16168(a,1,2,2))].">
      <j1 rule="para" parents="9865 16168"/>
    </justification>
  </clause>

  <clause id="16193">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = T(x,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,7330,a,b,16180,a),flip(a)].">
      <j1 rule="hyper" parents="347 7330 16180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16194">
    <literal><![CDATA[
      T(x,K(y,T(z,u) * w)) = T(x,K(y,z * w))
    ]]></literal>
    <justification jstring="[para(4946(a,1),16180(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4946 16180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16195">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(16180(a,2),7362(a,1))].">
      <j1 rule="para" parents="16180 7362"/>
    </justification>
  </clause>

  <clause id="16196">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w)) = K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(13490,a,16186,a)].">
      <j1 rule="hyper" parents="13490 16186"/>
    </justification>
  </clause>

  <clause id="16197">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(7328,a,16186,a)].">
      <j1 rule="hyper" parents="7328 16186"/>
    </justification>
  </clause>

  <clause id="16198">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(16186(a,2),7328(a,1))].">
      <j1 rule="para" parents="16186 7328"/>
    </justification>
  </clause>

  <clause id="16199">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u * K(w,v5))) = T(y,K(u * K(w,v5),z) * x)
    ]]></literal>
    <justification jstring="[para(16187(a,1),15497(a,1,2,1,2))].">
      <j1 rule="para" parents="16187 15497"/>
    </justification>
  </clause>

  <clause id="16200">
    <literal><![CDATA[
      T(T(K(x,y) * z,K(x,y)) \ u,K(K(x,y) * z,w)) = (z * K(x,y)) \ T(u,K(z,w))
    ]]></literal>
    <justification jstring="[para(16193(a,1),15314(a,2,2))].">
      <j1 rule="para" parents="16193 15314"/>
    </justification>
  </clause>

  <clause id="16201">
    <literal><![CDATA[
      T(T(K(x,y) * z,K(x,y)) / u,K(K(x,y) * z,w)) = (z * K(x,y)) / T(u,K(z,w))
    ]]></literal>
    <justification jstring="[para(16193(a,1),15315(a,2,2))].">
      <j1 rule="para" parents="16193 15315"/>
    </justification>
  </clause>

  <clause id="16202">
    <literal><![CDATA[
      K(x,K(y,L(K(z,u) * w,v5,v6))) = K(x,K(w,L(y,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(8926,a,16196,a)].">
      <j1 rule="hyper" parents="8926 16196"/>
    </justification>
  </clause>

  <clause id="16203">
    <literal><![CDATA[
      K(x,K(T(y,z) / u,w)) = K(x,K(y / u,w))
    ]]></literal>
    <justification jstring="[para(5569(a,1),16196(a,1,2,1))].">
      <j1 rule="para" parents="5569 16196"/>
    </justification>
  </clause>

  <clause id="16204">
    <literal><![CDATA[
      T(x,K(y * K(z,u),w)) = T(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(132,a,16197,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 16197 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16205">
    <literal><![CDATA[
      T(T(x,K(y,z)),(y * K(u,w)) * z) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (y * K(u,w))) = v5
    ]]></literal>
    <justification jstring="[para(16204(a,1),10397(a,1,1))].">
      <j1 rule="para" parents="16204 10397"/>
    </justification>
  </clause>

  <clause id="16206">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,8814,a(flip),b,16171,a),flip(a)].">
      <j1 rule="hyper" parents="347 8814 16171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16208">
    <literal><![CDATA[
      K(x,K(y,L(K(z,u) / w,v5,v6))) = K(x,K(w,L(y,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(8957,a,16206,a)].">
      <j1 rule="hyper" parents="8957 16206"/>
    </justification>
  </clause>

  <clause id="16209">
    <literal><![CDATA[
      K(x,K(K(y,z) / u,w)) = K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(7328,a,16206,a)].">
      <j1 rule="hyper" parents="7328 16206"/>
    </justification>
  </clause>

  <clause id="16210">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) = K(x,K(z * y,y / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,13542,a,b,16206,a)].">
      <j1 rule="hyper" parents="63 13542 16206"/>
    </justification>
  </clause>

  <clause id="16211">
    <literal><![CDATA[
      K(x,K(K(y,z) / u,w)) = K(x,K(u * K(v5,v6),w))
    ]]></literal>
    <justification jstring="[hyper(347,a,16197,a,b,16209,a),flip(a)].">
      <j1 rule="hyper" parents="347 16197 16209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16212">
    <literal><![CDATA[
      K(x,K(y,z * T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u * z)) = v5
    ]]></literal>
    <justification jstring="[para(16172(a,2),13498(a,1))].">
      <j1 rule="para" parents="16172 13498"/>
    </justification>
  </clause>

  <clause id="16213">
    <literal><![CDATA[
      T(x,K(y \ ((z * u) / z),w)) = K(x,K(w,y * u)) * x
    ]]></literal>
    <justification jstring="[para(16172(a,1),15802(a,2,1))].">
      <j1 rule="para" parents="16172 15802"/>
    </justification>
  </clause>

  <clause id="16214">
    <literal><![CDATA[
      K(x,K(y / z,L(u,z,w))) = K(x,K(u,(y * w) / (w * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13873,a(flip),b,16203,a),flip(a)].">
      <j1 rule="hyper" parents="63 13873 16203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16215">
    <literal><![CDATA[
      K(x,K(y,z * (u * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z * (w * u))) = v5
    ]]></literal>
    <justification jstring="[para(6977(a,1),16198(a,1,2,2))].">
      <j1 rule="para" parents="6977 16198"/>
    </justification>
  </clause>

  <clause id="16218">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,w / (u * z)))
    ]]></literal>
    <justification jstring="[hyper(8849,a,16184,a),flip(a)].">
      <j1 rule="hyper" parents="8849 16184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16219">
    <literal><![CDATA[
      K(x,K(y,((z * u) * w) / (w * u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,13872,a(flip),b,16184,a),flip(a)].">
      <j1 rule="hyper" parents="347 13872 16184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16220">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * (w * z)) / T(w * u,a(w,z,z \ u)))) = K(x,K(y,a(w,z,z \ u)))
    ]]></literal>
    <justification jstring="[para(1076(a,1),16184(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1076 16184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16221">
    <literal><![CDATA[
      K(x,K(y,z / (K(u,w) * v5))) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(8849,a,16185,a)].">
      <j1 rule="hyper" parents="8849 16185"/>
    </justification>
  </clause>

  <clause id="16223">
    <literal><![CDATA[
      K(x,K(y,(z * T(u,w)) / v5)) = K(x,K(y,(z * u) / v5))
    ]]></literal>
    <justification jstring="[para(5573(a,1),16185(a,1,2,2,1))].">
      <j1 rule="para" parents="5573 16185"/>
    </justification>
  </clause>

  <clause id="16224">
    <literal><![CDATA[
      L(K(x,K(y,z / (u / w))),v5,v6) = K(y,K(z / (w \ u),L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[para(16188(a,2),8920(a,1,1))].">
      <j1 rule="para" parents="16188 8920"/>
    </justification>
  </clause>

  <clause id="16225">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) * v5)) = K(x,K(y,v5 * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,13476,a,b,16190,a),flip(a)].">
      <j1 rule="hyper" parents="347 13476 16190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16226">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / w) * v5)) = K(x,K(y,(z / w) * v5))
    ]]></literal>
    <justification jstring="[para(1439(a,1),16190(a,1,2,2,1))].">
      <j1 rule="para" parents="1439 16190"/>
    </justification>
  </clause>

  <clause id="16227">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * v5)) = K(x,K(y,((u \ z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(7768(a,1),16190(a,1,2,2,1))].">
      <j1 rule="para" parents="7768 16190"/>
    </justification>
  </clause>

  <clause id="16228">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,v5 * z)) = v6
    ]]></literal>
    <justification jstring="[para(16190(a,2),13498(a,1))].">
      <j1 rule="para" parents="16190 13498"/>
    </justification>
  </clause>

  <clause id="16229">
    <literal><![CDATA[
      K(x,K(y * K(z,u),L(w,K(v5,v6),v7))) = K(x,K(w,L(K(v5,v6) / y,y,v7)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8932,a(flip),b,16211,a),flip(a)].">
      <j1 rule="hyper" parents="63 8932 16211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16230">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,(u * z) / w)) = v5
    ]]></literal>
    <justification jstring="[para(16218(a,2),8849(a,1))].">
      <j1 rule="para" parents="16218 8849"/>
    </justification>
  </clause>

  <clause id="16231">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) = K(x,K(y,(v5 * v6) / z))
    ]]></literal>
    <justification jstring="[para(6511(a,1),16221(a,1,2,2,2))].">
      <j1 rule="para" parents="6511 16221"/>
    </justification>
  </clause>

  <clause id="16232">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) / v5)) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[para(7427(a,1),16221(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7427 16221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16233">
    <literal><![CDATA[
      K(x,K(y,(z / T(u,w)) * v5)) = K(x,K(y,v5 * (z / u)))
    ]]></literal>
    <justification jstring="[para(6102(a,1),16225(a,1,2,2,1))].">
      <j1 rule="para" parents="6102 16225"/>
    </justification>
  </clause>

  <clause id="16235">
    <literal><![CDATA[
      K(x,K(y,z / u)) * (w * K(x,y)) = w * K(x,T(y,(u * K(v5,v6)) / z))
    ]]></literal>
    <justification jstring="[para(16232(a,1),13720(a,1,1))].">
      <j1 rule="para" parents="16232 13720"/>
    </justification>
  </clause>

  <clause id="16236">
    <literal><![CDATA[
      K(x,y) * ((1 / y) * K(z,u)) = ((1 / y) * K(z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(3892(a,1),16132(a,1,1))].">
      <j1 rule="para" parents="3892 16132"/>
    </justification>
  </clause>

  <clause id="16237">
    <literal><![CDATA[
      T(x,T(y,(z * T(u,w)) * v5)) = T(x,T(y,(u * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,16143,a,b,16142,a)].">
      <j1 rule="hyper" parents="63 16143 16142"/>
    </justification>
  </clause>

  <clause id="16238">
    <literal><![CDATA[
      T(x * K(y,z),K(u,w)) = T(x,K(u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(7306,a,16191,a),flip(a)].">
      <j1 rule="hyper" parents="7306 16191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16239">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,w)) = K(x,y) * T(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(35,a,5895,a(flip),b,16238,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 5895 16238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16246">
    <literal><![CDATA[
      K(x,K(y,L(K(z,u) / w,v5,v6))) = K(x,K(y,L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(347,a,8925,a,b,16208,a),flip(a)].">
      <j1 rule="hyper" parents="347 8925 16208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16247">
    <literal><![CDATA[
      T(x,K(y \ ((z * u) / z),w)) = T(x,K(w,y * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,4977,a,b,16213,a),flip(a)].">
      <j1 rule="hyper" parents="347 4977 16213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16249">
    <literal><![CDATA[
      T(x,K(y \ T(z,u),w)) = T(x,K(w,y * z))
    ]]></literal>
    <justification jstring="[para(15581(a,1),16247(a,1,2))].">
      <j1 rule="para" parents="15581 16247"/>
    </justification>
  </clause>

  <clause id="16250">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),z \ T(u,w)) = T(x,T(z \ T(u,w),y))
    ]]></literal>
    <justification jstring="[para(16249(a,1),6814(a,1,1))].">
      <j1 rule="para" parents="16249 6814"/>
    </justification>
  </clause>

  <clause id="16251">
    <literal><![CDATA[
      K(x,K(y,z / (T(u,w) * v5))) = K(x,K(y,(v5 * u) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16218,a(flip),b,16223,a)].">
      <j1 rule="hyper" parents="63 16218 16223"/>
    </justification>
  </clause>

  <clause id="16252">
    <literal><![CDATA[
      K(x,K(y,((z / (z / u)) / w) * v5)) = K(x,K(y,(u / w) * v5))
    ]]></literal>
    <justification jstring="[para(275(a,1),16226(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="275 16226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16253">
    <literal><![CDATA[
      T(x,T(T(y * T(z,u),w),(z * y) * v5)) = T(x,T(T(y * T(z,u),w),v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,7765,a(flip),b,16237,a),flip(a)].">
      <j1 rule="hyper" parents="63 7765 16237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16254">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) / v5)) = K(x,K(y,v5 / ((w \ u) * z)))
    ]]></literal>
    <justification jstring="[para(113(a,1),16251(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="113 16251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16255">
    <literal><![CDATA[
      K(L(x,y,z),T(u,w * (v5 \ v6))) = K(x,L(T(u,w * (v6 / v5)),y,z))
    ]]></literal>
    <justification jstring="[hyper(16161,a,11108,a)].">
      <j1 rule="hyper" parents="16161 11108"/>
    </justification>
  </clause>

  <clause id="16257">
    <literal><![CDATA[
      K(x,K(y / (z \ u),L(w,u,z))) = K(x,K(w,(y * z) / (z * (z \ u))))
    ]]></literal>
    <justification jstring="[hyper(63,a,15155,a(flip),b,16214,a)].">
      <j1 rule="hyper" parents="63 15155 16214"/>
    </justification>
  </clause>

  <clause id="16258">
    <literal><![CDATA[
      K(x,K(T(R(y,K(z,u),w),K(z,u)),L(v5,K(z,u) * w,v6))) = K(x,K(v5,(((K(z,u) * y) * w) * v6) / (v6 * (K(z,u) * w))))
    ]]></literal>
    <justification jstring="[para(7357(a,1),16214(a,1,2,1))].">
      <j1 rule="para" parents="7357 16214"/>
    </justification>
  </clause>

  <clause id="16259">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,u * (y * z)))
    ]]></literal>
    <justification jstring="[para(13282(a,1),16163(a,1,1,2))].">
      <j1 rule="para" parents="13282 16163"/>
    </justification>
  </clause>

  <clause id="16260">
    <literal><![CDATA[
      T(x,K(y,z * (y * u))) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(7764,a,16259,a),flip(a)].">
      <j1 rule="hyper" parents="7764 16259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16261">
    <literal><![CDATA[
      K(x,K(y,((z \ (z * ((1 / z) * u))) * w) * v5)) = K(x,K(y,(L(u / z,z,1 / z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(963(a,1),16227(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="963 16227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16262">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) = K(x,K(y,z / (v5 * v6)))
    ]]></literal>
    <justification jstring="[hyper(347,a,8823,a,b,16231,a),flip(a)].">
      <j1 rule="hyper" parents="347 8823 16231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16263">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(u,x) / (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(13705,a,16236,a),flip(a)].">
      <j1 rule="hyper" parents="13705 16236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16264">
    <literal><![CDATA[
      K(x,y) / (K(z,u) * y) = (K(x,y) / y) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13842,a(flip),b,16263,a),flip(a)].">
      <j1 rule="hyper" parents="63 13842 16263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16265">
    <literal><![CDATA[
      K(x,L(K(y,z),K(u,w) / w,v5)) * K(K(y,z),x) = a(v5,K(u,w) / (K(z,y) * w),K(K(y,z),x))
    ]]></literal>
    <justification jstring="[para(16264(a,2),9256(a,2,2))].">
      <j1 rule="para" parents="16264 9256"/>
    </justification>
  </clause>

  <clause id="16266">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),u \ T(z,w)) = T(x,T(u \ T(z,w),y))
    ]]></literal>
    <justification jstring="[para(13483(a,1),16250(a,1,1))].">
      <j1 rule="para" parents="13483 16250"/>
    </justification>
  </clause>

  <clause id="16267">
    <literal><![CDATA[
      K(x,K(y,z * ((u / (u / w)) / v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(13498,a,16252,a)].">
      <j1 rule="hyper" parents="13498 16252"/>
    </justification>
  </clause>

  <clause id="16268">
    <literal><![CDATA[
      K(x,K(y,z / (u * (K(w,v5) * v6)))) = K(x,K(y,z / (v6 * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16192,a,b,16262,a)].">
      <j1 rule="hyper" parents="63 16192 16262"/>
    </justification>
  </clause>

  <clause id="16269">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),T(u \ T(z,w),y)) = T(x,u \ T(z,w))
    ]]></literal>
    <justification jstring="[para(7334(a,1),16266(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7334 16266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16270">
    <literal><![CDATA[
      K(x,K(y,((z \ u) / w) * v5)) = K(x,K(y,v5 * ((u / z) / w)))
    ]]></literal>
    <justification jstring="[para(80(a,1),16267(a,1,2,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="80 16267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16271">
    <literal><![CDATA[
      K(x,K(y,z / (u * (K(w,v5) * v6)))) = K(x,K(y,z / (u * v6)))
    ]]></literal>
    <justification jstring="[hyper(347,a,16192,a,b,16268,a),flip(a)].">
      <j1 rule="hyper" parents="347 16192 16268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16272">
    <literal><![CDATA[
      K(x,K((1 / y) / z,L(z / u,u,y))) = K(x,K(y * z,z / u))
    ]]></literal>
    <justification jstring="[hyper(13540,a,16210,a)].">
      <j1 rule="hyper" parents="13540 16210"/>
    </justification>
  </clause>

  <clause id="16274">
    <literal><![CDATA[
      K(x,K((y \ z) * u,u / y)) = K(x,K(z,(1 / (y \ z)) / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14109,a(flip),b,16272,a),flip(a)].">
      <j1 rule="hyper" parents="63 14109 16272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16275">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,(1 / (z \ u)) / y))
    ]]></literal>
    <justification jstring="[hyper(7328,a,16274,a)].">
      <j1 rule="hyper" parents="7328 16274"/>
    </justification>
  </clause>

  <clause id="16276">
    <literal><![CDATA[
      K(x,K(y,(1 / (z \ y)) / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13500,a(flip),b,16275,a),flip(a)].">
      <j1 rule="hyper" parents="63 13500 16275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16277">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u / (y / z)))
    ]]></literal>
    <justification jstring="[para(83(a,1),16276(a,1,2,2,1,2))].">
      <j1 rule="para" parents="83 16276"/>
    </justification>
  </clause>

  <clause id="16278">
    <literal><![CDATA[
      K(x,K(y,z / (y / u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12744,a(flip),b,16277,a),flip(a)].">
      <j1 rule="hyper" parents="63 12744 16277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16279">
    <literal><![CDATA[
      K(x,K(y,z * (y / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16189,a(flip),b,16278,a),flip(a)].">
      <j1 rule="hyper" parents="63 16189 16278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16280">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(y,K(x,z / u))
    ]]></literal>
    <justification jstring="[hyper(7281,a,16279,a)].">
      <j1 rule="hyper" parents="7281 16279"/>
    </justification>
  </clause>

  <clause id="16281">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(347,a,7279,a,b,16280,a),flip(a)].">
      <j1 rule="hyper" parents="347 7279 16280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16282">
    <literal><![CDATA[
      K(x,L(T(y,z * (u / w)),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z * (w \ u)),v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(16255(a,1),11169(a,1))].">
      <j1 rule="para" parents="16255 11169"/>
    </justification>
  </clause>

  <clause id="16283">
    <literal><![CDATA[
      T(x,(y * (y * T(z,y * y))) * u) = T(x,(y * (y * z)) * u)
    ]]></literal>
    <justification jstring="[hyper(13494,a,16116,a),flip(a)].">
      <j1 rule="hyper" parents="13494 16116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16284">
    <literal><![CDATA[
      T(x,(L(y,z,z) * (z * z)) * u) = T(x,(z * (z * y)) * u)
    ]]></literal>
    <justification jstring="[para(734(a,1),16283(a,1,2,1))].">
      <j1 rule="para" parents="734 16283"/>
    </justification>
  </clause>

  <clause id="16285">
    <literal><![CDATA[
      T(x,L(y,z,z) * ((z * z) * u)) = T(x,(z * (z * y)) * u)
    ]]></literal>
    <justification jstring="[para(32(a,1),16284(a,1,2))].">
      <j1 rule="para" parents="32 16284"/>
    </justification>
  </clause>

  <clause id="16286">
    <literal><![CDATA[
      T(x,y * (K(z,u) * (K(z,u) * (w * v5)))) = T(x,y * (w * (v5 * (K(z,u) * K(z,u)))))
    ]]></literal>
    <justification jstring="[para(33(a,1),16117(a,2,2,2))].">
      <j1 rule="para" parents="33 16117"/>
    </justification>
  </clause>

  <clause id="16287">
    <literal><![CDATA[
      K(x,K(y * K(z,u),L(w,K(v5,v6),v7))) = K(x,K(w,L(y,y,v7)))
    ]]></literal>
    <justification jstring="[hyper(347,a,16246,a(flip),b,16229,a),flip(a)].">
      <j1 rule="hyper" parents="347 16246 16229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16289">
    <literal><![CDATA[
      K(x,K(y * K(z,u),L(w,K(v5,v6),v7))) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,7625,a(flip),b,16287,a),flip(a)].">
      <j1 rule="hyper" parents="347 7625 16287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16291">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w),v5))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16197,a(flip),b,16289,a)].">
      <j1 rule="hyper" parents="63 16197 16289"/>
    </justification>
  </clause>

  <clause id="16292">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,w)) / v5)) = K(x,T(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(13731,a,16235,a),flip(a)].">
      <j1 rule="hyper" parents="13731 16235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16293">
    <literal><![CDATA[
      K(x,T(y,(z / T(u,w)) / v5)) = K(x,T(y,v5 / (z / u)))
    ]]></literal>
    <justification jstring="[para(6102(a,1),16292(a,1,2,2,1))].">
      <j1 rule="para" parents="6102 16292"/>
    </justification>
  </clause>

  <clause id="16294">
    <literal><![CDATA[
      K(x,T(y,z / (u / T(w,v5)))) = K(x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(8879,a,16293,a)].">
      <j1 rule="hyper" parents="8879 16293"/>
    </justification>
  </clause>

  <clause id="16295">
    <literal><![CDATA[
      K(x,T(L(y,z,T(x,u)),w / (v5 / T(v6,v7)))) = K(x,T(y,w / (v5 / v6)))
    ]]></literal>
    <justification jstring="[hyper(347,a,8586,a(flip),b,16294,a),flip(a)].">
      <j1 rule="hyper" parents="347 8586 16294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16296">
    <literal><![CDATA[
      K(x,T(y,z / (u / (w / v5)))) = K(x,T(y,z / (u / (v5 \ w))))
    ]]></literal>
    <justification jstring="[para(113(a,1),16294(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="113 16294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16297">
    <literal><![CDATA[
      T(1 / x,T(y,z / (u / T(w,v5)))) = K(1 / x,T(y,z / (u / w))) / x
    ]]></literal>
    <justification jstring="[para(16294(a,1),5092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16294 5092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16298">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u / w)))) = K(1 / x,T(y,z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,16165,a(flip),b,16296,a),flip(a)].">
      <j1 rule="hyper" parents="347 16165 16296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16299">
    <literal><![CDATA[
      K(1 / x,T(y,z / (u / w))) = K(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(13419,a,16298,a),flip(a)].">
      <j1 rule="hyper" parents="13419 16298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16300">
    <literal><![CDATA[
      T(x,T(T(y * T(y \ z,u),w),T(z,y) * v5)) = T(x,T(T(y * T(y \ z,u),w),v5))
    ]]></literal>
    <justification jstring="[para(12091(a,1),16253(a,1,2))].">
      <j1 rule="para" parents="12091 16253"/>
    </justification>
  </clause>

  <clause id="16301">
    <literal><![CDATA[
      T(1 / x,T(y,z / (u / T(w,v5)))) = K(1 / x,T(y,(w / u) * z)) / x
    ]]></literal>
    <justification jstring="[para(16299(a,1),16297(a,2,1))].">
      <j1 rule="para" parents="16299 16297"/>
    </justification>
  </clause>

  <clause id="16302">
    <literal><![CDATA[
      T(1 / x,T(y,z / (u / T(w,v5)))) = T(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,5092,a(flip),b,16301,a),flip(a)].">
      <j1 rule="hyper" parents="347 5092 16301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16303">
    <literal><![CDATA[
      T(T(1 / (1 / L(x,y,z)),T(u,(w / v5) * v6)),1 / x) = T(L(x,y,z),T(u,v6 / (v5 / T(w,v7))))
    ]]></literal>
    <justification jstring="[para(16302(a,1),4673(a,1,1))].">
      <j1 rule="para" parents="16302 4673"/>
    </justification>
  </clause>

  <clause id="16304">
    <literal><![CDATA[
      K(x,L(T(y \ z,y * (z \ u)),y,z \ u)) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(16282,a,14588,a)].">
      <j1 rule="hyper" parents="16282 14588"/>
    </justification>
  </clause>

  <clause id="16305">
    <literal><![CDATA[
      K(x,L(T(y \ z,z * (y \ u)),y,y \ u)) = K(x,((u / y) * z) / u)
    ]]></literal>
    <justification jstring="[hyper(16282,a,14587,a)].">
      <j1 rule="hyper" parents="16282 14587"/>
    </justification>
  </clause>

  <clause id="16306">
    <literal><![CDATA[
      K(x,T((y * (y \ z)) \ (u * (y \ z)),y)) = K(x,((z / y) * u) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14106,a(flip),b,16305,a)].">
      <j1 rule="hyper" parents="63 14106 16305"/>
    </justification>
  </clause>

  <clause id="16307">
    <literal><![CDATA[
      K(x,T(y \ (z * (u \ y)),u)) = K(x,((y / u) * z) / y)
    ]]></literal>
    <justification jstring="[para(10(a,1),16306(a,1,2,1,1))].">
      <j1 rule="para" parents="10 16306"/>
    </justification>
  </clause>

  <clause id="16309">
    <literal><![CDATA[
      T(x,T(y / (y / z),u) * K(z \ y,w)) = T(x,(y * K(z,u)) / T(y / z,w))
    ]]></literal>
    <justification jstring="[hyper(15727,a,15541,a)].">
      <j1 rule="hyper" parents="15727 15541"/>
    </justification>
  </clause>

  <clause id="16310">
    <literal><![CDATA[
      K(x,y \ (z / T(z / u,w))) = K(x,y \ (T(u \ z,w) \ z))
    ]]></literal>
    <justification jstring="[para(10578(a,1),15623(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10578 15623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16311">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ T(z,v5 * K(w,u))) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,7977,a(flip),b,15647,a)].">
      <j1 rule="hyper" parents="63 7977 15647"/>
    </justification>
  </clause>

  <clause id="16312">
    <literal><![CDATA[
      K(x,((K(y,z) * u) / (y \ z)) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15863,a(flip),b,15661,a),flip(a)].">
      <j1 rule="hyper" parents="63 15863 15661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16313">
    <literal><![CDATA[
      K(x,(K(y,z) * (u / (y \ z))) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[para(11446(a,1),16312(a,1,2,1))].">
      <j1 rule="para" parents="11446 16312"/>
    </justification>
  </clause>

  <clause id="16314">
    <literal><![CDATA[
      K(((T(T(x,y),y) \ z) * K(x,y)) * u,w) = K(T(T(x,y) \ z,K(y,x)) * u,w)
    ]]></literal>
    <justification jstring="[para(6117(a,1),15746(a,1,1,1))].">
      <j1 rule="para" parents="6117 15746"/>
    </justification>
  </clause>

  <clause id="16315">
    <literal><![CDATA[
      K(x \ (y * ((z * (y \ u)) / z)),w) = K(x \ (y * T(y \ u,z)),w)
    ]]></literal>
    <justification jstring="[para(1857(a,1),15781(a,1,1))].">
      <j1 rule="para" parents="1857 15781"/>
    </justification>
  </clause>

  <clause id="16316">
    <literal><![CDATA[
      K(x \ (y * T(y \ 1,z)),u) = K(x \ K(z,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(4965(a,1),16315(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4965 16315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16317">
    <literal><![CDATA[
      K(x \ K(y \ 1,z),u) = K(x \ K(z,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(4925(a,1),16316(a,1,1,2))].">
      <j1 rule="para" parents="4925 16316"/>
    </justification>
  </clause>

  <clause id="16318">
    <literal><![CDATA[
      (x \ K(y \ K(z,u \ 1),w)) \ (x \ 1) = K(w,y \ K(u \ 1,z))
    ]]></literal>
    <justification jstring="[para(16317(a,1),13022(a,1,1,2))].">
      <j1 rule="para" parents="16317 13022"/>
    </justification>
  </clause>

  <clause id="16319">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(u,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(13023,a,16318,a),flip(a)].">
      <j1 rule="hyper" parents="13023 16318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16320">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y \ z) / y) = K(x,T(y \ ((z / y) \ u),z))
    ]]></literal>
    <justification jstring="[hyper(13673,a,16105,a),flip(a)].">
      <j1 rule="hyper" parents="13673 16105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16321">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y \ z) / y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = w
    ]]></literal>
    <justification jstring="[para(16320(a,2),15100(a,1))].">
      <j1 rule="para" parents="16320 15100"/>
    </justification>
  </clause>

  <clause id="16322">
    <literal><![CDATA[
      T(x,K(y * K(z,u),w) * v5) = v5 \ T(x * T(v5,K(w,y)),K(w,y))
    ]]></literal>
    <justification jstring="[para(16187(a,1),16199(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16187 16199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16323">
    <literal><![CDATA[
      T(x,K(y * K(z,u),w) * v5) = T(x,K(y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,15497,a(flip),b,16322,a),flip(a)].">
      <j1 rule="hyper" parents="347 15497 16322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16324">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = v5 \ T(x * T(v5,K(w,u)),K(w,u))
    ]]></literal>
    <justification jstring="[para(7076(a,1),16322(a,1,2,1,1))].">
      <j1 rule="para" parents="7076 16322"/>
    </justification>
  </clause>

  <clause id="16326">
    <literal><![CDATA[
      T(x,y * K(z \ K(u,w),v5)) = T(x,K(z,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(15872,a,16323,a)].">
      <j1 rule="hyper" parents="15872 16323"/>
    </justification>
  </clause>

  <clause id="16328">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = T(x,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[para(7076(a,1),16323(a,1,2,1,1))].">
      <j1 rule="para" parents="7076 16323"/>
    </justification>
  </clause>

  <clause id="16329">
    <literal><![CDATA[
      T(x,K(y,z) * ((K(u,w) / y) \ v5)) = T(x,T(K(u,w) / y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,15784,a(flip),b,16326,a),flip(a)].">
      <j1 rule="hyper" parents="63 15784 16326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16330">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = T(x,v5 * K(u \ K(v6,v7),w))
    ]]></literal>
    <justification jstring="[hyper(347,a,16326,a,b,16328,a),flip(a)].">
      <j1 rule="hyper" parents="347 16326 16328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16331">
    <literal><![CDATA[
      T(x,K(y \ K(z,u),w) * v5) = T(x,K(K(v6,v7) * y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,13555,a,b,16330,a)].">
      <j1 rule="hyper" parents="347 13555 16330"/>
    </justification>
  </clause>

  <clause id="16332">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * K(v5,v6)) = T(x,u * T(u \ K(v6,v5),w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15519,a(flip),b,16331,a),flip(a)].">
      <j1 rule="hyper" parents="63 15519 16331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16333">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(16324(a,2),15506(a,1))].">
      <j1 rule="para" parents="16324 15506"/>
    </justification>
  </clause>

  <clause id="16334">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,w) * ((K(y,z) * u) \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(15529(a,1),16333(a,1))].">
      <j1 rule="para" parents="15529 16333"/>
    </justification>
  </clause>

  <clause id="16336">
    <literal><![CDATA[
      T(x,y * T(y \ K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,w) * K(u,z)) = v5
    ]]></literal>
    <justification jstring="[para(16332(a,1),16333(a,1))].">
      <j1 rule="para" parents="16332 16333"/>
    </justification>
  </clause>

  <clause id="16337">
    <literal><![CDATA[
      T(x,K(y,z) * ((K(u,w) * y) \ v5)) = T(x,T(y \ K(w,u),z) * v5)
    ]]></literal>
    <justification jstring="[hyper(16334,a,15899,a)].">
      <j1 rule="hyper" parents="16334 15899"/>
    </justification>
  </clause>

  <clause id="16338">
    <literal><![CDATA[
      K(K(x * 1,y) * ((z / (x * z)) \ u),w) = K(T(z / (x * z),y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(15709,a,15877,a),flip(a)].">
      <j1 rule="hyper" parents="15709 15877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16339">
    <literal><![CDATA[
      K(K(x,y) * ((z / (x * z)) \ u),w) = K(T(z / (x * z),y) \ u,w)
    ]]></literal>
    <justification jstring="[para(8(a,1),16338(a,1,1,1,1))].">
      <j1 rule="para" parents="8 16338"/>
    </justification>
  </clause>

  <clause id="16340">
    <literal><![CDATA[
      L(K(x,y * K(z,T(u * K(w,v5),v6))),x,v7) = (x * K(v8,v9)) \ (T(x,K(u,z) * y) * K(v8,v9))
    ]]></literal>
    <justification jstring="[para(16323(a,1),15725(a,2,2,1))].">
      <j1 rule="para" parents="16323 15725"/>
    </justification>
  </clause>

  <clause id="16341">
    <literal><![CDATA[
      K(x,y \ (((1 / z) \ u) * w)) = K(x,y \ (((z \ 1) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(15731,a,15864,a),flip(a)].">
      <j1 rule="hyper" parents="15731 15864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16342">
    <literal><![CDATA[
      K(T(x,y) / (((z \ 1) / y) * y),u) = K(T(z,y) * x,T(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(15762,a,15892,a)].">
      <j1 rule="hyper" parents="15762 15892"/>
    </justification>
  </clause>

  <clause id="16343">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,y * x)) = K(T(z,y) / (x \ 1),u)
    ]]></literal>
    <justification jstring="[para(12(a,1),16342(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 16342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16344">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,y * x)) = K(T(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,13221,a(flip),b,16343,a),flip(a)].">
      <j1 rule="hyper" parents="347 13221 16343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16346">
    <literal><![CDATA[
      K(x * T(y,z),T(u,z * y)) = K(T(x,z) * y,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(13782,a,16344,a)].">
      <j1 rule="hyper" parents="13782 16344"/>
    </justification>
  </clause>

  <clause id="16347">
    <literal><![CDATA[
      K(x * T(y,z),T(u,z * y)) = K(y * T(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,10371,a(flip),b,16346,a),flip(a)].">
      <j1 rule="hyper" parents="347 10371 16346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16348">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * T(z * y,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13700,a(flip),b,16347,a)].">
      <j1 rule="hyper" parents="63 13700 16347"/>
    </justification>
  </clause>

  <clause id="16349">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,15820,a(flip),b,16348,a),flip(a)].">
      <j1 rule="hyper" parents="347 15820 16348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16350">
    <literal><![CDATA[
      K(x * (y * z),z * x) = K(x * (z * y),x * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13726,a(flip),b,16349,a)].">
      <j1 rule="hyper" parents="63 13726 16349"/>
    </justification>
  </clause>

  <clause id="16351">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),T(u,w)) \ K(x * (y * z),K(u,w)) = K(u,(x * y) * R(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(128,a,16349,a(flip),b,7508,a)].">
      <j1 rule="hyper" parents="128 16349 7508"/>
    </justification>
  </clause>

  <clause id="16352">
    <literal><![CDATA[
      K(x * (((y \ z) * (z \ y)) * (1 / (z \ y))),(1 / (z \ y)) * x) = K(x * (y \ z),x * (1 / (z \ y)))
    ]]></literal>
    <justification jstring="[para(1638(a,1),16350(a,2,1,2))].">
      <j1 rule="para" parents="1638 16350"/>
    </justification>
  </clause>

  <clause id="16353">
    <literal><![CDATA[
      T(x,T(((y \ z) \ z) / u,K(y \ z,y)) \ w) = T(x,((y / u) * K(y,y \ z)) \ w)
    ]]></literal>
    <justification jstring="[para(6117(a,1),15602(a,2,2,1))].">
      <j1 rule="para" parents="6117 15602"/>
    </justification>
  </clause>

  <clause id="16354">
    <literal><![CDATA[
      K(x,y * T(((z \ u) \ u) / w,K(z \ u,z))) = K(x,y * ((z / w) * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(6117(a,1),15692(a,2,2,2))].">
      <j1 rule="para" parents="6117 15692"/>
    </justification>
  </clause>

  <clause id="16355">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * (((1 / z) * u) * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(12993(a,1),15695(a,2,2,2,2))].">
      <j1 rule="para" parents="12993 15695"/>
    </justification>
  </clause>

  <clause id="16356">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * ((1 / z) * (z * (u / z))))
    ]]></literal>
    <justification jstring="[para(9564(a,1),16355(a,2,2,2))].">
      <j1 rule="para" parents="9564 16355"/>
    </justification>
  </clause>

  <clause id="16357">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * ((((1 / u) * z) \ z) \ z))
    ]]></literal>
    <justification jstring="[para(2939(a,1),16356(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2939 16356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16358">
    <literal><![CDATA[
      K(x,y * T((1 / z) * u,u)) = K(x,y * L(u / z,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(347,a,11976,a(flip),b,16357,a)].">
      <j1 rule="hyper" parents="347 11976 16357"/>
    </justification>
  </clause>

  <clause id="16359">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * (z * (1 / u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15681,a(flip),b,16358,a),flip(a)].">
      <j1 rule="hyper" parents="63 15681 16358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16360">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(347,a,5418,a(flip),b,16359,a),flip(a)].">
      <j1 rule="hyper" parents="347 5418 16359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16361">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) * (w / T(u,w)))) = T(x,y * (K(w,u) * ((w / u) * z)))
    ]]></literal>
    <justification jstring="[para(11932(a,1),15696(a,1,2,2,1))].">
      <j1 rule="para" parents="11932 15696"/>
    </justification>
  </clause>

  <clause id="16362">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) * (u \ w))) = T(x,y * (K(w,u) * ((w / u) * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12175,a(flip),b,16361,a)].">
      <j1 rule="hyper" parents="63 12175 16361"/>
    </justification>
  </clause>

  <clause id="16363">
    <literal><![CDATA[
      T(x,y * (K(z,u) * ((z / u) * w))) = T(x,y * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(15701,a,16362,a),flip(a)].">
      <j1 rule="hyper" parents="15701 16362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16364">
    <literal><![CDATA[
      T(x,y * ((z / T(u,z)) * w)) = T(x,y * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(11437(a,1),16363(a,1,2,2))].">
      <j1 rule="para" parents="11437 16363"/>
    </justification>
  </clause>

  <clause id="16365">
    <literal><![CDATA[
      T(x,y * ((T(z,u) / T(u,z)) * w)) = T(x,y * ((u \ T(z,u)) * w))
    ]]></literal>
    <justification jstring="[para(4270(a,1),16364(a,1,2,2,1,2))].">
      <j1 rule="para" parents="4270 16364"/>
    </justification>
  </clause>

  <clause id="16366">
    <literal><![CDATA[
      T(x,y * ((T(z,u) \ u) * ((u / z) * w))) = T(x,y * ((z \ u) * ((z \ u) * w)))
    ]]></literal>
    <justification jstring="[para(11523(a,1),16364(a,1,2,2))].">
      <j1 rule="para" parents="11523 16364"/>
    </justification>
  </clause>

  <clause id="16367">
    <literal><![CDATA[
      K(x,T((y \ (z * u)) \ 1,y) * T(u,z)) = K(x,T(u * ((y \ (z * u)) \ 1),z))
    ]]></literal>
    <justification jstring="[hyper(12117,a,16108,a)].">
      <j1 rule="hyper" parents="12117 16108"/>
    </justification>
  </clause>

  <clause id="16368">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,K(x,y) \ z) = (K(x,y) \ z) \ (u * (z * K(y,x)))
    ]]></literal>
    <justification jstring="[para(7335(a,1),16176(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7335 16176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16369">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * (z * K(y,x))) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16068,a(flip),b,16368,a),flip(a)].">
      <j1 rule="hyper" parents="63 16068 16368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16370">
    <literal><![CDATA[
      (x * K(y,z)) \ (u * (K(z,y) \ x)) = x \ T(u * x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15173,a(flip),b,16369,a)].">
      <j1 rule="hyper" parents="63 15173 16369"/>
    </justification>
  </clause>

  <clause id="16371">
    <literal><![CDATA[
      (x * K(y,z)) \ (u * (K(z,y) \ x)) = x \ T(u * x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7330(a,1),16370(a,2,2))].">
      <j1 rule="para" parents="7330 16370"/>
    </justification>
  </clause>

  <clause id="16372">
    <literal><![CDATA[
      T((x * K(y,z)) \ u,K(K(y,z) * x,w)) = (x * K(y,z)) \ T(u,K(x,w))
    ]]></literal>
    <justification jstring="[para(6872(a,1),16200(a,1,1,1))].">
      <j1 rule="para" parents="6872 16200"/>
    </justification>
  </clause>

  <clause id="16374">
    <literal><![CDATA[
      T((x * K(y,z)) \ u,K(w,K(y,z) * x)) = (x * K(y,z)) \ T(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(7362,a,16372,a)].">
      <j1 rule="hyper" parents="7362 16372"/>
    </justification>
  </clause>

  <clause id="16375">
    <literal><![CDATA[
      T((x * K(y,z)) \ u,K(x,w)) = (x * K(y,z)) \ T(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(16195,a,16374,a)].">
      <j1 rule="hyper" parents="16195 16374"/>
    </justification>
  </clause>

  <clause id="16377">
    <literal><![CDATA[
      K(x,T((y * K(z,u)) / T(w,K(y,v5)),T((y * K(z,u)) \ w,K(y,v5)))) = K(x,(y * K(z,u)) / T(w,K(y,v5)))
    ]]></literal>
    <justification jstring="[para(16375(a,2),3895(a,1,2,2))].">
      <j1 rule="para" parents="16375 3895"/>
    </justification>
  </clause>

  <clause id="16378">
    <literal><![CDATA[
      T((x * K(y,z)) / u,K(K(y,z) * x,w)) = (x * K(y,z)) / T(u,K(x,w))
    ]]></literal>
    <justification jstring="[para(6872(a,1),16201(a,1,1,1))].">
      <j1 rule="para" parents="6872 16201"/>
    </justification>
  </clause>

  <clause id="16380">
    <literal><![CDATA[
      T((x * K(y,z)) / u,K(w,K(y,z) * x)) = (x * K(y,z)) / T(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(7362,a,16378,a)].">
      <j1 rule="hyper" parents="7362 16378"/>
    </justification>
  </clause>

  <clause id="16381">
    <literal><![CDATA[
      (x * K(y,z)) / T(u,K(x,w)) = T((x * K(y,z)) / u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(16195,a,16380,a),flip(a)].">
      <j1 rule="hyper" parents="16195 16380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16383">
    <literal><![CDATA[
      T(x,y * ((z / u) * (w * (K(z,u) * K(z,u))))) = T(x,y * (K(z,u) * ((z / T(u,z)) * w)))
    ]]></literal>
    <justification jstring="[para(11437(a,1),16286(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11437 16286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16384">
    <literal><![CDATA[
      T(x,T(T(y * T(y \ z,u),w),z * v5)) = T(x,T(T(y * T(y \ z,u),w),v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,16141,a(flip),b,16300,a)].">
      <j1 rule="hyper" parents="63 16141 16300"/>
    </justification>
  </clause>

  <clause id="16385">
    <literal><![CDATA[
      T(x,T(T(y * T(y \ z,u),y),w)) = T(x,T(y * T(z / y,u),z * w))
    ]]></literal>
    <justification jstring="[hyper(10431,a,16384,a),flip(a)].">
      <j1 rule="hyper" parents="10431 16384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16387">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),z * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),w)) = v5
    ]]></literal>
    <justification jstring="[para(16385(a,1),10431(a,1))].">
      <j1 rule="para" parents="16385 10431"/>
    </justification>
  </clause>

  <clause id="16388">
    <literal><![CDATA[
      K(x,y * T(((z \ u) \ u) / w,K(z \ u,z))) = K(x,y * (K(z,u) * (z / w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,14861,a(flip),b,16354,a),flip(a)].">
      <j1 rule="hyper" parents="347 14861 16354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16389">
    <literal><![CDATA[
      K(x,y * T(((z \ u) \ u) / w,K(z \ u,z))) = K(x,y * (T(z,u) / w))
    ]]></literal>
    <justification jstring="[para(13192(a,1),16388(a,2,2,2))].">
      <j1 rule="para" parents="13192 16388"/>
    </justification>
  </clause>

  <clause id="16390">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) / w)) = K(x,y * (T(z,u) / w))
    ]]></literal>
    <justification jstring="[hyper(14822,a,16389,a)].">
      <j1 rule="hyper" parents="14822 16389"/>
    </justification>
  </clause>

  <clause id="16391">
    <literal><![CDATA[
      K(x,T(y,T(z,u) / w) * (T(z,u) / w)) = K(x,(((z \ u) \ u) / w) * y)
    ]]></literal>
    <justification jstring="[hyper(12138,a,16390,a),flip(a)].">
      <j1 rule="hyper" parents="12138 16390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16393">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) / u) * w) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(10409,a,16391,a),flip(a)].">
      <j1 rule="hyper" parents="10409 16391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16394">
    <literal><![CDATA[
      K(x,K(y,L(y \ z,u,w)) * (v5 * L(z / y,u,w))) = K(x,v5 * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(278(a,1),15591(a,2,2,2))].">
      <j1 rule="para" parents="278 15591"/>
    </justification>
  </clause>

  <clause id="16395">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w * v5)) * T(u,w * v5))) = K(x,y * (T(u,w \ v5) * z))
    ]]></literal>
    <justification jstring="[hyper(15754,a,16065,a),flip(a)].">
      <j1 rule="hyper" parents="15754 16065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16396">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) * v5)) = K(x,y * (T(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(15753,a,16395,a),flip(a)].">
      <j1 rule="hyper" parents="15753 16395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16397">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) * v5)) = T(x,y * (T(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(132,a,16396,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 16396 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16398">
    <literal><![CDATA[
      x * K(x,y * (T(z,u * w) * v5)) = T(x,y * (T(z,u \ w) * v5))
    ]]></literal>
    <justification jstring="[hyper(134,a,16396,a(flip),b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 16396 4924"/>
    </justification>
  </clause>

  <clause id="16399">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (T(z,u * w) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(16398(a,1),4984(a,1))].">
      <j1 rule="para" parents="16398 4984"/>
    </justification>
  </clause>

  <clause id="16400">
    <literal><![CDATA[
      T(x,((y * z) / T(y,u)) * K(w,T(y,u) * z)) = T(x,T(y * (z * K(u,y)),w) / y)
    ]]></literal>
    <justification jstring="[para(15596(a,1),15544(a,1,2,2))].">
      <j1 rule="para" parents="15596 15544"/>
    </justification>
  </clause>

  <clause id="16401">
    <literal><![CDATA[
      K(x,y \ T(z,u)) * a(w,v5,K(y \ T(z,u),x)) = K(x,L(y \ T(z,u \ 1),v5,w))
    ]]></literal>
    <justification jstring="[para(15926(a,1),15908(a,1,1))].">
      <j1 rule="para" parents="15926 15908"/>
    </justification>
  </clause>

  <clause id="16402">
    <literal><![CDATA[
      K(x,L(y \ T(z,u \ 1),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ T(z,u),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(16401(a,1),11093(a,1))].">
      <j1 rule="para" parents="16401 11093"/>
    </justification>
  </clause>

  <clause id="16403">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,z),y,z)) = K(x,(z \ y) \ (((z \ 1) \ u) * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(16402,a,15086,a)].">
      <j1 rule="hyper" parents="16402 15086"/>
    </justification>
  </clause>

  <clause id="16404">
    <literal><![CDATA[
      K(x,(y \ z) \ (((y \ 1) \ u) * (y \ 1))) = K(x,(y * z) \ ((y * u) * y))
    ]]></literal>
    <justification jstring="[para(480(a,1),16403(a,1,2)),flip(a)].">
      <j1 rule="para" parents="480 16403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16405">
    <literal><![CDATA[
      K(x,(y \ z) \ (((y \ 1) \ u) * (y \ 1))) = K(x,(y * z) \ (y * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(347,a,12005,a(flip),b,16404,a),flip(a)].">
      <j1 rule="hyper" parents="347 12005 16404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16406">
    <literal><![CDATA[
      T(x,y * K(z,u)) \ T(y * T(T(x,K(z,u)),y * K(z,u)),K(u,z)) = T(y,x * K(z,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),16011(a,1,2,1,2))].">
      <j1 rule="para" parents="23 16011"/>
    </justification>
  </clause>

  <clause id="16407">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * (w * z)) / T(w * u,a(w,z,z \ u)))) = a(y,z,K(x,K(z \ u,w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,14015,a,b,16220,a),flip(a)].">
      <j1 rule="hyper" parents="347 14015 16220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16408">
    <literal><![CDATA[
      K(x * (y * z),T(u,w)) \ K(x * (y * z),K(u,w)) = K(u,(x * y) * R(z,y,x))
    ]]></literal>
    <justification jstring="[para(16349(a,1),16351(a,1,1))].">
      <j1 rule="para" parents="16349 16351"/>
    </justification>
  </clause>

  <clause id="16409">
    <literal><![CDATA[
      K(x,(y * z) * R(u,z,y)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(7517,a,16408,a),flip(a)].">
      <j1 rule="hyper" parents="7517 16408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16410">
    <literal><![CDATA[
      K(x,(y * z) * R(T(u,y * z),z,y)) = K(x,L(u,z,y) * (y * z))
    ]]></literal>
    <justification jstring="[para(734(a,1),16409(a,2,2))].">
      <j1 rule="para" parents="734 16409"/>
    </justification>
  </clause>

  <clause id="16412">
    <literal><![CDATA[
      K(x,R(y,z,u) * (u * z)) = K(x,L(y,z,u) * (u * z))
    ]]></literal>
    <justification jstring="[para(268(a,1),16410(a,1,2))].">
      <j1 rule="para" parents="268 16410"/>
    </justification>
  </clause>

  <clause id="16413">
    <literal><![CDATA[
      K(x,L(y,z,u) * (u * z)) = K(x,(y * z) * T(u,z))
    ]]></literal>
    <justification jstring="[para(9598(a,1),16412(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9598 16412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16414">
    <literal><![CDATA[
      K(x,L(y,z,u) * (T(u,z) * z)) = K(x,(y * z) * T(T(u,z),z))
    ]]></literal>
    <justification jstring="[para(10142(a,1),16413(a,1,2,1))].">
      <j1 rule="para" parents="10142 16413"/>
    </justification>
  </clause>

  <clause id="16415">
    <literal><![CDATA[
      K(x,L(y,z,u) * (T(u,z) * z)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,15689,a(flip),b,16414,a),flip(a)].">
      <j1 rule="hyper" parents="347 15689 16414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16416">
    <literal><![CDATA[
      K(x,L(y,z,u) * (z * u)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(15753,a,16415,a)].">
      <j1 rule="hyper" parents="15753 16415"/>
    </justification>
  </clause>

  <clause id="16418">
    <literal><![CDATA[
      T(x,L(y,z,u) * (z * u)) = T(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(132,a,16416,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 16416 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16419">
    <literal><![CDATA[
      K(x,L(y,z,z \ u) * u) = K(x,(y * z) * (z \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),16416(a,1,2,2))].">
      <j1 rule="para" parents="10 16416"/>
    </justification>
  </clause>

  <clause id="16420">
    <literal><![CDATA[
      T(x,L(y,z \ K(u,z \ 1),u) * (u * (z \ 1))) = T(x,(y * (z \ K(u,z \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(5054(a,1),16418(a,1,2,2))].">
      <j1 rule="para" parents="5054 16418"/>
    </justification>
  </clause>

  <clause id="16424">
    <literal><![CDATA[
      T(x,y * ((z / u) * (w * (K(z,u) * K(z,u))))) = T(x,y * ((T(z,u) / T(u,z)) * w))
    ]]></literal>
    <justification jstring="[para(11530(a,1),16383(a,2,2,2))].">
      <j1 rule="para" parents="11530 16383"/>
    </justification>
  </clause>

  <clause id="16425">
    <literal><![CDATA[
      T(x,y * ((T(z,u) / T(u,z)) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * ((z / u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(16424(a,1),15777(a,1))].">
      <j1 rule="para" parents="16424 15777"/>
    </justification>
  </clause>

  <clause id="16426">
    <literal><![CDATA[
      T(x,y * ((z \ T(u,z)) * w)) = T(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(16425,a,16365,a),flip(a)].">
      <j1 rule="hyper" parents="16425 16365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16428">
    <literal><![CDATA[
      T(x,y * ((T(z,u) \ u) * w)) = T(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(4281(a,2),16426(a,1,2,2,1))].">
      <j1 rule="para" parents="4281 16426"/>
    </justification>
  </clause>

  <clause id="16429">
    <literal><![CDATA[
      T(x,y * ((z / u) * ((z / u) * w))) = T(x,y * ((u \ z) * ((u \ z) * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16366,a(flip),b,16428,a),flip(a)].">
      <j1 rule="hyper" parents="63 16366 16428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16430">
    <literal><![CDATA[
      T(x,y * ((R(T(z,u),z,z) \ u) * w)) = T(x,y * ((u / ((z \ 1) \ 1)) * w))
    ]]></literal>
    <justification jstring="[para(797(a,1),16428(a,1,2,2,1,1))].">
      <j1 rule="para" parents="797 16428"/>
    </justification>
  </clause>

  <clause id="16431">
    <literal><![CDATA[
      T(x,y * ((z / ((u \ 1) \ 1)) * w)) = T(x,y * (((u \ (u \ z)) * u) * w))
    ]]></literal>
    <justification jstring="[para(13257(a,1),16430(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="13257 16430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16432">
    <literal><![CDATA[
      T(x,y * K(z,u)) \ T(y * T(T(x,K(z,u)),y * K(z,u)),K(z,u)) = T(y,x * K(z,u))
    ]]></literal>
    <justification jstring="[para(7330(a,1),16406(a,1,2))].">
      <j1 rule="para" parents="7330 16406"/>
    </justification>
  </clause>

  <clause id="16433">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * (w * z)) / T(w * u,a(w,z,z \ u)))) = a(y,z,K(x,K(w,u / z)))
    ]]></literal>
    <justification jstring="[para(13506(a,1),16407(a,2,3))].">
      <j1 rule="para" parents="13506 16407"/>
    </justification>
  </clause>

  <clause id="16434">
    <literal><![CDATA[
      T(x,y * K(z,u)) \ (T(x,K(z,u)) * T(y,K(z,u))) = T(y,x * K(z,u))
    ]]></literal>
    <justification jstring="[para(15736(a,1),16432(a,1,2))].">
      <j1 rule="para" parents="15736 16432"/>
    </justification>
  </clause>

  <clause id="16435">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(u * K(y,z),x) * T(u,K(y,z))) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(9945,a,16434,a)].">
      <j1 rule="hyper" parents="9945 16434"/>
    </justification>
  </clause>

  <clause id="16436">
    <literal><![CDATA[
      K(x,K(y,z)) * T(K(u * K(y,z),x) * u,K(y,z)) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(16239(a,2),16435(a,1,2))].">
      <j1 rule="para" parents="16239 16435"/>
    </justification>
  </clause>

  <clause id="16437">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(y,z) \ T(u * K(y,z),x)) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(13338(a,1),16436(a,1,2))].">
      <j1 rule="para" parents="13338 16436"/>
    </justification>
  </clause>

  <clause id="16438">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * T(u * K(y,z),x)) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(5256(a,1),16437(a,1,2))].">
      <j1 rule="para" parents="5256 16437"/>
    </justification>
  </clause>

  <clause id="16439">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u * K(y,x),z) = T(u,z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(8552,a,16438,a)].">
      <j1 rule="hyper" parents="8552 16438"/>
    </justification>
  </clause>

  <clause id="16440">
    <literal><![CDATA[
      K(x,y) * T(z * K(y,T(x,u)),u) = T(z,u * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,15198,a(flip),b,16439,a)].">
      <j1 rule="hyper" parents="63 15198 16439"/>
    </justification>
  </clause>

  <clause id="16441">
    <literal><![CDATA[
      T(x * K(y,T(z,u)),u) = K(y,z) * T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5273,a,16440,a),flip(a)].">
      <j1 rule="hyper" parents="5273 16440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16442">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * K(z,T(u,y)),y) = R(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[hyper(220,a,16441,a,b,13920,a)].">
      <j1 rule="hyper" parents="220 16441 13920"/>
    </justification>
  </clause>

  <clause id="16444">
    <literal><![CDATA[
      L(x,K(y,T(z,x)),u) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(13777,a,16442,a)].">
      <j1 rule="hyper" parents="13777 16442"/>
    </justification>
  </clause>

  <clause id="16445">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * (w * z)) / (w * u))) = a(y,z,K(x,K(w,u / z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16174,a(flip),b,16433,a)].">
      <j1 rule="hyper" parents="63 16174 16433"/>
    </justification>
  </clause>

  <clause id="16447">
    <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(7897(a,1),16064(a,1,2,2,2))].">
      <j1 rule="para" parents="7897 16064"/>
    </justification>
  </clause>

  <clause id="16448">
    <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(7283(a,2),16447(a,1,2,2))].">
      <j1 rule="para" parents="7283 16447"/>
    </justification>
  </clause>

  <clause id="16451">
    <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(9615(a,1),16448(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9615 16448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16452">
    <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(347,a,6265,a(flip),b,16451,a),flip(a)].">
      <j1 rule="hyper" parents="347 6265 16451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16453">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(12113,a,16452,a)].">
      <j1 rule="hyper" parents="12113 16452"/>
    </justification>
  </clause>

  <clause id="16454">
    <literal><![CDATA[
      K(x,y \ K(z,u \ 1)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(6318,a,16453,a),flip(a)].">
      <j1 rule="hyper" parents="6318 16453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16456">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16319,a,b,16454,a)].">
      <j1 rule="hyper" parents="63 16319 16454"/>
    </justification>
  </clause>

  <clause id="16457">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(3885(a,1),16454(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3885 16454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16458">
    <literal><![CDATA[
      K(x,y \ K(z,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16456,a(flip),b,16457,a)].">
      <j1 rule="hyper" parents="63 16456 16457"/>
    </justification>
  </clause>

  <clause id="16459">
    <literal><![CDATA[
      K(x,y \ K(z \ u,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12011,a(flip),b,16457,a)].">
      <j1 rule="hyper" parents="63 12011 16457"/>
    </justification>
  </clause>

  <clause id="16461">
    <literal><![CDATA[
      K(x,y \ K(z,u \ z)) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16458,a,b,16459,a)].">
      <j1 rule="hyper" parents="63 16458 16459"/>
    </justification>
  </clause>

  <clause id="16462">
    <literal><![CDATA[
      K(x,(y \ (z * (u \ y))) \ K(z,u)) = K(x,z \ ((y \ (z * (u \ y))) \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14877,a(flip),b,16461,a),flip(a)].">
      <j1 rule="hyper" parents="63 14877 16461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16463">
    <literal><![CDATA[
      K(x,(y \ (z * (u \ y))) \ K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T((z * (u \ y)) \ y,z)) = w
    ]]></literal>
    <justification jstring="[para(16462(a,2),8607(a,1))].">
      <j1 rule="para" parents="16462 8607"/>
    </justification>
  </clause>

  <clause id="16464">
    <literal><![CDATA[
      K(x,K(y,(L(z / u,u,1 / u) * w) * v5)) = K(x,K(y,(((1 / u) * z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(9(a,1),16261(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 16261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16465">
    <literal><![CDATA[
      K(x,K(y,(z * u) * R(L(w / v5,v5,1 / v5),z,u))) = K(x,K(y,(((1 / v5) * w) * z) * u))
    ]]></literal>
    <justification jstring="[hyper(13689,a,16464,a)].">
      <j1 rule="hyper" parents="13689 16464"/>
    </justification>
  </clause>

  <clause id="16467">
    <literal><![CDATA[
      K(x,K(y,(z * u) * L(R(w / v5,z,u),v5,1 / v5))) = K(x,K(y,(((1 / v5) * w) * z) * u))
    ]]></literal>
    <justification jstring="[para(29(a,1),16465(a,1,2,2,2))].">
      <j1 rule="para" parents="29 16465"/>
    </justification>
  </clause>

  <clause id="16468">
    <literal><![CDATA[
      L(K(x,y * K(z,T(u * K(w,v5),v6))),x,v7) = L(K(x,y * K(u,z)),x,v8)
    ]]></literal>
    <justification jstring="[hyper(347,a,13779,a,b,16340,a),flip(a)].">
      <j1 rule="hyper" parents="347 13779 16340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16469">
    <literal><![CDATA[
      L(K(x,y * K(z,T(u * K(w,v5),v6))),x,v7) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,14012,a(flip),b,16468,a),flip(a)].">
      <j1 rule="hyper" parents="347 14012 16468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16470">
    <literal><![CDATA[
      L(K(x,y * K(z,u * K(w,v5))),x,v6) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(110(a,1),16469(a,1,1,2,2,2))].">
      <j1 rule="para" parents="110 16469"/>
    </justification>
  </clause>

  <clause id="16471">
    <literal><![CDATA[
      K(x,y * K(z,u * K(w,v5))) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(13957,a,16470,a)].">
      <j1 rule="hyper" parents="13957 16470"/>
    </justification>
  </clause>

  <clause id="16472">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * v5) = K(x,v5 * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(13608,a,16471,a)].">
      <j1 rule="hyper" parents="13608 16471"/>
    </justification>
  </clause>

  <clause id="16473">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * K(y,w)) = K(x,T(y * K(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(7497,a,16471,a),flip(a)].">
      <j1 rule="hyper" parents="7497 16471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16474">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * v5) = K(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,13579,a,b,16472,a),flip(a)].">
      <j1 rule="hyper" parents="347 13579 16472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16475">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) = K(x,K(w,u) * v5)
    ]]></literal>
    <justification jstring="[para(7087(a,1),16474(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7087 16474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16476">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) = K(x,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,15545,a,b,16475,a),flip(a)].">
      <j1 rule="hyper" parents="347 15545 16475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16478">
    <literal><![CDATA[
      K(x,T(y * K(z,u),w)) = K(x,T(y,w) * K(z,u))
    ]]></literal>
    <justification jstring="[para(13573(a,1),16473(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13573 16473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16479">
    <literal><![CDATA[
      K(x,T(y * K(z,u),w)) = K(x,K(u,z) * T(y,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,15548,a,b,16478,a),flip(a)].">
      <j1 rule="hyper" parents="347 15548 16478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16480">
    <literal><![CDATA[
      K(x,T(y * K(z,u),w)) = K(x,K(u,z) \ T(y,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,13592,a,b,16478,a),flip(a)].">
      <j1 rule="hyper" parents="347 13592 16478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16481">
    <literal><![CDATA[
      T(x,T(y * K(z,u),w)) = T(x,K(u,z) * T(y,w))
    ]]></literal>
    <justification jstring="[hyper(132,a,16479,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 16479 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16482">
    <literal><![CDATA[
      K(x,K(y,z) \ T(u / y,w)) = K(x,T(u / T(y,z),w))
    ]]></literal>
    <justification jstring="[para(6102(a,1),16480(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6102 16480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16483">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,K(y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15848,a,b,16481,a)].">
      <j1 rule="hyper" parents="63 15848 16481"/>
    </justification>
  </clause>

  <clause id="16484">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,T(u,w) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,15510,a(flip),b,16483,a),flip(a)].">
      <j1 rule="hyper" parents="347 15510 16483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16485">
    <literal><![CDATA[
      T(x,T(K(y / z,u) * T(y,z),w)) = T(x,(z * K(y,w)) * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(15768,a,16483,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="15768 16483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16486">
    <literal><![CDATA[
      T(x,((y \ z) * y) * K(u,w)) = T(x,T(K(u,w) * z,y))
    ]]></literal>
    <justification jstring="[hyper(13693,a,16483,a(flip))].">
      <j1 rule="hyper" parents="13693 16483"/>
    </justification>
  </clause>

  <clause id="16487">
    <literal><![CDATA[
      T(x,T(K(y,z \ u) * (u / (u / z)),w)) = T(x,(u * K(z,w)) / T(u / z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,16309,a(flip),b,16484,a),flip(a)].">
      <j1 rule="hyper" parents="347 16309 16484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16488">
    <literal><![CDATA[
      K(x,T(y / T(z,K(u,w)),v5)) = K(x,T(y / z,v5))
    ]]></literal>
    <justification jstring="[hyper(14827,a,16482,a),flip(a)].">
      <j1 rule="hyper" parents="14827 16482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16489">
    <literal><![CDATA[
      K(x,T(y / (T(z,u) * T(w,z)),v5)) = K(x,T(y / (w * T(z,u)),v5))
    ]]></literal>
    <justification jstring="[para(7740(a,1),16488(a,1,2,1,2))].">
      <j1 rule="para" parents="7740 16488"/>
    </justification>
  </clause>

  <clause id="16490">
    <literal><![CDATA[
      K(x,T(y / (K(T(z,u),T(z,u) \ w) \ w),v5)) = K(x,T(y / (T(z,u) * T(T(z,u) \ w,z)),v5))
    ]]></literal>
    <justification jstring="[para(4912(a,2),16489(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4912 16489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16491">
    <literal><![CDATA[
      T(x,T(T(y * K(y / z,u),z),w)) = T(x,(z * K(y,w)) * T(y / z,u))
    ]]></literal>
    <justification jstring="[para(13938(a,2),16485(a,1,2,1))].">
      <j1 rule="para" parents="13938 16485"/>
    </justification>
  </clause>

  <clause id="16492">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * T(z / y,w)) = T(x,T(y * T(z / y,w),u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14539,a(flip),b,16491,a),flip(a)].">
      <j1 rule="hyper" parents="63 14539 16491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16493">
    <literal><![CDATA[
      T(x,(y * K(z,u)) / T(y / z,w)) = T(x,T(y / T(y / z,w),u))
    ]]></literal>
    <justification jstring="[para(8538(a,1),16487(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8538 16487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16494">
    <literal><![CDATA[
      T(x,(y * K(z,u)) / T(y / z,w)) = T(x,T(T(z \ y,w) \ y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,10579,a(flip),b,16493,a),flip(a)].">
      <j1 rule="hyper" parents="347 10579 16493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16495">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w) / w,v5))) * K(K(z,y),x) = a(v5,K(u,w) / (K(y,z) * w),K(K(z,y),x))
    ]]></literal>
    <justification jstring="[para(8929(a,1),16265(a,1,1))].">
      <j1 rule="para" parents="8929 16265"/>
    </justification>
  </clause>

  <clause id="16496">
    <literal><![CDATA[
      T(L(x,y,z),T(u,w / (v5 / T(v6,v7)))) = T(L(x,y,z),T(u,(v6 / v5) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,4673,a(flip),b,16303,a),flip(a)].">
      <j1 rule="hyper" parents="63 4673 16303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16497">
    <literal><![CDATA[
      K(x,T(y / (K(T(z,u),T(z,u) \ w) \ w),v5)) = K(x,T(y / ((z \ w) * z),v5))
    ]]></literal>
    <justification jstring="[para(7251(a,1),16490(a,2,2,1,2))].">
      <j1 rule="para" parents="7251 16490"/>
    </justification>
  </clause>

  <clause id="16498">
    <literal><![CDATA[
      K(x,T(y / (K(z,T(T(z,u) \ w,u)) \ w),v5)) = K(x,T(y / ((z \ w) * z),v5))
    ]]></literal>
    <justification jstring="[para(7093(a,1),16497(a,1,2,1,2,1))].">
      <j1 rule="para" parents="7093 16497"/>
    </justification>
  </clause>

  <clause id="16500">
    <literal><![CDATA[
      K(x,T(y / (K(z,z \ T(u,w)) \ u),v5)) = K(x,T(y / ((z \ u) * z),v5))
    ]]></literal>
    <justification jstring="[para(10468(a,1),16498(a,1,2,1,2,1))].">
      <j1 rule="para" parents="10468 16498"/>
    </justification>
  </clause>

  <clause id="16503">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = L(T(x,K(z,y) * (x \ u)),u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,25,a,b,15723,a),flip(a)].">
      <j1 rule="hyper" parents="347 25 15723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16504">
    <literal><![CDATA[
      T((x * K(y,z)) / (u * K(y,z)),u * K(y,T(z,x))) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(7126(a,1),16146(a,1,2))].">
      <j1 rule="para" parents="7126 16146"/>
    </justification>
  </clause>

  <clause id="16506">
    <literal><![CDATA[
      K(x * (y \ z),(1 / (z \ y)) * x) = K(x * (y \ z),x * (1 / (z \ y)))
    ]]></literal>
    <justification jstring="[para(2054(a,1),16352(a,1,1,2))].">
      <j1 rule="para" parents="2054 16352"/>
    </justification>
  </clause>

  <clause id="16507">
    <literal><![CDATA[
      K(x * (y \ z),x * (1 / (z \ y))) = K(x * (y \ z),(z \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(13291,a,16506,a),flip(a)].">
      <j1 rule="hyper" parents="13291 16506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16508">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ z),x / (z \ y)) = u
    ]]></literal>
    <justification jstring="[para(16507(a,1),13334(a,1))].">
      <j1 rule="para" parents="16507 13334"/>
    </justification>
  </clause>

  <clause id="16509">
    <literal><![CDATA[
      (x \ (K(y,L(z,u,x)) * u)) \ (K(y,z) * ((u * x) / x)) = L(T(x,K(z,y) * (x \ u)),u,K(y,z))
    ]]></literal>
    <justification jstring="[para(14205(a,1),16503(a,1,1,2,1))].">
      <j1 rule="para" parents="14205 16503"/>
    </justification>
  </clause>

  <clause id="16510">
    <literal><![CDATA[
      ((x \ y) * K(z,T(u,y))) \ (K(z,u) * ((y * x) / x)) = L(T(x,K(u,z) * (x \ y)),y,K(z,u))
    ]]></literal>
    <justification jstring="[para(14220(a,1),16509(a,1,1))].">
      <j1 rule="para" parents="14220 16509"/>
    </justification>
  </clause>

  <clause id="16511">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),u,K(z,y)) = ((x \ u) * K(z,T(y,u))) \ (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(11(a,1),16510(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 16510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16512">
    <literal><![CDATA[
      T((x * K(y,z)) / (u * K(y,z)),K(z,y) * u) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(15722,a,16504,a)].">
      <j1 rule="hyper" parents="15722 16504"/>
    </justification>
  </clause>

  <clause id="16513">
    <literal><![CDATA[
      (x / T(K(y,z),u * K(z,y))) \ (K(z,y) * u) = (x * K(z,y)) \ (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(15517,a,16512,a),flip(a)].">
      <j1 rule="hyper" parents="15517 16512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16515">
    <literal><![CDATA[
      (x / K(y,T(z,u))) \ (K(z,y) * u) = (x * K(z,y)) \ (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(16133(a,1),16513(a,1,1,2))].">
      <j1 rule="para" parents="16133 16513"/>
    </justification>
  </clause>

  <clause id="16516">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ (K(y,z) * u) = (x * K(y,z)) \ (u * K(y,z))
    ]]></literal>
    <justification jstring="[para(7126(a,1),16515(a,1,1))].">
      <j1 rule="para" parents="7126 16515"/>
    </justification>
  </clause>

  <clause id="16518">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),u,K(z,y)) = ((x \ u) * K(z,y)) \ (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16511,a,b,16516,a)].">
      <j1 rule="hyper" parents="63 16511 16516"/>
    </justification>
  </clause>

  <clause id="16519">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K((((z \ u) * y) \ y) * ((z \ u) * y),z))
    ]]></literal>
    <justification jstring="[hyper(15712,a,15656,a)].">
      <j1 rule="hyper" parents="15712 15656"/>
    </justification>
  </clause>

  <clause id="16520">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K((u \ z) * (y / (u \ z)),z))
    ]]></literal>
    <justification jstring="[para(15404(a,1),16519(a,2,3,1))].">
      <j1 rule="para" parents="15404 16519"/>
    </justification>
  </clause>

  <clause id="16521">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K(y,T(z,u \ z)))
    ]]></literal>
    <justification jstring="[para(10382(a,1),16520(a,2,3))].">
      <j1 rule="para" parents="10382 16520"/>
    </justification>
  </clause>

  <clause id="16522">
    <literal><![CDATA[
      K((x \ K(x * (y \ T(z,u \ w)),x \ 1)) \ (y \ T(z,u * w)),v5) = K((y \ T(z,u \ w)) * x,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,13221,a(flip),b,15990,a),flip(a)].">
      <j1 rule="hyper" parents="347 13221 15990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16523">
    <literal><![CDATA[
      K((x \ K(x * (y \ T(z,u * w)),x \ 1)) \ (y \ T(z,u * w)),v5) = K((y \ T(z,u \ w)) * x,v5)
    ]]></literal>
    <justification jstring="[para(15991(a,1),16522(a,1,1,1,2))].">
      <j1 rule="para" parents="15991 16522"/>
    </justification>
  </clause>

  <clause id="16524">
    <literal><![CDATA[
      K((x \ T(y,z * u)) / (w \ 1),v5) = K((x \ T(y,z \ u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(5655(a,1),16523(a,1,1))].">
      <j1 rule="para" parents="5655 16523"/>
    </justification>
  </clause>

  <clause id="16525">
    <literal><![CDATA[
      K((x \ T(y,z \ u)) * w,v5) = K((x \ T(y,z * u)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(13222,a,16524,a),flip(a)].">
      <j1 rule="hyper" parents="13222 16524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16526">
    <literal><![CDATA[
      K((x \ T(y,y * z)) * u,w) = K((x \ ((y \ z) \ z)) * u,w)
    ]]></literal>
    <justification jstring="[para(112(a,1),16525(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="112 16525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16527">
    <literal><![CDATA[
      K((T(x,x \ ((y \ z) \ z)) \ T(y,y * z)) * u,w) = K(T(x \ ((y \ z) \ z),x) * u,w)
    ]]></literal>
    <justification jstring="[para(4301(a,1),16526(a,2,1,1))].">
      <j1 rule="para" parents="4301 16526"/>
    </justification>
  </clause>

  <clause id="16528">
    <literal><![CDATA[
      K((T(x,x \ T(y,z)) \ T(y,y * z)) * u,w) = K(T(x \ ((y \ z) \ z),x) * u,w)
    ]]></literal>
    <justification jstring="[para(12213(a,1),16527(a,1,1,1,1))].">
      <j1 rule="para" parents="12213 16527"/>
    </justification>
  </clause>

  <clause id="16529">
    <literal><![CDATA[
      K((T(x,T(x \ y,z)) \ T(y,y * z)) * u,w) = K(T(x \ ((y \ z) \ z),x) * u,w)
    ]]></literal>
    <justification jstring="[para(10467(a,2),16528(a,1,1,1,1))].">
      <j1 rule="para" parents="10467 16528"/>
    </justification>
  </clause>

  <clause id="16530">
    <literal><![CDATA[
      K(x,T(T((y * K(z,u)) / w,K(y,v5)),T((y * K(z,u)) \ w,K(y,v5)))) = K(x,(y * K(z,u)) / T(w,K(y,v5)))
    ]]></literal>
    <justification jstring="[para(16381(a,1),16377(a,1,2,1))].">
      <j1 rule="para" parents="16381 16377"/>
    </justification>
  </clause>

  <clause id="16531">
    <literal><![CDATA[
      K(x,T(T((y * K(z,u)) / w,K(y,v5)),(y * K(z,u)) \ w)) = K(x,(y * K(z,u)) / T(w,K(y,v5)))
    ]]></literal>
    <justification jstring="[hyper(13638,a,16530,a)].">
      <j1 rule="hyper" parents="13638 16530"/>
    </justification>
  </clause>

  <clause id="16533">
    <literal><![CDATA[
      K(x,R(y * z,K(u,L(w,y,z)),K(u,L(w,y,z))) \ v5) = K(x,((K(L(w,y,z),u) * 1) * ((K(u,w) * y) * z)) \ v5)
    ]]></literal>
    <justification jstring="[para(5256(a,1),15973(a,2,2,1,1))].">
      <j1 rule="para" parents="5256 15973"/>
    </justification>
  </clause>

  <clause id="16534">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u * w)),K(T(u,v5 * (v5 * v6)) * w,z)) = T(y,K(z,T(u,v6) * w) * x)
    ]]></literal>
    <justification jstring="[para(16194(a,1),16101(a,1,2,1,2))].">
      <j1 rule="para" parents="16194 16101"/>
    </justification>
  </clause>

  <clause id="16535">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u * w)),K(z,T(u,v5 * (v5 * v6)) * w)) = T(y,K(z,T(u,v6) * w) * x)
    ]]></literal>
    <justification jstring="[para(7330(a,1),16534(a,1,2))].">
      <j1 rule="para" parents="7330 16534"/>
    </justification>
  </clause>

  <clause id="16537">
    <literal><![CDATA[
      T(x,K(y,T(z,u) * w) * v5) = v5 \ T(x * T(v5,K(y,z * w)),K(y,z * w))
    ]]></literal>
    <justification jstring="[para(16194(a,1),16535(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16194 16535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16538">
    <literal><![CDATA[
      T(x,K(y,T(z,u) * w) * v5) = T(x,K(z * w,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,15497,a(flip),b,16537,a),flip(a)].">
      <j1 rule="hyper" parents="347 15497 16537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16540">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w) * v5)) = T(x,K(u * v5,z) * y)
    ]]></literal>
    <justification jstring="[hyper(13563,a,16538,a)].">
      <j1 rule="hyper" parents="13563 16538"/>
    </justification>
  </clause>

  <clause id="16541">
    <literal><![CDATA[
      T(x,K(y * z,u) * ((y * z) / T(y,w))) = T(x,T(y * (z * K(w,y)),u) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16400,a(flip),b,16540,a),flip(a)].">
      <j1 rule="hyper" parents="63 16400 16540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16543">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,y)),w) / y) = T(x,T(y * z,w) / T(y,u))
    ]]></literal>
    <justification jstring="[para(13192(a,1),16541(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13192 16541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16544">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,y)),w) / y) = T(x,T(y,u) \ T(z * y,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,13688,a(flip),b,16543,a),flip(a)].">
      <j1 rule="hyper" parents="347 13688 16543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16545">
    <literal><![CDATA[
      T(x,y \ T((z * K(u,y)) * y,w)) = T(x,T(y,u) \ T(z * y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,7467,a(flip),b,16544,a)].">
      <j1 rule="hyper" parents="63 7467 16544"/>
    </justification>
  </clause>

  <clause id="16546">
    <literal><![CDATA[
      T(x,y \ T(z * (y * K(u,y)),w)) = T(x,T(y,u) \ T(z * y,w))
    ]]></literal>
    <justification jstring="[para(6051(a,1),16545(a,1,2,2,1))].">
      <j1 rule="para" parents="6051 16545"/>
    </justification>
  </clause>

  <clause id="16547">
    <literal><![CDATA[
      K(x,R(y * z,K(u,L(w,y,z)),K(u,L(w,y,z))) \ v5) = K(x,((K(w,L(u,y,z)) * 1) * ((K(u,w) * y) * z)) \ v5)
    ]]></literal>
    <justification jstring="[para(11108(a,1),16533(a,2,2,1,1,1))].">
      <j1 rule="para" parents="11108 16533"/>
    </justification>
  </clause>

  <clause id="16548">
    <literal><![CDATA[
      K(x,R(y * z,K(u,L(w,y,z)),K(u,L(w,y,z))) \ v5) = K(x,(K(w,L(u,y,z)) * ((K(u,w) * y) * z)) \ v5)
    ]]></literal>
    <justification jstring="[para(8(a,1),16547(a,2,2,1,1))].">
      <j1 rule="para" parents="8 16547"/>
    </justification>
  </clause>

  <clause id="16549">
    <literal><![CDATA[
      K(x,(1 \ T(1 / (y / z),y)) * L(T(1 / (y / z),y) \ 1,u,w)) = K(x,L(y / ((y \ z) * y),u,w) / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,11972,a(flip),b,16012,a),flip(a)].">
      <j1 rule="hyper" parents="63 11972 16012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16550">
    <literal><![CDATA[
      K(x,T(1 / (y / z),y) * L(T(1 / (y / z),y) \ 1,u,w)) = K(x,L(y / ((y \ z) * y),u,w) / (z \ y))
    ]]></literal>
    <justification jstring="[para(66(a,1),16549(a,1,2,1))].">
      <j1 rule="para" parents="66 16549"/>
    </justification>
  </clause>

  <clause id="16551">
    <literal><![CDATA[
      K(x,K(y,(((K(z,u) * w) * v5) * v6) / (v6 * (K(z,u) * v5)))) = K(x,K(R(w,K(z,u),v5),L(y,K(z,u) * v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(13672,a,16258,a),flip(a)].">
      <j1 rule="hyper" parents="13672 16258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16553">
    <literal><![CDATA[
      K(x,K(y,(((K(z,u) * w) * v5) * v6) / (v6 * (K(z,u) * v5)))) = K(x,K(w,L(L(y,K(z,u) * v5,v6),K(z,u),v5)))
    ]]></literal>
    <justification jstring="[para(14080(a,1),16551(a,2,2))].">
      <j1 rule="para" parents="14080 16551"/>
    </justification>
  </clause>

  <clause id="16554">
    <literal><![CDATA[
      K(x,K(y,(((K(z,u) * w) * v5) * v6) / (v6 * (K(z,u) * v5)))) = K(x,K(w,L(y,K(z,u) * v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(347,a,16291,a(flip),b,16553,a),flip(a)].">
      <j1 rule="hyper" parents="347 16291 16553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16556">
    <literal><![CDATA[
      K(x,K(y,(((K(z,u) * w) * v5) * v6) / (v6 * v5))) = K(x,K(w,L(y,K(z,u) * v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16271,a(flip),b,16554,a)].">
      <j1 rule="hyper" parents="63 16271 16554"/>
    </justification>
  </clause>

  <clause id="16558">
    <literal><![CDATA[
      K(x,K(y,L(K(z,u) * w,v5,v6))) = K(x,K(w,L(y,K(z,u) * v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16219,a(flip),b,16556,a)].">
      <j1 rule="hyper" parents="63 16219 16556"/>
    </justification>
  </clause>

  <clause id="16559">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w) * v5,v6))) = K(x,K(y,L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16202,a(flip),b,16558,a),flip(a)].">
      <j1 rule="hyper" parents="63 16202 16558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16560">
    <literal><![CDATA[
      L(K(x,K(y,z)),K(u,w) * v5,v6) = K(y,K(z,L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(11122,a,16559,a)].">
      <j1 rule="hyper" parents="11122 16559"/>
    </justification>
  </clause>

  <clause id="16562">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w) / v5,v6))) = K(x,K(y,L(z,1 / v5,v6)))
    ]]></literal>
    <justification jstring="[para(12988(a,1),16559(a,1,2,2,2))].">
      <j1 rule="para" parents="12988 16559"/>
    </justification>
  </clause>

  <clause id="16563">
    <literal><![CDATA[
      L(K(x,K(y,z)),K(u,w) * v5,v6) = a(x,v5,K(v6,K(y,z))) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,14155,a,b,16560,a),flip(a)].">
      <j1 rule="hyper" parents="347 14155 16560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16564">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w) / v5,v6))) = K(x,K(z,L(y,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(347,a,8928,a(flip),b,16562,a),flip(a)].">
      <j1 rule="hyper" parents="347 8928 16562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16565">
    <literal><![CDATA[
      a(x,K(y,z) / (K(u,w) * z),K(K(w,u),v5)) = K(v5,K(w,L(u,z,x))) * K(K(w,u),v5)
    ]]></literal>
    <justification jstring="[para(16564(a,1),16495(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16564 16495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16566">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,K(v5,v6))) = a(x,u,K(w,K(v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(14156,a,16563,a)].">
      <j1 rule="hyper" parents="14156 16563"/>
    </justification>
  </clause>

  <clause id="16567">
    <literal><![CDATA[
      a(x,y * (z / y),K(u,K(w,v5))) = a(x,z,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(4899(a,1),16566(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4899 16566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16568">
    <literal><![CDATA[
      a(x,y / z,K(u,K(w,v5))) = a(x,z \ y,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(5012(a,1),16566(a,1,2))].">
      <j1 rule="para" parents="5012 16566"/>
    </justification>
  </clause>

  <clause id="16569">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w * y))) = a(x,w,K((1 / y) / w,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12747,a(flip),b,16567,a),flip(a)].">
      <j1 rule="hyper" parents="63 12747 16567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16570">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w * y))) = a(x,w,K(z,K(u,(1 / y) / w)))
    ]]></literal>
    <justification jstring="[para(7283(a,2),16569(a,2,3))].">
      <j1 rule="para" parents="7283 16569"/>
    </justification>
  </clause>

  <clause id="16571">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w * y))) = a(x,w,K(z,K(u,w * y)))
    ]]></literal>
    <justification jstring="[para(12744(a,1),16570(a,2,3))].">
      <j1 rule="para" parents="12744 16570"/>
    </justification>
  </clause>

  <clause id="16572">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(u,K(w,z))) = a(x,y,K(u,K(w,y * (y \ z))))
    ]]></literal>
    <justification jstring="[para(10(a,1),16571(a,1,3,2,2))].">
      <j1 rule="para" parents="10 16571"/>
    </justification>
  </clause>

  <clause id="16573">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(u,K(w,y * (y \ z))))
    ]]></literal>
    <justification jstring="[para(7283(a,1),16572(a,1,3))].">
      <j1 rule="para" parents="7283 16572"/>
    </justification>
  </clause>

  <clause id="16574">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(u,K(w,z)))
    ]]></literal>
    <justification jstring="[para(10(a,1),16573(a,2,3,2,2))].">
      <j1 rule="para" parents="10 16573"/>
    </justification>
  </clause>

  <clause id="16575">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(7283(a,1),16574(a,2,3))].">
      <j1 rule="para" parents="7283 16574"/>
    </justification>
  </clause>

  <clause id="16576">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,z / y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(83(a,1),16575(a,1,2,2))].">
      <j1 rule="para" parents="83 16575"/>
    </justification>
  </clause>

  <clause id="16577">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(w,K(z,u)))
    ]]></literal>
    <justification jstring="[para(7283(a,2),16576(a,1,3))].">
      <j1 rule="para" parents="7283 16576"/>
    </justification>
  </clause>

  <clause id="16578">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(7283(a,2),16577(a,2,3))].">
      <j1 rule="para" parents="7283 16577"/>
    </justification>
  </clause>

  <clause id="16579">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14068,a,b,16578,a)].">
      <j1 rule="hyper" parents="63 14068 16578"/>
    </justification>
  </clause>

  <clause id="16580">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(u,x)))
    ]]></literal>
    <justification jstring="[para(7293(a,1),16579(a,2,3))].">
      <j1 rule="para" parents="7293 16579"/>
    </justification>
  </clause>

  <clause id="16581">
    <literal><![CDATA[
      a(x,K(y,z) / (K(u,w) * z),K(K(w,u),v5)) = K(v5,K(w,L(u,z,x))) * K(v5,K(w,u))
    ]]></literal>
    <justification jstring="[para(7292(a,1),16565(a,2,2))].">
      <j1 rule="para" parents="7292 16565"/>
    </justification>
  </clause>

  <clause id="16583">
    <literal><![CDATA[
      a(x,K(y,z) / (K(u,w) * z),K(K(w,u),v5)) = K(K(w,L(u,z,x)) * K(u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,10692,a(flip),b,16581,a),flip(a)].">
      <j1 rule="hyper" parents="347 10692 16581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16584">
    <literal><![CDATA[
      a(x,K(y,z) / (K(u,w) * z),K(K(w,u),v5)) = K(a(x,z * u,K(u,w)),v5)
    ]]></literal>
    <justification jstring="[para(9256(a,1),16583(a,2,1))].">
      <j1 rule="para" parents="9256 16583"/>
    </justification>
  </clause>

  <clause id="16585">
    <literal><![CDATA[
      a(x,K(y,z) / (K(u,w) * z),K(K(w,u),v5)) = a(u,z,K(v5,K(w,x)))
    ]]></literal>
    <justification jstring="[hyper(347,a,14519,a(flip),b,16584,a),flip(a)].">
      <j1 rule="hyper" parents="347 14519 16584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16586">
    <literal><![CDATA[
      a(x,(K(y,z) / z) * K(u,w),K(K(u,w),v5)) = a(w,z,K(v5,K(u,x)))
    ]]></literal>
    <justification jstring="[para(16264(a,1),16585(a,1,2))].">
      <j1 rule="para" parents="16264 16585"/>
    </justification>
  </clause>

  <clause id="16587">
    <literal><![CDATA[
      a(x,(K(y,z) / z) * K(u,w),K(v5,K(u,w))) = a(w,z,K(v5,K(u,x)))
    ]]></literal>
    <justification jstring="[para(7292(a,1),16586(a,1,3))].">
      <j1 rule="para" parents="7292 16586"/>
    </justification>
  </clause>

  <clause id="16588">
    <literal><![CDATA[
      a(x,K(y,z) / z,K(u,K(w,v5))) = a(v5,z,K(u,K(w,x)))
    ]]></literal>
    <justification jstring="[hyper(11175,a,16587,a)].">
      <j1 rule="hyper" parents="11175 16587"/>
    </justification>
  </clause>

  <clause id="16589">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,y,K(z,K(u,x)))
    ]]></literal>
    <justification jstring="[para(186(a,1),16588(a,1,2,1))].">
      <j1 rule="para" parents="186 16588"/>
    </justification>
  </clause>

  <clause id="16590">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(x,z,K(u,K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16580,a(flip),b,16589,a)].">
      <j1 rule="hyper" parents="63 16580 16589"/>
    </justification>
  </clause>

  <clause id="16591">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(y,z,K(u,K(x,w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,14069,a,b,16590,a),flip(a)].">
      <j1 rule="hyper" parents="347 14069 16590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16592">
    <literal><![CDATA[
      T((K(x,L(x \ K(y,z),u,w)) \ K(x,x \ K(y,z))) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(11049(a,1),15795(a,1,1,1,1))].">
      <j1 rule="para" parents="11049 15795"/>
    </justification>
  </clause>

  <clause id="16593">
    <literal><![CDATA[
      T((K(L(x \ K(y,z),u,w),x) * K(x,x \ K(y,z))) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(5256(a,1),16592(a,1,1,1))].">
      <j1 rule="para" parents="5256 16592"/>
    </justification>
  </clause>

  <clause id="16594">
    <literal><![CDATA[
      T((K(x \ K(y,z),L(x,u,w)) * K(x,x \ K(y,z))) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(11108(a,1),16593(a,1,1,1,1))].">
      <j1 rule="para" parents="11108 16593"/>
    </justification>
  </clause>

  <clause id="16595">
    <literal><![CDATA[
      T(a(x \ K(y,z),u,K(w,x)) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(13969(a,1),16594(a,1,1,1))].">
      <j1 rule="para" parents="13969 16594"/>
    </justification>
  </clause>

  <clause id="16596">
    <literal><![CDATA[
      T(a(K(x,y),z,K(u,w)) * L(K(w,w \ K(x,y)),z,u),K(K(y,x) * w,w \ 1)) = K(K(y,x) * w,w \ 1)
    ]]></literal>
    <justification jstring="[para(14028(a,1),16595(a,1,1,1))].">
      <j1 rule="para" parents="14028 16595"/>
    </justification>
  </clause>

  <clause id="16597">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * L(L(L(L(z \ 1,z,y),y * z,x),u,w),v5,v6)) = L(z,y,x) \ L(L((x * y) \ (x * (y * z)),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),4099(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 4099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16598">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * L(L(L(L(z \ 1,z,y),y * z,x),u,w),v5,v6)) = L(z,y,x) \ L(L(L(z,y,x),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),16597(a,2,2,1,1))].">
      <j1 rule="para" parents="18 16597"/>
    </justification>
  </clause>

  <clause id="16599">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * L(L(L(z \ 1,z,y),u,w),v5,v6))) = L(z,y,x) \ L(L(L(z,y,x),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(1180(a,1),16598(a,1,2))].">
      <j1 rule="para" parents="1180 16598"/>
    </justification>
  </clause>

  <clause id="16600">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * L(L(z \ 1,u,w),v5,v6)))) = L(z,y,x) \ L(L(L(z,y,x),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(1180(a,1),16599(a,1,2,2))].">
      <j1 rule="para" parents="1180 16599"/>
    </justification>
  </clause>

  <clause id="16601">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z \ L(L(z,u,w),v5,v6)))) = L(z,y,x) \ L(L(L(z,y,x),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(3540(a,1),16600(a,1,2,2,2))].">
      <j1 rule="para" parents="3540 16600"/>
    </justification>
  </clause>

  <clause id="16602">
    <literal><![CDATA[
      L(x,y,z) \ L(L(L(x,y,z),u,w),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x \ L(L(x,u,w),v5,v6),y,z) = v7
    ]]></literal>
    <justification jstring="[para(16601(a,1),545(a,1))].">
      <j1 rule="para" parents="16601 545"/>
    </justification>
  </clause>

  <clause id="16603">
    <literal><![CDATA[
      a(x,y,L(z * (a(u,w,u) \ v5),(a(u,w,u) \ z) * v5,L(v5 \ 1,v5,a(u,w,u) \ z))) = a(x,y,((a(u,w,u) \ z) * (((a(u,w,u) \ z) * v5) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(11883(a,1),12452(a,1,3,1))].">
      <j1 rule="para" parents="11883 12452"/>
    </justification>
  </clause>

  <clause id="16604">
    <literal><![CDATA[
      a(x,y,L(z * (a(u,w,u) \ v5),z * (a(u,w,u) \ v5),L(v5 \ 1,v5,a(u,w,u) \ z))) = a(x,y,((a(u,w,u) \ z) * (((a(u,w,u) \ z) * v5) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(11883(a,1),16603(a,1,3,2))].">
      <j1 rule="para" parents="11883 16603"/>
    </justification>
  </clause>

  <clause id="16605">
    <literal><![CDATA[
      a(x,y,L(z * (a(u,w,u) \ v5),z * (a(u,w,u) \ v5),L(v5 \ 1,v5,z))) = a(x,y,((a(u,w,u) \ z) * (((a(u,w,u) \ z) * v5) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(11421(a,1),16604(a,1,3,3))].">
      <j1 rule="para" parents="11421 16604"/>
    </justification>
  </clause>

  <clause id="16615">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) * u) * a(u,z \ L(z,y,x),u)) \ ((u * (a(x,y,z) \ 1)) * u) = R(T(u,a(x,y,z) \ u),(a(x,y,z) \ 1) * u,a(u,a(x,y,z) \ 1,u))
    ]]></literal>
    <justification jstring="[para(1799(a,1),12421(a,2,1))].">
      <j1 rule="para" parents="1799 12421"/>
    </justification>
  </clause>

  <clause id="16616">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) * u) * a(u,z \ L(z,y,x),u)) \ ((u * (a(x,y,z) \ 1)) * u) = T(u,a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,11856,a(flip),b,16615,a),flip(a)].">
      <j1 rule="hyper" parents="347 11856 16615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16618">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * R(u,z \ L(z,y,x),u)) \ ((u * (a(x,y,z) \ 1)) * u) = T(u,a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(10964(a,1),16616(a,1,1))].">
      <j1 rule="para" parents="10964 16616"/>
    </justification>
  </clause>

  <clause id="16619">
    <literal><![CDATA[
      L(T(x,a(y,z,u) \ 1),u \ L(u,z,y),x) = T(x,a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(11043,a,16618,a)].">
      <j1 rule="hyper" parents="11043 16618"/>
    </justification>
  </clause>

  <clause id="16620">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,12618,a(flip),b,16619,a),flip(a)].">
      <j1 rule="hyper" parents="63 12618 16619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16621">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,13984,a(flip),b,16620,a),flip(a)].">
      <j1 rule="hyper" parents="347 13984 16620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16622">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,13978,a(flip),b,16620,a),flip(a)].">
      <j1 rule="hyper" parents="347 13978 16620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16623">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(13299,a,16621,a)].">
      <j1 rule="hyper" parents="13299 16621"/>
    </justification>
  </clause>

  <clause id="16624">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,14337,a,b,16623,a),flip(a)].">
      <j1 rule="hyper" parents="347 14337 16623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16625">
    <literal><![CDATA[
      T(x,y \ L(y,z,u)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(12617,a,16624,a)].">
      <j1 rule="hyper" parents="12617 16624"/>
    </justification>
  </clause>

  <clause id="16626">
    <literal><![CDATA[
      K(x,a(y,z,u) \ x) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(5005,a,16622,a)].">
      <j1 rule="hyper" parents="5005 16622"/>
    </justification>
  </clause>

  <clause id="16627">
    <literal><![CDATA[
      a(x,y,K(z,a(x,y,z) \ u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12729,a(flip),b,16626,a)].">
      <j1 rule="hyper" parents="63 12729 16626"/>
    </justification>
  </clause>

  <clause id="16628">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = a(z,y,u) * (x / a(z,y,u))
    ]]></literal>
    <justification jstring="[para(16627(a,1),12686(a,1,1))].">
      <j1 rule="para" parents="16627 12686"/>
    </justification>
  </clause>

  <clause id="16629">
    <literal><![CDATA[
      a(x,y,z) \ L(u,y,K(x,z)) = u / a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(14494,a,16628,a)].">
      <j1 rule="hyper" parents="14494 16628"/>
    </justification>
  </clause>

  <clause id="16630">
    <literal><![CDATA[
      L(x * a(y,z,u),z,K(y,u)) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(709,a,16629,a),flip(a)].">
      <j1 rule="hyper" parents="709 16629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16631">
    <literal><![CDATA[
      a(x,y,z) \ L(u,y,K(z,x)) = u / a(x,y,z)
    ]]></literal>
    <justification jstring="[para(14399(a,1),16629(a,1,2))].">
      <j1 rule="para" parents="14399 16629"/>
    </justification>
  </clause>

  <clause id="16632">
    <literal><![CDATA[
      T(x * a(y,z,u),a(u,z,y)) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(14386,a,16630,a)].">
      <j1 rule="hyper" parents="14386 16630"/>
    </justification>
  </clause>

  <clause id="16633">
    <literal><![CDATA[
      (a(x,y,z) * u) * a(x,y,z) = a(x,y,z) * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,16630,a(flip),b,14340,a)].">
      <j1 rule="hyper" parents="133 16630 14340"/>
    </justification>
  </clause>

  <clause id="16634">
    <literal><![CDATA[
      a(x,y,z) \ L(u * (1 / a(x,y,z)),y,K(z,x)) = u * ((1 / a(x,y,z)) / a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,6388,a(flip),b,16631,a),flip(a)].">
      <j1 rule="hyper" parents="347 6388 16631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16635">
    <literal><![CDATA[
      T(x * a(y,z,u),a(u,z,y)) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ (a(y,z,u) * x) = v5
    ]]></literal>
    <justification jstring="[para(16632(a,2),613(a,1))].">
      <j1 rule="para" parents="16632 613"/>
    </justification>
  </clause>

  <clause id="16636">
    <literal><![CDATA[
      L(a(x,y,z),u,a(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(12406,a,16633,a)].">
      <j1 rule="hyper" parents="12406 16633"/>
    </justification>
  </clause>

  <clause id="16637">
    <literal><![CDATA[
      a(x,y,z) \ L(u * (a(x,y,z) \ 1),y,K(z,x)) = u * ((1 / a(x,y,z)) / a(x,y,z))
    ]]></literal>
    <justification jstring="[para(12593(a,1),16634(a,1,2,1,2))].">
      <j1 rule="para" parents="12593 16634"/>
    </justification>
  </clause>

  <clause id="16638">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) \ 1) * u) = u * ((1 / a(x,y,z)) / a(x,y,z))
    ]]></literal>
    <justification jstring="[para(15421(a,1),16637(a,1,2))].">
      <j1 rule="para" parents="15421 16637"/>
    </justification>
  </clause>

  <clause id="16639">
    <literal><![CDATA[
      x * ((1 / a(y,z,u)) / a(y,z,u)) = (a(y,z,u) * a(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(524,a,16638,a),flip(a)].">
      <j1 rule="hyper" parents="524 16638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16640">
    <literal><![CDATA[
      x * ((a(y,z,u) \ 1) / a(y,z,u)) = (a(y,z,u) * a(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(12593(a,1),16639(a,1,2,1))].">
      <j1 rule="para" parents="12593 16639"/>
    </justification>
  </clause>

  <clause id="16641">
    <literal><![CDATA[
      x * (a(y,z,u) \ (1 / a(y,z,u))) = (a(y,z,u) * a(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(888(a,1),16640(a,1,2))].">
      <j1 rule="para" parents="888 16640"/>
    </justification>
  </clause>

  <clause id="16642">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * ((a(x,y,z) * a(x,y,z)) \ u) = T(u,a(x,y,z) \ (a(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(16641(a,1),12598(a,1,2))].">
      <j1 rule="para" parents="16641 12598"/>
    </justification>
  </clause>

  <clause id="16643">
    <literal><![CDATA[
      T(x,a(y,z,u) \ (a(y,z,u) \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(287,a,16642,a),flip(a)].">
      <j1 rule="hyper" parents="287 16642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16644">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ (u \ a(x,y,z)) = u \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,1120,a(flip),b,16642,a),flip(a)].">
      <j1 rule="hyper" parents="34 1120 16642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16645">
    <literal><![CDATA[
      T(x,a(y,z,u) \ (a(y,z,u) \ w)) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(13808,a,16643,a)].">
      <j1 rule="hyper" parents="13808 16643"/>
    </justification>
  </clause>

  <clause id="16647">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) = T(x,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(40,a,13847,a,b,16645,a),flip(a)].">
      <j1 rule="hyper" parents="40 13847 16645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16648">
    <literal><![CDATA[
      x / T(x,a(y,z,u) * w) = K(a(y,z,u) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(220,a,16647,a(flip),b,4939,a(flip))].">
      <j1 rule="hyper" parents="220 16647 4939"/>
    </justification>
  </clause>

  <clause id="16649">
    <literal><![CDATA[
      x \ T(x,a(y,z,u) * w) = K(x,a(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(128,a,16647,a(flip),b,4929,a(flip))].">
      <j1 rule="hyper" parents="128 16647 4929"/>
    </justification>
  </clause>

  <clause id="16650">
    <literal><![CDATA[
      K(a(x,y,z) \ u,w) = K(a(x,y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(5013,a,16648,a),flip(a)].">
      <j1 rule="hyper" parents="5013 16648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16651">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) = K(x,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(5006,a,16649,a),flip(a)].">
      <j1 rule="hyper" parents="5006 16649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16652">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,a(y,z,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(16649(a,1),5006(a,1))].">
      <j1 rule="para" parents="16649 5006"/>
    </justification>
  </clause>

  <clause id="16653">
    <literal><![CDATA[
      K(x,a(y,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(z,y,y) * u) = w
    ]]></literal>
    <justification jstring="[para(16056(a,1),16652(a,1))].">
      <j1 rule="para" parents="16056 16652"/>
    </justification>
  </clause>

  <clause id="16654">
    <literal><![CDATA[
      K(x,a(y,y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(z,y,y) * u) = w
    ]]></literal>
    <justification jstring="[para(16651(a,2),16653(a,1))].">
      <j1 rule="para" parents="16651 16653"/>
    </justification>
  </clause>

  <clause id="16655">
    <literal><![CDATA[
      K(x,L(y,z,z) * (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(y,z,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15326(a,2),16654(a,1))].">
      <j1 rule="para" parents="15326 16654"/>
    </justification>
  </clause>

  <clause id="16656">
    <literal><![CDATA[
      K(x,1 / (K(1 / y,y) \ R(1 / L(y,z,u),L(y,z,u),K(1 / y,y)))) = K(1 / y,y) \ ((1 / L(y,z,u)) * ((x * (1 / (1 / L(y,z,u)))) / x))
    ]]></literal>
    <justification jstring="[para(2218(a,1),8197(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2218 8197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16658">
    <literal><![CDATA[
      K(x,1 / (K(1 / y,y) \ R(1 / L(y,z,u),L(y,z,u),K(1 / y,y)))) = K(1 / y,y) \ ((1 / L(y,z,u)) * (1 / (1 / ((x * L(y,z,u)) / x))))
    ]]></literal>
    <justification jstring="[para(2844(a,1),16656(a,2,2,2))].">
      <j1 rule="para" parents="2844 16656"/>
    </justification>
  </clause>

  <clause id="16659">
    <literal><![CDATA[
      K(x,1 / (K(1 / y,y) \ R(1 / L(y,z,u),L(y,z,u),K(1 / y,y)))) = K(1 / y,y) \ ((T(L(y,z,u),x) \ 1) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11778(a,1),16658(a,2,2))].">
      <j1 rule="para" parents="11778 16658"/>
    </justification>
  </clause>

  <clause id="16660">
    <literal><![CDATA[
      K(x,1 / (K(1 / y,y) \ R(1 / L(y,z,u),L(y,z,u),K(1 / y,y)))) = K(y,1 / y) * ((T(L(y,z,u),x) \ 1) * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,5256,a(flip),b,16659,a),flip(a)].">
      <j1 rule="hyper" parents="347 5256 16659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16661">
    <literal><![CDATA[
      K(x,1 / (K(1 / y,y) \ R(1 / L(y,z,u),L(y,z,u),K(1 / y,y)))) = (T(L(y,z,u),x) \ 1) * L((y \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,6375,a(flip),b,16660,a),flip(a)].">
      <j1 rule="hyper" parents="347 6375 16660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16662">
    <literal><![CDATA[
      K(x,1 / (K(1 / y,y) \ (1 / L(y,z,u)))) = (T(L(y,z,u),x) \ 1) * L((y \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(2218(a,1),16661(a,1,2,2,2))].">
      <j1 rule="para" parents="2218 16661"/>
    </justification>
  </clause>

  <clause id="16664">
    <literal><![CDATA[
      K(x,1 / (K(y,1 / y) * (1 / L(y,z,u)))) = (T(L(y,z,u),x) \ 1) * L((y \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(5256(a,1),16662(a,1,2,2))].">
      <j1 rule="para" parents="5256 16662"/>
    </justification>
  </clause>

  <clause id="16665">
    <literal><![CDATA[
      (T(L(x,y,z),u) \ 1) * L((x \ 1) \ 1,y,z) = K(u,1 / (1 / (1 / (1 / L(x,y,z)))))
    ]]></literal>
    <justification jstring="[para(9737(a,1),16664(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9737 16664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16666">
    <literal><![CDATA[
      (T(L(x,y,z),u) \ 1) * L((x \ 1) \ 1,y,z) = K(u,T(L(x,y,z),1))
    ]]></literal>
    <justification jstring="[hyper(347,a,8483,a(flip),b,16665,a),flip(a)].">
      <j1 rule="hyper" parents="347 8483 16665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16667">
    <literal><![CDATA[
      (T(L(x,y,z),u) \ 1) * L((x \ 1) \ 1,y,z) = K(u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(223(a,1),16666(a,2,2))].">
      <j1 rule="para" parents="223 16666"/>
    </justification>
  </clause>

  <clause id="16668">
    <literal><![CDATA[
      K(T(x,y / (z / T(u,w))),L(v5,v6,v7)) = (T(L(v5,v6,v7),T(x,(u / z) * y)) \ 1) * L((v5 \ 1) \ 1,v6,v7)
    ]]></literal>
    <justification jstring="[para(16496(a,1),16667(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="16496 16667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16669">
    <literal><![CDATA[
      K(T(x,y / (z / T(u,w))),L(v5,v6,v7)) = K(T(x,(u / z) * y),L(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(347,a,16667,a(flip),b,16668,a),flip(a)].">
      <j1 rule="hyper" parents="347 16667 16668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16670">
    <literal><![CDATA[
      K(T(x,y / (z / T(u,w))),L(v5,v6,v7)) = K(x,T(L(v5,v6,v7),(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,7093,a(flip),b,16669,a),flip(a)].">
      <j1 rule="hyper" parents="347 7093 16669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16671">
    <literal><![CDATA[
      K(x,T(L(y,z,u),w / (v5 / T(v6,v7)))) = K(x,T(L(y,z,u),(v6 / v5) * w))
    ]]></literal>
    <justification jstring="[hyper(7488,a,16670,a)].">
      <j1 rule="hyper" parents="7488 16670"/>
    </justification>
  </clause>

  <clause id="16672">
    <literal><![CDATA[
      K(x,T(L(y,z,u),w / (v5 / v6))) = K(x,T(L(y,z,u),(v6 / v5) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16294,a(flip),b,16671,a)].">
      <j1 rule="hyper" parents="63 16294 16671"/>
    </justification>
  </clause>

  <clause id="16673">
    <literal><![CDATA[
      K(x,T(L(y,z,T(x,u)),(T(w,v5) / v6) * v7)) = K(x,T(y,v7 / (v6 / w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16295,a(flip),b,16672,a),flip(a)].">
      <j1 rule="hyper" parents="63 16295 16672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16674">
    <literal><![CDATA[
      K(x,T(y,(T(z,u) / w) * v5)) = K(x,T(y,v5 / (w / z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,8586,a(flip),b,16673,a)].">
      <j1 rule="hyper" parents="63 8586 16673"/>
    </justification>
  </clause>

  <clause id="16675">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[para(110(a,1),16674(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="110 16674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16677">
    <literal><![CDATA[
      K(x,T(y,z / (u \ w))) = K(x,T(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16137,a(flip),b,16675,a)].">
      <j1 rule="hyper" parents="63 16137 16675"/>
    </justification>
  </clause>

  <clause id="16678">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,(z / u) * w)) = K(x,T(y,w / (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,7267,a,b,16677,a)].">
      <j1 rule="hyper" parents="347 7267 16677"/>
    </justification>
  </clause>

  <clause id="16679">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(34,a,16164,a,b,16678,a)].">
      <j1 rule="hyper" parents="34 16164 16678"/>
    </justification>
  </clause>

  <clause id="16680">
    <literal><![CDATA[
      K(x,K(y,(z / u) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(8849,a,16679,a)].">
      <j1 rule="hyper" parents="8849 16679"/>
    </justification>
  </clause>

  <clause id="16681">
    <literal><![CDATA[
      K(x,K(y,((z / u) / z) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16189,a(flip),b,16679,a),flip(a)].">
      <j1 rule="hyper" parents="63 16189 16679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16682">
    <literal><![CDATA[
      K(x,K(y,(z / (z * u)) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16175,a(flip),b,16679,a),flip(a)].">
      <j1 rule="hyper" parents="63 16175 16679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16683">
    <literal><![CDATA[
      L(K(x,K(y,(z / u) * w)),v5,v6) = K(y,K(w / (z \ u),L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[para(16679(a,1),16224(a,1,1))].">
      <j1 rule="para" parents="16679 16224"/>
    </justification>
  </clause>

  <clause id="16684">
    <literal><![CDATA[
      K(x,K(y,z * (u / (u * w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[hyper(13498,a,16682,a)].">
      <j1 rule="hyper" parents="13498 16682"/>
    </justification>
  </clause>

  <clause id="16685">
    <literal><![CDATA[
      K(x,K(y,z / (u \ w))) = K(x,K(y,z * (u / w)))
    ]]></literal>
    <justification jstring="[para(10(a,1),16684(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 16684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16686">
    <literal><![CDATA[
      K(x,K(y / (z \ u),L(w,v5,v6))) = K(x,K((z / u) * y,L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(8962,a,16683,a),flip(a)].">
      <j1 rule="hyper" parents="8962 16683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16687">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(u * y) / (y * (y \ z))))
    ]]></literal>
    <justification jstring="[hyper(63,a,16257,a(flip),b,16686,a),flip(a)].">
      <j1 rule="hyper" parents="63 16257 16686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16688">
    <literal><![CDATA[
      K(x,K(((y / z) / y) * u,L(w,v5,v6))) = K(x,K(u / z,L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(83(a,1),16686(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="83 16686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16689">
    <literal><![CDATA[
      K(x,K(y * ((z / u) / z),L(w,v5,v6))) = K(x,K(y / u,L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(13499,a,16688,a)].">
      <j1 rule="hyper" parents="13499 16688"/>
    </justification>
  </clause>

  <clause id="16690">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(u * y) / z))
    ]]></literal>
    <justification jstring="[para(10(a,1),16687(a,2,2,2,2))].">
      <j1 rule="para" parents="10 16687"/>
    </justification>
  </clause>

  <clause id="16691">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(y * u) / z))
    ]]></literal>
    <justification jstring="[hyper(347,a,16184,a,b,16690,a),flip(a)].">
      <j1 rule="hyper" parents="347 16184 16690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16692">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,z,y))) = K(x,K(w,(y * ((v5 / u) / v5)) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16689,a(flip),b,16691,a)].">
      <j1 rule="hyper" parents="63 16689 16691"/>
    </justification>
  </clause>

  <clause id="16693">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,z,y))) = K(x,K(w,(y * (1 / u)) / z))
    ]]></literal>
    <justification jstring="[para(13224(a,1),16691(a,1,2))].">
      <j1 rule="para" parents="13224 16691"/>
    </justification>
  </clause>

  <clause id="16694">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,(u * y) / z)) = v5
    ]]></literal>
    <justification jstring="[para(16691(a,2),16230(a,1))].">
      <j1 rule="para" parents="16691 16230"/>
    </justification>
  </clause>

  <clause id="16695">
    <literal><![CDATA[
      K(x,K(y,(z * ((u / w) / u)) / v5)) = K(x,K(y,(z * (1 / w)) / v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,16693,a(flip),b,16692,a),flip(a)].">
      <j1 rule="hyper" parents="63 16693 16692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16696">
    <literal><![CDATA[
      K(x,K((y / z) / (1 / u),L(w,z,y))) = K(x,K(w,(T(y,u) / (1 / u)) / z))
    ]]></literal>
    <justification jstring="[para(3809(a,2),16692(a,2,2,2,1))].">
      <j1 rule="para" parents="3809 16692"/>
    </justification>
  </clause>

  <clause id="16697">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(T(y,u) / (1 / u)) / z))
    ]]></literal>
    <justification jstring="[para(13223(a,1),16696(a,1,2))].">
      <j1 rule="para" parents="13223 16696"/>
    </justification>
  </clause>

  <clause id="16698">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / (1 / u)) / w)) = K(x,K(y,(z * u) / w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16691,a(flip),b,16697,a),flip(a)].">
      <j1 rule="hyper" parents="63 16691 16697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16699">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / T(u,z)) * w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16680,a(flip),b,16698,a)].">
      <j1 rule="hyper" parents="63 16680 16698"/>
    </justification>
  </clause>

  <clause id="16700">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) / w))) = K(x,K(y,(w * u) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16233,a(flip),b,16699,a)].">
      <j1 rule="hyper" parents="63 16233 16699"/>
    </justification>
  </clause>

  <clause id="16701">
    <literal><![CDATA[
      K(x,K(y,((z \ 1) / u) * w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16270,a,b,16700,a)].">
      <j1 rule="hyper" parents="63 16270 16700"/>
    </justification>
  </clause>

  <clause id="16703">
    <literal><![CDATA[
      K(x,K(y,(z * (1 / u)) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16267,a(flip),b,16700,a),flip(a)].">
      <j1 rule="hyper" parents="63 16267 16700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16704">
    <literal><![CDATA[
      K(x,K(y,((z / (z / (u \ 1))) / w) * v5)) = K(x,K(y,(w * u) / v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,16252,a,b,16701,a)].">
      <j1 rule="hyper" parents="63 16252 16701"/>
    </justification>
  </clause>

  <clause id="16705">
    <literal><![CDATA[
      K(x,K(y,(z * ((u / w) / u)) / v5)) = K(x,K(y,(w / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,16695,a,b,16703,a)].">
      <j1 rule="hyper" parents="63 16695 16703"/>
    </justification>
  </clause>

  <clause id="16706">
    <literal><![CDATA[
      K(x,K(y,z / ((1 / u) * w))) = K(x,K(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16218,a(flip),b,16703,a)].">
      <j1 rule="hyper" parents="63 16218 16703"/>
    </justification>
  </clause>

  <clause id="16707">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,y / z,z))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14523,a,b,16706,a)].">
      <j1 rule="hyper" parents="63 14523 16706"/>
    </justification>
  </clause>

  <clause id="16708">
    <literal><![CDATA[
      K(x,K(y,((1 / z) * u) / (((1 / z) * u) * w))) = K(x,K(y,(z / u) * (((1 / z) * u) / w)))
    ]]></literal>
    <justification jstring="[para(7822(a,1),16706(a,1,2))].">
      <j1 rule="para" parents="7822 16706"/>
    </justification>
  </clause>

  <clause id="16709">
    <literal><![CDATA[
      K(x,K(y,((z / (z / ((u / z) \ 1))) / w) * v5)) = K(x,K(y,v5 / (((z / (z / u)) / z) * w)))
    ]]></literal>
    <justification jstring="[para(15224(a,1),16706(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="15224 16706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16710">
    <literal><![CDATA[
      K(x,K(y,z / (((u / w) / u) * v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16218,a(flip),b,16705,a)].">
      <j1 rule="hyper" parents="63 16218 16705"/>
    </justification>
  </clause>

  <clause id="16711">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,y,z))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15156,a(flip),b,16707,a)].">
      <j1 rule="hyper" parents="63 15156 16707"/>
    </justification>
  </clause>

  <clause id="16712">
    <literal><![CDATA[
      K(x,K(y,(z / u) * (((1 / z) * u) / (((1 / z) * u) * w)))) = K(x,K(y,1 / (w * ((1 / z) * u))))
    ]]></literal>
    <justification jstring="[para(14289(a,1),16708(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14289 16708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16713">
    <literal><![CDATA[
      K(x,K(y,((z / (z / ((u / z) \ 1))) / w) * v5)) = K(x,K(y,((z / u) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,16710,a(flip),b,16709,a),flip(a)].">
      <j1 rule="hyper" parents="347 16710 16709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16715">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) / v5)) = K(x,K(y,((w / u) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,16704,a(flip),b,16713,a)].">
      <j1 rule="hyper" parents="63 16704 16713"/>
    </justification>
  </clause>

  <clause id="16716">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) / v5)) = K(x,K(y,((u / z) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(16230,a,16715,a)].">
      <j1 rule="hyper" parents="16230 16715"/>
    </justification>
  </clause>

  <clause id="16718">
    <literal><![CDATA[
      K(x,K(y,z / ((u \ w) * v5))) = K(x,K(y,((u / w) / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16254,a(flip),b,16715,a)].">
      <j1 rule="hyper" parents="63 16254 16715"/>
    </justification>
  </clause>

  <clause id="16719">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * w) / v5)) = K(x,K(y,((z / u) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(8849,a,16718,a)].">
      <j1 rule="hyper" parents="8849 16718"/>
    </justification>
  </clause>

  <clause id="16720">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(y,z,K(x,K(w,u / z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16445,a(flip),b,16719,a),flip(a)].">
      <j1 rule="hyper" parents="63 16445 16719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16721">
    <literal><![CDATA[
      K(x,K(y,(z * u) * ((w / u) / (z * w)))) = a(x,w,K(y,K(z,u / w)))
    ]]></literal>
    <justification jstring="[hyper(13489,a,16720,a)].">
      <j1 rule="hyper" parents="13489 16720"/>
    </justification>
  </clause>

  <clause id="16722">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(x,z,K(y,K(w,u / z)))
    ]]></literal>
    <justification jstring="[hyper(7281,a,16720,a)].">
      <j1 rule="hyper" parents="7281 16720"/>
    </justification>
  </clause>

  <clause id="16723">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(y,(u / z) * z,K(x,K(w,u / z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,14273,a,b,16720,a),flip(a)].">
      <j1 rule="hyper" parents="347 14273 16720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16724">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(x,u,K(y,K(z / u,w / u)))
    ]]></literal>
    <justification jstring="[para(12(a,1),16721(a,1,2,2,2,2))].">
      <j1 rule="para" parents="12 16721"/>
    </justification>
  </clause>

  <clause id="16725">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(y,u,K(x,K(w,u / z)))
    ]]></literal>
    <justification jstring="[para(12(a,1),16723(a,2,2))].">
      <j1 rule="para" parents="12 16723"/>
    </justification>
  </clause>

  <clause id="16726">
    <literal><![CDATA[
      K(x,K(y,(z / u) * (((1 / z) * u) / (((1 / z) * u) * w)))) = K(x,K(y,w * ((1 / z) * u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,8822,a(flip),b,16712,a),flip(a)].">
      <j1 rule="hyper" parents="347 8822 16712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16727">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(u / w) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16684,a(flip),b,16726,a),flip(a)].">
      <j1 rule="hyper" parents="63 16684 16726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16729">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,16680,a(flip),b,16727,a),flip(a)].">
      <j1 rule="hyper" parents="347 16680 16727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16730">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[para(291(a,1),16729(a,1,2,2,2))].">
      <j1 rule="para" parents="291 16729"/>
    </justification>
  </clause>

  <clause id="16731">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,16170,a(flip),b,16730,a),flip(a)].">
      <j1 rule="hyper" parents="347 16170 16730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16733">
    <literal><![CDATA[
      K(x,K(y,R(z / u,w,v5) * (w * v5))) = K(x,K(y,(((1 / u) * z) * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,16467,a(flip),b,16731,a),flip(a)].">
      <j1 rule="hyper" parents="63 16467 16731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16735">
    <literal><![CDATA[
      K(x,K(y,(((1 / z) * u) * w) * v5)) = K(x,K(y,((u / z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(107(a,1),16733(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 16733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16736">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) * v5)) = K(x,K(y,((w / u) * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,16173,a,b,16735,a)].">
      <j1 rule="hyper" parents="63 16173 16735"/>
    </justification>
  </clause>

  <clause id="16737">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * T(v5,v6))) = K(x,K(y,v5 * (w * ((1 / u) * z))))
    ]]></literal>
    <justification jstring="[hyper(16212,a,16736,a),flip(a)].">
      <j1 rule="hyper" parents="16212 16736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16738">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((w / u) * z) * (1 / v5)))
    ]]></literal>
    <justification jstring="[hyper(13785,a,16736,a)].">
      <j1 rule="hyper" parents="13785 16736"/>
    </justification>
  </clause>

  <clause id="16739">
    <literal><![CDATA[
      K(x,K(y,z * (u * ((1 / w) * v5)))) = K(x,K(y,z * ((v5 / w) * u)))
    ]]></literal>
    <justification jstring="[hyper(16212,a,16737,a),flip(a)].">
      <j1 rule="hyper" parents="16212 16737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16740">
    <literal><![CDATA[
      K(x,K(y,z * (((1 / u) * w) * v5))) = K(x,K(y,z * ((w / u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(16215,a,16739,a)].">
      <j1 rule="hyper" parents="16215 16739"/>
    </justification>
  </clause>

  <clause id="16741">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((w / u) * z) / v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,12735,a(flip),b,16738,a),flip(a)].">
      <j1 rule="hyper" parents="347 12735 16738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16742">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((u / w) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,16716,a(flip),b,16741,a),flip(a)].">
      <j1 rule="hyper" parents="347 16716 16741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16743">
    <literal><![CDATA[
      K(x,K(y,z / (u * ((1 / w) * v5)))) = K(x,K(y,((w / v5) / u) * z))
    ]]></literal>
    <justification jstring="[hyper(8849,a,16742,a)].">
      <j1 rule="hyper" parents="8849 16742"/>
    </justification>
  </clause>

  <clause id="16744">
    <literal><![CDATA[
      K(x,K(y,((z / u) / w) * ((w * (1 / z)) * u))) = K(x,K(y,a(w,1 / z,u)))
    ]]></literal>
    <justification jstring="[para(13371(a,2),16743(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13371 16743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16745">
    <literal><![CDATA[
      K(x,K(y,((z / u) / w) * ((w * (1 / z)) * u))) = a(x,1 / z,K(y,K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,14158,a,b,16744,a),flip(a)].">
      <j1 rule="hyper" parents="347 14158 16744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16746">
    <literal><![CDATA[
      K(x,K(y,((z / u) / w) * ((w * (1 / z)) * u))) = a(u,z,K(y,K(w,x)))
    ]]></literal>
    <justification jstring="[hyper(347,a,16589,a(flip),b,16745,a),flip(a)].">
      <j1 rule="hyper" parents="347 16589 16745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16747">
    <literal><![CDATA[
      K(x,K(y,((z / u) / w) * ((w * (1 / z)) * u))) = a(u,z,K(x,K(y,w)))
    ]]></literal>
    <justification jstring="[para(7283(a,1),16746(a,2,3))].">
      <j1 rule="para" parents="7283 16746"/>
    </justification>
  </clause>

  <clause id="16748">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (1 / (K(w,1 / z) / w))) * (((1 / z) * (1 / (1 / w))) * u))) = a(u,z,K(x,K(y,1 / (K(w,1 / z) / w))))
    ]]></literal>
    <justification jstring="[para(5550(a,1),16747(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5550 16747"/>
    </justification>
  </clause>

  <clause id="16749">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (1 / (K(w,1 / z) / w))) * (((1 / z) * w) * u))) = a(u,z,K(x,K(y,1 / (K(w,1 / z) / w))))
    ]]></literal>
    <justification jstring="[para(6951(a,1),16748(a,1,2))].">
      <j1 rule="para" parents="6951 16748"/>
    </justification>
  </clause>

  <clause id="16750">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * K(1 / z,w))) * (((1 / z) * w) * u))) = a(u,z,K(x,K(y,1 / (K(w,1 / z) / w))))
    ]]></literal>
    <justification jstring="[para(13151(a,1),16749(a,1,2))].">
      <j1 rule="para" parents="13151 16749"/>
    </justification>
  </clause>

  <clause id="16751">
    <literal><![CDATA[
      K(x,K(y,(((z / u) / w) * K(w,1 / z)) * (((1 / z) * w) * u))) = a(u,z,K(x,K(y,1 / (K(w,1 / z) / w))))
    ]]></literal>
    <justification jstring="[para(6217(a,1),16750(a,1,2,2,1))].">
      <j1 rule="para" parents="6217 16750"/>
    </justification>
  </clause>

  <clause id="16752">
    <literal><![CDATA[
      K(x,K(y,(((z / u) / w) * K(w,1 / z)) * ((w / z) * u))) = a(u,z,K(x,K(y,1 / (K(w,1 / z) / w))))
    ]]></literal>
    <justification jstring="[hyper(63,a,16740,a(flip),b,16751,a)].">
      <j1 rule="hyper" parents="63 16740 16751"/>
    </justification>
  </clause>

  <clause id="16753">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(w,u,K(x,K(y,1 / (K(z,1 / u) / z))))
    ]]></literal>
    <justification jstring="[hyper(16228,a,16752,a)].">
      <j1 rule="hyper" parents="16228 16752"/>
    </justification>
  </clause>

  <clause id="16755">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(w,u,K(x,K(y,z * K(1 / u,z))))
    ]]></literal>
    <justification jstring="[para(6153(a,1),16753(a,2,3,2))].">
      <j1 rule="para" parents="6153 16753"/>
    </justification>
  </clause>

  <clause id="16756">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(w,u,K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(16168(a,1),16755(a,2,3))].">
      <j1 rule="para" parents="16168 16755"/>
    </justification>
  </clause>

  <clause id="16757">
    <literal><![CDATA[
      a(x,y,K(z,K(u / y,w / y))) = a(w,y,K(x,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16724,a(flip),b,16756,a)].">
      <j1 rule="hyper" parents="63 16724 16756"/>
    </justification>
  </clause>

  <clause id="16759">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(y,w / (y \ z)))) = a(w,y \ z,K(x,K(u,z)))
    ]]></literal>
    <justification jstring="[para(80(a,1),16757(a,1,3,2,1))].">
      <j1 rule="para" parents="80 16757"/>
    </justification>
  </clause>

  <clause id="16760">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(y,w * (y / z)))) = a(w,y \ z,K(x,K(u,z)))
    ]]></literal>
    <justification jstring="[para(16685(a,1),16759(a,1,3))].">
      <j1 rule="para" parents="16685 16759"/>
    </justification>
  </clause>

  <clause id="16761">
    <literal><![CDATA[
      a(x,y \ z,K(y,K(u,w * (y / z)))) = a(w,y \ z,K(x,K(u,z)))
    ]]></literal>
    <justification jstring="[para(7279(a,1),16760(a,1,3))].">
      <j1 rule="para" parents="7279 16760"/>
    </justification>
  </clause>

  <clause id="16762">
    <literal><![CDATA[
      a(x,y \ z,K(y,K(u,w / z))) = a(w,y \ z,K(x,K(u,z)))
    ]]></literal>
    <justification jstring="[para(16281(a,1),16761(a,1,3))].">
      <j1 rule="para" parents="16281 16761"/>
    </justification>
  </clause>

  <clause id="16763">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(w,z))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14269,a(flip),b,16762,a),flip(a)].">
      <j1 rule="hyper" parents="63 14269 16762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16764">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(z,w))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[para(7293(a,1),16763(a,1,3))].">
      <j1 rule="para" parents="7293 16763"/>
    </justification>
  </clause>

  <clause id="16765">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(u,y,K(z,K(w,x / y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16568,a,b,16764,a)].">
      <j1 rule="hyper" parents="63 16568 16764"/>
    </justification>
  </clause>

  <clause id="16766">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(y,z,K(x,K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16591,a(flip),b,16765,a),flip(a)].">
      <j1 rule="hyper" parents="63 16591 16765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16767">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(y,z,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(7279(a,1),16766(a,2,3))].">
      <j1 rule="para" parents="7279 16766"/>
    </justification>
  </clause>

  <clause id="16768">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(u,K(x,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16722,a,b,16767,a)].">
      <j1 rule="hyper" parents="63 16722 16767"/>
    </justification>
  </clause>

  <clause id="16769">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(x,K(w,u)))
    ]]></literal>
    <justification jstring="[para(7283(a,2),16768(a,2,3))].">
      <j1 rule="para" parents="7283 16768"/>
    </justification>
  </clause>

  <clause id="16770">
    <literal><![CDATA[
      a(x,y,K(z,K(u,y / w))) = a(w,x,K(z,K(u,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16725,a(flip),b,16769,a)].">
      <j1 rule="hyper" parents="63 16725 16769"/>
    </justification>
  </clause>

  <clause id="16771">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(u,y)))
    ]]></literal>
    <justification jstring="[para(8823(a,1),16770(a,1,3))].">
      <j1 rule="para" parents="8823 16770"/>
    </justification>
  </clause>

  <clause id="16772">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(y,u)))
    ]]></literal>
    <justification jstring="[para(7293(a,1),16771(a,2,3))].">
      <j1 rule="para" parents="7293 16771"/>
    </justification>
  </clause>

  <clause id="16773">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,z,K(x,K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16767,a(flip),b,16772,a),flip(a)].">
      <j1 rule="hyper" parents="63 16767 16772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16774">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) * K(z,K(x,w)) = L(K(z,K(x,w)),u,y)
    ]]></literal>
    <justification jstring="[para(16773(a,1),14140(a,1,1))].">
      <j1 rule="para" parents="16773 14140"/>
    </justification>
  </clause>

  <clause id="16775">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) * K(x,K(z,w)) = L(K(z,K(x,w)),u,y)
    ]]></literal>
    <justification jstring="[para(7279(a,1),16774(a,1,2))].">
      <j1 rule="para" parents="7279 16774"/>
    </justification>
  </clause>

  <clause id="16776">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(z,L(y,w,u)))
    ]]></literal>
    <justification jstring="[hyper(14651,a,16775,a),flip(a)].">
      <j1 rule="hyper" parents="14651 16775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16777">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,L(z,w,u)))
    ]]></literal>
    <justification jstring="[hyper(8958,a,16776,a)].">
      <j1 rule="hyper" parents="8958 16776"/>
    </justification>
  </clause>

  <clause id="16778">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,16711,a(flip),b,16777,a),flip(a)].">
      <j1 rule="hyper" parents="347 16711 16777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16779">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,v5 \ ((v5 / (w * u)) * (w * (u * z)))))
    ]]></literal>
    <justification jstring="[para(894(a,1),16777(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="894 16777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16780">
    <literal><![CDATA[
      K(x,K(y,L(L(1 / z,z,u),w,u * z))) = K(x,K(y,1 / L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(6411(a,1),16777(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6411 16777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16781">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(z / w) * u))
    ]]></literal>
    <justification jstring="[hyper(16694,a,16778,a)].">
      <j1 rule="hyper" parents="16694 16778"/>
    </justification>
  </clause>

  <clause id="16782">
    <literal><![CDATA[
      K(x,K(y,L(L(1 / z,z,u),w,u * z))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,8822,a(flip),b,16780,a),flip(a)].">
      <j1 rule="hyper" parents="347 8822 16780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16783">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,((v5 / (w * u)) * (w * (u * z))) / v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,13512,a,b,16779,a),flip(a)].">
      <j1 rule="hyper" parents="347 13512 16779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16784">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,((v5 / (w * u)) / v5) * (w * (u * z))))
    ]]></literal>
    <justification jstring="[hyper(347,a,16781,a(flip),b,16783,a),flip(a)].">
      <j1 rule="hyper" parents="347 16781 16783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16785">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,(w * (u * z)) / (w * u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,16681,a(flip),b,16784,a),flip(a)].">
      <j1 rule="hyper" parents="347 16681 16784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16788">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,T(L(z,u,w),w * u)))
    ]]></literal>
    <justification jstring="[para(7462(a,1),16785(a,2,2))].">
      <j1 rule="para" parents="7462 16785"/>
    </justification>
  </clause>

  <clause id="16789">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,13502,a(flip),b,16788,a),flip(a)].">
      <j1 rule="hyper" parents="347 13502 16788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16792">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5,w * u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15156,a(flip),b,16789,a)].">
      <j1 rule="hyper" parents="63 15156 16789"/>
    </justification>
  </clause>

  <clause id="16794">
    <literal><![CDATA[
      K(x,K(y,L(1 / z,z,u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16782,a(flip),b,16792,a),flip(a)].">
      <j1 rule="hyper" parents="63 16782 16792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16796">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,1 / z))
    ]]></literal>
    <justification jstring="[para(6287(a,1),16794(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6287 16794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16798">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,8828,a(flip),b,16796,a),flip(a)].">
      <j1 rule="hyper" parents="347 8828 16796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16799">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,8822,a(flip),b,16796,a),flip(a)].">
      <j1 rule="hyper" parents="347 8822 16796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16802">
    <literal><![CDATA[
      (x * y) * K(z,K(u,w)) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(16798(a,1),8924(a,1,2))].">
      <j1 rule="para" parents="16798 8924"/>
    </justification>
  </clause>

  <clause id="16812">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(132,a,16799,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 16799 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16813">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = x * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,16799,a(flip),b,4924,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 16799 4924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16814">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,L(z,u,w) / y) = K(x,y \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(16799(a,1),8944(a,1,1))].">
      <j1 rule="para" parents="16799 8944"/>
    </justification>
  </clause>

  <clause id="16815">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(16799(a,1),13550(a,1,1))].">
      <j1 rule="para" parents="16799 13550"/>
    </justification>
  </clause>

  <clause id="16816">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(14081(a,2),16799(a,1,2))].">
      <j1 rule="para" parents="14081 16799"/>
    </justification>
  </clause>

  <clause id="16817">
    <literal><![CDATA[
      T(x * (T(y,x) * K(z,u)),K(z,u)) = K(z,L(u,y,x)) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(11163,a,16812,a),flip(a)].">
      <j1 rule="hyper" parents="11163 16812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16819">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,L(x,u,w))) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,7336,a(flip),b,16812,a),flip(a)].">
      <j1 rule="hyper" parents="347 7336 16812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16821">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8933,a,b,16812,a)].">
      <j1 rule="hyper" parents="63 8933 16812"/>
    </justification>
  </clause>

  <clause id="16822">
    <literal><![CDATA[
      K(x,L(y,z,u)) * T(w,K(x,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      w * K(x,L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(16812(a,1),315(a,1,2))].">
      <j1 rule="para" parents="16812 315"/>
    </justification>
  </clause>

  <clause id="16824">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8917,a,b,16816,a)].">
      <j1 rule="hyper" parents="63 8917 16816"/>
    </justification>
  </clause>

  <clause id="16827">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(14049,a,16821,a)].">
      <j1 rule="hyper" parents="14049 16821"/>
    </justification>
  </clause>

  <clause id="16829">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,14364,a(flip),b,16821,a),flip(a)].">
      <j1 rule="hyper" parents="40 14364 16821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16832">
    <literal><![CDATA[
      T(x,L(y,z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(14451,a,16827,a)].">
      <j1 rule="hyper" parents="14451 16827"/>
    </justification>
  </clause>

  <clause id="16833">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(1852,a,16827,a),flip(a)].">
      <j1 rule="hyper" parents="1852 16827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16836">
    <literal><![CDATA[
      a(K(x,y),z,K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,16827,a(flip),b,14059,a),flip(a)].">
      <j1 rule="hyper" parents="129 16827 14059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16837">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      w * a(x,y,K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(16827(a,1),315(a,1,2))].">
      <j1 rule="para" parents="16827 315"/>
    </justification>
  </clause>

  <clause id="16839">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w))) = x
    ]]></literal>
    <justification jstring="[para(12651(a,1),16827(a,1,2))].">
      <j1 rule="para" parents="12651 16827"/>
    </justification>
  </clause>

  <clause id="16840">
    <literal><![CDATA[
      T(x,K(a(y,z,u),w)) = x
    ]]></literal>
    <justification jstring="[para(12681(a,1),16827(a,1,2))].">
      <j1 rule="para" parents="12681 16827"/>
    </justification>
  </clause>

  <clause id="16841">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w) \ z)) = x
    ]]></literal>
    <justification jstring="[para(14009(a,2),16827(a,1,2))].">
      <j1 rule="para" parents="14009 16827"/>
    </justification>
  </clause>

  <clause id="16842">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(16827(a,1),14423(a,1))].">
      <j1 rule="para" parents="16827 14423"/>
    </justification>
  </clause>

  <clause id="16844">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(14440,a,16829,a)].">
      <j1 rule="hyper" parents="14440 16829"/>
    </justification>
  </clause>

  <clause id="16845">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) = L(x,y,w * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(10573,a,16829,a),flip(a)].">
      <j1 rule="hyper" parents="10573 16829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16846">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = K(x,K(y,z)) * (u * w)
    ]]></literal>
    <justification jstring="[hyper(1362,a,16829,a),flip(a)].">
      <j1 rule="hyper" parents="1362 16829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16847">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = u \ (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(651,a,16829,a),flip(a)].">
      <j1 rule="hyper" parents="651 16829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16849">
    <literal><![CDATA[
      L(x,y,K(z,u) / w) = L(x,y,w \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14457,a(flip),b,16829,a)].">
      <j1 rule="hyper" parents="63 14457 16829"/>
    </justification>
  </clause>

  <clause id="16851">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) / w = K(x,K(y,z)) * (u / w)
    ]]></literal>
    <justification jstring="[hyper(220,a,16829,a(flip),b,9645,a(flip))].">
      <j1 rule="hyper" parents="220 16829 9645"/>
    </justification>
  </clause>

  <clause id="16852">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = (K(x,K(y,z)) \ u) * w
    ]]></literal>
    <justification jstring="[para(16829(a,1),538(a,1,2,2))].">
      <j1 rule="para" parents="16829 538"/>
    </justification>
  </clause>

  <clause id="16853">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ ((K(x,K(y,z)) * u) * (w * v5)) = L(v5,L(w,u,K(x,K(y,z))),K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(16829(a,1),541(a,1,2,2,1))].">
      <j1 rule="para" parents="16829 541"/>
    </justification>
  </clause>

  <clause id="16854">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * (w * v5))) \ ((x * (K(y,K(z,u)) * w)) * v5) = a(x,K(y,K(z,u)) * w,L(v5,w,K(y,K(z,u))))
    ]]></literal>
    <justification jstring="[para(16829(a,1),539(a,1,2,2))].">
      <j1 rule="para" parents="16829 539"/>
    </justification>
  </clause>

  <clause id="16855">
    <literal><![CDATA[
      x \ (y * K(z,K(u,w))) = (x \ y) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[para(16829(a,1),14376(a,1,1))].">
      <j1 rule="para" parents="16829 14376"/>
    </justification>
  </clause>

  <clause id="16856">
    <literal><![CDATA[
      K(x,(y * K(z,K(u,w))) / (T(K(z,K(u,w)) \ v5,v6) * K(z,K(u,w)))) = K(x,y / T(v5 * K(z,K(u,w)),v6))
    ]]></literal>
    <justification jstring="[para(16829(a,1),15407(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16829 15407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16858">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11128,a,16836,a)].">
      <j1 rule="hyper" parents="11128 16836"/>
    </justification>
  </clause>

  <clause id="16859">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,w) = K(x,y) * (z * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(1093,a,16836,a)].">
      <j1 rule="hyper" parents="1093 16836"/>
    </justification>
  </clause>

  <clause id="16861">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(52,a,16836,a)].">
      <j1 rule="hyper" parents="52 16836"/>
    </justification>
  </clause>

  <clause id="16862">
    <literal><![CDATA[
      K(x,y) \ (z * K(u,w)) = (K(x,y) \ z) * K(u,w)
    ]]></literal>
    <justification jstring="[hyper(189,a,14704,a,b,16836,a(flip))].">
      <j1 rule="hyper" parents="189 14704 16836"/>
    </justification>
  </clause>

  <clause id="16863">
    <literal><![CDATA[
      T(1 * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(16836(a,1),16596(a,1,1,1))].">
      <j1 rule="para" parents="16836 16596"/>
    </justification>
  </clause>

  <clause id="16864">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = T(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10367,a,16839,a)].">
      <j1 rule="hyper" parents="10367 16839"/>
    </justification>
  </clause>

  <clause id="16866">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7763,a,16839,a)].">
      <j1 rule="hyper" parents="7763 16839"/>
    </justification>
  </clause>

  <clause id="16867">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(7539,a,16839,a)].">
      <j1 rule="hyper" parents="7539 16839"/>
    </justification>
  </clause>

  <clause id="16871">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(16839(a,1),49(a,2))].">
      <j1 rule="para" parents="16839 49"/>
    </justification>
  </clause>

  <clause id="16872">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(16839(a,1),6819(a,2))].">
      <j1 rule="para" parents="16839 6819"/>
    </justification>
  </clause>

  <clause id="16873">
    <literal><![CDATA[
      T(x,y / a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,a(z,u,w) \ y) = v5
    ]]></literal>
    <justification jstring="[para(16839(a,1),8886(a,1,1))].">
      <j1 rule="para" parents="16839 8886"/>
    </justification>
  </clause>

  <clause id="16874">
    <literal><![CDATA[
      T(x,y * a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,a(z,u,w) * y) = v5
    ]]></literal>
    <justification jstring="[para(16839(a,1),10367(a,1))].">
      <j1 rule="para" parents="16839 10367"/>
    </justification>
  </clause>

  <clause id="16875">
    <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(16839(a,1),10398(a,1,1))].">
      <j1 rule="para" parents="16839 10398"/>
    </justification>
  </clause>

  <clause id="16876">
    <literal><![CDATA[
      x \ T(y * x,K(a(z,u,w),v5)) = T(y,K(v5,a(z,u,w)) * x)
    ]]></literal>
    <justification jstring="[para(16839(a,1),15501(a,1,2,1,2))].">
      <j1 rule="para" parents="16839 15501"/>
    </justification>
  </clause>

  <clause id="16877">
    <literal><![CDATA[
      ((x * L(x \ y,z,u)) \ y) \ y = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,15369,a(flip),b,16832,a)].">
      <j1 rule="hyper" parents="63 15369 16832"/>
    </justification>
  </clause>

  <clause id="16878">
    <literal><![CDATA[
      L(x,y,K(z,u)) * T(w,x) != v5
    ]]></literal>
    <literal><![CDATA[
      w * L(x,y,K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(16832(a,1),315(a,1,2))].">
      <j1 rule="para" parents="16832 315"/>
    </justification>
  </clause>

  <clause id="16880">
    <literal><![CDATA[
      T(x,L(y,z,T(u,w))) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(6642(a,1),16832(a,1,2))].">
      <j1 rule="para" parents="6642 16832"/>
    </justification>
  </clause>

  <clause id="16881">
    <literal><![CDATA[
      ((x * y) * ((K(y,x) * z) * u)) / T((y * x) * z,u) = L(u,z,x * y)
    ]]></literal>
    <justification jstring="[para(16832(a,1),15212(a,1,2))].">
      <j1 rule="para" parents="16832 15212"/>
    </justification>
  </clause>

  <clause id="16882">
    <literal><![CDATA[
      K(L(x,y,z) \ x,T(u,w)) = K(L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(8213,a,16841,a)].">
      <j1 rule="hyper" parents="8213 16841"/>
    </justification>
  </clause>

  <clause id="16883">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w) \ z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7763,a,16841,a)].">
      <j1 rule="hyper" parents="7763 16841"/>
    </justification>
  </clause>

  <clause id="16884">
    <literal><![CDATA[
      T(x,K(L(y,z,u) \ y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(16841(a,1),7538(a,1,1))].">
      <j1 rule="para" parents="16841 7538"/>
    </justification>
  </clause>

  <clause id="16886">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) \ w) = K(x,u \ (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15083,a(flip),b,16858,a)].">
      <j1 rule="hyper" parents="63 15083 16858"/>
    </justification>
  </clause>

  <clause id="16888">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,u \ (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(5277(a,1),16858(a,1,2))].">
      <j1 rule="para" parents="5277 16858"/>
    </justification>
  </clause>

  <clause id="16889">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(6642(a,1),16858(a,1,2))].">
      <j1 rule="para" parents="6642 16858"/>
    </justification>
  </clause>

  <clause id="16890">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(14348(a,1),16858(a,1,2))].">
      <j1 rule="para" parents="14348 16858"/>
    </justification>
  </clause>

  <clause id="16891">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y / (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(14372(a,1),16858(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14372 16858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16892">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(16858(a,1),15077(a,1))].">
      <j1 rule="para" parents="16858 15077"/>
    </justification>
  </clause>

  <clause id="16893">
    <literal><![CDATA[
      K(x,T(y,z \ L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(16625(a,2),16858(a,1,2))].">
      <j1 rule="para" parents="16625 16858"/>
    </justification>
  </clause>

  <clause id="16894">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K(z \ (K(y,x) * u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,7026,a(flip),b,16861,a),flip(a)].">
      <j1 rule="hyper" parents="63 7026 16861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16897">
    <literal><![CDATA[
      (K(x,y) * z) * L(K(u,w),v5,v6) = K(x,y) * (z * L(K(u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(16861(a,1),474(a,1,2,1))].">
      <j1 rule="para" parents="16861 474"/>
    </justification>
  </clause>

  <clause id="16898">
    <literal><![CDATA[
      T(x * K(y,z),a(u,w,x)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(16861(a,1),14362(a,2,2))].">
      <j1 rule="para" parents="16861 14362"/>
    </justification>
  </clause>

  <clause id="16899">
    <literal><![CDATA[
      (L(K(x,y),z,u) * w) * K(v5,v6) = L(K(x,y),z,u) * (w * K(v5,v6))
    ]]></literal>
    <justification jstring="[para(16861(a,1),14114(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="16861 14114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16901">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ T(y,x)) = a(z,u,w) \ y
    ]]></literal>
    <justification jstring="[hyper(133,a,16866,a(flip),b,13246,a)].">
      <j1 rule="hyper" parents="133 16866 13246"/>
    </justification>
  </clause>

  <clause id="16903">
    <literal><![CDATA[
      K(x / a(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(a(y,z,u) \ x,w) = v5
    ]]></literal>
    <justification jstring="[para(16866(a,1),7481(a,1))].">
      <j1 rule="para" parents="16866 7481"/>
    </justification>
  </clause>

  <clause id="16904">
    <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(16866(a,1),7491(a,1))].">
      <j1 rule="para" parents="16866 7491"/>
    </justification>
  </clause>

  <clause id="16905">
    <literal><![CDATA[
      K(a(x,y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u * a(x,y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(16866(a,1),10383(a,1))].">
      <j1 rule="para" parents="16866 10383"/>
    </justification>
  </clause>

  <clause id="16906">
    <literal><![CDATA[
      K(x,y * a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,a(z,u,w) * y) = v5
    ]]></literal>
    <justification jstring="[para(16866(a,1),10406(a,1))].">
      <j1 rule="para" parents="16866 10406"/>
    </justification>
  </clause>

  <clause id="16907">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ 1) = a(z,u,w) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(16866(a,1),13015(a,1,1))].">
      <j1 rule="para" parents="16866 13015"/>
    </justification>
  </clause>

  <clause id="16908">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ x) = a(z,u,w) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(16866(a,1),13104(a,1,1))].">
      <j1 rule="para" parents="16866 13104"/>
    </justification>
  </clause>

  <clause id="16909">
    <literal><![CDATA[
      T(K(x,T(y,a(z,u,w))) * (v5 / T(y,a(z,u,w))),y) = T(T(y,a(z,u,w)),x) \ v5
    ]]></literal>
    <justification jstring="[hyper(63,a,7678,a(flip),b,16867,a),flip(a)].">
      <j1 rule="hyper" parents="63 7678 16867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16910">
    <literal><![CDATA[
      R(x,y,T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(14371(a,1),16842(a,1))].">
      <j1 rule="para" parents="14371 16842"/>
    </justification>
  </clause>

  <clause id="16911">
    <literal><![CDATA[
      L(x,y,z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,w) * z) = v5
    ]]></literal>
    <justification jstring="[para(14492(a,1),16842(a,1))].">
      <j1 rule="para" parents="14492 16842"/>
    </justification>
  </clause>

  <clause id="16912">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) = L(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11187,a(flip),b,16844,a),flip(a)].">
      <j1 rule="hyper" parents="63 11187 16844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16913">
    <literal><![CDATA[
      L(x,y,K(z,u) * (w * z)) = L(x,y,w * T(z,u))
    ]]></literal>
    <justification jstring="[para(6191(a,1),16844(a,1,3))].">
      <j1 rule="para" parents="6191 16844"/>
    </justification>
  </clause>

  <clause id="16916">
    <literal><![CDATA[
      K(x,T(y * L(z,u,w),z)) = K(x,L(z,u,w) * y)
    ]]></literal>
    <justification jstring="[hyper(10406,a,16890,a),flip(a)].">
      <j1 rule="hyper" parents="10406 16890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16918">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) = K(x,T(y,u \ (z \ w)))
    ]]></literal>
    <justification jstring="[para(329(a,1),16890(a,1,2,2))].">
      <j1 rule="para" parents="329 16890"/>
    </justification>
  </clause>

  <clause id="16920">
    <literal><![CDATA[
      K(L(x,y,z) \ u,T(w,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u / L(x,y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(16890(a,1),7485(a,1))].">
      <j1 rule="para" parents="16890 7485"/>
    </justification>
  </clause>

  <clause id="16921">
    <literal><![CDATA[
      K(x,T(y,(z / u) / w)) = K(x,T(y,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(14124(a,1),16890(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14124 16890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16922">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = K(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(10406,a,16893,a)].">
      <j1 rule="hyper" parents="10406 16893"/>
    </justification>
  </clause>

  <clause id="16923">
    <literal><![CDATA[
      T(a(x,y,z) \ u,T(w,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(a(x,y,z) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(7553(a,2),16872(a,1))].">
      <j1 rule="para" parents="7553 16872"/>
    </justification>
  </clause>

  <clause id="16924">
    <literal><![CDATA[
      L(T(x,y),z,T(u,w)) \ T(x,L(y,z,u)) = L(x,z,T(u,w)) \ x
    ]]></literal>
    <justification jstring="[para(16880(a,1),11200(a,1,2))].">
      <j1 rule="para" parents="16880 11200"/>
    </justification>
  </clause>

  <clause id="16925">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z * y) \ u,u,y * z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11768,a(flip),b,16889,a),flip(a)].">
      <j1 rule="hyper" parents="63 11768 16889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16926">
    <literal><![CDATA[
      (K(x,L(y,z * u,z)) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(16889(a,1),15331(a,1,1,1))].">
      <j1 rule="para" parents="16889 15331"/>
    </justification>
  </clause>

  <clause id="16927">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ (K(y,z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ w) = v5
    ]]></literal>
    <justification jstring="[para(99(a,1),16892(a,1,2))].">
      <j1 rule="para" parents="99 16892"/>
    </justification>
  </clause>

  <clause id="16928">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(6642(a,1),16892(a,1,2))].">
      <j1 rule="para" parents="6642 16892"/>
    </justification>
  </clause>

  <clause id="16929">
    <literal><![CDATA[
      K(x,L(y,z,u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(6958(a,1),16892(a,1,2))].">
      <j1 rule="para" parents="6958 16892"/>
    </justification>
  </clause>

  <clause id="16931">
    <literal><![CDATA[
      K(x,y / (z * K(u,y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) / z) = w
    ]]></literal>
    <justification jstring="[para(14472(a,1),16892(a,1,2))].">
      <j1 rule="para" parents="14472 16892"/>
    </justification>
  </clause>

  <clause id="16932">
    <literal><![CDATA[
      K(x,L(y,z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w * u)) = v5
    ]]></literal>
    <justification jstring="[para(14492(a,1),16892(a,1,2))].">
      <j1 rule="para" parents="14492 16892"/>
    </justification>
  </clause>

  <clause id="16933">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(16813(a,2),4984(a,1))].">
      <j1 rule="para" parents="16813 4984"/>
    </justification>
  </clause>

  <clause id="16934">
    <literal><![CDATA[
      1 / T((x * K(y,z)) * K(a(u,w,x),v5),a(u,w,x)) = K(v5,a(u,w,x)) / (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(16898(a,1),13142(a,2,2))].">
      <j1 rule="para" parents="16898 13142"/>
    </justification>
  </clause>

  <clause id="16935">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,x)) = L(x,u,K(w,z)) \ y
    ]]></literal>
    <justification jstring="[hyper(14464,a,16833,a),flip(a)].">
      <j1 rule="hyper" parents="14464 16833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16936">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,x)) = T(x,a(z,u,w)) \ y
    ]]></literal>
    <justification jstring="[hyper(12692,a,16833,a),flip(a)].">
      <j1 rule="hyper" parents="12692 16833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16937">
    <literal><![CDATA[
      (x * y) * a(z,u,K(x,w)) = T(x,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(12661,a,16833,a),flip(a)].">
      <j1 rule="hyper" parents="12661 16833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16939">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = a(w,z,K(u,y)) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,13975,a,b,16833,a)].">
      <j1 rule="hyper" parents="347 13975 16833"/>
    </justification>
  </clause>

  <clause id="16940">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w \ x) = w \ L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,14365,a(flip),b,16833,a),flip(a)].">
      <j1 rule="hyper" parents="347 14365 16833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16941">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) * a(u,y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[hyper(133,a,16833,a,b,13975,a)].">
      <j1 rule="hyper" parents="133 16833 13975"/>
    </justification>
  </clause>

  <clause id="16943">
    <literal><![CDATA[
      x \ (L(y,a(z,u,K(w,v5)),x) * (x * a(z,u,K(w,v5)))) = T(y,x * a(z,u,K(w,v5))) * a(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,735,a,b,16833,a)].">
      <j1 rule="hyper" parents="63 735 16833"/>
    </justification>
  </clause>

  <clause id="16944">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u,K(w,z)) \ y = v5
    ]]></literal>
    <justification jstring="[para(16833(a,1),14464(a,1))].">
      <j1 rule="para" parents="16833 14464"/>
    </justification>
  </clause>

  <clause id="16945">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ w)) = L(x,y,K(u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,11495,a,b,16845,a)].">
      <j1 rule="hyper" parents="347 11495 16845"/>
    </justification>
  </clause>

  <clause id="16946">
    <literal><![CDATA[
      L(x,y,z \ K(z,z \ u)) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11554,a,b,16849,a),flip(a)].">
      <j1 rule="hyper" parents="63 11554 16849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16947">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) = T(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16647,a,b,16864,a)].">
      <j1 rule="hyper" parents="63 16647 16864"/>
    </justification>
  </clause>

  <clause id="16948">
    <literal><![CDATA[
      T(x,(K(a(y,z,u),w) * v5) * a(y,z,u)) = T(x,T(a(y,z,u),w) * v5)
    ]]></literal>
    <justification jstring="[para(4943(a,1),16864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4943 16864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16950">
    <literal><![CDATA[
      x / L(y,z,(y * z) \ x) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(220,a,16912,a(flip),b,13465,a(flip))].">
      <j1 rule="hyper" parents="220 16912 13465"/>
    </justification>
  </clause>

  <clause id="16951">
    <literal><![CDATA[
      L(x,y,(x * y) \ (y * (x * z))) = L(x,y,L(z,x,y))
    ]]></literal>
    <justification jstring="[para(18(a,2),16912(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18 16912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16952">
    <literal><![CDATA[
      T(x,K(L(y,z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(9768(a,1),16933(a,1,2))].">
      <j1 rule="para" parents="9768 16933"/>
    </justification>
  </clause>

  <clause id="16954">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) / K(x,L(x,y,z) \ u) = a(x,y,K(z,u)) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,15252,a,b,16939,a)].">
      <j1 rule="hyper" parents="63 15252 16939"/>
    </justification>
  </clause>

  <clause id="16955">
    <literal><![CDATA[
      K(x,L(y,z,u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w / u)) = v5
    ]]></literal>
    <justification jstring="[para(113(a,1),16928(a,1,2,3))].">
      <j1 rule="para" parents="113 16928"/>
    </justification>
  </clause>

  <clause id="16956">
    <literal><![CDATA[
      L(K(K(x,y),z) * ((u * w) \ v5),K(z,K(x,y)),u * w) = (u * (w * K(z,K(x,y)))) \ v5
    ]]></literal>
    <justification jstring="[para(16802(a,1),5278(a,2,1))].">
      <j1 rule="para" parents="16802 5278"/>
    </justification>
  </clause>

  <clause id="16959">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(347,a,13533,a,b,16815,a),flip(a)].">
      <j1 rule="hyper" parents="347 13533 16815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16960">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * (w \ x)) = u * (w \ T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(12783(a,1),16815(a,2,2))].">
      <j1 rule="para" parents="12783 16815"/>
    </justification>
  </clause>

  <clause id="16962">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,16815,a(flip),b,16846,a),flip(a)].">
      <j1 rule="hyper" parents="347 16815 16846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16964">
    <literal><![CDATA[
      K(x,K(y,z)) * ((u \ 1) * w) = (u \ K(x,K(y,z))) * w
    ]]></literal>
    <justification jstring="[para(13534(a,1),16846(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13534 16846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16965">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ (K(x,K(y,z)) \ w) = u \ w
    ]]></literal>
    <justification jstring="[para(10(a,1),16847(a,2,2))].">
      <j1 rule="para" parents="10 16847"/>
    </justification>
  </clause>

  <clause id="16966">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = u \ (K(x,K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(7318(a,2),16847(a,2,2))].">
      <j1 rule="para" parents="7318 16847"/>
    </justification>
  </clause>

  <clause id="16967">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) / w = (u / w) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,13514,a(flip),b,16851,a),flip(a)].">
      <j1 rule="hyper" parents="347 13514 16851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16968">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,y) / u) = T(x,T(y,z)) / u
    ]]></literal>
    <justification jstring="[para(7192(a,1),16851(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7192 16851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16969">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) / w = K(x,K(y,z)) * (u / w)
    ]]></literal>
    <justification jstring="[para(7318(a,2),16851(a,1,1))].">
      <j1 rule="para" parents="7318 16851"/>
    </justification>
  </clause>

  <clause id="16970">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = (K(y,K(x,z)) \ u) * w
    ]]></literal>
    <justification jstring="[para(7279(a,1),16852(a,1,1))].">
      <j1 rule="para" parents="7279 16852"/>
    </justification>
  </clause>

  <clause id="16971">
    <literal><![CDATA[
      x \ (y * K(z,K(u,w))) = K(z,K(u,w)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,13514,a,b,16855,a),flip(a)].">
      <j1 rule="hyper" parents="347 13514 16855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16972">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,K(u,w)) = x \ (y * T(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(5926(a,1),16855(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5926 16855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16973">
    <literal><![CDATA[
      x \ T(K(y,K(z,u)) * w,v5) = (x \ T(w,v5)) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(14302(a,2),16855(a,1,2))].">
      <j1 rule="para" parents="14302 16855"/>
    </justification>
  </clause>

  <clause id="16974">
    <literal><![CDATA[
      x \ (y * (z * K(u,K(w,v5)))) = (x \ (y * z)) * K(u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(16802(a,1),16855(a,1,2))].">
      <j1 rule="para" parents="16802 16855"/>
    </justification>
  </clause>

  <clause id="16976">
    <literal><![CDATA[
      ((K(x,y) * (z * K(u,w))) * v5) / (K(u,w) * v5) = R(K(x,y) * z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(16859(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="16859 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16977">
    <literal><![CDATA[
      T((K(x,y) * K(z,u)) \ (K(x,y) * (w * K(z,u))),K(x,y)) = R(T(w,K(x,y) * K(z,u)),K(x,y),K(z,u))
    ]]></literal>
    <justification jstring="[para(16859(a,1),1211(a,1,1,2))].">
      <j1 rule="para" parents="16859 1211"/>
    </justification>
  </clause>

  <clause id="16979">
    <literal><![CDATA[
      T(L(x,y,z) \ x,T(u,w)) = T(L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,16882,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 16882 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16980">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) \ w) = K(x,u \ (K(z,y) \ w))
    ]]></literal>
    <justification jstring="[para(5256(a,2),16886(a,2,2,2))].">
      <j1 rule="para" parents="5256 16886"/>
    </justification>
  </clause>

  <clause id="16981">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (w * K(z,y))) = v5
    ]]></literal>
    <justification jstring="[para(16888(a,2),14854(a,1))].">
      <j1 rule="para" parents="16888 14854"/>
    </justification>
  </clause>

  <clause id="16982">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,u / (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(14831,a,16891,a)].">
      <j1 rule="hyper" parents="14831 16891"/>
    </justification>
  </clause>

  <clause id="16983">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,14862,a(flip),b,16891,a),flip(a)].">
      <j1 rule="hyper" parents="347 14862 16891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16984">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (w \ K(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(16891(a,2),14863(a,1))].">
      <j1 rule="para" parents="16891 14863"/>
    </justification>
  </clause>

  <clause id="16985">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K(x \ (K(z,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(14847,a,16894,a)].">
      <j1 rule="hyper" parents="14847 16894"/>
    </justification>
  </clause>

  <clause id="16987">
    <literal><![CDATA[
      ((x * y) / x) \ (a(z,u,w) \ y) = y \ (a(z,u,w) \ T(y,x))
    ]]></literal>
    <justification jstring="[hyper(128,a,16901,a(flip),b,5428,a)].">
      <j1 rule="hyper" parents="128 16901 5428"/>
    </justification>
  </clause>

  <clause id="16989">
    <literal><![CDATA[
      T(x,y) \ (a(z,u,w) \ K(x,y)) = x \ (a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,16907,a(flip),b,4944,a)].">
      <j1 rule="hyper" parents="128 16907 4944"/>
    </justification>
  </clause>

  <clause id="16990">
    <literal><![CDATA[
      (a(x,y,z) \ K(u,w)) \ T(u,w) = (a(x,y,z) \ 1) \ u
    ]]></literal>
    <justification jstring="[para(16907(a,1),13154(a,1,1))].">
      <j1 rule="para" parents="16907 13154"/>
    </justification>
  </clause>

  <clause id="16991">
    <literal><![CDATA[
      K(x,y \ (z * L(y,u,w))) = K(x,L(y,u,w) * (z / y))
    ]]></literal>
    <justification jstring="[para(1997(a,1),16916(a,1,2))].">
      <j1 rule="para" parents="1997 16916"/>
    </justification>
  </clause>

  <clause id="16992">
    <literal><![CDATA[
      K(x,T(T((y * K(z,u)) / w,K(y,v5)),K(z,u) \ (y \ w))) = K(x,(y * K(z,u)) / T(w,K(y,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16531,a(flip),b,16918,a),flip(a)].">
      <j1 rule="hyper" parents="63 16531 16918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16993">
    <literal><![CDATA[
      K(x * y,T(z,y \ (x \ u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(16918(a,1),7495(a,1))].">
      <j1 rule="para" parents="16918 7495"/>
    </justification>
  </clause>

  <clause id="16994">
    <literal><![CDATA[
      K(x,T(y,z / (u * w))) = K(x,T(y,u \ (z / w)))
    ]]></literal>
    <justification jstring="[hyper(13645,a,16921,a),flip(a)].">
      <j1 rule="hyper" parents="13645 16921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16995">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ R(x,y,z) != w
    ]]></literal>
    <literal><![CDATA[
      (u * (x \ R(x,y,z))) / u = w
    ]]></literal>
    <justification jstring="[para(16935(a,1),14041(a,1))].">
      <j1 rule="para" parents="16935 14041"/>
    </justification>
  </clause>

  <clause id="16996">
    <literal><![CDATA[
      T(x \ 1,a(y,z,u)) = T(x,a(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(12702,a,16936,a)].">
      <j1 rule="hyper" parents="12702 16936"/>
    </justification>
  </clause>

  <clause id="16997">
    <literal><![CDATA[
      K(x,y) / T(z \ 1,a(u,w,v5)) = K(x,y) * T(z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(220,a,16996,a,b,13130,a)].">
      <j1 rule="hyper" parents="220 16996 13130"/>
    </justification>
  </clause>

  <clause id="16998">
    <literal><![CDATA[
      L(x,y,K(z,u) * (w * (z \ u))) = L(x,y,w * (u / z))
    ]]></literal>
    <justification jstring="[para(6075(a,1),16945(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6075 16945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16999">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(7326,a,16959,a)].">
      <j1 rule="hyper" parents="7326 16959"/>
    </justification>
  </clause>

  <clause id="17000">
    <literal><![CDATA[
      x \ (K(y,K(z,u)) * w) = K(y,K(z,u)) * (x \ w)
    ]]></literal>
    <justification jstring="[hyper(678,a,16959,a)].">
      <j1 rule="hyper" parents="678 16959"/>
    </justification>
  </clause>

  <clause id="17003">
    <literal><![CDATA[
      (x * (y * (z * K(u,K(w,v5))))) \ ((x * (K(u,K(w,v5)) * y)) * z) = a(x,K(u,K(w,v5)) * y,z)
    ]]></literal>
    <justification jstring="[para(16962(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="16962 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17005">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = x * (w * K(y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(13514(a,1),16962(a,1,1))].">
      <j1 rule="para" parents="13514 16962"/>
    </justification>
  </clause>

  <clause id="17006">
    <literal><![CDATA[
      (x \ 1) * (y * K(z,K(u,w))) = (x \ K(z,K(u,w))) * y
    ]]></literal>
    <justification jstring="[para(13534(a,1),16962(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13534 16962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17007">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) * v5 = (x * w) * (v5 * K(y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(16959(a,1),16962(a,1,1))].">
      <j1 rule="para" parents="16959 16962"/>
    </justification>
  </clause>

  <clause id="17009">
    <literal><![CDATA[
      (x * K(y,K(z,u))) / w = (x / w) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(13514(a,1),16967(a,1,1))].">
      <j1 rule="para" parents="13514 16967"/>
    </justification>
  </clause>

  <clause id="17011">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,u)) = (T(x,T(y,u)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(16968(a,1),13178(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16968 13178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17012">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) / w != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / w) = v5
    ]]></literal>
    <justification jstring="[para(16969(a,2),7326(a,1))].">
      <j1 rule="para" parents="16969 7326"/>
    </justification>
  </clause>

  <clause id="17013">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * K(u,K(w,v5))) = K(u,K(w,v5)) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(18(a,2),16971(a,2,2))].">
      <j1 rule="para" parents="18 16971"/>
    </justification>
  </clause>

  <clause id="17014">
    <literal><![CDATA[
      x \ T(y * K(z,K(u,w)),v5) = K(z,K(u,w)) * (x \ T(y,v5))
    ]]></literal>
    <justification jstring="[para(14306(a,2),16971(a,1,2))].">
      <j1 rule="para" parents="14306 16971"/>
    </justification>
  </clause>

  <clause id="17015">
    <literal><![CDATA[
      T(x,L(y,z,u)) / (L(T(x,y),z,u) * K(w,L(x,z,u) \ x)) = T(L(x,z,u) \ x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11203,a,b,16979,a)].">
      <j1 rule="hyper" parents="63 11203 16979"/>
    </justification>
  </clause>

  <clause id="17016">
    <literal><![CDATA[
      K(x,(K(y,z) * ((K(u,w) \ v5) / K(y,z))) \ v6) = K(x,v5 \ (K(w,u) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,14805,a,b,16980,a)].">
      <j1 rule="hyper" parents="63 14805 16980"/>
    </justification>
  </clause>

  <clause id="17017">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) \ (K(y,z) \ w)) = K(x,(y \ u) \ w)
    ]]></literal>
    <justification jstring="[para(5322(a,1),16980(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5322 16980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17018">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,14862,a(flip),b,16982,a),flip(a)].">
      <j1 rule="hyper" parents="347 14862 16982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17019">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (w \ K(y,z))) = v5
    ]]></literal>
    <justification jstring="[para(16982(a,2),14863(a,1))].">
      <j1 rule="para" parents="16982 14863"/>
    </justification>
  </clause>

  <clause id="17020">
    <literal><![CDATA[
      T(x,(y * K(z,u)) / w) = T(x,y * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(132,a,16983,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 16983 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17021">
    <literal><![CDATA[
      K(x,T(y * z,x) * (u \ K(w,L(v5,z,y)))) = K(x,(y * (z * K(w,v5))) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11138,a(flip),b,16983,a),flip(a)].">
      <j1 rule="hyper" parents="63 11138 16983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17022">
    <literal><![CDATA[
      K(x,T(y / (z \ u),x) * (w \ K(z \ u,z))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8747,a(flip),b,16983,a),flip(a)].">
      <j1 rule="hyper" parents="63 8747 16983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17023">
    <literal><![CDATA[
      K(x,(y / z) * (u \ K(w,z))) = K(x,(y / T(z,w)) / u)
    ]]></literal>
    <justification jstring="[para(6102(a,1),16983(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6102 16983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17024">
    <literal><![CDATA[
      K(x,(y / z) * (u \ K(w,T(z,v5)))) = K(x,(y / T(z,T(w,v5))) / u)
    ]]></literal>
    <justification jstring="[para(7128(a,1),16983(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7128 16983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17025">
    <literal><![CDATA[
      K(x,T(y,z) * (u \ K(w,y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(T(y,w),z) / u) = v5
    ]]></literal>
    <justification jstring="[para(16983(a,1),15815(a,1))].">
      <j1 rule="para" parents="16983 15815"/>
    </justification>
  </clause>

  <clause id="17026">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K((x \ K(y,z)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,14869,a(flip),b,16985,a),flip(a)].">
      <j1 rule="hyper" parents="63 14869 16985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17027">
    <literal><![CDATA[
      K(x,T(y,z \ (u / w))) = K(x,T(y,(z * w) * u))
    ]]></literal>
    <justification jstring="[hyper(13668,a,16994,a),flip(a)].">
      <j1 rule="hyper" parents="13668 16994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17028">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) = K(x,T(y,z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(13645,a,16994,a)].">
      <j1 rule="hyper" parents="13645 16994"/>
    </justification>
  </clause>

  <clause id="17029">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ (T(x,K(y,z)) \ w)) = u \ (x \ w)
    ]]></literal>
    <justification jstring="[para(5159(a,1),17000(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5159 17000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17030">
    <literal><![CDATA[
      x \ (K(K(y,z),u) * w) = K(u,K(y,z)) * (x \ w)
    ]]></literal>
    <justification jstring="[para(7292(a,2),17000(a,1,2,1))].">
      <j1 rule="para" parents="7292 17000"/>
    </justification>
  </clause>

  <clause id="17031">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = x * (K(y,K(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(347,a,13533,a,b,17005,a),flip(a)].">
      <j1 rule="hyper" parents="347 13533 17005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17032">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) \ (x * (y * (v5 * K(z,K(u,w))))) != v6
    ]]></literal>
    <literal><![CDATA[
      L(v5,y * K(z,K(u,w)),x) = v6
    ]]></literal>
    <justification jstring="[para(17005(a,1),545(a,1,2,2))].">
      <j1 rule="para" parents="17005 545"/>
    </justification>
  </clause>

  <clause id="17033">
    <literal><![CDATA[
      K(x,(y * K(z,K(u,w))) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * v5) = v6
    ]]></literal>
    <justification jstring="[para(17005(a,2),14832(a,1,2))].">
      <j1 rule="para" parents="17005 14832"/>
    </justification>
  </clause>

  <clause id="17034">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / w) = T(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(132,a,17018,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 17018 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17035">
    <literal><![CDATA[
      K(x,(y / (z \ u)) * (w \ K(z,u))) = K(x,(y / (T(z,u) \ u)) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,16313,a(flip),b,17018,a),flip(a)].">
      <j1 rule="hyper" parents="63 16313 17018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17036">
    <literal><![CDATA[
      T(x,y * (T(y / z,u) \ K(z,w))) = T(x,T(T(z \ y,u) \ y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16494,a(flip),b,17020,a),flip(a)].">
      <j1 rule="hyper" parents="63 16494 17020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17037">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,z)) * u,w) = K(x * (K(y,z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(13369,a,17026,a),flip(a)].">
      <j1 rule="hyper" parents="13369 17026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17038">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w)) = K(x,T(y,z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(13421,a,17027,a),flip(a)].">
      <j1 rule="hyper" parents="13421 17027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17039">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ w))) = K(x,T(y,u \ (w / z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16918,a(flip),b,17028,a)].">
      <j1 rule="hyper" parents="63 16918 17028"/>
    </justification>
  </clause>

  <clause id="17040">
    <literal><![CDATA[
      R(x,K(y,K(z,u)),w) = x
    ]]></literal>
    <justification jstring="[hyper(2384,a,17031,a)].">
      <j1 rule="hyper" parents="2384 17031"/>
    </justification>
  </clause>

  <clause id="17041">
    <literal><![CDATA[
      L(x,K(y,K(z,u)),w) = x
    ]]></literal>
    <justification jstring="[hyper(544,a,17031,a)].">
      <j1 rule="hyper" parents="544 17031"/>
    </justification>
  </clause>

  <clause id="17042">
    <literal><![CDATA[
      (x / (K(y,K(z,u)) * w)) * K(y,K(z,u)) = x / w
    ]]></literal>
    <justification jstring="[hyper(131,a,12,a(flip),b,17031,a),flip(a)].">
      <j1 rule="hyper" parents="131 12 17031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17043">
    <literal><![CDATA[
      (x * K(y,K(z,u))) \ w = K(y,K(z,u)) \ (x \ w)
    ]]></literal>
    <justification jstring="[hyper(128,a,76,a(flip),b,17031,a)].">
      <j1 rule="hyper" parents="128 76 17031"/>
    </justification>
  </clause>

  <clause id="17044">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * (w * v5))) \ (((x * K(y,K(z,u))) * w) * v5) = a(x * K(y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(17031(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="17031 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17045">
    <literal><![CDATA[
      ((x * y) * (K(z,K(u,w)) * v5)) / ((y * K(z,K(u,w))) * v5) = R(x,R(y,K(z,K(u,w)),v5),K(z,K(u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(17040(a,1),592(a,1,1,1,2))].">
      <j1 rule="para" parents="17040 592"/>
    </justification>
  </clause>

  <clause id="17047">
    <literal><![CDATA[
      L(x,K(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(17041(a,1),50(a,2))].">
      <j1 rule="para" parents="17041 50"/>
    </justification>
  </clause>

  <clause id="17048">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ (K(y,w) * z)) = T(x,z * (T(z / y,u) \ K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15810,a(flip),b,17034,a)].">
      <j1 rule="hyper" parents="63 15810 17034"/>
    </justification>
  </clause>

  <clause id="17049">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) / w) / T(v5,u * (w \ K(y,z)))) * v6) = K(x,(v5 \ ((K(y,z) * u) / w)) * v6)
    ]]></literal>
    <justification jstring="[para(17034(a,1),12064(a,1,2,1,2))].">
      <j1 rule="para" parents="17034 12064"/>
    </justification>
  </clause>

  <clause id="17050">
    <literal><![CDATA[
      K(((x \ y) / z) \ u,T(w,x \ (y / z))) = K(u / ((x \ y) / z),w)
    ]]></literal>
    <justification jstring="[hyper(13666,a,17039,a),flip(a)].">
      <j1 rule="hyper" parents="13666 17039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17051">
    <literal><![CDATA[
      x / (K(y,K(z,u)) * w) = K(y,K(z,u)) \ (x / w)
    ]]></literal>
    <justification jstring="[hyper(128,a,17042,a(flip),b,13514,a),flip(a)].">
      <j1 rule="hyper" parents="128 17042 13514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17052">
    <literal><![CDATA[
      (x * K(y,K(z,u))) \ w = (x \ w) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,13547,a(flip),b,17043,a),flip(a)].">
      <j1 rule="hyper" parents="347 13547 17043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17053">
    <literal><![CDATA[
      K(x,K(y,z)) \ (K(y,x) \ u) = K(y,T(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(7311(a,1),17043(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7311 17043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17054">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = K(x,K(y,z)) \ (u \ w)
    ]]></literal>
    <justification jstring="[para(13547(a,2),17043(a,1,1))].">
      <j1 rule="para" parents="13547 17043"/>
    </justification>
  </clause>

  <clause id="17055">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / (K(x,K(y,z)) \ w)) = u / w
    ]]></literal>
    <justification jstring="[para(10(a,1),17051(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 17051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17056">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ w = (u \ w) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(13514(a,2),17052(a,1,1))].">
      <j1 rule="para" parents="13514 17052"/>
    </justification>
  </clause>

  <clause id="17057">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) \ w) = K(x,K(y,z) \ w)
    ]]></literal>
    <justification jstring="[para(17053(a,1),14799(a,1,2))].">
      <j1 rule="para" parents="17053 14799"/>
    </justification>
  </clause>

  <clause id="17058">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) \ w) = v5
    ]]></literal>
    <justification jstring="[para(17057(a,2),15563(a,1))].">
      <j1 rule="para" parents="17057 15563"/>
    </justification>
  </clause>

  <clause id="17059">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u \ w) = u \ (K(x,K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,16966,a(flip),b,17054,a),flip(a)].">
      <j1 rule="hyper" parents="63 16966 17054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17060">
    <literal><![CDATA[
      K(x,y \ (K(z,K(u,w)) \ v5)) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[para(17059(a,1),14799(a,1,2))].">
      <j1 rule="para" parents="17059 14799"/>
    </justification>
  </clause>

  <clause id="17061">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,K(w,v5)))) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(5571(a,1),17060(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5571 17060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17062">
    <literal><![CDATA[
      K(x,y \ (T(z,T(u,w)) * v5)) = K(x,y \ (T(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(9740(a,1),17060(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9740 17060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17063">
    <literal><![CDATA[
      K(x,y \ ((z / K(u,w)) \ (v5 * (K(u,w) \ z)))) = K(x,y \ T(v5,z / K(u,w)))
    ]]></literal>
    <justification jstring="[para(13722(a,1),17060(a,1,2,2))].">
      <j1 rule="para" parents="13722 17060"/>
    </justification>
  </clause>

  <clause id="17064">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      w * a(z,y,K(u,x)) = v5
    ]]></literal>
    <justification jstring="[para(13959(a,1),16837(a,1,1))].">
      <j1 rule="para" parents="13959 16837"/>
    </justification>
  </clause>

  <clause id="17065">
    <literal><![CDATA[
      K(x,a(y,z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      w * a(x,z,K(u,y)) = v5
    ]]></literal>
    <justification jstring="[para(13960(a,1),16837(a,1,1))].">
      <j1 rule="para" parents="13960 16837"/>
    </justification>
  </clause>

  <clause id="17066">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(16947(a,2),16874(a,1))].">
      <j1 rule="para" parents="16947 16874"/>
    </justification>
  </clause>

  <clause id="17067">
    <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(16647(a,2),16875(a,1))].">
      <j1 rule="para" parents="16647 16875"/>
    </justification>
  </clause>

  <clause id="17068">
    <literal><![CDATA[
      K(x,y * (z \ K(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) / z) = w
    ]]></literal>
    <justification jstring="[para(14862(a,1),16931(a,1))].">
      <j1 rule="para" parents="14862 16931"/>
    </justification>
  </clause>

  <clause id="17069">
    <literal><![CDATA[
      L(x,y,L(K(y,x) * z,x,y)) = L(x,y,L(z,x,y))
    ]]></literal>
    <justification jstring="[para(10173(a,1),16951(a,1,3))].">
      <j1 rule="para" parents="10173 16951"/>
    </justification>
  </clause>

  <clause id="17070">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,w / u))
    ]]></literal>
    <justification jstring="[hyper(16955,a,13990,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16955 13990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17071">
    <literal><![CDATA[
      K(x,K(y,z / u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z) * w) = v5
    ]]></literal>
    <justification jstring="[para(8942(a,1),17033(a,1,2,1))].">
      <j1 rule="para" parents="8942 17033"/>
    </justification>
  </clause>

  <clause id="17072">
    <literal><![CDATA[
      (K(x,y) * z) * u != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * (z * u)) * a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(13381(a,1),17065(a,1))].">
      <j1 rule="para" parents="13381 17065"/>
    </justification>
  </clause>

  <clause id="17073">
    <literal><![CDATA[
      K(x,L(y,z,u) * (y \ w)) = K(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15323,a(flip),b,16922,a)].">
      <j1 rule="hyper" parents="63 15323 16922"/>
    </justification>
  </clause>

  <clause id="17074">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1) / u) = L(x,y,u \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(12126,a,16946,a),flip(a)].">
      <j1 rule="hyper" parents="12126 16946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17075">
    <literal><![CDATA[
      L(x,y,z \ K(u,z \ 1)) = L(x,y,z \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16849,a(flip),b,17074,a)].">
      <j1 rule="hyper" parents="63 16849 17074"/>
    </justification>
  </clause>

  <clause id="17076">
    <literal><![CDATA[
      L(x,y,z \ K(z,y)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(10238,a,17075,a),flip(a)].">
      <j1 rule="hyper" parents="10238 17075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17077">
    <literal><![CDATA[
      L(x,T(y,z),(z \ T(y,z \ y)) \ 1) = L(x,T(y,z),(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(13933(a,1),17076(a,1,3))].">
      <j1 rule="para" parents="13933 17076"/>
    </justification>
  </clause>

  <clause id="17078">
    <literal><![CDATA[
      R(K(x,K(y,z)),(u \ 1) * w,v5) \ (v5 * ((u \ K(x,K(y,z))) * w)) = ((u \ 1) * w) * T(v5,K(x,K(y,z)) * ((u \ 1) * w))
    ]]></literal>
    <justification jstring="[para(16964(a,1),13920(a,1,2,2))].">
      <j1 rule="para" parents="16964 13920"/>
    </justification>
  </clause>

  <clause id="17079">
    <literal><![CDATA[
      T((x \ (y * z)) / ((K(u,w) * z) / K(u,w)),z) = z \ (x \ (y * T(z,K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(6228,a,16972,a)].">
      <j1 rule="hyper" parents="6228 16972"/>
    </justification>
  </clause>

  <clause id="17080">
    <literal><![CDATA[
      K(x,y \ (z * T(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * u)) = v6
    ]]></literal>
    <justification jstring="[para(16972(a,1),14826(a,1,2))].">
      <j1 rule="para" parents="16972 14826"/>
    </justification>
  </clause>

  <clause id="17081">
    <literal><![CDATA[
      (x \ K(y,K(z,u))) * (K(y,K(z,u)) * w) = (x \ 1) * w
    ]]></literal>
    <justification jstring="[para(13548(a,1),17006(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13548 17006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17082">
    <literal><![CDATA[
      (T(x,T(y,z)) / z) \ 1 = K(y,x) * ((x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(13935,a,17011,a),flip(a)].">
      <j1 rule="hyper" parents="13935 17011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17083">
    <literal><![CDATA[
      x / L(K(y,z),(z / u) \ 1,((T(z,T(y,u)) / u) \ 1) \ x) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(17082(a,2),16950(a,1,2,3,1))].">
      <j1 rule="para" parents="17082 16950"/>
    </justification>
  </clause>

  <clause id="17084">
    <literal><![CDATA[
      K((x * K(y,z)) * u,w) = K(x * (K(y,z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(13744,a,17037,a)].">
      <j1 rule="hyper" parents="13744 17037"/>
    </justification>
  </clause>

  <clause id="17085">
    <literal><![CDATA[
      K((K(x,y) * z) * u,w) = K(z * (K(x,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(14846,a,17084,a)].">
      <j1 rule="hyper" parents="14846 17084"/>
    </justification>
  </clause>

  <clause id="17086">
    <literal><![CDATA[
      K((T(T(x,y),y) \ z) * (K(x,y) * u),w) = K(T(T(x,y) \ z,K(y,x)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,16314,a(flip),b,17084,a),flip(a)].">
      <j1 rule="hyper" parents="63 16314 17084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17087">
    <literal><![CDATA[
      K((x / y) * (K(x,z) * u),w) = K((T(x,z) / y) * u,w)
    ]]></literal>
    <justification jstring="[para(13192(a,1),17085(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13192 17085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17088">
    <literal><![CDATA[
      K(x,(y * T(z,u)) \ (T(y,z) * w)) = K(x,(T(z,u) * y) \ (y * w))
    ]]></literal>
    <justification jstring="[para(10307(a,1),17062(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10307 17062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17089">
    <literal><![CDATA[
      a(x,y,K(z / u,w)) = a(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(34,a,13990,a,b,17070,a)].">
      <j1 rule="hyper" parents="34 13990 17070"/>
    </justification>
  </clause>

  <clause id="17090">
    <literal><![CDATA[
      a(x,y,K(z,x \ (u * (x / w)))) = a(z,y,K(w \ u,x))
    ]]></literal>
    <justification jstring="[hyper(14056,a,17089,a)].">
      <j1 rule="hyper" parents="14056 17089"/>
    </justification>
  </clause>

  <clause id="17091">
    <literal><![CDATA[
      K(x,y / z) * a(x,u,K(z \ y,w)) = K(x,L(y / z,u,w \ 1))
    ]]></literal>
    <justification jstring="[para(17089(a,1),14076(a,1,2))].">
      <j1 rule="para" parents="17089 14076"/>
    </justification>
  </clause>

  <clause id="17092">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,w / (y * u)))
    ]]></literal>
    <justification jstring="[para(17089(a,1),14542(a,1,2))].">
      <j1 rule="para" parents="17089 14542"/>
    </justification>
  </clause>

  <clause id="17093">
    <literal><![CDATA[
      K(T(x,y),z * (u \ L(u,w,v5))) = K(x,T(L(u,w,v5) * (u \ z),y))
    ]]></literal>
    <justification jstring="[hyper(7488,a,17073,a),flip(a)].">
      <j1 rule="hyper" parents="7488 17073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17094">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * (y \ u)) = K(x,u * a(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(15980,a,17073,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="15980 17073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17095">
    <literal><![CDATA[
      a(x,y,K(z * (u / w),u)) = a(x,y,K(w \ z,u))
    ]]></literal>
    <justification jstring="[hyper(14168,a,17090,a)].">
      <j1 rule="hyper" parents="14168 17090"/>
    </justification>
  </clause>

  <clause id="17096">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),w)) = a(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(8412(a,1),17095(a,1,3))].">
      <j1 rule="para" parents="8412 17095"/>
    </justification>
  </clause>

  <clause id="17097">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ T(y,v5)))) = K(x,y) * a(x,z,K(w \ u,y))
    ]]></literal>
    <justification jstring="[para(17096(a,1),14079(a,2,2))].">
      <j1 rule="para" parents="17096 14079"/>
    </justification>
  </clause>

  <clause id="17098">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * x) = w * L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(16878,a,14367,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16878 14367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17099">
    <literal><![CDATA[
      K(L(x / y,z,u) \ w,T(v5,y * x)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(w / L(x / y,z,u),v5) = v6
    ]]></literal>
    <justification jstring="[para(13664(a,1),16920(a,1))].">
      <j1 rule="para" parents="13664 16920"/>
    </justification>
  </clause>

  <clause id="17100">
    <literal><![CDATA[
      K(x,(y * z) \ (K(u,y) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,u) * z) \ w) = v5
    ]]></literal>
    <justification jstring="[para(4946(a,1),16927(a,1,2,1))].">
      <j1 rule="para" parents="4946 16927"/>
    </justification>
  </clause>

  <clause id="17101">
    <literal><![CDATA[
      (x \ y) * a(x,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(w,u)) \ y = v5
    ]]></literal>
    <justification jstring="[para(13959(a,1),16944(a,1,2))].">
      <j1 rule="para" parents="13959 16944"/>
    </justification>
  </clause>

  <clause id="17102">
    <literal><![CDATA[
      K(x,T(y * K(z,u),u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) * (w \ K(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(7253(a,2),16984(a,1,2,1))].">
      <j1 rule="para" parents="7253 16984"/>
    </justification>
  </clause>

  <clause id="17103">
    <literal><![CDATA[
      K(x * L(x \ y,z,u),T(w,y)) = K(x * L(x \ y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(16993,a,16883,a)].">
      <j1 rule="hyper" parents="16993 16883"/>
    </justification>
  </clause>

  <clause id="17104">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(y * (u / z),u) * w)
    ]]></literal>
    <justification jstring="[hyper(17071,a,14516,a)].">
      <j1 rule="hyper" parents="17071 14516"/>
    </justification>
  </clause>

  <clause id="17105">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,w) * (v5 \ u)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * (v5 \ T(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(13116(a,1),17080(a,1,2,2,2))].">
      <j1 rule="para" parents="13116 17080"/>
    </justification>
  </clause>

  <clause id="17106">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ R(x,y,u) = T(x \ R(x,y,u),z)
    ]]></literal>
    <justification jstring="[hyper(17101,a,14147,a)].">
      <j1 rule="hyper" parents="17101 14147"/>
    </justification>
  </clause>

  <clause id="17107">
    <literal><![CDATA[
      R(L(x,y,K(x * z,u)) \ R(x,y,u),x,z) = T((x * z) \ (R(x,y,u) * z),x)
    ]]></literal>
    <justification jstring="[para(17106(a,2),1209(a,1,1))].">
      <j1 rule="para" parents="17106 1209"/>
    </justification>
  </clause>

  <clause id="17109">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ R(x,y,z) = T(x \ R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(14399(a,1),17106(a,1,1))].">
      <j1 rule="para" parents="14399 17106"/>
    </justification>
  </clause>

  <clause id="17110">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) = v5 \ (x * v5)
    ]]></literal>
    <justification jstring="[para(16840(a,1),16876(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16840 16876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17111">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(17110(a,2),360(a,1))].">
      <j1 rule="para" parents="17110 360"/>
    </justification>
  </clause>

  <clause id="17113">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y * v5) = v6
    ]]></literal>
    <justification jstring="[para(4974(a,1),17111(a,1,2))].">
      <j1 rule="para" parents="4974 17111"/>
    </justification>
  </clause>

  <clause id="17114">
    <literal><![CDATA[
      T(x,(a(y,z,u) * w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,(w * a(y,z,u)) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(10274(a,1),17111(a,1,2))].">
      <j1 rule="para" parents="10274 17111"/>
    </justification>
  </clause>

  <clause id="17115">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(12651(a,2),17111(a,1,2,1))].">
      <j1 rule="para" parents="12651 17111"/>
    </justification>
  </clause>

  <clause id="17116">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w)) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ v5) = v6
    ]]></literal>
    <justification jstring="[para(15529(a,1),17111(a,1))].">
      <j1 rule="para" parents="15529 17111"/>
    </justification>
  </clause>

  <clause id="17117">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * v5) = T(x,v5)
    ]]></literal>
    <justification jstring="[hyper(17115,a,xx),flip(a)].">
      <j1 rule="hyper" parents="17115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17118">
    <literal><![CDATA[
      T(x,(y * z) * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (z * K(u,w))) = v5
    ]]></literal>
    <justification jstring="[para(13372(a,1),17115(a,1,2))].">
      <j1 rule="para" parents="13372 17115"/>
    </justification>
  </clause>

  <clause id="17119">
    <literal><![CDATA[
      T(x,y * a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v6
    ]]></literal>
    <justification jstring="[para(16833(a,1),17115(a,1,2))].">
      <j1 rule="para" parents="16833 17115"/>
    </justification>
  </clause>

  <clause id="17120">
    <literal><![CDATA[
      T(x,y * L(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(17098(a,1),17115(a,1,2))].">
      <j1 rule="para" parents="17098 17115"/>
    </justification>
  </clause>

  <clause id="17121">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) = v5 / T(v5,w)
    ]]></literal>
    <justification jstring="[hyper(220,a,17117,a(flip),b,4939,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="220 17117 4939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17122">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(9259(a,1),17117(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9259 17117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17123">
    <literal><![CDATA[
      T(x,(y * z) * K(u,w)) = T(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(13372(a,1),17117(a,1,2))].">
      <j1 rule="para" parents="13372 17117"/>
    </justification>
  </clause>

  <clause id="17124">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(w,v5) = v6
    ]]></literal>
    <justification jstring="[para(17121(a,2),5013(a,1))].">
      <j1 rule="para" parents="17121 5013"/>
    </justification>
  </clause>

  <clause id="17125">
    <literal><![CDATA[
      K(T(x,a(y,z,u)) \ w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x \ w,v5) = v6
    ]]></literal>
    <justification jstring="[para(12690(a,1),17124(a,1,1))].">
      <j1 rule="para" parents="12690 17124"/>
    </justification>
  </clause>

  <clause id="17126">
    <literal><![CDATA[
      K(x * a(y,z,K(u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(16833(a,1),17124(a,1,1))].">
      <j1 rule="para" parents="16833 17124"/>
    </justification>
  </clause>

  <clause id="17127">
    <literal><![CDATA[
      T(x * a(y,z,K(u,w)),v5) / (x * a(y,z,K(u,w))) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(17126,a,4969,a),flip(a)].">
      <j1 rule="hyper" parents="17126 4969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17128">
    <literal><![CDATA[
      K(x * T(y,a(z,u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * y,v5) = v6
    ]]></literal>
    <justification jstring="[para(12654(a,1),17126(a,1,1))].">
      <j1 rule="para" parents="12654 17126"/>
    </justification>
  </clause>

  <clause id="17129">
    <literal><![CDATA[
      K(x / L(y,z,K(u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x / y,v5) = v6
    ]]></literal>
    <justification jstring="[para(14458(a,1),17126(a,1,1))].">
      <j1 rule="para" parents="14458 17126"/>
    </justification>
  </clause>

  <clause id="17130">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(7610(a,1),17122(a,1,2,1))].">
      <j1 rule="para" parents="7610 17122"/>
    </justification>
  </clause>

  <clause id="17131">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[para(8255(a,2),17122(a,1,2))].">
      <j1 rule="para" parents="8255 17122"/>
    </justification>
  </clause>

  <clause id="17132">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,15511,a,b,17130,a),flip(a)].">
      <j1 rule="hyper" parents="347 15511 17130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17133">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) = x \ T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(128,a,17130,a(flip),b,4929,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 17130 4929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17134">
    <literal><![CDATA[
      x / T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,L(z,v5,v6)) * u,x) = w
    ]]></literal>
    <justification jstring="[para(17130(a,1),5013(a,1,2))].">
      <j1 rule="para" parents="17130 5013"/>
    </justification>
  </clause>

  <clause id="17135">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,9936,a,b,17131,a),flip(a)].">
      <j1 rule="hyper" parents="347 9936 17131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17136">
    <literal><![CDATA[
      T(x,(K(y,z) * u) * w) = T(x,K(z,y) * (u * w))
    ]]></literal>
    <justification jstring="[para(14092(a,1),17132(a,1,2))].">
      <j1 rule="para" parents="14092 17132"/>
    </justification>
  </clause>

  <clause id="17137">
    <literal><![CDATA[
      (T(x,K(y,z) * u) * K(z,L(T(y,x),w,v5))) / (K(z,L(y,w,v5)) * x) = K(x,u * K(z,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(17132(a,1),13928(a,1,1,1))].">
      <j1 rule="para" parents="17132 13928"/>
    </justification>
  </clause>

  <clause id="17138">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = x \ T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(128,a,17135,a(flip),b,4929,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 17135 4929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17139">
    <literal><![CDATA[
      T(x,(a(y,z,u) / w) * v5) = T(x,(w \ a(y,z,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(17113,a,15629,a),flip(a)].">
      <j1 rule="hyper" parents="17113 15629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17140">
    <literal><![CDATA[
      T(x,y * (z / a(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (a(u,w,v5) \ z)) = v6
    ]]></literal>
    <justification jstring="[para(14432(a,1),17120(a,1,2,2))].">
      <j1 rule="para" parents="14432 17120"/>
    </justification>
  </clause>

  <clause id="17141">
    <literal><![CDATA[
      T(x,K(y,z) * (u * w)) = T(x,u * (w * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(13564,a,17123,a)].">
      <j1 rule="hyper" parents="13564 17123"/>
    </justification>
  </clause>

  <clause id="17142">
    <literal><![CDATA[
      T(x,(y \ z) * (y * K(u,w))) = T(x,T(K(u,w) * z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16486,a(flip),b,17123,a),flip(a)].">
      <j1 rule="hyper" parents="63 16486 17123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17143">
    <literal><![CDATA[
      x \ T(x,y * (z * K(u,w))) = K(x,(y * z) * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(128,a,17123,a(flip),b,4929,a(flip))].">
      <j1 rule="hyper" parents="128 17123 4929"/>
    </justification>
  </clause>

  <clause id="17144">
    <literal><![CDATA[
      T(x,y * (T(z,(u * w) \ K(v5,v6)) * v7)) = T(x,y * (T(z,u * (w * K(v5,v6))) * v7))
    ]]></literal>
    <justification jstring="[para(17123(a,1),16397(a,2,2,2,1))].">
      <j1 rule="para" parents="17123 16397"/>
    </justification>
  </clause>

  <clause id="17145">
    <literal><![CDATA[
      K(T(x,y) * L(y,z,u),w) = K(L(y,z,u) * x,w)
    ]]></literal>
    <justification jstring="[hyper(17128,a,14050,a),flip(a)].">
      <j1 rule="hyper" parents="17128 14050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17146">
    <literal><![CDATA[
      T(x,(K(a(y,z,u),w) * v5) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      T(x,v5 * v6) = v7
    ]]></literal>
    <justification jstring="[para(17136(a,2),17111(a,1))].">
      <j1 rule="para" parents="17136 17111"/>
    </justification>
  </clause>

  <clause id="17147">
    <literal><![CDATA[
      T(x,K(y,z) * (u * w)) = T(x,u * (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,14788,a,b,17141,a),flip(a)].">
      <j1 rule="hyper" parents="347 14788 17141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17148">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = K(u * L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,8281,a(flip),b,17145,a),flip(a)].">
      <j1 rule="hyper" parents="63 8281 17145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17149">
    <literal><![CDATA[
      T(x,y * (K(z,z \ u) * w)) = T(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(11990,a,17147,a),flip(a)].">
      <j1 rule="hyper" parents="11990 17147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17150">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (z * w))) = T(x,u * (z * (K(y,z) * w)))
    ]]></literal>
    <justification jstring="[para(5353(a,1),17147(a,2,2,2))].">
      <j1 rule="para" parents="5353 17147"/>
    </justification>
  </clause>

  <clause id="17151">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * v5) = v6
    ]]></literal>
    <justification jstring="[para(17133(a,2),5006(a,1))].">
      <j1 rule="para" parents="17133 5006"/>
    </justification>
  </clause>

  <clause id="17152">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(17138(a,2),5006(a,1))].">
      <j1 rule="para" parents="17138 5006"/>
    </justification>
  </clause>

  <clause id="17153">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(5006,a,17143,a),flip(a)].">
      <j1 rule="hyper" parents="5006 17143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17154">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * K(u,w))) = v5
    ]]></literal>
    <justification jstring="[para(17143(a,1),5006(a,1))].">
      <j1 rule="para" parents="17143 5006"/>
    </justification>
  </clause>

  <clause id="17155">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15640,a,17153,a)].">
      <j1 rule="hyper" parents="15640 17153"/>
    </justification>
  </clause>

  <clause id="17156">
    <literal><![CDATA[
      K(x,y * ((1 / z) * K(u,y / z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(13884,a,17153,a),flip(a)].">
      <j1 rule="hyper" parents="13884 17153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17157">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(13608,a,17153,a)].">
      <j1 rule="hyper" parents="13608 17153"/>
    </justification>
  </clause>

  <clause id="17158">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,14810,a,b,17155,a),flip(a)].">
      <j1 rule="hyper" parents="347 14810 17155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17159">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w * z))) = K(x,u * (w * T(z,y)))
    ]]></literal>
    <justification jstring="[para(5926(a,1),17155(a,2,2,2))].">
      <j1 rule="para" parents="5926 17155"/>
    </justification>
  </clause>

  <clause id="17160">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w \ 1))) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[para(12973(a,1),17155(a,2,2,2))].">
      <j1 rule="para" parents="12973 17155"/>
    </justification>
  </clause>

  <clause id="17161">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (K(z,y) * w)) = v5
    ]]></literal>
    <justification jstring="[para(17155(a,2),14835(a,1))].">
      <j1 rule="para" parents="17155 14835"/>
    </justification>
  </clause>

  <clause id="17162">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (z / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (T(z,y) / w)) = v5
    ]]></literal>
    <justification jstring="[para(17155(a,2),14851(a,1))].">
      <j1 rule="para" parents="17155 14851"/>
    </justification>
  </clause>

  <clause id="17163">
    <literal><![CDATA[
      K(x,y * (z * K(u,w))) = K(x,y * (z * K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17155,a(flip),b,17157,a)].">
      <j1 rule="hyper" parents="63 17155 17157"/>
    </justification>
  </clause>

  <clause id="17164">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17157,a(flip),b,17158,a),flip(a)].">
      <j1 rule="hyper" parents="63 17157 17158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17165">
    <literal><![CDATA[
      K(x,y * (K(z,x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * u) = w
    ]]></literal>
    <justification jstring="[para(17158(a,1),7871(a,1))].">
      <j1 rule="para" parents="17158 7871"/>
    </justification>
  </clause>

  <clause id="17166">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w,u))) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(13045(a,1),17163(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13045 17163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17167">
    <literal><![CDATA[
      K(x,y * (z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (K(w,u) * z)) = v5
    ]]></literal>
    <justification jstring="[para(17163(a,1),14835(a,1))].">
      <j1 rule="para" parents="17163 14835"/>
    </justification>
  </clause>

  <clause id="17168">
    <literal><![CDATA[
      K(x,y * (z * K(u,u \ w))) = K(x,y * (z * K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14861,a,b,17164,a)].">
      <j1 rule="hyper" parents="63 14861 17164"/>
    </justification>
  </clause>

  <clause id="17169">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * u))) = K(x,y * (w * T(u,z)))
    ]]></literal>
    <justification jstring="[para(5926(a,1),17164(a,2,2,2))].">
      <j1 rule="para" parents="5926 17164"/>
    </justification>
  </clause>

  <clause id="17170">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u * L(z / y,w,v5))) = K(x,u * L(y \ z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(17151,a,16394,a)].">
      <j1 rule="hyper" parents="17151 16394"/>
    </justification>
  </clause>

  <clause id="17171">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(9768(a,1),17151(a,1,2,1))].">
      <j1 rule="para" parents="9768 17151"/>
    </justification>
  </clause>

  <clause id="17172">
    <literal><![CDATA[
      K(x,K((y \ z) \ u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z \ (y * u),w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(15074(a,1),17151(a,1,2,1))].">
      <j1 rule="para" parents="15074 17151"/>
    </justification>
  </clause>

  <clause id="17173">
    <literal><![CDATA[
      K(x,y * (K(z,u \ y) / u)) = K(x,T(y / u,z))
    ]]></literal>
    <justification jstring="[para(13342(a,1),17156(a,1,2,2))].">
      <j1 rule="para" parents="13342 17156"/>
    </justification>
  </clause>

  <clause id="17174">
    <literal><![CDATA[
      K(x,y * (z \ K(u,z \ y))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(15705,a,17173,a)].">
      <j1 rule="hyper" parents="15705 17173"/>
    </justification>
  </clause>

  <clause id="17175">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(u,T(u \ z,y)))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[para(11644(a,1),17174(a,1,2,2,2))].">
      <j1 rule="para" parents="11644 17174"/>
    </justification>
  </clause>

  <clause id="17176">
    <literal><![CDATA[
      K(x,K(y,z \ u) * (w * (v5 * (u / z)))) = K(x,w * (v5 * T(u / z,y)))
    ]]></literal>
    <justification jstring="[hyper(17071,a,17159,a)].">
      <j1 rule="hyper" parents="17071 17159"/>
    </justification>
  </clause>

  <clause id="17177">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (1 / w))) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(12176,a,17160,a)].">
      <j1 rule="hyper" parents="12176 17160"/>
    </justification>
  </clause>

  <clause id="17178">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(w,z \ u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,w)) = v5
    ]]></literal>
    <justification jstring="[para(17160(a,1),15149(a,1))].">
      <j1 rule="para" parents="17160 15149"/>
    </justification>
  </clause>

  <clause id="17179">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w * v5,u))) = K(x,y * (z \ T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15993,a(flip),b,17166,a)].">
      <j1 rule="hyper" parents="63 15993 17166"/>
    </justification>
  </clause>

  <clause id="17180">
    <literal><![CDATA[
      K(x,y * (z \ (u * (w / u)))) = K(x,y * ((z \ w) * K(w,u)))
    ]]></literal>
    <justification jstring="[para(14664(a,1),17168(a,1,2,2))].">
      <j1 rule="para" parents="14664 17168"/>
    </justification>
  </clause>

  <clause id="17181">
    <literal><![CDATA[
      K(x,y * (z * (u * (w / u)))) = K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14890,a(flip),b,17169,a)].">
      <j1 rule="hyper" parents="63 14890 17169"/>
    </justification>
  </clause>

  <clause id="17182">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) * v5) = K(x,K(y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(17171,a,xx),flip(a)].">
      <j1 rule="hyper" parents="17171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17183">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[para(14172(a,1),17182(a,1,2))].">
      <j1 rule="para" parents="14172 17182"/>
    </justification>
  </clause>

  <clause id="17184">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * w) = K(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(14833,a,17183,a)].">
      <j1 rule="hyper" parents="14833 17183"/>
    </justification>
  </clause>

  <clause id="17185">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ w) = K(x,K(u,z) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(13316,a,17183,a)].">
      <j1 rule="hyper" parents="13316 17183"/>
    </justification>
  </clause>

  <clause id="17186">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,K(z,y) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,15545,a,b,17183,a),flip(a)].">
      <j1 rule="hyper" parents="347 15545 17183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17187">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) * w)) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[para(5209(a,1),17183(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5209 17183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17188">
    <literal><![CDATA[
      K(x,K(y,z) * ((y \ u) * w)) = K(x,(((z * y) / z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(5161(a,2),17183(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5161 17183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17189">
    <literal><![CDATA[
      K(x,K(y,z) * ((y / u) * w)) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[para(13192(a,1),17183(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13192 17183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17190">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * w) = K(x,K(u,z) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,15545,a,b,17184,a),flip(a)].">
      <j1 rule="hyper" parents="347 15545 17184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17191">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * w) = T(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(132,a,17184,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 17184 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17192">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) * w)) = K(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(13045(a,1),17184(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13045 17184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17193">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * (y * w)) = v5
    ]]></literal>
    <justification jstring="[para(17184(a,2),15546(a,1))].">
      <j1 rule="para" parents="17184 15546"/>
    </justification>
  </clause>

  <clause id="17194">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ w) = K(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,15545,a,b,17185,a),flip(a)].">
      <j1 rule="hyper" parents="347 15545 17185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17195">
    <literal><![CDATA[
      K(x,K(y,z) * (((z * y) / u) * w)) = K(x,(((y * z) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(13754(a,1),17185(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13754 17185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17196">
    <literal><![CDATA[
      K(x,K(y,z) * ((y \ u) * w)) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(5209(a,1),17186(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5209 17186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17197">
    <literal><![CDATA[
      K(x,K(y,z) * ((z / u) * w)) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[para(13192(a,1),17186(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13192 17186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17198">
    <literal><![CDATA[
      K(x,K(y,z) * (((z * y) / u) * w)) = K(x,((T(z,y) * y) / u) * w)
    ]]></literal>
    <justification jstring="[para(13923(a,1),17186(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13923 17186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17199">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,K(u,w) * (z * x)) = K(y,x * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[para(17186(a,1),16183(a,1,2))].">
      <j1 rule="para" parents="17186 16183"/>
    </justification>
  </clause>

  <clause id="17200">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(13292,a,17190,a)].">
      <j1 rule="hyper" parents="13292 17190"/>
    </justification>
  </clause>

  <clause id="17201">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * ((w * u) * v5)) = K(x,(w * (u * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[para(11109(a,1),17190(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11109 17190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17202">
    <literal><![CDATA[
      K(x,K(y \ z,y) * ((u \ z) * w)) = K(x,(u \ (y * (z / y))) * w)
    ]]></literal>
    <justification jstring="[para(14664(a,1),17190(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14664 17190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17203">
    <literal><![CDATA[
      T(K(x,K(y \ z,y) * (u * w)),w \ T(w * (u * K(y,y \ z)),x)) = (w \ T(w * (u * K(y,y \ z)),x)) \ ((u / y) * ((y \ z) \ z))
    ]]></literal>
    <justification jstring="[para(17190(a,1),13259(a,1,1))].">
      <j1 rule="para" parents="17190 13259"/>
    </justification>
  </clause>

  <clause id="17204">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) * (y * w)) = v5
    ]]></literal>
    <justification jstring="[para(17191(a,2),15522(a,1))].">
      <j1 rule="para" parents="17191 15522"/>
    </justification>
  </clause>

  <clause id="17205">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,w) * (y * z)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (y * K(u,w))) = v5
    ]]></literal>
    <justification jstring="[para(17191(a,1),16205(a,1))].">
      <j1 rule="para" parents="17191 16205"/>
    </justification>
  </clause>

  <clause id="17206">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) \ w) = T(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(132,a,17194,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 17194 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17207">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * (y * u)) = K(x,T(y \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[para(4935(a,1),17194(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4935 17194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17208">
    <literal><![CDATA[
      T(x,(K(y,z) / u) \ w) = T(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(132,a,17200,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 17200 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17209">
    <literal><![CDATA[
      K(x,L(K(y,z) / u,w,v5) * (1 / (u \ K(y,z)))) = K(x,K(y,z) * (u * L(K(y,z) * (u \ 1),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15423,a(flip),b,17200,a)].">
      <j1 rule="hyper" parents="63 15423 17200"/>
    </justification>
  </clause>

  <clause id="17210">
    <literal><![CDATA[
      T(x,K(y,z \ u) * ((u \ z) * w)) = T(x,T((u \ z) \ 1,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15737,a(flip),b,17206,a),flip(a)].">
      <j1 rule="hyper" parents="63 15737 17206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17211">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) * (y * w)) = v5
    ]]></literal>
    <justification jstring="[para(17206(a,2),15522(a,1))].">
      <j1 rule="para" parents="17206 15522"/>
    </justification>
  </clause>

  <clause id="17212">
    <literal><![CDATA[
      K(x,L(T(1 / y,K(z,u) * (y * z)) \ w,w,(K(z,u) / y) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(17208(a,1),13455(a,1,2,1,1))].">
      <j1 rule="para" parents="17208 13455"/>
    </justification>
  </clause>

  <clause id="17213">
    <literal><![CDATA[
      K(x,y * (z \ K(u,L(w,v5,v6)))) = K(x,K(w,u) * (y * (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(17171,a,17177,a),flip(a)].">
      <j1 rule="hyper" parents="17171 17177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17214">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (1 / w))) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(15546,a,17177,a)].">
      <j1 rule="hyper" parents="15546 17177"/>
    </justification>
  </clause>

  <clause id="17215">
    <literal><![CDATA[
      K(x,y * (z * T(u * w,w))) = K(x,y * (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(11(a,1),17181(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 17181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17216">
    <literal><![CDATA[
      K(x,(y \ z) * (u * K(w,y))) = K(x,(T(y,w) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17157,a(flip),b,17187,a)].">
      <j1 rule="hyper" parents="63 17157 17187"/>
    </justification>
  </clause>

  <clause id="17217">
    <literal><![CDATA[
      K(x,(K(y,z) * (z / u)) * w) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17186,a,b,17189,a)].">
      <j1 rule="hyper" parents="63 17186 17189"/>
    </justification>
  </clause>

  <clause id="17218">
    <literal><![CDATA[
      K(x,((y \ z) * K(u,z)) * w) = K(x,(y \ T(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17190,a,b,17192,a)].">
      <j1 rule="hyper" parents="63 17190 17192"/>
    </justification>
  </clause>

  <clause id="17219">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12034,a(flip),b,17196,a),flip(a)].">
      <j1 rule="hyper" parents="63 12034 17196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17220">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(4281(a,1),17219(a,1,2,1))].">
      <j1 rule="para" parents="4281 17219"/>
    </justification>
  </clause>

  <clause id="17221">
    <literal><![CDATA[
      K(x,T(y \ z,z) * u) = K(x,(y \ T(z,y)) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,15612,a,b,17220,a)].">
      <j1 rule="hyper" parents="347 15612 17220"/>
    </justification>
  </clause>

  <clause id="17222">
    <literal><![CDATA[
      (x * K(y,(z / u) * w)) \ x != v5
    ]]></literal>
    <literal><![CDATA[
      K((u \ T(z,u)) * w,y) = v5
    ]]></literal>
    <justification jstring="[para(17220(a,1),6141(a,1,1,2))].">
      <j1 rule="para" parents="17220 6141"/>
    </justification>
  </clause>

  <clause id="17223">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) * u) = w
    ]]></literal>
    <justification jstring="[para(17221(a,1),15741(a,1))].">
      <j1 rule="para" parents="17221 15741"/>
    </justification>
  </clause>

  <clause id="17224">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) * u) = w
    ]]></literal>
    <justification jstring="[para(4281(a,2),17223(a,1,2,1))].">
      <j1 rule="para" parents="4281 17223"/>
    </justification>
  </clause>

  <clause id="17225">
    <literal><![CDATA[
      K(x,(T(y,T(z,u)) \ (u * (z / u))) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,((u * (z / u)) / y) * w) = v5
    ]]></literal>
    <justification jstring="[para(10339(a,1),17224(a,1,2,1,1))].">
      <j1 rule="para" parents="10339 17224"/>
    </justification>
  </clause>

  <clause id="17226">
    <literal><![CDATA[
      K(x,K(y,z) * ((y / u) * w)) = K(x,(T(y,K(v5,v6) * z) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,16475,a(flip),b,17197,a)].">
      <j1 rule="hyper" parents="63 16475 17197"/>
    </justification>
  </clause>

  <clause id="17227">
    <literal><![CDATA[
      K(x,L(y,z,z \ u) * u) = K(x,(T(u,y) / z) * (z * y))
    ]]></literal>
    <justification jstring="[para(14626(a,1),17197(a,1,2))].">
      <j1 rule="para" parents="14626 17197"/>
    </justification>
  </clause>

  <clause id="17228">
    <literal><![CDATA[
      K(x,K(y * 1,z) * (y * u)) = K(x,T(y \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(15880,a,17207,a)].">
      <j1 rule="hyper" parents="15880 17207"/>
    </justification>
  </clause>

  <clause id="17229">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17177,a(flip),b,17214,a)].">
      <j1 rule="hyper" parents="63 17177 17214"/>
    </justification>
  </clause>

  <clause id="17230">
    <literal><![CDATA[
      K(x,y * (z \ K(z,u))) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(13333,a,17229,a),flip(a)].">
      <j1 rule="hyper" parents="13333 17229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17231">
    <literal><![CDATA[
      K(x,y * (z \ K(u,u \ w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,12128,a,b,17229,a)].">
      <j1 rule="hyper" parents="347 12128 17229"/>
    </justification>
  </clause>

  <clause id="17232">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(u,w))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,14870,a(flip),b,17229,a),flip(a)].">
      <j1 rule="hyper" parents="347 14870 17229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17233">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,u))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,12128,a(flip),b,17229,a),flip(a)].">
      <j1 rule="hyper" parents="347 12128 17229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17234">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K((z \ 1) * u,u))) = K(x,y / ((z \ K(z \ u,u)) * u))
    ]]></literal>
    <justification jstring="[para(13336(a,2),17230(a,2,2,2))].">
      <j1 rule="para" parents="13336 17230"/>
    </justification>
  </clause>

  <clause id="17235">
    <literal><![CDATA[
      K(x,y * ((z * u) * u)) = K(x,y * (u * (u * z)))
    ]]></literal>
    <justification jstring="[para(111(a,1),17215(a,1,2,2))].">
      <j1 rule="para" parents="111 17215"/>
    </justification>
  </clause>

  <clause id="17236">
    <literal><![CDATA[
      K(x,y * (((z * T(u,w)) * K(v5,u)) * K(v5,u))) = K(x,y * (K(v5,u) * ((K(v5,u) * z) * T(u,w))))
    ]]></literal>
    <justification jstring="[para(7673(a,2),17235(a,2,2,2,2))].">
      <j1 rule="para" parents="7673 17235"/>
    </justification>
  </clause>

  <clause id="17237">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * (w \ (y * z))) = K(x,(y \ u) * (w \ (z * y)))
    ]]></literal>
    <justification jstring="[para(13906(a,1),17216(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13906 17216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17238">
    <literal><![CDATA[
      K(x,(T(y \ z,y) / u) * w) = K(x,((z / y) / u) * w)
    ]]></literal>
    <justification jstring="[para(13361(a,1),17217(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13361 17217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17239">
    <literal><![CDATA[
      K(x,(y \ ((z * u) / z)) * w) = K(x,(y \ T(u,z)) * w)
    ]]></literal>
    <justification jstring="[para(14224(a,2),17218(a,1,2,1))].">
      <j1 rule="para" parents="14224 17218"/>
    </justification>
  </clause>

  <clause id="17240">
    <literal><![CDATA[
      K(x,T(y \ 1,L(z,u,w)) \ v5) = K(x,K(y * 1,z) * (y * v5))
    ]]></literal>
    <justification jstring="[hyper(17151,a,17228,a),flip(a)].">
      <j1 rule="hyper" parents="17151 17228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17241">
    <literal><![CDATA[
      K(x,y / (z * (u * K(w,u)))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14872,a,b,17232,a)].">
      <j1 rule="hyper" parents="63 14872 17232"/>
    </justification>
  </clause>

  <clause id="17242">
    <literal><![CDATA[
      K(x,(K(y \ z,y) * u) / w) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17018,a,b,17233,a)].">
      <j1 rule="hyper" parents="63 17018 17233"/>
    </justification>
  </clause>

  <clause id="17243">
    <literal><![CDATA[
      K(x,(T((K(y,z) * u) \ w,K(z,y) * u) / v5) * v6) = K(x,((w / (K(y,z) * u)) / v5) * v6)
    ]]></literal>
    <justification jstring="[para(15511(a,1),17238(a,1,2,1,1))].">
      <j1 rule="para" parents="15511 17238"/>
    </justification>
  </clause>

  <clause id="17244">
    <literal><![CDATA[
      T(x,(y \ ((z * u) / z)) * w) = T(x,(y \ T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(132,a,17239,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 17239 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17245">
    <literal><![CDATA[
      K(x,y / (z * T(T(u,w),w))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(4972(a,1),17241(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4972 17241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17246">
    <literal><![CDATA[
      K(x,y / (z * T(u \ w,u))) = K(x,y / (z * (w / u)))
    ]]></literal>
    <justification jstring="[para(4990(a,1),17241(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4990 17241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17247">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,T(y * (1 / z),z) / u)
    ]]></literal>
    <justification jstring="[para(5767(a,1),17242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5767 17242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17248">
    <literal><![CDATA[
      T(x,K(y,z) * (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u * (w * K(y,z))) = v5
    ]]></literal>
    <justification jstring="[para(13555(a,2),17118(a,1))].">
      <j1 rule="para" parents="13555 17118"/>
    </justification>
  </clause>

  <clause id="17249">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (w * K(y,z))) = v5
    ]]></literal>
    <justification jstring="[para(13579(a,2),17154(a,1))].">
      <j1 rule="para" parents="13579 17154"/>
    </justification>
  </clause>

  <clause id="17250">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (w * K(z,y))) = v5
    ]]></literal>
    <justification jstring="[para(15548(a,2),17154(a,1))].">
      <j1 rule="para" parents="15548 17154"/>
    </justification>
  </clause>

  <clause id="17251">
    <literal><![CDATA[
      T(x,K(y,z) * (u * T(z / u,w))) = T(x,T(u * T(z / u,w),y))
    ]]></literal>
    <justification jstring="[hyper(17204,a,16492,a)].">
      <j1 rule="hyper" parents="17204 16492"/>
    </justification>
  </clause>

  <clause id="17252">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * (u * z)) = K(x,(z * u) * (u \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16419,a(flip),b,17227,a),flip(a)].">
      <j1 rule="hyper" parents="63 16419 17227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17253">
    <literal><![CDATA[
      K(x,(T(y,((z \ 1) \ u) / u) / u) * ((z \ K(z,u)) \ u)) = K(x,((((z \ 1) \ u) / u) * u) * (u \ y))
    ]]></literal>
    <justification jstring="[para(7723(a,2),17252(a,1,2,2))].">
      <j1 rule="para" parents="7723 17252"/>
    </justification>
  </clause>

  <clause id="17254">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * K(u * K(v6,v7),w))) = v5
    ]]></literal>
    <justification jstring="[para(16472(a,1),17250(a,1))].">
      <j1 rule="para" parents="16472 17250"/>
    </justification>
  </clause>

  <clause id="17256">
    <literal><![CDATA[
      L(x * L(x \ y,z,u),z,K(x \ y,u)) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14392,a,b,16877,a)].">
      <j1 rule="hyper" parents="63 14392 16877"/>
    </justification>
  </clause>

  <clause id="17257">
    <literal><![CDATA[
      x \ T(K(y,K(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,u)) * (x \ T(w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(16973(a,2),13531(a,1))].">
      <j1 rule="para" parents="16973 13531"/>
    </justification>
  </clause>

  <clause id="17258">
    <literal><![CDATA[
      x \ (y * (K(z,K(u,w)) * v5)) = (x \ (y * v5)) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[para(13514(a,2),16974(a,1,2,2))].">
      <j1 rule="para" parents="13514 16974"/>
    </justification>
  </clause>

  <clause id="17259">
    <literal><![CDATA[
      (x \ (y * z)) * K(y,K(u,w)) = x \ (T(y,K(u,w)) * z)
    ]]></literal>
    <justification jstring="[para(13530(a,1),16974(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13530 16974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17260">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,K(w,v5)) * v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ (u * v6))) = v7
    ]]></literal>
    <justification jstring="[para(17259(a,1),14832(a,1,2,2))].">
      <j1 rule="para" parents="17259 14832"/>
    </justification>
  </clause>

  <clause id="17261">
    <literal><![CDATA[
      K(x,y) / L(z \ 1,u,K(w,v5)) = K(x,y) * T(z,a(v5,u,w))
    ]]></literal>
    <justification jstring="[para(14337(a,2),16997(a,1,2))].">
      <j1 rule="para" parents="14337 16997"/>
    </justification>
  </clause>

  <clause id="17262">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) * v5 = (x * w) * (K(y,K(z,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,13533,a,b,17007,a),flip(a)].">
      <j1 rule="hyper" parents="347 13533 17007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17263">
    <literal><![CDATA[
      K(x,L(y,z,u / (y * w))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(13995,a,17092,a),flip(a)].">
      <j1 rule="hyper" parents="13995 17092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17264">
    <literal><![CDATA[
      K(x,L(y,z,(y * u) \ w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(16929,a,17263,a)].">
      <j1 rule="hyper" parents="16929 17263"/>
    </justification>
  </clause>

  <clause id="17265">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) \ u) = K(x,u * a(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,15325,a(flip),b,17094,a)].">
      <j1 rule="hyper" parents="63 15325 17094"/>
    </justification>
  </clause>

  <clause id="17266">
    <literal><![CDATA[
      K(x * L(x \ y,z,u),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * L(x \ y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(17103(a,1),7478(a,1))].">
      <j1 rule="para" parents="17103 7478"/>
    </justification>
  </clause>

  <clause id="17267">
    <literal><![CDATA[
      T(x * a(y,z,K(u,w)),v5) = T(x,v5) * a(y,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(37,a,4963,a,b,17127,a),flip(a)].">
      <j1 rule="hyper" parents="37 4963 17127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17268">
    <literal><![CDATA[
      T(x,y * a(z,u,K(w,v5))) * a(v6,v7,K(v8,v9)) = T(x * a(v6,v7,K(v8,v9)),y)
    ]]></literal>
    <justification jstring="[hyper(17119,a,17267,a),flip(a)].">
      <j1 rule="hyper" parents="17119 17267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17269">
    <literal><![CDATA[
      T(x * a(y,z,K(u,w)),v5) = a(y,z,K(u,w)) * T(x,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,16833,a,b,17267,a),flip(a)].">
      <j1 rule="hyper" parents="347 16833 17267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17270">
    <literal><![CDATA[
      T(a(x,y,K(z,u)) * w,v5) = T(w,v5) * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(16833(a,2),17267(a,1,1))].">
      <j1 rule="para" parents="16833 17267"/>
    </justification>
  </clause>

  <clause id="17271">
    <literal><![CDATA[
      x / T((a(y,z,K(u,w)) * x) * a(w,z,K(u,y)),v5) = K(v5,x / a(w,z,K(u,y)))
    ]]></literal>
    <justification jstring="[para(17269(a,2),14071(a,1,2))].">
      <j1 rule="para" parents="17269 14071"/>
    </justification>
  </clause>

  <clause id="17272">
    <literal><![CDATA[
      K(K(x,L(y,z,u)) * w,v5) = K(K(x,y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(17134,a,4920,a(flip))].">
      <j1 rule="hyper" parents="17134 4920"/>
    </justification>
  </clause>

  <clause id="17273">
    <literal><![CDATA[
      K(K(L(x,y,z),u) * w,v5) = K(K(x,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(9768(a,1),17272(a,1,1,1))].">
      <j1 rule="para" parents="9768 17272"/>
    </justification>
  </clause>

  <clause id="17274">
    <literal><![CDATA[
      K(x * K(L(y,z,u),w),v5) = K(K(y,w) * x,v5)
    ]]></literal>
    <justification jstring="[hyper(13606,a,17273,a)].">
      <j1 rule="hyper" parents="13606 17273"/>
    </justification>
  </clause>

  <clause id="17275">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),v5) = K(K(y,z) * x,v5)
    ]]></literal>
    <justification jstring="[para(7037(a,1),17274(a,1,1,2))].">
      <j1 rule="para" parents="7037 17274"/>
    </justification>
  </clause>

  <clause id="17276">
    <literal><![CDATA[
      K(x,y * (z \ (u * (w / u)))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[para(13045(a,1),17180(a,2,2,2))].">
      <j1 rule="para" parents="13045 17180"/>
    </justification>
  </clause>

  <clause id="17277">
    <literal><![CDATA[
      K(x,T(y * ((z * y) \ u),z)) = K(x,y * ((z * y) \ T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14695,a(flip),b,17276,a)].">
      <j1 rule="hyper" parents="63 14695 17276"/>
    </justification>
  </clause>

  <clause id="17278">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z))) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(9(a,1),17276(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 17276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17279">
    <literal><![CDATA[
      K(x,y * (z \ T(u * w,w))) = K(x,y * (z \ (w * u)))
    ]]></literal>
    <justification jstring="[para(11(a,1),17276(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 17276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17280">
    <literal><![CDATA[
      K(x,x * (((y * x) * z) \ T(u,(y * x) * z))) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,11485,a(flip),b,17278,a),flip(a)].">
      <j1 rule="hyper" parents="347 11485 17278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17281">
    <literal><![CDATA[
      K(x,y * (T(z,u) \ u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(4281(a,2),17278(a,1,2,2))].">
      <j1 rule="para" parents="4281 17278"/>
    </justification>
  </clause>

  <clause id="17282">
    <literal><![CDATA[
      K(x,(((y * z) / y) \ u) * w) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17196,a(flip),b,17188,a),flip(a)].">
      <j1 rule="hyper" parents="63 17196 17188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17283">
    <literal><![CDATA[
      K(x,(T(T(y,z),z) \ u) * w) = K(x,(y \ u) * w)
    ]]></literal>
    <justification jstring="[para(255(a,1),17282(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="255 17282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17284">
    <literal><![CDATA[
      K((T(T(x,y),y) \ z) * u,w) = (v5 * K(w,(x \ z) * u)) \ v5
    ]]></literal>
    <justification jstring="[para(17283(a,1),6123(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="17283 6123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17285">
    <literal><![CDATA[
      K(x,y) / L(z \ 1,u,K(w,v5)) = K(x,y) * L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(14337(a,2),17261(a,2,2))].">
      <j1 rule="para" parents="14337 17261"/>
    </justification>
  </clause>

  <clause id="17286">
    <literal><![CDATA[
      K(x,y * ((z * y) \ T(u,z))) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,16107,a(flip),b,17277,a),flip(a)].">
      <j1 rule="hyper" parents="63 16107 17277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17287">
    <literal><![CDATA[
      K(x,((y * z) / (u * y)) * u) = K(x,u * ((y * u) \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12097,a(flip),b,17286,a),flip(a)].">
      <j1 rule="hyper" parents="63 12097 17286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17288">
    <literal><![CDATA[
      K(x,y * ((T(z,u) * y) \ u)) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[para(13194(a,2),17286(a,1,2,2))].">
      <j1 rule="para" parents="13194 17286"/>
    </justification>
  </clause>

  <clause id="17289">
    <literal><![CDATA[
      K((T(T(x,y),y) \ z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((x \ z) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(17284(a,2),6141(a,1))].">
      <j1 rule="para" parents="17284 6141"/>
    </justification>
  </clause>

  <clause id="17290">
    <literal><![CDATA[
      T(x * (T(y,x) * K(z,u)),K(z,u)) = (K(z,u) * y) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,14092,a(flip),b,16817,a),flip(a)].">
      <j1 rule="hyper" parents="347 14092 16817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17291">
    <literal><![CDATA[
      T((K(x,y) * z) * u,K(x,y)) = u * (T(z,u) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(7352,a,17290,a)].">
      <j1 rule="hyper" parents="7352 17290"/>
    </justification>
  </clause>

  <clause id="17292">
    <literal><![CDATA[
      K(x,(y * (T(z,y) * K(u,w))) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,((K(u,w) * z) * y) * v5) = v6
    ]]></literal>
    <justification jstring="[para(17291(a,1),14821(a,1,2,1))].">
      <j1 rule="para" parents="17291 14821"/>
    </justification>
  </clause>

  <clause id="17293">
    <literal><![CDATA[
      K(x,y \ (z * (T(u,z) * K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((K(w,v5) * u) * z)) = v6
    ]]></literal>
    <justification jstring="[para(17291(a,1),14824(a,1,2,2))].">
      <j1 rule="para" parents="17291 14824"/>
    </justification>
  </clause>

  <clause id="17294">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(z,y,x)) = x * (y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(16822,a,14678,a)].">
      <j1 rule="hyper" parents="16822 14678"/>
    </justification>
  </clause>

  <clause id="17295">
    <literal><![CDATA[
      K(x,y * ((z * (u / w)) * K(L(w,u,z),v5))) = K(x,y * (z * (u / T(w,v5))))
    ]]></literal>
    <justification jstring="[para(17294(a,1),17163(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="17294 17163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17296">
    <literal><![CDATA[
      K(x,y * (z \ K(u,L(w,v5,v6)))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,17177,a(flip),b,17213,a),flip(a)].">
      <j1 rule="hyper" parents="347 17177 17213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17297">
    <literal><![CDATA[
      K((x \ T(y,x)) * z,u) = K((y / x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(17222,a,13585,a)].">
      <j1 rule="hyper" parents="17222 13585"/>
    </justification>
  </clause>

  <clause id="17298">
    <literal><![CDATA[
      K((T(x,x \ y) \ T(y,T(x,x \ y))) * z,u) = K((x \ y) * z,u)
    ]]></literal>
    <justification jstring="[para(296(a,1),17297(a,2,1,1))].">
      <j1 rule="para" parents="296 17297"/>
    </justification>
  </clause>

  <clause id="17299">
    <literal><![CDATA[
      K(x,T(y \ 1,L(z,u,w)) \ v5) = K(x,K(y,z) * (y * v5))
    ]]></literal>
    <justification jstring="[para(8(a,1),17240(a,2,2,1,1))].">
      <j1 rule="para" parents="8 17240"/>
    </justification>
  </clause>

  <clause id="17300">
    <literal><![CDATA[
      K(x,T(y \ 1,L(z,u,w)) \ v5) = K(x,T(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(14900,a,17299,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14900 17299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17301">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(398(a,1),17300(a,1,2,1,2))].">
      <j1 rule="para" parents="398 17300"/>
    </justification>
  </clause>

  <clause id="17302">
    <literal><![CDATA[
      K(x,T(1 / y,z) \ u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(12029,a,17301,a)].">
      <j1 rule="hyper" parents="12029 17301"/>
    </justification>
  </clause>

  <clause id="17303">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z) \ u,w,v5)) = K(L(x,w,v5),T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(11169,a,17301,a)].">
      <j1 rule="hyper" parents="11169 17301"/>
    </justification>
  </clause>

  <clause id="17304">
    <literal><![CDATA[
      K(x,(((y * z) \ y) \ 1) \ u) = K(x,T((z * y) \ y,y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15622,a(flip),b,17301,a)].">
      <j1 rule="hyper" parents="63 15622 17301"/>
    </justification>
  </clause>

  <clause id="17305">
    <literal><![CDATA[
      K(x,T(y \ 1,z) * u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(80(a,1),17302(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="80 17302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17306">
    <literal><![CDATA[
      K(x,T(y * ((z \ (u * y)) \ 1),u)) = K(x,T(z \ (u * y),z) \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16367,a(flip),b,17305,a)].">
      <j1 rule="hyper" parents="63 16367 17305"/>
    </justification>
  </clause>

  <clause id="17307">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z) \ u,w,v5)) = K(x,L(T(y,z) * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,11108,a(flip),b,17303,a),flip(a)].">
      <j1 rule="hyper" parents="347 11108 17303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17308">
    <literal><![CDATA[
      K(x,(((y * z) \ y) \ 1) \ u) = K(x,(y / (z * y)) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,15612,a(flip),b,17304,a),flip(a)].">
      <j1 rule="hyper" parents="347 15612 17304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17309">
    <literal><![CDATA[
      K(x,(y / (z * y)) * u) = K(x,((y * z) \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(13242,a,17308,a),flip(a)].">
      <j1 rule="hyper" parents="13242 17308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17310">
    <literal><![CDATA[
      K(x,(y / (z * y)) * u) = K(x,(y \ (y / z)) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,5476,a(flip),b,17309,a),flip(a)].">
      <j1 rule="hyper" parents="347 5476 17309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17312">
    <literal><![CDATA[
      (x / T((y / (z * y)) * u,w)) \ (x * K(w,(y \ (y / z)) * u)) = (y / (z * y)) * u
    ]]></literal>
    <justification jstring="[para(17310(a,1),6170(a,1,2,2))].">
      <j1 rule="para" parents="17310 6170"/>
    </justification>
  </clause>

  <clause id="17313">
    <literal><![CDATA[
      K(x,L(T(1 / y,z) * u,w,v5)) = K(x,L(T(y,z) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(83(a,1),17307(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="83 17307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17314">
    <literal><![CDATA[
      K(x,L(T(1 / y,z) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(17313(a,1),14692(a,1))].">
      <j1 rule="para" parents="17313 14692"/>
    </justification>
  </clause>

  <clause id="17315">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) \ v5) \ v6) = K(x,v5 \ (L(K(y,z),u,w) * v6))
    ]]></literal>
    <justification jstring="[hyper(6481,a,16899,a),flip(a)].">
      <j1 rule="hyper" parents="6481 16899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17316">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) / x = T(y \ R(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(16995,a,17109,a)].">
      <j1 rule="hyper" parents="16995 17109"/>
    </justification>
  </clause>

  <clause id="17317">
    <literal><![CDATA[
      (a(x,y,x) * R(x,z,u)) / R(x,y,x) = T(x \ R(x,z,u),R(x,y,x))
    ]]></literal>
    <justification jstring="[para(10975(a,1),17316(a,1,1))].">
      <j1 rule="para" parents="10975 17316"/>
    </justification>
  </clause>

  <clause id="17318">
    <literal><![CDATA[
      K(x,(y / T(z,T(u,w))) / v5) = K(x,(y / z) * (v5 \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(14883,a,17024,a),flip(a)].">
      <j1 rule="hyper" parents="14883 17024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17319">
    <literal><![CDATA[
      K(x,(y / T(z,T(u,w))) / v5) = K(x,(y / T(z,u)) / v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,17023,a(flip),b,17318,a),flip(a)].">
      <j1 rule="hyper" parents="347 17023 17318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17320">
    <literal><![CDATA[
      K(x,(y / T(z,u)) / T(w,T(z,u) \ y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w \ (y / T(z,T(u,v6)))) = v5
    ]]></literal>
    <justification jstring="[para(17319(a,1),14897(a,1))].">
      <j1 rule="para" parents="17319 14897"/>
    </justification>
  </clause>

  <clause id="17321">
    <literal><![CDATA[
      K(((x \ y) / z) \ u,T(w,x * (y / z))) = K(u / ((x \ y) / z),w)
    ]]></literal>
    <justification jstring="[hyper(13421,a,17050,a)].">
      <j1 rule="hyper" parents="13421 17050"/>
    </justification>
  </clause>

  <clause id="17322">
    <literal><![CDATA[
      L(x,T(y,z),(y / z) \ 1) = L(x,T(y,z),(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,11458,a(flip),b,17077,a)].">
      <j1 rule="hyper" parents="63 11458 17077"/>
    </justification>
  </clause>

  <clause id="17323">
    <literal><![CDATA[
      L(x,T(y,z),(z \ y) \ 1) = L(x,y,(y / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(14445,a,17322,a),flip(a)].">
      <j1 rule="hyper" parents="14445 17322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17324">
    <literal><![CDATA[
      L(x,y,(y / z) \ 1) = L(x,y,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(12394,a,17323,a),flip(a)].">
      <j1 rule="hyper" parents="12394 17323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17325">
    <literal><![CDATA[
      L(x,(y * z) / y,(T(y,z) \ ((y * z) / y)) \ 1) = L(x,(y * z) / y,(z / y) \ 1)
    ]]></literal>
    <justification jstring="[para(1520(a,1),17324(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1520 17324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17326">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(x,w,K(u \ y,z)) = K(x,L((y * z) / u,w,z \ 1))
    ]]></literal>
    <justification jstring="[para(11290(a,1),17091(a,1,2))].">
      <j1 rule="para" parents="11290 17091"/>
    </justification>
  </clause>

  <clause id="17327">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ T(y,v5)))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,13990,a(flip),b,17097,a),flip(a)].">
      <j1 rule="hyper" parents="347 13990 17097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17328">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(y * (z \ u),u) * w)
    ]]></literal>
    <justification jstring="[para(8412(a,1),17104(a,2,2,1))].">
      <j1 rule="para" parents="8412 17104"/>
    </justification>
  </clause>

  <clause id="17329">
    <literal><![CDATA[
      K(x,y * (z \ T(u,w \ v5))) = K(x,y * (z \ T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17166,a(flip),b,17179,a),flip(a)].">
      <j1 rule="hyper" parents="63 17166 17179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17330">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ 1) \ w) = K(x,((T(z,y) * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17195,a(flip),b,17198,a)].">
      <j1 rule="hyper" parents="63 17195 17198"/>
    </justification>
  </clause>

  <clause id="17331">
    <literal><![CDATA[
      K(x,((T(y,z) * z) / u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,((z * y) / u) * w) = v5
    ]]></literal>
    <justification jstring="[para(17330(a,1),13242(a,1))].">
      <j1 rule="para" parents="17330 13242"/>
    </justification>
  </clause>

  <clause id="17332">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) * K(x,K(u,w)) = K(x,w * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(13691,a,17199,a)].">
      <j1 rule="hyper" parents="13691 17199"/>
    </justification>
  </clause>

  <clause id="17333">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) * w)) = K(x,(u \ (z * (y / z))) * w)
    ]]></literal>
    <justification jstring="[hyper(12116,a,17202,a)].">
      <j1 rule="hyper" parents="12116 17202"/>
    </justification>
  </clause>

  <clause id="17334">
    <literal><![CDATA[
      K(x,(y \ (z * (u / z))) * w) = K(x,(y \ T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17192,a(flip),b,17333,a),flip(a)].">
      <j1 rule="hyper" parents="63 17192 17333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17335">
    <literal><![CDATA[
      T(x,(y \ z) * (u * K(w,z \ y))) = T(x,T((y \ z) \ 1,w) \ u)
    ]]></literal>
    <justification jstring="[hyper(17248,a,17210,a)].">
      <j1 rule="hyper" parents="17248 17210"/>
    </justification>
  </clause>

  <clause id="17336">
    <literal><![CDATA[
      K(x,(T(y,K(z,u) * w) / v5) * v6) = K(x,(T(y,w) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,17189,a(flip),b,17226,a),flip(a)].">
      <j1 rule="hyper" parents="63 17189 17226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17337">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,((1 / z) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(347,a,12226,a(flip),b,17247,a),flip(a)].">
      <j1 rule="hyper" parents="347 12226 17247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17338">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(347,a,5594,a(flip),b,17337,a),flip(a)].">
      <j1 rule="hyper" parents="347 5594 17337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17339">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,(y * x) * z)) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(11748,a,17280,a)].">
      <j1 rule="hyper" parents="11748 17280"/>
    </justification>
  </clause>

  <clause id="17340">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,z * (y * x))) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(14856,a,17339,a)].">
      <j1 rule="hyper" parents="14856 17339"/>
    </justification>
  </clause>

  <clause id="17341">
    <literal><![CDATA[
      K((T(x,x \ y) \ T(y,x)) * z,u) = K((x \ y) * z,u)
    ]]></literal>
    <justification jstring="[para(4172(a,1),17298(a,1,1,1,2))].">
      <j1 rule="para" parents="4172 17298"/>
    </justification>
  </clause>

  <clause id="17342">
    <literal><![CDATA[
      K((T(x \ y,x) * K(y,x)) * z,u) = K((x \ y) * z,u)
    ]]></literal>
    <justification jstring="[para(13114(a,1),17341(a,1,1,1))].">
      <j1 rule="para" parents="13114 17341"/>
    </justification>
  </clause>

  <clause id="17343">
    <literal><![CDATA[
      K(T((x \ y) * K(y,x),x) * z,u) = K((x \ y) * z,u)
    ]]></literal>
    <justification jstring="[para(7253(a,2),17342(a,1,1,1))].">
      <j1 rule="para" parents="7253 17342"/>
    </justification>
  </clause>

  <clause id="17344">
    <literal><![CDATA[
      K(T(x \ T(y,x),x) * z,u) = K((x \ y) * z,u)
    ]]></literal>
    <justification jstring="[para(6106(a,1),17343(a,1,1,1,1))].">
      <j1 rule="para" parents="6106 17343"/>
    </justification>
  </clause>

  <clause id="17345">
    <literal><![CDATA[
      K((T(x,y) / y) * z,u) = K((y \ x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(15743,a,17344,a)].">
      <j1 rule="hyper" parents="15743 17344"/>
    </justification>
  </clause>

  <clause id="17346">
    <literal><![CDATA[
      K((T(T(x,y),z) / y) * u,w) = K((y \ T(x,z)) * u,w)
    ]]></literal>
    <justification jstring="[para(23(a,1),17345(a,1,1,1,1))].">
      <j1 rule="para" parents="23 17345"/>
    </justification>
  </clause>

  <clause id="17347">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) * v5) \ v6) = K(x,v5 \ (L(K(z,y),u,w) * v6))
    ]]></literal>
    <justification jstring="[para(8255(a,1),17315(a,1,2,1))].">
      <j1 rule="para" parents="8255 17315"/>
    </justification>
  </clause>

  <clause id="17348">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(347,a,14866,a(flip),b,17328,a),flip(a)].">
      <j1 rule="hyper" parents="347 14866 17328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17349">
    <literal><![CDATA[
      K(x,K(y \ z,u) * (w * (u / (y / z)))) = K(x,w * T((y / z) \ u,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15225,a(flip),b,17348,a),flip(a)].">
      <j1 rule="hyper" parents="63 15225 17348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17350">
    <literal><![CDATA[
      K(x,K(y * z,u) * (w * v5)) * K(x,K(w,v5)) = K(x,v5 * (K(u,z \ y) * w))
    ]]></literal>
    <justification jstring="[para(15884(a,1),17332(a,1,1))].">
      <j1 rule="para" parents="15884 17332"/>
    </justification>
  </clause>

  <clause id="17351">
    <literal><![CDATA[
      T(x,T(K(y,z \ u) * z,u)) = T(x,T((u \ z) \ 1,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17142,a(flip),b,17335,a)].">
      <j1 rule="hyper" parents="63 17142 17335"/>
    </justification>
  </clause>

  <clause id="17352">
    <literal><![CDATA[
      T(x,T(y * K(z,y \ u),u)) = T(x,T((u \ y) \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(13578,a,17351,a)].">
      <j1 rule="hyper" parents="13578 17351"/>
    </justification>
  </clause>

  <clause id="17353">
    <literal><![CDATA[
      T(x,T((y \ z) \ 1,u) \ y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z \ y,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(17352(a,1),7585(a,1))].">
      <j1 rule="para" parents="17352 7585"/>
    </justification>
  </clause>

  <clause id="17354">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ z) = T(x,T(z \ y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(17353,a,15900,a)].">
      <j1 rule="hyper" parents="17353 15900"/>
    </justification>
  </clause>

  <clause id="17355">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ z) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z * T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(17354(a,2),10394(a,1))].">
      <j1 rule="para" parents="17354 10394"/>
    </justification>
  </clause>

  <clause id="17356">
    <literal><![CDATA[
      K(x,((K(y,z) \ u) * L((K(y,z) \ u) \ u,w,v5)) \ v6) = K(x,(K(y,z) \ u) \ (L(K(z,y),w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(742(a,2),17347(a,1,2,1))].">
      <j1 rule="para" parents="742 17347"/>
    </justification>
  </clause>

  <clause id="17357">
    <literal><![CDATA[
      L(x,K(y,z) * u,z * y) = L(x,u,z * y)
    ]]></literal>
    <justification jstring="[hyper(13778,a,16881,a)].">
      <j1 rule="hyper" parents="13778 16881"/>
    </justification>
  </clause>

  <clause id="17359">
    <literal><![CDATA[
      L(x,K(y,z / y) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),17357(a,1,3))].">
      <j1 rule="para" parents="12 17357"/>
    </justification>
  </clause>

  <clause id="17360">
    <literal><![CDATA[
      L(x,K(y,y \ z) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[para(5098(a,1),17359(a,1,2,1))].">
      <j1 rule="para" parents="5098 17359"/>
    </justification>
  </clause>

  <clause id="17361">
    <literal><![CDATA[
      L(x,K(y,z) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[hyper(12402,a,17360,a)].">
      <j1 rule="hyper" parents="12402 17360"/>
    </justification>
  </clause>

  <clause id="17362">
    <literal><![CDATA[
      L(x,K(y,z) * u,z) = L(x,u,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),17361(a,2,3))].">
      <j1 rule="para" parents="12 17361"/>
    </justification>
  </clause>

  <clause id="17363">
    <literal><![CDATA[
      L(x,T(y,z) \ u,y) = L(x,y \ u,y)
    ]]></literal>
    <justification jstring="[para(5209(a,1),17362(a,1,2))].">
      <j1 rule="para" parents="5209 17362"/>
    </justification>
  </clause>

  <clause id="17364">
    <literal><![CDATA[
      L(x,y * K(z,u),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(7432(a,1),17362(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7432 17362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17365">
    <literal><![CDATA[
      L(x,y \ K(z,u),z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(12973(a,1),17364(a,1,2))].">
      <j1 rule="para" parents="12973 17364"/>
    </justification>
  </clause>

  <clause id="17366">
    <literal><![CDATA[
      T(x,L(y,z \ 1,u) * (u * (z \ 1))) = T(x,(y * (z \ K(u,z \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(17365(a,1),16420(a,1,2,1))].">
      <j1 rule="para" parents="17365 16420"/>
    </justification>
  </clause>

  <clause id="17367">
    <literal><![CDATA[
      T(x,T(a(y,z,u),w) * v5) = T(x,v5 * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(17146,a,16948,a),flip(a)].">
      <j1 rule="hyper" parents="17146 16948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17368">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,u * a(w,v5,v6)) \ z) != v7
    ]]></literal>
    <literal><![CDATA[
      T(x,z / T(y,T(a(w,v5,v6),v8) * u)) = v7
    ]]></literal>
    <justification jstring="[para(17367(a,1),13539(a,1,2,1))].">
      <j1 rule="para" parents="17367 13539"/>
    </justification>
  </clause>

  <clause id="17369">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * K(u,K(w,v5)))) = K(u,K(w,v5)) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(16802(a,1),17013(a,1,2))].">
      <j1 rule="para" parents="16802 17013"/>
    </justification>
  </clause>

  <clause id="17370">
    <literal><![CDATA[
      K(x,K(y \ (z * (u \ 1)),w) * v5) = K(x,K(w,u * (z \ y)) * v5)
    ]]></literal>
    <justification jstring="[hyper(17172,a,15837,a)].">
      <j1 rule="hyper" parents="17172 15837"/>
    </justification>
  </clause>

  <clause id="17371">
    <literal><![CDATA[
      T(x,K(y \ (z * (u \ 1)),w) * v5) = T(x,K(w,u * (z \ y)) * v5)
    ]]></literal>
    <justification jstring="[hyper(132,a,17370,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 17370 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17372">
    <literal><![CDATA[
      T(K(x,K(y,z * (u \ w)) * v5),v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) = (v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) \ K(w \ (u * (1 / z)),y)
    ]]></literal>
    <justification jstring="[para(17370(a,1),13260(a,1,1))].">
      <j1 rule="para" parents="17370 13260"/>
    </justification>
  </clause>

  <clause id="17373">
    <literal><![CDATA[
      T(x,y * K(z,u \ (w * (v5 \ 1)))) = T(x,K(z,v5 * (w \ u)) * y)
    ]]></literal>
    <justification jstring="[hyper(15530,a,17371,a)].">
      <j1 rule="hyper" parents="15530 17371"/>
    </justification>
  </clause>

  <clause id="17374">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) * v5) = K(x,K(w,u) * ((y * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(17151,a,17201,a),flip(a)].">
      <j1 rule="hyper" parents="17151 17201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17375">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,u) * ((y * z) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(17201(a,1),17151(a,1))].">
      <j1 rule="para" parents="17201 17151"/>
    </justification>
  </clause>

  <clause id="17376">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,w) * (y * z)) = T(x,z * (y * K(w * u,w)))
    ]]></literal>
    <justification jstring="[hyper(17205,a,12088,a),flip(a)].">
      <j1 rule="hyper" parents="17205 12088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17377">
    <literal><![CDATA[
      T(x,y * (z * K(u * w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (z * K(w,u))) = v5
    ]]></literal>
    <justification jstring="[para(17376(a,1),17205(a,1))].">
      <j1 rule="para" parents="17376 17205"/>
    </justification>
  </clause>

  <clause id="17378">
    <literal><![CDATA[
      T(x,y * ((z * u) * K(u,w))) = T(x,y * (z * ((w \ u) * w)))
    ]]></literal>
    <justification jstring="[hyper(17377,a,15997,a)].">
      <j1 rule="hyper" parents="17377 15997"/>
    </justification>
  </clause>

  <clause id="17379">
    <literal><![CDATA[
      T(x,y * (z * ((u \ w) * u))) = T(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[para(5926(a,1),17378(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5926 17378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17380">
    <literal><![CDATA[
      T(x,y * T(z * ((u \ w) * u),z)) = T(x,y * (z * T((z * w) / z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15688,a(flip),b,17379,a)].">
      <j1 rule="hyper" parents="63 15688 17379"/>
    </justification>
  </clause>

  <clause id="17381">
    <literal><![CDATA[
      K(x,y * (z * K(u * K(w,v5),v6 \ v7))) = K(x,(y * z) * K(u,v7 * v6))
    ]]></literal>
    <justification jstring="[hyper(17254,a,15984,a)].">
      <j1 rule="hyper" parents="17254 15984"/>
    </justification>
  </clause>

  <clause id="17382">
    <literal><![CDATA[
      R(a(x,y,x) * x,z,u) / R(x,y,x) = T(x \ R(x,z,u),R(x,y,x))
    ]]></literal>
    <justification jstring="[para(11534(a,2),17317(a,1,1))].">
      <j1 rule="para" parents="11534 17317"/>
    </justification>
  </clause>

  <clause id="17383">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * K(u,K(w,v5))))) = K(u,K(w,v5)) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(16802(a,1),17369(a,1,2,2))].">
      <j1 rule="para" parents="16802 17369"/>
    </justification>
  </clause>

  <clause id="17384">
    <literal><![CDATA[
      R(R(x,y,x),z,u) / R(x,y,x) = T(x \ R(x,z,u),R(x,y,x))
    ]]></literal>
    <justification jstring="[para(8342(a,1),17382(a,1,1,1))].">
      <j1 rule="para" parents="8342 17382"/>
    </justification>
  </clause>

  <clause id="17385">
    <literal><![CDATA[
      R(x,y,x) \ R(R(x,y,x),z,u) = T(x \ R(x,z,u),R(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(3689,a,17384,a)].">
      <j1 rule="hyper" parents="3689 17384"/>
    </justification>
  </clause>

  <clause id="17386">
    <literal><![CDATA[
      R(x,y,x) \ R(R(x,y,x),z,u) = x \ R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,5802,a(flip),b,17385,a),flip(a)].">
      <j1 rule="hyper" parents="347 5802 17385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17388">
    <literal><![CDATA[
      L(x * K(y,K(z,u)),w,v5) = K(y,K(z,u)) * L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(545,a,17383,a)].">
      <j1 rule="hyper" parents="545 17383"/>
    </justification>
  </clause>

  <clause id="17389">
    <literal><![CDATA[
      ((x * y) \ (x * (y * (z * K(u,K(w,v5)))))) * K(u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = v6
    ]]></literal>
    <justification jstring="[para(17383(a,2),13557(a,1,1))].">
      <j1 rule="para" parents="17383 13557"/>
    </justification>
  </clause>

  <clause id="17390">
    <literal><![CDATA[
      L(x * K(y,K(z,u)),w,v5) = L(x,w,v5) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,13514,a(flip),b,17388,a),flip(a)].">
      <j1 rule="hyper" parents="347 13514 17388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17391">
    <literal><![CDATA[
      K(x,L(y * K(z,K(u,w)),v5,v6)) = K(x,L(y,v5,v6))
    ]]></literal>
    <justification jstring="[para(17388(a,2),14795(a,1,2))].">
      <j1 rule="para" parents="17388 14795"/>
    </justification>
  </clause>

  <clause id="17392">
    <literal><![CDATA[
      K(x,y * L(z * K(u,K(w,v5)),v6,v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      K(x,y * L(z,v6,v7)) = v8
    ]]></literal>
    <justification jstring="[para(17388(a,2),14879(a,1,2,2))].">
      <j1 rule="para" parents="17388 14879"/>
    </justification>
  </clause>

  <clause id="17393">
    <literal><![CDATA[
      K(x,L(y \ K(z,T(u,w)),v5,v6)) = K(x,L(y \ K(z,u),v5,v6))
    ]]></literal>
    <justification jstring="[para(13344(a,1),17391(a,1,2,1))].">
      <j1 rule="para" parents="13344 17391"/>
    </justification>
  </clause>

  <clause id="17395">
    <literal><![CDATA[
      L(K(x,K(y,z)) * u,w,v5) = L(u,w,v5) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(13514(a,2),17390(a,1,1))].">
      <j1 rule="para" parents="13514 17390"/>
    </justification>
  </clause>

  <clause id="17396">
    <literal><![CDATA[
      K(x,y * L(K(z,K(u,w)) * v5,v6,v7)) = K(x,y * L(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(17395(a,2),14808(a,1,2,2))].">
      <j1 rule="para" parents="17395 14808"/>
    </justification>
  </clause>

  <clause id="17397">
    <literal><![CDATA[
      K(x,T((y * K(z,T(u,w))) / v5,y \ v5)) = K(x,L((v5 / y) \ K(z,T(u,y)),v5 / y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14765,a(flip),b,17393,a)].">
      <j1 rule="hyper" parents="63 14765 17393"/>
    </justification>
  </clause>

  <clause id="17398">
    <literal><![CDATA[
      K(x,y * L((z / K(u,w)) \ v5,v6,v7)) = K(x,y * L((K(u,w) \ z) \ v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(5441(a,1),17396(a,1,2,2,1))].">
      <j1 rule="para" parents="5441 17396"/>
    </justification>
  </clause>

  <clause id="17400">
    <literal><![CDATA[
      K(x,(K(y,z) * ((K(u,T(w,v5)) \ v6) / K(y,z))) \ v7) = K(x,v6 \ (K(w,T(u,v5)) \ v7))
    ]]></literal>
    <justification jstring="[para(7093(a,1),17016(a,1,2,1,2,1,1))].">
      <j1 rule="para" parents="7093 17016"/>
    </justification>
  </clause>

  <clause id="17401">
    <literal><![CDATA[
      K(x,T(y / (z \ u),x) * (w \ K(z,u))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17233,a(flip),b,17022,a)].">
      <j1 rule="hyper" parents="63 17233 17022"/>
    </justification>
  </clause>

  <clause id="17402">
    <literal><![CDATA[
      K(x,(y / (z \ u)) * (w \ K(z,u))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(8046,a,17401,a)].">
      <j1 rule="hyper" parents="8046 17401"/>
    </justification>
  </clause>

  <clause id="17403">
    <literal><![CDATA[
      K(x,(y / (T(z,u) \ u)) / w) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17035,a(flip),b,17402,a)].">
      <j1 rule="hyper" parents="63 17035 17402"/>
    </justification>
  </clause>

  <clause id="17404">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ (K(y,w) * z)) = T(x,T(T(y \ z,u) \ z,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,17036,a(flip),b,17048,a),flip(a)].">
      <j1 rule="hyper" parents="347 17036 17048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17405">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(z / y,w,v5))) = K(x,u * L(y \ z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(11993,a,17170,a)].">
      <j1 rule="hyper" parents="11993 17170"/>
    </justification>
  </clause>

  <clause id="17406">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * L(y / z,w,v5)) = K(x,(y \ u) * L(z \ y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,17187,a(flip),b,17405,a)].">
      <j1 rule="hyper" parents="63 17187 17405"/>
    </justification>
  </clause>

  <clause id="17407">
    <literal><![CDATA[
      K(x,K((y * z) / y,y) * (u * L(K(z,y) * (y / z),w,v5))) = K(x,u * L(((y * z) / y) \ y,w,v5))
    ]]></literal>
    <justification jstring="[para(6836(a,1),17405(a,1,2,2,2,1))].">
      <j1 rule="para" parents="6836 17405"/>
    </justification>
  </clause>

  <clause id="17408">
    <literal><![CDATA[
      K(x,y * (K(z \ u,w) * (v5 * (u / z)))) = K(x,y * (v5 * T(u / z,w)))
    ]]></literal>
    <justification jstring="[hyper(17161,a,17176,a)].">
      <j1 rule="hyper" parents="17161 17176"/>
    </justification>
  </clause>

  <clause id="17409">
    <literal><![CDATA[
      K(x,T(y * ((z \ (u * y)) \ 1),u)) = K(x,((u * y) / z) \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,15593,a(flip),b,17306,a),flip(a)].">
      <j1 rule="hyper" parents="347 15593 17306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17410">
    <literal><![CDATA[
      K(x,((y * z) / u) \ T(z,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z / (u \ (y * z)),y)) = w
    ]]></literal>
    <justification jstring="[para(17409(a,1),13328(a,1))].">
      <j1 rule="para" parents="17409 13328"/>
    </justification>
  </clause>

  <clause id="17411">
    <literal><![CDATA[
      T(x,y * T(z * ((u \ w) * u),z)) = T(x,y * (z * T(T(w,u),z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,15859,a(flip),b,17380,a),flip(a)].">
      <j1 rule="hyper" parents="347 15859 17380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17412">
    <literal><![CDATA[
      T(x,y * T(z * ((u \ w) * u),z)) = T(x,y * (T(w,u) * z))
    ]]></literal>
    <justification jstring="[para(111(a,1),17411(a,2,2,2))].">
      <j1 rule="para" parents="111 17411"/>
    </justification>
  </clause>

  <clause id="17413">
    <literal><![CDATA[
      T(x,y * (((z \ u) * z) * w)) = T(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(12218,a,17412,a)].">
      <j1 rule="hyper" parents="12218 17412"/>
    </justification>
  </clause>

  <clause id="17414">
    <literal><![CDATA[
      T(x,y * (T(z \ u,z) * w)) = T(x,y * ((u / ((z \ 1) \ 1)) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16431,a,b,17413,a),flip(a)].">
      <j1 rule="hyper" parents="63 16431 17413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17415">
    <literal><![CDATA[
      T(x,y * ((z / ((u \ 1) \ 1)) * w)) = T(x,y * ((z / u) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15857,a(flip),b,17414,a),flip(a)].">
      <j1 rule="hyper" parents="63 15857 17414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17416">
    <literal><![CDATA[
      K(x,y * (z * K(u * K(w,v5),v6 \ v7))) = K(x,y * (z * K(u,v7 * v6)))
    ]]></literal>
    <justification jstring="[hyper(347,a,17153,a(flip),b,17381,a),flip(a)].">
      <j1 rule="hyper" parents="347 17153 17381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17418">
    <literal><![CDATA[
      K(x,(y / z) * L(z / y,u,w)) = K(x,(z \ y) * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(17224,a,17406,a)].">
      <j1 rule="hyper" parents="17224 17406"/>
    </justification>
  </clause>

  <clause id="17419">
    <literal><![CDATA[
      K(x,y * (z * K(u,w \ v5))) = K(x,y * (z * K(u,v5 * w)))
    ]]></literal>
    <justification jstring="[para(203(a,1),17416(a,1,2,2,2,1))].">
      <j1 rule="para" parents="203 17416"/>
    </justification>
  </clause>

  <clause id="17420">
    <literal><![CDATA[
      K(x,y * (z * K(u,w / v5))) = K(x,y * (z * K(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(14901,a,17419,a)].">
      <j1 rule="hyper" parents="14901 17419"/>
    </justification>
  </clause>

  <clause id="17421">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(z,w * v5))) = K(x,y * (T(z,w / v5) / u))
    ]]></literal>
    <justification jstring="[hyper(14851,a,17420,a),flip(a)].">
      <j1 rule="hyper" parents="14851 17420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17422">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) / v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(z,u * w) / v5)) = v6
    ]]></literal>
    <justification jstring="[para(17421(a,1),14851(a,1))].">
      <j1 rule="para" parents="17421 14851"/>
    </justification>
  </clause>

  <clause id="17423">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) / v5)) = K(x,y * (T(z,w * u) / v5))
    ]]></literal>
    <justification jstring="[hyper(17422,a,14868,a),flip(a)].">
      <j1 rule="hyper" parents="17422 14868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17424">
    <literal><![CDATA[
      K(x,T(y * z,x) * (u \ K(w,v5))) = K(x,(y * (z * K(w,v5))) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17296,a(flip),b,17021,a)].">
      <j1 rule="hyper" parents="63 17296 17021"/>
    </justification>
  </clause>

  <clause id="17426">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) / v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) * (v5 \ K(u,w))) = v6
    ]]></literal>
    <justification jstring="[para(17424(a,1),8046(a,1))].">
      <j1 rule="para" parents="17424 8046"/>
    </justification>
  </clause>

  <clause id="17427">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,z)) = w
    ]]></literal>
    <justification jstring="[para(17231(a,1),17178(a,1))].">
      <j1 rule="para" parents="17231 17178"/>
    </justification>
  </clause>

  <clause id="17428">
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,z)) = K(x,y / (z / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(17427,a,14871,a)].">
      <j1 rule="hyper" parents="17427 14871"/>
    </justification>
  </clause>

  <clause id="17429">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y / T(z / u,z))
    ]]></literal>
    <justification jstring="[hyper(16006,a,17428,a),flip(a)].">
      <j1 rule="hyper" parents="16006 17428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17430">
    <literal><![CDATA[
      x \ y != T(z,x * a(u,w,K(v5,v6))) * a(v7,v8,K(v9,v10))
    ]]></literal>
    <literal><![CDATA[
      (z * a(v7,v8,K(v9,v10))) * x = y
    ]]></literal>
    <justification jstring="[para(17268(a,2),152(a,1)),flip(a)].">
      <j1 rule="para" parents="17268 152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17431">
    <literal><![CDATA[
      K(x,K(y,z) * ((u * T(w,u)) * v5)) = K(x,((K(z,y) * w) * u) * v5)
    ]]></literal>
    <justification jstring="[hyper(17292,a,17374,a),flip(a)].">
      <j1 rule="hyper" parents="17292 17374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17432">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) * v5) = K(x,K(z,y) * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[para(111(a,1),17431(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="111 17431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17433">
    <literal><![CDATA[
      K(x,((y / K(z,u)) * w) * v5) = K(x,K(z,u) * ((y * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,14859,a,b,17432,a)].">
      <j1 rule="hyper" parents="63 14859 17432"/>
    </justification>
  </clause>

  <clause id="17434">
    <literal><![CDATA[
      K(x,((y * K(z,u)) * w) * v5) = K(x,K(u,z) * ((y * w) * v5))
    ]]></literal>
    <justification jstring="[para(6117(a,1),17433(a,1,2,1,1))].">
      <j1 rule="para" parents="6117 17433"/>
    </justification>
  </clause>

  <clause id="17435">
    <literal><![CDATA[
      T(K(x,K(y,z) * ((u * w) * v5)),v5 \ T(v5 * ((u * K(z,y)) * w),x)) = (v5 \ T(v5 * ((u * K(z,y)) * w),x)) \ T((u * K(z,y)) * w,K(u,w))
    ]]></literal>
    <justification jstring="[para(17434(a,1),13728(a,1,1))].">
      <j1 rule="para" parents="17434 13728"/>
    </justification>
  </clause>

  <clause id="17436">
    <literal><![CDATA[
      K(x,y * ((z * (u / w)) * K(w,L(v5,u,z)))) = K(x,y * (z * (u / T(w,v5))))
    ]]></literal>
    <justification jstring="[para(11108(a,1),17295(a,1,2,2,2))].">
      <j1 rule="para" parents="11108 17295"/>
    </justification>
  </clause>

  <clause id="17437">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,u * ((z \ 1) * T(y,u / z)))
    ]]></literal>
    <justification jstring="[para(13133(a,1),17366(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13133 17366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17439">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,u * ((z \ 1) * T(y,z \ u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,14911,a(flip),b,17437,a),flip(a)].">
      <j1 rule="hyper" parents="347 14911 17437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17440">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * T(u,z \ y))) = T(x,(u * (z \ 1)) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16020,a(flip),b,17439,a),flip(a)].">
      <j1 rule="hyper" parents="63 16020 17439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17441">
    <literal><![CDATA[
      K(x,y * (z * ((u / w) * K(w,v5)))) = K(x,y * (z * (u / T(w,v5))))
    ]]></literal>
    <justification jstring="[para(11174(a,1),17436(a,1,2,2))].">
      <j1 rule="para" parents="11174 17436"/>
    </justification>
  </clause>

  <clause id="17442">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * (u * z)) * (u \ K(z,u)) = K(x,y) * R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(14201(a,1),16926(a,1,1,1))].">
      <j1 rule="para" parents="14201 16926"/>
    </justification>
  </clause>

  <clause id="17444">
    <literal><![CDATA[
      ((K(x,y) * z) * T(u,z)) * (u \ K(z,u)) = K(x,y) * R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(14091(a,1),17442(a,1,1))].">
      <j1 rule="para" parents="14091 17442"/>
    </justification>
  </clause>

  <clause id="17445">
    <literal><![CDATA[
      R(K(x,y) * z,u,u \ 1) = K(x,y) * R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,6539,a(flip),b,17444,a)].">
      <j1 rule="hyper" parents="63 6539 17444"/>
    </justification>
  </clause>

  <clause id="17447">
    <literal><![CDATA[
      R(K(x,y) * (z / u),u,u \ 1) = K(x,y) * (z * (u \ 1))
    ]]></literal>
    <justification jstring="[para(691(a,1),17445(a,2,2))].">
      <j1 rule="para" parents="691 17445"/>
    </justification>
  </clause>

  <clause id="17448">
    <literal><![CDATA[
      x \ R(K(y,z) * (K(z,y) * x),u,u \ 1) = a(K(z,y) * x,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(17445(a,2),15210(a,1,2))].">
      <j1 rule="para" parents="17445 15210"/>
    </justification>
  </clause>

  <clause id="17449">
    <literal><![CDATA[
      (K(x,y) * (z * (u \ 1))) / (u \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * (z / u)) * u = w
    ]]></literal>
    <justification jstring="[para(17447(a,1),698(a,1,1))].">
      <j1 rule="para" parents="17447 698"/>
    </justification>
  </clause>

  <clause id="17450">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) / u)) * u = z * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(17449,a,14672,a)].">
      <j1 rule="hyper" parents="17449 14672"/>
    </justification>
  </clause>

  <clause id="17451">
    <literal><![CDATA[
      (K(x,y) * (K(K(y,x),z) * u)) * (u \ (z * K(y,x))) = z * a(u \ (z * K(y,x)),z,K(y,x))
    ]]></literal>
    <justification jstring="[para(13746(a,1),17450(a,1,1,2))].">
      <j1 rule="para" parents="13746 17450"/>
    </justification>
  </clause>

  <clause id="17452">
    <literal><![CDATA[
      a(K(x,y) * z,u,u \ 1) = z \ R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5261(a,1),17448(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5261 17448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17453">
    <literal><![CDATA[
      a(K(x,y) * z,u,u \ 1) = a(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,853,a(flip),b,17452,a),flip(a)].">
      <j1 rule="hyper" parents="347 853 17452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17454">
    <literal><![CDATA[
      a(T(x,y),z,z \ 1) = a(x,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(1324(a,2),17453(a,1,1))].">
      <j1 rule="para" parents="1324 17453"/>
    </justification>
  </clause>

  <clause id="17455">
    <literal><![CDATA[
      T(x,y) * a(x,z,z \ 1) = R(T(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,17454,a(flip),b,853,a)].">
      <j1 rule="hyper" parents="134 17454 853"/>
    </justification>
  </clause>

  <clause id="17456">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = y * R(T(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(17455(a,1),4795(a,2,2))].">
      <j1 rule="para" parents="17455 4795"/>
    </justification>
  </clause>

  <clause id="17457">
    <literal><![CDATA[
      (R(x,y,y \ 1) * z) / R(x,y,y \ 1) = (x * z) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,268,a(flip),b,17456,a)].">
      <j1 rule="hyper" parents="131 268 17456"/>
    </justification>
  </clause>

  <clause id="17458">
    <literal><![CDATA[
      (L(x,y,y \ 1) * z) / L(x,y,y \ 1) = (x * z) / x
    ]]></literal>
    <justification jstring="[hyper(63,a,15213,a(flip),b,17457,a)].">
      <j1 rule="hyper" parents="63 15213 17457"/>
    </justification>
  </clause>

  <clause id="17459">
    <literal><![CDATA[
      (L(x \ T(y,z),u,u \ 1) * K(z,y)) / L(x \ T(y,z),u,u \ 1) = (x \ y) / (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(13102(a,1),17458(a,2,1))].">
      <j1 rule="para" parents="13102 17458"/>
    </justification>
  </clause>

  <clause id="17460">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) / K(x,L(x,y,z) \ u) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,13999,a(flip),b,16954,a),flip(a)].">
      <j1 rule="hyper" parents="347 13999 16954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17461">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) * K(L(x,y,z) \ u,x) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(6140,a,17460,a)].">
      <j1 rule="hyper" parents="6140 17460"/>
    </justification>
  </clause>

  <clause id="17462">
    <literal><![CDATA[
      L(x,y,z) * T(u / L(x,y,z),T(x,u)) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(7194,a,17461,a)].">
      <j1 rule="hyper" parents="7194 17461"/>
    </justification>
  </clause>

  <clause id="17463">
    <literal><![CDATA[
      L(x,y,z) * T(u / L(x,y,z),x) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(8999(a,1),17462(a,1,2))].">
      <j1 rule="para" parents="8999 17462"/>
    </justification>
  </clause>

  <clause id="17464">
    <literal><![CDATA[
      T(x * L(y,z,u),a(u,z,y)) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),17463(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 17463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17465">
    <literal><![CDATA[
      K(x,L(y,z,u) * T(w,y)) = K(x,w * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(17464(a,1),16866(a,1,2))].">
      <j1 rule="para" parents="17464 16866"/>
    </justification>
  </clause>

  <clause id="17466">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) * T(y,z)) = K(x,y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(12155,a,17465,a)].">
      <j1 rule="hyper" parents="12155 17465"/>
    </justification>
  </clause>

  <clause id="17467">
    <literal><![CDATA[
      K(x,L(y,z,u) * (y \ w)) = K(x,(w / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(113(a,1),17465(a,1,2,2))].">
      <j1 rule="para" parents="113 17465"/>
    </justification>
  </clause>

  <clause id="17468">
    <literal><![CDATA[
      K(x,(y / z) * L(z,u,u)) = K(x,a(z,u,u) * y)
    ]]></literal>
    <justification jstring="[hyper(16655,a,17467,a),flip(a)].">
      <j1 rule="hyper" parents="16655 17467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17469">
    <literal><![CDATA[
      K(x,(y / z) * L(z,u,w)) = K(x,y * (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17073,a(flip),b,17467,a),flip(a)].">
      <j1 rule="hyper" parents="63 17073 17467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17470">
    <literal><![CDATA[
      K(x,a(y,z,z) * (u * y)) = K(x,u * L(y,z,z))
    ]]></literal>
    <justification jstring="[para(11(a,1),17468(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 17468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17471">
    <literal><![CDATA[
      K(x,L((y / (z \ 1)) / z,u,w) * T(z,y / (z \ K(y,z)))) = K(x,z * L(z \ (y / (z \ K(y,z))),u,w))
    ]]></literal>
    <justification jstring="[para(6537(a,1),17466(a,1,2,1,1))].">
      <j1 rule="para" parents="6537 17466"/>
    </justification>
  </clause>

  <clause id="17472">
    <literal><![CDATA[
      K(x,y \ ((z * K(u,w)) \ (v5 * (K(w,u) \ z)))) = K(x,y \ T(v5,z / K(w,u)))
    ]]></literal>
    <justification jstring="[para(6117(a,1),17063(a,1,2,2,1))].">
      <j1 rule="para" parents="6117 17063"/>
    </justification>
  </clause>

  <clause id="17473">
    <literal><![CDATA[
      T((x \ (y * z)) / T(z,K(u,w)),z) = z \ (x \ (y * T(z,K(u,w))))
    ]]></literal>
    <justification jstring="[para(7355(a,1),17079(a,1,1,2))].">
      <j1 rule="para" parents="7355 17079"/>
    </justification>
  </clause>

  <clause id="17474">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u \ (w * x)) = x \ (u \ (w * T(x,K(y,z))))
    ]]></literal>
    <justification jstring="[hyper(13570,a,17473,a)].">
      <j1 rule="hyper" parents="13570 17473"/>
    </justification>
  </clause>

  <clause id="17475">
    <literal><![CDATA[
      K(T(T(x,y) \ z,K(y,x)) * u,w) = K((x \ z) * (K(x,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(17289,a,17086,a),flip(a)].">
      <j1 rule="hyper" parents="17289 17086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17476">
    <literal><![CDATA[
      K((x \ y) * (K(x,z) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((T(x,z) \ y) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(17475(a,1),14818(a,1))].">
      <j1 rule="para" parents="17475 14818"/>
    </justification>
  </clause>

  <clause id="17477">
    <literal><![CDATA[
      K((T(x,T(y,z)) \ u) * w,v5) = K((x \ u) * (K(x,y) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(17476,a,14876,a)].">
      <j1 rule="hyper" parents="17476 14876"/>
    </justification>
  </clause>

  <clause id="17478">
    <literal><![CDATA[
      K((T(x,T(y,z)) \ u) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K((T(x,y) \ u) * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(17477(a,2),17476(a,1))].">
      <j1 rule="para" parents="17477 17476"/>
    </justification>
  </clause>

  <clause id="17479">
    <literal><![CDATA[
      K(T(x \ ((y \ z) \ z),x) * u,w) = K((T(x,x \ y) \ T(y,y * z)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(17478,a,16529,a),flip(a)].">
      <j1 rule="hyper" parents="17478 16529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17480">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(u,u \ z))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[hyper(14883,a,17175,a)].">
      <j1 rule="hyper" parents="14883 17175"/>
    </justification>
  </clause>

  <clause id="17481">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(z,u))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[hyper(63,a,17231,a(flip),b,17480,a)].">
      <j1 rule="hyper" parents="63 17231 17480"/>
    </justification>
  </clause>

  <clause id="17482">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (T(z,u) \ (u * y))) = w
    ]]></literal>
    <justification jstring="[para(17481(a,1),13335(a,1))].">
      <j1 rule="para" parents="17481 13335"/>
    </justification>
  </clause>

  <clause id="17483">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) / (u / w))) = K(x,y * T((u / w) \ z,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(17162,a,17349,a)].">
      <j1 rule="hyper" parents="17162 17349"/>
    </justification>
  </clause>

  <clause id="17484">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) / (u / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u / w) \ z)) = v5
    ]]></literal>
    <justification jstring="[para(17483(a,2),14822(a,1))].">
      <j1 rule="para" parents="17483 14822"/>
    </justification>
  </clause>

  <clause id="17485">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) / (w / u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((w / u) \ z)) = v5
    ]]></literal>
    <justification jstring="[para(17423(a,1),17484(a,1))].">
      <j1 rule="para" parents="17423 17484"/>
    </justification>
  </clause>

  <clause id="17486">
    <literal><![CDATA[
      K(x,y * (K(z,u \ w) * v5)) = K(x,y * (K(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,17332,a(flip),b,17350,a),flip(a)].">
      <j1 rule="hyper" parents="63 17332 17350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17487">
    <literal><![CDATA[
      K(x,y * (K(z \ u,w * v5) * (v6 * (u / z)))) = K(x,y * (v6 * T(u / z,v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17408,a(flip),b,17486,a),flip(a)].">
      <j1 rule="hyper" parents="63 17408 17486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17488">
    <literal><![CDATA[
      K(x,y * L((K(z,u) \ w) \ v5,v6,v7)) = K(x,y * L((w * K(u,z)) \ v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(6117(a,1),17398(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6117 17398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17489">
    <literal><![CDATA[
      K(x,y \ (z \ T(u * z,K(w,v5)))) = K(x,y \ T(u,z / K(v5,w)))
    ]]></literal>
    <justification jstring="[para(16371(a,1),17472(a,1,2,2))].">
      <j1 rule="para" parents="16371 17472"/>
    </justification>
  </clause>

  <clause id="17490">
    <literal><![CDATA[
      K(x,y \ T(z,u / K(w,v5))) = K(x,y \ (u \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17061,a(flip),b,17489,a),flip(a)].">
      <j1 rule="hyper" parents="63 17061 17489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17492">
    <literal><![CDATA[
      K(x,y \ T(z,u / K(w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),17490(a,2,2,2))].">
      <j1 rule="para" parents="22 17490"/>
    </justification>
  </clause>

  <clause id="17493">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w / v5))) = K(x,y \ T(z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(6074(a,1),17492(a,1,2,2,2))].">
      <j1 rule="para" parents="6074 17492"/>
    </justification>
  </clause>

  <clause id="17494">
    <literal><![CDATA[
      K(x,y \ T(z,u * T(w,v5))) = K(x,y \ T(z,u * w))
    ]]></literal>
    <justification jstring="[para(6144(a,1),17492(a,1,2,2,2))].">
      <j1 rule="para" parents="6144 17492"/>
    </justification>
  </clause>

  <clause id="17495">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w) * v5)) = K(x,y \ T(z,v5))
    ]]></literal>
    <justification jstring="[para(7086(a,1),17492(a,1,2,2,2))].">
      <j1 rule="para" parents="7086 17492"/>
    </justification>
  </clause>

  <clause id="17496">
    <literal><![CDATA[
      K(x,R(y / z,z,y \ T(u,K(w,v5) * v6)) \ T(u,v6)) = K(x,z * (y \ T(u,K(w,v5) * v6)))
    ]]></literal>
    <justification jstring="[para(693(a,1),17495(a,1,2)),flip(a)].">
      <j1 rule="para" parents="693 17495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17497">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(17495(a,1),16098(a,1))].">
      <j1 rule="para" parents="17495 16098"/>
    </justification>
  </clause>

  <clause id="17498">
    <literal><![CDATA[
      K(x,y \ T(z,u * T(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,w * u)) = v6
    ]]></literal>
    <justification jstring="[para(17494(a,2),14856(a,1))].">
      <j1 rule="para" parents="17494 14856"/>
    </justification>
  </clause>

  <clause id="17499">
    <literal><![CDATA[
      K(T(x \ ((y \ z) \ z),x) * u,w) = K((T(x \ y,x) * K(y,y * z)) * u,w)
    ]]></literal>
    <justification jstring="[para(13114(a,1),17479(a,2,1,1))].">
      <j1 rule="para" parents="13114 17479"/>
    </justification>
  </clause>

  <clause id="17500">
    <literal><![CDATA[
      K(T(x \ ((y \ z) \ z),x) * u,w) = K(T(x \ y,x) * (K(y,y * z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,17084,a(flip),b,17499,a),flip(a)].">
      <j1 rule="hyper" parents="347 17084 17499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17501">
    <literal><![CDATA[
      K(T(x \ ((y \ z) \ z),x) * u,w) = K(T(x \ y,x) * (K(y,z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,14684,a(flip),b,17500,a),flip(a)].">
      <j1 rule="hyper" parents="347 14684 17500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17502">
    <literal><![CDATA[
      K(T(x \ ((y \ z) \ z),x) * u,w) = K((y / x) * (K(y,z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,15742,a(flip),b,17501,a),flip(a)].">
      <j1 rule="hyper" parents="347 15742 17501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17503">
    <literal><![CDATA[
      K(T(x \ ((y \ z) \ z),x) * u,w) = K((T(y,z) / x) * u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,17087,a(flip),b,17502,a),flip(a)].">
      <j1 rule="hyper" parents="347 17087 17502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17504">
    <literal><![CDATA[
      K((((x \ y) \ y) / z) * u,w) = K((T(x,y) / z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(15743,a,17503,a)].">
      <j1 rule="hyper" parents="15743 17503"/>
    </justification>
  </clause>

  <clause id="17505">
    <literal><![CDATA[
      K((((T(x,y) \ z) \ z) / y) * u,w) = K((y \ T(x,z)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,17346,a(flip),b,17504,a),flip(a)].">
      <j1 rule="hyper" parents="347 17346 17504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17506">
    <literal><![CDATA[
      K((T((x \ y) \ y,z) / z) * u,w) = K((z \ T(x,y)) * u,w)
    ]]></literal>
    <justification jstring="[para(7558(a,2),17505(a,1,1,1,1))].">
      <j1 rule="para" parents="7558 17505"/>
    </justification>
  </clause>

  <clause id="17507">
    <literal><![CDATA[
      K((x \ ((y \ z) \ z)) * u,w) = K((x \ T(y,z)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17345,a(flip),b,17506,a)].">
      <j1 rule="hyper" parents="63 17345 17506"/>
    </justification>
  </clause>

  <clause id="17508">
    <literal><![CDATA[
      K((((x \ (y \ x)) * ((y \ x) \ x)) \ T(y,x)) * z,u) = K(((x \ (y \ x)) \ 1) * z,u)
    ]]></literal>
    <justification jstring="[para(1639(a,1),17507(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1639 17507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17509">
    <literal><![CDATA[
      T(K(x,y) * (z / T(y,a(u,w,v5))),y) = T(T(y,a(u,w,v5)),x) \ z
    ]]></literal>
    <justification jstring="[para(16866(a,1),16909(a,1,1,1))].">
      <j1 rule="para" parents="16866 16909"/>
    </justification>
  </clause>

  <clause id="17510">
    <literal><![CDATA[
      (T(x,y) \ z) * K(a(u,w,v5),x) = T(T(x,a(u,w,v5)),y) \ z
    ]]></literal>
    <justification jstring="[hyper(8413,a,17509,a)].">
      <j1 rule="hyper" parents="8413 17509"/>
    </justification>
  </clause>

  <clause id="17512">
    <literal><![CDATA[
      (T(x,y) \ z) * a(u,w,K(v5,x)) = T(T(x,a(u,w,v5)),y) \ z
    ]]></literal>
    <justification jstring="[para(12681(a,2),17510(a,1,2))].">
      <j1 rule="para" parents="12681 17510"/>
    </justification>
  </clause>

  <clause id="17513">
    <literal><![CDATA[
      T(T(T(x,a(y,z,u)),y) \ R(T(x,y),z,u),y) = T(x,y) \ R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(17512(a,1),14042(a,1,1))].">
      <j1 rule="para" parents="17512 14042"/>
    </justification>
  </clause>

  <clause id="17514">
    <literal><![CDATA[
      T(T(x,L(y,z,u)) \ R(T(x,y),z,u),y) = T(x,y) \ R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(14033(a,1),17513(a,1,1,1))].">
      <j1 rule="para" parents="14033 17513"/>
    </justification>
  </clause>

  <clause id="17515">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,u) = T(x \ R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(14682(a,1),17514(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14682 17514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17516">
    <literal><![CDATA[
      L(T(x \ R(x,y,z),u),T(x,u),y * z) = a(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(17515(a,1),14250(a,2,1)),flip(a)].">
      <j1 rule="para" parents="17515 14250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17518">
    <literal><![CDATA[
      L(T(x \ R(x,K(y,z),T(u * K(z,y),w)),v5),T(x,v5),T(u * K(u * K(z,y),w),K(z,y))) = a(T(x,v5),K(y,z),T(u * K(z,y),w))
    ]]></literal>
    <justification jstring="[para(14575(a,2),17516(a,1,3))].">
      <j1 rule="para" parents="14575 17516"/>
    </justification>
  </clause>

  <clause id="17519">
    <literal><![CDATA[
      K(x,(T(y,T(z,u)) \ T(z,u)) * w) = K(x,((u * (z / u)) / y) * w)
    ]]></literal>
    <justification jstring="[hyper(17225,a,17334,a),flip(a)].">
      <j1 rule="hyper" parents="17225 17334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17520">
    <literal><![CDATA[
      K(x,((y * (z / y)) / u) * w) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(17224,a,17519,a),flip(a)].">
      <j1 rule="hyper" parents="17224 17519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17521">
    <literal><![CDATA[
      K(x,(T(y * z,y) / u) * w) = K(x,((T(y,z) * z) / u) * w)
    ]]></literal>
    <justification jstring="[para(4149(a,2),17520(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4149 17520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17522">
    <literal><![CDATA[
      K(x,(T(y * z,y) / u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,((z * y) / u) * w) = v5
    ]]></literal>
    <justification jstring="[para(17521(a,2),17331(a,1))].">
      <j1 rule="para" parents="17521 17331"/>
    </justification>
  </clause>

  <clause id="17523">
    <literal><![CDATA[
      K(x,y / a(z,u,K(w,v5))) = y / T(y,x)
    ]]></literal>
    <justification jstring="[para(16941(a,1),17271(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16941 17271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17524">
    <literal><![CDATA[
      K(x,y / a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v6
    ]]></literal>
    <justification jstring="[para(17523(a,2),5013(a,1))].">
      <j1 rule="para" parents="17523 5013"/>
    </justification>
  </clause>

  <clause id="17525">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(16939(a,1),17524(a,1,2))].">
      <j1 rule="para" parents="16939 17524"/>
    </justification>
  </clause>

  <clause id="17526">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(17525,a,xx),flip(a)].">
      <j1 rule="hyper" parents="17525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17527">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w)) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ v5) = v6
    ]]></literal>
    <justification jstring="[para(12690(a,1),17525(a,1,2))].">
      <j1 rule="para" parents="12690 17525"/>
    </justification>
  </clause>

  <clause id="17528">
    <literal><![CDATA[
      K(x,y * L(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(17098(a,1),17525(a,1,2))].">
      <j1 rule="para" parents="17098 17525"/>
    </justification>
  </clause>

  <clause id="17529">
    <literal><![CDATA[
      K(x,K(a(y,z,u),w) * v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[para(12681(a,1),17526(a,1,2,1))].">
      <j1 rule="para" parents="12681 17526"/>
    </justification>
  </clause>

  <clause id="17530">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w)) \ v5) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[para(14363(a,1),17526(a,1,2))].">
      <j1 rule="para" parents="14363 17526"/>
    </justification>
  </clause>

  <clause id="17531">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) = K(x,(y \ z) * K(u,w))
    ]]></literal>
    <justification jstring="[para(14734(a,1),17526(a,1,2))].">
      <j1 rule="para" parents="14734 17526"/>
    </justification>
  </clause>

  <clause id="17532">
    <literal><![CDATA[
      K(x,y * a(z,u,K(w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(16833(a,1),17526(a,1,2))].">
      <j1 rule="para" parents="16833 17526"/>
    </justification>
  </clause>

  <clause id="17533">
    <literal><![CDATA[
      K(x,y \ L(z,u,K(w,v5))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(16940(a,1),17526(a,1,2))].">
      <j1 rule="para" parents="16940 17526"/>
    </justification>
  </clause>

  <clause id="17534">
    <literal><![CDATA[
      K(x,y * L(z,u,K(w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(17098(a,1),17526(a,1,2))].">
      <j1 rule="para" parents="17098 17526"/>
    </justification>
  </clause>

  <clause id="17535">
    <literal><![CDATA[
      K(x,y * (z * K(a(u,w,v5),v6))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(17249,a,17529,a)].">
      <j1 rule="hyper" parents="17249 17529"/>
    </justification>
  </clause>

  <clause id="17536">
    <literal><![CDATA[
      T(x,K(y,z)) / ((z * a(u,w,K(v5,v6))) * T((z * a(u,w,K(v5,v6))) \ x,y)) = K(y,(x \ (z * a(u,w,K(v5,v6)))) \ 1)
    ]]></literal>
    <justification jstring="[para(17532(a,1),9424(a,1,1,2))].">
      <j1 rule="para" parents="17532 9424"/>
    </justification>
  </clause>

  <clause id="17537">
    <literal><![CDATA[
      K(x,y / L(z,u,K(w,v5))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(14458(a,1),17532(a,1,2))].">
      <j1 rule="para" parents="14458 17532"/>
    </justification>
  </clause>

  <clause id="17538">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w)) \ v5) = K(x,L(y,z,u) \ v5)
    ]]></literal>
    <justification jstring="[para(6642(a,1),17530(a,1,2,1))].">
      <j1 rule="para" parents="6642 17530"/>
    </justification>
  </clause>

  <clause id="17539">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w)) \ v5) = K(x,T(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(14348(a,1),17530(a,1,2,1))].">
      <j1 rule="para" parents="14348 17530"/>
    </justification>
  </clause>

  <clause id="17540">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ (K(z,w) * v5))) = K(x,y \ ((T(z,w) \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(5328(a,1),17533(a,1,2,2))].">
      <j1 rule="para" parents="5328 17533"/>
    </justification>
  </clause>

  <clause id="17541">
    <literal><![CDATA[
      K(x,y \ T(z,L(u,w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(14348(a,1),17533(a,1,2,2))].">
      <j1 rule="para" parents="14348 17533"/>
    </justification>
  </clause>

  <clause id="17542">
    <literal><![CDATA[
      K(x,y * L((K(z,u) * w) \ v5,v6,v7)) = K(x,y * L(w \ (K(z,u) \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(622(a,1),17534(a,1,2,2))].">
      <j1 rule="para" parents="622 17534"/>
    </justification>
  </clause>

  <clause id="17543">
    <literal><![CDATA[
      K(x,y / ((z * ((K(u,w) * z) \ v5)) / z)) = K(x,y / ((K(u,w) \ v5) / z))
    ]]></literal>
    <justification jstring="[para(962(a,1),17537(a,1,2,2))].">
      <j1 rule="para" parents="962 17537"/>
    </justification>
  </clause>

  <clause id="17544">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) \ v5)) = K(x,y / (w \ (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(5277(a,1),17537(a,1,2,2))].">
      <j1 rule="para" parents="5277 17537"/>
    </justification>
  </clause>

  <clause id="17545">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,K(v5,v6)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(12681(a,2),17535(a,1,2,2,2))].">
      <j1 rule="para" parents="12681 17535"/>
    </justification>
  </clause>

  <clause id="17546">
    <literal><![CDATA[
      K(x,T(y,z) \ L(z,u,w)) = K(x,L(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(12071,a,17539,a),flip(a)].">
      <j1 rule="hyper" parents="12071 17539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17547">
    <literal><![CDATA[
      K(x,y \ T(z,L(u / w,v5,v6))) = K(x,y \ T(z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,14809,a(flip),b,17541,a),flip(a)].">
      <j1 rule="hyper" parents="347 14809 17541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17549">
    <literal><![CDATA[
      K(x,y * (T(z,y) * a(u,w,K(v5,v6)))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(111(a,1),17545(a,2,2))].">
      <j1 rule="para" parents="111 17545"/>
    </justification>
  </clause>

  <clause id="17550">
    <literal><![CDATA[
      K(x,y * ((z * u) * K(w,v5))) = K(x,y * (z * (u * K(w,v5))))
    ]]></literal>
    <justification jstring="[para(86(a,1),17545(a,1,2,2))].">
      <j1 rule="para" parents="86 17545"/>
    </justification>
  </clause>

  <clause id="17551">
    <literal><![CDATA[
      K(x,y * (R(z,z \ (u / a(w,v5,K(v6,v7))),a(w,v5,K(v6,v7))) \ u)) = K(x,y * (z \ (u / a(w,v5,K(v6,v7)))))
    ]]></literal>
    <justification jstring="[para(899(a,2),17545(a,1,2,2))].">
      <j1 rule="para" parents="899 17545"/>
    </justification>
  </clause>

  <clause id="17552">
    <literal><![CDATA[
      K(x,y * (z \ (u * K(w,v5)))) = K(x,y * ((z \ u) * K(w,v5)))
    ]]></literal>
    <justification jstring="[para(14725(a,1),17545(a,1,2,2))].">
      <j1 rule="para" parents="14725 17545"/>
    </justification>
  </clause>

  <clause id="17553">
    <literal><![CDATA[
      K(x,y * (L(z,u,K(w,v5)) \ v6)) = K(x,y * (z \ v6))
    ]]></literal>
    <justification jstring="[para(16935(a,1),17545(a,1,2,2))].">
      <j1 rule="para" parents="16935 17545"/>
    </justification>
  </clause>

  <clause id="17554">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) \ ((w * v5) * K(z,u)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (v5 * K(w * v5,K(z,u)))) = v6
    ]]></literal>
    <justification jstring="[para(13232(a,1),17528(a,1,2,2))].">
      <j1 rule="para" parents="13232 17528"/>
    </justification>
  </clause>

  <clause id="17555">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) = K(x,K(u,w) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,13579,a,b,17531,a),flip(a)].">
      <j1 rule="hyper" parents="347 13579 17531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17556">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * K(w,L(v5,u,z))) = K(x,y \ (z * (u * K(w,v5))))
    ]]></literal>
    <justification jstring="[para(11073(a,1),17531(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11073 17531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17557">
    <literal><![CDATA[
      T(L(x,y,T(z,u)) \ x,w) \ T(x,u) = L(T(x,u),y,z) * K(w,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(17538(a,1),15255(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17538 15255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17558">
    <literal><![CDATA[
      K(x,L(y / z,u,w) / (1 / (z / y))) = K(x,(1 / (z / y)) \ L(y / z,u,w))
    ]]></literal>
    <justification jstring="[para(672(a,1),17546(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="672 17546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17559">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(14836,a,17555,a)].">
      <j1 rule="hyper" parents="14836 17555"/>
    </justification>
  </clause>

  <clause id="17560">
    <literal><![CDATA[
      T(x,y \ (z * K(u,w))) = T(x,K(u,w) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(132,a,17555,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 17555 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17561">
    <literal><![CDATA[
      K(x,R(y,y \ (x * z),y) / z) = K(x,K(z * x,y) * ((y \ (x * z)) \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,10392,a(flip),b,17555,a)].">
      <j1 rule="hyper" parents="63 10392 17555"/>
    </justification>
  </clause>

  <clause id="17562">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * y))) = K(x,u \ (w * T(y,z)))
    ]]></literal>
    <justification jstring="[para(5926(a,1),17555(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5926 17555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17563">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ (w / (y \ z)))) = K(x,u \ (w / (z / y)))
    ]]></literal>
    <justification jstring="[para(6125(a,1),17555(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6125 17555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17564">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u \ (w * z))) = K(x,u \ (w * (y * (z / y))))
    ]]></literal>
    <justification jstring="[para(9564(a,1),17555(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9564 17555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17565">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ (w * z))) = K(x,u \ (w * ((y \ z) * y)))
    ]]></literal>
    <justification jstring="[para(9585(a,1),17555(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9585 17555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17566">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,w / T(y,z)) \ (w / y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,((w / y) * K(y,z)) / u) = v5
    ]]></literal>
    <justification jstring="[para(17555(a,1),15543(a,1))].">
      <j1 rule="para" parents="17555 15543"/>
    </justification>
  </clause>

  <clause id="17567">
    <literal><![CDATA[
      K(x,K(y,z) * ((z * u) \ w)) = K(x,(T(z,y) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(17100,a,17559,a),flip(a)].">
      <j1 rule="hyper" parents="17100 17559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17568">
    <literal><![CDATA[
      K(x,K(y \ z,z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(y \ z,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(15873,a,17559,a),flip(a)].">
      <j1 rule="hyper" parents="15873 17559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17569">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (T(u,K(z,y) * w) \ w)) = K(x,(K(y \ z,y) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(12090,a,17559,a),flip(a)].">
      <j1 rule="hyper" parents="12090 17559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17570">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * w)) = T(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(132,a,17559,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 17559 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17571">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16888,a,b,17559,a)].">
      <j1 rule="hyper" parents="63 16888 17559"/>
    </justification>
  </clause>

  <clause id="17572">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (y * w))) = K(x,u \ (T(y,z) * w))
    ]]></literal>
    <justification jstring="[para(4974(a,1),17559(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4974 17559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17573">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * (w \ (u / z))) = K(x,w \ (u / T(z,y)))
    ]]></literal>
    <justification jstring="[para(8536(a,1),17559(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8536 17559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17574">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((z * y) * w))) = K(x,u \ ((y * z) * w))
    ]]></literal>
    <justification jstring="[para(10281(a,1),17559(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10281 17559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17575">
    <literal><![CDATA[
      T(x,y \ (z * K(u,w))) = T(x,K(w,u) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,15511,a,b,17560,a),flip(a)].">
      <j1 rule="hyper" parents="347 15511 17560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17576">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ T(v5,K(u,w) * (y \ z))) = K(x,v5 / T(y \ (z * K(u,w)),K(v6,v7)))
    ]]></literal>
    <justification jstring="[para(17560(a,1),14815(a,1,2,2))].">
      <j1 rule="para" parents="17560 14815"/>
    </justification>
  </clause>

  <clause id="17577">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * w)) = T(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(347,a,15511,a,b,17570,a),flip(a)].">
      <j1 rule="hyper" parents="347 15511 17570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17578">
    <literal><![CDATA[
      T(x,K(y,z) * (T(y \ u,w) \ u)) = T(x,T(T(y \ u,w) \ u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,17404,a(flip),b,17570,a),flip(a)].">
      <j1 rule="hyper" parents="63 17404 17570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17579">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ (z \ w))) = T(x,u \ (T(z,y) \ w))
    ]]></literal>
    <justification jstring="[para(5209(a,1),17570(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5209 17570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17580">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(14814,a,17571,a)].">
      <j1 rule="hyper" parents="14814 17571"/>
    </justification>
  </clause>

  <clause id="17581">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(132,a,17571,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 17571 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17582">
    <literal><![CDATA[
      K(x,R(y * z,K(u,L(w,y,z)),K(u,L(w,y,z))) \ v5) = K(x,K(L(u,y,z),w) * (((K(u,w) * y) * z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,16548,a,b,17571,a)].">
      <j1 rule="hyper" parents="63 16548 17571"/>
    </justification>
  </clause>

  <clause id="17583">
    <literal><![CDATA[
      K(x,K(y,z) * ((y \ u) \ w)) = K(x,(T(y,z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(5209(a,1),17571(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5209 17571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17584">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ (w \ z))) = T(x,u \ (w \ T(z,y)))
    ]]></literal>
    <justification jstring="[para(13045(a,1),17575(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13045 17575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17585">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) = T(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(132,a,17580,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 17580 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17586">
    <literal><![CDATA[
      K(x,K(y,z) * ((u / y) \ w)) = K(x,(u / T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(6102(a,1),17580(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6102 17580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17587">
    <literal><![CDATA[
      T(x,K(y,z) * ((z / u) \ w)) = T(x,(T(z,y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(13192(a,1),17581(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13192 17581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17588">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) = T(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(347,a,15511,a,b,17585,a),flip(a)].">
      <j1 rule="hyper" parents="347 15511 17585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17589">
    <literal><![CDATA[
      T(x,T(((y \ z) \ z) / u,K(y \ z,y)) \ w) = T(x,K(y \ z,y) * ((y / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16353,a,b,17585,a)].">
      <j1 rule="hyper" parents="63 16353 17585"/>
    </justification>
  </clause>

  <clause id="17590">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / y) \ w)) = T(x,(u / T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(6102(a,1),17585(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6102 17585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17591">
    <literal><![CDATA[
      T(x,K(y \ z,y) * ((u \ (y \ z)) \ w)) = T(x,(u \ (z / y)) \ w)
    ]]></literal>
    <justification jstring="[para(13354(a,1),17585(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13354 17585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17592">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * y) \ w)) = T(x,(u * T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(5926(a,1),17588(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5926 17588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17593">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ y) \ w)) = T(x,(u \ T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(13045(a,1),17588(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13045 17588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17594">
    <literal><![CDATA[
      K(x,y * T(a(z,u,K(w,v5)) * v6,y)) = K(x,v6 * y)
    ]]></literal>
    <justification jstring="[para(17270(a,2),17549(a,1,2,2))].">
      <j1 rule="para" parents="17270 17549"/>
    </justification>
  </clause>

  <clause id="17595">
    <literal><![CDATA[
      K(x,y * (L(z,u,a(w,v5,K(v6,v7))) \ v8)) = K(x,y * (z \ v8))
    ]]></literal>
    <justification jstring="[para(11127(a,1),17553(a,1,2,2,1,3))].">
      <j1 rule="para" parents="11127 17553"/>
    </justification>
  </clause>

  <clause id="17596">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) * v6) = K(x,v5 * v6)
    ]]></literal>
    <justification jstring="[para(111(a,1),17594(a,1,2))].">
      <j1 rule="para" parents="111 17594"/>
    </justification>
  </clause>

  <clause id="17597">
    <literal><![CDATA[
      K(x,(L(y,z,K(u,w)) / v5) * v6) = K(x,(y / v5) * v6)
    ]]></literal>
    <justification jstring="[para(14366(a,1),17596(a,1,2,1))].">
      <j1 rule="para" parents="14366 17596"/>
    </justification>
  </clause>

  <clause id="17598">
    <literal><![CDATA[
      K(x,(y \ L(z,u,K(w,v5))) * v6) = K(x,(y \ z) * v6)
    ]]></literal>
    <justification jstring="[para(16940(a,1),17596(a,1,2,1))].">
      <j1 rule="para" parents="16940 17596"/>
    </justification>
  </clause>

  <clause id="17599">
    <literal><![CDATA[
      K(x,(T((K(y,z) * u) \ w,v5) / v6) * v7) = K(x,(T(u \ (K(y,z) \ w),v5) / v6) * v7)
    ]]></literal>
    <justification jstring="[para(621(a,1),17597(a,1,2,1,1))].">
      <j1 rule="para" parents="621 17597"/>
    </justification>
  </clause>

  <clause id="17600">
    <literal><![CDATA[
      K(x,(y \ ((K(z,u) * (w * v5)) / (K(z,u) * w))) * v6) = K(x,(y \ (v5 * K(K(z,u) * w,v5))) * v6)
    ]]></literal>
    <justification jstring="[para(5071(a,1),17598(a,1,2,1,2))].">
      <j1 rule="para" parents="5071 17598"/>
    </justification>
  </clause>

  <clause id="17601">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * z))) = K(x,u \ (w * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15546,a,17562,a)].">
      <j1 rule="hyper" parents="15546 17562"/>
    </justification>
  </clause>

  <clause id="17602">
    <literal><![CDATA[
      K(x,K(y,z) * ((y * u) \ w)) = K(x,(T(y,z) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(15546,a,17567,a)].">
      <j1 rule="hyper" parents="15546 17567"/>
    </justification>
  </clause>

  <clause id="17603">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z * w))) = K(x,u \ (T(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(15546,a,17572,a)].">
      <j1 rule="hyper" parents="15546 17572"/>
    </justification>
  </clause>

  <clause id="17604">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * (z \ w))) = T(x,y \ (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,17577,a,b,17579,a)].">
      <j1 rule="hyper" parents="63 17577 17579"/>
    </justification>
  </clause>

  <clause id="17605">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ w)) = K(x,(T(z,y) \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(15546,a,17583,a)].">
      <j1 rule="hyper" parents="15546 17583"/>
    </justification>
  </clause>

  <clause id="17606">
    <literal><![CDATA[
      T(x,K(y * z,u) * (w \ (v5 \ u))) = T(x,w \ (v5 \ T(u,y \ z)))
    ]]></literal>
    <justification jstring="[hyper(15867,a,17584,a)].">
      <j1 rule="hyper" parents="15867 17584"/>
    </justification>
  </clause>

  <clause id="17607">
    <literal><![CDATA[
      K(K(x,y) * ((z / x) \ u),w) = (v5 * K(w,(z / T(x,y)) \ u)) \ v5
    ]]></literal>
    <justification jstring="[para(17586(a,1),6123(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="17586 6123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17608">
    <literal><![CDATA[
      T(x,(K(y,z) / T(u,w)) \ v5) = T(x,T(K(y,z) / u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,16329,a(flip),b,17590,a),flip(a)].">
      <j1 rule="hyper" parents="63 16329 17590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17609">
    <literal><![CDATA[
      T(x,(K(y,z) * T(u,w)) \ v5) = T(x,T(u \ K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,16337,a(flip),b,17592,a),flip(a)].">
      <j1 rule="hyper" parents="63 16337 17592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17610">
    <literal><![CDATA[
      T(x,(y * T(z,u)) \ T(z,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(y * z) \ T(T(z,w),u)) = v5
    ]]></literal>
    <justification jstring="[para(17592(a,1),15726(a,1))].">
      <j1 rule="para" parents="17592 15726"/>
    </justification>
  </clause>

  <clause id="17611">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z * x))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (x * T(z,y))) = w
    ]]></literal>
    <justification jstring="[para(17603(a,2),9548(a,1))].">
      <j1 rule="para" parents="17603 9548"/>
    </justification>
  </clause>

  <clause id="17612">
    <literal><![CDATA[
      T(x,y \ (T(z \ u,z) \ w)) = T(x,y \ ((u / z) \ w))
    ]]></literal>
    <justification jstring="[para(5441(a,1),17604(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5441 17604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17613">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12063,a(flip),b,17605,a),flip(a)].">
      <j1 rule="hyper" parents="63 12063 17605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17614">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,y / z)) = K(x,u / (T(z,y) \ y))
    ]]></literal>
    <justification jstring="[hyper(12079,a,17613,a),flip(a)].">
      <j1 rule="hyper" parents="12079 17613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17615">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(132,a,17613,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 17613 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17616">
    <literal><![CDATA[
      T(x,(T(y,z / u) \ T(u \ z,u)) \ w) = T(x,(T(u \ z,u) / y) \ w)
    ]]></literal>
    <justification jstring="[para(7419(a,1),17615(a,1,2,1,1))].">
      <j1 rule="para" parents="7419 17615"/>
    </justification>
  </clause>

  <clause id="17617">
    <literal><![CDATA[
      K(x,(y / (T(z,u) \ u)) / T(w,(u / z) \ y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w \ (y / (T(z,u) \ u))) = v5
    ]]></literal>
    <justification jstring="[para(17615(a,1),14865(a,1,2,2))].">
      <j1 rule="para" parents="17615 14865"/>
    </justification>
  </clause>

  <clause id="17618">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(17614(a,1),12077(a,1))].">
      <j1 rule="para" parents="17614 12077"/>
    </justification>
  </clause>

  <clause id="17619">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(4281(a,1),17618(a,1,2,2))].">
      <j1 rule="para" parents="4281 17618"/>
    </justification>
  </clause>

  <clause id="17620">
    <literal><![CDATA[
      K(x,y \ T(z,u / (w * v5))) = K(x,y \ T(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[para(14124(a,1),17547(a,1,2,2))].">
      <j1 rule="para" parents="14124 17547"/>
    </justification>
  </clause>

  <clause id="17621">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * v5))) = K(x,y * (w * (v5 * K(u,z))))
    ]]></literal>
    <justification jstring="[hyper(17167,a,17550,a)].">
      <j1 rule="hyper" parents="17167 17550"/>
    </justification>
  </clause>

  <clause id="17622">
    <literal><![CDATA[
      K(x,y * (z * (u * K(y,w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w) * (z * u)) = v5
    ]]></literal>
    <justification jstring="[para(17550(a,1),13639(a,1))].">
      <j1 rule="para" parents="17550 13639"/>
    </justification>
  </clause>

  <clause id="17623">
    <literal><![CDATA[
      K(x,y * (z \ (u * K(w,v5)))) = K(x,y * (K(w,v5) * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,14810,a,b,17552,a),flip(a)].">
      <j1 rule="hyper" parents="347 14810 17552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17624">
    <literal><![CDATA[
      K(x,y * (z \ (u * K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (K(w,v5) * (z \ u))) = v6
    ]]></literal>
    <justification jstring="[para(17552(a,2),14835(a,1))].">
      <j1 rule="para" parents="17552 14835"/>
    </justification>
  </clause>

  <clause id="17625">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w / y))) = K(x,u \ (w / T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(15641,a,17573,a)].">
      <j1 rule="hyper" parents="15641 17573"/>
    </justification>
  </clause>

  <clause id="17626">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * (v5 \ ((y * z) * v6))) = K(x,v5 \ ((z * y) * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,16474,a,b,17574,a)].">
      <j1 rule="hyper" parents="63 16474 17574"/>
    </justification>
  </clause>

  <clause id="17627">
    <literal><![CDATA[
      T(x,T(K(y,z) / u,w) \ v5) = T(x,K(y,z) * (T(u,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,17208,a(flip),b,17608,a),flip(a)].">
      <j1 rule="hyper" parents="63 17208 17608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17628">
    <literal><![CDATA[
      T(x,T(y \ K(z,u),w) * v5) = T(x,K(z,u) * (T(y,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,17581,a(flip),b,17609,a),flip(a)].">
      <j1 rule="hyper" parents="63 17581 17609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17629">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) \ v5)) = K(x,y \ T(z,u \ (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(14855,a,17620,a)].">
      <j1 rule="hyper" parents="14855 17620"/>
    </justification>
  </clause>

  <clause id="17630">
    <literal><![CDATA[
      K(x,y * (z * (K(u,z) * w))) = K(x,y * (z * (w * K(z,u))))
    ]]></literal>
    <justification jstring="[para(5353(a,1),17621(a,1,2,2))].">
      <j1 rule="para" parents="5353 17621"/>
    </justification>
  </clause>

  <clause id="17631">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ (v5 \ 1)))) = K(x,y * (w \ (v5 \ K(z,u))))
    ]]></literal>
    <justification jstring="[para(12973(a,1),17623(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="12973 17623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17632">
    <literal><![CDATA[
      T(x,T(y * K(z,u),w) * v5) = T(x,K(u,z) * (T(y,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,15898,a(flip),b,17627,a)].">
      <j1 rule="hyper" parents="63 15898 17627"/>
    </justification>
  </clause>

  <clause id="17633">
    <literal><![CDATA[
      T(x,K(y,z) * (T(y \ u,w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(17628(a,1),15902(a,1))].">
      <j1 rule="para" parents="17628 15902"/>
    </justification>
  </clause>

  <clause id="17634">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w / v5))) = K(x,y \ T(z,(u * v5) * w))
    ]]></literal>
    <justification jstring="[hyper(15924,a,17629,a),flip(a)].">
      <j1 rule="hyper" parents="15924 17629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17635">
    <literal><![CDATA[
      K(x,y * (z * (K(u,z) * w))) = K(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(14848,a,17630,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14848 17630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17636">
    <literal><![CDATA[
      T(x,y * (z * (K(u,z) * w))) = T(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(132,a,17635,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 17635 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17637">
    <literal><![CDATA[
      K(x,y * (((z * u) / z) * w)) = K(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,9272,a,b,17635,a)].">
      <j1 rule="hyper" parents="63 9272 17635"/>
    </justification>
  </clause>

  <clause id="17638">
    <literal><![CDATA[
      K(x,y * (T(T(z,u),u) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(5366(a,1),17635(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5366 17635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17639">
    <literal><![CDATA[
      K(x,y * (z * (T(T(z,u),u) \ w))) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),17638(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 17638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17640">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (K(z,u) * w))) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(5781(a,2),17639(a,1,2,2))].">
      <j1 rule="para" parents="5781 17639"/>
    </justification>
  </clause>

  <clause id="17641">
    <literal><![CDATA[
      K(x,(y * T(T(z,u),u)) * w) = K(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[para(9941(a,1),17640(a,1,2))].">
      <j1 rule="para" parents="9941 17640"/>
    </justification>
  </clause>

  <clause id="17642">
    <literal><![CDATA[
      K(x,(y * (z * K(u,z))) * w) = K(x,(y * T(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(5058(a,1),17641(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5058 17641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17643">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (z * w))) = T(x,u * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,17150,a,b,17636,a)].">
      <j1 rule="hyper" parents="63 17150 17636"/>
    </justification>
  </clause>

  <clause id="17644">
    <literal><![CDATA[
      K(x,y * (T(z / u,u) * (w \ 1))) = K(x,y * ((z / u) * (w \ K(u,z))))
    ]]></literal>
    <justification jstring="[hyper(63,a,15193,a(flip),b,17637,a),flip(a)].">
      <j1 rule="hyper" parents="63 15193 17637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17645">
    <literal><![CDATA[
      T(x,(y * (z * K(u,z))) * w) = T(x,(y * T(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(132,a,17642,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 17642 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17646">
    <literal><![CDATA[
      T(x,y * (K(z,z \ u) * (u * w))) = T(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,17149,a,b,17643,a)].">
      <j1 rule="hyper" parents="63 17149 17643"/>
    </justification>
  </clause>

  <clause id="17647">
    <literal><![CDATA[
      T(x,(y * T(z,u)) * (w \ K(y * T(z,u),v5))) = T(x,T(y * (z * K(u,z)),v5) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15783,a(flip),b,17645,a),flip(a)].">
      <j1 rule="hyper" parents="63 15783 17645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17648">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w) * v5) = T(x,K(z,y) * (T(u,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(15646,a,17632,a)].">
      <j1 rule="hyper" parents="15646 17632"/>
    </justification>
  </clause>

  <clause id="17649">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) * v5)) = K(x,y \ T(z,u * (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(15924,a,17634,a),flip(a)].">
      <j1 rule="hyper" parents="15924 17634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17650">
    <literal><![CDATA[
      T(x,y * ((z * (u / z)) * w)) = T(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[para(10145(a,1),17646(a,1,2,2))].">
      <j1 rule="para" parents="10145 17646"/>
    </justification>
  </clause>

  <clause id="17651">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * K(u \ 1,(1 / z) * u)) * w)) = T(x,y * (T(1 / z,u \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,5754,a,b,17650,a)].">
      <j1 rule="hyper" parents="63 5754 17650"/>
    </justification>
  </clause>

  <clause id="17652">
    <literal><![CDATA[
      T(x,y * (T(z / (u \ 1),z) * w)) = T(x,y * ((T(z,u) / (u \ 1)) * w))
    ]]></literal>
    <justification jstring="[para(3807(a,2),17650(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3807 17650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17653">
    <literal><![CDATA[
      T(x,K(y,z) * (T(u \ z,w) * u)) = T(x,u * T(T(z,T(y,u)) / u,w))
    ]]></literal>
    <justification jstring="[hyper(13248,a,17648,a),flip(a)].">
      <j1 rule="hyper" parents="13248 17648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17654">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) * v5)) = K(x,y \ T(z,u * (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(347,a,17493,a(flip),b,17649,a),flip(a)].">
      <j1 rule="hyper" parents="347 17493 17649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17655">
    <literal><![CDATA[
      K(x,T(y,z) * (u * (w / y))) = K(x,y * (u * (w / T(y,z))))
    ]]></literal>
    <justification jstring="[hyper(17622,a,17441,a)].">
      <j1 rule="hyper" parents="17622 17441"/>
    </justification>
  </clause>

  <clause id="17656">
    <literal><![CDATA[
      K(x,y * (z * (u / T(y,u * z)))) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14913,a(flip),b,17655,a),flip(a)].">
      <j1 rule="hyper" parents="63 14913 17655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17657">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ (u / (z \ y)))
    ]]></literal>
    <justification jstring="[para(5608(a,1),17563(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5608 17563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17658">
    <literal><![CDATA[
      K(x,y \ (z * (u * (w / u)))) = K(x,K(u,w) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(11993,a,17564,a),flip(a)].">
      <j1 rule="hyper" parents="11993 17564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17659">
    <literal><![CDATA[
      K(x,y \ (z * (u * (w / u)))) = K(x,y \ (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,17601,a(flip),b,17658,a),flip(a)].">
      <j1 rule="hyper" parents="347 17601 17658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17660">
    <literal><![CDATA[
      K(x,y \ (z * T(u * w,w))) = K(x,y \ (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(11(a,1),17659(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 17659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17661">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * (u * w))) = K(x,y \ (T(w * u,u) * z))
    ]]></literal>
    <justification jstring="[hyper(15730,a,17660,a),flip(a)].">
      <j1 rule="hyper" parents="15730 17660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17662">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) * u))) = K(x,K(w,u) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(12116,a,17565,a),flip(a)].">
      <j1 rule="hyper" parents="12116 17565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17663">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) * u))) = K(x,y \ (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,17562,a(flip),b,17662,a),flip(a)].">
      <j1 rule="hyper" parents="347 17562 17662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17664">
    <literal><![CDATA[
      K(x,y \ (z * T(u * w,u))) = K(x,y \ (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(9(a,1),17663(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 17663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17665">
    <literal><![CDATA[
      T(x,(y \ T(z \ u,z)) \ w) = T(x,(y \ (u / z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17593,a(flip),b,17591,a)].">
      <j1 rule="hyper" parents="63 17593 17591"/>
    </justification>
  </clause>

  <clause id="17666">
    <literal><![CDATA[
      T(x,y \ (z \ T(u,w \ v5))) = T(x,y \ (z \ T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17584,a(flip),b,17606,a),flip(a)].">
      <j1 rule="hyper" parents="63 17584 17606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17667">
    <literal><![CDATA[
      K(K(x,y) * ((z / x) \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((z / T(x,y)) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(17607(a,2),6141(a,1))].">
      <j1 rule="para" parents="17607 6141"/>
    </justification>
  </clause>

  <clause id="17668">
    <literal><![CDATA[
      K(K(x,y) * ((z / y) \ u),w) = K((z / T(y,x)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(17667,a,15570,a),flip(a)].">
      <j1 rule="hyper" parents="17667 15570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17669">
    <literal><![CDATA[
      K(x,y * ((T(z,u) \ u) \ (w \ K(u,z)))) = K(x,y * ((z \ u) \ (w \ 1)))
    ]]></literal>
    <justification jstring="[para(12230(a,1),17631(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12230 17631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17670">
    <literal><![CDATA[
      K(x,y \ (T(z * u,u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(15707,a,17661,a),flip(a)].">
      <j1 rule="hyper" parents="15707 17661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17671">
    <literal><![CDATA[
      K(x,y \ (T(z * u,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((u * z) * w)) = v5
    ]]></literal>
    <justification jstring="[para(17661(a,1),15707(a,1))].">
      <j1 rule="para" parents="17661 15707"/>
    </justification>
  </clause>

  <clause id="17672">
    <literal><![CDATA[
      K(x,y \ ((z * (u / z)) * w)) = K(x,y \ (T(u,z) * w))
    ]]></literal>
    <justification jstring="[para(12(a,1),17670(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 17670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17673">
    <literal><![CDATA[
      R(T(K(x,y \ z),y * u),y,u) = K(x,(y * u) \ (T(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(15111,a,17672,a)].">
      <j1 rule="hyper" parents="15111 17672"/>
    </justification>
  </clause>

  <clause id="17674">
    <literal><![CDATA[
      R(K(x,T(y \ z,y * u)),y,u) = K(x,(y * u) \ (T(z,y) * u))
    ]]></literal>
    <justification jstring="[para(7091(a,2),17673(a,1,1))].">
      <j1 rule="para" parents="7091 17673"/>
    </justification>
  </clause>

  <clause id="17675">
    <literal><![CDATA[
      K(x,L(T(y \ z,y * u),y,u)) = K(x,(y * u) \ (T(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(14117,a,17674,a)].">
      <j1 rule="hyper" parents="14117 17674"/>
    </justification>
  </clause>

  <clause id="17676">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (T(z,y) * (z \ u))) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16304,a(flip),b,17675,a),flip(a)].">
      <j1 rule="hyper" parents="63 16304 17675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17677">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (K(z,y) * u)) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[para(4944(a,1),17676(a,1,2,2))].">
      <j1 rule="para" parents="4944 17676"/>
    </justification>
  </clause>

  <clause id="17678">
    <literal><![CDATA[
      K(x,(T(y,z) * (z \ u)) \ u) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(17100,a,17677,a)].">
      <j1 rule="hyper" parents="17100 17677"/>
    </justification>
  </clause>

  <clause id="17679">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,y \ u),(x * y) \ T(T(y,u),z)) = (x * T(y,z)) \ ((y \ u) \ u)
    ]]></literal>
    <justification jstring="[hyper(17610,a,12215,a)].">
      <j1 rule="hyper" parents="17610 12215"/>
    </justification>
  </clause>

  <clause id="17680">
    <literal><![CDATA[
      K(x,y / T((K(z,u) * w) \ v5,w)) = K(x,y / ((K(z,u) \ v5) / w))
    ]]></literal>
    <justification jstring="[hyper(15747,a,17543,a)].">
      <j1 rule="hyper" parents="15747 17543"/>
    </justification>
  </clause>

  <clause id="17681">
    <literal><![CDATA[
      T(x,(T(y,z / u) \ (z / u)) \ w) = T(x,(T(u \ z,u) / y) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17665,a(flip),b,17616,a)].">
      <j1 rule="hyper" parents="63 17665 17616"/>
    </justification>
  </clause>

  <clause id="17682">
    <literal><![CDATA[
      T(x,(T(y \ z,y) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17615,a(flip),b,17681,a),flip(a)].">
      <j1 rule="hyper" parents="63 17615 17681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17683">
    <literal><![CDATA[
      T(x,((((y \ z) \ z) \ z) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(4320(a,1),17682(a,1,2,1,1))].">
      <j1 rule="para" parents="4320 17682"/>
    </justification>
  </clause>

  <clause id="17684">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w \ K(u,z)))) = K(x,y * ((u \ z) * (w \ 1)))
    ]]></literal>
    <justification jstring="[para(113(a,1),17644(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="113 17644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17685">
    <literal><![CDATA[
      T(x,y * ((T(z,u) / (u \ 1)) * w)) = T(x,y * (((u \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12098,a(flip),b,17652,a),flip(a)].">
      <j1 rule="hyper" parents="63 12098 17652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17686">
    <literal><![CDATA[
      T(x,K(y,z) * (u * T(z / u,w))) = T(x,u * T(T(z,T(y,u)) / u,w))
    ]]></literal>
    <justification jstring="[hyper(15729,a,17653,a)].">
      <j1 rule="hyper" parents="15729 17653"/>
    </justification>
  </clause>

  <clause id="17687">
    <literal><![CDATA[
      T(x,y * T(T(z,T(u,y)) / y,w)) = T(x,T(y * T(z / y,w),u))
    ]]></literal>
    <justification jstring="[hyper(63,a,17251,a(flip),b,17686,a),flip(a)].">
      <j1 rule="hyper" parents="63 17251 17686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17688">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,T(T(y,w) \ z,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(17633,a,17578,a),flip(a)].">
      <j1 rule="hyper" parents="17633 17578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17689">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,z * T(T(y,w) / z,u))
    ]]></literal>
    <justification jstring="[hyper(17355,a,17688,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="17355 17688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17691">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,T(w,z))) = T(x,T(z * T(y / z,u),w))
    ]]></literal>
    <justification jstring="[hyper(347,a,17687,a(flip),b,17689,a),flip(a)].">
      <j1 rule="hyper" parents="347 17687 17689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17692">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,T(z * T(y / z,u),w))
    ]]></literal>
    <justification jstring="[hyper(13633,a,17691,a)].">
      <j1 rule="hyper" parents="13633 17691"/>
    </justification>
  </clause>

  <clause id="17694">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),w)) = T(x,y * T(T(z,w) / y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,17689,a(flip),b,17692,a),flip(a)].">
      <j1 rule="hyper" parents="63 17689 17692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17696">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),z * y)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,16019,a(flip),b,17694,a),flip(a)].">
      <j1 rule="hyper" parents="347 16019 17694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17697">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),y)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(16387,a,17696,a)].">
      <j1 rule="hyper" parents="16387 17696"/>
    </justification>
  </clause>

  <clause id="17698">
    <literal><![CDATA[
      T(x,T(y,z) \ T(z * y,u)) = T(x,T(z / y,u) * y)
    ]]></literal>
    <justification jstring="[hyper(10401,a,17697,a),flip(a)].">
      <j1 rule="hyper" parents="10401 17697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17699">
    <literal><![CDATA[
      T(x,T(y,z) \ T(z * y,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(484(a,1),17698(a,2,2))].">
      <j1 rule="para" parents="484 17698"/>
    </justification>
  </clause>

  <clause id="17700">
    <literal><![CDATA[
      K(x,y * L((K(z,u) * w) \ v5,v6,v7)) = K(x,y * L(w \ (K(u,z) * v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(5256(a,1),17542(a,2,2,2,1,2))].">
      <j1 rule="para" parents="5256 17542"/>
    </justification>
  </clause>

  <clause id="17701">
    <literal><![CDATA[
      K(x,L(y / z,u,w) / (1 / (z / y))) = K(x,(z / y) * L(y / z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,13049,a(flip),b,17558,a),flip(a)].">
      <j1 rule="hyper" parents="347 13049 17558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17702">
    <literal><![CDATA[
      K(x,(y / z) * L(z / y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z / y,u,w) * (y / z)) = v5
    ]]></literal>
    <justification jstring="[para(17701(a,1),13310(a,1))].">
      <j1 rule="para" parents="17701 13310"/>
    </justification>
  </clause>

  <clause id="17703">
    <literal><![CDATA[
      K(x,(y \ z) * L(z \ y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / z,u,w) * (z / y)) = v5
    ]]></literal>
    <justification jstring="[para(17418(a,1),17702(a,1))].">
      <j1 rule="para" parents="17418 17702"/>
    </justification>
  </clause>

  <clause id="17704">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(y \ z,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(15838,a,17568,a)].">
      <j1 rule="hyper" parents="15838 17568"/>
    </justification>
  </clause>

  <clause id="17705">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(z \ y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(12116,a,17569,a)].">
      <j1 rule="hyper" parents="12116 17569"/>
    </justification>
  </clause>

  <clause id="17706">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = K(x,w * (u \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(347,a,17242,a(flip),b,17705,a),flip(a)].">
      <j1 rule="hyper" parents="347 17242 17705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17707">
    <literal><![CDATA[
      K(x,(K(y \ z,z) * u) / w) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17704,a(flip),b,17706,a)].">
      <j1 rule="hyper" parents="63 17704 17706"/>
    </justification>
  </clause>

  <clause id="17708">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(17019,a,17707,a)].">
      <j1 rule="hyper" parents="17019 17707"/>
    </justification>
  </clause>

  <clause id="17709">
    <literal><![CDATA[
      K(x,y \ (z / T(u,T(w,v5)))) = K(x,y \ (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(17320,a,14864,a)].">
      <j1 rule="hyper" parents="17320 14864"/>
    </justification>
  </clause>

  <clause id="17711">
    <literal><![CDATA[
      (T(L(x,y,T(z,u)) \ x,w) \ T(x,u)) \ L(T(x,u),y,z) = K(L(x,y,z) \ x,w)
    ]]></literal>
    <justification jstring="[para(17557(a,2),6123(a,1,1))].">
      <j1 rule="para" parents="17557 6123"/>
    </justification>
  </clause>

  <clause id="17714">
    <literal><![CDATA[
      T(x,L(y,z,u)) / (L(T(x,y),z,u) * a(w,z,K(x,u))) = T(L(x,z,u) \ x,w)
    ]]></literal>
    <justification jstring="[para(14009(a,1),17015(a,1,2,2))].">
      <j1 rule="para" parents="14009 17015"/>
    </justification>
  </clause>

  <clause id="17715">
    <literal><![CDATA[
      T(x,y * (T(z,u * (w * K(v5,K(v6,v7)))) * v8)) = T(x,y * (T(z,(u * w) \ 1) * v8))
    ]]></literal>
    <justification jstring="[para(14784(a,1),17144(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14784 17144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17716">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(z \ u,u))) = K(x,y / ((z \ K(z \ u,u)) * u))
    ]]></literal>
    <justification jstring="[para(7789(a,1),17234(a,1,2,2,2))].">
      <j1 rule="para" parents="7789 17234"/>
    </justification>
  </clause>

  <clause id="17717">
    <literal><![CDATA[
      K(x,y / ((z \ K(z \ u,u)) * u)) = K(x,y * (((z \ 1) * u) \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17708,a(flip),b,17716,a),flip(a)].">
      <j1 rule="hyper" parents="63 17708 17716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17718">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(u,z))) = K(x,y / T((z \ 1) * u,u))
    ]]></literal>
    <justification jstring="[para(13336(a,1),17717(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13336 17717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17719">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(347,a,15672,a(flip),b,17718,a),flip(a)].">
      <j1 rule="hyper" parents="347 15672 17718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17720">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17232,a(flip),b,17719,a)].">
      <j1 rule="hyper" parents="63 17232 17719"/>
    </justification>
  </clause>

  <clause id="17721">
    <literal><![CDATA[
      K(x,y / (T(z,u) * (u \ 1))) = K(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,17245,a(flip),b,17720,a),flip(a)].">
      <j1 rule="hyper" parents="63 17245 17720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17722">
    <literal><![CDATA[
      (x / T((y / (z * y)) * z,u)) \ (x * 1) = (y / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(6622(a,1),17312(a,1,2,2))].">
      <j1 rule="para" parents="6622 17312"/>
    </justification>
  </clause>

  <clause id="17723">
    <literal><![CDATA[
      (x / T((y / (z * y)) * z,u)) \ x = (y / (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(363,a,17722,a)].">
      <j1 rule="hyper" parents="363 17722"/>
    </justification>
  </clause>

  <clause id="17724">
    <literal><![CDATA[
      T(x,(y / (z * y)) * z) = x
    ]]></literal>
    <justification jstring="[hyper(4299,a,17723,a)].">
      <j1 rule="hyper" parents="4299 17723"/>
    </justification>
  </clause>

  <clause id="17726">
    <literal><![CDATA[
      T(x,y * R(y \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[para(867(a,1),17724(a,1,2))].">
      <j1 rule="para" parents="867 17724"/>
    </justification>
  </clause>

  <clause id="17727">
    <literal><![CDATA[
      T(x * R(x \ 1,x,y),z) = x * R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(54,a,17726,a)].">
      <j1 rule="hyper" parents="54 17726"/>
    </justification>
  </clause>

  <clause id="17728">
    <literal><![CDATA[
      L(x,(y * z) / y,(T(y,z) \ ((y * z) / y)) \ 1) = L(x,y * (z / y),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,12399,a(flip),b,17325,a),flip(a)].">
      <j1 rule="hyper" parents="347 12399 17325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17729">
    <literal><![CDATA[
      K(x,(K(y,T(z,u)) * ((K(w,T(v5,v6)) \ v7) * K(z,T(y,u)))) \ v8) = K(x,v7 \ (K(v5,T(w,v6)) \ v8))
    ]]></literal>
    <justification jstring="[para(7126(a,1),17400(a,1,2,1,2))].">
      <j1 rule="para" parents="7126 17400"/>
    </justification>
  </clause>

  <clause id="17730">
    <literal><![CDATA[
      K(x,y * (z * T(u / w,v5 \ v6))) = K(x,y * (z * T(u / w,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17408,a(flip),b,17487,a),flip(a)].">
      <j1 rule="hyper" parents="63 17408 17487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17731">
    <literal><![CDATA[
      K((((x \ (y \ x)) * ((y \ x) \ x)) \ T(y,x)) * z,u) = K((x \ (y \ x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,13029,a(flip),b,17508,a),flip(a)].">
      <j1 rule="hyper" parents="347 13029 17508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17732">
    <literal><![CDATA[
      T(x,T(((y \ z) \ z) / u,K(y \ z,y)) \ w) = T(x,K(z,y) * ((y / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(347,a,12062,a(flip),b,17589,a),flip(a)].">
      <j1 rule="hyper" parents="347 12062 17589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17733">
    <literal><![CDATA[
      T(x,K(y,z) * ((z / u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(((z \ y) \ y) / u) \ w) = v5
    ]]></literal>
    <justification jstring="[para(17732(a,1),15636(a,1))].">
      <j1 rule="para" parents="17732 15636"/>
    </justification>
  </clause>

  <clause id="17734">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / u) \ w) = T(x,(T(y,z) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(17733,a,17587,a)].">
      <j1 rule="hyper" parents="17733 17587"/>
    </justification>
  </clause>

  <clause id="17735">
    <literal><![CDATA[
      T(x,(T(y \ z,z) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17683,a(flip),b,17734,a),flip(a)].">
      <j1 rule="hyper" parents="63 17683 17734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17736">
    <literal><![CDATA[
      T(x,((y / z) / y) \ u) = T(x,(y \ (z \ y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12067,a(flip),b,17735,a),flip(a)].">
      <j1 rule="hyper" parents="63 12067 17735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17737">
    <literal><![CDATA[
      T(x,(y \ ((z \ K(z,y)) \ y)) \ u) = T(x,(y \ (y / (z \ 1))) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15861,a(flip),b,17736,a),flip(a)].">
      <j1 rule="hyper" parents="63 15861 17736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17738">
    <literal><![CDATA[
      T(x,(((y \ 1) \ z) / z) \ u) = T(x,(z \ (z / (y \ 1))) \ u)
    ]]></literal>
    <justification jstring="[para(7724(a,1),17737(a,1,2,1))].">
      <j1 rule="para" parents="7724 17737"/>
    </justification>
  </clause>

  <clause id="17739">
    <literal><![CDATA[
      T(x,(y \ (y / ((z \ 1) \ 1))) \ u) = T(x,((z \ y) / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(12106,a,17738,a),flip(a)].">
      <j1 rule="hyper" parents="12106 17738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17740">
    <literal><![CDATA[
      T(x,((y \ z) / z) \ u) = T(x,(z \ (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(12105,a,17739,a),flip(a)].">
      <j1 rule="hyper" parents="12105 17739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17741">
    <literal><![CDATA[
      K(x,(T((K(y,z) * u) \ w,v5) / v6) * v7) = K(x,(T(u \ (K(z,y) * w),v5) / v6) * v7)
    ]]></literal>
    <justification jstring="[para(5256(a,1),17599(a,2,2,1,1,1,2))].">
      <j1 rule="para" parents="5256 17599"/>
    </justification>
  </clause>

  <clause id="17742">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,z)),w) / v5) = T(x,T(y * T(z,u),w) / v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,14874,a(flip),b,17647,a),flip(a)].">
      <j1 rule="hyper" parents="63 14874 17647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17743">
    <literal><![CDATA[
      T(x,y * (T(z,u * (w * K(v5,K(v6,v7)))) * v8)) = T(x,y * (T(z,w \ (u \ 1)) * v8))
    ]]></literal>
    <justification jstring="[para(13214(a,1),17715(a,2,2,2,1))].">
      <j1 rule="para" parents="13214 17715"/>
    </justification>
  </clause>

  <clause id="17744">
    <literal><![CDATA[
      L(x,(y * z) / y,(y \ z) \ 1) = L(x,y * (z / y),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[para(4175(a,1),17728(a,1,3,1))].">
      <j1 rule="para" parents="4175 17728"/>
    </justification>
  </clause>

  <clause id="17745">
    <literal><![CDATA[
      L(x,y * (z / y),(z / y) \ 1) = L(x,y * (z / y),(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,12399,a(flip),b,17744,a),flip(a)].">
      <j1 rule="hyper" parents="63 12399 17744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17746">
    <literal><![CDATA[
      L(x,y * (z / y),(z / y) \ 1) = L(x,z,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,12412,a(flip),b,17745,a),flip(a)].">
      <j1 rule="hyper" parents="347 12412 17745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17747">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,z,(y \ z) \ 1)) = K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u))
    ]]></literal>
    <justification jstring="[para(17746(a,1),6544(a,1,2))].">
      <j1 rule="para" parents="17746 6544"/>
    </justification>
  </clause>

  <clause id="17748">
    <literal><![CDATA[
      T(x,y * (T(z,u * (w * K(v5,K(v6,v7)))) * v8)) = T(x,y * (T(z,w * (u \ 1)) * v8))
    ]]></literal>
    <justification jstring="[hyper(347,a,16397,a(flip),b,17743,a),flip(a)].">
      <j1 rule="hyper" parents="347 16397 17743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17749">
    <literal><![CDATA[
      T(x,y * (T(z,u * (w * K(v5,K(v6,v7)))) * v8)) = T(x,y * (T(z,w / u) * v8))
    ]]></literal>
    <justification jstring="[para(13069(a,1),17748(a,2,2,2,1))].">
      <j1 rule="para" parents="13069 17748"/>
    </justification>
  </clause>

  <clause id="17750">
    <literal><![CDATA[
      T(x,y * (T(z,u / w) * v5)) = T(x,y * (T(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[para(203(a,1),17749(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="203 17749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17751">
    <literal><![CDATA[
      T(1 * K(x,L(x \ K(y,z),u,w)),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(7610(a,1),16863(a,1,1,2))].">
      <j1 rule="para" parents="7610 16863"/>
    </justification>
  </clause>

  <clause id="17753">
    <literal><![CDATA[
      1 / T((x * K(y,z)) * a(u,w,K(x,v5)),a(u,w,x)) = K(v5,a(u,w,x)) / (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(12681(a,2),16934(a,1,2,1,2))].">
      <j1 rule="para" parents="12681 16934"/>
    </justification>
  </clause>

  <clause id="17754">
    <literal><![CDATA[
      L(K(x,K(y,z)) * ((u * w) \ v5),K(x,K(y,z)),u * w) = (u * (w * K(x,K(y,z)))) \ v5
    ]]></literal>
    <justification jstring="[para(7292(a,1),16956(a,1,1,1))].">
      <j1 rule="para" parents="7292 16956"/>
    </justification>
  </clause>

  <clause id="17756">
    <literal><![CDATA[
      K(x,T((y * K(z,T(u,w))) / v5,y \ v5)) = K(x,(y * (v5 / y)) \ (K(z,u) * y))
    ]]></literal>
    <justification jstring="[para(7114(a,1),17397(a,2,2))].">
      <j1 rule="para" parents="7114 17397"/>
    </justification>
  </clause>

  <clause id="17757">
    <literal><![CDATA[
      K(x,T(y,z / T(u,w)) \ (z / T(u,w))) = K(x,((z / u) * K(u,w)) / y)
    ]]></literal>
    <justification jstring="[hyper(17566,a,17625,a),flip(a)].">
      <j1 rule="hyper" parents="17566 17625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17758">
    <literal><![CDATA[
      K(x,((y / z) * K(z,u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / T(z,u)) / w) = v5
    ]]></literal>
    <justification jstring="[para(17757(a,1),12071(a,1))].">
      <j1 rule="para" parents="17757 12071"/>
    </justification>
  </clause>

  <clause id="17759">
    <literal><![CDATA[
      K(x,((y * z) / T(y,u)) / w) = K(x,T(z * K(y,u),y) / w)
    ]]></literal>
    <justification jstring="[hyper(17758,a,15666,a)].">
      <j1 rule="hyper" parents="17758 15666"/>
    </justification>
  </clause>

  <clause id="17760">
    <literal><![CDATA[
      K(x,T(y * K(z,u),u) / w) = K(x,T(y * K(u,z),u) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15665,a(flip),b,17759,a)].">
      <j1 rule="hyper" parents="63 15665 17759"/>
    </justification>
  </clause>

  <clause id="17761">
    <literal><![CDATA[
      K(x,T(y * K(z,u),z) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * (w \ K(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(17760(a,1),17102(a,1))].">
      <j1 rule="para" parents="17760 17102"/>
    </justification>
  </clause>

  <clause id="17762">
    <literal><![CDATA[
      K(x,(y / (z / u)) / T(w,(z / u) \ y)) = K(x,w \ (y / (T(u,z) \ z)))
    ]]></literal>
    <justification jstring="[hyper(17617,a,17403,a),flip(a)].">
      <j1 rule="hyper" parents="17617 17403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17763">
    <literal><![CDATA[
      K(x,y \ (z / (T(u,w) \ w))) = K(x,y \ (z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(14865,a,17762,a),flip(a)].">
      <j1 rule="hyper" parents="14865 17762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17764">
    <literal><![CDATA[
      K(x,y \ (T(z,u / w) / (u / w))) = K(x,y \ ((T(w,u) \ u) \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12075,a(flip),b,17763,a),flip(a)].">
      <j1 rule="hyper" parents="63 12075 17763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17765">
    <literal><![CDATA[
      K(x,y \ (z / (z / u))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(80(a,1),17763(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="80 17763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17766">
    <literal><![CDATA[
      K(x,y \ T(z \ u,u)) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[para(80(a,1),17765(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="80 17765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17767">
    <literal><![CDATA[
      K(x,y \ T(z * (u * K(w,u \ 1)),z)) = K(x,y \ (z / T(z / (z * u),w)))
    ]]></literal>
    <justification jstring="[para(8073(a,1),17765(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8073 17765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17768">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,z \ 1))) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15800,a(flip),b,17766,a)].">
      <j1 rule="hyper" parents="63 15800 17766"/>
    </justification>
  </clause>

  <clause id="17769">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((z \ y) \ T(u,(y / z) \ 1)))
    ]]></literal>
    <justification jstring="[para(5637(a,1),17768(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5637 17768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17770">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) \ u) \ w)) = K(x,y \ ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12006,a(flip),b,17764,a),flip(a)].">
      <j1 rule="hyper" parents="63 12006 17764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17771">
    <literal><![CDATA[
      K(x,(y \ 1) \ ((z / u) \ w)) = K(x,y * ((u \ T(z,u)) \ w))
    ]]></literal>
    <justification jstring="[hyper(13308,a,17770,a),flip(a)].">
      <j1 rule="hyper" parents="13308 17770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17772">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,z)) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u / z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(17771(a,1),13242(a,1))].">
      <j1 rule="para" parents="17771 13242"/>
    </justification>
  </clause>

  <clause id="17773">
    <literal><![CDATA[
      K(x,y * ((T(z,u) \ u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u / z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(4281(a,2),17772(a,1,2,2,1))].">
      <j1 rule="para" parents="4281 17772"/>
    </justification>
  </clause>

  <clause id="17774">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ (w \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u / z) \ (w \ K(u,z)))) = v5
    ]]></literal>
    <justification jstring="[para(17669(a,1),17773(a,1))].">
      <j1 rule="para" parents="17669 17773"/>
    </justification>
  </clause>

  <clause id="17775">
    <literal><![CDATA[
      K(x,y \ T(z * (u * K(w,u \ 1)),z)) = K(x,y \ (T((z * u) \ z,w) \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,16310,a(flip),b,17767,a),flip(a)].">
      <j1 rule="hyper" parents="347 16310 17767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17776">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((z \ y) \ T(u,z / y)))
    ]]></literal>
    <justification jstring="[para(4435(a,1),17769(a,2,2,2,2))].">
      <j1 rule="para" parents="4435 17769"/>
    </justification>
  </clause>

  <clause id="17777">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ ((u * K(w,u \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12007,a(flip),b,17775,a),flip(a)].">
      <j1 rule="hyper" parents="63 12007 17775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17778">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ (u * (K(w,u \ 1) * z)))
    ]]></literal>
    <justification jstring="[para(5815(a,1),17777(a,2,2,2))].">
      <j1 rule="para" parents="5815 17777"/>
    </justification>
  </clause>

  <clause id="17779">
    <literal><![CDATA[
      T(K(x,L(x \ K(y,z),u,w)),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),17751(a,1,1))].">
      <j1 rule="para" parents="7 17751"/>
    </justification>
  </clause>

  <clause id="17780">
    <literal><![CDATA[
      K(x,L(x \ K(y,z),u,w)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(13596,a,17779,a)].">
      <j1 rule="hyper" parents="13596 17779"/>
    </justification>
  </clause>

  <clause id="17781">
    <literal><![CDATA[
      K(x,L(x \ K(y,z),u,w)) = K(x,x \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,15794,a(flip),b,17780,a),flip(a)].">
      <j1 rule="hyper" parents="347 15794 17780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17782">
    <literal><![CDATA[
      K(x,L(y \ K(z,u),w,v5) * (K(y,y \ K(z,u)) * v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,T(L(y \ K(z,u),w,v5),y) * v6) = v7
    ]]></literal>
    <justification jstring="[para(17781(a,1),15674(a,1,2,2,1))].">
      <j1 rule="para" parents="17781 15674"/>
    </justification>
  </clause>

  <clause id="17783">
    <literal><![CDATA[
      1 / T(T(x,a(y,z,u)) * K(w,v5),a(y,z,x)) = K(u,a(y,z,x)) / (x * K(w,v5))
    ]]></literal>
    <justification jstring="[para(16937(a,1),17753(a,1,2,1))].">
      <j1 rule="para" parents="16937 17753"/>
    </justification>
  </clause>

  <clause id="17784">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) \ v5 = K(z,K(u,w)) * ((x * y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(17047,a,17754,a),flip(a)].">
      <j1 rule="hyper" parents="17047 17754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17786">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) \ v5 = K(y,K(z,u)) * ((x * w) \ v5)
    ]]></literal>
    <justification jstring="[para(13514(a,2),17784(a,1,1,2))].">
      <j1 rule="para" parents="13514 17784"/>
    </justification>
  </clause>

  <clause id="17787">
    <literal><![CDATA[
      K(x,(T(y \ (K(z,u) * w),K(z,u) * y) / v5) * v6) = K(x,((w / (K(u,z) * y)) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,17741,a(flip),b,17243,a)].">
      <j1 rule="hyper" parents="63 17741 17243"/>
    </justification>
  </clause>

  <clause id="17789">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * K(u \ 1,(1 / z) * u)) * w)) = T(x,y * (T(1 / z,u * 1) * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,16397,a(flip),b,17651,a),flip(a)].">
      <j1 rule="hyper" parents="347 16397 17651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17790">
    <literal><![CDATA[
      T((x * T(y,y \ z)) \ T(y,y \ u),(x * y) \ T(T(y,u),z)) = (x * T(y,y \ z)) \ ((y \ u) \ u)
    ]]></literal>
    <justification jstring="[hyper(12217,a,17679,a)].">
      <j1 rule="hyper" parents="12217 17679"/>
    </justification>
  </clause>

  <clause id="17791">
    <literal><![CDATA[
      K(x,(T(y \ (K(z,u) * w),y) / v5) * v6) = K(x,((w / (K(u,z) * y)) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,17336,a(flip),b,17787,a)].">
      <j1 rule="hyper" parents="63 17336 17787"/>
    </justification>
  </clause>

  <clause id="17793">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) / w) / v5) * v6) = K(x,((u / (K(z,y) * w)) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,17238,a(flip),b,17791,a)].">
      <j1 rule="hyper" parents="63 17238 17791"/>
    </justification>
  </clause>

  <clause id="17794">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * K(u \ 1,(1 / z) * u)) * w)) = T(x,y * (T(1 / z,u) * w))
    ]]></literal>
    <justification jstring="[para(8(a,1),17789(a,2,2,2,1,2))].">
      <j1 rule="para" parents="8 17789"/>
    </justification>
  </clause>

  <clause id="17795">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * K(u \ 1,(1 / z) * u)) * w)) = T(x,y * (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,4014,a(flip),b,17794,a),flip(a)].">
      <j1 rule="hyper" parents="347 4014 17794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17796">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * K(u \ 1,z \ u)) * w)) = T(x,y * (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[para(12993(a,1),17795(a,1,2,2,1,2))].">
      <j1 rule="para" parents="12993 17795"/>
    </justification>
  </clause>

  <clause id="17797">
    <literal><![CDATA[
      T(x,y * ((z \ K(u \ 1,z \ u)) * w)) = T(x,y * (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[para(12973(a,1),17796(a,1,2,2,1))].">
      <j1 rule="para" parents="12973 17796"/>
    </justification>
  </clause>

  <clause id="17798">
    <literal><![CDATA[
      (x * (y * (z * K(u,K(w,v5))))) \ ((x * y) * (z * K(u,K(w,v5)))) = a(x,K(u,K(w,v5)) * y,z)
    ]]></literal>
    <justification jstring="[para(17007(a,1),17003(a,1,2))].">
      <j1 rule="para" parents="17007 17003"/>
    </justification>
  </clause>

  <clause id="17799">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * (w * v5))) \ ((x * (K(y,K(z,u)) * w)) * v5) = a(x * K(y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(17031(a,1),17044(a,1,2,1))].">
      <j1 rule="para" parents="17031 17044"/>
    </justification>
  </clause>

  <clause id="17800">
    <literal><![CDATA[
      (K(x,y) * (K(x,K(y,z)) * u)) * (u \ (z * K(y,x))) = z * a(u \ (z * K(y,x)),z,K(y,x))
    ]]></literal>
    <justification jstring="[para(7282(a,1),17451(a,1,1,2,1))].">
      <j1 rule="para" parents="7282 17451"/>
    </justification>
  </clause>

  <clause id="17801">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) \ (w * v5)))) = K(x,y * (v5 * K(w * v5,K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(17554,a,17623,a),flip(a)].">
      <j1 rule="hyper" parents="17554 17623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17802">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,z,z \ y)) = K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(14511,a,17747,a)].">
      <j1 rule="hyper" parents="14511 17747"/>
    </justification>
  </clause>

  <clause id="17803">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u)) = K(x,L(T(z,y) \ u,z,z \ y))
    ]]></literal>
    <justification jstring="[hyper(15807,a,17802,a),flip(a)].">
      <j1 rule="hyper" parents="15807 17802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17804">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,12171,a(flip),b,17803,a),flip(a)].">
      <j1 rule="hyper" parents="347 12171 17803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17805">
    <literal><![CDATA[
      K(x,(y * ((y / z) \ 1)) \ (((y / z) \ 1) * u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(15732,a,17804,a)].">
      <j1 rule="hyper" parents="15732 17804"/>
    </justification>
  </clause>

  <clause id="17806">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ ((y / z) \ u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16042,a(flip),b,17805,a)].">
      <j1 rule="hyper" parents="63 16042 17805"/>
    </justification>
  </clause>

  <clause id="17807">
    <literal><![CDATA[
      K(x,y \ ((y \ z) \ u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[para(5637(a,1),17806(a,1,2))].">
      <j1 rule="para" parents="5637 17806"/>
    </justification>
  </clause>

  <clause id="17808">
    <literal><![CDATA[
      T(x,y \ ((y \ z) \ u)) = T(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(132,a,17807,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 17807 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17809">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((y \ z) * T(u,z / y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17776,a,b,17807,a)].">
      <j1 rule="hyper" parents="63 17776 17807"/>
    </justification>
  </clause>

  <clause id="17810">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * (K(y,u) * w))) = K(x,y \ ((T(y,u) \ z) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,17540,a(flip),b,17807,a),flip(a)].">
      <j1 rule="hyper" parents="63 17540 17807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17811">
    <literal><![CDATA[
      K(x,y \ (((K(z,y) * u) \ y) * w)) = K(x,y \ ((T(y,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(5198(a,1),17807(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5198 17807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17812">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((z \ y) * u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(17807(a,1),9425(a,1,2))].">
      <j1 rule="para" parents="17807 9425"/>
    </justification>
  </clause>

  <clause id="17813">
    <literal><![CDATA[
      T(T(x,K(y,z * (y * u))),y \ ((z \ y) * u)) = T(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13481,a(flip),b,17808,a),flip(a)].">
      <j1 rule="hyper" parents="63 13481 17808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17814">
    <literal><![CDATA[
      K(x,y \ ((T(y,z) \ u) \ w)) = K(x,y \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[para(13175(a,1),17811(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="13175 17811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17815">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ T(u * (y \ z),K(y,z)))
    ]]></literal>
    <justification jstring="[para(8799(a,2),17809(a,2,2,2))].">
      <j1 rule="para" parents="8799 17809"/>
    </justification>
  </clause>

  <clause id="17816">
    <literal><![CDATA[
      K(x,((y \ z) \ u) / y) = K(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[hyper(13418,a,17812,a),flip(a)].">
      <j1 rule="hyper" parents="13418 17812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17817">
    <literal><![CDATA[
      K(x,((y \ z) \ (((z \ y) * u) * (u / ((z \ y) * u)))) / y) = K(x,((((z \ y) * u) \ u) \ u) / y)
    ]]></literal>
    <justification jstring="[para(4233(a,1),17816(a,2,2,1))].">
      <j1 rule="para" parents="4233 17816"/>
    </justification>
  </clause>

  <clause id="17818">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y \ ((u \ y) * z)) = T(x,((y \ u) \ z) / y)
    ]]></literal>
    <justification jstring="[para(16260(a,1),17813(a,1,1))].">
      <j1 rule="para" parents="16260 17813"/>
    </justification>
  </clause>

  <clause id="17819">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ (u * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,14797,a(flip),b,17815,a),flip(a)].">
      <j1 rule="hyper" parents="347 14797 17815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17821">
    <literal><![CDATA[
      K(x,y \ (z / (y \ u))) = K(x,y \ (z * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17657,a(flip),b,17819,a)].">
      <j1 rule="hyper" parents="63 17657 17819"/>
    </justification>
  </clause>

  <clause id="17822">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * T(y,y \ z)) \ ((y \ z) \ z)))) = K(x,((y \ z) \ z) \ (u / T(w,T(y,z))))
    ]]></literal>
    <justification jstring="[para(7084(a,1),17821(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7084 17821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17823">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) * w,v5) = a(x,w,v5 * K(y,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(836,a,17798,a),flip(a)].">
      <j1 rule="hyper" parents="836 17798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17824">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * (w * v5))) \ ((x * w) * (K(y,K(z,u)) * v5)) = a(x * K(y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(17262(a,1),17799(a,1,2))].">
      <j1 rule="para" parents="17262 17799"/>
    </justification>
  </clause>

  <clause id="17825">
    <literal><![CDATA[
      (x * (T(T(x,K(y,z)),y) \ u)) * (u \ (z * K(x,y))) = z * a(u \ (z * K(x,y)),z,K(x,y))
    ]]></literal>
    <justification jstring="[para(13521(a,1),17800(a,1,1))].">
      <j1 rule="para" parents="13521 17800"/>
    </justification>
  </clause>

  <clause id="17826">
    <literal><![CDATA[
      ((x * (K(y,K(z,u)) * (w * v5))) \ ((x * w) * v5)) * K(y,K(z,u)) = a(x * K(y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,17258,a(flip),b,17824,a)].">
      <j1 rule="hyper" parents="63 17258 17824"/>
    </justification>
  </clause>

  <clause id="17827">
    <literal><![CDATA[
      (x * (T(x,T(y,z)) \ u)) * (u \ (z * K(x,y))) = z * a(u \ (z * K(x,y)),z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6814(a,1),17825(a,1,1,2,1))].">
      <j1 rule="para" parents="6814 17825"/>
    </justification>
  </clause>

  <clause id="17828">
    <literal><![CDATA[
      (K(T(x,y),z) * u) * (u \ (y * K(z,x))) = y * a(u \ (y * K(z,x)),y,K(z,x))
    ]]></literal>
    <justification jstring="[para(4947(a,1),17827(a,1,1))].">
      <j1 rule="para" parents="4947 17827"/>
    </justification>
  </clause>

  <clause id="17829">
    <literal><![CDATA[
      (K(x,K(y,z)) * ((u * (w * v5)) \ ((u * w) * v5))) * K(x,K(y,z)) = a(u * K(x,K(y,z)),w,v5)
    ]]></literal>
    <justification jstring="[para(17786(a,1),17826(a,1,1))].">
      <j1 rule="para" parents="17786 17826"/>
    </justification>
  </clause>

  <clause id="17830">
    <literal><![CDATA[
      (K(x,K(y,z)) * a(u,w,v5)) * K(x,K(y,z)) = a(u * K(x,K(y,z)),w,v5)
    ]]></literal>
    <justification jstring="[para(14(a,2),17829(a,1,1,2))].">
      <j1 rule="para" parents="14 17829"/>
    </justification>
  </clause>

  <clause id="17831">
    <literal><![CDATA[
      a(x * K(y,K(z,u)),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(17830(a,1),13557(a,1))].">
      <j1 rule="para" parents="17830 13557"/>
    </justification>
  </clause>

  <clause id="17832">
    <literal><![CDATA[
      a(x * K(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(K(y,z) * x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(91(a,1),17831(a,1,1))].">
      <j1 rule="para" parents="91 17831"/>
    </justification>
  </clause>

  <clause id="17833">
    <literal><![CDATA[
      a(x \ T(y,K(z,u)),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x \ y,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(1438(a,1),17831(a,1,1))].">
      <j1 rule="para" parents="1438 17831"/>
    </justification>
  </clause>

  <clause id="17834">
    <literal><![CDATA[
      a(T(x,K(y,z)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(4929(a,2),17831(a,1,1))].">
      <j1 rule="para" parents="4929 17831"/>
    </justification>
  </clause>

  <clause id="17835">
    <literal><![CDATA[
      a(K(x,K(y,z)) * u,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(7076(a,1),17831(a,1,1))].">
      <j1 rule="para" parents="7076 17831"/>
    </justification>
  </clause>

  <clause id="17836">
    <literal><![CDATA[
      a(T(x,T(y,z)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(T(x,y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(7246(a,1),17831(a,1,1))].">
      <j1 rule="para" parents="7246 17831"/>
    </justification>
  </clause>

  <clause id="17837">
    <literal><![CDATA[
      a(T(x,K(y,z)) \ u,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x \ u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(13546(a,1),17831(a,1,1))].">
      <j1 rule="para" parents="13546 17831"/>
    </justification>
  </clause>

  <clause id="17838">
    <literal><![CDATA[
      a(T(x,K(y,z)),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(17834,a,xx),flip(a)].">
      <j1 rule="hyper" parents="17834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17839">
    <literal><![CDATA[
      a(K(x,y) * (z \ 1),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z \ K(x,y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(13024(a,1),17834(a,1,1))].">
      <j1 rule="para" parents="13024 17834"/>
    </justification>
  </clause>

  <clause id="17840">
    <literal><![CDATA[
      a(K(x,y) * (z \ x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z \ T(x,y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(13116(a,1),17834(a,1,1))].">
      <j1 rule="para" parents="13116 17834"/>
    </justification>
  </clause>

  <clause id="17841">
    <literal><![CDATA[
      a(K(x,K(y,z)) * u,w,v5) = a(u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(17835,a,11589,a),flip(a)].">
      <j1 rule="hyper" parents="17835 11589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17842">
    <literal><![CDATA[
      a(x * (y \ T(z,K(u,w))),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x * (y \ z),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(16960(a,1),17835(a,1,1))].">
      <j1 rule="para" parents="16960 17835"/>
    </justification>
  </clause>

  <clause id="17843">
    <literal><![CDATA[
      a(x * (K(y,K(z,u)) * w),v5,v6) = a(x * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(16959(a,1),17841(a,1,1))].">
      <j1 rule="para" parents="16959 17841"/>
    </justification>
  </clause>

  <clause id="17844">
    <literal><![CDATA[
      a(x * (T(y,K(z,u)) \ w),v5,v6) = a(x * (y \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(5159(a,1),17843(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5159 17843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17845">
    <literal><![CDATA[
      a(x * (y \ T(z * y,K(u,w))),v5,v6) = a(x * T(z,y * K(u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(16070(a,1),17844(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="16070 17844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17846">
    <literal><![CDATA[
      a(x * T(y,z * K(u,w)),v5,v6) = a(x * (z \ (y * z)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(17842,a,17845,a),flip(a)].">
      <j1 rule="hyper" parents="17842 17845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17847">
    <literal><![CDATA[
      a(x * T(y,z * K(u,w)),v5,v6) = a(x * T(y,z),v5,v6)
    ]]></literal>
    <justification jstring="[para(22(a,2),17846(a,2,1,2))].">
      <j1 rule="para" parents="22 17846"/>
    </justification>
  </clause>

  <clause id="17848">
    <literal><![CDATA[
      a((x / y) * T(y,z),u,w) = a(x * K(y,z * K(v5,v6)),u,w)
    ]]></literal>
    <justification jstring="[para(5925(a,1),17847(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5925 17847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17849">
    <literal><![CDATA[
      a(x * K(y,z * K(u,w)),v5,v6) = a(x * K(y,z),v5,v6)
    ]]></literal>
    <justification jstring="[para(5925(a,1),17848(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5925 17848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17850">
    <literal><![CDATA[
      a(x * K(y,K(z,u) * w),v5,v6) = a(x * K(y,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(7076(a,1),17849(a,1,1,2,2))].">
      <j1 rule="para" parents="7076 17849"/>
    </justification>
  </clause>

  <clause id="17851">
    <literal><![CDATA[
      a(K(x,K(y,z) * u) * w,v5,v6) = a(w * K(x,u),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(17832,a,17850,a)].">
      <j1 rule="hyper" parents="17832 17850"/>
    </justification>
  </clause>

  <clause id="17852">
    <literal><![CDATA[
      a(K(x,T(y,z)) * u,w,v5) = a(u * K(x,y),w,v5)
    ]]></literal>
    <justification jstring="[para(1324(a,2),17851(a,1,1,1,2))].">
      <j1 rule="para" parents="1324 17851"/>
    </justification>
  </clause>

  <clause id="17853">
    <literal><![CDATA[
      K(x,T(T((y * K(z,u)) / w,K(y,v5)),y \ w)) = K(x,(y * K(z,u)) / T(w,K(y,v5)))
    ]]></literal>
    <justification jstring="[hyper(16140,a,16992,a)].">
      <j1 rule="hyper" parents="16140 16992"/>
    </justification>
  </clause>

  <clause id="17854">
    <literal><![CDATA[
      K(x,T((y * K(z,u)) / w,y \ w)) = K(x,(y * K(z,u)) / T(w,K(y,v5)))
    ]]></literal>
    <justification jstring="[hyper(13602,a,17853,a)].">
      <j1 rule="hyper" parents="13602 17853"/>
    </justification>
  </clause>

  <clause id="17855">
    <literal><![CDATA[
      K(x,T((y * K(z,u)) / w,y \ w)) = K(x,(y * K(z,u)) / w)
    ]]></literal>
    <justification jstring="[hyper(347,a,14806,a(flip),b,17854,a),flip(a)].">
      <j1 rule="hyper" parents="347 14806 17854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17857">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ (K(u,w) * y)) = K(x,(y * K(u,T(w,v5))) / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,17756,a(flip),b,17855,a)].">
      <j1 rule="hyper" parents="63 17756 17855"/>
    </justification>
  </clause>

  <clause id="17858">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ (K(u,w) * y)) = K(x,(y * K(u,w)) / z)
    ]]></literal>
    <justification jstring="[para(110(a,1),17857(a,2,2,1,2,2))].">
      <j1 rule="para" parents="110 17857"/>
    </justification>
  </clause>

  <clause id="17859">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ (K(u,w) * y)) = K(x,y / (z * K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,16891,a(flip),b,17858,a),flip(a)].">
      <j1 rule="hyper" parents="347 16891 17858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17860">
    <literal><![CDATA[
      K(x,K(y,z)) * ((u * w) \ (u * (w * (v5 * K(x,K(y,z)))))) = L(v5,w * K(x,K(y,z)),u)
    ]]></literal>
    <justification jstring="[hyper(17032,a,17784,a),flip(a)].">
      <j1 rule="hyper" parents="17032 17784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17861">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ (u * (w * (v5 * K(x,K(y,z))))) != v6
    ]]></literal>
    <literal><![CDATA[
      L(v5,w * K(x,K(y,z)),u) = v6
    ]]></literal>
    <justification jstring="[para(16815(a,2),17032(a,1,1))].">
      <j1 rule="para" parents="16815 17032"/>
    </justification>
  </clause>

  <clause id="17862">
    <literal><![CDATA[
      K(x,K(y,z)) * L(u * K(x,K(y,z)),w,v5) = L(u,w * K(x,K(y,z)),v5)
    ]]></literal>
    <justification jstring="[para(18(a,2),17860(a,1,2))].">
      <j1 rule="para" parents="18 17860"/>
    </justification>
  </clause>

  <clause id="17863">
    <literal><![CDATA[
      K(x,K(y,z)) * L(K(x,K(y,z)) * u,w,v5) = L(u,w * K(x,K(y,z)),v5)
    ]]></literal>
    <justification jstring="[para(13514(a,2),17862(a,1,2,1))].">
      <j1 rule="para" parents="13514 17862"/>
    </justification>
  </clause>

  <clause id="17864">
    <literal><![CDATA[
      L(K(x,K(y,z)) * (u * K(x,K(y,z))),w,v5) = L(u,w * K(x,K(y,z)),v5)
    ]]></literal>
    <justification jstring="[hyper(34,a,17388,a(flip),b,17863,a),flip(a)].">
      <j1 rule="hyper" parents="34 17388 17863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17865">
    <literal><![CDATA[
      L(x,y * K(z,K(u,w)),v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(13549(a,1),17864(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13549 17864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17866">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) * L(v5,y,x) = x * ((y * K(z,K(u,w))) * v5)
    ]]></literal>
    <justification jstring="[hyper(134,a,17865,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 17865 18"/>
    </justification>
  </clause>

  <clause id="17867">
    <literal><![CDATA[
      L(x,T(y,K(z,u)),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(4929(a,2),17865(a,1,2))].">
      <j1 rule="para" parents="4929 17865"/>
    </justification>
  </clause>

  <clause id="17868">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) = L(x,K(y,z),w)
    ]]></literal>
    <justification jstring="[para(7094(a,1),17865(a,1,2))].">
      <j1 rule="para" parents="7094 17865"/>
    </justification>
  </clause>

  <clause id="17869">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),v5) = L(x,y \ (w * K(z,u)),v5)
    ]]></literal>
    <justification jstring="[para(13432(a,1),17865(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13432 17865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17870">
    <literal><![CDATA[
      L(x,K(y,z) * (u * K(y,z)),w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,8636,a,b,17867,a)].">
      <j1 rule="hyper" parents="63 8636 17867"/>
    </justification>
  </clause>

  <clause id="17871">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) = L(x,K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,5181,a,b,17868,a),flip(a)].">
      <j1 rule="hyper" parents="347 5181 17868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17872">
    <literal><![CDATA[
      R(x,K(y,z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16444,a(flip),b,17868,a)].">
      <j1 rule="hyper" parents="63 16444 17868"/>
    </justification>
  </clause>

  <clause id="17873">
    <literal><![CDATA[
      L(x * K(y,z),K(z,y),u) = (x * u) / (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(6150,a,17872,a),flip(a)].">
      <j1 rule="hyper" parents="6150 17872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17874">
    <literal><![CDATA[
      L((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(6149,a,17872,a),flip(a)].">
      <j1 rule="hyper" parents="6149 17872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17875">
    <literal><![CDATA[
      ((x * K(y,z)) * u) / (K(y,z) * u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(993,a,17872,a)].">
      <j1 rule="hyper" parents="993 17872"/>
    </justification>
  </clause>

  <clause id="17877">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(x,T(y,z))) = L(z * K(x,K(y,u)),K(x,T(y,z)),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13525,a,b,17872,a)].">
      <j1 rule="hyper" parents="63 13525 17872"/>
    </justification>
  </clause>

  <clause id="17878">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u * K(y,z)) = (x * (u * K(y,z))) / u
    ]]></literal>
    <justification jstring="[hyper(63,a,9688,a(flip),b,17872,a),flip(a)].">
      <j1 rule="hyper" parents="63 9688 17872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17879">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,T(y,u)),u) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,8733,a(flip),b,17872,a),flip(a)].">
      <j1 rule="hyper" parents="63 8733 17872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17880">
    <literal><![CDATA[
      L(x,K(y,z),u) * (K(y,z) * u) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(133,a,17872,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="133 17872 20"/>
    </justification>
  </clause>

  <clause id="17881">
    <literal><![CDATA[
      L(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(17872(a,1),9366(a,1,1))].">
      <j1 rule="para" parents="17872 9366"/>
    </justification>
  </clause>

  <clause id="17882">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(17872(a,1),14334(a,1,1,2))].">
      <j1 rule="para" parents="17872 14334"/>
    </justification>
  </clause>

  <clause id="17883">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,K(y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(17871(a,2),5182(a,1))].">
      <j1 rule="para" parents="17871 5182"/>
    </justification>
  </clause>

  <clause id="17885">
    <literal><![CDATA[
      L(x,K(y,z) * (u * z),w) = L(x,u * T(z,y),w)
    ]]></literal>
    <justification jstring="[para(6111(a,1),17870(a,1,2,2))].">
      <j1 rule="para" parents="6111 17870"/>
    </justification>
  </clause>

  <clause id="17886">
    <literal><![CDATA[
      R(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(16444(a,1),17883(a,1))].">
      <j1 rule="para" parents="16444 17883"/>
    </justification>
  </clause>

  <clause id="17887">
    <literal><![CDATA[
      ((K(x,y) * (z * K(u,w))) * v5) / (K(u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y) * z,K(u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(16976(a,2),17886(a,1))].">
      <j1 rule="para" parents="16976 17886"/>
    </justification>
  </clause>

  <clause id="17888">
    <literal><![CDATA[
      K(x,y) * L(K(y,x) * z,K(x,y),u) = ((z * u) / (K(x,y) * u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(17873(a,1),6212(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17873 6212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17890">
    <literal><![CDATA[
      L(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(17875(a,1),595(a,1))].">
      <j1 rule="para" parents="17875 595"/>
    </justification>
  </clause>

  <clause id="17891">
    <literal><![CDATA[
      (x * y) \ (L(x,K(z,u),K(z,u) \ y) * (K(z,u) * (K(z,u) \ y))) = a(x,K(z,u),K(z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(128,a,17880,a,b,834,a)].">
      <j1 rule="hyper" parents="128 17880 834"/>
    </justification>
  </clause>

  <clause id="17893">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(17883,a,17879,a)].">
      <j1 rule="hyper" parents="17883 17879"/>
    </justification>
  </clause>

  <clause id="17895">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * T(u,K(x,y))) = (u * z) / (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,13719,a,b,17893,a)].">
      <j1 rule="hyper" parents="63 13719 17893"/>
    </justification>
  </clause>

  <clause id="17896">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),x,u * K(y,z)) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(17882,a,16845,a),flip(a)].">
      <j1 rule="hyper" parents="17882 16845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17897">
    <literal><![CDATA[
      (x * ((y * K(z,u)) * w)) \ (x * ((y * K(z,u)) * L(w,K(z,u),y))) = L(a(w,K(z,u),y),(y * K(z,u)) * w,x)
    ]]></literal>
    <justification jstring="[para(17896(a,1),575(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17896 575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17898">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) * v5 != x * ((y * K(z,K(u,w))) * v6)
    ]]></literal>
    <literal><![CDATA[
      L(v6,y,x) = v5
    ]]></literal>
    <justification jstring="[para(17866(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="17866 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17899">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(x,T(y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      L(z * K(x,K(y,u)),K(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(17877(a,2),17883(a,1))].">
      <j1 rule="para" parents="17877 17883"/>
    </justification>
  </clause>

  <clause id="17900">
    <literal><![CDATA[
      K(x,((y / (K(z,u) * w)) / T(v5,y * (w \ K(u,z)))) * v6) = K(x,(v5 \ ((K(u,z) * y) / w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,17793,a(flip),b,17049,a)].">
      <j1 rule="hyper" parents="63 17793 17049"/>
    </justification>
  </clause>

  <clause id="17901">
    <literal><![CDATA[
      K(x,y * ((z * (T(u,w) * K(v5,u))) * K(v5,u))) = K(x,y * (K(v5,u) * ((K(v5,u) * z) * T(u,w))))
    ]]></literal>
    <justification jstring="[para(8429(a,1),17236(a,1,2,2,1))].">
      <j1 rule="para" parents="8429 17236"/>
    </justification>
  </clause>

  <clause id="17902">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ T(v5,y \ z)) = K(x,v5 / T(y \ (z * K(u,w)),K(v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(17497,a,17576,a)].">
      <j1 rule="hyper" parents="17497 17576"/>
    </justification>
  </clause>

  <clause id="17904">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ T(v5,y \ z)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5 / (y \ (z * K(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(17902(a,2),14829(a,1))].">
      <j1 rule="para" parents="17902 14829"/>
    </justification>
  </clause>

  <clause id="17905">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ T(v5,y * z)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5 / (y \ (z * K(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(15923(a,1),17904(a,1))].">
      <j1 rule="para" parents="15923 17904"/>
    </justification>
  </clause>

  <clause id="17906">
    <literal><![CDATA[
      K(x,(K(y,T(z,u)) * (K(w,T(v5,v6)) \ (v7 * K(z,T(y,u))))) \ v8) = K(x,v7 \ (K(v5,T(w,v6)) \ v8))
    ]]></literal>
    <justification jstring="[para(16862(a,2),17729(a,1,2,1,2))].">
      <j1 rule="para" parents="16862 17729"/>
    </justification>
  </clause>

  <clause id="17907">
    <literal><![CDATA[
      K(x,((((y \ z) * u) \ u) \ u) / z) = K(x,((z \ y) \ (((z \ y) \ u) * (z \ y))) / z)
    ]]></literal>
    <justification jstring="[para(15394(a,1),17817(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="15394 17817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17908">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y \ z) / y) = K(x,((((z \ y) * u) \ u) \ u) / y)
    ]]></literal>
    <justification jstring="[para(22(a,2),17907(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="22 17907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17909">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,((((z \ y) * u) \ u) \ u) / y)
    ]]></literal>
    <justification jstring="[hyper(16321,a,17908,a)].">
      <j1 rule="hyper" parents="16321 17908"/>
    </justification>
  </clause>

  <clause id="17910">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,T((z \ y) * u,u) / y)
    ]]></literal>
    <justification jstring="[hyper(347,a,12133,a(flip),b,17909,a),flip(a)].">
      <j1 rule="hyper" parents="347 12133 17909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17911">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * (z \ y)) / y) = w
    ]]></literal>
    <justification jstring="[para(17910(a,2),15955(a,1))].">
      <j1 rule="para" parents="17910 15955"/>
    </justification>
  </clause>

  <clause id="17912">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ (u * (w * (v5 * K(x,K(y,z))))) = L(v5,w * K(x,K(y,z)),u)
    ]]></literal>
    <justification jstring="[hyper(17861,a,xx),flip(a)].">
      <j1 rule="hyper" parents="17861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17913">
    <literal><![CDATA[
      (x * y) \ (L(x,K(z,u),K(u,z) * y) * (K(z,u) * (K(z,u) \ y))) = a(x,K(z,u),K(z,u) \ y)
    ]]></literal>
    <justification jstring="[para(5256(a,1),17891(a,1,2,1,3))].">
      <j1 rule="para" parents="5256 17891"/>
    </justification>
  </clause>

  <clause id="17914">
    <literal><![CDATA[
      K(x,(y \ ((K(z,u) * w) / v5)) * v6) = K(x,(y \ (w / (K(u,z) * v5))) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,13460,a(flip),b,17900,a),flip(a)].">
      <j1 rule="hyper" parents="63 13460 17900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17915">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) * T(u,v5)))) = K(x,y * (w * ((T(u,v5) * K(z,u)) * K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(63,a,17550,a(flip),b,17901,a),flip(a)].">
      <j1 rule="hyper" parents="63 17550 17901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17916">
    <literal><![CDATA[
      K(x,(y * K(z,T(u,w))) \ v5) = K(x,y \ (K(z,T(u,w)) \ v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),17906(a,1,2,1))].">
      <j1 rule="para" parents="10 17906"/>
    </justification>
  </clause>

  <clause id="17917">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) * T(u,v5)))) = K(x,y * (w * (T(u,v5) * (K(z,u) * K(z,u)))))
    ]]></literal>
    <justification jstring="[para(5463(a,1),17915(a,2,2,2,2))].">
      <j1 rule="para" parents="5463 17915"/>
    </justification>
  </clause>

  <clause id="17918">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) * T(u,v5)))) = K(x,y * (w * T(u * (K(z,u) * K(z,u)),v5)))
    ]]></literal>
    <justification jstring="[para(16033(a,2),17917(a,2,2,2,2))].">
      <j1 rule="para" parents="16033 17917"/>
    </justification>
  </clause>

  <clause id="17919">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) * T(u,v5)))) = K(x,y * (w * T((T(z,u) * u) / z,v5)))
    ]]></literal>
    <justification jstring="[para(7780(a,1),17918(a,2,2,2,2,1))].">
      <j1 rule="para" parents="7780 17918"/>
    </justification>
  </clause>

  <clause id="17920">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (K(z,u) * (w * T(u,v5))))) = K(x,y * (w * T((T(z,u) * u) / z,v5)))
    ]]></literal>
    <justification jstring="[para(7673(a,1),17919(a,1,2,2,2))].">
      <j1 rule="para" parents="7673 17919"/>
    </justification>
  </clause>

  <clause id="17921">
    <literal><![CDATA[
      K(x,y * (z * T((T(u,w) * w) / u,v5))) = K(x,y * (z * T(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17640,a(flip),b,17920,a),flip(a)].">
      <j1 rule="hyper" parents="63 17640 17920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17923">
    <literal><![CDATA[
      K(x,y * (z * T(T(u * K(w,u),v5),w))) = K(x,y * (z * T((T(v6,u) * u) / v6,v5)))
    ]]></literal>
    <justification jstring="[para(5059(a,2),17921(a,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5059 17921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17924">
    <literal><![CDATA[
      K(x,y * (z * T(T(u * K(w,u),v5 \ v6),w))) = K(x,y * (z * T((T(v7,u) * u) / v7,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(347,a,17730,a(flip),b,17923,a),flip(a)].">
      <j1 rule="hyper" parents="347 17730 17923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17925">
    <literal><![CDATA[
      K(x,y * (z * T(T(u * K(w,u),v5 \ v6),w))) = K(x,y * (z * T(u,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(347,a,17921,a(flip),b,17924,a),flip(a)].">
      <j1 rule="hyper" parents="347 17921 17924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17926">
    <literal><![CDATA[
      K(x,y * (z * T(u,w \ v5))) = K(x,y * (z * T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[para(5058(a,1),17925(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5058 17925"/>
    </justification>
  </clause>

  <clause id="17927">
    <literal><![CDATA[
      K(x,y * (z * T(u,w / v5))) = K(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(14893,a,17926,a)].">
      <j1 rule="hyper" parents="14893 17926"/>
    </justification>
  </clause>

  <clause id="17928">
    <literal><![CDATA[
      T(x,y * (z * T(u,w \ v5))) = T(x,y * (z * T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(132,a,17926,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 17926 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17929">
    <literal><![CDATA[
      K(x,y * (T(z,T(u \ w,u)) * v5)) = K(x,y * (T(v5,z) * T(z,w * u)))
    ]]></literal>
    <justification jstring="[hyper(15822,a,17927,a)].">
      <j1 rule="hyper" parents="15822 17927"/>
    </justification>
  </clause>

  <clause id="17930">
    <literal><![CDATA[
      T(x,y * (z * T(u,w / v5))) = T(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(132,a,17927,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 17927 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17931">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * T(u,y * z))) = T(x,(u * (z \ 1)) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,17440,a(flip),b,17928,a),flip(a)].">
      <j1 rule="hyper" parents="63 17440 17928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17932">
    <literal><![CDATA[
      K(T(x,y / z),(u * w) \ T(v5,w * (u * T(x,y * z)))) = K(T(x,y / z),v5 / (u * w))
    ]]></literal>
    <justification jstring="[para(17930(a,1),17340(a,1,2,2))].">
      <j1 rule="para" parents="17930 17340"/>
    </justification>
  </clause>

  <clause id="17933">
    <literal><![CDATA[
      K(x,y * (T(z,T(u \ w,u)) * v5)) = K(x,y * (T(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,15698,a(flip),b,17929,a),flip(a)].">
      <j1 rule="hyper" parents="347 15698 17929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17934">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) * v5)) = K(x,y * (T(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(14886,a,17933,a)].">
      <j1 rule="hyper" parents="14886 17933"/>
    </justification>
  </clause>

  <clause id="17936">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) * (u / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u / w) * z)) = v5
    ]]></literal>
    <justification jstring="[para(17934(a,1),15756(a,1))].">
      <j1 rule="para" parents="17934 15756"/>
    </justification>
  </clause>

  <clause id="17937">
    <literal><![CDATA[
      K(T(x,y / z),((z \ 1) * y) \ T(u,(x * (z \ 1)) * T(y,z))) = K(T(x,y / z),u / ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[para(17931(a,1),17932(a,1,2,2))].">
      <j1 rule="para" parents="17931 17932"/>
    </justification>
  </clause>

  <clause id="17939">
    <literal><![CDATA[
      K(x,L(T(y,z * y) * u,u,y * z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,17307,a(flip),b,16925,a)].">
      <j1 rule="hyper" parents="63 17307 16925"/>
    </justification>
  </clause>

  <clause id="17940">
    <literal><![CDATA[
      K(x,L(T(y,y * z) * u,u,y * z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(4323(a,1),17939(a,1,2,1,1))].">
      <j1 rule="para" parents="4323 17939"/>
    </justification>
  </clause>

  <clause id="17941">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(12209,a,17940,a)].">
      <j1 rule="hyper" parents="12209 17940"/>
    </justification>
  </clause>

  <clause id="17942">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * T(w,K(y,x) * v5)) / (K(x,L(y,z,u)) * w) = K(w,v5 * K(x,L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(13729(a,1),17137(a,1,1))].">
      <j1 rule="para" parents="13729 17137"/>
    </justification>
  </clause>

  <clause id="17944">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,K(z,L(y,w,v5)))) = K(x,u * K(z,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(7704,a,17942,a)].">
      <j1 rule="hyper" parents="7704 17942"/>
    </justification>
  </clause>

  <clause id="17945">
    <literal><![CDATA[
      K(x,y * K(z,L(u,w,v5))) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(16819(a,1),17944(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16819 17944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17946">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,(y \ (z * u)) * K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,17556,a(flip),b,17945,a)].">
      <j1 rule="hyper" parents="63 17556 17945"/>
    </justification>
  </clause>

  <clause id="17948">
    <literal><![CDATA[
      K(x,(y \ (z * T(u,z))) * K(w,v5)) = K(x,y \ ((K(v5,w) * u) * z))
    ]]></literal>
    <justification jstring="[hyper(17293,a,17946,a),flip(a)].">
      <j1 rule="hyper" parents="17293 17946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17950">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,K(w,v5) * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,15548,a,b,17946,a),flip(a)].">
      <j1 rule="hyper" parents="347 15548 17946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17951">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * (w \ (v5 * u))) = K(x,w \ (v5 * (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[para(7104(a,1),17950(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7104 17950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17952">
    <literal><![CDATA[
      K(x,y \ ((K(z,u) * w) * v5)) = K(x,(y \ (w * v5)) * K(u,z))
    ]]></literal>
    <justification jstring="[para(111(a,1),17948(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="111 17948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17953">
    <literal><![CDATA[
      K(x,y \ ((K(z,u) * w) * v5)) = K(x,K(z,u) * (y \ (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(347,a,15548,a,b,17952,a),flip(a)].">
      <j1 rule="hyper" parents="347 15548 17952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17954">
    <literal><![CDATA[
      K(x,K(y,z) * (((K(y,z) * u) * w) \ (u * (w * v5)))) = K(x,L(v5,w,K(y,z) * u))
    ]]></literal>
    <justification jstring="[para(18(a,2),17953(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 17953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17955">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y * w) * v5))) = K(x,u \ ((T(y,z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(4974(a,1),17953(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4974 17953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17956">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,w) * v5))) = K(x,K(w,u) * (y \ (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(15641,a,17951,a),flip(a)].">
      <j1 rule="hyper" parents="15641 17951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17957">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,w) * v5))) = K(x,K(u,w) * (y \ (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14802,a(flip),b,17951,a),flip(a)].">
      <j1 rule="hyper" parents="63 14802 17951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17958">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * (v5 \ z)))) = K(x,u \ (w * (v5 \ T(z,y))))
    ]]></literal>
    <justification jstring="[hyper(17105,a,17956,a),flip(a)].">
      <j1 rule="hyper" parents="17105 17956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17959">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,K(u \ 1,w) * (y \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17778,a,b,17956,a)].">
      <j1 rule="hyper" parents="63 17778 17956"/>
    </justification>
  </clause>

  <clause id="17960">
    <literal><![CDATA[
      K(x,K(y,z) * (z \ ((u \ z) * w))) = K(x,z \ ((T(z,y) \ u) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,17810,a(flip),b,17956,a),flip(a)].">
      <j1 rule="hyper" parents="63 17810 17956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17961">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u \ (z * w))) = K(x,u \ (((y \ z) * y) * w))
    ]]></literal>
    <justification jstring="[para(10277(a,1),17956(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10277 17956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17963">
    <literal><![CDATA[
      K(x,y \ ((T(z,u * K(w,v5)) * u) * v6)) = K(x,y \ ((u * z) * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,17626,a(flip),b,17955,a),flip(a)].">
      <j1 rule="hyper" parents="63 17626 17955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17964">
    <literal><![CDATA[
      K(x,T(y,z) \ (u * (w \ y))) = K(x,y \ (u * (w \ T(y,z))))
    ]]></literal>
    <justification jstring="[hyper(12153,a,17958,a)].">
      <j1 rule="hyper" parents="12153 17958"/>
    </justification>
  </clause>

  <clause id="17965">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ y) * w)) = K(x,y \ ((T(y,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[hyper(12153,a,17960,a)].">
      <j1 rule="hyper" parents="12153 17960"/>
    </justification>
  </clause>

  <clause id="17966">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ y) * w)) = K(x,y \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,17814,a(flip),b,17965,a),flip(a)].">
      <j1 rule="hyper" parents="347 17814 17965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17967">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * z) * w)) = K(x,K(z,u) * (y \ (u * w)))
    ]]></literal>
    <justification jstring="[hyper(11993,a,17961,a),flip(a)].">
      <j1 rule="hyper" parents="11993 17961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17968">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * z) * w)) = K(x,y \ (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,17603,a(flip),b,17967,a),flip(a)].">
      <j1 rule="hyper" parents="347 17603 17967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17969">
    <literal><![CDATA[
      K(x,y \ ((z / (T(u,z) \ 1)) * w)) = K(x,y \ (T(z / (u \ 1),z) * w))
    ]]></literal>
    <justification jstring="[para(6533(a,1),17968(a,1,2,2,1))].">
      <j1 rule="para" parents="6533 17968"/>
    </justification>
  </clause>

  <clause id="17970">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) * u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(203(a,1),17963(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="203 17963"/>
    </justification>
  </clause>

  <clause id="17971">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,K(u,w) * (y \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,15832,a(flip),b,17959,a),flip(a)].">
      <j1 rule="hyper" parents="347 15832 17959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17972">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,17572,a(flip),b,17971,a),flip(a)].">
      <j1 rule="hyper" parents="347 17572 17971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17973">
    <literal><![CDATA[
      K(x,y \ T(z * (1 / T(u,w)),z)) = K(x,y \ (T(1 / u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(15826,a,17972,a)].">
      <j1 rule="hyper" parents="15826 17972"/>
    </justification>
  </clause>

  <clause id="17974">
    <literal><![CDATA[
      K(x,y \ T(z * (1 / T(u,w)),z)) = K(x,y \ (T(u \ 1,w) * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,5705,a(flip),b,17973,a),flip(a)].">
      <j1 rule="hyper" parents="347 5705 17973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17975">
    <literal><![CDATA[
      K(x,y \ ((1 / T(z,u)) * w)) = K(x,y \ (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12007,a(flip),b,17974,a)].">
      <j1 rule="hyper" parents="63 12007 17974"/>
    </justification>
  </clause>

  <clause id="17976">
    <literal><![CDATA[
      K(x,y \ (T(z \ 1,u) * w)) = K(x,y \ ((T(z,u) \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(13952,a,17975,a),flip(a)].">
      <j1 rule="hyper" parents="13952 17975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17977">
    <literal><![CDATA[
      K(x,((y \ 1) * T(z \ u,y)) \ (T(y \ 1,z \ u) * u)) = K(x,L(T(z,u),u,T(y,z \ u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(347,a,11159,a(flip),b,17976,a),flip(a)].">
      <j1 rule="hyper" parents="347 11159 17976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17978">
    <literal><![CDATA[
      K(x,y \ ((z / (T(u,z) \ 1)) * w)) = K(x,y \ (((u \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,12163,a(flip),b,17969,a),flip(a)].">
      <j1 rule="hyper" parents="347 12163 17969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17979">
    <literal><![CDATA[
      K(x,L(T(y,z),z,T(u,y \ z) \ 1)) = K(x,(T(y \ z,u) * (u \ 1)) \ ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,17088,a(flip),b,17977,a),flip(a)].">
      <j1 rule="hyper" parents="63 17088 17977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17980">
    <literal><![CDATA[
      K(x,L(T(y,z),z,T(u,y \ z) \ 1)) = K(x,(T(y \ z,u) / u) \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,16042,a(flip),b,17979,a),flip(a)].">
      <j1 rule="hyper" parents="347 16042 17979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17981">
    <literal><![CDATA[
      K(x,L(T(y,z),z,T(u,y \ z) \ 1)) = K(x,(u \ (y \ z)) \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,12018,a(flip),b,17980,a),flip(a)].">
      <j1 rule="hyper" parents="347 12018 17980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17982">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * (u \ 1),w,v5))) = K(x,L(K(y,z) / u,w,v5) * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[para(13126(a,1),17209(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13126 17209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17983">
    <literal><![CDATA[
      K(x,(T(y,(z \ 1) \ 1) / u) * ((z \ K(z,u)) \ u)) = K(x,((((z \ 1) \ u) / u) * u) * (u \ y))
    ]]></literal>
    <justification jstring="[para(4431(a,1),17253(a,1,2,1,1))].">
      <j1 rule="para" parents="4431 17253"/>
    </justification>
  </clause>

  <clause id="17984">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * ((z \ K(z,u)) \ u)) = K(x,((((z \ 1) \ u) / u) * u) * (u \ y))
    ]]></literal>
    <justification jstring="[para(2966(a,1),17983(a,1,2,1,1))].">
      <j1 rule="para" parents="2966 17983"/>
    </justification>
  </clause>

  <clause id="17986">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * (u / (z \ 1))) = K(x,((((z \ 1) \ u) / u) * u) * (u \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15938,a(flip),b,17984,a)].">
      <j1 rule="hyper" parents="63 15938 17984"/>
    </justification>
  </clause>

  <clause id="17987">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * (u / (z \ 1))) = K(x,((z \ 1) \ u) * (u \ y))
    ]]></literal>
    <justification jstring="[para(12(a,1),17986(a,2,2,1))].">
      <j1 rule="para" parents="12 17986"/>
    </justification>
  </clause>

  <clause id="17988">
    <literal><![CDATA[
      K(x,((((y * z) \ y) \ y) / u) * (u / ((z \ 1) \ 1))) = K(x,(((z \ 1) \ 1) \ u) * (u \ (y * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,9415,a(flip),b,17987,a)].">
      <j1 rule="hyper" parents="63 9415 17987"/>
    </justification>
  </clause>

  <clause id="17990">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,((((u * y) \ u) \ u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,5419,a(flip),b,17988,a),flip(a)].">
      <j1 rule="hyper" parents="63 5419 17988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17991">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,(T(u * y,u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(347,a,16393,a(flip),b,17990,a),flip(a)].">
      <j1 rule="hyper" parents="347 16393 17990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17992">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,((y * u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(17522,a,17991,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="17522 17991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17993">
    <literal><![CDATA[
      K(x,(T(y,1) \ z) * (z \ (u * y))) = K(x,((y * u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,12103,a(flip),b,17992,a)].">
      <j1 rule="hyper" parents="63 12103 17992"/>
    </justification>
  </clause>

  <clause id="17994">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,(y \ u) * (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(223(a,1),17993(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="223 17993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17995">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * L((K(z,y) \ u) \ u,w,v5)) \ v6) = K(x,(K(z,y) \ u) \ (L(K(y,z),w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(5256(a,1),17356(a,1,2,1,1))].">
      <j1 rule="para" parents="5256 17356"/>
    </justification>
  </clause>

  <clause id="17996">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * (z / y),w,v5))) = K(x,u * L(((z * y) / z) \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(5140(a,1),17407(a,1,2,1))].">
      <j1 rule="para" parents="5140 17407"/>
    </justification>
  </clause>

  <clause id="17998">
    <literal><![CDATA[
      T((x * T(y,y \ z)) \ T(y,y \ z),(x * y) \ y) = (x * T(y,y \ z)) \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(15634,a,17790,a)].">
      <j1 rule="hyper" parents="15634 17790"/>
    </justification>
  </clause>

  <clause id="17999">
    <literal><![CDATA[
      T((x * y) \ y,K(y,y \ z)) = (x * T(y,y \ z)) \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,15177,a(flip),b,17998,a)].">
      <j1 rule="hyper" parents="63 15177 17998"/>
    </justification>
  </clause>

  <clause id="18000">
    <literal><![CDATA[
      (x * T(y,y \ z)) \ ((y \ z) \ z) = T((x * y) \ y,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8800,a,17999,a),flip(a)].">
      <j1 rule="hyper" parents="8800 17999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18001">
    <literal><![CDATA[
      K(T(x,y / z),((z \ 1) * y) \ T(u,y * (x * (z \ 1)))) = K(T(x,y / z),u / ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(17498,a,17937,a)].">
      <j1 rule="hyper" parents="17498 17937"/>
    </justification>
  </clause>

  <clause id="18002">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * L(K(z,T(y,u)),w,v5)) \ v6) = K(x,(K(z,y) \ u) \ (L(K(y,z),w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(7164(a,1),17995(a,1,2,1,2,1))].">
      <j1 rule="para" parents="7164 17995"/>
    </justification>
  </clause>

  <clause id="18003">
    <literal><![CDATA[
      K(x,(K(y,z) * (u * L(K(z,T(y,u)),w,v5))) \ v6) = K(x,(K(z,y) \ u) \ (L(K(y,z),w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(16897(a,1),18002(a,1,2,1))].">
      <j1 rule="para" parents="16897 18002"/>
    </justification>
  </clause>

  <clause id="18004">
    <literal><![CDATA[
      K(x,(K(y,z) * (L(K(z,y),u,w) * v5)) \ v6) = K(x,(K(z,y) \ v5) \ (L(K(y,z),u,w) * v6))
    ]]></literal>
    <justification jstring="[para(7113(a,1),18003(a,1,2,1,2))].">
      <j1 rule="para" parents="7113 18003"/>
    </justification>
  </clause>

  <clause id="18005">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) \ (L(K(z,y),w,v5) * v6)) = K(x,(a(y,w,K(v5,z)) * u) \ v6)
    ]]></literal>
    <justification jstring="[para(13988(a,1),18004(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13988 18004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18006">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)),v5) * (v5 * a(y,z,K(u,w))) = (x * a(y,z,K(u,w))) * v5
    ]]></literal>
    <justification jstring="[hyper(17430,a,16943,a),flip(a)].">
      <j1 rule="hyper" parents="17430 16943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18007">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * v5 != v6 * (v5 * a(y,z,K(u,w)))
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)),v5) = v6
    ]]></literal>
    <justification jstring="[para(18006(a,1),44(a,1))].">
      <j1 rule="para" parents="18006 44"/>
    </justification>
  </clause>

  <clause id="18008">
    <literal><![CDATA[
      R(T(x,K(y,z) * K(u,w)),K(y,z),K(u,w)) = T(L(T(x,K(u,w)),K(u,w),K(y,z)),K(y,z))
    ]]></literal>
    <justification jstring="[para(263(a,1),16977(a,1,1)),flip(a)].">
      <j1 rule="para" parents="263 16977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18009">
    <literal><![CDATA[
      K(x,L(y \ K(z,u),w,v5) * (K(y,K(z,u)) * v6)) = K(x,T(L(y \ K(z,u),w,v5),y) * v6)
    ]]></literal>
    <justification jstring="[hyper(17782,a,12010,a),flip(a)].">
      <j1 rule="hyper" parents="17782 12010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18010">
    <literal><![CDATA[
      K(x,T(L(y \ K(z,u),w,v5),y) * v6) = K(x,L(y \ K(z,u),w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(14879,a,18009,a),flip(a)].">
      <j1 rule="hyper" parents="14879 18009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18012">
    <literal><![CDATA[
      K(x,L(K(y,z) / u,w,v5) * v6) = K(x,L(u \ K(y,z),w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,15587,a(flip),b,18010,a)].">
      <j1 rule="hyper" parents="63 15587 18010"/>
    </justification>
  </clause>

  <clause id="18013">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * (u \ 1),w,v5))) = K(x,L(u \ K(y,z),w,v5) * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,17982,a,b,18012,a)].">
      <j1 rule="hyper" parents="63 17982 18012"/>
    </justification>
  </clause>

  <clause id="18014">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * w)) \ ((K(x,K(y,z)) * u) * (w * v5)) = L(v5,L(w,u,K(x,K(y,z))),K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(7318(a,2),16853(a,1,1))].">
      <j1 rule="para" parents="7318 16853"/>
    </justification>
  </clause>

  <clause id="18016">
    <literal><![CDATA[
      K(x,(y * K(z,K(u,w))) / (T(K(z,K(u,w)) * v5,v6) * K(z,K(u,w)))) = K(x,y / T(v5 * K(z,K(u,w)),v6))
    ]]></literal>
    <justification jstring="[para(7318(a,1),16856(a,1,2,2,1,1))].">
      <j1 rule="para" parents="7318 16856"/>
    </justification>
  </clause>

  <clause id="18017">
    <literal><![CDATA[
      (K(x,K(y,z)) \ ((u * w) * v5)) / ((w * K(x,K(y,z))) * v5) = R(u,R(w,K(x,K(y,z)),v5),K(x,K(y,z)) * v5)
    ]]></literal>
    <justification jstring="[para(16999(a,2),17045(a,1,1))].">
      <j1 rule="para" parents="16999 17045"/>
    </justification>
  </clause>

  <clause id="18018">
    <literal><![CDATA[
      K(x,L((y / (z \ 1)) / z,u,w) * T(z,y * (K(z,y) * z))) = K(x,z * L(z \ (y / (z \ K(y,z))),u,w))
    ]]></literal>
    <justification jstring="[para(13185(a,1),17471(a,1,2,2))].">
      <j1 rule="para" parents="13185 17471"/>
    </justification>
  </clause>

  <clause id="18019">
    <literal><![CDATA[
      K(x,y * (R(z,z \ (a(u,w,K(v5,v6)) * v7),a(v6,w,K(v5,u))) \ v7)) = K(x,y * (z \ (v7 / a(v6,w,K(v5,u)))))
    ]]></literal>
    <justification jstring="[para(16939(a,1),17551(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="16939 17551"/>
    </justification>
  </clause>

  <clause id="18020">
    <literal><![CDATA[
      K(x,R(y * z,K(u,L(w,y,z)),K(u,L(w,y,z))) \ v5) = K(x,K(u,w) * (((K(u,w) * y) * z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,17182,a(flip),b,17582,a),flip(a)].">
      <j1 rule="hyper" parents="347 17182 17582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18022">
    <literal><![CDATA[
      K(x,K(y,z) * (((K(y,z) * u) * w) \ v5)) = K(x,(u * w) \ v5)
    ]]></literal>
    <justification jstring="[para(6198(a,1),18020(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6198 18020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18023">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,(v5 * z) \ (v5 * (z * y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17954,a(flip),b,18022,a)].">
      <j1 rule="hyper" parents="63 17954 18022"/>
    </justification>
  </clause>

  <clause id="18026">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,L(y,z,v5))
    ]]></literal>
    <justification jstring="[para(18(a,2),18023(a,2,2))].">
      <j1 rule="para" parents="18 18023"/>
    </justification>
  </clause>

  <clause id="18027">
    <literal><![CDATA[
      K(x,L(y,z,u * K(w,v5))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(16932,a,18026,a)].">
      <j1 rule="hyper" parents="16932 18026"/>
    </justification>
  </clause>

  <clause id="18028">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) \ v5,K(z,u) * w)) = K(x,L(y,v5,w))
    ]]></literal>
    <justification jstring="[hyper(14332,a,18026,a)].">
      <j1 rule="hyper" parents="14332 18026"/>
    </justification>
  </clause>

  <clause id="18029">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,(z * v5) / ((y \ z) * v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,14082,a,b,18026,a),flip(a)].">
      <j1 rule="hyper" parents="347 14082 18026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18030">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * K(w,L(v5,u,z)) = (K(x,y) * z) * (u * K(w,v5))
    ]]></literal>
    <justification jstring="[para(18026(a,1),11073(a,1,2))].">
      <j1 rule="para" parents="18026 11073"/>
    </justification>
  </clause>

  <clause id="18031">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * (K(w,v5) * u)) = (K(x,y) * z) * (K(w,v5) * u)
    ]]></literal>
    <justification jstring="[para(18026(a,1),14092(a,1,1))].">
      <j1 rule="para" parents="18026 14092"/>
    </justification>
  </clause>

  <clause id="18032">
    <literal><![CDATA[
      K(x,L(y,z,u * (w / v5))) = K(x,L(y,z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(16998(a,1),18026(a,1,2))].">
      <j1 rule="para" parents="16998 18026"/>
    </justification>
  </clause>

  <clause id="18033">
    <literal><![CDATA[
      K(x,L(y,(z \ u) / w,w)) = K(x,L(y,u / z,w * K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15227,a(flip),b,18027,a),flip(a)].">
      <j1 rule="hyper" parents="63 15227 18027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18034">
    <literal><![CDATA[
      K(x,L(y,z,u \ (w / v5))) = K(x,L(y,z,u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(13113(a,1),18027(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="13113 18027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18035">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) = K(v5,x) * K(x,L(v5,y,z))
    ]]></literal>
    <justification jstring="[para(18027(a,1),13968(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18027 13968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18036">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * (u * K(w,v5))) = (K(x,y) * z) * (u * K(w,v5))
    ]]></literal>
    <justification jstring="[para(18027(a,1),14092(a,1,1))].">
      <j1 rule="para" parents="18027 14092"/>
    </justification>
  </clause>

  <clause id="18037">
    <literal><![CDATA[
      (K(x,L(y,z,K(u,w))) * z) / (K(v5,v6) * K(u,w)) = K(x,y) * (z / (K(u,w) * K(v5,v6)))
    ]]></literal>
    <justification jstring="[para(18027(a,1),14241(a,1,1,1))].">
      <j1 rule="para" parents="18027 14241"/>
    </justification>
  </clause>

  <clause id="18038">
    <literal><![CDATA[
      K(x,L(y,z,u \ (w \ v5))) * (z * (u \ (v5 / w))) = (K(x,y) * z) * (u \ (v5 / w))
    ]]></literal>
    <justification jstring="[para(18034(a,1),14092(a,1,1))].">
      <j1 rule="para" parents="18034 14092"/>
    </justification>
  </clause>

  <clause id="18039">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) = a(x,y,K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,13968,a(flip),b,18035,a),flip(a)].">
      <j1 rule="hyper" parents="347 13968 18035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18040">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(18035(a,2),14052(a,1))].">
      <j1 rule="para" parents="18035 14052"/>
    </justification>
  </clause>

  <clause id="18041">
    <literal><![CDATA[
      a(x * K(y,z),u,K(w,v5)) = a(v5,u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(14019,a,18039,a)].">
      <j1 rule="hyper" parents="14019 18039"/>
    </justification>
  </clause>

  <clause id="18042">
    <literal><![CDATA[
      a(x,y,K(z * u,w)) = a(x,y,K(u * z,w))
    ]]></literal>
    <justification jstring="[para(91(a,1),18039(a,1,3,1))].">
      <j1 rule="para" parents="91 18039"/>
    </justification>
  </clause>

  <clause id="18043">
    <literal><![CDATA[
      a(x,y,K(K(z,u) * w,v5)) = a(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(7076(a,1),18039(a,1,3,1))].">
      <j1 rule="para" parents="7076 18039"/>
    </justification>
  </clause>

  <clause id="18044">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(7408(a,1),18039(a,1,3))].">
      <j1 rule="para" parents="7408 18039"/>
    </justification>
  </clause>

  <clause id="18045">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,13959,a,b,18044,a),flip(a)].">
      <j1 rule="hyper" parents="347 13959 18044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18046">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16521,a,b,18044,a)].">
      <j1 rule="hyper" parents="63 16521 18044"/>
    </justification>
  </clause>

  <clause id="18047">
    <literal><![CDATA[
      a(x,y,K(z,u / w)) = a(x,y,K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(113(a,1),18044(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="113 18044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18048">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(134,a,18045,a(flip),b,12653,a),flip(a)].">
      <j1 rule="hyper" parents="134 18045 12653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18049">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(w,z,K(y * x,u))
    ]]></literal>
    <justification jstring="[para(10369(a,1),18045(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10369 18045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18050">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(18045(a,2),14016(a,1))].">
      <j1 rule="para" parents="18045 14016"/>
    </justification>
  </clause>

  <clause id="18051">
    <literal><![CDATA[
      L(1 / (x * K(y,z)),u,K(w,v5)) = a(w,u,K(x,v5)) / (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(18041(a,1),14347(a,2,1))].">
      <j1 rule="para" parents="18041 14347"/>
    </justification>
  </clause>

  <clause id="18052">
    <literal><![CDATA[
      a(x,y,K((z / (u / w)) * K(w,z),v5)) = a(x,y,K(z / (u / T(w,z)),v5))
    ]]></literal>
    <justification jstring="[para(13266(a,1),18042(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="13266 18042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18053">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * v5)) = a(z,y,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(14016,a,18043,a)].">
      <j1 rule="hyper" parents="14016 18043"/>
    </justification>
  </clause>

  <clause id="18054">
    <literal><![CDATA[
      a(x,y,K((z / u) \ w,v5)) = a(x,y,K((u \ z) \ w,v5))
    ]]></literal>
    <justification jstring="[para(5441(a,1),18043(a,1,3,1))].">
      <j1 rule="para" parents="5441 18043"/>
    </justification>
  </clause>

  <clause id="18055">
    <literal><![CDATA[
      a(x,y,K(y * z,u \ w)) * K(x,(y * (w / u)) / ((z \ 1) * (w / u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(18047(a,1),14259(a,1,1))].">
      <j1 rule="para" parents="18047 14259"/>
    </justification>
  </clause>

  <clause id="18056">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) \ K(z,(y * x) / u) = K(z,y / (u / x))
    ]]></literal>
    <justification jstring="[para(18047(a,1),14679(a,1,1))].">
      <j1 rule="para" parents="18047 14679"/>
    </justification>
  </clause>

  <clause id="18057">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,(u * w) \ v5)) = K(x,L(y,z,v5 / (T(u,x) * w)))
    ]]></literal>
    <justification jstring="[para(18047(a,1),14133(a,1,2))].">
      <j1 rule="para" parents="18047 14133"/>
    </justification>
  </clause>

  <clause id="18058">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(18048(a,2),14002(a,1))].">
      <j1 rule="para" parents="18048 14002"/>
    </justification>
  </clause>

  <clause id="18059">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(u,z,K(w,y * x))
    ]]></literal>
    <justification jstring="[hyper(347,a,13959,a(flip),b,18049,a),flip(a)].">
      <j1 rule="hyper" parents="347 13959 18049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18061">
    <literal><![CDATA[
      a(x,y,K(z \ T(u,w),v5)) = a(v5,y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[para(5456(a,1),18053(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5456 18053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18062">
    <literal><![CDATA[
      a(x * (T(y,z) / z),u,K(w,v5)) = a(w,u,K(v5,(z \ y) * x))
    ]]></literal>
    <justification jstring="[para(12015(a,1),18059(a,2,3))].">
      <j1 rule="para" parents="12015 18059"/>
    </justification>
  </clause>

  <clause id="18063">
    <literal><![CDATA[
      a(x,y,K(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,w * u)) = v5
    ]]></literal>
    <justification jstring="[para(18059(a,1),14019(a,1))].">
      <j1 rule="para" parents="18059 14019"/>
    </justification>
  </clause>

  <clause id="18064">
    <literal><![CDATA[
      a(x * (y \ T(z,y)),u,K(w,v5)) = a(w,u,K(v5,(z / y) * x))
    ]]></literal>
    <justification jstring="[para(17220(a,1),18059(a,2,3))].">
      <j1 rule="para" parents="17220 18059"/>
    </justification>
  </clause>

  <clause id="18066">
    <literal><![CDATA[
      a(T(x,y),z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(14060(a,2),18050(a,1))].">
      <j1 rule="para" parents="14060 18050"/>
    </justification>
  </clause>

  <clause id="18067">
    <literal><![CDATA[
      T(T(x,y) * K(z,u),a(w,v5,x)) = T(x,y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(18058,a,16898,a)].">
      <j1 rule="hyper" parents="18058 16898"/>
    </justification>
  </clause>

  <clause id="18069">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = a(x,y,K(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(18066,a,14514,a),flip(a)].">
      <j1 rule="hyper" parents="18066 14514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18070">
    <literal><![CDATA[
      a(x / y,z,K(u,w)) = a(y \ x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(18066,a,11574,a)].">
      <j1 rule="hyper" parents="18066 11574"/>
    </justification>
  </clause>

  <clause id="18072">
    <literal><![CDATA[
      a(K(x,y),z,u \ w) = a(w / u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,13971,a,b,18070,a)].">
      <j1 rule="hyper" parents="347 13971 18070"/>
    </justification>
  </clause>

  <clause id="18073">
    <literal><![CDATA[
      (x * K(y,z)) / a((1 / u) \ x,u \ 1,K(y,z)) = (x / (1 / u)) * (K(y,T(z,u)) / u)
    ]]></literal>
    <justification jstring="[para(18070(a,1),15203(a,1,2))].">
      <j1 rule="para" parents="18070 15203"/>
    </justification>
  </clause>

  <clause id="18074">
    <literal><![CDATA[
      a(x / y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y \ x,z,K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(18072(a,1),14055(a,1))].">
      <j1 rule="para" parents="18072 14055"/>
    </justification>
  </clause>

  <clause id="18075">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,14029,a(flip),b,18069,a),flip(a)].">
      <j1 rule="hyper" parents="347 14029 18069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18076">
    <literal><![CDATA[
      K(x * L(y,z,u),y * x) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,17148,a(flip),b,18075,a)].">
      <j1 rule="hyper" parents="63 17148 18075"/>
    </justification>
  </clause>

  <clause id="18077">
    <literal><![CDATA[
      K(x * (1 / (1 / (y \ z))),(1 / (z \ y)) * x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[para(3294(a,1),18076(a,1,1,2))].">
      <j1 rule="para" parents="3294 18076"/>
    </justification>
  </clause>

  <clause id="18078">
    <literal><![CDATA[
      a(x,y,K(z * (u / w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z * (w \ u),v5)) = v6
    ]]></literal>
    <justification jstring="[para(6075(a,1),18040(a,1,3,1))].">
      <j1 rule="para" parents="6075 18040"/>
    </justification>
  </clause>

  <clause id="18079">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(v5,u,K(z,w)) = v6
    ]]></literal>
    <justification jstring="[para(18049(a,2),18040(a,1))].">
      <j1 rule="para" parents="18049 18040"/>
    </justification>
  </clause>

  <clause id="18080">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * (v5 * v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,v6 * (v5 * K(w,u)))) = v7
    ]]></literal>
    <justification jstring="[para(17190(a,1),18063(a,1,3))].">
      <j1 rule="para" parents="17190 18063"/>
    </justification>
  </clause>

  <clause id="18081">
    <literal><![CDATA[
      K(x,a(y,z,u)) / (u * K(w,v5)) = 1 / (T(u,a(y,z,x)) * K(w,v5))
    ]]></literal>
    <justification jstring="[para(18067(a,1),17783(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18067 17783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18082">
    <literal><![CDATA[
      a(x * K(y,z),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x \ K(z,y),u,K(v5,w)) = v6
    ]]></literal>
    <justification jstring="[para(14166(a,1),18074(a,1))].">
      <j1 rule="para" parents="14166 18074"/>
    </justification>
  </clause>

  <clause id="18083">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(18029(a,2),14129(a,1))].">
      <j1 rule="para" parents="18029 14129"/>
    </justification>
  </clause>

  <clause id="18084">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(5209(a,1),18083(a,1,2,3))].">
      <j1 rule="para" parents="5209 18083"/>
    </justification>
  </clause>

  <clause id="18085">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,(w * u) \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(10274(a,1),18083(a,1,2,3))].">
      <j1 rule="para" parents="10274 18083"/>
    </justification>
  </clause>

  <clause id="18086">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) \ (y \ u)) = K(x,L(T(z,u),u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(18084,a,17981,a),flip(a)].">
      <j1 rule="hyper" parents="18084 17981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18087">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) / u,z \ y,y \ (z \ y))) = K(x,(z \ y) / (u * T(y \ (z \ y),y)))
    ]]></literal>
    <justification jstring="[hyper(18084,a,14261,a)].">
      <j1 rule="hyper" parents="18084 14261"/>
    </justification>
  </clause>

  <clause id="18088">
    <literal><![CDATA[
      T(K(x,L(T(y,z * y),z,u \ 1)),K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))) = K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(468,a,11191,a(flip),b,18086,a)].">
      <j1 rule="hyper" parents="468 11191 18086"/>
    </justification>
  </clause>

  <clause id="18089">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) \ v5,w)) = K(x,L(y,v5,w))
    ]]></literal>
    <justification jstring="[hyper(18083,a,18028,a)].">
      <j1 rule="hyper" parents="18083 18028"/>
    </justification>
  </clause>

  <clause id="18091">
    <literal><![CDATA[
      K(x,L(y,z \ (u \ w),z)) = K(x,L(y,w / u,z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(14182,a,18033,a)].">
      <j1 rule="hyper" parents="14182 18033"/>
    </justification>
  </clause>

  <clause id="18093">
    <literal><![CDATA[
      K(x,L(y,z / u,w * K(u,z))) = K(x,L(y,u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(14198,a,18091,a),flip(a)].">
      <j1 rule="hyper" parents="14198 18091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18094">
    <literal><![CDATA[
      K(x,L(y,z / u,w)) = K(x,L(y,u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18027,a(flip),b,18093,a)].">
      <j1 rule="hyper" parents="63 18027 18093"/>
    </justification>
  </clause>

  <clause id="18096">
    <literal><![CDATA[
      K(x,L(y,(z * u) / z,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),18094(a,2,2,2))].">
      <j1 rule="para" parents="9 18094"/>
    </justification>
  </clause>

  <clause id="18098">
    <literal><![CDATA[
      K(x,L(y,T(z,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[para(255(a,1),18096(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="255 18096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18103">
    <literal><![CDATA[
      K(x,L(y \ z,T(y,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ z,z,w)) = v5
    ]]></literal>
    <justification jstring="[para(18098(a,2),11167(a,1))].">
      <j1 rule="para" parents="18098 11167"/>
    </justification>
  </clause>

  <clause id="18104">
    <literal><![CDATA[
      K(x,L(y,z * u,w)) = K(x,L(y,u * z,w))
    ]]></literal>
    <justification jstring="[para(12382(a,1),18098(a,1,2))].">
      <j1 rule="para" parents="12382 18098"/>
    </justification>
  </clause>

  <clause id="18105">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) \ v5,v6)) = K(x,L(y,w \ (K(u,z) * v5),v6))
    ]]></literal>
    <justification jstring="[para(14383(a,1),18098(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14383 18098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18106">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,z,u)) = K(x,L(y * z,T(y \ 1,w),u))
    ]]></literal>
    <justification jstring="[hyper(18103,a,12986,a)].">
      <j1 rule="hyper" parents="18103 12986"/>
    </justification>
  </clause>

  <clause id="18107">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,T((y / z) \ 1,w),u))
    ]]></literal>
    <justification jstring="[para(12(a,1),18106(a,2,2,1))].">
      <j1 rule="para" parents="12 18106"/>
    </justification>
  </clause>

  <clause id="18108">
    <literal><![CDATA[
      a(x \ y,x,K(z,u)) * K(z,(x * u) / y) = K(z,x / (y / u))
    ]]></literal>
    <justification jstring="[hyper(14065,a,18056,a)].">
      <j1 rule="hyper" parents="14065 18056"/>
    </justification>
  </clause>

  <clause id="18109">
    <literal><![CDATA[
      a(x,y,K(z * (T(u,x) \ w),v5)) = a(v5,y,K(x,z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(18078,a,13986,a)].">
      <j1 rule="hyper" parents="18078 13986"/>
    </justification>
  </clause>

  <clause id="18110">
    <literal><![CDATA[
      a(x,y,K(z,u * (w / v5))) = a(x,y,K(z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13987,a(flip),b,18109,a),flip(a)].">
      <j1 rule="hyper" parents="63 13987 18109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18111">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5 * (v6 \ v7))) = a(v5 * (v7 / v6),u,K(z,w))
    ]]></literal>
    <justification jstring="[hyper(18079,a,18110,a),flip(a)].">
      <j1 rule="hyper" parents="18079 18110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18112">
    <literal><![CDATA[
      a(x \ K(y,z),u,K(w,v5)) = a(w,u,K(x,v5))
    ]]></literal>
    <justification jstring="[hyper(18082,a,18041,a)].">
      <j1 rule="hyper" parents="18082 18041"/>
    </justification>
  </clause>

  <clause id="18113">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ w)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(18085,a,14506,a)].">
      <j1 rule="hyper" parents="18085 14506"/>
    </justification>
  </clause>

  <clause id="18115">
    <literal><![CDATA[
      K(x,L(y,z,u \ (w \ u))) = K(x,L(y,z,w \ 1))
    ]]></literal>
    <justification jstring="[para(10(a,1),18113(a,1,2,3,1))].">
      <j1 rule="para" parents="10 18113"/>
    </justification>
  </clause>

  <clause id="18116">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,((u / (z * u)) * y) \ u)
    ]]></literal>
    <justification jstring="[para(13462(a,1),18113(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13462 18113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18117">
    <literal><![CDATA[
      (x \ y) * K(z,L(u,y,x \ 1)) = ((x \ y) / y) * (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(18115(a,1),11069(a,1,2))].">
      <j1 rule="para" parents="18115 11069"/>
    </justification>
  </clause>

  <clause id="18118">
    <literal><![CDATA[
      a(x,y,K(z,u \ y)) * K(z,(y * x) / u) = K(z,y / (u / x))
    ]]></literal>
    <justification jstring="[para(13974(a,1),18108(a,1,1))].">
      <j1 rule="para" parents="13974 18108"/>
    </justification>
  </clause>

  <clause id="18119">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,(y * T(z,w)) / u) = K(x,y / (u / T(z,w)))
    ]]></literal>
    <justification jstring="[para(18045(a,1),18108(a,1,1))].">
      <j1 rule="para" parents="18045 18108"/>
    </justification>
  </clause>

  <clause id="18120">
    <literal><![CDATA[
      K(x,((y / (z * y)) * u) \ y) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14564,a(flip),b,18116,a),flip(a)].">
      <j1 rule="hyper" parents="63 14564 18116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18121">
    <literal><![CDATA[
      K(x,((y / z) \ u) \ z) = K(x,((z / y) * u) \ z)
    ]]></literal>
    <justification jstring="[para(12(a,1),18120(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 18120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18122">
    <literal><![CDATA[
      ((x \ y) / y) * (y * K(z,u)) = x \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14549,a(flip),b,18117,a),flip(a)].">
      <j1 rule="hyper" parents="63 14549 18117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18123">
    <literal><![CDATA[
      (x / y) \ (x * K(z,u)) = (y / x) * (x * K(z,u))
    ]]></literal>
    <justification jstring="[para(83(a,1),18122(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="83 18122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18124">
    <literal><![CDATA[
      K(x,(T((y \ z) / z,x) * (z * K(u,w))) * v5) = K(x,(y \ (z * K(u,w))) * v5)
    ]]></literal>
    <justification jstring="[para(18122(a,1),7976(a,2,2,1))].">
      <j1 rule="para" parents="18122 7976"/>
    </justification>
  </clause>

  <clause id="18125">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(x,y,K(u \ y,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(17064,a,18118,a)].">
      <j1 rule="hyper" parents="17064 18118"/>
    </justification>
  </clause>

  <clause id="18126">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(z,y,K(x,u \ y)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(16837,a,18118,a)].">
      <j1 rule="hyper" parents="16837 18118"/>
    </justification>
  </clause>

  <clause id="18127">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,17326,a(flip),b,18125,a)].">
      <j1 rule="hyper" parents="63 17326 18125"/>
    </justification>
  </clause>

  <clause id="18128">
    <literal><![CDATA[
      K(x,L((y * z) * (u \ T(w,w \ u)),y,z \ 1)) = K(x,y / (T((u \ w) \ 1,w) / z))
    ]]></literal>
    <justification jstring="[hyper(13859,a,18127,a)].">
      <j1 rule="hyper" parents="13859 18127"/>
    </justification>
  </clause>

  <clause id="18129">
    <literal><![CDATA[
      K(x,L((y * z) * u,y,z \ 1)) = K(x,y / ((u \ 1) / z))
    ]]></literal>
    <justification jstring="[hyper(13444,a,18127,a)].">
      <j1 rule="hyper" parents="13444 18127"/>
    </justification>
  </clause>

  <clause id="18130">
    <literal><![CDATA[
      K(x,y / (z * (y / (u * y)))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15481,a(flip),b,18127,a)].">
      <j1 rule="hyper" parents="63 15481 18127"/>
    </justification>
  </clause>

  <clause id="18131">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / (u * (z \ 1))) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15065,a(flip),b,18127,a)].">
      <j1 rule="hyper" parents="63 15065 18127"/>
    </justification>
  </clause>

  <clause id="18132">
    <literal><![CDATA[
      K(x,y / (z * ((y * u) \ y))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14508,a(flip),b,18127,a)].">
      <j1 rule="hyper" parents="63 14508 18127"/>
    </justification>
  </clause>

  <clause id="18133">
    <literal><![CDATA[
      K(x,(y \ z) / (u * ((y \ z) / z))) = K(x,(y \ z) / (u / y))
    ]]></literal>
    <justification jstring="[para(10(a,1),18130(a,1,2,2,2,2))].">
      <j1 rule="para" parents="10 18130"/>
    </justification>
  </clause>

  <clause id="18134">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / ((z \ 1) * u)) = K(x,y / (T(u,z) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,17721,a(flip),b,18131,a)].">
      <j1 rule="hyper" parents="63 17721 18131"/>
    </justification>
  </clause>

  <clause id="18136">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y / (u \ z))) * K(x,L(y / (u \ z),u \ z,u) / (y * (z \ u))) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16814,a,b,18046,a)].">
      <j1 rule="hyper" parents="63 16814 18046"/>
    </justification>
  </clause>

  <clause id="18137">
    <literal><![CDATA[
      a(x,y,K(z,u)) / (z * K(w,v5)) = L(K(v5,w) / z,y,K(x,u))
    ]]></literal>
    <justification jstring="[para(13074(a,1),18051(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13074 18051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18138">
    <literal><![CDATA[
      K(x,a(y,z,u)) / (u * K(w,v5)) = K(v5,w) / T(u,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,13074,a(flip),b,18081,a),flip(a)].">
      <j1 rule="hyper" parents="347 13074 18081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18140">
    <literal><![CDATA[
      a(x,y,K(z,u)) / (z * K(w,v5)) = K(v5,w) / T(z,a(u,y,x))
    ]]></literal>
    <justification jstring="[para(13960(a,2),18138(a,1,1))].">
      <j1 rule="para" parents="13960 18138"/>
    </justification>
  </clause>

  <clause id="18141">
    <literal><![CDATA[
      a(x,y,K(z,u)) / (z * K(w,v5)) = K(v5,w) / L(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[para(14337(a,2),18140(a,2,2))].">
      <j1 rule="para" parents="14337 18140"/>
    </justification>
  </clause>

  <clause id="18142">
    <literal><![CDATA[
      L(K(x,y) / z,u,K(w,v5)) = K(x,y) / L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,18137,a(flip),b,18141,a)].">
      <j1 rule="hyper" parents="63 18137 18141"/>
    </justification>
  </clause>

  <clause id="18143">
    <literal><![CDATA[
      L(K(x,y) / (z \ 1),u,K(w,v5)) = K(x,y) * L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,17285,a(flip),b,18142,a),flip(a)].">
      <j1 rule="hyper" parents="347 17285 18142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18144">
    <literal><![CDATA[
      L(K(x,y) * z,u,K(w,v5)) = K(x,y) * L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(13064(a,1),18143(a,1,1))].">
      <j1 rule="para" parents="13064 18143"/>
    </justification>
  </clause>

  <clause id="18145">
    <literal><![CDATA[
      L(K(x,y) * (K(y,T(x,z)) * (z / a(u,w,v5))),w,K(v5,u)) = T(a(u,w,v5) \ z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,15334,a(flip),b,18144,a),flip(a)].">
      <j1 rule="hyper" parents="347 15334 18144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18147">
    <literal><![CDATA[
      K(x,L(y,z \ (K(u,w) * v5),z)) = K(x,L(y,v5,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18089,a(flip),b,18105,a),flip(a)].">
      <j1 rule="hyper" parents="63 18089 18105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18148">
    <literal><![CDATA[
      K(x,L(y,K(z,u) * w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(14198,a,18147,a)].">
      <j1 rule="hyper" parents="14198 18147"/>
    </justification>
  </clause>

  <clause id="18149">
    <literal><![CDATA[
      K(x,L(y,K(z,u) * w,v5)) = a(y,w,K(x,v5)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,13994,a,b,18148,a),flip(a)].">
      <j1 rule="hyper" parents="347 13994 18148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18152">
    <literal><![CDATA[
      K(x,L(y,K(z,u),w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,11058,a(flip),b,18148,a),flip(a)].">
      <j1 rule="hyper" parents="63 11058 18148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18157">
    <literal><![CDATA[
      K(L(x,K(y,z),u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(11194,a,18152,a)].">
      <j1 rule="hyper" parents="11194 18152"/>
    </justification>
  </clause>

  <clause id="18158">
    <literal><![CDATA[
      L(K(x,y),K(z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11051,a,18152,a)].">
      <j1 rule="hyper" parents="11051 18152"/>
    </justification>
  </clause>

  <clause id="18159">
    <literal><![CDATA[
      T(x,L(y,K(z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,18152,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 18152 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18160">
    <literal><![CDATA[
      a(x,K(y,z),K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,18152,a,b,13992,a),flip(a)].">
      <j1 rule="hyper" parents="129 18152 13992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18161">
    <literal><![CDATA[
      K(x,R(y,K(z,u),w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14081,a,b,18152,a)].">
      <j1 rule="hyper" parents="63 14081 18152"/>
    </justification>
  </clause>

  <clause id="18164">
    <literal><![CDATA[
      K(x,(y * z) \ (y * K(u,w))) = K(x,z \ K(u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,11057,a(flip),b,18152,a)].">
      <j1 rule="hyper" parents="63 11057 18152"/>
    </justification>
  </clause>

  <clause id="18165">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) * K(w,u) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,18152,a(flip),b,11063,a)].">
      <j1 rule="hyper" parents="134 18152 11063"/>
    </justification>
  </clause>

  <clause id="18167">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(y,z) * K(u,w))
    ]]></literal>
    <justification jstring="[para(18152(a,1),11073(a,1,2))].">
      <j1 rule="para" parents="18152 11073"/>
    </justification>
  </clause>

  <clause id="18169">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) * w = K(x,y) * (K(z,u) * w)
    ]]></literal>
    <justification jstring="[para(18152(a,1),14092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18152 14092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18170">
    <literal><![CDATA[
      x \ (K(y,z) * K(u,w)) = (x \ K(y,z)) * K(u,w)
    ]]></literal>
    <justification jstring="[para(18152(a,1),14221(a,1,2,2))].">
      <j1 rule="para" parents="18152 14221"/>
    </justification>
  </clause>

  <clause id="18171">
    <literal><![CDATA[
      K(x,L(y,K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(18152(a,1),15077(a,1))].">
      <j1 rule="para" parents="18152 15077"/>
    </justification>
  </clause>

  <clause id="18172">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) \ (y \ w)) = v5
    ]]></literal>
    <justification jstring="[para(18152(a,1),15078(a,1))].">
      <j1 rule="para" parents="18152 15078"/>
    </justification>
  </clause>

  <clause id="18173">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,(y / w) * K(u,z))
    ]]></literal>
    <justification jstring="[para(17874(a,1),18152(a,1,2))].">
      <j1 rule="para" parents="17874 18152"/>
    </justification>
  </clause>

  <clause id="18174">
    <literal><![CDATA[
      L(x,K(y,z),T(u,w)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(189,a,14485,a,b,18160,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="189 14485 18160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18175">
    <literal><![CDATA[
      L(x,K(y,z),K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(189,a,14361,a,b,18160,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="189 14361 18160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18176">
    <literal><![CDATA[
      T(x,a(y,K(z,u),w)) = x
    ]]></literal>
    <justification jstring="[hyper(189,a,12679,a,b,18160,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="189 12679 18160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18178">
    <literal><![CDATA[
      R(x,K(y,z),T(u,w)) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(14482,a,18175,a)].">
      <j1 rule="hyper" parents="14482 18175"/>
    </justification>
  </clause>

  <clause id="18180">
    <literal><![CDATA[
      L(x,K(y,z),u / w) = L(x,K(y,z),w \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14457,a(flip),b,18175,a)].">
      <j1 rule="hyper" parents="63 14457 18175"/>
    </justification>
  </clause>

  <clause id="18181">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ w = K(u,z) * (K(y,x) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,5722,a(flip),b,18175,a)].">
      <j1 rule="hyper" parents="63 5722 18175"/>
    </justification>
  </clause>

  <clause id="18185">
    <literal><![CDATA[
      T(x,a(y,K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(18175(a,1),14423(a,1,1))].">
      <j1 rule="para" parents="18175 14423"/>
    </justification>
  </clause>

  <clause id="18186">
    <literal><![CDATA[
      R(T(x,K(y,z) * K(u,w)),K(y,z),K(u,w)) = T(T(x,K(u,w)),K(y,z))
    ]]></literal>
    <justification jstring="[para(18175(a,1),18008(a,2,1))].">
      <j1 rule="para" parents="18175 18008"/>
    </justification>
  </clause>

  <clause id="18187">
    <literal><![CDATA[
      T(x,a(y,K(z,u),w)) = v5 / (x \ v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,80,a,b,18176,a),flip(a)].">
      <j1 rule="hyper" parents="347 80 18176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18188">
    <literal><![CDATA[
      L(x,K(y,z),u) * T(w,x) = w * L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17464,a(flip),b,18176,a)].">
      <j1 rule="hyper" parents="63 17464 18176"/>
    </justification>
  </clause>

  <clause id="18189">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K((x \ u) * K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(14694,a,18157,a)].">
      <j1 rule="hyper" parents="14694 18157"/>
    </justification>
  </clause>

  <clause id="18191">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K(K(z,y) * (x \ u),w)
    ]]></literal>
    <justification jstring="[para(5278(a,1),18157(a,1,1))].">
      <j1 rule="para" parents="5278 18157"/>
    </justification>
  </clause>

  <clause id="18194">
    <literal><![CDATA[
      L(L(K(x,y),z,u),K(w,v5),v6) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(18158(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18158 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18197">
    <literal><![CDATA[
      K(x,T((y / z) / K(u,w),v5)) = K(x,T(y / (K(u,w) * z),v5))
    ]]></literal>
    <justification jstring="[para(704(a,1),18161(a,1,2)),flip(a)].">
      <j1 rule="para" parents="704 18161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18198">
    <literal><![CDATA[
      R(x,K(y,z),K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(14299(a,2),18185(a,1))].">
      <j1 rule="para" parents="14299 18185"/>
    </justification>
  </clause>

  <clause id="18199">
    <literal><![CDATA[
      T(x * K(y,z),a(u,x,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = v5
    ]]></literal>
    <justification jstring="[para(14191(a,1),18185(a,1))].">
      <j1 rule="para" parents="14191 18185"/>
    </justification>
  </clause>

  <clause id="18200">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * (y \ w)) = v5
    ]]></literal>
    <justification jstring="[para(5278(a,1),18171(a,1,2))].">
      <j1 rule="para" parents="5278 18171"/>
    </justification>
  </clause>

  <clause id="18201">
    <literal><![CDATA[
      L(K(x,y),K(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(11049(a,2),18171(a,1))].">
      <j1 rule="para" parents="11049 18171"/>
    </justification>
  </clause>

  <clause id="18202">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ y) \ K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(11068(a,1),18171(a,1))].">
      <j1 rule="para" parents="11068 18171"/>
    </justification>
  </clause>

  <clause id="18203">
    <literal><![CDATA[
      L(x,K(y,z),(u \ w) \ w) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(2111,a,18174,a)].">
      <j1 rule="hyper" parents="2111 18174"/>
    </justification>
  </clause>

  <clause id="18204">
    <literal><![CDATA[
      T(x \ L(x,K(y,z),u),w) = x \ L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(128,a,18174,a(flip),b,14469,a),flip(a)].">
      <j1 rule="hyper" parents="128 18174 14469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18205">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),x,K(y,z) * T(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,K(y,z),T(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(18174(a,1),17882(a,1,1,2))].">
      <j1 rule="para" parents="18174 17882"/>
    </justification>
  </clause>

  <clause id="18208">
    <literal><![CDATA[
      L(K(x,y),L(K(z,u),w,v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v7
    ]]></literal>
    <justification jstring="[para(5660(a,1),18201(a,1,2))].">
      <j1 rule="para" parents="5660 18201"/>
    </justification>
  </clause>

  <clause id="18210">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * L(K(u,w),v5,v6)) = x * L(K(u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(18194(a,1),6134(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18194 6134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18211">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ v6) = K(x,L(K(z,u),w,v5) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(18208,a,11074,a),flip(a)].">
      <j1 rule="hyper" parents="18208 11074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18212">
    <literal><![CDATA[
      K(x,(y * z) \ (K(u,w) * y)) = K(x,z \ K(u,w))
    ]]></literal>
    <justification jstring="[hyper(14836,a,18164,a)].">
      <j1 rule="hyper" parents="14836 18164"/>
    </justification>
  </clause>

  <clause id="18213">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) / (u * w) = (x * K(y,z)) / (w * u)
    ]]></literal>
    <justification jstring="[hyper(131,a,18165,a(flip),b,9588,a),flip(a)].">
      <j1 rule="hyper" parents="131 18165 9588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18214">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) * K(z,y) = x * K(u,w)
    ]]></literal>
    <justification jstring="[para(13590(a,1),18165(a,1,1,2))].">
      <j1 rule="para" parents="13590 18165"/>
    </justification>
  </clause>

  <clause id="18216">
    <literal><![CDATA[
      (L(K(x,y) * K(z,u),w,K(v5,v6)) * a(v5,w,v6)) / K(z,u) = a(v5,w,v6) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,14354,a,b,18167,a)].">
      <j1 rule="hyper" parents="131 14354 18167"/>
    </justification>
  </clause>

  <clause id="18218">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(w,v5) = x * (K(z,L(u,x,y \ x)) * K(w,v5))
    ]]></literal>
    <justification jstring="[para(14213(a,2),18167(a,1,1))].">
      <j1 rule="para" parents="14213 18167"/>
    </justification>
  </clause>

  <clause id="18220">
    <literal><![CDATA[
      K(x,y) * (K(z,T(y,x)) * u) = (T(T(y,z),x) \ y) * u
    ]]></literal>
    <justification jstring="[para(7584(a,1),18169(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7584 18169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18222">
    <literal><![CDATA[
      ((x * ((x \ (y \ 1)) * (y * K(z,u)))) \ K(y \ 1,y)) * K(z,u) = a(x,x \ (y \ 1),y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(13433,a,18170,a),flip(a)].">
      <j1 rule="hyper" parents="13433 18170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18223">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,K(u,z) * (y / w))
    ]]></literal>
    <justification jstring="[hyper(347,a,13579,a,b,18173,a),flip(a)].">
      <j1 rule="hyper" parents="347 13579 18173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18226">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ w = K(y,x) * (K(u,z) * w)
    ]]></literal>
    <justification jstring="[para(13590(a,1),18181(a,1,1))].">
      <j1 rule="para" parents="13590 18181"/>
    </justification>
  </clause>

  <clause id="18227">
    <literal><![CDATA[
      a(x \ (y * K(z,u)),w,K(v5,v6)) = a(v5,w,K((y \ x) * K(u,z),v6))
    ]]></literal>
    <justification jstring="[para(18189(a,1),13980(a,2,3))].">
      <j1 rule="para" parents="18189 13980"/>
    </justification>
  </clause>

  <clause id="18228">
    <literal><![CDATA[
      K((x / ((y * z) / y)) \ u,w) = K(K(y,z) * ((x / z) \ u),w)
    ]]></literal>
    <justification jstring="[para(6126(a,2),18191(a,1,1,1))].">
      <j1 rule="para" parents="6126 18191"/>
    </justification>
  </clause>

  <clause id="18229">
    <literal><![CDATA[
      x * K(a(y,x,z),L(x,u,w)) = T(x,a(w,u,a(y,x,z)))
    ]]></literal>
    <justification jstring="[hyper(18199,a,14231,a)].">
      <j1 rule="hyper" parents="18199 14231"/>
    </justification>
  </clause>

  <clause id="18230">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,(z / y) \ K(w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,17859,a(flip),b,18212,a)].">
      <j1 rule="hyper" parents="63 17859 18212"/>
    </justification>
  </clause>

  <clause id="18231">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) * (K(z,y) * K(w,u)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,18165,a(flip),b,18214,a),flip(a)].">
      <j1 rule="hyper" parents="35 18165 18214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18233">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (w \ z))) = K(x,u / (w \ T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(14858,a,18223,a),flip(a)].">
      <j1 rule="hyper" parents="14858 18223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18234">
    <literal><![CDATA[
      K(x,K(y,z) * (u / w)) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(13319,a,18223,a),flip(a)].">
      <j1 rule="hyper" parents="13319 18223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18235">
    <literal><![CDATA[
      K(x,K(y,z) * (u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (w \ K(y,z))) = v5
    ]]></literal>
    <justification jstring="[para(18223(a,1),13319(a,1))].">
      <j1 rule="para" parents="18223 13319"/>
    </justification>
  </clause>

  <clause id="18238">
    <literal><![CDATA[
      K(x,y) * (K(z,T(y,x)) * u) = (T(T(y,x),z) / y) \ u
    ]]></literal>
    <justification jstring="[para(7830(a,1),18226(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7830 18226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18239">
    <literal><![CDATA[
      K(x,(y / z) \ K(z,u)) = K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[hyper(16931,a,18230,a),flip(a)].">
      <j1 rule="hyper" parents="16931 18230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18240">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,(w / y) \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(14857,a,18230,a)].">
      <j1 rule="hyper" parents="14857 18230"/>
    </justification>
  </clause>

  <clause id="18242">
    <literal><![CDATA[
      K(x,(y / (z * K(u,w))) \ K(z,u)) = K(x,T(z * K(u,w),u) / y)
    ]]></literal>
    <justification jstring="[para(7903(a,1),18239(a,1,2,2))].">
      <j1 rule="para" parents="7903 18239"/>
    </justification>
  </clause>

  <clause id="18243">
    <literal><![CDATA[
      K(x,(y / (z * K(u,w))) \ K(z,T(z \ u,w))) = K(x,T(z * K(u,w),z \ u) / y)
    ]]></literal>
    <justification jstring="[para(13653(a,1),18239(a,1,2,2))].">
      <j1 rule="para" parents="13653 18239"/>
    </justification>
  </clause>

  <clause id="18244">
    <literal><![CDATA[
      x / (K(y,z) * K(u,w)) = x * (K(z,y) * K(w,u))
    ]]></literal>
    <justification jstring="[hyper(353,a,18231,a),flip(a)].">
      <j1 rule="hyper" parents="353 18231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18247">
    <literal><![CDATA[
      K(x,y * (z \ K(x,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = w
    ]]></literal>
    <justification jstring="[para(18234(a,1),7871(a,1))].">
      <j1 rule="para" parents="18234 7871"/>
    </justification>
  </clause>

  <clause id="18248">
    <literal><![CDATA[
      K(x,y / T(z / u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u \ z)) = w
    ]]></literal>
    <justification jstring="[para(13856(a,2),18247(a,1))].">
      <j1 rule="para" parents="13856 18247"/>
    </justification>
  </clause>

  <clause id="18249">
    <literal><![CDATA[
      K(x,(y / z) \ K(u,w)) = K(x,K(u,w) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,18223,a(flip),b,18240,a),flip(a)].">
      <j1 rule="hyper" parents="63 18223 18240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18250">
    <literal><![CDATA[
      K(x,(y / z) \ K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z / T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(18249(a,2),15749(a,1))].">
      <j1 rule="para" parents="18249 15749"/>
    </justification>
  </clause>

  <clause id="18251">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u \ z)) = w
    ]]></literal>
    <justification jstring="[para(17429(a,2),18248(a,1))].">
      <j1 rule="para" parents="17429 18248"/>
    </justification>
  </clause>

  <clause id="18252">
    <literal><![CDATA[
      K(x,(y / z) \ K(y,u / (w * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,z / T(y,L((u / v5) / w,w,v5))) = v6
    ]]></literal>
    <justification jstring="[para(14108(a,1),18250(a,1,2,2))].">
      <j1 rule="para" parents="14108 18250"/>
    </justification>
  </clause>

  <clause id="18253">
    <literal><![CDATA[
      K(x,y / (T(z,u) / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u \ z)) = w
    ]]></literal>
    <justification jstring="[para(4279(a,2),18251(a,1,2,2))].">
      <j1 rule="para" parents="4279 18251"/>
    </justification>
  </clause>

  <clause id="18254">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / ((z \ 1) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (z \ u)) = w
    ]]></literal>
    <justification jstring="[para(18134(a,2),18253(a,1))].">
      <j1 rule="para" parents="18134 18253"/>
    </justification>
  </clause>

  <clause id="18255">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = a(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(14141,a,18149,a)].">
      <j1 rule="hyper" parents="14141 18149"/>
    </justification>
  </clause>

  <clause id="18256">
    <literal><![CDATA[
      K(x,L(y,K(z,u) * w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(18149(a,2),14151(a,1))].">
      <j1 rule="para" parents="18149 14151"/>
    </justification>
  </clause>

  <clause id="18259">
    <literal><![CDATA[
      a(x,y \ K(z,u),K(w,v5)) = a(x,y \ 1,K(w,v5))
    ]]></literal>
    <justification jstring="[para(13015(a,1),18255(a,1,2))].">
      <j1 rule="para" parents="13015 18255"/>
    </justification>
  </clause>

  <clause id="18261">
    <literal><![CDATA[
      T(x,a(y,z \ K(u,w),v5)) = x * a(x,z \ 1,K(v5,y))
    ]]></literal>
    <justification jstring="[para(18259(a,1),13976(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18259 13976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18264">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) * v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,w * v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(6511(a,1),18256(a,1,2,2))].">
      <j1 rule="para" parents="6511 18256"/>
    </justification>
  </clause>

  <clause id="18265">
    <literal><![CDATA[
      (T(T(x,y),z) \ x) * u != w
    ]]></literal>
    <literal><![CDATA[
      x * (T(T(x,z),y) \ u) = w
    ]]></literal>
    <justification jstring="[para(18220(a,1),5518(a,1))].">
      <j1 rule="para" parents="18220 5518"/>
    </justification>
  </clause>

  <clause id="18266">
    <literal><![CDATA[
      x * a(y,x,K(z,L(x,u,w))) = T(x,a(w,u,a(y,x,z)))
    ]]></literal>
    <justification jstring="[para(12681(a,2),18229(a,1,2))].">
      <j1 rule="para" parents="12681 18229"/>
    </justification>
  </clause>

  <clause id="18267">
    <literal><![CDATA[
      K(x,y / (z \ T(u,K(w,v5)))) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(14825,a,18233,a),flip(a)].">
      <j1 rule="hyper" parents="14825 18233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18268">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (y \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (z / y)) = w
    ]]></literal>
    <justification jstring="[para(18233(a,2),17619(a,1))].">
      <j1 rule="para" parents="18233 17619"/>
    </justification>
  </clause>

  <clause id="18269">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * v5))) = K(x,y / (z \ (v5 * K(u,w))))
    ]]></literal>
    <justification jstring="[para(6121(a,1),18267(a,1,2,2,2))].">
      <j1 rule="para" parents="6121 18267"/>
    </justification>
  </clause>

  <clause id="18270">
    <literal><![CDATA[
      K(x,y / (z \ (u * T(z,K(w,v5))))) = K(x,y / T(u,K(v5,w) * z))
    ]]></literal>
    <justification jstring="[para(15497(a,1),18267(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15497 18267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18271">
    <literal><![CDATA[
      (T(T(x,y),z) / x) \ u = (T(T(x,z),y) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,18220,a(flip),b,18238,a),flip(a)].">
      <j1 rule="hyper" parents="63 18220 18238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18272">
    <literal><![CDATA[
      (x \ T(T(x,y),z)) \ u = (T(T(x,z),y) \ x) * u
    ]]></literal>
    <justification jstring="[para(4820(a,1),18271(a,1,1))].">
      <j1 rule="para" parents="4820 18271"/>
    </justification>
  </clause>

  <clause id="18273">
    <literal><![CDATA[
      T(x,a(y,z \ K(u,w),v5)) = T(x,a(y,z \ 1,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,13976,a(flip),b,18261,a),flip(a)].">
      <j1 rule="hyper" parents="347 13976 18261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18274">
    <literal><![CDATA[
      L(x,y \ K(z,u),K(w,v5)) = T(x,a(v5,y \ 1,w))
    ]]></literal>
    <justification jstring="[hyper(14338,a,18273,a)].">
      <j1 rule="hyper" parents="14338 18273"/>
    </justification>
  </clause>

  <clause id="18275">
    <literal><![CDATA[
      L(x,y \ K(z,u),K(w,v5)) = L(x,y \ 1,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,14337,a,b,18274,a),flip(a)].">
      <j1 rule="hyper" parents="347 14337 18274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18276">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,K(z,u)) = L(x,y * K(w,v5),K(z,u))
    ]]></literal>
    <justification jstring="[hyper(13743,a,18275,a),flip(a)].">
      <j1 rule="hyper" parents="13743 18275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18277">
    <literal><![CDATA[
      T(x,a(y,z,a(u,x,w))) = x * 1
    ]]></literal>
    <justification jstring="[para(9771(a,1),18266(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9771 18266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18278">
    <literal><![CDATA[
      a(x,y,a(z,x,K(u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(14262,a,18277,a)].">
      <j1 rule="hyper" parents="14262 18277"/>
    </justification>
  </clause>

  <clause id="18279">
    <literal><![CDATA[
      T(x,a(y,z,a(u,x,w))) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,8,a(flip),b,18277,a),flip(a)].">
      <j1 rule="hyper" parents="347 8 18277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18281">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),w,y) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(52,a,18278,a)].">
      <j1 rule="hyper" parents="52 18278"/>
    </justification>
  </clause>

  <clause id="18282">
    <literal><![CDATA[
      T(x,L(a(y,x,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(14522,a,18279,a)].">
      <j1 rule="hyper" parents="14522 18279"/>
    </justification>
  </clause>

  <clause id="18283">
    <literal><![CDATA[
      T(a(x,y,z),a(y,u,w)) = (y * a(x,y,z)) / y
    ]]></literal>
    <justification jstring="[para(18282(a,1),14032(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18282 14032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18284">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,y))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,11650,a,b,18281,a)].">
      <j1 rule="hyper" parents="63 11650 18281"/>
    </justification>
  </clause>

  <clause id="18285">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,z))) = K(x,y) * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(18284(a,1),13991(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18284 13991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18286">
    <literal><![CDATA[
      T(a(x,y,z),a(y,u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,12676,a(flip),b,18283,a),flip(a)].">
      <j1 rule="hyper" parents="347 12676 18283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18287">
    <literal><![CDATA[
      T(a(x,y,z),a(u,w,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(14037,a,18286,a)].">
      <j1 rule="hyper" parents="14037 18286"/>
    </justification>
  </clause>

  <clause id="18288">
    <literal><![CDATA[
      T(a(x,y,z),a(u,z,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,18287,a)].">
      <j1 rule="hyper" parents="54 18287"/>
    </justification>
  </clause>

  <clause id="18289">
    <literal><![CDATA[
      L(a(x,y,z),u,K(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(18287(a,1),14422(a,1,1)),flip(b)].">
      <j1 rule="para" parents="18287 14422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18290">
    <literal><![CDATA[
      L(a(x,y,z),z,K(u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(14431,a,18288,a)].">
      <j1 rule="hyper" parents="14431 18288"/>
    </justification>
  </clause>

  <clause id="18291">
    <literal><![CDATA[
      a(T(x,y),y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(15321,a,18290,a)].">
      <j1 rule="hyper" parents="15321 18290"/>
    </justification>
  </clause>

  <clause id="18292">
    <literal><![CDATA[
      a(T(x,y),T(y,z),u) = a(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(17836,a,18291,a)].">
      <j1 rule="hyper" parents="17836 18291"/>
    </justification>
  </clause>

  <clause id="18293">
    <literal><![CDATA[
      a(x * (y / x),x,z) = a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(11585,a,18291,a),flip(a)].">
      <j1 rule="hyper" parents="11585 18291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18294">
    <literal><![CDATA[
      a(x * y,y,z) = a(y * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(11584,a,18291,a)].">
      <j1 rule="hyper" parents="11584 18291"/>
    </justification>
  </clause>

  <clause id="18295">
    <literal><![CDATA[
      a(x,T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11578,a(flip),b,18293,a)].">
      <j1 rule="hyper" parents="63 11578 18293"/>
    </justification>
  </clause>

  <clause id="18296">
    <literal><![CDATA[
      a(x,y,z) * (x * (T(y,x) * z)) = (y * x) * z
    ]]></literal>
    <justification jstring="[para(18293(a,1),13942(a,1,1))].">
      <j1 rule="para" parents="18293 13942"/>
    </justification>
  </clause>

  <clause id="18297">
    <literal><![CDATA[
      a(x \ y,(x \ y) \ y,z) = a(x \ y,x,z)
    ]]></literal>
    <justification jstring="[hyper(14999,a,18295,a)].">
      <j1 rule="hyper" parents="14999 18295"/>
    </justification>
  </clause>

  <clause id="18298">
    <literal><![CDATA[
      a(x,y,z) = (L(z,y,x) * (y * x)) \ (z * (y * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,14598,a,b,18295,a),flip(a)].">
      <j1 rule="hyper" parents="63 14598 18295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18299">
    <literal><![CDATA[
      (a(x,y,z) \ (y * x)) * z = x * ((x \ (y * x)) * z)
    ]]></literal>
    <justification jstring="[para(18295(a,1),14632(a,1,1,1))].">
      <j1 rule="para" parents="18295 14632"/>
    </justification>
  </clause>

  <clause id="18300">
    <literal><![CDATA[
      a(x,T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(18292(a,1),4807(a,1))].">
      <j1 rule="para" parents="18292 4807"/>
    </justification>
  </clause>

  <clause id="18301">
    <literal><![CDATA[
      (x * (T(y,x) * z)) \ ((y * x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(259(a,2),18300(a,1))].">
      <j1 rule="para" parents="259 18300"/>
    </justification>
  </clause>

  <clause id="18302">
    <literal><![CDATA[
      (L(x,y,z) * (y * z)) \ (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(14598(a,2),18300(a,1))].">
      <j1 rule="para" parents="14598 18300"/>
    </justification>
  </clause>

  <clause id="18304">
    <literal><![CDATA[
      a(x \ y,x,x) * (x * ((x \ y) \ y)) = (x \ y) \ (y * x)
    ]]></literal>
    <justification jstring="[para(18297(a,1),14754(a,1,1))].">
      <j1 rule="para" parents="18297 14754"/>
    </justification>
  </clause>

  <clause id="18305">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * z) = x * (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(138,a,18296,a)].">
      <j1 rule="hyper" parents="138 18296"/>
    </justification>
  </clause>

  <clause id="18306">
    <literal><![CDATA[
      a(x,y,T(z,x * T(y,x))) \ ((y * x) * T(z,x * T(y,x))) = L(z,T(y,x),x) * (x * T(y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,734,a(flip),b,18305,a),flip(a)].">
      <j1 rule="hyper" parents="347 734 18305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18307">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,z))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,13991,a(flip),b,18285,a),flip(a)].">
      <j1 rule="hyper" parents="347 13991 18285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18308">
    <literal><![CDATA[
      K(x,L(y,z,(z * u) \ w)) = K(x,L(y,z,u \ (z \ w)))
    ]]></literal>
    <justification jstring="[para(329(a,1),18307(a,1,2,3))].">
      <j1 rule="para" parents="329 18307"/>
    </justification>
  </clause>

  <clause id="18309">
    <literal><![CDATA[
      (a(x,y,z) \ (y * x)) * z = x * (T(y,x) * z)
    ]]></literal>
    <justification jstring="[para(22(a,2),18299(a,2,2,1))].">
      <j1 rule="para" parents="22 18299"/>
    </justification>
  </clause>

  <clause id="18310">
    <literal><![CDATA[
      L(x,y * K(z,u),K(w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(3526,a,18276,a),flip(a)].">
      <j1 rule="hyper" parents="3526 18276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18311">
    <literal><![CDATA[
      L((x * K(y,z)) \ u,x,K(z,y)) = x \ (K(z,T(y,x)) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10453,a(flip),b,18310,a),flip(a)].">
      <j1 rule="hyper" parents="63 10453 18310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18312">
    <literal><![CDATA[
      L(x,K(y,z) * u,K(w,v5)) = L(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(7076(a,1),18310(a,1,2))].">
      <j1 rule="para" parents="7076 18310"/>
    </justification>
  </clause>

  <clause id="18313">
    <literal><![CDATA[
      L(x,y \ (z * K(u,w)),K(v5,v6)) = L(x,y \ z,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(14549(a,1),18310(a,1,2))].">
      <j1 rule="para" parents="14549 18310"/>
    </justification>
  </clause>

  <clause id="18315">
    <literal><![CDATA[
      T(x,K(y,z)) * L(u,x,K(y,z)) = K(y,z) * ((x * K(z,y)) * u)
    ]]></literal>
    <justification jstring="[para(18312(a,1),10565(a,1,2))].">
      <j1 rule="para" parents="18312 10565"/>
    </justification>
  </clause>

  <clause id="18316">
    <literal><![CDATA[
      L(x,K(y,z) * u,a(w,v5,K(v6,v7))) = L(x,u,K(a(w,v5,v6),v7))
    ]]></literal>
    <justification jstring="[para(12681(a,2),18312(a,1,3))].">
      <j1 rule="para" parents="12681 18312"/>
    </justification>
  </clause>

  <clause id="18317">
    <literal><![CDATA[
      K(x,L(y,z,u \ (z \ w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,(u * z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(18308(a,1),18085(a,1))].">
      <j1 rule="para" parents="18308 18085"/>
    </justification>
  </clause>

  <clause id="18318">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),K(v5,v6)) = L(x,y \ w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,17869,a,b,18313,a)].">
      <j1 rule="hyper" parents="63 17869 18313"/>
    </justification>
  </clause>

  <clause id="18319">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),x \ u,K(z,y)) = (K(z,y) * (x \ (K(y,z) * u))) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,10022,a(flip),b,18318,a),flip(a)].">
      <j1 rule="hyper" parents="63 10022 18318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18320">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) \ (w \ v5)) = K(x,w \ (K(y,T(z,u)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(18172,a,17916,a)].">
      <j1 rule="hyper" parents="18172 17916"/>
    </justification>
  </clause>

  <clause id="18321">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * (u \ w)) = v5
    ]]></literal>
    <justification jstring="[para(14804(a,2),18200(a,1))].">
      <j1 rule="para" parents="14804 18200"/>
    </justification>
  </clause>

  <clause id="18322">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,w)) = K(x,K(u,w) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(18202,a,17555,a)].">
      <j1 rule="hyper" parents="18202 17555"/>
    </justification>
  </clause>

  <clause id="18323">
    <literal><![CDATA[
      K(x,K(y,z) * ((y * (z \ u)) \ u)) = K(x,T((y * (z \ u)) \ u,y))
    ]]></literal>
    <justification jstring="[hyper(16463,a,18322,a),flip(a)].">
      <j1 rule="hyper" parents="16463 18322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18324">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ T(w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * (u \ K(y,z))) = v5
    ]]></literal>
    <justification jstring="[para(17278(a,2),18235(a,1))].">
      <j1 rule="para" parents="17278 18235"/>
    </justification>
  </clause>

  <clause id="18325">
    <literal><![CDATA[
      (x \ T(T(x,y),z)) \ u = x * (T(T(x,y),z) \ u)
    ]]></literal>
    <justification jstring="[hyper(18265,a,18272,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18265 18272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18326">
    <literal><![CDATA[
      K(x,K(y,z) * (u / ((K(w,v5) * y) \ z))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (z / (K(w,v5) * y))) = v6
    ]]></literal>
    <justification jstring="[para(16476(a,1),18268(a,1))].">
      <j1 rule="para" parents="16476 18268"/>
    </justification>
  </clause>

  <clause id="18328">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * x))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * ((z \ y) \ x)) = w
    ]]></literal>
    <justification jstring="[para(6484(a,1),18321(a,1))].">
      <j1 rule="para" parents="6484 18321"/>
    </justification>
  </clause>

  <clause id="18329">
    <literal><![CDATA[
      K(x,T((y / z) / K(u,w),v5)) = K(x,T(y / (K(w,u) \ z),v5))
    ]]></literal>
    <justification jstring="[para(5256(a,2),18197(a,2,2,1,2))].">
      <j1 rule="para" parents="5256 18197"/>
    </justification>
  </clause>

  <clause id="18330">
    <literal><![CDATA[
      (x * K(y,z)) / (z * y) = x / (T(z,y) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,15813,a(flip),b,18213,a),flip(a)].">
      <j1 rule="hyper" parents="63 15813 18213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18331">
    <literal><![CDATA[
      (x / (y * z)) * K(z,y) = x / (T(y,z) * z)
    ]]></literal>
    <justification jstring="[hyper(9880,a,18330,a)].">
      <j1 rule="hyper" parents="9880 18330"/>
    </justification>
  </clause>

  <clause id="18332">
    <literal><![CDATA[
      K((x / ((y * z) / y)) \ u,w) = K((x / T(z,y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,17668,a(flip),b,18228,a),flip(a)].">
      <j1 rule="hyper" parents="347 17668 18228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18333">
    <literal><![CDATA[
      K((x \ (x / T(y,y * x))) \ z,u) = K((x / T(y * x,y)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(13871,a,18332,a)].">
      <j1 rule="hyper" parents="13871 18332"/>
    </justification>
  </clause>

  <clause id="18334">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)) * v5,a(v6,v7,K(v8,v9))) = L(x,v5,K(a(v6,v7,v8),v9))
    ]]></literal>
    <justification jstring="[para(11127(a,1),18316(a,1,2,1))].">
      <j1 rule="para" parents="11127 18316"/>
    </justification>
  </clause>

  <clause id="18335">
    <literal><![CDATA[
      K(x,y \ (K(z,T(u,w)) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) \ (y \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(18320(a,1),17058(a,1))].">
      <j1 rule="para" parents="18320 17058"/>
    </justification>
  </clause>

  <clause id="18336">
    <literal><![CDATA[
      K(x,T(y / (K(z,u) \ w),v5)) = K(x,T((y / w) * K(z,u),v5))
    ]]></literal>
    <justification jstring="[para(6117(a,1),18329(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6117 18329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18337">
    <literal><![CDATA[
      K(x,T(y / (K(z,u) \ w),v5)) = K(x,K(u,z) \ T(y / w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,16480,a(flip),b,18336,a),flip(a)].">
      <j1 rule="hyper" parents="347 16480 18336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18338">
    <literal><![CDATA[
      K(x,K(y \ T(z,u),y) \ T(w / z,v5)) = K(x,T(w / ((y \ z) * y),v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,16500,a(flip),b,18337,a),flip(a)].">
      <j1 rule="hyper" parents="63 16500 18337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18339">
    <literal><![CDATA[
      K(x,L(y,z * (K(u,w) * v5),v6)) = K(x,L(y,v5 * z,v6))
    ]]></literal>
    <justification jstring="[hyper(18264,a,18104,a),flip(a)].">
      <j1 rule="hyper" parents="18264 18104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18340">
    <literal><![CDATA[
      K(x,L(y,z * (u * K(w,v5)),v6)) = K(x,L(y,u * z,v6))
    ]]></literal>
    <justification jstring="[para(7372(a,1),18339(a,1,2,2,2))].">
      <j1 rule="para" parents="7372 18339"/>
    </justification>
  </clause>

  <clause id="18342">
    <literal><![CDATA[
      K(x \ 1,L(y,z,(x * z) \ u)) = K(x \ 1,L(y,z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(18317,a,14770,a)].">
      <j1 rule="hyper" parents="18317 14770"/>
    </justification>
  </clause>

  <clause id="18343">
    <literal><![CDATA[
      K(x \ 1,L(T(y,z),u,u \ z)) = K(z \ (u * ((x * u) \ z)),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14153,a(flip),b,18342,a),flip(a)].">
      <j1 rule="hyper" parents="63 14153 18342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18344">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ w) \ T(v5,u * w))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5 * ((u \ w) \ K(y,z))) = v6
    ]]></literal>
    <justification jstring="[para(17329(a,1),18324(a,1))].">
      <j1 rule="para" parents="17329 18324"/>
    </justification>
  </clause>

  <clause id="18345">
    <literal><![CDATA[
      K(x,y \ (K(z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) \ (y \ w)) = v5
    ]]></literal>
    <justification jstring="[para(110(a,1),18335(a,1,2,2,1,2))].">
      <j1 rule="para" parents="110 18335"/>
    </justification>
  </clause>

  <clause id="18346">
    <literal><![CDATA[
      K(x,K(y,z) \ ((T(z,y) \ u) \ w)) = K(x,(z \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(18345,a,17017,a)].">
      <j1 rule="hyper" parents="18345 17017"/>
    </justification>
  </clause>

  <clause id="18347">
    <literal><![CDATA[
      K(x,K(y,z) * ((T(y,z) \ u) \ w)) = K(x,(y \ u) \ w)
    ]]></literal>
    <justification jstring="[para(5256(a,1),18346(a,1,2))].">
      <j1 rule="para" parents="5256 18346"/>
    </justification>
  </clause>

  <clause id="18348">
    <literal><![CDATA[
      a(x,y,K((T(z,u) \ w) \ v5,v6)) = a(v6,y,K(x,(z \ w) \ v5))
    ]]></literal>
    <justification jstring="[para(18347(a,1),18053(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18347 18053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18349">
    <literal><![CDATA[
      K(x \ (y * (((z / y) * y) \ x)),u) = K((z * (y \ x)) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14650,a(flip),b,18343,a),flip(a)].">
      <j1 rule="hyper" parents="63 14650 18343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18350">
    <literal><![CDATA[
      K((x * (y \ z)) \ z,u) = K(z \ (y * (x \ z)),u)
    ]]></literal>
    <justification jstring="[para(12(a,1),18349(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 18349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18352">
    <literal><![CDATA[
      x / (K(y \ (z * (u \ y)),w) * x) = K(w,(u * (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[para(18350(a,1),5259(a,1,2,1))].">
      <j1 rule="para" parents="18350 5259"/>
    </justification>
  </clause>

  <clause id="18353">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z \ (u * (w \ z)),y))) / x) = K(y,T((w * (u \ z)) \ z,x))
    ]]></literal>
    <justification jstring="[para(18350(a,1),8525(a,1,2,1,2,2))].">
      <j1 rule="para" parents="18350 8525"/>
    </justification>
  </clause>

  <clause id="18354">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (z * (y \ u))) = w
    ]]></literal>
    <justification jstring="[para(18352(a,1),5276(a,1))].">
      <j1 rule="para" parents="18352 5276"/>
    </justification>
  </clause>

  <clause id="18355">
    <literal><![CDATA[
      K(x,y \ ((y * z) * (u \ y))) = K(x,(u / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(18354,a,16029,a)].">
      <j1 rule="hyper" parents="18354 16029"/>
    </justification>
  </clause>

  <clause id="18356">
    <literal><![CDATA[
      K(x,y \ (z * (((y * u) \ y) \ y))) = K(x,(u \ (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(18354,a,16022,a)].">
      <j1 rule="hyper" parents="18354 16022"/>
    </justification>
  </clause>

  <clause id="18357">
    <literal><![CDATA[
      K(x,((y / z) / u) \ y) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[para(83(a,1),18355(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="83 18355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18358">
    <literal><![CDATA[
      K(x,((y * ((y * z) / y)) / u) \ z) = K(x,z \ ((z * u) * ((y * z) \ T(z,y))))
    ]]></literal>
    <justification jstring="[para(13264(a,1),18355(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13264 18355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18359">
    <literal><![CDATA[
      K(x,T(y,z * u) / ((y / z) / u)) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15971,a,b,18357,a)].">
      <j1 rule="hyper" parents="63 15971 18357"/>
    </justification>
  </clause>

  <clause id="18360">
    <literal><![CDATA[
      K(x,y \ (z * T(y * u,y))) = K(x,(u \ (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,12101,a(flip),b,18356,a)].">
      <j1 rule="hyper" parents="63 12101 18356"/>
    </justification>
  </clause>

  <clause id="18361">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) \ u) = K(x,u \ (z * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17664,a(flip),b,18360,a),flip(a)].">
      <j1 rule="hyper" parents="63 17664 18360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18362">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * y))) = K(x,(u \ z) \ y)
    ]]></literal>
    <justification jstring="[para(83(a,1),18361(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="83 18361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18363">
    <literal><![CDATA[
      K(x,(y \ (z * u)) \ u) = K(x,u \ (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15097,a(flip),b,18362,a),flip(a)].">
      <j1 rule="hyper" parents="63 15097 18362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18364">
    <literal><![CDATA[
      K(x,((y / z) \ u) \ z) = K(x,z \ ((z / u) * y))
    ]]></literal>
    <justification jstring="[para(12(a,1),18362(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="12 18362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18365">
    <literal><![CDATA[
      T(K(x,y \ (z \ (u * y))),y) = K(x,y / (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(18363(a,1),7648(a,1,1))].">
      <j1 rule="para" parents="18363 7648"/>
    </justification>
  </clause>

  <clause id="18366">
    <literal><![CDATA[
      K(x,((y / z) * u) \ y) = K(x,y \ ((y / u) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18121,a(flip),b,18364,a)].">
      <j1 rule="hyper" parents="63 18121 18364"/>
    </justification>
  </clause>

  <clause id="18367">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,w)) = T(K(x,y \ ((y / u) * z)),w)
    ]]></literal>
    <justification jstring="[para(18366(a,1),7091(a,2,1))].">
      <j1 rule="para" parents="18366 7091"/>
    </justification>
  </clause>

  <clause id="18368">
    <literal><![CDATA[
      T(x,K(y,x \ (z \ ((u * z) * x)))) \ (z \ ((K(y,u) * z) * x)) = K(y,x / ((u * z) \ (z * x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14675,a,b,18365,a)].">
      <j1 rule="hyper" parents="63 14675 18365"/>
    </justification>
  </clause>

  <clause id="18369">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,w)) = K(x,T(y \ ((y / u) * z),w))
    ]]></literal>
    <justification jstring="[hyper(347,a,7091,a,b,18367,a),flip(a)].">
      <j1 rule="hyper" parents="347 7091 18367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18370">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,y / (z * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15992,a(flip),b,18369,a),flip(a)].">
      <j1 rule="hyper" parents="63 15992 18369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18371">
    <literal><![CDATA[
      K(x,(y * (z \ u)) / u) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(17911,a,18370,a)].">
      <j1 rule="hyper" parents="17911 18370"/>
    </justification>
  </clause>

  <clause id="18372">
    <literal><![CDATA[
      K(x,y / ((z \ y) * (u \ y))) = K(x,(u * T(z,y)) / y)
    ]]></literal>
    <justification jstring="[hyper(63,a,12099,a(flip),b,18371,a),flip(a)].">
      <j1 rule="hyper" parents="63 12099 18371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18373">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) / K(z,u)) = K(x,(L(y \ K(z,u),w,v5) \ (y \ K(z,u))) \ 1)
    ]]></literal>
    <justification jstring="[para(14498(a,1),18372(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14498 18372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18374">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,(y / z) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,18098,a(flip),b,18107,a),flip(a)].">
      <j1 rule="hyper" parents="347 18098 18107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18375">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,(z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(12413(a,1),18374(a,2,2))].">
      <j1 rule="para" parents="12413 18374"/>
    </justification>
  </clause>

  <clause id="18376">
    <literal><![CDATA[
      K(x,L((y / z) * z,z,u)) = K(x,L(y,(z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(13440,a,18375,a)].">
      <j1 rule="hyper" parents="13440 18375"/>
    </justification>
  </clause>

  <clause id="18377">
    <literal><![CDATA[
      K(x,L(y,(z \ y) \ 1,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),18376(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 18376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18378">
    <literal><![CDATA[
      a(x * (y / z),u,K(w,v5)) = a(x * (z \ y),u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(18079,a,18111,a),flip(a)].">
      <j1 rule="hyper" parents="18079 18111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18379">
    <literal><![CDATA[
      a(x * (y \ T(z,y)),u,K(w,v5)) = a(w,u,K(v5,(y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,18062,a(flip),b,18378,a),flip(a)].">
      <j1 rule="hyper" parents="63 18062 18378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18380">
    <literal><![CDATA[
      a(x,y,K(z,(u / w) * v5)) = a(x,y,K(z,(w \ u) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,18064,a(flip),b,18379,a)].">
      <j1 rule="hyper" parents="63 18064 18379"/>
    </justification>
  </clause>

  <clause id="18381">
    <literal><![CDATA[
      (T(x,L(K(y,z),u,w)) * K(v5,v6)) * (K(v6,v5) * L(K(y,z),u,w)) = x * ((x * L(K(y,z),u,w)) / x)
    ]]></literal>
    <justification jstring="[hyper(347,a,4149,a(flip),b,18210,a),flip(a)].">
      <j1 rule="hyper" parents="347 4149 18210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18382">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ v6) = K(x,K(z,u) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(17152,a,18211,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="17152 18211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18383">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,K(u,w) \ ((y * z) \ v5))
    ]]></literal>
    <justification jstring="[para(97(a,1),18382(a,1,2,1))].">
      <j1 rule="para" parents="97 18382"/>
    </justification>
  </clause>

  <clause id="18384">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,K(w,u) * ((y * z) \ v5))
    ]]></literal>
    <justification jstring="[para(5256(a,1),18383(a,2,2))].">
      <j1 rule="para" parents="5256 18383"/>
    </justification>
  </clause>

  <clause id="18385">
    <literal><![CDATA[
      K(x,T(y \ (z * K(u,w)),K(v5,v6)) \ v7) = K(x,K(w,u) * ((((v7 * y) \ v7) * z) \ v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,16024,a,b,18384,a)].">
      <j1 rule="hyper" parents="63 16024 18384"/>
    </justification>
  </clause>

  <clause id="18386">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) * ((((v5 * u) \ v5) * z) \ v5)) = K(x,((u \ z) * K(w,y)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,16027,a(flip),b,18384,a),flip(a)].">
      <j1 rule="hyper" parents="63 16027 18384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18387">
    <literal><![CDATA[
      a(x \ (y * K(z,u)),w,K(v5,v6)) = a(v5,w,K(y \ x,v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,18039,a(flip),b,18227,a),flip(a)].">
      <j1 rule="hyper" parents="347 18039 18227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18389">
    <literal><![CDATA[
      K(x,y / T(z * K(u,K(w,v5)),u)) = K(x,y / T(z,K(v5,w) * u))
    ]]></literal>
    <justification jstring="[para(5916(a,2),18270(a,1,2,2))].">
      <j1 rule="para" parents="5916 18270"/>
    </justification>
  </clause>

  <clause id="18390">
    <literal><![CDATA[
      K(x,T((y * (z \ u)) \ u,y)) = K(x,(T(y,z) * (z \ u)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17602,a(flip),b,18323,a),flip(a)].">
      <j1 rule="hyper" parents="63 17602 18323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18391">
    <literal><![CDATA[
      K(x,T((y * (z \ u)) \ u,y)) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,17678,a(flip),b,18390,a),flip(a)].">
      <j1 rule="hyper" parents="347 17678 18390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18392">
    <literal><![CDATA[
      K((x \ (x / T(y,x * y))) \ z,u) = K((x / T(y * x,y)) \ z,u)
    ]]></literal>
    <justification jstring="[para(4323(a,2),18333(a,1,1,1,2,2))].">
      <j1 rule="para" parents="4323 18333"/>
    </justification>
  </clause>

  <clause id="18393">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,w)) = T(x,K(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(18198,a,18186,a),flip(a)].">
      <j1 rule="hyper" parents="18198 18186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18396">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,w)) = T(x,K(y,z) * K(w,u))
    ]]></literal>
    <justification jstring="[hyper(7346,a,18393,a)].">
      <j1 rule="hyper" parents="7346 18393"/>
    </justification>
  </clause>

  <clause id="18399">
    <literal><![CDATA[
      T(T(T(x,K(y,z)),u),K(w,v5)) = T(T(x,u),K(z,y) * K(v5,w))
    ]]></literal>
    <justification jstring="[para(7339(a,2),18396(a,1,1))].">
      <j1 rule="para" parents="7339 18396"/>
    </justification>
  </clause>

  <clause id="18400">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ x)) = K(x,K(y,z) * (u \ (z * x)))
    ]]></literal>
    <justification jstring="[hyper(18328,a,17957,a)].">
      <j1 rule="hyper" parents="18328 17957"/>
    </justification>
  </clause>

  <clause id="18401">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (x * T(z,y))) = w
    ]]></literal>
    <justification jstring="[para(18400(a,2),17611(a,1))].">
      <j1 rule="para" parents="18400 17611"/>
    </justification>
  </clause>

  <clause id="18402">
    <literal><![CDATA[
      K(x,(x * y) \ (x * T(z,y * x))) = K(x,R(z,z \ (x * y),z) / y)
    ]]></literal>
    <justification jstring="[hyper(18401,a,17561,a(flip))].">
      <j1 rule="hyper" parents="18401 17561"/>
    </justification>
  </clause>

  <clause id="18403">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)) * v5,a(v6,v7,K(v8,v9))) = L(x,v5,a(v6,v7,K(v8,v9)))
    ]]></literal>
    <justification jstring="[para(12681(a,2),18334(a,2,3))].">
      <j1 rule="para" parents="12681 18334"/>
    </justification>
  </clause>

  <clause id="18404">
    <literal><![CDATA[
      K(x,y \ (x \ (x * T(z,y * x)))) = K(x,R(z,z \ (x * y),z) / y)
    ]]></literal>
    <justification jstring="[hyper(7209,a,18402,a)].">
      <j1 rule="hyper" parents="7209 18402"/>
    </justification>
  </clause>

  <clause id="18405">
    <literal><![CDATA[
      K(x,R(y,y \ (x * z),y) / z) = K(x,z \ T(y,z * x))
    ]]></literal>
    <justification jstring="[para(9(a,1),18404(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 18404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18406">
    <literal><![CDATA[
      K(x,y \ T(z,y * x)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(11987,a,18405,a),flip(a)].">
      <j1 rule="hyper" parents="11987 18405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18408">
    <literal><![CDATA[
      K(x,y \ T(z,y \ x)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(16110,a,18406,a)].">
      <j1 rule="hyper" parents="16110 18406"/>
    </justification>
  </clause>

  <clause id="18409">
    <literal><![CDATA[
      K(x,x \ (y * (x / z))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14860,a(flip),b,18408,a)].">
      <j1 rule="hyper" parents="63 14860 18408"/>
    </justification>
  </clause>

  <clause id="18410">
    <literal><![CDATA[
      K(x,y / (z \ x)) = K(x,x \ (y * z))
    ]]></literal>
    <justification jstring="[para(80(a,1),18409(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="80 18409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18411">
    <literal><![CDATA[
      K(x,y / (x / z)) = K(x,x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,8406,a,b,18410,a)].">
      <j1 rule="hyper" parents="63 8406 18410"/>
    </justification>
  </clause>

  <clause id="18412">
    <literal><![CDATA[
      K(x,x \ (y * (z \ x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(80(a,1),18411(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="80 18411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18413">
    <literal><![CDATA[
      (x * ((y \ x) \ z)) * K(z,x / (y \ x)) = z * R(y,y \ x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[para(18412(a,1),5319(a,1,2))].">
      <j1 rule="para" parents="18412 5319"/>
    </justification>
  </clause>

  <clause id="18414">
    <literal><![CDATA[
      a(x,y,K((z / (u / w)) * K(w,z),v5)) = a(x,y,K((u / T(w,z)) \ z,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,17089,a(flip),b,18052,a),flip(a)].">
      <j1 rule="hyper" parents="347 17089 18052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18415">
    <literal><![CDATA[
      K(x,L(y,z,u / (T(w,x) * v5))) = K(x,L(y,z,(w * v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(13996,a,18057,a),flip(a)].">
      <j1 rule="hyper" parents="13996 18057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18416">
    <literal><![CDATA[
      K(x,L(y,z,(T(u,x) * w) \ v5)) = K(x,L(y,z,(u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(16929,a,18415,a)].">
      <j1 rule="hyper" parents="16929 18415"/>
    </justification>
  </clause>

  <clause id="18417">
    <literal><![CDATA[
      K(x,L(y,z,(y * z) \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(18416(a,1),14243(a,1,1))].">
      <j1 rule="para" parents="18416 14243"/>
    </justification>
  </clause>

  <clause id="18418">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(17264(a,1),18417(a,1,1))].">
      <j1 rule="para" parents="17264 18417"/>
    </justification>
  </clause>

  <clause id="18419">
    <literal><![CDATA[
      (x * y) * ((T(x,z) * y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      (K(z,x) * y) * (y \ u) = w
    ]]></literal>
    <justification jstring="[para(18418(a,1),14095(a,1))].">
      <j1 rule="para" parents="18418 14095"/>
    </justification>
  </clause>

  <clause id="18420">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (K(z,T(x,z)) * y) * (y \ u)
    ]]></literal>
    <justification jstring="[hyper(18419,a,15775,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18419 15775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18421">
    <literal><![CDATA[
      K(x,K(y \ z,T(y,u)) \ T(w / z,v5)) = K(x,T(w / ((y \ z) * y),v5))
    ]]></literal>
    <justification jstring="[para(10475(a,1),18338(a,1,2,1))].">
      <j1 rule="para" parents="10475 18338"/>
    </justification>
  </clause>

  <clause id="18422">
    <literal><![CDATA[
      a(x,y,K((z / T(u,w)) \ w,v5)) = a(x,y,K(T(w,u) / (z / u),v5))
    ]]></literal>
    <justification jstring="[para(15573(a,1),18414(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15573 18414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18423">
    <literal><![CDATA[
      a(x,y,K((z / T(u,w)) \ w,v5)) = a(x,y,K((z / u) \ T(w,u),v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,17089,a(flip),b,18422,a),flip(a)].">
      <j1 rule="hyper" parents="347 17089 18422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18424">
    <literal><![CDATA[
      a(x,y,K((z / T(u,w)) \ w,v5)) = a(v5,y,K(x,(z / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(347,a,18061,a(flip),b,18423,a),flip(a)].">
      <j1 rule="hyper" parents="347 18061 18423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18426">
    <literal><![CDATA[
      a(x,y,K((T(z,u) \ w) \ u,v5)) = a(v5,y,K(x,(w / z) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18054,a(flip),b,18424,a)].">
      <j1 rule="hyper" parents="63 18054 18424"/>
    </justification>
  </clause>

  <clause id="18427">
    <literal><![CDATA[
      a(x,y,K(z,(u / w) \ v5)) = a(x,y,K(z,(w \ u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,18348,a(flip),b,18426,a),flip(a)].">
      <j1 rule="hyper" parents="63 18348 18426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18428">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,(v5 \ v6) \ v7)) = a((v6 / v5) \ v7,u,K(z,w))
    ]]></literal>
    <justification jstring="[hyper(18079,a,18427,a),flip(a)].">
      <j1 rule="hyper" parents="18079 18427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18430">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) / (w / u)) = K(z,y / ((w / u) / x))
    ]]></literal>
    <justification jstring="[para(18427(a,1),18118(a,1,1))].">
      <j1 rule="para" parents="18427 18118"/>
    </justification>
  </clause>

  <clause id="18431">
    <literal><![CDATA[
      a((x / y) \ z,u,K(w,v5)) = a((y \ x) \ z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(18079,a,18428,a),flip(a)].">
      <j1 rule="hyper" parents="18079 18428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18432">
    <literal><![CDATA[
      K(x,K(y,y \ z) \ T(u / z,w)) = K(x,T(u / ((y \ z) * y),w))
    ]]></literal>
    <justification jstring="[hyper(17058,a,18421,a)].">
      <j1 rule="hyper" parents="17058 18421"/>
    </justification>
  </clause>

  <clause id="18433">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),w)) = K(x,K(u,z) \ T(y / u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,15642,a(flip),b,18432,a),flip(a)].">
      <j1 rule="hyper" parents="63 15642 18432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18434">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),w)) = K(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(347,a,16482,a(flip),b,18433,a),flip(a)].">
      <j1 rule="hyper" parents="347 16482 18433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18435">
    <literal><![CDATA[
      K(x,T(y / T(z,u),z * u)) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15801,a(flip),b,18434,a),flip(a)].">
      <j1 rule="hyper" parents="63 15801 18434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18436">
    <literal><![CDATA[
      K(x,T(y / T(z,u * a(w,v5,v6)),z * (a(w,v5,v6) * u))) = K(x,z \ T(y,a(w,v5,v6) * u))
    ]]></literal>
    <justification jstring="[para(16864(a,1),18435(a,1,2,1,2))].">
      <j1 rule="para" parents="16864 18435"/>
    </justification>
  </clause>

  <clause id="18437">
    <literal><![CDATA[
      a(x,y,K(z,u * (w * K(v5,v6)))) = a(z,y,K(w * u,x))
    ]]></literal>
    <justification jstring="[hyper(18080,a,18053,a)].">
      <j1 rule="hyper" parents="18080 18053"/>
    </justification>
  </clause>

  <clause id="18438">
    <literal><![CDATA[
      K(x,L(y,z,u / (K(w,v5) / v6))) = K(x,y) * a(x,z,K(v6 * u,y))
    ]]></literal>
    <justification jstring="[para(18437(a,1),14136(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18437 14136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18439">
    <literal><![CDATA[
      K(x,L(y,z,u / (K(w,v5) / v6))) = K(x,L(y,z,v6 * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,13990,a(flip),b,18438,a),flip(a)].">
      <j1 rule="hyper" parents="347 13990 18438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18441">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = x * a(z,x,K(y \ x,u))
    ]]></literal>
    <justification jstring="[para(13969(a,1),18218(a,2,2))].">
      <j1 rule="para" parents="13969 18218"/>
    </justification>
  </clause>

  <clause id="18442">
    <literal><![CDATA[
      x * R(y,y \ z,(y \ z) \ x) = (z * ((y \ z) \ x)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(80(a,1),18413(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="80 18413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18443">
    <literal><![CDATA[
      K(x,K(y,z) * ((T((u \ w) / w,x) * w) * v5)) = K(x,(u \ (w * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[hyper(17375,a,18124,a)].">
      <j1 rule="hyper" parents="17375 18124"/>
    </justification>
  </clause>

  <clause id="18444">
    <literal><![CDATA[
      K(x,K(y,z) * ((u * T(u \ (w \ u),x)) * v5)) = K(x,(w \ (u * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[para(484(a,1),18443(a,1,2,2,1))].">
      <j1 rule="para" parents="484 18443"/>
    </justification>
  </clause>

  <clause id="18445">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) * (z * (w \ (w / u))) = (K(x,y) * z) * (w \ (w / u))
    ]]></literal>
    <justification jstring="[para(18115(a,1),18038(a,1,1))].">
      <j1 rule="para" parents="18115 18038"/>
    </justification>
  </clause>

  <clause id="18446">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) * (z / u) = (K(x,y) * z) * (z \ (z / u))
    ]]></literal>
    <justification jstring="[hyper(357,a,18445,a)].">
      <j1 rule="hyper" parents="357 18445"/>
    </justification>
  </clause>

  <clause id="18447">
    <literal><![CDATA[
      (K(x,y) * z) \ ((K(x,y) * z) / u) = z \ (z / u)
    ]]></literal>
    <justification jstring="[hyper(128,a,14550,a(flip),b,18446,a(flip))].">
      <j1 rule="hyper" parents="128 14550 18446"/>
    </justification>
  </clause>

  <clause id="18448">
    <literal><![CDATA[
      x * L(y \ 1,y,y \ (K(z,u) * x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(5514,a,18447,a)].">
      <j1 rule="hyper" parents="5514 18447"/>
    </justification>
  </clause>

  <clause id="18449">
    <literal><![CDATA[
      x * L(y \ 1,y,y \ (x * K(z,u))) = x / y
    ]]></literal>
    <justification jstring="[para(7372(a,1),18448(a,1,2,3,2))].">
      <j1 rule="para" parents="7372 18448"/>
    </justification>
  </clause>

  <clause id="18450">
    <literal><![CDATA[
      x * L((y \ (x * K(z,u))) \ 1,y \ (x * K(z,u)),y) = x / (y \ (x * K(z,u)))
    ]]></literal>
    <justification jstring="[para(10151(a,1),18449(a,1,2))].">
      <j1 rule="para" parents="10151 18449"/>
    </justification>
  </clause>

  <clause id="18451">
    <literal><![CDATA[
      K(x * (1 / (1 / (y \ z))),(z \ y) \ x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(13291,a,18077,a)].">
      <j1 rule="hyper" parents="13291 18077"/>
    </justification>
  </clause>

  <clause id="18452">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(3926,a,18451,a)].">
      <j1 rule="hyper" parents="3926 18451"/>
    </justification>
  </clause>

  <clause id="18453">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(347,a,12981,a(flip),b,18452,a),flip(a)].">
      <j1 rule="hyper" parents="347 12981 18452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18454">
    <literal><![CDATA[
      K(x * (y \ z),x / (z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(16508,a,18453,a)].">
      <j1 rule="hyper" parents="16508 18453"/>
    </justification>
  </clause>

  <clause id="18456">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),u,K(z,y)) = (K(z,y) * (x \ (K(y,z) * u))) \ u
    ]]></literal>
    <justification jstring="[hyper(14465,a,18319,a)].">
      <j1 rule="hyper" parents="14465 18319"/>
    </justification>
  </clause>

  <clause id="18458">
    <literal><![CDATA[
      (K(x,y) * (z \ (K(y,x) * u))) \ u = ((z \ u) * K(x,y)) \ (u * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16518,a(flip),b,18456,a),flip(a)].">
      <j1 rule="hyper" parents="63 16518 18456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18459">
    <literal><![CDATA[
      L(((x \ y) * K(z,u)) \ (y * K(z,u)),x \ (K(u,z) * y),K(u,z)) = (x \ (K(u,z) * y)) \ (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(18458(a,1),14385(a,1,1))].">
      <j1 rule="para" parents="18458 14385"/>
    </justification>
  </clause>

  <clause id="18460">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) \ T(v5,w))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (v5 / (K(z,u) * w))) = v6
    ]]></literal>
    <justification jstring="[para(18233(a,1),18326(a,1))].">
      <j1 rule="para" parents="18233 18326"/>
    </justification>
  </clause>

  <clause id="18461">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * T(v5,z)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (v5 / (K(w,u) * z))) = v6
    ]]></literal>
    <justification jstring="[para(17544(a,1),18460(a,1))].">
      <j1 rule="para" parents="17544 18460"/>
    </justification>
  </clause>

  <clause id="18462">
    <literal><![CDATA[
      K(x,K(y,z) * ((((u * w) \ u) * v5) \ u)) = K(x,((w \ v5) * K(z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(17171,a,18386,a)].">
      <j1 rule="hyper" parents="17171 18386"/>
    </justification>
  </clause>

  <clause id="18464">
    <literal><![CDATA[
      K(x,K(y,z) * ((((u * w) \ u) * v5) \ u)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * ((w \ v5) \ u)) = v6
    ]]></literal>
    <justification jstring="[para(18462(a,2),18200(a,1))].">
      <j1 rule="para" parents="18462 18200"/>
    </justification>
  </clause>

  <clause id="18465">
    <literal><![CDATA[
      x / (y \ (x * K(z,u))) = x * ((x * K(z,u)) \ y)
    ]]></literal>
    <justification jstring="[para(408(a,1),18450(a,1,2)),flip(a)].">
      <j1 rule="para" parents="408 18450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18466">
    <literal><![CDATA[
      x / ((y / x) * (x * K(z,u))) = x * ((x * K(z,u)) \ (x / y))
    ]]></literal>
    <justification jstring="[para(18123(a,1),18465(a,1,2))].">
      <j1 rule="para" parents="18123 18465"/>
    </justification>
  </clause>

  <clause id="18467">
    <literal><![CDATA[
      K(x,(y / (z * K(u,w))) \ K(z,z \ u)) = K(x,T(z * K(u,w),z \ u) / y)
    ]]></literal>
    <justification jstring="[hyper(14830,a,18243,a)].">
      <j1 rule="hyper" parents="14830 18243"/>
    </justification>
  </clause>

  <clause id="18468">
    <literal><![CDATA[
      K(x,T(y * K(z,u),y \ z) / w) = K(x,(w / (y * K(z,u))) \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(12127,a,18467,a),flip(a)].">
      <j1 rule="hyper" parents="12127 18467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18469">
    <literal><![CDATA[
      K(x,T(y * K(z,u),y \ z) / w) = K(x,T(y * K(z,u),z) / w)
    ]]></literal>
    <justification jstring="[hyper(347,a,18242,a(flip),b,18468,a),flip(a)].">
      <j1 rule="hyper" parents="347 18242 18468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18470">
    <literal><![CDATA[
      K(x,(T(y,z) / (y / u)) / w) = K(x,T(u * K(y,z),y) / w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15849,a(flip),b,18469,a)].">
      <j1 rule="hyper" parents="63 15849 18469"/>
    </justification>
  </clause>

  <clause id="18471">
    <literal><![CDATA[
      K(x,(T(y,z) / (y / u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u,y) * (w \ K(z,y))) = v5
    ]]></literal>
    <justification jstring="[para(18470(a,2),17761(a,1))].">
      <j1 rule="para" parents="18470 17761"/>
    </justification>
  </clause>

  <clause id="18472">
    <literal><![CDATA[
      K(x,T(y * T(z,u),T(z,u)) / w) = K(x,T(y * z,z) * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(18471,a,15962,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18471 15962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18473">
    <literal><![CDATA[
      K(x,T(y * T(z,u),T(z,u)) / w) = K(x,(z * y) * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,15791,a(flip),b,18472,a),flip(a)].">
      <j1 rule="hyper" parents="347 15791 18472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18474">
    <literal><![CDATA[
      K(x,(y * z) * (u \ K(w,y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,w) * z) / u) = v5
    ]]></literal>
    <justification jstring="[para(18473(a,1),15955(a,1))].">
      <j1 rule="para" parents="18473 15955"/>
    </justification>
  </clause>

  <clause id="18475">
    <literal><![CDATA[
      K(x,(T(y,z) * (1 / z)) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(18474,a,17338,a)].">
      <j1 rule="hyper" parents="18474 17338"/>
    </justification>
  </clause>

  <clause id="18476">
    <literal><![CDATA[
      K(x,(y * (1 / T(z,y))) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[para(5356(a,1),18475(a,1,2,1))].">
      <j1 rule="para" parents="5356 18475"/>
    </justification>
  </clause>

  <clause id="18477">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,((z \ 1) * y) / ((u \ 1) * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15215,a(flip),b,18476,a)].">
      <j1 rule="hyper" parents="63 15215 18476"/>
    </justification>
  </clause>

  <clause id="18478">
    <literal><![CDATA[
      K(x,T(y \ (z * K(u,w)),K(v5,v6)) \ v7) = K(x,K(w,u) * ((y \ z) \ v7))
    ]]></literal>
    <justification jstring="[hyper(18464,a,18385,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18464 18385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18479">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ v5) = K(x,K(w,u) * ((y \ z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(14828,a,18478,a)].">
      <j1 rule="hyper" parents="14828 18478"/>
    </justification>
  </clause>

  <clause id="18480">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ w) \ T(v5,u * w))) = K(x,v5 / (u \ (w * K(z,y))))
    ]]></literal>
    <justification jstring="[hyper(17905,a,18479,a),flip(a)].">
      <j1 rule="hyper" parents="17905 18479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18481">
    <literal><![CDATA[
      K(x,y / (z \ (u * K(w,v5)))) = K(x,y * ((z \ u) \ K(v5,w)))
    ]]></literal>
    <justification jstring="[hyper(18344,a,18480,a),flip(a)].">
      <j1 rule="hyper" parents="18344 18480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18482">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * v5))) = K(x,y * ((z \ v5) \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18269,a,b,18481,a)].">
      <j1 rule="hyper" parents="63 18269 18481"/>
    </justification>
  </clause>

  <clause id="18483">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,z)) \ K(w,v5))) = K(x,y / (u / (K(w,v5) * z)))
    ]]></literal>
    <justification jstring="[hyper(18461,a,18482,a),flip(a)].">
      <j1 rule="hyper" parents="18461 18482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18484">
    <literal><![CDATA[
      K(x,y / (z / (K(u,w) * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((z / v5) \ K(u,w))) = v6
    ]]></literal>
    <justification jstring="[para(18483(a,1),17772(a,1))].">
      <j1 rule="para" parents="18483 17772"/>
    </justification>
  </clause>

  <clause id="18485">
    <literal><![CDATA[
      (K(x,y) * z) / (K(u,w) * K(v5,v6)) = K(x,y) * (z / (K(v5,v6) * K(u,w)))
    ]]></literal>
    <justification jstring="[para(16858(a,1),18037(a,1,1,1))].">
      <j1 rule="para" parents="16858 18037"/>
    </justification>
  </clause>

  <clause id="18487">
    <literal><![CDATA[
      (K(x,y) * z) * (K(u,w) * K(v5,v6)) = K(x,y) * (z / (K(v6,v5) * K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18244,a(flip),b,18485,a)].">
      <j1 rule="hyper" parents="63 18244 18485"/>
    </justification>
  </clause>

  <clause id="18489">
    <literal><![CDATA[
      (K(x,y) * z) * (K(u,w) * K(v5,v6)) = K(x,y) * (z * (K(v5,v6) * K(u,w)))
    ]]></literal>
    <justification jstring="[para(18244(a,1),18487(a,2,2))].">
      <j1 rule="para" parents="18244 18487"/>
    </justification>
  </clause>

  <clause id="18490">
    <literal><![CDATA[
      L(K(x,y) * K(z,u),w,K(v5,v6)) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(17898,a,18489,a)].">
      <j1 rule="hyper" parents="17898 18489"/>
    </justification>
  </clause>

  <clause id="18491">
    <literal><![CDATA[
      ((K(x,y) * K(z,u)) * a(w,v5,v6)) / K(x,y) = a(w,v5,v6) * K(z,u)
    ]]></literal>
    <justification jstring="[para(18490(a,1),18216(a,1,1,1))].">
      <j1 rule="para" parents="18490 18216"/>
    </justification>
  </clause>

  <clause id="18492">
    <literal><![CDATA[
      (K(x,y) * (K(z,u) * a(w,v5,v6))) / K(x,y) = a(w,v5,v6) * K(z,u)
    ]]></literal>
    <justification jstring="[para(18169(a,1),18491(a,1,1))].">
      <j1 rule="para" parents="18169 18491"/>
    </justification>
  </clause>

  <clause id="18494">
    <literal><![CDATA[
      T(K(x,y) * a(z,u,w),K(v5,v6)) = a(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7360,a,18492,a)].">
      <j1 rule="hyper" parents="7360 18492"/>
    </justification>
  </clause>

  <clause id="18495">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,(y * (u / y)) / (((u \ z) \ 1) * (u / y))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(13799(a,1),18055(a,1,1))].">
      <j1 rule="para" parents="13799 18055"/>
    </justification>
  </clause>

  <clause id="18496">
    <literal><![CDATA[
      (x * K(y,z)) / a((u \ 1) \ x,u \ 1,K(y,z)) = (x / (1 / u)) * (K(y,T(z,u)) / u)
    ]]></literal>
    <justification jstring="[para(18431(a,1),18073(a,1,2))].">
      <j1 rule="para" parents="18431 18073"/>
    </justification>
  </clause>

  <clause id="18497">
    <literal><![CDATA[
      K(x,L((y * z) * (u / w),y,z \ 1)) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[hyper(16031,a,18128,a)].">
      <j1 rule="hyper" parents="16031 18128"/>
    </justification>
  </clause>

  <clause id="18498">
    <literal><![CDATA[
      K(x,y / (T((z \ u) \ 1,u) / w)) = K(x,y / (((u / z) \ 1) / w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18129,a(flip),b,18497,a),flip(a)].">
      <j1 rule="hyper" parents="63 18129 18497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18499">
    <literal><![CDATA[
      T(K(x,(y * z) / ((u / w) \ 1)) * a(z,y,K(x,((u / w) \ 1) \ y)),K(x,y / (T((w \ u) \ 1,u) / z))) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[hyper(468,a,18126,a,b,18498,a)].">
      <j1 rule="hyper" parents="468 18126 18498"/>
    </justification>
  </clause>

  <clause id="18500">
    <literal><![CDATA[
      L(K(x,K(y,z)) * (z / a(u,w,v5)),w,K(v5,u)) = T(a(u,w,v5) \ z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8665(a,1),18145(a,1,1))].">
      <j1 rule="para" parents="8665 18145"/>
    </justification>
  </clause>

  <clause id="18501">
    <literal><![CDATA[
      L(T(x,K(y,z)) / a(u,w,v5),w,K(v5,u)) = T(a(u,w,v5) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12750(a,1),18500(a,1,1))].">
      <j1 rule="para" parents="12750 18500"/>
    </justification>
  </clause>

  <clause id="18502">
    <literal><![CDATA[
      T(a(x,y,z) \ u,K(w,v5)) = a(x,y,z) \ T(u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(14359,a,18501,a),flip(a)].">
      <j1 rule="hyper" parents="14359 18501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18503">
    <literal><![CDATA[
      T(a(x,y,z) \ (a(x,y,z) * u),K(w,v5)) = u * K(w,K(v5,u * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,13491,a(flip),b,18502,a),flip(a)].">
      <j1 rule="hyper" parents="347 13491 18502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18504">
    <literal><![CDATA[
      x * K(y,K(z,x * a(u,w,v5))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),18503(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 18503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18505">
    <literal><![CDATA[
      T(a(x,y,z) * u,K(w,v5)) = a(x,y,z) * T(u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(134,a,18504,a(flip),b,13491,a),flip(a)].">
      <j1 rule="hyper" parents="134 18504 13491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18506">
    <literal><![CDATA[
      x \ T(a(y,z,u) * (a(y,z,u) \ x),K(w,v5)) = K(w,K(v5,a(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(128,a,18505,a,b,7300,a(flip))].">
      <j1 rule="hyper" parents="128 18505 7300"/>
    </justification>
  </clause>

  <clause id="18507">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w) \ v5)) = v5 \ T(v5,K(x,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),18506(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 18506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18508">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w) \ v5)) = K(v5,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,4924,a,b,18507,a),flip(a)].">
      <j1 rule="hyper" parents="347 4924 18507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18509">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(y,z)) = u * K(y,T(z,a(w,v5,v6) \ x))
    ]]></literal>
    <justification jstring="[para(18508(a,1),13720(a,1,1))].">
      <j1 rule="para" parents="18508 13720"/>
    </justification>
  </clause>

  <clause id="18510">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w) \ v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(13865,a,18509,a),flip(a)].">
      <j1 rule="hyper" parents="13865 18509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18511">
    <literal><![CDATA[
      K(x,T(y,z * a(u,w,v5))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(13420,a,18510,a)].">
      <j1 rule="hyper" parents="13420 18510"/>
    </justification>
  </clause>

  <clause id="18512">
    <literal><![CDATA[
      K(x,T(y,z)) * (a(u,w,v5) \ z) != v6
    ]]></literal>
    <literal><![CDATA[
      (a(u,w,v5) \ z) * K(x,y) = v6
    ]]></literal>
    <justification jstring="[para(18510(a,1),7442(a,1,1))].">
      <j1 rule="para" parents="18510 7442"/>
    </justification>
  </clause>

  <clause id="18513">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w)) = K(x,T(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(13379(a,1),18510(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13379 18510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18514">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) = T(x,K(y,z * a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(18511(a,1),7564(a,1,1,2))].">
      <j1 rule="para" parents="18511 7564"/>
    </justification>
  </clause>

  <clause id="18515">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w)) = K(x,T(y,z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,16129,a,b,18513,a),flip(a)].">
      <j1 rule="hyper" parents="347 16129 18513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18517">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * (w * u))) = v5
    ]]></literal>
    <justification jstring="[para(18513(a,2),16162(a,1))].">
      <j1 rule="para" parents="18513 16162"/>
    </justification>
  </clause>

  <clause id="18518">
    <literal><![CDATA[
      K(x,T(y,z * (a(u,w,v5) * v6))) = K(x,T(y,z * v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,18511,a(flip),b,18515,a),flip(a)].">
      <j1 rule="hyper" parents="63 18511 18515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18519">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * (u * w))) = v5
    ]]></literal>
    <justification jstring="[para(18515(a,2),16162(a,1))].">
      <j1 rule="para" parents="18515 16162"/>
    </justification>
  </clause>

  <clause id="18520">
    <literal><![CDATA[
      T(x,K(y,z * a(u,w,v5))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7764,a,18514,a),flip(a)].">
      <j1 rule="hyper" parents="7764 18514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18521">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w) * v5)) = T(x,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(13677,a,18520,a)].">
      <j1 rule="hyper" parents="13677 18520"/>
    </justification>
  </clause>

  <clause id="18522">
    <literal><![CDATA[
      T(x,K(y,(z * u) * w)) = T(x,K(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(86(a,1),18520(a,1,2,2))].">
      <j1 rule="para" parents="86 18520"/>
    </justification>
  </clause>

  <clause id="18524">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u * a(w,v5,v6))) = T(y,K(u * a(w,v5,v6),z) * x)
    ]]></literal>
    <justification jstring="[para(18520(a,1),15497(a,1,2,1,2))].">
      <j1 rule="para" parents="18520 15497"/>
    </justification>
  </clause>

  <clause id="18525">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (a(u,w,v5) \ z)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,(a(u,w,v5) \ z) * y) = v6
    ]]></literal>
    <justification jstring="[para(18521(a,1),13482(a,1,1))].">
      <j1 rule="para" parents="18521 13482"/>
    </justification>
  </clause>

  <clause id="18526">
    <literal><![CDATA[
      K(x,T(y,z * (u / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * (w * u))) = v5
    ]]></literal>
    <justification jstring="[para(17038(a,1),18519(a,1))].">
      <j1 rule="para" parents="17038 18519"/>
    </justification>
  </clause>

  <clause id="18527">
    <literal><![CDATA[
      K(((x \ y) / z) \ u,T(w,x * (z * y))) = K(u / ((x \ y) / z),w)
    ]]></literal>
    <justification jstring="[hyper(18526,a,17321,a)].">
      <j1 rule="hyper" parents="18526 17321"/>
    </justification>
  </clause>

  <clause id="18528">
    <literal><![CDATA[
      T(x,K(y * a(z,u,w),v5) * v6) = v6 \ T(x * T(v6,K(v5,y)),K(v5,y))
    ]]></literal>
    <justification jstring="[para(18520(a,1),18524(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18520 18524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18529">
    <literal><![CDATA[
      T(x,K(y * a(z,u,w),v5) * v6) = T(x,K(y,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,15497,a(flip),b,18528,a),flip(a)].">
      <j1 rule="hyper" parents="347 15497 18528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18531">
    <literal><![CDATA[
      T(x,T(y,z * a(u,w,v5)) \ v6) = T(x,K(z,y) * (y \ v6))
    ]]></literal>
    <justification jstring="[para(5209(a,1),18529(a,1,2))].">
      <j1 rule="para" parents="5209 18529"/>
    </justification>
  </clause>

  <clause id="18532">
    <literal><![CDATA[
      T(x,T(y,z * a(u,w,v5)) \ v6) = T(x,T(y,z) \ v6)
    ]]></literal>
    <justification jstring="[para(5209(a,1),18531(a,2,2))].">
      <j1 rule="para" parents="5209 18531"/>
    </justification>
  </clause>

  <clause id="18533">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,u) \ z) = T(x,z / T(y,T(a(w,v5,v6),v7) * u))
    ]]></literal>
    <justification jstring="[hyper(17368,a,18532,a),flip(a)].">
      <j1 rule="hyper" parents="17368 18532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18534">
    <literal><![CDATA[
      T(x,y / T(z,T(a(u,w,v5),v6) * v7)) = T(x,y / T(z,v7))
    ]]></literal>
    <justification jstring="[hyper(13539,a,18533,a),flip(a)].">
      <j1 rule="hyper" parents="13539 18533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18535">
    <literal><![CDATA[
      T(x,y / T(z,u * a(w,v5,v6))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(10361(a,1),18534(a,1,2,2))].">
      <j1 rule="para" parents="10361 18534"/>
    </justification>
  </clause>

  <clause id="18536">
    <literal><![CDATA[
      K(x,T(y / T(z,u * a(w,v5,v6)),v7)) = (x * v7) \ (T(x,y / T(z,u)) * v7)
    ]]></literal>
    <justification jstring="[para(18535(a,1),7236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18535 7236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18537">
    <literal><![CDATA[
      K(x,T(y / T(z,u * a(w,v5,v6)),v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / T(z,u),v7)) = v8
    ]]></literal>
    <justification jstring="[para(18536(a,2),7792(a,1))].">
      <j1 rule="para" parents="18536 7792"/>
    </justification>
  </clause>

  <clause id="18542">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,T(u,y)) / y) = (x / (y \ 1)) * (y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15140,a(flip),b,18496,a),flip(a)].">
      <j1 rule="hyper" parents="63 15140 18496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18543">
    <literal><![CDATA[
      K(x,T((y * (z \ u)) \ u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u \ (z * (y \ u)),w)) = v5
    ]]></literal>
    <justification jstring="[para(18353(a,1),8526(a,1))].">
      <j1 rule="para" parents="18353 8526"/>
    </justification>
  </clause>

  <clause id="18544">
    <literal><![CDATA[
      K(x,T(y \ (z * (u \ y)),u)) = K(x,y / ((y / z) * u))
    ]]></literal>
    <justification jstring="[hyper(18543,a,18391,a)].">
      <j1 rule="hyper" parents="18543 18391"/>
    </justification>
  </clause>

  <clause id="18545">
    <literal><![CDATA[
      K(x,((y / z) * u) / y) = K(x,y / ((y / u) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,16307,a(flip),b,18544,a)].">
      <j1 rule="hyper" parents="63 16307 18544"/>
    </justification>
  </clause>

  <clause id="18546">
    <literal><![CDATA[
      K(x,((y / ((y * z) \ y)) * u) / y) = K(x,y / ((y / u) / z))
    ]]></literal>
    <justification jstring="[hyper(347,a,18132,a(flip),b,18545,a),flip(a)].">
      <j1 rule="hyper" parents="347 18132 18545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18547">
    <literal><![CDATA[
      K(x,((y * z) * u) / y) = K(x,y / ((y / u) / z))
    ]]></literal>
    <justification jstring="[para(80(a,1),18546(a,1,2,1,1))].">
      <j1 rule="para" parents="80 18546"/>
    </justification>
  </clause>

  <clause id="18549">
    <literal><![CDATA[
      K(x,T(y,z) / ((T(y,z) / u) / (K(z,y) * w))) = K(x,((y * w) * u) / T(y,z))
    ]]></literal>
    <justification jstring="[para(5213(a,1),18547(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5213 18547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18550">
    <literal><![CDATA[
      K(x,((y * z) * (u * K(y,w))) / y) = K(x,y / ((K(w,y) * (y / u)) / z))
    ]]></literal>
    <justification jstring="[para(13201(a,1),18547(a,2,2,2,1))].">
      <j1 rule="para" parents="13201 18547"/>
    </justification>
  </clause>

  <clause id="18551">
    <literal><![CDATA[
      K(x,y / ((K(z,y) * (y / u)) / w)) = K(x,((y * w) * u) * (y \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(17426,a,18550,a),flip(a)].">
      <j1 rule="hyper" parents="17426 18550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18552">
    <literal><![CDATA[
      K(x,y / ((K(z,y) * (y / u)) / w)) = K(x,((y * w) * u) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,17230,a(flip),b,18551,a),flip(a)].">
      <j1 rule="hyper" parents="347 17230 18551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18553">
    <literal><![CDATA[
      K(x,T(y,z) * (((T(y,z) / u) / w) \ K(z,y))) = K(x,((y * w) * u) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(18484,a,18549,a)].">
      <j1 rule="hyper" parents="18484 18549"/>
    </justification>
  </clause>

  <clause id="18554">
    <literal><![CDATA[
      K(x,T(T(y,z),z) / ((T(y,z) / u) / w)) = K(x,((y * w) * u) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(17025,a,18553,a)].">
      <j1 rule="hyper" parents="17025 18553"/>
    </justification>
  </clause>

  <clause id="18555">
    <literal><![CDATA[
      K(x,((y * z) * u) / T(y,w)) = K(x,y / ((T(y,w) / u) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,15664,a(flip),b,18554,a),flip(a)].">
      <j1 rule="hyper" parents="63 15664 18554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18557">
    <literal><![CDATA[
      K(x,y / ((K(z,y) * (y / u)) / w)) = K(x,y / ((T(y,z) / u) / w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18552,a,b,18555,a)].">
      <j1 rule="hyper" parents="63 18552 18555"/>
    </justification>
  </clause>

  <clause id="18558">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (K(z,x) * y) * (y \ u)
    ]]></literal>
    <justification jstring="[para(5095(a,1),18420(a,2,1,1))].">
      <j1 rule="para" parents="5095 18420"/>
    </justification>
  </clause>

  <clause id="18559">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((T(x,z) * (y * K(x,z))) \ u) = (K(z,x) * y) * (y \ u)
    ]]></literal>
    <justification jstring="[para(4974(a,1),18558(a,1,2,1))].">
      <j1 rule="para" parents="4974 18558"/>
    </justification>
  </clause>

  <clause id="18560">
    <literal><![CDATA[
      (K(x,y) * (z * K(y,x))) * ((z * K(y,x)) \ u) = (K(x,y) * z) * (z \ u)
    ]]></literal>
    <justification jstring="[hyper(18419,a,18559,a)].">
      <j1 rule="hyper" parents="18419 18559"/>
    </justification>
  </clause>

  <clause id="18561">
    <literal><![CDATA[
      T(x,K(y,z)) * ((x * K(y,z)) \ u) = (K(z,y) * x) * (x \ u)
    ]]></literal>
    <justification jstring="[para(5265(a,1),18560(a,1,1))].">
      <j1 rule="para" parents="5265 18560"/>
    </justification>
  </clause>

  <clause id="18562">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ u) = z * ((K(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(10297,a,18561,a),flip(a)].">
      <j1 rule="hyper" parents="10297 18561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18563">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * u) = z \ ((K(y,x) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(706,a,18562,a),flip(a)].">
      <j1 rule="hyper" parents="706 18562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18564">
    <literal><![CDATA[
      x * a(y \ (x * K(z,u)),x,K(z,u)) = y * ((K(z,T(u,x)) * y) \ (x * K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17828,a(flip),b,18562,a)].">
      <j1 rule="hyper" parents="63 17828 18562"/>
    </justification>
  </clause>

  <clause id="18565">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * (K(z,T(y,x)) * u)) = L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(10233,a,18563,a),flip(a)].">
      <j1 rule="hyper" parents="10233 18563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18566">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * T(u,K(z,y))) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,17895,a(flip),b,18563,a),flip(a)].">
      <j1 rule="hyper" parents="63 17895 18563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18567">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ ((K(u,z) * w) * v5)))) = K(x,y * (v5 * K(w * v5,K(z,u))))
    ]]></literal>
    <justification jstring="[para(18563(a,1),17801(a,1,2,2,2))].">
      <j1 rule="para" parents="18563 17801"/>
    </justification>
  </clause>

  <clause id="18568">
    <literal><![CDATA[
      x \ ((x * K(y,z)) * (K(z,y) * u)) = L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[para(10285(a,1),18565(a,1,2))].">
      <j1 rule="para" parents="10285 18565"/>
    </justification>
  </clause>

  <clause id="18569">
    <literal><![CDATA[
      L(x,K(y,z),u * K(z,y)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(6142,a,18568,a)].">
      <j1 rule="hyper" parents="6142 18568"/>
    </justification>
  </clause>

  <clause id="18570">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * u) = x * L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(150,a,18568,a),flip(a)].">
      <j1 rule="hyper" parents="150 18568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18571">
    <literal><![CDATA[
      L(x,K(y,z),K(z,y) * u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(16911,a,18569,a)].">
      <j1 rule="hyper" parents="16911 18569"/>
    </justification>
  </clause>

  <clause id="18572">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u) = (x * (u * K(y,z))) / u
    ]]></literal>
    <justification jstring="[hyper(63,a,17878,a(flip),b,18569,a),flip(a)].">
      <j1 rule="hyper" parents="63 17878 18569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18573">
    <literal><![CDATA[
      L(x,K(y,z),u \ T(z,y)) = L(x,K(y,z),u \ z)
    ]]></literal>
    <justification jstring="[para(13045(a,1),18569(a,1,3))].">
      <j1 rule="para" parents="13045 18569"/>
    </justification>
  </clause>

  <clause id="18574">
    <literal><![CDATA[
      L(x,K(y,z),u) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(18569(a,1),17881(a,1,1))].">
      <j1 rule="para" parents="18569 17881"/>
    </justification>
  </clause>

  <clause id="18575">
    <literal><![CDATA[
      (x * y) \ (L(x,K(z,u),y) * (K(z,u) * (K(z,u) \ y))) = a(x,K(z,u),K(z,u) \ y)
    ]]></literal>
    <justification jstring="[para(18571(a,1),17913(a,1,2,1))].">
      <j1 rule="para" parents="18571 17913"/>
    </justification>
  </clause>

  <clause id="18576">
    <literal><![CDATA[
      x * L(K(y,z) * u,K(z,y),x) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(5261(a,1),18570(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5261 18570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18577">
    <literal><![CDATA[
      L(K(x,y) * z,K(y,x),u) * u = T(z,K(y,x)) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(6880(a,1),18574(a,2,1))].">
      <j1 rule="para" parents="6880 18574"/>
    </justification>
  </clause>

  <clause id="18578">
    <literal><![CDATA[
      L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z)) = (x * K(y,z)) * (K(z,y) * L(K(K(y,z),x) * u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(17069(a,1),18574(a,1,1))].">
      <j1 rule="para" parents="17069 18574"/>
    </justification>
  </clause>

  <clause id="18579">
    <literal><![CDATA[
      (x * K(y,z)) * (x \ u) = x * ((x * K(z,y)) \ u)
    ]]></literal>
    <justification jstring="[para(5278(a,1),18576(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5278 18576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18580">
    <literal><![CDATA[
      K(x,y * (z \ T((u * K(w,v5)) * v6,L(K(w,v5) * v6,K(v5,w),u)))) = K(x,y * (z \ (L(K(w,v5) * v6,K(v5,w),u) * u)))
    ]]></literal>
    <justification jstring="[para(18576(a,1),17279(a,1,2,2,2,1))].">
      <j1 rule="para" parents="18576 17279"/>
    </justification>
  </clause>

  <clause id="18581">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * L(u \ 1,u,u \ (x * K(z,y)))) = x \ ((x * K(z,y)) / u)
    ]]></literal>
    <justification jstring="[hyper(128,a,5511,a,b,18579,a)].">
      <j1 rule="hyper" parents="128 5511 18579"/>
    </justification>
  </clause>

  <clause id="18582">
    <literal><![CDATA[
      (x * (y * K(z,u))) / y = (x * y) / (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,17893,a(flip),b,18572,a),flip(a)].">
      <j1 rule="hyper" parents="63 17893 18572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18583">
    <literal><![CDATA[
      ((x * y) / (y * K(z,u))) * y = x * (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,17893,a(flip),b,18572,a(flip))].">
      <j1 rule="hyper" parents="133 17893 18572"/>
    </justification>
  </clause>

  <clause id="18584">
    <literal><![CDATA[
      K(K(x,y),z) \ ((u * (T(z,K(x,y)) * K(y,x))) / T(z,K(x,y))) = T((u * T(z,K(x,y))) / (z * K(x,y)),K(K(x,y),z))
    ]]></literal>
    <justification jstring="[hyper(462,a,18582,a,b,18331,a),flip(a)].">
      <j1 rule="hyper" parents="462 18582 18331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18585">
    <literal><![CDATA[
      (x / (y * K(z,u))) * y = (x / y) * (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,171,a(flip),b,18582,a)].">
      <j1 rule="hyper" parents="133 171 18582"/>
    </justification>
  </clause>

  <clause id="18586">
    <literal><![CDATA[
      (K(x,L(y,z * (u * K(w,v5)),u)) * (z * (u * K(w,v5)))) / u = K(x,y) * ((z * u) / (u * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(18582(a,1),14240(a,2,2))].">
      <j1 rule="para" parents="18582 14240"/>
    </justification>
  </clause>

  <clause id="18587">
    <literal><![CDATA[
      (x * (y * K(z,u))) / y != w
    ]]></literal>
    <literal><![CDATA[
      (x * y) / (y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(18583(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="18583 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18588">
    <literal><![CDATA[
      (x / ((y \ 1) * K(z,u))) * (y \ 1) = (x / (y \ 1)) * (y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,13014,a(flip),b,18585,a),flip(a)].">
      <j1 rule="hyper" parents="347 13014 18585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18589">
    <literal><![CDATA[
      (x / y) * (y * K(z,T(u,y))) = (x / (K(u,z) * y)) * y
    ]]></literal>
    <justification jstring="[para(7076(a,1),18585(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7076 18585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18590">
    <literal><![CDATA[
      (x / (K(y,z) * u)) * u = (x / u) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(7115,a,18589,a),flip(a)].">
      <j1 rule="hyper" parents="7115 18589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18591">
    <literal><![CDATA[
      (x / (K(y,z) * (1 / u))) * (1 / u) = (x / (1 / u)) * (K(z,y) / u)
    ]]></literal>
    <justification jstring="[para(12988(a,1),18590(a,2,2))].">
      <j1 rule="para" parents="12988 18590"/>
    </justification>
  </clause>

  <clause id="18592">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * T(u,K(y,z))) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(7330(a,1),18566(a,1,2,2))].">
      <j1 rule="para" parents="7330 18566"/>
    </justification>
  </clause>

  <clause id="18593">
    <literal><![CDATA[
      x \ ((K(y,z) * (x * K(u,K(y,z)))) * u) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(6848(a,2),18592(a,1,2))].">
      <j1 rule="para" parents="6848 18592"/>
    </justification>
  </clause>

  <clause id="18594">
    <literal><![CDATA[
      (x / (K(y,z) / u)) * (1 / u) = (x / (1 / u)) * (K(z,y) / u)
    ]]></literal>
    <justification jstring="[para(12988(a,1),18591(a,1,1,2))].">
      <j1 rule="para" parents="12988 18591"/>
    </justification>
  </clause>

  <clause id="18595">
    <literal><![CDATA[
      x \ ((K(y,z) * (x * K(y,K(z,u)))) * u) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(7283(a,2),18593(a,1,2,1,2,2))].">
      <j1 rule="para" parents="7283 18593"/>
    </justification>
  </clause>

  <clause id="18596">
    <literal><![CDATA[
      x \ ((K(y,T(z,u)) * x) * u) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(13558(a,1),18595(a,1,2,1))].">
      <j1 rule="para" parents="13558 18595"/>
    </justification>
  </clause>

  <clause id="18597">
    <literal><![CDATA[
      (x * y) / (y * K(z,T(u,x))) = y \ ((K(u,z) * y) * x)
    ]]></literal>
    <justification jstring="[para(7380(a,1),18596(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7380 18596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18598">
    <literal><![CDATA[
      x * a(y \ (x * K(z,u)),x,K(z,u)) = y * ((K(z,u) * y) \ (K(z,u) * x))
    ]]></literal>
    <justification jstring="[para(13752(a,1),18564(a,2,2))].">
      <j1 rule="para" parents="13752 18564"/>
    </justification>
  </clause>

  <clause id="18599">
    <literal><![CDATA[
      x * a(y,x,K(x \ z,u)) = z * ((K(y,u) * z) \ (K(y,u) * x))
    ]]></literal>
    <justification jstring="[para(18387(a,1),18598(a,1,2))].">
      <j1 rule="para" parents="18387 18598"/>
    </justification>
  </clause>

  <clause id="18600">
    <literal><![CDATA[
      (x * y) * ((x * T(y,T(z,x))) \ (K(y,z) * u)) = u * a(y,u,K(u \ (x * y),z))
    ]]></literal>
    <justification jstring="[para(7697(a,1),18599(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7697 18599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18602">
    <literal><![CDATA[
      (x * K(y,z)) \ (x / u) = x \ ((x * K(z,y)) / u)
    ]]></literal>
    <justification jstring="[para(18449(a,1),18581(a,1,2))].">
      <j1 rule="para" parents="18449 18581"/>
    </justification>
  </clause>

  <clause id="18604">
    <literal><![CDATA[
      x / ((y / x) * (x * K(z,u))) = x * (x \ ((x * K(u,z)) / y))
    ]]></literal>
    <justification jstring="[para(18602(a,1),18466(a,2,2))].">
      <j1 rule="para" parents="18602 18466"/>
    </justification>
  </clause>

  <clause id="18605">
    <literal><![CDATA[
      x / ((y / x) * (x * K(z,u))) = (x * K(u,z)) / y
    ]]></literal>
    <justification jstring="[hyper(347,a,10,a(flip),b,18604,a),flip(a)].">
      <j1 rule="hyper" parents="347 10 18604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18607">
    <literal><![CDATA[
      x / (((T(y,y \ 1) * (x * K(z,u))) / x) * (x * K(u,z))) = R(y \ 1,y,x * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,2298,a(flip),b,18605,a),flip(a)].">
      <j1 rule="hyper" parents="347 2298 18605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18608">
    <literal><![CDATA[
      (x * y) * ((x * T(y,T(z,x))) \ (K(y,z) * u)) = u * a(z,u,K(y,u \ x))
    ]]></literal>
    <justification jstring="[para(14025(a,1),18600(a,2,2))].">
      <j1 rule="para" parents="14025 18600"/>
    </justification>
  </clause>

  <clause id="18609">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,x,K(y,u)) = z * a(u,z,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(14400(a,1),18608(a,1,2))].">
      <j1 rule="para" parents="14400 18608"/>
    </justification>
  </clause>

  <clause id="18610">
    <literal><![CDATA[
      x * a(y,x,K(z,x \ u)) = u * (z * L(z \ (u \ x),u,K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(1196,a,18609,a),flip(a)].">
      <j1 rule="hyper" parents="1196 18609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18611">
    <literal><![CDATA[
      x * L(y * (y \ (x \ z)),x,K(y,u)) = z * a(u,z,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(14406(a,2),18610(a,2,2)),flip(a)].">
      <j1 rule="para" parents="14406 18610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18612">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,y,K(z,y \ x))
    ]]></literal>
    <justification jstring="[para(10(a,1),18611(a,1,2,1))].">
      <j1 rule="para" parents="10 18611"/>
    </justification>
  </clause>

  <clause id="18614">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,y,K(x \ y,z))
    ]]></literal>
    <justification jstring="[para(11302(a,2),18612(a,2,2))].">
      <j1 rule="para" parents="11302 18612"/>
    </justification>
  </clause>

  <clause id="18615">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = y * L(y \ x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,18441,a,b,18614,a)].">
      <j1 rule="hyper" parents="347 18441 18614"/>
    </justification>
  </clause>

  <clause id="18616">
    <literal><![CDATA[
      a(x,K(y,z),K(y,z) \ u) = (x * u) \ (L(x,K(y,z),u) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),18575(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 18575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18618">
    <literal><![CDATA[
      a(x,K(y,z),K(z,y) * u) = (x * u) \ (L(x,K(y,z),u) * u)
    ]]></literal>
    <justification jstring="[para(5256(a,1),18616(a,1,3))].">
      <j1 rule="para" parents="5256 18616"/>
    </justification>
  </clause>

  <clause id="18619">
    <literal><![CDATA[
      (x * L(K(K(y,z),x) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),K(z,y) * L(K(K(y,z),x) * u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(17069(a,1),18618(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="17069 18618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18620">
    <literal><![CDATA[
      x / (((T(y,y \ 1) * x) / (x * K(z,u))) * (x * K(z,u))) = R(y \ 1,y,x * K(u,z))
    ]]></literal>
    <justification jstring="[para(18582(a,1),18607(a,1,2,1))].">
      <j1 rule="para" parents="18582 18607"/>
    </justification>
  </clause>

  <clause id="18621">
    <literal><![CDATA[
      R(x \ 1,x,y * K(z,u)) = y / (T(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),18620(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 18620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18623">
    <literal><![CDATA[
      R(x \ 1,x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x \ 1,x,y) = w
    ]]></literal>
    <justification jstring="[para(18621(a,2),2368(a,1))].">
      <j1 rule="para" parents="18621 2368"/>
    </justification>
  </clause>

  <clause id="18624">
    <literal><![CDATA[
      R(x \ 1,x,T(y,z)) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(18623,a,5358,a),flip(a)].">
      <j1 rule="hyper" parents="18623 5358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18625">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) / u,z \ y,z \ 1)) = K(x,(z \ y) / (u * T(y \ (z \ y),y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18115,a(flip),b,18087,a)].">
      <j1 rule="hyper" parents="63 18115 18087"/>
    </justification>
  </clause>

  <clause id="18626">
    <literal><![CDATA[
      K(x,(y \ z) / (u * T(z \ (y \ z),z))) = K(x,L(T(z,y \ 1) / u,z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(14216,a,18625,a),flip(a)].">
      <j1 rule="hyper" parents="14216 18625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18628">
    <literal><![CDATA[
      K(x,(y \ z) / (u * T(z \ (y \ z),z))) = K(x,((y \ 1) * z) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(347,a,15969,a(flip),b,18626,a),flip(a)].">
      <j1 rule="hyper" parents="347 15969 18626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18629">
    <literal><![CDATA[
      K(x,(y \ z) / (u * ((y \ z) / z))) = K(x,((y \ 1) * z) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17246,a(flip),b,18628,a)].">
      <j1 rule="hyper" parents="63 17246 18628"/>
    </justification>
  </clause>

  <clause id="18630">
    <literal><![CDATA[
      K(x,((y \ 1) * z) / (u * (y \ 1))) = K(x,(y \ z) / (u / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,18133,a(flip),b,18629,a),flip(a)].">
      <j1 rule="hyper" parents="63 18133 18629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18631">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,(z \ y) / ((u \ 1) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18477,a,b,18630,a)].">
      <j1 rule="hyper" parents="63 18477 18630"/>
    </justification>
  </clause>

  <clause id="18632">
    <literal><![CDATA[
      K(x,T(y / T(z,u * a(w,v5,v6)),z * u)) = K(x,z \ T(y,a(w,v5,v6) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18518,a(flip),b,18436,a)].">
      <j1 rule="hyper" parents="63 18518 18436"/>
    </justification>
  </clause>

  <clause id="18633">
    <literal><![CDATA[
      K(x,T(y / T(z,u),z * u)) = K(x,z \ T(y,a(w,v5,v6) * u))
    ]]></literal>
    <justification jstring="[hyper(18537,a,18632,a)].">
      <j1 rule="hyper" parents="18537 18632"/>
    </justification>
  </clause>

  <clause id="18635">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * v6)) = K(x,y \ T(z,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,18435,a(flip),b,18633,a),flip(a)].">
      <j1 rule="hyper" parents="63 18435 18633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18636">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,u / (((u \ z) \ 1) * (y \ u))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(13919(a,1),18495(a,1,2,2))].">
      <j1 rule="para" parents="13919 18495"/>
    </justification>
  </clause>

  <clause id="18637">
    <literal><![CDATA[
      a(x,y,T(z,x * T(y,x))) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (x * T(y,x))
    ]]></literal>
    <justification jstring="[para(10165(a,1),18306(a,2,1))].">
      <j1 rule="para" parents="10165 18306"/>
    </justification>
  </clause>

  <clause id="18638">
    <literal><![CDATA[
      a(x,y,T(z,x * T(y,x))) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,251,a(flip),b,18637,a),flip(a)].">
      <j1 rule="hyper" parents="347 251 18637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18639">
    <literal><![CDATA[
      a(x,y,T(z,y * x)) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(111(a,1),18638(a,1,1,3,2))].">
      <j1 rule="para" parents="111 18638"/>
    </justification>
  </clause>

  <clause id="18640">
    <literal><![CDATA[
      T(x,K(y,z \ ((u * z) * x))) \ (z \ ((K(y,u) * z) * x)) = K(y,x / ((u * z) \ (z * x)))
    ]]></literal>
    <justification jstring="[para(8898(a,1),18368(a,1,1))].">
      <j1 rule="para" parents="8898 18368"/>
    </justification>
  </clause>

  <clause id="18641">
    <literal><![CDATA[
      T(x,K(y,((z * u) * x) * u)) \ (u \ ((K(y,z) * u) * x)) = K(y,x / ((z * u) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(13475(a,1),18640(a,1,1))].">
      <j1 rule="para" parents="13475 18640"/>
    </justification>
  </clause>

  <clause id="18642">
    <literal><![CDATA[
      T(x,K(y,(z * u) * (x * u))) \ (u \ ((K(y,z) * u) * x)) = K(y,x / ((z * u) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(18522(a,1),18641(a,1,1))].">
      <j1 rule="para" parents="18522 18641"/>
    </justification>
  </clause>

  <clause id="18643">
    <literal><![CDATA[
      T(x,K(y,z * (u * z))) \ (z \ ((K(y,u) * z) * x)) = K(y,x / ((u * z) \ (z * x)))
    ]]></literal>
    <justification jstring="[para(13817(a,1),18642(a,1,1))].">
      <j1 rule="para" parents="13817 18642"/>
    </justification>
  </clause>

  <clause id="18644">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u \ ((K(y,z) * u) * x)) = K(y,x / ((z * u) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(13676(a,1),18643(a,1,1))].">
      <j1 rule="para" parents="13676 18643"/>
    </justification>
  </clause>

  <clause id="18645">
    <literal><![CDATA[
      x \ (y \ ((K(z,u) * y) * T(x,K(z,u)))) = K(z,x / ((u * y) \ (y * x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17474,a(flip),b,18644,a)].">
      <j1 rule="hyper" parents="63 17474 18644"/>
    </justification>
  </clause>

  <clause id="18647">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = y \ ((y * u) / (u * K(z,x)))
    ]]></literal>
    <justification jstring="[para(18592(a,1),18645(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18592 18645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18648">
    <literal><![CDATA[
      (T(x,K(y,z)) * K(u,w)) * (K(w,u) * L(K(y,z),v5,v6)) = x * ((x * L(K(y,z),v5,v6)) / x)
    ]]></literal>
    <justification jstring="[para(16821(a,1),18381(a,1,1,1))].">
      <j1 rule="para" parents="16821 18381"/>
    </justification>
  </clause>

  <clause id="18649">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * L(K(x,y),u,w)) = z * ((z * L(K(x,y),u,w)) / z)
    ]]></literal>
    <justification jstring="[para(7351(a,1),18648(a,1,1))].">
      <j1 rule="para" parents="7351 18648"/>
    </justification>
  </clause>

  <clause id="18651">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * L(K(x,y),u,w)) = z * L(K(x,T(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(7444(a,1),18649(a,2,2))].">
      <j1 rule="para" parents="7444 18649"/>
    </justification>
  </clause>

  <clause id="18652">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * L(K(x,y),u,w)) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[hyper(347,a,7113,a(flip),b,18651,a),flip(a)].">
      <j1 rule="hyper" parents="347 7113 18651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18653">
    <literal><![CDATA[
      (K(x,y) * (z * (K(y,x) * L(K(x,y),u,w)))) * a(x,z,K(K(y,x) * L(K(x,y),u,w),y)) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[hyper(17072,a,18652,a)].">
      <j1 rule="hyper" parents="17072 18652"/>
    </justification>
  </clause>

  <clause id="18654">
    <literal><![CDATA[
      (K(x,L(y,z * u,z)) * (u * (z * K(w,v5)))) / z = K(x,y) * ((u * z) / (z * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(18340(a,1),18586(a,1,1,1))].">
      <j1 rule="para" parents="18340 18586"/>
    </justification>
  </clause>

  <clause id="18655">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * (z * (u * K(w,v5)))) / u = K(x,y) * ((z * u) / (u * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(14201(a,1),18654(a,1,1,1))].">
      <j1 rule="para" parents="14201 18654"/>
    </justification>
  </clause>

  <clause id="18657">
    <literal><![CDATA[
      ((K(x,y) * z) * (u * K(w,v5))) / u = K(x,y) * ((z * u) / (u * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(18036(a,1),18655(a,1,1))].">
      <j1 rule="para" parents="18036 18655"/>
    </justification>
  </clause>

  <clause id="18658">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(w,v5)) = K(x,y) * ((z * u) / (u * K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(18587,a,18657,a)].">
      <j1 rule="hyper" parents="18587 18657"/>
    </justification>
  </clause>

  <clause id="18659">
    <literal><![CDATA[
      K(x,y) * ((z * u) / (u * K(x,T(y,z)))) = L(z * K(x,K(y,u)),K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(17899,a,18658,a),flip(a)].">
      <j1 rule="hyper" parents="17899 18658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18660">
    <literal><![CDATA[
      K(x,y) * (z \ ((K(y,x) * z) * u)) = L(u * K(x,K(y,z)),K(x,y),z)
    ]]></literal>
    <justification jstring="[para(18597(a,1),18659(a,1,2))].">
      <j1 rule="para" parents="18597 18659"/>
    </justification>
  </clause>

  <clause id="18661">
    <literal><![CDATA[
      K(x,y * L(z * K(u,K(w,v5)),K(u,w),v5)) = K(x,y * (z * K(v5 * z,K(u,w))))
    ]]></literal>
    <justification jstring="[para(18660(a,1),18567(a,1,2,2))].">
      <j1 rule="para" parents="18660 18567"/>
    </justification>
  </clause>

  <clause id="18662">
    <literal><![CDATA[
      K(x,y * (z * K(u * z,K(w,v5)))) = K(x,y * L(z,K(w,v5),u))
    ]]></literal>
    <justification jstring="[hyper(17392,a,18661,a),flip(a)].">
      <j1 rule="hyper" parents="17392 18661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18663">
    <literal><![CDATA[
      K(x,y * L(z,K(u,w),v5)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(14832,a,18662,a),flip(a)].">
      <j1 rule="hyper" parents="14832 18662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18664">
    <literal><![CDATA[
      K(x,y * L(z,K(u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(18662(a,1),14832(a,1))].">
      <j1 rule="para" parents="18662 14832"/>
    </justification>
  </clause>

  <clause id="18666">
    <literal><![CDATA[
      K(x,y * L((z * K(u,w)) \ v5,v6,v7)) = K(x,y * L(K(u,w) \ (z \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(622(a,1),18663(a,1,2,2))].">
      <j1 rule="para" parents="622 18663"/>
    </justification>
  </clause>

  <clause id="18667">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * (K(u,z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * w) = v5
    ]]></literal>
    <justification jstring="[para(6134(a,1),18664(a,1,2))].">
      <j1 rule="para" parents="6134 18664"/>
    </justification>
  </clause>

  <clause id="18668">
    <literal><![CDATA[
      K(x,y * L((z * K(u,w)) \ v5,v6,v7)) = K(x,y * L(K(w,u) * (z \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(5256(a,1),18666(a,2,2,2,1))].">
      <j1 rule="para" parents="5256 18666"/>
    </justification>
  </clause>

  <clause id="18669">
    <literal><![CDATA[
      K(x,y * L((K(z,u) \ w) \ v5,v6,v7)) = K(x,y * L(K(z,u) * (w \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,17488,a,b,18668,a)].">
      <j1 rule="hyper" parents="63 17488 18668"/>
    </justification>
  </clause>

  <clause id="18670">
    <literal><![CDATA[
      K(x,y * L((K(z,u) * w) \ v5,v6,v7)) = K(x,y * L(K(u,z) * (w \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(5256(a,1),18669(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5256 18669"/>
    </justification>
  </clause>

  <clause id="18671">
    <literal><![CDATA[
      K(x,y * L(z \ (K(u,w) * v5),v6,v7)) = K(x,y * L(K(u,w) * (z \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,17700,a(flip),b,18670,a)].">
      <j1 rule="hyper" parents="63 17700 18670"/>
    </justification>
  </clause>

  <clause id="18672">
    <literal><![CDATA[
      K(x,y * L(K(z,u) * (w \ v5),w,v6)) = K(x,y * ((v6 * w) \ (v6 * (K(z,u) * v5))))
    ]]></literal>
    <justification jstring="[hyper(13646,a,18671,a),flip(a)].">
      <j1 rule="hyper" parents="13646 18671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18673">
    <literal><![CDATA[
      K(x,y * ((z * u) \ (z * (K(w,v5) * (u * v6))))) = K(x,y * L(K(w,v5) * v6,u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),18672(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 18672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18674">
    <literal><![CDATA[
      L(((x \ y) * K(z,u)) \ (y * K(z,u)),x \ y,K(u,z)) = (x \ (K(u,z) * y)) \ (K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,18318,a(flip),b,18459,a)].">
      <j1 rule="hyper" parents="63 18318 18459"/>
    </justification>
  </clause>

  <clause id="18676">
    <literal><![CDATA[
      (x \ y) \ (K(z,T(u,x \ y)) * (y * K(u,z))) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,18311,a(flip),b,18674,a)].">
      <j1 rule="hyper" parents="63 18311 18674"/>
    </justification>
  </clause>

  <clause id="18677">
    <literal><![CDATA[
      (x \ y) \ (K(z,T(u,y * x)) * (y * K(u,z))) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(13270(a,1),18676(a,1,2,1))].">
      <j1 rule="para" parents="13270 18676"/>
    </justification>
  </clause>

  <clause id="18678">
    <literal><![CDATA[
      (x \ y) \ T(K(z,K(u,y * x)) * y,K(z,u)) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(8715(a,2),18677(a,1,2))].">
      <j1 rule="para" parents="8715 18677"/>
    </justification>
  </clause>

  <clause id="18679">
    <literal><![CDATA[
      K(x,K(y,z * u)) * ((u \ z) \ T(z,K(x,y))) = (u \ (K(x,y) * z)) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(17257,a,18678,a)].">
      <j1 rule="hyper" parents="17257 18678"/>
    </justification>
  </clause>

  <clause id="18680">
    <literal><![CDATA[
      T(x \ y,K(z,u)) \ T(y,K(z,u)) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(13477,a,18679,a)].">
      <j1 rule="hyper" parents="13477 18679"/>
    </justification>
  </clause>

  <clause id="18681">
    <literal><![CDATA[
      R(x,y,z \ (T(u \ w,K(v5,v6)) \ T(w,K(v5,v6)))) = R(x,y,z \ T(u,K(v5,v6) * w))
    ]]></literal>
    <justification jstring="[para(18680(a,2),12267(a,1,3,2))].">
      <j1 rule="para" parents="18680 12267"/>
    </justification>
  </clause>

  <clause id="18682">
    <literal><![CDATA[
      R(x,y,z \ (T(u \ w,K(v5,v6)) \ T(w,K(v5,v6)))) = R(x,y,z \ T(u,K(v6,v5) * w))
    ]]></literal>
    <justification jstring="[para(15511(a,1),18681(a,2,3,2))].">
      <j1 rule="para" parents="15511 18681"/>
    </justification>
  </clause>

  <clause id="18683">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * T(y,y \ z)) \ ((y \ z) \ z)))) = K(x,((y \ z) \ z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(347,a,17709,a(flip),b,17822,a),flip(a)].">
      <j1 rule="hyper" parents="347 17709 17822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18685">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * T(y,y \ z)) \ ((y \ z) \ z)))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(347,a,11974,a(flip),b,18683,a),flip(a)].">
      <j1 rule="hyper" parents="347 11974 18683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18686">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * T((w * y) \ y,K(y,z)))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[para(18000(a,1),18685(a,1,2,2,2))].">
      <j1 rule="para" parents="18000 18685"/>
    </justification>
  </clause>

  <clause id="18687">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * y) \ y))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(17080,a,18686,a)].">
      <j1 rule="hyper" parents="17080 18686"/>
    </justification>
  </clause>

  <clause id="18688">
    <literal><![CDATA[
      K(x,T(y,z) \ (u * ((w * y) \ y))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(12151,a,18687,a)].">
      <j1 rule="hyper" parents="12151 18687"/>
    </justification>
  </clause>

  <clause id="18689">
    <literal><![CDATA[
      K(x,y \ (z * ((u * y) \ T(y,w)))) = K(x,T(y,w) \ (z / T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17964,a(flip),b,18688,a)].">
      <j1 rule="hyper" parents="63 17964 18688"/>
    </justification>
  </clause>

  <clause id="18690">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y * u) / T(z,y))) = K(x,((z * ((z * y) / z)) / u) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,18358,a,b,18689,a),flip(a)].">
      <j1 rule="hyper" parents="63 18358 18689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18691">
    <literal><![CDATA[
      K(x,((y * ((y * z) / y)) / u) \ z) = K(x,z \ ((z * u) / y))
    ]]></literal>
    <justification jstring="[hyper(13641,a,18690,a),flip(a)].">
      <j1 rule="hyper" parents="13641 18690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18692">
    <literal><![CDATA[
      K(x,((y * z) / u) \ T(z,y)) = K(x,z \ ((z * u) / y))
    ]]></literal>
    <justification jstring="[para(14536(a,1),18691(a,1,2))].">
      <j1 rule="para" parents="14536 18691"/>
    </justification>
  </clause>

  <clause id="18693">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),u)) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(17410,a,18692,a)].">
      <j1 rule="hyper" parents="17410 18692"/>
    </justification>
  </clause>

  <clause id="18694">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ (u * y))) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(17482,a,18693,a)].">
      <j1 rule="hyper" parents="17482 18693"/>
    </justification>
  </clause>

  <clause id="18695">
    <literal><![CDATA[
      K(x,y / (z \ (T(u,z) * y))) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[para(4767(a,1),18694(a,1,2,2))].">
      <j1 rule="para" parents="4767 18694"/>
    </justification>
  </clause>

  <clause id="18696">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * w)) \ ((K(K(y,z),x) \ u) * (w * v5)) = L(v5,L(w,u,K(x,K(y,z))),K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(5256(a,2),18014(a,1,2,1))].">
      <j1 rule="para" parents="5256 18014"/>
    </justification>
  </clause>

  <clause id="18697">
    <literal><![CDATA[
      K(x,(y * K(z,K(u,w))) / T((K(z,K(u,w)) * v5) * K(z,K(u,w)),v6)) = K(x,y / T(v5 * K(z,K(u,w)),v6))
    ]]></literal>
    <justification jstring="[para(14306(a,2),18016(a,1,2,2))].">
      <j1 rule="para" parents="14306 18016"/>
    </justification>
  </clause>

  <clause id="18698">
    <literal><![CDATA[
      (K(x,K(y,z)) \ ((u * w) * v5)) / ((K(x,K(y,z)) \ w) * v5) = R(u,R(w,K(x,K(y,z)),v5),K(x,K(y,z)) * v5)
    ]]></literal>
    <justification jstring="[para(13547(a,2),18017(a,1,2,1))].">
      <j1 rule="para" parents="13547 18017"/>
    </justification>
  </clause>

  <clause id="18699">
    <literal><![CDATA[
      K(x,L((y / (z \ 1)) / z,u,w) * T(z,y * z)) = K(x,z * L(z \ (y / (z \ K(y,z))),u,w))
    ]]></literal>
    <justification jstring="[para(7997(a,1),18018(a,1,2,2))].">
      <j1 rule="para" parents="7997 18018"/>
    </justification>
  </clause>

  <clause id="18701">
    <literal><![CDATA[
      K(x,y * L(y \ (z / (y \ K(z,y))),u,w)) = K(x,L(z,u,w) / (T(y,z * y) \ 1))
    ]]></literal>
    <justification jstring="[para(10100(a,1),18699(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10100 18699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18702">
    <literal><![CDATA[
      K(x,y * L(y \ (z / (y \ K(z,y))),u,w)) = K(x,L(z,u,w) * T(y,z * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,13072,a(flip),b,18701,a),flip(a)].">
      <j1 rule="hyper" parents="347 13072 18701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18703">
    <literal><![CDATA[
      K(x,y * L(y \ (z / (y \ K(z,y))),u,w)) = K(x,L(z,u,w) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,12044,a(flip),b,18702,a),flip(a)].">
      <j1 rule="hyper" parents="347 12044 18702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18704">
    <literal><![CDATA[
      K(x,y * L(y \ (z / (y \ K(z,y))),u,w)) = K(x,y * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,17465,a(flip),b,18703,a),flip(a)].">
      <j1 rule="hyper" parents="347 17465 18703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18705">
    <literal><![CDATA[
      K(x,y * L((z / (y \ 1)) / y,u,w)) = K(x,y * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(6537(a,1),18704(a,1,2,2,1))].">
      <j1 rule="para" parents="6537 18704"/>
    </justification>
  </clause>

  <clause id="18706">
    <literal><![CDATA[
      K(x,y * (L(z,z \ (a(u,w,K(v5,v6)) * v7),a(v6,w,K(v5,u))) \ v7)) = K(x,y * (z \ (v7 / a(v6,w,K(v5,u)))))
    ]]></literal>
    <justification jstring="[para(14449(a,1),18019(a,1,2,2,1))].">
      <j1 rule="para" parents="14449 18019"/>
    </justification>
  </clause>

  <clause id="18707">
    <literal><![CDATA[
      K(x,1) * K(x,L(y / (z \ u),z \ u,z) / (y * (u \ z))) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(18454(a,1),18136(a,1,1,2))].">
      <j1 rule="para" parents="18454 18136"/>
    </justification>
  </clause>

  <clause id="18708">
    <literal><![CDATA[
      K(x,L(y / (z \ u),z \ u,z) / (y * (u \ z))) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(234,a,18707,a)].">
      <j1 rule="hyper" parents="234 18707"/>
    </justification>
  </clause>

  <clause id="18710">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) / K(z,u)) = K(x,(y \ K(z,u)) \ L(y \ K(z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,6250,a(flip),b,18373,a),flip(a)].">
      <j1 rule="hyper" parents="347 6250 18373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18711">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) / K(z,u)) = a(y \ K(z,u),w,K(x,v5))
    ]]></literal>
    <justification jstring="[hyper(126,a,14572,a(flip),b,18710,a),flip(a)].">
      <j1 rule="hyper" parents="126 14572 18710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18712">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) / K(z,u)) = a(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,18112,a(flip),b,18711,a),flip(a)].">
      <j1 rule="hyper" parents="347 18112 18711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18714">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) * K(u,z)) = a(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[para(6117(a,1),18712(a,1,2))].">
      <j1 rule="para" parents="6117 18712"/>
    </justification>
  </clause>

  <clause id="18715">
    <literal><![CDATA[
      K(x,L(y \ K(z,u),w,v5) * (T(y,K(z,u)) * K(u,z))) = a(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(17154,a,18714,a)].">
      <j1 rule="hyper" parents="17154 18714"/>
    </justification>
  </clause>

  <clause id="18716">
    <literal><![CDATA[
      K(x,L(y \ K(z,u),w,v5) * (K(u,z) * y)) = a(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[para(6885(a,1),18715(a,1,2,2))].">
      <j1 rule="para" parents="6885 18715"/>
    </justification>
  </clause>

  <clause id="18717">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * (u \ 1),w,v5))) = a(x,w,K(u,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,18013,a,b,18716,a)].">
      <j1 rule="hyper" parents="63 18013 18716"/>
    </justification>
  </clause>

  <clause id="18719">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * w)) \ ((K(y,K(x,z)) \ u) * (w * v5)) = L(v5,L(w,u,K(x,K(y,z))),K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(7291(a,1),18696(a,1,2,1,1))].">
      <j1 rule="para" parents="7291 18696"/>
    </justification>
  </clause>

  <clause id="18720">
    <literal><![CDATA[
      K(x,(y * K(z,K(u,w))) / T(v5,v6)) = K(x,y / T(v5 * K(z,K(u,w)),v6))
    ]]></literal>
    <justification jstring="[para(13548(a,1),18697(a,1,2,2,1))].">
      <j1 rule="para" parents="13548 18697"/>
    </justification>
  </clause>

  <clause id="18721">
    <literal><![CDATA[
      K(x,y / T(z * K(u,K(w,v5)),v6)) = K(x,(y / T(z,v6)) * K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(17009(a,1),18720(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17009 18720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18722">
    <literal><![CDATA[
      K(x,y / T(z * K(u,K(w,v5)),v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,v6)) = v7
    ]]></literal>
    <justification jstring="[para(18721(a,2),14826(a,1))].">
      <j1 rule="para" parents="18721 14826"/>
    </justification>
  </clause>

  <clause id="18723">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w) * v5)) = K(x,y / T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(18722,a,18389,a),flip(a)].">
      <j1 rule="hyper" parents="18722 18389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18725">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w) * v5)) = T(x,y / T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(132,a,18723,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 18723 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18726">
    <literal><![CDATA[
      K(x,y / T((K(z,u) * w) \ v5,w)) = K(x,y / (v5 / (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15600,a(flip),b,18723,a),flip(a)].">
      <j1 rule="hyper" parents="63 15600 18723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18727">
    <literal><![CDATA[
      T(x,y / T(z,u * T(w,v5))) = T(x,y / T(z,u * w))
    ]]></literal>
    <justification jstring="[para(5573(a,1),18725(a,1,2,2,2))].">
      <j1 rule="para" parents="5573 18725"/>
    </justification>
  </clause>

  <clause id="18728">
    <literal><![CDATA[
      T(x,T(y * T(z,u),w) / T(v5,y * z)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5 \ T(y * T(z,u),w)) = v6
    ]]></literal>
    <justification jstring="[para(18727(a,1),14837(a,1))].">
      <j1 rule="para" parents="18727 14837"/>
    </justification>
  </clause>

  <clause id="18729">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,z)),w) / T(v5,y * z)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5 \ T(y * (z * K(u,z)),w)) = v6
    ]]></literal>
    <justification jstring="[para(18727(a,1),15653(a,1))].">
      <j1 rule="para" parents="18727 15653"/>
    </justification>
  </clause>

  <clause id="18730">
    <literal><![CDATA[
      K(x,y / ((K(z,u) \ w) / v5)) = K(x,y / (w / (K(z,u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17680,a(flip),b,18726,a)].">
      <j1 rule="hyper" parents="63 17680 18726"/>
    </justification>
  </clause>

  <clause id="18731">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) = K(x,y / (w / (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(5256(a,1),18730(a,1,2,2,1))].">
      <j1 rule="para" parents="5256 18730"/>
    </justification>
  </clause>

  <clause id="18732">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((w / v5) \ K(u,z))) = v6
    ]]></literal>
    <justification jstring="[para(18731(a,2),18484(a,1))].">
      <j1 rule="para" parents="18731 18484"/>
    </justification>
  </clause>

  <clause id="18733">
    <literal><![CDATA[
      K(x,y * (((y / z) / u) \ K(y,w))) = K(x,y / ((T(y,w) / z) / u))
    ]]></literal>
    <justification jstring="[hyper(18732,a,18557,a)].">
      <j1 rule="hyper" parents="18732 18557"/>
    </justification>
  </clause>

  <clause id="18734">
    <literal><![CDATA[
      K(x,T(y,z) / ((y / u) / w)) = K(x,y / ((T(y,z) / u) / w))
    ]]></literal>
    <justification jstring="[hyper(17068,a,18733,a)].">
      <j1 rule="hyper" parents="17068 18733"/>
    </justification>
  </clause>

  <clause id="18735">
    <literal><![CDATA[
      K(x,y / ((T(y,z * u) / z) / u)) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18359,a(flip),b,18734,a),flip(a)].">
      <j1 rule="hyper" parents="63 18359 18734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18736">
    <literal><![CDATA[
      T(x,T(y * T(z,u),w) / T(v5,y * z)) = T(x,v5 \ T(y * (z * K(u,z)),w))
    ]]></literal>
    <justification jstring="[hyper(18729,a,17742,a),flip(a)].">
      <j1 rule="hyper" parents="18729 17742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18738">
    <literal><![CDATA[
      T(x,y \ T(z * (u * K(w,u)),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(z * T(u,w),v5)) = v6
    ]]></literal>
    <justification jstring="[para(18736(a,1),18728(a,1))].">
      <j1 rule="para" parents="18736 18728"/>
    </justification>
  </clause>

  <clause id="18739">
    <literal><![CDATA[
      T(x,T(y,z) \ T(u * y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(u * T(y,z),w)) = v5
    ]]></literal>
    <justification jstring="[para(16546(a,1),18738(a,1))].">
      <j1 rule="para" parents="16546 18738"/>
    </justification>
  </clause>

  <clause id="18740">
    <literal><![CDATA[
      T(x,y \ T(z * T(y,z),u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(18739,a,17699,a)].">
      <j1 rule="hyper" parents="18739 17699"/>
    </justification>
  </clause>

  <clause id="18741">
    <literal><![CDATA[
      T(x,y \ T(y * z,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(111(a,1),18740(a,1,2,2,1))].">
      <j1 rule="para" parents="111 18740"/>
    </justification>
  </clause>

  <clause id="18742">
    <literal><![CDATA[
      (K(x,K(y,z)) \ ((u * w) * v5)) / (K(x,K(y,z)) \ (w * v5)) = R(u,R(w,K(x,K(y,z)),v5),K(x,K(y,z)) * v5)
    ]]></literal>
    <justification jstring="[para(16852(a,2),18698(a,1,2))].">
      <j1 rule="para" parents="16852 18698"/>
    </justification>
  </clause>

  <clause id="18743">
    <literal><![CDATA[
      K(x,y * (L(z,a(u,w,K(v5,v6)) * v7,a(v6,w,K(v5,u))) \ v7)) = K(x,y * (z \ (v7 / a(v6,w,K(v5,u)))))
    ]]></literal>
    <justification jstring="[para(14488(a,1),18706(a,1,2,2,1))].">
      <j1 rule="para" parents="14488 18706"/>
    </justification>
  </clause>

  <clause id="18744">
    <literal><![CDATA[
      K(x,y * (L(z,u,a(w,v5,K(v6,v7))) \ u)) = K(x,y * (z \ (u / a(w,v5,K(v6,v7)))))
    ]]></literal>
    <justification jstring="[para(18403(a,1),18743(a,1,2,2,1))].">
      <j1 rule="para" parents="18403 18743"/>
    </justification>
  </clause>

  <clause id="18745">
    <literal><![CDATA[
      K(x,y * (L(z,u,a(w,v5,K(v6,v7))) \ u)) = K(x,y * (z \ (a(v7,v5,K(v6,w)) * u)))
    ]]></literal>
    <justification jstring="[para(16939(a,1),18744(a,2,2,2,2))].">
      <j1 rule="para" parents="16939 18744"/>
    </justification>
  </clause>

  <clause id="18747">
    <literal><![CDATA[
      K(x,y * (z \ (a(u,w,K(v5,v6)) * v7))) = K(x,y * (z \ v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,17595,a(flip),b,18745,a),flip(a)].">
      <j1 rule="hyper" parents="63 17595 18745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18749">
    <literal><![CDATA[
      K(x,y * (z \ ((u * w) * K(v5,v6)))) = K(x,y * (z \ (u * (w * K(v5,v6)))))
    ]]></literal>
    <justification jstring="[para(13372(a,1),18747(a,1,2,2,2))].">
      <j1 rule="para" parents="13372 18747"/>
    </justification>
  </clause>

  <clause id="18750">
    <literal><![CDATA[
      K(x,y * (z \ (u * (w * K(v5,v6))))) = K(x,y * (K(v5,v6) * (z \ (u * w))))
    ]]></literal>
    <justification jstring="[hyper(17624,a,18749,a),flip(a)].">
      <j1 rule="hyper" parents="17624 18749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18751">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * w)) \ (K(x,K(y,z)) \ (u * (w * v5))) = L(v5,L(w,u,K(x,K(y,z))),K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(16970(a,2),18719(a,1,2))].">
      <j1 rule="para" parents="16970 18719"/>
    </justification>
  </clause>

  <clause id="18752">
    <literal><![CDATA[
      K(x,K(y,z)) \ (((u * w) * v5) / (K(x,K(y,z)) \ (w * v5))) = R(u,R(w,K(x,K(y,z)),v5),K(x,K(y,z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(17012,a,18742,a)].">
      <j1 rule="hyper" parents="17012 18742"/>
    </justification>
  </clause>

  <clause id="18753">
    <literal><![CDATA[
      L(x,L(y,z,K(u,K(w,v5))),K(u,K(w,v5)) * z) = (z * y) \ (z * (y * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,16965,a(flip),b,18751,a),flip(a)].">
      <j1 rule="hyper" parents="63 16965 18751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18755">
    <literal><![CDATA[
      L(x,L(y,z,K(u,K(w,v5))),K(u,K(w,v5)) * z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,18,a,b,18753,a),flip(a)].">
      <j1 rule="hyper" parents="347 18 18753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18756">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w)) * v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(16829(a,1),18755(a,1,2))].">
      <j1 rule="para" parents="16829 18755"/>
    </justification>
  </clause>

  <clause id="18757">
    <literal><![CDATA[
      L(x,y * K(z,K(u,w)),v5) = L(x,y,K(v6,K(v7,v8)) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,17865,a,b,18756,a)].">
      <j1 rule="hyper" parents="347 17865 18756"/>
    </justification>
  </clause>

  <clause id="18758">
    <literal><![CDATA[
      L(x,y,z * T(u,K(w,v5))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16913,a(flip),b,18756,a)].">
      <j1 rule="hyper" parents="63 16913 18756"/>
    </justification>
  </clause>

  <clause id="18759">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w)) \ v5) = L(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(5159(a,1),18756(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5159 18756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18760">
    <literal><![CDATA[
      L(x,y,K(z,T(u,w))) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(7263(a,1),18756(a,1,3))].">
      <j1 rule="para" parents="7263 18756"/>
    </justification>
  </clause>

  <clause id="18761">
    <literal><![CDATA[
      L(x,y,K(z,u / w)) = L(x,y,K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(8939(a,1),18756(a,1,3))].">
      <j1 rule="para" parents="8939 18756"/>
    </justification>
  </clause>

  <clause id="18762">
    <literal><![CDATA[
      L(x,y,z / T(u,K(w,v5))) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(13551(a,1),18756(a,1,3))].">
      <j1 rule="para" parents="13551 18756"/>
    </justification>
  </clause>

  <clause id="18763">
    <literal><![CDATA[
      L(x,y,z * K(u,T(w,v5))) = L(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(13720(a,1),18756(a,1,3))].">
      <j1 rule="para" parents="13720 18756"/>
    </justification>
  </clause>

  <clause id="18764">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),K(z,y)) = a(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(10581,a,18760,a),flip(a)].">
      <j1 rule="hyper" parents="10581 18760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18765">
    <literal><![CDATA[
      L(x,y,z * (T(u,T(w,v5)) / v5)) = L(x,y,z * (T(u,w) / v5))
    ]]></literal>
    <justification jstring="[para(8543(a,1),18758(a,1,3,2))].">
      <j1 rule="para" parents="8543 18758"/>
    </justification>
  </clause>

  <clause id="18766">
    <literal><![CDATA[
      L(x,y,((1 / z) * K(u,w)) \ v5) = L(x,y,(K(u,w) / z) \ v5)
    ]]></literal>
    <justification jstring="[para(13065(a,1),18759(a,1,3,1))].">
      <j1 rule="para" parents="13065 18759"/>
    </justification>
  </clause>

  <clause id="18767">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(z,(x * (y \ u)) \ (x * u))) = (x * u) \ (K(z,(x * u) / (x * (y \ u))) * ((x * K(y,z)) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5889,a(flip),b,18761,a),flip(a)].">
      <j1 rule="hyper" parents="63 5889 18761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18768">
    <literal><![CDATA[
      L(x,y,z / ((1 / u) * K(w,v5))) = L(x,y,z / (K(w,v5) / u))
    ]]></literal>
    <justification jstring="[para(13065(a,1),18762(a,1,3,2))].">
      <j1 rule="para" parents="13065 18762"/>
    </justification>
  </clause>

  <clause id="18769">
    <literal><![CDATA[
      L(x,y,T(K(z,u) * w,v5)) = L(x,y,T(w,v5) * K(z,u))
    ]]></literal>
    <justification jstring="[para(14301(a,1),18763(a,1,3))].">
      <j1 rule="para" parents="14301 18763"/>
    </justification>
  </clause>

  <clause id="18770">
    <literal><![CDATA[
      a(x,y,T(z,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(18289,a,18764,a),flip(a)].">
      <j1 rule="hyper" parents="18289 18764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18772">
    <literal><![CDATA[
      a(x,y,z) = (x * (z * y)) \ ((x * y) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,258,a,b,18770,a),flip(a)].">
      <j1 rule="hyper" parents="63 258 18770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18773">
    <literal><![CDATA[
      a(x,y,z * y) = a(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12444,a(flip),b,18770,a)].">
      <j1 rule="hyper" parents="63 12444 18770"/>
    </justification>
  </clause>

  <clause id="18774">
    <literal><![CDATA[
      a(x,y / z,z) = a(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,6410,a(flip),b,18770,a)].">
      <j1 rule="hyper" parents="63 6410 18770"/>
    </justification>
  </clause>

  <clause id="18775">
    <literal><![CDATA[
      x \ ((x * y) * T(z,y)) = (z * y) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,18770,a(flip),b,14703,a),flip(a)].">
      <j1 rule="hyper" parents="134 18770 14703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18776">
    <literal><![CDATA[
      a(x,y,z) * (x * (z * y)) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,18770,a(flip),b,13385,a)].">
      <j1 rule="hyper" parents="133 18770 13385"/>
    </justification>
  </clause>

  <clause id="18778">
    <literal><![CDATA[
      a(x,y \ z,(y \ z) \ z) = a(x,y \ z,y)
    ]]></literal>
    <justification jstring="[para(112(a,1),18770(a,1,3))].">
      <j1 rule="para" parents="112 18770"/>
    </justification>
  </clause>

  <clause id="18779">
    <literal><![CDATA[
      a(x,y,z) * ((z * y) * x) = (z * y) * R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[para(18770(a,1),15207(a,1,1))].">
      <j1 rule="para" parents="18770 15207"/>
    </justification>
  </clause>

  <clause id="18781">
    <literal><![CDATA[
      (x * y) \ ((x * (y / z)) * z) = a(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,89,a,b,18774,a)].">
      <j1 rule="hyper" parents="63 89 18774"/>
    </justification>
  </clause>

  <clause id="18782">
    <literal><![CDATA[
      x \ ((x * y) * T(z,y)) = z * (y * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,12362,a(flip),b,18775,a),flip(a)].">
      <j1 rule="hyper" parents="347 12362 18775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18783">
    <literal><![CDATA[
      x * (y * (z * a(x,z,y))) = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,12362,a(flip),b,18775,a)].">
      <j1 rule="hyper" parents="134 12362 18775"/>
    </justification>
  </clause>

  <clause id="18784">
    <literal><![CDATA[
      a(x,y,z) * (x * (z * y)) = R(x,y,z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,9598,a,b,18776,a),flip(a)].">
      <j1 rule="hyper" parents="347 9598 18776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18785">
    <literal><![CDATA[
      (x * y) \ ((x * z) * T(y,z)) = L(z * a(x,z,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,18783,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="128 18783 97"/>
    </justification>
  </clause>

  <clause id="18786">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,z * y)
    ]]></literal>
    <justification jstring="[hyper(35,a,14668,a,b,18784,a),flip(a)].">
      <j1 rule="hyper" parents="35 14668 18784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18787">
    <literal><![CDATA[
      a(x,y,z) = ((z * y) * x) \ ((z * y) * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,14667,a,b,18784,a),flip(a)].">
      <j1 rule="hyper" parents="35 14667 18784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18788">
    <literal><![CDATA[
      ((x * y) * z) * a(z,y,x) = (x * y) * R(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,18786,a,b,99,a(flip))].">
      <j1 rule="hyper" parents="134 18786 99"/>
    </justification>
  </clause>

  <clause id="18789">
    <literal><![CDATA[
      L(x \ R(x,y \ z,y),x,z) = a(x,y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),18786(a,2,3)),flip(a)].">
      <j1 rule="para" parents="10 18786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18790">
    <literal><![CDATA[
      L(x,y,z * u) != a(y,u,z)
    ]]></literal>
    <literal><![CDATA[
      y \ R(y,u,z) = x
    ]]></literal>
    <justification jstring="[para(18786(a,2),50(a,1)),flip(a)].">
      <j1 rule="para" parents="18786 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18791">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w)) * v5) = (K(v6,K(v7,v8)) * (v5 * y)) \ (v5 * (y * (x * K(v6,K(v7,v8)))))
    ]]></literal>
    <justification jstring="[hyper(63,a,17912,a,b,18757,a),flip(a)].">
      <j1 rule="hyper" parents="63 17912 18757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18792">
    <literal><![CDATA[
      L(x,y,T(K(z,u) * w,v5)) = L(x,y,K(z,u) * T(w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,16845,a,b,18769,a),flip(a)].">
      <j1 rule="hyper" parents="347 16845 18769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18793">
    <literal><![CDATA[
      a(x,y,z) * ((z * y) * x) = (z * y) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,9594,a(flip),b,18779,a),flip(a)].">
      <j1 rule="hyper" parents="347 9594 18779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18794">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),x,T(K(y,z) * u,w)) = a(x,K(y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(18205,a,18792,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18205 18792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18795">
    <literal><![CDATA[
      L(x,y,(K(z,u) / w) \ v5) = L(x,y,(w \ K(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,13886,a(flip),b,18766,a),flip(a)].">
      <j1 rule="hyper" parents="63 13886 18766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18796">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ 1),x,(u \ K(z,y)) \ x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(18795(a,1),15216(a,1,2,2))].">
      <j1 rule="para" parents="18795 15216"/>
    </justification>
  </clause>

  <clause id="18797">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,(x \ K(x,y)) \ u))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(18795(a,1),14565(a,1,2,2,2))].">
      <j1 rule="para" parents="18795 14565"/>
    </justification>
  </clause>

  <clause id="18798">
    <literal><![CDATA[
      L(x,y,z / (K(u,w) / v5)) = L(x,y,z / (v5 \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,13885,a(flip),b,18768,a),flip(a)].">
      <j1 rule="hyper" parents="63 13885 18768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18799">
    <literal><![CDATA[
      K(x,L(y,z,u / (w \ K(v5,v6)))) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[para(18798(a,1),18439(a,1,2))].">
      <j1 rule="para" parents="18798 18439"/>
    </justification>
  </clause>

  <clause id="18800">
    <literal><![CDATA[
      K(x,L(y,z,(u \ K(w,v5)) \ v6)) = K(x,L(y,z,u * v6))
    ]]></literal>
    <justification jstring="[hyper(16929,a,18799,a)].">
      <j1 rule="hyper" parents="16929 18799"/>
    </justification>
  </clause>

  <clause id="18801">
    <literal><![CDATA[
      K(x,L(y,z,(u \ 1) * w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[para(388(a,1),18800(a,1,2,3,1)),flip(a)].">
      <j1 rule="para" parents="388 18800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18802">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ 1))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(16932,a,18801,a)].">
      <j1 rule="hyper" parents="16932 18801"/>
    </justification>
  </clause>

  <clause id="18803">
    <literal><![CDATA[
      K(x,L(y,z,(u \ 1) \ w)) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[para(3940(a,1),18802(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3940 18802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18804">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,u * y)) = K(x,u \ ((u / (y \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14212,a(flip),b,18803,a),flip(a)].">
      <j1 rule="hyper" parents="63 14212 18803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18805">
    <literal><![CDATA[
      K(x,L(y * z,u,u * y)) = K(x,u \ ((u / (y \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(13440,a,18804,a)].">
      <j1 rule="hyper" parents="13440 18804"/>
    </justification>
  </clause>

  <clause id="18806">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ ((z / (T(y,z) \ 1)) * u))
    ]]></literal>
    <justification jstring="[para(111(a,1),18805(a,1,2,3))].">
      <j1 rule="para" parents="111 18805"/>
    </justification>
  </clause>

  <clause id="18807">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,17978,a(flip),b,18806,a),flip(a)].">
      <j1 rule="hyper" parents="347 17978 18806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18808">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ 1),x,u * x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(18800(a,1),18796(a,1,2))].">
      <j1 rule="para" parents="18800 18796"/>
    </justification>
  </clause>

  <clause id="18809">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u * x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(9392(a,1),18808(a,1,2))].">
      <j1 rule="para" parents="9392 18808"/>
    </justification>
  </clause>

  <clause id="18811">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u * x)) = (x / (1 / u)) * (K(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(347,a,18594,a(flip),b,18809,a),flip(a)].">
      <j1 rule="hyper" parents="347 18594 18809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18812">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w)) * v5) = ((v5 * y) \ (v5 * (y * (x * K(v6,K(v7,v8)))))) * K(v6,K(v7,v8))
    ]]></literal>
    <justification jstring="[hyper(347,a,17056,a(flip),b,18791,a),flip(a)].">
      <j1 rule="hyper" parents="347 17056 18791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18814">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,v5) = v6
    ]]></literal>
    <justification jstring="[para(18812(a,2),17389(a,1))].">
      <j1 rule="para" parents="18812 17389"/>
    </justification>
  </clause>

  <clause id="18815">
    <literal><![CDATA[
      L(x,y,T(T(z,K(u,w)),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,T(z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(5026(a,1),18814(a,1,3))].">
      <j1 rule="para" parents="5026 18814"/>
    </justification>
  </clause>

  <clause id="18816">
    <literal><![CDATA[
      L(x,y,K(z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(7263(a,1),18814(a,1,3))].">
      <j1 rule="para" parents="7263 18814"/>
    </justification>
  </clause>

  <clause id="18817">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,K(x,y) \ x))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14503(a,1),18797(a,1,2,2))].">
      <j1 rule="para" parents="14503 18797"/>
    </justification>
  </clause>

  <clause id="18818">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,x * K(y,x)))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(5233(a,1),18817(a,1,2,2,2,3))].">
      <j1 rule="para" parents="5233 18817"/>
    </justification>
  </clause>

  <clause id="18819">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,x))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(11470(a,1),18818(a,1,2,2,2))].">
      <j1 rule="para" parents="11470 18818"/>
    </justification>
  </clause>

  <clause id="18820">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y,x))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14205(a,1),18819(a,1,2,2))].">
      <j1 rule="para" parents="14205 18819"/>
    </justification>
  </clause>

  <clause id="18822">
    <literal><![CDATA[
      (K(x,y) / x) * (x * (T(y,x) * K(z,u))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(11072(a,1),18820(a,1,2))].">
      <j1 rule="para" parents="11072 18820"/>
    </justification>
  </clause>

  <clause id="18823">
    <literal><![CDATA[
      L(x * K(y,z),u,u \ 1) = L(x,u,u \ 1) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6495,a,18822,a)].">
      <j1 rule="hyper" parents="6495 18822"/>
    </justification>
  </clause>

  <clause id="18824">
    <literal><![CDATA[
      L(K(x,y) * z,u,u \ 1) = K(x,y) * L(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,3376,a(flip),b,18823,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 3376 18823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18825">
    <literal><![CDATA[
      L((x \ T(y,z)) * K(z,y),u,u \ 1) / L(x \ T(y,z),u,u \ 1) = (x \ y) / (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(18823(a,2),17459(a,1,1))].">
      <j1 rule="para" parents="18823 17459"/>
    </justification>
  </clause>

  <clause id="18826">
    <literal><![CDATA[
      T(x,y) * L(K(y,x) * z,u,u \ 1) = x * L(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,18824,a,b,5210,a)].">
      <j1 rule="hyper" parents="134 18824 5210"/>
    </justification>
  </clause>

  <clause id="18827">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ z,u,u \ 1) = x * L(x \ z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5209(a,1),18826(a,1,2,1))].">
      <j1 rule="para" parents="5209 18826"/>
    </justification>
  </clause>

  <clause id="18828">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,z \ 1),u) = L(x \ T(y,u),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(2134,a,18827,a)].">
      <j1 rule="hyper" parents="2134 18827"/>
    </justification>
  </clause>

  <clause id="18829">
    <literal><![CDATA[
      (x \ (x * L(x \ y,z,z \ 1))) / L(x \ T(y,u),z,z \ 1) = K(u,T(x * L(x \ y,z,z \ 1),x))
    ]]></literal>
    <justification jstring="[para(18828(a,1),13246(a,1,2))].">
      <j1 rule="para" parents="18828 13246"/>
    </justification>
  </clause>

  <clause id="18830">
    <literal><![CDATA[
      K(x,y * L(((z \ T(u,w)) / (y \ 1)) / y,v5,v5 \ 1)) = K(x,y * (z \ T(z * L(z \ u,v5,v5 \ 1),w)))
    ]]></literal>
    <justification jstring="[para(18828(a,2),18705(a,2,2,2))].">
      <j1 rule="para" parents="18828 18705"/>
    </justification>
  </clause>

  <clause id="18831">
    <literal><![CDATA[
      L(x \ y,z,z \ 1) / L(x \ T(y,u),z,z \ 1) = (x \ y) / (x \ T(y,u))
    ]]></literal>
    <justification jstring="[para(13102(a,1),18825(a,1,1,1))].">
      <j1 rule="para" parents="13102 18825"/>
    </justification>
  </clause>

  <clause id="18832">
    <literal><![CDATA[
      L(x \ y,z,z \ 1) / L(x \ T(y,u),z,z \ 1) = K(u,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,13246,a(flip),b,18831,a),flip(a)].">
      <j1 rule="hyper" parents="347 13246 18831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18834">
    <literal><![CDATA[
      K(x,T(y * L(y \ z,u,u \ 1),y)) = L(y \ z,u,u \ 1) / L(y \ T(z,x),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),18829(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 18829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18835">
    <literal><![CDATA[
      K(x,T(y * L(y \ z,u,u \ 1),y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,18832,a(flip),b,18834,a),flip(a)].">
      <j1 rule="hyper" parents="347 18832 18834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18837">
    <literal><![CDATA[
      K(x,y * L(z / y,u,u \ 1)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(10407,a,18835,a)].">
      <j1 rule="hyper" parents="10407 18835"/>
    </justification>
  </clause>

  <clause id="18839">
    <literal><![CDATA[
      R(x,R(y,K(z,K(u,w)),v5),K(z,K(u,w)) * v5) = ((x * y) * v5) / (y * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,17055,a(flip),b,18752,a),flip(a)].">
      <j1 rule="hyper" parents="63 17055 18752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18841">
    <literal><![CDATA[
      R(x,R(y,K(z,K(u,w)),v5),K(z,K(u,w)) * v5) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,20,a,b,18839,a),flip(a)].">
      <j1 rule="hyper" parents="347 20 18839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18842">
    <literal><![CDATA[
      R(x,y,K(z,K(u,w)) * v5) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[para(17040(a,1),18841(a,1,2))].">
      <j1 rule="para" parents="17040 18841"/>
    </justification>
  </clause>

  <clause id="18843">
    <literal><![CDATA[
      R(x,y,z \ (T(u,K(w,v5)) \ v6)) = R(x,y,z \ (u \ v6))
    ]]></literal>
    <justification jstring="[para(17029(a,1),18842(a,1,3)),flip(a)].">
      <j1 rule="para" parents="17029 18842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18844">
    <literal><![CDATA[
      R(x,y,z \ ((u \ w) \ T(w,K(v5,v6)))) = R(x,y,z \ T(u,K(v6,v5) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18682,a(flip),b,18843,a),flip(a)].">
      <j1 rule="hyper" parents="63 18682 18843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18846">
    <literal><![CDATA[
      R(x,y,z \ T(u * K(w,K(v5,v6)),w)) = R(x,y,z \ T(u,K(v6,v5) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,14690,a,b,18844,a)].">
      <j1 rule="hyper" parents="63 14690 18844"/>
    </justification>
  </clause>

  <clause id="18847">
    <literal><![CDATA[
      R(x,y,K(z,K(u,w)) * (v5 \ T(v6,z))) = R(x,y,v5 \ T(v6,K(w,u) * z))
    ]]></literal>
    <justification jstring="[para(17014(a,1),18846(a,1,3))].">
      <j1 rule="para" parents="17014 18846"/>
    </justification>
  </clause>

  <clause id="18848">
    <literal><![CDATA[
      R(x,y,z \ T(u,K(w,v5) * v6)) = R(x,y,z \ T(u,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,18842,a(flip),b,18847,a),flip(a)].">
      <j1 rule="hyper" parents="63 18842 18847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18850">
    <literal><![CDATA[
      K(x,R(y / z,z,y \ T(u,w)) \ T(u,w)) = K(x,z * (y \ T(u,K(v5,v6) * w)))
    ]]></literal>
    <justification jstring="[para(18848(a,1),17496(a,1,2,1))].">
      <j1 rule="para" parents="18848 17496"/>
    </justification>
  </clause>

  <clause id="18851">
    <literal><![CDATA[
      K(x,y * (z \ T(u,K(w,v5) * v6))) = K(x,y * (z \ T(u,v6)))
    ]]></literal>
    <justification jstring="[para(693(a,1),18850(a,1,2)),flip(a)].">
      <j1 rule="para" parents="693 18850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18853">
    <literal><![CDATA[
      K(x,T((y \ T(z,u)) / (w \ 1),w)) = K(x,w * (y \ T(y * L(y \ z,v5,v5 \ 1),u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18837,a(flip),b,18830,a)].">
      <j1 rule="hyper" parents="63 18837 18830"/>
    </justification>
  </clause>

  <clause id="18854">
    <literal><![CDATA[
      K(x,y * (z \ T(z * L(z \ u,w,w \ 1),v5))) = K(x,y * (z \ T(u,v5)))
    ]]></literal>
    <justification jstring="[hyper(13305,a,18853,a),flip(a)].">
      <j1 rule="hyper" parents="13305 18853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18856">
    <literal><![CDATA[
      K(x,y * L(z \ T(u,w),v5,v5 \ 1)) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(18828(a,1),18854(a,1,2,2))].">
      <j1 rule="para" parents="18828 18854"/>
    </justification>
  </clause>

  <clause id="18857">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,w)) \ L(z \ T(u,w),v5,v5 \ 1))) = K(x,(y / (z \ T(u,w))) * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17469,a(flip),b,18856,a)].">
      <j1 rule="hyper" parents="63 17469 18856"/>
    </justification>
  </clause>

  <clause id="18858">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,w)) \ L(z \ T(u,w),v5,v5 \ 1))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),18857(a,2,2))].">
      <j1 rule="para" parents="12 18857"/>
    </justification>
  </clause>

  <clause id="18859">
    <literal><![CDATA[
      K(x,y * a(z \ T(u,w),v5,v5 \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15980,a,18858,a)].">
      <j1 rule="hyper" parents="15980 18858"/>
    </justification>
  </clause>

  <clause id="18862">
    <literal><![CDATA[
      K(x,y * a(z,u,u \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(83(a,1),18859(a,1,2,2,1))].">
      <j1 rule="para" parents="83 18859"/>
    </justification>
  </clause>

  <clause id="18863">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17265,a,b,18862,a)].">
      <j1 rule="hyper" parents="63 17265 18862"/>
    </justification>
  </clause>

  <clause id="18864">
    <literal><![CDATA[
      K(x,y * a(z,u,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(14922(a,1),18862(a,1,2,2))].">
      <j1 rule="para" parents="14922 18862"/>
    </justification>
  </clause>

  <clause id="18865">
    <literal><![CDATA[
      K(x,a(y,z,z) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(16906,a,18864,a)].">
      <j1 rule="hyper" parents="16906 18864"/>
    </justification>
  </clause>

  <clause id="18866">
    <literal><![CDATA[
      T(x,y * a(z,u,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(132,a,18864,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 18864 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18867">
    <literal><![CDATA[
      1 * K(x,a(y,z,z) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(237,a,18865,a)].">
      <j1 rule="hyper" parents="237 18865"/>
    </justification>
  </clause>

  <clause id="18868">
    <literal><![CDATA[
      T(x,a(y,z,z) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,18865,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 18865 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18869">
    <literal><![CDATA[
      K(x,y * L(z,u,u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,17470,a(flip),b,18865,a)].">
      <j1 rule="hyper" parents="63 17470 18865"/>
    </justification>
  </clause>

  <clause id="18870">
    <literal><![CDATA[
      K(x,y / a(z \ 1,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(16904,a,18863,a)].">
      <j1 rule="hyper" parents="16904 18863"/>
    </justification>
  </clause>

  <clause id="18871">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(16652,a,18863,a)].">
      <j1 rule="hyper" parents="16652 18863"/>
    </justification>
  </clause>

  <clause id="18873">
    <literal><![CDATA[
      K(x,a(y,z,z)) * K(u,a(w,v5,v5) * v6) = K(u,v6)
    ]]></literal>
    <justification jstring="[para(12658(a,2),18867(a,1,1))].">
      <j1 rule="para" parents="12658 18867"/>
    </justification>
  </clause>

  <clause id="18875">
    <literal><![CDATA[
      T(x,y * L(z,u,u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(132,a,18869,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 18869 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18876">
    <literal><![CDATA[
      K(x,y * (z / (u \ 1))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15946,a(flip),b,18869,a),flip(a)].">
      <j1 rule="hyper" parents="63 15946 18869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18877">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3188(a,1),18869(a,1,2,2))].">
      <j1 rule="para" parents="3188 18869"/>
    </justification>
  </clause>

  <clause id="18878">
    <literal><![CDATA[
      K(x,y * (a(z \ 1,z,u) \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13309,a,18870,a)].">
      <j1 rule="hyper" parents="13309 18870"/>
    </justification>
  </clause>

  <clause id="18879">
    <literal><![CDATA[
      K(x,a(y,y,z) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16057,a(flip),b,18871,a)].">
      <j1 rule="hyper" parents="63 16057 18871"/>
    </justification>
  </clause>

  <clause id="18881">
    <literal><![CDATA[
      T(x,a(y,y,z) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(132,a,18879,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 18879 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18882">
    <literal><![CDATA[
      T(x,a(y,y,z) * u) = T(x,u * a(w,v5,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,18866,a,b,18881,a),flip(a)].">
      <j1 rule="hyper" parents="347 18866 18881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18883">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y * a(u,u,w)) = z
    ]]></literal>
    <justification jstring="[para(18881(a,1),16875(a,1))].">
      <j1 rule="para" parents="18881 16875"/>
    </justification>
  </clause>

  <clause id="18884">
    <literal><![CDATA[
      T(x,a(y,y,z) * (u * w)) = T(x,u * L(w,v5,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,18881,a,b,18875,a)].">
      <j1 rule="hyper" parents="347 18881 18875"/>
    </justification>
  </clause>

  <clause id="18886">
    <literal><![CDATA[
      T(x,y * L(z,u,u)) = T(x,y * (w * (w \ z)))
    ]]></literal>
    <justification jstring="[para(169(a,2),18875(a,2,2))].">
      <j1 rule="para" parents="169 18875"/>
    </justification>
  </clause>

  <clause id="18887">
    <literal><![CDATA[
      T(x,(y * z) * L(L(u,z,y),w,w)) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(97(a,1),18875(a,2,2))].">
      <j1 rule="para" parents="97 18875"/>
    </justification>
  </clause>

  <clause id="18888">
    <literal><![CDATA[
      T(x,y * ((z * z) \ u)) = T(x,y * (z \ (z \ u)))
    ]]></literal>
    <justification jstring="[para(329(a,1),18875(a,1,2,2))].">
      <j1 rule="para" parents="329 18875"/>
    </justification>
  </clause>

  <clause id="18889">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ u)) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(3192(a,1),18875(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3192 18875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18890">
    <literal><![CDATA[
      T(x,a(y,z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * a(v5,v5,v6)) = w
    ]]></literal>
    <justification jstring="[para(18868(a,2),18883(a,1))].">
      <j1 rule="para" parents="18868 18883"/>
    </justification>
  </clause>

  <clause id="18891">
    <literal><![CDATA[
      K(x,y \ L(z,u,u \ 1)) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(13062,a,18877,a)].">
      <j1 rule="hyper" parents="13062 18877"/>
    </justification>
  </clause>

  <clause id="18892">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,12984,a,b,18877,a),flip(a)].">
      <j1 rule="hyper" parents="347 12984 18877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18894">
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16360,a(flip),b,18877,a)].">
      <j1 rule="hyper" parents="63 16360 18877"/>
    </justification>
  </clause>

  <clause id="18895">
    <literal><![CDATA[
      K(x,y * L(y \ z,u,u \ 1)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),18877(a,2,2))].">
      <j1 rule="para" parents="10 18877"/>
    </justification>
  </clause>

  <clause id="18896">
    <literal><![CDATA[
      (x * (a(y \ 1,y,z) \ 1)) / T(x * (a(y \ 1,y,z) \ 1),u) = K(u,x)
    ]]></literal>
    <justification jstring="[hyper(4940,a,18878,a)].">
      <j1 rule="hyper" parents="4940 18878"/>
    </justification>
  </clause>

  <clause id="18898">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(737(a,1),18895(a,1,2))].">
      <j1 rule="para" parents="737 18895"/>
    </justification>
  </clause>

  <clause id="18900">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(3339(a,1),18895(a,1,2))].">
      <j1 rule="para" parents="3339 18895"/>
    </justification>
  </clause>

  <clause id="18901">
    <literal><![CDATA[
      K(x,y \ L(z,u,u \ 1)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3341(a,1),18895(a,1,2))].">
      <j1 rule="para" parents="3341 18895"/>
    </justification>
  </clause>

  <clause id="18902">
    <literal><![CDATA[
      T(x,L(y,z,z \ 1) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[hyper(132,a,18898,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 18898 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18903">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(18254,a,18900,a),flip(a)].">
      <j1 rule="hyper" parents="18254 18900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18904">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ u) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16050,a(flip),b,18901,a),flip(a)].">
      <j1 rule="hyper" parents="63 16050 18901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18905">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16023,a(flip),b,18901,a),flip(a)].">
      <j1 rule="hyper" parents="63 16023 18901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18906">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) \ u)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(2943(a,1),18901(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2943 18901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18907">
    <literal><![CDATA[
      T(x,((y \ 1) \ z) * u) = T(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(2943(a,1),18902(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2943 18902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18909">
    <literal><![CDATA[
      T(T(x,K(y,z * (z * u))),y / (z \ (z / (u \ 1)))) = T(x,L(u,u,z) \ y)
    ]]></literal>
    <justification jstring="[para(18876(a,1),13823(a,1,1,2))].">
      <j1 rule="para" parents="18876 13823"/>
    </justification>
  </clause>

  <clause id="18910">
    <literal><![CDATA[
      T(x,a(y,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(18882(a,2),11921(a,1))].">
      <j1 rule="para" parents="18882 11921"/>
    </justification>
  </clause>

  <clause id="18911">
    <literal><![CDATA[
      T(x,(y \ 1) \ (z * u)) = T(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,13054,a,b,18889,a)].">
      <j1 rule="hyper" parents="347 13054 18889"/>
    </justification>
  </clause>

  <clause id="18912">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * u)) = T(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,4011,a(flip),b,18889,a),flip(a)].">
      <j1 rule="hyper" parents="63 4011 18889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18914">
    <literal><![CDATA[
      T(x,y * (z * (u \ 1))) = T(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(132,a,18894,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 18894 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18915">
    <literal><![CDATA[
      K(x,T(y,z \ u) * (u / z)) = K(x,(u * (z \ 1)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14842,a(flip),b,18894,a),flip(a)].">
      <j1 rule="hyper" parents="63 14842 18894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18916">
    <literal><![CDATA[
      K(x,y * (z / (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * u)) = w
    ]]></literal>
    <justification jstring="[para(18894(a,1),12132(a,1))].">
      <j1 rule="para" parents="18894 12132"/>
    </justification>
  </clause>

  <clause id="18917">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17720,a(flip),b,18903,a),flip(a)].">
      <j1 rule="hyper" parents="63 17720 18903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18918">
    <literal><![CDATA[
      K(x,y / ((z \ 1) \ u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5597,a(flip),b,18903,a),flip(a)].">
      <j1 rule="hyper" parents="63 5597 18903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18919">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,u / ((u \ z) \ (y \ u))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(18903(a,1),18636(a,1,2))].">
      <j1 rule="para" parents="18903 18636"/>
    </justification>
  </clause>

  <clause id="18921">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ u) = T(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(132,a,18904,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 18904 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18923">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ u)) = T(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(132,a,18906,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 18906 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18924">
    <literal><![CDATA[
      T(x,((y \ 1) * z) * u) = T(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(12023,a,18907,a),flip(a)].">
      <j1 rule="hyper" parents="12023 18907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18925">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * ((z \ 1) * u))) = T(x,y * ((z * z) \ u))
    ]]></literal>
    <justification jstring="[para(499(a,1),18912(a,2,2,2))].">
      <j1 rule="para" parents="499 18912"/>
    </justification>
  </clause>

  <clause id="18926">
    <literal><![CDATA[
      K(x,(y / (z * u)) * a(w,v5,v5 \ 1)) = K(x,y / ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,18862,a,b,18918,a)].">
      <j1 rule="hyper" parents="347 18862 18918"/>
    </justification>
  </clause>

  <clause id="18927">
    <literal><![CDATA[
      T(x,y \ ((1 / z) * u)) = T(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(83(a,1),18923(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="83 18923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18928">
    <literal><![CDATA[
      T(x,L(y,z,u) \ ((y \ 1) \ w)) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(1407(a,1),18923(a,2,2))].">
      <j1 rule="para" parents="1407 18923"/>
    </justification>
  </clause>

  <clause id="18929">
    <literal><![CDATA[
      T(x,a(y,y,z) * (((u \ 1) * w) * v5)) = T(x,(u \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,18881,a,b,18924,a)].">
      <j1 rule="hyper" parents="63 18881 18924"/>
    </justification>
  </clause>

  <clause id="18930">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) * u)) = T(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,5707,a(flip),b,18927,a)].">
      <j1 rule="hyper" parents="63 5707 18927"/>
    </justification>
  </clause>

  <clause id="18931">
    <literal><![CDATA[
      T(x,y * L(z,u,u)) = T(x,y * ((w \ 1) \ (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,18889,a,b,18886,a),flip(a)].">
      <j1 rule="hyper" parents="347 18889 18886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18932">
    <literal><![CDATA[
      K(x,y \ L(z,u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = w
    ]]></literal>
    <justification jstring="[para(18891(a,2),13062(a,1))].">
      <j1 rule="para" parents="18891 13062"/>
    </justification>
  </clause>

  <clause id="18933">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = w
    ]]></literal>
    <justification jstring="[para(18892(a,2),13242(a,1))].">
      <j1 rule="para" parents="18892 13242"/>
    </justification>
  </clause>

  <clause id="18934">
    <literal><![CDATA[
      (x * a(y,z,z)) / T(a(y,z,z) * x,u) = K(u,x)
    ]]></literal>
    <justification jstring="[hyper(6312,a,18873,a)].">
      <j1 rule="hyper" parents="6312 18873"/>
    </justification>
  </clause>

  <clause id="18935">
    <literal><![CDATA[
      T(x,y * L(z,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = w
    ]]></literal>
    <justification jstring="[para(18884(a,1),11983(a,1))].">
      <j1 rule="para" parents="18884 11983"/>
    </justification>
  </clause>

  <clause id="18936">
    <literal><![CDATA[
      T(x,(y \ z) * L(u,w,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,((y \ 1) * z) * u) = v5
    ]]></literal>
    <justification jstring="[para(18924(a,1),18935(a,1))].">
      <j1 rule="para" parents="18924 18935"/>
    </justification>
  </clause>

  <clause id="18937">
    <literal><![CDATA[
      T(T(x,y * (z \ (z \ u))),w) = T(T(x,y * u),z \ (z \ w))
    ]]></literal>
    <justification jstring="[para(18888(a,1),16103(a,1,1))].">
      <j1 rule="para" parents="18888 16103"/>
    </justification>
  </clause>

  <clause id="18938">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (z * u)) = w
    ]]></literal>
    <justification jstring="[para(18911(a,1),13173(a,1))].">
      <j1 rule="para" parents="18911 13173"/>
    </justification>
  </clause>

  <clause id="18939">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (z / u)) = w
    ]]></literal>
    <justification jstring="[para(18917(a,1),17619(a,1))].">
      <j1 rule="para" parents="18917 17619"/>
    </justification>
  </clause>

  <clause id="18940">
    <literal><![CDATA[
      K(x,y \ (z * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z / u)) = w
    ]]></literal>
    <justification jstring="[para(15950(a,1),18932(a,1))].">
      <j1 rule="para" parents="15950 18932"/>
    </justification>
  </clause>

  <clause id="18941">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ L(u,w,w \ 1)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ z) \ u) = v5
    ]]></literal>
    <justification jstring="[para(18905(a,2),18932(a,1))].">
      <j1 rule="para" parents="18905 18932"/>
    </justification>
  </clause>

  <clause id="18942">
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z / u)) = w
    ]]></literal>
    <justification jstring="[para(16360(a,1),18933(a,1))].">
      <j1 rule="para" parents="16360 18933"/>
    </justification>
  </clause>

  <clause id="18943">
    <literal><![CDATA[
      T(a(x,y,y) * z,u) = T(z,u) * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,5196,a,b,18934,a),flip(a)].">
      <j1 rule="hyper" parents="36 5196 18934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18944">
    <literal><![CDATA[
      T(x,y * L(z,u,u)) = T(x,y * (z * a(w,w,z)))
    ]]></literal>
    <justification jstring="[para(15286(a,1),18931(a,2,2,2))].">
      <j1 rule="para" parents="15286 18931"/>
    </justification>
  </clause>

  <clause id="18946">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / (u * (w \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / w)) = v5
    ]]></literal>
    <justification jstring="[para(18900(a,2),18939(a,1))].">
      <j1 rule="para" parents="18900 18939"/>
    </justification>
  </clause>

  <clause id="18947">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w \ K(u,z)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u \ z) / w)) = v5
    ]]></literal>
    <justification jstring="[para(17684(a,2),18942(a,1))].">
      <j1 rule="para" parents="17684 18942"/>
    </justification>
  </clause>

  <clause id="18948">
    <literal><![CDATA[
      T(x,y * (z * L(u,w,w))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(474(a,1),18887(a,1,2))].">
      <j1 rule="para" parents="474 18887"/>
    </justification>
  </clause>

  <clause id="18949">
    <literal><![CDATA[
      T(x,y * (z * ((u * u) \ w))) = T(x,y * (z * (u \ (u \ w))))
    ]]></literal>
    <justification jstring="[para(329(a,1),18948(a,1,2,2,2))].">
      <j1 rule="para" parents="329 18948"/>
    </justification>
  </clause>

  <clause id="18950">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14840,a(flip),b,18915,a),flip(a)].">
      <j1 rule="hyper" parents="63 14840 18915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18951">
    <literal><![CDATA[
      K(x,(y / (1 / z)) * u) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(83(a,1),18950(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="83 18950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18952">
    <literal><![CDATA[
      K(x,(y / (z \ 1)) * u) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(12026,a,18951,a)].">
      <j1 rule="hyper" parents="12026 18951"/>
    </justification>
  </clause>

  <clause id="18953">
    <literal><![CDATA[
      T(x,(y / (z \ 1)) * u) = T(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(132,a,18952,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 18952 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18954">
    <literal><![CDATA[
      T(x,a(y,y,z) * ((u \ K(w \ 1,(w \ 1) \ (u \ 1))) * v5)) = T(x,(w \ ((u \ 1) / (w \ 1))) * v5)
    ]]></literal>
    <justification jstring="[para(9560(a,2),18929(a,1,2,2,1))].">
      <j1 rule="para" parents="9560 18929"/>
    </justification>
  </clause>

  <clause id="18955">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * ((z \ 1) * u))) = T(x,y * (z \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,18888,a(flip),b,18925,a),flip(a)].">
      <j1 rule="hyper" parents="347 18888 18925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18956">
    <literal><![CDATA[
      T(x,L(y,z,u) \ (y * w)) = T(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18923,a(flip),b,18928,a)].">
      <j1 rule="hyper" parents="63 18923 18928"/>
    </justification>
  </clause>

  <clause id="18957">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ (y \ w))) = T(x,L(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(10(a,1),18956(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 18956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18958">
    <literal><![CDATA[
      T(T(x,y * ((z / u) * (u \ z))),(z / u) \ ((z / u) \ w)) = T(T(x,y * (u \ (z / T(z / u,z / u)))),w)
    ]]></literal>
    <justification jstring="[para(8710(a,1),18937(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8710 18937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18959">
    <literal><![CDATA[
      T(T(x,y * (z * (u \ (u \ w)))),v5) = T(T(x,y * (z * w)),u \ (u \ v5))
    ]]></literal>
    <justification jstring="[para(18949(a,1),16113(a,1,1))].">
      <j1 rule="para" parents="18949 16113"/>
    </justification>
  </clause>

  <clause id="18960">
    <literal><![CDATA[
      K(x,y / ((z \ 1) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (z * u)) = w
    ]]></literal>
    <justification jstring="[para(18926(a,1),11946(a,1))].">
      <j1 rule="para" parents="18926 11946"/>
    </justification>
  </clause>

  <clause id="18962">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ z) \ u) = w
    ]]></literal>
    <justification jstring="[para(534(a,1),18941(a,1,2,2))].">
      <j1 rule="para" parents="534 18941"/>
    </justification>
  </clause>

  <clause id="18963">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ R(u,w,w \ 1)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ z) \ u) = v5
    ]]></literal>
    <justification jstring="[para(15948(a,2),18941(a,1))].">
      <j1 rule="para" parents="15948 18941"/>
    </justification>
  </clause>

  <clause id="18965">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(15065(a,2),18946(a,1))].">
      <j1 rule="para" parents="15065 18946"/>
    </justification>
  </clause>

  <clause id="18966">
    <literal><![CDATA[
      K(x,L((y * z) * u,y,z \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / ((u \ 1) / z)) = w
    ]]></literal>
    <justification jstring="[para(13443(a,1),18965(a,1))].">
      <j1 rule="para" parents="13443 18965"/>
    </justification>
  </clause>

  <clause id="18967">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15947(a,2),18963(a,1))].">
      <j1 rule="para" parents="15947 18963"/>
    </justification>
  </clause>

  <clause id="18968">
    <literal><![CDATA[
      K(x,((y / (z * y)) * u) \ y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ u) \ y) = w
    ]]></literal>
    <justification jstring="[para(18116(a,1),18967(a,1))].">
      <j1 rule="para" parents="18116 18967"/>
    </justification>
  </clause>

  <clause id="18969">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u \ z) \ y) = w
    ]]></literal>
    <justification jstring="[para(18366(a,1),18968(a,1))].">
      <j1 rule="para" parents="18366 18968"/>
    </justification>
  </clause>

  <clause id="18970">
    <literal><![CDATA[
      K(x,y / (T((z \ u) \ 1,u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (((u / z) \ 1) / w)) = v5
    ]]></literal>
    <justification jstring="[para(18497(a,1),18966(a,1))].">
      <j1 rule="para" parents="18497 18966"/>
    </justification>
  </clause>

  <clause id="18971">
    <literal><![CDATA[
      T(x * (a(y \ 1,y,z) \ 1),u) = T(x,u) * (a(y \ 1,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,5196,a,b,18896,a),flip(a)].">
      <j1 rule="hyper" parents="36 5196 18896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18972">
    <literal><![CDATA[
      T(x * (a(y \ 1,y,z) \ 1),u) / (x * (a(y \ 1,y,z) \ 1)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(131,a,18971,a,b,4974,a)].">
      <j1 rule="hyper" parents="131 18971 4974"/>
    </justification>
  </clause>

  <clause id="18973">
    <literal><![CDATA[
      K(x * (a(y \ 1,y,z) \ 1),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(5031,a,18972,a)].">
      <j1 rule="hyper" parents="5031 18972"/>
    </justification>
  </clause>

  <clause id="18974">
    <literal><![CDATA[
      K(x / a(y \ 1,y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(13302,a,18973,a)].">
      <j1 rule="hyper" parents="13302 18973"/>
    </justification>
  </clause>

  <clause id="18975">
    <literal><![CDATA[
      K(a(x \ 1,x,y) \ z,u) = K(z,u)
    ]]></literal>
    <justification jstring="[hyper(16903,a,18974,a)].">
      <j1 rule="hyper" parents="16903 18974"/>
    </justification>
  </clause>

  <clause id="18976">
    <literal><![CDATA[
      K(a(x \ 1,x,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = w
    ]]></literal>
    <justification jstring="[para(18975(a,1),7205(a,1))].">
      <j1 rule="para" parents="18975 7205"/>
    </justification>
  </clause>

  <clause id="18977">
    <literal><![CDATA[
      K(a(x,x,y) * z,u) = K(z,u)
    ]]></literal>
    <justification jstring="[hyper(18976,a,16060,a),flip(a)].">
      <j1 rule="hyper" parents="18976 16060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18978">
    <literal><![CDATA[
      (a(x,x,y) * z) * K(z,u) = T(a(x,x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(134,a,18977,a(flip),b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 18977 4924"/>
    </justification>
  </clause>

  <clause id="18979">
    <literal><![CDATA[
      T(a(x,x,y) * z,u) = a(x,x,y) * T(z,u)
    ]]></literal>
    <justification jstring="[hyper(5973,a,18978,a),flip(a)].">
      <j1 rule="hyper" parents="5973 18978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18980">
    <literal><![CDATA[
      T(a(x,x,y) * (x \ 1),y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,14746,a(flip),b,18979,a),flip(a)].">
      <j1 rule="hyper" parents="347 14746 18979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18981">
    <literal><![CDATA[
      T(x \ a(x,x,y),y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[para(15268(a,1),18980(a,1,1))].">
      <j1 rule="para" parents="15268 18980"/>
    </justification>
  </clause>

  <clause id="18982">
    <literal><![CDATA[
      x \ a(x,x,y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(279,a,18981,a),flip(a)].">
      <j1 rule="hyper" parents="279 18981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18983">
    <literal><![CDATA[
      (x \ a(x,x,y)) * y = x \ y
    ]]></literal>
    <justification jstring="[hyper(152,a,18981,a)].">
      <j1 rule="hyper" parents="152 18981"/>
    </justification>
  </clause>

  <clause id="18984">
    <literal><![CDATA[
      T(x,T(y \ a(y,y,z \ 1),z \ 1) * u) = T(x,((1 / z) \ (y \ (z \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(18981(a,2),14689(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="18981 14689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18985">
    <literal><![CDATA[
      a(x,x,y) / ((x \ y) / y) = x
    ]]></literal>
    <justification jstring="[hyper(222,a,18982,a)].">
      <j1 rule="hyper" parents="222 18982"/>
    </justification>
  </clause>

  <clause id="18986">
    <literal><![CDATA[
      x * ((x \ y) / y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(150,a,18982,a)].">
      <j1 rule="hyper" parents="150 18982"/>
    </justification>
  </clause>

  <clause id="18987">
    <literal><![CDATA[
      x * (y \ a(y,y,x)) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,18982,a,b,3836,a)].">
      <j1 rule="hyper" parents="134 18982 3836"/>
    </justification>
  </clause>

  <clause id="18988">
    <literal><![CDATA[
      x \ R(x,x,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(38,a,2376,a,b,18982,a)].">
      <j1 rule="hyper" parents="38 2376 18982"/>
    </justification>
  </clause>

  <clause id="18989">
    <literal><![CDATA[
      L(x \ y,x,z \ a(z,z,x)) = (z \ x) \ (((z \ x) / x) * y)
    ]]></literal>
    <justification jstring="[para(18982(a,2),565(a,1,3))].">
      <j1 rule="para" parents="18982 565"/>
    </justification>
  </clause>

  <clause id="18990">
    <literal><![CDATA[
      x * a(x,x,y) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(150,a,18988,a)].">
      <j1 rule="hyper" parents="150 18988"/>
    </justification>
  </clause>

  <clause id="18991">
    <literal><![CDATA[
      a(x,x,x * y) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,2378,a(flip),b,18988,a),flip(a)].">
      <j1 rule="hyper" parents="63 2378 18988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18992">
    <literal><![CDATA[
      K(x,x \ y) * R(x,x,z) = ((x \ y) \ y) * a(x,x,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,18988,a(flip),b,5194,a),flip(a)].">
      <j1 rule="hyper" parents="134 18988 5194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18993">
    <literal><![CDATA[
      a(x,x,y) * x = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,18988,a(flip),b,3675,a)].">
      <j1 rule="hyper" parents="133 18988 3675"/>
    </justification>
  </clause>

  <clause id="18994">
    <literal><![CDATA[
      (a(x,x,y) / x) * y = L(x,x,x) \ y
    ]]></literal>
    <justification jstring="[para(18988(a,1),3450(a,1,1,1))].">
      <j1 rule="para" parents="18988 3450"/>
    </justification>
  </clause>

  <clause id="18995">
    <literal><![CDATA[
      R(x,x,y) \ x = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(18988(a,1),4742(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18988 4742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18996">
    <literal><![CDATA[
      x \ R(x,x,y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * a(x,x,y) = u
    ]]></literal>
    <justification jstring="[para(18990(a,1),637(a,1,2))].">
      <j1 rule="para" parents="18990 637"/>
    </justification>
  </clause>

  <clause id="18997">
    <literal><![CDATA[
      (a(x,x,y) * z) \ (x \ (R(x,x,y) * z)) = a(x,a(x,x,y),z)
    ]]></literal>
    <justification jstring="[para(18990(a,1),14699(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="18990 14699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18998">
    <literal><![CDATA[
      (x \ y) * L(z,y,x \ a(x,x,y)) = (x \ a(x,x,y)) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,18983,a(flip),b,212,a)].">
      <j1 rule="hyper" parents="133 18983 212"/>
    </justification>
  </clause>

  <clause id="18999">
    <literal><![CDATA[
      (x \ a(x,x,y * z)) * (z * y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(14642(a,1),18983(a,1,1,2))].">
      <j1 rule="para" parents="14642 18983"/>
    </justification>
  </clause>

  <clause id="19000">
    <literal><![CDATA[
      (x \ y) \ (z \ ((z * (x \ a(x,x,y))) * y)) = a(z,x \ a(x,x,y),y)
    ]]></literal>
    <justification jstring="[para(18983(a,1),14699(a,2,1)),flip(a)].">
      <j1 rule="para" parents="18983 14699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19001">
    <literal><![CDATA[
      (x \ a(x,x,y)) * (y \ 1) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(14922(a,1),18983(a,1,1,2))].">
      <j1 rule="para" parents="14922 18983"/>
    </justification>
  </clause>

  <clause id="19002">
    <literal><![CDATA[
      T(x,(y * ((z \ a(z,z,y)) * (y \ 1))) * u) = T(x,((y \ 1) * (z \ y)) * u)
    ]]></literal>
    <justification jstring="[para(18983(a,1),16030(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="18983 16030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19003">
    <literal><![CDATA[
      a(x \ y,x \ y,y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(13348,a,18986,a),flip(a)].">
      <j1 rule="hyper" parents="13348 18986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19004">
    <literal><![CDATA[
      a(x \ y,x \ y,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y / x) * (x / y) = z
    ]]></literal>
    <justification jstring="[para(18986(a,1),13348(a,1))].">
      <j1 rule="para" parents="18986 13348"/>
    </justification>
  </clause>

  <clause id="19005">
    <literal><![CDATA[
      L(x,R(y,y,z) \ y,R(y,y,z) \ y) / (((R(y,y,z) \ y) \ 1) * x) = a(y,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,3201,a,b,18995,a)].">
      <j1 rule="hyper" parents="63 3201 18995"/>
    </justification>
  </clause>

  <clause id="19006">
    <literal><![CDATA[
      x * R(1 / x,x,y) = a(x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,418,a,b,18991,a)].">
      <j1 rule="hyper" parents="347 418 18991"/>
    </justification>
  </clause>

  <clause id="19008">
    <literal><![CDATA[
      (x * y) * (x * (y / (x * y))) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(18991(a,1),15282(a,1,2))].">
      <j1 rule="para" parents="18991 15282"/>
    </justification>
  </clause>

  <clause id="19009">
    <literal><![CDATA[
      T(a(x,x,y) / x,y) = y \ (L(x,x,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(462,a,xx,b,18994,a)].">
      <j1 rule="hyper" parents="462 18994"/>
    </justification>
  </clause>

  <clause id="19010">
    <literal><![CDATA[
      x \ a(x,x,y * x) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,18773,a,b,19006,a)].">
      <j1 rule="hyper" parents="128 18773 19006"/>
    </justification>
  </clause>

  <clause id="19011">
    <literal><![CDATA[
      (x * y) \ ((x \ 1) \ y) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(138,a,19008,a)].">
      <j1 rule="hyper" parents="138 19008"/>
    </justification>
  </clause>

  <clause id="19012">
    <literal><![CDATA[
      (x * y) \ ((y \ 1) \ x) = T(y,x) * (x / (y * x))
    ]]></literal>
    <justification jstring="[hyper(128,a,19008,a(flip),b,10284,a)].">
      <j1 rule="hyper" parents="128 19008 10284"/>
    </justification>
  </clause>

  <clause id="19013">
    <literal><![CDATA[
      x \ y != z * (u / (z * u))
    ]]></literal>
    <literal><![CDATA[
      x * a(z,z,z * u) = y
    ]]></literal>
    <justification jstring="[para(2378(a,1),18996(a,1)),flip(a)].">
      <j1 rule="para" parents="2378 18996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19014">
    <literal><![CDATA[
      (x * y) \ ((y \ 1) \ x) = y * (x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,9875,a(flip),b,19012,a),flip(a)].">
      <j1 rule="hyper" parents="347 9875 19012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19015">
    <literal><![CDATA[
      (a(x,x,y) * z) \ (R(x,x,y) * (x \ z)) = a(x,a(x,x,y),z)
    ]]></literal>
    <justification jstring="[para(1746(a,1),18997(a,1,2))].">
      <j1 rule="para" parents="1746 18997"/>
    </justification>
  </clause>

  <clause id="19016">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / (u \ (u / (z \ 1)))) = T(x,L(z,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(13479(a,1),18909(a,1,1))].">
      <j1 rule="para" parents="13479 18909"/>
    </justification>
  </clause>

  <clause id="19018">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,u / ((z \ u) * (y \ u))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(16032(a,1),18919(a,1,2))].">
      <j1 rule="para" parents="16032 18919"/>
    </justification>
  </clause>

  <clause id="19019">
    <literal><![CDATA[
      T(x,((y \ 1) * (z \ y)) * u) = T(x,(y * (z \ (y \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(19001(a,1),19002(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="19001 19002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19020">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,(y * T(z,u)) / u) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(18372(a,1),19018(a,1,2))].">
      <j1 rule="para" parents="18372 19018"/>
    </justification>
  </clause>

  <clause id="19021">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18119,a(flip),b,19020,a)].">
      <j1 rule="hyper" parents="63 18119 19020"/>
    </justification>
  </clause>

  <clause id="19022">
    <literal><![CDATA[
      K(x,y / (z \ u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(18251,a,19021,a)].">
      <j1 rule="hyper" parents="18251 19021"/>
    </justification>
  </clause>

  <clause id="19023">
    <literal><![CDATA[
      K(x,y * (z \ (u \ 1))) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(18960,a,19022,a),flip(a)].">
      <j1 rule="hyper" parents="18960 19022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19024">
    <literal><![CDATA[
      T(x,y / (z \ u)) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(132,a,19022,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 19022 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19025">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y * (T(z,u) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18917,a(flip),b,19022,a)].">
      <j1 rule="hyper" parents="63 18917 19022"/>
    </justification>
  </clause>

  <clause id="19026">
    <literal><![CDATA[
      K(x,y * ((T(z,u) * y) \ u)) = K(x,y \ ((y * u) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18695,a(flip),b,19022,a),flip(a)].">
      <j1 rule="hyper" parents="63 18695 19022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19027">
    <literal><![CDATA[
      x * K(y,x * ((z * x) \ (u * z))) = (x * z) / (z * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(134,a,19022,a(flip),b,18647,a(flip))].">
      <j1 rule="hyper" parents="134 19022 18647"/>
    </justification>
  </clause>

  <clause id="19028">
    <literal><![CDATA[
      K(x,y * (z \ u)) * x = T(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(133,a,19022,a(flip),b,4969,a(flip))].">
      <j1 rule="hyper" parents="133 19022 4969"/>
    </justification>
  </clause>

  <clause id="19029">
    <literal><![CDATA[
      K(x,y * ((z / u) \ (w \ K(z,u)))) = K(x,y / (w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(17774,a,19023,a)].">
      <j1 rule="hyper" parents="17774 19023"/>
    </justification>
  </clause>

  <clause id="19030">
    <literal><![CDATA[
      T(x,y / (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u \ z)) = w
    ]]></literal>
    <justification jstring="[para(19028(a,1),4987(a,1))].">
      <j1 rule="para" parents="19028 4987"/>
    </justification>
  </clause>

  <clause id="19031">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(347,a,17281,a(flip),b,19025,a),flip(a)].">
      <j1 rule="hyper" parents="347 17281 19025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19032">
    <literal><![CDATA[
      K(x,y / (z / u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(18939,a,19031,a)].">
      <j1 rule="hyper" parents="18939 19031"/>
    </justification>
  </clause>

  <clause id="19033">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,(z \ y) * (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18631,a,b,19032,a)].">
      <j1 rule="hyper" parents="63 18631 19032"/>
    </justification>
  </clause>

  <clause id="19034">
    <literal><![CDATA[
      K(x,y \ ((y * z) / u)) = K(x,(z / (y * u)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,17288,a(flip),b,19026,a),flip(a)].">
      <j1 rule="hyper" parents="63 17288 19026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19035">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,(z \ y) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,18876,a(flip),b,19033,a),flip(a)].">
      <j1 rule="hyper" parents="347 18876 19033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19036">
    <literal><![CDATA[
      T(x,T(y \ a(y,y,z \ 1),z \ 1) * u) = T(x,((z \ 1) \ (y \ (z \ 1))) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,14689,a(flip),b,18984,a),flip(a)].">
      <j1 rule="hyper" parents="347 14689 18984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19037">
    <literal><![CDATA[
      T(x,T(y \ a(y,y,z),z \ 1) * u) = T(x,((z \ 1) \ (y \ (z \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(14922(a,1),19036(a,1,2,1,1,2))].">
      <j1 rule="para" parents="14922 19036"/>
    </justification>
  </clause>

  <clause id="19038">
    <literal><![CDATA[
      T(x,T(y \ a(y,y,z),z) * u) = T(x,((z \ 1) \ (y \ (z \ 1))) * u)
    ]]></literal>
    <justification jstring="[hyper(16109,a,19037,a)].">
      <j1 rule="hyper" parents="16109 19037"/>
    </justification>
  </clause>

  <clause id="19039">
    <literal><![CDATA[
      T(x,((y \ 1) \ (z \ (y \ 1))) * u) = T(x,(y \ (z \ y)) * u)
    ]]></literal>
    <justification jstring="[para(18981(a,1),19038(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18981 19038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19041">
    <literal><![CDATA[
      T(x,a(y,y,z) * ((u \ K(w \ 1,w / u)) * v5)) = T(x,(w \ ((u \ 1) / (w \ 1))) * v5)
    ]]></literal>
    <justification jstring="[para(13070(a,1),18954(a,1,2,2,1,2))].">
      <j1 rule="para" parents="13070 18954"/>
    </justification>
  </clause>

  <clause id="19042">
    <literal><![CDATA[
      T(x,a(y,y,z) * ((u \ K(w \ 1,u \ w)) * v5)) = T(x,(w \ ((u \ 1) / (w \ 1))) * v5)
    ]]></literal>
    <justification jstring="[para(7644(a,1),19041(a,1,2,2,1,2))].">
      <j1 rule="para" parents="7644 19041"/>
    </justification>
  </clause>

  <clause id="19043">
    <literal><![CDATA[
      T(x,a(y,y,z) * (T(u \ 1,w) * v5)) = T(x,(w \ ((u \ 1) / (w \ 1))) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,17797,a(flip),b,19042,a)].">
      <j1 rule="hyper" parents="63 17797 19042"/>
    </justification>
  </clause>

  <clause id="19044">
    <literal><![CDATA[
      T(x,(y \ ((z \ 1) / (y \ 1))) * u) = T(x,T(z \ 1,y) * u)
    ]]></literal>
    <justification jstring="[hyper(18910,a,19043,a),flip(a)].">
      <j1 rule="hyper" parents="18910 19043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19045">
    <literal><![CDATA[
      T(x,(y \ ((z \ 1) / (y \ 1))) * u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,15896,a(flip),b,19044,a),flip(a)].">
      <j1 rule="hyper" parents="347 15896 19044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19046">
    <literal><![CDATA[
      T(x,(a(y,z,z) \ ((a(y,z,z) \ 1) \ (u \ 1))) * w) = T(x,T(u,a(y,z,z)) \ w)
    ]]></literal>
    <justification jstring="[para(14935(a,1),19045(a,1,2,1,2))].">
      <j1 rule="para" parents="14935 19045"/>
    </justification>
  </clause>

  <clause id="19047">
    <literal><![CDATA[
      T(T(x,y * ((z / u) * (u \ z))),(z / u) \ ((z / u) \ w)) = T(T(x,y * (u \ (z / (z / u)))),w)
    ]]></literal>
    <justification jstring="[para(110(a,1),18958(a,2,1,2,2,2,2))].">
      <j1 rule="para" parents="110 18958"/>
    </justification>
  </clause>

  <clause id="19048">
    <literal><![CDATA[
      T(T(x,y * ((z / u) * (u \ z))),(z / u) \ ((z / u) \ w)) = T(T(x,y * K(u \ z,u)),w)
    ]]></literal>
    <justification jstring="[para(4893(a,1),19047(a,2,1,2,2))].">
      <j1 rule="para" parents="4893 19047"/>
    </justification>
  </clause>

  <clause id="19049">
    <literal><![CDATA[
      T(T(x,y * ((z / u) * (u \ z))),(z / u) \ ((z / u) \ w)) = T(T(x,K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[para(13650(a,1),19048(a,2,1))].">
      <j1 rule="para" parents="13650 19048"/>
    </justification>
  </clause>

  <clause id="19050">
    <literal><![CDATA[
      x / K(y,L(z,(z / u) \ 1,((T(z,T(y,u)) / u) \ 1) \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(11049(a,1),17083(a,1,2))].">
      <j1 rule="para" parents="11049 17083"/>
    </justification>
  </clause>

  <clause id="19051">
    <literal><![CDATA[
      (x * ((y * K(z,u)) * w)) \ (x * (y * (K(z,u) * w))) = L(a(w,K(z,u),y),(y * K(z,u)) * w,x)
    ]]></literal>
    <justification jstring="[para(97(a,1),17897(a,1,2,2))].">
      <j1 rule="para" parents="97 17897"/>
    </justification>
  </clause>

  <clause id="19052">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,((T(z,T(y,u)) / u) \ 1) \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(12413(a,1),19050(a,1,2,2))].">
      <j1 rule="para" parents="12413 19050"/>
    </justification>
  </clause>

  <clause id="19053">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,x * (T(z,T(y,u)) / u))) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(18803(a,1),19052(a,1,2))].">
      <j1 rule="para" parents="18803 19052"/>
    </justification>
  </clause>

  <clause id="19054">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,x * (T(z,y) / u))) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(18765(a,1),19053(a,1,2,2))].">
      <j1 rule="para" parents="18765 19053"/>
    </justification>
  </clause>

  <clause id="19055">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,x * (u \ T(z,y)))) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(18032(a,1),19054(a,1,2))].">
      <j1 rule="para" parents="18032 19054"/>
    </justification>
  </clause>

  <clause id="19056">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,u \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(17327(a,1),19055(a,1,2))].">
      <j1 rule="para" parents="17327 19055"/>
    </justification>
  </clause>

  <clause id="19058">
    <literal><![CDATA[
      x / K(y,L(z,u,u \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(18377(a,1),19056(a,1,2))].">
      <j1 rule="para" parents="18377 19056"/>
    </justification>
  </clause>

  <clause id="19059">
    <literal><![CDATA[
      (x / (((y / z) \ 1) * K(u,y))) * ((y / z) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(19058(a,1),13786(a,1))].">
      <j1 rule="para" parents="19058 13786"/>
    </justification>
  </clause>

  <clause id="19060">
    <literal><![CDATA[
      (x / ((y / z) \ 1)) * ((y / z) \ K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(18588(a,1),19059(a,1))].">
      <j1 rule="para" parents="18588 19059"/>
    </justification>
  </clause>

  <clause id="19061">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * (w * v5))) \ ((u * (K(x,K(y,z)) * w)) * v5) = a(u,K(x,K(y,z)) * w,L(v5,w,K(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(16999(a,2),16854(a,1,1))].">
      <j1 rule="para" parents="16999 16854"/>
    </justification>
  </clause>

  <clause id="19062">
    <literal><![CDATA[
      (K(x,y) * (z * (K(y,x) * L(K(x,y),u,w)))) * a(x,z,K(K(x,y) * K(y,x),y)) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[para(17275(a,1),18653(a,1,2,3))].">
      <j1 rule="para" parents="17275 18653"/>
    </justification>
  </clause>

  <clause id="19063">
    <literal><![CDATA[
      (K(x,y) * (z * (K(y,x) * L(K(x,y),u,w)))) * a(x,z,K(1,y)) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[para(5160(a,1),19062(a,1,2,3,1))].">
      <j1 rule="para" parents="5160 19062"/>
    </justification>
  </clause>

  <clause id="19065">
    <literal><![CDATA[
      (K(x,y) * (z * (K(y,x) * L(K(x,y),u,w)))) * 1 = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[para(557(a,1),19063(a,1,2))].">
      <j1 rule="para" parents="557 19063"/>
    </justification>
  </clause>

  <clause id="19067">
    <literal><![CDATA[
      K(x,y) * (z * (K(y,x) * L(K(x,y),u,w))) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[hyper(142,a,19065,a)].">
      <j1 rule="hyper" parents="142 19065"/>
    </justification>
  </clause>

  <clause id="19069">
    <literal><![CDATA[
      K(x,y) * (z * a(x,u,K(w,y))) = L(K(x,y),u,w) * z
    ]]></literal>
    <justification jstring="[para(13970(a,1),19067(a,1,2,2))].">
      <j1 rule="para" parents="13970 19067"/>
    </justification>
  </clause>

  <clause id="19070">
    <literal><![CDATA[
      L(K(x,y),z * a(x,u,K(w,y)),v5) \ ((L(K(x,y),u,w) * z) * v5) = (z * a(x,u,K(w,y))) * v5
    ]]></literal>
    <justification jstring="[para(19069(a,1),14113(a,1,2,1))].">
      <j1 rule="para" parents="19069 14113"/>
    </justification>
  </clause>

  <clause id="19071">
    <literal><![CDATA[
      K(x,y) \ ((L(K(x,y),z,u) * w) * K(v5,v6)) = (w * a(x,z,K(u,y))) * K(v5,v6)
    ]]></literal>
    <justification jstring="[para(16861(a,1),19070(a,1,1))].">
      <j1 rule="para" parents="16861 19070"/>
    </justification>
  </clause>

  <clause id="19072">
    <literal><![CDATA[
      K(x,y) \ (L(K(x,y),z,u) * (w * K(v5,v6))) = (w * a(x,z,K(u,y))) * K(v5,v6)
    ]]></literal>
    <justification jstring="[para(16899(a,1),19071(a,1,2))].">
      <j1 rule="para" parents="16899 19071"/>
    </justification>
  </clause>

  <clause id="19073">
    <literal><![CDATA[
      T(x * a(y,z,K(u,w)),K(y,w)) = L(K(y,w),z,u) * (x * K(w,y))
    ]]></literal>
    <justification jstring="[hyper(7534,a,19072,a)].">
      <j1 rule="hyper" parents="7534 19072"/>
    </justification>
  </clause>

  <clause id="19074">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * (w * v5))) \ ((K(x,K(y,z)) \ (u * w)) * v5) = a(u,K(x,K(y,z)) * w,L(v5,w,K(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(16999(a,2),19061(a,1,2,1))].">
      <j1 rule="para" parents="16999 19061"/>
    </justification>
  </clause>

  <clause id="19075">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * (w * v5))) \ (K(x,K(y,z)) \ ((u * w) * v5)) = a(u,K(x,K(y,z)) * w,L(v5,w,K(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(16852(a,2),19074(a,1,2))].">
      <j1 rule="para" parents="16852 19074"/>
    </justification>
  </clause>

  <clause id="19076">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) * w,L(v5,w,K(y,K(z,u)))) = (x * (w * v5)) \ ((x * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,16965,a(flip),b,19075,a),flip(a)].">
      <j1 rule="hyper" parents="63 16965 19075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19078">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) * w,L(v5,w,K(y,K(z,u)))) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,14,a,b,19076,a),flip(a)].">
      <j1 rule="hyper" parents="347 14 19076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19079">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) * w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(16829(a,1),19078(a,1,3))].">
      <j1 rule="para" parents="16829 19078"/>
    </justification>
  </clause>

  <clause id="19080">
    <literal><![CDATA[
      a(x,T(y,K(z,u)),w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(15000,a,19079,a),flip(a)].">
      <j1 rule="hyper" parents="15000 19079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19081">
    <literal><![CDATA[
      a(x,K(y,z) * u,w) = a(x,u * K(y,z),w)
    ]]></literal>
    <justification jstring="[para(4909(a,1),19079(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4909 19079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19082">
    <literal><![CDATA[
      a(x,y * K(z,K(u,w)),v5) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[para(7372(a,1),19079(a,1,2))].">
      <j1 rule="para" parents="7372 19079"/>
    </justification>
  </clause>

  <clause id="19083">
    <literal><![CDATA[
      a(x,K(y,T(z,u)),w) = a(x,K(y,z),w)
    ]]></literal>
    <justification jstring="[para(7263(a,1),19079(a,1,2))].">
      <j1 rule="para" parents="7263 19079"/>
    </justification>
  </clause>

  <clause id="19085">
    <literal><![CDATA[
      a(x,y \ (T(z,K(u,w)) \ v5),v6) = a(x,y \ (z \ v5),v6)
    ]]></literal>
    <justification jstring="[para(17029(a,1),19079(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17029 19079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19086">
    <literal><![CDATA[
      a(T(x,K(y,z)),u,w) = a(x,u * K(v5,K(v6,v7)),w)
    ]]></literal>
    <justification jstring="[hyper(17834,a,19082,a),flip(a)].">
      <j1 rule="hyper" parents="17834 19082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19087">
    <literal><![CDATA[
      a(x,y * K(z,K(u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,v5) = v6
    ]]></literal>
    <justification jstring="[para(19086(a,1),17834(a,1))].">
      <j1 rule="para" parents="19086 17834"/>
    </justification>
  </clause>

  <clause id="19088">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(7076(a,1),19087(a,1,2))].">
      <j1 rule="para" parents="7076 19087"/>
    </justification>
  </clause>

  <clause id="19089">
    <literal><![CDATA[
      a(x,y,z * K(u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(17823(a,1),19088(a,1))].">
      <j1 rule="para" parents="17823 19088"/>
    </justification>
  </clause>

  <clause id="19091">
    <literal><![CDATA[
      a(x,y,T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(4929(a,2),19089(a,1,3))].">
      <j1 rule="para" parents="4929 19089"/>
    </justification>
  </clause>

  <clause id="19092">
    <literal><![CDATA[
      a(x,y,T(z,K(u,w))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(19091,a,xx),flip(a)].">
      <j1 rule="hyper" parents="19091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19093">
    <literal><![CDATA[
      a(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,T(z,T(u,v5))) = w
    ]]></literal>
    <justification jstring="[para(7356(a,1),19091(a,1,3))].">
      <j1 rule="para" parents="7356 19091"/>
    </justification>
  </clause>

  <clause id="19094">
    <literal><![CDATA[
      a(x,y,L(z / K(u,w),v5,v6) * K(v7,K(u,w))) = a(x,y,L(K(u,w) \ z,v5,v6) * K(v7,K(u,w)))
    ]]></literal>
    <justification jstring="[para(7513(a,1),19092(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7513 19092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19095">
    <literal><![CDATA[
      a(x,y,T(z,T(x * y,u))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(19093,a,14593,a)].">
      <j1 rule="hyper" parents="19093 14593"/>
    </justification>
  </clause>

  <clause id="19096">
    <literal><![CDATA[
      a(x,y,T(z,y * x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(10334(a,1),19095(a,1,3))].">
      <j1 rule="para" parents="10334 19095"/>
    </justification>
  </clause>

  <clause id="19097">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(19096(a,1),18639(a,1,1))].">
      <j1 rule="para" parents="19096 18639"/>
    </justification>
  </clause>

  <clause id="19098">
    <literal><![CDATA[
      a(x,y \ (T(z,z \ u) \ w),v5) = a(x,y \ (((z \ u) \ u) \ w),v5)
    ]]></literal>
    <justification jstring="[para(3574(a,1),19085(a,1,2,2,1))].">
      <j1 rule="para" parents="3574 19085"/>
    </justification>
  </clause>

  <clause id="19099">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * T(z,y * x)) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(111(a,1),19097(a,1,2,2,2))].">
      <j1 rule="para" parents="111 19097"/>
    </justification>
  </clause>

  <clause id="19100">
    <literal><![CDATA[
      a(x,y,z) \ (z * (y * x)) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,250,a(flip),b,19099,a)].">
      <j1 rule="hyper" parents="63 250 19099"/>
    </justification>
  </clause>

  <clause id="19101">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * (v5 * (w * u)))) = K(x,y \ T(z,L(v5,w,u) * (w * u)))
    ]]></literal>
    <justification jstring="[para(19100(a,1),15923(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="19100 15923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19102">
    <literal><![CDATA[
      a(x,y \ ((z * (1 / z)) \ (z \ u)),w) = a(x,y \ (((z \ 1) \ 1) \ u),w)
    ]]></literal>
    <justification jstring="[para(3415(a,2),19098(a,1,2,2))].">
      <j1 rule="para" parents="3415 19098"/>
    </justification>
  </clause>

  <clause id="19103">
    <literal><![CDATA[
      a(x,y \ (((z \ 1) \ 1) \ u),w) = a(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,12445,a(flip),b,19102,a),flip(a)].">
      <j1 rule="hyper" parents="63 12445 19102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19105">
    <literal><![CDATA[
      a(x,y \ (((z * u) \ z) \ w),v5) = a(x,y \ ((z \ (z / u)) \ w),v5)
    ]]></literal>
    <justification jstring="[para(3256(a,1),19103(a,1,2,2,1))].">
      <j1 rule="para" parents="3256 19103"/>
    </justification>
  </clause>

  <clause id="19106">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * (v5 * (w * u)))) = K(x,y \ T(z,(v5 * w) * u))
    ]]></literal>
    <justification jstring="[para(16418(a,1),19101(a,2,2,2))].">
      <j1 rule="para" parents="16418 19101"/>
    </justification>
  </clause>

  <clause id="19107">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * (v5 * (w * u)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,17654,a(flip),b,19106,a),flip(a)].">
      <j1 rule="hyper" parents="347 17654 19106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19108">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w \ v5))) = K(x,y \ T(z,u * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18635,a(flip),b,19107,a),flip(a)].">
      <j1 rule="hyper" parents="63 18635 19107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19110">
    <literal><![CDATA[
      a(x,y,L(z / K(u,w),v5,v6) * K(v7,K(u,w))) = a(x,y,L(K(w,u) * z,v5,v6) * K(v7,K(u,w)))
    ]]></literal>
    <justification jstring="[para(5256(a,1),19094(a,2,3,1,1))].">
      <j1 rule="para" parents="5256 19094"/>
    </justification>
  </clause>

  <clause id="19111">
    <literal><![CDATA[
      a(x,y,L(z / K(u,w),v5,v6) * K(v7,K(u,w))) = a(x,y,L(K(w,u) * z,v5,v6) * K(u,K(w,v7)))
    ]]></literal>
    <justification jstring="[para(7283(a,2),19110(a,2,3,2))].">
      <j1 rule="para" parents="7283 19110"/>
    </justification>
  </clause>

  <clause id="19112">
    <literal><![CDATA[
      a(x,y,L(K(z,K(u,w)) * (K(u,z) * v5),v6,v7)) = a(x,y,L(v5 / K(z,u),v6,v7) * K(w,K(z,u)))
    ]]></literal>
    <justification jstring="[para(17395(a,2),19111(a,2,3)),flip(a)].">
      <j1 rule="para" parents="17395 19111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19113">
    <literal><![CDATA[
      a(x,y,L(z / K(u,w),v5,v6) * K(v7,K(u,w))) = a(x,y,L(K(w,T(u,v7)) * z,v5,v6))
    ]]></literal>
    <justification jstring="[para(8069(a,1),19112(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="8069 19112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19114">
    <literal><![CDATA[
      a(x,y,L(z * K(u,w),v5,v6) * K(v7,K(w,u))) = a(x,y,L(K(u,T(w,v7)) * z,v5,v6))
    ]]></literal>
    <justification jstring="[para(6117(a,1),19113(a,1,3,1,1))].">
      <j1 rule="para" parents="6117 19113"/>
    </justification>
  </clause>

  <clause id="19115">
    <literal><![CDATA[
      a(x,y,L(K(z,T(u,w)) * v5,v6,v7)) = a(x,y,L(v5 * K(z,u),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(19089,a,19114,a),flip(a)].">
      <j1 rule="hyper" parents="19089 19114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19116">
    <literal><![CDATA[
      K(x,L(T(1 / y,y * T(z,u)) \ w,w,(K(z,u) / y) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(13571(a,1),17212(a,1,2,1,1))].">
      <j1 rule="para" parents="13571 17212"/>
    </justification>
  </clause>

  <clause id="19117">
    <literal><![CDATA[
      K(x,L(T(1 / y,T(z * y,u)) \ w,w,(K(z,u) / y) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(10489(a,2),19116(a,1,2,1,1))].">
      <j1 rule="para" parents="10489 19116"/>
    </justification>
  </clause>

  <clause id="19118">
    <literal><![CDATA[
      K(x,L(T(1 / y,T(z * y,u)) \ w,w,(y \ K(z,u)) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(18795(a,1),19117(a,1,2))].">
      <j1 rule="para" parents="18795 19117"/>
    </justification>
  </clause>

  <clause id="19119">
    <literal><![CDATA[
      K(x,L(T(1 / y,T(z * y,u)) \ w,w,y * z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18800,a(flip),b,19118,a)].">
      <j1 rule="hyper" parents="63 18800 19118"/>
    </justification>
  </clause>

  <clause id="19120">
    <literal><![CDATA[
      K(x,L(T(1 / y,z * y) \ u,u,y * z)) = K(x,(z * K(w,z)) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(14904,a,19119,a)].">
      <j1 rule="hyper" parents="14904 19119"/>
    </justification>
  </clause>

  <clause id="19122">
    <literal><![CDATA[
      K(x,L(T(y,z * y) * u,u,y * z)) = K(x,(z * K(w,z)) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(17314,a,19120,a)].">
      <j1 rule="hyper" parents="17314 19120"/>
    </justification>
  </clause>

  <clause id="19123">
    <literal><![CDATA[
      K(x,L(T(y,y * z) * u,u,y * z)) = K(x,(z * K(w,z)) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[para(4323(a,1),19122(a,1,2,1,1))].">
      <j1 rule="para" parents="4323 19122"/>
    </justification>
  </clause>

  <clause id="19124">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,(z * K(w,z)) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(12209,a,19123,a)].">
      <j1 rule="hyper" parents="12209 19123"/>
    </justification>
  </clause>

  <clause id="19125">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,K(z,w) * (z \ (((K(z,w) / y) \ z) * u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,17580,a(flip),b,19124,a),flip(a)].">
      <j1 rule="hyper" parents="347 17580 19124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19126">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,T(z,w) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,15549,a(flip),b,19125,a),flip(a)].">
      <j1 rule="hyper" parents="347 15549 19125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19127">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((K(z,w) / y) \ T(z,w)) * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,17966,a(flip),b,19126,a),flip(a)].">
      <j1 rule="hyper" parents="347 17966 19126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19128">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((1 / y) \ z) * u))
    ]]></literal>
    <justification jstring="[para(12322(a,1),19127(a,2,2,2,1))].">
      <j1 rule="para" parents="12322 19127"/>
    </justification>
  </clause>

  <clause id="19129">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,16341,a(flip),b,19128,a),flip(a)].">
      <j1 rule="hyper" parents="347 16341 19128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19130">
    <literal><![CDATA[
      K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,17941,a(flip),b,19129,a)].">
      <j1 rule="hyper" parents="63 17941 19129"/>
    </justification>
  </clause>

  <clause id="19131">
    <literal><![CDATA[
      K(x,((y * z) * (y \ 1)) \ (T(y * z,z) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12102,a(flip),b,19130,a)].">
      <j1 rule="hyper" parents="63 12102 19130"/>
    </justification>
  </clause>

  <clause id="19132">
    <literal><![CDATA[
      K(x,((y * z) * (y \ 1)) \ ((z * y) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(17671,a,19131,a)].">
      <j1 rule="hyper" parents="17671 19131"/>
    </justification>
  </clause>

  <clause id="19133">
    <literal><![CDATA[
      K(x,((y * z) / y) \ ((z * y) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18904,a(flip),b,19132,a)].">
      <j1 rule="hyper" parents="63 18904 19132"/>
    </justification>
  </clause>

  <clause id="19134">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,y \ ((T(y,z) * z) * u))
    ]]></literal>
    <justification jstring="[para(10140(a,1),19133(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10140 19133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19135">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,y \ ((z * y) * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,17970,a(flip),b,19134,a),flip(a)].">
      <j1 rule="hyper" parents="347 17970 19134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19136">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18807,a,b,19135,a)].">
      <j1 rule="hyper" parents="63 18807 19135"/>
    </justification>
  </clause>

  <clause id="19137">
    <literal><![CDATA[
      T(x,K(y,z)) / (z * (a(u,w,K(v5,v6)) * T(a(u,w,K(v5,v6)) \ (z \ x),y))) = K(y,(x \ (z * a(u,w,K(v5,v6)))) \ 1)
    ]]></literal>
    <justification jstring="[para(1022(a,1),17536(a,1,2))].">
      <j1 rule="para" parents="1022 17536"/>
    </justification>
  </clause>

  <clause id="19138">
    <literal><![CDATA[
      T(x,K(y,z)) / (z * (a(u,w,K(v5,v6)) * T(a(v6,w,K(v5,u)) * (z \ x),y))) = K(y,(x \ (z * a(u,w,K(v5,v6)))) \ 1)
    ]]></literal>
    <justification jstring="[para(13989(a,1),19137(a,1,2,2,2,1))].">
      <j1 rule="para" parents="13989 19137"/>
    </justification>
  </clause>

  <clause id="19139">
    <literal><![CDATA[
      T(x,K(y,z)) / (z * T((a(u,w,K(v5,v6)) * (z \ x)) * a(v6,w,K(v5,u)),y)) = K(y,(x \ (z * a(v6,w,K(v5,u)))) \ 1)
    ]]></literal>
    <justification jstring="[para(17269(a,2),19138(a,1,2,2))].">
      <j1 rule="para" parents="17269 19138"/>
    </justification>
  </clause>

  <clause id="19140">
    <literal><![CDATA[
      K(x,(y \ (z * a(u,w,K(v5,v6)))) \ 1) = T(y,K(x,z)) / (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[para(16941(a,1),19139(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="16941 19139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19141">
    <literal><![CDATA[
      K(x,(y \ (z * a(u,w,K(v5,v6)))) \ 1) = K(x,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,9424,a(flip),b,19140,a),flip(a)].">
      <j1 rule="hyper" parents="347 9424 19140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19143">
    <literal><![CDATA[
      K(x,(y \ (a(z,u,K(w,v5)) * v6)) \ 1) = K(x,(y \ v6) \ 1)
    ]]></literal>
    <justification jstring="[para(16833(a,2),19141(a,1,2,1,2))].">
      <j1 rule="para" parents="16833 19141"/>
    </justification>
  </clause>

  <clause id="19144">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) \ v6) = K(x,(v6 \ v5) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6269,a,19143,a)].">
      <j1 rule="hyper" parents="6269 19143"/>
    </justification>
  </clause>

  <clause id="19145">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) \ v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,v5 \ v6) = v7
    ]]></literal>
    <justification jstring="[para(19144(a,2),6269(a,1))].">
      <j1 rule="para" parents="19144 6269"/>
    </justification>
  </clause>

  <clause id="19146">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) \ (L(K(z,y),w,v5) * v6)) = K(x,u \ v6)
    ]]></literal>
    <justification jstring="[hyper(19145,a,18005,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19145 18005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19147">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ (L(K(y,z),w,v5) * v6)) = K(x,u \ v6)
    ]]></literal>
    <justification jstring="[para(5256(a,1),19146(a,1,2,1))].">
      <j1 rule="para" parents="5256 19146"/>
    </justification>
  </clause>

  <clause id="19148">
    <literal><![CDATA[
      K(x,y \ ((L(K(z,u),w,v5) * v6) * K(u,z))) = K(x,y \ v6)
    ]]></literal>
    <justification jstring="[hyper(16981,a,19147,a)].">
      <j1 rule="hyper" parents="16981 19147"/>
    </justification>
  </clause>

  <clause id="19149">
    <literal><![CDATA[
      K(x,y \ (L(K(z,u),w,v5) * (v6 * K(u,z)))) = K(x,y \ v6)
    ]]></literal>
    <justification jstring="[para(16899(a,1),19148(a,1,2,2))].">
      <j1 rule="para" parents="16899 19148"/>
    </justification>
  </clause>

  <clause id="19150">
    <literal><![CDATA[
      K(x,y \ T(z * a(u,w,K(v5,v6)),K(u,v6))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(19073(a,2),19149(a,1,2,2))].">
      <j1 rule="para" parents="19073 19149"/>
    </justification>
  </clause>

  <clause id="19151">
    <literal><![CDATA[
      K(x,y \ (z * a(u,w,K(v5,v6)))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(14824,a,19150,a)].">
      <j1 rule="hyper" parents="14824 19150"/>
    </justification>
  </clause>

  <clause id="19153">
    <literal><![CDATA[
      K(x,y \ K(z,L(u,w,v5))) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[para(11061(a,1),19151(a,1,2,2))].">
      <j1 rule="para" parents="11061 19151"/>
    </justification>
  </clause>

  <clause id="19154">
    <literal><![CDATA[
      K(x,y \ K(z,(u / w) / v5)) = K(x,y \ K(z,u / (v5 * w)))
    ]]></literal>
    <justification jstring="[para(14108(a,1),19153(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14108 19153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19155">
    <literal><![CDATA[
      K(x,y \ K(z,u / (w * v5))) = K(x,y \ K(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[hyper(14878,a,19154,a),flip(a)].">
      <j1 rule="hyper" parents="14878 19154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19156">
    <literal><![CDATA[
      K(x,(y / z) \ K(y,u \ (w / v5))) = K(x,z / T(y,L((w / v5) / u,u,v5)))
    ]]></literal>
    <justification jstring="[hyper(18252,a,19155,a),flip(a)].">
      <j1 rule="hyper" parents="18252 19155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19157">
    <literal><![CDATA[
      K(x,y / T(z,L((u / w) / v5,v5,w))) = K(x,y / T(z,v5 \ (u / w)))
    ]]></literal>
    <justification jstring="[hyper(18250,a,19156,a),flip(a)].">
      <j1 rule="hyper" parents="18250 19156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19158">
    <literal><![CDATA[
      K(x,y * T(z,L((u / w) / v5,v5,w))) = K(x,y / T(z \ 1,v5 \ (u / w)))
    ]]></literal>
    <justification jstring="[hyper(16013,a,19157,a)].">
      <j1 rule="hyper" parents="16013 19157"/>
    </justification>
  </clause>

  <clause id="19159">
    <literal><![CDATA[
      K(x,y * T(z,L((u / w) / v5,v5,w))) = K(x,y * T(z,v5 \ (u / w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,16000,a(flip),b,19158,a),flip(a)].">
      <j1 rule="hyper" parents="347 16000 19158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19160">
    <literal><![CDATA[
      K(x,y * T(z,u / (w * v5))) = K(x,y * T(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[para(14124(a,1),19159(a,1,2,2))].">
      <j1 rule="para" parents="14124 19159"/>
    </justification>
  </clause>

  <clause id="19161">
    <literal><![CDATA[
      K(x,y * T(z,(u * w) \ v5)) = K(x,y * T(z,u \ (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(14849,a,19160,a)].">
      <j1 rule="hyper" parents="14849 19160"/>
    </justification>
  </clause>

  <clause id="19162">
    <literal><![CDATA[
      K(x,y * T(z,(u * w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u \ (w \ v5))) = v6
    ]]></literal>
    <justification jstring="[para(19161(a,2),15853(a,1))].">
      <j1 rule="para" parents="19161 15853"/>
    </justification>
  </clause>

  <clause id="19163">
    <literal><![CDATA[
      K(x,y * T(z,u \ (w \ v5))) = K(x,y * T(z,v5 * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(19162,a,15930,a)].">
      <j1 rule="hyper" parents="19162 15930"/>
    </justification>
  </clause>

  <clause id="19164">
    <literal><![CDATA[
      K(x,y * T(z,(u \ w) * v5)) = K(x,y * T(z,w * (v5 * u)))
    ]]></literal>
    <justification jstring="[hyper(15932,a,19163,a)].">
      <j1 rule="hyper" parents="15932 19163"/>
    </justification>
  </clause>

  <clause id="19165">
    <literal><![CDATA[
      K(T(x,y),(z \ u) * T(w,u * (x * z))) = K(T(x,y),w * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16010,a(flip),b,19164,a),flip(a)].">
      <j1 rule="hyper" parents="63 16010 19164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19166">
    <literal><![CDATA[
      K(x,T((y \ z) * T(u,z * (x * y)),w)) = K(T(x,w),u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(7488,a,19165,a)].">
      <j1 rule="hyper" parents="7488 19165"/>
    </justification>
  </clause>

  <clause id="19167">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(T(x,z * u),y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(13276,a,19166,a)].">
      <j1 rule="hyper" parents="13276 19166"/>
    </justification>
  </clause>

  <clause id="19168">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(x,T(y * (u \ z),z * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,7093,a(flip),b,19167,a),flip(a)].">
      <j1 rule="hyper" parents="347 7093 19167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19169">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u \ z) * y) = w
    ]]></literal>
    <justification jstring="[para(19168(a,2),13277(a,1))].">
      <j1 rule="para" parents="19168 13277"/>
    </justification>
  </clause>

  <clause id="19170">
    <literal><![CDATA[
      K(x,y * (z \ T((u * K(w,v5)) * v6,K(w,v5) * v6))) = K(x,y * (z \ (L(K(w,v5) * v6,K(v5,w),u) * u)))
    ]]></literal>
    <justification jstring="[para(18159(a,1),18580(a,1,2,2,2))].">
      <j1 rule="para" parents="18159 18580"/>
    </justification>
  </clause>

  <clause id="19171">
    <literal><![CDATA[
      K(x,y * (z \ T((u * K(w,v5)) * v6,v6))) = K(x,y * (z \ (L(K(w,v5) * v6,K(v5,w),u) * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18851,a(flip),b,19170,a)].">
      <j1 rule="hyper" parents="63 18851 19170"/>
    </justification>
  </clause>

  <clause id="19174">
    <literal><![CDATA[
      K(x,y * (z \ (L(K(u,w) * v5,K(w,u),v6) * v6))) = K(x,y * (z \ (v5 * (v6 * K(u,w)))))
    ]]></literal>
    <justification jstring="[hyper(63,a,17279,a(flip),b,19171,a),flip(a)].">
      <j1 rule="hyper" parents="63 17279 19171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19175">
    <literal><![CDATA[
      K(x,y * (z \ (L(K(u,w) * v5,K(w,u),v6) * v6))) = K(x,y * (K(u,w) * (z \ (v5 * v6))))
    ]]></literal>
    <justification jstring="[hyper(347,a,18750,a(flip),b,19174,a),flip(a)].">
      <j1 rule="hyper" parents="347 18750 19174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19176">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,K(w,v5)) * (K(v5,w) * v6)))) = K(x,y * (K(v5,w) * (z \ (u * v6))))
    ]]></literal>
    <justification jstring="[para(18577(a,1),19175(a,1,2,2,2))].">
      <j1 rule="para" parents="18577 19175"/>
    </justification>
  </clause>

  <clause id="19177">
    <literal><![CDATA[
      K(x,y * (z \ (u * (K(w,v5) * v6)))) = K(x,y * (K(w,v5) * (z \ (u * v6))))
    ]]></literal>
    <justification jstring="[hyper(17260,a,19176,a)].">
      <j1 rule="hyper" parents="17260 19176"/>
    </justification>
  </clause>

  <clause id="19178">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((w * v5) \ (w * (v5 * v6))))) = K(x,y * L(K(z,u) * v6,v5,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18673,a(flip),b,19177,a),flip(a)].">
      <j1 rule="hyper" parents="63 18673 19177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19179">
    <literal><![CDATA[
      K(x,y * L(K(z,u) * w,v5,v6)) = K(x,y * (K(z,u) * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(18(a,2),19178(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="18 19178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19180">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * L(K(u,z) * w,v5,v6)) = K(x,y * L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(18667,a,19179,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18667 19179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19181">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * w,v5,v6))) = K(x,u * L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(17193,a,19180,a)].">
      <j1 rule="hyper" parents="17193 19180"/>
    </justification>
  </clause>

  <clause id="19182">
    <literal><![CDATA[
      K(x,y * L(y \ 1,z,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18717,a(flip),b,19181,a),flip(a)].">
      <j1 rule="hyper" parents="63 18717 19181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19183">
    <literal><![CDATA[
      K(x,y * L(((z * u) / z) \ z,w,v5)) = K(x,y * L(z / u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,17996,a(flip),b,19181,a)].">
      <j1 rule="hyper" parents="63 17996 19181"/>
    </justification>
  </clause>

  <clause id="19184">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(T(1 / (y / z),y),w))
    ]]></literal>
    <justification jstring="[hyper(63,a,16550,a(flip),b,19182,a)].">
      <j1 rule="hyper" parents="63 16550 19182"/>
    </justification>
  </clause>

  <clause id="19185">
    <literal><![CDATA[
      K(x,(y \ ((y * (z * y)) / y)) * L(y / (z * y),u,w)) = K(x,z * L((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(15428,a,19183,a),flip(a)].">
      <j1 rule="hyper" parents="15428 19183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19187">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(1 / (y / z),T(w,y)))
    ]]></literal>
    <justification jstring="[para(7093(a,1),19184(a,2,3))].">
      <j1 rule="para" parents="7093 19184"/>
    </justification>
  </clause>

  <clause id="19188">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(z / y,T(w,y)))
    ]]></literal>
    <justification jstring="[para(5554(a,1),19187(a,2,3))].">
      <j1 rule="para" parents="5554 19187"/>
    </justification>
  </clause>

  <clause id="19189">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[para(7135(a,1),19188(a,2,3))].">
      <j1 rule="para" parents="7135 19188"/>
    </justification>
  </clause>

  <clause id="19190">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) * (y \ z)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19022,a(flip),b,19189,a)].">
      <j1 rule="hyper" parents="63 19022 19189"/>
    </justification>
  </clause>

  <clause id="19191">
    <literal><![CDATA[
      K(x,(y \ T(z * y,y)) * L(y / (z * y),u,w)) = K(x,z * L((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,17239,a(flip),b,19185,a)].">
      <j1 rule="hyper" parents="63 17239 19185"/>
    </justification>
  </clause>

  <clause id="19192">
    <literal><![CDATA[
      K(x,((y * z) / z) * L(z / (y * z),u,w)) = K(x,y * L((z * y) \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(17223,a,19191,a)].">
      <j1 rule="hyper" parents="17223 19191"/>
    </justification>
  </clause>

  <clause id="19193">
    <literal><![CDATA[
      K(x,y * L(z / (y * z),u,w)) = K(x,y * L((z * y) \ z,u,w))
    ]]></literal>
    <justification jstring="[para(11(a,1),19192(a,1,2,1))].">
      <j1 rule="para" parents="11 19192"/>
    </justification>
  </clause>

  <clause id="19194">
    <literal><![CDATA[
      K(x,L(y / (z * y),u,w) * z) = K(x,z * L((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(14686,a,19193,a)].">
      <j1 rule="hyper" parents="14686 19193"/>
    </justification>
  </clause>

  <clause id="19195">
    <literal><![CDATA[
      K(x,(y \ z) * L((y * (y \ z)) \ y,u,w)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19190,a(flip),b,19194,a),flip(a)].">
      <j1 rule="hyper" parents="63 19190 19194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19196">
    <literal><![CDATA[
      K(x,(y \ z) * L(z \ y,u,w)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),19195(a,1,2,2,1,1))].">
      <j1 rule="para" parents="10 19195"/>
    </justification>
  </clause>

  <clause id="19197">
    <literal><![CDATA[
      K(x,L(y / z,u,w) * (z / y)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(17703,a,19196,a)].">
      <j1 rule="hyper" parents="17703 19196"/>
    </justification>
  </clause>

  <clause id="19199">
    <literal><![CDATA[
      K(K(x,y),z) \ ((u * (T(z,K(x,y)) * K(y,x))) / T(z,K(x,y))) = T((u * z) / (K(x,y) * z),K(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(9621(a,1),18584(a,2,1))].">
      <j1 rule="para" parents="9621 18584"/>
    </justification>
  </clause>

  <clause id="19200">
    <literal><![CDATA[
      K(K(x,y),z) \ ((u * (T(z,K(x,y)) * K(y,x))) / T(z,K(x,y))) = (u * z) / (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,13543,a(flip),b,19199,a),flip(a)].">
      <j1 rule="hyper" parents="347 13543 19199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19202">
    <literal><![CDATA[
      K(x,K(y,z)) \ ((u * (T(x,K(y,z)) * K(z,y))) / T(x,K(y,z))) = (u * x) / (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(7292(a,1),19200(a,1,1))].">
      <j1 rule="para" parents="7292 19200"/>
    </justification>
  </clause>

  <clause id="19203">
    <literal><![CDATA[
      K(x,K(y,z)) \ ((u * (K(z,y) * x)) / T(x,K(y,z))) = (u * x) / (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(6885(a,1),19202(a,1,2,1,2))].">
      <j1 rule="para" parents="6885 19202"/>
    </justification>
  </clause>

  <clause id="19204">
    <literal><![CDATA[
      (x * (K(y,z) * u)) / u = (x * u) / (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(13680,a,19203,a)].">
      <j1 rule="hyper" parents="13680 19203"/>
    </justification>
  </clause>

  <clause id="19205">
    <literal><![CDATA[
      (x * (y / z)) / (K(u,y) * (y / z)) = (x * (T(y,u) / z)) / (y / z)
    ]]></literal>
    <justification jstring="[para(13192(a,1),19204(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13192 19204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19206">
    <literal><![CDATA[
      (K(x,L(y,z * (K(u,w) * v5),v5)) * (z * (K(u,w) * v5))) / v5 = K(x,y) * ((z * v5) / (K(w,u) * v5))
    ]]></literal>
    <justification jstring="[para(19204(a,1),14240(a,2,2))].">
      <j1 rule="para" parents="19204 14240"/>
    </justification>
  </clause>

  <clause id="19207">
    <literal><![CDATA[
      (K(x,L(y,z * u,z)) * (u * (K(w,v5) * z))) / z = K(x,y) * ((u * z) / (K(v5,w) * z))
    ]]></literal>
    <justification jstring="[para(18339(a,1),19206(a,1,1,1))].">
      <j1 rule="para" parents="18339 19206"/>
    </justification>
  </clause>

  <clause id="19208">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * (z * (K(w,v5) * u))) / u = K(x,y) * ((z * u) / (K(v5,w) * u))
    ]]></literal>
    <justification jstring="[para(14201(a,1),19207(a,1,1,1))].">
      <j1 rule="para" parents="14201 19207"/>
    </justification>
  </clause>

  <clause id="19210">
    <literal><![CDATA[
      ((K(x,y) * z) * (K(u,w) * v5)) / v5 = K(x,y) * ((z * v5) / (K(w,u) * v5))
    ]]></literal>
    <justification jstring="[para(18031(a,1),19208(a,1,1))].">
      <j1 rule="para" parents="18031 19208"/>
    </justification>
  </clause>

  <clause id="19211">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (K(w,v5) * u) = K(x,y) * ((z * u) / (K(w,v5) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19204,a(flip),b,19210,a)].">
      <j1 rule="hyper" parents="63 19204 19210"/>
    </justification>
  </clause>

  <clause id="19212">
    <literal><![CDATA[
      K(x,y) * (((z * K(u,w)) * v5) / (K(u,w) * v5)) = L(K(x,y) * z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(17887,a,19211,a),flip(a)].">
      <j1 rule="hyper" parents="17887 19211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19213">
    <literal><![CDATA[
      L(K(x,y) * z,K(u,w),v5) = K(x,y) * L(z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(17875(a,1),19212(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17875 19212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19214">
    <literal><![CDATA[
      L(K(x,y) * (K(y,x) * z),K(x,y),u) = ((z * u) / (K(x,y) * u)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,17888,a(flip),b,19213,a),flip(a)].">
      <j1 rule="hyper" parents="347 17888 19213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19215">
    <literal><![CDATA[
      ((x * y) / (K(z,u) * y)) * K(z,u) = L(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(5261(a,1),19214(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5261 19214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19216">
    <literal><![CDATA[
      ((x * (T(y,z) / u)) / (y / u)) * K(z,y) = L(x,K(z,y),T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(13202(a,1),19215(a,1,1,2))].">
      <j1 rule="para" parents="13202 19215"/>
    </justification>
  </clause>

  <clause id="19217">
    <literal><![CDATA[
      ((x * (T(y,z) / u)) / (y / u)) * K(z,y) = L(x,K(z,y),u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,18180,a(flip),b,19216,a),flip(a)].">
      <j1 rule="hyper" parents="347 18180 19216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19218">
    <literal><![CDATA[
      ((x * (T(y,z) / u)) / (y / u)) * K(z,y) = L(x,K(z,y),u \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,18573,a(flip),b,19217,a),flip(a)].">
      <j1 rule="hyper" parents="347 18573 19217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19219">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * ((w \ K(x,K(y,z))) * v5)) = ((w \ 1) * v5) * T(u,K(x,K(y,z)) * ((w \ 1) * v5))
    ]]></literal>
    <justification jstring="[para(16824(a,1),17078(a,1,1))].">
      <j1 rule="para" parents="16824 17078"/>
    </justification>
  </clause>

  <clause id="19220">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * ((w \ K(x,K(y,z))) * v5)) = ((w \ 1) * v5) * T(u,K(x,K(y,z)) * ((w \ 1) * v5))
    ]]></literal>
    <justification jstring="[hyper(7325,a,19219,a)].">
      <j1 rule="hyper" parents="7325 19219"/>
    </justification>
  </clause>

  <clause id="19222">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * ((w \ K(x,K(y,z))) * v5)) = ((w \ 1) * v5) * T(u,K(x,K(y,z)) * (w \ v5))
    ]]></literal>
    <justification jstring="[para(18912(a,1),19220(a,2,2))].">
      <j1 rule="para" parents="18912 19220"/>
    </justification>
  </clause>

  <clause id="19223">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * ((w \ K(x,K(y,z))) * v5)) = ((w \ 1) * v5) * T(u,w \ v5)
    ]]></literal>
    <justification jstring="[para(14783(a,1),19222(a,2,2))].">
      <j1 rule="para" parents="14783 19222"/>
    </justification>
  </clause>

  <clause id="19224">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * ((w \ K(x,K(y,z))) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      u * ((w \ 1) * v5) = v6
    ]]></literal>
    <justification jstring="[para(19223(a,2),13170(a,1))].">
      <j1 rule="para" parents="19223 13170"/>
    </justification>
  </clause>

  <clause id="19226">
    <literal><![CDATA[
      T(K(x,L(T(y,z),z,u \ 1)),K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))) = K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(8731(a,1),18088(a,1,1))].">
      <j1 rule="para" parents="8731 18088"/>
    </justification>
  </clause>

  <clause id="19227">
    <literal><![CDATA[
      K(x,(y \ (z \ (u * z))) \ (y \ (u * z))) = K(x,L(T(z,u),u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(13596,a,19226,a),flip(a)].">
      <j1 rule="hyper" parents="13596 19226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19228">
    <literal><![CDATA[
      K(x,(y \ T(z,u)) \ (y \ (z * u))) = K(x,L(T(u,z),z,y \ 1))
    ]]></literal>
    <justification jstring="[para(22(a,2),19227(a,1,2,1,2))].">
      <j1 rule="para" parents="22 19227"/>
    </justification>
  </clause>

  <clause id="19230">
    <literal><![CDATA[
      L(T(x \ L(x,K(y,z),T(u * K(z,y),w)),v5),T(x,v5),T(u * K(u * K(z,y),w),K(z,y))) = a(T(x,v5),K(y,z),T(u * K(z,y),w))
    ]]></literal>
    <justification jstring="[para(17872(a,1),17518(a,1,1,1,2))].">
      <j1 rule="para" parents="17872 17518"/>
    </justification>
  </clause>

  <clause id="19231">
    <literal><![CDATA[
      L(T(x \ L(x,K(y,z),u * K(z,y)),w),T(x,w),T(u * K(u * K(z,y),v5),K(z,y))) = a(T(x,w),K(y,z),T(u * K(z,y),v5))
    ]]></literal>
    <justification jstring="[para(18174(a,1),19230(a,1,1,1,2))].">
      <j1 rule="para" parents="18174 19230"/>
    </justification>
  </clause>

  <clause id="19233">
    <literal><![CDATA[
      L(T(x \ L(x,K(y,z),u),w),T(x,w),T(u * K(u * K(z,y),v5),K(z,y))) = a(T(x,w),K(y,z),T(u * K(z,y),v5))
    ]]></literal>
    <justification jstring="[para(18569(a,1),19231(a,1,1,1,2))].">
      <j1 rule="para" parents="18569 19231"/>
    </justification>
  </clause>

  <clause id="19234">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),T(x,w),T(u * K(u * K(z,y),v5),K(z,y))) = a(T(x,w),K(y,z),T(u * K(z,y),v5))
    ]]></literal>
    <justification jstring="[para(18204(a,1),19233(a,1,1))].">
      <j1 rule="para" parents="18204 19233"/>
    </justification>
  </clause>

  <clause id="19235">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),T(x,w),K(y,z) * T(u * K(z,y),v5)) = a(T(x,w),K(y,z),T(u * K(z,y),v5))
    ]]></literal>
    <justification jstring="[para(14575(a,1),19234(a,1,3))].">
      <j1 rule="para" parents="14575 19234"/>
    </justification>
  </clause>

  <clause id="19237">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),T(x,w),T(K(y,z) * (u * K(z,y)),v5)) = a(T(x,w),K(y,z),T(u * K(z,y),v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,18792,a,b,19235,a)].">
      <j1 rule="hyper" parents="63 18792 19235"/>
    </justification>
  </clause>

  <clause id="19238">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),T(x,w),T(T(u,K(y,z)),v5)) = a(T(x,w),K(y,z),T(u * K(z,y),v5))
    ]]></literal>
    <justification jstring="[para(7341(a,1),19237(a,1,3,1))].">
      <j1 rule="para" parents="7341 19237"/>
    </justification>
  </clause>

  <clause id="19239">
    <literal><![CDATA[
      a(T(x,y),K(z,u),T(w * K(u,z),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x \ L(x,K(z,u),w),T(x,y),T(w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(19238(a,1),18815(a,1))].">
      <j1 rule="para" parents="19238 18815"/>
    </justification>
  </clause>

  <clause id="19240">
    <literal><![CDATA[
      T(K(x,K(y,z) * (u * w)),w \ T(w * (u * K(z,z \ y)),x)) = (w \ T(w * (u * K(z,z \ y)),x)) \ ((u / z) * ((z \ y) \ y))
    ]]></literal>
    <justification jstring="[para(12013(a,1),17203(a,1,1))].">
      <j1 rule="para" parents="12013 17203"/>
    </justification>
  </clause>

  <clause id="19241">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),w \ T(w * (u * K(z,z \ y)),x))) = (w \ T(w * (u * K(z,z \ y)),x)) \ ((u / z) * ((z \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(7480,a,19240,a)].">
      <j1 rule="hyper" parents="7480 19240"/>
    </justification>
  </clause>

  <clause id="19242">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),w \ (w * (u * K(z,z \ y))))) = (w \ T(w * (u * K(z,z \ y)),x)) \ ((u / z) * ((z \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(16160,a,19241,a)].">
      <j1 rule="hyper" parents="16160 19241"/>
    </justification>
  </clause>

  <clause id="19243">
    <literal><![CDATA[
      (x \ T(x * (y * K(z,z \ u)),w)) \ ((y / z) * ((z \ u) \ u)) = K(w,T(K(u,z) * (y * x),y * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(9(a,1),19242(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 19242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19245">
    <literal><![CDATA[
      (x \ T(x * (y * K(z,z \ u)),w)) \ ((y / z) * ((z \ u) \ u)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(w,T(K(u,z) * (y * x),y)) = v5
    ]]></literal>
    <justification jstring="[para(19243(a,2),16158(a,1))].">
      <j1 rule="para" parents="19243 16158"/>
    </justification>
  </clause>

  <clause id="19246">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),u)) = K(x,w * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(19245,a,15191,a)].">
      <j1 rule="hyper" parents="19245 15191"/>
    </justification>
  </clause>

  <clause id="19247">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(L(z,u,x),T(y,u))) = (x * u) \ (K(z,(x * u) / (x * (y \ u))) * ((x * K(y,z)) * u))
    ]]></literal>
    <justification jstring="[para(11106(a,1),18767(a,1,3))].">
      <j1 rule="para" parents="11106 18767"/>
    </justification>
  </clause>

  <clause id="19248">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(L(z,u,x),y)) = (x * u) \ (K(z,(x * u) / (x * (y \ u))) * ((x * K(y,z)) * u))
    ]]></literal>
    <justification jstring="[hyper(18816,a,19247,a)].">
      <j1 rule="hyper" parents="18816 19247"/>
    </justification>
  </clause>

  <clause id="19250">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(z,L(y,u,x))) = (x * u) \ (K(z,(x * u) / (x * (y \ u))) * ((x * K(y,z)) * u))
    ]]></literal>
    <justification jstring="[para(11108(a,1),19248(a,1,3))].">
      <j1 rule="para" parents="11108 19248"/>
    </justification>
  </clause>

  <clause id="19251">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(z,L(y,u,x))) = ((x * u) \ (K(z,(x * u) / (x * (y \ u))) * ((x * K(y,z)) * u))) / 1
    ]]></literal>
    <justification jstring="[hyper(347,a,78,a,b,19250,a),flip(a)].">
      <j1 rule="hyper" parents="347 78 19250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19252">
    <literal><![CDATA[
      ((x * y) \ (K(z,(x * y) / (x * (u \ y))) * ((x * K(u,z)) * y))) / a(z,x * (K(u,z) * y),K(L(u,y,x),a(x,K(u,z),y))) = a(x,K(u,z),y)
    ]]></literal>
    <justification jstring="[hyper(131,a,19250,a(flip),b,14342,a)].">
      <j1 rule="hyper" parents="131 19250 14342"/>
    </justification>
  </clause>

  <clause id="19253">
    <literal><![CDATA[
      (x * y) \ (((x * K(z,u)) * y) * K(u,T((x * y) / (x * (z \ y)),(x * K(z,u)) * y))) = L(a(x,K(z,u),y),x * (K(z,u) * y),K(u,L(z,y,x)))
    ]]></literal>
    <justification jstring="[para(7104(a,2),19250(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7104 19250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19255">
    <literal><![CDATA[
      K(x,T(K(y,z) * ((u * w) * v5),v5 \ T(v5 * ((u * K(z,y)) * w),x))) = (v5 \ T(v5 * ((u * K(z,y)) * w),x)) \ T((u * K(z,y)) * w,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(7480,a,17435,a)].">
      <j1 rule="hyper" parents="7480 17435"/>
    </justification>
  </clause>

  <clause id="19256">
    <literal><![CDATA[
      ((x * y) \ (K(z,(x * y) / (x * (u \ y))) * ((x * K(u,z)) * y))) / a(z,x * (K(u,z) * y),a(L(u,y,x),K(u,z),K(y,x))) = a(x,K(u,z),y)
    ]]></literal>
    <justification jstring="[para(13960(a,2),19252(a,1,2,3))].">
      <j1 rule="para" parents="13960 19252"/>
    </justification>
  </clause>

  <clause id="19257">
    <literal><![CDATA[
      K(x,T(K(y,z) * ((u * w) * v5),v5 \ (v5 * ((u * K(z,y)) * w)))) = (v5 \ T(v5 * ((u * K(z,y)) * w),x)) \ T((u * K(z,y)) * w,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(16160,a,19255,a)].">
      <j1 rule="hyper" parents="16160 19255"/>
    </justification>
  </clause>

  <clause id="19258">
    <literal><![CDATA[
      (x \ T(x * ((y * K(z,u)) * w),v5)) \ T((y * K(z,u)) * w,K(y,w)) = K(v5,T(K(u,z) * ((y * w) * x),(y * K(z,u)) * w))
    ]]></literal>
    <justification jstring="[para(9(a,1),19257(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 19257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19259">
    <literal><![CDATA[
      (x \ T(x * ((y * K(z,u)) * w),v5)) \ T((y * K(z,u)) * w,K(y,w)) = K(v5,T(K(u,z) * ((y * w) * x),y * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,16138,a(flip),b,19258,a),flip(a)].">
      <j1 rule="hyper" parents="347 16138 19258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19262">
    <literal><![CDATA[
      (x \ T(x * ((y * K(z,u)) * w),v5)) \ T((y * K(z,u)) * w,K(y,w)) = K(v5,x * (K(z,u) * (y * w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,19246,a(flip),b,19259,a),flip(a)].">
      <j1 rule="hyper" parents="347 19246 19259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19263">
    <literal><![CDATA[
      (x \ T(x * ((y * K(z,u)) * w),v5)) \ ((y * K(z,u)) * w) = K(v5,x * (K(z,u) * (y * w)))
    ]]></literal>
    <justification jstring="[para(13685(a,1),19262(a,1,2))].">
      <j1 rule="para" parents="13685 19262"/>
    </justification>
  </clause>

  <clause id="19264">
    <literal><![CDATA[
      K(x,y * ((z * K(u,w)) * v5)) = K(x,y * (K(u,w) * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(13235,a,19263,a)].">
      <j1 rule="hyper" parents="13235 19263"/>
    </justification>
  </clause>

  <clause id="19265">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((w * z) * v5))) = K(x,y * ((w * T(z,u)) * v5))
    ]]></literal>
    <justification jstring="[para(5926(a,1),19264(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5926 19264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19266">
    <literal><![CDATA[
      K(x,y * ((z * T(u,x)) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((z * u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(19265(a,1),17165(a,1))].">
      <j1 rule="para" parents="19265 17165"/>
    </justification>
  </clause>

  <clause id="19267">
    <literal><![CDATA[
      K(x,K(y,z) * ((u * (u \ (w \ u))) * v5)) = K(x,(w \ (u * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[hyper(19266,a,18444,a)].">
      <j1 rule="hyper" parents="19266 18444"/>
    </justification>
  </clause>

  <clause id="19268">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) * v5) = K(x,K(w,u) * ((y \ z) * v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),19267(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 19267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19269">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w) * ((v5 \ y) * v6)) = K(x,(v5 \ ((K(z,u) * (w * y)) / (K(z,u) * w))) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,17600,a,b,19268,a),flip(a)].">
      <j1 rule="hyper" parents="63 17600 19268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19271">
    <literal><![CDATA[
      K(x,(y \ ((K(z,u) * (w * v5)) / (K(z,u) * w))) * v6) = K(x,(y \ T(v5,K(z,u) * w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,17192,a(flip),b,19269,a),flip(a)].">
      <j1 rule="hyper" parents="63 17192 19269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19272">
    <literal><![CDATA[
      K(x,(y \ ((z * u) / (K(w,v5) * (K(v5,w) * z)))) * v6) = K(x,(y \ T(u,K(v5,w) * z)) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,17914,a(flip),b,19271,a)].">
      <j1 rule="hyper" parents="63 17914 19271"/>
    </justification>
  </clause>

  <clause id="19273">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ ((v5 * z) / v5)) * v6)
    ]]></literal>
    <justification jstring="[para(5261(a,1),19272(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5261 19272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19274">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ T(z,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,17239,a(flip),b,19273,a),flip(a)].">
      <j1 rule="hyper" parents="347 17239 19273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19275">
    <literal><![CDATA[
      K(x,(y \ T(z,u * K(w,v5))) * v6) = K(x,(y \ T(z,u)) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,16311,a(flip),b,19274,a)].">
      <j1 rule="hyper" parents="63 16311 19274"/>
    </justification>
  </clause>

  <clause id="19277">
    <literal><![CDATA[
      ((x * y) \ (K(z,(x * y) / (x * (u \ y))) * ((x * K(u,z)) * y))) / a(z,x * (K(u,z) * y),1) = a(x,K(u,z),y)
    ]]></literal>
    <justification jstring="[para(18160(a,1),19256(a,1,2,3))].">
      <j1 rule="para" parents="18160 19256"/>
    </justification>
  </clause>

  <clause id="19278">
    <literal><![CDATA[
      ((x * y) \ (K(z,(x * y) / (x * (u \ y))) * ((x * K(u,z)) * y))) / 1 = a(x,K(u,z),y)
    ]]></literal>
    <justification jstring="[para(555(a,1),19277(a,1,2))].">
      <j1 rule="para" parents="555 19277"/>
    </justification>
  </clause>

  <clause id="19280">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(z,L(y,u,x))) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19251,a,b,19278,a)].">
      <j1 rule="hyper" parents="63 19251 19278"/>
    </justification>
  </clause>

  <clause id="19282">
    <literal><![CDATA[
      T(K(x,(y * z) * (u / w)) * a(z,y,K(x,((u / w) \ 1) \ y)),K(x,y / (T((w \ u) \ 1,u) / z))) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[para(13072(a,1),18499(a,1,1,1))].">
      <j1 rule="para" parents="13072 18499"/>
    </justification>
  </clause>

  <clause id="19283">
    <literal><![CDATA[
      T(K(x,(y * z) * (u / w)) * a(z,y,K(x,(u / w) * y)),K(x,y / (T((w \ u) \ 1,u) / z))) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[para(12984(a,1),19282(a,1,1,2,3))].">
      <j1 rule="para" parents="12984 19282"/>
    </justification>
  </clause>

  <clause id="19284">
    <literal><![CDATA[
      T(K(x,(y * z) * (u / w)) * a(z,y,K(x,(w \ u) * y)),K(x,y / (T((w \ u) \ 1,u) / z))) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[para(18380(a,1),19283(a,1,1,2))].">
      <j1 rule="para" parents="18380 19283"/>
    </justification>
  </clause>

  <clause id="19285">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) * y)) * K(z,(y * x) * (w / u)) = K(z,y / (T((u \ w) \ 1,w) / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,18494,a(flip),b,19284,a)].">
      <j1 rule="hyper" parents="63 18494 19284"/>
    </justification>
  </clause>

  <clause id="19287">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) * y)) * K(z,(y * x) * (w / u)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z,y / (((w / u) \ 1) / x)) = v5
    ]]></literal>
    <justification jstring="[para(19285(a,2),18970(a,1))].">
      <j1 rule="para" parents="19285 18970"/>
    </justification>
  </clause>

  <clause id="19288">
    <literal><![CDATA[
      (x * y) \ (((x * K(z,u)) * y) * K(u,T((x * y) / (x * (z \ y)),(x * K(z,u)) * y))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,19280,a(flip),b,19253,a),flip(a)].">
      <j1 rule="hyper" parents="347 19280 19253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19289">
    <literal><![CDATA[
      (x * y) \ (((x * K(z,u)) * y) * K(u,T((x * y) / (x * (z \ y)),x * y))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(9018(a,1),19288(a,1,2,2))].">
      <j1 rule="para" parents="9018 19288"/>
    </justification>
  </clause>

  <clause id="19290">
    <literal><![CDATA[
      (x * y) \ (((x * K(z,u)) * y) * K(u,(x * (z \ y)) \ (x * y))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(7626(a,1),19289(a,1,2,2))].">
      <j1 rule="para" parents="7626 19289"/>
    </justification>
  </clause>

  <clause id="19293">
    <literal><![CDATA[
      (x * y) \ (((x * K(z,u)) * y) * K(L(u,y,x),T(z,y))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(11106(a,1),19290(a,1,2,2))].">
      <j1 rule="para" parents="11106 19290"/>
    </justification>
  </clause>

  <clause id="19294">
    <literal><![CDATA[
      (x * y) \ (((K(z,u) * x) * y) * K(L(T(u,x),y,x),T(z,y))) = a(x,K(z,T(u,x)),y)
    ]]></literal>
    <justification jstring="[para(7104(a,1),19293(a,1,2,1,1))].">
      <j1 rule="para" parents="7104 19293"/>
    </justification>
  </clause>

  <clause id="19295">
    <literal><![CDATA[
      (x * y) \ (((K(z,u) * x) * y) * K(L(u,y,x),T(T(z,y),x))) = a(x,K(z,T(u,x)),y)
    ]]></literal>
    <justification jstring="[para(7132(a,1),19294(a,1,2,2))].">
      <j1 rule="para" parents="7132 19294"/>
    </justification>
  </clause>

  <clause id="19296">
    <literal><![CDATA[
      (x * y) \ (((K(z,u) * x) * y) * K(L(u,y,x),T(T(z,y),x))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,19083,a(flip),b,19295,a),flip(a)].">
      <j1 rule="hyper" parents="347 19083 19295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19298">
    <literal><![CDATA[
      (x * y) \ (((K(z,u) * x) * y) * K(u,L(T(T(z,y),x),y,x))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(11108(a,1),19296(a,1,2,2))].">
      <j1 rule="para" parents="11108 19296"/>
    </justification>
  </clause>

  <clause id="19299">
    <literal><![CDATA[
      (x * y) \ ((K(z,u) * x) * (y * K(u,T(T(z,y),x)))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(18030(a,1),19298(a,1,2))].">
      <j1 rule="para" parents="18030 19298"/>
    </justification>
  </clause>

  <clause id="19300">
    <literal><![CDATA[
      (x * y) \ ((K(z,u) * x) * (K(u,T(z,x)) * y)) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(7172(a,1),19299(a,1,2,2))].">
      <j1 rule="para" parents="7172 19299"/>
    </justification>
  </clause>

  <clause id="19301">
    <literal><![CDATA[
      (x * y) \ ((x * K(z,u)) * (K(u,z) * y)) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(10285(a,1),19300(a,1,2))].">
      <j1 rule="para" parents="10285 19300"/>
    </justification>
  </clause>

  <clause id="19302">
    <literal><![CDATA[
      a(x,K(y,z),K(z,y) * u) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(5291,a,19301,a)].">
      <j1 rule="hyper" parents="5291 19301"/>
    </justification>
  </clause>

  <clause id="19303">
    <literal><![CDATA[
      ((K(x,y) * (K(y,x) * z)) * u) \ (R(u,K(x,y),K(y,x) * z) * T(K(x,y) * (K(y,x) * z),u)) = a(u,K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,10457,a(flip),b,19302,a)].">
      <j1 rule="hyper" parents="63 10457 19302"/>
    </justification>
  </clause>

  <clause id="19304">
    <literal><![CDATA[
      (x * y) \ (R(y,K(z,u),K(u,z) * x) * T(K(z,u) * (K(u,z) * x),y)) = a(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[para(5261(a,1),19303(a,1,1,1))].">
      <j1 rule="para" parents="5261 19303"/>
    </justification>
  </clause>

  <clause id="19305">
    <literal><![CDATA[
      (x * y) \ (L(y,K(z,u),K(u,z) * x) * T(K(z,u) * (K(u,z) * x),y)) = a(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[para(17872(a,1),19304(a,1,2,1))].">
      <j1 rule="para" parents="17872 19304"/>
    </justification>
  </clause>

  <clause id="19306">
    <literal><![CDATA[
      (x * y) \ (L(y,K(z,u),K(u,z) * x) * T(x,y)) = a(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[para(5261(a,1),19305(a,1,2,2,1))].">
      <j1 rule="para" parents="5261 19305"/>
    </justification>
  </clause>

  <clause id="19307">
    <literal><![CDATA[
      (x * y) \ (x * L(y,K(z,u),K(u,z) * x)) = a(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[para(18188(a,1),19306(a,1,2))].">
      <j1 rule="para" parents="18188 19306"/>
    </justification>
  </clause>

  <clause id="19308">
    <literal><![CDATA[
      (x * y) \ ((x * K(z,u)) * (K(u,z) * y)) = a(y,K(u,z),x)
    ]]></literal>
    <justification jstring="[para(10461(a,1),19307(a,1,2))].">
      <j1 rule="para" parents="10461 19307"/>
    </justification>
  </clause>

  <clause id="19309">
    <literal><![CDATA[
      a(x,K(y,z),u) = a(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,19301,a(flip),b,19308,a)].">
      <j1 rule="hyper" parents="63 19301 19308"/>
    </justification>
  </clause>

  <clause id="19310">
    <literal><![CDATA[
      a(x,K(y,z),u) / (w \ T(a(u,K(z,y),x),w)) = T(w,a(u,K(z,y),x))
    ]]></literal>
    <justification jstring="[hyper(131,a,19309,a,b,4300,a)].">
      <j1 rule="hyper" parents="131 19309 4300"/>
    </justification>
  </clause>

  <clause id="19311">
    <literal><![CDATA[
      T(a(x,K(y,z),u),w) = a(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(37,a,18187,a(flip),b,19310,a)].">
      <j1 rule="hyper" parents="37 18187 19310"/>
    </justification>
  </clause>

  <clause id="19312">
    <literal><![CDATA[
      a(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,K(z,y),x) = w
    ]]></literal>
    <justification jstring="[para(19311(a,1),201(a,1)),flip(b)].">
      <j1 rule="para" parents="19311 201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19313">
    <literal><![CDATA[
      L(a(x,K(y,z),u),w,K(v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(u,K(z,y),x) = v7
    ]]></literal>
    <justification jstring="[para(19311(a,1),14422(a,1,1)),flip(b)].">
      <j1 rule="para" parents="19311 14422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19314">
    <literal><![CDATA[
      T(K(x,K(y,z * (u \ w)) * v5),v5 * T(v5 \ K(w \ (u * (z \ 1)),y),x)) = (v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) \ K(w \ (u * (1 / z)),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,18741,a(flip),b,17372,a)].">
      <j1 rule="hyper" parents="63 18741 17372"/>
    </justification>
  </clause>

  <clause id="19315">
    <literal><![CDATA[
      T(K(x,K(y,z * (u \ w)) * v5),K(v5,x) * K(y,w \ (u * (z \ 1)))) = (v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) \ K(w \ (u * (1 / z)),y)
    ]]></literal>
    <justification jstring="[hyper(16336,a,19314,a)].">
      <j1 rule="hyper" parents="16336 19314"/>
    </justification>
  </clause>

  <clause id="19316">
    <literal><![CDATA[
      T(K(x,K(y,z * (u \ w)) * v5),K(y,z * (u \ w)) * K(v5,x)) = (v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) \ K(w \ (u * (1 / z)),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,17373,a(flip),b,19315,a)].">
      <j1 rule="hyper" parents="63 17373 19315"/>
    </justification>
  </clause>

  <clause id="19317">
    <literal><![CDATA[
      (x \ T(x * K(y \ (z * (u \ 1)),w),v5)) \ K(y \ (z * (1 / u)),w) = K(v5,T(K(w,u * (z \ y)) * x,K(w,u * (z \ y))))
    ]]></literal>
    <justification jstring="[hyper(16154,a,19316,a),flip(a)].">
      <j1 rule="hyper" parents="16154 19316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19319">
    <literal><![CDATA[
      (x \ T(x * K(y \ (z * (u \ 1)),w),v5)) \ K(y \ (z * (1 / u)),w) = K(v5,x * K(w,u * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(347,a,10345,a(flip),b,19317,a),flip(a)].">
      <j1 rule="hyper" parents="347 10345 19317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19320">
    <literal><![CDATA[
      (x \ T(x * K(y \ (z * (u \ 1)),w),v5)) \ K(y \ (z * (u \ 1)),w) = K(v5,x * K(w,u * (z \ y)))
    ]]></literal>
    <justification jstring="[para(3915(a,1),19319(a,1,2))].">
      <j1 rule="para" parents="3915 19319"/>
    </justification>
  </clause>

  <clause id="19321">
    <literal><![CDATA[
      K(x,y * K(z \ (u * (w \ 1)),v5)) = K(x,y * K(v5,w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(13235,a,19320,a)].">
      <j1 rule="hyper" parents="13235 19320"/>
    </justification>
  </clause>

  <clause id="19322">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = K(x,(y \ z) * K(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(15675,a,19321,a)].">
      <j1 rule="hyper" parents="15675 19321"/>
    </justification>
  </clause>

  <clause id="19323">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[para(13045(a,1),19322(a,2,2))].">
      <j1 rule="para" parents="13045 19322"/>
    </justification>
  </clause>

  <clause id="19324">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[para(5704(a,1),19323(a,1,2,2))].">
      <j1 rule="para" parents="5704 19323"/>
    </justification>
  </clause>

  <clause id="19325">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,v5 * (w * (u \ 1)))) = v6
    ]]></literal>
    <justification jstring="[para(19324(a,1),15924(a,1))].">
      <j1 rule="para" parents="19324 15924"/>
    </justification>
  </clause>

  <clause id="19326">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(19325,a,19108,a)].">
      <j1 rule="hyper" parents="19325 19108"/>
    </justification>
  </clause>

  <clause id="19327">
    <literal><![CDATA[
      K(T(x,y / z),((z \ 1) * y) \ T(u,z * (x * y))) = K(T(x,y / z),u / ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,18001,a(flip),b,19326,a),flip(a)].">
      <j1 rule="hyper" parents="63 18001 19326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19328">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ T(u,y * (x * z)),z / y)) = K(T(x,z / y),u / ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(7488,a,19327,a)].">
      <j1 rule="hyper" parents="7488 19327"/>
    </justification>
  </clause>

  <clause id="19329">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ T(u,y * (x * z)),z * y)) = K(T(x,z / y),u / ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(13667,a,19328,a)].">
      <j1 rule="hyper" parents="13667 19328"/>
    </justification>
  </clause>

  <clause id="19330">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / ((z \ 1) * u)) = K(T(x,u / z),y / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(14577,a,19329,a)].">
      <j1 rule="hyper" parents="14577 19329"/>
    </justification>
  </clause>

  <clause id="19331">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / ((z \ 1) * u)) = K(x,T(y / ((z \ 1) * u),u / z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7093,a(flip),b,19330,a),flip(a)].">
      <j1 rule="hyper" parents="347 7093 19330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19332">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / ((z \ 1) * u)) = K(x,T(((z \ 1) * u) \ y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(15247(a,1),19331(a,2,2))].">
      <j1 rule="para" parents="15247 19331"/>
    </justification>
  </clause>

  <clause id="19333">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / ((z \ 1) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z \ 1) * u) \ y) = w
    ]]></literal>
    <justification jstring="[para(19332(a,2),13598(a,1))].">
      <j1 rule="para" parents="19332 13598"/>
    </justification>
  </clause>

  <clause id="19334">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z \ 1) * u) \ y) = w
    ]]></literal>
    <justification jstring="[para(18903(a,1),19333(a,1))].">
      <j1 rule="para" parents="18903 19333"/>
    </justification>
  </clause>

  <clause id="19335">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(x,((z \ 1) * u) \ y)
    ]]></literal>
    <justification jstring="[hyper(19334,a,19022,a),flip(a)].">
      <j1 rule="hyper" parents="19334 19022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19336">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(19169,a,19335,a),flip(a)].">
      <j1 rule="hyper" parents="19169 19335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19337">
    <literal><![CDATA[
      K(x,(y \ z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(18962,a,19336,a)].">
      <j1 rule="hyper" parents="18962 19336"/>
    </justification>
  </clause>

  <clause id="19338">
    <literal><![CDATA[
      T(x,(y \ z) \ u) = T(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(132,a,19337,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 19337 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19339">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * (u \ (y * z))) = K(x,L(T(z,y),y,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,19228,a(flip),b,19337,a),flip(a)].">
      <j1 rule="hyper" parents="63 19228 19337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19340">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) * y)) * K(z,(y * x) / (u / w)) = K(z,y / ((u / w) / x))
    ]]></literal>
    <justification jstring="[para(19337(a,1),18430(a,1,1,3))].">
      <j1 rule="para" parents="19337 18430"/>
    </justification>
  </clause>

  <clause id="19341">
    <literal><![CDATA[
      T(x,(y \ (y / z)) * u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(83(a,1),19338(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 19338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19342">
    <literal><![CDATA[
      T(x,(y \ (y / z)) \ u) = T(x,z * u)
    ]]></literal>
    <justification jstring="[para(83(a,1),19338(a,2,2,1))].">
      <j1 rule="para" parents="83 19338"/>
    </justification>
  </clause>

  <clause id="19343">
    <literal><![CDATA[
      K(T(x,(y \ z) * u) * ((z \ y) \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(((z \ y) \ u) * x,w) = v5
    ]]></literal>
    <justification jstring="[para(19338(a,1),10389(a,1,1,1))].">
      <j1 rule="para" parents="19338 10389"/>
    </justification>
  </clause>

  <clause id="19344">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * T(w,(L(x,y,z) \ x) * u) = w * (((x \ L(x,y,z)) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(19338(a,1),13459(a,1,2))].">
      <j1 rule="para" parents="19338 13459"/>
    </justification>
  </clause>

  <clause id="19345">
    <literal><![CDATA[
      T(T(x,y \ (y \ 1)),z / (u \ (u / y))) = T(x,z * (u \ (u / y)))
    ]]></literal>
    <justification jstring="[para(19341(a,1),14480(a,1,1))].">
      <j1 rule="para" parents="19341 14480"/>
    </justification>
  </clause>

  <clause id="19346">
    <literal><![CDATA[
      T(x,(y \ (y / z)) \ (u \ w)) = T(x,z / (w \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,19024,a,b,19342,a),flip(a)].">
      <j1 rule="hyper" parents="347 19024 19342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19347">
    <literal><![CDATA[
      T(x,((y \ z) / z) \ u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17740,a,b,19342,a)].">
      <j1 rule="hyper" parents="63 17740 19342"/>
    </justification>
  </clause>

  <clause id="19349">
    <literal><![CDATA[
      T(x,(y / z) \ u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(83(a,1),19347(a,1,2,1,1))].">
      <j1 rule="para" parents="83 19347"/>
    </justification>
  </clause>

  <clause id="19350">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) \ u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18921,a,b,19349,a)].">
      <j1 rule="hyper" parents="63 18921 19349"/>
    </justification>
  </clause>

  <clause id="19351">
    <literal><![CDATA[
      T(x,((y \ 1) / z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(19350(a,1),12024(a,1))].">
      <j1 rule="para" parents="19350 12024"/>
    </justification>
  </clause>

  <clause id="19352">
    <literal><![CDATA[
      T(x,(y \ (y / z)) \ u) = T(x,z / (w \ (w / u)))
    ]]></literal>
    <justification jstring="[para(83(a,1),19346(a,1,2,2))].">
      <j1 rule="para" parents="83 19346"/>
    </justification>
  </clause>

  <clause id="19353">
    <literal><![CDATA[
      T(T(x,K(y,z)),(u \ (u / y)) \ (z \ 1)) = T(x,L(z,z,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,19016,a(flip),b,19352,a),flip(a)].">
      <j1 rule="hyper" parents="347 19016 19352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19354">
    <literal><![CDATA[
      K(x,(y \ z) * (z \ (u * y))) = K(x,L(T(u,y),y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,17237,a(flip),b,19339,a)].">
      <j1 rule="hyper" parents="63 17237 19339"/>
    </justification>
  </clause>

  <clause id="19355">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,L(T(z,y),y,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,17994,a,b,19354,a)].">
      <j1 rule="hyper" parents="63 17994 19354"/>
    </justification>
  </clause>

  <clause id="19357">
    <literal><![CDATA[
      T(T(x,y \ (y \ 1)),(z \ (z / u)) \ y) = T(x,u * (w \ (w / y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19352,a,b,19345,a)].">
      <j1 rule="hyper" parents="63 19352 19345"/>
    </justification>
  </clause>

  <clause id="19359">
    <literal><![CDATA[
      T(x,y \ (y \ ((z \ (z / u)) \ y))) = T(x,u * (w \ (w / y)))
    ]]></literal>
    <justification jstring="[hyper(13810,a,19357,a)].">
      <j1 rule="hyper" parents="13810 19357"/>
    </justification>
  </clause>

  <clause id="19361">
    <literal><![CDATA[
      T(x,(y \ (y / z)) \ (u \ 1)) = T(x,z * (w \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(13901,a,19359,a)].">
      <j1 rule="hyper" parents="13901 19359"/>
    </justification>
  </clause>

  <clause id="19362">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (u \ (u / z))) = T(x,L(z,z,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,19353,a(flip),b,19361,a),flip(a)].">
      <j1 rule="hyper" parents="63 19353 19361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19363">
    <literal><![CDATA[
      T(x,L(y,y,z) \ u) = T(x,(w \ (w / y)) * u)
    ]]></literal>
    <justification jstring="[hyper(13949,a,19362,a),flip(a)].">
      <j1 rule="hyper" parents="13949 19362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19364">
    <literal><![CDATA[
      T(x,L(y / (y / z),y / (y / z),u) \ w) = T(x,(y \ ((z * (y / z)) / z)) * w)
    ]]></literal>
    <justification jstring="[para(4396(a,2),19363(a,2,2,1,2))].">
      <j1 rule="para" parents="4396 19363"/>
    </justification>
  </clause>

  <clause id="19365">
    <literal><![CDATA[
      T(x,(y \ (y / z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ u) = w
    ]]></literal>
    <justification jstring="[para(19363(a,1),11982(a,1))].">
      <j1 rule="para" parents="19363 11982"/>
    </justification>
  </clause>

  <clause id="19366">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) * y)) * K(z,(y * x) * (w / u)) = K(z,y / ((u / w) / x))
    ]]></literal>
    <justification jstring="[para(19032(a,1),19340(a,1,2))].">
      <j1 rule="para" parents="19032 19340"/>
    </justification>
  </clause>

  <clause id="19367">
    <literal><![CDATA[
      T(x,L(y / (y / z),(y / z) \ y,y) \ u) = T(x,(y \ ((z * (y / z)) / z)) * u)
    ]]></literal>
    <justification jstring="[para(12398(a,1),19364(a,1,2,1))].">
      <j1 rule="para" parents="12398 19364"/>
    </justification>
  </clause>

  <clause id="19368">
    <literal><![CDATA[
      K(x,y / (((z / u) \ 1) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(19287,a,19366,a)].">
      <j1 rule="hyper" parents="19287 19366"/>
    </justification>
  </clause>

  <clause id="19369">
    <literal><![CDATA[
      K(x,y * (z / ((u / w) \ 1))) = K(x,y / ((w / u) / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19032,a(flip),b,19368,a)].">
      <j1 rule="hyper" parents="63 19032 19368"/>
    </justification>
  </clause>

  <clause id="19370">
    <literal><![CDATA[
      K(x,y / ((z / u) / w)) = K(x,y * (w * (u / z)))
    ]]></literal>
    <justification jstring="[hyper(18916,a,19369,a),flip(a)].">
      <j1 rule="hyper" parents="18916 19369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19371">
    <literal><![CDATA[
      K(x,y * (z / (u / w))) = K(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19032,a(flip),b,19370,a)].">
      <j1 rule="hyper" parents="63 19032 19370"/>
    </justification>
  </clause>

  <clause id="19372">
    <literal><![CDATA[
      K(x,y * (z * (u / T(y,u * z)))) = K(x,y \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18735,a(flip),b,19370,a),flip(a)].">
      <j1 rule="hyper" parents="63 18735 19370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19373">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) * (u / w))) = K(x,y * ((w / u) \ z))
    ]]></literal>
    <justification jstring="[hyper(17485,a,19371,a),flip(a)].">
      <j1 rule="hyper" parents="17485 19371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19374">
    <literal><![CDATA[
      K(x,y \ ((y * z) * u)) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,17656,a(flip),b,19372,a),flip(a)].">
      <j1 rule="hyper" parents="63 17656 19372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19375">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) / u)) * u) = K(x,u \ ((u * y) / z))
    ]]></literal>
    <justification jstring="[hyper(18940,a,19374,a),flip(a)].">
      <j1 rule="hyper" parents="18940 19374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19376">
    <literal><![CDATA[
      K(x,y \ ((T(z,y * K(u,w)) * y) * v5)) = K(x,(z * (v5 / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,17963,a,b,19374,a)].">
      <j1 rule="hyper" parents="63 17963 19374"/>
    </justification>
  </clause>

  <clause id="19377">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) / u)) * u) = K(x,(y / (u * z)) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,19034,a(flip),b,19375,a),flip(a)].">
      <j1 rule="hyper" parents="347 19034 19375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19378">
    <literal><![CDATA[
      K(x,y * ((z / u) \ w)) = K(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(17936,a,19373,a),flip(a)].">
      <j1 rule="hyper" parents="17936 19373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19379">
    <literal><![CDATA[
      T(x,y * ((z / u) \ w)) = T(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(132,a,19378,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 19378 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19380">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w \ K(u,z)))) = K(x,y / (w * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19029,a(flip),b,19378,a),flip(a)].">
      <j1 rule="hyper" parents="63 19029 19378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19381">
    <literal><![CDATA[
      K(x,y / (z * (u \ w))) = K(x,y * ((w \ u) / z))
    ]]></literal>
    <justification jstring="[hyper(18947,a,19380,a),flip(a)].">
      <j1 rule="hyper" parents="18947 19380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19382">
    <literal><![CDATA[
      K(x,L(y / (z \ u),z \ u,z) * ((z \ u) / y)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18708,a(flip),b,19381,a),flip(a)].">
      <j1 rule="hyper" parents="63 18708 19381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19383">
    <literal><![CDATA[
      a(x,y \ z,K(u \ (y \ z),y)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19197,a(flip),b,19382,a)].">
      <j1 rule="hyper" parents="63 19197 19382"/>
    </justification>
  </clause>

  <clause id="19384">
    <literal><![CDATA[
      a(x,y \ z,K(u \ z,y)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(14167,a,19383,a)].">
      <j1 rule="hyper" parents="14167 19383"/>
    </justification>
  </clause>

  <clause id="19385">
    <literal><![CDATA[
      a(x,y,K(z \ y,u)) = a(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(14270,a,19384,a)].">
      <j1 rule="hyper" parents="14270 19384"/>
    </justification>
  </clause>

  <clause id="19386">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19383,a(flip),b,19385,a),flip(a)].">
      <j1 rule="hyper" parents="63 19383 19385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19387">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = x * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(19385(a,1),18441(a,2,2))].">
      <j1 rule="para" parents="19385 18441"/>
    </justification>
  </clause>

  <clause id="19388">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,u,K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(19387(a,2),14402(a,1))].">
      <j1 rule="para" parents="19387 14402"/>
    </justification>
  </clause>

  <clause id="19389">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = L(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(19388,a,18615,a),flip(a)].">
      <j1 rule="hyper" parents="19388 18615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19390">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,K(u,w)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,7672,a(flip),b,19389,a),flip(a)].">
      <j1 rule="hyper" parents="128 7672 19389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19391">
    <literal><![CDATA[
      x * a(y,x,K(z,x \ u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18612,a(flip),b,19389,a)].">
      <j1 rule="hyper" parents="63 18612 19389"/>
    </justification>
  </clause>

  <clause id="19392">
    <literal><![CDATA[
      x * a(y,x,K(z,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(19386(a,1),19391(a,1,2))].">
      <j1 rule="para" parents="19386 19391"/>
    </justification>
  </clause>

  <clause id="19393">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(34,a,14390,a,b,19392,a),flip(a)].">
      <j1 rule="hyper" parents="34 14390 19392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19394">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,19393,a,b,14355,a)].">
      <j1 rule="hyper" parents="134 19393 14355"/>
    </justification>
  </clause>

  <clause id="19395">
    <literal><![CDATA[
      K(x,y) * a(x,y,K(z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(19393(a,2),11198(a,1,2))].">
      <j1 rule="para" parents="19393 11198"/>
    </justification>
  </clause>

  <clause id="19396">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(19393(a,1),13997(a,1,2))].">
      <j1 rule="para" parents="19393 13997"/>
    </justification>
  </clause>

  <clause id="19397">
    <literal><![CDATA[
      L(x,y,K(z,u)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(14428,a,19394,a)].">
      <j1 rule="hyper" parents="14428 19394"/>
    </justification>
  </clause>

  <clause id="19398">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(19393(a,2),19394(a,1,2))].">
      <j1 rule="para" parents="19393 19394"/>
    </justification>
  </clause>

  <clause id="19399">
    <literal><![CDATA[
      L(x,T(y,z),K(u,w)) = L(x,u,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(18816,a,19397,a),flip(a)].">
      <j1 rule="hyper" parents="18816 19397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19400">
    <literal><![CDATA[
      L(R(x,y,z),u,K(y,z)) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(14482,a,19397,a),flip(a)].">
      <j1 rule="hyper" parents="14482 19397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19401">
    <literal><![CDATA[
      L(x,y * z,K(y,u)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(14437,a,19397,a)].">
      <j1 rule="hyper" parents="14437 19397"/>
    </justification>
  </clause>

  <clause id="19402">
    <literal><![CDATA[
      L(x,y,K(x * z,u)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,14427,a,b,19397,a)].">
      <j1 rule="hyper" parents="347 14427 19397"/>
    </justification>
  </clause>

  <clause id="19403">
    <literal><![CDATA[
      L(T(x,y),z,K(y,u)) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,14348,a(flip),b,19397,a),flip(a)].">
      <j1 rule="hyper" parents="347 14348 19397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19405">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,y,K(z,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (z * u) = w
    ]]></literal>
    <justification jstring="[para(19397(a,1),322(a,1,2))].">
      <j1 rule="para" parents="19397 322"/>
    </justification>
  </clause>

  <clause id="19406">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,u,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(19397(a,2),3524(a,1))].">
      <j1 rule="para" parents="19397 3524"/>
    </justification>
  </clause>

  <clause id="19407">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ R(x,u,z) = T(x \ R(x,u,z),y)
    ]]></literal>
    <justification jstring="[para(19397(a,2),17106(a,1,1))].">
      <j1 rule="para" parents="19397 17106"/>
    </justification>
  </clause>

  <clause id="19408">
    <literal><![CDATA[
      L(x,T(y,z),K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u,K(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(19397(a,1),18816(a,1))].">
      <j1 rule="para" parents="19397 18816"/>
    </justification>
  </clause>

  <clause id="19409">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,u,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(19398(a,1),14402(a,1))].">
      <j1 rule="para" parents="19398 14402"/>
    </justification>
  </clause>

  <clause id="19410">
    <literal><![CDATA[
      L(x,T(y,z),K((u \ 1) \ w,v5)) = L(x,u \ w,K(v5,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,3608,a(flip),b,19399,a),flip(a)].">
      <j1 rule="hyper" parents="347 3608 19399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19411">
    <literal><![CDATA[
      ((x * y) * K(z,u)) / (z * (y * K(z,u))) = L(R(x / z,z,y),u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14375,a(flip),b,19401,a)].">
      <j1 rule="hyper" parents="63 14375 19401"/>
    </justification>
  </clause>

  <clause id="19412">
    <literal><![CDATA[
      R(L(x,y,K(z,u)) \ R(x,u,z),x,y) = T((x * y) \ (R(x,u,z) * y),x)
    ]]></literal>
    <justification jstring="[para(19402(a,1),17107(a,1,1,1))].">
      <j1 rule="para" parents="19402 17107"/>
    </justification>
  </clause>

  <clause id="19413">
    <literal><![CDATA[
      T(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(19403(a,1),14452(a,1))].">
      <j1 rule="para" parents="19403 14452"/>
    </justification>
  </clause>

  <clause id="19414">
    <literal><![CDATA[
      L(R(x,y,z),u,K(z,y)) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(14430,a,19400,a)].">
      <j1 rule="hyper" parents="14430 19400"/>
    </justification>
  </clause>

  <clause id="19415">
    <literal><![CDATA[
      K(x,L(y,z,u * z)) = K(x,y) * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(11297(a,1),19395(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11297 19395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19416">
    <literal><![CDATA[
      K(x,L(y,z,u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(14148,a,19396,a)].">
      <j1 rule="hyper" parents="14148 19396"/>
    </justification>
  </clause>

  <clause id="19417">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(19396(a,1),14148(a,1))].">
      <j1 rule="para" parents="19396 14148"/>
    </justification>
  </clause>

  <clause id="19418">
    <literal><![CDATA[
      K(x,L((y * z) \ u,y,z)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(15078,a,19416,a),flip(a)].">
      <j1 rule="hyper" parents="15078 19416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19419">
    <literal><![CDATA[
      K(x,L(y,z,(u \ 1) * w)) = K(x,L(y,u \ w,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,18801,a,b,19416,a)].">
      <j1 rule="hyper" parents="347 18801 19416"/>
    </justification>
  </clause>

  <clause id="19420">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,y,x)) = K((x * y) \ (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,11120,a(flip),b,19416,a),flip(a)].">
      <j1 rule="hyper" parents="347 11120 19416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19421">
    <literal><![CDATA[
      (x * y) * K(z,L(u,x,y)) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ (x * (y * K(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(19416(a,1),11077(a,1,2))].">
      <j1 rule="para" parents="19416 11077"/>
    </justification>
  </clause>

  <clause id="19422">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,x,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x * z),u) = w
    ]]></literal>
    <justification jstring="[para(19416(a,1),15081(a,1))].">
      <j1 rule="para" parents="19416 15081"/>
    </justification>
  </clause>

  <clause id="19423">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(13998(a,2),19417(a,1))].">
      <j1 rule="para" parents="13998 19417"/>
    </justification>
  </clause>

  <clause id="19424">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,T(u,w)) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(19390(a,1),14439(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19390 14439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19425">
    <literal><![CDATA[
      K(x,T(y,z) \ (z \ u)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15093,a(flip),b,19418,a)].">
      <j1 rule="hyper" parents="63 15093 19418"/>
    </justification>
  </clause>

  <clause id="19427">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(132,a,19425,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 19425 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19428">
    <literal><![CDATA[
      K(x,y \ (T(z,y) \ u)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15618,a(flip),b,19425,a),flip(a)].">
      <j1 rule="hyper" parents="63 15618 19425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19429">
    <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(19425(a,1),17527(a,1))].">
      <j1 rule="para" parents="19425 17527"/>
    </justification>
  </clause>

  <clause id="19430">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ (y \ u)) = T(x,y \ ((z * (y \ 1)) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15919,a(flip),b,19427,a)].">
      <j1 rule="hyper" parents="63 15919 19427"/>
    </justification>
  </clause>

  <clause id="19431">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ u)) = T(x,T(z,y) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15900,a(flip),b,19427,a),flip(a)].">
      <j1 rule="hyper" parents="63 15900 19427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19432">
    <literal><![CDATA[
      T(x,T(T(y,z) \ (z \ u),w)) = K(x,w) * T(x * K(w,x),z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(134,a,19427,a(flip),b,8681,a),flip(a)].">
      <j1 rule="hyper" parents="134 19427 8681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19433">
    <literal><![CDATA[
      T(x,y \ (T(z,y) \ u)) = x * K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(134,a,19428,a(flip),b,4924,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 19428 4924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19434">
    <literal><![CDATA[
      K(x \ (T(y,x) \ z),u) = (w * K(u,y \ (x \ z))) \ w
    ]]></literal>
    <justification jstring="[para(19428(a,1),6123(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="19428 6123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19435">
    <literal><![CDATA[
      K(x,L(y,z,u * z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,19395,a(flip),b,19415,a),flip(a)].">
      <j1 rule="hyper" parents="347 19395 19415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19436">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y)) = K(x,z \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19136,a(flip),b,19435,a),flip(a)].">
      <j1 rule="hyper" parents="63 19136 19435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19437">
    <literal><![CDATA[
      K(x,L(y,z,u / z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),19435(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="12 19435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19438">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,u) / y) = x * K(z,L(T(u,y),x,y))
    ]]></literal>
    <justification jstring="[para(19435(a,1),18811(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19435 18811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19439">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) = K(x,u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,6468,a(flip),b,19437,a),flip(a)].">
      <j1 rule="hyper" parents="63 6468 19437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19440">
    <literal><![CDATA[
      K(x,(y * z) \ (y * u)) = K(x,y \ ((y / z) * u))
    ]]></literal>
    <justification jstring="[hyper(6472,a,19439,a)].">
      <j1 rule="hyper" parents="6472 19439"/>
    </justification>
  </clause>

  <clause id="19441">
    <literal><![CDATA[
      K(x,L(y,(z \ 1) * u,w)) = K(x,L(y,z \ u,w))
    ]]></literal>
    <justification jstring="[hyper(19417,a,19419,a)].">
      <j1 rule="hyper" parents="19417 19419"/>
    </justification>
  </clause>

  <clause id="19442">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w)) * (a(z,u,w) \ v5)) = T(x,a(z,u,w) * ((y \ 1) \ v5))
    ]]></literal>
    <justification jstring="[hyper(17066,a,19431,a),flip(a)].">
      <j1 rule="hyper" parents="17066 19431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19443">
    <literal><![CDATA[
      T(x,y \ (T(z,y) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(19433(a,2),4984(a,1))].">
      <j1 rule="para" parents="19433 4984"/>
    </justification>
  </clause>

  <clause id="19444">
    <literal><![CDATA[
      K(x,(y \ z) \ (((y \ 1) \ u) * (y \ 1))) = K(x,y \ ((y / z) * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,16405,a,b,19440,a)].">
      <j1 rule="hyper" parents="63 16405 19440"/>
    </justification>
  </clause>

  <clause id="19445">
    <literal><![CDATA[
      K(x,L(y,z \ u,w)) = K(x,L(y,z * u,w))
    ]]></literal>
    <justification jstring="[para(3599(a,1),19441(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3599 19441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19446">
    <literal><![CDATA[
      K((x \ y) \ (z * u),L(w,x * y,z)) = K((z \ (x \ y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(15080,a,19445,a),flip(a)].">
      <j1 rule="hyper" parents="15080 19445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19447">
    <literal><![CDATA[
      K(x,y) * a(x,z,a(y,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,a(v5,u,w),z)) = v6
    ]]></literal>
    <justification jstring="[para(13960(a,2),19423(a,1,2,3))].">
      <j1 rule="para" parents="13960 19423"/>
    </justification>
  </clause>

  <clause id="19448">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(14076(a,1),19423(a,1))].">
      <j1 rule="para" parents="14076 19423"/>
    </justification>
  </clause>

  <clause id="19449">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y)) = K(x,(z \ y) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(19448,a,19035,a)].">
      <j1 rule="hyper" parents="19448 19035"/>
    </justification>
  </clause>

  <clause id="19450">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(z,y),u,y)) = w
    ]]></literal>
    <justification jstring="[para(19355(a,2),19448(a,1))].">
      <j1 rule="para" parents="19355 19448"/>
    </justification>
  </clause>

  <clause id="19451">
    <literal><![CDATA[
      T(x,(y / z) \ (T(u,T(z \ y,z)) \ w)) = T(x,u \ (T(z \ y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(19443,a,15566,a),flip(a)].">
      <j1 rule="hyper" parents="19443 15566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19452">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(15565(a,2),19443(a,1))].">
      <j1 rule="para" parents="15565 19443"/>
    </justification>
  </clause>

  <clause id="19453">
    <literal><![CDATA[
      K(x,y \ ((z * y) * u)) = K(x,(y \ z) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19436,a(flip),b,19449,a)].">
      <j1 rule="hyper" parents="63 19436 19449"/>
    </justification>
  </clause>

  <clause id="19454">
    <literal><![CDATA[
      K(x,(y \ T(z,y * K(u,w))) * (y * v5)) = K(x,(z * (v5 / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,19376,a(flip),b,19453,a),flip(a)].">
      <j1 rule="hyper" parents="63 19376 19453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19455">
    <literal><![CDATA[
      T(x,L(y \ z,u,w) \ (y \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (L(z / y,u,w) \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(278(a,1),19452(a,1,2,1))].">
      <j1 rule="para" parents="278 19452"/>
    </justification>
  </clause>

  <clause id="19456">
    <literal><![CDATA[
      L(x,T(y,z),K(u * w,v5)) = L(x,u \ w,K(v5,y))
    ]]></literal>
    <justification jstring="[para(12975(a,1),19410(a,1,3))].">
      <j1 rule="para" parents="12975 19410"/>
    </justification>
  </clause>

  <clause id="19457">
    <literal><![CDATA[
      L(x,y \ z,K(u,w)) = L(x,y * z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(19408,a,19456,a),flip(a)].">
      <j1 rule="hyper" parents="19408 19456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19458">
    <literal><![CDATA[
      L(x,y * z,K(u,w \ 1)) = L(x,w,K(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(19406,a,19457,a),flip(a)].">
      <j1 rule="hyper" parents="19406 19457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19459">
    <literal><![CDATA[
      L(x,y,K(z \ u,w)) = L(x,y,K(z * u,w))
    ]]></literal>
    <justification jstring="[hyper(19406,a,19458,a),flip(a)].">
      <j1 rule="hyper" parents="19406 19458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19460">
    <literal><![CDATA[
      x \ L(x,y,K(z * u,w)) = a(x,y,K(z \ u,w))
    ]]></literal>
    <justification jstring="[hyper(128,a,19459,a(flip),b,14343,a)].">
      <j1 rule="hyper" parents="128 19459 14343"/>
    </justification>
  </clause>

  <clause id="19461">
    <literal><![CDATA[
      a(x,y,K(z \ u,w)) = a(x,y,K(z * u,w))
    ]]></literal>
    <justification jstring="[hyper(14391,a,19460,a),flip(a)].">
      <j1 rule="hyper" parents="14391 19460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19462">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u * w,y)) = K(x,L(y,z,w / u))
    ]]></literal>
    <justification jstring="[para(19461(a,1),17070(a,1,2))].">
      <j1 rule="para" parents="19461 17070"/>
    </justification>
  </clause>

  <clause id="19463">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),x,K(y,z) * u) = a(x,K(y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,18794,a(flip),b,19424,a),flip(a)].">
      <j1 rule="hyper" parents="63 18794 19424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19464">
    <literal><![CDATA[
      K(x \ (T(y,x) \ z),u) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,13585,a(flip),b,19434,a),flip(a)].">
      <j1 rule="hyper" parents="347 13585 19434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19465">
    <literal><![CDATA[
      K(T(x,y) \ (y \ z),u) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(15710,a,19464,a)].">
      <j1 rule="hyper" parents="15710 19464"/>
    </justification>
  </clause>

  <clause id="19466">
    <literal><![CDATA[
      K(a(x,y,z) \ (u \ w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(u \ (a(x,y,z) \ w),v5) = v6
    ]]></literal>
    <justification jstring="[para(19465(a,1),17125(a,1))].">
      <j1 rule="para" parents="19465 17125"/>
    </justification>
  </clause>

  <clause id="19467">
    <literal><![CDATA[
      K(x,L(y,z,u / w)) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[hyper(13995,a,19462,a),flip(a)].">
      <j1 rule="hyper" parents="13995 19462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19468">
    <literal><![CDATA[
      K(x,L(y,z,u \ w)) = K(x,L(y,z,u * w))
    ]]></literal>
    <justification jstring="[hyper(16929,a,19467,a)].">
      <j1 rule="hyper" parents="16929 19467"/>
    </justification>
  </clause>

  <clause id="19469">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,y,x * y)) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(15090,a,19468,a),flip(a)].">
      <j1 rule="hyper" parents="15090 19468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19470">
    <literal><![CDATA[
      x * K(x,L(y,z,u * w)) = T(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(134,a,19468,a(flip),b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 19468 4924"/>
    </justification>
  </clause>

  <clause id="19471">
    <literal><![CDATA[
      T(x,L(y,z,u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,u * w)) = v5
    ]]></literal>
    <justification jstring="[para(19470(a,1),4984(a,1))].">
      <j1 rule="para" parents="19470 4984"/>
    </justification>
  </clause>

  <clause id="19472">
    <literal><![CDATA[
      T(x,L((y \ z) \ ((y \ 1) * u),y \ z,y * 1)) = T(x,((y \ z) / T(y \ 1,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(19471,a,15088,a)].">
      <j1 rule="hyper" parents="19471 15088"/>
    </justification>
  </clause>

  <clause id="19473">
    <literal><![CDATA[
      K(T(x,y) \ z,L(u,y,x)) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19435,a(flip),b,19469,a)].">
      <j1 rule="hyper" parents="63 19435 19469"/>
    </justification>
  </clause>

  <clause id="19474">
    <literal><![CDATA[
      K((x * y) \ (y * z),u) = K(y \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19420,a(flip),b,19473,a)].">
      <j1 rule="hyper" parents="63 19420 19473"/>
    </justification>
  </clause>

  <clause id="19475">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ (y \ u)) = T(x,y * ((z * y) \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,13171,a(flip),b,19430,a),flip(a)].">
      <j1 rule="hyper" parents="347 13171 19430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19476">
    <literal><![CDATA[
      K((x \ y) \ (y * z),L(u,x,y)) = K((y \ (x \ y)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(14211,a,19446,a)].">
      <j1 rule="hyper" parents="14211 19446"/>
    </justification>
  </clause>

  <clause id="19477">
    <literal><![CDATA[
      K((x \ (y \ x)) \ z,u) = K(x \ (y * (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(19422,a,19476,a),flip(a)].">
      <j1 rule="hyper" parents="19422 19476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19478">
    <literal><![CDATA[
      K((((x \ (y \ x)) * ((y \ x) \ x)) \ T(y,x)) * z,u) = K(x \ (y * (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17731,a,b,19477,a)].">
      <j1 rule="hyper" parents="63 17731 19477"/>
    </justification>
  </clause>

  <clause id="19479">
    <literal><![CDATA[
      a(x,K(y,z),T(u,w)) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(17882,a,19463,a),flip(a)].">
      <j1 rule="hyper" parents="17882 19463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19482">
    <literal><![CDATA[
      a(T(x,y),K(z,u),w) = a(w,K(u,z),x)
    ]]></literal>
    <justification jstring="[hyper(19312,a,19479,a)].">
      <j1 rule="hyper" parents="19312 19479"/>
    </justification>
  </clause>

  <clause id="19483">
    <literal><![CDATA[
      a(x,K(y,z),L(u,w,K(v5,v6))) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(14337(a,2),19479(a,1,3))].">
      <j1 rule="para" parents="14337 19479"/>
    </justification>
  </clause>

  <clause id="19484">
    <literal><![CDATA[
      a(T(x,y),K(z,u),w * K(u,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x \ L(x,K(z,u),w),T(x,y),T(w,v6)) = v5
    ]]></literal>
    <justification jstring="[para(19479(a,1),19239(a,1))].">
      <j1 rule="para" parents="19479 19239"/>
    </justification>
  </clause>

  <clause id="19487">
    <literal><![CDATA[
      K(x \ (a(y,z,u) \ w),v5) = K(a(y,z,u) * (x \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(19466,a,16650,a)].">
      <j1 rule="hyper" parents="19466 16650"/>
    </justification>
  </clause>

  <clause id="19488">
    <literal><![CDATA[
      x \ (y * (x * K(z,u))) = T(y,x) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(19421,a,11072,a)].">
      <j1 rule="hyper" parents="19421 11072"/>
    </justification>
  </clause>

  <clause id="19489">
    <literal><![CDATA[
      x * (T(y,x) * K(z,u)) = y * (x * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(150,a,19488,a)].">
      <j1 rule="hyper" parents="150 19488"/>
    </justification>
  </clause>

  <clause id="19491">
    <literal><![CDATA[
      L((T(x,y) * K(z,T(u,w))) / K(z,T(u,w)),K(z,T(u,w)),y) = T((K(z,T(u,w)) * x) / K(z,T(u,w)),K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(19488(a,1),15724(a,1,1,1))].">
      <j1 rule="para" parents="19488 15724"/>
    </justification>
  </clause>

  <clause id="19492">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * (y * K(w,v5)) = y * (L(x,z,u) * K(w,v5))
    ]]></literal>
    <justification jstring="[para(5077(a,1),19489(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5077 19489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19494">
    <literal><![CDATA[
      x * (T(y,x) * a(z,u,K(w,v5))) = y * (x * K(a(z,u,w),v5))
    ]]></literal>
    <justification jstring="[para(12681(a,2),19489(a,1,2,2))].">
      <j1 rule="para" parents="12681 19489"/>
    </justification>
  </clause>

  <clause id="19495">
    <literal><![CDATA[
      x * T(y * a(z,u,K(w,v5)),x) = y * (x * K(a(z,u,w),v5))
    ]]></literal>
    <justification jstring="[para(17267(a,2),19494(a,1,2))].">
      <j1 rule="para" parents="17267 19494"/>
    </justification>
  </clause>

  <clause id="19496">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * v5 = x * (v5 * K(a(y,z,u),w))
    ]]></literal>
    <justification jstring="[hyper(315,a,19495,a)].">
      <j1 rule="hyper" parents="315 19495"/>
    </justification>
  </clause>

  <clause id="19497">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * v5 = x * (v5 * a(y,z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(12681(a,2),19496(a,2,2,2))].">
      <j1 rule="para" parents="12681 19496"/>
    </justification>
  </clause>

  <clause id="19498">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)),v5) = x
    ]]></literal>
    <justification jstring="[hyper(18007,a,19497,a)].">
      <j1 rule="hyper" parents="18007 19497"/>
    </justification>
  </clause>

  <clause id="19499">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,y,T(z,u)) * w) = a(x,y,K(z,u)) * w
    ]]></literal>
    <justification jstring="[hyper(63,a,15365,a(flip),b,19498,a)].">
      <j1 rule="hyper" parents="63 15365 19498"/>
    </justification>
  </clause>

  <clause id="19500">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      x = v6
    ]]></literal>
    <justification jstring="[para(19498(a,1),50(a,2))].">
      <j1 rule="para" parents="19498 50"/>
    </justification>
  </clause>

  <clause id="19502">
    <literal><![CDATA[
      L(x,y,T(z,u)) * (L(x,y,z) \ w) = a(x,y,K(z,u)) * w
    ]]></literal>
    <justification jstring="[hyper(63,a,15151,a(flip),b,19499,a)].">
      <j1 rule="hyper" parents="63 15151 19499"/>
    </justification>
  </clause>

  <clause id="19503">
    <literal><![CDATA[
      L(x,y,T(z,u)) * (L(x,y,z) \ u) = T(u,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,14038,a,b,19502,a),flip(a)].">
      <j1 rule="hyper" parents="347 14038 19502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19504">
    <literal><![CDATA[
      T(L(x,y,z) \ x,u) \ x = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,13262,a,b,19503,a)].">
      <j1 rule="hyper" parents="35 13262 19503"/>
    </justification>
  </clause>

  <clause id="19505">
    <literal><![CDATA[
      T(L(x,y,z) \ x,u) = L(x,y,T(z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(39,a,3309,a,b,19504,a),flip(a)].">
      <j1 rule="hyper" parents="39 3309 19504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19506">
    <literal><![CDATA[
      L(T(x,y),z,T(u,w)) \ T(x,L(y,z,u)) = T(L(x,z,u) \ x,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,16924,a,b,19505,a)].">
      <j1 rule="hyper" parents="347 16924 19505"/>
    </justification>
  </clause>

  <clause id="19507">
    <literal><![CDATA[
      T(T(L(x,y,z) \ x,u),w) \ T(x,u) = L(T(x,u),y,z) * K(w,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(19505(a,2),17557(a,1,1,1))].">
      <j1 rule="para" parents="19505 17557"/>
    </justification>
  </clause>

  <clause id="19508">
    <literal><![CDATA[
      (T(T(L(x,y,z) \ x,u),w) \ T(x,u)) \ L(T(x,u),y,z) = K(L(x,y,z) \ x,w)
    ]]></literal>
    <justification jstring="[para(19505(a,2),17711(a,1,1,1,1))].">
      <j1 rule="para" parents="19505 17711"/>
    </justification>
  </clause>

  <clause id="19509">
    <literal><![CDATA[
      T(x,L(y,z,u)) / L(T(x,y),z,T(u,w)) = T(L(x,z,u) \ x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,9498,a,b,19506,a)].">
      <j1 rule="hyper" parents="63 9498 19506"/>
    </justification>
  </clause>

  <clause id="19510">
    <literal><![CDATA[
      L(T(x,y),z,u) * a(w,z,K(x,u)) = L(T(x,y),z,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(36,a,17714,a,b,19509,a)].">
      <j1 rule="hyper" parents="36 17714 19509"/>
    </justification>
  </clause>

  <clause id="19511">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * (y * u)) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,19275,a(flip),b,19454,a)].">
      <j1 rule="hyper" parents="63 19275 19454"/>
    </justification>
  </clause>

  <clause id="19512">
    <literal><![CDATA[
      K(x,(y * (z / u)) * u) = K(x,(y / u) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(17223,a,19511,a),flip(a)].">
      <j1 rule="hyper" parents="17223 19511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19513">
    <literal><![CDATA[
      K(x,(y / z) * (z * (u \ 1))) = K(x,(y / (z * u)) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,19377,a(flip),b,19512,a),flip(a)].">
      <j1 rule="hyper" parents="63 19377 19512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19514">
    <literal><![CDATA[
      K(x,(y / (z * u)) * z) = K(x,(y / z) * (z / u))
    ]]></literal>
    <justification jstring="[hyper(18942,a,19513,a),flip(a)].">
      <j1 rule="hyper" parents="18942 19513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19515">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,u * ((y * u) \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,17287,a(flip),b,19514,a),flip(a)].">
      <j1 rule="hyper" parents="63 17287 19514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19516">
    <literal><![CDATA[
      K(x,y * ((z * y) \ (u * z))) = K(x,L(T(u,z),y,z))
    ]]></literal>
    <justification jstring="[hyper(19450,a,19515,a),flip(a)].">
      <j1 rule="hyper" parents="19450 19515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19517">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u)) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(19516(a,1),19027(a,1,2))].">
      <j1 rule="para" parents="19516 19027"/>
    </justification>
  </clause>

  <clause id="19518">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,u) / y) = (x * y) / (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19438,a,b,19517,a)].">
      <j1 rule="hyper" parents="63 19438 19517"/>
    </justification>
  </clause>

  <clause id="19519">
    <literal><![CDATA[
      (x * y) / (y * K(T(z,y),u)) = (x / (y \ 1)) * (y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,18542,a(flip),b,19518,a),flip(a)].">
      <j1 rule="hyper" parents="63 18542 19518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19520">
    <literal><![CDATA[
      (x / (y \ 1)) * (y \ K(z,u)) = (x * y) / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(7076(a,1),19519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7076 19519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19521">
    <literal><![CDATA[
      (x * (y / z)) / (K(u,y) * (y / z)) = (x / z) * (z * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(19060,a,19520,a),flip(a)].">
      <j1 rule="hyper" parents="19060 19520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19522">
    <literal><![CDATA[
      (x * (T(y,z) / u)) / (y / u) = (x / u) * (u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19205,a(flip),b,19521,a)].">
      <j1 rule="hyper" parents="63 19205 19521"/>
    </justification>
  </clause>

  <clause id="19523">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = L(x,K(u,z),y \ z)
    ]]></literal>
    <justification jstring="[para(19522(a,1),19218(a,1,1))].">
      <j1 rule="para" parents="19522 19218"/>
    </justification>
  </clause>

  <clause id="19524">
    <literal><![CDATA[
      L(x,K(y,z),u \ z) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(19388,a,19523,a),flip(a)].">
      <j1 rule="hyper" parents="19388 19523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19525">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18203,a(flip),b,19524,a),flip(a)].">
      <j1 rule="hyper" parents="63 18203 19524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19526">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(11471,a,19525,a),flip(a)].">
      <j1 rule="hyper" parents="11471 19525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19527">
    <literal><![CDATA[
      R(x,K(y,z),u) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(17890,a,19526,a)].">
      <j1 rule="hyper" parents="17890 19526"/>
    </justification>
  </clause>

  <clause id="19528">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,y,K(z,x)) = z * (T(K(x,y),z) * u)
    ]]></literal>
    <justification jstring="[para(19526(a,1),10167(a,1,2))].">
      <j1 rule="para" parents="19526 10167"/>
    </justification>
  </clause>

  <clause id="19529">
    <literal><![CDATA[
      L(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(19526(a,2),19409(a,1))].">
      <j1 rule="para" parents="19526 19409"/>
    </justification>
  </clause>

  <clause id="19530">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = R(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,19394,a,b,19527,a)].">
      <j1 rule="hyper" parents="347 19394 19527"/>
    </justification>
  </clause>

  <clause id="19532">
    <literal><![CDATA[
      x * a(x,T(y,z),K(u,w)) = R(x,K(u,w),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,18178,a(flip),b,19530,a),flip(a)].">
      <j1 rule="hyper" parents="347 18178 19530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19533">
    <literal><![CDATA[
      ((x * K(y,z)) * u) / (K(y,z) * u) = x * a(x,T(u,w),K(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,20,a(flip),b,19532,a)].">
      <j1 rule="hyper" parents="347 20 19532"/>
    </justification>
  </clause>

  <clause id="19534">
    <literal><![CDATA[
      x * (T(K(y,z),x) * u) = K(y,z) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(19405,a,19528,a),flip(a)].">
      <j1 rule="hyper" parents="19405 19528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19536">
    <literal><![CDATA[
      x * (K(y,T(z,x)) * u) = K(y,z) * (x * u)
    ]]></literal>
    <justification jstring="[para(7091(a,2),19534(a,1,2,1))].">
      <j1 rule="para" parents="7091 19534"/>
    </justification>
  </clause>

  <clause id="19537">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * u) = z * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(7371(a,1),19534(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7371 19534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19538">
    <literal><![CDATA[
      K(x,y * z) * (y * u) = y * (K(x,z * y) * u)
    ]]></literal>
    <justification jstring="[para(10344(a,1),19534(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10344 19534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19539">
    <literal><![CDATA[
      x \ (K(y,z) * (x * u)) = K(y,T(z,x)) * u
    ]]></literal>
    <justification jstring="[hyper(138,a,19536,a)].">
      <j1 rule="hyper" parents="138 19536"/>
    </justification>
  </clause>

  <clause id="19540">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ u) = z \ (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(128,a,169,a(flip),b,19536,a),flip(a)].">
      <j1 rule="hyper" parents="128 169 19536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19541">
    <literal><![CDATA[
      x \ (K(y,z) * (x * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) * u = w
    ]]></literal>
    <justification jstring="[para(19536(a,1),356(a,1,2))].">
      <j1 rule="para" parents="19536 356"/>
    </justification>
  </clause>

  <clause id="19542">
    <literal><![CDATA[
      x * (K(y,T(z,x)) * ((x \ 1) * u)) = K(y,z) * L(u,x,x)
    ]]></literal>
    <justification jstring="[para(3197(a,1),19536(a,2,2))].">
      <j1 rule="para" parents="3197 19536"/>
    </justification>
  </clause>

  <clause id="19543">
    <literal><![CDATA[
      K(x,T(y,z)) * ((z \ 1) * u) = (z \ 1) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(8853(a,1),19536(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8853 19536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19544">
    <literal><![CDATA[
      x \ (K(y,T(z,x)) * u) = K(y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(678,a,19537,a)].">
      <j1 rule="hyper" parents="678 19537"/>
    </justification>
  </clause>

  <clause id="19545">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * (y \ u)) = z * (T(y,x) \ u)
    ]]></literal>
    <justification jstring="[para(5209(a,1),19537(a,2,2))].">
      <j1 rule="para" parents="5209 19537"/>
    </justification>
  </clause>

  <clause id="19546">
    <literal><![CDATA[
      K(x,T(y,z)) * L(1 / u,u,z) = z \ (K(x,y) * (z / u))
    ]]></literal>
    <justification jstring="[para(3266(a,1),19539(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3266 19539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19547">
    <literal><![CDATA[
      a(x,y,z) \ (K(u,w) * v5) = K(u,w) * (a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(16866(a,1),19540(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16866 19540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19548">
    <literal><![CDATA[
      K(x,y) * (K(z,T(u,x)) * w) = T(x,y) * (K(z,u) * (x \ w))
    ]]></literal>
    <justification jstring="[hyper(134,a,19544,a(flip),b,5189,a),flip(a)].">
      <j1 rule="hyper" parents="134 19544 5189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19549">
    <literal><![CDATA[
      x \ (x \ (K(y,z) * u)) = K(y,z) * (x \ (x \ u))
    ]]></literal>
    <justification jstring="[para(19540(a,1),19544(a,1,2))].">
      <j1 rule="para" parents="19540 19544"/>
    </justification>
  </clause>

  <clause id="19550">
    <literal><![CDATA[
      K(x \ y,x) * (a(z,u,w) \ y) = a(z,u,w) \ ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(4898(a,1),19547(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4898 19547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19551">
    <literal><![CDATA[
      x * ((x \ 1) * (K(y,z) * u)) = K(y,z) * L(u,x,x)
    ]]></literal>
    <justification jstring="[para(19543(a,1),19542(a,1,2))].">
      <j1 rule="para" parents="19543 19542"/>
    </justification>
  </clause>

  <clause id="19552">
    <literal><![CDATA[
      L(K(x,y) * z,u,u) = K(x,y) * L(z,u,u)
    ]]></literal>
    <justification jstring="[hyper(3226,a,19551,a)].">
      <j1 rule="hyper" parents="3226 19551"/>
    </justification>
  </clause>

  <clause id="19553">
    <literal><![CDATA[
      L(K(x,y) * (K(y,x) * z),u,u) \ z = a(u,u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(19552(a,2),15328(a,1,1))].">
      <j1 rule="para" parents="19552 15328"/>
    </justification>
  </clause>

  <clause id="19554">
    <literal><![CDATA[
      a(x,x,K(y,z) * u) = L(u,x,x) \ u
    ]]></literal>
    <justification jstring="[para(5261(a,1),19553(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5261 19553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19555">
    <literal><![CDATA[
      a(x,x,K(y,z) * u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,14600,a(flip),b,19554,a),flip(a)].">
      <j1 rule="hyper" parents="347 14600 19554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19556">
    <literal><![CDATA[
      a(x,x,T(y * (z \ u),K(z,u))) = a(x,x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(8806(a,1),19555(a,1,3))].">
      <j1 rule="para" parents="8806 19555"/>
    </justification>
  </clause>

  <clause id="19557">
    <literal><![CDATA[
      a(x,x,y * (z / u)) = a(x,x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(19091,a,19556,a),flip(a)].">
      <j1 rule="hyper" parents="19091 19556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19560">
    <literal><![CDATA[
      ((x * (y * (x \ 1))) / x) \ (x \ (x * (y / x))) = K(x \ 1,y) * a(x,x,x * (x \ y))
    ]]></literal>
    <justification jstring="[para(19557(a,1),15336(a,2,2))].">
      <j1 rule="para" parents="19557 15336"/>
    </justification>
  </clause>

  <clause id="19561">
    <literal><![CDATA[
      ((x * K(y,z)) * u) / L(K(y,z) * u,w,a(w,v5,K(v6,v7))) = x * a(x,T(u,v8),K(y,z))
    ]]></literal>
    <justification jstring="[para(14012(a,2),19533(a,1,2))].">
      <j1 rule="para" parents="14012 19533"/>
    </justification>
  </clause>

  <clause id="19562">
    <literal><![CDATA[
      ((x * y) * K(z,u)) / (z * (y * K(z,u))) = R(x / z,z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,19414,a(flip),b,19411,a),flip(a)].">
      <j1 rule="hyper" parents="347 19414 19411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19563">
    <literal><![CDATA[
      T((x * y) \ (R(x,z,u) * y),x) = R(T(x \ R(x,z,u),y),x,y)
    ]]></literal>
    <justification jstring="[para(19407(a,1),19412(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19407 19412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19564">
    <literal><![CDATA[
      T(x \ R(x,y,z),x * u) = T(x \ R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(1212,a,19563,a)].">
      <j1 rule="hyper" parents="1212 19563"/>
    </justification>
  </clause>

  <clause id="19565">
    <literal><![CDATA[
      R(T(x \ R(x,y,z),u),x,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x * u) \ (R(x,y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(19563(a,1),3735(a,1))].">
      <j1 rule="para" parents="19563 3735"/>
    </justification>
  </clause>

  <clause id="19566">
    <literal><![CDATA[
      T(x \ 1,x * y) * R((((x \ 1) \ y) \ y) \ 1,z,u) = T(x \ R(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4528,a,b,19564,a)].">
      <j1 rule="hyper" parents="63 4528 19564"/>
    </justification>
  </clause>

  <clause id="19567">
    <literal><![CDATA[
      x \ (y \ ((L(y \ R(y,z,u),x,y) * y) * x)) = R(T(y \ R(y,z,u),x),y,x)
    ]]></literal>
    <justification jstring="[para(19564(a,1),1331(a,2,1))].">
      <j1 rule="para" parents="19564 1331"/>
    </justification>
  </clause>

  <clause id="19568">
    <literal><![CDATA[
      T(x,T(T(y,z) \ (z \ u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z \ (y \ u),w)) = v5
    ]]></literal>
    <justification jstring="[para(19432(a,2),8683(a,1))].">
      <j1 rule="para" parents="19432 8683"/>
    </justification>
  </clause>

  <clause id="19569">
    <literal><![CDATA[
      K(x,(y \ z) \ T(u,y \ 1)) = K(x,y \ ((y / z) * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(15824,a,19444,a)].">
      <j1 rule="hyper" parents="15824 19444"/>
    </justification>
  </clause>

  <clause id="19570">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * y))) = K(x,(y \ z) \ T(u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,15926,a(flip),b,19569,a),flip(a)].">
      <j1 rule="hyper" parents="63 15926 19569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19571">
    <literal><![CDATA[
      K(x,(y \ z) \ T(u,y)) = K(x,(u \ z) \ y)
    ]]></literal>
    <justification jstring="[hyper(18969,a,19570,a),flip(a)].">
      <j1 rule="hyper" parents="18969 19570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19572">
    <literal><![CDATA[
      T(x,(y \ z) \ T(u,y)) = T(x,(u \ z) \ y)
    ]]></literal>
    <justification jstring="[hyper(132,a,19571,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 19571 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19573">
    <literal><![CDATA[
      T(x,(y / z) \ (T(u,y / z) \ w)) = T(x,u \ (T(z \ y,z) \ w))
    ]]></literal>
    <justification jstring="[para(7419(a,1),19451(a,1,2,2,1))].">
      <j1 rule="para" parents="7419 19451"/>
    </justification>
  </clause>

  <clause id="19574">
    <literal><![CDATA[
      T(x,y \ (T(z \ u,z) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ ((u / z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(19573(a,1),19443(a,1))].">
      <j1 rule="para" parents="19573 19443"/>
    </justification>
  </clause>

  <clause id="19575">
    <literal><![CDATA[
      T(x,a(y,z,u) * ((w \ 1) \ v5)) = T(x,w * (a(y,z,u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(17113,a,19442,a),flip(a)].">
      <j1 rule="hyper" parents="17113 19442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19576">
    <literal><![CDATA[
      T(x,a(y,z,u) * (w * v5)) = T(x,w * (a(y,z,u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(18938,a,19575,a)].">
      <j1 rule="hyper" parents="18938 19575"/>
    </justification>
  </clause>

  <clause id="19577">
    <literal><![CDATA[
      T(x,((y \ 1) \ z) * a(u,u,w)) = T(x,y * (a(v5,v6,v6) \ z))
    ]]></literal>
    <justification jstring="[hyper(18890,a,19575,a)].">
      <j1 rule="hyper" parents="18890 19575"/>
    </justification>
  </clause>

  <clause id="19578">
    <literal><![CDATA[
      T(x,((y \ 1) \ z) * a(u,w,v5)) = T(x,y * (a(u,w,v5) \ z))
    ]]></literal>
    <justification jstring="[hyper(16875,a,19575,a)].">
      <j1 rule="hyper" parents="16875 19575"/>
    </justification>
  </clause>

  <clause id="19579">
    <literal><![CDATA[
      T(x,y * (a(z,z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * w) = v5
    ]]></literal>
    <justification jstring="[para(19576(a,1),18910(a,1))].">
      <j1 rule="para" parents="19576 18910"/>
    </justification>
  </clause>

  <clause id="19580">
    <literal><![CDATA[
      T(x,y * (a(z,u,u) \ w)) = T(x,y * (a(v5,v5,v6) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19577,a(flip),b,19578,a)].">
      <j1 rule="hyper" parents="63 19577 19578"/>
    </justification>
  </clause>

  <clause id="19581">
    <literal><![CDATA[
      K((((x \ (x / y)) * y) \ T(y,x)) * z,u) = K(x \ (y * (x * z)),u)
    ]]></literal>
    <justification jstring="[para(13356(a,1),19478(a,1,1,1,1))].">
      <j1 rule="para" parents="13356 19478"/>
    </justification>
  </clause>

  <clause id="19582">
    <literal><![CDATA[
      K(((x * ((y * x) \ y)) \ T(x,y)) * z,u) = K(y \ (x * (y * z)),u)
    ]]></literal>
    <justification jstring="[para(3261(a,1),19581(a,1,1,1,1))].">
      <j1 rule="para" parents="3261 19581"/>
    </justification>
  </clause>

  <clause id="19583">
    <literal><![CDATA[
      K((1 / ((x * y) \ y)) * z,u) = K(y \ (x * (y * z)),u)
    ]]></literal>
    <justification jstring="[para(9320(a,1),19582(a,1,1,1))].">
      <j1 rule="para" parents="9320 19582"/>
    </justification>
  </clause>

  <clause id="19584">
    <literal><![CDATA[
      K(((x * y) \ y) \ z,u) = K(y \ (x * (y * z)),u)
    ]]></literal>
    <justification jstring="[hyper(13290,a,19583,a)].">
      <j1 rule="hyper" parents="13290 19583"/>
    </justification>
  </clause>

  <clause id="19585">
    <literal><![CDATA[
      T(R(x,y,x) \ 1,R(x * K(z,x),y,x)) * R((((R(x,y,x) \ 1) \ K(z,x)) \ K(z,x)) \ 1,u,w) = T(R(x,y,x) \ R(R(x,y,x),u,w),K(z,x))
    ]]></literal>
    <justification jstring="[para(7632(a,2),19566(a,1,1,2))].">
      <j1 rule="para" parents="7632 19566"/>
    </justification>
  </clause>

  <clause id="19586">
    <literal><![CDATA[
      T(x,L(y / (y / z),z,y) \ u) = T(x,(y \ ((z * (y / z)) / z)) * u)
    ]]></literal>
    <justification jstring="[para(83(a,1),19367(a,1,2,1,2))].">
      <j1 rule="para" parents="83 19367"/>
    </justification>
  </clause>

  <clause id="19587">
    <literal><![CDATA[
      T(x,(y \ ((z * (y / z)) / z)) * u) = T(x,(y / (y * (1 / z))) \ u)
    ]]></literal>
    <justification jstring="[para(9704(a,1),19586(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9704 19586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19588">
    <literal><![CDATA[
      T(T(L(x,y,z) \ x,u),w) \ T(x,u) = L(T(x,u),y,z) * a(w,y,K(x,z))
    ]]></literal>
    <justification jstring="[para(14009(a,1),19507(a,2,2))].">
      <j1 rule="para" parents="14009 19507"/>
    </justification>
  </clause>

  <clause id="19589">
    <literal><![CDATA[
      T(T(L(x,y,z) \ x,u),w) \ T(x,u) = L(T(x,u),y,T(z,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,19510,a(flip),b,19588,a),flip(a)].">
      <j1 rule="hyper" parents="347 19510 19588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19590">
    <literal><![CDATA[
      L(T(x,y),z,T(u,w)) \ L(T(x,y),z,u) = K(L(x,z,u) \ x,w)
    ]]></literal>
    <justification jstring="[para(19589(a,1),19508(a,1,1))].">
      <j1 rule="para" parents="19589 19508"/>
    </justification>
  </clause>

  <clause id="19591">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = a(u,y,K(z,T(x,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,14485,a(flip),b,19590,a),flip(a)].">
      <j1 rule="hyper" parents="63 14485 19590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19592">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,18044,a(flip),b,19591,a),flip(a)].">
      <j1 rule="hyper" parents="347 18044 19591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19593">
    <literal><![CDATA[
      L(x,y,z) * T(L(x,y,z) \ x,u) = x * a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(134,a,19592,a(flip),b,5940,a),flip(a)].">
      <j1 rule="hyper" parents="134 19592 5940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19594">
    <literal><![CDATA[
      L(x,y,z) * T(L(x,y,z) \ x,u) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,14342,a(flip),b,19593,a),flip(a)].">
      <j1 rule="hyper" parents="347 14342 19593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19595">
    <literal><![CDATA[
      L(x,y,z) \ L(x,y,K(z,u)) = T(L(x,y,z) \ x,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,11518,a(flip),b,19594,a)].">
      <j1 rule="hyper" parents="128 11518 19594"/>
    </justification>
  </clause>

  <clause id="19596">
    <literal><![CDATA[
      L(x,y,z) \ L(x,y,K(z,u)) = L(x,y,T(z,u \ 1)) \ x
    ]]></literal>
    <justification jstring="[hyper(347,a,19505,a(flip),b,19595,a),flip(a)].">
      <j1 rule="hyper" parents="347 19505 19595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19597">
    <literal><![CDATA[
      (L(x * K(y,x),z,u) \ x) * K(y,x) = L(x,z,T(u,y \ 1)) \ x
    ]]></literal>
    <justification jstring="[hyper(14669,a,19596,a)].">
      <j1 rule="hyper" parents="14669 19596"/>
    </justification>
  </clause>

  <clause id="19598">
    <literal><![CDATA[
      (L(x * K(y,x),z,u) \ x) * K(y,x) = x / L(x,z,T(u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(347,a,3308,a,b,19597,a),flip(a)].">
      <j1 rule="hyper" parents="347 3308 19597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19599">
    <literal><![CDATA[
      (x * L(y,z,u)) / T(x,y) = L(y,z,T(u,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(36,a,15138,a(flip),b,19598,a(flip))].">
      <j1 rule="hyper" parents="36 15138 19598"/>
    </justification>
  </clause>

  <clause id="19600">
    <literal><![CDATA[
      (a(x,y,z) * L(y,u,w)) / a(x,y,z) = L(y,u,T(w,a(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(12675(a,1),19599(a,1,2))].">
      <j1 rule="para" parents="12675 19599"/>
    </justification>
  </clause>

  <clause id="19601">
    <literal><![CDATA[
      L((a(x,y,z) * y) / a(x,y,z),u,w) = L(y,u,T(w,a(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(951,a,19600,a)].">
      <j1 rule="hyper" parents="951 19600"/>
    </justification>
  </clause>

  <clause id="19602">
    <literal><![CDATA[
      L((x * a(y,x,z)) / a(y,x,z),u,w) = L(x,u,T(w,a(y,x,z) \ 1))
    ]]></literal>
    <justification jstring="[para(12674(a,1),19601(a,1,1,1))].">
      <j1 rule="para" parents="12674 19601"/>
    </justification>
  </clause>

  <clause id="19603">
    <literal><![CDATA[
      L(x,y,T(z,a(u,x,w) \ 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),19602(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 19602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19604">
    <literal><![CDATA[
      L(x,y,L(z,x,K(u,w))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14384,a(flip),b,19603,a)].">
      <j1 rule="hyper" parents="63 14384 19603"/>
    </justification>
  </clause>

  <clause id="19605">
    <literal><![CDATA[
      L(x,K(y,z),u) * L(K(K(y,z),x) * u,x,K(y,z)) = (x * K(y,z)) * (K(z,y) * L(K(K(y,z),x) * u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(19604(a,1),18578(a,1,1))].">
      <j1 rule="para" parents="19604 18578"/>
    </justification>
  </clause>

  <clause id="19607">
    <literal><![CDATA[
      T(x,L((y \ z) \ ((y \ 1) * u),y \ z,y)) = T(x,((y \ z) / T(y \ 1,z)) \ u)
    ]]></literal>
    <justification jstring="[para(8(a,1),19472(a,1,2,3))].">
      <j1 rule="para" parents="8 19472"/>
    </justification>
  </clause>

  <clause id="19608">
    <literal><![CDATA[
      T(x,((y \ z) / T(y \ 1,z)) \ u) = T(x,z \ (y * ((y \ 1) * u)))
    ]]></literal>
    <justification jstring="[para(561(a,1),19607(a,1,2)),flip(a)].">
      <j1 rule="para" parents="561 19607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19609">
    <literal><![CDATA[
      T(x,((y \ z) / T(y \ 1,z)) \ u) = T(x,z \ L(u,y,y))
    ]]></literal>
    <justification jstring="[para(3197(a,1),19608(a,2,2,2))].">
      <j1 rule="para" parents="3197 19608"/>
    </justification>
  </clause>

  <clause id="19610">
    <literal><![CDATA[
      T(x,((y \ 1) \ (y \ z)) \ u) = T(x,z \ L(u,y,y))
    ]]></literal>
    <justification jstring="[para(4420(a,1),19609(a,1,2,1))].">
      <j1 rule="para" parents="4420 19609"/>
    </justification>
  </clause>

  <clause id="19611">
    <literal><![CDATA[
      T(x,(y * z) \ L(u,y,y)) = T(x,((y \ 1) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),19610(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 19610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19612">
    <literal><![CDATA[
      T(x,(y * a(z,z,y)) \ u) = T(x,y \ L(u,z,z))
    ]]></literal>
    <justification jstring="[para(15286(a,1),19610(a,1,2,1))].">
      <j1 rule="para" parents="15286 19610"/>
    </justification>
  </clause>

  <clause id="19613">
    <literal><![CDATA[
      T(x,L(y \ 1,z,z) * u) = T(x,y \ L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(14646,a,19612,a)].">
      <j1 rule="hyper" parents="14646 19612"/>
    </justification>
  </clause>

  <clause id="19614">
    <literal><![CDATA[
      T(x,(y \ 1) \ L(z,u,u)) = T(x,L(y,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(12108,a,19613,a),flip(a)].">
      <j1 rule="hyper" parents="12108 19613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19615">
    <literal><![CDATA[
      T(x,L(y,z,z) * u) = T(x,y * L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(13173,a,19614,a),flip(a)].">
      <j1 rule="hyper" parents="13173 19614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19616">
    <literal><![CDATA[
      T(x,y * L((z * z) * u,z,z)) = T(x,(z * (z * y)) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16285,a(flip),b,19615,a),flip(a)].">
      <j1 rule="hyper" parents="63 16285 19615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19617">
    <literal><![CDATA[
      T(x,(y * (y * z)) * u) = T(x,z * (y * (y * u)))
    ]]></literal>
    <justification jstring="[para(3180(a,1),19616(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3180 19616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19618">
    <literal><![CDATA[
      T(x,(K(y,z) * (K(y,z) * u)) * ((z * y) * w)) = T(x,u * (K(y,z) * ((y * z) * w)))
    ]]></literal>
    <justification jstring="[para(10281(a,1),19617(a,2,2,2,2))].">
      <j1 rule="para" parents="10281 19617"/>
    </justification>
  </clause>

  <clause id="19619">
    <literal><![CDATA[
      T(x,(y * (T(T(y,z),z) \ u)) * ((y * z) * w)) = T(x,u * (K(z,y) * ((z * y) * w)))
    ]]></literal>
    <justification jstring="[para(5781(a,1),19618(a,1,2,1))].">
      <j1 rule="para" parents="5781 19618"/>
    </justification>
  </clause>

  <clause id="19620">
    <literal><![CDATA[
      T(x,y * (z * (T(T(z,u),u) \ ((z * u) * w)))) = T(x,y * (K(u,z) * ((u * z) * w)))
    ]]></literal>
    <justification jstring="[para(15814(a,1),19619(a,1,2))].">
      <j1 rule="para" parents="15814 19619"/>
    </justification>
  </clause>

  <clause id="19621">
    <literal><![CDATA[
      T(x,y * (K(z,u) * ((z * u) * w))) = T(x,y * ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(15778,a,19620,a),flip(a)].">
      <j1 rule="hyper" parents="15778 19620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19622">
    <literal><![CDATA[
      T(x,y * ((T(z,u) * u) * w)) = T(x,y * ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(10131(a,1),19621(a,1,2,2))].">
      <j1 rule="para" parents="10131 19621"/>
    </justification>
  </clause>

  <clause id="19623">
    <literal><![CDATA[
      ((x * (y * (x \ 1))) / x) \ (x \ (x * (y / x))) = K(x \ 1,y) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),19560(a,2,2,3))].">
      <j1 rule="para" parents="10 19560"/>
    </justification>
  </clause>

  <clause id="19624">
    <literal><![CDATA[
      ((x * (y * (x \ 1))) / x) \ (x \ (x * (y / x))) = (y * (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,14716,a(flip),b,19623,a),flip(a)].">
      <j1 rule="hyper" parents="347 14716 19623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19625">
    <literal><![CDATA[
      ((x * (y / x)) * (x \ 1)) \ (x \ (x * (y / x))) = (y * (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(1085(a,1),19624(a,1,1))].">
      <j1 rule="para" parents="1085 19624"/>
    </justification>
  </clause>

  <clause id="19626">
    <literal><![CDATA[
      ((x * (y / x)) * (x \ 1)) \ (y / x) = (y * (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(9(a,1),19625(a,1,2))].">
      <j1 rule="para" parents="9 19625"/>
    </justification>
  </clause>

  <clause id="19628">
    <literal><![CDATA[
      ((x * K(y,z)) * u) / L(T(u,K(z,y)) * K(y,z),w,a(w,v5,K(v6,v7))) = x * a(x,T(u,v8),K(y,z))
    ]]></literal>
    <justification jstring="[para(6885(a,2),19561(a,1,2,1))].">
      <j1 rule="para" parents="6885 19561"/>
    </justification>
  </clause>

  <clause id="19629">
    <literal><![CDATA[
      (x * T(y,K(z,u))) * K(u,z) = (x * K(u,z)) * y
    ]]></literal>
    <justification jstring="[hyper(15150,a,19628,a)].">
      <j1 rule="hyper" parents="15150 19628"/>
    </justification>
  </clause>

  <clause id="19630">
    <literal><![CDATA[
      (x * K(y,z)) * T(u,K(y,z)) = (x * u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6888(a,1),19629(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6888 19629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19631">
    <literal><![CDATA[
      T((x * T(y,K(z,u))) \ ((x * y) * K(z,u)),x) = R(T(K(z,u),x * T(y,K(z,u))),x,T(y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(19630(a,1),1211(a,1,1,2))].">
      <j1 rule="para" parents="19630 1211"/>
    </justification>
  </clause>

  <clause id="19632">
    <literal><![CDATA[
      (x * T(y,z)) * T(u,K(y,z)) = ((x * y) * u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(5926(a,1),19630(a,1,1))].">
      <j1 rule="para" parents="5926 19630"/>
    </justification>
  </clause>

  <clause id="19633">
    <literal><![CDATA[
      (((x * y) * z) * K(y,u)) / (T(y,u) * T(z,K(y,u))) = R(x,T(y,u),T(z,K(y,u)))
    ]]></literal>
    <justification jstring="[hyper(131,a,19632,a(flip),b,107,a)].">
      <j1 rule="hyper" parents="131 19632 107"/>
    </justification>
  </clause>

  <clause id="19634">
    <literal><![CDATA[
      (((x * y) * z) * K(y,u)) / (y * (z * K(y,u))) = R(x,T(y,u),T(z,K(y,u)))
    ]]></literal>
    <justification jstring="[para(5154(a,1),19633(a,1,2))].">
      <j1 rule="para" parents="5154 19633"/>
    </justification>
  </clause>

  <clause id="19635">
    <literal><![CDATA[
      R((x * y) / y,y,T(z,u)) = R(x,T(y,u),T(z,K(y,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19562,a(flip),b,19634,a)].">
      <j1 rule="hyper" parents="63 19562 19634"/>
    </justification>
  </clause>

  <clause id="19636">
    <literal><![CDATA[
      R(x,T(y,z),T(u,K(y,z))) = R(x,y,T(u,z))
    ]]></literal>
    <justification jstring="[para(11(a,1),19635(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 19635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19637">
    <literal><![CDATA[
      R(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,T(y,u),z) = w
    ]]></literal>
    <justification jstring="[para(19636(a,1),16910(a,1))].">
      <j1 rule="para" parents="19636 16910"/>
    </justification>
  </clause>

  <clause id="19638">
    <literal><![CDATA[
      R(x \ 1,T(x,y),z) = R(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(19637,a,18624,a)].">
      <j1 rule="hyper" parents="19637 18624"/>
    </justification>
  </clause>

  <clause id="19641">
    <literal><![CDATA[
      T(x * R(x \ 1,x,y),z) = (y / (T(x,z) * y)) * T(x,z)
    ]]></literal>
    <justification jstring="[para(19638(a,1),2150(a,1,1,2))].">
      <j1 rule="para" parents="19638 2150"/>
    </justification>
  </clause>

  <clause id="19642">
    <literal><![CDATA[
      (x / (T(y,z) * x)) * T(y,z) = y * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,17727,a(flip),b,19641,a),flip(a)].">
      <j1 rule="hyper" parents="63 17727 19641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19645">
    <literal><![CDATA[
      (x / (T(y,z) * x)) * T(y,z) = (x / (y * x)) * y
    ]]></literal>
    <justification jstring="[hyper(347,a,867,a,b,19642,a),flip(a)].">
      <j1 rule="hyper" parents="347 867 19642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19646">
    <literal><![CDATA[
      (x / (y * x)) * K(z,y) = x / (T(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(6112,a,19645,a)].">
      <j1 rule="hyper" parents="6112 19645"/>
    </justification>
  </clause>

  <clause id="19647">
    <literal><![CDATA[
      K(x,y) * ((z / (x * z)) \ u) = (z / (T(x,y) * z)) \ u
    ]]></literal>
    <justification jstring="[para(19646(a,1),5823(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19646 5823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19648">
    <literal><![CDATA[
      K((x / (T(y,z) * x)) \ u,w) = K(T(x / (y * x),z) \ u,w)
    ]]></literal>
    <justification jstring="[para(19647(a,1),16339(a,1,1))].">
      <j1 rule="para" parents="19647 16339"/>
    </justification>
  </clause>

  <clause id="19649">
    <literal><![CDATA[
      K(T(x / (y * x),z) \ u,w) = K((x \ (x / T(y,z))) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(13851,a,19648,a),flip(a)].">
      <j1 rule="hyper" parents="13851 19648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19650">
    <literal><![CDATA[
      K(T(x / (y * x),x * y) \ z,u) = K((x / T(y * x,y)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,18392,a(flip),b,19649,a),flip(a)].">
      <j1 rule="hyper" parents="347 18392 19649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19651">
    <literal><![CDATA[
      K(T((x * y) \ y,K(y,x)) \ z,u) = K((y / T(x * y,x)) \ z,u)
    ]]></literal>
    <justification jstring="[para(10364(a,1),19650(a,1,1,1))].">
      <j1 rule="para" parents="10364 19650"/>
    </justification>
  </clause>

  <clause id="19652">
    <literal><![CDATA[
      K((x / T(y * x,y)) \ z,u) = K(((y * x) \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(14820,a,19651,a),flip(a)].">
      <j1 rule="hyper" parents="14820 19651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19653">
    <literal><![CDATA[
      K((x / T(y * x,y)) \ z,u) = K(x \ (y * (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,19584,a(flip),b,19652,a),flip(a)].">
      <j1 rule="hyper" parents="347 19584 19652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19655">
    <literal><![CDATA[
      R(T(K(x,y),z * T(u,K(x,y))),z,T(u,K(x,y))) = T(T(K(x,y),u),z)
    ]]></literal>
    <justification jstring="[para(6173(a,1),19631(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6173 19631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19657">
    <literal><![CDATA[
      R(T(K(x,y),z * T(u,K(x,y))),z,T(u,K(x,y))) = T(K(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(7091(a,2),19655(a,2,1))].">
      <j1 rule="para" parents="7091 19655"/>
    </justification>
  </clause>

  <clause id="19658">
    <literal><![CDATA[
      R(T(K(x,y),z * T(u,K(x,y))),z,T(u,K(x,y))) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[hyper(347,a,7091,a,b,19657,a),flip(a)].">
      <j1 rule="hyper" parents="347 7091 19657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19659">
    <literal><![CDATA[
      R(T(K(x,y),z * u),z,T(u,K(x,y))) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[para(7853(a,1),19658(a,1,1))].">
      <j1 rule="para" parents="7853 19658"/>
    </justification>
  </clause>

  <clause id="19660">
    <literal><![CDATA[
      R(K(x,T(y,z * u)),z,T(u,K(x,y))) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[para(7091(a,2),19659(a,1,1))].">
      <j1 rule="para" parents="7091 19659"/>
    </justification>
  </clause>

  <clause id="19661">
    <literal><![CDATA[
      R(K(x,T(y,z * u)),z,u) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[hyper(16910,a,19660,a)].">
      <j1 rule="hyper" parents="16910 19660"/>
    </justification>
  </clause>

  <clause id="19662">
    <literal><![CDATA[
      K(x,L(T(y,z * u),z,u)) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[hyper(14117,a,19661,a)].">
      <j1 rule="hyper" parents="14117 19661"/>
    </justification>
  </clause>

  <clause id="19663">
    <literal><![CDATA[
      K((x * y) \ (z * y),u) = K(z / x,T(T(u,y),x))
    ]]></literal>
    <justification jstring="[hyper(14100,a,19662,a)].">
      <j1 rule="hyper" parents="14100 19662"/>
    </justification>
  </clause>

  <clause id="19664">
    <literal><![CDATA[
      K((x * y) \ (z * y),u) = K(x \ z,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,7135,a(flip),b,19663,a),flip(a)].">
      <j1 rule="hyper" parents="347 7135 19663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19665">
    <literal><![CDATA[
      K((x * y) \ (y * z),u) = K(x \ T(z,y),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(15913,a,19664,a)].">
      <j1 rule="hyper" parents="15913 19664"/>
    </justification>
  </clause>

  <clause id="19666">
    <literal><![CDATA[
      K((x * y) \ (z * x),u) = K(T(y,x) \ z,T(u,x))
    ]]></literal>
    <justification jstring="[hyper(15811,a,19664,a)].">
      <j1 rule="hyper" parents="15811 19664"/>
    </justification>
  </clause>

  <clause id="19667">
    <literal><![CDATA[
      K((x / y) \ z,T(u,y)) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(12(a,1),19664(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 19664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19668">
    <literal><![CDATA[
      K(T(x,y) / (z \ y),u) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(15767,a,19667,a)].">
      <j1 rule="hyper" parents="15767 19667"/>
    </justification>
  </clause>

  <clause id="19669">
    <literal><![CDATA[
      K(x \ (y * z),T(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K((x / z) \ y,u) = w
    ]]></literal>
    <justification jstring="[para(19667(a,1),7478(a,1))].">
      <j1 rule="para" parents="19667 7478"/>
    </justification>
  </clause>

  <clause id="19670">
    <literal><![CDATA[
      K(x \ (T(y,x) * z),u) = K(y / (z \ x),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15818,a(flip),b,19668,a),flip(a)].">
      <j1 rule="hyper" parents="63 15818 19668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19671">
    <literal><![CDATA[
      K(x \ (T(y,x) * z),u) = (w * K(u,y / (z \ x))) \ w
    ]]></literal>
    <justification jstring="[hyper(347,a,6123,a,b,19670,a),flip(a)].">
      <j1 rule="hyper" parents="347 6123 19670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19672">
    <literal><![CDATA[
      K(x \ ((y \ x) * z),u) = K(y \ T(z,x),T(u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,19474,a(flip),b,19665,a)].">
      <j1 rule="hyper" parents="63 19474 19665"/>
    </justification>
  </clause>

  <clause id="19673">
    <literal><![CDATA[
      (x * K(T(y,z) \ u,T(w,z))) \ x = K(w,(z * y) \ (u * z))
    ]]></literal>
    <justification jstring="[para(19666(a,1),6123(a,1,1,2))].">
      <j1 rule="para" parents="19666 6123"/>
    </justification>
  </clause>

  <clause id="19674">
    <literal><![CDATA[
      (x * K(y \ T(z,u),T(w,u))) \ (x * w) = T(w,u \ ((y \ u) * z))
    ]]></literal>
    <justification jstring="[para(19672(a,1),6100(a,1,1,2))].">
      <j1 rule="para" parents="19672 6100"/>
    </justification>
  </clause>

  <clause id="19675">
    <literal><![CDATA[
      K(x \ (y * T(z * u,z)),T(w,u * z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K((x / T(z * u,z)) \ y,w) = v5
    ]]></literal>
    <justification jstring="[para(10350(a,1),19669(a,1,2))].">
      <j1 rule="para" parents="10350 19669"/>
    </justification>
  </clause>

  <clause id="19676">
    <literal><![CDATA[
      T(x,y \ (T(z,y) * u)) = x * K(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[hyper(4916,a,19671,a)].">
      <j1 rule="hyper" parents="4916 19671"/>
    </justification>
  </clause>

  <clause id="19677">
    <literal><![CDATA[
      T(x,y \ (T(z,y) * u)) = T(x,z / (u \ y))
    ]]></literal>
    <justification jstring="[hyper(347,a,4929,a,b,19676,a),flip(a)].">
      <j1 rule="hyper" parents="347 4929 19676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19678">
    <literal><![CDATA[
      T(x,y \ (T(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(19677(a,2),19030(a,1))].">
      <j1 rule="para" parents="19677 19030"/>
    </justification>
  </clause>

  <clause id="19679">
    <literal><![CDATA[
      T(x,T(y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (y \ (z \ u))) = w
    ]]></literal>
    <justification jstring="[para(4772(a,1),19678(a,1,2))].">
      <j1 rule="para" parents="4772 19678"/>
    </justification>
  </clause>

  <clause id="19680">
    <literal><![CDATA[
      K(x,T(T(y,z) \ u,z)) = K(x,(z * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(7155,a,19673,a)].">
      <j1 rule="hyper" parents="7155 19673"/>
    </justification>
  </clause>

  <clause id="19681">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,z)) = T(x,(z * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(132,a,19680,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 19680 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19682">
    <literal><![CDATA[
      T(x,T(T(y,z \ 1) \ ((z \ 1) \ u),z \ 1)) = T(x,((z \ 1) * y) \ (z \ T(z * u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(1137(a,2),19681(a,2,2,2))].">
      <j1 rule="para" parents="1137 19681"/>
    </justification>
  </clause>

  <clause id="19683">
    <literal><![CDATA[
      T(x,y \ ((z \ y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z \ T(u,y),y)) = w
    ]]></literal>
    <justification jstring="[para(19674(a,1),7158(a,1))].">
      <j1 rule="para" parents="19674 7158"/>
    </justification>
  </clause>

  <clause id="19684">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),T(u \ T(z,y),y)) = T(x,((y \ u) \ z) / y)
    ]]></literal>
    <justification jstring="[hyper(19683,a,17818,a)].">
      <j1 rule="hyper" parents="19683 17818"/>
    </justification>
  </clause>

  <clause id="19685">
    <literal><![CDATA[
      T(x,((y \ z) \ u) / y) = T(x,z \ T(u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,16269,a(flip),b,19684,a),flip(a)].">
      <j1 rule="hyper" parents="63 16269 19684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19687">
    <literal><![CDATA[
      T(x,y \ (K(z * z,u) * (z \ (z \ u)))) = T(x,(((z \ 1) \ y) \ ((z \ u) / z)) / (z \ 1))
    ]]></literal>
    <justification jstring="[para(14775(a,2),19685(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14775 19685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19688">
    <literal><![CDATA[
      K(x \ (y * (z * u)),T(w,z * u)) = K((x / T(u * z,u)) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(19675,a,12279,a),flip(a)].">
      <j1 rule="hyper" parents="19675 12279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19689">
    <literal><![CDATA[
      K((x / T(y * z,y)) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((x / (z * y)) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(19688(a,1),19669(a,1))].">
      <j1 rule="para" parents="19688 19669"/>
    </justification>
  </clause>

  <clause id="19690">
    <literal><![CDATA[
      K((x / (x * y)) \ z,u) = K(x \ (y * (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(19689,a,19653,a)].">
      <j1 rule="hyper" parents="19689 19653"/>
    </justification>
  </clause>

  <clause id="19691">
    <literal><![CDATA[
      (x * K(y \ (z * (y * u)),w)) \ (x * w) = T(w,(y / (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(19690(a,1),6100(a,1,1,2))].">
      <j1 rule="para" parents="19690 6100"/>
    </justification>
  </clause>

  <clause id="19692">
    <literal><![CDATA[
      T(x,(y / (y * z)) \ u) = T(x,y \ (z * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(6114,a,19691,a),flip(a)].">
      <j1 rule="hyper" parents="6114 19691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19693">
    <literal><![CDATA[
      T(x,(y \ ((z * (y / z)) / z)) * u) = T(x,y \ ((1 / z) * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19587,a,b,19692,a)].">
      <j1 rule="hyper" parents="63 19587 19692"/>
    </justification>
  </clause>

  <clause id="19694">
    <literal><![CDATA[
      T(x,(y \ ((z * (y / z)) / z)) * u) = T(x,y \ ((z \ 1) * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,5707,a(flip),b,19693,a),flip(a)].">
      <j1 rule="hyper" parents="347 5707 19693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19695">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) * (y * u))) = T(x,(y \ T(y / z,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17244,a(flip),b,19694,a),flip(a)].">
      <j1 rule="hyper" parents="63 17244 19694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19696">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) * (y * u))) = T(x,(y \ (z \ y)) * u)
    ]]></literal>
    <justification jstring="[para(113(a,1),19695(a,2,2,1,2))].">
      <j1 rule="para" parents="113 19695"/>
    </justification>
  </clause>

  <clause id="19697">
    <literal><![CDATA[
      T(x,((y \ 1) \ (z \ (y \ 1))) * (u * a(y,y,u))) = T(x,(y \ 1) \ ((z \ 1) * (y \ u)))
    ]]></literal>
    <justification jstring="[para(15291(a,1),19696(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="15291 19696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19698">
    <literal><![CDATA[
      T(x,((y \ 1) \ (z \ (y \ 1))) * (u * a(y,y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * ((z \ 1) * (y \ u))) = w
    ]]></literal>
    <justification jstring="[para(19697(a,2),13173(a,1))].">
      <j1 rule="para" parents="19697 13173"/>
    </justification>
  </clause>

  <clause id="19699">
    <literal><![CDATA[
      T(x,y \ (K(z * z,u) * (z \ (z \ u)))) = T(x,(((z \ 1) \ y) \ ((z \ u) / z)) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,13139,a(flip),b,19687,a),flip(a)].">
      <j1 rule="hyper" parents="347 13139 19687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19700">
    <literal><![CDATA[
      T(x,((y \ 1) \ (z \ (y \ 1))) * L(u,w,w)) = T(x,y * ((z \ 1) * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(19698,a,18944,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19698 18944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19701">
    <literal><![CDATA[
      T(x,(y \ (z \ y)) * L(u,w,w)) = T(x,y * ((z \ 1) * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19039,a(flip),b,19700,a)].">
      <j1 rule="hyper" parents="63 19039 19700"/>
    </justification>
  </clause>

  <clause id="19702">
    <literal><![CDATA[
      T(x,((y \ 1) * (z \ y)) * u) = T(x,y * ((z \ 1) * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(18936,a,19701,a)].">
      <j1 rule="hyper" parents="18936 19701"/>
    </justification>
  </clause>

  <clause id="19703">
    <literal><![CDATA[
      T(x,(y * (z \ (y \ 1))) * u) = T(x,y * ((z \ 1) * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19019,a(flip),b,19702,a)].">
      <j1 rule="hyper" parents="63 19019 19702"/>
    </justification>
  </clause>

  <clause id="19704">
    <literal><![CDATA[
      T(x,y * (((z * y) \ 1) * (y \ u))) = T(x,(z \ (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12868,a(flip),b,19703,a),flip(a)].">
      <j1 rule="hyper" parents="63 12868 19703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19705">
    <literal><![CDATA[
      T(x,T(T(y,z \ 1) \ ((z \ 1) \ u),z \ 1)) = T(x,((z \ 1) * y) \ (z \ T(z * u,z * 1)))
    ]]></literal>
    <justification jstring="[hyper(347,a,17666,a(flip),b,19682,a),flip(a)].">
      <j1 rule="hyper" parents="347 17666 19682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19706">
    <literal><![CDATA[
      T(x,T(T(y,z \ 1) \ ((z \ 1) \ u),z \ 1)) = T(x,((z \ 1) * y) \ (z \ T(z * u,z)))
    ]]></literal>
    <justification jstring="[para(8(a,1),19705(a,2,2,2,2,2))].">
      <j1 rule="para" parents="8 19705"/>
    </justification>
  </clause>

  <clause id="19707">
    <literal><![CDATA[
      T(x,T(T(y,z \ 1) \ ((z \ 1) \ u),z \ 1)) = T(x,((z \ 1) * y) \ ((z * u) / z))
    ]]></literal>
    <justification jstring="[hyper(347,a,15734,a(flip),b,19706,a),flip(a)].">
      <j1 rule="hyper" parents="347 15734 19706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19708">
    <literal><![CDATA[
      T(x,T(T(y,z \ 1) \ ((z \ 1) \ u),z \ 1)) = T(x,((z \ 1) * y) \ T(u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,15625,a(flip),b,19707,a),flip(a)].">
      <j1 rule="hyper" parents="347 15625 19707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19709">
    <literal><![CDATA[
      T(x,T(T(y,z \ 1) \ ((z \ 1) \ u),z)) = T(x,((z \ 1) * y) \ T(u,z))
    ]]></literal>
    <justification jstring="[hyper(8869,a,19708,a)].">
      <j1 rule="hyper" parents="8869 19708"/>
    </justification>
  </clause>

  <clause id="19710">
    <literal><![CDATA[
      T(x,T((y \ 1) \ (z \ u),y)) = T(x,((y \ 1) * z) \ T(u,y))
    ]]></literal>
    <justification jstring="[hyper(19568,a,19709,a)].">
      <j1 rule="hyper" parents="19568 19709"/>
    </justification>
  </clause>

  <clause id="19711">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ T(u,y)) = T(x,T(y * (z \ u),y))
    ]]></literal>
    <justification jstring="[hyper(63,a,13321,a(flip),b,19710,a),flip(a)].">
      <j1 rule="hyper" parents="63 13321 19710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19712">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ u) * y) = w
    ]]></literal>
    <justification jstring="[para(19711(a,2),10401(a,1))].">
      <j1 rule="para" parents="19711 10401"/>
    </justification>
  </clause>

  <clause id="19713">
    <literal><![CDATA[
      T(x,((y \ 1) * z) \ (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ (u / y)) * y) = w
    ]]></literal>
    <justification jstring="[para(113(a,1),19712(a,1,2,2))].">
      <j1 rule="para" parents="113 19712"/>
    </justification>
  </clause>

  <clause id="19714">
    <literal><![CDATA[
      T(x,(y \ (z / u)) * u) = T(x,u * ((y * u) \ z))
    ]]></literal>
    <justification jstring="[hyper(19713,a,19475,a)].">
      <j1 rule="hyper" parents="19713 19475"/>
    </justification>
  </clause>

  <clause id="19715">
    <literal><![CDATA[
      T(x,y \ (K(z * z,u) * (z \ (z \ u)))) = T(x,z * ((((z \ 1) \ y) * z) \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19699,a,b,19714,a)].">
      <j1 rule="hyper" parents="63 19699 19714"/>
    </justification>
  </clause>

  <clause id="19716">
    <literal><![CDATA[
      T((K(x,T(y,z)) * u) / K(x,T(y,z)),K(y,x) * w) = L(T(u,w),K(x,T(y,z)),w)
    ]]></literal>
    <justification jstring="[para(11(a,1),19491(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 19491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19717">
    <literal><![CDATA[
      T((K(x,T(y,z)) * u) / K(x,T(y,z)),K(y,x) * w) = L(T(u,w),K(y,x),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,17871,a(flip),b,19716,a),flip(a)].">
      <j1 rule="hyper" parents="347 17871 19716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19720">
    <literal><![CDATA[
      T((K(x,T(y,z)) * u) * K(y,T(x,z)),K(y,x) * w) = L(T(u,w),K(y,x),w)
    ]]></literal>
    <justification jstring="[para(7126(a,1),19717(a,1,1))].">
      <j1 rule="para" parents="7126 19717"/>
    </justification>
  </clause>

  <clause id="19721">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * u) = L(T(x,u),K(z,y),u)
    ]]></literal>
    <justification jstring="[para(13718(a,1),19720(a,1,1))].">
      <j1 rule="para" parents="13718 19720"/>
    </justification>
  </clause>

  <clause id="19722">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * u) = L(T(x,u),y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(19529,a,19721,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19529 19721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19723">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * u) = T(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,14348,a(flip),b,19722,a),flip(a)].">
      <j1 rule="hyper" parents="347 14348 19722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19724">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(19723(a,2),19413(a,1))].">
      <j1 rule="para" parents="19723 19413"/>
    </justification>
  </clause>

  <clause id="19725">
    <literal><![CDATA[
      L(x,K(y,z),u) * L(K(x,K(y,z)) * u,x,K(y,z)) = (x * K(y,z)) * (K(z,y) * L(K(K(y,z),x) * u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(7292(a,1),19605(a,1,2,1,1))].">
      <j1 rule="para" parents="7292 19605"/>
    </justification>
  </clause>

  <clause id="19727">
    <literal><![CDATA[
      L(T(x,K(y,z)),K(y,z),u) * L(u,x,K(y,z)) = (x * K(y,z)) * (K(z,y) * L(K(K(y,z),x) * u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,10427,a(flip),b,19725,a)].">
      <j1 rule="hyper" parents="63 10427 19725"/>
    </justification>
  </clause>

  <clause id="19728">
    <literal><![CDATA[
      L(T(x,K(y,z)),K(y,z),u) * L(u,x,K(y,z)) = (x * K(y,z)) * (K(z,y) * L(K(x,K(y,z)) * u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(7292(a,1),19727(a,2,2,2,1,1))].">
      <j1 rule="para" parents="7292 19727"/>
    </justification>
  </clause>

  <clause id="19729">
    <literal><![CDATA[
      L(T(x,K(y,z)),K(y,z),u) * L(u,x,K(y,z)) = (x * K(y,z)) * L(K(z,y) * (K(x,K(y,z)) * u),x,K(y,z))
    ]]></literal>
    <justification jstring="[para(18144(a,2),19728(a,2,2))].">
      <j1 rule="para" parents="18144 19728"/>
    </justification>
  </clause>

  <clause id="19730">
    <literal><![CDATA[
      L(T(x,K(y,z)),K(y,z),u) * L(u,x,K(y,z)) = (x * K(y,z)) * L(y * (T(T(y,K(x,z)),z) \ u),x,K(y,z))
    ]]></literal>
    <justification jstring="[para(13521(a,1),19729(a,2,2,1))].">
      <j1 rule="para" parents="13521 19729"/>
    </justification>
  </clause>

  <clause id="19731">
    <literal><![CDATA[
      L(T(x,K(y,z)),K(y,z),u) * L(u,x,K(y,z)) = (x * K(y,z)) * L(y * (T(y,T(z,x)) \ u),x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7349(a,1),19730(a,2,2,1,2,1))].">
      <j1 rule="para" parents="7349 19730"/>
    </justification>
  </clause>

  <clause id="19732">
    <literal><![CDATA[
      L(T(x,K(y,z)),K(y,z),u) * L(u,x,K(y,z)) = (x * K(y,z)) * L(K(T(z,x),y) * u,x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4947(a,1),19731(a,2,2,1))].">
      <j1 rule="para" parents="4947 19731"/>
    </justification>
  </clause>

  <clause id="19733">
    <literal><![CDATA[
      L(T(x,K(y,z)),K(y,z),u) * L(u,x,K(y,z)) = (x * K(y,z)) * L(K(z,T(y,x)) * u,x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7093(a,1),19732(a,2,2,1,1))].">
      <j1 rule="para" parents="7093 19732"/>
    </justification>
  </clause>

  <clause id="19734">
    <literal><![CDATA[
      L(T(x,K(y,z)),K(y,z),u) * L(u,x,K(y,z)) = K(y,z) * (T(x,K(y,z)) * (K(z,T(y,x)) * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,10150,a(flip),b,19733,a),flip(a)].">
      <j1 rule="hyper" parents="347 10150 19733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19735">
    <literal><![CDATA[
      L(T(x,K(y,z)),K(y,z),u) * L(u,x,K(y,z)) = K(y,z) * (x * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[para(8296(a,1),19734(a,2,2))].">
      <j1 rule="para" parents="8296 19734"/>
    </justification>
  </clause>

  <clause id="19736">
    <literal><![CDATA[
      T(L(x \ 1,y,x),R(x * K(z,x),y,x)) * R((((R(x,y,x) \ 1) \ K(z,x)) \ K(z,x)) \ 1,u,w) = T(R(x,y,x) \ R(R(x,y,x),u,w),K(z,x))
    ]]></literal>
    <justification jstring="[para(8391(a,2),19585(a,1,1,1))].">
      <j1 rule="para" parents="8391 19585"/>
    </justification>
  </clause>

  <clause id="19737">
    <literal><![CDATA[
      T(L(x \ 1,y,x),L(x * K(z,x),y,x)) * R((((R(x,y,x) \ 1) \ K(z,x)) \ K(z,x)) \ 1,u,w) = T(R(x,y,x) \ R(R(x,y,x),u,w),K(z,x))
    ]]></literal>
    <justification jstring="[para(14104(a,1),19736(a,1,1))].">
      <j1 rule="para" parents="14104 19736"/>
    </justification>
  </clause>

  <clause id="19738">
    <literal><![CDATA[
      T(L(x \ 1,y,x),L(T(x,z),y,x)) * R((((R(x,y,x) \ 1) \ K(z,x)) \ K(z,x)) \ 1,u,w) = T(R(x,y,x) \ R(R(x,y,x),u,w),K(z,x))
    ]]></literal>
    <justification jstring="[para(8068(a,1),19737(a,1,1))].">
      <j1 rule="para" parents="8068 19737"/>
    </justification>
  </clause>

  <clause id="19739">
    <literal><![CDATA[
      T(L(x \ 1,y,x),T(x,z)) * R((((R(x,y,x) \ 1) \ K(z,x)) \ K(z,x)) \ 1,u,w) = T(R(x,y,x) \ R(R(x,y,x),u,w),K(z,x))
    ]]></literal>
    <justification jstring="[para(7259(a,1),19738(a,1,1))].">
      <j1 rule="para" parents="7259 19738"/>
    </justification>
  </clause>

  <clause id="19740">
    <literal><![CDATA[
      L(T(x \ 1,T(x,y)),z,x) * R((((R(x,z,x) \ 1) \ K(y,x)) \ K(y,x)) \ 1,u,w) = T(R(x,z,x) \ R(R(x,z,x),u,w),K(y,x))
    ]]></literal>
    <justification jstring="[para(25(a,2),19739(a,1,1))].">
      <j1 rule="para" parents="25 19739"/>
    </justification>
  </clause>

  <clause id="19742">
    <literal><![CDATA[
      L(T(x \ 1,x),y,x) * R((((R(x,y,x) \ 1) \ K(z,x)) \ K(z,x)) \ 1,u,w) = T(R(x,y,x) \ R(R(x,y,x),u,w),K(z,x))
    ]]></literal>
    <justification jstring="[para(3088(a,1),19740(a,1,1,1))].">
      <j1 rule="para" parents="3088 19740"/>
    </justification>
  </clause>

  <clause id="19744">
    <literal><![CDATA[
      L(T(x \ 1,x),y,x) * R(((L(x \ 1,y,x) \ K(z,x)) \ K(z,x)) \ 1,u,w) = T(R(x,y,x) \ R(R(x,y,x),u,w),K(z,x))
    ]]></literal>
    <justification jstring="[para(8391(a,2),19742(a,1,2,1,1,1,1))].">
      <j1 rule="para" parents="8391 19742"/>
    </justification>
  </clause>

  <clause id="19745">
    <literal><![CDATA[
      L(T(x \ 1,x),y,x) * R(L(((x \ 1) \ K(z,x)) \ K(z,x),y,x) \ 1,u,w) = T(R(x,y,x) \ R(R(x,y,x),u,w),K(z,x))
    ]]></literal>
    <justification jstring="[para(9708(a,2),19744(a,1,2,1,1))].">
      <j1 rule="para" parents="9708 19744"/>
    </justification>
  </clause>

  <clause id="19746">
    <literal><![CDATA[
      T(R(x,y,x) \ R(R(x,y,x),z,u),K(w,x)) = L(T(x \ 1,x),y,x) * R(L(T(x \ 1,x),y,x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(8071(a,1),19745(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8071 19745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19747">
    <literal><![CDATA[
      T(R(x,y,x) \ R(R(x,y,x),z,u),K(w,x)) = L(T(x \ 1,x) * R(T(x \ 1,x) \ 1,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,4605,a(flip),b,19746,a),flip(a)].">
      <j1 rule="hyper" parents="347 4605 19746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19749">
    <literal><![CDATA[
      T(R(x,y,x) \ R(R(x,y,x),z,u),K(w,x)) = L(T((x \ 1) * R((x \ 1) \ 1,z,u),x),y,x)
    ]]></literal>
    <justification jstring="[para(2148(a,1),19747(a,2,1))].">
      <j1 rule="para" parents="2148 19747"/>
    </justification>
  </clause>

  <clause id="19750">
    <literal><![CDATA[
      T(R(x,y,x) \ R(R(x,y,x),z,u),K(w,x)) = L(T(x \ R(x,z,u),x),y,x)
    ]]></literal>
    <justification jstring="[para(1462(a,1),19749(a,2,1,1))].">
      <j1 rule="para" parents="1462 19749"/>
    </justification>
  </clause>

  <clause id="19751">
    <literal><![CDATA[
      T(R(x,y,x) \ R(R(x,y,x),z,u),K(w,x)) = L(x \ R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(3685(a,1),19750(a,2,1))].">
      <j1 rule="para" parents="3685 19750"/>
    </justification>
  </clause>

  <clause id="19752">
    <literal><![CDATA[
      T(x \ R(x,y,z),K(u,x)) = L(x \ R(x,y,z),w,x)
    ]]></literal>
    <justification jstring="[para(17386(a,1),19751(a,1,1))].">
      <j1 rule="para" parents="17386 19751"/>
    </justification>
  </clause>

  <clause id="19753">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(16884,a,19752,a),flip(a)].">
      <j1 rule="hyper" parents="16884 19752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19755">
    <literal><![CDATA[
      x \ (y \ (((y \ R(y,z,u)) * y) * x)) = R(T(y \ R(y,z,u),x),y,x)
    ]]></literal>
    <justification jstring="[para(19753(a,1),19567(a,1,2,2,1,1))].">
      <j1 rule="para" parents="19753 19567"/>
    </justification>
  </clause>

  <clause id="19756">
    <literal><![CDATA[
      R(T(x \ R(x,y,z),u),x,u) = u \ (x \ (R(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(3678(a,1),19755(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3678 19755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19758">
    <literal><![CDATA[
      R(T(x \ R(x,y,z),u),x,u) = u \ (R(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[para(1746(a,1),19756(a,2,2))].">
      <j1 rule="para" parents="1746 19756"/>
    </justification>
  </clause>

  <clause id="19759">
    <literal><![CDATA[
      (x * y) \ (R(x,z,u) * y) = y \ (R(x,z,u) * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(19565,a,19758,a)].">
      <j1 rule="hyper" parents="19565 19758"/>
    </justification>
  </clause>

  <clause id="19760">
    <literal><![CDATA[
      (x * y) \ (R(x,z,z \ y) * y) = y \ (x \ ((x * z) * (z \ y)))
    ]]></literal>
    <justification jstring="[para(1763(a,1),19759(a,2,2))].">
      <j1 rule="para" parents="1763 19759"/>
    </justification>
  </clause>

  <clause id="19761">
    <literal><![CDATA[
      (x * y) \ (R(x,x,x * y) * y) = y \ (x \ ((x * x) * (x \ y)))
    ]]></literal>
    <justification jstring="[para(3388(a,1),19760(a,1,2,1))].">
      <j1 rule="para" parents="3388 19760"/>
    </justification>
  </clause>

  <clause id="19762">
    <literal><![CDATA[
      x \ (y \ ((y * y) * (y \ x))) = (y * x) \ ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(3390(a,1),19761(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3390 19761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19763">
    <literal><![CDATA[
      x \ (y \ ((y * y) * (y \ x))) = y * (x / (y * x))
    ]]></literal>
    <justification jstring="[hyper(347,a,19011,a(flip),b,19762,a),flip(a)].">
      <j1 rule="hyper" parents="347 19011 19762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19764">
    <literal><![CDATA[
      x \ (y \ ((y \ 1) \ x)) = y * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(495(a,1),19763(a,1,2,2))].">
      <j1 rule="para" parents="495 19763"/>
    </justification>
  </clause>

  <clause id="19765">
    <literal><![CDATA[
      x * a(y,y,y * x) = y \ ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(19013,a,19764,a)].">
      <j1 rule="hyper" parents="19013 19764"/>
    </justification>
  </clause>

  <clause id="19766">
    <literal><![CDATA[
      K(x \ 1,x * y) * (x * (y / (x * y))) = ((x * y) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(19764(a,1),15357(a,1,2))].">
      <j1 rule="para" parents="19764 15357"/>
    </justification>
  </clause>

  <clause id="19767">
    <literal><![CDATA[
      x * a(y,y,x * y) = y \ ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(14642(a,1),19765(a,1,2))].">
      <j1 rule="para" parents="14642 19765"/>
    </justification>
  </clause>

  <clause id="19768">
    <literal><![CDATA[
      x * (K(x \ 1,y * x) * (y / (x * y))) = ((x * y) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,19538,a(flip),b,19766,a)].">
      <j1 rule="hyper" parents="63 19538 19766"/>
    </justification>
  </clause>

  <clause id="19769">
    <literal><![CDATA[
      x * T(y / (x * y),y * x) = ((x * y) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(5557(a,1),19768(a,1,2))].">
      <j1 rule="para" parents="5557 19768"/>
    </justification>
  </clause>

  <clause id="19770">
    <literal><![CDATA[
      x * T((x * y) \ y,K(y,x)) = ((x * y) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(10364(a,1),19769(a,1,2))].">
      <j1 rule="para" parents="10364 19769"/>
    </justification>
  </clause>

  <clause id="19771">
    <literal><![CDATA[
      ((x * y) * (x \ 1)) \ y = x * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(6901(a,1),19770(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6901 19770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19772">
    <literal><![CDATA[
      x * ((x * (y / x)) \ (y / x)) = (y * (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,19626,a(flip),b,19771,a),flip(a)].">
      <j1 rule="hyper" parents="63 19626 19771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19774">
    <literal><![CDATA[
      (x * (y \ 1)) \ (y \ x) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(10315(a,1),19772(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10315 19772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19775">
    <literal><![CDATA[
      ((1 / (x \ 1)) \ (x \ 1)) * (x * (y \ (x \ y))) = (y * (1 / (x \ 1))) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(19774(a,1),6660(a,1,2))].">
      <j1 rule="para" parents="19774 6660"/>
    </justification>
  </clause>

  <clause id="19776">
    <literal><![CDATA[
      (x \ (x \ 1)) * (x * (y \ (x \ y))) = (y * (1 / (x \ 1))) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(80(a,1),19775(a,1,1,1))].">
      <j1 rule="para" parents="80 19775"/>
    </justification>
  </clause>

  <clause id="19777">
    <literal><![CDATA[
      (x * (1 / (y \ 1))) \ (y \ x) = (y * y) \ (y * (x \ (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(981,a,19776,a),flip(a)].">
      <j1 rule="hyper" parents="981 19776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19778">
    <literal><![CDATA[
      L(x \ (y \ (x \ y)),x,x) = (y * (1 / (x \ 1))) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,99,a,b,19777,a)].">
      <j1 rule="hyper" parents="347 99 19777"/>
    </justification>
  </clause>

  <clause id="19779">
    <literal><![CDATA[
      (x * (1 / (y \ 1))) \ (y \ x) = y \ (x \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(9455,a,19778,a),flip(a)].">
      <j1 rule="hyper" parents="9455 19778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19780">
    <literal><![CDATA[
      (x * y) \ (y \ x) = y \ (x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(80(a,1),19779(a,1,1,2))].">
      <j1 rule="para" parents="80 19779"/>
    </justification>
  </clause>

  <clause id="19781">
    <literal><![CDATA[
      (x / y) \ (x \ ((x / y) \ x)) = (x * (x / y)) \ y
    ]]></literal>
    <justification jstring="[para(83(a,1),19780(a,1,2)),flip(a)].">
      <j1 rule="para" parents="83 19780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19783">
    <literal><![CDATA[
      (x * (x / y)) \ y = (x / y) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(83(a,1),19781(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="83 19781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19784">
    <literal><![CDATA[
      (x * L(K(K(y,z),x) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),K(z,y) * L(K(x,K(y,z)) * u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(7292(a,1),18619(a,2,3,2,1,1))].">
      <j1 rule="para" parents="7292 18619"/>
    </justification>
  </clause>

  <clause id="19785">
    <literal><![CDATA[
      (x * L(K(K(y,z),x) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),L(K(z,y) * (K(x,K(y,z)) * u),x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(18144(a,2),19784(a,2,3))].">
      <j1 rule="para" parents="18144 19784"/>
    </justification>
  </clause>

  <clause id="19786">
    <literal><![CDATA[
      (x * L(K(K(y,z),x) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),L(y * (T(T(y,K(x,z)),z) \ u),x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(13521(a,1),19785(a,2,3,1))].">
      <j1 rule="para" parents="13521 19785"/>
    </justification>
  </clause>

  <clause id="19787">
    <literal><![CDATA[
      (x * L(K(K(y,z),x) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),L(y * (T(y,T(z,x)) \ u),x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(7349(a,1),19786(a,2,3,1,2,1))].">
      <j1 rule="para" parents="7349 19786"/>
    </justification>
  </clause>

  <clause id="19788">
    <literal><![CDATA[
      (x * L(K(K(y,z),x) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),L(K(T(z,x),y) * u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(4947(a,1),19787(a,2,3,1))].">
      <j1 rule="para" parents="4947 19787"/>
    </justification>
  </clause>

  <clause id="19789">
    <literal><![CDATA[
      (x * L(K(K(y,z),x) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),L(K(z,T(y,x)) * u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(7093(a,1),19788(a,2,3,1,1))].">
      <j1 rule="para" parents="7093 19788"/>
    </justification>
  </clause>

  <clause id="19790">
    <literal><![CDATA[
      (x * L(K(K(y,z),x) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),L(u * K(z,y),x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,19115,a(flip),b,19789,a),flip(a)].">
      <j1 rule="hyper" parents="347 19115 19789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19792">
    <literal><![CDATA[
      (x * L(K(K(y,z),x) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,19483,a(flip),b,19790,a),flip(a)].">
      <j1 rule="hyper" parents="347 19483 19790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19794">
    <literal><![CDATA[
      (x * L(K(x,K(y,z)) * u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),u * K(z,y))
    ]]></literal>
    <justification jstring="[para(7292(a,1),19792(a,1,1,2,1,1))].">
      <j1 rule="para" parents="7292 19792"/>
    </justification>
  </clause>

  <clause id="19795">
    <literal><![CDATA[
      (T(x,K(y,z)) * L(u,x,K(y,z))) \ (L(x,K(y,z),L(u,x,K(y,z))) * L(K(K(y,z),x) * u,x,K(y,z))) = a(x,K(y,z),u * K(z,y))
    ]]></literal>
    <justification jstring="[para(10426(a,1),19794(a,1,1))].">
      <j1 rule="para" parents="10426 19794"/>
    </justification>
  </clause>

  <clause id="19796">
    <literal><![CDATA[
      (K(x,y) * ((z * K(y,x)) * u)) \ (L(z,K(x,y),L(u,z,K(x,y))) * L(K(K(x,y),z) * u,z,K(x,y))) = a(z,K(x,y),u * K(y,x))
    ]]></literal>
    <justification jstring="[para(18315(a,1),19795(a,1,1))].">
      <j1 rule="para" parents="18315 19795"/>
    </justification>
  </clause>

  <clause id="19797">
    <literal><![CDATA[
      (K(x,y) * ((z * K(y,x)) * u)) \ (L(z,K(x,y),u) * L(K(K(x,y),z) * u,z,K(x,y))) = a(z,K(x,y),u * K(y,x))
    ]]></literal>
    <justification jstring="[para(19604(a,1),19796(a,1,2,1))].">
      <j1 rule="para" parents="19604 19796"/>
    </justification>
  </clause>

  <clause id="19798">
    <literal><![CDATA[
      (K(x,y) * ((z * K(y,x)) * u)) \ (L(z,K(x,y),u) * L(K(z,K(x,y)) * u,z,K(x,y))) = a(z,K(x,y),u * K(y,x))
    ]]></literal>
    <justification jstring="[para(7292(a,1),19797(a,1,2,2,1,1))].">
      <j1 rule="para" parents="7292 19797"/>
    </justification>
  </clause>

  <clause id="19800">
    <literal><![CDATA[
      (K(x,y) * ((z * K(y,x)) * u)) \ (L(T(z,K(x,y)),K(x,y),u) * L(u,z,K(x,y))) = a(z,K(x,y),u * K(y,x))
    ]]></literal>
    <justification jstring="[para(10427(a,1),19798(a,1,2))].">
      <j1 rule="para" parents="10427 19798"/>
    </justification>
  </clause>

  <clause id="19801">
    <literal><![CDATA[
      (K(x,y) * ((z * K(y,x)) * u)) \ (K(x,y) * (z * (K(y,x) * u))) = a(z,K(x,y),u * K(y,x))
    ]]></literal>
    <justification jstring="[para(19735(a,1),19800(a,1,2))].">
      <j1 rule="para" parents="19735 19800"/>
    </justification>
  </clause>

  <clause id="19802">
    <literal><![CDATA[
      L(a(x,K(y,z),u),(u * K(y,z)) * x,K(z,y)) = a(u,K(z,y),x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,19051,a(flip),b,19801,a)].">
      <j1 rule="hyper" parents="63 19051 19801"/>
    </justification>
  </clause>

  <clause id="19803">
    <literal><![CDATA[
      a(x,K(y,z),u * K(z,y)) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(19313,a,19802,a),flip(a)].">
      <j1 rule="hyper" parents="19313 19802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19804">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),T(x,w),T(u,v5)) = a(T(x,w),K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(19484,a,19803,a)].">
      <j1 rule="hyper" parents="19484 19803"/>
    </justification>
  </clause>

  <clause id="19805">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),T(x,w),T(u,v5)) = a(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,19482,a(flip),b,19804,a),flip(a)].">
      <j1 rule="hyper" parents="347 19482 19804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19807">
    <literal><![CDATA[
      L(x \ L(x,y,K(z,u)),T(x,w),T(z,v5)) = a(z,K(u,y),x)
    ]]></literal>
    <justification jstring="[para(19526(a,1),19805(a,1,1,2))].">
      <j1 rule="para" parents="19526 19805"/>
    </justification>
  </clause>

  <clause id="19808">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),T(z,w),T(u,v5)) = a(u,K(x,y),z)
    ]]></literal>
    <justification jstring="[para(14355(a,1),19807(a,1,1))].">
      <j1 rule="para" parents="14355 19807"/>
    </justification>
  </clause>

  <clause id="19809">
    <literal><![CDATA[
      a(x,y,K(z,L(u,T(z,w),T(u,v5)))) = a(u,K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11650,a,b,19808,a)].">
      <j1 rule="hyper" parents="63 11650 19808"/>
    </justification>
  </clause>

  <clause id="19810">
    <literal><![CDATA[
      a(x,K(y,z),u) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[para(11050(a,1),19809(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11050 19809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19812">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,K(y,x),u) = w
    ]]></literal>
    <justification jstring="[para(19810(a,1),19312(a,1))].">
      <j1 rule="para" parents="19810 19312"/>
    </justification>
  </clause>

  <clause id="19813">
    <literal><![CDATA[
      a(x,K(y,z),u) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(19812,a,13959,a(flip))].">
      <j1 rule="hyper" parents="19812 13959"/>
    </justification>
  </clause>

  <clause id="19814">
    <literal><![CDATA[
      a(x,a(y,z,K(u,w)),v5) = a(x,a(y,z,u),K(v5,w))
    ]]></literal>
    <justification jstring="[para(12681(a,2),19813(a,1,2))].">
      <j1 rule="para" parents="12681 19813"/>
    </justification>
  </clause>

  <clause id="19815">
    <literal><![CDATA[
      a(x,a(y,z,K(u,w)),v5) = a(x,y,K(v5,a(w,z,u)))
    ]]></literal>
    <justification jstring="[para(13960(a,2),19813(a,1,2))].">
      <j1 rule="para" parents="13960 19813"/>
    </justification>
  </clause>

  <clause id="19816">
    <literal><![CDATA[
      a(x,a(y,z,u),K(w,v5)) = a(x,y,K(w,a(v5,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19814,a(flip),b,19815,a)].">
      <j1 rule="hyper" parents="63 19814 19815"/>
    </justification>
  </clause>

  <clause id="19817">
    <literal><![CDATA[
      a(x,a(y,z,u),K(w,v5)) = a(x,y,a(w,z,K(u,v5)))
    ]]></literal>
    <justification jstring="[para(13960(a,2),19816(a,2,3))].">
      <j1 rule="para" parents="13960 19816"/>
    </justification>
  </clause>

  <clause id="19818">
    <literal><![CDATA[
      K(x,y) * a(x,z,a(y,u,K(w,v5))) = K(x,L(y,v5,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(19817(a,1),19396(a,1,2))].">
      <j1 rule="para" parents="19817 19396"/>
    </justification>
  </clause>

  <clause id="19819">
    <literal><![CDATA[
      K(x,L(y,a(z,u,w),v5)) = K(x,L(y,z,a(v5,u,w)))
    ]]></literal>
    <justification jstring="[hyper(19447,a,19818,a)].">
      <j1 rule="hyper" parents="19447 19818"/>
    </justification>
  </clause>

  <clause id="19820">
    <literal><![CDATA[
      T(x * K(y,L(x,z,a(u,w,v5))),y) = L(x,a(z,w,v5),K(u,y))
    ]]></literal>
    <justification jstring="[para(19819(a,1),14433(a,1,1,2))].">
      <j1 rule="para" parents="19819 14433"/>
    </justification>
  </clause>

  <clause id="19821">
    <literal><![CDATA[
      L(x,a(y,z,u),K(w,v5)) = L(x,y,K(a(w,z,u),v5))
    ]]></literal>
    <justification jstring="[hyper(14434,a,19820,a),flip(a)].">
      <j1 rule="hyper" parents="14434 19820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19822">
    <literal><![CDATA[
      L(x,a(y,z,u),K(w,v5)) = L(x,y,a(w,z,K(u,v5)))
    ]]></literal>
    <justification jstring="[para(12681(a,2),19821(a,2,3))].">
      <j1 rule="para" parents="12681 19821"/>
    </justification>
  </clause>

  <clause id="19823">
    <literal><![CDATA[
      L(x,K(a(y,z,u),w),v5) = L(x,y,a(v5,z,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19526,a,b,19822,a)].">
      <j1 rule="hyper" parents="63 19526 19822"/>
    </justification>
  </clause>

  <clause id="19824">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)),v5) = L(x,y,a(v5,z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(12681(a,2),19823(a,1,2))].">
      <j1 rule="para" parents="12681 19823"/>
    </justification>
  </clause>

  <clause id="19825">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(19500,a,19824,a),flip(a)].">
      <j1 rule="hyper" parents="19500 19824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19828">
    <literal><![CDATA[
      L(x,a(y,z,u),K(w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,19822,a,b,19825,a)].">
      <j1 rule="hyper" parents="63 19822 19825"/>
    </justification>
  </clause>

  <clause id="19834">
    <literal><![CDATA[
      a(a(x,y,z),u,K(w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(127,a,19828,a(flip),b,19398,a),flip(a)].">
      <j1 rule="hyper" parents="127 19828 19398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19835">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11128,a,19834,a)].">
      <j1 rule="hyper" parents="11128 19834"/>
    </justification>
  </clause>

  <clause id="19838">
    <literal><![CDATA[
      K((a(x,y,z) * u) \ w,v5) = K(u \ (a(x,y,z) \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(15079,a,19835,a),flip(a)].">
      <j1 rule="hyper" parents="15079 19835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19840">
    <literal><![CDATA[
      K((a(x,y,z) * u) \ w,v5) = K(a(x,y,z) * (u \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,19487,a(flip),b,19838,a),flip(a)].">
      <j1 rule="hyper" parents="347 19487 19838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19841">
    <literal><![CDATA[
      (x * K(a(y,z,u) * (w \ v5),v6)) \ (x * v6) = T(v6,(a(y,z,u) * w) \ v5)
    ]]></literal>
    <justification jstring="[para(19840(a,1),6100(a,1,1,2))].">
      <j1 rule="para" parents="19840 6100"/>
    </justification>
  </clause>

  <clause id="19842">
    <literal><![CDATA[
      T(x,(a(y,z,u) * w) \ v5) = T(x,a(y,z,u) * (w \ v5))
    ]]></literal>
    <justification jstring="[hyper(6114,a,19841,a),flip(a)].">
      <j1 rule="hyper" parents="6114 19841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19843">
    <literal><![CDATA[
      T(x,(y * a(z,u,w)) \ v5) = T(x,a(z,u,w) * (y \ v5))
    ]]></literal>
    <justification jstring="[hyper(17114,a,19842,a)].">
      <j1 rule="hyper" parents="17114 19842"/>
    </justification>
  </clause>

  <clause id="19844">
    <literal><![CDATA[
      T(x,T(y * (z * (a(u,w,v5) \ 1)),a(u,w,v5) * a(u,w,v5))) = T(x,a(u,w,v5) * (a(u,w,v5) \ (y * (z * a(u,w,v5)))))
    ]]></literal>
    <justification jstring="[para(967(a,2),19842(a,1,2))].">
      <j1 rule="para" parents="967 19842"/>
    </justification>
  </clause>

  <clause id="19845">
    <literal><![CDATA[
      T(x,a(y,y,z) * (z \ u)) = T(x,z \ L(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,19612,a(flip),b,19843,a),flip(a)].">
      <j1 rule="hyper" parents="63 19612 19843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19846">
    <literal><![CDATA[
      T(x,y \ L(z,u,u)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(18910,a,19845,a),flip(a)].">
      <j1 rule="hyper" parents="18910 19845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19848">
    <literal><![CDATA[
      T(x,T(y,z) \ L(u,w,w)) = T(x,z * (y \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(19679,a,19846,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19679 19846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19849">
    <literal><![CDATA[
      R(T(x \ 1,x \ (y * z)),x,y \ z) = (x * L(y * z,y,y)) \ L(y * z,y,y)
    ]]></literal>
    <justification jstring="[para(19846(a,1),15307(a,1,1))].">
      <j1 rule="para" parents="19846 15307"/>
    </justification>
  </clause>

  <clause id="19850">
    <literal><![CDATA[
      T(x,(y * z) \ L(u,w,w)) = T(x,y * ((z * y) \ (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(15719,a,19848,a)].">
      <j1 rule="hyper" parents="15719 19848"/>
    </justification>
  </clause>

  <clause id="19851">
    <literal><![CDATA[
      T(x,T(y,z) * L(u,w,w)) = T(x,z * ((y \ 1) \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,15900,a(flip),b,19848,a)].">
      <j1 rule="hyper" parents="63 15900 19848"/>
    </justification>
  </clause>

  <clause id="19852">
    <literal><![CDATA[
      T(x,y * ((z * y) \ (y \ u))) = T(x,((y \ 1) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19611,a(flip),b,19850,a),flip(a)].">
      <j1 rule="hyper" parents="63 19611 19850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19854">
    <literal><![CDATA[
      T(x,y \ (K(z * z,u) * (z \ (z \ u)))) = T(x,((z \ 1) \ ((z \ 1) \ y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19715,a,b,19852,a)].">
      <j1 rule="hyper" parents="63 19715 19852"/>
    </justification>
  </clause>

  <clause id="19855">
    <literal><![CDATA[
      T(x,T(y,z) * L(u,w,w)) = T(x,z * (y * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,18889,a(flip),b,19851,a),flip(a)].">
      <j1 rule="hyper" parents="347 18889 19851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19856">
    <literal><![CDATA[
      T(x,y * (z * (y \ u))) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(18935,a,19855,a),flip(a)].">
      <j1 rule="hyper" parents="18935 19855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19857">
    <literal><![CDATA[
      T(x,T((y * z) \ 1,z) * u) = T(x,(y \ (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19704,a(flip),b,19856,a),flip(a)].">
      <j1 rule="hyper" parents="63 19704 19856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19858">
    <literal><![CDATA[
      T(x,T(y,z) * (z * u)) = T(x,z * (y * u))
    ]]></literal>
    <justification jstring="[para(9(a,1),19856(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 19856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19859">
    <literal><![CDATA[
      T(x,y * (T(z,y) * u)) = T(x,z * (y * u))
    ]]></literal>
    <justification jstring="[hyper(15779,a,19858,a),flip(a)].">
      <j1 rule="hyper" parents="15779 19858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19860">
    <literal><![CDATA[
      T(x,y * (T(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (y * u)) = w
    ]]></literal>
    <justification jstring="[para(19858(a,1),15779(a,1))].">
      <j1 rule="para" parents="19858 15779"/>
    </justification>
  </clause>

  <clause id="19861">
    <literal><![CDATA[
      T(x,((y \ 1) / z) * (T(u,y \ (z \ 1)) * w)) = T(x,u * (((y \ 1) / z) * w))
    ]]></literal>
    <justification jstring="[para(13166(a,1),19859(a,1,2,2,1))].">
      <j1 rule="para" parents="13166 19859"/>
    </justification>
  </clause>

  <clause id="19862">
    <literal><![CDATA[
      T(x,(y / (z \ 1)) * (T(u,y * z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u * ((y / (z \ 1)) * w)) = v5
    ]]></literal>
    <justification jstring="[para(13139(a,1),19860(a,1,2,2,1))].">
      <j1 rule="para" parents="13139 19860"/>
    </justification>
  </clause>

  <clause id="19863">
    <literal><![CDATA[
      T(x,T(y * z,z) \ u) = T(x,(y \ (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(15901,a,19857,a)].">
      <j1 rule="hyper" parents="15901 19857"/>
    </justification>
  </clause>

  <clause id="19864">
    <literal><![CDATA[
      T(x,(y \ (z \ 1)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(19863(a,1),15719(a,1))].">
      <j1 rule="para" parents="19863 15719"/>
    </justification>
  </clause>

  <clause id="19865">
    <literal><![CDATA[
      T(x,y \ (K(z * z,u) * (z \ (z \ u)))) = T(x,y \ ((z \ 1) * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,15087,a(flip),b,19854,a),flip(a)].">
      <j1 rule="hyper" parents="347 15087 19854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19866">
    <literal><![CDATA[
      T(x,((y \ 1) / z) * (T(u,y * (z \ 1)) * w)) = T(x,u * (((y \ 1) / z) * w))
    ]]></literal>
    <justification jstring="[hyper(16399,a,19861,a)].">
      <j1 rule="hyper" parents="16399 19861"/>
    </justification>
  </clause>

  <clause id="19867">
    <literal><![CDATA[
      T(x,y \ T((z \ u) / z,z \ 1)) = T(x,y \ ((z \ 1) * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[para(14775(a,1),19865(a,1,2,2))].">
      <j1 rule="para" parents="14775 19865"/>
    </justification>
  </clause>

  <clause id="19868">
    <literal><![CDATA[
      T(x,y \ T((z \ u) / z,z)) = T(x,y \ ((z \ 1) * ((z \ 1) * u)))
    ]]></literal>
    <justification jstring="[hyper(15841,a,19867,a)].">
      <j1 rule="hyper" parents="15841 19867"/>
    </justification>
  </clause>

  <clause id="19869">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) * ((z \ 1) * u))) = T(x,y \ (z \ (z \ u)))
    ]]></literal>
    <justification jstring="[para(113(a,1),19868(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 19868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19870">
    <literal><![CDATA[
      T(x,(y \ K(y,(z \ 1) * ((z \ 1) * u))) \ (z \ (z \ u))) = T(x,(y \ 1) \ T((z \ 1) * ((z \ 1) * u),y))
    ]]></literal>
    <justification jstring="[para(7721(a,1),19869(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7721 19869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19871">
    <literal><![CDATA[
      T(x,((y \ 1) / z) * (T(u,y / z) * w)) = T(x,u * (((y \ 1) / z) * w))
    ]]></literal>
    <justification jstring="[para(13069(a,1),19866(a,1,2,2,1))].">
      <j1 rule="para" parents="13069 19866"/>
    </justification>
  </clause>

  <clause id="19872">
    <literal><![CDATA[
      T(x,((y \ 1) / z) * (T(u,z * y) * w)) = T(x,u * (((y \ 1) / z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,17750,a(flip),b,19871,a)].">
      <j1 rule="hyper" parents="63 17750 19871"/>
    </justification>
  </clause>

  <clause id="19873">
    <literal><![CDATA[
      T(x,(y * z) \ (T(u,y * z) * w)) = T(x,u * (((z \ 1) / y) * w))
    ]]></literal>
    <justification jstring="[hyper(19351,a,19872,a)].">
      <j1 rule="hyper" parents="19351 19872"/>
    </justification>
  </clause>

  <clause id="19874">
    <literal><![CDATA[
      T(x,y * (((z \ 1) / u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * ((u * z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(19873(a,1),19678(a,1))].">
      <j1 rule="para" parents="19873 19678"/>
    </justification>
  </clause>

  <clause id="19876">
    <literal><![CDATA[
      T(x,(y * z) * (T(u,y * z) * w)) = T(x,u * ((y / (z \ 1)) * w))
    ]]></literal>
    <justification jstring="[hyper(19862,a,18953,a),flip(a)].">
      <j1 rule="hyper" parents="19862 18953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19877">
    <literal><![CDATA[
      T(x,y * ((z / (u \ 1)) * w)) = T(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[hyper(19860,a,19876,a),flip(a)].">
      <j1 rule="hyper" parents="19860 19876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19878">
    <literal><![CDATA[
      T(x,y * (((z \ 1) \ u) * w)) = T(x,y * ((T(u,z) * z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,17685,a(flip),b,19877,a)].">
      <j1 rule="hyper" parents="63 17685 19877"/>
    </justification>
  </clause>

  <clause id="19879">
    <literal><![CDATA[
      T(x,y * ((z * (u \ 1)) * w)) = T(x,y * ((z / u) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,17415,a(flip),b,19877,a),flip(a)].">
      <j1 rule="hyper" parents="63 17415 19877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19880">
    <literal><![CDATA[
      T(x,y * (((z \ 1) \ u) * w)) = T(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,19622,a(flip),b,19878,a),flip(a)].">
      <j1 rule="hyper" parents="347 19622 19878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19881">
    <literal><![CDATA[
      T(x,y * (((z \ 1) * u) * w)) = T(x,y * ((z \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,4013,a(flip),b,19880,a),flip(a)].">
      <j1 rule="hyper" parents="63 4013 19880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19882">
    <literal><![CDATA[
      T(x,y * (((z \ 1) / u) * w)) = T(x,y * ((z \ (u \ 1)) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19879,a(flip),b,19881,a)].">
      <j1 rule="hyper" parents="63 19879 19881"/>
    </justification>
  </clause>

  <clause id="19883">
    <literal><![CDATA[
      T(x,y * ((z \ (u \ 1)) * w)) = T(x,y * ((u * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(19874,a,19882,a),flip(a)].">
      <j1 rule="hyper" parents="19874 19882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19884">
    <literal><![CDATA[
      T(x,y * (((z / u) \ (z \ 1)) * u)) = T(x,y * ((z / u) \ (z \ u)))
    ]]></literal>
    <justification jstring="[para(19783(a,1),19883(a,2,2,2))].">
      <j1 rule="para" parents="19783 19883"/>
    </justification>
  </clause>

  <clause id="19885">
    <literal><![CDATA[
      T(x,y * ((z / u) \ (z \ u))) = T(x,y * ((u / (z * z)) * u))
    ]]></literal>
    <justification jstring="[para(821(a,1),19884(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="821 19884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19886">
    <literal><![CDATA[
      T(x,y * ((z / u) \ (z \ u))) = T(x,y * (u * ((z * z) \ u)))
    ]]></literal>
    <justification jstring="[para(803(a,1),19885(a,2,2,2))].">
      <j1 rule="para" parents="803 19885"/>
    </justification>
  </clause>

  <clause id="19887">
    <literal><![CDATA[
      T(x,y * ((z / u) \ (z \ u))) = T(x,y * (u * (z \ (z \ u))))
    ]]></literal>
    <justification jstring="[hyper(347,a,18949,a(flip),b,19886,a),flip(a)].">
      <j1 rule="hyper" parents="347 18949 19886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19888">
    <literal><![CDATA[
      T(x,y * ((z / u) * (u \ z))) = T(x,y * (z * (u \ (u \ z))))
    ]]></literal>
    <justification jstring="[hyper(63,a,19379,a(flip),b,19887,a)].">
      <j1 rule="hyper" parents="63 19379 19887"/>
    </justification>
  </clause>

  <clause id="19889">
    <literal><![CDATA[
      T(T(x,y * (z * (u \ (u \ z)))),(z / u) \ ((z / u) \ w)) = T(T(x,K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[para(19888(a,1),19049(a,1,1))].">
      <j1 rule="para" parents="19888 19049"/>
    </justification>
  </clause>

  <clause id="19890">
    <literal><![CDATA[
      T(x,(y \ K(y,(z \ 1) * ((z \ 1) * u))) \ (z \ (z \ u))) = T(x,(((z \ 1) * ((z \ 1) * u)) \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,19572,a(flip),b,19870,a),flip(a)].">
      <j1 rule="hyper" parents="347 19572 19870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19891">
    <literal><![CDATA[
      T(x,(y \ K(y,(z \ 1) * ((z \ 1) * u))) \ (z \ (z \ u))) = T(x,((z \ 1) * ((z \ 1) * u)) * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,13054,a(flip),b,19890,a),flip(a)].">
      <j1 rule="hyper" parents="347 13054 19890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19892">
    <literal><![CDATA[
      T(x,(y \ K(y,(z \ 1) * ((z \ 1) * u))) \ (z \ (z \ u))) = T(x,u * ((z \ 1) * ((z \ 1) * y)))
    ]]></literal>
    <justification jstring="[hyper(347,a,19617,a(flip),b,19891,a),flip(a)].">
      <j1 rule="hyper" parents="347 19617 19891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19893">
    <literal><![CDATA[
      T(x,(y \ K(y,(z \ 1) * ((z \ 1) * u))) \ (z \ (z \ u))) = T(x,u * (z \ (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(347,a,18955,a(flip),b,19892,a),flip(a)].">
      <j1 rule="hyper" parents="347 18955 19892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19894">
    <literal><![CDATA[
      T(x,(y \ K(y,z \ ((z \ 1) * u))) \ (z \ (z \ u))) = T(x,u * (z \ (z \ y)))
    ]]></literal>
    <justification jstring="[para(13050(a,1),19893(a,1,2,1,2))].">
      <j1 rule="para" parents="13050 19893"/>
    </justification>
  </clause>

  <clause id="19895">
    <literal><![CDATA[
      T(x,(y \ K(y,(z * z) \ u)) \ (z \ (z \ u))) = T(x,u * (z \ (z \ y)))
    ]]></literal>
    <justification jstring="[para(499(a,1),19894(a,1,2,1,2,2))].">
      <j1 rule="para" parents="499 19894"/>
    </justification>
  </clause>

  <clause id="19896">
    <literal><![CDATA[
      T(x,(y \ K(y,z \ (z \ u))) \ (z \ (z \ u))) = T(x,u * (z \ (z \ y)))
    ]]></literal>
    <justification jstring="[para(12972(a,1),19895(a,1,2,1,2))].">
      <j1 rule="para" parents="12972 19895"/>
    </justification>
  </clause>

  <clause id="19897">
    <literal><![CDATA[
      T(x,K(y \ (y \ z),u) * (u * (y \ (y \ z)))) = T(x,z * (y \ (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(17211,a,19896,a)].">
      <j1 rule="hyper" parents="17211 19896"/>
    </justification>
  </clause>

  <clause id="19898">
    <literal><![CDATA[
      T(x,(y \ (y \ z)) * u) = T(x,z * (y \ (y \ u)))
    ]]></literal>
    <justification jstring="[para(4909(a,1),19897(a,1,2))].">
      <j1 rule="para" parents="4909 19897"/>
    </justification>
  </clause>

  <clause id="19899">
    <literal><![CDATA[
      T(x,a(y,z,u) * (a(y,z,u) \ (w * (v5 * a(y,z,u))))) = T(x,w * (v5 * (a(y,z,u) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(9172,a,19844,a),flip(a)].">
      <j1 rule="hyper" parents="9172 19844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19901">
    <literal><![CDATA[
      T(x,y * (z * (a(u,w,v5) \ 1))) = T(x,y * (z * a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(10(a,1),19899(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 19899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19902">
    <literal><![CDATA[
      T(x,y * (z / a(u,w,v5))) = T(x,y * (z * a(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,18914,a(flip),b,19901,a)].">
      <j1 rule="hyper" parents="63 18914 19901"/>
    </justification>
  </clause>

  <clause id="19904">
    <literal><![CDATA[
      T(x,y * (a(z,u,w) \ v5)) = T(x,y * (v5 * a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(17140,a,19902,a)].">
      <j1 rule="hyper" parents="17140 19902"/>
    </justification>
  </clause>

  <clause id="19905">
    <literal><![CDATA[
      T(x,y * (a(z,z,u) \ w)) = T(x,y * (w * a(v5,v6,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,19580,a(flip),b,19904,a)].">
      <j1 rule="hyper" parents="63 19580 19904"/>
    </justification>
  </clause>

  <clause id="19906">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (z * a(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,(a(u,w,v5) \ z) * y) = v6
    ]]></literal>
    <justification jstring="[para(19904(a,1),18525(a,1))].">
      <j1 rule="para" parents="19904 18525"/>
    </justification>
  </clause>

  <clause id="19907">
    <literal><![CDATA[
      T(x,y * (z * a(u,w,w))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(19579,a,19905,a),flip(a)].">
      <j1 rule="hyper" parents="19579 19905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19908">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * z) = T(x,(a(u,w,w) \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(19906,a,19907,a),flip(a)].">
      <j1 rule="hyper" parents="19906 19907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19909">
    <literal><![CDATA[
      T(x,(a(y,z,z) \ u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u * w) = v5
    ]]></literal>
    <justification jstring="[para(19908(a,1),10397(a,1))].">
      <j1 rule="para" parents="19908 10397"/>
    </justification>
  </clause>

  <clause id="19910">
    <literal><![CDATA[
      T(x,((a(y,z,z) \ 1) \ (u \ 1)) * w) = T(x,T(u,a(y,z,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(19909,a,19046,a)].">
      <j1 rule="hyper" parents="19909 19046"/>
    </justification>
  </clause>

  <clause id="19911">
    <literal><![CDATA[
      T(x,(y * (a(z,u,u) \ 1)) \ w) = T(x,T(y,a(z,u,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(19864,a,19910,a)].">
      <j1 rule="hyper" parents="19864 19910"/>
    </justification>
  </clause>

  <clause id="19912">
    <literal><![CDATA[
      T(x,T(y,a(z,u,u)) \ w) = T(x,(a(z,u,u) / y) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,19350,a(flip),b,19911,a),flip(a)].">
      <j1 rule="hyper" parents="63 19350 19911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19913">
    <literal><![CDATA[
      T(x,T(y,a(z,u,u)) \ w) = T(x,(y \ a(z,u,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(347,a,17139,a(flip),b,19912,a),flip(a)].">
      <j1 rule="hyper" parents="347 17139 19912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19914">
    <literal><![CDATA[
      T(x,(y \ a(z,u,u)) * w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(17116,a,19913,a),flip(a)].">
      <j1 rule="hyper" parents="17116 19913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19915">
    <literal><![CDATA[
      T(x,y \ (T(z \ u,z) \ w)) = T(x,(y \ a(v5,v6,v6)) * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(347,a,17612,a,b,19914,a)].">
      <j1 rule="hyper" parents="347 17612 19914"/>
    </justification>
  </clause>

  <clause id="19916">
    <literal><![CDATA[
      T(x,y \ (T(z \ u,z) \ w)) = T(x,(y \ a(v5,v6,v6)) * ((z / u) * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,19379,a(flip),b,19915,a),flip(a)].">
      <j1 rule="hyper" parents="347 19379 19915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19917">
    <literal><![CDATA[
      T(x,y \ (T(z \ u,z) \ w)) = T(x,y \ ((z / u) * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,19914,a(flip),b,19916,a),flip(a)].">
      <j1 rule="hyper" parents="347 19914 19916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19918">
    <literal><![CDATA[
      T(x,y \ ((z / u) \ w)) = T(x,y \ ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(19574,a,19917,a)].">
      <j1 rule="hyper" parents="19574 19917"/>
    </justification>
  </clause>

  <clause id="19919">
    <literal><![CDATA[
      T(T(x,y * (z * (u \ (u \ z)))),(z / u) \ ((u / z) * w)) = T(T(x,K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,19889,a(flip),b,19918,a),flip(a)].">
      <j1 rule="hyper" parents="63 19889 19918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19920">
    <literal><![CDATA[
      T(T(x,y * (z * (u \ (u \ z)))),(u / z) * ((u / z) * w)) = T(T(x,K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,19349,a(flip),b,19919,a)].">
      <j1 rule="hyper" parents="63 19349 19919"/>
    </justification>
  </clause>

  <clause id="19921">
    <literal><![CDATA[
      T(T(x,y * (z * z)),u \ (u \ ((u / z) * ((u / z) * w)))) = T(T(x,K(z,u) * y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,18959,a(flip),b,19920,a)].">
      <j1 rule="hyper" parents="63 18959 19920"/>
    </justification>
  </clause>

  <clause id="19922">
    <literal><![CDATA[
      T(T(x,y),(z \ (z \ ((z / u) * ((z / u) * w)))) * (u * u)) = T(T(x,K(u,z) * y),w)
    ]]></literal>
    <justification jstring="[hyper(10399,a,19921,a)].">
      <j1 rule="hyper" parents="10399 19921"/>
    </justification>
  </clause>

  <clause id="19923">
    <literal><![CDATA[
      T(T(x,y),((z / u) * ((z / u) * w)) * (z \ (z \ (u * u)))) = T(T(x,K(u,z) * y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,19898,a(flip),b,19922,a)].">
      <j1 rule="hyper" parents="63 19898 19922"/>
    </justification>
  </clause>

  <clause id="19924">
    <literal><![CDATA[
      T(T(x,y),z * ((u / w) * ((u / w) * (u \ (u \ (w * w)))))) = T(T(x,K(w,u) * y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,19617,a(flip),b,19923,a)].">
      <j1 rule="hyper" parents="63 19617 19923"/>
    </justification>
  </clause>

  <clause id="19925">
    <literal><![CDATA[
      T(T(x,y),z * ((u \ w) * ((u \ w) * (w \ (w \ (u * u)))))) = T(T(x,K(u,w) * y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,16429,a(flip),b,19924,a)].">
      <j1 rule="hyper" parents="63 16429 19924"/>
    </justification>
  </clause>

  <clause id="19926">
    <literal><![CDATA[
      T(T(T(x,y),z),T(T(x,y),u) * ((w \ v5) * ((w \ v5) * (v5 \ (v5 \ (w * w)))))) = T(T(T(x,K(w,v5) * y),T(x,y)),z)
    ]]></literal>
    <justification jstring="[para(19925(a,1),7869(a,2,1))].">
      <j1 rule="para" parents="19925 7869"/>
    </justification>
  </clause>

  <clause id="19927">
    <literal><![CDATA[
      T(T(T(x,y),K(z,u) * w),T(T(x,y),v5)) = T(T(T(x,K(z,u) * y),T(x,y)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,19925,a(flip),b,19926,a)].">
      <j1 rule="hyper" parents="63 19925 19926"/>
    </justification>
  </clause>

  <clause id="19928">
    <literal><![CDATA[
      T(T(x,K(y,z) * u),w) = T(T(x,u),K(y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(40,a,4282,a,b,19927,a)].">
      <j1 rule="hyper" parents="40 4282 19927"/>
    </justification>
  </clause>

  <clause id="19929">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(40,a,18399,a,b,19928,a)].">
      <j1 rule="hyper" parents="40 18399 19928"/>
    </justification>
  </clause>

  <clause id="19932">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,15528,a(flip),b,19929,a),flip(a)].">
      <j1 rule="hyper" parents="347 15528 19929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19935">
    <literal><![CDATA[
      x * T(y,K(z,u) * x) = T(y,K(u,z)) * x
    ]]></literal>
    <justification jstring="[hyper(134,a,19929,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 19929 22"/>
    </justification>
  </clause>

  <clause id="19937">
    <literal><![CDATA[
      T(x,L(y,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(19724,a,19932,a)].">
      <j1 rule="hyper" parents="19724 19932"/>
    </justification>
  </clause>

  <clause id="19938">
    <literal><![CDATA[
      T(x,(y \ z) \ u) = T(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(15089,a,19937,a)].">
      <j1 rule="hyper" parents="15089 19937"/>
    </justification>
  </clause>

  <clause id="19939">
    <literal><![CDATA[
      T(x,a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(14049,a,19937,a)].">
      <j1 rule="hyper" parents="14049 19937"/>
    </justification>
  </clause>

  <clause id="19940">
    <literal><![CDATA[
      T(x / L(y,z,u),T(y,x)) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(7541,a,19937,a),flip(a)].">
      <j1 rule="hyper" parents="7541 19937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19941">
    <literal><![CDATA[
      T(x / L(y,z,u),y) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(386,a,19937,a),flip(a)].">
      <j1 rule="hyper" parents="386 19937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19951">
    <literal><![CDATA[
      T(x,R(y,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14104,a,b,19937,a)].">
      <j1 rule="hyper" parents="63 14104 19937"/>
    </justification>
  </clause>

  <clause id="19952">
    <literal><![CDATA[
      L(x,y,K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,14364,a(flip),b,19937,a),flip(a)].">
      <j1 rule="hyper" parents="40 14364 19937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19953">
    <literal><![CDATA[
      L(x,y,z) * T(u,x) = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,19937,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 19937 22"/>
    </justification>
  </clause>

  <clause id="19954">
    <literal><![CDATA[
      K(x,a(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,19937,a(flip),b,14287,a),flip(a)].">
      <j1 rule="hyper" parents="129 19937 14287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19955">
    <literal><![CDATA[
      T(x,y) != L(y,z,u) \ w
    ]]></literal>
    <literal><![CDATA[
      w / L(y,z,u) = x
    ]]></literal>
    <justification jstring="[para(19937(a,1),279(a,1))].">
      <j1 rule="para" parents="19937 279"/>
    </justification>
  </clause>

  <clause id="19956">
    <literal><![CDATA[
      L(x,y,z) * T(u,x) != w
    ]]></literal>
    <literal><![CDATA[
      u * L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(19937(a,1),315(a,1,2))].">
      <j1 rule="para" parents="19937 315"/>
    </justification>
  </clause>

  <clause id="19959">
    <literal><![CDATA[
      T(x,T((y \ z) \ u,w)) = T(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[para(891(a,1),19937(a,1,2)),flip(a)].">
      <j1 rule="para" parents="891 19937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19960">
    <literal><![CDATA[
      (x * L(L(y,z,u),w,v5)) / T(x,L(y,z,u)) = L(L(y,w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(19937(a,1),295(a,1,2))].">
      <j1 rule="para" parents="19937 295"/>
    </justification>
  </clause>

  <clause id="19962">
    <literal><![CDATA[
      T(x * L(y,z,u),K(L(y,z,u),w)) = L(y,z,u) * T(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(19937(a,1),6062(a,2,2))].">
      <j1 rule="para" parents="19937 6062"/>
    </justification>
  </clause>

  <clause id="19964">
    <literal><![CDATA[
      L(T(x,y),z,u) \ T(x,y) = L(x,z,u) \ x
    ]]></literal>
    <justification jstring="[para(19937(a,1),11200(a,1,2))].">
      <j1 rule="para" parents="19937 11200"/>
    </justification>
  </clause>

  <clause id="19966">
    <literal><![CDATA[
      R(x,y,z) * T(u,x) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(19937(a,1),14122(a,1,2))].">
      <j1 rule="para" parents="19937 14122"/>
    </justification>
  </clause>

  <clause id="19967">
    <literal><![CDATA[
      R(x,y,z) * T(u,x) != w
    ]]></literal>
    <literal><![CDATA[
      u * R(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(19937(a,1),14123(a,1,2))].">
      <j1 rule="para" parents="19937 14123"/>
    </justification>
  </clause>

  <clause id="19968">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,u) = x \ R(x,z,u)
    ]]></literal>
    <justification jstring="[para(19937(a,1),14682(a,1,1))].">
      <j1 rule="para" parents="19937 14682"/>
    </justification>
  </clause>

  <clause id="19972">
    <literal><![CDATA[
      T(x,L(y,z,u) \ (T(w,y) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,w \ (L(y,z,u) \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(19937(a,1),19443(a,1,2,2,1))].">
      <j1 rule="para" parents="19937 19443"/>
    </justification>
  </clause>

  <clause id="19974">
    <literal><![CDATA[
      x \ (a(y,z,u) * x) = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(16635,a,19939,a)].">
      <j1 rule="hyper" parents="16635 19939"/>
    </justification>
  </clause>

  <clause id="19975">
    <literal><![CDATA[
      T(x,y \ R(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(14233,a,19939,a)].">
      <j1 rule="hyper" parents="14233 19939"/>
    </justification>
  </clause>

  <clause id="19976">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ (v5 * a(x,y,z)) = a(x,y,z) * (L(a(x,y,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(11226,a,19939,a),flip(a)].">
      <j1 rule="hyper" parents="11226 19939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19977">
    <literal><![CDATA[
      x / a(y,z,u) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(7761,a,19939,a),flip(a)].">
      <j1 rule="hyper" parents="7761 19939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19978">
    <literal><![CDATA[
      x * K(a(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[hyper(7760,a,19939,a)].">
      <j1 rule="hyper" parents="7760 19939"/>
    </justification>
  </clause>

  <clause id="19979">
    <literal><![CDATA[
      x * K(y,a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(6059,a,19939,a)].">
      <j1 rule="hyper" parents="6059 19939"/>
    </justification>
  </clause>

  <clause id="19980">
    <literal><![CDATA[
      x * (a(y,z,u) * w) = x * (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(5904,a,19939,a),flip(a)].">
      <j1 rule="hyper" parents="5904 19939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19982">
    <literal><![CDATA[
      (x * a(y,z,u)) / x = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(5640,a,19939,a)].">
      <j1 rule="hyper" parents="5640 19939"/>
    </justification>
  </clause>

  <clause id="19984">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ u = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(4352,a,19939,a)].">
      <j1 rule="hyper" parents="4352 19939"/>
    </justification>
  </clause>

  <clause id="19985">
    <literal><![CDATA[
      a(x,y,z) * u = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1852,a,19939,a),flip(a)].">
      <j1 rule="hyper" parents="1852 19939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19986">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(x,y,z) = u
    ]]></literal>
    <justification jstring="[hyper(1847,a,19939,a)].">
      <j1 rule="hyper" parents="1847 19939"/>
    </justification>
  </clause>

  <clause id="19987">
    <literal><![CDATA[
      (a(x,y,z) * u) * w = (u * a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(1283,a,19939,a),flip(a)].">
      <j1 rule="hyper" parents="1283 19939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19988">
    <literal><![CDATA[
      a(x,y,z) \ (u * a(x,y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(439,a,19939,a)].">
      <j1 rule="hyper" parents="439 19939"/>
    </justification>
  </clause>

  <clause id="20000">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,16623,a,b,19939,a)].">
      <j1 rule="hyper" parents="63 16623 19939"/>
    </justification>
  </clause>

  <clause id="20001">
    <literal><![CDATA[
      R(x,y,K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,14299,a,b,19939,a)].">
      <j1 rule="hyper" parents="63 14299 19939"/>
    </justification>
  </clause>

  <clause id="20002">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,12580,a,b,19939,a)].">
      <j1 rule="hyper" parents="63 12580 19939"/>
    </justification>
  </clause>

  <clause id="20003">
    <literal><![CDATA[
      (K(x,y) * z) \ u = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14383,a(flip),b,19939,a),flip(a)].">
      <j1 rule="hyper" parents="63 14383 19939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20005">
    <literal><![CDATA[
      T(a(x,y,z),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,19939,a)].">
      <j1 rule="hyper" parents="54 19939"/>
    </justification>
  </clause>

  <clause id="20006">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) / (x * y) = L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(220,a,19939,a(flip),b,13762,a)].">
      <j1 rule="hyper" parents="220 19939 13762"/>
    </justification>
  </clause>

  <clause id="20007">
    <literal><![CDATA[
      a(x,y,z) * (u / a(x,y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(134,a,14035,a(flip),b,19939,a(flip))].">
      <j1 rule="hyper" parents="134 14035 19939"/>
    </justification>
  </clause>

  <clause id="20008">
    <literal><![CDATA[
      (K(x,y) * z) * u = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(134,a,19939,a(flip),b,14336,a)].">
      <j1 rule="hyper" parents="134 19939 14336"/>
    </justification>
  </clause>

  <clause id="20009">
    <literal><![CDATA[
      K(a(x,y,z),u) * w = w
    ]]></literal>
    <justification jstring="[hyper(132,a,19939,a(flip),b,5212,a),flip(a)].">
      <j1 rule="hyper" parents="132 19939 5212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20011">
    <literal><![CDATA[
      T(x * a(y,z,u),a(y,z,u) \ 1) = ((a(y,z,u) * x) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,19939,a(flip),b,6351,a),flip(a)].">
      <j1 rule="hyper" parents="128 19939 6351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20013">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(19939(a,1),49(a,2))].">
      <j1 rule="para" parents="19939 49"/>
    </justification>
  </clause>

  <clause id="20014">
    <literal><![CDATA[
      a(x,y,z) \ u != w
    ]]></literal>
    <literal><![CDATA[
      w * a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(19939(a,1),152(a,1)),flip(a)].">
      <j1 rule="para" parents="19939 152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20015">
    <literal><![CDATA[
      a(x,y,z) \ (u * a(x,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(19939(a,1),155(a,1)),flip(a)].">
      <j1 rule="para" parents="19939 155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20016">
    <literal><![CDATA[
      a(x,y,z) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(19939(a,1),315(a,1,2))].">
      <j1 rule="para" parents="19939 315"/>
    </justification>
  </clause>

  <clause id="20017">
    <literal><![CDATA[
      x \ (a(y,z,u) * x) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(19939(a,1),361(a,1,2,2))].">
      <j1 rule="para" parents="19939 361"/>
    </justification>
  </clause>

  <clause id="20018">
    <literal><![CDATA[
      x / a(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(19939(a,1),386(a,1))].">
      <j1 rule="para" parents="19939 386"/>
    </justification>
  </clause>

  <clause id="20019">
    <literal><![CDATA[
      x * (a(y,z,u) \ (w * a(y,z,u))) = x * w
    ]]></literal>
    <justification jstring="[para(19939(a,1),167(a,2,2))].">
      <j1 rule="para" parents="19939 167"/>
    </justification>
  </clause>

  <clause id="20020">
    <literal><![CDATA[
      x \ (a(y,z,u) * w) = x \ (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(19939(a,1),250(a,1,2,2))].">
      <j1 rule="para" parents="19939 250"/>
    </justification>
  </clause>

  <clause id="20022">
    <literal><![CDATA[
      (a(x,y,z) * u) * w != v5
    ]]></literal>
    <literal><![CDATA[
      (u * a(x,y,z)) * w = v5
    ]]></literal>
    <justification jstring="[para(19939(a,1),629(a,1,1,2))].">
      <j1 rule="para" parents="19939 629"/>
    </justification>
  </clause>

  <clause id="20023">
    <literal><![CDATA[
      x * (a(y,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (w * a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(19939(a,1),639(a,1,2,2))].">
      <j1 rule="para" parents="19939 639"/>
    </justification>
  </clause>

  <clause id="20024">
    <literal><![CDATA[
      (a(x,y,z) * u) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      (u * a(x,y,z)) \ w = v5
    ]]></literal>
    <justification jstring="[para(19939(a,1),650(a,1,1,2))].">
      <j1 rule="para" parents="19939 650"/>
    </justification>
  </clause>

  <clause id="20025">
    <literal><![CDATA[
      L(x \ y,x,a(z,u,w)) = (x * a(z,u,w)) \ (a(z,u,w) * y)
    ]]></literal>
    <justification jstring="[para(19939(a,1),10169(a,1,1,1))].">
      <j1 rule="para" parents="19939 10169"/>
    </justification>
  </clause>

  <clause id="20028">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (u * w) = w * (T(u,w) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(19939(a,1),13468(a,1,2))].">
      <j1 rule="para" parents="19939 13468"/>
    </justification>
  </clause>

  <clause id="20029">
    <literal><![CDATA[
      L(a(x,y,z),u \ w,u) * w = u * ((u \ w) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(19939(a,1),13767(a,1,2))].">
      <j1 rule="para" parents="19939 13767"/>
    </justification>
  </clause>

  <clause id="20030">
    <literal><![CDATA[
      ((x / y) * (y * a(z,u,w))) / x = L(a(z,u,w),y,y \ x)
    ]]></literal>
    <justification jstring="[para(19939(a,1),13867(a,1,2))].">
      <j1 rule="para" parents="19939 13867"/>
    </justification>
  </clause>

  <clause id="20031">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      T(y,a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[para(19939(a,1),14037(a,1))].">
      <j1 rule="para" parents="19939 14037"/>
    </justification>
  </clause>

  <clause id="20033">
    <literal><![CDATA[
      (x * y) * K(z,u) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(19939(a,1),14297(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19939 14297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20035">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(19939(a,1),14423(a,1))].">
      <j1 rule="para" parents="19939 14423"/>
    </justification>
  </clause>

  <clause id="20039">
    <literal><![CDATA[
      x \ ((x * a(y,z,u)) * w) = w * (a(y,z,u) * a(x,a(y,z,u),w))
    ]]></literal>
    <justification jstring="[para(19939(a,1),18782(a,1,2,2))].">
      <j1 rule="para" parents="19939 18782"/>
    </justification>
  </clause>

  <clause id="20040">
    <literal><![CDATA[
      R(x,y,T(z,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(14482,a,19952,a)].">
      <j1 rule="hyper" parents="14482 19952"/>
    </justification>
  </clause>

  <clause id="20041">
    <literal><![CDATA[
      L(x,y,T(z,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(14440,a,19952,a)].">
      <j1 rule="hyper" parents="14440 19952"/>
    </justification>
  </clause>

  <clause id="20042">
    <literal><![CDATA[
      L(x,y,z * u) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(10573,a,19952,a)].">
      <j1 rule="hyper" parents="10573 19952"/>
    </justification>
  </clause>

  <clause id="20043">
    <literal><![CDATA[
      L(x,y,(z \ u) * z) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(10571,a,19952,a)].">
      <j1 rule="hyper" parents="10571 19952"/>
    </justification>
  </clause>

  <clause id="20046">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,y) * u) = z \ u
    ]]></literal>
    <justification jstring="[hyper(569,a,19952,a),flip(a)].">
      <j1 rule="hyper" parents="569 19952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20075">
    <literal><![CDATA[
      L(x,K(y,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,19526,a,b,19952,a)].">
      <j1 rule="hyper" parents="63 19526 19952"/>
    </justification>
  </clause>

  <clause id="20076">
    <literal><![CDATA[
      T(x,y \ L(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,16625,a,b,19952,a)].">
      <j1 rule="hyper" parents="63 16625 19952"/>
    </justification>
  </clause>

  <clause id="20077">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),y) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17256,a(flip),b,19952,a)].">
      <j1 rule="hyper" parents="63 17256 19952"/>
    </justification>
  </clause>

  <clause id="20078">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * u = u * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,15421,a(flip),b,19952,a)].">
      <j1 rule="hyper" parents="63 15421 19952"/>
    </justification>
  </clause>

  <clause id="20079">
    <literal><![CDATA[
      L(x,y,z / u) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14457,a(flip),b,19952,a)].">
      <j1 rule="hyper" parents="63 14457 19952"/>
    </justification>
  </clause>

  <clause id="20080">
    <literal><![CDATA[
      (x * K(y,z)) / u = x / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14372,a(flip),b,19952,a),flip(a)].">
      <j1 rule="hyper" parents="63 14372 19952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20083">
    <literal><![CDATA[
      (x \ y) \ (K(x,z) * u) = (T(x,z) \ y) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,5328,a(flip),b,19952,a)].">
      <j1 rule="hyper" parents="63 5328 19952"/>
    </justification>
  </clause>

  <clause id="20087">
    <literal><![CDATA[
      T(a(x,y,z) \ 1,u) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(269,a,15421,a(flip),b,19952,a(flip))].">
      <j1 rule="hyper" parents="269 15421 19952"/>
    </justification>
  </clause>

  <clause id="20088">
    <literal><![CDATA[
      (K(x,y) * z) / u = K(x,y) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(220,a,19952,a(flip),b,9645,a(flip))].">
      <j1 rule="hyper" parents="220 19952 9645"/>
    </justification>
  </clause>

  <clause id="20090">
    <literal><![CDATA[
      (T(x,y) * z) * L(u,z,x) = T(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(134,a,19952,a(flip),b,6641,a(flip))].">
      <j1 rule="hyper" parents="134 19952 6641"/>
    </justification>
  </clause>

  <clause id="20092">
    <literal><![CDATA[
      T(L(x,y,z) \ x,u) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,19952,a(flip),b,19594,a),flip(a)].">
      <j1 rule="hyper" parents="128 19952 19594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20093">
    <literal><![CDATA[
      (K(x,y) * z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (z * u) = w
    ]]></literal>
    <justification jstring="[para(19952(a,1),322(a,1,2))].">
      <j1 rule="para" parents="19952 322"/>
    </justification>
  </clause>

  <clause id="20101">
    <literal><![CDATA[
      (K(x,y) * z) \ u != w
    ]]></literal>
    <literal><![CDATA[
      z \ (K(y,x) * u) = w
    ]]></literal>
    <justification jstring="[para(19952(a,1),5290(a,1)),flip(a)].">
      <j1 rule="para" parents="19952 5290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20103">
    <literal><![CDATA[
      L(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(19952(a,1),6972(a,1))].">
      <j1 rule="para" parents="19952 6972"/>
    </justification>
  </clause>

  <clause id="20105">
    <literal><![CDATA[
      L(x,y,z * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(19952(a,1),10573(a,1))].">
      <j1 rule="para" parents="19952 10573"/>
    </justification>
  </clause>

  <clause id="20107">
    <literal><![CDATA[
      T(K(x,y) * (z / u),u) = u \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(19952(a,1),13764(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19952 13764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20109">
    <literal><![CDATA[
      x \ (y * K(z,u)) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(19952(a,1),14376(a,1,1))].">
      <j1 rule="para" parents="19952 14376"/>
    </justification>
  </clause>

  <clause id="20110">
    <literal><![CDATA[
      R(x,y,z) * (x \ u) = (u / x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(19952(a,1),14415(a,1,2))].">
      <j1 rule="para" parents="19952 14415"/>
    </justification>
  </clause>

  <clause id="20111">
    <literal><![CDATA[
      R(x,y,z) * (x \ u) != w
    ]]></literal>
    <literal><![CDATA[
      (u / x) * R(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(19952(a,1),14416(a,1,2))].">
      <j1 rule="para" parents="19952 14416"/>
    </justification>
  </clause>

  <clause id="20112">
    <literal><![CDATA[
      x \ (y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * K(z,u) = w
    ]]></literal>
    <justification jstring="[para(19952(a,1),14489(a,1,1))].">
      <j1 rule="para" parents="19952 14489"/>
    </justification>
  </clause>

  <clause id="20119">
    <literal><![CDATA[
      (a(x,y,z) * u) \ w = (u * a(x,y,z)) \ w
    ]]></literal>
    <justification jstring="[hyper(193,a,10293,a,b,19954,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="193 10293 19954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20120">
    <literal><![CDATA[
      x / (a(y,z,u) * w) = x / (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(189,a,9868,a,b,19954,a(flip))].">
      <j1 rule="hyper" parents="189 9868 19954"/>
    </justification>
  </clause>

  <clause id="20126">
    <literal><![CDATA[
      R(x,y,z / u) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(10646,a,20001,a)].">
      <j1 rule="hyper" parents="10646 20001"/>
    </justification>
  </clause>

  <clause id="20137">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * K(u,w)) = (x * (y * z)) * K(u,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,20001,a(flip),b,543,a)].">
      <j1 rule="hyper" parents="133 20001 543"/>
    </justification>
  </clause>

  <clause id="20140">
    <literal><![CDATA[
      R(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(20001(a,1),51(a,2))].">
      <j1 rule="para" parents="20001 51"/>
    </justification>
  </clause>

  <clause id="20146">
    <literal><![CDATA[
      (x * K(y,z)) / u != w
    ]]></literal>
    <literal><![CDATA[
      x / (u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(20001(a,1),6148(a,1))].">
      <j1 rule="para" parents="20001 6148"/>
    </justification>
  </clause>

  <clause id="20151">
    <literal><![CDATA[
      (x * K(y,z)) * u = x * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(1362,a,20075,a),flip(a)].">
      <j1 rule="hyper" parents="1362 20075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20165">
    <literal><![CDATA[
      x / (K(y,z) * u) = (x / u) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,17874,a(flip),b,20075,a)].">
      <j1 rule="hyper" parents="63 17874 20075"/>
    </justification>
  </clause>

  <clause id="20166">
    <literal><![CDATA[
      (x * K(y,z)) \ u = K(z,y) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,5278,a(flip),b,20075,a)].">
      <j1 rule="hyper" parents="63 5278 20075"/>
    </justification>
  </clause>

  <clause id="20172">
    <literal><![CDATA[
      L(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(20075(a,1),50(a,2))].">
      <j1 rule="para" parents="20075 50"/>
    </justification>
  </clause>

  <clause id="20173">
    <literal><![CDATA[
      (x * K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(20075(a,1),322(a,1,2))].">
      <j1 rule="para" parents="20075 322"/>
    </justification>
  </clause>

  <clause id="20177">
    <literal><![CDATA[
      ((x * K(y,z)) * (u * w)) \ ((x * (T(u,K(z,y)) * K(y,z))) * w) = a(x * K(y,z),L(u,K(y,z),x),w)
    ]]></literal>
    <justification jstring="[para(20075(a,1),6892(a,1,1,2,1))].">
      <j1 rule="para" parents="20075 6892"/>
    </justification>
  </clause>

  <clause id="20179">
    <literal><![CDATA[
      (x \ y) * (K(y,z) * u) = (x \ T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(20075(a,1),13109(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20075 13109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20181">
    <literal><![CDATA[
      T(x / R(y,z,u),y) = R(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(386,a,19951,a),flip(a)].">
      <j1 rule="hyper" parents="386 19951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20190">
    <literal><![CDATA[
      R(x,y,z) * L(T(u,x),w,v5) = L(u,w,v5) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(19951(a,1),267(a,1,2,1))].">
      <j1 rule="para" parents="19951 267"/>
    </justification>
  </clause>

  <clause id="20191">
    <literal><![CDATA[
      T(x,y \ (z * (u \ y))) = T(x,T(z / u,y))
    ]]></literal>
    <justification jstring="[para(1077(a,1),19951(a,1,2))].">
      <j1 rule="para" parents="1077 19951"/>
    </justification>
  </clause>

  <clause id="20196">
    <literal><![CDATA[
      L(x,y,y \ R(y,z,u)) * ((y \ R(y,z,u)) * y) = (y \ R(y,z,u)) * (y * T(x,y))
    ]]></literal>
    <justification jstring="[para(19951(a,1),3691(a,2,2,2))].">
      <j1 rule="para" parents="19951 3691"/>
    </justification>
  </clause>

  <clause id="20199">
    <literal><![CDATA[
      x / (y \ R(y,z,u)) = (y \ R(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(7761,a,19975,a),flip(a)].">
      <j1 rule="hyper" parents="7761 19975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20202">
    <literal><![CDATA[
      (x \ R(x,y,z)) * u = u * (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(1852,a,19975,a),flip(a)].">
      <j1 rule="hyper" parents="1852 19975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20206">
    <literal><![CDATA[
      T(x,y \ R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(19975(a,1),49(a,2))].">
      <j1 rule="para" parents="19975 49"/>
    </justification>
  </clause>

  <clause id="20216">
    <literal><![CDATA[
      K(L(x,y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14159,a(flip),b,19978,a)].">
      <j1 rule="hyper" parents="63 14159 19978"/>
    </justification>
  </clause>

  <clause id="20217">
    <literal><![CDATA[
      K(x,L(y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14078,a(flip),b,19978,a)].">
      <j1 rule="hyper" parents="63 14078 19978"/>
    </justification>
  </clause>

  <clause id="20219">
    <literal><![CDATA[
      x * (x \ (y * a(z,u,w))) = a(z,u,w) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,19978,a(flip),b,13906,a(flip))].">
      <j1 rule="hyper" parents="134 19978 13906"/>
    </justification>
  </clause>

  <clause id="20220">
    <literal><![CDATA[
      x / (y * a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x / (a(z,u,w) * y) = v5
    ]]></literal>
    <justification jstring="[para(19978(a,1),9873(a,2))].">
      <j1 rule="para" parents="19978 9873"/>
    </justification>
  </clause>

  <clause id="20221">
    <literal><![CDATA[
      x / (a(y,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      x / (w * a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(19978(a,1),9874(a,1))].">
      <j1 rule="para" parents="19978 9874"/>
    </justification>
  </clause>

  <clause id="20224">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * v5 = v5 * L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(19979(a,1),5067(a,1,1,1))].">
      <j1 rule="para" parents="19979 5067"/>
    </justification>
  </clause>

  <clause id="20226">
    <literal><![CDATA[
      x / (a(y,z,u) \ 1) = (a(y,z,u) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(7761,a,20000,a),flip(a)].">
      <j1 rule="hyper" parents="7761 20000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20229">
    <literal><![CDATA[
      K(x,a(y,z,u) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,20000,a)].">
      <j1 rule="hyper" parents="55 20000"/>
    </justification>
  </clause>

  <clause id="20230">
    <literal><![CDATA[
      (a(x,y,z) \ u) / u = u \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(220,a,20000,a(flip),b,4219,a)].">
      <j1 rule="hyper" parents="220 20000 4219"/>
    </justification>
  </clause>

  <clause id="20231">
    <literal><![CDATA[
      K(x,y \ L(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(127,a,20000,a(flip),b,12615,a),flip(a)].">
      <j1 rule="hyper" parents="127 20000 12615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20232">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * (a(x,y,z) \ 1) = w
    ]]></literal>
    <justification jstring="[para(20000(a,1),315(a,1,2))].">
      <j1 rule="para" parents="20000 315"/>
    </justification>
  </clause>

  <clause id="20234">
    <literal><![CDATA[
      x / (L(y,z,u) \ y) = (L(y,z,u) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(7761,a,20002,a),flip(a)].">
      <j1 rule="hyper" parents="7761 20002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20236">
    <literal><![CDATA[
      (L(x,y,z) \ x) * u = u * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(1852,a,20002,a),flip(a)].">
      <j1 rule="hyper" parents="1852 20002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20237">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * w = (u * (L(x,y,z) \ x)) * w
    ]]></literal>
    <justification jstring="[hyper(1283,a,20002,a),flip(a)].">
      <j1 rule="hyper" parents="1283 20002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20240">
    <literal><![CDATA[
      (x * y) / (x * L(y,z,u)) = (x * L(y,z,u)) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(220,a,20002,a(flip),b,13773,a(flip))].">
      <j1 rule="hyper" parents="220 20002 13773"/>
    </justification>
  </clause>

  <clause id="20241">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) * (w * u) = w * (u * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[hyper(134,a,20002,a(flip),b,13762,a)].">
      <j1 rule="hyper" parents="134 20002 13762"/>
    </justification>
  </clause>

  <clause id="20242">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * w != v5
    ]]></literal>
    <literal><![CDATA[
      (u * (L(x,y,z) \ x)) * w = v5
    ]]></literal>
    <justification jstring="[para(20002(a,1),629(a,1,1,2))].">
      <j1 rule="para" parents="20002 629"/>
    </justification>
  </clause>

  <clause id="20248">
    <literal><![CDATA[
      (x * a(y,z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,u) * x) * w = v5
    ]]></literal>
    <justification jstring="[para(20009(a,1),10292(a,1,2))].">
      <j1 rule="para" parents="20009 10292"/>
    </justification>
  </clause>

  <clause id="20250">
    <literal><![CDATA[
      x / (y \ L(y,z,u)) = (y \ L(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(7761,a,20076,a),flip(a)].">
      <j1 rule="hyper" parents="7761 20076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20251">
    <literal><![CDATA[
      K(x \ L(x,y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(4952,a,20076,a)].">
      <j1 rule="hyper" parents="4952 20076"/>
    </justification>
  </clause>

  <clause id="20253">
    <literal><![CDATA[
      (x \ L(x,y,z)) * u = u * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(1852,a,20076,a),flip(a)].">
      <j1 rule="hyper" parents="1852 20076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20259">
    <literal><![CDATA[
      T(x \ L(x,y,z),u) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(54,a,20076,a)].">
      <j1 rule="hyper" parents="54 20076"/>
    </justification>
  </clause>

  <clause id="20260">
    <literal><![CDATA[
      (x * (y * (z \ L(z,u,w)))) / (x * y) = L(z \ L(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(220,a,20076,a(flip),b,13762,a)].">
      <j1 rule="hyper" parents="220 20076 13762"/>
    </justification>
  </clause>

  <clause id="20262">
    <literal><![CDATA[
      x \ ((y \ L(y,z,u)) * x) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(20076(a,1),256(a,1,2,2))].">
      <j1 rule="para" parents="20076 256"/>
    </justification>
  </clause>

  <clause id="20284">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14098,a,b,20216,a)].">
      <j1 rule="hyper" parents="63 14098 20216"/>
    </justification>
  </clause>

  <clause id="20286">
    <literal><![CDATA[
      L(L(x / (x / y),z,u),w,v5) \ L(L(y,z,u),w,v5) = K(L(y,z,u),y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,5838,a,b,20216,a)].">
      <j1 rule="hyper" parents="63 5838 20216"/>
    </justification>
  </clause>

  <clause id="20288">
    <literal><![CDATA[
      K(x,y) * (L(T(x,y),z,u) \ w) = L(x,z,u) \ w
    ]]></literal>
    <justification jstring="[hyper(133,a,20216,a(flip),b,5833,a)].">
      <j1 rule="hyper" parents="133 20216 5833"/>
    </justification>
  </clause>

  <clause id="20294">
    <literal><![CDATA[
      K((x \ y) \ z,u) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(561(a,1),20216(a,1,1)),flip(a)].">
      <j1 rule="para" parents="561 20216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20300">
    <literal><![CDATA[
      K(x,y) * (L(x,z,u) * w) = L(T(x,y),z,u) * w
    ]]></literal>
    <justification jstring="[para(20216(a,1),5235(a,1,1))].">
      <j1 rule="para" parents="20216 5235"/>
    </justification>
  </clause>

  <clause id="20301">
    <literal><![CDATA[
      L(x \ y,z,u) \ K(x \ y,x) = L(y / x,z,u) \ 1
    ]]></literal>
    <justification jstring="[para(20216(a,1),5303(a,1,2))].">
      <j1 rule="para" parents="20216 5303"/>
    </justification>
  </clause>

  <clause id="20305">
    <literal><![CDATA[
      K(x,y) * R(x,z,u) = R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(20216(a,1),14119(a,1,1))].">
      <j1 rule="para" parents="20216 14119"/>
    </justification>
  </clause>

  <clause id="20337">
    <literal><![CDATA[
      K(x,R(y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14081,a,b,20217,a)].">
      <j1 rule="hyper" parents="63 14081 20217"/>
    </justification>
  </clause>

  <clause id="20338">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14072,a,b,20217,a)].">
      <j1 rule="hyper" parents="63 14072 20217"/>
    </justification>
  </clause>

  <clause id="20340">
    <literal><![CDATA[
      K(x / ((1 / y) * z),u) = K((x / z) * y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15147,a(flip),b,20217,a)].">
      <j1 rule="hyper" parents="63 15147 20217"/>
    </justification>
  </clause>

  <clause id="20341">
    <literal><![CDATA[
      K(x,(y / z) / u) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14236,a(flip),b,20217,a),flip(a)].">
      <j1 rule="hyper" parents="63 14236 20217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20344">
    <literal><![CDATA[
      K(x,y) * ((T(y,x) * z) * u) = (y * z) * u
    ]]></literal>
    <justification jstring="[hyper(133,a,20217,a(flip),b,14105,a)].">
      <j1 rule="hyper" parents="133 20217 14105"/>
    </justification>
  </clause>

  <clause id="20345">
    <literal><![CDATA[
      K(x,y) * (L(y,z,u) * x) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,20217,a(flip),b,4908,a(flip))].">
      <j1 rule="hyper" parents="133 20217 4908"/>
    </justification>
  </clause>

  <clause id="20351">
    <literal><![CDATA[
      x * (T(L(y,z,u),w) \ 1) = x * (L(y,z,u) \ K(w,y))
    ]]></literal>
    <justification jstring="[para(20217(a,1),5042(a,2,2,2))].">
      <j1 rule="para" parents="20217 5042"/>
    </justification>
  </clause>

  <clause id="20353">
    <literal><![CDATA[
      K(x,y) * (L(y,z,u) \ w) = L(T(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(20217(a,1),5343(a,1,1))].">
      <j1 rule="para" parents="20217 5343"/>
    </justification>
  </clause>

  <clause id="20354">
    <literal><![CDATA[
      (x / L(y,z,u)) * K(w,y) = x / L(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(20217(a,1),6177(a,1,2))].">
      <j1 rule="para" parents="20217 6177"/>
    </justification>
  </clause>

  <clause id="20359">
    <literal><![CDATA[
      (x * y) * K(z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(20217(a,1),11076(a,1,2))].">
      <j1 rule="para" parents="20217 11076"/>
    </justification>
  </clause>

  <clause id="20369">
    <literal><![CDATA[
      (x \ y) * K(z,T(u,y)) = x \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(20217(a,1),14220(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20217 14220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20374">
    <literal><![CDATA[
      x \ (K(y,z) * (x * u)) = u * K(y,T(z,x * u))
    ]]></literal>
    <justification jstring="[para(20217(a,1),14554(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20217 14554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20388">
    <literal><![CDATA[
      K(x,y \ (a(z,u,w) \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(7601,a,20229,a)].">
      <j1 rule="hyper" parents="7601 20229"/>
    </justification>
  </clause>

  <clause id="20393">
    <literal><![CDATA[
      x \ ((y \ (x * L(x \ y,z,u))) * y) = L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(189,a,5992,a,b,20251,a(flip))].">
      <j1 rule="hyper" parents="189 5992 20251"/>
    </justification>
  </clause>

  <clause id="20394">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * R(u,x,L(x \ 1,y,z)) = 1 * ((u * x) * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(20251(a,1),14257(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20251 14257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20406">
    <literal><![CDATA[
      (x \ K(y,x \ 1)) * R(y,z,u) = R(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(20284(a,1),5054(a,1,1,2))].">
      <j1 rule="para" parents="20284 5054"/>
    </justification>
  </clause>

  <clause id="20407">
    <literal><![CDATA[
      K(x,y) * (R(x,z,u) * w) = R(T(x,y),z,u) * w
    ]]></literal>
    <justification jstring="[para(20284(a,1),5236(a,1,1))].">
      <j1 rule="para" parents="20284 5236"/>
    </justification>
  </clause>

  <clause id="20408">
    <literal><![CDATA[
      K(x,y) * (R(T(x,y),z,u) \ w) = R(x,z,u) \ w
    ]]></literal>
    <justification jstring="[para(20284(a,1),5327(a,1,1))].">
      <j1 rule="para" parents="20284 5327"/>
    </justification>
  </clause>

  <clause id="20412">
    <literal><![CDATA[
      R(x,y,z) \ (R((x \ u) \ u,y,z) * w) = K((x \ u) \ u,x \ u) * w
    ]]></literal>
    <justification jstring="[para(20284(a,1),10705(a,2,1))].">
      <j1 rule="para" parents="20284 10705"/>
    </justification>
  </clause>

  <clause id="20425">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ u) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,8544,a(flip),b,20337,a)].">
      <j1 rule="hyper" parents="63 8544 20337"/>
    </justification>
  </clause>

  <clause id="20431">
    <literal><![CDATA[
      K(x,y \ (z * (u \ y))) = K(x,T(z / u,y))
    ]]></literal>
    <justification jstring="[para(1077(a,1),20337(a,1,2))].">
      <j1 rule="para" parents="1077 20337"/>
    </justification>
  </clause>

  <clause id="20433">
    <literal><![CDATA[
      (x * (K(y,x) * z)) * u = K(y,x) * ((x * z) * u)
    ]]></literal>
    <justification jstring="[para(20337(a,1),6721(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20337 6721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20434">
    <literal><![CDATA[
      K(x,y) * (R(z,u,w) * K(y,T(z,x))) = (y * R(z,u,w)) / T(y,x)
    ]]></literal>
    <justification jstring="[para(20337(a,1),8183(a,1,2,2))].">
      <j1 rule="para" parents="20337 8183"/>
    </justification>
  </clause>

  <clause id="20438">
    <literal><![CDATA[
      ((x * y) * T(z,y)) * K(z * y,T(x,z * y)) = (z * y) * (((x * y) * T(z,y)) / (z * y))
    ]]></literal>
    <justification jstring="[para(20337(a,1),9661(a,1,2))].">
      <j1 rule="para" parents="20337 9661"/>
    </justification>
  </clause>

  <clause id="20439">
    <literal><![CDATA[
      K(x,y) * ((y \ z) * u) = (T(y,x) \ z) * u
    ]]></literal>
    <justification jstring="[para(20337(a,1),11712(a,1,1))].">
      <j1 rule="para" parents="20337 11712"/>
    </justification>
  </clause>

  <clause id="20460">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,6694,a(flip),b,20338,a)].">
      <j1 rule="hyper" parents="63 6694 20338"/>
    </justification>
  </clause>

  <clause id="20471">
    <literal><![CDATA[
      (T(x,y) \ z) * T(u,K(x,y) * (T(x,y) \ z)) = K(x,y) \ (u * (x \ z))
    ]]></literal>
    <justification jstring="[para(20338(a,1),13921(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20338 13921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20479">
    <literal><![CDATA[
      x * a(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(20005(a,1),315(a,1,2))].">
      <j1 rule="para" parents="20005 315"/>
    </justification>
  </clause>

  <clause id="20480">
    <literal><![CDATA[
      x * (y * a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (a(z,u,w) * y) = v5
    ]]></literal>
    <justification jstring="[para(20005(a,1),639(a,1,2,2))].">
      <j1 rule="para" parents="20005 639"/>
    </justification>
  </clause>

  <clause id="20481">
    <literal><![CDATA[
      T(a(x,y,z) * u,K(u,w)) = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(20005(a,1),6060(a,2,2))].">
      <j1 rule="para" parents="20005 6060"/>
    </justification>
  </clause>

  <clause id="20482">
    <literal><![CDATA[
      x / L(a(y,z,u),w,v5) = L(a(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[para(20005(a,1),9695(a,1,2,1))].">
      <j1 rule="para" parents="20005 9695"/>
    </justification>
  </clause>

  <clause id="20487">
    <literal><![CDATA[
      T(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(14046(a,1),20013(a,1))].">
      <j1 rule="para" parents="14046 20013"/>
    </justification>
  </clause>

  <clause id="20488">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(16621(a,2),20013(a,1))].">
      <j1 rule="para" parents="16621 20013"/>
    </justification>
  </clause>

  <clause id="20489">
    <literal><![CDATA[
      (x * K(y,z)) \ (K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(570(a,1),20035(a,1))].">
      <j1 rule="para" parents="570 20035"/>
    </justification>
  </clause>

  <clause id="20491">
    <literal><![CDATA[
      L(x,y,z / u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(6958(a,1),20035(a,1))].">
      <j1 rule="para" parents="6958 20035"/>
    </justification>
  </clause>

  <clause id="20492">
    <literal><![CDATA[
      L(x,y,(z \ u) * z) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(11452(a,1),20035(a,1))].">
      <j1 rule="para" parents="11452 20035"/>
    </justification>
  </clause>

  <clause id="20496">
    <literal><![CDATA[
      R(x,T(y,z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(19637,a,20040,a)].">
      <j1 rule="hyper" parents="19637 20040"/>
    </justification>
  </clause>

  <clause id="20497">
    <literal><![CDATA[
      R(x,y,z * u) = R(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(12269,a,20040,a)].">
      <j1 rule="hyper" parents="12269 20040"/>
    </justification>
  </clause>

  <clause id="20513">
    <literal><![CDATA[
      (x * T(y,z * y)) / (L(y,z,y) * z) = R(x / z,z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,4359,a,b,20040,a)].">
      <j1 rule="hyper" parents="63 4359 20040"/>
    </justification>
  </clause>

  <clause id="20514">
    <literal><![CDATA[
      R(x,y,R(T(z,u),w,v5)) = R(x,y,R(z,w,v5))
    ]]></literal>
    <justification jstring="[para(27(a,2),20040(a,1,3))].">
      <j1 rule="para" parents="27 20040"/>
    </justification>
  </clause>

  <clause id="20516">
    <literal><![CDATA[
      R(x,x \ y,z) \ (y * T(z,u)) = (x \ y) * T(z,u)
    ]]></literal>
    <justification jstring="[para(20040(a,1),578(a,1,1))].">
      <j1 rule="para" parents="20040 578"/>
    </justification>
  </clause>

  <clause id="20517">
    <literal><![CDATA[
      R(x,y,z * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(20040(a,1),12269(a,1))].">
      <j1 rule="para" parents="20040 12269"/>
    </justification>
  </clause>

  <clause id="20520">
    <literal><![CDATA[
      L((T(x,y) \ z) \ u,T(x,y) \ z,x) = z \ (T(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(651,a,20041,a),flip(a)].">
      <j1 rule="hyper" parents="651 20041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20529">
    <literal><![CDATA[
      L(x \ T(y,T(z,u)),x,z) = (T(z,u) * x) \ (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,480,a(flip),b,20041,a),flip(a)].">
      <j1 rule="hyper" parents="63 480 20041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20531">
    <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),20041(a,1,3))].">
      <j1 rule="para" parents="25 20041"/>
    </justification>
  </clause>

  <clause id="20536">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,u) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[para(20041(a,1),14467(a,2,2))].">
      <j1 rule="para" parents="20041 14467"/>
    </justification>
  </clause>

  <clause id="20539">
    <literal><![CDATA[
      R(x,y,z / u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(10645(a,1),20140(a,1))].">
      <j1 rule="para" parents="10645 20140"/>
    </justification>
  </clause>

  <clause id="20552">
    <literal><![CDATA[
      R(x,(y \ z) * y,u) = R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12338,a,b,20496,a)].">
      <j1 rule="hyper" parents="63 12338 20496"/>
    </justification>
  </clause>

  <clause id="20553">
    <literal><![CDATA[
      R(x,y * z,u) = R(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12336,a(flip),b,20496,a)].">
      <j1 rule="hyper" parents="63 12336 20496"/>
    </justification>
  </clause>

  <clause id="20554">
    <literal><![CDATA[
      R(x,L(T(y,z),u,w),v5) = R(x,L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(25(a,2),20496(a,1,2))].">
      <j1 rule="para" parents="25 20496"/>
    </justification>
  </clause>

  <clause id="20555">
    <literal><![CDATA[
      R(x,y / z,u) = R(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(113(a,1),20496(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 20496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20558">
    <literal><![CDATA[
      R(1 / T(x,y),x,z) \ z = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(20496(a,1),420(a,1,1))].">
      <j1 rule="para" parents="20496 420"/>
    </justification>
  </clause>

  <clause id="20559">
    <literal><![CDATA[
      R(x,L(y / z,u,w),v5) = R(x,L(z \ y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(278(a,1),20496(a,1,2)),flip(a)].">
      <j1 rule="para" parents="278 20496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20560">
    <literal><![CDATA[
      R(R(x,y,z),u,w) * (T(y,v5) * z) = (R(x,u,w) * T(y,v5)) * z
    ]]></literal>
    <justification jstring="[para(20496(a,1),469(a,1,1,1))].">
      <j1 rule="para" parents="20496 469"/>
    </justification>
  </clause>

  <clause id="20561">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (T(y,v5) * z) = (L(x,u,w) * T(y,v5)) * z
    ]]></literal>
    <justification jstring="[para(20496(a,1),471(a,1,1,1))].">
      <j1 rule="para" parents="20496 471"/>
    </justification>
  </clause>

  <clause id="20565">
    <literal><![CDATA[
      R(x,y * z,z) * R(y,z,z) = (x * (y * z)) * (z \ 1)
    ]]></literal>
    <justification jstring="[para(20496(a,1),9690(a,1,1))].">
      <j1 rule="para" parents="20496 9690"/>
    </justification>
  </clause>

  <clause id="20569">
    <literal><![CDATA[
      T(x \ (a(y,z,u) \ x),w) = x \ (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(5039,a,20388,a)].">
      <j1 rule="hyper" parents="5039 20388"/>
    </justification>
  </clause>

  <clause id="20570">
    <literal><![CDATA[
      x * T(a(y,z,u),w) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(134,a,20005,a,b,19974,a)].">
      <j1 rule="hyper" parents="134 20005 19974"/>
    </justification>
  </clause>

  <clause id="20571">
    <literal><![CDATA[
      (x \ 1) \ (a(y,z,u) * x) = (x * x) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(134,a,19974,a(flip),b,500,a),flip(a)].">
      <j1 rule="hyper" parents="134 19974 500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20572">
    <literal><![CDATA[
      x \ L(a(y,z,u) * x,w,v5) = x * L(x \ a(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(19974(a,1),3341(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="19974 3341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20575">
    <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(133,a,735,a(flip),b,19977,a)].">
      <j1 rule="hyper" parents="133 735 19977"/>
    </justification>
  </clause>

  <clause id="20577">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ u != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(19977(a,1),359(a,1,1))].">
      <j1 rule="para" parents="19977 359"/>
    </justification>
  </clause>

  <clause id="20578">
    <literal><![CDATA[
      x \ y != (a(z,u,w) \ v5) * a(z,u,w)
    ]]></literal>
    <literal><![CDATA[
      x * v5 = y
    ]]></literal>
    <justification jstring="[para(19977(a,1),636(a,2,1))].">
      <j1 rule="para" parents="19977 636"/>
    </justification>
  </clause>

  <clause id="20579">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ u != w \ v5
    ]]></literal>
    <literal><![CDATA[
      w * a(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(19977(a,1),638(a,1,1))].">
      <j1 rule="para" parents="19977 638"/>
    </justification>
  </clause>

  <clause id="20580">
    <literal><![CDATA[
      R((a(x,y,z) \ u) / w,w,a(x,y,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      u / (w * a(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(19977(a,1),682(a,1,1,1))].">
      <j1 rule="para" parents="19977 682"/>
    </justification>
  </clause>

  <clause id="20581">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) \ ((a(y,z,u) \ x) * w) = x \ (((x / a(y,z,u)) * w) / (a(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(19977(a,1),3986(a,1,2,1))].">
      <j1 rule="para" parents="19977 3986"/>
    </justification>
  </clause>

  <clause id="20582">
    <literal><![CDATA[
      L(a(x,y,z) \ (u \ w),a(x,y,z),u) \ (u \ w) = (u \ w) / ((u * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(19977(a,1),9701(a,1,1,1))].">
      <j1 rule="para" parents="19977 9701"/>
    </justification>
  </clause>

  <clause id="20586">
    <literal><![CDATA[
      x * (a(y,z,u) \ (w * a(y,z,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      x * w = v5
    ]]></literal>
    <justification jstring="[para(19982(a,1),644(a,1,2,1))].">
      <j1 rule="para" parents="19982 644"/>
    </justification>
  </clause>

  <clause id="20587">
    <literal><![CDATA[
      x \ ((y * y) * a(z,u,w)) = (x \ a(z,u,w)) * (y * y)
    ]]></literal>
    <justification jstring="[para(19982(a,1),729(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="19982 729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20588">
    <literal><![CDATA[
      ((x * a(y,z,u)) * (x \ w)) / w = R(a(y,z,u),x,x \ w)
    ]]></literal>
    <justification jstring="[para(19982(a,1),606(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19982 606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20593">
    <literal><![CDATA[
      a(x,y,z) != u \ w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) \ w = u
    ]]></literal>
    <justification jstring="[para(19984(a,1),48(a,1))].">
      <j1 rule="para" parents="19984 48"/>
    </justification>
  </clause>

  <clause id="20594">
    <literal><![CDATA[
      x * a(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) \ w = x
    ]]></literal>
    <justification jstring="[para(19984(a,1),143(a,1,2))].">
      <j1 rule="para" parents="19984 143"/>
    </justification>
  </clause>

  <clause id="20597">
    <literal><![CDATA[
      a(x,y,z) * (z * u) = z * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,12362,a(flip),b,19985,a),flip(a)].">
      <j1 rule="hyper" parents="347 12362 19985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20600">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (u * a(x,y,z)) = (a(x,y,z) * a(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(128,a,19985,a(flip),b,302,a)].">
      <j1 rule="hyper" parents="128 19985 302"/>
    </justification>
  </clause>

  <clause id="20601">
    <literal><![CDATA[
      x * (x \ (y \ (a(z,u,w) * v5))) = y \ (v5 * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(128,a,19985,a(flip),b,76,a),flip(a)].">
      <j1 rule="hyper" parents="128 19985 76"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20602">
    <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(19985(a,2),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="19985 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20603">
    <literal><![CDATA[
      L(a(x,y,z) \ T(u,w),a(x,y,z),w) = (a(x,y,z) * w) \ (u * w)
    ]]></literal>
    <justification jstring="[para(19985(a,2),480(a,2,1))].">
      <j1 rule="para" parents="19985 480"/>
    </justification>
  </clause>

  <clause id="20606">
    <literal><![CDATA[
      x \ (a(y,z,u) * L(x,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,w,v5) * (x \ a(y,z,u)) = v6
    ]]></literal>
    <justification jstring="[para(19985(a,2),1426(a,1,2))].">
      <j1 rule="para" parents="19985 1426"/>
    </justification>
  </clause>

  <clause id="20607">
    <literal><![CDATA[
      (a(x,y,z) * u) * T(w,u) = (((w * u) / w) * a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[para(19985(a,1),6300(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19985 6300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20609">
    <literal><![CDATA[
      (a(x,y,z) * u) * u = u * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(19985(a,2),12635(a,1,1))].">
      <j1 rule="para" parents="19985 12635"/>
    </justification>
  </clause>

  <clause id="20610">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) / T(x * a(z,u,w),y) = L(y,a(z,u,w),x)
    ]]></literal>
    <justification jstring="[para(19985(a,1),13760(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="19985 13760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20611">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) / T(x * a(z,u,w),y) != v5
    ]]></literal>
    <literal><![CDATA[
      L(y,a(z,u,w),x) = v5
    ]]></literal>
    <justification jstring="[para(19985(a,1),13768(a,1,1,2))].">
      <j1 rule="para" parents="19985 13768"/>
    </justification>
  </clause>

  <clause id="20612">
    <literal><![CDATA[
      (x * y) / (T(x,y) * a(z,u,w)) = (y * x) / (a(z,u,w) * x)
    ]]></literal>
    <justification jstring="[para(19985(a,1),13912(a,1,2))].">
      <j1 rule="para" parents="19985 13912"/>
    </justification>
  </clause>

  <clause id="20617">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (u * a(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(19988(a,1),526(a,1,2))].">
      <j1 rule="para" parents="19988 526"/>
    </justification>
  </clause>

  <clause id="20620">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (z * y) \ ((z * (y * x)) / x) = u
    ]]></literal>
    <justification jstring="[para(20042(a,1),12306(a,1))].">
      <j1 rule="para" parents="20042 12306"/>
    </justification>
  </clause>

  <clause id="20621">
    <literal><![CDATA[
      L(x,y,z * (u \ (w \ a(v5,v6,v5)))) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(u \ (w \ 1)) * z) = v7
    ]]></literal>
    <justification jstring="[para(20042(a,1),12228(a,1))].">
      <j1 rule="para" parents="20042 12228"/>
    </justification>
  </clause>

  <clause id="20626">
    <literal><![CDATA[
      L(x,y,z * (u \ (1 / u))) = L(x,y,(u * u) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13818,a,b,20079,a)].">
      <j1 rule="hyper" parents="63 13818 20079"/>
    </justification>
  </clause>

  <clause id="20629">
    <literal><![CDATA[
      L(x,y,((z * z) \ u) \ w) = L(x,y,(w / u) * (z * z))
    ]]></literal>
    <justification jstring="[para(896(a,1),20079(a,1,3)),flip(a)].">
      <j1 rule="para" parents="896 20079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20631">
    <literal><![CDATA[
      L(x,y,(z * T(u,w * z)) \ (u * (w * z))) = L(x,y,R(w,z,u))
    ]]></literal>
    <justification jstring="[para(13917(a,2),20079(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13917 20079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20634">
    <literal><![CDATA[
      R(x,y,(z * u) / (w * (v5 * v5))) = R(x,y,w \ (z * (u / (v5 * v5))))
    ]]></literal>
    <justification jstring="[para(813(a,1),20126(a,1,3))].">
      <j1 rule="para" parents="813 20126"/>
    </justification>
  </clause>

  <clause id="20635">
    <literal><![CDATA[
      T(x,(y * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(329(a,1),20487(a,1,2))].">
      <j1 rule="para" parents="329 20487"/>
    </justification>
  </clause>

  <clause id="20636">
    <literal><![CDATA[
      T(x,(y \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y * u)) = w
    ]]></literal>
    <justification jstring="[para(15084(a,1),20487(a,1))].">
      <j1 rule="para" parents="15084 20487"/>
    </justification>
  </clause>

  <clause id="20637">
    <literal><![CDATA[
      T(a(x,y,z) / u,u \ 1) = a(x,y,z) / u
    ]]></literal>
    <justification jstring="[hyper(20488,a,6279,a),flip(a)].">
      <j1 rule="hyper" parents="20488 6279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20638">
    <literal><![CDATA[
      R(x,y,z * u) * (y * (u * z)) = (x * y) * (u * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,20497,a,b,20,a(flip))].">
      <j1 rule="hyper" parents="133 20497 20"/>
    </justification>
  </clause>

  <clause id="20639">
    <literal><![CDATA[
      R(x,y,L(z,u,w) * (w * u)) = R(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[para(97(a,1),20497(a,1,3)),flip(a)].">
      <j1 rule="para" parents="97 20497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20640">
    <literal><![CDATA[
      R(x,y,(z * u) * R(w,z,u)) = R(x,y,(w * z) * u)
    ]]></literal>
    <justification jstring="[para(107(a,1),20497(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 20497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20641">
    <literal><![CDATA[
      R(x,y,(z * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(20497(a,1),2186(a,1))].">
      <j1 rule="para" parents="20497 2186"/>
    </justification>
  </clause>

  <clause id="20643">
    <literal><![CDATA[
      R(x,(y * y) \ z,u) = R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2245,a(flip),b,20552,a)].">
      <j1 rule="hyper" parents="63 2245 20552"/>
    </justification>
  </clause>

  <clause id="20644">
    <literal><![CDATA[
      R(x,(y \ 1) * z,u) = R(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(2365,a,20553,a),flip(a)].">
      <j1 rule="hyper" parents="2365 20553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20646">
    <literal><![CDATA[
      R(x,(y * (z \ 1)) * u,w) = R(x,u * (y * z),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,2381,a(flip),b,20553,a),flip(a)].">
      <j1 rule="hyper" parents="347 2381 20553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20647">
    <literal><![CDATA[
      R(x,(y * y) * z,u) = R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,2245,a(flip),b,20553,a),flip(a)].">
      <j1 rule="hyper" parents="347 2245 20553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20648">
    <literal><![CDATA[
      R(x,T(y,z * z) * (u \ (z * z)),w) = R(x,(u \ 1) * (y * (z * z)),w)
    ]]></literal>
    <justification jstring="[para(936(a,1),20553(a,1,2)),flip(a)].">
      <j1 rule="para" parents="936 20553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20653">
    <literal><![CDATA[
      R(x,L(y \ z,y,u),w) = R(x,(u * z) / (u * y),w)
    ]]></literal>
    <justification jstring="[para(99(a,2),20555(a,2,2)),flip(a)].">
      <j1 rule="para" parents="99 20555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20654">
    <literal><![CDATA[
      R(x,((y * y) \ z) \ u,w) = R(x,(u / z) * (y * y),w)
    ]]></literal>
    <justification jstring="[para(896(a,1),20555(a,1,2)),flip(a)].">
      <j1 rule="para" parents="896 20555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20655">
    <literal><![CDATA[
      R(x,(y \ 1) \ z,u) = R(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(500(a,1),20643(a,1,2)),flip(a)].">
      <j1 rule="para" parents="500 20643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20656">
    <literal><![CDATA[
      R(x,(y * (z \ 1)) \ u,w) = R(x,(y * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(973(a,1),20643(a,1,2)),flip(a)].">
      <j1 rule="para" parents="973 20643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20659">
    <literal><![CDATA[
      L(x,y,L(T(z,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(z,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(25(a,2),20103(a,1,3))].">
      <j1 rule="para" parents="25 20103"/>
    </justification>
  </clause>

  <clause id="20661">
    <literal><![CDATA[
      L(x,y,R(z,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(u * z) * (u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(915(a,1),20103(a,1,3))].">
      <j1 rule="para" parents="915 20103"/>
    </justification>
  </clause>

  <clause id="20662">
    <literal><![CDATA[
      L(x,y,L((z \ u) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(z,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(342(a,1),20103(a,1,3))].">
      <j1 rule="para" parents="342 20103"/>
    </justification>
  </clause>

  <clause id="20670">
    <literal><![CDATA[
      T(x,(T(y,z) / z) \ u) = T(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,12067,a,b,19938,a)].">
      <j1 rule="hyper" parents="63 12067 19938"/>
    </justification>
  </clause>

  <clause id="20671">
    <literal><![CDATA[
      T(x,y \ (z * u)) = T(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19338,a(flip),b,19938,a),flip(a)].">
      <j1 rule="hyper" parents="63 19338 19938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20673">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(11226,a,19941,a),flip(a)].">
      <j1 rule="hyper" parents="11226 19941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20674">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) / x = u / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(305,a,19941,a)].">
      <j1 rule="hyper" parents="305 19941"/>
    </justification>
  </clause>

  <clause id="20675">
    <literal><![CDATA[
      x / L(y \ L(y,z,u),w,v5) = L(y \ L(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,20076,a(flip),b,19941,a)].">
      <j1 rule="hyper" parents="63 20076 19941"/>
    </justification>
  </clause>

  <clause id="20676">
    <literal><![CDATA[
      (x / L(y,z,u)) * y = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(134,a,19941,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 19941 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20677">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) / x != w
    ]]></literal>
    <literal><![CDATA[
      u / L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(19941(a,1),318(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="19941 318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20678">
    <literal><![CDATA[
      T(L(x / y,z,u) \ x,y \ x) = L(y \ x,z,u) \ x
    ]]></literal>
    <justification jstring="[para(9697(a,1),19941(a,1,1))].">
      <j1 rule="para" parents="9697 19941"/>
    </justification>
  </clause>

  <clause id="20680">
    <literal><![CDATA[
      (L(x,y,z) \ u) * L(x,y,z) = (x \ u) * x
    ]]></literal>
    <justification jstring="[hyper(11231,a,19953,a),flip(a)].">
      <j1 rule="hyper" parents="11231 19953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20681">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) * x = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,11219,a,b,19953,a)].">
      <j1 rule="hyper" parents="63 11219 19953"/>
    </justification>
  </clause>

  <clause id="20682">
    <literal><![CDATA[
      T(x,y) * L(T(y,x),z,u) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,4288,a,b,19953,a)].">
      <j1 rule="hyper" parents="63 4288 19953"/>
    </justification>
  </clause>

  <clause id="20683">
    <literal><![CDATA[
      L(x,y,z) * (x \ (u * x)) = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,167,a,b,19953,a)].">
      <j1 rule="hyper" parents="63 167 19953"/>
    </justification>
  </clause>

  <clause id="20684">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ y) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,338,a(flip),b,19953,a)].">
      <j1 rule="hyper" parents="63 338 19953"/>
    </justification>
  </clause>

  <clause id="20685">
    <literal><![CDATA[
      T(L(x,y,z) * (x \ u),x) = x \ (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(462,a,19953,a(flip),b,11219,a)].">
      <j1 rule="hyper" parents="462 19953 11219"/>
    </justification>
  </clause>

  <clause id="20686">
    <literal><![CDATA[
      L(x,y,z) * (u * x) = x * (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,19953,a(flip),b,1411,a),flip(a)].">
      <j1 rule="hyper" parents="134 19953 1411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20687">
    <literal><![CDATA[
      (x * L(y,z,u)) / y = L(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(131,a,19953,a(flip),b,11219,a)].">
      <j1 rule="hyper" parents="131 19953 11219"/>
    </justification>
  </clause>

  <clause id="20688">
    <literal><![CDATA[
      L(x,y,z) * (x \ T(u,x)) = x \ (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,19953,a(flip),b,1404,a),flip(a)].">
      <j1 rule="hyper" parents="128 19953 1404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20689">
    <literal><![CDATA[
      L(x,y,z) * (x \ u) = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(113(a,1),19953(a,1,2))].">
      <j1 rule="para" parents="113 19953"/>
    </justification>
  </clause>

  <clause id="20690">
    <literal><![CDATA[
      ((x * y) / x) * L(x,z,u) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[para(254(a,1),19953(a,1,2)),flip(a)].">
      <j1 rule="para" parents="254 19953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20691">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * T(v5,x) = v5 * L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(19951(a,1),19953(a,1,2))].">
      <j1 rule="para" parents="19951 19953"/>
    </justification>
  </clause>

  <clause id="20692">
    <literal><![CDATA[
      (x * R(y,z,u)) / y = R(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(131,a,19966,a(flip),b,15129,a)].">
      <j1 rule="hyper" parents="131 19966 15129"/>
    </justification>
  </clause>

  <clause id="20693">
    <literal><![CDATA[
      (x * R(y,z,u)) \ (R(y,z,u) * (T(x,y) * w)) = L(w,T(x,y),R(y,z,u))
    ]]></literal>
    <justification jstring="[para(19966(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="19966 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20697">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ u) = (K(y,x) * z) \ u
    ]]></literal>
    <justification jstring="[hyper(347,a,19540,a,b,20003,a)].">
      <j1 rule="hyper" parents="347 19540 20003"/>
    </justification>
  </clause>

  <clause id="20701">
    <literal><![CDATA[
      (T(x,y) * z) \ (K(x,y) * u) = (x * z) \ u
    ]]></literal>
    <justification jstring="[para(4946(a,1),20003(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4946 20003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20702">
    <literal><![CDATA[
      (x * y) \ (K(z,x) * u) = (T(x,z) * y) \ u
    ]]></literal>
    <justification jstring="[para(4974(a,1),20003(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4974 20003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20703">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ u = (x * z) \ (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(5353(a,1),20003(a,1,1))].">
      <j1 rule="para" parents="5353 20003"/>
    </justification>
  </clause>

  <clause id="20705">
    <literal><![CDATA[
      (x * T(y,z)) \ (K(y,z) * u) = T(x * y,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(5955(a,1),20003(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5955 20003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20706">
    <literal><![CDATA[
      (x * T(y,T(z,x))) \ u = (x * y) \ (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(7697(a,1),20003(a,1,1))].">
      <j1 rule="para" parents="7697 20003"/>
    </justification>
  </clause>

  <clause id="20707">
    <literal><![CDATA[
      ((x * y) * z) \ (K(x,y) * u) = ((y * x) * z) \ u
    ]]></literal>
    <justification jstring="[para(10281(a,1),20003(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10281 20003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20709">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (K(u,w) * v5) = (a(x,y,z) \ K(w,u)) \ v5
    ]]></literal>
    <justification jstring="[para(16907(a,1),20003(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16907 20003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20710">
    <literal><![CDATA[
      R(x,K(y,z) * u,w) * (K(y,z) * (u * w)) = (x * (K(y,z) * u)) * w
    ]]></literal>
    <justification jstring="[hyper(134,a,20008,a(flip),b,209,a)].">
      <j1 rule="hyper" parents="134 20008 209"/>
    </justification>
  </clause>

  <clause id="20711">
    <literal><![CDATA[
      (K(x,y) * (z * u)) \ ((K(x,y) * z) * (u * w)) = L(w,u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(20008(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="20008 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20715">
    <literal><![CDATA[
      (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,K(y,z) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(20008(a,1),836(a,1,1,2))].">
      <j1 rule="para" parents="20008 836"/>
    </justification>
  </clause>

  <clause id="20718">
    <literal><![CDATA[
      K(x,y) * ((T(x,y) \ z) * u) = (x \ z) * u
    ]]></literal>
    <justification jstring="[para(5159(a,1),20008(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5159 20008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20721">
    <literal><![CDATA[
      K(x \ y,x) * (((x \ y) \ z) * u) = ((y / x) \ z) * u
    ]]></literal>
    <justification jstring="[para(5441(a,1),20008(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5441 20008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20724">
    <literal><![CDATA[
      K(x,y) * (((y * x) * z) * u) = ((x * y) * z) * u
    ]]></literal>
    <justification jstring="[para(10281(a,1),20008(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10281 20008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20727">
    <literal><![CDATA[
      K(x,y) * ((K(y,x) / z) * u) = (1 / z) * u
    ]]></literal>
    <justification jstring="[para(13063(a,1),20008(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13063 20008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20728">
    <literal><![CDATA[
      K(x,y) * ((x / z) * u) = (T(x,y) / z) * u
    ]]></literal>
    <justification jstring="[para(13192(a,1),20008(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13192 20008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20740">
    <literal><![CDATA[
      K(x,y) * (z * (u * K(y,x))) = T(z * u,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(269,a,20033,a,b,5261,a),flip(a)].">
      <j1 rule="hyper" parents="269 20033 5261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20742">
    <literal><![CDATA[
      x * R(y,y \ z,(y \ z) \ x) = z * (((y \ z) \ x) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,18442,a,b,20033,a)].">
      <j1 rule="hyper" parents="63 18442 20033"/>
    </justification>
  </clause>

  <clause id="20750">
    <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(20033(a,2),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="20033 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20753">
    <literal><![CDATA[
      ((x * y) * (z * K(u,w))) / ((y * z) * K(u,w)) = R(R(x,y,z),y * z,K(u,w))
    ]]></literal>
    <justification jstring="[para(20033(a,1),591(a,1,1))].">
      <j1 rule="para" parents="20033 591"/>
    </justification>
  </clause>

  <clause id="20762">
    <literal><![CDATA[
      x * ((R(x,y,x) \ z) * K(u,w)) = (a(x,y,x) \ z) * K(u,w)
    ]]></literal>
    <justification jstring="[para(10991(a,1),20033(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10991 20033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20769">
    <literal><![CDATA[
      R(K(x,T(y,z)) / u,u,z) = z / ((u * z) * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(7437,a,20080,a)].">
      <j1 rule="hyper" parents="7437 20080"/>
    </justification>
  </clause>

  <clause id="20772">
    <literal><![CDATA[
      (K(x,y) * z) / (u * K(x,y)) = T(z,K(y,x)) / u
    ]]></literal>
    <justification jstring="[para(6880(a,1),20080(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6880 20080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20775">
    <literal><![CDATA[
      (x * (y * K(z,u))) / w = (x * y) / (w * K(u,z))
    ]]></literal>
    <justification jstring="[para(20033(a,1),20080(a,1,1))].">
      <j1 rule="para" parents="20033 20080"/>
    </justification>
  </clause>

  <clause id="20776">
    <literal><![CDATA[
      K(x,y) * ((T(y,x) * z) / u) = (y * z) / u
    ]]></literal>
    <justification jstring="[para(4946(a,1),20088(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4946 20088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20783">
    <literal><![CDATA[
      T(L(x,y,z) \ x,u) = x * (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,1409,a,b,20092,a),flip(a)].">
      <j1 rule="hyper" parents="347 1409 20092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20784">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x,y,z) * L(x,y,z)) = (L(x,y,z) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,20092,a(flip),b,4883,a)].">
      <j1 rule="hyper" parents="133 20092 4883"/>
    </justification>
  </clause>

  <clause id="20785">
    <literal><![CDATA[
      ((x * x) \ (L(y,z,u) \ y)) * w = (L(y,z,u) \ y) * ((x * x) \ w)
    ]]></literal>
    <justification jstring="[para(20092(a,1),829(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20092 829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20786">
    <literal><![CDATA[
      T((x * x) \ (L(y,z,u) \ y),w) = T(x * x,w) \ (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(20092(a,1),10450(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20092 10450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20791">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,u) = x \ (y * T(z,u))
    ]]></literal>
    <justification jstring="[para(5926(a,1),20109(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5926 20109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20792">
    <literal><![CDATA[
      (x \ (y / z)) * K(u,z) = x \ (y / T(z,u))
    ]]></literal>
    <justification jstring="[para(6102(a,1),20109(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6102 20109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20794">
    <literal><![CDATA[
      (x \ (y \ z)) * K(z,u) = x \ (y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(13045(a,1),20109(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13045 20109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20801">
    <literal><![CDATA[
      ((x * K(y,z)) * u) \ (x * (K(y,z) * (u * w))) = L(w,u,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,20151,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="128 20151 97"/>
    </justification>
  </clause>

  <clause id="20804">
    <literal><![CDATA[
      ((x * y) * (K(z,u) * w)) / ((y * K(z,u)) * w) = R(R(x,y,K(z,u)),y * K(z,u),w)
    ]]></literal>
    <justification jstring="[para(20151(a,1),591(a,1,1))].">
      <j1 rule="para" parents="20151 591"/>
    </justification>
  </clause>

  <clause id="20808">
    <literal><![CDATA[
      (x * y) * (K(y,z) * u) = (x * T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(5926(a,1),20151(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5926 20151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20809">
    <literal><![CDATA[
      (x / y) * (K(z,y) * u) = (x / T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(6102(a,1),20151(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6102 20151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20810">
    <literal><![CDATA[
      (x * T(y,z)) * (K(z,y) * u) = (x * y) * u
    ]]></literal>
    <justification jstring="[para(6111(a,1),20151(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6111 20151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20814">
    <literal><![CDATA[
      (x * (y * z)) * (K(y,z) * u) = (x * (T(y,z) * z)) * u
    ]]></literal>
    <justification jstring="[para(9653(a,1),20151(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9653 20151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20815">
    <literal><![CDATA[
      (x \ 1) * (K(y,z) * u) = (x \ K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(12973(a,1),20151(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12973 20151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20816">
    <literal><![CDATA[
      (x \ K(y,z)) * (K(z,y) * u) = (x \ 1) * u
    ]]></literal>
    <justification jstring="[para(13009(a,1),20151(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13009 20151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20819">
    <literal><![CDATA[
      (x * (y * K(z,u))) * w = (x * y) * (K(z,u) * w)
    ]]></literal>
    <justification jstring="[para(20033(a,1),20151(a,1,1))].">
      <j1 rule="para" parents="20033 20151"/>
    </justification>
  </clause>

  <clause id="20822">
    <literal><![CDATA[
      (x / (y \ z)) * K(y,u) = x / (T(y,u) \ z)
    ]]></literal>
    <justification jstring="[para(5209(a,1),20165(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5209 20165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20823">
    <literal><![CDATA[
      x / T(K(y,z) * u,z) = (x / T(u,z)) * K(z,y)
    ]]></literal>
    <justification jstring="[para(7515(a,2),20165(a,1,2))].">
      <j1 rule="para" parents="7515 20165"/>
    </justification>
  </clause>

  <clause id="20827">
    <literal><![CDATA[
      K(x,y) * ((z / T(y,x)) \ u) = (z / y) \ u
    ]]></literal>
    <justification jstring="[para(5922(a,1),20166(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5922 20166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20828">
    <literal><![CDATA[
      K(x,y) * ((z * y) \ u) = (z * T(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(5926(a,1),20166(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5926 20166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20829">
    <literal><![CDATA[
      K(x,T(y,z)) * ((y * z) \ u) = (T(y,x) * z) \ u
    ]]></literal>
    <justification jstring="[para(5924(a,1),20166(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5924 20166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20831">
    <literal><![CDATA[
      K(x,y) * ((z * T(x,y)) \ u) = (z * x) \ u
    ]]></literal>
    <justification jstring="[para(6111(a,1),20166(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6111 20166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20832">
    <literal><![CDATA[
      K(x,y) * ((z \ 1) \ u) = (z \ K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(12973(a,1),20166(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12973 20166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20833">
    <literal><![CDATA[
      K(x,y) * ((z \ K(x,y)) \ u) = (z \ 1) \ u
    ]]></literal>
    <justification jstring="[para(13009(a,1),20166(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13009 20166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20834">
    <literal><![CDATA[
      K(x,y) * ((z \ y) \ u) = (z \ T(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(13045(a,1),20166(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13045 20166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20837">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ w = K(u,z) * ((x * y) \ w)
    ]]></literal>
    <justification jstring="[para(20033(a,1),20166(a,1,1))].">
      <j1 rule="para" parents="20033 20166"/>
    </justification>
  </clause>

  <clause id="20839">
    <literal><![CDATA[
      (x * (R(x,y,z) \ u)) / x = u / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(305,a,20181,a)].">
      <j1 rule="hyper" parents="305 20181"/>
    </justification>
  </clause>

  <clause id="20843">
    <literal><![CDATA[
      T((x \ y) \ L(x \ y,z,u),w) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,3354,a(flip),b,20259,a),flip(a)].">
      <j1 rule="hyper" parents="347 3354 20259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20846">
    <literal><![CDATA[
      K(x \ (y * z),T(u,z)) = K(z / (y \ x),u)
    ]]></literal>
    <justification jstring="[hyper(7492,a,20294,a),flip(a)].">
      <j1 rule="hyper" parents="7492 20294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20853">
    <literal><![CDATA[
      K(x \ (y * (z * u)),T(w,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(((y \ x) / u) \ z,w) = v5
    ]]></literal>
    <justification jstring="[para(20294(a,1),19669(a,1))].">
      <j1 rule="para" parents="20294 19669"/>
    </justification>
  </clause>

  <clause id="20855">
    <literal><![CDATA[
      ((x \ y) \ y) * a(x,x,z) = R(T(x,x \ y),x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,18992,a(flip),b,20305,a)].">
      <j1 rule="hyper" parents="63 18992 20305"/>
    </justification>
  </clause>

  <clause id="20857">
    <literal><![CDATA[
      K(x,y) * (z \ (z \ R(x,u,w))) = z \ (z \ R(T(x,y),u,w))
    ]]></literal>
    <justification jstring="[para(20305(a,1),19549(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="20305 19549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20861">
    <literal><![CDATA[
      x * K(x,y / (z * u)) = T(x,(y / u) / z)
    ]]></literal>
    <justification jstring="[hyper(134,a,20341,a(flip),b,4924,a(flip))].">
      <j1 rule="hyper" parents="134 20341 4924"/>
    </justification>
  </clause>

  <clause id="20865">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) / (a(x,y,z) * w) = R(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(220,a,20570,a(flip),b,13920,a)].">
      <j1 rule="hyper" parents="220 20570 13920"/>
    </justification>
  </clause>

  <clause id="20869">
    <literal><![CDATA[
      R(x,L(y * z,y,y),u) = R(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15284,a,b,20655,a)].">
      <j1 rule="hyper" parents="63 15284 20655"/>
    </justification>
  </clause>

  <clause id="20870">
    <literal><![CDATA[
      R(x,y \ (y \ z),u) = R(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15297,a(flip),b,20655,a),flip(a)].">
      <j1 rule="hyper" parents="63 15297 20655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20871">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ u)) = T(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,18923,a,b,20671,a)].">
      <j1 rule="hyper" parents="63 18923 20671"/>
    </justification>
  </clause>

  <clause id="20872">
    <literal><![CDATA[
      T(x,((y \ z) \ u) * w) = T(x,(z \ y) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,19338,a(flip),b,20671,a),flip(a)].">
      <j1 rule="hyper" parents="63 19338 20671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20873">
    <literal><![CDATA[
      T(x,(y \ (z \ 1)) * u) = T(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,18930,a(flip),b,20671,a),flip(a)].">
      <j1 rule="hyper" parents="63 18930 20671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20874">
    <literal><![CDATA[
      T(x,(y \ z) * (z \ u)) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),20671(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 20671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20875">
    <literal><![CDATA[
      T(x,y \ (z * ((y \ z) \ u))) = T(x,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),20671(a,2,2))].">
      <j1 rule="para" parents="10 20671"/>
    </justification>
  </clause>

  <clause id="20876">
    <literal><![CDATA[
      R(T(x \ 1,(x \ y) * z),x,y \ z) = (x * L(y * z,y,y)) \ L(y * z,y,y)
    ]]></literal>
    <justification jstring="[para(20671(a,1),19849(a,1,1))].">
      <j1 rule="para" parents="20671 19849"/>
    </justification>
  </clause>

  <clause id="20877">
    <literal><![CDATA[
      T(x,y \ ((z / y) \ u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[hyper(19365,a,20874,a)].">
      <j1 rule="hyper" parents="19365 20874"/>
    </justification>
  </clause>

  <clause id="20878">
    <literal><![CDATA[
      T(x,(y / z) \ u) = T(x,z * (y \ u))
    ]]></literal>
    <justification jstring="[para(83(a,1),20874(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 20874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20879">
    <literal><![CDATA[
      T(x,(y * z) * (((u * y) * z) \ w)) = T(x,R(u,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(209(a,1),20874(a,1,2,1))].">
      <j1 rule="para" parents="209 20874"/>
    </justification>
  </clause>

  <clause id="20880">
    <literal><![CDATA[
      T(x,R(y / z,z,y \ u) \ w) = T(x,(z * (y \ u)) * (u \ w))
    ]]></literal>
    <justification jstring="[para(693(a,1),20874(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="693 20874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20881">
    <literal><![CDATA[
      T(x * ((a(y,z,u) \ x) \ w),w) = x * ((a(y,z,u) \ x) \ w)
    ]]></literal>
    <justification jstring="[hyper(20488,a,20875,a),flip(a)].">
      <j1 rule="hyper" parents="20488 20875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20882">
    <literal><![CDATA[
      T(x,(y * L(y \ z,u,w)) \ v5) = T(x,y \ (L(z / y,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(759(a,1),20877(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="759 20877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20883">
    <literal><![CDATA[
      T(x,(y / z) * u) = T(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,19349,a(flip),b,20878,a)].">
      <j1 rule="hyper" parents="63 19349 20878"/>
    </justification>
  </clause>

  <clause id="20884">
    <literal><![CDATA[
      T(x \ 1,(x \ y) * z) = T(x \ 1,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9124,a(flip),b,20883,a)].">
      <j1 rule="hyper" parents="63 9124 20883"/>
    </justification>
  </clause>

  <clause id="20885">
    <literal><![CDATA[
      (x * (y * (a(z,u,w) \ 1))) / (a(z,u,w) \ 1) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,w) \ (x * (y * a(z,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(966(a,2),20018(a,1))].">
      <j1 rule="para" parents="966 20018"/>
    </justification>
  </clause>

  <clause id="20887">
    <literal><![CDATA[
      L(x,y,z * (T(u,z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(w,u,z) * (u * z)) = v5
    ]]></literal>
    <justification jstring="[para(10150(a,1),20105(a,1,3))].">
      <j1 rule="para" parents="10150 20105"/>
    </justification>
  </clause>

  <clause id="20889">
    <literal><![CDATA[
      x * T(a(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) * x = v5
    ]]></literal>
    <justification jstring="[para(20005(a,2),20479(a,1,2))].">
      <j1 rule="para" parents="20005 20479"/>
    </justification>
  </clause>

  <clause id="20891">
    <literal><![CDATA[
      L(x,y,R(z * K(u,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(u * w) \ ((u * z) * w)) = v5
    ]]></literal>
    <justification jstring="[para(5061(a,2),20491(a,1,3))].">
      <j1 rule="para" parents="5061 20491"/>
    </justification>
  </clause>

  <clause id="20894">
    <literal><![CDATA[
      L(x,y,((z * u) \ (((z \ 1) \ u) \ w)) * ((z \ 1) \ u)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z * u) \ w) = v5
    ]]></literal>
    <justification jstring="[para(3736(a,1),20492(a,1,3,1))].">
      <j1 rule="para" parents="3736 20492"/>
    </justification>
  </clause>

  <clause id="20895">
    <literal><![CDATA[
      R(x,y,z / (u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,L(u,u,z) * z) = w
    ]]></literal>
    <justification jstring="[para(2008(a,1),20517(a,1,3))].">
      <j1 rule="para" parents="2008 20517"/>
    </justification>
  </clause>

  <clause id="20896">
    <literal><![CDATA[
      R(x,y,z * (u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(2204(a,2),20517(a,1))].">
      <j1 rule="para" parents="2204 20517"/>
    </justification>
  </clause>

  <clause id="20898">
    <literal><![CDATA[
      R(x,y,R(z * K(u,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,(u * w) \ ((u * z) * w)) = v5
    ]]></literal>
    <justification jstring="[para(5061(a,2),20539(a,1,3))].">
      <j1 rule="para" parents="5061 20539"/>
    </justification>
  </clause>

  <clause id="20900">
    <literal><![CDATA[
      R(x,y,z * (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,L(u,z,z)) = w
    ]]></literal>
    <justification jstring="[para(97(a,1),20641(a,1,3))].">
      <j1 rule="para" parents="97 20641"/>
    </justification>
  </clause>

  <clause id="20901">
    <literal><![CDATA[
      R(x,y,(z * (u \ 1)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,(z * u) \ w) = v5
    ]]></literal>
    <justification jstring="[para(819(a,1),20641(a,1,3))].">
      <j1 rule="para" parents="819 20641"/>
    </justification>
  </clause>

  <clause id="20902">
    <literal><![CDATA[
      R(x,y * (z * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(1805(a,2),20641(a,1))].">
      <j1 rule="para" parents="1805 20641"/>
    </justification>
  </clause>

  <clause id="20903">
    <literal><![CDATA[
      R(x,y * (z * (u * u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y * z,w) = v5
    ]]></literal>
    <justification jstring="[para(1806(a,2),20641(a,1))].">
      <j1 rule="para" parents="1806 20641"/>
    </justification>
  </clause>

  <clause id="20904">
    <literal><![CDATA[
      R(x,y \ z,x) = R(x,y * z,x)
    ]]></literal>
    <justification jstring="[hyper(12186,a,20869,a),flip(a)].">
      <j1 rule="hyper" parents="12186 20869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20905">
    <literal><![CDATA[
      R(T(x,y),z * u,T(x,y)) = R(T(x,y),z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(6797,a,20904,a),flip(a)].">
      <j1 rule="hyper" parents="6797 20904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20906">
    <literal><![CDATA[
      R(x,(y * z) * (z \ y),u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,a(y,z,z \ y),u) = w
    ]]></literal>
    <justification jstring="[para(13395(a,1),20902(a,1,2))].">
      <j1 rule="para" parents="13395 20902"/>
    </justification>
  </clause>

  <clause id="20907">
    <literal><![CDATA[
      R(x,(y * y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(20553(a,1),20902(a,1))].">
      <j1 rule="para" parents="20553 20902"/>
    </justification>
  </clause>

  <clause id="20908">
    <literal><![CDATA[
      R(x,(y \ 1) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(495(a,1),20907(a,1,2))].">
      <j1 rule="para" parents="495 20907"/>
    </justification>
  </clause>

  <clause id="20909">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(z,u)) = T(x,K(u,z)) * y
    ]]></literal>
    <justification jstring="[hyper(15512,a,19935,a)].">
      <j1 rule="hyper" parents="15512 19935"/>
    </justification>
  </clause>

  <clause id="20910">
    <literal><![CDATA[
      x * T(y,x * K(z,u)) = T(y,K(z,u)) * x
    ]]></literal>
    <justification jstring="[para(15510(a,1),19935(a,1,2))].">
      <j1 rule="para" parents="15510 19935"/>
    </justification>
  </clause>

  <clause id="20911">
    <literal><![CDATA[
      T(L(x / y,z,u) \ x,T(y \ x,x)) = L(y \ x,z,u) \ x
    ]]></literal>
    <justification jstring="[para(9697(a,1),19940(a,1,1))].">
      <j1 rule="para" parents="9697 19940"/>
    </justification>
  </clause>

  <clause id="20912">
    <literal><![CDATA[
      L(T(x,x \ y),z,u) \ ((x \ y) \ y) = L(x,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(774,a,19964,a)].">
      <j1 rule="hyper" parents="774 19964"/>
    </justification>
  </clause>

  <clause id="20913">
    <literal><![CDATA[
      L(K(x,y) * (z / y),u,w) \ T(z / T(y,x),K(y,x)) = L(z / T(y,x),u,w) \ (z / T(y,x))
    ]]></literal>
    <justification jstring="[para(5938(a,1),19964(a,1,1,1))].">
      <j1 rule="para" parents="5938 19964"/>
    </justification>
  </clause>

  <clause id="20917">
    <literal><![CDATA[
      x * (T(a(y,z,u),w) * v5) = x * (v5 * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(20005(a,2),19980(a,1,2,1))].">
      <j1 rule="para" parents="20005 19980"/>
    </justification>
  </clause>

  <clause id="20918">
    <literal><![CDATA[
      a(x,y,z) * (u * a(w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      (a(w,v5,v6) * u) * a(x,y,z) = v7
    ]]></literal>
    <justification jstring="[para(19980(a,1),20016(a,1))].">
      <j1 rule="para" parents="19980 20016"/>
    </justification>
  </clause>

  <clause id="20920">
    <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(347,a,15418,a(flip),b,20078,a),flip(a)].">
      <j1 rule="hyper" parents="347 15418 20078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20921">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ L(u,a(x,y,z),a(x,y,z)) = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,15418,a(flip),b,20078,a)].">
      <j1 rule="hyper" parents="128 15418 20078"/>
    </justification>
  </clause>

  <clause id="20922">
    <literal><![CDATA[
      (x * y) \ ((y * (a(z,u,w) \ 1)) * T(x,y)) = R(T(a(z,u,w) \ 1,x * y),y,x)
    ]]></literal>
    <justification jstring="[para(20078(a,1),9627(a,1,2,1))].">
      <j1 rule="para" parents="20078 9627"/>
    </justification>
  </clause>

  <clause id="20926">
    <literal><![CDATA[
      K(x,y) * ((x \ z) \ ((x \ z) \ u)) = (x \ z) \ ((T(x,y) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(20083(a,1),19549(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20083 19549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20928">
    <literal><![CDATA[
      x * L(y \ R(y,z,u),y,x) = R(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,4071,a,b,20110,a)].">
      <j1 rule="hyper" parents="347 4071 20110"/>
    </justification>
  </clause>

  <clause id="20929">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,u) = u \ (R(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(128,a,20110,a,b,4071,a),flip(a)].">
      <j1 rule="hyper" parents="128 20110 4071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20930">
    <literal><![CDATA[
      x * ((y / x) * R(x,z,u)) = R(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,20110,a(flip),b,1746,a)].">
      <j1 rule="hyper" parents="134 20110 1746"/>
    </justification>
  </clause>

  <clause id="20931">
    <literal><![CDATA[
      R(x / (x / y),z,u) * ((x / (x / y)) \ x) = ((y * (x / y)) / y) * R(x / (x / y),z,u)
    ]]></literal>
    <justification jstring="[para(4396(a,2),20110(a,2,1))].">
      <j1 rule="para" parents="4396 20110"/>
    </justification>
  </clause>

  <clause id="20935">
    <literal><![CDATA[
      T(x,R(y,z,u) * (y \ w)) = T(x,w * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(20110(a,2),20883(a,1,2))].">
      <j1 rule="para" parents="20110 20883"/>
    </justification>
  </clause>

  <clause id="20936">
    <literal><![CDATA[
      a(x,y,z) * ((u * a(w,v5,v6)) \ v7) = ((a(w,v5,v6) * u) \ v7) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,20119,a(flip),b,19988,a)].">
      <j1 rule="hyper" parents="134 20119 19988"/>
    </justification>
  </clause>

  <clause id="20937">
    <literal><![CDATA[
      ((1 / x) \ a(y,z,x)) \ u = (a(y,z,x) * x) \ u
    ]]></literal>
    <justification jstring="[para(14326(a,2),20119(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14326 20119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20938">
    <literal><![CDATA[
      (x \ T(y,z)) * (T(y,z) \ u) = (x \ y) * (y \ u)
    ]]></literal>
    <justification jstring="[hyper(5324,a,20179,a),flip(a)].">
      <j1 rule="hyper" parents="5324 20179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20941">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ x = x * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10762,a(flip),b,20199,a),flip(a)].">
      <j1 rule="hyper" parents="63 10762 20199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20942">
    <literal><![CDATA[
      x \ (a(y,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      x \ (w * a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(20219(a,1),356(a,1,2))].">
      <j1 rule="para" parents="20219 356"/>
    </justification>
  </clause>

  <clause id="20944">
    <literal><![CDATA[
      (x \ ((L(y,z,u) \ y) * (L(y,z,u) \ y))) \ (x \ 1) = ((L(y,z,u) \ y) \ 1) / (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,1379,a,b,20234,a)].">
      <j1 rule="hyper" parents="347 1379 20234"/>
    </justification>
  </clause>

  <clause id="20945">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),y * L(y,z,u),x) = (L(y,z,u) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,10889,a,b,20234,a)].">
      <j1 rule="hyper" parents="63 10889 20234"/>
    </justification>
  </clause>

  <clause id="20947">
    <literal><![CDATA[
      (x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))) * (L(x,y,z) \ x) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3534,a(flip),b,20236,a),flip(a)].">
      <j1 rule="hyper" parents="63 3534 20236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20948">
    <literal><![CDATA[
      (L(x,y,z) \ x) / T(u * u,w) = T(u * u,w) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(34,a,6580,a(flip),b,20236,a),flip(a)].">
      <j1 rule="hyper" parents="34 6580 20236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20949">
    <literal><![CDATA[
      (x * ((L(y,z,u) \ y) * w)) / T(x * w,L(y,z,u) \ y) = L(L(y,z,u) \ y,w,x)
    ]]></literal>
    <justification jstring="[para(20236(a,2),13760(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="20236 13760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20951">
    <literal><![CDATA[
      T(L(x,y,z) * ((x \ L(x,u,w)) \ v5),x \ L(x,u,w)) = (x \ L(x,u,w)) \ (L(x,y,z) * v5)
    ]]></literal>
    <justification jstring="[para(20250(a,1),12308(a,1,1,2))].">
      <j1 rule="para" parents="20250 12308"/>
    </justification>
  </clause>

  <clause id="20952">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * u) = x * (u * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,12287,a(flip),b,20253,a),flip(a)].">
      <j1 rule="hyper" parents="347 12287 20253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20953">
    <literal><![CDATA[
      (x \ L(x,y,z)) * R(u,x,L(x,y,z)) = (u * (1 / x)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,3726,a(flip),b,20253,a),flip(a)].">
      <j1 rule="hyper" parents="347 3726 20253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20954">
    <literal><![CDATA[
      x \ ((x \ L(x,y,z)) * u) = (x \ u) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,20253,a,b,12286,a)].">
      <j1 rule="hyper" parents="128 20253 12286"/>
    </justification>
  </clause>

  <clause id="20955">
    <literal><![CDATA[
      (x \ y) * (x \ L(x,z,u)) = y * L(y \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3359,a(flip),b,20253,a),flip(a)].">
      <j1 rule="hyper" parents="63 3359 20253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20956">
    <literal><![CDATA[
      (x / y) \ L(x / y,z,u) = y \ (x * L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(128,a,3360,a(flip),b,20253,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 3360 20253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20957">
    <literal><![CDATA[
      ((x * x) * (y \ L(y,z,u))) / w = (y \ L(y,z,u)) / (w / (x * x))
    ]]></literal>
    <justification jstring="[para(20253(a,1),902(a,1,1))].">
      <j1 rule="para" parents="20253 902"/>
    </justification>
  </clause>

  <clause id="20958">
    <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(20253(a,1),88(a,1,1,2))].">
      <j1 rule="para" parents="20253 88"/>
    </justification>
  </clause>

  <clause id="20959">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * (x \ L(x,y,z)))) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(20253(a,1),3651(a,1,2,2))].">
      <j1 rule="para" parents="20253 3651"/>
    </justification>
  </clause>

  <clause id="20960">
    <literal><![CDATA[
      (x * y) \ ((y * (z \ L(z,u,w))) * T(x,y)) = R(T(z \ L(z,u,w),x * y),y,x)
    ]]></literal>
    <justification jstring="[para(20253(a,1),9627(a,1,2,1))].">
      <j1 rule="para" parents="20253 9627"/>
    </justification>
  </clause>

  <clause id="20961">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (u * (x \ L(x,y,z))) = w
    ]]></literal>
    <justification jstring="[para(20253(a,2),12289(a,1))].">
      <j1 rule="para" parents="20253 12289"/>
    </justification>
  </clause>

  <clause id="20962">
    <literal><![CDATA[
      K(x * L(y \ z,y,z \ 1),u) = K((x / y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(13467,a,20340,a)].">
      <j1 rule="hyper" parents="13467 20340"/>
    </justification>
  </clause>

  <clause id="20965">
    <literal><![CDATA[
      T(x,y) \ ((T(x,y) * z) * u) = x \ ((x * z) * u)
    ]]></literal>
    <justification jstring="[hyper(128,a,20344,a(flip),b,4947,a),flip(a)].">
      <j1 rule="hyper" parents="128 20344 4947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20967">
    <literal><![CDATA[
      (x \ y) * (K(z,T(u,y)) * w) = (x \ (K(z,u) * y)) * w
    ]]></literal>
    <justification jstring="[para(20369(a,1),20151(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20369 20151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20969">
    <literal><![CDATA[
      T(x,(y * (z \ u)) \ u) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(132,a,20425,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 20425 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20970">
    <literal><![CDATA[
      ((x * (y \ z)) \ z) \ K((x * (y \ z)) \ z,T(x / y,z)) = 1 / ((x * (y \ z)) \ z)
    ]]></literal>
    <justification jstring="[hyper(128,a,20431,a(flip),b,2598,a)].">
      <j1 rule="hyper" parents="128 20431 2598"/>
    </justification>
  </clause>

  <clause id="20971">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ z) * u) = x * ((x \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(134,a,20439,a(flip),b,5210,a)].">
      <j1 rule="hyper" parents="134 20439 5210"/>
    </justification>
  </clause>

  <clause id="20974">
    <literal><![CDATA[
      T(a(x,y,z) * u,K(w,u) * v5) = T(u * a(x,y,z),v5)
    ]]></literal>
    <justification jstring="[para(20481(a,1),19929(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20481 19929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20980">
    <literal><![CDATA[
      T(x,y) * (y \ L(T(y,x),z,u)) = x * (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(20536(a,1),5342(a,2,2))].">
      <j1 rule="para" parents="20536 5342"/>
    </justification>
  </clause>

  <clause id="20983">
    <literal><![CDATA[
      x * (((x \ y) \ y) * a(x \ y,x,x)) = (x \ y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,18304,a(flip),b,20597,a),flip(a)].">
      <j1 rule="hyper" parents="63 18304 20597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20984">
    <literal><![CDATA[
      (x * (y * a(z,u,x))) \ ((a(z,u,x) * x) * y) = a(a(z,u,x),x,y)
    ]]></literal>
    <justification jstring="[para(20597(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="20597 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20985">
    <literal><![CDATA[
      x \ T(x / (a(y,z,u) * x),(a(y,z,u) * x) \ 1) = x / ((a(y,z,u) * x) * x)
    ]]></literal>
    <justification jstring="[para(20609(a,2),9706(a,2,2))].">
      <j1 rule="para" parents="20609 9706"/>
    </justification>
  </clause>

  <clause id="20986">
    <literal><![CDATA[
      a(x,y,z) / (a(x,y,z) * u) = a(x,y,z) \ (a(x,y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(128,a,20637,a(flip),b,9707,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 20637 9707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20987">
    <literal><![CDATA[
      T(x,(y / L(T(z,y),u,w)) \ v5) = T(x,y \ (L(z,u,w) * v5))
    ]]></literal>
    <justification jstring="[para(4298(a,1),20670(a,1,2,1))].">
      <j1 rule="para" parents="4298 20670"/>
    </justification>
  </clause>

  <clause id="20988">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) \ (u * x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(214,a,20673,a)].">
      <j1 rule="hyper" parents="214 20673"/>
    </justification>
  </clause>

  <clause id="20989">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * L(x,y,z) = u * x
    ]]></literal>
    <justification jstring="[hyper(148,a,20673,a)].">
      <j1 rule="hyper" parents="148 20673"/>
    </justification>
  </clause>

  <clause id="20990">
    <literal><![CDATA[
      R(R(x,y,(z * y) \ z),y * ((z * y) \ z),y) = y * (L(y,y,z) \ ((x * y) * ((z * y) \ z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3352,a,b,20673,a)].">
      <j1 rule="hyper" parents="63 3352 20673"/>
    </justification>
  </clause>

  <clause id="20991">
    <literal><![CDATA[
      (x / L(x,y,z)) * L(T(L(x,y,z),x),u,w) = x * (L(x,y,z) \ L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,2181,a,b,20673,a)].">
      <j1 rule="hyper" parents="63 2181 20673"/>
    </justification>
  </clause>

  <clause id="20992">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * (x \ L(x,y,z)))) = R(u,x \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3165,a(flip),b,20673,a),flip(a)].">
      <j1 rule="hyper" parents="63 3165 20673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20994">
    <literal><![CDATA[
      (L(x / y,z,u) \ x) * (y \ x) = (y \ x) * (L(y \ x,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(133,a,9697,a(flip),b,20674,a)].">
      <j1 rule="hyper" parents="133 9697 20674"/>
    </justification>
  </clause>

  <clause id="20995">
    <literal><![CDATA[
      (L(x,y,z) * u) / L(x,y,z) = (x * u) / x
    ]]></literal>
    <justification jstring="[para(9(a,1),20674(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 20674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20996">
    <literal><![CDATA[
      (x / L(y,z,u)) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * (L(y,z,u) \ x) = w
    ]]></literal>
    <justification jstring="[para(20674(a,1),280(a,1,1))].">
      <j1 rule="para" parents="20674 280"/>
    </justification>
  </clause>

  <clause id="20997">
    <literal><![CDATA[
      ((x * (L(x,y,z) \ u)) * w) / (x * w) = R(u / L(x,y,z),x,w)
    ]]></literal>
    <justification jstring="[para(20674(a,1),108(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20674 108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20998">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) / (x \ 1) = u / L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(3439(a,1),20674(a,1,1))].">
      <j1 rule="para" parents="3439 20674"/>
    </justification>
  </clause>

  <clause id="20999">
    <literal><![CDATA[
      x * (((x * (L(x,y,z) \ u)) / (x \ 1)) \ w) = (1 / x) * ((u / L(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(20674(a,1),6489(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20674 6489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21001">
    <literal><![CDATA[
      ((L(x,y,z) \ u) / x) * L(x,y,z) = x \ u
    ]]></literal>
    <justification jstring="[hyper(2013,a,20680,a)].">
      <j1 rule="hyper" parents="2013 20680"/>
    </justification>
  </clause>

  <clause id="21002">
    <literal><![CDATA[
      a(x,y,z) \ (u * L(a(x,y,z),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(a(x,y,z),w,v5) * (a(x,y,z) \ u) = v6
    ]]></literal>
    <justification jstring="[para(20681(a,1),20015(a,1,2))].">
      <j1 rule="para" parents="20681 20015"/>
    </justification>
  </clause>

  <clause id="21003">
    <literal><![CDATA[
      ((x \ y) \ y) * L(T(x \ y,x),z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(804,a,20682,a)].">
      <j1 rule="hyper" parents="804 20682"/>
    </justification>
  </clause>

  <clause id="21004">
    <literal><![CDATA[
      x * L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (L(y,z,u) * x) = w
    ]]></literal>
    <justification jstring="[para(20682(a,1),5647(a,1))].">
      <j1 rule="para" parents="20682 5647"/>
    </justification>
  </clause>

  <clause id="21005">
    <literal><![CDATA[
      L(x,y,z) * (x \ (u * (x \ 1))) = u * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3438,a(flip),b,20683,a)].">
      <j1 rule="hyper" parents="63 3438 20683"/>
    </justification>
  </clause>

  <clause id="21006">
    <literal><![CDATA[
      L(x \ 1,y,z) * (u * x) = (x \ 1) * (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(20683(a,1),3545(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20683 3545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21007">
    <literal><![CDATA[
      x * ((y / x) * L(x,z,u)) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(641,a,20686,a),flip(a)].">
      <j1 rule="hyper" parents="641 20686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21008">
    <literal><![CDATA[
      x \ (L(x,y,z) * u) = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,168,a(flip),b,20686,a(flip))].">
      <j1 rule="hyper" parents="128 168 20686"/>
    </justification>
  </clause>

  <clause id="21009">
    <literal><![CDATA[
      x * ((y \ a(y,y,x)) * L(x,z,u)) = L(x,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[para(18983(a,1),20686(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18983 20686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21010">
    <literal><![CDATA[
      L(x,y,z) * (x \ u) != w
    ]]></literal>
    <literal><![CDATA[
      (u / x) * L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(20687(a,1),2014(a,1))].">
      <j1 rule="para" parents="20687 2014"/>
    </justification>
  </clause>

  <clause id="21011">
    <literal><![CDATA[
      (L(x,y,z) * u) / T(x,u) = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(11224,a,20689,a)].">
      <j1 rule="hyper" parents="11224 20689"/>
    </justification>
  </clause>

  <clause id="21012">
    <literal><![CDATA[
      (x / (y \ 1)) * L(y \ 1,z,u) = L(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3438,a(flip),b,20689,a),flip(a)].">
      <j1 rule="hyper" parents="63 3438 20689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21013">
    <literal><![CDATA[
      L(x,y,z) * (x \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      (z * (T(y,z) * x)) / x = u
    ]]></literal>
    <justification jstring="[para(20689(a,2),10186(a,1))].">
      <j1 rule="para" parents="20689 10186"/>
    </justification>
  </clause>

  <clause id="21014">
    <literal><![CDATA[
      ((L(x,y,z) * u) / L(x,y,z)) * L(L(x,w,v5),y,z) = L(L(x,y,z),w,v5) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,166,a,b,20690,a)].">
      <j1 rule="hyper" parents="63 166 20690"/>
    </justification>
  </clause>

  <clause id="21015">
    <literal><![CDATA[
      ((x * ((y / (x \ 1)) \ z)) / (1 / x)) * L(1 / x,u,w) = L(1 / x,u,w) * ((y / x) \ z)
    ]]></literal>
    <justification jstring="[para(6489(a,1),20690(a,1,1,1))].">
      <j1 rule="para" parents="6489 20690"/>
    </justification>
  </clause>

  <clause id="21016">
    <literal><![CDATA[
      (x * (R(x,y,z) \ u)) * R(x,y,z) = u * x
    ]]></literal>
    <justification jstring="[hyper(673,a,20692,a),flip(a)].">
      <j1 rule="hyper" parents="673 20692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21017">
    <literal><![CDATA[
      (R(x,y,z) \ u) * R(x,y,z) = (x \ u) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,1747,a(flip),b,20692,a),flip(a)].">
      <j1 rule="hyper" parents="133 1747 20692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21019">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) * (z \ w) = (K(y,T(x,u)) * z) \ w
    ]]></literal>
    <justification jstring="[hyper(7790,a,20697,a)].">
      <j1 rule="hyper" parents="7790 20697"/>
    </justification>
  </clause>

  <clause id="21020">
    <literal><![CDATA[
      (T(x,y) * z) * T(u,x * z) = K(x,y) * (u * (x * z))
    ]]></literal>
    <justification jstring="[hyper(134,a,22,a,b,20701,a)].">
      <j1 rule="hyper" parents="134 22 20701"/>
    </justification>
  </clause>

  <clause id="21021">
    <literal><![CDATA[
      (T(x,y) * z) \ (T(x,y) * u) = (x * z) \ (x * u)
    ]]></literal>
    <justification jstring="[para(4974(a,1),20701(a,1,2))].">
      <j1 rule="para" parents="4974 20701"/>
    </justification>
  </clause>

  <clause id="21022">
    <literal><![CDATA[
      (x * y) \ T(z \ (u * x),K(x,u)) = (T(x,u) * y) \ (z \ (x * u))
    ]]></literal>
    <justification jstring="[para(13909(a,2),20702(a,1,2))].">
      <j1 rule="para" parents="13909 20702"/>
    </justification>
  </clause>

  <clause id="21023">
    <literal><![CDATA[
      (T(x,y) * z) \ (L(x,u,w) * y) = (x * z) \ (y * L(x,u,w))
    ]]></literal>
    <justification jstring="[para(20345(a,1),20702(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20345 20702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21024">
    <literal><![CDATA[
      K(x,y) * ((K(y,x) / z) * (L((1 / z) \ 1,u,w) * v5)) = L(1 / z,u,w) * (((1 / z) \ 1) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,3440,a,b,20727,a),flip(a)].">
      <j1 rule="hyper" parents="347 3440 20727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21025">
    <literal><![CDATA[
      L(x \ y,x,x \ 1) = K(z,u) * ((K(u,z) / x) * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,2938,a,b,20727,a)].">
      <j1 rule="hyper" parents="347 2938 20727"/>
    </justification>
  </clause>

  <clause id="21027">
    <literal><![CDATA[
      K(x,y) * (x \ ((x / z) * u)) = x \ ((T(x,y) / z) * u)
    ]]></literal>
    <justification jstring="[hyper(128,a,20728,a(flip),b,5191,a),flip(a)].">
      <j1 rule="hyper" parents="128 20728 5191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21028">
    <literal><![CDATA[
      T(L(x,y,z) \ x,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = w
    ]]></literal>
    <justification jstring="[para(20783(a,2),1422(a,1))].">
      <j1 rule="para" parents="20783 1422"/>
    </justification>
  </clause>

  <clause id="21030">
    <literal><![CDATA[
      x \ (y * T(z,z \ (x \ (y * z)))) = z * ((x \ (y * z)) / z)
    ]]></literal>
    <justification jstring="[hyper(5314,a,20791,a),flip(a)].">
      <j1 rule="hyper" parents="5314 20791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21031">
    <literal><![CDATA[
      (x \ (y * z)) * (K(z,u) * w) = (x \ (y * T(z,u))) * w
    ]]></literal>
    <justification jstring="[para(20791(a,1),20151(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20791 20151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21032">
    <literal><![CDATA[
      K(x,y) * (z \ (u / T(x,y))) = T(z \ (u / x),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(134,a,20792,a(flip),b,7345,a)].">
      <j1 rule="hyper" parents="134 20792 7345"/>
    </justification>
  </clause>

  <clause id="21034">
    <literal><![CDATA[
      (x \ (y \ z)) * (K(z,u) * w) = (x \ (y \ T(z,u))) * w
    ]]></literal>
    <justification jstring="[para(20794(a,1),20151(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20794 20151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21035">
    <literal><![CDATA[
      (x * T(y,z)) * (T(y,z) \ u) = (x * y) * (y \ u)
    ]]></literal>
    <justification jstring="[hyper(5324,a,20808,a),flip(a)].">
      <j1 rule="hyper" parents="5324 20808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21036">
    <literal><![CDATA[
      K(x,y) * ((T(x,y) * z) \ z) = (z * x) \ T(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(128,a,6348,a,b,20808,a),flip(a)].">
      <j1 rule="hyper" parents="128 6348 20808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21038">
    <literal><![CDATA[
      (x / T(y,z)) * (a(u,w,v5) \ T(y,z)) = (x / y) * (a(u,w,v5) \ y)
    ]]></literal>
    <justification jstring="[para(16901(a,1),20809(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16901 20809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21039">
    <literal><![CDATA[
      (x * T(y,z)) \ (K(x,y) * u) = K(z,y) * ((y * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(128,a,10301,a(flip),b,20810,a)].">
      <j1 rule="hyper" parents="128 10301 20810"/>
    </justification>
  </clause>

  <clause id="21040">
    <literal><![CDATA[
      (T(x,y) \ z) \ (((T(x,y) \ z) * x) * u) = (z / T(x,y)) \ (z * (K(y,x) * u))
    ]]></literal>
    <justification jstring="[hyper(128,a,20810,a(flip),b,10240,a)].">
      <j1 rule="hyper" parents="128 20810 10240"/>
    </justification>
  </clause>

  <clause id="21042">
    <literal><![CDATA[
      (x \ K(y,z)) * (u * K(z,y)) = (x \ 1) * T(u,K(y,z))
    ]]></literal>
    <justification jstring="[para(7341(a,1),20815(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7341 20815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21044">
    <literal><![CDATA[
      K(x,y) * ((z / T(y,x)) \ R((z / y) * u,z / y,z / y)) = (u * (z / y)) * (1 / (z / y))
    ]]></literal>
    <justification jstring="[hyper(347,a,2520,a(flip),b,20827,a),flip(a)].">
      <j1 rule="hyper" parents="347 2520 20827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21047">
    <literal><![CDATA[
      K(x,y) * (((z * y) \ u) * w) = ((z * T(y,x)) \ u) * w
    ]]></literal>
    <justification jstring="[para(20828(a,1),20008(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20828 20008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21050">
    <literal><![CDATA[
      ((x \ K(y,z)) \ u) \ 1 = ((x \ 1) \ u) \ K(y,z)
    ]]></literal>
    <justification jstring="[para(20832(a,1),13174(a,1,1))].">
      <j1 rule="para" parents="20832 13174"/>
    </justification>
  </clause>

  <clause id="21051">
    <literal><![CDATA[
      ((x \ K(y,z)) \ u) \ (K(z,y) * w) = ((x \ 1) \ u) \ w
    ]]></literal>
    <justification jstring="[para(20832(a,1),20046(a,1,1))].">
      <j1 rule="para" parents="20832 20046"/>
    </justification>
  </clause>

  <clause id="21052">
    <literal><![CDATA[
      T(x,y) * ((z \ T(x,y)) \ u) = x * ((z \ x) \ u)
    ]]></literal>
    <justification jstring="[hyper(134,a,20834,a(flip),b,5210,a)].">
      <j1 rule="hyper" parents="134 20834 5210"/>
    </justification>
  </clause>

  <clause id="21053">
    <literal><![CDATA[
      x * (L(x,y,z) \ (L(x,y,z) * (R(L(x,y,z),u,w) \ v5))) = (v5 / R(L(x,y,z),u,w)) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,20839,a(flip),b,20674,a),flip(a)].">
      <j1 rule="hyper" parents="133 20839 20674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21055">
    <literal><![CDATA[
      K(x / (y \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K((z / x) \ y,u) = w
    ]]></literal>
    <justification jstring="[para(20846(a,1),19669(a,1))].">
      <j1 rule="para" parents="20846 19669"/>
    </justification>
  </clause>

  <clause id="21056">
    <literal><![CDATA[
      T(x,(y / z) / u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y / (u * z)) = w
    ]]></literal>
    <justification jstring="[para(20861(a,1),4984(a,1))].">
      <j1 rule="para" parents="20861 4984"/>
    </justification>
  </clause>

  <clause id="21057">
    <literal><![CDATA[
      T(x,T(y,z) * (z \ u)) = T(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,19431,a(flip),b,20871,a)].">
      <j1 rule="hyper" parents="63 19431 20871"/>
    </justification>
  </clause>

  <clause id="21058">
    <literal><![CDATA[
      R(T(x \ 1,(x \ y) * z),x,y \ z) = (x * ((y \ 1) \ z)) \ ((y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(20871(a,1),13816(a,1,1))].">
      <j1 rule="para" parents="20871 13816"/>
    </justification>
  </clause>

  <clause id="21059">
    <literal><![CDATA[
      T(x / y,y * K(z,u)) = T(y \ x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(491,a,20910,a)].">
      <j1 rule="hyper" parents="491 20910"/>
    </justification>
  </clause>

  <clause id="21061">
    <literal><![CDATA[
      ((x / y) * R(y,z,u)) * K(y,(x / y) * R(y,z,u)) = (R(y,z,u) * x) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,20930,a(flip),b,4989,a),flip(a)].">
      <j1 rule="hyper" parents="131 20930 4989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21062">
    <literal><![CDATA[
      ((x \ (x \ R(x,y,z))) * (x * (R(x,y,z) \ x))) * ((x \ (x \ R(x,y,z))) \ 1) = (x \ R(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[para(20941(a,1),1640(a,1,1,2))].">
      <j1 rule="para" parents="20941 1640"/>
    </justification>
  </clause>

  <clause id="21063">
    <literal><![CDATA[
      T(x,T(y / z,y * u)) = T(x,(z * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(9(a,1),20969(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 20969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21064">
    <literal><![CDATA[
      (x * y) / L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      y * (L(y,z,u) \ x) = w
    ]]></literal>
    <justification jstring="[para(20988(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="20988 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21065">
    <literal><![CDATA[
      (x * (x \ (L(1 / x,y,z) \ u))) * L(x,y,z) = ((1 / x) \ u) * x
    ]]></literal>
    <justification jstring="[para(3636(a,1),20989(a,1,1,2))].">
      <j1 rule="para" parents="3636 20989"/>
    </justification>
  </clause>

  <clause id="21067">
    <literal><![CDATA[
      (x / L(L(y,z,u),w,v5)) * y = y * (L(L(y,z,u),w,v5) \ x)
    ]]></literal>
    <justification jstring="[hyper(133,a,20674,a(flip),b,20995,a(flip))].">
      <j1 rule="hyper" parents="133 20674 20995"/>
    </justification>
  </clause>

  <clause id="21069">
    <literal><![CDATA[
      (x / y) * L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) * (y \ x) = w
    ]]></literal>
    <justification jstring="[para(21008(a,1),1426(a,1))].">
      <j1 rule="para" parents="21008 1426"/>
    </justification>
  </clause>

  <clause id="21070">
    <literal><![CDATA[
      (x * (R(x,y,z) \ (u * K(w,v5)))) * R(x,y,z) = u * (K(w,v5) * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,20151,a(flip),b,21016,a),flip(a)].">
      <j1 rule="hyper" parents="347 20151 21016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21071">
    <literal><![CDATA[
      (x * y) / R(y,z,u) = y * (R(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,21016,a)].">
      <j1 rule="hyper" parents="145 21016"/>
    </justification>
  </clause>

  <clause id="21073">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) \ v5 != v6
    ]]></literal>
    <literal><![CDATA[
      v5 / L(a(x,y,z) \ 1,u,w) = v6
    ]]></literal>
    <justification jstring="[para(20000(a,1),19955(a,1)),flip(a)].">
      <j1 rule="para" parents="20000 19955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21074">
    <literal><![CDATA[
      L(x,y,z) * (((x \ 1) \ 1) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      (u / ((x \ 1) \ 1)) * L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(2968(a,1),19956(a,1,2))].">
      <j1 rule="para" parents="2968 19956"/>
    </justification>
  </clause>

  <clause id="21075">
    <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(19939(a,1),19956(a,1,2))].">
      <j1 rule="para" parents="19939 19956"/>
    </justification>
  </clause>

  <clause id="21076">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) * v5 != v6
    ]]></literal>
    <literal><![CDATA[
      v5 * L(a(x,y,z) \ 1,u,w) = v6
    ]]></literal>
    <justification jstring="[para(20000(a,1),19956(a,1,2))].">
      <j1 rule="para" parents="20000 19956"/>
    </justification>
  </clause>

  <clause id="21077">
    <literal><![CDATA[
      R(x,y,z) * u != w
    ]]></literal>
    <literal><![CDATA[
      ((x * u) / x) * R(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(254(a,1),19967(a,1,2))].">
      <j1 rule="para" parents="254 19967"/>
    </justification>
  </clause>

  <clause id="21079">
    <literal><![CDATA[
      R(x,y,z) * (R(x,u,w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      (v5 / R(x,u,w)) * R(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(20181(a,1),19967(a,1,2))].">
      <j1 rule="para" parents="20181 19967"/>
    </justification>
  </clause>

  <clause id="21080">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) * L(z,1 / T(x,y),x) = T(x,y) * ((1 / T(x,y)) * z)
    ]]></literal>
    <justification jstring="[hyper(126,a,10291,a,b,20090,a(flip))].">
      <j1 rule="hyper" parents="126 10291 20090"/>
    </justification>
  </clause>

  <clause id="21081">
    <literal><![CDATA[
      (x * y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ (K(y,x) * z) = u
    ]]></literal>
    <justification jstring="[para(4909(a,1),20101(a,1,1))].">
      <j1 rule="para" parents="4909 20101"/>
    </justification>
  </clause>

  <clause id="21082">
    <literal><![CDATA[
      (x * T(y,z)) / u != w
    ]]></literal>
    <literal><![CDATA[
      (x * y) / (u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(5926(a,1),20146(a,1,1))].">
      <j1 rule="para" parents="5926 20146"/>
    </justification>
  </clause>

  <clause id="21085">
    <literal><![CDATA[
      (x * (y * K(z,u))) * w != v5
    ]]></literal>
    <literal><![CDATA[
      (x * y) * (K(z,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(20033(a,1),20173(a,1,1))].">
      <j1 rule="para" parents="20033 20173"/>
    </justification>
  </clause>

  <clause id="21087">
    <literal><![CDATA[
      T(x,(y \ L(z,u,w)) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y \ (y \ z),u,w) \ (y \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(3341(a,1),20635(a,1,2,1))].">
      <j1 rule="para" parents="3341 20635"/>
    </justification>
  </clause>

  <clause id="21088">
    <literal><![CDATA[
      R(x,y,(z \ 1) * u) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(20896,a,20497,a),flip(a)].">
      <j1 rule="hyper" parents="20896 20497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21089">
    <literal><![CDATA[
      R(x,y,(z \ 1) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z * u) = w
    ]]></literal>
    <justification jstring="[para(20497(a,1),20896(a,1))].">
      <j1 rule="para" parents="20497 20896"/>
    </justification>
  </clause>

  <clause id="21090">
    <literal><![CDATA[
      R(x,L(y * z,y,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(15284(a,2),20908(a,1))].">
      <j1 rule="para" parents="15284 20908"/>
    </justification>
  </clause>

  <clause id="21092">
    <literal><![CDATA[
      T(x,T(y \ (z * u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / (z \ y)) = w
    ]]></literal>
    <justification jstring="[para(19959(a,1),7809(a,1))].">
      <j1 rule="para" parents="19959 7809"/>
    </justification>
  </clause>

  <clause id="21094">
    <literal><![CDATA[
      T(x,y * L(y \ x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(54,a,20077,a)].">
      <j1 rule="hyper" parents="54 20077"/>
    </justification>
  </clause>

  <clause id="21096">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,u) \ w) = x * (L(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(134,a,20288,a(flip),b,5157,a),flip(a)].">
      <j1 rule="hyper" parents="134 20288 5157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21097">
    <literal><![CDATA[
      L(x,y,z) \ T(L(T(x,u),y,z),w) = K(x,u) * K(L(T(x,u),y,z),w)
    ]]></literal>
    <justification jstring="[para(4924(a,2),20288(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4924 20288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21098">
    <literal><![CDATA[
      K(x,y) * (L(y,z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(T(y,x),z,u) \ w = v5
    ]]></literal>
    <justification jstring="[para(20288(a,1),5274(a,1,2)),flip(b)].">
      <j1 rule="para" parents="20288 5274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21099">
    <literal><![CDATA[
      ((x \ y) \ y) \ (L(T(x,x \ y),z,u) * w) = x \ (L(x,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(128,a,20300,a(flip),b,5188,a)].">
      <j1 rule="hyper" parents="128 20300 5188"/>
    </justification>
  </clause>

  <clause id="21100">
    <literal><![CDATA[
      L(T(x,y),z,x) * (x \ u) = K(x,y) * (a(x,z,x) \ u)
    ]]></literal>
    <justification jstring="[para(9981(a,1),20300(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9981 20300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21102">
    <literal><![CDATA[
      L(T(x,y),z,u) * T(w,x) = K(x,y) * (w * L(x,z,u))
    ]]></literal>
    <justification jstring="[para(19953(a,1),20300(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19953 20300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21103">
    <literal><![CDATA[
      K(x,y) * ((z / x) * L(x,u,w)) = L(T(x,y),u,w) * (x \ z)
    ]]></literal>
    <justification jstring="[para(20689(a,1),20300(a,1,2))].">
      <j1 rule="para" parents="20689 20300"/>
    </justification>
  </clause>

  <clause id="21104">
    <literal><![CDATA[
      K(x,y) * (L(y,z,u) \ y) = y * (L(T(y,x),z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(20353(a,1),5467(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20353 5467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21106">
    <literal><![CDATA[
      (L(x,y,z) \ T(T(L(x,y,z),u),w)) * K(v5,x) = T(T(L(x,y,z),u),w) / L(T(x,v5),y,z)
    ]]></literal>
    <justification jstring="[para(4820(a,1),20354(a,1,1))].">
      <j1 rule="para" parents="4820 20354"/>
    </justification>
  </clause>

  <clause id="21108">
    <literal><![CDATA[
      x * K(y,T(z,u * x)) = K(y,T(z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(19541,a,20374,a),flip(a)].">
      <j1 rule="hyper" parents="19541 20374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21110">
    <literal><![CDATA[
      K(x * y,T(z,u * x)) = K(y * x,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(10377,a,21108,a)].">
      <j1 rule="hyper" parents="10377 21108"/>
    </justification>
  </clause>

  <clause id="21111">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(34,a,7104,a,b,21108,a)].">
      <j1 rule="hyper" parents="34 7104 21108"/>
    </justification>
  </clause>

  <clause id="21112">
    <literal><![CDATA[
      T(x,T(T(y,z),u)) = T(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(132,a,21111,a,b,5455,a),flip(a)].">
      <j1 rule="hyper" parents="132 21111 5455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21113">
    <literal><![CDATA[
      T(x,T(y / z,y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z \ y,u)) = w
    ]]></literal>
    <justification jstring="[para(21112(a,1),8709(a,1))].">
      <j1 rule="para" parents="21112 8709"/>
    </justification>
  </clause>

  <clause id="21114">
    <literal><![CDATA[
      K(x * y,T(z,u * (x * w))) = K(y * x,T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(18517,a,21110,a)].">
      <j1 rule="hyper" parents="18517 21110"/>
    </justification>
  </clause>

  <clause id="21116">
    <literal><![CDATA[
      R(T(x,y),z,u) * T(w,x) = K(x,y) * (w * R(x,z,u))
    ]]></literal>
    <justification jstring="[para(19966(a,1),20407(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19966 20407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21117">
    <literal><![CDATA[
      T(x,y) * (R(T(x,y),z,u) \ w) = x * (R(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(134,a,20408,a(flip),b,5157,a),flip(a)].">
      <j1 rule="hyper" parents="134 20408 5157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21122">
    <literal><![CDATA[
      R(x,(y \ ((y \ z) / z)) \ u,w) = R(x,(((y \ z) / z) * y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,12422,a(flip),b,20656,a)].">
      <j1 rule="hyper" parents="63 12422 20656"/>
    </justification>
  </clause>

  <clause id="21123">
    <literal><![CDATA[
      R(x,(y \ (z \ (z / y))) \ u,w) = R(x,((z \ (z / y)) * y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,12341,a(flip),b,20656,a)].">
      <j1 rule="hyper" parents="63 12341 20656"/>
    </justification>
  </clause>

  <clause id="21124">
    <literal><![CDATA[
      x \ (y * L(x,z \ (x \ y),z)) = T(z * ((z \ (y / x)) * x),x)
    ]]></literal>
    <justification jstring="[para(13709(a,1),20685(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13709 20685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21125">
    <literal><![CDATA[
      K(T(x,y),z * (y \ L(y,u,w))) = K(x,y \ (z * L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(20685(a,1),17093(a,2,2))].">
      <j1 rule="para" parents="20685 17093"/>
    </justification>
  </clause>

  <clause id="21126">
    <literal><![CDATA[
      (x * T(y,T(z,x))) \ T(u,T(z,w)) = (x * y) \ T(K(z,y) * u,T(z,w))
    ]]></literal>
    <justification jstring="[para(8523(a,2),20706(a,2,2))].">
      <j1 rule="para" parents="8523 20706"/>
    </justification>
  </clause>

  <clause id="21127">
    <literal><![CDATA[
      R(x,y,((z * u) * (u * z)) \ w) = R(x,y,K(u,z) * w)
    ]]></literal>
    <justification jstring="[para(20707(a,1),2238(a,1,3))].">
      <j1 rule="para" parents="20707 2238"/>
    </justification>
  </clause>

  <clause id="21128">
    <literal><![CDATA[
      ((x * y) * z) \ (y * (T(x,y) * u)) = ((y * x) * z) \ (y * (x * u))
    ]]></literal>
    <justification jstring="[para(5231(a,1),20707(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5231 20707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21129">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(z,u)) = K(u,z) * (x * (K(z,u) * y))
    ]]></literal>
    <justification jstring="[para(7351(a,1),20740(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7351 20740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21130">
    <literal><![CDATA[
      K(x,y) * (z * (u \ T(y,x))) = T(z * (u \ y),K(y,x))
    ]]></literal>
    <justification jstring="[para(13045(a,1),20740(a,1,2,2))].">
      <j1 rule="para" parents="13045 20740"/>
    </justification>
  </clause>

  <clause id="21131">
    <literal><![CDATA[
      K(x,y) * (z / (u * K(x,y))) = T(z,K(y,x)) / u
    ]]></literal>
    <justification jstring="[hyper(63,a,20088,a(flip),b,20772,a)].">
      <j1 rule="hyper" parents="63 20088 20772"/>
    </justification>
  </clause>

  <clause id="21136">
    <literal><![CDATA[
      L(x,y,(z * u) / (w * K(v5,v6))) = L(x,y,w \ (z * (u * K(v6,v5))))
    ]]></literal>
    <justification jstring="[para(20775(a,1),20079(a,1,3))].">
      <j1 rule="para" parents="20775 20079"/>
    </justification>
  </clause>

  <clause id="21137">
    <literal><![CDATA[
      (x * (y * z)) * (K(z,u) * w) = (x * (y * T(z,u))) * w
    ]]></literal>
    <justification jstring="[para(5926(a,1),20819(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5926 20819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21138">
    <literal><![CDATA[
      (x * y) * (K(z,T(u,y)) * w) = (x * (K(z,u) * y)) * w
    ]]></literal>
    <justification jstring="[para(7104(a,1),20819(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7104 20819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21139">
    <literal><![CDATA[
      (x * (y \ K(z,u))) * (K(u,z) * w) = (x * (y \ 1)) * w
    ]]></literal>
    <justification jstring="[para(13009(a,1),20819(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13009 20819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21140">
    <literal><![CDATA[
      (x * (y * (z * K(u,w)))) * v5 = (x * (y * z)) * (K(u,w) * v5)
    ]]></literal>
    <justification jstring="[para(20033(a,1),20819(a,1,1,2))].">
      <j1 rule="para" parents="20033 20819"/>
    </justification>
  </clause>

  <clause id="21142">
    <literal><![CDATA[
      K(x,y) * ((z * (u * y)) \ w) = (z * (u * T(y,x))) \ w
    ]]></literal>
    <justification jstring="[para(5926(a,1),20837(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5926 20837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21143">
    <literal><![CDATA[
      K(x,y) * ((T(x,y) * z) \ u) = T(x * z,K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(7742(a,1),20837(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7742 20837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21144">
    <literal><![CDATA[
      (x * (y * (z * K(u,w)))) \ v5 = K(w,u) * ((x * (y * z)) \ v5)
    ]]></literal>
    <justification jstring="[para(20033(a,1),20837(a,1,1,2))].">
      <j1 rule="para" parents="20033 20837"/>
    </justification>
  </clause>

  <clause id="21145">
    <literal><![CDATA[
      R(x,y,(z * u) * z) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,L(u,z,z)) = w
    ]]></literal>
    <justification jstring="[para(20497(a,1),20900(a,1))].">
      <j1 rule="para" parents="20497 20900"/>
    </justification>
  </clause>

  <clause id="21146">
    <literal><![CDATA[
      R(T(x,y),z \ u,x) = R(T(x,y),z * u,x)
    ]]></literal>
    <justification jstring="[hyper(6797,a,20905,a),flip(a)].">
      <j1 rule="hyper" parents="6797 20905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21148">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (u * (w * a(x,y,z))) = L(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(128,a,20917,a(flip),b,10150,a)].">
      <j1 rule="hyper" parents="128 20917 10150"/>
    </justification>
  </clause>

  <clause id="21149">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (u * (w * a(x,y,z))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(w,a(x,y,z),u) = v5
    ]]></literal>
    <justification jstring="[para(20917(a,1),10185(a,1,2))].">
      <j1 rule="para" parents="20917 10185"/>
    </justification>
  </clause>

  <clause id="21150">
    <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(20917(a,1),18301(a,1,1))].">
      <j1 rule="para" parents="20917 18301"/>
    </justification>
  </clause>

  <clause id="21151">
    <literal><![CDATA[
      ((1 / x) \ a(y,z,x)) \ (a(y,z,x) * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x \ u,x,a(y,z,x)) = w
    ]]></literal>
    <justification jstring="[para(20937(a,2),686(a,1))].">
      <j1 rule="para" parents="20937 686"/>
    </justification>
  </clause>

  <clause id="21152">
    <literal><![CDATA[
      (x \ (y \ z)) * (T(z / y,y) \ u) = (x \ (z / y)) * ((z / y) \ u)
    ]]></literal>
    <justification jstring="[para(113(a,1),20938(a,1,1,2))].">
      <j1 rule="para" parents="113 20938"/>
    </justification>
  </clause>

  <clause id="21154">
    <literal><![CDATA[
      T(x,y) * (z * ((T(x,y) * z) \ T(x,y))) = x * ((x \ (T(x,y) / z)) * z)
    ]]></literal>
    <justification jstring="[para(3261(a,1),20971(a,1,2))].">
      <j1 rule="para" parents="3261 20971"/>
    </justification>
  </clause>

  <clause id="21155">
    <literal><![CDATA[
      (T(x,y) * ((x * x) \ z)) \ (T(x,y) * u) = ((x \ 1) * z) \ (x * u)
    ]]></literal>
    <justification jstring="[para(497(a,1),21021(a,2,1))].">
      <j1 rule="para" parents="497 21021"/>
    </justification>
  </clause>

  <clause id="21156">
    <literal><![CDATA[
      T(x,T(y / z,y * u)) = T(x,u \ (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(20635,a,21063,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="20635 21063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21157">
    <literal><![CDATA[
      K(x,y) * (z / (u * K(x,y))) = T(z,K(x,y)) / u
    ]]></literal>
    <justification jstring="[para(7330(a,1),21131(a,2,1))].">
      <j1 rule="para" parents="7330 21131"/>
    </justification>
  </clause>

  <clause id="21158">
    <literal><![CDATA[
      R(x * y,x * y,L(y,x,x)) = (((x * y) \ 1) \ T(x,z)) / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(21145,a,13249,a)].">
      <j1 rule="hyper" parents="21145 13249"/>
    </justification>
  </clause>

  <clause id="21159">
    <literal><![CDATA[
      (x \ 1) / L(a(y,z,u),x,x) = x / (x * (x * a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(220,a,20006,a(flip),b,821,a)].">
      <j1 rule="hyper" parents="220 20006 821"/>
    </justification>
  </clause>

  <clause id="21160">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) / (x * w) = L(a(y,z,u),w,x)
    ]]></literal>
    <justification jstring="[para(19985(a,2),20006(a,1,1,2))].">
      <j1 rule="para" parents="19985 20006"/>
    </justification>
  </clause>

  <clause id="21161">
    <literal><![CDATA[
      a(x,y,z) * (u * a(w,v5,a(x,y,z))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(w,v5,a(x,y,z)) * (u * a(x,y,z)) = v6
    ]]></literal>
    <justification jstring="[para(20597(a,1),20023(a,1))].">
      <j1 rule="para" parents="20597 20023"/>
    </justification>
  </clause>

  <clause id="21164">
    <literal><![CDATA[
      R(x,R(1 / y,y,z),u * w) * (R(1 / y,y,z) * (w * u)) = (x * (z / (y * z))) * (w * u)
    ]]></literal>
    <justification jstring="[para(418(a,1),20638(a,2,1))].">
      <j1 rule="para" parents="418 20638"/>
    </justification>
  </clause>

  <clause id="21165">
    <literal><![CDATA[
      R(x,y,(((T(z,u) * w) / v5) * v6) * R(K(u,z),(T(z,u) * w) / v5,v6)) = R(x,y,((z * w) / v5) * v6)
    ]]></literal>
    <justification jstring="[para(20776(a,1),20640(a,2,3,1))].">
      <j1 rule="para" parents="20776 20640"/>
    </justification>
  </clause>

  <clause id="21166">
    <literal><![CDATA[
      R(x,y * (z / (y * y)),u) = R(x,L(y \ z,y,y),u)
    ]]></literal>
    <justification jstring="[para(464(a,1),20653(a,2,2)),flip(a)].">
      <j1 rule="para" parents="464 20653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21167">
    <literal><![CDATA[
      R(K(x,T(y,z)) / u,u,z) = z / (u * (z * K(y,x)))
    ]]></literal>
    <justification jstring="[para(20033(a,1),20769(a,2,2))].">
      <j1 rule="para" parents="20033 20769"/>
    </justification>
  </clause>

  <clause id="21168">
    <literal><![CDATA[
      R(x,y * (((z * u) * z) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y * a(z * u,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(13372(a,1),20903(a,1,2,2))].">
      <j1 rule="para" parents="13372 20903"/>
    </justification>
  </clause>

  <clause id="21169">
    <literal><![CDATA[
      (x * y) \ (((x * y) / x) * R(x,z,u)) = y \ (R(x,z,u) * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,10193,a,b,20929,a)].">
      <j1 rule="hyper" parents="63 10193 20929"/>
    </justification>
  </clause>

  <clause id="21170">
    <literal><![CDATA[
      x \ (R(y,y,z) * (y \ x)) = L(a(y,y,z),y,x)
    ]]></literal>
    <justification jstring="[para(18988(a,1),20929(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18988 20929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21171">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * x)) = w
    ]]></literal>
    <justification jstring="[para(20673(a,1),20996(a,1,1))].">
      <j1 rule="para" parents="20673 20996"/>
    </justification>
  </clause>

  <clause id="21172">
    <literal><![CDATA[
      L(x * K(y,z),u,w) * (K(z,y) * (x \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      (v5 / (x * K(y,z))) * L(x * K(y,z),u,w) = v6
    ]]></literal>
    <justification jstring="[para(20166(a,1),21010(a,1,2))].">
      <j1 rule="para" parents="20166 21010"/>
    </justification>
  </clause>

  <clause id="21173">
    <literal><![CDATA[
      K(x,y) * ((K(y,x) / z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      (1 / z) * u = w
    ]]></literal>
    <justification jstring="[para(21025(a,1),2947(a,1))].">
      <j1 rule="para" parents="21025 2947"/>
    </justification>
  </clause>

  <clause id="21174">
    <literal><![CDATA[
      ((x / y) / (1 / y)) * L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) * (y \ (x / (y \ 1))) = w
    ]]></literal>
    <justification jstring="[para(2287(a,1),21069(a,1,1))].">
      <j1 rule="para" parents="2287 21069"/>
    </justification>
  </clause>

  <clause id="21175">
    <literal><![CDATA[
      (L(x,y,z) * u) / (T(x,T(u,w)) * K(w,u)) = (T(u,w) / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(21082,a,21011,a)].">
      <j1 rule="hyper" parents="21082 21011"/>
    </justification>
  </clause>

  <clause id="21176">
    <literal><![CDATA[
      T(x,y \ (z \ (u * y))) = T(x,T(z \ u,y))
    ]]></literal>
    <justification jstring="[hyper(21113,a,21156,a),flip(a)].">
      <j1 rule="hyper" parents="21113 21156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21177">
    <literal><![CDATA[
      L(x,y,z) * (a(u,w,x) * v5) = a(u,w,x) * (L(x,y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(133,a,12369,a(flip),b,21160,a),flip(a)].">
      <j1 rule="hyper" parents="133 12369 21160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21178">
    <literal><![CDATA[
      L(a(x,y,z),u,a(x,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(21160(a,1),282(a,1)),flip(b)].">
      <j1 rule="para" parents="21160 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21179">
    <literal><![CDATA[
      ((a(x,y,z) * u) * u) / ((a(x,y,z) * u) * (a(x,y,z) * u)) = L(a(x,y,z),u,a(x,y,z) * u) \ 1
    ]]></literal>
    <justification jstring="[para(21160(a,1),515(a,1,1)),flip(a)].">
      <j1 rule="para" parents="21160 515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21180">
    <literal><![CDATA[
      L(a(x,y,z),u,a(x,y,z)) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) \ w = v5
    ]]></literal>
    <justification jstring="[para(21160(a,1),371(a,1,1))].">
      <j1 rule="para" parents="21160 371"/>
    </justification>
  </clause>

  <clause id="21181">
    <literal><![CDATA[
      L((x * y) / x,z,u) * R(x,w,v5) = R(x,w,v5) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(254(a,1),20190(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="254 20190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21182">
    <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(347,a,250,a(flip),b,20240,a),flip(a)].">
      <j1 rule="hyper" parents="347 250 20240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21183">
    <literal><![CDATA[
      (L(x / y,z,u) \ 1) * K(y,y \ x) = L(y \ x,z,u) \ 1
    ]]></literal>
    <justification jstring="[para(20301(a,1),13009(a,1,1))].">
      <j1 rule="para" parents="20301 13009"/>
    </justification>
  </clause>

  <clause id="21185">
    <literal><![CDATA[
      x * (L(T(y,z),u,w) \ 1) = x * (L(y,u,w) \ K(z,y))
    ]]></literal>
    <justification jstring="[para(25(a,2),20351(a,1,2,1))].">
      <j1 rule="para" parents="25 20351"/>
    </justification>
  </clause>

  <clause id="21188">
    <literal><![CDATA[
      x \ (y * a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x \ (a(z,u,w) * y) = v5
    ]]></literal>
    <justification jstring="[para(20601(a,1),230(a,1))].">
      <j1 rule="para" parents="20601 230"/>
    </justification>
  </clause>

  <clause id="21189">
    <literal><![CDATA[
      R(x,((y * y) \ z) \ u,w) = R(x,u / z,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,2245,a(flip),b,20654,a),flip(a)].">
      <j1 rule="hyper" parents="347 2245 20654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21191">
    <literal><![CDATA[
      R(x,((y * y) \ z) \ u,w) = R(x,z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,20555,a(flip),b,21189,a),flip(a)].">
      <j1 rule="hyper" parents="347 20555 21189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21192">
    <literal><![CDATA[
      R(x,((y \ 1) \ z) \ u,w) = R(x,(y \ z) \ u,w)
    ]]></literal>
    <justification jstring="[para(500(a,1),21191(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="500 21191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21193">
    <literal><![CDATA[
      T(L(x \ y,z,u),(x \ y) \ y) * ((x \ y) \ y) = L(x \ y,z,u) * ((x * L(x \ y,z,u)) / L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(20684(a,1),4149(a,2,2,1))].">
      <j1 rule="para" parents="20684 4149"/>
    </justification>
  </clause>

  <clause id="21194">
    <literal><![CDATA[
      ((K(x,y) * z) * (R(K(x,y) * z,u,w) \ (v5 * (x * y)))) * R(K(x,y) * z,u,w) = (v5 * (T(x,y) * y)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,21016,a,b,20814,a)].">
      <j1 rule="hyper" parents="63 21016 20814"/>
    </justification>
  </clause>

  <clause id="21195">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,L(z,z,u) * u) = w
    ]]></literal>
    <justification jstring="[para(20126(a,1),20895(a,1))].">
      <j1 rule="para" parents="20126 20895"/>
    </justification>
  </clause>

  <clause id="21196">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,L(T(x,x \ 1),y,z) \ (x \ 1),L(T(x,x \ 1),y,z)) = ((x \ 1) \ 1) \ (L(T(x,x \ 1),y,z) * u)
    ]]></literal>
    <justification jstring="[para(20912(a,1),3252(a,1,1,1))].">
      <j1 rule="para" parents="20912 3252"/>
    </justification>
  </clause>

  <clause id="21197">
    <literal><![CDATA[
      (x * (y * (x \ L(x,z,u)))) * a(L(y,x,x \ L(x,z,u)),x \ L(x,z,u),x) = (x \ L(x,z,u)) * (x * R(y,x \ L(x,z,u),x))
    ]]></literal>
    <justification jstring="[para(20952(a,1),14570(a,1,1))].">
      <j1 rule="para" parents="20952 14570"/>
    </justification>
  </clause>

  <clause id="21198">
    <literal><![CDATA[
      L(((x \ y) \ y) \ (x \ L(x,z,u)),x,x \ y) = y \ (y * L(y \ (x \ y),z,u))
    ]]></literal>
    <justification jstring="[para(20955(a,1),10212(a,2,2))].">
      <j1 rule="para" parents="20955 10212"/>
    </justification>
  </clause>

  <clause id="21199">
    <literal><![CDATA[
      (x / y) \ L(x / y,z,u) = (y \ x) \ L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,3354,a,b,20956,a),flip(a)].">
      <j1 rule="hyper" parents="347 3354 20956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21200">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) * (y / x) = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,20956,a(flip),b,3161,a)].">
      <j1 rule="hyper" parents="133 20956 3161"/>
    </justification>
  </clause>

  <clause id="21201">
    <literal><![CDATA[
      ((x \ y) * (K(z,x) * u)) \ ((x \ y) * K(z,x)) = ((x \ (K(z,x) * y)) * u) \ (T(x,z) \ y)
    ]]></literal>
    <justification jstring="[para(20967(a,1),15352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20967 15352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21202">
    <literal><![CDATA[
      T(x * a(y,z,u),w / x) != v5
    ]]></literal>
    <literal><![CDATA[
      T(a(y,z,u) * x,w / T(x,v6)) = v5
    ]]></literal>
    <justification jstring="[para(20974(a,1),13631(a,1))].">
      <j1 rule="para" parents="20974 13631"/>
    </justification>
  </clause>

  <clause id="21203">
    <literal><![CDATA[
      T(x * x,y) * (y \ L(T(y,x * x),z,u)) = x * (R(x,x,y \ L(y,z,u)) * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,1750,a,b,20980,a),flip(a)].">
      <j1 rule="hyper" parents="347 1750 20980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21204">
    <literal><![CDATA[
      L(x,y,z) * (u * (x \ 1)) = x * (u * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,21005,a(flip),b,1402,a),flip(a)].">
      <j1 rule="hyper" parents="134 21005 1402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21205">
    <literal><![CDATA[
      K(x,T(y,z * u)) * (z \ w) = (K(y,T(x,u)) * z) \ w
    ]]></literal>
    <justification jstring="[para(21111(a,1),21019(a,1,1))].">
      <j1 rule="para" parents="21111 21019"/>
    </justification>
  </clause>

  <clause id="21206">
    <literal><![CDATA[
      K(x,y) * (((z \ K(x,y)) * u) \ w) = ((z \ 1) * T(u,K(x,y))) \ w
    ]]></literal>
    <justification jstring="[para(21042(a,1),20837(a,1,1)),flip(a)].">
      <j1 rule="para" parents="21042 20837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21207">
    <literal><![CDATA[
      (T(x,y) \ 1) * (L(T(x,y) \ 1,z,u) \ w) = x * (L(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3439,a,b,21096,a)].">
      <j1 rule="hyper" parents="63 3439 21096"/>
    </justification>
  </clause>

  <clause id="21208">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * L(T(x,w),y,z) = u * T(x,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,21096,a(flip),b,20673,a)].">
      <j1 rule="hyper" parents="133 21096 20673"/>
    </justification>
  </clause>

  <clause id="21210">
    <literal><![CDATA[
      T(x,y) * R(L(T(y,z),u,w),T(x,y),L(T(y,z),u,w)) = T(K(y,z) * (x * L(y,u,w)),L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(21102(a,1),4378(a,2,1))].">
      <j1 rule="para" parents="21102 4378"/>
    </justification>
  </clause>

  <clause id="21211">
    <literal><![CDATA[
      K(x,y) * ((x \ (1 / x)) * R(x,z,u)) = R(T(x,y),z,u) * (x \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(887(a,1),21116(a,1,2)),flip(a)].">
      <j1 rule="para" parents="887 21116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21212">
    <literal><![CDATA[
      T(x,y) * (R(T(x,y),z,x) \ u) = a(x,z,x) \ u
    ]]></literal>
    <justification jstring="[hyper(347,a,10991,a(flip),b,21117,a),flip(a)].">
      <j1 rule="hyper" parents="347 10991 21117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21213">
    <literal><![CDATA[
      T(x,y) * (R(T(x,y),x \ z,u) \ (z * T(u,w))) = x * ((x \ z) * T(u,w))
    ]]></literal>
    <justification jstring="[para(20516(a,1),21117(a,2,2))].">
      <j1 rule="para" parents="20516 21117"/>
    </justification>
  </clause>

  <clause id="21214">
    <literal><![CDATA[
      R(T(x,y),z,x) \ (u * T(x,y)) = T(a(x,z,x) \ u,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(269,a,11374,a(flip),b,21212,a),flip(a)].">
      <j1 rule="hyper" parents="269 11374 21212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21216">
    <literal><![CDATA[
      R(x,(K(y,z) * u) * (w * (v5 \ K(z,y))),v6) = R(x,(w * (v5 \ 1)) * u,v6)
    ]]></literal>
    <justification jstring="[para(21139(a,1),20553(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21139 20553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21217">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ ((x * y) * z) = K(u,z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(14(a,2),21142(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14 21142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21218">
    <literal><![CDATA[
      a(x,y,L((z * (u * T(w,v5))) \ 1,v6,v7)) = a(x,y,L(K(v5,w) * (z * (u * w)),v6,v7))
    ]]></literal>
    <justification jstring="[para(21142(a,1),15030(a,1,3,1))].">
      <j1 rule="para" parents="21142 15030"/>
    </justification>
  </clause>

  <clause id="21219">
    <literal><![CDATA[
      T(x * y,K(x,z)) \ y = (y * x) \ T(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,21036,a(flip),b,21143,a),flip(a)].">
      <j1 rule="hyper" parents="63 21036 21143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21220">
    <literal><![CDATA[
      R(x,y,L(z,z,u) * u) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(21195,a,2241,a)].">
      <j1 rule="hyper" parents="21195 2241"/>
    </justification>
  </clause>

  <clause id="21221">
    <literal><![CDATA[
      R(x,y,z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,L(z,z,u) * u) = w
    ]]></literal>
    <justification jstring="[para(2241(a,1),21195(a,1))].">
      <j1 rule="para" parents="2241 21195"/>
    </justification>
  </clause>

  <clause id="21222">
    <literal><![CDATA[
      ((x \ y) \ y) \ L((x \ y) \ y,z,u) = x \ L(y / (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(646,a,21199,a),flip(a)].">
      <j1 rule="hyper" parents="646 21199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21223">
    <literal><![CDATA[
      (L(x \ y,z,u) \ (x \ y)) \ 1 = (y / x) \ L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,10888,a,b,21199,a)].">
      <j1 rule="hyper" parents="347 10888 21199"/>
    </justification>
  </clause>

  <clause id="21224">
    <literal><![CDATA[
      ((x \ y) \ L(x \ y,z,u)) * (y / x) = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(38,a,20262,a,b,21199,a)].">
      <j1 rule="hyper" parents="38 20262 21199"/>
    </justification>
  </clause>

  <clause id="21225">
    <literal><![CDATA[
      (x / y) \ L(x / y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      y \ (x * L(x \ y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(21199(a,2),3365(a,1))].">
      <j1 rule="para" parents="21199 3365"/>
    </justification>
  </clause>

  <clause id="21226">
    <literal><![CDATA[
      L(x / L(x,y,z),u,L(x,w,v5)) = (L(x,y,z) \ (x * (x \ L(x,y,z)))) * (x / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(12283(a,1),21200(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12283 21200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21227">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * z)) * ((z \ u) \ w) = (z \ (K(y,x) * u)) \ w
    ]]></literal>
    <justification jstring="[para(19540(a,1),21205(a,2,1))].">
      <j1 rule="para" parents="19540 21205"/>
    </justification>
  </clause>

  <clause id="21228">
    <literal><![CDATA[
      (L(x,y,z) \ u) * L(T(x,w),y,z) = (x \ u) * T(x,w)
    ]]></literal>
    <justification jstring="[para(1408(a,1),21208(a,1,1))].">
      <j1 rule="para" parents="1408 21208"/>
    </justification>
  </clause>

  <clause id="21229">
    <literal><![CDATA[
      (x \ 1) \ (x * (((x * x) \ y) * a(z,u,w))) = L(a(z,u,w),(x * x) \ y,x * x) * y
    ]]></literal>
    <justification jstring="[hyper(347,a,494,a,b,20029,a)].">
      <j1 rule="hyper" parents="347 494 20029"/>
    </justification>
  </clause>

  <clause id="21230">
    <literal><![CDATA[
      (((a(x,y,z) \ u) \ w) * (u / a(x,y,z))) \ (((a(x,y,z) \ u) \ w) * u) = ((w / (a(x,y,z) \ u)) * ((a(x,y,z) \ u) * a(x,y,z))) / w
    ]]></literal>
    <justification jstring="[hyper(347,a,9645,a(flip),b,20030,a)].">
      <j1 rule="hyper" parents="347 9645 20030"/>
    </justification>
  </clause>

  <clause id="21231">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * K(u,w)) = x * ((y * z) * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,20033,a(flip),b,20137,a),flip(a)].">
      <j1 rule="hyper" parents="347 20033 20137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21233">
    <literal><![CDATA[
      K(x,y) * (z \ (K(y,x) * u)) = T(z,K(y,x)) \ u
    ]]></literal>
    <justification jstring="[hyper(20489,a,20166,a),flip(a)].">
      <j1 rule="hyper" parents="20489 20166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21234">
    <literal><![CDATA[
      T(K(x,y) * (z / (u * K(x,y))),u * K(x,y)) = T(u,K(x,y)) \ z
    ]]></literal>
    <justification jstring="[hyper(20489,a,20107,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="20489 20107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21235">
    <literal><![CDATA[
      K(x,y) * (z \ (T(y,x) * u)) = T(z,K(y,x)) \ (y * u)
    ]]></literal>
    <justification jstring="[para(4974(a,1),21233(a,1,2,2))].">
      <j1 rule="para" parents="4974 21233"/>
    </justification>
  </clause>

  <clause id="21236">
    <literal><![CDATA[
      L((T(x,y) \ z) \ u,x \ z,x) = z \ (T(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,17363,a(flip),b,20520,a)].">
      <j1 rule="hyper" parents="63 17363 20520"/>
    </justification>
  </clause>

  <clause id="21238">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ u,x \ R(T(x,w),y,z),x) = R(T(x,w),y,z) \ (T(x,w) * u)
    ]]></literal>
    <justification jstring="[para(19968(a,1),21236(a,1,1,1))].">
      <j1 rule="para" parents="19968 21236"/>
    </justification>
  </clause>

  <clause id="21239">
    <literal><![CDATA[
      x * (L(T(x,y),z,u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(x,y),z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(21104(a,1),21098(a,1))].">
      <j1 rule="para" parents="21104 21098"/>
    </justification>
  </clause>

  <clause id="21240">
    <literal><![CDATA[
      L(a(x,y,z),u,u) \ (u \ 1) = u / (u * (u * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,20482,a(flip),b,21159,a)].">
      <j1 rule="hyper" parents="63 20482 21159"/>
    </justification>
  </clause>

  <clause id="21241">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * z) * y) = K(z,y) * a(x,z,y)
    ]]></literal>
    <justification jstring="[para(111(a,1),21217(a,1,1,2))].">
      <j1 rule="para" parents="111 21217"/>
    </justification>
  </clause>

  <clause id="21242">
    <literal><![CDATA[
      K(x \ y,z) * a(x,x \ y,z) = (x * (z * (x \ y))) \ (y * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),21241(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 21241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21243">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * K(u,w)) = x * (y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(20033(a,1),21231(a,2,2))].">
      <j1 rule="para" parents="20033 21231"/>
    </justification>
  </clause>

  <clause id="21244">
    <literal><![CDATA[
      x * (L(x,y,z) \ K(u,x)) = L(T(x,u),y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(21239,a,21185,a),flip(a)].">
      <j1 rule="hyper" parents="21239 21185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21245">
    <literal><![CDATA[
      (x / y) * (L(x / y,z,u) \ K(y,y \ x)) = L(T(x / y,y),z,u) \ (x / y)
    ]]></literal>
    <justification jstring="[para(5098(a,1),21244(a,1,2,2))].">
      <j1 rule="para" parents="5098 21244"/>
    </justification>
  </clause>

  <clause id="21246">
    <literal><![CDATA[
      L(a(x,y,z),u,u) \ (u \ 1) = u / (u * (a(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(19985(a,2),21240(a,2,2,2))].">
      <j1 rule="para" parents="19985 21240"/>
    </justification>
  </clause>

  <clause id="21247">
    <literal><![CDATA[
      L(x * K(y,z),u,w) = L(x,u,w) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(544,a,21243,a)].">
      <j1 rule="hyper" parents="544 21243"/>
    </justification>
  </clause>

  <clause id="21249">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) \ T(x * u,w) = L(T(x,u) * K(x * u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(13293,a,21247,a(flip))].">
      <j1 rule="hyper" parents="13293 21247"/>
    </justification>
  </clause>

  <clause id="21250">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) = K(x,y) * L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(35,a,3376,a(flip),b,21247,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 3376 21247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21255">
    <literal><![CDATA[
      1 / L((x \ K(y,z)) * K(z,y),u,w) = L(K(y,z) / x,u,w) \ K(y,z)
    ]]></literal>
    <justification jstring="[para(21247(a,2),13147(a,1,2))].">
      <j1 rule="para" parents="21247 13147"/>
    </justification>
  </clause>

  <clause id="21256">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * (y * K(w,v5)) = y * L(x * K(w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(21247(a,2),19492(a,2,2))].">
      <j1 rule="para" parents="21247 19492"/>
    </justification>
  </clause>

  <clause id="21258">
    <literal><![CDATA[
      x \ L(y * K(z,u),w,v5) = (x \ L(y,w,v5)) * K(z,u)
    ]]></literal>
    <justification jstring="[para(21247(a,2),20109(a,1,2))].">
      <j1 rule="para" parents="21247 20109"/>
    </justification>
  </clause>

  <clause id="21259">
    <literal><![CDATA[
      L(x * K(y,z),u,w) * v5 = L(x,u,w) * (K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(21247(a,2),20151(a,1,1))].">
      <j1 rule="para" parents="21247 20151"/>
    </justification>
  </clause>

  <clause id="21260">
    <literal><![CDATA[
      L(x * K(y,z),u,w) \ v5 = K(z,y) * (L(x,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(21247(a,2),20166(a,1,1))].">
      <j1 rule="para" parents="21247 20166"/>
    </justification>
  </clause>

  <clause id="21261">
    <literal><![CDATA[
      L(K(x,T(y,z)) * (1 / u),u,z) = z \ (K(x,y) * (z / u))
    ]]></literal>
    <justification jstring="[hyper(347,a,19546,a(flip),b,21250,a),flip(a)].">
      <j1 rule="hyper" parents="347 19546 21250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21262">
    <literal><![CDATA[
      L(K(x \ y,x) * z,z,x \ y) = (y / x) \ ((x \ y) / (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(347,a,5606,a(flip),b,21250,a),flip(a)].">
      <j1 rule="hyper" parents="347 5606 21250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21264">
    <literal><![CDATA[
      x * L(K(x,y) * z,u,w) = T(x,y) * L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(134,a,21250,a,b,5157,a)].">
      <j1 rule="hyper" parents="134 21250 5157"/>
    </justification>
  </clause>

  <clause id="21265">
    <literal><![CDATA[
      L(K(x,y) * (1 / z),z,y) = T(y,x) \ (y / z)
    ]]></literal>
    <justification jstring="[hyper(5521,a,21250,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="5521 21250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21266">
    <literal><![CDATA[
      L(L(K(x,y) * ((x \ 1) \ ((x \ 1) \ z)),u,w),x,x) = T(x,y) * ((x \ 1) \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(21250(a,2),5876(a,1,1))].">
      <j1 rule="para" parents="21250 5876"/>
    </justification>
  </clause>

  <clause id="21268">
    <literal><![CDATA[
      L(K(x,y) * (T(z,u) \ w),z,u) = K(x,y) * ((z * u) \ (u * w))
    ]]></literal>
    <justification jstring="[para(10169(a,1),21250(a,2,2))].">
      <j1 rule="para" parents="10169 21250"/>
    </justification>
  </clause>

  <clause id="21270">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) \ v5 = L(z,u,w) \ (K(y,x) * v5)
    ]]></literal>
    <justification jstring="[para(21250(a,2),20003(a,1,1))].">
      <j1 rule="para" parents="21250 20003"/>
    </justification>
  </clause>

  <clause id="21271">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) * v5 = K(x,y) * (L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(21250(a,2),20008(a,1,1))].">
      <j1 rule="para" parents="21250 20008"/>
    </justification>
  </clause>

  <clause id="21272">
    <literal><![CDATA[
      (x / y) * L(K(z,y) * u,w,v5) = (x / T(y,z)) * L(u,w,v5)
    ]]></literal>
    <justification jstring="[para(21250(a,2),20809(a,1,2))].">
      <j1 rule="para" parents="21250 20809"/>
    </justification>
  </clause>

  <clause id="21273">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) \ v5 != v6
    ]]></literal>
    <literal><![CDATA[
      L(z,u,w) \ (K(y,x) * v5) = v6
    ]]></literal>
    <justification jstring="[para(21250(a,2),20101(a,1,1))].">
      <j1 rule="para" parents="21250 20101"/>
    </justification>
  </clause>

  <clause id="21274">
    <literal><![CDATA[
      L(K(x,y) / z,z,y) = T(y,x) \ (y / z)
    ]]></literal>
    <justification jstring="[para(12988(a,1),21265(a,1,1))].">
      <j1 rule="para" parents="12988 21265"/>
    </justification>
  </clause>

  <clause id="21275">
    <literal><![CDATA[
      T(x,y) * L(x \ 1,z,u) = x * L(x \ K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4521(a,1),21264(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4521 21264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21276">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ z,u,w) = x * L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(5159(a,1),21264(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5159 21264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21277">
    <literal><![CDATA[
      L(x \ y,z,u) * (K(x,x \ y) * w) = L(y / x,z,u) * w
    ]]></literal>
    <justification jstring="[para(4990(a,1),21259(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4990 21259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21279">
    <literal><![CDATA[
      K(x \ y,x) * (L(x \ y,z,u) \ w) = L(y / x,z,u) \ w
    ]]></literal>
    <justification jstring="[para(4990(a,1),21260(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4990 21260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21280">
    <literal><![CDATA[
      (x / (K(y,z) * u)) * L(K(y,z) * u,w,v5) = K(y,z) * (L(u,w,v5) * ((K(y,z) * u) \ x))
    ]]></literal>
    <justification jstring="[hyper(21010,a,21271,a)].">
      <j1 rule="hyper" parents="21010 21271"/>
    </justification>
  </clause>

  <clause id="21281">
    <literal><![CDATA[
      K(x,y) * (L(y * x,z,u) * w) = L(x * y,z,u) * w
    ]]></literal>
    <justification jstring="[para(4909(a,1),21271(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4909 21271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21282">
    <literal><![CDATA[
      T(x,y) * L(x \ 1,z,u) = x \ L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,4988,a(flip),b,21275,a),flip(a)].">
      <j1 rule="hyper" parents="347 4988 21275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21285">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),w) = x * L(x \ T(y,w),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2132,a(flip),b,21276,a)].">
      <j1 rule="hyper" parents="63 2132 21276"/>
    </justification>
  </clause>

  <clause id="21286">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (y * z),u,w) = y * (x * L(x \ z,u,w))
    ]]></literal>
    <justification jstring="[para(21276(a,1),1634(a,2,2))].">
      <j1 rule="para" parents="21276 1634"/>
    </justification>
  </clause>

  <clause id="21287">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * T(w,y) = x * (w * L(w \ (x \ (w * y)),z,u))
    ]]></literal>
    <justification jstring="[para(21276(a,1),2064(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21276 2064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21288">
    <literal><![CDATA[
      (x \ y) * L(T(y / x,T(x,y)) \ z,u,w) = (y / x) * L((y / x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(4173(a,1),21276(a,1,1))].">
      <j1 rule="para" parents="4173 21276"/>
    </justification>
  </clause>

  <clause id="21290">
    <literal><![CDATA[
      K(x,y) * (L(y * x,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x * y,z,u) * w = v5
    ]]></literal>
    <justification jstring="[para(21281(a,1),5274(a,1,2)),flip(b)].">
      <j1 rule="para" parents="21281 5274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21293">
    <literal><![CDATA[
      L(K(x,T(y,z)) / u,u,z) = z \ (K(x,y) * (z / u))
    ]]></literal>
    <justification jstring="[para(12988(a,1),21261(a,1,1))].">
      <j1 rule="para" parents="12988 21261"/>
    </justification>
  </clause>

  <clause id="21294">
    <literal><![CDATA[
      R(x,K(y,T(z,u)) / w,L(K(y,T(z,u)) / w,w,u)) = R(x,u \ (K(y,z) * (u / w)),K(y,T(z,u)) / w)
    ]]></literal>
    <justification jstring="[para(21293(a,1),2044(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21293 2044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21295">
    <literal><![CDATA[
      L(x,(K(y,T(z,u)) / w) * L(K(y,T(z,u)) / w,w,u),v5) = L(x,(K(y,T(z,u)) / w) \ (u \ (K(y,z) * (u / w))),v5)
    ]]></literal>
    <justification jstring="[para(21293(a,1),3603(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="21293 3603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21296">
    <literal><![CDATA[
      L(x \ y,x,a(z,u,w)) = (x * a(z,u,w)) \ (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,20020,a(flip),b,20025,a),flip(a)].">
      <j1 rule="hyper" parents="347 20020 20025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21297">
    <literal><![CDATA[
      L(x \ y,x,a(y,z,z)) = (x * a(y,z,z)) \ R(y,z,z)
    ]]></literal>
    <justification jstring="[para(13403(a,1),20025(a,2,2))].">
      <j1 rule="para" parents="13403 20025"/>
    </justification>
  </clause>

  <clause id="21298">
    <literal><![CDATA[
      (((x * y) / x) * a(z,u,w)) * x = (y * a(z,u,w)) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(20022,a,20607,a),flip(a)].">
      <j1 rule="hyper" parents="20022 20607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21299">
    <literal><![CDATA[
      (a(x,y,z) * (u \ 1)) * T(w,u \ 1) = ((u \ K(w,u \ 1)) * a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[para(4979(a,2),20607(a,2,1,1))].">
      <j1 rule="para" parents="4979 20607"/>
    </justification>
  </clause>

  <clause id="21300">
    <literal><![CDATA[
      x * ((R(x,y,x) \ z) * K(u,w)) = z * (a(x,y,x) \ K(u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,11883,a(flip),b,20762,a),flip(a)].">
      <j1 rule="hyper" parents="347 11883 20762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21301">
    <literal><![CDATA[
      T(x \ (y * L(y \ x,z,u)),w) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(3354(a,1),20843(a,1,1))].">
      <j1 rule="para" parents="3354 20843"/>
    </justification>
  </clause>

  <clause id="21302">
    <literal><![CDATA[
      R(x,(y \ z) * (z * y),u) = R(x,a(z,y,y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(20906,a,20553,a),flip(a)].">
      <j1 rule="hyper" parents="20906 20553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21303">
    <literal><![CDATA[
      T(L(x / y,z,u) \ x,x / y) = L(y \ x,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(7809,a,20911,a)].">
      <j1 rule="hyper" parents="7809 20911"/>
    </justification>
  </clause>

  <clause id="21304">
    <literal><![CDATA[
      L(x / y,z,u) \ (x * K(y,y \ x)) = L(y \ x,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,11309,a,b,21303,a)].">
      <j1 rule="hyper" parents="63 11309 21303"/>
    </justification>
  </clause>

  <clause id="21305">
    <literal><![CDATA[
      a(x,y,z) / (u * a(x,y,z)) = a(x,y,z) \ (a(x,y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(20221,a,20986,a)].">
      <j1 rule="hyper" parents="20221 20986"/>
    </justification>
  </clause>

  <clause id="21306">
    <literal><![CDATA[
      T(x,L(T(y,z),u,w) * (z \ v5)) = T(x,z \ (L(y,u,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,20878,a(flip),b,20987,a)].">
      <j1 rule="hyper" parents="63 20878 20987"/>
    </justification>
  </clause>

  <clause id="21307">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * ((L(T(x \ y,x),z,u) * ((x \ y) \ y)) / L(T(x \ y,x),z,u)) = (L(T(x \ y,x),z,u) * ((x \ y) \ y)) * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(21003(a,1),4468(a,1,1))].">
      <j1 rule="para" parents="21003 4468"/>
    </justification>
  </clause>

  <clause id="21308">
    <literal><![CDATA[
      x \ (y * T(z,T(x \ y,z))) = z * ((x \ (y * z)) / z)
    ]]></literal>
    <justification jstring="[para(21176(a,1),21030(a,1,2,2))].">
      <j1 rule="para" parents="21176 21030"/>
    </justification>
  </clause>

  <clause id="21309">
    <literal><![CDATA[
      x \ (y * T(z,x \ y)) = z * ((x \ (y * z)) / z)
    ]]></literal>
    <justification jstring="[para(4270(a,1),21308(a,1,2,2))].">
      <j1 rule="para" parents="4270 21308"/>
    </justification>
  </clause>

  <clause id="21310">
    <literal><![CDATA[
      T(x,T(y \ (z * u),u)) = T(x,y \ (z * T(u,y \ z)))
    ]]></literal>
    <justification jstring="[para(21309(a,2),10339(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21309 10339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21311">
    <literal><![CDATA[
      T(x,y \ (z * T(u,y \ z))) = T(x,u / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(21092,a,21310,a),flip(a)].">
      <j1 rule="hyper" parents="21092 21310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21312">
    <literal><![CDATA[
      T(x,y \ (z * (u * T(w,(z \ y) \ u)))) = T(x,w / (u \ (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(20636,a,21311,a)].">
      <j1 rule="hyper" parents="20636 21311"/>
    </justification>
  </clause>

  <clause id="21313">
    <literal><![CDATA[
      x * (L(L(x,y,z),u,w) \ v5) != v6 * v7
    ]]></literal>
    <literal><![CDATA[
      v6 \ ((v5 / L(L(x,y,z),u,w)) * x) = v7
    ]]></literal>
    <justification jstring="[para(21067(a,1),613(a,1))].">
      <j1 rule="para" parents="21067 613"/>
    </justification>
  </clause>

  <clause id="21314">
    <literal><![CDATA[
      L(T(x,T(y,(z / x) * L(x,u,w))),u,w) * (x \ z) = ((z / x) * L(x,u,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7442,a,21103,a),flip(a)].">
      <j1 rule="hyper" parents="7442 21103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21315">
    <literal><![CDATA[
      K(T(x,y),z * (y \ L(y,u,w))) = K(x,L(y,u,w) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(347,a,16991,a(flip),b,21125,a),flip(a)].">
      <j1 rule="hyper" parents="347 16991 21125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21316">
    <literal><![CDATA[
      K(x,y) * (z * (K(y,x) * u)) = T(z,K(x,y)) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,20909,a(flip),b,21129,a),flip(a)].">
      <j1 rule="hyper" parents="63 20909 21129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21317">
    <literal><![CDATA[
      K(x,y) * (T(z,K(y,x)) * u) = z * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5273,a,21316,a)].">
      <j1 rule="hyper" parents="5273 21316"/>
    </justification>
  </clause>

  <clause id="21318">
    <literal><![CDATA[
      T(x,K(y,z)) * (K(y,z) * u) = K(y,z) * (x * u)
    ]]></literal>
    <justification jstring="[para(5261(a,1),21316(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5261 21316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21320">
    <literal><![CDATA[
      K(x,y) * (z * (K(y,x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) * u = w
    ]]></literal>
    <justification jstring="[para(21317(a,1),5274(a,1,2)),flip(b)].">
      <j1 rule="para" parents="21317 5274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21321">
    <literal><![CDATA[
      K(x,y) * (T(z,K(x,y)) * u) = z * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(7330(a,1),21317(a,1,2,1))].">
      <j1 rule="para" parents="7330 21317"/>
    </justification>
  </clause>

  <clause id="21322">
    <literal><![CDATA[
      T(x,K(y,z)) * (K(z,y) * u) = K(z,y) * (x * u)
    ]]></literal>
    <justification jstring="[para(7334(a,1),21317(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7334 21317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21323">
    <literal><![CDATA[
      (K(x,y) * (z * u)) \ (T(z,K(x,y)) * w) = (z * (K(x,y) * u)) \ (z * w)
    ]]></literal>
    <justification jstring="[para(21318(a,1),21021(a,1,1))].">
      <j1 rule="para" parents="21318 21021"/>
    </justification>
  </clause>

  <clause id="21324">
    <literal><![CDATA[
      K(x,y) * ((T(z,K(x,y)) * u) * w) = (z * (K(x,y) * u)) * w
    ]]></literal>
    <justification jstring="[para(21321(a,1),20008(a,1,1)),flip(a)].">
      <j1 rule="para" parents="21321 20008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21325">
    <literal><![CDATA[
      ((K(x,y) * (z * u)) * w) / (L(u,K(x,y),T(z,K(y,x))) * w) = R(K(x,y) * z,L(u,K(x,y),T(z,K(y,x))),w)
    ]]></literal>
    <justification jstring="[para(21322(a,1),6891(a,1,1,1))].">
      <j1 rule="para" parents="21322 6891"/>
    </justification>
  </clause>

  <clause id="21326">
    <literal><![CDATA[
      K(x,y) * (z * L(K(y,x) * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) * L(u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(21250(a,2),21320(a,1,2,2))].">
      <j1 rule="para" parents="21250 21320"/>
    </justification>
  </clause>

  <clause id="21327">
    <literal><![CDATA[
      R(x,(y * (z * u)) * (K(w,v5) * v6),v7) = R(x,v6 * (y * (z * (u * K(w,v5)))),v7)
    ]]></literal>
    <justification jstring="[para(21140(a,1),20553(a,1,2))].">
      <j1 rule="para" parents="21140 20553"/>
    </justification>
  </clause>

  <clause id="21328">
    <literal><![CDATA[
      (K(x,y) * ((z * ((z \ (u \ 1)) * u)) \ K(u \ 1,u))) * K(y,x) = a(z,z \ (u \ 1),u * K(y,x))
    ]]></literal>
    <justification jstring="[para(21144(a,1),18222(a,1,1))].">
      <j1 rule="para" parents="21144 18222"/>
    </justification>
  </clause>

  <clause id="21329">
    <literal><![CDATA[
      (a(x,y,z) * u) * a(w,v5,u) = u * (a(w,v5,u) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,12360,a(flip),b,21148,a)].">
      <j1 rule="hyper" parents="134 12360 21148"/>
    </justification>
  </clause>

  <clause id="21330">
    <literal><![CDATA[
      L(x / y,z,u) \ K(y,y \ x) = L(y \ x,z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(13077,a,21183,a)].">
      <j1 rule="hyper" parents="13077 21183"/>
    </justification>
  </clause>

  <clause id="21331">
    <literal><![CDATA[
      L(x / y,z,u) \ (x / y) = L(y \ x,z,u) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(39,a,10888,a,b,21223,a)].">
      <j1 rule="hyper" parents="39 10888 21223"/>
    </justification>
  </clause>

  <clause id="21332">
    <literal><![CDATA[
      L((x * x) \ y,z,u) \ ((x * x) \ y) = L(y,z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(3868,a,21331,a),flip(a)].">
      <j1 rule="hyper" parents="3868 21331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21333">
    <literal><![CDATA[
      ((x / y) \ 1) * (L(y \ x,z,u) \ (y \ x)) = L(x / y,z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(134,a,21331,a(flip),b,10873,a)].">
      <j1 rule="hyper" parents="134 21331 10873"/>
    </justification>
  </clause>

  <clause id="21334">
    <literal><![CDATA[
      L((x * K(y,z)) \ z,u,w) \ ((x * K(y,z)) \ z) = L(T(z,y) / x,u,w) \ (z / (x * K(y,z)))
    ]]></literal>
    <justification jstring="[para(13098(a,1),21331(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13098 21331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21337">
    <literal><![CDATA[
      (x / T(y,z)) * L((u / T(y,z)) \ w,v5,v6) = (x / y) * L((u / y) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(20827(a,1),21272(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20827 21272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21338">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * u) = x * (L(1 / x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(21277(a,1),3548(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21277 3548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21339">
    <literal><![CDATA[
      L(x / y,z,u) * ((x / y) \ w) = L(y \ x,z,u) * ((y \ x) \ w)
    ]]></literal>
    <justification jstring="[para(5603(a,1),21277(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5603 21277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21340">
    <literal><![CDATA[
      (x / y) * (L(x / y,z,u) \ w) = (y \ x) * (L(y \ x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(21279(a,1),5451(a,1,2))].">
      <j1 rule="para" parents="21279 5451"/>
    </justification>
  </clause>

  <clause id="21341">
    <literal><![CDATA[
      K(x \ 1,x) * (L(x,y,z) \ x) = L(1 / x,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(10875(a,1),21279(a,1,2))].">
      <j1 rule="para" parents="10875 21279"/>
    </justification>
  </clause>

  <clause id="21342">
    <literal><![CDATA[
      T(x * a(y,z,u),L(x \ w,x,a(y,z,u))) = T(x * a(y,z,u),w / x)
    ]]></literal>
    <justification jstring="[para(21296(a,2),14329(a,1,2))].">
      <j1 rule="para" parents="21296 14329"/>
    </justification>
  </clause>

  <clause id="21343">
    <literal><![CDATA[
      x * (a(y,y * x,y) \ K(y,z)) = (y * ((y \ x) * T(y,z))) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,15063,a(flip),b,21300,a),flip(a)].">
      <j1 rule="hyper" parents="63 15063 21300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21344">
    <literal><![CDATA[
      x / (y \ (z * L(z \ y,u,w))) = (y \ (z * L(z \ y,u,w))) \ x
    ]]></literal>
    <justification jstring="[hyper(220,a,21301,a(flip),b,15397,a(flip))].">
      <j1 rule="hyper" parents="220 21301 15397"/>
    </justification>
  </clause>

  <clause id="21345">
    <literal><![CDATA[
      L(x / y,z,u) \ (y * (x / y)) = L(y \ x,z,u) \ x
    ]]></literal>
    <justification jstring="[para(5111(a,1),21304(a,1,2))].">
      <j1 rule="para" parents="5111 21304"/>
    </justification>
  </clause>

  <clause id="21346">
    <literal><![CDATA[
      L(x / T(y,z),y,z) \ (T(y,z) * (x / T(y,z))) = ((y * z) \ (z * x)) \ x
    ]]></literal>
    <justification jstring="[para(10169(a,1),21345(a,2,1))].">
      <j1 rule="para" parents="10169 21345"/>
    </justification>
  </clause>

  <clause id="21347">
    <literal><![CDATA[
      a(x,y,z) / ((a(x,y,z) \ u) * a(x,y,z)) = 1 / (1 / (u \ a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,3396,a(flip),b,21305,a),flip(a)].">
      <j1 rule="hyper" parents="347 3396 21305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21348">
    <literal><![CDATA[
      K(x,T(y * (z \ L(z,u,w)),z)) = K(x,L(z,u,w) * (y / z))
    ]]></literal>
    <justification jstring="[hyper(7488,a,21315,a)].">
      <j1 rule="hyper" parents="7488 21315"/>
    </justification>
  </clause>

  <clause id="21349">
    <literal><![CDATA[
      R(x,y,(K(z,u) * (((T(w,K(z,u)) * v5) * v6) \ 1)) \ v7) = R(x,y,((w * (K(z,u) * v5)) * v6) \ v7)
    ]]></literal>
    <justification jstring="[para(21324(a,1),2243(a,2,3,1))].">
      <j1 rule="para" parents="21324 2243"/>
    </justification>
  </clause>

  <clause id="21350">
    <literal><![CDATA[
      L(1 / x,y,z) \ (x \ 1) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,2909,a(flip),b,21341,a),flip(a)].">
      <j1 rule="hyper" parents="63 2909 21341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21351">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * (1 / x) = x * (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,4661,a(flip),b,21350,a),flip(a)].">
      <j1 rule="hyper" parents="63 4661 21350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21352">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (1 / x) = x * (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,9330,a(flip),b,21351,a)].">
      <j1 rule="hyper" parents="63 9330 21351"/>
    </justification>
  </clause>

  <clause id="21353">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ 1) * (x \ 1) = x * (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,13359,a,b,21352,a)].">
      <j1 rule="hyper" parents="63 13359 21352"/>
    </justification>
  </clause>

  <clause id="21354">
    <literal><![CDATA[
      L(x,y,z) != (u * L(L(w,y,z),v5,v6)) / T(u,L(w,y,z))
    ]]></literal>
    <literal><![CDATA[
      L(w,v5,v6) = x
    ]]></literal>
    <justification jstring="[para(19960(a,2),50(a,1)),flip(a)].">
      <j1 rule="para" parents="19960 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21356">
    <literal><![CDATA[
      T(x * L(y,z,u),K(y,w)) = L(y,z,u) * T(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(16952,a,19962,a)].">
      <j1 rule="hyper" parents="16952 19962"/>
    </justification>
  </clause>

  <clause id="21359">
    <literal><![CDATA[
      ((a(x,y,z) * u) \ u) \ u = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,20000,a(flip),b,20011,a),flip(a)].">
      <j1 rule="hyper" parents="63 20000 20011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21361">
    <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(347,a,10169,a(flip),b,20260,a),flip(a)].">
      <j1 rule="hyper" parents="347 10169 20260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21362">
    <literal><![CDATA[
      (x * (y * (y \ L(y,z,u)))) / (x * y) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,3965,a(flip),b,20260,a),flip(a)].">
      <j1 rule="hyper" parents="347 3965 20260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21363">
    <literal><![CDATA[
      x * R(y,y \ z,(y \ z) \ x) = z * ((y \ z) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(13045(a,1),20742(a,2,2))].">
      <j1 rule="para" parents="13045 20742"/>
    </justification>
  </clause>

  <clause id="21364">
    <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(20480,a,20920,a)].">
      <j1 rule="hyper" parents="20480 20920"/>
    </justification>
  </clause>

  <clause id="21365">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ L(u,a(x,y,z),a(x,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      u * a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(20920(a,1),356(a,1,2))].">
      <j1 rule="para" parents="20920 356"/>
    </justification>
  </clause>

  <clause id="21366">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),a(x,y,z)) = (a(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[para(19986(a,1),20920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19986 20920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21367">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ u != w * a(x,y,z)
    ]]></literal>
    <literal><![CDATA[
      L(w,a(x,y,z),a(x,y,z)) = u
    ]]></literal>
    <justification jstring="[para(20921(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="20921 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21368">
    <literal><![CDATA[
      a(x,x \ y,z) * K(x \ y,z) = (x * (z * (x \ y))) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(20479,a,21242,a)].">
      <j1 rule="hyper" parents="20479 21242"/>
    </justification>
  </clause>

  <clause id="21369">
    <literal><![CDATA[
      (x * (y * (x \ z))) \ (z * y) = (y * (x \ z)) \ (x \ (z * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,14740,a(flip),b,21242,a),flip(a)].">
      <j1 rule="hyper" parents="63 14740 21242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21370">
    <literal><![CDATA[
      L(x * K(x \ y,x),x,x \ y) = (y / x) \ ((x \ y) / (x \ 1))
    ]]></literal>
    <justification jstring="[para(3025(a,1),21262(a,1,1))].">
      <j1 rule="para" parents="3025 21262"/>
    </justification>
  </clause>

  <clause id="21371">
    <literal><![CDATA[
      x * (y \ L(T(y,z),y * x,y)) = (y * ((y \ x) * T(y,z))) / y
    ]]></literal>
    <justification jstring="[hyper(63,a,9990,a(flip),b,21343,a)].">
      <j1 rule="hyper" parents="63 9990 21343"/>
    </justification>
  </clause>

  <clause id="21372">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z),a(x,y,z)) = a(x,y,z) * L(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,523,a(flip),b,21364,a),flip(a)].">
      <j1 rule="hyper" parents="63 523 21364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21373">
    <literal><![CDATA[
      L(x * (a(y,z,u) \ 1),a(y,z,u),a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u)) * (a(y,z,u) \ 1) = w
    ]]></literal>
    <justification jstring="[para(21364(a,1),3213(a,1))].">
      <j1 rule="para" parents="21364 3213"/>
    </justification>
  </clause>

  <clause id="21374">
    <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(63,a,329,a(flip),b,21366,a),flip(a)].">
      <j1 rule="hyper" parents="63 329 21366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21375">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u)) != (a(y,z,u) \ 1) * w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) \ w = x
    ]]></literal>
    <justification jstring="[para(21366(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="21366 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21376">
    <literal><![CDATA[
      (x \ (y * z)) / (z * (x \ y)) = (x * (z * (x \ y))) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14753,a(flip),b,21368,a)].">
      <j1 rule="hyper" parents="63 14753 21368"/>
    </justification>
  </clause>

  <clause id="21377">
    <literal><![CDATA[
      (x \ (y * z)) / (z * (x \ y)) = (z * (x \ y)) \ (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,21369,a(flip),b,21376,a),flip(a)].">
      <j1 rule="hyper" parents="347 21369 21376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21378">
    <literal><![CDATA[
      ((x * (y \ z)) \ (y \ (z * x))) * (x * (y \ z)) = y \ (z * x)
    ]]></literal>
    <justification jstring="[hyper(133,a,21369,a(flip),b,21376,a)].">
      <j1 rule="hyper" parents="133 21369 21376"/>
    </justification>
  </clause>

  <clause id="21379">
    <literal><![CDATA[
      (x / y) \ ((y \ x) / (y \ 1)) = (x \ (y \ x)) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10224,a(flip),b,21370,a),flip(a)].">
      <j1 rule="hyper" parents="63 10224 21370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21381">
    <literal><![CDATA[
      x \ ((a(y,z,u) \ 1) \ ((x * (((a(y,z,u) * a(y,z,u)) * x) \ (x * w))) * a(y,z,u))) = (a(y,z,u) * a(y,z,u)) * L((a(y,z,u) * a(y,z,u)) \ w,x,a(y,z,u) * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(128,a,20600,a,b,10435,a)].">
      <j1 rule="hyper" parents="128 20600 10435"/>
    </justification>
  </clause>

  <clause id="21382">
    <literal><![CDATA[
      ((x / (y * y)) * (a(z,u,w) * v5)) \ (((a(z,u,w) * x) / (y * y)) * v5) = a(x / (y * y),a(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(464(a,2),20602(a,1,2,1))].">
      <j1 rule="para" parents="464 20602"/>
    </justification>
  </clause>

  <clause id="21383">
    <literal><![CDATA[
      R(x,y,(z * (u * u)) \ (w * v5)) = R(x,y,z \ (w * (v5 / (u * u))))
    ]]></literal>
    <justification jstring="[hyper(20539,a,20634,a)].">
      <j1 rule="hyper" parents="20539 20634"/>
    </justification>
  </clause>

  <clause id="21384">
    <literal><![CDATA[
      x * (L(x,y,z) \ (L(x,y,z) * L(x,y,z))) = (L(x,y,z) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(1434,a,20784,a)].">
      <j1 rule="hyper" parents="1434 20784"/>
    </justification>
  </clause>

  <clause id="21385">
    <literal><![CDATA[
      T(x,y \ (L((z / y) / y,u,w) \ v5)) = T(x,(L(z,u,w) / y) \ v5)
    ]]></literal>
    <justification jstring="[para(3339(a,1),20882(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3339 20882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21386">
    <literal><![CDATA[
      T(x * x,y) \ (L(z,u,w) \ z) = L(z,u,w) \ (z / T(x * x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,1107,a(flip),b,20948,a),flip(a)].">
      <j1 rule="hyper" parents="63 1107 20948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21387">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (u * L(x,y,z)) = R(u / (1 / x),x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,164,a(flip),b,20953,a)].">
      <j1 rule="hyper" parents="128 164 20953"/>
    </justification>
  </clause>

  <clause id="21388">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),y) = L(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,20959,a(flip),b,20992,a),flip(a)].">
      <j1 rule="hyper" parents="63 20959 20992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21389">
    <literal><![CDATA[
      (L(1 / x,y,z) \ u) * L(x,y,z) = ((1 / x) \ u) * x
    ]]></literal>
    <justification jstring="[hyper(628,a,21065,a)].">
      <j1 rule="hyper" parents="628 21065"/>
    </justification>
  </clause>

  <clause id="21391">
    <literal><![CDATA[
      (x * ((R(x,y,z) \ u) * K(w,v5))) * R(x,y,z) = u * (K(w,v5) * x)
    ]]></literal>
    <justification jstring="[para(20109(a,1),21070(a,1,1,2))].">
      <j1 rule="para" parents="20109 21070"/>
    </justification>
  </clause>

  <clause id="21392">
    <literal><![CDATA[
      ((x \ y) \ y) \ (L(T(x,x \ y),z,u) * w) = L(x,z,u) * (x \ w)
    ]]></literal>
    <justification jstring="[hyper(347,a,1402,a(flip),b,21099,a),flip(a)].">
      <j1 rule="hyper" parents="347 1402 21099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21393">
    <literal><![CDATA[
      ((x * y) * z) \ (y * (T(x,y) * z)) = (y * x) \ ((y * (x * z)) / z)
    ]]></literal>
    <justification jstring="[hyper(347,a,3980,a(flip),b,21128,a),flip(a)].">
      <j1 rule="hyper" parents="347 3980 21128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21394">
    <literal><![CDATA[
      L(x,y,(z * K(u,w)) \ (v5 * v6)) = L(x,y,z \ (v5 * (v6 * K(w,u))))
    ]]></literal>
    <justification jstring="[hyper(20491,a,21136,a)].">
      <j1 rule="hyper" parents="20491 21136"/>
    </justification>
  </clause>

  <clause id="21395">
    <literal><![CDATA[
      (x \ (y / z)) * ((y / z) \ u) = (x \ (z \ y)) * ((z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(113(a,1),21152(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 21152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21396">
    <literal><![CDATA[
      L(1 / x,x,y) * ((y / x) \ z) = (y \ (x \ y)) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(3271,a,21395,a)].">
      <j1 rule="hyper" parents="3271 21395"/>
    </justification>
  </clause>

  <clause id="21397">
    <literal><![CDATA[
      ((x \ K(x,y)) * z) \ (T(x,y) * u) = ((x \ 1) * z) \ (x * u)
    ]]></literal>
    <justification jstring="[para(5646(a,1),21155(a,1,1))].">
      <j1 rule="para" parents="5646 21155"/>
    </justification>
  </clause>

  <clause id="21398">
    <literal><![CDATA[
      ((x \ y) \ y) \ L((x \ y) \ y,z,u) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[para(80(a,1),21222(a,2,2,1))].">
      <j1 rule="para" parents="80 21222"/>
    </justification>
  </clause>

  <clause id="21399">
    <literal><![CDATA[
      ((x \ y) \ y) \ (x \ L(x,z,u)) = L(((x \ y) \ y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(128,a,21398,a(flip),b,3343,a)].">
      <j1 rule="hyper" parents="128 21398 3343"/>
    </justification>
  </clause>

  <clause id="21400">
    <literal><![CDATA[
      T(T(x,K(y,z)) / u,u * K(y,z)) = T(u,K(y,z)) \ x
    ]]></literal>
    <justification jstring="[para(21157(a,1),21234(a,1,1))].">
      <j1 rule="para" parents="21157 21234"/>
    </justification>
  </clause>

  <clause id="21401">
    <literal><![CDATA[
      T(x \ T(y,K(z,u)),K(z,u)) = T(x,K(z,u)) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,21059,a(flip),b,21400,a)].">
      <j1 rule="hyper" parents="63 21059 21400"/>
    </justification>
  </clause>

  <clause id="21402">
    <literal><![CDATA[
      T(x \ (y * z),K(z,y)) = T(x,K(z,y)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(4906(a,1),21401(a,1,1,2))].">
      <j1 rule="para" parents="4906 21401"/>
    </justification>
  </clause>

  <clause id="21403">
    <literal><![CDATA[
      L(x,y,z) * (K(u,x) * (u * K(w,v5))) = u * L(x * K(w,v5),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21259,a(flip),b,21256,a)].">
      <j1 rule="hyper" parents="63 21259 21256"/>
    </justification>
  </clause>

  <clause id="21404">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * w != (x * v5) * L((x * v5) \ (v5 * y),z,u)
    ]]></literal>
    <literal><![CDATA[
      T(v5,x * L(x \ y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(21286(a,2),270(a,2))].">
      <j1 rule="para" parents="21286 270"/>
    </justification>
  </clause>

  <clause id="21405">
    <literal><![CDATA[
      (x * x) \ (x * (y * L(y \ x,z,u))) = (y * x) \ L(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(21286(a,1),4058(a,1,2))].">
      <j1 rule="para" parents="21286 4058"/>
    </justification>
  </clause>

  <clause id="21407">
    <literal><![CDATA[
      T(x,y \ (z * (u * T(w,(y \ z) * u)))) = T(x,w / (u \ (z \ y)))
    ]]></literal>
    <justification jstring="[para(19338(a,1),21312(a,1,2,2,2,2))].">
      <j1 rule="para" parents="19338 21312"/>
    </justification>
  </clause>

  <clause id="21408">
    <literal><![CDATA[
      L(1 / x,y,z) * ((1 / x) \ u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,3438,a(flip),b,21339,a),flip(a)].">
      <j1 rule="hyper" parents="347 3438 21339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21409">
    <literal><![CDATA[
      L(1 / (x \ 1),x,y * x) * ((1 / (x \ 1)) \ z) = L(x,x,y) * (((x \ 1) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(4601(a,1),21339(a,2,1))].">
      <j1 rule="para" parents="4601 21339"/>
    </justification>
  </clause>

  <clause id="21410">
    <literal><![CDATA[
      L(1 / x,y,z) * (a(x,u,w) * x) = L(x,y,z) * (x \ a(x,u,w))
    ]]></literal>
    <justification jstring="[para(15261(a,1),21408(a,1,2))].">
      <j1 rule="para" parents="15261 21408"/>
    </justification>
  </clause>

  <clause id="21411">
    <literal><![CDATA[
      ((x \ y) * (L(x \ y,z,u) \ w)) / (y / x) = w / L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(131,a,21340,a(flip),b,20676,a)].">
      <j1 rule="hyper" parents="131 21340 20676"/>
    </justification>
  </clause>

  <clause id="21412">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,z,u) \ x) != w
    ]]></literal>
    <literal><![CDATA[
      L(y / x,z,u) \ y = w
    ]]></literal>
    <justification jstring="[para(21340(a,1),1433(a,1))].">
      <j1 rule="para" parents="21340 1433"/>
    </justification>
  </clause>

  <clause id="21413">
    <literal><![CDATA[
      (x \ ((y \ x) * L((y \ x) \ x,z,u))) \ w = w / (x \ (L(y,z,u) * (y \ x)))
    ]]></literal>
    <justification jstring="[para(742(a,1),21344(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="742 21344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21414">
    <literal><![CDATA[
      (x * L(y,z,u)) / (x * y) = x \ ((x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),21362(a,1,1,2))].">
      <j1 rule="para" parents="10 21362"/>
    </justification>
  </clause>

  <clause id="21415">
    <literal><![CDATA[
      ((x * y) * L(z,y,x)) / ((x * y) * z) = ((x * y) * z) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,3967,a(flip),b,21414,a),flip(a)].">
      <j1 rule="hyper" parents="347 3967 21414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21417">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      (a(x,y,z) \ u) * (a(x,y,z) \ 1) = w
    ]]></literal>
    <justification jstring="[para(21374(a,1),20232(a,1))].">
      <j1 rule="para" parents="21374 20232"/>
    </justification>
  </clause>

  <clause id="21418">
    <literal><![CDATA[
      R(x,y,(z * z) \ (u \ (w * v5))) = R(x,y,u \ (w * (v5 / (z * z))))
    ]]></literal>
    <justification jstring="[para(459(a,1),21383(a,1,3))].">
      <j1 rule="para" parents="459 21383"/>
    </justification>
  </clause>

  <clause id="21419">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ x = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(620,a,21384,a),flip(a)].">
      <j1 rule="hyper" parents="620 21384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21421">
    <literal><![CDATA[
      (x * y) / (x * (y * (x * y))) = L(x * y,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(220,a,97,a(flip),b,21419,a)].">
      <j1 rule="hyper" parents="220 97 21419"/>
    </justification>
  </clause>

  <clause id="21422">
    <literal><![CDATA[
      (x \ (y \ z)) * L(x \ (y \ z),x,y) = (((y * x) \ z) \ 1) \ (x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(329(a,1),21419(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="329 21419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21423">
    <literal><![CDATA[
      R(x,y,z * L(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,L(z,u,w) \ z) = v5
    ]]></literal>
    <justification jstring="[para(21419(a,1),2379(a,1,3))].">
      <j1 rule="para" parents="21419 2379"/>
    </justification>
  </clause>

  <clause id="21424">
    <literal><![CDATA[
      R(x,y,(z * (u * (z * u))) \ (z * u)) = R(x,y,L(z * u,u,z) \ 1)
    ]]></literal>
    <justification jstring="[para(21421(a,1),20126(a,1,3)),flip(a)].">
      <j1 rule="para" parents="21421 20126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21425">
    <literal><![CDATA[
      T((x * x) \ (L(y,z,u) \ y),w) = L(y,z,u) \ (y / T(x * x,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,20786,a,b,21386,a)].">
      <j1 rule="hyper" parents="63 20786 21386"/>
    </justification>
  </clause>

  <clause id="21426">
    <literal><![CDATA[
      (x * (R(x,y,z) \ u)) * (K(w,v5) * R(x,y,z)) = u * (K(w,v5) * x)
    ]]></literal>
    <justification jstring="[hyper(21085,a,21391,a)].">
      <j1 rule="hyper" parents="21085 21391"/>
    </justification>
  </clause>

  <clause id="21427">
    <literal><![CDATA[
      L(x,y,z \ (u * (w * K(v5,v6)))) = L(x,y,K(v5,v6) * (z \ (u * w)))
    ]]></literal>
    <justification jstring="[para(20166(a,1),21394(a,1,3)),flip(a)].">
      <j1 rule="para" parents="20166 21394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21428">
    <literal><![CDATA[
      L(x,y,z) * ((x \ u) * K(w,v5)) = (u / x) * L(x * K(w,v5),y,z)
    ]]></literal>
    <justification jstring="[para(5237(a,1),21403(a,1,2))].">
      <j1 rule="para" parents="5237 21403"/>
    </justification>
  </clause>

  <clause id="21429">
    <literal><![CDATA[
      L(x \ (y * L(y \ x,z,u)),x,x) = (y * x) \ L(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(686,a,21405,a)].">
      <j1 rule="hyper" parents="686 21405"/>
    </justification>
  </clause>

  <clause id="21430">
    <literal><![CDATA[
      T(x,(y \ z) * (u * T(w,(y \ z) * u))) = T(x,w / (u \ (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,20671,a(flip),b,21407,a)].">
      <j1 rule="hyper" parents="63 20671 21407"/>
    </justification>
  </clause>

  <clause id="21431">
    <literal><![CDATA[
      ((x \ 1) * (L(x \ 1,y,z) \ u)) * x = R(u / L(1 / x,y,z),x,x)
    ]]></literal>
    <justification jstring="[para(21411(a,1),2262(a,1,1)),flip(a)].">
      <j1 rule="para" parents="21411 2262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21432">
    <literal><![CDATA[
      R(x,y,z \ (u * (w / (v5 * v5)))) = R(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[hyper(2239,a,21418,a),flip(a)].">
      <j1 rule="hyper" parents="2239 21418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21434">
    <literal><![CDATA[
      R(x,y,z \ (u * (w * (v5 \ 1)))) = R(x,y,z \ (u * (w * v5)))
    ]]></literal>
    <justification jstring="[para(780(a,1),21432(a,1,3,2,2))].">
      <j1 rule="para" parents="780 21432"/>
    </justification>
  </clause>

  <clause id="21435">
    <literal><![CDATA[
      L(x,y,z) * ((x \ u) * K(x,w)) = (u / x) * L(T(x,w),y,z)
    ]]></literal>
    <justification jstring="[para(4929(a,2),21428(a,2,2,1))].">
      <j1 rule="para" parents="4929 21428"/>
    </justification>
  </clause>

  <clause id="21436">
    <literal><![CDATA[
      ((x / y) * L(T(y,z),(y \ x) * K(y,z),y)) \ ((y \ x) * K(y,z)) = L(T(y,y * ((y \ x) * K(y,z))) \ 1,y,(y \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[para(21435(a,1),9317(a,2,1)),flip(a)].">
      <j1 rule="para" parents="21435 9317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21437">
    <literal><![CDATA[
      T(x,L(y,z,u \ w) * ((u \ w) * z)) = T(x,y / (z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(734(a,1),21430(a,1,2))].">
      <j1 rule="para" parents="734 21430"/>
    </justification>
  </clause>

  <clause id="21438">
    <literal><![CDATA[
      a(x,y,z) * (z \ L(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(z,u,w) * (z \ a(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(12714(a,1),20606(a,1))].">
      <j1 rule="para" parents="12714 20606"/>
    </justification>
  </clause>

  <clause id="21439">
    <literal><![CDATA[
      (K(x,y) * (z * u)) \ (K(x,y) * (z * (u * w))) = L(w,u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(20008(a,1),20711(a,1,2))].">
      <j1 rule="para" parents="20008 20711"/>
    </justification>
  </clause>

  <clause id="21440">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * (K(y,z) * (u * w))) = L(w,u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(20151(a,1),20801(a,1,1))].">
      <j1 rule="para" parents="20151 20801"/>
    </justification>
  </clause>

  <clause id="21441">
    <literal><![CDATA[
      (1 / R(x,y,z)) * R(x,u,w) = R(x,y,z) \ R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(21079,a,2521,a)].">
      <j1 rule="hyper" parents="21079 2521"/>
    </justification>
  </clause>

  <clause id="21442">
    <literal><![CDATA[
      L(x,y,z) \ T(L(T(x,u),y,z),w) = K(x,u) * K(T(x,u),w)
    ]]></literal>
    <justification jstring="[para(20216(a,1),21097(a,2,2))].">
      <j1 rule="para" parents="20216 21097"/>
    </justification>
  </clause>

  <clause id="21443">
    <literal><![CDATA[
      L(x,y,z) \ T(L(T(x,u),y,z),w) = K(x,u) * K(x,T(w,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,7124,a(flip),b,21442,a),flip(a)].">
      <j1 rule="hyper" parents="347 7124 21442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21445">
    <literal><![CDATA[
      L(x,y,z) \ T(L(T(x,u),y,z),w) = x \ T(T(x,u),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,7828,a(flip),b,21443,a),flip(a)].">
      <j1 rule="hyper" parents="347 7828 21443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21446">
    <literal><![CDATA[
      (x * (y * z)) / ((x * y) * z) = ((x * y) * z) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[para(97(a,1),21415(a,1,1))].">
      <j1 rule="para" parents="97 21415"/>
    </justification>
  </clause>

  <clause id="21447">
    <literal><![CDATA[
      ((x * y) \ ((x * (y * z)) / z)) * ((x * y) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,3980,a(flip),b,21446,a)].">
      <j1 rule="hyper" parents="133 3980 21446"/>
    </justification>
  </clause>

  <clause id="21448">
    <literal><![CDATA[
      ((x * y) * (x * y)) \ (x * (y * (x * y))) = a(x,y,x * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,13387,a(flip),b,21446,a),flip(a)].">
      <j1 rule="hyper" parents="63 13387 21446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21449">
    <literal><![CDATA[
      (x * (y * z)) / ((x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) / z) = u
    ]]></literal>
    <justification jstring="[para(21446(a,2),12307(a,1))].">
      <j1 rule="para" parents="21446 12307"/>
    </justification>
  </clause>

  <clause id="21450">
    <literal><![CDATA[
      R(x,(a(y,z,y * z) \ 1) \ u,w) = R(x,(y * (z * (y * z))) \ u,w)
    ]]></literal>
    <justification jstring="[para(21448(a,1),21191(a,1,2,1))].">
      <j1 rule="para" parents="21448 21191"/>
    </justification>
  </clause>

  <clause id="21451">
    <literal><![CDATA[
      R(x,y,(z * (u * (z * u))) \ (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,L(z * u,u,z)) = w
    ]]></literal>
    <justification jstring="[para(21424(a,2),2232(a,1))].">
      <j1 rule="para" parents="21424 2232"/>
    </justification>
  </clause>

  <clause id="21452">
    <literal><![CDATA[
      R(x / L(1 / y,z,u),y,y) = (y * (L(y,z,u) \ x)) * y
    ]]></literal>
    <justification jstring="[para(3439(a,1),21431(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3439 21431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21453">
    <literal><![CDATA[
      R(x / L(1 / y,z,u),y,y) = y * (L(y,z,u) \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(21171,a,21452,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="21171 21452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21454">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,w)) = L(x,y,K(u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(942,a,21439,a)].">
      <j1 rule="hyper" parents="942 21439"/>
    </justification>
  </clause>

  <clause id="21456">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(20035,a,21454,a),flip(a)].">
      <j1 rule="hyper" parents="20035 21454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21458">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(21454(a,1),20035(a,1))].">
      <j1 rule="para" parents="21454 20035"/>
    </justification>
  </clause>

  <clause id="21459">
    <literal><![CDATA[
      L(x,y,z * K(u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(20105,a,21456,a)].">
      <j1 rule="hyper" parents="20105 21456"/>
    </justification>
  </clause>

  <clause id="21464">
    <literal><![CDATA[
      L(x,y,z \ (u * (w * K(v5,v6)))) = L(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,21427,a,b,21456,a)].">
      <j1 rule="hyper" parents="63 21427 21456"/>
    </justification>
  </clause>

  <clause id="21465">
    <literal><![CDATA[
      L(x,y,z * (u / w)) = L(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,16998,a(flip),b,21456,a)].">
      <j1 rule="hyper" parents="63 16998 21456"/>
    </justification>
  </clause>

  <clause id="21466">
    <literal><![CDATA[
      L(x,y,z * T(u,w)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,16913,a(flip),b,21456,a)].">
      <j1 rule="hyper" parents="63 16913 21456"/>
    </justification>
  </clause>

  <clause id="21468">
    <literal><![CDATA[
      L(x,y,T(z,u) \ w) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(5159(a,1),21456(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5159 21456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21469">
    <literal><![CDATA[
      L(x,y,(z / u) * w) = L(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[para(5237(a,1),21456(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5237 21456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21470">
    <literal><![CDATA[
      L(x,y,((z \ u) \ u) \ w) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(5340(a,2),21456(a,1,3))].">
      <j1 rule="para" parents="5340 21456"/>
    </justification>
  </clause>

  <clause id="21471">
    <literal><![CDATA[
      L(x,y,(z / u) \ w) = L(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(5441(a,1),21456(a,1,3))].">
      <j1 rule="para" parents="5441 21456"/>
    </justification>
  </clause>

  <clause id="21472">
    <literal><![CDATA[
      L(x,y,z \ T(u,w)) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(5456(a,1),21456(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5456 21456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21473">
    <literal><![CDATA[
      L(x,y,R(T(z,u),w,v5) * v6) = L(x,y,R(z,w,v5) * v6)
    ]]></literal>
    <justification jstring="[para(5236(a,1),21456(a,1,3))].">
      <j1 rule="para" parents="5236 21456"/>
    </justification>
  </clause>

  <clause id="21474">
    <literal><![CDATA[
      L(x,y,z * (K(u,w) * v5)) = L(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(5885(a,1),21456(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5885 21456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21479">
    <literal><![CDATA[
      L(x,y,(K(z,u) * w) \ v5) = L(x,y,w \ v5)
    ]]></literal>
    <justification jstring="[para(20697(a,1),21456(a,1,3))].">
      <j1 rule="para" parents="20697 21456"/>
    </justification>
  </clause>

  <clause id="21480">
    <literal><![CDATA[
      L(x,y,(z * T(u,w)) \ v5) = L(x,y,(z * u) \ v5)
    ]]></literal>
    <justification jstring="[para(20828(a,1),21456(a,1,3))].">
      <j1 rule="para" parents="20828 21456"/>
    </justification>
  </clause>

  <clause id="21481">
    <literal><![CDATA[
      L(x,y,(z \ T(u,w)) \ v5) = L(x,y,(z \ u) \ v5)
    ]]></literal>
    <justification jstring="[para(20834(a,1),21456(a,1,3))].">
      <j1 rule="para" parents="20834 21456"/>
    </justification>
  </clause>

  <clause id="21482">
    <literal><![CDATA[
      L(x,y,L(K(z,u) * w,v5,v6)) = L(x,y,L(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(21250(a,2),21456(a,1,3))].">
      <j1 rule="para" parents="21250 21456"/>
    </justification>
  </clause>

  <clause id="21492">
    <literal><![CDATA[
      (L(x,y * K(x,z),x) * (y * K(x,z))) \ (y * K(x,z)) = L(T(x,x * y) \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9319,a,b,21459,a)].">
      <j1 rule="hyper" parents="63 9319 21459"/>
    </justification>
  </clause>

  <clause id="21493">
    <literal><![CDATA[
      L(R(R(x * K(y,z),u,x * K(y,z)),w,v5),u,x) = R(x * K(y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,4376,a(flip),b,21459,a),flip(a)].">
      <j1 rule="hyper" parents="63 4376 21459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21498">
    <literal><![CDATA[
      L(x,y,z \ (u / w)) = L(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(13113(a,1),21459(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13113 21459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21504">
    <literal><![CDATA[
      ((x * y) * T(y,z)) \ (x * T(y,z)) = L(y \ 1,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1509,a,b,21466,a)].">
      <j1 rule="hyper" parents="63 1509 21466"/>
    </justification>
  </clause>

  <clause id="21505">
    <literal><![CDATA[
      L(x,y,z * L(u / w,v5,v6)) = L(x,y,z * L(w \ u,v5,v6))
    ]]></literal>
    <justification jstring="[para(278(a,1),21466(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="278 21466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21509">
    <literal><![CDATA[
      L(L(x \ 1,x,x \ y) \ z,(y * K(u,x)) \ (y / T(x,u)),(y / T(x,u)) * x) = (y / T(x,u)) \ (((y / T(x,u)) * x) * z)
    ]]></literal>
    <justification jstring="[para(21468(a,1),13352(a,1,1,1))].">
      <j1 rule="para" parents="21468 13352"/>
    </justification>
  </clause>

  <clause id="21514">
    <literal><![CDATA[
      L(x,y,((z \ u) \ u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ w) = v5
    ]]></literal>
    <justification jstring="[para(5340(a,2),21458(a,1,3))].">
      <j1 rule="para" parents="5340 21458"/>
    </justification>
  </clause>

  <clause id="21515">
    <literal><![CDATA[
      L(x,y,(z / u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(u \ z) * w) = v5
    ]]></literal>
    <justification jstring="[para(5479(a,1),21458(a,1,3))].">
      <j1 rule="para" parents="5479 21458"/>
    </justification>
  </clause>

  <clause id="21516">
    <literal><![CDATA[
      L(x,y,z * T(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * u) = v5
    ]]></literal>
    <justification jstring="[para(5573(a,1),21458(a,1,3))].">
      <j1 rule="para" parents="5573 21458"/>
    </justification>
  </clause>

  <clause id="21517">
    <literal><![CDATA[
      L(x,y,z \ T(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ u) = v5
    ]]></literal>
    <justification jstring="[para(5570(a,1),21458(a,1,3))].">
      <j1 rule="para" parents="5570 21458"/>
    </justification>
  </clause>

  <clause id="21518">
    <literal><![CDATA[
      L(x,y,L(T(z,u),w,v5) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(z,w,v5) * v6) = v7
    ]]></literal>
    <justification jstring="[para(5235(a,1),21458(a,1,3))].">
      <j1 rule="para" parents="5235 21458"/>
    </justification>
  </clause>

  <clause id="21519">
    <literal><![CDATA[
      L(x,y,R(T(z,u),w,v5) \ v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y,R(z,w,v5) \ v6) = v7
    ]]></literal>
    <justification jstring="[para(5344(a,1),21458(a,1,3))].">
      <j1 rule="para" parents="5344 21458"/>
    </justification>
  </clause>

  <clause id="21520">
    <literal><![CDATA[
      L(x,y,z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(7372(a,1),21458(a,1,3))].">
      <j1 rule="para" parents="7372 21458"/>
    </justification>
  </clause>

  <clause id="21521">
    <literal><![CDATA[
      L(x,y,(z * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(u * z) \ w) = v5
    ]]></literal>
    <justification jstring="[para(10274(a,1),21458(a,1,3))].">
      <j1 rule="para" parents="10274 21458"/>
    </justification>
  </clause>

  <clause id="21523">
    <literal><![CDATA[
      L(x,y,z * (u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * (w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(16998(a,1),21458(a,1))].">
      <j1 rule="para" parents="16998 21458"/>
    </justification>
  </clause>

  <clause id="21524">
    <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(19545(a,1),21458(a,1,3))].">
      <j1 rule="para" parents="19545 21458"/>
    </justification>
  </clause>

  <clause id="21525">
    <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(20828(a,1),21458(a,1,3))].">
      <j1 rule="para" parents="20828 21458"/>
    </justification>
  </clause>

  <clause id="21526">
    <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(21250(a,2),21458(a,1,3))].">
      <j1 rule="para" parents="21250 21458"/>
    </justification>
  </clause>

  <clause id="21527">
    <literal><![CDATA[
      L(x,y,L(z / u,w,v5) \ v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(u \ z,w,v5) \ v6) = v7
    ]]></literal>
    <justification jstring="[para(21279(a,1),21458(a,1,3))].">
      <j1 rule="para" parents="21279 21458"/>
    </justification>
  </clause>

  <clause id="21528">
    <literal><![CDATA[
      L(x,y,(z \ (K(u,w) * v5)) \ v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z \ v5) \ v6) = v7
    ]]></literal>
    <justification jstring="[para(21227(a,1),21458(a,1,3))].">
      <j1 rule="para" parents="21227 21458"/>
    </justification>
  </clause>

  <clause id="21530">
    <literal><![CDATA[
      L(x,y,z * ((u \ w) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * u) = v5
    ]]></literal>
    <justification jstring="[para(5954(a,1),21520(a,1,3))].">
      <j1 rule="para" parents="5954 21520"/>
    </justification>
  </clause>

  <clause id="21531">
    <literal><![CDATA[
      L(x,y,z \ (u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ (w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(13354(a,1),21520(a,1,3))].">
      <j1 rule="para" parents="13354 21520"/>
    </justification>
  </clause>

  <clause id="21532">
    <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(20791(a,1),21520(a,1,3))].">
      <j1 rule="para" parents="20791 21520"/>
    </justification>
  </clause>

  <clause id="21534">
    <literal><![CDATA[
      L(x,y,((z * z) \ u) \ w) = L(x,y,(u \ w) * (z * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,20629,a,b,21469,a)].">
      <j1 rule="hyper" parents="63 20629 21469"/>
    </justification>
  </clause>

  <clause id="21535">
    <literal><![CDATA[
      1 / (x * (L(x,1 / x,(x \ 1) * y) \ x)) = L(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(21469(a,1),10569(a,1,2,2,1))].">
      <j1 rule="para" parents="21469 10569"/>
    </justification>
  </clause>

  <clause id="21537">
    <literal><![CDATA[
      L(x,y,((z * z) \ (u \ z)) \ w) = L(x,y,(u \ (z \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(820(a,1),21471(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="820 21471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21538">
    <literal><![CDATA[
      L(x,y,(z \ u) \ (1 / u)) = L(x,y,z * (u \ (1 / u)))
    ]]></literal>
    <justification jstring="[para(911(a,1),21471(a,1,3)),flip(a)].">
      <j1 rule="para" parents="911 21471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21539">
    <literal><![CDATA[
      L(x,y,z * (T(u,w) * v5)) = L(x,y,z * (u * v5))
    ]]></literal>
    <justification jstring="[para(4946(a,1),21474(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="4946 21474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21540">
    <literal><![CDATA[
      L(x,y,z * ((u * w) \ v5)) = L(x,y,z * ((w * u) \ v5))
    ]]></literal>
    <justification jstring="[para(10274(a,1),21474(a,1,3,2))].">
      <j1 rule="para" parents="10274 21474"/>
    </justification>
  </clause>

  <clause id="21542">
    <literal><![CDATA[
      L(x,y,z * (u \ (K(w,v5) * v6))) = L(x,y,z * (u \ v6))
    ]]></literal>
    <justification jstring="[para(19540(a,1),21474(a,1,3,2))].">
      <j1 rule="para" parents="19540 21474"/>
    </justification>
  </clause>

  <clause id="21543">
    <literal><![CDATA[
      L(x,y,z * ((u * K(w,v5)) \ v6)) = L(x,y,z * (u \ v6))
    ]]></literal>
    <justification jstring="[para(20166(a,2),21474(a,1,3,2))].">
      <j1 rule="para" parents="20166 21474"/>
    </justification>
  </clause>

  <clause id="21544">
    <literal><![CDATA[
      L(x,y,(z \ T(u,w)) * v5) = L(x,y,(z \ u) * v5)
    ]]></literal>
    <justification jstring="[para(20179(a,1),21474(a,1,3))].">
      <j1 rule="para" parents="20179 21474"/>
    </justification>
  </clause>

  <clause id="21545">
    <literal><![CDATA[
      L(x,y,z * ((T(u,w) * v5) \ v6)) = L(x,y,z * ((u * v5) \ v6))
    ]]></literal>
    <justification jstring="[para(20829(a,1),21474(a,1,3,2))].">
      <j1 rule="para" parents="20829 21474"/>
    </justification>
  </clause>

  <clause id="21546">
    <literal><![CDATA[
      L(x,y,(z \ (K(u,w) * v5)) * v6) = L(x,y,(z \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(20967(a,1),21474(a,1,3))].">
      <j1 rule="para" parents="20967 21474"/>
    </justification>
  </clause>

  <clause id="21547">
    <literal><![CDATA[
      L(x,y,(z \ (u * T(w,v5))) * v6) = L(x,y,(z \ (u * w)) * v6)
    ]]></literal>
    <justification jstring="[para(21031(a,1),21474(a,1,3))].">
      <j1 rule="para" parents="21031 21474"/>
    </justification>
  </clause>

  <clause id="21548">
    <literal><![CDATA[
      L(x,y,(T(z,u) \ w) \ v5) = L(x,y,(z \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(5159(a,1),21479(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5159 21479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21549">
    <literal><![CDATA[
      L(x,y,(z * (u * w)) \ v5) = L(x,y,(z * (w * u)) \ v5)
    ]]></literal>
    <justification jstring="[para(9586(a,1),21479(a,1,3,1))].">
      <j1 rule="para" parents="9586 21479"/>
    </justification>
  </clause>

  <clause id="21550">
    <literal><![CDATA[
      L(x,y,y \ (x \ z)) * (x \ z) = ((z / x) / y) * (y * x)
    ]]></literal>
    <justification jstring="[para(21498(a,1),13869(a,1,1))].">
      <j1 rule="para" parents="21498 13869"/>
    </justification>
  </clause>

  <clause id="21551">
    <literal><![CDATA[
      L(x,y,(z * (u / w)) \ v5) = L(x,y,(z * (w \ u)) \ v5)
    ]]></literal>
    <justification jstring="[para(113(a,1),21480(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="113 21480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21553">
    <literal><![CDATA[
      L(x,y,(z \ (u / w)) \ v5) = L(x,y,(z \ (w \ u)) \ v5)
    ]]></literal>
    <justification jstring="[para(113(a,1),21481(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="113 21481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21554">
    <literal><![CDATA[
      L(x,y,(z \ u) \ (L(w,(z \ T(u,v5)) \ v6,z \ T(u,v5)) * v6)) = L(x,y,((z \ T(u,v5)) \ v6) * T(w,v6))
    ]]></literal>
    <justification jstring="[para(874(a,1),21481(a,1,3)),flip(a)].">
      <j1 rule="para" parents="874 21481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21555">
    <literal><![CDATA[
      L(x,y,L(z \ T(u,w),v5,v6)) = L(x,y,L(z \ u,v5,v6))
    ]]></literal>
    <justification jstring="[para(5456(a,1),21482(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5456 21482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21559">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * (u * w)) = L(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(20887,a,21539,a)].">
      <j1 rule="hyper" parents="20887 21539"/>
    </justification>
  </clause>

  <clause id="21560">
    <literal><![CDATA[
      L(x,y,((z * (L(z,u,w) \ v5)) \ T(z * v5,v6)) * v7) = L(x,y,L(T(z,v5),u,w) * v7)
    ]]></literal>
    <justification jstring="[para(9713(a,1),21544(a,2,3,1))].">
      <j1 rule="para" parents="9713 21544"/>
    </justification>
  </clause>

  <clause id="21561">
    <literal><![CDATA[
      L(x,y,(z / T(u,w)) \ v5) = L(x,y,(u \ z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,21471,a,b,21548,a)].">
      <j1 rule="hyper" parents="63 21471 21548"/>
    </justification>
  </clause>

  <clause id="21563">
    <literal><![CDATA[
      L(x,y,(z * ((z * u) \ z)) \ w) = L(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(3263(a,1),21561(a,1,3,1))].">
      <j1 rule="para" parents="3263 21561"/>
    </justification>
  </clause>

  <clause id="21567">
    <literal><![CDATA[
      L(x,y,z \ (u * (w / v5))) = L(x,y,z \ (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(4949(a,1),21464(a,1,3,2,2))].">
      <j1 rule="para" parents="4949 21464"/>
    </justification>
  </clause>

  <clause id="21568">
    <literal><![CDATA[
      L(x,y,z \ (u * (K(w,v5) * v6))) = L(x,y,z \ (u * v6))
    ]]></literal>
    <justification jstring="[para(7076(a,1),21464(a,1,3,2,2))].">
      <j1 rule="para" parents="7076 21464"/>
    </justification>
  </clause>

  <clause id="21569">
    <literal><![CDATA[
      L(x,y,z \ ((u \ w) * K(v5,w))) = L(x,y,z \ (u \ L(w,v5,w)))
    ]]></literal>
    <justification jstring="[para(12129(a,1),21464(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="12129 21464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21570">
    <literal><![CDATA[
      L(x,y,(z \ u) \ (1 / u)) = L(x,y,(u * u) \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,20626,a(flip),b,21538,a),flip(a)].">
      <j1 rule="hyper" parents="347 20626 21538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21571">
    <literal><![CDATA[
      L(x,y,(z \ u) \ (u \ 1)) = L(x,y,(u * u) \ z)
    ]]></literal>
    <justification jstring="[hyper(21531,a,21570,a)].">
      <j1 rule="hyper" parents="21531 21570"/>
    </justification>
  </clause>

  <clause id="21572">
    <literal><![CDATA[
      L(x,y,(z \ u) \ (u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(u * u) \ z) = w
    ]]></literal>
    <justification jstring="[para(21571(a,2),21521(a,1))].">
      <j1 rule="para" parents="21571 21521"/>
    </justification>
  </clause>

  <clause id="21573">
    <literal><![CDATA[
      L(x,y,z * (u \ (w / v5))) = L(x,y,z * (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(5012(a,1),21542(a,1,3,2,2))].">
      <j1 rule="para" parents="5012 21542"/>
    </justification>
  </clause>

  <clause id="21574">
    <literal><![CDATA[
      L(x,y,z * (u \ L(T(w,v5),v6,v7))) = L(x,y,z * (u \ L(w,v6,v7)))
    ]]></literal>
    <justification jstring="[para(5028(a,1),21542(a,1,3,2,2))].">
      <j1 rule="para" parents="5028 21542"/>
    </justification>
  </clause>

  <clause id="21575">
    <literal><![CDATA[
      L(x,y,z * (u \ (w * (K(v5,v6) * v7)))) = L(x,y,z * (u \ (w * v7)))
    ]]></literal>
    <justification jstring="[para(5885(a,1),21542(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="5885 21542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21576">
    <literal><![CDATA[
      L(x,y,((T(z,u) * w) \ v5) * v6) = L(x,y,((z * w) \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(20701(a,1),21546(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="20701 21546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21577">
    <literal><![CDATA[
      L(x,y,(z * ((z \ u) * w)) \ (u * w)) = L(x,y,(w * (z \ u)) \ (z \ (u * w)))
    ]]></literal>
    <justification jstring="[para(21369(a,1),21549(a,1,3)),flip(a)].">
      <j1 rule="para" parents="21369 21549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21578">
    <literal><![CDATA[
      L(x,y,((z * u) \ z) \ w) = L(x,y,(z \ (u \ z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3950,a,b,21553,a)].">
      <j1 rule="hyper" parents="63 3950 21553"/>
    </justification>
  </clause>

  <clause id="21579">
    <literal><![CDATA[
      L(x,y,z \ ((u * T(w,v5)) * v6)) = L(x,y,z \ ((u * w) * v6))
    ]]></literal>
    <justification jstring="[para(20808(a,1),21568(a,1,3,2))].">
      <j1 rule="para" parents="20808 21568"/>
    </justification>
  </clause>

  <clause id="21580">
    <literal><![CDATA[
      L(x,y,z * ((u * w) \ u)) = L(x,y,z * (u \ (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,3949,a,b,21573,a)].">
      <j1 rule="hyper" parents="63 3949 21573"/>
    </justification>
  </clause>

  <clause id="21581">
    <literal><![CDATA[
      L(x,y,(((z * u) * (z \ 1)) \ (z * u)) \ w) = L(x,y,((z * u) \ ((z * z) * u)) \ w)
    ]]></literal>
    <justification jstring="[para(494(a,1),21578(a,2,3,1,2))].">
      <j1 rule="para" parents="494 21578"/>
    </justification>
  </clause>

  <clause id="21582">
    <literal><![CDATA[
      L(x,y,((z * T(u,z)) \ z) \ w) = L(x,y,(z \ (u \ T(z,u))) \ w)
    ]]></literal>
    <justification jstring="[para(4281(a,1),21578(a,2,3,1,2))].">
      <j1 rule="para" parents="4281 21578"/>
    </justification>
  </clause>

  <clause id="21583">
    <literal><![CDATA[
      L(x,y,z * ((u * w) \ w)) = L(x,y,z * (w \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21540,a,b,21580,a)].">
      <j1 rule="hyper" parents="63 21540 21580"/>
    </justification>
  </clause>

  <clause id="21584">
    <literal><![CDATA[
      L(x,y,z \ L(z,z,u)) = L(x,y,z * (u \ (z \ u)))
    ]]></literal>
    <justification jstring="[para(3348(a,2),21580(a,1,3))].">
      <j1 rule="para" parents="3348 21580"/>
    </justification>
  </clause>

  <clause id="21585">
    <literal><![CDATA[
      L(x,y,z \ L(z,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(u \ (z \ u)) * z) = w
    ]]></literal>
    <justification jstring="[para(21584(a,2),20105(a,1))].">
      <j1 rule="para" parents="21584 20105"/>
    </justification>
  </clause>

  <clause id="21586">
    <literal><![CDATA[
      L(x,y,z * (u \ ((w * ((w * u) \ w)) \ u))) = L(x,y,z * ((w * K(u \ 1,u)) \ u))
    ]]></literal>
    <justification jstring="[para(3274(a,1),21583(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="3274 21583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21588">
    <literal><![CDATA[
      (x \ 1) * ((((y * x) * T(x,z)) \ (y * T(x,z))) \ 1) = (L(1 / x,x,y * x) \ 1) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(21504(a,2),20994(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="21504 20994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21589">
    <literal><![CDATA[
      L(x,y,R(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(u * w) \ (w * (z * u))) = v5
    ]]></literal>
    <justification jstring="[para(20631(a,1),21525(a,1))].">
      <j1 rule="para" parents="20631 21525"/>
    </justification>
  </clause>

  <clause id="21590">
    <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(5012(a,1),21526(a,1,3,1))].">
      <j1 rule="para" parents="5012 21526"/>
    </justification>
  </clause>

  <clause id="21591">
    <literal><![CDATA[
      (((x / y) / z) * (z * y)) \ x = a(z \ (y \ x),z,y)
    ]]></literal>
    <justification jstring="[para(21550(a,1),14757(a,1,1))].">
      <j1 rule="para" parents="21550 14757"/>
    </justification>
  </clause>

  <clause id="21592">
    <literal><![CDATA[
      L(x,y,((z * (u \ 1)) \ (u \ 1)) \ w) = L(x,y,((z * u) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(973(a,1),21537(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="973 21537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21593">
    <literal><![CDATA[
      L(x,y,z * ((u * T(w,v5)) \ v6)) = L(x,y,z * ((w * u) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,21540,a,b,21545,a)].">
      <j1 rule="hyper" parents="63 21540 21545"/>
    </justification>
  </clause>

  <clause id="21594">
    <literal><![CDATA[
      L(x,y,R(T(z,T(u,w) * v5),v5,T(u,w)) * v6) = L(x,y,((u * v5) \ ((z * v5) * T(T(u,w),v5))) * v6)
    ]]></literal>
    <justification jstring="[para(9627(a,1),21576(a,1,3,1))].">
      <j1 rule="para" parents="9627 21576"/>
    </justification>
  </clause>

  <clause id="21595">
    <literal><![CDATA[
      L(x,y,z \ T(u * (w * T(v5,v6)),K(w * T(v5,v6),v7))) = L(x,y,z \ ((w * v5) * T(u,T(w * T(v5,v6),v7))))
    ]]></literal>
    <justification jstring="[para(6060(a,2),21579(a,1,3,2))].">
      <j1 rule="para" parents="6060 21579"/>
    </justification>
  </clause>

  <clause id="21596">
    <literal><![CDATA[
      L(x,y,(z \ ((u \ w) \ w)) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z \ u) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(5017(a,2),21528(a,1,3,1,2))].">
      <j1 rule="para" parents="5017 21528"/>
    </justification>
  </clause>

  <clause id="21598">
    <literal><![CDATA[
      L(x,y,(z \ (u \ T(w,v5))) \ v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z \ (u \ w)) \ v6) = v7
    ]]></literal>
    <justification jstring="[para(5570(a,1),21528(a,1,3,1,2))].">
      <j1 rule="para" parents="5570 21528"/>
    </justification>
  </clause>

  <clause id="21599">
    <literal><![CDATA[
      L(x,y,(z \ (u \ w)) * K(v5,w)) = L(x,y,z \ (u \ L(w,v5,w)))
    ]]></literal>
    <justification jstring="[para(20109(a,1),21569(a,1,3))].">
      <j1 rule="para" parents="20109 21569"/>
    </justification>
  </clause>

  <clause id="21600">
    <literal><![CDATA[
      L(x,y,z \ (u \ L(w,v5,w))) = L(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(21520,a,21599,a),flip(a)].">
      <j1 rule="hyper" parents="21520 21599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21602">
    <literal><![CDATA[
      1 / (x * (L(x,x,(x \ 1) * y) \ x)) = L(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(3189(a,1),21535(a,1,2,2,1))].">
      <j1 rule="para" parents="3189 21535"/>
    </justification>
  </clause>

  <clause id="21603">
    <literal><![CDATA[
      L(1 / x,x,(x \ 1) * y) = L(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(3648,a,21602,a)].">
      <j1 rule="hyper" parents="3648 21602"/>
    </justification>
  </clause>

  <clause id="21604">
    <literal><![CDATA[
      L(x,y,z * (u * L(1 / u,w,v5))) = L(x,y,z * (u \ L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(5667(a,1),21574(a,1,3,2))].">
      <j1 rule="para" parents="5667 21574"/>
    </justification>
  </clause>

  <clause id="21605">
    <literal><![CDATA[
      L(x,y,z * (u \ ((w * T(v5,v6)) * v7))) = L(x,y,z * (u \ ((w * v5) * v7)))
    ]]></literal>
    <justification jstring="[para(20808(a,1),21575(a,1,3,2,2))].">
      <j1 rule="para" parents="20808 21575"/>
    </justification>
  </clause>

  <clause id="21606">
    <literal><![CDATA[
      L(x,y,(z \ (u \ T(z,u))) \ w) = L(x,y,((u * z) \ z) \ w)
    ]]></literal>
    <justification jstring="[para(111(a,1),21582(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="111 21582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21607">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,w) = L(x,y,w * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(942,a,21440,a)].">
      <j1 rule="hyper" parents="942 21440"/>
    </justification>
  </clause>

  <clause id="21608">
    <literal><![CDATA[
      L(x,K(y,z) * u,w) = L(x,u,w * K(y,z))
    ]]></literal>
    <justification jstring="[para(19952(a,1),21607(a,1,1))].">
      <j1 rule="para" parents="19952 21607"/>
    </justification>
  </clause>

  <clause id="21609">
    <literal><![CDATA[
      L(x,K(y,z) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,21459,a(flip),b,21608,a),flip(a)].">
      <j1 rule="hyper" parents="347 21459 21608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21612">
    <literal><![CDATA[
      L(x,K(y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(21608(a,2),21520(a,1))].">
      <j1 rule="para" parents="21608 21520"/>
    </justification>
  </clause>

  <clause id="21614">
    <literal><![CDATA[
      L(x,y * T(z,u),w) = L(x,y * z,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17885,a(flip),b,21609,a)].">
      <j1 rule="hyper" parents="63 17885 21609"/>
    </justification>
  </clause>

  <clause id="21615">
    <literal><![CDATA[
      L(x,y * K(z,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17870,a(flip),b,21609,a),flip(a)].">
      <j1 rule="hyper" parents="63 17870 21609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21616">
    <literal><![CDATA[
      L(x,T(y,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(1324(a,2),21609(a,1,2))].">
      <j1 rule="para" parents="1324 21609"/>
    </justification>
  </clause>

  <clause id="21617">
    <literal><![CDATA[
      L(x,y * z,u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(4909(a,1),21609(a,1,2))].">
      <j1 rule="para" parents="4909 21609"/>
    </justification>
  </clause>

  <clause id="21619">
    <literal><![CDATA[
      L(x,y / z,u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(5012(a,1),21609(a,1,2))].">
      <j1 rule="para" parents="5012 21609"/>
    </justification>
  </clause>

  <clause id="21622">
    <literal><![CDATA[
      L(x,(y / z) * u,w) = L(x,(z \ y) * u,w)
    ]]></literal>
    <justification jstring="[para(5237(a,1),21609(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5237 21609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21625">
    <literal><![CDATA[
      L(x,L(T(y,z),u,w),v5) = L(x,L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(5028(a,1),21609(a,1,2))].">
      <j1 rule="para" parents="5028 21609"/>
    </justification>
  </clause>

  <clause id="21626">
    <literal><![CDATA[
      L(x,y \ T(z,u),w) = L(x,y \ z,w)
    ]]></literal>
    <justification jstring="[para(5456(a,1),21609(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5456 21609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21628">
    <literal><![CDATA[
      L(x,(T(y,z) * u) * w,v5) = L(x,(y * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(5846(a,1),21609(a,1,2))].">
      <j1 rule="para" parents="5846 21609"/>
    </justification>
  </clause>

  <clause id="21629">
    <literal><![CDATA[
      L(x,y * (K(z,u) * w),v5) = L(x,y * w,v5)
    ]]></literal>
    <justification jstring="[para(5885(a,1),21609(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5885 21609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21630">
    <literal><![CDATA[
      L(x,(y * z) \ u,w) = L(x,(z * y) \ u,w)
    ]]></literal>
    <justification jstring="[para(10274(a,1),21609(a,1,2))].">
      <j1 rule="para" parents="10274 21609"/>
    </justification>
  </clause>

  <clause id="21633">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),v5) = L(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(19540(a,1),21609(a,1,2))].">
      <j1 rule="para" parents="19540 21609"/>
    </justification>
  </clause>

  <clause id="21634">
    <literal><![CDATA[
      L(x,(y * T(z,u)) \ w,v5) = L(x,(y * z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(20828(a,1),21609(a,1,2))].">
      <j1 rule="para" parents="20828 21609"/>
    </justification>
  </clause>

  <clause id="21635">
    <literal><![CDATA[
      L(x,(y \ T(z,u)) \ w,v5) = L(x,(y \ z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(20834(a,1),21609(a,1,2))].">
      <j1 rule="para" parents="20834 21609"/>
    </justification>
  </clause>

  <clause id="21636">
    <literal><![CDATA[
      L(x,(T(y,K(z,u)) * w) * v5,v6) = L(x,(y * (K(z,u) * w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(21324(a,1),21609(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21324 21609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21652">
    <literal><![CDATA[
      (x * T(y,z)) \ ((T(y,z) * z) * x) = L(z * K(z * y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13758,a,b,21616,a)].">
      <j1 rule="hyper" parents="63 13758 21616"/>
    </justification>
  </clause>

  <clause id="21653">
    <literal><![CDATA[
      L(1 / T(x,x \ y),x,y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3267,a(flip),b,21616,a),flip(a)].">
      <j1 rule="hyper" parents="63 3267 21616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21654">
    <literal><![CDATA[
      L(T(x,y) \ (z \ u),x,z) = (z * T(x,y)) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,329,a(flip),b,21616,a),flip(a)].">
      <j1 rule="hyper" parents="63 329 21616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21655">
    <literal><![CDATA[
      L(T(x,y) \ z,x,u) = (u * T(x,y)) \ (u * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,99,a(flip),b,21616,a),flip(a)].">
      <j1 rule="hyper" parents="63 99 21616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21656">
    <literal><![CDATA[
      (x * T(y,z)) * L(u,y,x) = x * (T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(134,a,21616,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="134 21616 18"/>
    </justification>
  </clause>

  <clause id="21659">
    <literal><![CDATA[
      L(x,L(y / z,u,w),v5) = L(x,L(z \ y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(278(a,1),21616(a,1,2)),flip(a)].">
      <j1 rule="para" parents="278 21616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21666">
    <literal><![CDATA[
      L(x,y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z * y,u) = w
    ]]></literal>
    <justification jstring="[para(21616(a,1),12403(a,1))].">
      <j1 rule="para" parents="21616 12403"/>
    </justification>
  </clause>

  <clause id="21681">
    <literal><![CDATA[
      L(x,y * (z / u),w) = L(x,y * (u \ z),w)
    ]]></literal>
    <justification jstring="[para(5927(a,1),21615(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5927 21615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21682">
    <literal><![CDATA[
      L(x,y * (z * K(u,w)),v5) = L(x,y * z,v5)
    ]]></literal>
    <justification jstring="[para(7609(a,1),21615(a,1,2))].">
      <j1 rule="para" parents="7609 21615"/>
    </justification>
  </clause>

  <clause id="21688">
    <literal><![CDATA[
      L(x,y \ (z / u),w) = L(x,y \ (u \ z),w)
    ]]></literal>
    <justification jstring="[para(13113(a,1),21615(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13113 21615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21691">
    <literal><![CDATA[
      L(x,y \ (z * T(u,w)),v5) = L(x,y \ (z * u),v5)
    ]]></literal>
    <justification jstring="[para(20791(a,1),21615(a,1,2))].">
      <j1 rule="para" parents="20791 21615"/>
    </justification>
  </clause>

  <clause id="21692">
    <literal><![CDATA[
      L(x,y \ (z \ T(u,w)),v5) = L(x,y \ (z \ u),v5)
    ]]></literal>
    <justification jstring="[para(20794(a,1),21615(a,1,2))].">
      <j1 rule="para" parents="20794 21615"/>
    </justification>
  </clause>

  <clause id="21693">
    <literal><![CDATA[
      L(x,L(y * K(z,u),w,v5),v6) = L(x,L(y,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(21247(a,2),21615(a,1,2))].">
      <j1 rule="para" parents="21247 21615"/>
    </justification>
  </clause>

  <clause id="21695">
    <literal><![CDATA[
      L(x,(y \ 1) * z,u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(3528,a,21617,a),flip(a)].">
      <j1 rule="hyper" parents="3528 21617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21697">
    <literal><![CDATA[
      L(x,y * ((z * z) * u),w) = L(x,u * y,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,3596,a,b,21617,a)].">
      <j1 rule="hyper" parents="347 3596 21617"/>
    </justification>
  </clause>

  <clause id="21698">
    <literal><![CDATA[
      L(x,(y * z) * y,u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,3609,a(flip),b,21617,a),flip(a)].">
      <j1 rule="hyper" parents="347 3609 21617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21699">
    <literal><![CDATA[
      L(x,y \ (z * (u * u)),w) = L(x,(u * u) * (y \ z),w)
    ]]></literal>
    <justification jstring="[para(456(a,2),21617(a,1,2))].">
      <j1 rule="para" parents="456 21617"/>
    </justification>
  </clause>

  <clause id="21700">
    <literal><![CDATA[
      L(x,L(y,y,z) * z,u) = L(x,z / (y \ 1),u)
    ]]></literal>
    <justification jstring="[para(2008(a,1),21617(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2008 21617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21701">
    <literal><![CDATA[
      L(x,(1 / (1 / (y \ z))) * z,u) = L(x,z / (z \ y),u)
    ]]></literal>
    <justification jstring="[para(3397(a,1),21617(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3397 21617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21702">
    <literal><![CDATA[
      L(x,(y * y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(21617(a,1),3518(a,1))].">
      <j1 rule="para" parents="21617 3518"/>
    </justification>
  </clause>

  <clause id="21703">
    <literal><![CDATA[
      L(x,(y \ 1) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z * y,u) = w
    ]]></literal>
    <justification jstring="[para(21617(a,1),3528(a,1))].">
      <j1 rule="para" parents="21617 3528"/>
    </justification>
  </clause>

  <clause id="21704">
    <literal><![CDATA[
      L(x,((y \ 1) \ z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u * (y \ z),w) = v5
    ]]></literal>
    <justification jstring="[para(21617(a,1),3617(a,1))].">
      <j1 rule="para" parents="21617 3617"/>
    </justification>
  </clause>

  <clause id="21705">
    <literal><![CDATA[
      L(x,a(y,z,y) * (u * w),v5) = L(x,w * (a(y,z,y) * u),v5)
    ]]></literal>
    <justification jstring="[para(11372(a,1),21617(a,1,2))].">
      <j1 rule="para" parents="11372 21617"/>
    </justification>
  </clause>

  <clause id="21706">
    <literal><![CDATA[
      L(x,(K(y,z) * u) * (w \ 1),v5) = L(x,(w \ K(y,z)) * u,v5)
    ]]></literal>
    <justification jstring="[para(20815(a,1),21617(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20815 21617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21707">
    <literal><![CDATA[
      L(x,K(y,z) * (L(u,w,v5) * v6),v7) = L(x,v6 * L(K(y,z) * u,w,v5),v7)
    ]]></literal>
    <justification jstring="[para(21271(a,1),21617(a,1,2))].">
      <j1 rule="para" parents="21271 21617"/>
    </justification>
  </clause>

  <clause id="21717">
    <literal><![CDATA[
      L(x,L(y * z,y,y),u) = L(x,y \ T(z,w),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,15304,a,b,21626,a)].">
      <j1 rule="hyper" parents="347 15304 21626"/>
    </justification>
  </clause>

  <clause id="21719">
    <literal><![CDATA[
      L((T(x,y) \ T(z,u)) \ w,x \ z,x) = T(z,u) \ (T(x,y) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21236,a(flip),b,21626,a),flip(a)].">
      <j1 rule="hyper" parents="63 21236 21626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21720">
    <literal><![CDATA[
      L(x,y \ L(z / u,w,v5),v6) = L(x,y \ L(u \ z,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(278(a,1),21626(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="278 21626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21722">
    <literal><![CDATA[
      L(x,T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(1324(a,2),21612(a,1,2))].">
      <j1 rule="para" parents="1324 21612"/>
    </justification>
  </clause>

  <clause id="21723">
    <literal><![CDATA[
      L(x,(y \ z) * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(4898(a,1),21612(a,1,2))].">
      <j1 rule="para" parents="4898 21612"/>
    </justification>
  </clause>

  <clause id="21725">
    <literal><![CDATA[
      L(x,y / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z \ y,u) = w
    ]]></literal>
    <justification jstring="[para(5012(a,1),21612(a,1,2))].">
      <j1 rule="para" parents="5012 21612"/>
    </justification>
  </clause>

  <clause id="21726">
    <literal><![CDATA[
      L(x,(y \ z) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(5017(a,2),21612(a,1,2))].">
      <j1 rule="para" parents="5017 21612"/>
    </justification>
  </clause>

  <clause id="21727">
    <literal><![CDATA[
      L(x,(y / z) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,(z \ y) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(5441(a,1),21612(a,1,2))].">
      <j1 rule="para" parents="5441 21612"/>
    </justification>
  </clause>

  <clause id="21728">
    <literal><![CDATA[
      L(x,(y / z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,(z \ y) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(5479(a,1),21612(a,1,2))].">
      <j1 rule="para" parents="5479 21612"/>
    </justification>
  </clause>

  <clause id="21729">
    <literal><![CDATA[
      L(x,y * T(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,w) = v5
    ]]></literal>
    <justification jstring="[para(5573(a,1),21612(a,1,2))].">
      <j1 rule="para" parents="5573 21612"/>
    </justification>
  </clause>

  <clause id="21730">
    <literal><![CDATA[
      L(x,y \ T(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ z,w) = v5
    ]]></literal>
    <justification jstring="[para(5570(a,1),21612(a,1,2))].">
      <j1 rule="para" parents="5570 21612"/>
    </justification>
  </clause>

  <clause id="21731">
    <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(5343(a,1),21612(a,1,2))].">
      <j1 rule="para" parents="5343 21612"/>
    </justification>
  </clause>

  <clause id="21732">
    <literal><![CDATA[
      L(x,R(T(y,z),u,w) \ v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,R(y,u,w) \ v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(5344(a,1),21612(a,1,2))].">
      <j1 rule="para" parents="5344 21612"/>
    </justification>
  </clause>

  <clause id="21734">
    <literal><![CDATA[
      L(x,y * K(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(7372(a,1),21612(a,1,2))].">
      <j1 rule="para" parents="7372 21612"/>
    </justification>
  </clause>

  <clause id="21735">
    <literal><![CDATA[
      L(x,(y * z) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,(z * y) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(10274(a,1),21612(a,1,2))].">
      <j1 rule="para" parents="10274 21612"/>
    </justification>
  </clause>

  <clause id="21736">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ w,v5) = v6
    ]]></literal>
    <justification jstring="[para(19540(a,1),21612(a,1,2))].">
      <j1 rule="para" parents="19540 21612"/>
    </justification>
  </clause>

  <clause id="21737">
    <literal><![CDATA[
      L(x,y * (T(z,u) \ w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y * (z \ w),v5) = v6
    ]]></literal>
    <justification jstring="[para(19545(a,1),21612(a,1,2))].">
      <j1 rule="para" parents="19545 21612"/>
    </justification>
  </clause>

  <clause id="21738">
    <literal><![CDATA[
      L(x,(K(y,z) * u) \ w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,u \ w,v5) = v6
    ]]></literal>
    <justification jstring="[para(20697(a,1),21612(a,1,2))].">
      <j1 rule="para" parents="20697 21612"/>
    </justification>
  </clause>

  <clause id="21739">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,(y \ K(v5,v6)) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(20833(a,1),21612(a,1,2))].">
      <j1 rule="para" parents="20833 21612"/>
    </justification>
  </clause>

  <clause id="21740">
    <literal><![CDATA[
      L(x,(y \ T(z,u)) \ w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,(y \ z) \ w,v5) = v6
    ]]></literal>
    <justification jstring="[para(20834(a,1),21612(a,1,2))].">
      <j1 rule="para" parents="20834 21612"/>
    </justification>
  </clause>

  <clause id="21744">
    <literal><![CDATA[
      (L(x,y,x) * y) \ y = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13278,a(flip),b,21653,a)].">
      <j1 rule="hyper" parents="63 13278 21653"/>
    </justification>
  </clause>

  <clause id="21745">
    <literal><![CDATA[
      L(T(x,x * y) \ 1,x,y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[para(13272(a,1),21653(a,1,1))].">
      <j1 rule="para" parents="13272 21653"/>
    </justification>
  </clause>

  <clause id="21746">
    <literal><![CDATA[
      (a(x,y,z) * u) \ u = u \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(16636(a,1),21744(a,1,1,1))].">
      <j1 rule="para" parents="16636 21744"/>
    </justification>
  </clause>

  <clause id="21748">
    <literal><![CDATA[
      L(x,a(y,z,z \ y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,(z \ y) * (y * z),u) = w
    ]]></literal>
    <justification jstring="[para(3611(a,1),21666(a,1))].">
      <j1 rule="para" parents="3611 21666"/>
    </justification>
  </clause>

  <clause id="21751">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(495(a,1),21702(a,1,2))].">
      <j1 rule="para" parents="495 21702"/>
    </justification>
  </clause>

  <clause id="21752">
    <literal><![CDATA[
      L(x,y * (y * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,L(z,y,y),u) = w
    ]]></literal>
    <justification jstring="[para(97(a,1),21702(a,1,2))].">
      <j1 rule="para" parents="97 21702"/>
    </justification>
  </clause>

  <clause id="21753">
    <literal><![CDATA[
      L(x,y * (y * L(z,u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,L(L(z,y,y),u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(474(a,1),21702(a,1,2))].">
      <j1 rule="para" parents="474 21702"/>
    </justification>
  </clause>

  <clause id="21754">
    <literal><![CDATA[
      L(x,(y * y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(3178(a,1),21723(a,1))].">
      <j1 rule="para" parents="3178 21723"/>
    </justification>
  </clause>

  <clause id="21755">
    <literal><![CDATA[
      L(x,y \ (z * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(3616(a,1),21726(a,1))].">
      <j1 rule="para" parents="3616 21726"/>
    </justification>
  </clause>

  <clause id="21756">
    <literal><![CDATA[
      L(x,(y * T(z,u * y)) \ (z * (u * y)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,R(u,y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(13920(a,1),21726(a,1,2,1))].">
      <j1 rule="para" parents="13920 21726"/>
    </justification>
  </clause>

  <clause id="21758">
    <literal><![CDATA[
      L(x,y * ((z \ u) \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,w) = v5
    ]]></literal>
    <justification jstring="[para(5954(a,1),21734(a,1,2))].">
      <j1 rule="para" parents="5954 21734"/>
    </justification>
  </clause>

  <clause id="21759">
    <literal><![CDATA[
      L(x,y * (z / u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * (u \ z),w) = v5
    ]]></literal>
    <justification jstring="[para(6075(a,1),21734(a,1,2))].">
      <j1 rule="para" parents="6075 21734"/>
    </justification>
  </clause>

  <clause id="21760">
    <literal><![CDATA[
      L(x,y \ R(T(z,u),w,v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ R(z,w,v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(5796(a,1),21734(a,1,2))].">
      <j1 rule="para" parents="5796 21734"/>
    </justification>
  </clause>

  <clause id="21761">
    <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(6975(a,1),21734(a,1,2))].">
      <j1 rule="para" parents="6975 21734"/>
    </justification>
  </clause>

  <clause id="21762">
    <literal><![CDATA[
      L(x,y \ (z \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ (u / z),w) = v5
    ]]></literal>
    <justification jstring="[para(13113(a,1),21734(a,1,2))].">
      <j1 rule="para" parents="13113 21734"/>
    </justification>
  </clause>

  <clause id="21763">
    <literal><![CDATA[
      L(x,y \ (z / u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ (u \ z),w) = v5
    ]]></literal>
    <justification jstring="[para(13354(a,1),21734(a,1,2))].">
      <j1 rule="para" parents="13354 21734"/>
    </justification>
  </clause>

  <clause id="21764">
    <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(20791(a,1),21734(a,1,2))].">
      <j1 rule="para" parents="20791 21734"/>
    </justification>
  </clause>

  <clause id="21765">
    <literal><![CDATA[
      (T(x,x * y) \ 1) * L(T(x,x * y) \ 1,x,y) = ((T(x,x * y) \ 1) \ 1) \ (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(21745(a,1),3974(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21745 3974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21766">
    <literal><![CDATA[
      L(T(x,y * x) \ 1,x,y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[para(4323(a,2),21745(a,1,1,1))].">
      <j1 rule="para" parents="4323 21745"/>
    </justification>
  </clause>

  <clause id="21767">
    <literal><![CDATA[
      (T(x,y * x) \ 1) * ((y \ (x \ y)) \ (y \ (L(x,y,x) * y))) = 1 / ((L(x,y,x) * y) \ y)
    ]]></literal>
    <justification jstring="[para(21745(a,1),10844(a,1,2,1))].">
      <j1 rule="para" parents="21745 10844"/>
    </justification>
  </clause>

  <clause id="21768">
    <literal><![CDATA[
      L(x,L(y \ z,y,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,u) = w
    ]]></literal>
    <justification jstring="[para(99(a,2),21754(a,1,2))].">
      <j1 rule="para" parents="99 21754"/>
    </justification>
  </clause>

  <clause id="21769">
    <literal><![CDATA[
      L(x,a(y,z,z \ y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,(y * z) * (z \ y),u) = w
    ]]></literal>
    <justification jstring="[para(87(a,1),21754(a,1,2))].">
      <j1 rule="para" parents="87 21754"/>
    </justification>
  </clause>

  <clause id="21770">
    <literal><![CDATA[
      L(x,L((y * y) \ z,u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,L(z,u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(3181(a,2),21754(a,1,2))].">
      <j1 rule="para" parents="3181 21754"/>
    </justification>
  </clause>

  <clause id="21771">
    <literal><![CDATA[
      L(x,y \ (z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(3612(a,1),21754(a,1))].">
      <j1 rule="para" parents="3612 21754"/>
    </justification>
  </clause>

  <clause id="21772">
    <literal><![CDATA[
      L(x,y / (z * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(21619(a,2),21754(a,1))].">
      <j1 rule="para" parents="21619 21754"/>
    </justification>
  </clause>

  <clause id="21773">
    <literal><![CDATA[
      (T(x,y * x) \ 1) * ((y \ (x \ y)) \ z) = x * (L(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(21766(a,1),21207(a,1,2,1))].">
      <j1 rule="para" parents="21766 21207"/>
    </justification>
  </clause>

  <clause id="21774">
    <literal><![CDATA[
      L(x,y * (z * (u \ 1)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * (z * u),w) = v5
    ]]></literal>
    <justification jstring="[para(792(a,1),21772(a,1,2))].">
      <j1 rule="para" parents="792 21772"/>
    </justification>
  </clause>

  <clause id="21775">
    <literal><![CDATA[
      L(x,(((y * z) \ y) \ 1) * u,w) = L(x,((y \ (y / z)) \ 1) * u,w)
    ]]></literal>
    <justification jstring="[para(3259(a,1),21622(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3259 21622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21776">
    <literal><![CDATA[
      L(x,L((y * y) \ (z * y),u,w),v5) = L(x,L(z * (y \ 1),u,w),v5)
    ]]></literal>
    <justification jstring="[para(791(a,1),21625(a,1,2,1))].">
      <j1 rule="para" parents="791 21625"/>
    </justification>
  </clause>

  <clause id="21777">
    <literal><![CDATA[
      L(x,y * (T(z,u) * w),v5) = L(x,y * (z * w),v5)
    ]]></literal>
    <justification jstring="[para(4946(a,1),21629(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4946 21629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21780">
    <literal><![CDATA[
      L(x,y * (z \ (K(u,w) * v5)),v6) = L(x,y * (z \ v5),v6)
    ]]></literal>
    <justification jstring="[para(19540(a,1),21629(a,1,2,2))].">
      <j1 rule="para" parents="19540 21629"/>
    </justification>
  </clause>

  <clause id="21781">
    <literal><![CDATA[
      L(x,(y \ T(z,u)) * w,v5) = L(x,(y \ z) * w,v5)
    ]]></literal>
    <justification jstring="[para(20179(a,1),21629(a,1,2))].">
      <j1 rule="para" parents="20179 21629"/>
    </justification>
  </clause>

  <clause id="21783">
    <literal><![CDATA[
      L(x,(y * ((z * z) * u)) \ w,v5) = L(x,(u * (y * (z * z))) \ w,v5)
    ]]></literal>
    <justification jstring="[para(32(a,1),21630(a,1,2,1))].">
      <j1 rule="para" parents="32 21630"/>
    </justification>
  </clause>

  <clause id="21784">
    <literal><![CDATA[
      L(x,(((y \ z) * u) * y) \ (z * u),w) = L(x,a(y,y \ z,u),w)
    ]]></literal>
    <justification jstring="[para(88(a,1),21630(a,1,2)),flip(a)].">
      <j1 rule="para" parents="88 21630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21785">
    <literal><![CDATA[
      L(x,(K(y,z) * (u \ (w * y))) \ v5,v6) = L(x,(u \ (w * T(y,z))) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(20791(a,1),21630(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20791 21630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21786">
    <literal><![CDATA[
      L(x,y \ ((z * u) * w),v5) = L(x,y \ ((u * z) * w),v5)
    ]]></literal>
    <justification jstring="[para(10281(a,1),21633(a,1,2,2))].">
      <j1 rule="para" parents="10281 21633"/>
    </justification>
  </clause>

  <clause id="21788">
    <literal><![CDATA[
      L(x,y * (z \ (y \ z)),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(18986(a,1),21681(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18986 21681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21789">
    <literal><![CDATA[
      L(x,y * (z \ (u / w)),v5) = L(x,y * (z \ (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(13113(a,1),21682(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13113 21682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21790">
    <literal><![CDATA[
      L(x,y * (z \ (u \ T(w,v5))),v6) = L(x,y * (z \ (u \ w)),v6)
    ]]></literal>
    <justification jstring="[para(20794(a,1),21682(a,1,2,2))].">
      <j1 rule="para" parents="20794 21682"/>
    </justification>
  </clause>

  <clause id="21791">
    <literal><![CDATA[
      L((x \ (y / z)) \ u,x \ (z \ y),x) = (y / z) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(651,a,21688,a),flip(a)].">
      <j1 rule="hyper" parents="651 21688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21792">
    <literal><![CDATA[
      L(x,y \ ((z * z) \ (u \ z)),w) = L(x,y \ (u \ (z \ 1)),w)
    ]]></literal>
    <justification jstring="[para(820(a,1),21688(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="820 21688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21793">
    <literal><![CDATA[
      L(x,((y * y) * z) * u,w) = L(x,z * u,w)
    ]]></literal>
    <justification jstring="[hyper(21666,a,21697,a)].">
      <j1 rule="hyper" parents="21666 21697"/>
    </justification>
  </clause>

  <clause id="21795">
    <literal><![CDATA[
      (x * a(y,z,u)) \ x = x \ (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(20024,a,21746,a)].">
      <j1 rule="hyper" parents="20024 21746"/>
    </justification>
  </clause>

  <clause id="21796">
    <literal><![CDATA[
      K(x,y) * ((a(z,u,w) * T(x,y)) \ T(x,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      x \ (a(z,u,w) \ T(x,y)) = v5
    ]]></literal>
    <justification jstring="[para(21746(a,2),5323(a,1,2))].">
      <j1 rule="para" parents="21746 5323"/>
    </justification>
  </clause>

  <clause id="21797">
    <literal><![CDATA[
      (x \ ((x * y) * z)) \ (y * z) = (y * z) \ (a(x,y,z) \ (y * z))
    ]]></literal>
    <justification jstring="[para(14721(a,2),21746(a,1,1))].">
      <j1 rule="para" parents="14721 21746"/>
    </justification>
  </clause>

  <clause id="21798">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ x)) \ x = x * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(21746(a,1),21359(a,1,1))].">
      <j1 rule="para" parents="21746 21359"/>
    </justification>
  </clause>

  <clause id="21799">
    <literal><![CDATA[
      L(x,(((y * z) * y) * z) * u,w) = L(x,a(y * z,y,z) * u,w)
    ]]></literal>
    <justification jstring="[para(86(a,1),21793(a,1,2,1))].">
      <j1 rule="para" parents="86 21793"/>
    </justification>
  </clause>

  <clause id="21800">
    <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(21795(a,1),1015(a,1,2,1))].">
      <j1 rule="para" parents="21795 1015"/>
    </justification>
  </clause>

  <clause id="21801">
    <literal><![CDATA[
      x / (a(y,z,u) * x) = x \ (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(220,a,19985,a,b,21798,a)].">
      <j1 rule="hyper" parents="220 19985 21798"/>
    </justification>
  </clause>

  <clause id="21802">
    <literal><![CDATA[
      x \ y != y * a(z,u,w)
    ]]></literal>
    <literal><![CDATA[
      y \ (a(z,u,w) \ y) = x
    ]]></literal>
    <justification jstring="[para(21798(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="21798 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21803">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ z = z * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(12720(a,1),21798(a,1,1))].">
      <j1 rule="para" parents="12720 21798"/>
    </justification>
  </clause>

  <clause id="21804">
    <literal><![CDATA[
      a(a(x,y,z) \ 1,z * a(x,y,z),u) * (((a(x,y,z) \ 1) \ z) * u) = (a(x,y,z) \ 1) \ (z * u)
    ]]></literal>
    <justification jstring="[para(21803(a,1),14734(a,1,1,2))].">
      <j1 rule="para" parents="21803 14734"/>
    </justification>
  </clause>

  <clause id="21805">
    <literal><![CDATA[
      a(L(T(x,y) \ z,x,u),u * T(x,y),w) = (L(w,u * T(x,y),(u * T(x,y)) \ (u * z)) * (u * z)) \ (w * (u * z))
    ]]></literal>
    <justification jstring="[para(21655(a,2),14749(a,2,1)),flip(a)].">
      <j1 rule="para" parents="21655 14749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21808">
    <literal><![CDATA[
      (x * T(y,z)) * L((x * y) \ x,u,w) = x * (T(y,z) * L(y \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(416(a,1),21656(a,1,2))].">
      <j1 rule="para" parents="416 21656"/>
    </justification>
  </clause>

  <clause id="21809">
    <literal><![CDATA[
      L(x,L(y,y,z) * z,u) = L(x,(y \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,21619,a(flip),b,21700,a),flip(a)].">
      <j1 rule="hyper" parents="347 21619 21700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21810">
    <literal><![CDATA[
      L(x,L(y * z,y,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(21717(a,2),21730(a,1))].">
      <j1 rule="para" parents="21717 21730"/>
    </justification>
  </clause>

  <clause id="21811">
    <literal><![CDATA[
      L(x,(y \ (z \ y)) * z,u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(21666,a,21788,a)].">
      <j1 rule="hyper" parents="21666 21788"/>
    </justification>
  </clause>

  <clause id="21812">
    <literal><![CDATA[
      L(x,L(y,y,z) * z,u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,3608,a(flip),b,21809,a),flip(a)].">
      <j1 rule="hyper" parents="347 3608 21809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21813">
    <literal><![CDATA[
      L(x,L(y,y,z) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(21809(a,2),21751(a,1))].">
      <j1 rule="para" parents="21809 21751"/>
    </justification>
  </clause>

  <clause id="21814">
    <literal><![CDATA[
      L(1 / ((x \ (y \ x)) * y),a(y,y,x),y) = y \ R(1 / (x \ (y \ x)),x \ (y \ x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,3268,a(flip),b,21811,a),flip(a)].">
      <j1 rule="hyper" parents="63 3268 21811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21815">
    <literal><![CDATA[
      L((((x \ (y \ x)) * y) \ 1) \ z,a(y,y,x),(x \ (y \ x)) * y) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (y \ x)) * y) * z = u
    ]]></literal>
    <justification jstring="[para(21811(a,1),3204(a,1))].">
      <j1 rule="para" parents="21811 3204"/>
    </justification>
  </clause>

  <clause id="21816">
    <literal><![CDATA[
      L(x \ (y \ x),a(y,y,x),x \ (y \ x)) \ y = y / T(x \ (y \ x),y)
    ]]></literal>
    <justification jstring="[para(21811(a,1),12193(a,1,1))].">
      <j1 rule="para" parents="21811 12193"/>
    </justification>
  </clause>

  <clause id="21817">
    <literal><![CDATA[
      L(x,(T(y,z) * L(u,w,v5)) * y,v6) = L(x,L((y * u) * y,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(3376(a,2),21628(a,2,2))].">
      <j1 rule="para" parents="3376 21628"/>
    </justification>
  </clause>

  <clause id="21818">
    <literal><![CDATA[
      L(x,(T(y,z) * u) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,w * (y * u),v5) = v6
    ]]></literal>
    <justification jstring="[para(21628(a,2),21666(a,1))].">
      <j1 rule="para" parents="21628 21666"/>
    </justification>
  </clause>

  <clause id="21819">
    <literal><![CDATA[
      L(x,L((y / z) * (u * u),w,v5),v6) = L(x,L(z \ y,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,3191,a,b,21659,a)].">
      <j1 rule="hyper" parents="63 3191 21659"/>
    </justification>
  </clause>

  <clause id="21820">
    <literal><![CDATA[
      L(x,L(((y * y) \ z) \ u,w,v5),v6) = L(x,L((u / z) * (y * y),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(896(a,1),21659(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="896 21659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21821">
    <literal><![CDATA[
      L(x,L(y \ K(z,T(u,w)),y,w),v5) = L(x,w \ (K(z,u) * (w / y)),v5)
    ]]></literal>
    <justification jstring="[para(21293(a,1),21659(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21293 21659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21822">
    <literal><![CDATA[
      L(x,y \ (z * (u / w)),v5) = L(x,y \ (z * (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(113(a,1),21691(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="113 21691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21823">
    <literal><![CDATA[
      L(x,(y * z) * (((y * z) * y) * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,L(R(y * z,y,z),y * z,y * z),u) = w
    ]]></literal>
    <justification jstring="[para(582(a,1),21752(a,1,2,2))].">
      <j1 rule="para" parents="582 21752"/>
    </justification>
  </clause>

  <clause id="21824">
    <literal><![CDATA[
      L(x,y * (((z * u) * (z \ 1)) * w),v5) = L(x,y * (R(u,z,z) * w),v5)
    ]]></literal>
    <justification jstring="[para(915(a,1),21777(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="915 21777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21825">
    <literal><![CDATA[
      L(x,(y \ (z / u)) * w,v5) = L(x,(y \ (u \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(113(a,1),21781(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="113 21781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21827">
    <literal><![CDATA[
      L(x,L(T(y,z),z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,(z * u) \ (u * (y * z)),w) = v5
    ]]></literal>
    <justification jstring="[para(263(a,1),21735(a,1,2))].">
      <j1 rule="para" parents="263 21735"/>
    </justification>
  </clause>

  <clause id="21828">
    <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(5441(a,1),21736(a,1,2,2))].">
      <j1 rule="para" parents="5441 21736"/>
    </justification>
  </clause>

  <clause id="21829">
    <literal><![CDATA[
      L(x,y \ ((T(z,u) * w) * v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ ((z * w) * v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(5846(a,1),21736(a,1,2,2))].">
      <j1 rule="para" parents="5846 21736"/>
    </justification>
  </clause>

  <clause id="21830">
    <literal><![CDATA[
      L(x,y \ (z \ (K(u,w) * v5)),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ (z \ v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(19540(a,1),21736(a,1,2,2))].">
      <j1 rule="para" parents="19540 21736"/>
    </justification>
  </clause>

  <clause id="21831">
    <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(9586(a,1),21738(a,1,2,1))].">
      <j1 rule="para" parents="9586 21738"/>
    </justification>
  </clause>

  <clause id="21832">
    <literal><![CDATA[
      L(x,((T(y,z) * u) \ w) \ v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,((y * u) \ w) \ v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(20829(a,1),21738(a,1,2,1))].">
      <j1 rule="para" parents="20829 21738"/>
    </justification>
  </clause>

  <clause id="21833">
    <literal><![CDATA[
      L(x,(1 / (1 / (y \ z))) * z,u) = L(x,(z \ y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,21619,a(flip),b,21701,a),flip(a)].">
      <j1 rule="hyper" parents="347 21619 21701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21835">
    <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),21786(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14 21786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21836">
    <literal><![CDATA[
      L(x,y \ ((z * ((u * u) * w)) * v5),v6) = L(x,y \ ((w * (z * (u * u))) * v5),v6)
    ]]></literal>
    <justification jstring="[para(32(a,1),21786(a,1,2,2,1))].">
      <j1 rule="para" parents="32 21786"/>
    </justification>
  </clause>

  <clause id="21837">
    <literal><![CDATA[
      L(x,y \ T(z * (u * w),K(u * w,v5)),v6) = L(x,y \ ((w * u) * T(z,T(u * w,v5))),v6)
    ]]></literal>
    <justification jstring="[para(6060(a,2),21786(a,1,2,2))].">
      <j1 rule="para" parents="6060 21786"/>
    </justification>
  </clause>

  <clause id="21838">
    <literal><![CDATA[
      L(x,(y \ (z \ y)) * z,u) = L(x,z * L(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(3620,a,21825,a),flip(a)].">
      <j1 rule="hyper" parents="3620 21825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21839">
    <literal><![CDATA[
      L(x,y * L(y,y,z),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21811,a(flip),b,21838,a),flip(a)].">
      <j1 rule="hyper" parents="63 21811 21838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21840">
    <literal><![CDATA[
      L(x,((1 / (y \ z)) \ 1) * z,u) = L(x,(z \ y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(21728,a,21833,a)].">
      <j1 rule="hyper" parents="21728 21833"/>
    </justification>
  </clause>

  <clause id="21843">
    <literal><![CDATA[
      L(x,(y \ z) \ y,u) = L(x,(z \ y) * y,u)
    ]]></literal>
    <justification jstring="[para(83(a,1),21840(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 21840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21845">
    <literal><![CDATA[
      L(x,(T(y,z) \ u) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,w * (y \ u),v5) = v6
    ]]></literal>
    <justification jstring="[para(21617(a,1),21737(a,1))].">
      <j1 rule="para" parents="21617 21737"/>
    </justification>
  </clause>

  <clause id="21846">
    <literal><![CDATA[
      L(x,(y \ K(z,u)) \ w,v5) = L(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(21739,a,3608,a)].">
      <j1 rule="hyper" parents="21739 3608"/>
    </justification>
  </clause>

  <clause id="21847">
    <literal><![CDATA[
      L(x,(y * T(z,u)) * w,v5) = L(x,w * (y * z),v5)
    ]]></literal>
    <justification jstring="[hyper(21761,a,21617,a),flip(a)].">
      <j1 rule="hyper" parents="21761 21617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21848">
    <literal><![CDATA[
      L(x,(y * T(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,w * (y * z),v5) = v6
    ]]></literal>
    <justification jstring="[para(21617(a,1),21761(a,1))].">
      <j1 rule="para" parents="21617 21761"/>
    </justification>
  </clause>

  <clause id="21849">
    <literal><![CDATA[
      L(x,(y * z) * u,w) = L(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[para(111(a,1),21847(a,1,2,1))].">
      <j1 rule="para" parents="111 21847"/>
    </justification>
  </clause>

  <clause id="21850">
    <literal><![CDATA[
      L(x,(y \ z) * (y * z),u) = L(x,a(z,y,y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(13428,a,21849,a),flip(a)].">
      <j1 rule="hyper" parents="13428 21849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21851">
    <literal><![CDATA[
      L(x,(y * z) * R(u,z,y),w) = L(x,(u * z) * y,w)
    ]]></literal>
    <justification jstring="[para(107(a,1),21849(a,2,2))].">
      <j1 rule="para" parents="107 21849"/>
    </justification>
  </clause>

  <clause id="21852">
    <literal><![CDATA[
      L(x,((y / (z * z)) * u) * R(w,u,y / (z * z)),v5) = L(x,((w * u) * y) / (z * z),v5)
    ]]></literal>
    <justification jstring="[para(464(a,2),21851(a,2,2))].">
      <j1 rule="para" parents="464 21851"/>
    </justification>
  </clause>

  <clause id="21853">
    <literal><![CDATA[
      L(x,(y * ((z * z) \ u)) * R(w * z,(z * z) \ u,y),v5) = L(x,((w * (z \ 1)) * u) * y,v5)
    ]]></literal>
    <justification jstring="[para(828(a,1),21851(a,2,2,1))].">
      <j1 rule="para" parents="828 21851"/>
    </justification>
  </clause>

  <clause id="21854">
    <literal><![CDATA[
      L(x,y * (L(z,u,w) \ z),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y * (z * L(z,u,w)),v5) = v6
    ]]></literal>
    <justification jstring="[para(1409(a,1),21774(a,1,2,2))].">
      <j1 rule="para" parents="1409 21774"/>
    </justification>
  </clause>

  <clause id="21855">
    <literal><![CDATA[
      L(L(1 / x,x,y) \ z,y \ (x \ y),y) = (y / x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(3264(a,2),21791(a,1,1,1))].">
      <j1 rule="para" parents="3264 21791"/>
    </justification>
  </clause>

  <clause id="21856">
    <literal><![CDATA[
      L(L(x \ 1,x,x \ y) \ z,y \ (x \ y),y) = (y / x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(5508(a,2),21791(a,1,1,1))].">
      <j1 rule="para" parents="5508 21791"/>
    </justification>
  </clause>

  <clause id="21857">
    <literal><![CDATA[
      L(x,((y * z) * u) \ ((y * u) * z),w) = L(x,a(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(21735,a,21835,a)].">
      <j1 rule="hyper" parents="21735 21835"/>
    </justification>
  </clause>

  <clause id="21858">
    <literal><![CDATA[
      L(x,y * (a(z,u,z) * w),v5) = L(x,w * y,v5)
    ]]></literal>
    <justification jstring="[hyper(12377,a,21705,a),flip(a)].">
      <j1 rule="hyper" parents="12377 21705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21859">
    <literal><![CDATA[
      L(x,y * (a(z,u,z) \ w),v5) = L(x,w * y,v5)
    ]]></literal>
    <justification jstring="[hyper(8677,a,21858,a)].">
      <j1 rule="hyper" parents="8677 21858"/>
    </justification>
  </clause>

  <clause id="21861">
    <literal><![CDATA[
      a(x,y,L(z * (a(u,w,u) \ v5),v5 * z,L(v5 \ 1,v5,z))) = a(x,y,((a(u,w,u) \ z) * (((a(u,w,u) \ z) * v5) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(21859(a,1),16605(a,1,3))].">
      <j1 rule="para" parents="21859 16605"/>
    </justification>
  </clause>

  <clause id="21862">
    <literal><![CDATA[
      L(x,K(y,z) * (u * (w \ 1)),v5) = L(x,(w \ K(y,z)) * u,v5)
    ]]></literal>
    <justification jstring="[para(20008(a,1),21706(a,1,2))].">
      <j1 rule="para" parents="20008 21706"/>
    </justification>
  </clause>

  <clause id="21863">
    <literal><![CDATA[
      L(x,y \ L((z * z) \ z,u,w),v5) = L(x,y \ L(z \ 1,u,w),v5)
    ]]></literal>
    <justification jstring="[para(300(a,1),21720(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="300 21720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21864">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,x \ L(x \ 1,y,z),x) != w
    ]]></literal>
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) \ (x * u) = w
    ]]></literal>
    <justification jstring="[para(21720(a,1),3643(a,1))].">
      <j1 rule="para" parents="21720 3643"/>
    </justification>
  </clause>

  <clause id="21865">
    <literal><![CDATA[
      (x / y) \ (x * (L(1 / y,y,x) * z)) = L(z,x \ (y \ x),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),21855(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 21855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21866">
    <literal><![CDATA[
      L(x,(y \ K(z,u)) * w,v5) = L(x,w * (y \ 1),v5)
    ]]></literal>
    <justification jstring="[hyper(21612,a,21862,a),flip(a)].">
      <j1 rule="hyper" parents="21612 21862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21869">
    <literal><![CDATA[
      L(x,(y \ K(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,w * y,v5) = v6
    ]]></literal>
    <justification jstring="[para(21866(a,2),3528(a,1))].">
      <j1 rule="para" parents="21866 3528"/>
    </justification>
  </clause>

  <clause id="21871">
    <literal><![CDATA[
      (T(x,y) \ T(T(x,z),u)) \ w = T(T(x,z),u) \ (T(x,y) * w)
    ]]></literal>
    <justification jstring="[hyper(4151,a,21719,a)].">
      <j1 rule="hyper" parents="4151 21719"/>
    </justification>
  </clause>

  <clause id="21872">
    <literal><![CDATA[
      L(x,((y \ z) * z) * y,u) = L(x,a(y,y \ z,z),u)
    ]]></literal>
    <justification jstring="[hyper(21755,a,21784,a)].">
      <j1 rule="hyper" parents="21755 21784"/>
    </justification>
  </clause>

  <clause id="21873">
    <literal><![CDATA[
      L(x,y * (z * (y \ z)),u) = L(x,a(y,y \ z,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21849,a(flip),b,21872,a)].">
      <j1 rule="hyper" parents="63 21849 21872"/>
    </justification>
  </clause>

  <clause id="21874">
    <literal><![CDATA[
      L(x,a(y * z,y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u * (((y * z) * y) * z),w) = v5
    ]]></literal>
    <justification jstring="[para(21799(a,1),21666(a,1))].">
      <j1 rule="para" parents="21799 21666"/>
    </justification>
  </clause>

  <clause id="21875">
    <literal><![CDATA[
      L(x,y \ (z \ (u / w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ (z \ (w \ u)),v5) = v6
    ]]></literal>
    <justification jstring="[para(5012(a,1),21830(a,1,2,2,2))].">
      <j1 rule="para" parents="5012 21830"/>
    </justification>
  </clause>

  <clause id="21876">
    <literal><![CDATA[
      L(x,(y * (K(z,u) * w)) * v5,v6) = L(x,v5 * (y * w),v6)
    ]]></literal>
    <justification jstring="[hyper(21818,a,21636,a),flip(a)].">
      <j1 rule="hyper" parents="21818 21636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21877">
    <literal><![CDATA[
      L(x,(y * (T(z,u) * w)) * v5,v6) = L(x,v5 * (y * (z * w)),v6)
    ]]></literal>
    <justification jstring="[para(4974(a,1),21876(a,1,2,1,2))].">
      <j1 rule="para" parents="4974 21876"/>
    </justification>
  </clause>

  <clause id="21878">
    <literal><![CDATA[
      L(x,(((y * z) \ y) \ 1) * u,w) = L(x,u * (y \ (y / z)),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,21695,a(flip),b,21775,a),flip(a)].">
      <j1 rule="hyper" parents="347 21695 21775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21879">
    <literal><![CDATA[
      L(x,(((y * z) \ y) \ 1) * u,w) = L(x,u * (y \ (z \ y)),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,21789,a(flip),b,21878,a),flip(a)].">
      <j1 rule="hyper" parents="347 21789 21878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21880">
    <literal><![CDATA[
      L(x,y * ((z * u) \ z),w) = L(x,y * (z \ (u \ z)),w)
    ]]></literal>
    <justification jstring="[hyper(21703,a,21879,a)].">
      <j1 rule="hyper" parents="21703 21879"/>
    </justification>
  </clause>

  <clause id="21881">
    <literal><![CDATA[
      L(x,y * ((z * T(u,z)) \ z),w) = L(x,y * (z \ (u \ T(z,u))),w)
    ]]></literal>
    <justification jstring="[para(4281(a,1),21880(a,2,2,2,2))].">
      <j1 rule="para" parents="4281 21880"/>
    </justification>
  </clause>

  <clause id="21882">
    <literal><![CDATA[
      L(x,L(y * (z \ 1),u,w),v5) = L(x,L(y * z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(21770,a,21776,a),flip(a)].">
      <j1 rule="hyper" parents="21770 21776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21883">
    <literal><![CDATA[
      L(x,L((y * (z \ 1)) * K(u,w),v5,v6),v7) = L(x,L(y * z,v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,21693,a,b,21882,a)].">
      <j1 rule="hyper" parents="63 21693 21882"/>
    </justification>
  </clause>

  <clause id="21884">
    <literal><![CDATA[
      L(x,(y * ((z * z) * u)) \ w,v5) = L(x,(z * z) \ ((u * y) \ w),v5)
    ]]></literal>
    <justification jstring="[para(775(a,1),21783(a,2,2))].">
      <j1 rule="para" parents="775 21783"/>
    </justification>
  </clause>

  <clause id="21885">
    <literal><![CDATA[
      L(x,(y * z) \ (z * (u * y)),w) = L(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(21827,a,21625,a)].">
      <j1 rule="hyper" parents="21827 21625"/>
    </justification>
  </clause>

  <clause id="21887">
    <literal><![CDATA[
      L(x,y * (z \ (u \ T(z,u))),w) = L(x,y * ((u * z) \ z),w)
    ]]></literal>
    <justification jstring="[para(111(a,1),21881(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="111 21881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21888">
    <literal><![CDATA[
      L(x,y * ((z * u) \ u),w) = L(x,y * (u \ (z \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21790,a(flip),b,21887,a),flip(a)].">
      <j1 rule="hyper" parents="63 21790 21887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21890">
    <literal><![CDATA[
      L(x,L(y * ((z \ 1) * K(u,w)),v5,v6),v7) = L(x,L(y * z,v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(7609(a,1),21883(a,1,2,1))].">
      <j1 rule="para" parents="7609 21883"/>
    </justification>
  </clause>

  <clause id="21891">
    <literal><![CDATA[
      L(x,(y * ((z * z) * u)) \ w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,(u * y) \ w,v5) = v6
    ]]></literal>
    <justification jstring="[para(21884(a,2),21754(a,1))].">
      <j1 rule="para" parents="21884 21754"/>
    </justification>
  </clause>

  <clause id="21892">
    <literal><![CDATA[
      L(x,L(y * (z \ K(u,w)),v5,v6),v7) = L(x,L(y * z,v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(12973(a,1),21890(a,1,2,1,2))].">
      <j1 rule="para" parents="12973 21890"/>
    </justification>
  </clause>

  <clause id="21893">
    <literal><![CDATA[
      L(x,L((y * z) * y,u,w),v5) = L(x,L(R(z,y,y),u,w),v5)
    ]]></literal>
    <justification jstring="[para(6541(a,1),21892(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6541 21892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21894">
    <literal><![CDATA[
      L(x,(T(y,z) * L(u,w,v5)) * y,v6) = L(x,L(R(u,y,y),w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,21817,a,b,21893,a)].">
      <j1 rule="hyper" parents="63 21817 21893"/>
    </justification>
  </clause>

  <clause id="21895">
    <literal><![CDATA[
      L(x,y * (y * L(z,u,w)),v5) = L(x,L(R(z,y,y),u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(21818,a,21894,a)].">
      <j1 rule="hyper" parents="21818 21894"/>
    </justification>
  </clause>

  <clause id="21896">
    <literal><![CDATA[
      L(x,L(R(y,z,z),u,w),v5) = L(x,L(L(y,z,z),u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(21753,a,21895,a),flip(a)].">
      <j1 rule="hyper" parents="21753 21895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21897">
    <literal><![CDATA[
      L(x,L((y * z) * z,u,w),v5) = L(x,L(L(y,z,z),u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,3413,a,b,21896,a)].">
      <j1 rule="hyper" parents="63 3413 21896"/>
    </justification>
  </clause>

  <clause id="21898">
    <literal><![CDATA[
      L(x,L(L(y,z,z),y * z,y * z),u) = L(x,(y * z) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(21810,a,21897,a),flip(a)].">
      <j1 rule="hyper" parents="21810 21897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21899">
    <literal><![CDATA[
      R(x,(y * (z * (y * z))) \ u,w) = R(x,a(y,z,y * z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(20908,a,21450,a),flip(a)].">
      <j1 rule="hyper" parents="20908 21450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21900">
    <literal><![CDATA[
      L(x,y,((z * u) \ u) \ w) = L(x,y,(u \ (z \ u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(21598,a,21606,a),flip(a)].">
      <j1 rule="hyper" parents="21598 21606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21901">
    <literal><![CDATA[
      L(x,y,(z \ (u \ T(w,v5))) \ v6) = L(x,y,(z \ (u \ w)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(21598,a,xx),flip(a)].">
      <j1 rule="hyper" parents="21598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21902">
    <literal><![CDATA[
      L(x,y,((z * u) \ u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(u \ (z \ u)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(21606(a,1),21598(a,1))].">
      <j1 rule="para" parents="21606 21598"/>
    </justification>
  </clause>

  <clause id="21903">
    <literal><![CDATA[
      L(x,y,((z * (u \ 1)) \ (u \ 1)) \ w) = L(x,y,(u \ (z \ u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21592,a,b,21900,a)].">
      <j1 rule="hyper" parents="63 21592 21900"/>
    </justification>
  </clause>

  <clause id="21905">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ (u \ (z \ 1))) \ w) = L(x,y,(z \ (u \ z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(21902,a,21903,a)].">
      <j1 rule="hyper" parents="21902 21903"/>
    </justification>
  </clause>

  <clause id="21906">
    <literal><![CDATA[
      L(x,L(y \ K(z,T(u,w)),y,w),v5) = L(x,w \ (K(z,u) * (y \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,21822,a(flip),b,21821,a),flip(a)].">
      <j1 rule="hyper" parents="347 21822 21821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21907">
    <literal><![CDATA[
      L(x,L(y \ K(z,T(u,w)),y,w),v5) = L(x,w \ (y \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,21633,a(flip),b,21906,a),flip(a)].">
      <j1 rule="hyper" parents="347 21633 21906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21910">
    <literal><![CDATA[
      L(x,(y * z) \ (K(u,w) * y),v5) = L(x,y \ (z \ y),v5)
    ]]></literal>
    <justification jstring="[para(7114(a,1),21907(a,1,2))].">
      <j1 rule="para" parents="7114 21907"/>
    </justification>
  </clause>

  <clause id="21911">
    <literal><![CDATA[
      L(x,(y * z) \ y,u) = L(x,y \ (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(21736,a,21910,a)].">
      <j1 rule="hyper" parents="21736 21910"/>
    </justification>
  </clause>

  <clause id="21912">
    <literal><![CDATA[
      L(x,(y * z) \ z,u) = L(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[para(10299(a,1),21910(a,1,2))].">
      <j1 rule="para" parents="10299 21910"/>
    </justification>
  </clause>

  <clause id="21913">
    <literal><![CDATA[
      L(L(x,y \ (z \ y),z),z * ((y * z) \ y),z) = L(x,z,z)
    ]]></literal>
    <justification jstring="[para(21911(a,1),4091(a,1,1))].">
      <j1 rule="para" parents="21911 4091"/>
    </justification>
  </clause>

  <clause id="21914">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * (w \ y)),v5) = L(x,(w * y) \ y,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,21633,a,b,21912,a)].">
      <j1 rule="hyper" parents="347 21633 21912"/>
    </justification>
  </clause>

  <clause id="21915">
    <literal><![CDATA[
      L(x,(y * z) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z \ (y \ z),u) = w
    ]]></literal>
    <justification jstring="[para(21914(a,1),21736(a,1))].">
      <j1 rule="para" parents="21914 21736"/>
    </justification>
  </clause>

  <clause id="21916">
    <literal><![CDATA[
      L(x,(y * z) \ y,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ (z \ y),u) = w
    ]]></literal>
    <justification jstring="[para(21630(a,1),21915(a,1))].">
      <j1 rule="para" parents="21630 21915"/>
    </justification>
  </clause>

  <clause id="21917">
    <literal><![CDATA[
      L(x,L(L(y,z,z),y * z,y * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z \ (y \ z),u) = w
    ]]></literal>
    <justification jstring="[para(21898(a,2),21915(a,1))].">
      <j1 rule="para" parents="21898 21915"/>
    </justification>
  </clause>

  <clause id="21918">
    <literal><![CDATA[
      L(L(x,y \ (z \ y),z),z * (y \ (z \ y)),z) = L(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21880,a(flip),b,21913,a)].">
      <j1 rule="hyper" parents="63 21880 21913"/>
    </justification>
  </clause>

  <clause id="21919">
    <literal><![CDATA[
      L(L(x,y \ (z \ y),z),a(z,z,y),z) = L(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21788,a(flip),b,21918,a)].">
      <j1 rule="hyper" parents="63 21788 21918"/>
    </justification>
  </clause>

  <clause id="21920">
    <literal><![CDATA[
      R(x,y,z) \ (R((x \ u) \ u,y,z) * w) = K(x,x \ u) * w
    ]]></literal>
    <justification jstring="[para(5144(a,1),20412(a,2,1))].">
      <j1 rule="para" parents="5144 20412"/>
    </justification>
  </clause>

  <clause id="21922">
    <literal><![CDATA[
      (T(x,y) \ z) * T(u,K(x,y) * (T(x,y) \ z)) = K(y,x) * (u * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,5256,a(flip),b,20471,a),flip(a)].">
      <j1 rule="hyper" parents="347 5256 20471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21924">
    <literal><![CDATA[
      R(x,T(y,z * z) * (u \ (z * z)),w) = R(x,(u \ 1) * y,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,2244,a(flip),b,20648,a),flip(a)].">
      <j1 rule="hyper" parents="347 2244 20648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21926">
    <literal><![CDATA[
      R(x,T(y,z * z) * (u \ (z * z)),w) = R(x,y * u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,20644,a(flip),b,21924,a),flip(a)].">
      <j1 rule="hyper" parents="347 20644 21924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21927">
    <literal><![CDATA[
      (a(x,y,z) * ((u * a(w,v5,v6)) \ v7)) / (a(x,y,z) \ 1) = ((a(w,v5,v6) * u) \ v7) * ((1 / a(x,y,z)) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(20936(a,2),6386(a,1,1))].">
      <j1 rule="para" parents="20936 6386"/>
    </justification>
  </clause>

  <clause id="21928">
    <literal><![CDATA[
      (x * T(y,T(z,x))) \ T(y,T(z,u)) = (x * y) \ T(y * K(z,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(3025(a,1),21126(a,2,2,1))].">
      <j1 rule="para" parents="3025 21126"/>
    </justification>
  </clause>

  <clause id="21929">
    <literal><![CDATA[
      (L(x,y,z) * u) / T(K(w,u) * x,u) = (T(u,w) / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8522(a,1),21175(a,1,2))].">
      <j1 rule="para" parents="8522 21175"/>
    </justification>
  </clause>

  <clause id="21930">
    <literal><![CDATA[
      ((L(x,y,z) * u) / T(x,u)) * K(u,w) = (T(u,w) / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,20823,a(flip),b,21929,a)].">
      <j1 rule="hyper" parents="63 20823 21929"/>
    </justification>
  </clause>

  <clause id="21931">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) * K(x,w) = (T(x,w) / y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(21011(a,1),21930(a,1,1))].">
      <j1 rule="para" parents="21011 21930"/>
    </justification>
  </clause>

  <clause id="21932">
    <literal><![CDATA[
      (x / y) * (L(y,z,u) * K(x,w)) = (T(x,w) / y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(20359,a,21931,a)].">
      <j1 rule="hyper" parents="20359 21931"/>
    </justification>
  </clause>

  <clause id="21933">
    <literal><![CDATA[
      (x / y) * L(y * K(x,z),u,w) = (T(x,z) / y) * L(y,u,w)
    ]]></literal>
    <justification jstring="[para(21247(a,2),21932(a,1,2))].">
      <j1 rule="para" parents="21247 21932"/>
    </justification>
  </clause>

  <clause id="21934">
    <literal><![CDATA[
      (x * y) / (y * L(T(x,y),z,u)) = (y * L(T(x,y),z,u)) \ (x * y)
    ]]></literal>
    <justification jstring="[para(111(a,1),21182(a,1,1))].">
      <j1 rule="para" parents="111 21182"/>
    </justification>
  </clause>

  <clause id="21935">
    <literal><![CDATA[
      (x * L(T(y,x),z,u)) \ (y * x) = (y * x) / (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(267(a,1),21934(a,1,2)),flip(a)].">
      <j1 rule="para" parents="267 21934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21936">
    <literal><![CDATA[
      (x * y) / (L(x,z,u) * y) = (L(x,z,u) * y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(267(a,1),21935(a,1,1)),flip(a)].">
      <j1 rule="para" parents="267 21935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21937">
    <literal><![CDATA[
      (x * y) / ((L(x,z,u) * (y * (w * w))) / (w * w)) = (L(x,z,u) * (y * (w * w))) \ (x * (y * (w * w)))
    ]]></literal>
    <justification jstring="[hyper(1080,a,21936,a)].">
      <j1 rule="hyper" parents="1080 21936"/>
    </justification>
  </clause>

  <clause id="21938">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) \ (x * (x \ u)) = u / (L(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(391,a,21936,a),flip(a)].">
      <j1 rule="hyper" parents="391 21936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21939">
    <literal><![CDATA[
      x / (L(y,z,u) * (y \ x)) = (L(y,z,u) * (y \ x)) \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),21938(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 21938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21940">
    <literal><![CDATA[
      K(x,y) * ((x \ (1 / x)) * R(x,z,u)) = R(T(x,y),z,u) / (x * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,667,a(flip),b,21211,a),flip(a)].">
      <j1 rule="hyper" parents="347 667 21211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21941">
    <literal><![CDATA[
      K(x,y) * (x \ (x \ R(x,z,u))) = R(T(x,y),z,u) / (x * x)
    ]]></literal>
    <justification jstring="[para(3696(a,1),21940(a,1,2))].">
      <j1 rule="para" parents="3696 21940"/>
    </justification>
  </clause>

  <clause id="21942">
    <literal><![CDATA[
      R(T(x,y),z,u) / (x * x) = x \ (x \ R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,20857,a(flip),b,21941,a),flip(a)].">
      <j1 rule="hyper" parents="63 20857 21941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21943">
    <literal><![CDATA[
      (R(x,y,z) / (x * x)) \ K(T(x \ (x \ R(x,y,z)),x),x * x) = (x \ (x \ R(T(x,x \ 1),y,z))) \ 1
    ]]></literal>
    <justification jstring="[para(21942(a,1),11652(a,2,1))].">
      <j1 rule="para" parents="21942 11652"/>
    </justification>
  </clause>

  <clause id="21944">
    <literal><![CDATA[
      R(x,(K(y,z) * u) * (w * (v5 \ K(z,y))),v6) = R(x,u * (w * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,20646,a(flip),b,21216,a),flip(a)].">
      <j1 rule="hyper" parents="347 20646 21216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21945">
    <literal><![CDATA[
      R(x,K(y,z) * (u * (w * (v5 \ K(z,y)))),v6) = R(x,u * (w * v5),v6)
    ]]></literal>
    <justification jstring="[para(20008(a,1),21944(a,1,2))].">
      <j1 rule="para" parents="20008 21944"/>
    </justification>
  </clause>

  <clause id="21946">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) \ T(x * u,w) = L(u \ T(x * u,w),y,z)
    ]]></literal>
    <justification jstring="[para(13100(a,1),21249(a,2,1))].">
      <j1 rule="para" parents="13100 21249"/>
    </justification>
  </clause>

  <clause id="21947">
    <literal><![CDATA[
      L(K(x,y) / z,u,w) \ K(x,y) = 1 / L(z \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(13009(a,1),21255(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13009 21255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21948">
    <literal><![CDATA[
      L(K(x,y) / z,u,w) \ K(x,y) = L(1 / z,u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,9697,a(flip),b,21947,a),flip(a)].">
      <j1 rule="hyper" parents="347 9697 21947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21950">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * K(u,w) = L(K(w,u) / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(21948(a,1),13009(a,1,1))].">
      <j1 rule="para" parents="21948 13009"/>
    </justification>
  </clause>

  <clause id="21951">
    <literal><![CDATA[
      K(x,y) * (L(1 / z,u,w) \ 1) = 1 / L(z \ K(y,x),u,w)
    ]]></literal>
    <justification jstring="[para(21948(a,1),13128(a,1,2))].">
      <j1 rule="para" parents="21948 13128"/>
    </justification>
  </clause>

  <clause id="21952">
    <literal><![CDATA[
      L(K(x,y) / z,u,w) \ 1 != v5
    ]]></literal>
    <literal><![CDATA[
      L(1 / z,u,w) \ K(y,x) = v5
    ]]></literal>
    <justification jstring="[para(21950(a,1),13077(a,1))].">
      <j1 rule="para" parents="21950 13077"/>
    </justification>
  </clause>

  <clause id="21953">
    <literal><![CDATA[
      L((1 / x) * K(y,z),u,w) \ 1 = 1 / L(x \ K(y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21260,a,b,21951,a)].">
      <j1 rule="hyper" parents="63 21260 21951"/>
    </justification>
  </clause>

  <clause id="21954">
    <literal><![CDATA[
      K(x,y) * (z * (L(z,u,w) \ z)) = 1 / L(z \ K(y,x),u,w)
    ]]></literal>
    <justification jstring="[para(3638(a,1),21951(a,1,2))].">
      <j1 rule="para" parents="3638 21951"/>
    </justification>
  </clause>

  <clause id="21956">
    <literal><![CDATA[
      1 / L(x \ K(y,K(z,u)),w,v5) = L(K(y,K(z,u)) / x,w,v5) \ 1
    ]]></literal>
    <justification jstring="[para(13535(a,1),21953(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13535 21953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21957">
    <literal><![CDATA[
      1 / L(x \ K(y,K(z,u)),w,v5) = L(1 / x,w,v5) \ K(K(z,u),y)
    ]]></literal>
    <justification jstring="[hyper(21952,a,21956,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="21952 21956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21958">
    <literal><![CDATA[
      1 / L(x \ K(y,K(z,u)),w,v5) = L(1 / x,w,v5) \ K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(7291(a,1),21957(a,2,2))].">
      <j1 rule="para" parents="7291 21957"/>
    </justification>
  </clause>

  <clause id="21960">
    <literal><![CDATA[
      (x * y) \ (K(z,u) * (T(x,K(u,z)) * w)) = (x * (K(u,z) * y)) \ (x * w)
    ]]></literal>
    <justification jstring="[hyper(20101,a,21323,a)].">
      <j1 rule="hyper" parents="20101 21323"/>
    </justification>
  </clause>

  <clause id="21961">
    <literal><![CDATA[
      T(x * a(y,z,u),w / x) = T(x * a(y,z,u),x \ w)
    ]]></literal>
    <justification jstring="[hyper(20487,a,21342,a),flip(a)].">
      <j1 rule="hyper" parents="20487 21342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21962">
    <literal><![CDATA[
      T(a(x,y,z) * u,w / T(u,v5)) = T(u * a(x,y,z),u \ w)
    ]]></literal>
    <justification jstring="[hyper(21202,a,21961,a)].">
      <j1 rule="hyper" parents="21202 21961"/>
    </justification>
  </clause>

  <clause id="21964">
    <literal><![CDATA[
      1 / (1 / (x \ a(y,z,u))) = a(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(19986(a,1),21347(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19986 21347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21965">
    <literal><![CDATA[
      1 / (x \ a(y,z,u)) = (a(y,z,u) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(214,a,21964,a),flip(a)].">
      <j1 rule="hyper" parents="214 21964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21966">
    <literal><![CDATA[
      ((a(x,y,z) / u) \ 1) \ 1 = u \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(21964(a,1),219(a,1,1,1))].">
      <j1 rule="para" parents="21964 219"/>
    </justification>
  </clause>

  <clause id="21967">
    <literal><![CDATA[
      1 / ((x * (a(y,z,u) * a(y,z,u))) \ a(y,z,u)) = ((a(y,z,u) \ 1) / x) \ 1
    ]]></literal>
    <justification jstring="[para(812(a,1),21965(a,2,1))].">
      <j1 rule="para" parents="812 21965"/>
    </justification>
  </clause>

  <clause id="21968">
    <literal><![CDATA[
      L(x,y * L(K(z,u) * w,v5,v6),v7) = L(x,L(w,v5,v6) * y,v7)
    ]]></literal>
    <justification jstring="[hyper(21612,a,21707,a),flip(a)].">
      <j1 rule="hyper" parents="21612 21707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21970">
    <literal><![CDATA[
      L(x,y * L(z * T(z \ u,w),v5,v6),v7) = L(x,L(u,v5,v6) * y,v7)
    ]]></literal>
    <justification jstring="[para(1579(a,1),21968(a,1,2,2,1))].">
      <j1 rule="para" parents="1579 21968"/>
    </justification>
  </clause>

  <clause id="21971">
    <literal><![CDATA[
      L(x,y * L(z * K(u,w),v5,v6),v7) = L(x,L(z,v5,v6) * y,v7)
    ]]></literal>
    <justification jstring="[para(7372(a,1),21968(a,1,2,2,1))].">
      <j1 rule="para" parents="7372 21968"/>
    </justification>
  </clause>

  <clause id="21972">
    <literal><![CDATA[
      L(x,y * L(R(R(z,u,z),w,v5) * K(v6,v7),u,z),v8) = L(x,R(z,w,v5) * y,v8)
    ]]></literal>
    <justification jstring="[para(4376(a,1),21971(a,2,2,1))].">
      <j1 rule="para" parents="4376 21971"/>
    </justification>
  </clause>

  <clause id="21973">
    <literal><![CDATA[
      L(x,(y * z) \ (z * (u * y)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,R(u,y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(21634(a,1),21756(a,1))].">
      <j1 rule="para" parents="21634 21756"/>
    </justification>
  </clause>

  <clause id="21974">
    <literal><![CDATA[
      L(x,R(y,z,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(21973,a,21885,a)].">
      <j1 rule="hyper" parents="21973 21885"/>
    </justification>
  </clause>

  <clause id="21976">
    <literal><![CDATA[
      L(x,L(y,z,u * (w * w)),v5) = L(x,R(y,z,u),v5)
    ]]></literal>
    <justification jstring="[para(2185(a,1),21974(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2185 21974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21977">
    <literal><![CDATA[
      L(x,L(y,z,u * (w * w)),v5) = L(x,L(y,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,21974,a(flip),b,21976,a),flip(a)].">
      <j1 rule="hyper" parents="347 21974 21976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21978">
    <literal><![CDATA[
      L(x,L(((y * (z * z)) \ u) \ w,(y * (z * z)) \ u,y),v5) = L(x,u \ ((y * (z * z)) * w),v5)
    ]]></literal>
    <justification jstring="[para(561(a,1),21977(a,1,2)),flip(a)].">
      <j1 rule="para" parents="561 21977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21979">
    <literal><![CDATA[
      L(x,(y \ (z * T(u,w))) \ v5,v6) = L(x,(y \ (z * u)) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(21738,a,21785,a),flip(a)].">
      <j1 rule="hyper" parents="21738 21785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21980">
    <literal><![CDATA[
      L(x,((y * z) \ ((u * z) * y)) \ w,v5) = L(x,R(T(u,y * z),z,y) \ w,v5)
    ]]></literal>
    <justification jstring="[para(9627(a,1),21979(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9627 21979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21981">
    <literal><![CDATA[
      (x * T(y,z)) * L((x * y) \ x,u,w) = x * (y \ L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(21282(a,1),21808(a,2,2))].">
      <j1 rule="para" parents="21282 21808"/>
    </justification>
  </clause>

  <clause id="21982">
    <literal><![CDATA[
      x / T(y \ (x \ y),x) = (y \ (x \ y)) \ x
    ]]></literal>
    <justification jstring="[para(12630(a,1),21816(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12630 21816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21984">
    <literal><![CDATA[
      L(x,L(((y * y) \ z) \ u,w,v5),v6) = L(x,L(z \ u,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,21819,a(flip),b,21820,a),flip(a)].">
      <j1 rule="hyper" parents="347 21819 21820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21986">
    <literal><![CDATA[
      (x * T(y,T(z,x))) \ T(y,T(z,u)) = (x * y) \ T(y,K(u,z))
    ]]></literal>
    <justification jstring="[para(7364(a,1),21928(a,2,2))].">
      <j1 rule="para" parents="7364 21928"/>
    </justification>
  </clause>

  <clause id="21987">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * w) = (x * u) \ (x * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(21317(a,1),21960(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21317 21960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21988">
    <literal><![CDATA[
      (x * y) \ (x * (K(z,u) * 1)) = (x * (K(u,z) * y)) \ x
    ]]></literal>
    <justification jstring="[hyper(363,a,21987,a),flip(a)].">
      <j1 rule="hyper" parents="363 21987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21989">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ x = (x * u) \ (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(8(a,1),21988(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8 21988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21990">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ x = ((x * u) \ x) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,20109,a(flip),b,21989,a),flip(a)].">
      <j1 rule="hyper" parents="347 20109 21989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21991">
    <literal><![CDATA[
      ((x * (y \ z)) \ x) * K(y,u) = (x * (T(y,u) \ z)) \ x
    ]]></literal>
    <justification jstring="[para(5209(a,1),21990(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5209 21990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21993">
    <literal><![CDATA[
      L(L(x / (x / y),z,u),w,v5) \ L(L(y,z,u),w,v5) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,20216,a(flip),b,20286,a),flip(a)].">
      <j1 rule="hyper" parents="347 20216 20286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21995">
    <literal><![CDATA[
      a(x,x,L(L(x \ 1,y,z),u,w)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,15413,a,b,21993,a)].">
      <j1 rule="hyper" parents="63 15413 21993"/>
    </justification>
  </clause>

  <clause id="21996">
    <literal><![CDATA[
      a(x,x,L(L(x,y,z),u,w)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(15053,a,21995,a)].">
      <j1 rule="hyper" parents="15053 21995"/>
    </justification>
  </clause>

  <clause id="21998">
    <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(20151(a,1),20750(a,1,1,2))].">
      <j1 rule="para" parents="20151 20750"/>
    </justification>
  </clause>

  <clause id="21999">
    <literal><![CDATA[
      R(T(x \ 1,y * (x \ z)),x,y \ z) = (x * ((y \ 1) \ z)) \ ((y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(20884(a,1),21058(a,1,1))].">
      <j1 rule="para" parents="20884 21058"/>
    </justification>
  </clause>

  <clause id="22000">
    <literal><![CDATA[
      ((x / y) * R(y,z,u)) * K(y,y * (x / y)) = (R(y,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(10518(a,1),21061(a,1,2))].">
      <j1 rule="para" parents="10518 21061"/>
    </justification>
  </clause>

  <clause id="22001">
    <literal><![CDATA[
      ((x / y) * R(y,z,u)) * K(y,x) = (R(y,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(5298(a,1),22000(a,1,2))].">
      <j1 rule="para" parents="5298 22000"/>
    </justification>
  </clause>

  <clause id="22003">
    <literal><![CDATA[
      (x / y) * (R(y,z,u) * K(y,x)) = (R(y,z,u) * x) / y
    ]]></literal>
    <justification jstring="[hyper(20359,a,22001,a)].">
      <j1 rule="hyper" parents="20359 22001"/>
    </justification>
  </clause>

  <clause id="22004">
    <literal><![CDATA[
      T(x,L(y \ (y \ z),u,w) \ (y \ v5)) = T(x,L(z,u,w) \ (y * v5))
    ]]></literal>
    <justification jstring="[hyper(21087,a,19938,a)].">
      <j1 rule="hyper" parents="21087 19938"/>
    </justification>
  </clause>

  <clause id="22005">
    <literal><![CDATA[
      T(x,y \ (L((y \ z) / y,u,w) \ v5)) = T(x,L(z,u,w) \ (y * v5))
    ]]></literal>
    <justification jstring="[hyper(19455,a,22004,a)].">
      <j1 rule="hyper" parents="19455 22004"/>
    </justification>
  </clause>

  <clause id="22006">
    <literal><![CDATA[
      T(x,y \ (L((y \ z) / y,u,w) \ v5)) = T(x,(L(z,u,w) \ y) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,20671,a(flip),b,22005,a),flip(a)].">
      <j1 rule="hyper" parents="347 20671 22005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22007">
    <literal><![CDATA[
      a(a(x,y,z),z,u) = a(z,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(21150,a,20984,a),flip(a)].">
      <j1 rule="hyper" parents="21150 20984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22008">
    <literal><![CDATA[
      a(a(x,y,z),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,a(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(20984(a,1),21150(a,1))].">
      <j1 rule="para" parents="20984 21150"/>
    </justification>
  </clause>

  <clause id="22009">
    <literal><![CDATA[
      T(x,y) * (R(T(x,y),x * z,x) \ (z * T(x,u))) = x * ((x \ z) * T(x,u))
    ]]></literal>
    <justification jstring="[para(21146(a,1),21213(a,1,2,1))].">
      <j1 rule="para" parents="21146 21213"/>
    </justification>
  </clause>

  <clause id="22010">
    <literal><![CDATA[
      (((x * y) \ z) \ 1) \ (y \ (x \ z)) = (y \ (x \ z)) * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(329(a,1),21422(a,1,2)),flip(a)].">
      <j1 rule="para" parents="329 21422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22011">
    <literal><![CDATA[
      (x \ (y \ (y * z))) * ((y * x) \ (y * z)) = (((y * x) \ (y * z)) \ 1) \ (x \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),22010(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 22010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22012">
    <literal><![CDATA[
      L(x,((y * z) \ ((u * z) * y)) \ w,v5) = L(x,R(u,z,y) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(21732,a,21980,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="21732 21980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22013">
    <literal><![CDATA[
      L(x,((y * z) \ ((u * z) * y)) \ w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,R(u,z,y) \ w,v5) = v6
    ]]></literal>
    <justification jstring="[para(21980(a,2),21732(a,1))].">
      <j1 rule="para" parents="21980 21732"/>
    </justification>
  </clause>

  <clause id="22014">
    <literal><![CDATA[
      L(x,((y * z) \ ((u * z) * y)) \ (L(w,R(u,z,y) \ v5,R(u,z,y)) * v5),v6) = L(x,(R(u,z,y) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[para(874(a,1),22012(a,2,2))].">
      <j1 rule="para" parents="874 22012"/>
    </justification>
  </clause>

  <clause id="22015">
    <literal><![CDATA[
      L(x,((T(y,T(z * u,w)) * u) \ T(y * (z * u),K(z * u,w))) \ v5,v6) = L(x,R(z,u,T(y,T(z * u,w))) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(6060(a,2),22012(a,1,2,1,2))].">
      <j1 rule="para" parents="6060 22012"/>
    </justification>
  </clause>

  <clause id="22016">
    <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(20151(a,1),21998(a,1,2))].">
      <j1 rule="para" parents="20151 21998"/>
    </justification>
  </clause>

  <clause id="22017">
    <literal><![CDATA[
      T(x,y) * T(a(x,x * z,x) \ z,T(x,y)) = x * ((x \ z) * T(x,y))
    ]]></literal>
    <justification jstring="[para(21214(a,1),22009(a,1,2))].">
      <j1 rule="para" parents="21214 22009"/>
    </justification>
  </clause>

  <clause id="22018">
    <literal><![CDATA[
      T(x,y) * T((x \ z) * T(x,z),T(x,y)) = x * ((x \ z) * T(x,y))
    ]]></literal>
    <justification jstring="[para(12249(a,1),22017(a,1,2,1))].">
      <j1 rule="para" parents="12249 22017"/>
    </justification>
  </clause>

  <clause id="22019">
    <literal><![CDATA[
      ((x \ y) * T(x,y)) * T(x,z) = x * ((x \ y) * T(x,z))
    ]]></literal>
    <justification jstring="[hyper(315,a,22018,a)].">
      <j1 rule="hyper" parents="315 22018"/>
    </justification>
  </clause>

  <clause id="22020">
    <literal><![CDATA[
      a(x,y * K(z,u),w) = a(x,y,K(z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(836,a,22016,a),flip(a)].">
      <j1 rule="hyper" parents="836 22016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22022">
    <literal><![CDATA[
      ((x * y) * (z * K(u,w))) / (y * (z * K(u,w))) = R(R(x,y,z),y * z,K(u,w))
    ]]></literal>
    <justification jstring="[para(20033(a,1),20753(a,1,2))].">
      <j1 rule="para" parents="20033 20753"/>
    </justification>
  </clause>

  <clause id="22023">
    <literal><![CDATA[
      (1 / x) * ((y / L(x,z,u)) \ w) = x * ((y / L(x \ 1,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(20998(a,1),20999(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20998 20999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22024">
    <literal><![CDATA[
      ((x * y) / x) * L(L(x,z,u),w,v5) = L(L(x,w,v5),z,u) * y
    ]]></literal>
    <justification jstring="[para(20995(a,1),21014(a,1,1))].">
      <j1 rule="para" parents="20995 21014"/>
    </justification>
  </clause>

  <clause id="22025">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * T(v5,x) = v5 * L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(255(a,1),22024(a,1,1)),flip(a)].">
      <j1 rule="para" parents="255 22024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22027">
    <literal><![CDATA[
      (x / y) * (L(x / y,z,u) \ K(y,y \ x)) = L(y \ x,z,u) \ (x / y)
    ]]></literal>
    <justification jstring="[para(113(a,1),21245(a,2,1,1))].">
      <j1 rule="para" parents="113 21245"/>
    </justification>
  </clause>

  <clause id="22028">
    <literal><![CDATA[
      (x / y) * (L(y \ x,z,u) \ 1) = L(y \ x,z,u) \ (x / y)
    ]]></literal>
    <justification jstring="[para(21330(a,1),22027(a,1,2))].">
      <j1 rule="para" parents="21330 22027"/>
    </justification>
  </clause>

  <clause id="22029">
    <literal><![CDATA[
      (x / y) * L((x / y) \ z,u,w) = (y \ x) * L((y \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(4173(a,1),21288(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4173 21288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22030">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ (x \ 1),z,u) = (y / x) \ L(y / (x * x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3384,a(flip),b,22029,a),flip(a)].">
      <j1 rule="hyper" parents="63 3384 22029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22031">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ T(y,z),u,w) = (y / x) * L(x * K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(13044(a,1),22029(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13044 22029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22032">
    <literal><![CDATA[
      (x / y) \ L(x / (y * y),z,u) = y \ (x * L(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(1741,a,22030,a),flip(a)].">
      <j1 rule="hyper" parents="1741 22030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22033">
    <literal><![CDATA[
      (x / y) \ L(x / (y * y),z,u) = y \ (x \ L(x,z,u))
    ]]></literal>
    <justification jstring="[para(3343(a,1),22032(a,2,2))].">
      <j1 rule="para" parents="3343 22032"/>
    </justification>
  </clause>

  <clause id="22034">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ T(y,z),u,w) = (T(y,z) / x) * L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,21933,a(flip),b,22031,a),flip(a)].">
      <j1 rule="hyper" parents="347 21933 22031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22035">
    <literal><![CDATA[
      T((x \ y) * L((x \ y) \ y,z,u),w) = (T(y,w) / x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21285,a,b,22034,a)].">
      <j1 rule="hyper" parents="63 21285 22034"/>
    </justification>
  </clause>

  <clause id="22036">
    <literal><![CDATA[
      T(L(x,y,z) * (x \ u),w) = (T(u,w) / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(742(a,1),22035(a,1,1))].">
      <j1 rule="para" parents="742 22035"/>
    </justification>
  </clause>

  <clause id="22037">
    <literal><![CDATA[
      T(L(x,y,z) * (x \ u),K(w,u)) = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3027(a,1),22036(a,2,1,1))].">
      <j1 rule="para" parents="3027 22036"/>
    </justification>
  </clause>

  <clause id="22038">
    <literal><![CDATA[
      T((x / y) * L(y,z,u),K(x,w)) = L(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(6895,a,22037,a)].">
      <j1 rule="hyper" parents="6895 22037"/>
    </justification>
  </clause>

  <clause id="22039">
    <literal><![CDATA[
      T((x * (y \ x)) * L(((x \ y) \ 1) \ 1,z,u),K(x,w)) = L(((x \ y) \ 1) \ 1,z,u) * ((((x \ y) \ 1) \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(3258(a,1),22038(a,1,1,1))].">
      <j1 rule="para" parents="3258 22038"/>
    </justification>
  </clause>

  <clause id="22040">
    <literal><![CDATA[
      ((x \ K(x,x \ 1)) * a(y,z,u)) * x = (a(y,z,u) * (1 / x)) * x
    ]]></literal>
    <justification jstring="[hyper(9660,a,21299,a),flip(a)].">
      <j1 rule="hyper" parents="9660 21299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22041">
    <literal><![CDATA[
      ((x \ K(x,x \ 1)) * a(y,z,u)) * x = R(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,2259,a(flip),b,22040,a),flip(a)].">
      <j1 rule="hyper" parents="347 2259 22040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22042">
    <literal><![CDATA[
      ((x \ K(x,x \ 1)) * a(y,z,u)) * x = L(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,14319,a(flip),b,22041,a),flip(a)].">
      <j1 rule="hyper" parents="347 14319 22041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22043">
    <literal><![CDATA[
      L(a(x,y,z),u,u) / T(u,u \ 1) = a(x,y,z) * (u \ 1)
    ]]></literal>
    <justification jstring="[hyper(131,a,22042,a(flip),b,21299,a)].">
      <j1 rule="hyper" parents="131 22042 21299"/>
    </justification>
  </clause>

  <clause id="22044">
    <literal><![CDATA[
      ((1 / x) * a(y,z,u)) * x = L(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(1925(a,1),22042(a,1,1,1))].">
      <j1 rule="para" parents="1925 22042"/>
    </justification>
  </clause>

  <clause id="22045">
    <literal><![CDATA[
      (T(x,y) \ z) * L((T(x,y) \ z) \ u,w,v5) = (z / x) * L((z / x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22029,a(flip),b,21337,a)].">
      <j1 rule="hyper" parents="63 22029 21337"/>
    </justification>
  </clause>

  <clause id="22046">
    <literal><![CDATA[
      x / (y \ (L(z,u,w) * (z \ y))) = (y \ (L(z,u,w) * (z \ y))) \ x
    ]]></literal>
    <justification jstring="[para(742(a,1),21413(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="742 21413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22047">
    <literal><![CDATA[
      ((x \ (L(y,z,u) * (y \ x))) \ w) \ w = x \ (L(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(214,a,22046,a)].">
      <j1 rule="hyper" parents="214 22046"/>
    </justification>
  </clause>

  <clause id="22048">
    <literal><![CDATA[
      ((x \ (L(y,z,u) * (y \ x))) \ w) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      x \ (L(y,z,u) * (y \ x)) = v5
    ]]></literal>
    <justification jstring="[para(22046(a,1),359(a,1,1))].">
      <j1 rule="para" parents="22046 359"/>
    </justification>
  </clause>

  <clause id="22049">
    <literal><![CDATA[
      (x * ((L(y,z,u) * (y \ x)) \ x)) \ x = x \ (L(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3272,a(flip),b,22047,a)].">
      <j1 rule="hyper" parents="63 3272 22047"/>
    </justification>
  </clause>

  <clause id="22050">
    <literal><![CDATA[
      x / T(x * ((L(y,z,u) * (y \ x)) \ x),x \ (L(y,z,u) * (y \ x))) = x \ (L(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,6306,a,b,22049,a)].">
      <j1 rule="hyper" parents="63 6306 22049"/>
    </justification>
  </clause>

  <clause id="22051">
    <literal><![CDATA[
      L(x,y \ ((z * ((u * u) * w)) * v5),v6) = L(x,y \ ((w * z) * ((u * u) * v5)),v6)
    ]]></literal>
    <justification jstring="[para(125(a,1),21836(a,2,2,2))].">
      <j1 rule="para" parents="125 21836"/>
    </justification>
  </clause>

  <clause id="22052">
    <literal><![CDATA[
      1 / ((a(x,y,z) * a(x,y,z)) \ (u \ a(x,y,z))) = ((a(x,y,z) \ 1) / u) \ 1
    ]]></literal>
    <justification jstring="[para(459(a,1),21967(a,1,2))].">
      <j1 rule="para" parents="459 21967"/>
    </justification>
  </clause>

  <clause id="22053">
    <literal><![CDATA[
      (((x * y) \ (x * z)) \ 1) \ (y \ z) = (y \ z) * ((x * y) \ (x * z))
    ]]></literal>
    <justification jstring="[para(9(a,1),22011(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 22011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22054">
    <literal><![CDATA[
      R(x,((y * z) \ (y * u)) \ (z \ u),w) = R(x,(z \ u) * ((y * z) \ (y * u)),w)
    ]]></literal>
    <justification jstring="[para(22053(a,1),20655(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22053 20655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22055">
    <literal><![CDATA[
      R(R(x,y,z),y * z,K(u,w)) = R(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(595,a,22022,a),flip(a)].">
      <j1 rule="hyper" parents="595 22022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22056">
    <literal><![CDATA[
      R(x,y,z * K(u,w)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(20140,a,22055,a),flip(a)].">
      <j1 rule="hyper" parents="20140 22055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22057">
    <literal><![CDATA[
      R(x,y,z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(22055(a,1),20140(a,1))].">
      <j1 rule="para" parents="22055 20140"/>
    </justification>
  </clause>

  <clause id="22058">
    <literal><![CDATA[
      R(x,y,K(z,u) * w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(20517,a,22056,a)].">
      <j1 rule="hyper" parents="20517 22056"/>
    </justification>
  </clause>

  <clause id="22062">
    <literal><![CDATA[
      R(x,y,T(z,u) * w) = R(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(5564(a,1),22056(a,1,3))].">
      <j1 rule="para" parents="5564 22056"/>
    </justification>
  </clause>

  <clause id="22063">
    <literal><![CDATA[
      R(x,y,(z / u) * w) = R(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[para(7768(a,1),22056(a,1,3))].">
      <j1 rule="para" parents="7768 22056"/>
    </justification>
  </clause>

  <clause id="22064">
    <literal><![CDATA[
      R(x,y,z * (u * K(w,v5))) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(7609(a,1),22056(a,1,3))].">
      <j1 rule="para" parents="7609 22056"/>
    </justification>
  </clause>

  <clause id="22065">
    <literal><![CDATA[
      R(x,y,((z \ u) * z) \ w) = R(x,y,u \ w)
    ]]></literal>
    <justification jstring="[para(9886(a,1),22056(a,1,3))].">
      <j1 rule="para" parents="9886 22056"/>
    </justification>
  </clause>

  <clause id="22066">
    <literal><![CDATA[
      R(x,y,z * (K(u,w) * v5)) = R(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(11070(a,1),22056(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11070 22056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22067">
    <literal><![CDATA[
      R(x,y,z \ K(u,w)) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(12973(a,1),22056(a,1,3))].">
      <j1 rule="para" parents="12973 22056"/>
    </justification>
  </clause>

  <clause id="22068">
    <literal><![CDATA[
      R(x,y,z \ (u / w)) = R(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(13113(a,1),22056(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13113 22056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22069">
    <literal><![CDATA[
      R(x,y,z \ (u * (w / u))) = R(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(14664(a,1),22056(a,1,3))].">
      <j1 rule="para" parents="14664 22056"/>
    </justification>
  </clause>

  <clause id="22070">
    <literal><![CDATA[
      R(x,y,z \ (K(u,w) * v5)) = R(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(20369(a,1),22056(a,1,3))].">
      <j1 rule="para" parents="20369 22056"/>
    </justification>
  </clause>

  <clause id="22071">
    <literal><![CDATA[
      R(x,y,z \ (u * T(w,v5))) = R(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(20791(a,1),22056(a,1,3))].">
      <j1 rule="para" parents="20791 22056"/>
    </justification>
  </clause>

  <clause id="22072">
    <literal><![CDATA[
      L(R(R(x * K(y,z),u,x),w,v5),u,x) = R(x * K(y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(22056(a,1),21493(a,1,1,1))].">
      <j1 rule="para" parents="22056 21493"/>
    </justification>
  </clause>

  <clause id="22073">
    <literal><![CDATA[
      R(x,y * z,K(u,w) * v5) = R(x,z * y,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,20553,a,b,22058,a),flip(a)].">
      <j1 rule="hyper" parents="347 20553 22058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22076">
    <literal><![CDATA[
      R(x,y,((z * u) * (u * z)) \ w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21127,a,b,22058,a)].">
      <j1 rule="hyper" parents="63 21127 22058"/>
    </justification>
  </clause>

  <clause id="22077">
    <literal><![CDATA[
      R(x,y,(z * u) \ w) = R(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[para(10274(a,1),22058(a,1,3))].">
      <j1 rule="para" parents="10274 22058"/>
    </justification>
  </clause>

  <clause id="22078">
    <literal><![CDATA[
      R(x,y,(T(z,u) \ w) * v5) = R(x,y,(z \ w) * v5)
    ]]></literal>
    <justification jstring="[para(11712(a,1),22058(a,1,3))].">
      <j1 rule="para" parents="11712 22058"/>
    </justification>
  </clause>

  <clause id="22080">
    <literal><![CDATA[
      R(x,y,z * (T(u,w) \ v5)) = R(x,y,z * (u \ v5))
    ]]></literal>
    <justification jstring="[para(19545(a,1),22058(a,1,3))].">
      <j1 rule="para" parents="19545 22058"/>
    </justification>
  </clause>

  <clause id="22081">
    <literal><![CDATA[
      R(x,y,(z * T(u,w)) \ v5) = R(x,y,(z * u) \ v5)
    ]]></literal>
    <justification jstring="[para(20828(a,1),22058(a,1,3))].">
      <j1 rule="para" parents="20828 22058"/>
    </justification>
  </clause>

  <clause id="22082">
    <literal><![CDATA[
      R(x,y,(z \ K(u,w)) \ v5) = R(x,y,(z \ 1) \ v5)
    ]]></literal>
    <justification jstring="[para(20832(a,1),22058(a,1,3))].">
      <j1 rule="para" parents="20832 22058"/>
    </justification>
  </clause>

  <clause id="22083">
    <literal><![CDATA[
      R(x,y,((z / u) \ w) * v5) = R(x,y,((u \ z) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(20721(a,1),22058(a,1,3))].">
      <j1 rule="para" parents="20721 22058"/>
    </justification>
  </clause>

  <clause id="22084">
    <literal><![CDATA[
      R(x,y,(z * (u * T(w,v5))) \ v6) = R(x,y,(z * (u * w)) \ v6)
    ]]></literal>
    <justification jstring="[para(21142(a,1),22058(a,1,3))].">
      <j1 rule="para" parents="21142 22058"/>
    </justification>
  </clause>

  <clause id="22085">
    <literal><![CDATA[
      R(x / y,y,x \ 1) = K(z,u) / (y * (x \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(659,a,22067,a),flip(a)].">
      <j1 rule="hyper" parents="659 22067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22086">
    <literal><![CDATA[
      R(x,y,z \ K(u,w)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,2190,a(flip),b,22067,a),flip(a)].">
      <j1 rule="hyper" parents="347 2190 22067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22087">
    <literal><![CDATA[
      R(x,y,(z \ u) * z) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(330(a,1),22057(a,1,3))].">
      <j1 rule="para" parents="330 22057"/>
    </justification>
  </clause>

  <clause id="22088">
    <literal><![CDATA[
      R(x,y,L(z,u,w) * (w * u)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,w * (u * z)) = v5
    ]]></literal>
    <justification jstring="[para(537(a,1),22057(a,1,3))].">
      <j1 rule="para" parents="537 22057"/>
    </justification>
  </clause>

  <clause id="22089">
    <literal><![CDATA[
      R(x,y,z * (u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z * (w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(6075(a,1),22057(a,1,3))].">
      <j1 rule="para" parents="6075 22057"/>
    </justification>
  </clause>

  <clause id="22090">
    <literal><![CDATA[
      R(x,y,z * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,T(z,v5) * u) = w
    ]]></literal>
    <justification jstring="[para(6110(a,1),22057(a,1,3))].">
      <j1 rule="para" parents="6110 22057"/>
    </justification>
  </clause>

  <clause id="22091">
    <literal><![CDATA[
      R(x,y,K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(7076(a,1),22057(a,1,3))].">
      <j1 rule="para" parents="7076 22057"/>
    </justification>
  </clause>

  <clause id="22092">
    <literal><![CDATA[
      R(x,y,T(z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ w) = v5
    ]]></literal>
    <justification jstring="[para(8122(a,1),22057(a,1,3))].">
      <j1 rule="para" parents="8122 22057"/>
    </justification>
  </clause>

  <clause id="22093">
    <literal><![CDATA[
      R(x,y,(z / u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,(u \ z) * w) = v5
    ]]></literal>
    <justification jstring="[para(7768(a,1),22057(a,1,3))].">
      <j1 rule="para" parents="7768 22057"/>
    </justification>
  </clause>

  <clause id="22094">
    <literal><![CDATA[
      R(x,y,z \ (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ (w * u)) = v5
    ]]></literal>
    <justification jstring="[para(13432(a,1),22057(a,1,3))].">
      <j1 rule="para" parents="13432 22057"/>
    </justification>
  </clause>

  <clause id="22095">
    <literal><![CDATA[
      R(x,y,z \ (K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ v5) = v6
    ]]></literal>
    <justification jstring="[para(20369(a,1),22057(a,1,3))].">
      <j1 rule="para" parents="20369 22057"/>
    </justification>
  </clause>

  <clause id="22097">
    <literal><![CDATA[
      R(x,y,z * (K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z * v5) = v6
    ]]></literal>
    <justification jstring="[para(9400(a,1),22091(a,1,3))].">
      <j1 rule="para" parents="9400 22091"/>
    </justification>
  </clause>

  <clause id="22098">
    <literal><![CDATA[
      R(x,y,(z * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,(u * z) \ w) = v5
    ]]></literal>
    <justification jstring="[para(10274(a,1),22091(a,1,3))].">
      <j1 rule="para" parents="10274 22091"/>
    </justification>
  </clause>

  <clause id="22099">
    <literal><![CDATA[
      R(x,y,(T(z,u) \ w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y,(z \ w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(11712(a,1),22091(a,1,3))].">
      <j1 rule="para" parents="11712 22091"/>
    </justification>
  </clause>

  <clause id="22100">
    <literal><![CDATA[
      R(x,y,z * (u * (w / v5))) = R(x,y,z * (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(5927(a,1),22064(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5927 22064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22101">
    <literal><![CDATA[
      R(x,y,z * (u * ((w \ v5) \ v5))) = R(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(5954(a,1),22064(a,1,3,2))].">
      <j1 rule="para" parents="5954 22064"/>
    </justification>
  </clause>

  <clause id="22102">
    <literal><![CDATA[
      R(x,y,z * (u * (K(w,v5) * v6))) = R(x,y,z * (u * v6))
    ]]></literal>
    <justification jstring="[para(11070(a,1),22064(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="11070 22064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22103">
    <literal><![CDATA[
      R(x,y,z * (u \ K(w,v5))) = R(x,y,z * (u \ 1))
    ]]></literal>
    <justification jstring="[para(12973(a,1),22064(a,1,3,2))].">
      <j1 rule="para" parents="12973 22064"/>
    </justification>
  </clause>

  <clause id="22104">
    <literal><![CDATA[
      R(x,y,z * (u \ (w / v5))) = R(x,y,z * (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(13113(a,1),22064(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="13113 22064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22105">
    <literal><![CDATA[
      R(x,y,z * (K(u,w) * v5)) = R(x,y,v5 * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,20497,a,b,22066,a),flip(a)].">
      <j1 rule="hyper" parents="347 20497 22066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22106">
    <literal><![CDATA[
      R(x,y,z * ((u / w) \ v5)) = R(x,y,z * ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(5441(a,1),22066(a,1,3,2))].">
      <j1 rule="para" parents="5441 22066"/>
    </justification>
  </clause>

  <clause id="22107">
    <literal><![CDATA[
      R(x,y,(z \ T(u,w)) * v5) = R(x,y,(z \ u) * v5)
    ]]></literal>
    <justification jstring="[para(20179(a,1),22066(a,1,3))].">
      <j1 rule="para" parents="20179 22066"/>
    </justification>
  </clause>

  <clause id="22108">
    <literal><![CDATA[
      R(x,y,(z * T(u,w)) * v5) = R(x,y,(z * u) * v5)
    ]]></literal>
    <justification jstring="[para(20808(a,1),22066(a,1,3))].">
      <j1 rule="para" parents="20808 22066"/>
    </justification>
  </clause>

  <clause id="22109">
    <literal><![CDATA[
      R(x,y,z * ((u \ T(w,v5)) \ v6)) = R(x,y,z * ((u \ w) \ v6))
    ]]></literal>
    <justification jstring="[para(20834(a,1),22066(a,1,3,2))].">
      <j1 rule="para" parents="20834 22066"/>
    </justification>
  </clause>

  <clause id="22110">
    <literal><![CDATA[
      R(x,y,(z * (u * T(w,v5))) * v6) = R(x,y,(z * (u * w)) * v6)
    ]]></literal>
    <justification jstring="[para(21137(a,1),22066(a,1,3))].">
      <j1 rule="para" parents="21137 22066"/>
    </justification>
  </clause>

  <clause id="22111">
    <literal><![CDATA[
      R(x,y,z \ ((u \ 1) \ z)) = R(x,y,(z * u) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3621,a(flip),b,22068,a),flip(a)].">
      <j1 rule="hyper" parents="63 3621 22068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22112">
    <literal><![CDATA[
      R(x,y,z \ ((u * u) * w)) = R(x,y,z \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21432,a(flip),b,22069,a)].">
      <j1 rule="hyper" parents="63 21432 22069"/>
    </justification>
  </clause>

  <clause id="22114">
    <literal><![CDATA[
      R(x,y,z \ ((u / w) \ v5)) = R(x,y,z \ ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(5441(a,1),22070(a,1,3,2))].">
      <j1 rule="para" parents="5441 22070"/>
    </justification>
  </clause>

  <clause id="22115">
    <literal><![CDATA[
      R(x,y,z \ (u * (K(w,v5) * v6))) = R(x,y,z \ (u * v6))
    ]]></literal>
    <justification jstring="[para(5885(a,1),22070(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5885 22070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22116">
    <literal><![CDATA[
      R(x,y,z \ (u * (w * v5))) = R(x,y,z \ (u * (v5 * w)))
    ]]></literal>
    <justification jstring="[para(9586(a,1),22070(a,1,3,2))].">
      <j1 rule="para" parents="9586 22070"/>
    </justification>
  </clause>

  <clause id="22117">
    <literal><![CDATA[
      R(x,y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,z * y,u) = w
    ]]></literal>
    <justification jstring="[para(22073(a,1),22091(a,1))].">
      <j1 rule="para" parents="22073 22091"/>
    </justification>
  </clause>

  <clause id="22119">
    <literal><![CDATA[
      R(x,y,((z * u) * u) * z) = R(x,y,a(z * u,u,z))
    ]]></literal>
    <justification jstring="[para(14(a,2),22076(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14 22076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22120">
    <literal><![CDATA[
      R(x,y,((z \ 1) * u) \ w) = R(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(20901,a,22077,a),flip(a)].">
      <j1 rule="hyper" parents="20901 22077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22121">
    <literal><![CDATA[
      R(x,y,((z \ 1) * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,(u * z) \ w) = v5
    ]]></literal>
    <justification jstring="[para(22077(a,1),20901(a,1))].">
      <j1 rule="para" parents="22077 20901"/>
    </justification>
  </clause>

  <clause id="22122">
    <literal><![CDATA[
      R(x,y,z * L(T(u,w),v5,v6)) = R(x,y,L(u,v5,v6) * z)
    ]]></literal>
    <justification jstring="[para(5028(a,1),22105(a,1,3,2))].">
      <j1 rule="para" parents="5028 22105"/>
    </justification>
  </clause>

  <clause id="22123">
    <literal><![CDATA[
      R(x,y,z * (u * T(w,v5))) = R(x,y,(u * w) * z)
    ]]></literal>
    <justification jstring="[para(5573(a,1),22105(a,1,3,2))].">
      <j1 rule="para" parents="5573 22105"/>
    </justification>
  </clause>

  <clause id="22124">
    <literal><![CDATA[
      R(x,y,((z * u) \ w) * v5) = R(x,y,v5 * ((u * z) \ w))
    ]]></literal>
    <justification jstring="[para(10274(a,1),22105(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10274 22105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22125">
    <literal><![CDATA[
      R(x,y,(z \ (u \ T(w,v5))) * v6) = R(x,y,v6 * (z \ (u \ w)))
    ]]></literal>
    <justification jstring="[para(21034(a,1),22105(a,1,3))].">
      <j1 rule="para" parents="21034 22105"/>
    </justification>
  </clause>

  <clause id="22126">
    <literal><![CDATA[
      R(x,y,z \ ((u \ (1 / u)) * w)) = R(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(307(a,1),22112(a,1,3,2,1))].">
      <j1 rule="para" parents="307 22112"/>
    </justification>
  </clause>

  <clause id="22127">
    <literal><![CDATA[
      R(x,y,z \ ((u \ 1) \ w)) = R(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(495(a,1),22112(a,1,3,2))].">
      <j1 rule="para" parents="495 22112"/>
    </justification>
  </clause>

  <clause id="22128">
    <literal><![CDATA[
      R(x,y,(z * u) \ ((w * u) * z)) = R(x,y,R(T(w,z * u),u,z))
    ]]></literal>
    <justification jstring="[para(9627(a,1),22071(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9627 22071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22129">
    <literal><![CDATA[
      R(x,y,(((z * u) \ z) \ w) * v5) = R(x,y,((z \ (z / u)) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(3257(a,1),22078(a,1,3,1,1))].">
      <j1 rule="para" parents="3257 22078"/>
    </justification>
  </clause>

  <clause id="22130">
    <literal><![CDATA[
      R(x,y,z * (((u * w) \ u) \ v5)) = R(x,y,z * ((u \ (u / w)) \ v5))
    ]]></literal>
    <justification jstring="[para(3257(a,1),22080(a,1,3,2,1))].">
      <j1 rule="para" parents="3257 22080"/>
    </justification>
  </clause>

  <clause id="22131">
    <literal><![CDATA[
      R(x,y,(z * L(T(u,w),v5,v6)) \ v7) = R(x,y,(z * L(u,v5,v6)) \ v7)
    ]]></literal>
    <justification jstring="[para(25(a,2),22081(a,1,3,1,2))].">
      <j1 rule="para" parents="25 22081"/>
    </justification>
  </clause>

  <clause id="22132">
    <literal><![CDATA[
      R(x,y,(z * ((u * u) \ (w * u))) \ v5) = R(x,y,(z * (w * (u \ 1))) \ v5)
    ]]></literal>
    <justification jstring="[para(791(a,1),22081(a,1,3,1,2))].">
      <j1 rule="para" parents="791 22081"/>
    </justification>
  </clause>

  <clause id="22133">
    <literal><![CDATA[
      R(x,y,(z \ K(u,w)) \ v5) = R(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,2241,a(flip),b,22082,a),flip(a)].">
      <j1 rule="hyper" parents="347 2241 22082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22134">
    <literal><![CDATA[
      R(x,y,z * (u \ K(w,v5))) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,2204,a(flip),b,22103,a),flip(a)].">
      <j1 rule="hyper" parents="347 2204 22103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22135">
    <literal><![CDATA[
      R(x,y,(z \ (u / w)) * v5) = R(x,y,(z \ (w \ u)) * v5)
    ]]></literal>
    <justification jstring="[para(113(a,1),22107(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="113 22107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22136">
    <literal><![CDATA[
      R(x,y,(z \ (u \ T(u * w,w))) * v5) = R(x,y,(z \ R(w,u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(4214(a,1),22107(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="4214 22107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22137">
    <literal><![CDATA[
      R(x,y,(z * ((u * w) * (u \ 1))) * v5) = R(x,y,(z * R(w,u,u)) * v5)
    ]]></literal>
    <justification jstring="[para(915(a,1),22108(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="915 22108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22138">
    <literal><![CDATA[
      R(x,y,(K(z,u) * (w * (u \ v5))) * v6) = R(x,y,((T(u,z) \ v5) * w) * v6)
    ]]></literal>
    <justification jstring="[para(21922(a,1),22108(a,1,3,1))].">
      <j1 rule="para" parents="21922 22108"/>
    </justification>
  </clause>

  <clause id="22139">
    <literal><![CDATA[
      R(x,y,z * (u * L(T(w,v5),v6,v7))) = R(x,y,(u * L(w,v6,v7)) * z)
    ]]></literal>
    <justification jstring="[para(25(a,2),22123(a,1,3,2,2))].">
      <j1 rule="para" parents="25 22123"/>
    </justification>
  </clause>

  <clause id="22140">
    <literal><![CDATA[
      R(x,y,z * (u * R(T(w,v5),v6,v7))) = R(x,y,(u * R(w,v6,v7)) * z)
    ]]></literal>
    <justification jstring="[para(27(a,2),22123(a,1,3,2,2))].">
      <j1 rule="para" parents="27 22123"/>
    </justification>
  </clause>

  <clause id="22141">
    <literal><![CDATA[
      R(x,y,z \ ((u / (w \ 1)) \ v5)) = R(x,y,z \ ((u / w) \ v5))
    ]]></literal>
    <justification jstring="[para(6488(a,1),22126(a,1,3,2))].">
      <j1 rule="para" parents="6488 22126"/>
    </justification>
  </clause>

  <clause id="22142">
    <literal><![CDATA[
      R(x,y,(z * u) \ z) = R(x,y,z \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,22111,a(flip),b,22127,a)].">
      <j1 rule="hyper" parents="63 22111 22127"/>
    </justification>
  </clause>

  <clause id="22143">
    <literal><![CDATA[
      R(x,y,z \ (((u \ 1) \ (u \ w)) \ v5)) = R(x,y,z \ (L(1 / w,u,u) \ v5))
    ]]></literal>
    <justification jstring="[para(15287(a,1),22127(a,1,3,2,1))].">
      <j1 rule="para" parents="15287 22127"/>
    </justification>
  </clause>

  <clause id="22144">
    <literal><![CDATA[
      K(x,y) / (z * (u \ K(x,y))) = 1 / (z * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(659,a,22085,a),flip(a)].">
      <j1 rule="hyper" parents="659 22085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22145">
    <literal><![CDATA[
      R(x,y,z * ((u * u) \ w)) = R(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(22089,a,2203,a)].">
      <j1 rule="hyper" parents="22089 2203"/>
    </justification>
  </clause>

  <clause id="22146">
    <literal><![CDATA[
      R(x,y,z * ((u * u) * w)) = R(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),22145(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="9 22145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22147">
    <literal><![CDATA[
      R(x,y,z * L(T(u,w),w,w)) = R(x,y,z * (w * (u * w)))
    ]]></literal>
    <justification jstring="[para(263(a,1),22145(a,1,3,2))].">
      <j1 rule="para" parents="263 22145"/>
    </justification>
  </clause>

  <clause id="22148">
    <literal><![CDATA[
      R(x,y,(z * (u \ 1)) * w) = R(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[para(828(a,1),22145(a,1,3))].">
      <j1 rule="para" parents="828 22145"/>
    </justification>
  </clause>

  <clause id="22149">
    <literal><![CDATA[
      R(x,y,(z * (u * (w \ 1))) * v5) = R(x,y,(z * (u * w)) * v5)
    ]]></literal>
    <justification jstring="[para(968(a,1),22145(a,1,3))].">
      <j1 rule="para" parents="968 22145"/>
    </justification>
  </clause>

  <clause id="22150">
    <literal><![CDATA[
      R(x,y,(z * (z * u)) * u) = R(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15049,a(flip),b,22146,a),flip(a)].">
      <j1 rule="hyper" parents="63 15049 22146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22151">
    <literal><![CDATA[
      R(x,y,z * ((u \ (1 / u)) * w)) = R(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(307(a,1),22146(a,1,3,2,1))].">
      <j1 rule="para" parents="307 22146"/>
    </justification>
  </clause>

  <clause id="22152">
    <literal><![CDATA[
      R(x,y,((z * u) * u) * w) = R(x,y,R(z,u,u) * w)
    ]]></literal>
    <justification jstring="[para(593(a,1),22146(a,1,3))].">
      <j1 rule="para" parents="593 22146"/>
    </justification>
  </clause>

  <clause id="22154">
    <literal><![CDATA[
      R(x,y,(L(z,u,w) \ z) * v5) = R(x,y,(z * L(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(1409(a,1),22148(a,1,3,1))].">
      <j1 rule="para" parents="1409 22148"/>
    </justification>
  </clause>

  <clause id="22155">
    <literal><![CDATA[
      R(x,y,(z * a(u,u,z)) * w) = R(x,y,L(z,u,u) * w)
    ]]></literal>
    <justification jstring="[para(14611(a,1),22148(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="14611 22148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22156">
    <literal><![CDATA[
      R(x,y,z * ((u / (w \ 1)) \ v5)) = R(x,y,z * ((u / w) \ v5))
    ]]></literal>
    <justification jstring="[para(6488(a,1),22151(a,1,3,2))].">
      <j1 rule="para" parents="6488 22151"/>
    </justification>
  </clause>

  <clause id="22157">
    <literal><![CDATA[
      R(x,y,z \ ((u * (w \ 1)) * v5)) = R(x,y,z \ (v5 * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(22094,a,21434,a)].">
      <j1 rule="hyper" parents="22094 21434"/>
    </justification>
  </clause>

  <clause id="22158">
    <literal><![CDATA[
      R(x,y,z \ ((u \ 1) * w)) = R(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[hyper(22094,a,2388,a)].">
      <j1 rule="hyper" parents="22094 2388"/>
    </justification>
  </clause>

  <clause id="22159">
    <literal><![CDATA[
      R(x,y,z \ ((u * T(w,v5 * v5)) * v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ (((v5 * v5) * v6) * (u * ((v5 * v5) \ w)))) = v7
    ]]></literal>
    <justification jstring="[para(1092(a,1),22094(a,1,3,2))].">
      <j1 rule="para" parents="1092 22094"/>
    </justification>
  </clause>

  <clause id="22160">
    <literal><![CDATA[
      R(x,y,z \ (u \ ((1 / w) \ w))) = R(x,y,z \ (((1 / w) \ w) * u))
    ]]></literal>
    <justification jstring="[para(12273(a,1),22158(a,1,3,2))].">
      <j1 rule="para" parents="12273 22158"/>
    </justification>
  </clause>

  <clause id="22162">
    <literal><![CDATA[
      R(x,y,z \ ((u * w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ ((w * u) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(10281(a,1),22095(a,1,3,2))].">
      <j1 rule="para" parents="10281 22095"/>
    </justification>
  </clause>

  <clause id="22163">
    <literal><![CDATA[
      R(x,y,z \ (((u / w) \ v5) * v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ (((w \ u) \ v5) * v6)) = v7
    ]]></literal>
    <justification jstring="[para(20721(a,1),22095(a,1,3,2))].">
      <j1 rule="para" parents="20721 22095"/>
    </justification>
  </clause>

  <clause id="22164">
    <literal><![CDATA[
      R(x,y,z * (T(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z * (u * v5)) = v6
    ]]></literal>
    <justification jstring="[para(4974(a,1),22097(a,1,3,2))].">
      <j1 rule="para" parents="4974 22097"/>
    </justification>
  </clause>

  <clause id="22165">
    <literal><![CDATA[
      R(x,y,z * ((u / w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z * ((w \ u) \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(5441(a,1),22097(a,1,3,2))].">
      <j1 rule="para" parents="5441 22097"/>
    </justification>
  </clause>

  <clause id="22166">
    <literal><![CDATA[
      R(x,y,a(z * u,u,z)) = R(x,y,R(z,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,22119,a(flip),b,22152,a)].">
      <j1 rule="hyper" parents="63 22119 22152"/>
    </justification>
  </clause>

  <clause id="22167">
    <literal><![CDATA[
      R(x,y,a(z * u,u,z)) = R(x,y,z * R(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,20497,a,b,22166,a),flip(a)].">
      <j1 rule="hyper" parents="347 20497 22166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22168">
    <literal><![CDATA[
      R(x,y,a(z * u,u,z)) = R(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,15266,a(flip),b,22167,a),flip(a)].">
      <j1 rule="hyper" parents="347 15266 22167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22169">
    <literal><![CDATA[
      R(x,y,(z * z) * ((1 / z) * (u \ (z \ u)))) = R(x,y,z * R(z \ 1,z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,3958,a(flip),b,22100,a),flip(a)].">
      <j1 rule="hyper" parents="63 3958 22100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22170">
    <literal><![CDATA[
      R(x,y,(z * ((u \ w) \ w)) * v5) = R(x,y,v5 * (z * u))
    ]]></literal>
    <justification jstring="[hyper(20517,a,22101,a)].">
      <j1 rule="hyper" parents="20517 22101"/>
    </justification>
  </clause>

  <clause id="22171">
    <literal><![CDATA[
      R(x,y,(1 / z) * (u \ (z \ u))) = R(x,y,z * L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(12302,a,22104,a),flip(a)].">
      <j1 rule="hyper" parents="12302 22104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22172">
    <literal><![CDATA[
      R(x,y,z \ (((u * u) * w) * v5)) = R(x,y,z \ (w * ((u * u) * v5)))
    ]]></literal>
    <justification jstring="[para(6635(a,1),22115(a,1,3,2))].">
      <j1 rule="para" parents="6635 22115"/>
    </justification>
  </clause>

  <clause id="22173">
    <literal><![CDATA[
      R(x,y,z \ ((u * T(w,v5)) * v6)) = R(x,y,z \ ((u * w) * v6))
    ]]></literal>
    <justification jstring="[para(20808(a,1),22115(a,1,3,2))].">
      <j1 rule="para" parents="20808 22115"/>
    </justification>
  </clause>

  <clause id="22174">
    <literal><![CDATA[
      R(x,y,z \ ((u * (K(w,v5) * v6)) * v7)) = R(x,y,z \ ((u * v6) * v7))
    ]]></literal>
    <justification jstring="[para(21138(a,1),22115(a,1,3,2))].">
      <j1 rule="para" parents="21138 22115"/>
    </justification>
  </clause>

  <clause id="22175">
    <literal><![CDATA[
      R(x,y,z \ ((u * (w \ K(v5,v6))) * v7)) = R(x,y,z \ ((u * (w \ 1)) * v7))
    ]]></literal>
    <justification jstring="[para(21139(a,1),22115(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="21139 22115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22176">
    <literal><![CDATA[
      R(x,y,z \ (u * ((w * w) * v5))) = R(x,y,(z \ (u * v5)) * (w * w))
    ]]></literal>
    <justification jstring="[para(728(a,1),22116(a,1,3)),flip(a)].">
      <j1 rule="para" parents="728 22116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22177">
    <literal><![CDATA[
      R(x,y,((z * (z \ (u / z))) \ w) * v5) = R(x,y,v5 * ((R(z,u,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(12200(a,2),22124(a,2,3,2,1))].">
      <j1 rule="para" parents="12200 22124"/>
    </justification>
  </clause>

  <clause id="22178">
    <literal><![CDATA[
      R(x,y,(z \ L(u \ w,u,v5)) * v6) = R(x,y,(z \ ((v5 * w) / (v5 * u))) * v6)
    ]]></literal>
    <justification jstring="[para(99(a,2),22135(a,2,3,1,2)),flip(a)].">
      <j1 rule="para" parents="99 22135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22179">
    <literal><![CDATA[
      R(x,y,((z \ 1) \ (z \ u)) * w) = R(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[para(15286(a,2),22155(a,1,3,1))].">
      <j1 rule="para" parents="15286 22155"/>
    </justification>
  </clause>

  <clause id="22180">
    <literal><![CDATA[
      R(x,y,z * (u * (w * u))) = R(x,y,L(w,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,22122,a(flip),b,22147,a),flip(a)].">
      <j1 rule="hyper" parents="63 22122 22147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22181">
    <literal><![CDATA[
      R(x,y,L(z * u,u,u)) = R(x,y,L(z,u,u) * u)
    ]]></literal>
    <justification jstring="[hyper(20900,a,22180,a)].">
      <j1 rule="hyper" parents="20900 22180"/>
    </justification>
  </clause>

  <clause id="22183">
    <literal><![CDATA[
      R(x,y,L(1 / z,L(z,u,w),L(z,u,w)) * v5) = R(x,y,v5 * (L(z,u,w) * (z \ L(z,u,w))))
    ]]></literal>
    <justification jstring="[para(3162(a,1),22180(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="3162 22180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22184">
    <literal><![CDATA[
      R(x,y,z * (u * (u * z))) = R(x,y,a(z,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(22164,a,13953,a)].">
      <j1 rule="hyper" parents="22164 13953"/>
    </justification>
  </clause>

  <clause id="22185">
    <literal><![CDATA[
      R(x,y,(z * (z * u)) * u) = R(x,y,a(u,z,u * z))
    ]]></literal>
    <justification jstring="[hyper(20517,a,22184,a)].">
      <j1 rule="hyper" parents="20517 22184"/>
    </justification>
  </clause>

  <clause id="22186">
    <literal><![CDATA[
      R(x,y,a(z,u,z * u)) = R(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,22150,a(flip),b,22185,a),flip(a)].">
      <j1 rule="hyper" parents="63 22150 22185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22187">
    <literal><![CDATA[
      R(x * y,z,a(x,x,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(63,a,13954,a(flip),b,22186,a),flip(a)].">
      <j1 rule="hyper" parents="63 13954 22186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22188">
    <literal><![CDATA[
      a(x,x,y) * ((x * y) * z) = (x * y) * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,22187,a(flip),b,20865,a),flip(a)].">
      <j1 rule="hyper" parents="133 22187 20865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22189">
    <literal><![CDATA[
      (R(x,x,y) * y) * L(z,x * y,a(x,x,y)) = (x * y) * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,15116,a,b,22188,a)].">
      <j1 rule="hyper" parents="63 15116 22188"/>
    </justification>
  </clause>

  <clause id="22190">
    <literal><![CDATA[
      R(x,y,(z \ 1) * (u \ (z \ u))) = R(x,y,z * L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(22093,a,22171,a)].">
      <j1 rule="hyper" parents="22093 22171"/>
    </justification>
  </clause>

  <clause id="22191">
    <literal><![CDATA[
      R(x,y,z * L(z,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z * (u \ (z \ u))) = w
    ]]></literal>
    <justification jstring="[para(22190(a,1),21089(a,1))].">
      <j1 rule="para" parents="22190 21089"/>
    </justification>
  </clause>

  <clause id="22193">
    <literal><![CDATA[
      R(x,y,(z * (u * w)) \ v5) = R(x,y,(z * (w * u)) \ v5)
    ]]></literal>
    <justification jstring="[para(111(a,1),22084(a,1,3,1,2))].">
      <j1 rule="para" parents="111 22084"/>
    </justification>
  </clause>

  <clause id="22194">
    <literal><![CDATA[
      R(x,y,(z * ((u * u) * w)) \ v5) = R(x,y,(u * u) \ ((z * w) \ v5))
    ]]></literal>
    <justification jstring="[para(775(a,1),22193(a,1,3)),flip(a)].">
      <j1 rule="para" parents="775 22193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22195">
    <literal><![CDATA[
      R(x,y,(z * (K(u,w) * v5)) \ v6) = R(x,y,K(w,u) * ((z * v5) \ v6))
    ]]></literal>
    <justification jstring="[para(20837(a,1),22193(a,1,3)),flip(a)].">
      <j1 rule="para" parents="20837 22193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22196">
    <literal><![CDATA[
      R(x,y,z * ((u \ (w / v5)) \ v6)) = R(x,y,z * ((u \ (v5 \ w)) \ v6))
    ]]></literal>
    <justification jstring="[para(113(a,1),22109(a,1,3,2,1,2)),flip(a)].">
      <j1 rule="para" parents="113 22109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22197">
    <literal><![CDATA[
      R(x,y,(z * (u * w)) * v5) = R(x,y,(z * (w * u)) * v5)
    ]]></literal>
    <justification jstring="[para(111(a,1),22110(a,1,3,1,2))].">
      <j1 rule="para" parents="111 22110"/>
    </justification>
  </clause>

  <clause id="22198">
    <literal><![CDATA[
      R(x,y,(z * ((u * u) * w)) * v5) = R(x,y,(z * w) * ((u * u) * v5))
    ]]></literal>
    <justification jstring="[para(125(a,1),22197(a,1,3)),flip(a)].">
      <j1 rule="para" parents="125 22197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22199">
    <literal><![CDATA[
      R(x,y,z \ ((u / (w \ 1)) \ v5)) = R(x,y,z \ ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,22114,a(flip),b,22141,a),flip(a)].">
      <j1 rule="hyper" parents="347 22114 22141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22200">
    <literal><![CDATA[
      R(x,y,z * ((u / (w \ 1)) \ v5)) = R(x,y,z * ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,22106,a(flip),b,22156,a),flip(a)].">
      <j1 rule="hyper" parents="347 22106 22156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22201">
    <literal><![CDATA[
      L(x \ R(x,y,z \ ((u * w) * v5)),x,y * (z \ ((u * T(w,v6)) * v5))) = a(x,y,z \ ((u * T(w,v6)) * v5))
    ]]></literal>
    <justification jstring="[para(22173(a,1),14250(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22173 14250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22202">
    <literal><![CDATA[
      R(x,y,z \ (((u \ 1) \ w) \ v5)) = R(x,y,z \ ((u \ w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,22114,a(flip),b,22199,a)].">
      <j1 rule="hyper" parents="63 22114 22199"/>
    </justification>
  </clause>

  <clause id="22203">
    <literal><![CDATA[
      R(x,y,z * (((u \ 1) \ w) \ v5)) = R(x,y,z * ((u \ w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,22106,a(flip),b,22200,a)].">
      <j1 rule="hyper" parents="63 22106 22200"/>
    </justification>
  </clause>

  <clause id="22204">
    <literal><![CDATA[
      R(x,y,(z * u) \ ((w * u) * z)) = R(x,y,R(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,20514,a(flip),b,22128,a),flip(a)].">
      <j1 rule="hyper" parents="347 20514 22128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22206">
    <literal><![CDATA[
      R(x,y,(((z * u) \ z) \ 1) * w) = R(x,y,(z \ (z / u)) * w)
    ]]></literal>
    <justification jstring="[hyper(347,a,21088,a(flip),b,22129,a),flip(a)].">
      <j1 rule="hyper" parents="347 21088 22129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22207">
    <literal><![CDATA[
      R(x,y,(((z * u) \ z) \ 1) * w) = R(x,y,(z \ (u \ z)) * w)
    ]]></literal>
    <justification jstring="[hyper(347,a,22135,a(flip),b,22206,a),flip(a)].">
      <j1 rule="hyper" parents="347 22135 22206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22208">
    <literal><![CDATA[
      R(x,y,((z * u) \ z) * w) = R(x,y,(z \ (u \ z)) * w)
    ]]></literal>
    <justification jstring="[hyper(21089,a,22207,a)].">
      <j1 rule="hyper" parents="21089 22207"/>
    </justification>
  </clause>

  <clause id="22209">
    <literal><![CDATA[
      R(x,y,(z \ ((R(z,u,z) \ w) \ z)) * v5) = R(x,y,((a(z,u,z) \ w) \ z) * v5)
    ]]></literal>
    <justification jstring="[para(10991(a,1),22208(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="10991 22208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22210">
    <literal><![CDATA[
      R(x,y,K(z,u) * ((w * L(v5,v6,v7)) * v8)) = R(x,y,v8 * (w * L(T(v5,v9),v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(347,a,22058,a,b,22139,a)].">
      <j1 rule="hyper" parents="347 22058 22139"/>
    </justification>
  </clause>

  <clause id="22211">
    <literal><![CDATA[
      R(x,y,z \ ((L(u,w,v5) \ v6) \ ((1 / u) \ u))) = R(x,y,z \ (L(1 / u,w,v5) \ v6))
    ]]></literal>
    <justification jstring="[para(6663(a,1),22160(a,2,3,2))].">
      <j1 rule="para" parents="6663 22160"/>
    </justification>
  </clause>

  <clause id="22212">
    <literal><![CDATA[
      R(x,y,z \ (u * (w * (K(v5,v6) * v7)))) = R(x,y,z \ ((w * v7) * u))
    ]]></literal>
    <justification jstring="[hyper(22094,a,22174,a)].">
      <j1 rule="hyper" parents="22094 22174"/>
    </justification>
  </clause>

  <clause id="22213">
    <literal><![CDATA[
      R(x,y,z \ ((u * (w * v5)) * v6)) = R(x,y,z \ ((u * (v5 * w)) * v6))
    ]]></literal>
    <justification jstring="[para(4909(a,1),22174(a,1,3,2,1,2))].">
      <j1 rule="para" parents="4909 22174"/>
    </justification>
  </clause>

  <clause id="22214">
    <literal><![CDATA[
      R(x,y,z \ (u * ((w * w) * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ (u * v5)) = v6
    ]]></literal>
    <justification jstring="[para(22176(a,2),2186(a,1))].">
      <j1 rule="para" parents="22176 2186"/>
    </justification>
  </clause>

  <clause id="22215">
    <literal><![CDATA[
      R(x,y,z \ (((u * u) * w) * v5)) = R(x,y,z \ (w * v5))
    ]]></literal>
    <justification jstring="[hyper(22214,a,22172,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="22214 22172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22217">
    <literal><![CDATA[
      R(x,y,(z * ((u * u) * w)) \ v5) = R(x,y,(z * w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,2238,a(flip),b,22194,a),flip(a)].">
      <j1 rule="hyper" parents="347 2238 22194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22218">
    <literal><![CDATA[
      R(x,y,(z * ((u * u) * w)) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y,(z * w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(22194(a,2),2239(a,1))].">
      <j1 rule="para" parents="22194 2239"/>
    </justification>
  </clause>

  <clause id="22220">
    <literal><![CDATA[
      R(x,y,(z * ((u * u) \ w)) \ v5) = R(x,y,(z * w) \ v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),22217(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="10 22217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22221">
    <literal><![CDATA[
      R(x,y,(z * ((u * u) \ w)) \ v5) = R(x,y,(v6 * v6) * ((z * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,2240,a,b,22220,a),flip(a)].">
      <j1 rule="hyper" parents="347 2240 22220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22222">
    <literal><![CDATA[
      R(x,y,(z * L(T(u,w),w,w)) \ v5) = R(x,y,(z * (w * (u * w))) \ v5)
    ]]></literal>
    <justification jstring="[para(263(a,1),22220(a,1,3,1,2))].">
      <j1 rule="para" parents="263 22220"/>
    </justification>
  </clause>

  <clause id="22223">
    <literal><![CDATA[
      R(x,y,(z * (K(u,w) * v5)) \ v6) = R(x,y,(z * v5) \ v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,22058,a(flip),b,22195,a),flip(a)].">
      <j1 rule="hyper" parents="347 22058 22195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22225">
    <literal><![CDATA[
      R(x,K(y,z) * u,(x * u) \ w) \ w = (K(y,z) * u) * ((x * (K(y,z) * u)) \ w)
    ]]></literal>
    <justification jstring="[para(22223(a,1),581(a,1,1))].">
      <j1 rule="para" parents="22223 581"/>
    </justification>
  </clause>

  <clause id="22226">
    <literal><![CDATA[
      R(x,y,(z * (T(u,w) * v5)) \ v6) = R(x,y,(z * (u * v5)) \ v6)
    ]]></literal>
    <justification jstring="[para(4946(a,1),22223(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="4946 22223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22227">
    <literal><![CDATA[
      R(x,y,(z * ((u / w) * v5)) \ v6) = R(x,y,(z * ((w \ u) * v5)) \ v6)
    ]]></literal>
    <justification jstring="[para(5237(a,1),22223(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="5237 22223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22228">
    <literal><![CDATA[
      R(x,y,(z * ((K(u,w) / v5) * v6)) \ v7) = R(x,y,(z * ((1 / v5) * v6)) \ v7)
    ]]></literal>
    <justification jstring="[para(20727(a,1),22223(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="20727 22223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22229">
    <literal><![CDATA[
      R(x,y,((T(z,u) * w) * v5) \ v6) = R(x,y,(v5 * (z * w)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(22098,a,22226,a)].">
      <j1 rule="hyper" parents="22098 22226"/>
    </justification>
  </clause>

  <clause id="22230">
    <literal><![CDATA[
      R(x,y,((T(z,u) * w) * v5) \ v6) = R(x,y,(v5 * (z * w)) \ (K(v7,v8) * v6))
    ]]></literal>
    <justification jstring="[hyper(22095,a,22229,a)].">
      <j1 rule="hyper" parents="22095 22229"/>
    </justification>
  </clause>

  <clause id="22231">
    <literal><![CDATA[
      R(x,y,z * (((u * w) \ u) \ v5)) = R(x,y,z * ((u \ (w \ u)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,22130,a,b,22196,a)].">
      <j1 rule="hyper" parents="63 22130 22196"/>
    </justification>
  </clause>

  <clause id="22232">
    <literal><![CDATA[
      R(x,y,(z * ((u * u) * w)) * v5) = R(x,y,(z * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,22146,a(flip),b,22198,a),flip(a)].">
      <j1 rule="hyper" parents="347 22146 22198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22234">
    <literal><![CDATA[
      R(x,y,(z * ((u * u) \ w)) * v5) = R(x,y,(z * w) * v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),22232(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="10 22232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22235">
    <literal><![CDATA[
      R(x,y,((z * z) * u) * w) = R(x,y,u * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),22234(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 22234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22236">
    <literal><![CDATA[
      R(x,y,((z \ 1) \ u) * w) = R(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[para(495(a,1),22235(a,1,3,1))].">
      <j1 rule="para" parents="495 22235"/>
    </justification>
  </clause>

  <clause id="22237">
    <literal><![CDATA[
      R(x,y,(z \ (z \ u)) * w) = R(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,22179,a(flip),b,22236,a),flip(a)].">
      <j1 rule="hyper" parents="63 22179 22236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22238">
    <literal><![CDATA[
      R(x,y,L(z,u,u) * u) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(22087,a,22237,a),flip(a)].">
      <j1 rule="hyper" parents="22087 22237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22239">
    <literal><![CDATA[
      R(x,y,z * (u \ (u \ w))) = R(x,y,L(w,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(20517,a,22237,a)].">
      <j1 rule="hyper" parents="20517 22237"/>
    </justification>
  </clause>

  <clause id="22240">
    <literal><![CDATA[
      R(x,y,L(z,u,u) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(22237(a,1),22087(a,1))].">
      <j1 rule="para" parents="22237 22087"/>
    </justification>
  </clause>

  <clause id="22241">
    <literal><![CDATA[
      R(x,y,L(z * u,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(22181(a,2),22240(a,1))].">
      <j1 rule="para" parents="22181 22240"/>
    </justification>
  </clause>

  <clause id="22242">
    <literal><![CDATA[
      R(x,y,(z * u) \ ((z * w) * u)) = R(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[para(10172(a,2),22212(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10172 22212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22243">
    <literal><![CDATA[
      R(x,y,z \ ((u * ((w * w) * v5)) * v6)) = R(x,y,z \ ((u * v5) * ((w * w) * v6)))
    ]]></literal>
    <justification jstring="[para(125(a,1),22213(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="125 22213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22244">
    <literal><![CDATA[
      R(x,y,(z * ((u * u) \ w)) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y,(z * w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(22221(a,2),20641(a,1))].">
      <j1 rule="para" parents="22221 20641"/>
    </justification>
  </clause>

  <clause id="22245">
    <literal><![CDATA[
      R(x,y,(((z * z) \ u) * w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y,(w * u) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(22077(a,1),22244(a,1))].">
      <j1 rule="para" parents="22077 22244"/>
    </justification>
  </clause>

  <clause id="22246">
    <literal><![CDATA[
      R(x,y,(z \ R(u,w,u)) * v5) = R(x,y,v5 * (z \ (w \ (w * u))))
    ]]></literal>
    <justification jstring="[hyper(63,a,22125,a(flip),b,22136,a),flip(a)].">
      <j1 rule="hyper" parents="63 22125 22136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22248">
    <literal><![CDATA[
      R(x,y,(z \ R(u,w,u)) * v5) = R(x,y,v5 * (z \ u))
    ]]></literal>
    <justification jstring="[para(9(a,1),22246(a,2,3,2,2))].">
      <j1 rule="para" parents="9 22246"/>
    </justification>
  </clause>

  <clause id="22249">
    <literal><![CDATA[
      R(x,y,(z * ((u * w) * u)) * v5) = R(x,y,(z * R(w,u,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22149,a(flip),b,22137,a)].">
      <j1 rule="hyper" parents="63 22149 22137"/>
    </justification>
  </clause>

  <clause id="22250">
    <literal><![CDATA[
      R(x,y,(z * R(u,w,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y,v5 * (z * ((w * u) * w))) = v6
    ]]></literal>
    <justification jstring="[para(22249(a,1),20517(a,1))].">
      <j1 rule="para" parents="22249 20517"/>
    </justification>
  </clause>

  <clause id="22251">
    <literal><![CDATA[
      R(x,y,(z * (u * (w * u))) \ v5) = R(x,y,(z * L(w,u,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22131,a(flip),b,22222,a),flip(a)].">
      <j1 rule="hyper" parents="63 22131 22222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22252">
    <literal><![CDATA[
      R(x,y,(z * L(z,u,u)) \ (z * u)) = R(x,y,L(z * u,u,z))
    ]]></literal>
    <justification jstring="[hyper(21451,a,22251,a),flip(a)].">
      <j1 rule="hyper" parents="21451 22251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22254">
    <literal><![CDATA[
      R(x,y,a(z,z,u) \ (u * z)) = R(x,y,L(u * z,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,14645,a(flip),b,22252,a)].">
      <j1 rule="hyper" parents="63 14645 22252"/>
    </justification>
  </clause>

  <clause id="22255">
    <literal><![CDATA[
      R(x,y,z * (a(u,u,z) \ u)) = R(x,y,L(z * u,u,z))
    ]]></literal>
    <justification jstring="[para(12716(a,1),22254(a,1,3))].">
      <j1 rule="para" parents="12716 22254"/>
    </justification>
  </clause>

  <clause id="22256">
    <literal><![CDATA[
      R(x,y,(z * (u * (w \ 1))) \ v5) = R(x,y,(z * (u * w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(22244,a,22132,a),flip(a)].">
      <j1 rule="hyper" parents="22244 22132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22258">
    <literal><![CDATA[
      R(x,y,(z * ((u \ 1) * w)) \ v5) = R(x,y,(z * (w * u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22193,a,b,22256,a)].">
      <j1 rule="hyper" parents="63 22193 22256"/>
    </justification>
  </clause>

  <clause id="22259">
    <literal><![CDATA[
      R(x,y,(z * (u * (w \ 1))) \ ((z * u) * w)) = R(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(14(a,2),22256(a,2,3))].">
      <j1 rule="para" parents="14 22256"/>
    </justification>
  </clause>

  <clause id="22260">
    <literal><![CDATA[
      R(x,y,(z * (u * z)) \ w) = R(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[para(3197(a,1),22258(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="3197 22258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22261">
    <literal><![CDATA[
      R(x,y,((z * u) * u) \ w) = R(x,y,L(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(22098,a,22260,a)].">
      <j1 rule="hyper" parents="22098 22260"/>
    </justification>
  </clause>

  <clause id="22262">
    <literal><![CDATA[
      R(x,y,R(z,u,u) \ w) = R(x,y,L(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,2363,a(flip),b,22261,a)].">
      <j1 rule="hyper" parents="63 2363 22261"/>
    </justification>
  </clause>

  <clause id="22263">
    <literal><![CDATA[
      R(x,y,K(z,u) * ((w * (u \ v5)) * v6)) = R(x,y,((T(u,z) \ v5) * w) * v6)
    ]]></literal>
    <justification jstring="[para(20008(a,1),22138(a,1,3))].">
      <j1 rule="para" parents="20008 22138"/>
    </justification>
  </clause>

  <clause id="22264">
    <literal><![CDATA[
      R(x,y,z \ ((u * (w \ K(v5,v6))) * v7)) = R(x,y,z \ (v7 * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,22157,a(flip),b,22175,a),flip(a)].">
      <j1 rule="hyper" parents="347 22157 22175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22265">
    <literal><![CDATA[
      R(x,y,z \ (((u \ K(w,v5)) * v6) * v7)) = R(x,y,z \ (v7 * (v6 * u)))
    ]]></literal>
    <justification jstring="[hyper(22162,a,22264,a)].">
      <j1 rule="hyper" parents="22162 22264"/>
    </justification>
  </clause>

  <clause id="22266">
    <literal><![CDATA[
      R(x,y,(z * ((K(u,w) / v5) * v6)) \ v7) = R(x,y,(z * ((v5 \ 1) * v6)) \ v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,22227,a(flip),b,22228,a),flip(a)].">
      <j1 rule="hyper" parents="347 22227 22228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22267">
    <literal><![CDATA[
      R(x,y,((T(z,u) * w) * v5) \ v6) != v7
    ]]></literal>
    <literal><![CDATA[
      R(x,y,(v5 * (z * w)) \ v6) = v7
    ]]></literal>
    <justification jstring="[para(22230(a,2),22095(a,1))].">
      <j1 rule="para" parents="22230 22095"/>
    </justification>
  </clause>

  <clause id="22268">
    <literal><![CDATA[
      R(x,y,((T(z,u) \ w) * v5) * v6) = R(x,y,(v5 * (z \ w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(22091,a,22263,a),flip(a)].">
      <j1 rule="hyper" parents="22091 22263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22269">
    <literal><![CDATA[
      R(x,y,z * ((T(u,w) \ v5) * v6)) = R(x,y,(v6 * (u \ v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(20517,a,22268,a)].">
      <j1 rule="hyper" parents="20517 22268"/>
    </justification>
  </clause>

  <clause id="22271">
    <literal><![CDATA[
      R(x,y,(z * ((K(u,w) / v5) * v6)) \ v7) = R(x,y,(z * (v6 * v5)) \ v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,22258,a(flip),b,22266,a),flip(a)].">
      <j1 rule="hyper" parents="347 22258 22266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22272">
    <literal><![CDATA[
      R(x,y,(z * ((u \ K(w,v5)) * v6)) \ v7) = R(x,y,(z * (v6 * u)) \ v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,22227,a(flip),b,22271,a)].">
      <j1 rule="hyper" parents="63 22227 22271"/>
    </justification>
  </clause>

  <clause id="22273">
    <literal><![CDATA[
      R(x,y,z \ (L(1 / u,w,w) \ v5)) = R(x,y,z \ ((w \ (w \ u)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,22202,a(flip),b,22143,a),flip(a)].">
      <j1 rule="hyper" parents="63 22202 22143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22274">
    <literal><![CDATA[
      R(x,y,z \ (u \ ((1 / w) \ w))) = R(x,y,z \ (((w \ 1) \ w) * u))
    ]]></literal>
    <justification jstring="[hyper(22163,a,22160,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="22163 22160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22275">
    <literal><![CDATA[
      R(x,y,z \ (u \ ((1 / w) \ w))) = R(x,y,z \ ((w * w) * u))
    ]]></literal>
    <justification jstring="[para(301(a,1),22274(a,2,3,2,1))].">
      <j1 rule="para" parents="301 22274"/>
    </justification>
  </clause>

  <clause id="22276">
    <literal><![CDATA[
      R(x,y,z \ (u \ ((1 / w) \ w))) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,22112,a(flip),b,22275,a),flip(a)].">
      <j1 rule="hyper" parents="347 22112 22275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22278">
    <literal><![CDATA[
      R(x,y,z * ((R(u,w,u) \ w) \ v5)) = R(x,y,((w / u) \ v5) * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),22177(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="10 22177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22279">
    <literal><![CDATA[
      R(x,y,z * ((R(u,w,u) \ w) \ v5)) = R(x,y,((u \ w) \ v5) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,22083,a(flip),b,22278,a),flip(a)].">
      <j1 rule="hyper" parents="347 22083 22278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22281">
    <literal><![CDATA[
      R(x,y,z * ((u * ((w * u) \ u)) \ v5)) = R(x,y,((w \ u) \ v5) * z)
    ]]></literal>
    <justification jstring="[para(11739(a,1),22279(a,1,3,2,1))].">
      <j1 rule="para" parents="11739 22279"/>
    </justification>
  </clause>

  <clause id="22282">
    <literal><![CDATA[
      R(x,y,(z \ (u * w)) * ((u * u) \ v5)) = R(x,y,(z \ L(u \ w,u,u)) * v5)
    ]]></literal>
    <justification jstring="[para(830(a,1),22178(a,2,3)),flip(a)].">
      <j1 rule="para" parents="830 22178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22283">
    <literal><![CDATA[
      R(x,y,(z \ L(u \ w,u,u)) * v5) = R(x,y,(z \ (u * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22145,a(flip),b,22282,a),flip(a)].">
      <j1 rule="hyper" parents="63 22145 22282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22285">
    <literal><![CDATA[
      R(x,y,(z \ L(u \ (u * (w / u)),u,u)) * v5) = R(x,y,(z \ (T(u,u \ w) * w)) * v5)
    ]]></literal>
    <justification jstring="[para(4192(a,2),22283(a,2,3,1,2))].">
      <j1 rule="para" parents="4192 22283"/>
    </justification>
  </clause>

  <clause id="22286">
    <literal><![CDATA[
      (T(x,y) \ z) * L((T(x,y) \ z) \ u,w,v5) = (x \ z) * L((x \ z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,22029,a(flip),b,22045,a),flip(a)].">
      <j1 rule="hyper" parents="347 22029 22045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22287">
    <literal><![CDATA[
      1 / (x \ (a(y,z,u) \ 1)) = ((a(y,z,u) \ 1) / x) \ 1
    ]]></literal>
    <justification jstring="[para(16644(a,1),22052(a,1,2))].">
      <j1 rule="para" parents="16644 22052"/>
    </justification>
  </clause>

  <clause id="22288">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) / u) \ 1) \ 1 = u \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(214,a,22287,a)].">
      <j1 rule="hyper" parents="214 22287"/>
    </justification>
  </clause>

  <clause id="22289">
    <literal><![CDATA[
      1 / (x \ (a(y,z,u) \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      ((a(y,z,u) \ 1) / x) \ 1 = w
    ]]></literal>
    <justification jstring="[para(22288(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="22288 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22290">
    <literal><![CDATA[
      R(x,y,(z \ ((R(z,u,z) \ w) \ z)) * v5) = R(x,y,(w \ R(z,u,z)) * v5)
    ]]></literal>
    <justification jstring="[para(11406(a,1),22209(a,2,3,1))].">
      <j1 rule="para" parents="11406 22209"/>
    </justification>
  </clause>

  <clause id="22291">
    <literal><![CDATA[
      R(x,y,(z \ ((R(z,u,z) \ w) \ z)) * v5) = R(x,y,v5 * (w \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,22248,a(flip),b,22290,a),flip(a)].">
      <j1 rule="hyper" parents="347 22248 22290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22293">
    <literal><![CDATA[
      R(x,y,(z \ ((z \ u) \ R(z,w,z))) * v5) = R(x,y,v5 * (u \ z))
    ]]></literal>
    <justification jstring="[para(11408(a,1),22291(a,1,3,1,2))].">
      <j1 rule="para" parents="11408 22291"/>
    </justification>
  </clause>

  <clause id="22294">
    <literal><![CDATA[
      R(x,y,L(z,z,u \ ((u \ w) \ R(u,v5,u))) * (w \ u)) = R(x,y,(u \ ((u \ w) \ R(u,v5,u))) / (z \ 1))
    ]]></literal>
    <justification jstring="[para(2008(a,1),22293(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2008 22293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22295">
    <literal><![CDATA[
      R(x,y,z * (u * L(T(w,v5),v6,v7))) != v8
    ]]></literal>
    <literal><![CDATA[
      R(x,y,(u * L(w,v6,v7)) * z) = v8
    ]]></literal>
    <justification jstring="[para(22210(a,1),22091(a,1))].">
      <j1 rule="para" parents="22210 22091"/>
    </justification>
  </clause>

  <clause id="22296">
    <literal><![CDATA[
      R(x,y,z \ ((u * ((w * w) * v5)) * v6)) = R(x,y,z \ ((u * v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(22214,a,22243,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="22214 22243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22298">
    <literal><![CDATA[
      R(x,y,(z * ((u * u) * (w * (v5 \ 1)))) \ ((z * w) * v5)) = R(x,y,a(z * (u * u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,14930,a(flip),b,22296,a),flip(a)].">
      <j1 rule="hyper" parents="63 14930 22296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22299">
    <literal><![CDATA[
      (T(x,y) \ z) \ ((x * y) \ (y * z)) = (u * u) \ ((x \ z) * L((x \ z) \ (u * u),x,y))
    ]]></literal>
    <justification jstring="[para(22286(a,1),10211(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22286 10211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22300">
    <literal><![CDATA[
      R(T(x \ 1,y * (x \ z)),x,y \ z) = (x * L(y * z,y,y)) \ L(y * z,y,y)
    ]]></literal>
    <justification jstring="[para(20884(a,1),20876(a,1,1))].">
      <j1 rule="para" parents="20884 20876"/>
    </justification>
  </clause>

  <clause id="22301">
    <literal><![CDATA[
      (x * y) \ ((y * (a(z,u,w) \ 1)) * T(x,y)) = R(a(z,u,w) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(20087(a,1),20922(a,2,1))].">
      <j1 rule="para" parents="20087 20922"/>
    </justification>
  </clause>

  <clause id="22303">
    <literal><![CDATA[
      (x * y) \ ((y * (z \ L(z,u,w))) * T(x,y)) = R(z \ L(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(20259(a,1),20960(a,2,1))].">
      <j1 rule="para" parents="20259 20960"/>
    </justification>
  </clause>

  <clause id="22305">
    <literal><![CDATA[
      x \ T(x \ (a(y,z,u) \ x),(a(y,z,u) * x) \ 1) = x / ((a(y,z,u) * x) * x)
    ]]></literal>
    <justification jstring="[para(21801(a,1),20985(a,1,2,1))].">
      <j1 rule="para" parents="21801 20985"/>
    </justification>
  </clause>

  <clause id="22306">
    <literal><![CDATA[
      T(x,y) * ((1 / T(x,y)) * z) = K(x,x \ 1) * L(z,1 / T(x,y),x)
    ]]></literal>
    <justification jstring="[para(3005(a,1),21080(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3005 21080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22308">
    <literal><![CDATA[
      T(x,y) * ((1 / T(x,y)) * z) = K(x,x \ 1) * L(z,T(x,y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(3206(a,1),22306(a,2,2))].">
      <j1 rule="para" parents="3206 22306"/>
    </justification>
  </clause>

  <clause id="22309">
    <literal><![CDATA[
      T(x,y) * ((1 / T(x,y)) * z) = K(x,x \ 1) * L(z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(10724(a,1),22308(a,2,2))].">
      <j1 rule="para" parents="10724 22308"/>
    </justification>
  </clause>

  <clause id="22310">
    <literal><![CDATA[
      T(x,y) * ((1 / T(x,y)) * z) = x * ((1 / x) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,3433,a(flip),b,22309,a),flip(a)].">
      <j1 rule="hyper" parents="347 3433 22309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22312">
    <literal><![CDATA[
      L(L(((x \ y) \ y) \ 1,z,u),x,x \ y) = y \ (y * L(y \ (x \ y),z,u))
    ]]></literal>
    <justification jstring="[para(21399(a,1),21198(a,1,1))].">
      <j1 rule="para" parents="21399 21198"/>
    </justification>
  </clause>

  <clause id="22313">
    <literal><![CDATA[
      L(L(((x \ y) \ y) \ 1,z,u),x,x \ y) = L(y \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,9,a(flip),b,22312,a),flip(a)].">
      <j1 rule="hyper" parents="347 9 22312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22315">
    <literal><![CDATA[
      T(x \ ((y \ x) * 1),(y \ x) \ x) = L(x \ (y \ x),y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,10666,a,b,22313,a)].">
      <j1 rule="hyper" parents="63 10666 22313"/>
    </justification>
  </clause>

  <clause id="22316">
    <literal><![CDATA[
      T(x \ (y \ x),(y \ x) \ x) = L(x \ (y \ x),y,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),22315(a,1,1,2))].">
      <j1 rule="para" parents="8 22315"/>
    </justification>
  </clause>

  <clause id="22317">
    <literal><![CDATA[
      L(x \ (y \ x),y,y) = T(x \ (y \ x),y)
    ]]></literal>
    <justification jstring="[hyper(2904,a,22316,a),flip(a)].">
      <j1 rule="hyper" parents="2904 22316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22323">
    <literal><![CDATA[
      (a(x,y,z) * u) \ T(u,w) = u \ (a(x,y,z) \ T(u,w))
    ]]></literal>
    <justification jstring="[hyper(21796,a,20831,a),flip(a)].">
      <j1 rule="hyper" parents="21796 20831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22324">
    <literal><![CDATA[
      (x * a(y,z,u)) \ T(x,w) = x \ (a(y,z,u) \ T(x,w))
    ]]></literal>
    <justification jstring="[hyper(20024,a,22323,a)].">
      <j1 rule="hyper" parents="20024 22323"/>
    </justification>
  </clause>

  <clause id="22325">
    <literal><![CDATA[
      R(x,y,(1 / z) * (u \ (z \ u))) = R(x,y,z * R(z \ 1,z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(20641,a,22169,a)].">
      <j1 rule="hyper" parents="20641 22169"/>
    </justification>
  </clause>

  <clause id="22326">
    <literal><![CDATA[
      R(x,y,(z \ 1) * (u \ (z \ u))) = R(x,y,z * R(z \ 1,z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(22093,a,22325,a)].">
      <j1 rule="hyper" parents="22093 22325"/>
    </justification>
  </clause>

  <clause id="22328">
    <literal><![CDATA[
      R(x,y,z * R(z \ 1,z,z \ u)) = R(x,y,z * (u \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(21089,a,22326,a),flip(a)].">
      <j1 rule="hyper" parents="21089 22326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22329">
    <literal><![CDATA[
      x / ((a(y,z,u) * x) * x) = x \ (x \ (a(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(20569(a,1),22305(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20569 22305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22330">
    <literal><![CDATA[
      x / (x * (a(y,z,u) * x)) = x \ (x \ (a(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(20609(a,1),22329(a,1,2))].">
      <j1 rule="para" parents="20609 22329"/>
    </justification>
  </clause>

  <clause id="22332">
    <literal><![CDATA[
      L(a(x,y,z),u,u) \ (u \ 1) = u \ (u \ (a(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21246,a,b,22330,a)].">
      <j1 rule="hyper" parents="63 21246 22330"/>
    </justification>
  </clause>

  <clause id="22333">
    <literal><![CDATA[
      L(x,y,y \ R(y,z,u)) * ((y \ R(y,z,u)) * y) = (y \ R(y,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,251,a(flip),b,20196,a),flip(a)].">
      <j1 rule="hyper" parents="347 251 20196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22335">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * R(u,x,L(x \ 1,y,z)) = (u * x) * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7,a(flip),b,20394,a),flip(a)].">
      <j1 rule="hyper" parents="347 7 20394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22337">
    <literal><![CDATA[
      (x \ L(x,y,z)) * R(u,x,L(x \ 1,y,z)) = (u * x) * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(3343(a,1),22335(a,1,1))].">
      <j1 rule="para" parents="3343 22335"/>
    </justification>
  </clause>

  <clause id="22338">
    <literal><![CDATA[
      (x \ L(x,y,z)) * R(u,x,L(x,y,z)) = (u * x) * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(3328(a,1),22337(a,1,2))].">
      <j1 rule="para" parents="3328 22337"/>
    </justification>
  </clause>

  <clause id="22339">
    <literal><![CDATA[
      (x * (1 / y)) * L(y,z,u) = (x * y) * L(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,20953,a(flip),b,22338,a)].">
      <j1 rule="hyper" parents="63 20953 22338"/>
    </justification>
  </clause>

  <clause id="22340">
    <literal><![CDATA[
      (x / L(y,z,u)) / ((1 / y) * (1 / y)) = x / (((1 / y) * y) * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(22339(a,1),702(a,2,2))].">
      <j1 rule="para" parents="22339 702"/>
    </justification>
  </clause>

  <clause id="22341">
    <literal><![CDATA[
      ((x \ (1 * L(1 \ x,y,z))) * x) * L(x \ 1,u,w) = L(1 / x,y,z) * L(x,u,w)
    ]]></literal>
    <justification jstring="[para(21200(a,1),22339(a,1,1)),flip(a)].">
      <j1 rule="para" parents="21200 22339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22342">
    <literal><![CDATA[
      x / (((1 / y) * y) * L(y \ 1,z,u)) = (x / L(y,z,u)) / (y \ (1 / y))
    ]]></literal>
    <justification jstring="[para(307(a,1),22340(a,1,2)),flip(a)].">
      <j1 rule="para" parents="307 22340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22343">
    <literal><![CDATA[
      x / (((1 / y) * y) * L(y \ 1,z,u)) = (x / L(y,z,u)) * ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,6655,a(flip),b,22342,a),flip(a)].">
      <j1 rule="hyper" parents="347 6655 22342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22344">
    <literal><![CDATA[
      (x / L(y,z,u)) * ((1 / y) \ y) = x / L(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(81(a,1),22343(a,1,2)),flip(a)].">
      <j1 rule="para" parents="81 22343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22346">
    <literal><![CDATA[
      (x / L(y,z,u)) * (((1 / y) \ y) * w) = (x / L(y \ 1,z,u)) * w
    ]]></literal>
    <justification jstring="[para(22344(a,1),1125(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22344 1125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22347">
    <literal><![CDATA[
      (x \ y) / ((x * a(z,u,w)) \ y) = ((x * a(z,u,w)) \ y) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(329(a,1),20582(a,1,1)),flip(a)].">
      <j1 rule="para" parents="329 20582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22348">
    <literal><![CDATA[
      (((a(x,y,z) \ u) * a(x,y,z)) \ w) \ ((a(x,y,z) \ u) \ w) = ((a(x,y,z) \ u) \ w) / (u \ w)
    ]]></literal>
    <justification jstring="[para(19986(a,1),22347(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="19986 22347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22349">
    <literal><![CDATA[
      ((x * y) * (K(z,u) * w)) / (y * (K(z,u) * w)) = R(R(x,y,K(z,u)),y * K(z,u),w)
    ]]></literal>
    <justification jstring="[para(20151(a,1),20804(a,1,2))].">
      <j1 rule="para" parents="20151 20804"/>
    </justification>
  </clause>

  <clause id="22350">
    <literal><![CDATA[
      (x * ((L(y,z,u) \ y) * w)) / (x * w) = L(L(y,z,u) \ y,w,x)
    ]]></literal>
    <justification jstring="[para(20002(a,1),20949(a,1,2))].">
      <j1 rule="para" parents="20002 20949"/>
    </justification>
  </clause>

  <clause id="22351">
    <literal><![CDATA[
      (((L(x,y,z) \ x) * u) * T(w,w * ((L(x,y,z) \ x) * u))) / (L(w,(L(x,y,z) \ x) * u,w) * u) = L(L(x,y,z) \ x,u,L(w,(L(x,y,z) \ x) * u,w))
    ]]></literal>
    <justification jstring="[para(754(a,2),22350(a,1,1))].">
      <j1 rule="para" parents="754 22350"/>
    </justification>
  </clause>

  <clause id="22353">
    <literal><![CDATA[
      ((L(x,y,z) * (x \ u)) \ u) \ K((L(x,y,z) * (x \ u)) \ u,T(x \ L(x,y,z),u)) = 1 / ((L(x,y,z) * (x \ u)) \ u)
    ]]></literal>
    <justification jstring="[para(3161(a,1),20970(a,1,2,2,1))].">
      <j1 rule="para" parents="3161 20970"/>
    </justification>
  </clause>

  <clause id="22354">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(T(L(x,y,z),x),u,w) = x * (L(x,y,z) \ L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(3308(a,1),20991(a,1,1))].">
      <j1 rule="para" parents="3308 20991"/>
    </justification>
  </clause>

  <clause id="22355">
    <literal><![CDATA[
      a(x,y,L(K(z,u) * (w * (v5 * u)),v6,v7)) = a(x,y,L(w * (v5 * T(u,z)),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(15032,a,21218,a),flip(a)].">
      <j1 rule="hyper" parents="15032 21218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22356">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ u,x \ R(x,y,z),x) = R(T(x,w),y,z) \ (T(x,w) * u)
    ]]></literal>
    <justification jstring="[hyper(21760,a,21238,a)].">
      <j1 rule="hyper" parents="21760 21238"/>
    </justification>
  </clause>

  <clause id="22357">
    <literal><![CDATA[
      R(T(x,y),z,u) \ (T(x,y) * w) = R(x,z,u) \ (x * w)
    ]]></literal>
    <justification jstring="[hyper(651,a,22356,a),flip(a)].">
      <j1 rule="hyper" parents="651 22356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22358">
    <literal><![CDATA[
      (x * y) \ (y * L(T(x,y),z,u)) = (y * (x * (x \ L(x,z,u)))) / (y * x)
    ]]></literal>
    <justification jstring="[para(20536(a,1),21361(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="20536 21361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22359">
    <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),22358(a,2,1,2))].">
      <j1 rule="para" parents="10 22358"/>
    </justification>
  </clause>

  <clause id="22362">
    <literal><![CDATA[
      (x * L(y,z,u)) / (x * y) = (y * x) \ (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(267(a,1),22359(a,1,2)),flip(a)].">
      <j1 rule="para" parents="267 22359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22363">
    <literal><![CDATA[
      (x * y) \ (L(x,z,u) * y) = y \ ((y / x) * L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21414,a(flip),b,22362,a),flip(a)].">
      <j1 rule="hyper" parents="63 21414 22362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22364">
    <literal><![CDATA[
      (L(x,y,z) \ u) \ (((L(x,y,z) \ u) / x) * L(x,y,z)) = (x * (L(x,y,z) \ u)) \ u
    ]]></literal>
    <justification jstring="[para(10(a,1),22363(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 22363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22365">
    <literal><![CDATA[
      K(x,y) * (x \ ((x / y) * L(y,z,u))) = (T(y,x) * x) \ (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(22363(a,1),10330(a,1,2))].">
      <j1 rule="para" parents="22363 10330"/>
    </justification>
  </clause>

  <clause id="22366">
    <literal><![CDATA[
      (T(x,y) * y) \ (L(x,z,u) * y) = y \ ((T(y,x) / x) * L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21027,a(flip),b,22365,a),flip(a)].">
      <j1 rule="hyper" parents="63 21027 22365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22367">
    <literal><![CDATA[
      (T(x,y) * y) \ (L(x,z,u) * y) = y \ (x \ (y * L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(11233(a,1),22366(a,2,2))].">
      <j1 rule="para" parents="11233 22366"/>
    </justification>
  </clause>

  <clause id="22368">
    <literal><![CDATA[
      (x * y) \ (y * L(x,z,u)) = y \ (x \ (y * L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21023,a(flip),b,22367,a)].">
      <j1 rule="hyper" parents="63 21023 22367"/>
    </justification>
  </clause>

  <clause id="22369">
    <literal><![CDATA[
      (x * y) \ (z \ ((x * y) * L(z,y,x))) = (z * (x * y)) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[para(97(a,1),22368(a,1,2)),flip(a)].">
      <j1 rule="para" parents="97 22368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22370">
    <literal><![CDATA[
      (x * (y * z)) \ (y * (z * x)) = (y * z) \ (x \ (y * (z * x)))
    ]]></literal>
    <justification jstring="[para(97(a,1),22369(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="97 22369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22371">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z),a(x,y,z)) != a(x,y,z) * w
    ]]></literal>
    <literal><![CDATA[
      L(u,a(x,y,z),a(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(21372(a,2),43(a,1))].">
      <j1 rule="para" parents="21372 43"/>
    </justification>
  </clause>

  <clause id="22372">
    <literal><![CDATA[
      L(x,x,y * x) * ((1 / (x \ 1)) \ z) = L(x,x,y) * (((x \ 1) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(80(a,1),21409(a,1,1,1))].">
      <j1 rule="para" parents="80 21409"/>
    </justification>
  </clause>

  <clause id="22373">
    <literal><![CDATA[
      L(x,x,y * x) * (x \ z) = L(x,x,y) * (((x \ 1) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(80(a,1),22372(a,1,2,1))].">
      <j1 rule="para" parents="80 22372"/>
    </justification>
  </clause>

  <clause id="22375">
    <literal><![CDATA[
      (L(x,y * K(x,z),x) * (y * K(x,z))) \ (y * K(x,z)) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,21745,a(flip),b,21492,a),flip(a)].">
      <j1 rule="hyper" parents="347 21745 21492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22376">
    <literal><![CDATA[
      (L(x,y,x) * (y * K(x,z))) \ (y * K(x,z)) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[para(11177(a,1),22375(a,1,1,1))].">
      <j1 rule="para" parents="11177 22375"/>
    </justification>
  </clause>

  <clause id="22378">
    <literal><![CDATA[
      ((x * (y * T(x,z))) / x) \ (y * K(x,z)) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[para(15061(a,1),22376(a,1,1))].">
      <j1 rule="para" parents="15061 22376"/>
    </justification>
  </clause>

  <clause id="22380">
    <literal><![CDATA[
      L(x,y,L(z \ T(u * z,w),v5,v6) * v7) = L(x,y,L(T(u,z),v5,v6) * v7)
    ]]></literal>
    <justification jstring="[para(21946(a,1),21560(a,1,3,1))].">
      <j1 rule="para" parents="21946 21560"/>
    </justification>
  </clause>

  <clause id="22381">
    <literal><![CDATA[
      L(x,y,L(z \ T(u * z,w),v5,v6) * v7) != v8
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(u,v5,v6) * v7) = v8
    ]]></literal>
    <justification jstring="[para(22380(a,2),21518(a,1))].">
      <j1 rule="para" parents="22380 21518"/>
    </justification>
  </clause>

  <clause id="22382">
    <literal><![CDATA[
      L(x,y,((z * u) \ ((z * z) * u)) \ w) = L(x,y,L(z,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(10162(a,1),21581(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10162 21581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22383">
    <literal><![CDATA[
      L(x,y,R(T(z,z * u),z,u) \ w) = L(x,y,L(z,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(744(a,1),22382(a,1,3,1))].">
      <j1 rule="para" parents="744 22382"/>
    </justification>
  </clause>

  <clause id="22384">
    <literal><![CDATA[
      L(x,y,R(z,z,u) \ w) = L(x,y,L(z,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(21519,a,22383,a)].">
      <j1 rule="hyper" parents="21519 22383"/>
    </justification>
  </clause>

  <clause id="22385">
    <literal><![CDATA[
      L(x,R(y,y,z) \ y,L(y,y,z) \ y) / (((R(y,y,z) \ y) \ 1) * x) = a(y,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(22384(a,1),19005(a,1,1))].">
      <j1 rule="para" parents="22384 19005"/>
    </justification>
  </clause>

  <clause id="22386">
    <literal><![CDATA[
      L(x,y,z * (u \ ((w * ((w * u) \ w)) \ u))) = L(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,21543,a(flip),b,21586,a),flip(a)].">
      <j1 rule="hyper" parents="347 21543 21586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22388">
    <literal><![CDATA[
      R(x,y,z \ (L(1 / u,w,v5) \ v6)) = R(x,y,z \ (L(u,w,v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,22276,a(flip),b,22211,a),flip(a)].">
      <j1 rule="hyper" parents="63 22276 22211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22390">
    <literal><![CDATA[
      R(x,y,z \ ((u \ (u \ w)) \ v5)) = R(x,y,z \ (L(w,u,u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,22273,a(flip),b,22388,a)].">
      <j1 rule="hyper" parents="63 22273 22388"/>
    </justification>
  </clause>

  <clause id="22391">
    <literal><![CDATA[
      ((x \ (1 * L(x,y,z))) * x) * L(x \ 1,u,w) = L(1 / x,y,z) * L(x,u,w)
    ]]></literal>
    <justification jstring="[para(66(a,1),22341(a,1,1,1,2,2,1))].">
      <j1 rule="para" parents="66 22341"/>
    </justification>
  </clause>

  <clause id="22392">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * x) * L(x \ 1,u,w) = L(1 / x,y,z) * L(x,u,w)
    ]]></literal>
    <justification jstring="[para(7(a,1),22391(a,1,1,1,2))].">
      <j1 rule="para" parents="7 22391"/>
    </justification>
  </clause>

  <clause id="22393">
    <literal><![CDATA[
      L(1 / x,y,z) * L(x,u,w) = L(x,y,z) * L(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(3163(a,1),22392(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3163 22392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22394">
    <literal><![CDATA[
      R(R(x,y,K(z,u)),y * K(z,u),w) = R(x,y,K(z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(595,a,22349,a),flip(a)].">
      <j1 rule="hyper" parents="595 22349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22395">
    <literal><![CDATA[
      R(x,y * K(z,u),w) = R(x,y,K(z,u) * w)
    ]]></literal>
    <justification jstring="[para(20001(a,1),22394(a,1,1))].">
      <j1 rule="para" parents="20001 22394"/>
    </justification>
  </clause>

  <clause id="22396">
    <literal><![CDATA[
      R(x,y * K(z,u),w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,22058,a(flip),b,22395,a),flip(a)].">
      <j1 rule="hyper" parents="347 22058 22395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22398">
    <literal><![CDATA[
      R(x,y * K(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(22395(a,2),22091(a,1))].">
      <j1 rule="para" parents="22395 22091"/>
    </justification>
  </clause>

  <clause id="22399">
    <literal><![CDATA[
      R(x,K(y,z) * u,w) = R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(22117,a,22396,a)].">
      <j1 rule="hyper" parents="22117 22396"/>
    </justification>
  </clause>

  <clause id="22404">
    <literal><![CDATA[
      R(x,y * T(z,u),w) = R(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(1440(a,1),22396(a,1,2))].">
      <j1 rule="para" parents="1440 22396"/>
    </justification>
  </clause>

  <clause id="22407">
    <literal><![CDATA[
      R(x,T(y,z) * u,w) = R(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(5564(a,1),22396(a,1,2))].">
      <j1 rule="para" parents="5564 22396"/>
    </justification>
  </clause>

  <clause id="22408">
    <literal><![CDATA[
      R(x,y * (z * T(u,w)),v5) = R(x,y * (z * u),v5)
    ]]></literal>
    <justification jstring="[para(6975(a,1),22396(a,1,2))].">
      <j1 rule="para" parents="6975 22396"/>
    </justification>
  </clause>

  <clause id="22411">
    <literal><![CDATA[
      R(x,(y / z) * u,w) = R(x,(z \ y) * u,w)
    ]]></literal>
    <justification jstring="[para(7768(a,1),22396(a,1,2))].">
      <j1 rule="para" parents="7768 22396"/>
    </justification>
  </clause>

  <clause id="22412">
    <literal><![CDATA[
      R(x,y * (z * K(u,w)),v5) = R(x,y * z,v5)
    ]]></literal>
    <justification jstring="[para(7609(a,1),22396(a,1,2))].">
      <j1 rule="para" parents="7609 22396"/>
    </justification>
  </clause>

  <clause id="22414">
    <literal><![CDATA[
      R(x,((y \ z) * y) \ u,w) = R(x,z \ u,w)
    ]]></literal>
    <justification jstring="[para(9886(a,1),22396(a,1,2))].">
      <j1 rule="para" parents="9886 22396"/>
    </justification>
  </clause>

  <clause id="22415">
    <literal><![CDATA[
      R(x,y * (K(z,u) * w),v5) = R(x,y * w,v5)
    ]]></literal>
    <justification jstring="[para(11070(a,1),22396(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11070 22396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22416">
    <literal><![CDATA[
      R(x,y \ K(z,u),w) = R(x,y \ 1,w)
    ]]></literal>
    <justification jstring="[para(12973(a,1),22396(a,1,2))].">
      <j1 rule="para" parents="12973 22396"/>
    </justification>
  </clause>

  <clause id="22417">
    <literal><![CDATA[
      R(x,y \ (z / u),w) = R(x,y \ (u \ z),w)
    ]]></literal>
    <justification jstring="[para(13113(a,1),22396(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13113 22396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22418">
    <literal><![CDATA[
      R(x,y \ (K(z,u) * w),v5) = R(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(20369(a,1),22396(a,1,2))].">
      <j1 rule="para" parents="20369 22396"/>
    </justification>
  </clause>

  <clause id="22421">
    <literal><![CDATA[
      R(x,y * (z * (u \ K(w,v5))),v6) = R(x,y * (z * u),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,21945,a(flip),b,22399,a),flip(a)].">
      <j1 rule="hyper" parents="63 21945 22399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22422">
    <literal><![CDATA[
      R(x,(y / z) \ u,w) = R(x,(z \ y) \ u,w)
    ]]></literal>
    <justification jstring="[para(5441(a,1),22399(a,1,2))].">
      <j1 rule="para" parents="5441 22399"/>
    </justification>
  </clause>

  <clause id="22423">
    <literal><![CDATA[
      R(x,(T(y,z) * u) * w,v5) = R(x,(y * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(5846(a,1),22399(a,1,2))].">
      <j1 rule="para" parents="5846 22399"/>
    </justification>
  </clause>

  <clause id="22426">
    <literal><![CDATA[
      R(x,y * (T(z,u) \ w),v5) = R(x,y * (z \ w),v5)
    ]]></literal>
    <justification jstring="[para(19545(a,1),22399(a,1,2))].">
      <j1 rule="para" parents="19545 22399"/>
    </justification>
  </clause>

  <clause id="22427">
    <literal><![CDATA[
      R(x,(y * T(z,u)) \ w,v5) = R(x,(y * z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(20828(a,1),22399(a,1,2))].">
      <j1 rule="para" parents="20828 22399"/>
    </justification>
  </clause>

  <clause id="22428">
    <literal><![CDATA[
      R(x,(y \ K(z,u)) \ w,v5) = R(x,(y \ 1) \ w,v5)
    ]]></literal>
    <justification jstring="[para(20832(a,1),22399(a,1,2))].">
      <j1 rule="para" parents="20832 22399"/>
    </justification>
  </clause>

  <clause id="22429">
    <literal><![CDATA[
      R(x,(T(y,z) * u) \ w,v5) = R(x,(y * u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(20829(a,1),22399(a,1,2))].">
      <j1 rule="para" parents="20829 22399"/>
    </justification>
  </clause>

  <clause id="22430">
    <literal><![CDATA[
      R(x,((y / z) \ u) * w,v5) = R(x,((z \ y) \ u) * w,v5)
    ]]></literal>
    <justification jstring="[para(20721(a,1),22399(a,1,2))].">
      <j1 rule="para" parents="20721 22399"/>
    </justification>
  </clause>

  <clause id="22431">
    <literal><![CDATA[
      R(x,y,z) * (K(u,w) * (y * z)) = (x * (K(u,w) * y)) * z
    ]]></literal>
    <justification jstring="[para(22399(a,1),20710(a,1,1))].">
      <j1 rule="para" parents="22399 20710"/>
    </justification>
  </clause>

  <clause id="22432">
    <literal><![CDATA[
      R(x,y,(x * y) \ z) \ z = (K(u,w) * y) * ((x * (K(u,w) * y)) \ z)
    ]]></literal>
    <justification jstring="[para(22399(a,1),22225(a,1,1))].">
      <j1 rule="para" parents="22399 22225"/>
    </justification>
  </clause>

  <clause id="22433">
    <literal><![CDATA[
      R(x,y * ((z * z) \ (u / (z \ w))),v5) = R(x,y * (u / ((z \ 1) \ w)),v5)
    ]]></literal>
    <justification jstring="[para(2076(a,1),22404(a,1,2,2))].">
      <j1 rule="para" parents="2076 22404"/>
    </justification>
  </clause>

  <clause id="22434">
    <literal><![CDATA[
      R(x,y * (z \ (u * u)),w) = R(x,y * z,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21926,a(flip),b,22407,a),flip(a)].">
      <j1 rule="hyper" parents="63 21926 22407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22435">
    <literal><![CDATA[
      R(x,T(y / L(z,u,w),v5) * (((1 / z) \ z) * v6),v7) = R(x,(y / L(z \ 1,u,w)) * v6,v7)
    ]]></literal>
    <justification jstring="[para(22346(a,1),22407(a,2,2))].">
      <j1 rule="para" parents="22346 22407"/>
    </justification>
  </clause>

  <clause id="22436">
    <literal><![CDATA[
      R(x,y \ K(z,u),w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,2247,a(flip),b,22416,a),flip(a)].">
      <j1 rule="hyper" parents="347 2247 22416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22438">
    <literal><![CDATA[
      R(x,y * T(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y * z,w) = v5
    ]]></literal>
    <justification jstring="[para(1440(a,1),22398(a,1,2))].">
      <j1 rule="para" parents="1440 22398"/>
    </justification>
  </clause>

  <clause id="22439">
    <literal><![CDATA[
      R(x,T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(4929(a,2),22398(a,1,2))].">
      <j1 rule="para" parents="4929 22398"/>
    </justification>
  </clause>

  <clause id="22440">
    <literal><![CDATA[
      R(x,y * (z / u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y * (u \ z),w) = v5
    ]]></literal>
    <justification jstring="[para(6075(a,1),22398(a,1,2))].">
      <j1 rule="para" parents="6075 22398"/>
    </justification>
  </clause>

  <clause id="22441">
    <literal><![CDATA[
      R(x,y * (z * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y * (u * z),w) = v5
    ]]></literal>
    <justification jstring="[para(6977(a,1),22398(a,1,2))].">
      <j1 rule="para" parents="6977 22398"/>
    </justification>
  </clause>

  <clause id="22442">
    <literal><![CDATA[
      R(x,K(y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(7076(a,1),22398(a,1,2))].">
      <j1 rule="para" parents="7076 22398"/>
    </justification>
  </clause>

  <clause id="22443">
    <literal><![CDATA[
      R(x,y \ (z / u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ (u \ z),w) = v5
    ]]></literal>
    <justification jstring="[para(13354(a,1),22398(a,1,2))].">
      <j1 rule="para" parents="13354 22398"/>
    </justification>
  </clause>

  <clause id="22444">
    <literal><![CDATA[
      R(x,y \ (K(z,u) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ w,v5) = v6
    ]]></literal>
    <justification jstring="[para(20369(a,1),22398(a,1,2))].">
      <j1 rule="para" parents="20369 22398"/>
    </justification>
  </clause>

  <clause id="22446">
    <literal><![CDATA[
      R(x,y * (K(z,u) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(9400(a,1),22442(a,1,2))].">
      <j1 rule="para" parents="9400 22442"/>
    </justification>
  </clause>

  <clause id="22447">
    <literal><![CDATA[
      R(x,(T(y,z) * u) \ w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,(y * u) \ w,v5) = v6
    ]]></literal>
    <justification jstring="[para(20829(a,1),22442(a,1,2))].">
      <j1 rule="para" parents="20829 22442"/>
    </justification>
  </clause>

  <clause id="22448">
    <literal><![CDATA[
      R(x,((y / z) \ u) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,((z \ y) \ u) * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(20721(a,1),22442(a,1,2))].">
      <j1 rule="para" parents="20721 22442"/>
    </justification>
  </clause>

  <clause id="22449">
    <literal><![CDATA[
      R(x,(y / z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,u * (z \ y),w) = v5
    ]]></literal>
    <justification jstring="[para(22411(a,2),22117(a,1))].">
      <j1 rule="para" parents="22411 22117"/>
    </justification>
  </clause>

  <clause id="22450">
    <literal><![CDATA[
      R(x,y * (T(z,u) * w),v5) = R(x,y * (z * w),v5)
    ]]></literal>
    <justification jstring="[para(5564(a,1),22412(a,1,2,2))].">
      <j1 rule="para" parents="5564 22412"/>
    </justification>
  </clause>

  <clause id="22451">
    <literal><![CDATA[
      R(x,y * (z * (u / w)),v5) = R(x,y * (z * (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(5927(a,1),22412(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5927 22412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22452">
    <literal><![CDATA[
      R(x,y * ((z / u) * w),v5) = R(x,y * ((u \ z) * w),v5)
    ]]></literal>
    <justification jstring="[para(7768(a,1),22412(a,1,2,2))].">
      <j1 rule="para" parents="7768 22412"/>
    </justification>
  </clause>

  <clause id="22453">
    <literal><![CDATA[
      R(x,y * (z * (u * K(w,v5))),v6) = R(x,y * (z * u),v6)
    ]]></literal>
    <justification jstring="[para(7609(a,1),22412(a,1,2,2))].">
      <j1 rule="para" parents="7609 22412"/>
    </justification>
  </clause>

  <clause id="22454">
    <literal><![CDATA[
      R(x,y * (z * (u * (w * K(v5,v6)))),v7) = R(x,(z * (u * w)) * y,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,21327,a(flip),b,22415,a)].">
      <j1 rule="hyper" parents="63 21327 22415"/>
    </justification>
  </clause>

  <clause id="22455">
    <literal><![CDATA[
      R(x,y * ((z * T(u,w)) \ v5),v6) = R(x,y * ((z * u) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(20828(a,1),22415(a,1,2,2))].">
      <j1 rule="para" parents="20828 22415"/>
    </justification>
  </clause>

  <clause id="22456">
    <literal><![CDATA[
      R(x,(y * (K(z,u) * w)) * v5,v6) = R(x,(y * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(21138(a,1),22415(a,1,2))].">
      <j1 rule="para" parents="21138 22415"/>
    </justification>
  </clause>

  <clause id="22457">
    <literal><![CDATA[
      R(x,y \ (T(z,u) \ w),v5) = R(x,y \ (z \ w),v5)
    ]]></literal>
    <justification jstring="[para(5159(a,1),22418(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5159 22418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22458">
    <literal><![CDATA[
      R(x,y \ (z \ (K(u,w) * v5)),v6) = R(x,y \ (z \ v5),v6)
    ]]></literal>
    <justification jstring="[para(19540(a,1),22418(a,1,2,2))].">
      <j1 rule="para" parents="19540 22418"/>
    </justification>
  </clause>

  <clause id="22459">
    <literal><![CDATA[
      R(x * (y / (1 / z)),z,z) / z = R(x,(z \ 1) \ y,z) * y
    ]]></literal>
    <justification jstring="[para(22422(a,1),9674(a,2,1))].">
      <j1 rule="para" parents="22422 9674"/>
    </justification>
  </clause>

  <clause id="22460">
    <literal><![CDATA[
      R(x,((K(y,z) * u) / (y * T(z,w))) \ v5,v6) = R(x,(K(w,z) * ((z * y) \ u)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(21039(a,1),22422(a,2,2,1))].">
      <j1 rule="para" parents="21039 22422"/>
    </justification>
  </clause>

  <clause id="22461">
    <literal><![CDATA[
      R(x,(y \ (z * z)) * u,w) = R(x,u * y,w)
    ]]></literal>
    <justification jstring="[hyper(22117,a,22434,a)].">
      <j1 rule="hyper" parents="22117 22434"/>
    </justification>
  </clause>

  <clause id="22463">
    <literal><![CDATA[
      R(x,y * (K(z,u * z) * a(u,z,u * z)),w) = R(x,y * (u * ((u * z) * z)),w)
    ]]></literal>
    <justification jstring="[para(21241(a,1),22434(a,1,2,2))].">
      <j1 rule="para" parents="21241 22434"/>
    </justification>
  </clause>

  <clause id="22464">
    <literal><![CDATA[
      R(x,(y \ (z * z)) * (u * L(u,w,v5)),v6) = R(x,(L(u,w,v5) \ u) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,2382,a(flip),b,22461,a)].">
      <j1 rule="hyper" parents="63 2382 22461"/>
    </justification>
  </clause>

  <clause id="22465">
    <literal><![CDATA[
      R(x,(y * T(z,u)) * w,v5) = R(x,w * (y * z),v5)
    ]]></literal>
    <justification jstring="[hyper(22117,a,22408,a)].">
      <j1 rule="hyper" parents="22117 22408"/>
    </justification>
  </clause>

  <clause id="22466">
    <literal><![CDATA[
      R(x,y * ((z * (T(u,w) \ 1)) * u),v5) = R(x,y * ((z * (u \ 1)) * u),v5)
    ]]></literal>
    <justification jstring="[para(6360(a,1),22408(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6360 22408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22467">
    <literal><![CDATA[
      R(x,y * (K(z,u) * (w * (u \ v5))),v6) = R(x,y * ((T(u,z) \ v5) * w),v6)
    ]]></literal>
    <justification jstring="[para(21922(a,1),22408(a,1,2,2))].">
      <j1 rule="para" parents="21922 22408"/>
    </justification>
  </clause>

  <clause id="22468">
    <literal><![CDATA[
      R(x,(T(y,z) \ u) * w,v5) = R(x,w * (y \ u),v5)
    ]]></literal>
    <justification jstring="[hyper(22117,a,22426,a)].">
      <j1 rule="hyper" parents="22117 22426"/>
    </justification>
  </clause>

  <clause id="22469">
    <literal><![CDATA[
      R(x,(y * (z / u)) \ w,v5) = R(x,(y * (u \ z)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(113(a,1),22427(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="113 22427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22470">
    <literal><![CDATA[
      R(x,(y \ K(z,u)) \ w,v5) = R(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,20655,a(flip),b,22428,a),flip(a)].">
      <j1 rule="hyper" parents="347 20655 22428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22471">
    <literal><![CDATA[
      R(x,((y / z) * u) \ w,v5) = R(x,((z \ y) * u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(113(a,1),22429(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="113 22429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22472">
    <literal><![CDATA[
      R(x,(((y * T(z,u)) \ (y * w)) \ 1) \ (z \ w),v5) = R(x,(T(z,u) \ w) * ((y * T(z,u)) \ (y * w)),v5)
    ]]></literal>
    <justification jstring="[para(22053(a,1),22457(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22053 22457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22473">
    <literal><![CDATA[
      R(x,(y * z) * u,w) = R(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[para(111(a,1),22465(a,1,2,1))].">
      <j1 rule="para" parents="111 22465"/>
    </justification>
  </clause>

  <clause id="22474">
    <literal><![CDATA[
      R(x,y * ((y * y) \ z),u) = R(x,L(y \ z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(22440,a,21166,a)].">
      <j1 rule="hyper" parents="22440 21166"/>
    </justification>
  </clause>

  <clause id="22475">
    <literal><![CDATA[
      R(x,y \ R(y,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y * (z \ (y \ z)),u) = w
    ]]></literal>
    <justification jstring="[para(2377(a,2),22440(a,1,2))].">
      <j1 rule="para" parents="2377 22440"/>
    </justification>
  </clause>

  <clause id="22476">
    <literal><![CDATA[
      R(x,y * ((z * z) * u),w) = R(x,y * u,w)
    ]]></literal>
    <justification jstring="[hyper(22441,a,2244,a)].">
      <j1 rule="hyper" parents="22441 2244"/>
    </justification>
  </clause>

  <clause id="22477">
    <literal><![CDATA[
      R(x,(y * z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,u * (z * y),w) = v5
    ]]></literal>
    <justification jstring="[para(20553(a,1),22441(a,1))].">
      <j1 rule="para" parents="20553 22441"/>
    </justification>
  </clause>

  <clause id="22478">
    <literal><![CDATA[
      R(x,y * ((z * z) \ u),w) = R(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),22476(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 22476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22479">
    <literal><![CDATA[
      R(x,y * ((z \ 1) \ u),w) = R(x,y * (z \ u),w)
    ]]></literal>
    <justification jstring="[para(495(a,1),22476(a,1,2,2))].">
      <j1 rule="para" parents="495 22476"/>
    </justification>
  </clause>

  <clause id="22480">
    <literal><![CDATA[
      R(x,(y * T(z,u * u)) * w,v5) = R(x,(y * ((u * u) \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(1092(a,1),22476(a,1,2))].">
      <j1 rule="para" parents="1092 22476"/>
    </justification>
  </clause>

  <clause id="22481">
    <literal><![CDATA[
      R(x,y * (((1 / z) \ z) * u),w) = R(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(982(a,1),22478(a,1,2,2))].">
      <j1 rule="para" parents="982 22478"/>
    </justification>
  </clause>

  <clause id="22482">
    <literal><![CDATA[
      R(x,(y \ (z * (u \ 1))) * w,v5) = R(x,(y \ (z * u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(1104(a,1),22478(a,1,2))].">
      <j1 rule="para" parents="1104 22478"/>
    </justification>
  </clause>

  <clause id="22483">
    <literal><![CDATA[
      R(x,((y \ 1) \ z) * u,w) = R(x,u * (y \ z),w)
    ]]></literal>
    <justification jstring="[hyper(22117,a,22479,a)].">
      <j1 rule="hyper" parents="22117 22479"/>
    </justification>
  </clause>

  <clause id="22484">
    <literal><![CDATA[
      R(x,y * (z \ (z \ u)),w) = R(x,y * L(u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15298,a(flip),b,22479,a),flip(a)].">
      <j1 rule="hyper" parents="63 15298 22479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22485">
    <literal><![CDATA[
      R(x,y * ((z * (u \ 1)) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y * R(z,u,u),w) = v5
    ]]></literal>
    <justification jstring="[para(2903(a,1),22446(a,1,2,2))].">
      <j1 rule="para" parents="2903 22446"/>
    </justification>
  </clause>

  <clause id="22486">
    <literal><![CDATA[
      R(x,y * (z \ (K(u,w) * v5)),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      R(x,y * (z \ v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(19540(a,1),22446(a,1,2,2))].">
      <j1 rule="para" parents="19540 22446"/>
    </justification>
  </clause>

  <clause id="22487">
    <literal><![CDATA[
      R(x,L(y \ z,y,y),u) = R(x,(y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[para(497(a,1),22474(a,1,2)),flip(a)].">
      <j1 rule="para" parents="497 22474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22488">
    <literal><![CDATA[
      R(x,L(y \ z,y,y),u) = R(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,20644,a(flip),b,22487,a),flip(a)].">
      <j1 rule="hyper" parents="347 20644 22487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22489">
    <literal><![CDATA[
      R(x,(y * z) * y,u) = R(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),22488(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 22488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22490">
    <literal><![CDATA[
      R(x,L(a(y \ z,y,u),y * u,y * u),w) = R(x,((z / y) \ (z * u)) * (y * u),w)
    ]]></literal>
    <justification jstring="[para(14708(a,1),22488(a,1,2,1))].">
      <j1 rule="para" parents="14708 22488"/>
    </justification>
  </clause>

  <clause id="22491">
    <literal><![CDATA[
      R(x,(y \ (y \ z)) * u,w) = R(x,u * L(z,y,y),w)
    ]]></literal>
    <justification jstring="[hyper(22117,a,22484,a)].">
      <j1 rule="hyper" parents="22117 22484"/>
    </justification>
  </clause>

  <clause id="22493">
    <literal><![CDATA[
      R(x,y * (z * ((u \ w) / (v5 * v5))),v6) = R(x,y * (z * ((u * (v5 * v5)) \ w)),v6)
    ]]></literal>
    <justification jstring="[para(459(a,2),22451(a,2,2,2,2))].">
      <j1 rule="para" parents="459 22451"/>
    </justification>
  </clause>

  <clause id="22494">
    <literal><![CDATA[
      R(x,y * (z * (u \ T(w,v5))),v6) = R(x,y * (z * (u \ w)),v6)
    ]]></literal>
    <justification jstring="[para(1438(a,1),22453(a,1,2,2,2))].">
      <j1 rule="para" parents="1438 22453"/>
    </justification>
  </clause>

  <clause id="22495">
    <literal><![CDATA[
      R(x,y * (z * (u \ (w / v5))),v6) = R(x,y * (z * (u \ (v5 \ w))),v6)
    ]]></literal>
    <justification jstring="[para(13113(a,1),22453(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13113 22453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22496">
    <literal><![CDATA[
      R(x,y * (z * (K(u,w) * v5)),v6) = R(x,(z * v5) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(22117,a,22456,a)].">
      <j1 rule="hyper" parents="22117 22456"/>
    </justification>
  </clause>

  <clause id="22497">
    <literal><![CDATA[
      R(x,(y * (z / u)) * w,v5) = R(x,(y * (u \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(5012(a,1),22456(a,1,2,1,2))].">
      <j1 rule="para" parents="5012 22456"/>
    </justification>
  </clause>

  <clause id="22498">
    <literal><![CDATA[
      R(x,(y * (z \ T(u,w))) * v5,v6) = R(x,(y * (z \ u)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(5456(a,1),22456(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5456 22456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22499">
    <literal><![CDATA[
      R(x,((y \ T(z,u)) * w) * v5,v6) = R(x,((y \ z) * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(20179(a,1),22456(a,1,2,1))].">
      <j1 rule="para" parents="20179 22456"/>
    </justification>
  </clause>

  <clause id="22500">
    <literal><![CDATA[
      R(x,((y * T(z,u)) * w) * v5,v6) = R(x,((y * z) * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(20808(a,1),22456(a,1,2,1))].">
      <j1 rule="para" parents="20808 22456"/>
    </justification>
  </clause>

  <clause id="22501">
    <literal><![CDATA[
      R(x,y \ (z \ (u / w)),v5) = R(x,y \ (z \ (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(5012(a,1),22458(a,1,2,2,2))].">
      <j1 rule="para" parents="5012 22458"/>
    </justification>
  </clause>

  <clause id="22502">
    <literal><![CDATA[
      R(x,y \ (z \ (((u * u) \ u) \ w)),v5) = R(x,y \ (z \ ((u \ 1) \ w)),v5)
    ]]></literal>
    <justification jstring="[para(5345(a,1),22458(a,1,2,2,2))].">
      <j1 rule="para" parents="5345 22458"/>
    </justification>
  </clause>

  <clause id="22503">
    <literal><![CDATA[
      R(x,(y \ ((y \ z) / z)) \ u,w) = R(x,((z \ (y \ z)) * y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21122,a,b,22471,a)].">
      <j1 rule="hyper" parents="63 21122 22471"/>
    </justification>
  </clause>

  <clause id="22504">
    <literal><![CDATA[
      R(x,(y * (z * u)) * w,v5) = R(x,w * (y * (u * z)),v5)
    ]]></literal>
    <justification jstring="[para(4909(a,1),22496(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4909 22496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22505">
    <literal><![CDATA[
      R(x,y * (z * (T(u,w) \ v5)),v6) = R(x,(z * (u \ v5)) * y,v6)
    ]]></literal>
    <justification jstring="[para(5209(a,1),22496(a,1,2,2,2))].">
      <j1 rule="para" parents="5209 22496"/>
    </justification>
  </clause>

  <clause id="22506">
    <literal><![CDATA[
      R(x,(y * ((z * z) \ (u \ z))) * w,v5) = R(x,(y * (u \ (z \ 1))) * w,v5)
    ]]></literal>
    <justification jstring="[para(820(a,1),22497(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="820 22497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22507">
    <literal><![CDATA[
      R(x,(y * (1 / ((z \ (z / u)) \ 1))) * w,v5) = R(x,(y * ((z * u) \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(3256(a,1),22497(a,2,2,1,2))].">
      <j1 rule="para" parents="3256 22497"/>
    </justification>
  </clause>

  <clause id="22508">
    <literal><![CDATA[
      R(x,(y * ((z * T(u,T(w,z))) \ T(u,T(w,v5)))) * v6,v7) = R(x,(y * (T(u,K(v5,w)) / (z * u))) * v6,v7)
    ]]></literal>
    <justification jstring="[para(21986(a,2),22497(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="21986 22497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22509">
    <literal><![CDATA[
      R(x,y \ (z \ (((u * u) \ w) \ v5)),v6) = R(x,y \ (z \ ((v5 / w) * (u * u))),v6)
    ]]></literal>
    <justification jstring="[para(896(a,1),22501(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="896 22501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22510">
    <literal><![CDATA[
      R(x,(y * ((z * z) * u)) * w,v5) = R(x,w * (y * u),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,2300,a(flip),b,22504,a),flip(a)].">
      <j1 rule="hyper" parents="347 2300 22504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22511">
    <literal><![CDATA[
      R(x,(y * (z * u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,(y * (u * z)) * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(22504(a,2),22117(a,1))].">
      <j1 rule="para" parents="22504 22117"/>
    </justification>
  </clause>

  <clause id="22512">
    <literal><![CDATA[
      R(x,y * (z * ((u * u) \ w)),v5) = R(x,(z * w) * y,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),22510(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 22510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22513">
    <literal><![CDATA[
      R(x,((y * T(z,u * u)) * w) * v5,v6) = R(x,v5 * ((y * ((u * u) \ z)) * w),v6)
    ]]></literal>
    <justification jstring="[para(1092(a,1),22510(a,1,2,1))].">
      <j1 rule="para" parents="1092 22510"/>
    </justification>
  </clause>

  <clause id="22514">
    <literal><![CDATA[
      R(x,y * (z * (u / (w * w))),v5) = R(x,(z * u) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22451,a,b,22512,a)].">
      <j1 rule="hyper" parents="63 22451 22512"/>
    </justification>
  </clause>

  <clause id="22515">
    <literal><![CDATA[
      R(x,y * (z * L(u \ 1,w,v5)),v6) = R(x,(z * L(u,w,v5)) * y,v6)
    ]]></literal>
    <justification jstring="[para(3322(a,1),22514(a,1,2,2,2))].">
      <j1 rule="para" parents="3322 22514"/>
    </justification>
  </clause>

  <clause id="22517">
    <literal><![CDATA[
      R(x * (y / (1 / z)),z,z) / z = R(x,z \ y,z) * y
    ]]></literal>
    <justification jstring="[para(20655(a,1),22459(a,2,1))].">
      <j1 rule="para" parents="20655 22459"/>
    </justification>
  </clause>

  <clause id="22518">
    <literal><![CDATA[
      R(x * (y / (1 / z)),z,z) = ((x * (y / z)) * z) * z
    ]]></literal>
    <justification jstring="[hyper(9631,a,22517,a),flip(a)].">
      <j1 rule="hyper" parents="9631 22517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22519">
    <literal><![CDATA[
      R(x,y * ((z \ T(u,w)) * v5),v6) = R(x,y * (v5 * (z \ u)),v6)
    ]]></literal>
    <justification jstring="[hyper(22441,a,22494,a)].">
      <j1 rule="hyper" parents="22441 22494"/>
    </justification>
  </clause>

  <clause id="22520">
    <literal><![CDATA[
      R(x,y * (z \ (u / w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y * (z \ (w \ u)),v5) = v6
    ]]></literal>
    <justification jstring="[para(5012(a,1),22486(a,1,2,2,2))].">
      <j1 rule="para" parents="5012 22486"/>
    </justification>
  </clause>

  <clause id="22521">
    <literal><![CDATA[
      R(x,y * (((z \ 1) \ u) \ w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y * (((z \ K(v7,v8)) \ u) \ w),v5) = v6
    ]]></literal>
    <justification jstring="[para(21051(a,1),22486(a,1,2,2))].">
      <j1 rule="para" parents="21051 22486"/>
    </justification>
  </clause>

  <clause id="22522">
    <literal><![CDATA[
      R(x,(y * (((z * z) \ u) * w)) * v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      R(x,(y * (((z * z) \ w) * T(u,z * z))) * v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(829(a,1),22511(a,1,2,1,2))].">
      <j1 rule="para" parents="829 22511"/>
    </justification>
  </clause>

  <clause id="22523">
    <literal><![CDATA[
      R(x,(y * (z * u)) * ((w * w) \ v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      R(x,(y * ((u / (w * w)) * z)) * v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(1103(a,1),22511(a,1,2))].">
      <j1 rule="para" parents="1103 22511"/>
    </justification>
  </clause>

  <clause id="22524">
    <literal><![CDATA[
      R(x,(y \ (z / u)) * w,v5) = R(x,w * (y \ (u \ z)),v5)
    ]]></literal>
    <justification jstring="[hyper(22520,a,20553,a),flip(a)].">
      <j1 rule="hyper" parents="22520 20553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22525">
    <literal><![CDATA[
      R(x,(y * y) * (z \ ((y * y) \ u)),w) = R(x,z \ u,w)
    ]]></literal>
    <justification jstring="[para(729(a,1),22524(a,1,2)),flip(a)].">
      <j1 rule="para" parents="729 22524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22526">
    <literal><![CDATA[
      R(x,y * ((z * y) \ z),u) = R(x,y * (z \ (y \ z)),u)
    ]]></literal>
    <justification jstring="[para(3261(a,1),22524(a,1,2))].">
      <j1 rule="para" parents="3261 22524"/>
    </justification>
  </clause>

  <clause id="22527">
    <literal><![CDATA[
      R(x,y \ ((z * z) \ u),w) = R(x,y \ u,w)
    ]]></literal>
    <justification jstring="[hyper(20907,a,22525,a)].">
      <j1 rule="hyper" parents="20907 22525"/>
    </justification>
  </clause>

  <clause id="22529">
    <literal><![CDATA[
      R(x,y \ ((z \ 1) \ u),w) = R(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[para(500(a,1),22527(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="500 22527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22531">
    <literal><![CDATA[
      R(x,(y * (z * T(u,w))) * v5,v6) = R(x,v5 * (y * (z * u)),v6)
    ]]></literal>
    <justification jstring="[para(4915(a,1),22454(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4915 22454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22532">
    <literal><![CDATA[
      R(x,(y * ((z * z) \ u)) * w,v5) = R(x,w * (y * u),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22465,a(flip),b,22480,a),flip(a)].">
      <j1 rule="hyper" parents="63 22465 22480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22534">
    <literal><![CDATA[
      (K(x,y) * z) * ((u * (K(x,y) * z)) \ w) = z * ((u * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(1010,a,22432,a),flip(a)].">
      <j1 rule="hyper" parents="1010 22432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22536">
    <literal><![CDATA[
      (K(x,y) * z) * ((T(x,y) * z) \ u) = z * ((x * z) \ u)
    ]]></literal>
    <justification jstring="[para(4943(a,1),22534(a,1,2,1))].">
      <j1 rule="para" parents="4943 22534"/>
    </justification>
  </clause>

  <clause id="22537">
    <literal><![CDATA[
      K(x,y) * (z * ((T(x,y) * z) \ u)) = z * ((x * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(20093,a,22536,a)].">
      <j1 rule="hyper" parents="20093 22536"/>
    </justification>
  </clause>

  <clause id="22538">
    <literal><![CDATA[
      T(x,y) * (z * ((T(x,y) * z) \ u)) = x * (z * ((x * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(134,a,22537,a(flip),b,5157,a),flip(a)].">
      <j1 rule="hyper" parents="134 22537 5157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22539">
    <literal><![CDATA[
      x * ((x \ (T(x,y) / z)) * z) = x * (z * ((x * z) \ T(x,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21154,a(flip),b,22538,a)].">
      <j1 rule="hyper" parents="63 21154 22538"/>
    </justification>
  </clause>

  <clause id="22541">
    <literal><![CDATA[
      R(x,y * ((z * z) \ ((z \ u) \ w)),v5) = R(x,y * (w / ((z \ 1) \ u)),v5)
    ]]></literal>
    <justification jstring="[hyper(22520,a,22433,a)].">
      <j1 rule="hyper" parents="22520 22433"/>
    </justification>
  </clause>

  <clause id="22542">
    <literal><![CDATA[
      R(x,(L(y,z,u) \ y) * w,v5) = R(x,(y * L(y,z,u)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22461,a(flip),b,22464,a),flip(a)].">
      <j1 rule="hyper" parents="63 22461 22464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22543">
    <literal><![CDATA[
      R(x,y * ((z * (T(u,w) \ 1)) * u),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y * R(z,u,u),v5) = v6
    ]]></literal>
    <justification jstring="[para(22466(a,2),22485(a,1))].">
      <j1 rule="para" parents="22466 22485"/>
    </justification>
  </clause>

  <clause id="22544">
    <literal><![CDATA[
      R(x,y * ((T(z,u) \ w) * v5),v6) = R(x,y * (v5 * (z \ w)),v6)
    ]]></literal>
    <justification jstring="[hyper(22446,a,22467,a),flip(a)].">
      <j1 rule="hyper" parents="22446 22467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22546">
    <literal><![CDATA[
      R(x,(y * (z \ (u \ 1))) * w,v5) = R(x,w * (y * (z \ u)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22532,a(flip),b,22506,a),flip(a)].">
      <j1 rule="hyper" parents="63 22532 22506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22547">
    <literal><![CDATA[
      R(x,y * (z * (u \ (w \ 1))),v5) = R(x,y * (z * (u \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(22117,a,22546,a)].">
      <j1 rule="hyper" parents="22117 22546"/>
    </justification>
  </clause>

  <clause id="22549">
    <literal><![CDATA[
      R(x,y * (z / ((u \ 1) \ w)),v5) = R(x,y * ((u \ w) \ z),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22478,a(flip),b,22541,a),flip(a)].">
      <j1 rule="hyper" parents="63 22478 22541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22550">
    <literal><![CDATA[
      R(x,y * (((z \ 1) \ u) \ w),v5) = R(x,y * ((z \ u) \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(22440,a,22549,a)].">
      <j1 rule="hyper" parents="22440 22549"/>
    </justification>
  </clause>

  <clause id="22552">
    <literal><![CDATA[
      R(x,y * ((z * a(u,u,z)) \ w),v5) = R(x,y * ((u \ (u \ z)) \ w),v5)
    ]]></literal>
    <justification jstring="[para(15286(a,1),22550(a,1,2,2,1))].">
      <j1 rule="para" parents="15286 22550"/>
    </justification>
  </clause>

  <clause id="22553">
    <literal><![CDATA[
      R(x,y * (z * ((u * (w * w)) \ v5)),v6) = R(x,y * (z * (u \ (v5 / (w * w)))),v6)
    ]]></literal>
    <justification jstring="[para(779(a,1),22493(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="779 22493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22554">
    <literal><![CDATA[
      R(x,(y * ((z * u) \ z)) * w,v5) = R(x,(y * (z \ (z / u))) * w,v5)
    ]]></literal>
    <justification jstring="[para(80(a,1),22507(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="80 22507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22556">
    <literal><![CDATA[
      R(x,y \ (z \ (((u * u) \ w) \ v5)),v6) = R(x,y \ ((z \ (v5 / w)) * (u * u)),v6)
    ]]></literal>
    <justification jstring="[para(456(a,1),22509(a,2,2,2))].">
      <j1 rule="para" parents="456 22509"/>
    </justification>
  </clause>

  <clause id="22557">
    <literal><![CDATA[
      R(x,y * ((z * ((u * u) \ w)) * v5),v6) = R(x,((z * w) * v5) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,22500,a(flip),b,22513,a),flip(a)].">
      <j1 rule="hyper" parents="63 22500 22513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22559">
    <literal><![CDATA[
      R(x,y * (((z \ 1) * u) * w),v5) = R(x,((z * u) * w) * y,v5)
    ]]></literal>
    <justification jstring="[para(497(a,1),22557(a,1,2,2,1))].">
      <j1 rule="para" parents="497 22557"/>
    </justification>
  </clause>

  <clause id="22560">
    <literal><![CDATA[
      R(x,y * (((((z \ 1) * (z * u)) \ 1) * z) * w),v5) = R(x,(L(u * z,z,z) * w) * y,v5)
    ]]></literal>
    <justification jstring="[para(3217(a,1),22559(a,2,2,1,1))].">
      <j1 rule="para" parents="3217 22559"/>
    </justification>
  </clause>

  <clause id="22561">
    <literal><![CDATA[
      R(x,y * (z * ((u * (w * w)) \ v5)),v6) = R(x,y * (z * (u \ ((w * w) \ v5))),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,22495,a(flip),b,22553,a),flip(a)].">
      <j1 rule="hyper" parents="347 22495 22553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22562">
    <literal><![CDATA[
      R(x,y \ (z \ (((u * u) \ w) \ v5)),v6) = R(x,(y \ (z \ (v5 / w))) * (u * u),v6)
    ]]></literal>
    <justification jstring="[para(456(a,1),22556(a,2,2))].">
      <j1 rule="para" parents="456 22556"/>
    </justification>
  </clause>

  <clause id="22563">
    <literal><![CDATA[
      R(x,y * (z * ((u * u) \ (w \ v5))),v6) = R(x,y * (z * (w \ ((u * u) \ v5))),v6)
    ]]></literal>
    <justification jstring="[para(459(a,1),22561(a,1,2,2,2))].">
      <j1 rule="para" parents="459 22561"/>
    </justification>
  </clause>

  <clause id="22564">
    <literal><![CDATA[
      R(x,y \ (z \ (((u * u) \ w) \ v5)),v6) = R(x,y \ (z \ (v5 / w)),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,2245,a(flip),b,22562,a),flip(a)].">
      <j1 rule="hyper" parents="347 2245 22562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22566">
    <literal><![CDATA[
      R(x,y \ (z \ (((u * u) \ w) \ v5)),v6) = R(x,y \ (z \ (w \ v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,22501,a(flip),b,22564,a),flip(a)].">
      <j1 rule="hyper" parents="347 22501 22564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22567">
    <literal><![CDATA[
      R(x,y \ (z \ ((u \ 1) \ w)),v5) = R(x,y \ (z \ (u \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22502,a(flip),b,22566,a)].">
      <j1 rule="hyper" parents="63 22502 22566"/>
    </justification>
  </clause>

  <clause id="22569">
    <literal><![CDATA[
      R(x,y * (z * (u \ ((w * w) \ v5))),v6) = R(x,(z * (u \ v5)) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,22512,a(flip),b,22563,a),flip(a)].">
      <j1 rule="hyper" parents="63 22512 22563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22571">
    <literal><![CDATA[
      R(x,y * (z * ((z * u) * u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y * a(z,u,z * u),w) = v5
    ]]></literal>
    <justification jstring="[para(22463(a,1),22446(a,1))].">
      <j1 rule="para" parents="22463 22446"/>
    </justification>
  </clause>

  <clause id="22572">
    <literal><![CDATA[
      R(x,y * (((z \ K(u,w)) \ v5) \ v6),v7) = R(x,y * ((z \ v5) \ v6),v7)
    ]]></literal>
    <justification jstring="[hyper(22521,a,22550,a)].">
      <j1 rule="hyper" parents="22521 22550"/>
    </justification>
  </clause>

  <clause id="22573">
    <literal><![CDATA[
      R(x,y * ((z \ u) \ R(w,(z \ K(v5,v6)) \ u,(z \ K(v5,v6)) \ u)),v7) = R(x,y * T(w * (1 / ((z \ K(v5,v6)) \ u)),(z \ K(v5,v6)) \ u),v7)
    ]]></literal>
    <justification jstring="[para(2263(a,2),22572(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2263 22572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22574">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(L(x,y,z),u,w) = x * (L(x,y,z) \ L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(199(a,1),22354(a,1,2,1))].">
      <j1 rule="para" parents="199 22354"/>
    </justification>
  </clause>

  <clause id="22575">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(L(x,y,z),u,w) = x * L(x \ L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(4638(a,1),22574(a,2,2))].">
      <j1 rule="para" parents="4638 22574"/>
    </justification>
  </clause>

  <clause id="22576">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) \ u = (L(x,y,z) \ u) \ (x \ u)
    ]]></literal>
    <justification jstring="[para(21001(a,1),22364(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21001 22364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22577">
    <literal><![CDATA[
      x / T(y * (L(y,z,u) \ x),(y * (L(y,z,u) \ x)) \ x) = (L(y,z,u) \ x) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(658,a,22576,a)].">
      <j1 rule="hyper" parents="658 22576"/>
    </justification>
  </clause>

  <clause id="22578">
    <literal><![CDATA[
      (x * (x * (L(x,y,z) \ u))) \ (x * u) = (L(x,y,z) \ (x * u)) \ (x \ (x * u))
    ]]></literal>
    <justification jstring="[para(1407(a,1),22576(a,1,1,2))].">
      <j1 rule="para" parents="1407 22576"/>
    </justification>
  </clause>

  <clause id="22580">
    <literal><![CDATA[
      (x * (x * (L(x,y,z) \ u))) \ (x * u) = (x * (L(x,y,z) \ u)) \ (x \ (x * u))
    ]]></literal>
    <justification jstring="[para(1407(a,1),22578(a,2,1))].">
      <j1 rule="para" parents="1407 22578"/>
    </justification>
  </clause>

  <clause id="22581">
    <literal><![CDATA[
      (x * (x * (L(x,y,z) \ u))) \ (x * u) = (x * (L(x,y,z) \ u)) \ u
    ]]></literal>
    <justification jstring="[para(9(a,1),22580(a,2,2))].">
      <j1 rule="para" parents="9 22580"/>
    </justification>
  </clause>

  <clause id="22582">
    <literal><![CDATA[
      (x * (x * (L(x,y,z) \ u))) \ (x * u) = (L(x,y,z) \ u) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,22576,a(flip),b,22581,a),flip(a)].">
      <j1 rule="hyper" parents="347 22576 22581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22583">
    <literal><![CDATA[
      R(x,(K(y,z) * (u / (y * T(z,w)))) \ v5,v6) = R(x,(K(w,z) * ((z * y) \ u)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(20088(a,1),22460(a,1,2,1))].">
      <j1 rule="para" parents="20088 22460"/>
    </justification>
  </clause>

  <clause id="22584">
    <literal><![CDATA[
      R(x,(y / (z * T(u,w))) \ (K(u,z) * v5),v6) = R(x,(K(w,u) * ((u * z) \ y)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(20003(a,1),22583(a,1,2))].">
      <j1 rule="para" parents="20003 22583"/>
    </justification>
  </clause>

  <clause id="22585">
    <literal><![CDATA[
      R(x,(K(y,z) * ((z * u) \ w)) \ v5,v6) = R(x,(w / (u * T(z,y))) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(22444,a,22584,a),flip(a)].">
      <j1 rule="hyper" parents="22444 22584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22587">
    <literal><![CDATA[
      R(x,(K(y,z) * ((z * u) \ w)) \ v5,v6) = R(x,((u * T(z,y)) \ w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,22422,a(flip),b,22585,a),flip(a)].">
      <j1 rule="hyper" parents="347 22422 22585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22588">
    <literal><![CDATA[
      R(x,((y * z) \ u) \ (K(y,w) * v5),v6) = R(x,((z * T(y,w)) \ u) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(20003(a,1),22587(a,1,2))].">
      <j1 rule="para" parents="20003 22587"/>
    </justification>
  </clause>

  <clause id="22589">
    <literal><![CDATA[
      R(x,((y * T(z,u)) \ w) \ v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      R(x,((z * y) \ w) \ v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(22588(a,1),22444(a,1))].">
      <j1 rule="para" parents="22588 22444"/>
    </justification>
  </clause>

  <clause id="22591">
    <literal><![CDATA[
      L(L((x \ 1) \ ((T(x,y) \ 1) \ z),u,w),x,x) = T(x,y) * ((x \ 1) \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(20926(a,1),21266(a,1,1,1))].">
      <j1 rule="para" parents="20926 21266"/>
    </justification>
  </clause>

  <clause id="22592">
    <literal><![CDATA[
      L(x * ((T(x,y) \ 1) \ z),u,w) = T(x,y) * ((x \ 1) \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,3200,a(flip),b,22591,a)].">
      <j1 rule="hyper" parents="63 3200 22591"/>
    </justification>
  </clause>

  <clause id="22593">
    <literal><![CDATA[
      L(x,(y * ((z * z) \ u)) * R(w,u,y / (z * z)),v5) = L(x,((w * u) * y) / (z * z),v5)
    ]]></literal>
    <justification jstring="[para(803(a,1),21852(a,1,2,1))].">
      <j1 rule="para" parents="803 21852"/>
    </justification>
  </clause>

  <clause id="22594">
    <literal><![CDATA[
      R(x,y,(z \ L(u / w,w,w)) * v5) = R(x,y,(z \ (T(w,w \ u) * u)) * v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),22285(a,1,3,1,2,1))].">
      <j1 rule="para" parents="9 22285"/>
    </justification>
  </clause>

  <clause id="22596">
    <literal><![CDATA[
      R(x,y,a(z * (u * u),w,v5)) = R(x,y,(z * (w * (v5 \ 1))) \ ((z * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(22218,a,22298,a),flip(a)].">
      <j1 rule="hyper" parents="22218 22298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22599">
    <literal><![CDATA[
      R(x,y,a(z * (u * u),w,v5)) = R(x,y,a(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,22259,a(flip),b,22596,a),flip(a)].">
      <j1 rule="hyper" parents="347 22259 22596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22600">
    <literal><![CDATA[
      (T(x,y) \ z) \ ((x * y) \ (y * z)) = (x \ z) \ L(x \ z,x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,4058,a(flip),b,22299,a),flip(a)].">
      <j1 rule="hyper" parents="347 4058 22299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22602">
    <literal><![CDATA[
      (T(x,y) \ z) \ ((x * y) \ (y * z)) = x \ (z * L(z \ x,x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,3354,a(flip),b,22600,a),flip(a)].">
      <j1 rule="hyper" parents="347 3354 22600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22603">
    <literal><![CDATA[
      R(x,(y * ((z / (u * u)) * w)) * v5,v6) = R(x,(y * (w * z)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(22523,a,22478,a)].">
      <j1 rule="hyper" parents="22523 22478"/>
    </justification>
  </clause>

  <clause id="22604">
    <literal><![CDATA[
      R(x,(y * (z * ((u * u) \ w))) * v5,v6) = R(x,(y * (w * z)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(803(a,1),22603(a,1,2,1,2))].">
      <j1 rule="para" parents="803 22603"/>
    </justification>
  </clause>

  <clause id="22605">
    <literal><![CDATA[
      R(x,(y * (((z * z) \ u) * w)) * v5,v6) = R(x,(y * (u * w)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(22511,a,22604,a)].">
      <j1 rule="hyper" parents="22511 22604"/>
    </justification>
  </clause>

  <clause id="22606">
    <literal><![CDATA[
      x / T(y * (L(y,z,u) \ x),T(L(y,z,u) / y,x)) = (L(y,z,u) \ x) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(20969(a,1),22577(a,1,2))].">
      <j1 rule="para" parents="20969 22577"/>
    </justification>
  </clause>

  <clause id="22607">
    <literal><![CDATA[
      x / T(y * (L(y,z,u) \ x),T(y \ L(y,z,u),x)) = (L(y,z,u) \ x) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(3161(a,1),22606(a,1,2,2,1))].">
      <j1 rule="para" parents="3161 22606"/>
    </justification>
  </clause>

  <clause id="22608">
    <literal><![CDATA[
      x / T(y * (L(y,z,u) \ x),y \ L(y,z,u)) = (L(y,z,u) \ x) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(20259(a,1),22607(a,1,2,2))].">
      <j1 rule="para" parents="20259 22607"/>
    </justification>
  </clause>

  <clause id="22609">
    <literal><![CDATA[
      x / (y * (L(y,z,u) \ x)) = (L(y,z,u) \ x) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(20076(a,1),22608(a,1,2))].">
      <j1 rule="para" parents="20076 22608"/>
    </justification>
  </clause>

  <clause id="22612">
    <literal><![CDATA[
      L(x,(y * ((z * z) \ u)) * R(w,u,y),v5) = L(x,((w * u) * y) / (z * z),v5)
    ]]></literal>
    <justification jstring="[para(2188(a,1),22593(a,1,2,2))].">
      <j1 rule="para" parents="2188 22593"/>
    </justification>
  </clause>

  <clause id="22613">
    <literal><![CDATA[
      L(x,(y * ((z * z) \ u)) * R(w,u,y),v5) = L(x,(w * u) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,3186,a(flip),b,22612,a),flip(a)].">
      <j1 rule="hyper" parents="347 3186 22612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22616">
    <literal><![CDATA[
      ((x * y) * T(z,y)) * K(z * y,x) = (z * y) * (((x * y) * T(z,y)) / (z * y))
    ]]></literal>
    <justification jstring="[para(5095(a,1),20438(a,1,2))].">
      <j1 rule="para" parents="5095 20438"/>
    </justification>
  </clause>

  <clause id="22618">
    <literal><![CDATA[
      (x * y) * (((z * y) * T(x,y)) / (x * y)) = (z * y) * (T(x,y) * K(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(20359,a,22616,a),flip(a)].">
      <j1 rule="hyper" parents="20359 22616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22619">
    <literal><![CDATA[
      (x * y) * (T(z,y) * K(z * y,x)) = (z * y) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(9597(a,2),22618(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9597 22618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22620">
    <literal><![CDATA[
      (x * y) * R(z,y,x) = (z * y) * (y \ T(x * y,z))
    ]]></literal>
    <justification jstring="[para(13100(a,1),22619(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13100 22619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22621">
    <literal><![CDATA[
      (x * y) * R(a(z,u,w),y,x) = (a(z,u,w) * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(19979(a,1),22619(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19979 22619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22622">
    <literal><![CDATA[
      (x * y) \ ((y * a(z,u,w)) * T(x,y)) = R(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,19987,a(flip),b,22621,a)].">
      <j1 rule="hyper" parents="128 19987 22621"/>
    </justification>
  </clause>

  <clause id="22623">
    <literal><![CDATA[
      ((x * (y / x)) / x) * R(y / (y / x),z,u) = R(y / (y / x),z,u) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(644,a,20931,a),flip(a)].">
      <j1 rule="hyper" parents="644 20931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22625">
    <literal><![CDATA[
      ((x * (y / x)) / x) * R(y / (y / x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (y / x) * R(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(22623(a,2),1207(a,1))].">
      <j1 rule="para" parents="22623 1207"/>
    </justification>
  </clause>

  <clause id="22626">
    <literal><![CDATA[
      (x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))) * (L(x,y,z) \ x) = L(x / L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3308(a,2),20947(a,2,1))].">
      <j1 rule="para" parents="3308 20947"/>
    </justification>
  </clause>

  <clause id="22627">
    <literal><![CDATA[
      x * (L(x,y,z) \ (L(x,y,z) * (R(L(x,y,z),u,w) \ v5))) = (v5 / L(R(x,u,w),y,z)) * x
    ]]></literal>
    <justification jstring="[para(29(a,1),21053(a,2,1,2))].">
      <j1 rule="para" parents="29 21053"/>
    </justification>
  </clause>

  <clause id="22628">
    <literal><![CDATA[
      (L(x,y,z) \ T(L(T(x,u),y,z),w)) * K(v5,x) = T(T(L(x,y,z),u),w) / L(T(x,v5),y,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),21106(a,1,1,2,1))].">
      <j1 rule="para" parents="25 21106"/>
    </justification>
  </clause>

  <clause id="22629">
    <literal><![CDATA[
      ((x \ y) * (K(z,x) * u)) \ ((x \ y) * K(z,x)) = ((T(x,z) \ y) * u) \ (T(x,z) \ y)
    ]]></literal>
    <justification jstring="[para(5198(a,1),21201(a,2,1,1))].">
      <j1 rule="para" parents="5198 21201"/>
    </justification>
  </clause>

  <clause id="22630">
    <literal><![CDATA[
      (((x \ y) * (K(z,x) * u)) \ (x \ y)) * K(z,x) = ((T(x,z) \ y) * u) \ (T(x,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(20112,a,22629,a)].">
      <j1 rule="hyper" parents="20112 22629"/>
    </justification>
  </clause>

  <clause id="22631">
    <literal><![CDATA[
      ((((x \ y) * z) \ (x \ y)) * K(x,u)) * K(u,x) = ((T(x,u) \ y) * z) \ (T(x,u) \ y)
    ]]></literal>
    <justification jstring="[para(21990(a,1),22630(a,1,1))].">
      <j1 rule="para" parents="21990 22630"/>
    </justification>
  </clause>

  <clause id="22632">
    <literal><![CDATA[
      ((T(x,y) \ z) * u) \ (T(x,y) \ z) = ((x \ z) * u) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(6146,a,22631,a)].">
      <j1 rule="hyper" parents="6146 22631"/>
    </justification>
  </clause>

  <clause id="22634">
    <literal><![CDATA[
      L(x / L(x,y,z),u,L(x,w,v5)) = 1 * (x / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(284(a,1),21226(a,2,1))].">
      <j1 rule="para" parents="284 21226"/>
    </justification>
  </clause>

  <clause id="22636">
    <literal><![CDATA[
      L(x / L(x,y,z),u,L(x,w,v5)) = 1 * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(3308(a,1),22634(a,2,2))].">
      <j1 rule="para" parents="3308 22634"/>
    </justification>
  </clause>

  <clause id="22637">
    <literal><![CDATA[
      L(x / L(x,y,z),u,L(x,w,v5)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(347,a,7,a(flip),b,22636,a),flip(a)].">
      <j1 rule="hyper" parents="347 7 22636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22638">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,L(x,w,v5)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(3308(a,1),22637(a,1,1))].">
      <j1 rule="para" parents="3308 22637"/>
    </justification>
  </clause>

  <clause id="22640">
    <literal><![CDATA[
      (x / (K(y,z) * u)) * L(K(y,z) * u,w,v5) = K(y,z) * (L(u,w,v5) * (u \ (K(z,y) * x)))
    ]]></literal>
    <justification jstring="[para(20003(a,1),21280(a,2,2,2))].">
      <j1 rule="para" parents="20003 21280"/>
    </justification>
  </clause>

  <clause id="22641">
    <literal><![CDATA[
      (T(x,y * x) \ 1) * ((y \ (x \ y)) \ T(L(x,y,x),y)) = 1 / ((L(x,y,x) * y) \ y)
    ]]></literal>
    <justification jstring="[para(22(a,2),21767(a,1,2,2))].">
      <j1 rule="para" parents="22 21767"/>
    </justification>
  </clause>

  <clause id="22642">
    <literal><![CDATA[
      (T(x,y * x) \ 1) * ((y \ (x \ y)) \ T(x,y * x)) = 1 / ((L(x,y,x) * y) \ y)
    ]]></literal>
    <justification jstring="[para(4327(a,1),22641(a,1,2,2))].">
      <j1 rule="para" parents="4327 22641"/>
    </justification>
  </clause>

  <clause id="22643">
    <literal><![CDATA[
      1 / ((L(x,y,x) * y) \ y) = x * (L(x,x,y) \ T(x,y * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,21773,a(flip),b,22642,a),flip(a)].">
      <j1 rule="hyper" parents="63 21773 22642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22644">
    <literal><![CDATA[
      L(x,y \ ((z * u) * T(w,T(u * z,v5))),v6) = L(x,y \ (w * (u * z)),v6)
    ]]></literal>
    <justification jstring="[hyper(21730,a,21837,a),flip(a)].">
      <j1 rule="hyper" parents="21730 21837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22645">
    <literal><![CDATA[
      L(x,y \ ((z * u) * w),v5) = L(x,y \ (w * (u * z)),v5)
    ]]></literal>
    <justification jstring="[hyper(21764,a,22644,a)].">
      <j1 rule="hyper" parents="21764 22644"/>
    </justification>
  </clause>

  <clause id="22647">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * u) * z),w) = L(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,21885,a(flip),b,22645,a),flip(a)].">
      <j1 rule="hyper" parents="347 21885 22645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22648">
    <literal><![CDATA[
      L(x,y \ ((z * z) * u),w) = L(x,(z * z) * (y \ u),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,21699,a(flip),b,22645,a),flip(a)].">
      <j1 rule="hyper" parents="347 21699 22645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22651">
    <literal><![CDATA[
      L(x,(y * (z * u)) \ (u * (z * y)),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(14(a,2),22645(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14 22645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22652">
    <literal><![CDATA[
      L(x,y \ ((T(z,u * w) * w) * u),v5) = L(x,y \ (L(z,w,u) * (u * w)),v5)
    ]]></literal>
    <justification jstring="[para(734(a,1),22645(a,2,2,2))].">
      <j1 rule="para" parents="734 22645"/>
    </justification>
  </clause>

  <clause id="22653">
    <literal><![CDATA[
      L(x,y \ ((z * z) * u),w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,3604,a(flip),b,22648,a),flip(a)].">
      <j1 rule="hyper" parents="347 3604 22648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22655">
    <literal><![CDATA[
      L(x,y \ ((z * z) \ u),w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),22653(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 22653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22656">
    <literal><![CDATA[
      L(x,y \ ((z \ 1) \ u),w) = L(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[para(495(a,1),22653(a,1,2,2))].">
      <j1 rule="para" parents="495 22653"/>
    </justification>
  </clause>

  <clause id="22657">
    <literal><![CDATA[
      L(x,y \ L((z * z) \ u,w,v5),v6) = L(x,y \ L(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(3320(a,1),22653(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3320 22653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22658">
    <literal><![CDATA[
      L(x,y \ (z \ (u \ 1)),w) = L(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21792,a(flip),b,22655,a)].">
      <j1 rule="hyper" parents="63 21792 22655"/>
    </justification>
  </clause>

  <clause id="22659">
    <literal><![CDATA[
      L(x,(y \ (z \ u)) * (w * w),v5) = L(x,y \ ((z \ 1) \ u),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,3178,a,b,22656,a)].">
      <j1 rule="hyper" parents="347 3178 22656"/>
    </justification>
  </clause>

  <clause id="22662">
    <literal><![CDATA[
      L(x,(y * (z * u)) \ (z * (u * y)),w) = L(x,a(y,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(21831,a,22651,a)].">
      <j1 rule="hyper" parents="21831 22651"/>
    </justification>
  </clause>

  <clause id="22663">
    <literal><![CDATA[
      L(x,(((y \ 1) / z) * (z * y)) \ K(z,z \ (y \ 1)),u) = L(x,a((y \ 1) / z,z,y),u)
    ]]></literal>
    <justification jstring="[para(9559(a,1),22651(a,1,2,2))].">
      <j1 rule="para" parents="9559 22651"/>
    </justification>
  </clause>

  <clause id="22664">
    <literal><![CDATA[
      L(x,(y * z) \ (u \ (y * (z * u))),w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(22370(a,1),22662(a,1,2))].">
      <j1 rule="para" parents="22370 22662"/>
    </justification>
  </clause>

  <clause id="22665">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * (z * u)) / u),w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(21762,a,22664,a)].">
      <j1 rule="hyper" parents="21762 22664"/>
    </justification>
  </clause>

  <clause id="22666">
    <literal><![CDATA[
      L(x,(y * z) \ (u \ (z * (y * u))),w) = L(x,a(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(21735,a,22664,a)].">
      <j1 rule="hyper" parents="21735 22664"/>
    </justification>
  </clause>

  <clause id="22667">
    <literal><![CDATA[
      L(x,((y * z) \ ((y * (z * u)) / u)) \ 1,w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(3519,a,22665,a)].">
      <j1 rule="hyper" parents="3519 22665"/>
    </justification>
  </clause>

  <clause id="22668">
    <literal><![CDATA[
      L(x,(y * z) \ ((1 / y) \ (z * K(y,y \ 1))),u) = L(x,a(1 / y,y,z),u)
    ]]></literal>
    <justification jstring="[para(1924(a,2),22666(a,1,2,2,2,2))].">
      <j1 rule="para" parents="1924 22666"/>
    </justification>
  </clause>

  <clause id="22669">
    <literal><![CDATA[
      L(x,(y * z) \ (((z \ 1) / y) \ K(y,y \ (z \ 1))),u) = L(x,a((z \ 1) / y,y,z),u)
    ]]></literal>
    <justification jstring="[para(9559(a,1),22666(a,1,2,2,2))].">
      <j1 rule="para" parents="9559 22666"/>
    </justification>
  </clause>

  <clause id="22670">
    <literal><![CDATA[
      L(x,y \ L(z \ 1,u,w),v5) = L(x,y \ L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,21863,a(flip),b,22657,a)].">
      <j1 rule="hyper" parents="63 21863 22657"/>
    </justification>
  </clause>

  <clause id="22672">
    <literal><![CDATA[
      L(x,y \ ((z \ 1) \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ (z \ u),w) = v5
    ]]></literal>
    <justification jstring="[para(22659(a,1),3518(a,1))].">
      <j1 rule="para" parents="22659 3518"/>
    </justification>
  </clause>

  <clause id="22673">
    <literal><![CDATA[
      L(x,y \ (L(z,u,w) * (w * u)),v5) = L(x,y \ ((z * u) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(21829,a,22652,a),flip(a)].">
      <j1 rule="hyper" parents="21829 22652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22674">
    <literal><![CDATA[
      L(x,(y * z) \ (((1 / y) \ z) * K(y,y \ 1)),u) = L(x,a(1 / y,y,z),u)
    ]]></literal>
    <justification jstring="[para(2228(a,1),22668(a,1,2,2))].">
      <j1 rule="para" parents="2228 22668"/>
    </justification>
  </clause>

  <clause id="22675">
    <literal><![CDATA[
      L(x,(y * z) \ ((y \ 1) \ z),u) = L(x,a(1 / y,y,z),u)
    ]]></literal>
    <justification jstring="[para(2959(a,1),22674(a,1,2,2))].">
      <j1 rule="para" parents="2959 22674"/>
    </justification>
  </clause>

  <clause id="22676">
    <literal><![CDATA[
      L(x,(y * z) \ (y \ z),u) = L(x,a(1 / y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(22672,a,22675,a)].">
      <j1 rule="hyper" parents="22672 22675"/>
    </justification>
  </clause>

  <clause id="22682">
    <literal><![CDATA[
      L(x,((y \ (z \ 1)) * (y * z)) \ 1,u) = L(x,a((z \ 1) / y,y,z),u)
    ]]></literal>
    <justification jstring="[para(13177(a,1),22663(a,1,2))].">
      <j1 rule="para" parents="13177 22663"/>
    </justification>
  </clause>

  <clause id="22683">
    <literal><![CDATA[
      L(x,(y \ (z \ 1)) * (y * z),u) = L(x,a((z \ 1) / y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(3524,a,22682,a)].">
      <j1 rule="hyper" parents="3524 22682"/>
    </justification>
  </clause>

  <clause id="22684">
    <literal><![CDATA[
      L(x,a((y \ 1) / z,z,y),u) = L(x,(z \ y) * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3605,a(flip),b,22683,a),flip(a)].">
      <j1 rule="hyper" parents="63 3605 22683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22685">
    <literal><![CDATA[
      L(x,a((y \ 1) / z,z,y),u) = L(x,a(y,z,z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,21850,a(flip),b,22684,a),flip(a)].">
      <j1 rule="hyper" parents="347 21850 22684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22686">
    <literal><![CDATA[
      L(x,(y * z) \ ((y \ (z \ 1)) \ 1),u) = L(x,a((z \ 1) / y,y,z),u)
    ]]></literal>
    <justification jstring="[para(5251(a,1),22669(a,1,2,2))].">
      <j1 rule="para" parents="5251 22669"/>
    </justification>
  </clause>

  <clause id="22687">
    <literal><![CDATA[
      L(x,(y * z) \ (y \ (z \ 1)),u) = L(x,a((z \ 1) / y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(21771,a,22686,a)].">
      <j1 rule="hyper" parents="21771 22686"/>
    </justification>
  </clause>

  <clause id="22688">
    <literal><![CDATA[
      L(x,a((y \ 1) / z,z,y),u) = L(x,(z * y) \ (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,22658,a(flip),b,22687,a),flip(a)].">
      <j1 rule="hyper" parents="63 22658 22687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22689">
    <literal><![CDATA[
      R(x,T(y / L(z,u,w),v5) * v6,v7) = R(x,(y / L(z \ 1,u,w)) * v6,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,22481,a(flip),b,22435,a)].">
      <j1 rule="hyper" parents="63 22481 22435"/>
    </justification>
  </clause>

  <clause id="22691">
    <literal><![CDATA[
      R(x,(y / L(z \ 1,u,w)) * v5,v6) = R(x,(L(z,u,w) \ y) * v5,v6)
    ]]></literal>
    <justification jstring="[para(113(a,1),22689(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="113 22689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22692">
    <literal><![CDATA[
      R(x,y * (L(z \ 1,u,w) \ v5),v6) = R(x,(L(z,u,w) \ v5) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(22449,a,22691,a)].">
      <j1 rule="hyper" parents="22449 22691"/>
    </justification>
  </clause>

  <clause id="22693">
    <literal><![CDATA[
      (x * (L(x,y,z) \ L(x \ L(x,y,z),x,u))) * (L(x,y,z) \ x) = L(x / L(x,y,z),x,x \ u)
    ]]></literal>
    <justification jstring="[para(10190(a,1),22626(a,1,1,2,2))].">
      <j1 rule="para" parents="10190 22626"/>
    </justification>
  </clause>

  <clause id="22694">
    <literal><![CDATA[
      x * (L(x,y,z) \ (L(x,y,z) * (L(R(x,u,w),y,z) \ v5))) = (v5 / L(R(x,u,w),y,z)) * x
    ]]></literal>
    <justification jstring="[para(29(a,1),22627(a,1,2,2,2,1))].">
      <j1 rule="para" parents="29 22627"/>
    </justification>
  </clause>

  <clause id="22695">
    <literal><![CDATA[
      T(T(L(x,y,z),u),w) / L(T(x,v5),y,z) = (x \ T(T(x,u),w)) * K(v5,x)
    ]]></literal>
    <justification jstring="[para(21445(a,1),22628(a,1,1)),flip(a)].">
      <j1 rule="para" parents="21445 22628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22696">
    <literal><![CDATA[
      T(T(L(x,y,z),u),w) / L(T(x,v5),y,z) = T(T(x,u),w) / T(x,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,6165,a(flip),b,22695,a),flip(a)].">
      <j1 rule="hyper" parents="347 6165 22695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22697">
    <literal><![CDATA[
      (T(T(L(x,y,z),u),w) / L(T(x,v5),y,z)) \ v6 = K(x,v5) * ((x \ T(T(x,u),w)) \ v6)
    ]]></literal>
    <justification jstring="[para(22695(a,2),20166(a,1,1))].">
      <j1 rule="para" parents="22695 20166"/>
    </justification>
  </clause>

  <clause id="22699">
    <literal><![CDATA[
      (T(T(L(x,y,z),u),w) / L(T(x,v5),y,z)) \ v6 = K(x,v5) * (x * (T(T(x,u),w) \ v6))
    ]]></literal>
    <justification jstring="[para(18325(a,1),22697(a,2,2))].">
      <j1 rule="para" parents="18325 22697"/>
    </justification>
  </clause>

  <clause id="22700">
    <literal><![CDATA[
      (T(T(L(x,y,z),u),w) / L(T(x,v5),y,z)) \ v6 = T(x,v5) * (T(T(x,u),w) \ v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,4974,a(flip),b,22699,a),flip(a)].">
      <j1 rule="hyper" parents="347 4974 22699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22701">
    <literal><![CDATA[
      (T(T(x,y),z) / T(x,u)) \ w = T(x,u) * (T(T(x,y),z) \ w)
    ]]></literal>
    <justification jstring="[para(22696(a,1),22700(a,1,1))].">
      <j1 rule="para" parents="22696 22700"/>
    </justification>
  </clause>

  <clause id="22702">
    <literal><![CDATA[
      (T(x,y) \ T(T(x,z),u)) \ w = T(x,y) * (T(T(x,z),u) \ w)
    ]]></literal>
    <justification jstring="[para(10485(a,1),22701(a,1,1))].">
      <j1 rule="para" parents="10485 22701"/>
    </justification>
  </clause>

  <clause id="22703">
    <literal><![CDATA[
      T(T(x,y),z) \ (T(x,u) * w) = T(x,u) * (T(T(x,y),z) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21871,a(flip),b,22702,a)].">
      <j1 rule="hyper" parents="63 21871 22702"/>
    </justification>
  </clause>

  <clause id="22704">
    <literal><![CDATA[
      R(x,y * (T(T(z,u),w) \ (T(z,v5) * (T(T(z,u),w) \ v6))),v7) = R(x,y * L(T(z,v5) * v6,T(T(z,u),w),T(T(z,u),w)),v7)
    ]]></literal>
    <justification jstring="[para(22703(a,1),22484(a,1,2,2,2))].">
      <j1 rule="para" parents="22703 22484"/>
    </justification>
  </clause>

  <clause id="22705">
    <literal><![CDATA[
      K(x,y) * (L(z,u,w) * (z \ (K(y,x) * (w * u)))) != v5
    ]]></literal>
    <literal><![CDATA[
      (w * (u * (K(x,y) * z))) / (K(x,y) * z) = v5
    ]]></literal>
    <justification jstring="[para(22640(a,1),2021(a,1))].">
      <j1 rule="para" parents="22640 2021"/>
    </justification>
  </clause>

  <clause id="22706">
    <literal><![CDATA[
      ((x / y) * K(z,u)) * L(K(u,z) * y,w,v5) = K(u,z) * (L(y,w,v5) * (y \ (K(z,u) * x)))
    ]]></literal>
    <justification jstring="[para(20165(a,1),22640(a,1,1))].">
      <j1 rule="para" parents="20165 22640"/>
    </justification>
  </clause>

  <clause id="22707">
    <literal><![CDATA[
      (x / L(R(y,z,u),w,v5)) * y = y * (L(R(y,z,u),w,v5) \ x)
    ]]></literal>
    <justification jstring="[hyper(620,a,22694,a),flip(a)].">
      <j1 rule="hyper" parents="620 22694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22709">
    <literal><![CDATA[
      K(x,y) * (L(z,u,w) * (z \ (K(y,x) * v5))) = (v5 / z) * (K(y,x) * L(K(x,y) * z,u,w))
    ]]></literal>
    <justification jstring="[hyper(20173,a,22706,a),flip(a)].">
      <j1 rule="hyper" parents="20173 22706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22710">
    <literal><![CDATA[
      K(x,y) * (L(z,u,w) * (z \ (K(y,x) * v5))) = (v5 / z) * L(K(y,x) * (K(x,y) * z),u,w)
    ]]></literal>
    <justification jstring="[para(21250(a,2),22709(a,2,2))].">
      <j1 rule="para" parents="21250 22709"/>
    </justification>
  </clause>

  <clause id="22711">
    <literal><![CDATA[
      K(x,y) * (L(z,u,w) * (z \ (K(y,x) * v5))) = (v5 / z) * L(z,u,w)
    ]]></literal>
    <justification jstring="[para(5261(a,1),22710(a,2,2,1))].">
      <j1 rule="para" parents="5261 22710"/>
    </justification>
  </clause>

  <clause id="22712">
    <literal><![CDATA[
      K(x,y) * (L(z \ u,w,v5) * ((z \ u) \ (K(y,x) * v6))) = (v6 / (u / z)) * L(u / z,w,v5)
    ]]></literal>
    <justification jstring="[para(21339(a,1),22711(a,1,2))].">
      <j1 rule="para" parents="21339 22711"/>
    </justification>
  </clause>

  <clause id="22713">
    <literal><![CDATA[
      (x / (y / z)) * L(y / z,u,w) = (x / (z \ y)) * L(z \ y,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,22711,a(flip),b,22712,a),flip(a)].">
      <j1 rule="hyper" parents="63 22711 22712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22714">
    <literal><![CDATA[
      ((x * ((y / (x \ 1)) \ z)) / (x \ 1)) * L(x \ 1,u,w) = L(1 / x,u,w) * ((y / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21015,a(flip),b,22713,a),flip(a)].">
      <j1 rule="hyper" parents="63 21015 22713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22715">
    <literal><![CDATA[
      L(x,y,z) * (x \ (x * ((u / (x \ 1)) \ w))) = L(1 / x,y,z) * ((u / x) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21012,a(flip),b,22714,a)].">
      <j1 rule="hyper" parents="63 21012 22714"/>
    </justification>
  </clause>

  <clause id="22716">
    <literal><![CDATA[
      L(1 / x,y,z) * ((u / x) \ w) = L(x,y,z) * ((u / (x \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(620,a,22715,a),flip(a)].">
      <j1 rule="hyper" parents="620 22715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22718">
    <literal><![CDATA[
      L(x,x,y) * ((y / (x \ 1)) \ z) = (y \ (x \ y)) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21396,a(flip),b,22716,a),flip(a)].">
      <j1 rule="hyper" parents="63 21396 22716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22719">
    <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(20885,a,20226,a),flip(a)].">
      <j1 rule="hyper" parents="20885 20226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22721">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (L(x,u,w) * v5) = L(x,u,w) * ((x \ L(x,y,z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,20076,a(flip),b,20951,a),flip(a)].">
      <j1 rule="hyper" parents="63 20076 20951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22722">
    <literal><![CDATA[
      L(x,y,z) * ((x \ L(x,y,z)) \ u) = L((x \ 1) \ u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(3525,a,22721,a),flip(a)].">
      <j1 rule="hyper" parents="3525 22721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22724">
    <literal><![CDATA[
      R(R(x,y,(z * y) \ z),y * ((z * y) \ z),y) = y * (y \ ((x * y) * (y \ 1)))
    ]]></literal>
    <justification jstring="[para(6983(a,1),20990(a,2,2))].">
      <j1 rule="para" parents="6983 20990"/>
    </justification>
  </clause>

  <clause id="22725">
    <literal><![CDATA[
      R(R(x,y,(z * y) \ z),y * ((z * y) \ z),y) = y * (y \ R(x,y,y))
    ]]></literal>
    <justification jstring="[para(786(a,1),22724(a,2,2,2))].">
      <j1 rule="para" parents="786 22724"/>
    </justification>
  </clause>

  <clause id="22727">
    <literal><![CDATA[
      R(R(x,y,(z * y) \ z),y * ((z * y) \ z),y) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,10,a(flip),b,22725,a),flip(a)].">
      <j1 rule="hyper" parents="347 10 22725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22729">
    <literal><![CDATA[
      R(R(x,y,z \ (y \ z)),y * ((z * y) \ z),y) = R(x,y,y)
    ]]></literal>
    <justification jstring="[para(22142(a,1),22727(a,1,1))].">
      <j1 rule="para" parents="22142 22727"/>
    </justification>
  </clause>

  <clause id="22730">
    <literal><![CDATA[
      R(R(x,y,z \ (y \ z)),y * (z \ (y \ z)),y) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,22526,a(flip),b,22729,a)].">
      <j1 rule="hyper" parents="63 22526 22729"/>
    </justification>
  </clause>

  <clause id="22731">
    <literal><![CDATA[
      K(x,y) * ((z / T(y,x)) \ R((z / y) * u,z / y,y \ z)) = (u * (z / y)) * (1 / (z / y))
    ]]></literal>
    <justification jstring="[para(20126(a,1),21044(a,1,2,2))].">
      <j1 rule="para" parents="20126 21044"/>
    </justification>
  </clause>

  <clause id="22732">
    <literal><![CDATA[
      (x \ 1) * ((((y * x) * T(x,z)) \ (y * T(x,z))) \ 1) = (L(x \ 1,x,y) \ 1) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(10161(a,1),21588(a,2,1,1))].">
      <j1 rule="para" parents="10161 21588"/>
    </justification>
  </clause>

  <clause id="22733">
    <literal><![CDATA[
      (x \ 1) * ((((y * x) * T(x,z)) \ (y * T(x,z))) \ 1) = x * (1 / L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,21353,a(flip),b,22732,a),flip(a)].">
      <j1 rule="hyper" parents="347 21353 22732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22734">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,x,y * x) \ 1) = x * (1 / L(x,x,y))
    ]]></literal>
    <justification jstring="[para(21504(a,1),22733(a,1,2,1))].">
      <j1 rule="para" parents="21504 22733"/>
    </justification>
  </clause>

  <clause id="22735">
    <literal><![CDATA[
      L(x \ 1,x,y * x) \ (x \ 1) = x * (1 / L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(1422,a,22734,a)].">
      <j1 rule="hyper" parents="1422 22734"/>
    </justification>
  </clause>

  <clause id="22736">
    <literal><![CDATA[
      L(x,x,y * x) \ x = x * (1 / L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(10906,a,22735,a)].">
      <j1 rule="hyper" parents="10906 22735"/>
    </justification>
  </clause>

  <clause id="22737">
    <literal><![CDATA[
      (T(x,x * y) \ 1) * L(T(x,x * y) \ 1,x,y) = T((x \ 1) \ 1,x * y) \ (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(2727(a,2),21765(a,2,1))].">
      <j1 rule="para" parents="2727 21765"/>
    </justification>
  </clause>

  <clause id="22738">
    <literal><![CDATA[
      L(x,(y * ((z * z) \ u)) * R(w * z,u,y),v5) = L(x,((w * (z \ 1)) * u) * y,v5)
    ]]></literal>
    <justification jstring="[para(20643(a,1),21853(a,1,2,2))].">
      <j1 rule="para" parents="20643 21853"/>
    </justification>
  </clause>

  <clause id="22739">
    <literal><![CDATA[
      L(x,((y * (z \ 1)) * u) * w,v5) = L(x,((y * z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22613,a(flip),b,22738,a),flip(a)].">
      <j1 rule="hyper" parents="63 22613 22738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22741">
    <literal><![CDATA[
      L(x,y * ((z * (u \ 1)) * w),v5) = L(x,((z * u) * w) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(21666,a,22739,a)].">
      <j1 rule="hyper" parents="21666 22739"/>
    </justification>
  </clause>

  <clause id="22743">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,x \ L(x,y,z),x) = (L(1 / x,y,z) \ 1) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(21864,a,22670,a),flip(a)].">
      <j1 rule="hyper" parents="21864 22670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22744">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,x,x \ L(x,y,z)) = (L(1 / x,y,z) \ 1) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3652,a(flip),b,22743,a)].">
      <j1 rule="hyper" parents="63 3652 22743"/>
    </justification>
  </clause>

  <clause id="22745">
    <literal><![CDATA[
      L(x,L(((y * (z * z)) \ u) \ w,(y * (z * z)) \ u,y),v5) = L(x,u \ (y * ((z * z) * w)),v5)
    ]]></literal>
    <justification jstring="[para(32(a,1),21978(a,2,2,2))].">
      <j1 rule="para" parents="32 21978"/>
    </justification>
  </clause>

  <clause id="22746">
    <literal><![CDATA[
      R(x,y,z * (L(u,w,v5) * (u \ L(u,w,v5)))) = R(x,y,L(1 / u,L(u,w,v5),u) * z)
    ]]></literal>
    <justification jstring="[para(11041(a,1),22183(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="11041 22183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22747">
    <literal><![CDATA[
      R(x,y,z * (L(u,w,v5) * (u \ L(u,w,v5)))) = R(x,y,L(1 / u,u,L(u,w,v5)) * z)
    ]]></literal>
    <justification jstring="[para(1620(a,1),22746(a,2,3,1))].">
      <j1 rule="para" parents="1620 22746"/>
    </justification>
  </clause>

  <clause id="22749">
    <literal><![CDATA[
      R(x,y,z * (L(u,w,v5) * (u \ L(u,w,v5)))) = R(x,y,L(1 / u,u,u) * z)
    ]]></literal>
    <justification jstring="[para(11041(a,1),22747(a,2,3,1))].">
      <j1 rule="para" parents="11041 22747"/>
    </justification>
  </clause>

  <clause id="22750">
    <literal><![CDATA[
      R(x,y,z * (L(u,w,v5) * (u \ L(u,w,v5)))) = R(x,y,(u \ 1) * z)
    ]]></literal>
    <justification jstring="[para(760(a,1),22749(a,2,3,1))].">
      <j1 rule="para" parents="760 22749"/>
    </justification>
  </clause>

  <clause id="22752">
    <literal><![CDATA[
      R(x,y,z * (L(u,w,v5) * (u \ L(u,w,v5)))) = R(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,21088,a(flip),b,22750,a),flip(a)].">
      <j1 rule="hyper" parents="347 21088 22750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22753">
    <literal><![CDATA[
      K(x,y) * ((z / T(y,x)) \ R((z / y) * u,y \ z,y \ z)) = (u * (z / y)) * (1 / (z / y))
    ]]></literal>
    <justification jstring="[para(20555(a,1),22731(a,1,2,2))].">
      <j1 rule="para" parents="20555 22731"/>
    </justification>
  </clause>

  <clause id="22754">
    <literal><![CDATA[
      (T(x,x * y) \ 1) * L(T(x,x * y) \ 1,x,y) = T(x,x \ y) \ (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(13255(a,1),22737(a,2,1))].">
      <j1 rule="para" parents="13255 22737"/>
    </justification>
  </clause>

  <clause id="22755">
    <literal><![CDATA[
      L(x,L(((y * y) \ (z \ u)) \ w,(z * (y * y)) \ u,z),v5) = L(x,u \ (z * ((y * y) * w)),v5)
    ]]></literal>
    <justification jstring="[para(459(a,1),22745(a,1,2,1,1))].">
      <j1 rule="para" parents="459 22745"/>
    </justification>
  </clause>

  <clause id="22756">
    <literal><![CDATA[
      (x / y) \ R((x / y) * z,y \ x,y \ x) = (z * (x / y)) * (1 / (x / y))
    ]]></literal>
    <justification jstring="[hyper(63,a,20827,a(flip),b,22753,a)].">
      <j1 rule="hyper" parents="63 20827 22753"/>
    </justification>
  </clause>

  <clause id="22757">
    <literal><![CDATA[
      (x / y) \ R(x * K(y,z),y \ x,y \ x) = (T(y,z) * (x / y)) * (1 / (x / y))
    ]]></literal>
    <justification jstring="[para(5925(a,1),22756(a,1,2,1))].">
      <j1 rule="para" parents="5925 22756"/>
    </justification>
  </clause>

  <clause id="22758">
    <literal><![CDATA[
      L(x,L(((y * y) \ (z \ u)) \ w,(y * y) \ (z \ u),z),v5) = L(x,u \ (z * ((y * y) * w)),v5)
    ]]></literal>
    <justification jstring="[para(459(a,1),22755(a,1,2,2))].">
      <j1 rule="para" parents="459 22755"/>
    </justification>
  </clause>

  <clause id="22759">
    <literal><![CDATA[
      L(x,L(((y * y) \ (z \ u)) \ w,z \ u,z),v5) = L(x,u \ (z * ((y * y) * w)),v5)
    ]]></literal>
    <justification jstring="[para(3607(a,1),22758(a,1,2))].">
      <j1 rule="para" parents="3607 22758"/>
    </justification>
  </clause>

  <clause id="22760">
    <literal><![CDATA[
      L(x,L((y \ z) \ u,y \ z,y),w) = L(x,z \ (y * ((v5 * v5) * u)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21984,a(flip),b,22759,a)].">
      <j1 rule="hyper" parents="63 21984 22759"/>
    </justification>
  </clause>

  <clause id="22763">
    <literal><![CDATA[
      L(x,y \ (z * ((u * u) * w)),v5) = L(x,y \ (z * w),v5)
    ]]></literal>
    <justification jstring="[para(561(a,1),22760(a,1,2)),flip(a)].">
      <j1 rule="para" parents="561 22760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22764">
    <literal><![CDATA[
      L(x,y \ ((z * ((u * u) * w)) * v5),v6) = L(x,y \ ((w * z) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,22051,a,b,22763,a)].">
      <j1 rule="hyper" parents="63 22051 22763"/>
    </justification>
  </clause>

  <clause id="22766">
    <literal><![CDATA[
      L(x,(y * ((z * z) * (u * w))) \ ((u * y) * w),v5) = L(x,a(y * (z * z),u,w),v5)
    ]]></literal>
    <justification jstring="[para(1982(a,1),22764(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1982 22764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22767">
    <literal><![CDATA[
      L(x,a(y * (z * z),u,w),v5) = L(x,((u * w) * y) \ ((u * y) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(21891,a,22766,a),flip(a)].">
      <j1 rule="hyper" parents="21891 22766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22768">
    <literal><![CDATA[
      L(x,a(y * (z * z),u,w),v5) = L(x,a(y,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,21857,a(flip),b,22767,a),flip(a)].">
      <j1 rule="hyper" parents="347 21857 22767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22769">
    <literal><![CDATA[
      L(x,a(y \ 1,z,u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(240(a,1),22768(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="240 22768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22770">
    <literal><![CDATA[
      L(x,a(1 / y,z,u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(245(a,1),22768(a,1,2,1))].">
      <j1 rule="para" parents="245 22768"/>
    </justification>
  </clause>

  <clause id="22771">
    <literal><![CDATA[
      L(x,a(L(y,y,z),u,w),v5) = L(x,a((z * y) \ z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(730(a,1),22768(a,1,2,1))].">
      <j1 rule="para" parents="730 22768"/>
    </justification>
  </clause>

  <clause id="22772">
    <literal><![CDATA[
      L(x,(y * z) \ (y \ z),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,22676,a,b,22770,a)].">
      <j1 rule="hyper" parents="63 22676 22770"/>
    </justification>
  </clause>

  <clause id="22773">
    <literal><![CDATA[
      L(x,a((y \ 1) / z,z,y),u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,22688,a,b,22772,a)].">
      <j1 rule="hyper" parents="63 22688 22772"/>
    </justification>
  </clause>

  <clause id="22774">
    <literal><![CDATA[
      L(x,a(y,z,z \ y),u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,22685,a(flip),b,22773,a)].">
      <j1 rule="hyper" parents="63 22685 22773"/>
    </justification>
  </clause>

  <clause id="22775">
    <literal><![CDATA[
      L(x,(y * z) * (z \ y),u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(21769,a,22774,a)].">
      <j1 rule="hyper" parents="21769 22774"/>
    </justification>
  </clause>

  <clause id="22776">
    <literal><![CDATA[
      L(x,(y \ z) * (z * y),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(21748,a,22774,a)].">
      <j1 rule="hyper" parents="21748 22774"/>
    </justification>
  </clause>

  <clause id="22777">
    <literal><![CDATA[
      L(x,a(y \ z,y \ z,z),u) = L(x,a(z,y \ z,y),u)
    ]]></literal>
    <justification jstring="[para(18778(a,1),22774(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18778 22774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22778">
    <literal><![CDATA[
      L(x,(y / z) * (z / y),u) = L(x,a(y,z \ y,z),u)
    ]]></literal>
    <justification jstring="[para(19003(a,1),22777(a,1,2))].">
      <j1 rule="para" parents="19003 22777"/>
    </justification>
  </clause>

  <clause id="22779">
    <literal><![CDATA[
      L(x,(y / z) * (y \ z),u) = L(x,a(y,z \ y,z),u)
    ]]></literal>
    <justification jstring="[hyper(21759,a,22778,a)].">
      <j1 rule="hyper" parents="21759 22778"/>
    </justification>
  </clause>

  <clause id="22780">
    <literal><![CDATA[
      L(x,(y \ z) * (z \ y),u) = L(x,a(z,y \ z,y),u)
    ]]></literal>
    <justification jstring="[hyper(21728,a,22779,a)].">
      <j1 rule="hyper" parents="21728 22779"/>
    </justification>
  </clause>

  <clause id="22781">
    <literal><![CDATA[
      L(K(x,y) * (z / y),u,w) \ (K(x,y) * (z / y)) = L(z / T(y,x),u,w) \ (z / T(y,x))
    ]]></literal>
    <justification jstring="[para(5938(a,1),20913(a,1,2))].">
      <j1 rule="para" parents="5938 20913"/>
    </justification>
  </clause>

  <clause id="22782">
    <literal><![CDATA[
      L(x / y,z,u) \ (K(y,w) * (K(w,y) * (x / y))) = L(x / T(y,w),z,u) \ (x / T(y,w))
    ]]></literal>
    <justification jstring="[hyper(21273,a,22781,a)].">
      <j1 rule="hyper" parents="21273 22781"/>
    </justification>
  </clause>

  <clause id="22783">
    <literal><![CDATA[
      L(x / T(y,z),u,w) \ (x / T(y,z)) = L(x / y,u,w) \ (x / y)
    ]]></literal>
    <justification jstring="[para(5261(a,1),22782(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5261 22782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22784">
    <literal><![CDATA[
      L(x / T(y,z),u,w) \ (x / T(y,z)) = L(y \ x,u,w) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,21331,a(flip),b,22783,a),flip(a)].">
      <j1 rule="hyper" parents="347 21331 22783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22786">
    <literal><![CDATA[
      (x / T(y,z)) \ L(x / T(y,z),u,w) = (L(y \ x,u,w) \ (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[para(22784(a,1),10888(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22784 10888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22787">
    <literal><![CDATA[
      (x / T(y,z)) \ L(x / T(y,z),u,w) = (y \ x) \ L(y \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,10888,a(flip),b,22786,a),flip(a)].">
      <j1 rule="hyper" parents="347 10888 22786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22788">
    <literal><![CDATA[
      (x / T(y,z)) \ L(x / T(y,z),u,w) = y \ (x * L(x \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,3354,a(flip),b,22787,a),flip(a)].">
      <j1 rule="hyper" parents="347 3354 22787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22789">
    <literal><![CDATA[
      T(x,y) \ (z * L(z \ T(x,y),u,w)) = x \ (z * L(z \ x,u,w))
    ]]></literal>
    <justification jstring="[hyper(21225,a,22788,a)].">
      <j1 rule="hyper" parents="21225 22788"/>
    </justification>
  </clause>

  <clause id="22790">
    <literal><![CDATA[
      (x \ (y * (L(y,z,u) \ (L(y,z,u) \ y)))) \ (x \ 1) = ((L(y,z,u) \ y) \ 1) / (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(10928(a,1),20944(a,1,1,2))].">
      <j1 rule="para" parents="10928 20944"/>
    </justification>
  </clause>

  <clause id="22791">
    <literal><![CDATA[
      K(x,y) * ((K(y,x) / z) * (L((1 / z) \ 1,u,w) * v5)) = L(1 / z,u,w) * (z * v5)
    ]]></literal>
    <justification jstring="[para(83(a,1),21024(a,2,2,1))].">
      <j1 rule="para" parents="83 21024"/>
    </justification>
  </clause>

  <clause id="22792">
    <literal><![CDATA[
      K(x,y) * ((K(y,x) / z) * (L(z,u,w) * v5)) = L(1 / z,u,w) * (z * v5)
    ]]></literal>
    <justification jstring="[para(83(a,1),22791(a,1,2,2,1,1))].">
      <j1 rule="para" parents="83 22791"/>
    </justification>
  </clause>

  <clause id="22794">
    <literal><![CDATA[
      L(1 / x,y,z) * (x * u) = (1 / x) * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(21173,a,22792,a),flip(a)].">
      <j1 rule="hyper" parents="21173 22792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22795">
    <literal><![CDATA[
      T(x * x,y) * (y \ L(T(y,x * x),z,u)) = x * (R(x,x,y * L(y,z,u)) * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(3975(a,1),21203(a,2,2,1))].">
      <j1 rule="para" parents="3975 21203"/>
    </justification>
  </clause>

  <clause id="22796">
    <literal><![CDATA[
      L((x * K(y,z)) \ z,u,w) \ ((x * K(y,z)) \ z) = L(T(z,y) / x,u,w) \ (T(z,y) / x)
    ]]></literal>
    <justification jstring="[para(13098(a,1),21334(a,2,2))].">
      <j1 rule="para" parents="13098 21334"/>
    </justification>
  </clause>

  <clause id="22797">
    <literal><![CDATA[
      L((x * K(y,z)) \ z,u,w) \ ((x * K(y,z)) \ z) = L(x \ T(z,y),u,w) \ (x \ T(z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,21331,a(flip),b,22796,a),flip(a)].">
      <j1 rule="hyper" parents="347 21331 22796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22798">
    <literal><![CDATA[
      L(K(x,y) * (z \ x),u,w) \ ((z * K(y,x)) \ x) = L(z \ T(x,y),u,w) \ (z \ T(x,y))
    ]]></literal>
    <justification jstring="[para(13888(a,1),22797(a,1,1,1))].">
      <j1 rule="para" parents="13888 22797"/>
    </justification>
  </clause>

  <clause id="22799">
    <literal><![CDATA[
      L(K(x,y) * (z \ x),u,w) \ (K(x,y) * (z \ x)) = L(z \ T(x,y),u,w) \ (z \ T(x,y))
    ]]></literal>
    <justification jstring="[para(13888(a,1),22798(a,1,2))].">
      <j1 rule="para" parents="13888 22798"/>
    </justification>
  </clause>

  <clause id="22800">
    <literal><![CDATA[
      L(x \ y,z,u) \ (K(w,y) * (K(y,w) * (x \ y))) = L(x \ T(y,w),z,u) \ (x \ T(y,w))
    ]]></literal>
    <justification jstring="[hyper(21273,a,22799,a)].">
      <j1 rule="hyper" parents="21273 22799"/>
    </justification>
  </clause>

  <clause id="22801">
    <literal><![CDATA[
      L(x \ T(y,z),u,w) \ (x \ T(y,z)) = L(x \ y,u,w) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(5261(a,1),22800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5261 22800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22803">
    <literal><![CDATA[
      R(x,y,(((T(z,K(u,w)) * v5) * v6) \ 1) \ (K(w,u) * v7)) = R(x,y,((z * (K(u,w) * v5)) * v6) \ v7)
    ]]></literal>
    <justification jstring="[para(20003(a,1),21349(a,1,3))].">
      <j1 rule="para" parents="20003 21349"/>
    </justification>
  </clause>

  <clause id="22804">
    <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(3343(a,1),21800(a,2,2))].">
      <j1 rule="para" parents="3343 21800"/>
    </justification>
  </clause>

  <clause id="22805">
    <literal><![CDATA[
      K(x * a(y,z,u),x \ (a(y,z,u) \ x)) * (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(21004,a,22804,a)].">
      <j1 rule="hyper" parents="21004 22804"/>
    </justification>
  </clause>

  <clause id="22806">
    <literal><![CDATA[
      ((a(x,y,z) \ u) \ w) / (u \ w) = (u \ w) \ ((a(x,y,z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(19986(a,1),22348(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="19986 22348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22807">
    <literal><![CDATA[
      L(x / L(x,y,z),x,x \ u) = L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,20947,a(flip),b,22693,a),flip(a)].">
      <j1 rule="hyper" parents="63 20947 22693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22808">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,x \ u) = L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[para(3308(a,1),22807(a,1,1))].">
      <j1 rule="para" parents="3308 22807"/>
    </justification>
  </clause>

  <clause id="22809">
    <literal><![CDATA[
      (x \ (y * (L(y,z,u) \ (L(y,z,u) \ y)))) \ (x \ 1) = (y \ L(y,z,u)) / (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(10888(a,1),22790(a,2,1))].">
      <j1 rule="para" parents="10888 22790"/>
    </justification>
  </clause>

  <clause id="22810">
    <literal><![CDATA[
      (x \ (y * (L(y,z,u) \ (L(y,z,u) \ y)))) \ (x \ 1) = (L(y,z,u) \ y) \ (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,20234,a(flip),b,22809,a),flip(a)].">
      <j1 rule="hyper" parents="347 20234 22809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22811">
    <literal><![CDATA[
      (x \ (y * (L(y,z,u) \ (L(y,z,u) \ y)))) \ (x \ 1) = L(y,z,u) * L(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,10934,a(flip),b,22810,a),flip(a)].">
      <j1 rule="hyper" parents="347 10934 22810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22812">
    <literal><![CDATA[
      R(x,y,(((T(z,K(u,w)) * v5) * v6) \ 1) \ v7) = R(x,y,((z * (K(u,w) * v5)) * v6) \ v7)
    ]]></literal>
    <justification jstring="[hyper(22095,a,22803,a)].">
      <j1 rule="hyper" parents="22095 22803"/>
    </justification>
  </clause>

  <clause id="22813">
    <literal><![CDATA[
      R(x,y,((T(z,K(u,w)) * v5) * v6) \ v7) = R(x,y,((z * (K(u,w) * v5)) * v6) \ v7)
    ]]></literal>
    <justification jstring="[hyper(2379,a,22812,a)].">
      <j1 rule="hyper" parents="2379 22812"/>
    </justification>
  </clause>

  <clause id="22815">
    <literal><![CDATA[
      R(x,y,((z * (K(u,w) * v5)) * v6) \ v7) != v8
    ]]></literal>
    <literal><![CDATA[
      R(x,y,(v6 * (z * v5)) \ v7) = v8
    ]]></literal>
    <justification jstring="[para(22813(a,1),22267(a,1))].">
      <j1 rule="para" parents="22813 22267"/>
    </justification>
  </clause>

  <clause id="22816">
    <literal><![CDATA[
      R(x,y,(((T(z,u) * w) / v5) * v6) * K(u,z)) = R(x,y,((z * w) / v5) * v6)
    ]]></literal>
    <justification jstring="[para(20338(a,1),21165(a,1,3,2))].">
      <j1 rule="para" parents="20338 21165"/>
    </justification>
  </clause>

  <clause id="22817">
    <literal><![CDATA[
      R(x,y,((T(z,u) * w) / v5) * v6) = R(x,y,((z * w) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(22057,a,22816,a)].">
      <j1 rule="hyper" parents="22057 22816"/>
    </justification>
  </clause>

  <clause id="22819">
    <literal><![CDATA[
      R(x,y,(z \ (T(u,w) * v5)) * v6) = R(x,y,((u * v5) / z) * v6)
    ]]></literal>
    <justification jstring="[hyper(22093,a,22817,a)].">
      <j1 rule="hyper" parents="22093 22817"/>
    </justification>
  </clause>

  <clause id="22821">
    <literal><![CDATA[
      R(x,y,(z \ (T(u,w) * v5)) * v6) = R(x,y,(z \ (u * v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,22063,a(flip),b,22819,a),flip(a)].">
      <j1 rule="hyper" parents="347 22063 22819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22822">
    <literal><![CDATA[
      R(x,y,(z \ L(u / w,w,w)) * v5) = R(x,y,(z \ (w * u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22594,a,b,22821,a)].">
      <j1 rule="hyper" parents="63 22594 22821"/>
    </justification>
  </clause>

  <clause id="22824">
    <literal><![CDATA[
      R(x,y,(z \ L(((u \ w) / v5) / K(u,u \ w),K(u,u \ w),K(u,u \ w))) * v6) = R(x,y,(z \ ((w / u) / v5)) * v6)
    ]]></literal>
    <justification jstring="[para(13361(a,1),22822(a,2,3,1,2))].">
      <j1 rule="para" parents="13361 22822"/>
    </justification>
  </clause>

  <clause id="22825">
    <literal><![CDATA[
      L(x,y,z) * (K(u,w) * (K(w,u) * (x \ v5))) = (v5 / (x * K(u,w))) * L(x * K(u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(21172,a,21259,a),flip(a)].">
      <j1 rule="hyper" parents="21172 21259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22826">
    <literal><![CDATA[
      (x / (y * K(z,u))) * L(y * K(z,u),w,v5) = L(y,w,v5) * (y \ x)
    ]]></literal>
    <justification jstring="[para(5261(a,1),22825(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5261 22825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22827">
    <literal><![CDATA[
      R(L(x,y,z) \ x,L(x,y,z),x \ u) = u / ((u / (x * K(w,v5))) * L(x * K(w,v5),y,z))
    ]]></literal>
    <justification jstring="[para(22826(a,2),3315(a,2,2))].">
      <j1 rule="para" parents="22826 3315"/>
    </justification>
  </clause>

  <clause id="22829">
    <literal><![CDATA[
      (K(x,y) * ((L(z,u \ (z \ 1),u) * (z \ 1)) \ 1)) * K(y,x) = a(u,u \ (z \ 1),z * K(y,x))
    ]]></literal>
    <justification jstring="[para(13003(a,1),21328(a,1,1,2))].">
      <j1 rule="para" parents="13003 21328"/>
    </justification>
  </clause>

  <clause id="22830">
    <literal><![CDATA[
      (K(x,y) * ((L(z,u \ z,u) * (z \ 1)) \ 1)) * K(y,x) = a(u,u \ (z \ 1),z * K(y,x))
    ]]></literal>
    <justification jstring="[para(3230(a,1),22829(a,1,1,2,1,1))].">
      <j1 rule="para" parents="3230 22829"/>
    </justification>
  </clause>

  <clause id="22831">
    <literal><![CDATA[
      (K(x,y) * ((z \ L(z,u \ z,u)) \ 1)) * K(y,x) = a(u,u \ (z \ 1),z * K(y,x))
    ]]></literal>
    <justification jstring="[para(1295(a,1),22830(a,1,1,2,1))].">
      <j1 rule="para" parents="1295 22830"/>
    </justification>
  </clause>

  <clause id="22832">
    <literal><![CDATA[
      (K(x,y) * (L(z,u \ z,u) \ z)) * K(y,x) = a(u,u \ (z \ 1),z * K(y,x))
    ]]></literal>
    <justification jstring="[para(10882(a,1),22831(a,1,1,2))].">
      <j1 rule="para" parents="10882 22831"/>
    </justification>
  </clause>

  <clause id="22833">
    <literal><![CDATA[
      T(L(x,y \ x,y) \ x,K(z,u)) = a(y,y \ (x \ 1),x * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(6893,a,22832,a)].">
      <j1 rule="hyper" parents="6893 22832"/>
    </justification>
  </clause>

  <clause id="22834">
    <literal><![CDATA[
      a(x,x \ (y \ 1),y * K(z,u)) = L(y,x \ y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(21028,a,22833,a),flip(a)].">
      <j1 rule="hyper" parents="21028 22833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22835">
    <literal><![CDATA[
      a(x,x \ (y \ 1),y) = L(y,x \ y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(19089,a,22834,a)].">
      <j1 rule="hyper" parents="19089 22834"/>
    </justification>
  </clause>

  <clause id="22837">
    <literal><![CDATA[
      L(x,y \ x,y) \ x = a(y,y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,14971,a(flip),b,22835,a),flip(a)].">
      <j1 rule="hyper" parents="63 14971 22835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22838">
    <literal><![CDATA[
      L(x,y \ x,y) \ 1 = x \ a(y,y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,22837,a(flip),b,1409,a),flip(a)].">
      <j1 rule="hyper" parents="128 22837 1409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22839">
    <literal><![CDATA[
      L(x,y,((z * u) \ ((w * u) * T(T(z,v5),u))) * v6) = L(x,y,R(T(w,T(z,v5) * u),u,z) * v6)
    ]]></literal>
    <justification jstring="[para(20040(a,1),21594(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="20040 21594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22840">
    <literal><![CDATA[
      L(x,y,((z * u) \ ((w * u) * T(T(z,v5),u))) * v6) = L(x,y,R(w,u,z) * v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,21473,a(flip),b,22839,a),flip(a)].">
      <j1 rule="hyper" parents="347 21473 22839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22843">
    <literal><![CDATA[
      L(x,y,((z * u) \ ((w * u) * T(z,v5))) * v6) = L(x,y,R(w,u,z) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,21547,a(flip),b,22840,a)].">
      <j1 rule="hyper" parents="63 21547 22840"/>
    </justification>
  </clause>

  <clause id="22845">
    <literal><![CDATA[
      L(x,y,((z * u) \ ((w * u) * z)) * v5) = L(x,y,R(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,21547,a(flip),b,22843,a)].">
      <j1 rule="hyper" parents="63 21547 22843"/>
    </justification>
  </clause>

  <clause id="22846">
    <literal><![CDATA[
      L(x,y,((T(z,u) * u) \ ((w * u) * T(z,u))) * v5) = L(x,y,R(w,u * K(z,u),z) * v5)
    ]]></literal>
    <justification jstring="[para(6497(a,2),22845(a,2,3,1))].">
      <j1 rule="para" parents="6497 22845"/>
    </justification>
  </clause>

  <clause id="22847">
    <literal><![CDATA[
      L(x,y,L(z \ T(u * z,T(w,z)),z,w) * v5) = L(x,y,R(u,z * K(w,z),w) * v5)
    ]]></literal>
    <justification jstring="[para(20529(a,2),22846(a,1,3,1))].">
      <j1 rule="para" parents="20529 22846"/>
    </justification>
  </clause>

  <clause id="22848">
    <literal><![CDATA[
      L(x,y,R(z,u * K(w,u),w) * v5) = L(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(22381,a,22847,a),flip(a)].">
      <j1 rule="hyper" parents="22381 22847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22849">
    <literal><![CDATA[
      L(x,y,R(z,u,w) * v5) = L(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(9595(a,1),22848(a,1,3,1))].">
      <j1 rule="para" parents="9595 22848"/>
    </justification>
  </clause>

  <clause id="22850">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * (u * w)) = L(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[para(107(a,1),22849(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 22849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22851">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * R(1 / v5,v5,v5 \ R(z,u,w))) = L(x,y,v5 \ T(R(z,u,w),v5 \ 1))
    ]]></literal>
    <justification jstring="[para(3838(a,1),22849(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3838 22849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22852">
    <literal><![CDATA[
      L(x,y,T(z * R(u,w,v5),K(R(u,w,v5),v6))) = L(x,y,L(u,w,v5) * T(z,T(R(u,w,v5),v6)))
    ]]></literal>
    <justification jstring="[para(6060(a,2),22849(a,1,3))].">
      <j1 rule="para" parents="6060 22849"/>
    </justification>
  </clause>

  <clause id="22855">
    <literal><![CDATA[
      L(x,y,(z * u) * w) = L(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,21559,a(flip),b,22850,a),flip(a)].">
      <j1 rule="hyper" parents="63 21559 22850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22856">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * R(1 / v5,v5,v5 \ R(z,u,w))) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,v5 \ R(z,u,w)) = v6
    ]]></literal>
    <justification jstring="[para(22851(a,2),21517(a,1))].">
      <j1 rule="para" parents="22851 21517"/>
    </justification>
  </clause>

  <clause id="22857">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * T(v5,T(R(z,u,w),v6))) = L(x,y,v5 * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(20103,a,22852,a),flip(a)].">
      <j1 rule="hyper" parents="20103 22852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22859">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * T(v5,R(T(z,v6),u,w))) = L(x,y,v5 * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(27(a,2),22857(a,1,3,2,2))].">
      <j1 rule="para" parents="27 22857"/>
    </justification>
  </clause>

  <clause id="22860">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * T(v5,T(z,v6))) = L(x,y,v5 * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(19951(a,1),22859(a,1,3,2))].">
      <j1 rule="para" parents="19951 22859"/>
    </justification>
  </clause>

  <clause id="22862">
    <literal><![CDATA[
      L(x,y,T(z * L(u,w,v5),K(u,v6))) = L(x,y,z * R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(21356(a,2),22860(a,1,3))].">
      <j1 rule="para" parents="21356 22860"/>
    </justification>
  </clause>

  <clause id="22863">
    <literal><![CDATA[
      L(x,y,z * R(u,w,v5)) = L(x,y,z * L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(20103,a,22862,a),flip(a)].">
      <j1 rule="hyper" parents="20103 22862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22864">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * L(1 / v5,v5,v5 \ R(z,u,w))) = L(x,y,v5 \ R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(22856,a,22863,a),flip(a)].">
      <j1 rule="hyper" parents="22856 22863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22866">
    <literal><![CDATA[
      L(x,y,z * R(L(u,w,v5),v6,v7)) = L(x,y,z * L(L(u,v6,v7),w,v5))
    ]]></literal>
    <justification jstring="[para(30(a,1),22863(a,2,3,2))].">
      <j1 rule="para" parents="30 22863"/>
    </justification>
  </clause>

  <clause id="22867">
    <literal><![CDATA[
      L(x,y,z * L(K(u,w) / v5,v5,w)) = L(x,y,z * (w / (v5 * T(w,u))))
    ]]></literal>
    <justification jstring="[para(13456(a,1),22863(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="13456 22863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22868">
    <literal><![CDATA[
      L(x,y,z * L(R(u,w,v5),v6,v7)) = L(x,y,z * L(L(u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(29(a,1),22866(a,1,3,2))].">
      <j1 rule="para" parents="29 22866"/>
    </justification>
  </clause>

  <clause id="22869">
    <literal><![CDATA[
      L(x,y,(z * u) * L(R(w,v5,v6),u,z)) = L(x,y,z * (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(97(a,1),22868(a,2,3))].">
      <j1 rule="para" parents="97 22868"/>
    </justification>
  </clause>

  <clause id="22870">
    <literal><![CDATA[
      L(x,y,z * L(K(u,w) / v5,v5,w)) = L(x,y,z * ((v5 * T(w,u)) \ w))
    ]]></literal>
    <justification jstring="[hyper(347,a,21465,a(flip),b,22867,a),flip(a)].">
      <j1 rule="hyper" parents="347 21465 22867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22871">
    <literal><![CDATA[
      L(x,y,z * (u * R(w,v5,v6))) = L(x,y,z * (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(97(a,1),22869(a,1,3))].">
      <j1 rule="para" parents="97 22869"/>
    </justification>
  </clause>

  <clause id="22872">
    <literal><![CDATA[
      L(x,y,z * (u * R(T(w,u),v5,v6))) = L(x,y,z * (L(w,v5,v6) * u))
    ]]></literal>
    <justification jstring="[para(267(a,1),22871(a,2,3,2))].">
      <j1 rule="para" parents="267 22871"/>
    </justification>
  </clause>

  <clause id="22873">
    <literal><![CDATA[
      L(x,y,z * ((u \ a(u,u,R(w,v5,v6))) * L(w,v5,v6))) = L(x,y,z * (u \ R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(18983(a,1),22871(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="18983 22871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22874">
    <literal><![CDATA[
      L(x,y,(z \ a(z,z,u * R(w,v5,v6))) * (u * L(w,v5,v6))) = L(x,y,z \ (u * R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(18983(a,1),22871(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18983 22871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22875">
    <literal><![CDATA[
      L(x,y,z * (R(u,w,v5) * v6)) = L(x,y,z * (L(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(268(a,1),22872(a,1,3,2))].">
      <j1 rule="para" parents="268 22872"/>
    </justification>
  </clause>

  <clause id="22876">
    <literal><![CDATA[
      L(x,y,z * L(K(u,w) / v5,v5,w)) = L(x,y,z * ((w * v5) \ w))
    ]]></literal>
    <justification jstring="[hyper(347,a,21593,a(flip),b,22870,a),flip(a)].">
      <j1 rule="hyper" parents="347 21593 22870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22878">
    <literal><![CDATA[
      L(x,y,z * (T(u,w) \ (u / v5))) = L(x,y,z * ((u * v5) \ u))
    ]]></literal>
    <justification jstring="[para(21274(a,1),22876(a,1,3,2))].">
      <j1 rule="para" parents="21274 22876"/>
    </justification>
  </clause>

  <clause id="22879">
    <literal><![CDATA[
      L(x,y,z * (T(u,w) \ (v5 \ u))) = L(x,y,z * ((u * v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21573,a(flip),b,22878,a)].">
      <j1 rule="hyper" parents="63 21573 22878"/>
    </justification>
  </clause>

  <clause id="22880">
    <literal><![CDATA[
      L(x,y,z * ((u * w) \ u)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * (u \ (w \ u))) = v5
    ]]></literal>
    <justification jstring="[para(22879(a,1),21524(a,1))].">
      <j1 rule="para" parents="22879 21524"/>
    </justification>
  </clause>

  <clause id="22881">
    <literal><![CDATA[
      L(x,y,z * ((u * w) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * (w \ (u \ w))) = v5
    ]]></literal>
    <justification jstring="[para(21540(a,1),22880(a,1))].">
      <j1 rule="para" parents="21540 22880"/>
    </justification>
  </clause>

  <clause id="22882">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * L(v5 \ 1,v5,v5 \ R(z,u,w))) = L(x,y,v5 \ R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,21505,a(flip),b,22864,a)].">
      <j1 rule="hyper" parents="63 21505 22864"/>
    </justification>
  </clause>

  <clause id="22883">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * L(1 / v5,v5,R(z,u,w))) = L(x,y,v5 \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(5506(a,1),22882(a,1,3,2))].">
      <j1 rule="para" parents="5506 22882"/>
    </justification>
  </clause>

  <clause id="22887">
    <literal><![CDATA[
      x / T(x * ((L(y,z,u) * (y \ x)) \ x),T(L(y,z,u) / y,x)) = x \ (L(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[para(20191(a,1),22050(a,1,2))].">
      <j1 rule="para" parents="20191 22050"/>
    </justification>
  </clause>

  <clause id="22888">
    <literal><![CDATA[
      x / T(x * ((L(y,z,u) * (y \ x)) \ x),T(y \ L(y,z,u),x)) = x \ (L(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[para(3161(a,1),22887(a,1,2,2,1))].">
      <j1 rule="para" parents="3161 22887"/>
    </justification>
  </clause>

  <clause id="22889">
    <literal><![CDATA[
      x / T(x * ((L(y,z,u) * (y \ x)) \ x),y \ L(y,z,u)) = x \ (L(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[para(20259(a,1),22888(a,1,2,2))].">
      <j1 rule="para" parents="20259 22888"/>
    </justification>
  </clause>

  <clause id="22890">
    <literal><![CDATA[
      x / (x * ((L(y,z,u) * (y \ x)) \ x)) = x \ (L(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[para(20076(a,1),22889(a,1,2))].">
      <j1 rule="para" parents="20076 22889"/>
    </justification>
  </clause>

  <clause id="22893">
    <literal><![CDATA[
      R(x,y,z \ (((u * u) * w) * (v5 * ((u * u) \ v6)))) = R(x,y,z \ ((v5 * v6) * w))
    ]]></literal>
    <justification jstring="[hyper(22159,a,22173,a)].">
      <j1 rule="hyper" parents="22159 22173"/>
    </justification>
  </clause>

  <clause id="22894">
    <literal><![CDATA[
      R(x,y,z \ (u * (w * ((v5 * v5) \ v6)))) = R(x,y,z \ ((w * v6) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,22215,a(flip),b,22893,a)].">
      <j1 rule="hyper" parents="63 22215 22893"/>
    </justification>
  </clause>

  <clause id="22896">
    <literal><![CDATA[
      R(x,y,z \ (((u * u) * w) * (v5 * ((v6 * v6) \ v7)))) != v8
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ ((v5 * v7) * w)) = v8
    ]]></literal>
    <justification jstring="[para(22894(a,2),22214(a,1))].">
      <j1 rule="para" parents="22894 22214"/>
    </justification>
  </clause>

  <clause id="22897">
    <literal><![CDATA[
      R(x,y,z \ (u * (w * ((v5 * v5) \ v6)))) != v7
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ ((w * v6) * u)) = v7
    ]]></literal>
    <justification jstring="[para(22215(a,1),22896(a,1))].">
      <j1 rule="para" parents="22215 22896"/>
    </justification>
  </clause>

  <clause id="22898">
    <literal><![CDATA[
      R(x,(y * (((z * z) \ u) * T(w,z * z))) * v5,v6) = R(x,(y * (w * u)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(22522,a,22605,a)].">
      <j1 rule="hyper" parents="22522 22605"/>
    </justification>
  </clause>

  <clause id="22899">
    <literal><![CDATA[
      R(x,y * (z * (((u * u) \ w) * v5)),v6) = R(x,(z * (v5 * w)) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,22531,a(flip),b,22898,a)].">
      <j1 rule="hyper" parents="63 22531 22898"/>
    </justification>
  </clause>

  <clause id="22901">
    <literal><![CDATA[
      (x * (K(y,z) * (u * w))) \ ((x * (T(u,K(z,y)) * K(y,z))) * w) = a(x * K(y,z),L(u,K(y,z),x),w)
    ]]></literal>
    <justification jstring="[para(20151(a,1),20177(a,1,1))].">
      <j1 rule="para" parents="20151 20177"/>
    </justification>
  </clause>

  <clause id="22902">
    <literal><![CDATA[
      (R(x,y,z) * ((x * x) \ (x * (R(x,y,z) \ x)))) * ((x \ (x \ R(x,y,z))) \ 1) = (x \ R(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[para(1778(a,1),21062(a,1,1))].">
      <j1 rule="para" parents="1778 21062"/>
    </justification>
  </clause>

  <clause id="22903">
    <literal><![CDATA[
      (x * (a(y,z,u) * x)) / ((a(y,z,u) * x) * (a(y,z,u) * x)) = L(a(y,z,u),x,a(y,z,u) * x) \ 1
    ]]></literal>
    <justification jstring="[para(20609(a,1),21179(a,1,1))].">
      <j1 rule="para" parents="20609 21179"/>
    </justification>
  </clause>

  <clause id="22904">
    <literal><![CDATA[
      (x * ((y * y) \ (a(z,u,w) * v5))) \ (((a(z,u,w) * x) / (y * y)) * v5) = a(x / (y * y),a(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(803(a,1),21382(a,1,1))].">
      <j1 rule="para" parents="803 21382"/>
    </justification>
  </clause>

  <clause id="22905">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * w != x * (v5 * L(v5 \ (x \ (v5 * y)),z,u))
    ]]></literal>
    <literal><![CDATA[
      T(v5,x * L(x \ y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(1182(a,1),21404(a,2))].">
      <j1 rule="para" parents="1182 21404"/>
    </justification>
  </clause>

  <clause id="22906">
    <literal><![CDATA[
      (x * y) / ((L(x,z,u) * (y * (w * w))) / (w * w)) = ((L(x,z,u) * (y * (w * w))) \ (x * y)) * (w * w)
    ]]></literal>
    <justification jstring="[hyper(347,a,728,a(flip),b,21937,a),flip(a)].">
      <j1 rule="hyper" parents="347 728 21937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22907">
    <literal><![CDATA[
      R(x,(((y * T(z,u)) \ (y * w)) \ 1) \ (z \ w),v5) = R(x,(T(z,u) \ w) * ((y * z) \ (y * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,22455,a(flip),b,22472,a),flip(a)].">
      <j1 rule="hyper" parents="347 22455 22472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22909">
    <literal><![CDATA[
      R(x,(((y * T(z,u)) \ (y * w)) \ 1) \ (z \ w),v5) = R(x,((y * z) \ (y * w)) * (z \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,22468,a(flip),b,22907,a),flip(a)].">
      <j1 rule="hyper" parents="347 22468 22907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22911">
    <literal><![CDATA[
      R(x,(((y * T(z,u)) \ (y * w)) \ 1) \ (z \ w),v5) = R(x,(z \ w) * ((y * z) \ (y * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,20553,a,b,22909,a),flip(a)].">
      <j1 rule="hyper" parents="347 20553 22909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22912">
    <literal><![CDATA[
      R(x,(y * ((z * T(u,T(w,z))) \ T(u,T(w,v5)))) * v6,v7) = R(x,(y * (u / (z * T(u,K(v5,w))))) * v6,v7)
    ]]></literal>
    <justification jstring="[para(12788(a,1),22508(a,2,2,1,2))].">
      <j1 rule="para" parents="12788 22508"/>
    </justification>
  </clause>

  <clause id="22913">
    <literal><![CDATA[
      (x * (y * (K(z,u) * w))) / (K(z,u) * w) = ((x * y) / w) * L(w,y,x)
    ]]></literal>
    <justification jstring="[hyper(22705,a,22711,a)].">
      <j1 rule="hyper" parents="22705 22711"/>
    </justification>
  </clause>

  <clause id="22914">
    <literal><![CDATA[
      (x * (y * (K(z,u) * w))) / (K(z,u) * w) = (x * (y * w)) / w
    ]]></literal>
    <justification jstring="[hyper(347,a,2012,a(flip),b,22913,a),flip(a)].">
      <j1 rule="hyper" parents="347 2012 22913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22915">
    <literal><![CDATA[
      ((x * (y * z)) / z) / K(u,w) = (x * (y * (K(w,u) * z))) / z
    ]]></literal>
    <justification jstring="[hyper(131,a,22914,a(flip),b,20165,a(flip))].">
      <j1 rule="hyper" parents="131 22914 20165"/>
    </justification>
  </clause>

  <clause id="22916">
    <literal><![CDATA[
      (x * (y * (K(z,u) * w))) / w = ((x * (y * w)) / w) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(6140,a,22915,a),flip(a)].">
      <j1 rule="hyper" parents="6140 22915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22917">
    <literal><![CDATA[
      (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x * K(y,z),L(u,K(y,z),x),w)
    ]]></literal>
    <justification jstring="[para(6885(a,1),22901(a,1,2,1,2))].">
      <j1 rule="para" parents="6885 22901"/>
    </justification>
  </clause>

  <clause id="22918">
    <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(20075(a,1),22917(a,2,2))].">
      <j1 rule="para" parents="20075 22917"/>
    </justification>
  </clause>

  <clause id="22919">
    <literal><![CDATA[
      a(T(x,K(y,z)) * K(z,y),L(u,K(z,y),T(x,K(y,z))),w) = (K(z,y) * (x * (u * w))) \ ((T(x,K(y,z)) * (K(z,y) * u)) * w)
    ]]></literal>
    <justification jstring="[para(21322(a,1),22917(a,1,1)),flip(a)].">
      <j1 rule="para" parents="21322 22917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22920">
    <literal><![CDATA[
      a(x * K(y,z),u,w) = a(x,K(y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(20715,a,22918,a),flip(a)].">
      <j1 rule="hyper" parents="20715 22918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22922">
    <literal><![CDATA[
      (R(x,y,z) * L(x \ (R(x,y,z) \ x),x,x)) * ((x \ (x \ R(x,y,z))) \ 1) = (x \ R(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[para(99(a,2),22902(a,1,1,2))].">
      <j1 rule="para" parents="99 22902"/>
    </justification>
  </clause>

  <clause id="22923">
    <literal><![CDATA[
      (R(x,y,z) * L(R(x,y,z) \ 1,x,x)) * ((x \ (x \ R(x,y,z))) \ 1) = (x \ R(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[para(1758(a,1),22922(a,1,1,2,1))].">
      <j1 rule="para" parents="1758 22922"/>
    </justification>
  </clause>

  <clause id="22924">
    <literal><![CDATA[
      (R(x,y,z) \ L(R(x,y,z),x,x)) * ((x \ (x \ R(x,y,z))) \ 1) = (x \ R(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[para(3343(a,1),22923(a,1,1))].">
      <j1 rule="para" parents="3343 22923"/>
    </justification>
  </clause>

  <clause id="22925">
    <literal><![CDATA[
      L(a(x,y,z),u,a(x,y,z) * u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      u * ((a(x,y,z) * u) \ 1) = w
    ]]></literal>
    <justification jstring="[para(22903(a,1),802(a,1))].">
      <j1 rule="para" parents="22903 802"/>
    </justification>
  </clause>

  <clause id="22926">
    <literal><![CDATA[
      T(x,y * L(y \ z,u,w)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(22905,a,21287,a)].">
      <j1 rule="hyper" parents="22905 21287"/>
    </justification>
  </clause>

  <clause id="22927">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * T(w,y) = w * (x * L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,22926,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 22926 22"/>
    </justification>
  </clause>

  <clause id="22928">
    <literal><![CDATA[
      T(x,y * L(z,u,w)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),22926(a,1,2,2,1))].">
      <j1 rule="para" parents="9 22926"/>
    </justification>
  </clause>

  <clause id="22930">
    <literal><![CDATA[
      T(x,L(y,z,u) * w) = T(x,y * w)
    ]]></literal>
    <justification jstring="[para(737(a,1),22926(a,1,2))].">
      <j1 rule="para" parents="737 22926"/>
    </justification>
  </clause>

  <clause id="22932">
    <literal><![CDATA[
      T(x,y \ L(z,u,w)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3341(a,1),22926(a,1,2))].">
      <j1 rule="para" parents="3341 22926"/>
    </justification>
  </clause>

  <clause id="22936">
    <literal><![CDATA[
      T(x,(y * z) * u) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(97(a,1),22928(a,1,2)),flip(a)].">
      <j1 rule="para" parents="97 22928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22937">
    <literal><![CDATA[
      T(x,y * ((z * u) \ w)) = T(x,y * (u \ (z \ w)))
    ]]></literal>
    <justification jstring="[para(329(a,1),22928(a,1,2,2))].">
      <j1 rule="para" parents="329 22928"/>
    </justification>
  </clause>

  <clause id="22938">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ 1)) * ((L(y,z,u) * L(y \ 1,z,u)) \ w) = ((L(y,z,u) * L(y \ 1,z,u)) \ x) * w
    ]]></literal>
    <justification jstring="[para(22928(a,1),12463(a,1,1))].">
      <j1 rule="para" parents="22928 12463"/>
    </justification>
  </clause>

  <clause id="22939">
    <literal><![CDATA[
      L(T(x,T(y,(z / x) * x)),u,w) * (x \ z) = ((z / x) * L(x,u,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(22928(a,1),21314(a,1,1,1,2))].">
      <j1 rule="para" parents="22928 21314"/>
    </justification>
  </clause>

  <clause id="22943">
    <literal><![CDATA[
      T(x,y / (z \ (u \ w))) = T(x,y * ((w \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,21437,a(flip),b,22930,a)].">
      <j1 rule="hyper" parents="63 21437 22930"/>
    </justification>
  </clause>

  <clause id="22944">
    <literal><![CDATA[
      T(x,y \ (L(z,u,w) * v5)) = T(x,T(z,y) * (y \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,21306,a(flip),b,22930,a)].">
      <j1 rule="hyper" parents="63 21306 22930"/>
    </justification>
  </clause>

  <clause id="22945">
    <literal><![CDATA[
      (L(x,y,z) * u) * T(w,x * u) = w * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(134,a,22930,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 22930 22"/>
    </justification>
  </clause>

  <clause id="22946">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ w)) = T(x,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),22930(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 22930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22947">
    <literal><![CDATA[
      T(x,((y * z) \ u) * w) = T(x,(z \ (y \ u)) * w)
    ]]></literal>
    <justification jstring="[para(329(a,1),22930(a,1,2,1))].">
      <j1 rule="para" parents="329 22930"/>
    </justification>
  </clause>

  <clause id="22948">
    <literal><![CDATA[
      T(x,((y \ z) \ u) * w) = T(x,(z \ (y * u)) * w)
    ]]></literal>
    <justification jstring="[para(561(a,1),22930(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="561 22930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22950">
    <literal><![CDATA[
      T(x,x \ y) = (x \ L(y,z,u)) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(440,a,22932,a),flip(a)].">
      <j1 rule="hyper" parents="440 22932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22952">
    <literal><![CDATA[
      T(x,T(y / z,y)) = T(x,z \ L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,7064,a,b,22932,a)].">
      <j1 rule="hyper" parents="347 7064 22932"/>
    </justification>
  </clause>

  <clause id="22953">
    <literal><![CDATA[
      T(x,y \ L(R(y,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,19975,a(flip),b,22932,a),flip(a)].">
      <j1 rule="hyper" parents="347 19975 22932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22956">
    <literal><![CDATA[
      T(x,y \ L(R(y,z,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      x = v6
    ]]></literal>
    <justification jstring="[para(22932(a,2),20206(a,1))].">
      <j1 rule="para" parents="22932 20206"/>
    </justification>
  </clause>

  <clause id="22957">
    <literal><![CDATA[
      T(x \ y,z \ L(R(z,u,w),v5,v6)) != v7 \ y
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(22953(a,2),48(a,1))].">
      <j1 rule="para" parents="22953 48"/>
    </justification>
  </clause>

  <clause id="22958">
    <literal><![CDATA[
      T(x,L(y,z,u) \ w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,18957,a(flip),b,22946,a)].">
      <j1 rule="hyper" parents="63 18957 22946"/>
    </justification>
  </clause>

  <clause id="22960">
    <literal><![CDATA[
      T(x,y \ (T(z,y) \ u)) = T(x,z \ (L(y,w,v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(19972,a,22958,a),flip(a)].">
      <j1 rule="hyper" parents="19972 22958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22964">
    <literal><![CDATA[
      T(x,(((y * z) * u) \ ((y * (z * u)) * w)) \ v5) = T(x,(a(y,z,u) \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(837(a,1),22958(a,1,2,1))].">
      <j1 rule="para" parents="837 22958"/>
    </justification>
  </clause>

  <clause id="22969">
    <literal><![CDATA[
      T(x,y \ L(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = v5
    ]]></literal>
    <justification jstring="[para(22952(a,1),7081(a,1))].">
      <j1 rule="para" parents="22952 7081"/>
    </justification>
  </clause>

  <clause id="22970">
    <literal><![CDATA[
      ((x / y) \ L(x,z,u)) \ L(x,z,u) = y \ x
    ]]></literal>
    <justification jstring="[hyper(661,a,22950,a),flip(a)].">
      <j1 rule="hyper" parents="661 22950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22971">
    <literal><![CDATA[
      (x \ L(y,z,u)) \ L(y,z,u) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(440,a,22950,a),flip(a)].">
      <j1 rule="hyper" parents="440 22950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22972">
    <literal><![CDATA[
      L(x,y,z) / (u \ x) != w
    ]]></literal>
    <literal><![CDATA[
      (x / u) \ L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(22970(a,1),317(a,1,2)),flip(b)].">
      <j1 rule="para" parents="22970 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22973">
    <literal><![CDATA[
      ((L(x,y,z) / u) \ x) \ x = u \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(395,a,22971,a),flip(a)].">
      <j1 rule="hyper" parents="395 22971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22975">
    <literal><![CDATA[
      T(x,(y * z) * (z \ ((u * y) \ w))) = T(x,R(u,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,20879,a(flip),b,22937,a),flip(a)].">
      <j1 rule="hyper" parents="63 20879 22937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22976">
    <literal><![CDATA[
      T(x,y * (L(z \ (z \ u),w,v5) \ (z \ v6))) = T(x,y * ((z \ L(u,w,v5)) \ v6))
    ]]></literal>
    <justification jstring="[para(3341(a,1),22937(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3341 22937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22977">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ w)) = T(x,y * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(19030,a,22943,a)].">
      <j1 rule="hyper" parents="19030 22943"/>
    </justification>
  </clause>

  <clause id="22979">
    <literal><![CDATA[
      T(x,(y \ (z * u)) * w) = T(x,(y \ z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,20872,a(flip),b,22948,a),flip(a)].">
      <j1 rule="hyper" parents="63 20872 22948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22981">
    <literal><![CDATA[
      T(x,y \ (L(z,u,w) * v5)) = T(x,(y \ z) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,21057,a(flip),b,22944,a),flip(a)].">
      <j1 rule="hyper" parents="347 21057 22944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22982">
    <literal><![CDATA[
      T(x,y \ (((z * u) \ z) * w)) = T(x,(y \ (u \ 1)) * w)
    ]]></literal>
    <justification jstring="[para(244(a,1),22981(a,1,2,2,1))].">
      <j1 rule="para" parents="244 22981"/>
    </justification>
  </clause>

  <clause id="22983">
    <literal><![CDATA[
      T(x,y \ (L(z,u,w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (z \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(22960(a,1),19443(a,1))].">
      <j1 rule="para" parents="22960 19443"/>
    </justification>
  </clause>

  <clause id="22984">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ x,z,u) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(22972,a,3379,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="22972 3379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22985">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (y / x) \ L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(3379(a,2),22972(a,1))].">
      <j1 rule="para" parents="3379 22972"/>
    </justification>
  </clause>

  <clause id="22986">
    <literal><![CDATA[
      ((L(x,y,z) * u) * w) / T(x * u,w) = (w * (L(x,y,z) * u)) / (x * u)
    ]]></literal>
    <justification jstring="[para(22945(a,1),6181(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22945 6181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22987">
    <literal><![CDATA[
      T(x,y \ (((z * u) \ z) * w)) = T(x,y \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(347,a,20873,a(flip),b,22982,a),flip(a)].">
      <j1 rule="hyper" parents="347 20873 22982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22988">
    <literal><![CDATA[
      T(x,(y \ ((z * u) \ z)) * w) = T(x,y \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,20671,a(flip),b,22987,a)].">
      <j1 rule="hyper" parents="63 20671 22987"/>
    </justification>
  </clause>

  <clause id="22990">
    <literal><![CDATA[
      T(x,y \ (((y \ z) / y) \ u)) = T(x,(L(z,w,v5) \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(22983,a,22006,a)].">
      <j1 rule="hyper" parents="22983 22006"/>
    </justification>
  </clause>

  <clause id="22991">
    <literal><![CDATA[
      T(x,(L(y,z,u) / w) \ v5) = T(x,w \ (((y / w) / w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(22983,a,21385,a),flip(a)].">
      <j1 rule="hyper" parents="22983 21385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22992">
    <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(63,a,4095,a,b,22984,a)].">
      <j1 rule="hyper" parents="63 4095 22984"/>
    </justification>
  </clause>

  <clause id="22993">
    <literal><![CDATA[
      T(x,y * (z * (z \ ((u * y) \ w)))) = T(x,R(u,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,22936,a(flip),b,22975,a)].">
      <j1 rule="hyper" parents="63 22936 22975"/>
    </justification>
  </clause>

  <clause id="22994">
    <literal><![CDATA[
      T(x,(L(y,z,u) \ w) * v5) = T(x,(w \ y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,20877,a(flip),b,22990,a),flip(a)].">
      <j1 rule="hyper" parents="63 20877 22990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22996">
    <literal><![CDATA[
      T(x,(L(y,z,u) \ w) * v5) = T(x,(y \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,19338,a(flip),b,22994,a),flip(a)].">
      <j1 rule="hyper" parents="347 19338 22994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22997">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * T(w,(x \ x) * u) = w * (((x \ L(x,y,z)) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(22996(a,1),19344(a,1,2))].">
      <j1 rule="para" parents="22996 19344"/>
    </justification>
  </clause>

  <clause id="22998">
    <literal><![CDATA[
      T(x,(L(y,z,u) / w) \ v5) = T(x,(y / w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,20877,a(flip),b,22991,a),flip(a)].">
      <j1 rule="hyper" parents="347 20877 22991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23000">
    <literal><![CDATA[
      T(x,(L(y,z,u) / w) \ v5) = T(x,w * (y \ v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,20878,a(flip),b,22998,a),flip(a)].">
      <j1 rule="hyper" parents="347 20878 22998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23001">
    <literal><![CDATA[
      T(x,y * (L(z,u,w) \ v5)) = T(x,y * (z \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,20878,a(flip),b,23000,a)].">
      <j1 rule="hyper" parents="63 20878 23000"/>
    </justification>
  </clause>

  <clause id="23002">
    <literal><![CDATA[
      T(x,R(y,z,u) \ w) = T(x,z * ((y * z) \ w))
    ]]></literal>
    <justification jstring="[para(10(a,1),22993(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 22993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23003">
    <literal><![CDATA[
      T(x,R(y,z,u) \ w) = T(x,z * (z \ (y \ w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,22937,a(flip),b,23002,a),flip(a)].">
      <j1 rule="hyper" parents="347 22937 23002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23004">
    <literal><![CDATA[
      T(x,R(y,z,u) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,6623,a(flip),b,23002,a),flip(a)].">
      <j1 rule="hyper" parents="347 6623 23002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23006">
    <literal><![CDATA[
      x / (R(y,z,u) \ y) = (R(y,z,u) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(7761,a,23004,a),flip(a)].">
      <j1 rule="hyper" parents="7761 23004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23013">
    <literal><![CDATA[
      T(x,R(y,z,u) \ w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[para(10(a,1),23003(a,2,2))].">
      <j1 rule="para" parents="10 23003"/>
    </justification>
  </clause>

  <clause id="23014">
    <literal><![CDATA[
      T(x,(y * (z \ u)) * (u \ w)) = T(x,(z / y) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,20880,a(flip),b,23013,a)].">
      <j1 rule="hyper" parents="63 20880 23013"/>
    </justification>
  </clause>

  <clause id="23019">
    <literal><![CDATA[
      T(x,(y * (z \ u)) * (u \ w)) = T(x,y * (z \ w))
    ]]></literal>
    <justification jstring="[hyper(347,a,20878,a(flip),b,23014,a),flip(a)].">
      <j1 rule="hyper" parents="347 20878 23014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23020">
    <literal><![CDATA[
      T(x,y * ((z \ u) * (u \ w))) = T(x,y * (z \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,22936,a(flip),b,23019,a)].">
      <j1 rule="hyper" parents="63 22936 23019"/>
    </justification>
  </clause>

  <clause id="23022">
    <literal><![CDATA[
      (T(x,y) * (z * L(z \ y,u,w))) \ (x * (z * L(z \ y,u,w))) = K(z * L(z \ y,u,w),T(x,y))
    ]]></literal>
    <justification jstring="[hyper(128,a,22927,a(flip),b,91,a)].">
      <j1 rule="hyper" parents="128 22927 91"/>
    </justification>
  </clause>

  <clause id="23023">
    <literal><![CDATA[
      (x * (y * L(y \ z,u,w))) \ (T(x,z) * (y * L(y \ z,u,w))) = K(T(x,z),y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(22927(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="22927 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23024">
    <literal><![CDATA[
      (x * (y * L(y \ 1,z,u))) * T(w,x) = w * ((x * y) * L((x * y) \ x,z,u))
    ]]></literal>
    <justification jstring="[para(1015(a,1),22927(a,1,1))].">
      <j1 rule="para" parents="1015 22927"/>
    </justification>
  </clause>

  <clause id="23025">
    <literal><![CDATA[
      L(x * (y \ x),z,u) * (((x \ y) \ 1) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      (y / x) \ L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(4085(a,2),22985(a,1))].">
      <j1 rule="para" parents="4085 22985"/>
    </justification>
  </clause>

  <clause id="23026">
    <literal><![CDATA[
      T(x * x,y) * (y \ L(T(y,x * x),z,u)) = x * ((y / x) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(22992(a,1),22795(a,2,2))].">
      <j1 rule="para" parents="22992 22795"/>
    </justification>
  </clause>

  <clause id="23027">
    <literal><![CDATA[
      (x * x) * (y \ L(y,z,u)) = x * ((y / x) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,20980,a(flip),b,23026,a)].">
      <j1 rule="hyper" parents="63 20980 23026"/>
    </justification>
  </clause>

  <clause id="23028">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) \ (x \ (x * ((y / x) \ L(y,z,u)))) = a(x,x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(23027(a,1),14699(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="23027 14699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23029">
    <literal><![CDATA[
      (x * ((y / x) \ L(y,z,u))) / w = (y \ L(y,z,u)) / (w / (x * x))
    ]]></literal>
    <justification jstring="[para(23027(a,1),20957(a,1,1))].">
      <j1 rule="para" parents="23027 20957"/>
    </justification>
  </clause>

  <clause id="23030">
    <literal><![CDATA[
      ((x / y) \ L(x,z,u)) * K(y,(x / y) \ L(x,z,u)) = (x \ L(x,z,u)) / (y / (y * y))
    ]]></literal>
    <justification jstring="[hyper(5080,a,23029,a)].">
      <j1 rule="hyper" parents="5080 23029"/>
    </justification>
  </clause>

  <clause id="23031">
    <literal><![CDATA[
      T(x,(((y * (z * u)) * w) \ ((y * z) * u)) * v5) = T(x,(a(y,z,u) \ w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,19338,a(flip),b,22964,a)].">
      <j1 rule="hyper" parents="63 19338 22964"/>
    </justification>
  </clause>

  <clause id="23032">
    <literal><![CDATA[
      T(x,(((y * (z * u)) * w) \ (y * z)) * (u * v5)) = T(x,(a(y,z,u) \ w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22979,a(flip),b,23031,a)].">
      <j1 rule="hyper" parents="63 22979 23031"/>
    </justification>
  </clause>

  <clause id="23033">
    <literal><![CDATA[
      T(x,(((y * (z * u)) * w) \ y) * (z * (u * v5))) = T(x,(a(y,z,u) \ w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22979,a(flip),b,23032,a)].">
      <j1 rule="hyper" parents="63 22979 23032"/>
    </justification>
  </clause>

  <clause id="23034">
    <literal><![CDATA[
      T(x,(y \ ((z * (u * w)) \ z)) * (u * (w * v5))) = T(x,(a(z,u,w) \ y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22947,a(flip),b,23033,a)].">
      <j1 rule="hyper" parents="63 22947 23033"/>
    </justification>
  </clause>

  <clause id="23035">
    <literal><![CDATA[
      T(x,(a(y,z,u) \ w) \ v5) = T(x,w \ ((z * u) \ (z * (u * v5))))
    ]]></literal>
    <justification jstring="[hyper(63,a,22988,a(flip),b,23034,a),flip(a)].">
      <j1 rule="hyper" parents="63 22988 23034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23037">
    <literal><![CDATA[
      T(x,(a(y,z,u) \ w) \ v5) = T(x,w \ L(v5,u,z))
    ]]></literal>
    <justification jstring="[para(18(a,2),23035(a,2,2,2))].">
      <j1 rule="para" parents="18 23035"/>
    </justification>
  </clause>

  <clause id="23038">
    <literal><![CDATA[
      T(x,(a(y,z,u) \ w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,w \ v5) = v6
    ]]></literal>
    <justification jstring="[para(23037(a,2),22969(a,1))].">
      <j1 rule="para" parents="23037 22969"/>
    </justification>
  </clause>

  <clause id="23041">
    <literal><![CDATA[
      T(x,y \ a(z,u,w)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(23038,a,6258,a),flip(a)].">
      <j1 rule="hyper" parents="23038 6258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23042">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,w,v5) \ y) = z
    ]]></literal>
    <justification jstring="[para(190(a,1),23038(a,1,2))].">
      <j1 rule="para" parents="190 23038"/>
    </justification>
  </clause>

  <clause id="23043">
    <literal><![CDATA[
      a(x,y,z) / T(u,u \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      u \ a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(23041(a,1),345(a,1,2))].">
      <j1 rule="para" parents="23041 345"/>
    </justification>
  </clause>

  <clause id="23045">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(23042,a,xx)].">
      <j1 rule="hyper" parents="23042"/>
    </justification>
  </clause>

  <clause id="23047">
    <literal><![CDATA[
      T(x,y * a(z,u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(17067,a,23045,a)].">
      <j1 rule="hyper" parents="17067 23045"/>
    </justification>
  </clause>

  <clause id="23048">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(17066,a,23045,a)].">
      <j1 rule="hyper" parents="17066 23045"/>
    </justification>
  </clause>

  <clause id="23050">
    <literal><![CDATA[
      (a(x,y,z) \ u) * T(w,u) = w * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(134,a,23045,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 23045 22"/>
    </justification>
  </clause>

  <clause id="23051">
    <literal><![CDATA[
      (a(x,y,z) \ u) * T(w,u) != v5
    ]]></literal>
    <literal><![CDATA[
      w * (a(x,y,z) \ u) = v5
    ]]></literal>
    <justification jstring="[para(23045(a,1),315(a,1,2))].">
      <j1 rule="para" parents="23045 315"/>
    </justification>
  </clause>

  <clause id="23052">
    <literal><![CDATA[
      (x * y) / T(a(z,u,w) * x,y) = (a(z,u,w) * x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(23045(a,1),13941(a,1,2))].">
      <j1 rule="para" parents="23045 13941"/>
    </justification>
  </clause>

  <clause id="23054">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) = T(x,w * a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(347,a,23045,a,b,23047,a)].">
      <j1 rule="hyper" parents="347 23045 23047"/>
    </justification>
  </clause>

  <clause id="23057">
    <literal><![CDATA[
      T(x,a(y,z,u) * a(w,v5,v6)) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,19939,a(flip),b,23047,a),flip(a)].">
      <j1 rule="hyper" parents="347 19939 23047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23061">
    <literal><![CDATA[
      (x * a(y,z,u)) * T(w,x) = w * (x * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,23047,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="134 23047 22"/>
    </justification>
  </clause>

  <clause id="23074">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(z,u,w) * y) = (y * T(x,y)) * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(23048(a,1),20575(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="23048 20575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23075">
    <literal><![CDATA[
      ((a(x,y,z) * a(u,w,v5)) \ v6) * (a(x,y,z) * a(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[hyper(1847,a,23057,a)].">
      <j1 rule="hyper" parents="1847 23057"/>
    </justification>
  </clause>

  <clause id="23076">
    <literal><![CDATA[
      (a(x,x,y) * a(x,x,y)) \ ((x \ 1) \ (x \ y)) = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,15340,a,b,23057,a)].">
      <j1 rule="hyper" parents="63 15340 23057"/>
    </justification>
  </clause>

  <clause id="23077">
    <literal><![CDATA[
      T(a(x,y,z) * a(u,w,v5),v6) = a(x,y,z) * a(u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(54,a,23057,a)].">
      <j1 rule="hyper" parents="54 23057"/>
    </justification>
  </clause>

  <clause id="23078">
    <literal><![CDATA[
      (a(x,y,z) * a(u,w,v5)) * v6 != v7
    ]]></literal>
    <literal><![CDATA[
      v6 * (a(x,y,z) * a(u,w,v5)) = v7
    ]]></literal>
    <justification jstring="[para(23057(a,1),315(a,1,2))].">
      <j1 rule="para" parents="23057 315"/>
    </justification>
  </clause>

  <clause id="23080">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w) = v5
    ]]></literal>
    <justification jstring="[para(23054(a,2),11921(a,1))].">
      <j1 rule="para" parents="23054 11921"/>
    </justification>
  </clause>

  <clause id="23086">
    <literal><![CDATA[
      T(a(x,y,z) \ u,T(w,u)) = K(u,w) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(269,a,23050,a,b,5213,a)].">
      <j1 rule="hyper" parents="269 23050 5213"/>
    </justification>
  </clause>

  <clause id="23087">
    <literal><![CDATA[
      (a(x,y,z) \ u) * u = u * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(110(a,1),23050(a,1,2))].">
      <j1 rule="para" parents="110 23050"/>
    </justification>
  </clause>

  <clause id="23088">
    <literal><![CDATA[
      ((x * y) / x) * (a(z,u,w) \ x) = (a(z,u,w) \ x) * y
    ]]></literal>
    <justification jstring="[para(254(a,1),23050(a,1,2)),flip(a)].">
      <j1 rule="para" parents="254 23050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23089">
    <literal><![CDATA[
      L(((a(x,y,z) \ u) \ u) \ T(w,u),a(x,y,z),a(x,y,z) \ u) = u \ (w * (a(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(23050(a,1),10212(a,2,2))].">
      <j1 rule="para" parents="23050 10212"/>
    </justification>
  </clause>

  <clause id="23090">
    <literal><![CDATA[
      (x * (a(y,z,u) \ 1)) * T(w,a(y,z,u) \ T(x,1)) = w * ((a(y,z,u) \ 1) * T(x,1))
    ]]></literal>
    <justification jstring="[para(23050(a,1),13169(a,1,1))].">
      <j1 rule="para" parents="23050 13169"/>
    </justification>
  </clause>

  <clause id="23091">
    <literal><![CDATA[
      (x * (a(y,z,u) \ x)) / (x * x) = (a(y,z,u) \ x) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(23087(a,1),780(a,1,1))].">
      <j1 rule="para" parents="23087 780"/>
    </justification>
  </clause>

  <clause id="23092">
    <literal><![CDATA[
      (x * (a(y,z,u) \ x)) * (x \ (1 / x)) = (a(y,z,u) \ x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(23087(a,1),845(a,1,1))].">
      <j1 rule="para" parents="23087 845"/>
    </justification>
  </clause>

  <clause id="23093">
    <literal><![CDATA[
      (((x * y) / x) * a(z,u,w)) * x = x * (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,21298,a,b,23061,a)].">
      <j1 rule="hyper" parents="63 21298 23061"/>
    </justification>
  </clause>

  <clause id="23094">
    <literal><![CDATA[
      (x / y) * (y * a(z,u,w)) = (y * a(z,u,w)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(113(a,1),23061(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 23061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23095">
    <literal><![CDATA[
      (x * y) \ (x * (y * a(z,u,w))) = R(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(23061(a,1),22622(a,1,2))].">
      <j1 rule="para" parents="23061 22622"/>
    </justification>
  </clause>

  <clause id="23096">
    <literal><![CDATA[
      a(x,y,z) / (u \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      (1 / u) \ a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(749(a,1),23043(a,1,2))].">
      <j1 rule="para" parents="749 23043"/>
    </justification>
  </clause>

  <clause id="23097">
    <literal><![CDATA[
      R(a(x,y,z),u,w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(545,a,23095,a),flip(a)].">
      <j1 rule="hyper" parents="545 23095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23098">
    <literal><![CDATA[
      R(a(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(a(x,y,z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(23095(a,1),545(a,1))].">
      <j1 rule="para" parents="23095 545"/>
    </justification>
  </clause>

  <clause id="23100">
    <literal><![CDATA[
      L(a(x,y,z),u,w * w) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(598,a,23097,a),flip(a)].">
      <j1 rule="hyper" parents="598 23097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23101">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (u * w) = (a(x,y,z) * u) * w
    ]]></literal>
    <justification jstring="[hyper(133,a,23097,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="133 23097 20"/>
    </justification>
  </clause>

  <clause id="23104">
    <literal><![CDATA[
      x * L(a(y,z,u),a(y,z,u) \ w,(a(y,z,u) \ w) \ x) = w * ((a(y,z,u) \ w) \ T(x,a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(23097(a,1),21363(a,1,2))].">
      <j1 rule="para" parents="23097 21363"/>
    </justification>
  </clause>

  <clause id="23105">
    <literal><![CDATA[
      (x \ 1) \ (x * (((x * x) \ y) * a(z,u,w))) = a(z,u,w) * y
    ]]></literal>
    <justification jstring="[para(23100(a,1),21229(a,2,1))].">
      <j1 rule="para" parents="23100 21229"/>
    </justification>
  </clause>

  <clause id="23106">
    <literal><![CDATA[
      ((x * a(y,z,u)) * (x \ w)) / w != v5
    ]]></literal>
    <literal><![CDATA[
      L(a(y,z,u),x,x \ w) = v5
    ]]></literal>
    <justification jstring="[para(20588(a,2),23098(a,1))].">
      <j1 rule="para" parents="20588 23098"/>
    </justification>
  </clause>

  <clause id="23107">
    <literal><![CDATA[
      a(x,y,z) / (u \ 1) = (1 / u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(23096,a,xx),flip(a)].">
      <j1 rule="hyper" parents="23096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23108">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) = a(y,z,u) \ ((1 / x) \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(128,a,23107,a(flip),b,2008,a),flip(a)].">
      <j1 rule="hyper" parents="128 23107 2008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23109">
    <literal><![CDATA[
      T(a(x,y,z) * u,w) = T(u,w) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(269,a,23101,a(flip),b,20028,a(flip))].">
      <j1 rule="hyper" parents="269 23101 20028"/>
    </justification>
  </clause>

  <clause id="23110">
    <literal><![CDATA[
      (a(x,y,z) * u) * w != v5 * (u * w)
    ]]></literal>
    <literal><![CDATA[
      L(a(x,y,z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(23101(a,1),44(a,1))].">
      <j1 rule="para" parents="23101 44"/>
    </justification>
  </clause>

  <clause id="23111">
    <literal><![CDATA[
      (a(x,y,z) * u) * z = a(x,y,z) * (u * z)
    ]]></literal>
    <justification jstring="[para(12360(a,1),23101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12360 23101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23112">
    <literal><![CDATA[
      (a(x,y,z) * u) * L(z,w,v5) = a(x,y,z) * (u * L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(12369(a,1),23101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12369 23101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23113">
    <literal><![CDATA[
      T(a(x,y,z) * u,w) = a(x,y,z) * T(u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,19985,a,b,23109,a),flip(a)].">
      <j1 rule="hyper" parents="347 19985 23109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23116">
    <literal><![CDATA[
      T(a(x,y,z) * (u / w),w) = (w \ u) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(113(a,1),23109(a,2,1))].">
      <j1 rule="para" parents="113 23109"/>
    </justification>
  </clause>

  <clause id="23118">
    <literal><![CDATA[
      (x * y) / T(a(z,u,w) * x,y) = (y * x) / (a(z,u,w) * x)
    ]]></literal>
    <justification jstring="[para(23109(a,2),20612(a,1,2))].">
      <j1 rule="para" parents="23109 20612"/>
    </justification>
  </clause>

  <clause id="23119">
    <literal><![CDATA[
      (x * a(y,z,u)) * u = a(y,z,u) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(20022,a,23111,a)].">
      <j1 rule="hyper" parents="20022 23111"/>
    </justification>
  </clause>

  <clause id="23120">
    <literal><![CDATA[
      L(x,y,a(z,u,x)) = x
    ]]></literal>
    <justification jstring="[hyper(17898,a,23111,a)].">
      <j1 rule="hyper" parents="17898 23111"/>
    </justification>
  </clause>

  <clause id="23121">
    <literal><![CDATA[
      a(x,y,z) \ (u * z) = (a(x,y,z) \ u) * z
    ]]></literal>
    <justification jstring="[hyper(705,a,23111,a)].">
      <j1 rule="hyper" parents="705 23111"/>
    </justification>
  </clause>

  <clause id="23122">
    <literal><![CDATA[
      (x \ ((x * y) * z)) / z = a(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(131,a,14721,a,b,23111,a)].">
      <j1 rule="hyper" parents="131 14721 23111"/>
    </justification>
  </clause>

  <clause id="23123">
    <literal><![CDATA[
      (x * y) / L(y,x,z) = a(z,x,L(y,x,z)) * x
    ]]></literal>
    <justification jstring="[hyper(131,a,14730,a(flip),b,23111,a)].">
      <j1 rule="hyper" parents="131 14730 23111"/>
    </justification>
  </clause>

  <clause id="23125">
    <literal><![CDATA[
      a(a(x,y,z),u,z) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,23111,a(flip),b,13372,a),flip(a)].">
      <j1 rule="hyper" parents="129 23111 13372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23126">
    <literal><![CDATA[
      a(x,y,y) * (x * y) = R(x,y,y) * y
    ]]></literal>
    <justification jstring="[para(13403(a,1),23111(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13403 23111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23127">
    <literal><![CDATA[
      L(x,a(y,z,u) * (w * u),v5) = L(x,u * (a(y,z,u) * w),v5)
    ]]></literal>
    <justification jstring="[para(23111(a,1),21617(a,1,2))].">
      <j1 rule="para" parents="23111 21617"/>
    </justification>
  </clause>

  <clause id="23128">
    <literal><![CDATA[
      L(x,y,a(z,u,L(x,w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(161,a,23120,a)].">
      <j1 rule="hyper" parents="161 23120"/>
    </justification>
  </clause>

  <clause id="23129">
    <literal><![CDATA[
      L(R(x,y,z),u,a(w,v5,x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(23120(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23120 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23130">
    <literal><![CDATA[
      L(L(x,y,z),u,a(w,v5,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(23120(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23120 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23131">
    <literal><![CDATA[
      a(x,y,z) \ (u * z) != w
    ]]></literal>
    <literal><![CDATA[
      (a(x,y,z) \ u) * z = w
    ]]></literal>
    <justification jstring="[para(23120(a,1),876(a,1,2,2))].">
      <j1 rule="para" parents="23120 876"/>
    </justification>
  </clause>

  <clause id="23132">
    <literal><![CDATA[
      (a(x,y,z) * u) * R(z,w,v5) = a(x,y,z) * (u * R(z,w,v5))
    ]]></literal>
    <justification jstring="[para(23120(a,1),475(a,1,2,1))].">
      <j1 rule="para" parents="23120 475"/>
    </justification>
  </clause>

  <clause id="23133">
    <literal><![CDATA[
      L(L(L(x,y,z),u,w),v5,a(v6,v7,x)) = L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(23120(a,1),116(a,2,1,1))].">
      <j1 rule="para" parents="23120 116"/>
    </justification>
  </clause>

  <clause id="23134">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ z != u
    ]]></literal>
    <literal><![CDATA[
      z * a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(23120(a,1),21365(a,1,2))].">
      <j1 rule="para" parents="23120 21365"/>
    </justification>
  </clause>

  <clause id="23135">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,a(w,v5,a(z,y,x))) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(1787(a,2),23128(a,1,3,3))].">
      <j1 rule="para" parents="1787 23128"/>
    </justification>
  </clause>

  <clause id="23136">
    <literal><![CDATA[
      (a(x,y,z) \ u) * T(R(z,w,v5),u) = a(x,y,z) \ (R(z,w,v5) * u)
    ]]></literal>
    <justification jstring="[para(23129(a,1),874(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23129 874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23137">
    <literal><![CDATA[
      a(x,y,z) \ (u * L(z,w,v5)) = (a(x,y,z) \ u) * L(z,w,v5)
    ]]></literal>
    <justification jstring="[para(23130(a,1),538(a,1,2,2))].">
      <j1 rule="para" parents="23130 538"/>
    </justification>
  </clause>

  <clause id="23138">
    <literal><![CDATA[
      (x \ ((x * y) * z)) / z = y * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,19985,a(flip),b,23122,a),flip(a)].">
      <j1 rule="hyper" parents="347 19985 23122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23139">
    <literal><![CDATA[
      a(x,y,z) = y \ ((x \ ((x * y) * z)) / z)
    ]]></literal>
    <justification jstring="[hyper(128,a,23122,a,b,19985,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 23122 19985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23140">
    <literal><![CDATA[
      x / y != a(z,u,y) * u
    ]]></literal>
    <literal><![CDATA[
      z \ ((z * u) * y) = x
    ]]></literal>
    <justification jstring="[para(23122(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="23122 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23141">
    <literal><![CDATA[
      x \ a(x,x,(y \ ((y * x) * z)) / z) = R(1 / x,x,a(y,x,z))
    ]]></literal>
    <justification jstring="[para(23122(a,2),19010(a,1,2,3))].">
      <j1 rule="para" parents="23122 19010"/>
    </justification>
  </clause>

  <clause id="23142">
    <literal><![CDATA[
      (x \ (a(y,z,u) * (x * w))) / a(y,z,u) = a(x,w,a(y,z,u)) * w
    ]]></literal>
    <justification jstring="[para(19985(a,2),23122(a,1,1,2))].">
      <j1 rule="para" parents="19985 23122"/>
    </justification>
  </clause>

  <clause id="23143">
    <literal><![CDATA[
      (x \ (y * z)) / z = (x \ y) * a(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),23138(a,1,1,2,1))].">
      <j1 rule="para" parents="10 23138"/>
    </justification>
  </clause>

  <clause id="23145">
    <literal><![CDATA[
      (a(x,y,z) * u) \ T(a(x,y,z) * u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(128,a,23113,a,b,5926,a)].">
      <j1 rule="hyper" parents="128 23113 5926"/>
    </justification>
  </clause>

  <clause id="23146">
    <literal><![CDATA[
      T(a(x,y,z) * u,w) \ R(a(x,y,z),T(u,w),T(u,w)) = T(u,w) \ 1
    ]]></literal>
    <justification jstring="[para(23113(a,2),789(a,1,1))].">
      <j1 rule="para" parents="23113 789"/>
    </justification>
  </clause>

  <clause id="23148">
    <literal><![CDATA[
      K(x,y) * ((a(z,u,w) * y) \ v5) = T(a(z,u,w) * y,x) \ v5
    ]]></literal>
    <justification jstring="[para(23113(a,2),20828(a,2,1))].">
      <j1 rule="para" parents="23113 20828"/>
    </justification>
  </clause>

  <clause id="23149">
    <literal><![CDATA[
      T(a(x,y,z) * a(u,w,v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(u,w,v5) * a(x,y,z) = v7
    ]]></literal>
    <justification jstring="[para(23113(a,2),20889(a,1))].">
      <j1 rule="para" parents="23113 20889"/>
    </justification>
  </clause>

  <clause id="23150">
    <literal><![CDATA[
      a(x \ y,x,z) \ y = ((y / x) * (x * z)) / z
    ]]></literal>
    <justification jstring="[hyper(14755,a,23121,a),flip(a)].">
      <j1 rule="hyper" parents="14755 23121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23151">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) * y = z * (L(z,y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(21064,a,23123,a),flip(a)].">
      <j1 rule="hyper" parents="21064 23123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23152">
    <literal><![CDATA[
      (((x / y) * (y * z)) / z) \ x = a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[para(23150(a,1),19984(a,1,1))].">
      <j1 rule="para" parents="23150 19984"/>
    </justification>
  </clause>

  <clause id="23153">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ a(y,z,u) = (x \ 1) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,6354,a(flip),b,23116,a)].">
      <j1 rule="hyper" parents="63 6354 23116"/>
    </justification>
  </clause>

  <clause id="23154">
    <literal><![CDATA[
      K(a(x,y,z) * u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(5006,a,23145,a)].">
      <j1 rule="hyper" parents="5006 23145"/>
    </justification>
  </clause>

  <clause id="23157">
    <literal><![CDATA[
      K(a(x,y,z) \ u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,16650,a,b,23154,a)].">
      <j1 rule="hyper" parents="63 16650 23154"/>
    </justification>
  </clause>

  <clause id="23158">
    <literal><![CDATA[
      a(x,y,z) * K(u \ 1,u) = (u \ a(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(23154(a,1),5769(a,1,2))].">
      <j1 rule="para" parents="23154 5769"/>
    </justification>
  </clause>

  <clause id="23159">
    <literal><![CDATA[
      K((x * y) * z,u) = K(x * (y * z),u)
    ]]></literal>
    <justification jstring="[para(13372(a,1),23154(a,1,1))].">
      <j1 rule="para" parents="13372 23154"/>
    </justification>
  </clause>

  <clause id="23161">
    <literal><![CDATA[
      K(x \ (y * z),u) = K((x \ y) * z,u)
    ]]></literal>
    <justification jstring="[para(14734(a,1),23154(a,1,1))].">
      <j1 rule="para" parents="14734 23154"/>
    </justification>
  </clause>

  <clause id="23162">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * a(u,w,v5),y) = z
    ]]></literal>
    <justification jstring="[para(23154(a,1),16905(a,1))].">
      <j1 rule="para" parents="23154 16905"/>
    </justification>
  </clause>

  <clause id="23167">
    <literal><![CDATA[
      K(x * (y * z),T(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * (x * y),u) = w
    ]]></literal>
    <justification jstring="[para(23159(a,1),10376(a,1))].">
      <j1 rule="para" parents="23159 10376"/>
    </justification>
  </clause>

  <clause id="23168">
    <literal><![CDATA[
      K((x \ y) * (z * u),T(w,u)) = K(((y \ x) / u) \ z,w)
    ]]></literal>
    <justification jstring="[hyper(20853,a,23161,a),flip(a)].">
      <j1 rule="hyper" parents="20853 23161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23171">
    <literal><![CDATA[
      K(a(x,y,z) \ u,w) = K(u * a(v5,v6,v7),w)
    ]]></literal>
    <justification jstring="[hyper(23162,a,23157,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="23162 23157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23173">
    <literal><![CDATA[
      K(x \ (a(y,z,u) \ w),v5) = K((x \ w) * a(v6,v7,v8),v5)
    ]]></literal>
    <justification jstring="[hyper(19466,a,23171,a)].">
      <j1 rule="hyper" parents="19466 23171"/>
    </justification>
  </clause>

  <clause id="23174">
    <literal><![CDATA[
      T(a(x,y,z) \ u,T(w,u)) = a(x,y,z) \ T(u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,16908,a(flip),b,23086,a),flip(a)].">
      <j1 rule="hyper" parents="347 16908 23086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23175">
    <literal><![CDATA[
      T(a(x,y,z) \ u,w) = a(x,y,z) \ T(u,w)
    ]]></literal>
    <justification jstring="[hyper(16923,a,23174,a)].">
      <j1 rule="hyper" parents="16923 23174"/>
    </justification>
  </clause>

  <clause id="23177">
    <literal><![CDATA[
      (a(x,y,z) / u) * K(u \ 1,w) = T(a(x,y,z) / u,w)
    ]]></literal>
    <justification jstring="[hyper(38,a,5685,a,b,23175,a(flip))].">
      <j1 rule="hyper" parents="38 5685 23175"/>
    </justification>
  </clause>

  <clause id="23178">
    <literal><![CDATA[
      ((x * y) / x) \ (a(z,u,w) \ y) = y \ T(a(z,u,w) \ y,x)
    ]]></literal>
    <justification jstring="[para(23175(a,2),16987(a,2,2))].">
      <j1 rule="para" parents="23175 16987"/>
    </justification>
  </clause>

  <clause id="23179">
    <literal><![CDATA[
      L(T(a(x,y,z) \ u,w),a(x,y,z),w) = (a(x,y,z) * w) \ (u * w)
    ]]></literal>
    <justification jstring="[para(23175(a,2),20603(a,1,1))].">
      <j1 rule="para" parents="23175 20603"/>
    </justification>
  </clause>

  <clause id="23180">
    <literal><![CDATA[
      (x / T(y,z)) * T(a(u,w,v5) \ y,z) = (x / y) * (a(u,w,v5) \ y)
    ]]></literal>
    <justification jstring="[para(23175(a,2),21038(a,1,2))].">
      <j1 rule="para" parents="23175 21038"/>
    </justification>
  </clause>

  <clause id="23181">
    <literal><![CDATA[
      (x * a(y,z,u)) \ T(x,w) = x \ T(a(y,z,u) \ x,w)
    ]]></literal>
    <justification jstring="[para(23175(a,2),22324(a,2,2))].">
      <j1 rule="para" parents="23175 22324"/>
    </justification>
  </clause>

  <clause id="23182">
    <literal><![CDATA[
      ((((x * T(y,x)) / x) * a(z,u,w)) * x) \ (y * x) = (x * (y * a(z,u,w))) \ (x * y)
    ]]></literal>
    <justification jstring="[para(23093(a,2),13751(a,1,1))].">
      <j1 rule="para" parents="23093 13751"/>
    </justification>
  </clause>

  <clause id="23183">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) * a(y,z,u) = (1 / x) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,23108,a,b,19977,a)].">
      <j1 rule="hyper" parents="133 23108 19977"/>
    </justification>
  </clause>

  <clause id="23184">
    <literal><![CDATA[
      x \ a(y,z,u) != (w \ 1) * a(y,z,u)
    ]]></literal>
    <literal><![CDATA[
      L(w,w,a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[para(23153(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="23153 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23185">
    <literal><![CDATA[
      K(((x \ y) / z) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z * ((y \ x) * u),w) = v5
    ]]></literal>
    <justification jstring="[para(23168(a,1),23167(a,1))].">
      <j1 rule="para" parents="23168 23167"/>
    </justification>
  </clause>

  <clause id="23186">
    <literal><![CDATA[
      K((x \ y) * a(z,u,w),x) * (a(v5,v6,v7) \ y) = (x \ (a(v5,v6,v7) \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,23173,a(flip),b,4896,a)].">
      <j1 rule="hyper" parents="133 23173 4896"/>
    </justification>
  </clause>

  <clause id="23188">
    <literal><![CDATA[
      ((x \ ((x * y) * z)) / z) \ T(y,u) = y \ T(a(x,y,z) \ y,u)
    ]]></literal>
    <justification jstring="[para(23138(a,2),23181(a,1,1))].">
      <j1 rule="para" parents="23138 23181"/>
    </justification>
  </clause>

  <clause id="23189">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (u * (w * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      u * (a(x,y,z) \ (w * w)) = v5
    ]]></literal>
    <justification jstring="[para(936(a,1),23051(a,1))].">
      <j1 rule="para" parents="936 23051"/>
    </justification>
  </clause>

  <clause id="23191">
    <literal><![CDATA[
      x / (a(y,z,u) * a(w,v5,v6)) = (a(w,v5,v6) * a(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(131,a,23075,a(flip),b,19980,a)].">
      <j1 rule="hyper" parents="131 23075 19980"/>
    </justification>
  </clause>

  <clause id="23192">
    <literal><![CDATA[
      ((a(x,y,z) * a(x,y,z)) \ u) \ w = (a(x,y,z) * a(x,y,z)) * (u \ w)
    ]]></literal>
    <justification jstring="[para(23075(a,1),461(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23075 461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23193">
    <literal><![CDATA[
      x * ((a(y,z,u) \ x) / (x * x)) = (a(y,z,u) \ x) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,464,a(flip),b,23091,a)].">
      <j1 rule="hyper" parents="63 464 23091"/>
    </justification>
  </clause>

  <clause id="23194">
    <literal><![CDATA[
      (x * x) \ (a(y,z,u) * w) = ((x * x) \ w) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(128,a,23105,a(flip),b,494,a(flip))].">
      <j1 rule="hyper" parents="128 23105 494"/>
    </justification>
  </clause>

  <clause id="23196">
    <literal><![CDATA[
      (x * (((y * y) \ z) * a(u,w,v5))) \ (((a(u,w,v5) * x) / (y * y)) * z) = a(x / (y * y),a(u,w,v5),z)
    ]]></literal>
    <justification jstring="[para(23194(a,1),22904(a,1,1,2))].">
      <j1 rule="para" parents="23194 22904"/>
    </justification>
  </clause>

  <clause id="23197">
    <literal><![CDATA[
      (x * y) / (a(z,u,w) * y) = (a(z,u,w) * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,23052,a(flip),b,23118,a),flip(a)].">
      <j1 rule="hyper" parents="63 23052 23118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23198">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (u * (w * a(x,y,z))) = R(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(595,a,23197,a),flip(a)].">
      <j1 rule="hyper" parents="595 23197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23199">
    <literal><![CDATA[
      T(((x / a(y,z,u)) * w) / (a(y,z,u) * (x / a(y,z,u))),T(x,a(y,z,u))) = (w * (x / a(y,z,u))) / (a(y,z,u) * (x / a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,10342,a,b,23197,a)].">
      <j1 rule="hyper" parents="347 10342 23197"/>
    </justification>
  </clause>

  <clause id="23200">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (a(y,z,u) * w) = (x * a(y,z,u)) * w
    ]]></literal>
    <justification jstring="[hyper(133,a,21148,a(flip),b,23197,a)].">
      <j1 rule="hyper" parents="133 21148 23197"/>
    </justification>
  </clause>

  <clause id="23201">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (u * (w * a(x,y,z))) != v5
    ]]></literal>
    <literal><![CDATA[
      R(w,a(x,y,z),u) = v5
    ]]></literal>
    <justification jstring="[para(23197(a,1),595(a,1))].">
      <j1 rule="para" parents="23197 595"/>
    </justification>
  </clause>

  <clause id="23202">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (u * (u \ L(u,w,v5))) = L(u,w,v5) / (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(3163(a,1),23197(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3163 23197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23203">
    <literal><![CDATA[
      a(x,y,z) \ (u * L(z,w,v5)) != v6 * L(z,w,v5)
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) \ u = v6
    ]]></literal>
    <justification jstring="[para(23137(a,2),44(a,1))].">
      <j1 rule="para" parents="23137 44"/>
    </justification>
  </clause>

  <clause id="23204">
    <literal><![CDATA[
      K(x,a(y,z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(35,a,5209,a,b,23148,a)].">
      <j1 rule="hyper" parents="35 5209 23148"/>
    </justification>
  </clause>

  <clause id="23208">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,16651,a,b,23204,a)].">
      <j1 rule="hyper" parents="63 16651 23204"/>
    </justification>
  </clause>

  <clause id="23213">
    <literal><![CDATA[
      K(x,y \ (a(z,u,w) \ v5)) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[hyper(19429,a,23208,a)].">
      <j1 rule="hyper" parents="19429 23208"/>
    </justification>
  </clause>

  <clause id="23217">
    <literal><![CDATA[
      (a(x,y,z) \ u) * K(w,w \ u) = w * ((a(x,y,z) \ u) / w)
    ]]></literal>
    <justification jstring="[hyper(134,a,23213,a(flip),b,5110,a)].">
      <j1 rule="hyper" parents="134 23213 5110"/>
    </justification>
  </clause>

  <clause id="23218">
    <literal><![CDATA[
      K(x,x \ y) * (a(z,u,w) \ y) = x * ((a(z,u,w) \ y) / x)
    ]]></literal>
    <justification jstring="[hyper(133,a,23213,a(flip),b,5197,a)].">
      <j1 rule="hyper" parents="133 23213 5197"/>
    </justification>
  </clause>

  <clause id="23221">
    <literal><![CDATA[
      (a(x,y,z) * a(u,w,v5)) * v6 = v6 * (a(u,w,v5) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,9,a(flip),b,23191,a),flip(a)].">
      <j1 rule="hyper" parents="133 9 23191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23222">
    <literal><![CDATA[
      (x * ((a(y,z,u) * a(y,z,u)) \ w)) * v5 = (x * w) * ((a(y,z,u) * a(y,z,u)) \ v5)
    ]]></literal>
    <justification jstring="[para(23191(a,1),827(a,1,1,2))].">
      <j1 rule="para" parents="23191 827"/>
    </justification>
  </clause>

  <clause id="23223">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (u \ 1) = u * (a(x,y,z) \ (u \ 1))
    ]]></literal>
    <justification jstring="[para(820(a,1),23193(a,1,2)),flip(a)].">
      <j1 rule="para" parents="820 23193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23224">
    <literal><![CDATA[
      (x \ 1) * (a(y,z,u) \ ((x \ 1) \ 1)) = (a(y,z,u) \ x) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,988,a(flip),b,23223,a),flip(a)].">
      <j1 rule="hyper" parents="63 988 23223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23225">
    <literal><![CDATA[
      R(x,a(y,z,u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(21149,a,23198,a),flip(a)].">
      <j1 rule="hyper" parents="21149 23198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23226">
    <literal><![CDATA[
      R(x,a(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(23198(a,1),21149(a,1))].">
      <j1 rule="para" parents="23198 21149"/>
    </justification>
  </clause>

  <clause id="23227">
    <literal><![CDATA[
      L(x,a(y,z,u),(w \ 1) \ v5) = R(x,a(y,z,u),w \ v5)
    ]]></literal>
    <justification jstring="[hyper(2379,a,23225,a),flip(a)].">
      <j1 rule="hyper" parents="2379 23225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23229">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (x \ (a(y,z,u) * w)) = x \ ((x * a(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(133,a,23225,a(flip),b,1770,a(flip))].">
      <j1 rule="hyper" parents="133 23225 1770"/>
    </justification>
  </clause>

  <clause id="23230">
    <literal><![CDATA[
      L(x,a(y,z,u),(w \ 1) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,u),w \ v5) = v6
    ]]></literal>
    <justification jstring="[para(23227(a,2),23226(a,1))].">
      <j1 rule="para" parents="23227 23226"/>
    </justification>
  </clause>

  <clause id="23232">
    <literal><![CDATA[
      ((a(x,y,z) * u) * w) / (a(x,y,z) * w) = L(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(131,a,19987,a,b,23200,a)].">
      <j1 rule="hyper" parents="131 19987 23200"/>
    </justification>
  </clause>

  <clause id="23233">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) / ((x * a(y,z,u)) * w) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(220,a,23200,a(flip),b,19100,a)].">
      <j1 rule="hyper" parents="220 23200 19100"/>
    </justification>
  </clause>

  <clause id="23234">
    <literal><![CDATA[
      a(x,y,z) \ (u * (w / u)) = u * ((a(x,y,z) \ w) / u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14664,a(flip),b,23217,a)].">
      <j1 rule="hyper" parents="63 14664 23217"/>
    </justification>
  </clause>

  <clause id="23235">
    <literal><![CDATA[
      a(x,y,z) \ (u * (w / u)) != u * v5
    ]]></literal>
    <literal><![CDATA[
      (a(x,y,z) \ w) / u = v5
    ]]></literal>
    <justification jstring="[para(23234(a,2),43(a,1))].">
      <j1 rule="para" parents="23234 43"/>
    </justification>
  </clause>

  <clause id="23236">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (w * a(y,z,u)) = (a(y,z,u) * x) * w
    ]]></literal>
    <justification jstring="[hyper(133,a,23232,a(flip),b,20120,a(flip))].">
      <j1 rule="hyper" parents="133 23232 20120"/>
    </justification>
  </clause>

  <clause id="23237">
    <literal><![CDATA[
      L(x,a(y,z,u),w \ 1) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(23230,a,3937,a)].">
      <j1 rule="hyper" parents="23230 3937"/>
    </justification>
  </clause>

  <clause id="23238">
    <literal><![CDATA[
      (x \ a(x,y,z)) * L(u,a(x,y,z),x) = (x \ 1) * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(23237(a,1),15269(a,1,2))].">
      <j1 rule="para" parents="23237 15269"/>
    </justification>
  </clause>

  <clause id="23239">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(z,u,w) * y) = (x * y) * a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,252,a(flip),b,23074,a),flip(a)].">
      <j1 rule="hyper" parents="347 252 23074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23241">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (y * a(z,u,w)) = (x * y) * a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(20023,a,23239,a)].">
      <j1 rule="hyper" parents="20023 23239"/>
    </justification>
  </clause>

  <clause id="23242">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(z,u,w) * y) = a(z,u,w) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,19985,a,b,23239,a),flip(a)].">
      <j1 rule="hyper" parents="347 19985 23239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23243">
    <literal><![CDATA[
      L(1 / x,x,a(y,z,u)) \ a(y,z,u) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(128,a,81,a(flip),b,23239,a)].">
      <j1 rule="hyper" parents="128 81 23239"/>
    </justification>
  </clause>

  <clause id="23244">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) / w = w \ ((w * u) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,23239,a(flip),b,13775,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 23239 13775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23245">
    <literal><![CDATA[
      (x / y) \ (y \ ((y * (a(z,u,w) \ x)) * a(z,u,w))) = L(y,a(z,u,w) \ x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(23244(a,1),2020(a,1,2))].">
      <j1 rule="para" parents="23244 2020"/>
    </justification>
  </clause>

  <clause id="23246">
    <literal><![CDATA[
      L(x,x \ y,a(z,u,w)) \ (y * a(z,u,w)) = (x \ y) * a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(128,a,165,a(flip),b,23241,a)].">
      <j1 rule="hyper" parents="128 165 23241"/>
    </justification>
  </clause>

  <clause id="23247">
    <literal><![CDATA[
      R(x,y,a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(35,a,107,a,b,23241,a)].">
      <j1 rule="hyper" parents="35 107 23241"/>
    </justification>
  </clause>

  <clause id="23248">
    <literal><![CDATA[
      x \ ((x * y) * a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (x \ (y * a(z,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(23241(a,1),1426(a,1,2))].">
      <j1 rule="para" parents="23241 1426"/>
    </justification>
  </clause>

  <clause id="23249">
    <literal><![CDATA[
      ((x * y) * a(z,u,w)) \ (x * (y * a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(a(z,u,w),y,x) = v5
    ]]></literal>
    <justification jstring="[para(23241(a,1),18302(a,1,1))].">
      <j1 rule="para" parents="23241 18302"/>
    </justification>
  </clause>

  <clause id="23250">
    <literal><![CDATA[
      L((a(x,y,z) \ u) / w,w,a(x,y,z)) = u / (w * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(20580,a,23247,a),flip(a)].">
      <j1 rule="hyper" parents="20580 23247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23251">
    <literal><![CDATA[
      R(x,y,a(z,u,w) \ 1) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(2230,a,23247,a)].">
      <j1 rule="hyper" parents="2230 23247"/>
    </justification>
  </clause>

  <clause id="23253">
    <literal><![CDATA[
      L(x,y,a(z * (u * u),w,v5)) = R(x,y,a(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,22599,a(flip),b,23247,a),flip(a)].">
      <j1 rule="hyper" parents="63 22599 23247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23254">
    <literal><![CDATA[
      L(x * y,z,a(x,x,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(63,a,22187,a(flip),b,23247,a),flip(a)].">
      <j1 rule="hyper" parents="63 22187 23247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23255">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,y * a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(23247(a,1),14250(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="23247 14250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23256">
    <literal><![CDATA[
      L((a(x,y,z) \ u) / w,w,a(x,y,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      u / (w * a(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(23247(a,1),20580(a,1))].">
      <j1 rule="para" parents="23247 20580"/>
    </justification>
  </clause>

  <clause id="23257">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(23251(a,1),2232(a,1))].">
      <j1 rule="para" parents="23251 2232"/>
    </justification>
  </clause>

  <clause id="23258">
    <literal><![CDATA[
      L(x,y,a(z * (u * u),w,v5)) = L(x,y,a(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,23247,a(flip),b,23253,a),flip(a)].">
      <j1 rule="hyper" parents="347 23247 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23259">
    <literal><![CDATA[
      L(x,y,a(z \ 1,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(240(a,1),23258(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="240 23258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23260">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) / (a(x,y,z) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(u,w,a(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(23242(a,1),282(a,1,1)),flip(b)].">
      <j1 rule="para" parents="23242 282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23261">
    <literal><![CDATA[
      L(x,y,a(y,y,z)) * R(y,y,z) = a(y,y,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(18993(a,1),23242(a,1,2))].">
      <j1 rule="para" parents="18993 23242"/>
    </justification>
  </clause>

  <clause id="23262">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * (z * v5) = z * (a(x,y,L(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(23128(a,1),23242(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23128 23242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23263">
    <literal><![CDATA[
      a(x,x,y) * (z * x) != u * R(x,x,y)
    ]]></literal>
    <literal><![CDATA[
      L(z,x,a(x,x,y)) = u
    ]]></literal>
    <justification jstring="[para(23261(a,1),44(a,1))].">
      <j1 rule="para" parents="23261 44"/>
    </justification>
  </clause>

  <clause id="23264">
    <literal><![CDATA[
      (x / (y * a(z,u,w))) * y = y * ((a(z,u,w) * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(133,a,23250,a(flip),b,962,a(flip))].">
      <j1 rule="hyper" parents="133 23250 962"/>
    </justification>
  </clause>

  <clause id="23265">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) != v5 / (y * a(z,u,w))
    ]]></literal>
    <literal><![CDATA[
      (a(z,u,w) \ v5) / y = x
    ]]></literal>
    <justification jstring="[para(23250(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="23250 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23266">
    <literal><![CDATA[
      T((x / ((y \ 1) * a(z,u,w))) * (y \ 1),(x / ((y \ 1) * a(z,u,w))) / y) = (y \ 1) * ((a(z,u,w) * (y \ 1)) \ x)
    ]]></literal>
    <justification jstring="[hyper(13320,a,23264,a)].">
      <j1 rule="hyper" parents="13320 23264"/>
    </justification>
  </clause>

  <clause id="23267">
    <literal><![CDATA[
      (x / (a(y,z,u) * T(a(y,z,u) \ w,v5))) * T(w / a(y,z,u),v5) = T(w / a(y,z,u),v5) * ((a(y,z,u) * T(w / a(y,z,u),v5)) \ x)
    ]]></literal>
    <justification jstring="[para(484(a,1),23264(a,1,1,2))].">
      <j1 rule="para" parents="484 23264"/>
    </justification>
  </clause>

  <clause id="23268">
    <literal><![CDATA[
      x * ((a(y,z,u) \ x) * (x \ (1 / x))) = (a(y,z,u) \ x) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1098,a,23092,a)].">
      <j1 rule="hyper" parents="1098 23092"/>
    </justification>
  </clause>

  <clause id="23269">
    <literal><![CDATA[
      a(x,y,z) \ (R(z,u,w) * v5) = R(z,u,w) * (a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(23051,a,23136,a),flip(a)].">
      <j1 rule="hyper" parents="23051 23136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23270">
    <literal><![CDATA[
      a(x,y,z) \ (u \ (a(x,y,z) * (u * w))) = a(u,w,a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(20018,a,23142,a)].">
      <j1 rule="hyper" parents="20018 23142"/>
    </justification>
  </clause>

  <clause id="23271">
    <literal><![CDATA[
      (x \ 1) * (a(y,z,u) \ ((x \ 1) \ 1)) = x * (a(y,z,u) \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(347,a,23223,a(flip),b,23224,a),flip(a)].">
      <j1 rule="hyper" parents="347 23223 23224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23272">
    <literal><![CDATA[
      (x * a(y,z,u)) \ ((x * (a(y,z,u) * w)) / w) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(21449,a,23233,a)].">
      <j1 rule="hyper" parents="21449 23233"/>
    </justification>
  </clause>

  <clause id="23273">
    <literal><![CDATA[
      L(x,x \ y,a(y,y,z)) \ R(y,y,z) = (x \ y) * a(y,y,z)
    ]]></literal>
    <justification jstring="[para(18990(a,1),23246(a,1,2))].">
      <j1 rule="para" parents="18990 23246"/>
    </justification>
  </clause>

  <clause id="23274">
    <literal><![CDATA[
      (a(x,y,z) * u) \ ((a(x,y,z) * (u * w)) / w) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(20620,a,23255,a)].">
      <j1 rule="hyper" parents="20620 23255"/>
    </justification>
  </clause>

  <clause id="23275">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (1 / u) = u * (a(x,y,z) \ (1 / u))
    ]]></literal>
    <justification jstring="[para(912(a,1),23268(a,1,2)),flip(a)].">
      <j1 rule="para" parents="912 23268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23276">
    <literal><![CDATA[
      x * ((x * x) \ (a(y,z,u) \ (1 / (x \ 1)))) = (a(y,z,u) \ (x \ 1)) * (1 / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(347,a,497,a,b,23275,a)].">
      <j1 rule="hyper" parents="347 497 23275"/>
    </justification>
  </clause>

  <clause id="23277">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) * y,a(z,u,w),x) = (x * a(z,u,w)) \ (a(z,u,w) * (x * y))
    ]]></literal>
    <justification jstring="[para(23270(a,1),329(a,1,1))].">
      <j1 rule="para" parents="23270 329"/>
    </justification>
  </clause>

  <clause id="23278">
    <literal><![CDATA[
      (1 / x) * (a(y,z,u) \ x) = x * (a(y,z,u) \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(5729,a,23271,a)].">
      <j1 rule="hyper" parents="5729 23271"/>
    </justification>
  </clause>

  <clause id="23279">
    <literal><![CDATA[
      T(a(x,y,z) * u,w) \ R(a(x,y,z),T(u,w),u) = T(u,w) \ 1
    ]]></literal>
    <justification jstring="[para(20040(a,1),23146(a,1,2))].">
      <j1 rule="para" parents="20040 23146"/>
    </justification>
  </clause>

  <clause id="23281">
    <literal><![CDATA[
      T(a(x,y,z) * u,w) \ R(a(x,y,z),u,u) = T(u,w) \ 1
    ]]></literal>
    <justification jstring="[para(20496(a,1),23279(a,1,2))].">
      <j1 rule="para" parents="20496 23279"/>
    </justification>
  </clause>

  <clause id="23282">
    <literal><![CDATA[
      T(a(x,y,z) * u,w) \ L(a(x,y,z),u,u) = T(u,w) \ 1
    ]]></literal>
    <justification jstring="[para(14319(a,1),23281(a,1,2))].">
      <j1 rule="para" parents="14319 23281"/>
    </justification>
  </clause>

  <clause id="23284">
    <literal><![CDATA[
      R(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(20865(a,1),23260(a,1))].">
      <j1 rule="para" parents="20865 23260"/>
    </justification>
  </clause>

  <clause id="23285">
    <literal><![CDATA[
      R(x,y,a(z,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z * u,u,z)) = w
    ]]></literal>
    <justification jstring="[para(22168(a,1),23284(a,1))].">
      <j1 rule="para" parents="22168 23284"/>
    </justification>
  </clause>

  <clause id="23287">
    <literal><![CDATA[
      L(x,y,a(z * u,u,z)) = L(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(23285,a,23247,a)].">
      <j1 rule="hyper" parents="23285 23247"/>
    </justification>
  </clause>

  <clause id="23289">
    <literal><![CDATA[
      L((a(x,y,z) * a(x,y,z)) * (u \ w),(a(x,y,z) * a(x,y,z)) \ u,a(x,y,z) * a(x,y,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      u \ ((a(x,y,z) * a(x,y,z)) * w) = v5
    ]]></literal>
    <justification jstring="[para(23192(a,1),651(a,1,1))].">
      <j1 rule="para" parents="23192 651"/>
    </justification>
  </clause>

  <clause id="23290">
    <literal><![CDATA[
      L(x,y,z) / (a(u,w,v5) * x) = (a(u,w,v5) * x) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),23202(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 23202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23292">
    <literal><![CDATA[
      (x * (T(a(y,z,u),x) * w)) / w = w \ ((w * a(y,z,u)) * x)
    ]]></literal>
    <justification jstring="[hyper(21013,a,23229,a)].">
      <j1 rule="hyper" parents="21013 23229"/>
    </justification>
  </clause>

  <clause id="23293">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) / w = w \ ((w * a(y,z,u)) * x)
    ]]></literal>
    <justification jstring="[para(20005(a,1),23292(a,1,1,2,1))].">
      <j1 rule="para" parents="20005 23292"/>
    </justification>
  </clause>

  <clause id="23295">
    <literal><![CDATA[
      K(x \ y,x) * (a(z,u,w) \ y) = (x \ (a(z,u,w) \ y)) * x
    ]]></literal>
    <justification jstring="[para(5970(a,1),23186(a,1,1,1))].">
      <j1 rule="para" parents="5970 23186"/>
    </justification>
  </clause>

  <clause id="23296">
    <literal><![CDATA[
      a(x,y,z) \ ((u \ w) * u) = (u \ (a(x,y,z) \ w)) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,19550,a(flip),b,23295,a)].">
      <j1 rule="hyper" parents="63 19550 23295"/>
    </justification>
  </clause>

  <clause id="23297">
    <literal><![CDATA[
      L(x,y,z) \ (a(u,w,x) \ v5) = a(u,w,x) \ (L(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(23203,a,23296,a),flip(a)].">
      <j1 rule="hyper" parents="23203 23296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23298">
    <literal><![CDATA[
      a(x,y,z) * (L(z,u,w) \ (a(x,y,z) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(z,u,w) \ v5 = v6
    ]]></literal>
    <justification jstring="[para(23297(a,2),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="23297 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23299">
    <literal><![CDATA[
      (x * y) \ ((x * (y * a(z,u,w))) / a(z,u,w)) = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(23249,a,3980,a),flip(a)].">
      <j1 rule="hyper" parents="23249 3980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23300">
    <literal><![CDATA[
      L(T(x,T(y,z)),u,w) * (x \ z) = ((z / x) * L(x,u,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),22939(a,1,1,1,2,2))].">
      <j1 rule="para" parents="12 22939"/>
    </justification>
  </clause>

  <clause id="23302">
    <literal><![CDATA[
      L(T(x,T(y,z)),u,w) * (x \ z) = (z / x) * (L(x,u,w) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,20033,a(flip),b,23300,a),flip(a)].">
      <j1 rule="hyper" parents="347 20033 23300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23303">
    <literal><![CDATA[
      L(T(x,T(y,z)),u,w) * (x \ z) = (z / x) * L(x * K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(21247(a,2),23302(a,2,2))].">
      <j1 rule="para" parents="21247 23302"/>
    </justification>
  </clause>

  <clause id="23304">
    <literal><![CDATA[
      L(T(x,T(y,z)),u,w) * (x \ z) = (z / x) * L(T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(4929(a,2),23303(a,2,2,1))].">
      <j1 rule="para" parents="4929 23303"/>
    </justification>
  </clause>

  <clause id="23305">
    <literal><![CDATA[
      K(x,T(y,z)) * (a(x,u,x) \ z) = (z / x) * L(T(x,y),u,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,21100,a(flip),b,23304,a)].">
      <j1 rule="hyper" parents="63 21100 23304"/>
    </justification>
  </clause>

  <clause id="23306">
    <literal><![CDATA[
      (a(x,y,x) \ z) * K(x,u) = (z / x) * L(T(x,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(18512,a,23305,a)].">
      <j1 rule="hyper" parents="18512 23305"/>
    </justification>
  </clause>

  <clause id="23307">
    <literal><![CDATA[
      (x / y) * L(T(y,z),u,y) = x * (a(y,u,y) \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(11885,a,23306,a),flip(a)].">
      <j1 rule="hyper" parents="11885 23306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23308">
    <literal><![CDATA[
      (x / y) * L(T(y,z),u,y) = x * (y \ L(T(y,z),u,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,9990,a(flip),b,23307,a),flip(a)].">
      <j1 rule="hyper" parents="347 9990 23307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23309">
    <literal><![CDATA[
      T(x,y * (L(z \ (z \ u),w,v5) \ (z \ v6))) = T(x,y * ((L(u,w,v5) \ z) * v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,22977,a(flip),b,22976,a),flip(a)].">
      <j1 rule="hyper" parents="347 22977 22976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23310">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * T(w,u) = w * (((x \ L(x,y,z)) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(187(a,1),22997(a,1,2,2))].">
      <j1 rule="para" parents="187 22997"/>
    </justification>
  </clause>

  <clause id="23312">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * T(w,u) = w * ((L(x,y,z) \ x) * u)
    ]]></literal>
    <justification jstring="[para(10882(a,1),23310(a,2,2,1))].">
      <j1 rule="para" parents="10882 23310"/>
    </justification>
  </clause>

  <clause id="23313">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) * T(w,x) = w * ((L(y,z,u) \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(20242,a,23312,a)].">
      <j1 rule="hyper" parents="20242 23312"/>
    </justification>
  </clause>

  <clause id="23314">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) / T(w * w,x) = (w \ (w \ 1)) * ((L(y,z,u) \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13850,a(flip),b,23313,a)].">
      <j1 rule="hyper" parents="63 13850 23313"/>
    </justification>
  </clause>

  <clause id="23315">
    <literal><![CDATA[
      x * ((y * z) * L((y * z) \ y,u,w)) = (y * (z \ L(z,u,w))) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3343(a,1),23024(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3343 23024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23316">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * T(w,x) = w * (x * (y * L(y \ 1,z,u)))
    ]]></literal>
    <justification jstring="[para(1015(a,1),23315(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1015 23315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23317">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * T(w,x) = w * (x * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(3343(a,1),23316(a,2,2,2))].">
      <j1 rule="para" parents="3343 23316"/>
    </justification>
  </clause>

  <clause id="23318">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = 1
    ]]></literal>
    <justification jstring="[hyper(127,a,23317,a(flip),b,5926,a),flip(a)].">
      <j1 rule="hyper" parents="127 23317 5926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23319">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z \ L(z,u,w)))) = R(z \ L(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(23317(a,1),22303(a,1,2))].">
      <j1 rule="para" parents="23317 22303"/>
    </justification>
  </clause>

  <clause id="23320">
    <literal><![CDATA[
      K(x,T(x * (y \ L(y,z,u)),w)) = w / (w * 1)
    ]]></literal>
    <justification jstring="[para(23318(a,1),7428(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23318 7428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23321">
    <literal><![CDATA[
      K(x,T(x * (y \ L(y,z,u)),w)) = w / w
    ]]></literal>
    <justification jstring="[para(8(a,1),23320(a,2,2))].">
      <j1 rule="para" parents="8 23320"/>
    </justification>
  </clause>

  <clause id="23322">
    <literal><![CDATA[
      K(x,T(x * (y \ L(y,z,u)),w)) = 1
    ]]></literal>
    <justification jstring="[hyper(347,a,77,a(flip),b,23321,a),flip(a)].">
      <j1 rule="hyper" parents="347 77 23321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23324">
    <literal><![CDATA[
      K(x,L(y,z,u) * (x / y)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,21348,a(flip),b,23322,a)].">
      <j1 rule="hyper" parents="63 21348 23322"/>
    </justification>
  </clause>

  <clause id="23325">
    <literal><![CDATA[
      R(x \ L(x,y,z),u,w) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(545,a,23319,a),flip(a)].">
      <j1 rule="hyper" parents="545 23319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23326">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,L(x,y,z) \ u) \ u = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(23325(a,1),3164(a,1,1))].">
      <j1 rule="para" parents="23325 3164"/>
    </justification>
  </clause>

  <clause id="23327">
    <literal><![CDATA[
      T(x,y * ((z \ (z \ u)) \ (z \ w))) = T(x,y * ((L(u,v5,v6) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,23001,a(flip),b,23309,a)].">
      <j1 rule="hyper" parents="63 23001 23309"/>
    </justification>
  </clause>

  <clause id="23329">
    <literal><![CDATA[
      T(x,y * ((L(z,u,w) \ v5) * v6)) = T(x,y * (((v5 \ z) \ v5) * (v5 \ v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,22977,a(flip),b,23327,a),flip(a)].">
      <j1 rule="hyper" parents="63 22977 23327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23330">
    <literal><![CDATA[
      T(x,y * ((L(z,u,w) \ v5) * v6)) = T(x,y * ((v5 \ z) \ v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,23020,a(flip),b,23329,a),flip(a)].">
      <j1 rule="hyper" parents="347 23020 23329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23332">
    <literal><![CDATA[
      T(x,y * ((L(z,u,w) \ v5) * v6)) = T(x,y * ((z \ v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,22977,a(flip),b,23330,a),flip(a)].">
      <j1 rule="hyper" parents="347 22977 23330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23333">
    <literal><![CDATA[
      (x \ (x \ 1)) * ((L(y,z,u) \ y) * w) = w * ((L(y,z,u) \ y) / T(x * x,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,842,a(flip),b,23314,a),flip(a)].">
      <j1 rule="hyper" parents="63 842 23314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23334">
    <literal><![CDATA[
      (x \ (x \ 1)) * ((L(y,z,u) \ y) * w) = w * (L(y,z,u) \ (y / T(x * x,w)))
    ]]></literal>
    <justification jstring="[para(1107(a,1),23333(a,2,2))].">
      <j1 rule="para" parents="1107 23333"/>
    </justification>
  </clause>

  <clause id="23335">
    <literal><![CDATA[
      (x \ (x \ 1)) * ((L(y,z,u) \ y) * w) = w * T((x * x) \ (L(y,z,u) \ y),w)
    ]]></literal>
    <justification jstring="[para(21425(a,2),23334(a,2,2))].">
      <j1 rule="para" parents="21425 23334"/>
    </justification>
  </clause>

  <clause id="23336">
    <literal><![CDATA[
      (x \ (x \ 1)) * ((L(y,z,u) \ y) * w) = ((x * x) \ (L(y,z,u) \ y)) * w
    ]]></literal>
    <justification jstring="[hyper(347,a,111,a(flip),b,23335,a),flip(a)].">
      <j1 rule="hyper" parents="347 111 23335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23337">
    <literal><![CDATA[
      (x \ (x \ 1)) * ((L(y,z,u) \ y) * w) = (L(y,z,u) \ y) * ((x * x) \ w)
    ]]></literal>
    <justification jstring="[hyper(347,a,20785,a(flip),b,23336,a),flip(a)].">
      <j1 rule="hyper" parents="347 20785 23336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23338">
    <literal><![CDATA[
      (x * x) \ ((L(y,z,u) \ y) * w) = (L(y,z,u) \ y) * ((x * x) \ w)
    ]]></literal>
    <justification jstring="[hyper(981,a,23337,a)].">
      <j1 rule="hyper" parents="981 23337"/>
    </justification>
  </clause>

  <clause id="23339">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) * (x \ (x * a(y,z,u))) = (x \ a(y,z,u)) * (x * x)
    ]]></literal>
    <justification jstring="[hyper(23248,a,20587,a)].">
      <j1 rule="hyper" parents="23248 20587"/>
    </justification>
  </clause>

  <clause id="23340">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) * a(y,z,u) = (x \ a(y,z,u)) * (x * x)
    ]]></literal>
    <justification jstring="[hyper(620,a,23339,a)].">
      <j1 rule="hyper" parents="620 23339"/>
    </justification>
  </clause>

  <clause id="23342">
    <literal><![CDATA[
      (x \ a(y,z,u)) * (x * x) = (1 / x) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,23183,a(flip),b,23340,a),flip(a)].">
      <j1 rule="hyper" parents="63 23183 23340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23343">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) \ ((y / x) \ L(y,z,u)) = a(x,x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),23028(a,1,2))].">
      <j1 rule="para" parents="9 23028"/>
    </justification>
  </clause>

  <clause id="23345">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) \ ((y / x) \ L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,x,y * L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(23343(a,2),15027(a,1))].">
      <j1 rule="para" parents="23343 15027"/>
    </justification>
  </clause>

  <clause id="23346">
    <literal><![CDATA[
      a(x \ y,x,y \ L(y,z,u)) = a(x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(23345,a,14745,a),flip(a)].">
      <j1 rule="hyper" parents="23345 14745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23347">
    <literal><![CDATA[
      a(x \ y,x,y * L(y,z,u)) = a(x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(15027,a,23346,a)].">
      <j1 rule="hyper" parents="15027 23346"/>
    </justification>
  </clause>

  <clause id="23348">
    <literal><![CDATA[
      ((x * a(y,z,u)) * w) \ (x * w) = (w * (x * a(y,z,u))) \ (w * x)
    ]]></literal>
    <justification jstring="[para(255(a,1),23182(a,1,1,1,1))].">
      <j1 rule="para" parents="255 23182"/>
    </justification>
  </clause>

  <clause id="23349">
    <literal><![CDATA[
      x * ((x * x) \ (a(y,z,u) \ (1 / (x \ 1)))) = (a(y,z,u) \ (x \ 1)) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,207,a(flip),b,23276,a),flip(a)].">
      <j1 rule="hyper" parents="347 207 23276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23351">
    <literal><![CDATA[
      x * ((x * x) \ (a(y,z,u) \ x)) = (a(y,z,u) \ (x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(80(a,1),23349(a,1,2,2,2))].">
      <j1 rule="para" parents="80 23349"/>
    </justification>
  </clause>

  <clause id="23352">
    <literal><![CDATA[
      (a(x,y,z) \ (u \ 1)) * u = (u \ 1) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(525,a,23351,a),flip(a)].">
      <j1 rule="hyper" parents="525 23351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23353">
    <literal><![CDATA[
      a(x,y,z) \ ((z \ 1) * z) = (z \ 1) * (a(x,y,z) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,23121,a,b,23352,a)].">
      <j1 rule="hyper" parents="63 23121 23352"/>
    </justification>
  </clause>

  <clause id="23354">
    <literal><![CDATA[
      a(x,y,z) \ K(z \ 1,z) = (z \ 1) * (a(x,y,z) \ z)
    ]]></literal>
    <justification jstring="[para(290(a,2),23353(a,1,2))].">
      <j1 rule="para" parents="290 23353"/>
    </justification>
  </clause>

  <clause id="23355">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) * y,a(z,u,w),x) = L(K(a(z,u,w),x) * y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,10173,a(flip),b,23277,a),flip(a)].">
      <j1 rule="hyper" parents="347 10173 23277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23356">
    <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(20009(a,1),23355(a,2,1))].">
      <j1 rule="para" parents="20009 23355"/>
    </justification>
  </clause>

  <clause id="23357">
    <literal><![CDATA[
      L(1 * x,a(y,z,u),u) = L(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(12361(a,1),23356(a,1,1,1))].">
      <j1 rule="para" parents="12361 23356"/>
    </justification>
  </clause>

  <clause id="23358">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),a(z,u,w),y) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(12674(a,1),23356(a,1,1))].">
      <j1 rule="para" parents="12674 23356"/>
    </justification>
  </clause>

  <clause id="23359">
    <literal><![CDATA[
      L(x,a(y,z,u),u) = L(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),23357(a,1,1))].">
      <j1 rule="para" parents="7 23357"/>
    </justification>
  </clause>

  <clause id="23360">
    <literal><![CDATA[
      ((x / y) \ L(x,z,u)) * K(y,(x / y) \ L(x,z,u)) = (x \ L(x,z,u)) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(300(a,1),23030(a,2,2))].">
      <j1 rule="para" parents="300 23030"/>
    </justification>
  </clause>

  <clause id="23361">
    <literal><![CDATA[
      ((x / y) \ L(x,z,u)) * K(y,x \ (y * L(x,z,u))) = (x \ L(x,z,u)) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(7960(a,1),23360(a,1,2))].">
      <j1 rule="para" parents="7960 23360"/>
    </justification>
  </clause>

  <clause id="23362">
    <literal><![CDATA[
      ((x / y) \ L(x,z,u)) * K(y,L(x,z,u) * (y / x)) = (x \ L(x,z,u)) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(16991(a,1),23361(a,1,2))].">
      <j1 rule="para" parents="16991 23361"/>
    </justification>
  </clause>

  <clause id="23363">
    <literal><![CDATA[
      (x \ L(x,y,z)) / (u \ 1) = ((x / u) \ L(x,y,z)) * 1
    ]]></literal>
    <justification jstring="[para(23324(a,1),23362(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23324 23362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23364">
    <literal><![CDATA[
      (x \ L(x,y,z)) / (u \ 1) = (x / u) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,8,a(flip),b,23363,a),flip(a)].">
      <j1 rule="hyper" parents="347 8 23363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23365">
    <literal><![CDATA[
      (x \ L(x,y,z)) / (u \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      (x / u) \ L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(23363(a,2),141(a,1)),flip(b)].">
      <j1 rule="para" parents="23363 141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23367">
    <literal><![CDATA[
      (L(x,y,z) / u) \ L(L(x,y,z),w,v5) = L(x \ L(x,w,v5),y,z) / (u \ 1)
    ]]></literal>
    <justification jstring="[para(4638(a,1),23364(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4638 23364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23368">
    <literal><![CDATA[
      ((x / y) \ L(x,z,u)) * ((1 / (y \ 1)) \ (y \ 1)) = (x \ L(x,z,u)) / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(23364(a,1),6385(a,1,1))].">
      <j1 rule="para" parents="23364 6385"/>
    </justification>
  </clause>

  <clause id="23369">
    <literal><![CDATA[
      ((x / y) \ L(x,z,u)) * (y \ (y \ 1)) = (x \ L(x,z,u)) / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(80(a,1),23368(a,1,2,1))].">
      <j1 rule="para" parents="80 23368"/>
    </justification>
  </clause>

  <clause id="23370">
    <literal><![CDATA[
      ((x / y) \ L(x,z,u)) / (y * y) = (x \ L(x,z,u)) / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(913,a,23369,a)].">
      <j1 rule="hyper" parents="913 23369"/>
    </justification>
  </clause>

  <clause id="23371">
    <literal><![CDATA[
      (x / y) \ (L(x,z,u) / (y * y)) = (x \ L(x,z,u)) / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(817,a,23370,a)].">
      <j1 rule="hyper" parents="817 23370"/>
    </justification>
  </clause>

  <clause id="23372">
    <literal><![CDATA[
      (x / y) \ L(x / (y * y),z,u) = (x \ L(x,z,u)) / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3177(a,2),23371(a,1,2))].">
      <j1 rule="para" parents="3177 23371"/>
    </justification>
  </clause>

  <clause id="23373">
    <literal><![CDATA[
      (x \ L(x,y,z)) / ((u \ 1) \ 1) = u \ (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,22033,a(flip),b,23372,a),flip(a)].">
      <j1 rule="hyper" parents="63 22033 23372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23374">
    <literal><![CDATA[
      (x / (y \ 1)) \ L(x,z,u) = y \ (x \ L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(23365,a,23373,a)].">
      <j1 rule="hyper" parents="23365 23373"/>
    </justification>
  </clause>

  <clause id="23375">
    <literal><![CDATA[
      x / (((x \ L(x,y,z)) / u) \ 1) = L(x,y,z) / u
    ]]></literal>
    <justification jstring="[hyper(220,a,83,a(flip),b,23374,a),flip(a)].">
      <j1 rule="hyper" parents="220 83 23374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23376">
    <literal><![CDATA[
      (1 / x) \ (y \ L(y,z,u)) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(83(a,1),23374(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="83 23374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23377">
    <literal><![CDATA[
      (((L(x,y,z) / x) / (1 / u)) * ((1 / u) * x)) \ L(x,y,z) = a((x / u) \ L(x,y,z),1 / u,x)
    ]]></literal>
    <justification jstring="[para(23376(a,1),21591(a,2,1))].">
      <j1 rule="para" parents="23376 21591"/>
    </justification>
  </clause>

  <clause id="23378">
    <literal><![CDATA[
      (x * (a(y,z,u) \ 1)) * T(w,a(y,z,u) \ x) = w * ((a(y,z,u) \ 1) * T(x,1))
    ]]></literal>
    <justification jstring="[para(223(a,1),23090(a,1,2,2,2))].">
      <j1 rule="para" parents="223 23090"/>
    </justification>
  </clause>

  <clause id="23379">
    <literal><![CDATA[
      (x * (a(y,z,u) \ 1)) * T(w,x) = w * ((a(y,z,u) \ 1) * T(x,1))
    ]]></literal>
    <justification jstring="[para(23045(a,1),23378(a,1,2))].">
      <j1 rule="para" parents="23045 23378"/>
    </justification>
  </clause>

  <clause id="23380">
    <literal><![CDATA[
      (x * (a(y,z,u) \ 1)) * T(w,x) = w * ((a(y,z,u) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(223(a,1),23379(a,2,2,2))].">
      <j1 rule="para" parents="223 23379"/>
    </justification>
  </clause>

  <clause id="23382">
    <literal><![CDATA[
      (x * y) \ (x * ((a(z,u,w) \ 1) * y)) = R(a(z,u,w) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(23380(a,1),22301(a,1,2))].">
      <j1 rule="para" parents="23380 22301"/>
    </justification>
  </clause>

  <clause id="23383">
    <literal><![CDATA[
      L(T(a(x,y,z) \ 1,u),u,w) = R(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(881,a,23382,a)].">
      <j1 rule="hyper" parents="881 23382"/>
    </justification>
  </clause>

  <clause id="23384">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,u,w) = L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(20087(a,1),23383(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20087 23383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23385">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w \ 1) = R(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(2232,a,23384,a),flip(a)].">
      <j1 rule="hyper" parents="2232 23384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23386">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) * (u * w) = ((a(x,y,z) \ 1) * u) * w
    ]]></literal>
    <justification jstring="[hyper(133,a,23384,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="133 23384 20"/>
    </justification>
  </clause>

  <clause id="23388">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w \ 1) = L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,23384,a(flip),b,23385,a),flip(a)].">
      <j1 rule="hyper" parents="347 23384 23385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23389">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w \ 1) != v5
    ]]></literal>
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) = v5
    ]]></literal>
    <justification jstring="[para(23388(a,1),11399(a,1))].">
      <j1 rule="para" parents="23388 11399"/>
    </justification>
  </clause>

  <clause id="23390">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) = v5
    ]]></literal>
    <justification jstring="[para(23385(a,1),23389(a,1))].">
      <j1 rule="para" parents="23385 23389"/>
    </justification>
  </clause>

  <clause id="23391">
    <literal><![CDATA[
      (x / y) \ (y \ (a(z,u,w) * (y * (a(z,u,w) \ x)))) = L(y,a(z,u,w) \ x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(19985(a,2),23245(a,1,2,2))].">
      <j1 rule="para" parents="19985 23245"/>
    </justification>
  </clause>

  <clause id="23392">
    <literal><![CDATA[
      L(a(x,y,z) \ T(u,w),a(x,y,z),a(x,y,z) \ w) = w \ (u * (a(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[para(19984(a,1),23089(a,1,1,1))].">
      <j1 rule="para" parents="19984 23089"/>
    </justification>
  </clause>

  <clause id="23394">
    <literal><![CDATA[
      L(T(a(x,y,z) \ u,w),a(x,y,z),a(x,y,z) \ w) = w \ (u * (a(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[para(23175(a,2),23392(a,1,1))].">
      <j1 rule="para" parents="23175 23392"/>
    </justification>
  </clause>

  <clause id="23395">
    <literal><![CDATA[
      (((x \ L(x,y,z)) / (1 / u)) * ((1 / u) * x)) \ L(x,y,z) = a((x / u) \ L(x,y,z),1 / u,x)
    ]]></literal>
    <justification jstring="[para(3161(a,1),23377(a,1,1,1,1))].">
      <j1 rule="para" parents="3161 23377"/>
    </justification>
  </clause>

  <clause id="23396">
    <literal><![CDATA[
      (((x \ L(x,y,z)) / (u \ 1)) * ((u \ 1) * x)) \ L(x,y,z) = a((x / u) \ L(x,y,z),1 / u,x)
    ]]></literal>
    <justification jstring="[para(3515(a,1),23395(a,1,1))].">
      <j1 rule="para" parents="3515 23395"/>
    </justification>
  </clause>

  <clause id="23397">
    <literal><![CDATA[
      (((x / y) \ L(x,z,u)) * ((y \ 1) * x)) \ L(x,z,u) = a((x / y) \ L(x,z,u),1 / y,x)
    ]]></literal>
    <justification jstring="[para(23364(a,1),23396(a,1,1,1))].">
      <j1 rule="para" parents="23364 23396"/>
    </justification>
  </clause>

  <clause id="23398">
    <literal><![CDATA[
      K(x * L(x \ y,z,u),T(w,y)) = K(y,T(w,x * L(x \ y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(6202,a,23022,a),flip(a)].">
      <j1 rule="hyper" parents="6202 23022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23399">
    <literal><![CDATA[
      K(x * L(x \ y,z,u),T(w,y)) = K(y,T(w,y))
    ]]></literal>
    <justification jstring="[para(22926(a,1),23398(a,2,2))].">
      <j1 rule="para" parents="22926 23398"/>
    </justification>
  </clause>

  <clause id="23400">
    <literal><![CDATA[
      K(x * L(x \ y,z,u),T(w,y)) = K(y,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,5095,a(flip),b,23399,a),flip(a)].">
      <j1 rule="hyper" parents="347 5095 23399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23402">
    <literal><![CDATA[
      K(x * L(x \ y,z,u),w) = K(y,w)
    ]]></literal>
    <justification jstring="[hyper(17266,a,23400,a)].">
      <j1 rule="hyper" parents="17266 23400"/>
    </justification>
  </clause>

  <clause id="23404">
    <literal><![CDATA[
      K(x * L(y,z,u),w) = K(x * y,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),23402(a,1,1,2,1))].">
      <j1 rule="para" parents="9 23402"/>
    </justification>
  </clause>

  <clause id="23406">
    <literal><![CDATA[
      K(L(x,y,z) * u,w) = K(x * u,w)
    ]]></literal>
    <justification jstring="[para(737(a,1),23402(a,1,1))].">
      <j1 rule="para" parents="737 23402"/>
    </justification>
  </clause>

  <clause id="23408">
    <literal><![CDATA[
      K((x / y) * z,u) = K(x * (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,20962,a(flip),b,23404,a)].">
      <j1 rule="hyper" parents="63 20962 23404"/>
    </justification>
  </clause>

  <clause id="23410">
    <literal><![CDATA[
      K(x * (y \ (y / z)),u) = K(x * (z \ 1),u)
    ]]></literal>
    <justification jstring="[para(414(a,1),23404(a,1,1,2))].">
      <j1 rule="para" parents="414 23404"/>
    </justification>
  </clause>

  <clause id="23415">
    <literal><![CDATA[
      K(x * (L(x,y,z) \ u),w) = K(u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),23406(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 23406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23417">
    <literal><![CDATA[
      K(L(x,y,z) \ u,w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(1408(a,1),23415(a,1,1))].">
      <j1 rule="para" parents="1408 23415"/>
    </justification>
  </clause>

  <clause id="23421">
    <literal><![CDATA[
      K(L(x,y,z) \ (u * w),v5) = K((x \ u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,23161,a(flip),b,23417,a),flip(a)].">
      <j1 rule="hyper" parents="347 23161 23417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23425">
    <literal><![CDATA[
      K((x / y) \ z,T(u,y * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z / L(x / y,v5,v6),u) = w
    ]]></literal>
    <justification jstring="[para(23417(a,1),17099(a,1))].">
      <j1 rule="para" parents="23417 17099"/>
    </justification>
  </clause>

  <clause id="23427">
    <literal><![CDATA[
      K(x * (y \ z),T(u,x * y)) = K(z * (x / y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,13695,a(flip),b,23408,a),flip(a)].">
      <j1 rule="hyper" parents="63 13695 23408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23429">
    <literal><![CDATA[
      K(x * (y \ (y / z)),u) = K(x / z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,13226,a(flip),b,23410,a),flip(a)].">
      <j1 rule="hyper" parents="347 13226 23410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23430">
    <literal><![CDATA[
      K(x / (y \ z),u) = K(x * (z \ y),u)
    ]]></literal>
    <justification jstring="[para(80(a,1),23429(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="80 23429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23431">
    <literal><![CDATA[
      K((x / y) \ z,u) = K(y * (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(21055,a,23430,a)].">
      <j1 rule="hyper" parents="21055 23430"/>
    </justification>
  </clause>

  <clause id="23432">
    <literal><![CDATA[
      K(x * ((y \ z) \ u),w) = K(x * ((z \ y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(23185,a,23431,a),flip(a)].">
      <j1 rule="hyper" parents="23185 23431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23433">
    <literal><![CDATA[
      K(x * ((y \ z) \ u),T(w,y * (x * z))) = K(u / ((y \ z) / x),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,18527,a(flip),b,23431,a),flip(a)].">
      <j1 rule="hyper" parents="63 18527 23431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23435">
    <literal><![CDATA[
      K((L(x,y,z) \ u) * w,v5) = K((x \ u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,23161,a(flip),b,23421,a)].">
      <j1 rule="hyper" parents="63 23161 23421"/>
    </justification>
  </clause>

  <clause id="23436">
    <literal><![CDATA[
      T(x * K((y \ z) * u,x),x * ((L(y,w,v5) \ z) * u)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,(L(y,w,v5) \ z) * u,x) = v6
    ]]></literal>
    <justification jstring="[para(23435(a,1),8700(a,1,1,2))].">
      <j1 rule="para" parents="23435 8700"/>
    </justification>
  </clause>

  <clause id="23437">
    <literal><![CDATA[
      K(T(x,(y \ z) * u) * ((y \ z) * u),w) = K(((z \ y) \ u) * x,w)
    ]]></literal>
    <justification jstring="[hyper(19343,a,23432,a),flip(a)].">
      <j1 rule="hyper" parents="19343 23432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23438">
    <literal><![CDATA[
      K(x / L(y / z,u,w),v5) = K(z * (y \ x),T(v5,z * y))
    ]]></literal>
    <justification jstring="[hyper(23425,a,23431,a)].">
      <j1 rule="hyper" parents="23425 23431"/>
    </justification>
  </clause>

  <clause id="23440">
    <literal><![CDATA[
      K(x / L(y / z,u,w),v5) = K(x * (z / y),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,23427,a(flip),b,23438,a),flip(a)].">
      <j1 rule="hyper" parents="347 23427 23438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23441">
    <literal><![CDATA[
      K(x / (y / z),u) = K(x * (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(17129,a,23440,a)].">
      <j1 rule="hyper" parents="17129 23440"/>
    </justification>
  </clause>

  <clause id="23442">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,T(w,x * y)) = K(z / ((x \ y) / u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21114,a(flip),b,23433,a)].">
      <j1 rule="hyper" parents="63 21114 23433"/>
    </justification>
  </clause>

  <clause id="23443">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,w) = K(((y \ x) * z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(10389,a,23437,a),flip(a)].">
      <j1 rule="hyper" parents="10389 23437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23444">
    <literal><![CDATA[
      K(((x \ y) * z) * u,T(w,y * x)) = K(z / ((y \ x) / u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,23442,a(flip),b,23443,a),flip(a)].">
      <j1 rule="hyper" parents="63 23442 23443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23445">
    <literal><![CDATA[
      K(((x \ y) * z) * u,T(w,y * x)) = K(z * (u / (y \ x)),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,23441,a(flip),b,23444,a),flip(a)].">
      <j1 rule="hyper" parents="347 23441 23444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23446">
    <literal><![CDATA[
      K((x \ y) * (z * u),T(w,y * x)) = K(z * (u / (y \ x)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,23159,a(flip),b,23445,a)].">
      <j1 rule="hyper" parents="63 23159 23445"/>
    </justification>
  </clause>

  <clause id="23447">
    <literal><![CDATA[
      K((x * y) * (z \ u),w) = K(x * (y / (u \ z)),w)
    ]]></literal>
    <justification jstring="[hyper(13275,a,23446,a)].">
      <j1 rule="hyper" parents="13275 23446"/>
    </justification>
  </clause>

  <clause id="23448">
    <literal><![CDATA[
      K(x * (y / (z \ u)),w) = K(x * (y * (u \ z)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,23159,a(flip),b,23447,a),flip(a)].">
      <j1 rule="hyper" parents="63 23159 23447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23449">
    <literal><![CDATA[
      T(x * K((y \ z) * u,x),x * ((y \ z) * u)) = L(x,(L(y,w,v5) \ z) * u,x)
    ]]></literal>
    <justification jstring="[hyper(23436,a,23332,a),flip(a)].">
      <j1 rule="hyper" parents="23436 23332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23450">
    <literal><![CDATA[
      L(x,(L(y,z,u) \ w) * v5,x) = L(x,(y \ w) * v5,x)
    ]]></literal>
    <justification jstring="[hyper(8700,a,23449,a),flip(a)].">
      <j1 rule="hyper" parents="8700 23449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23451">
    <literal><![CDATA[
      L(x,(L(y,z,u) \ w) * v5,x) = L(x,w * (y * v5),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,12202,a(flip),b,23450,a),flip(a)].">
      <j1 rule="hyper" parents="347 12202 23450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23452">
    <literal><![CDATA[
      K(T(x,y),z * L(z \ y,u,w)) = K(x,T(y,z * L(z \ y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(7792,a,23023,a),flip(a)].">
      <j1 rule="hyper" parents="7792 23023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23453">
    <literal><![CDATA[
      K(T(x,y),z * L(z \ y,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(21094(a,1),23452(a,2,2))].">
      <j1 rule="para" parents="21094 23452"/>
    </justification>
  </clause>

  <clause id="23454">
    <literal><![CDATA[
      K(x,T(y * L(y \ z,u,w),z)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(7488,a,23453,a)].">
      <j1 rule="hyper" parents="7488 23453"/>
    </justification>
  </clause>

  <clause id="23455">
    <literal><![CDATA[
      K(x,y * L(y \ z,u,w)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(20077(a,1),23454(a,1,2))].">
      <j1 rule="para" parents="20077 23454"/>
    </justification>
  </clause>

  <clause id="23458">
    <literal><![CDATA[
      K(x,L(y,z,u) * w) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(737(a,1),23455(a,1,2))].">
      <j1 rule="para" parents="737 23455"/>
    </justification>
  </clause>

  <clause id="23462">
    <literal><![CDATA[
      K(x,y \ L(z,u,w)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3341(a,1),23455(a,1,2))].">
      <j1 rule="para" parents="3341 23455"/>
    </justification>
  </clause>

  <clause id="23463">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ w)) = K(x,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),23458(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 23458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23474">
    <literal><![CDATA[
      K(x,L(y,z,u) \ (y * w)) = K(x,w)
    ]]></literal>
    <justification jstring="[para(1407(a,2),23463(a,1,2))].">
      <j1 rule="para" parents="1407 23463"/>
    </justification>
  </clause>

  <clause id="23475">
    <literal><![CDATA[
      K(x,L(y,z,u) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(1408(a,1),23463(a,1,2))].">
      <j1 rule="para" parents="1408 23463"/>
    </justification>
  </clause>

  <clause id="23479">
    <literal><![CDATA[
      (x \ (y \ L(y,z,u))) \ K(x \ (y \ L(y,z,u)),x) = 1 / (x \ (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(23474(a,1),6479(a,1,2))].">
      <j1 rule="para" parents="23474 6479"/>
    </justification>
  </clause>

  <clause id="23488">
    <literal><![CDATA[
      (L(x,y,z) \ K(u,x \ 1)) * u = u * (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(23475(a,1),5054(a,1,1,2))].">
      <j1 rule="para" parents="23475 5054"/>
    </justification>
  </clause>

  <clause id="23490">
    <literal><![CDATA[
      1 / (x \ (y \ L(y,z,u))) = ((y \ L(y,z,u)) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(5732,a,23479,a),flip(a)].">
      <j1 rule="hyper" parents="5732 23479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23491">
    <literal><![CDATA[
      (x * y) / ((L(x,z,u) * (y * (w * w))) / (w * w)) = ((w * w) \ ((L(x,z,u) * y) \ (x * y))) * (w * w)
    ]]></literal>
    <justification jstring="[para(775(a,1),22906(a,2,1))].">
      <j1 rule="para" parents="775 22906"/>
    </justification>
  </clause>

  <clause id="23492">
    <literal><![CDATA[
      R(x,(y * ((z * T(u,T(w,z))) \ T(u,T(w,z)))) * v5,v6) = R(x,(y * (u / T(z * u,K(z,w)))) * v5,v6)
    ]]></literal>
    <justification jstring="[para(6810(a,2),22912(a,2,2,1,2,2))].">
      <j1 rule="para" parents="6810 22912"/>
    </justification>
  </clause>

  <clause id="23493">
    <literal><![CDATA[
      (x / (a(y,z,u) \ w)) * ((a(y,z,u) \ w) * a(y,z,u)) = w * ((a(y,z,u) \ w) \ T(x,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(10159,a,23104,a)].">
      <j1 rule="hyper" parents="10159 23104"/>
    </justification>
  </clause>

  <clause id="23494">
    <literal><![CDATA[
      x * ((a(y,z,u) \ x) \ T(w,a(y,z,u))) = (w / (a(y,z,u) \ x)) * x
    ]]></literal>
    <justification jstring="[para(19986(a,1),23493(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19986 23493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23495">
    <literal><![CDATA[
      (x / (a(y,z,u) \ w)) * w = w * ((a(y,z,u) \ w) \ x)
    ]]></literal>
    <justification jstring="[para(19939(a,1),23494(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="19939 23494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23496">
    <literal><![CDATA[
      (x * (((y * y) \ z) * a(u,w,v5))) \ ((a(u,w,v5) * x) * ((y * y) \ z)) = a(x / (y * y),a(u,w,v5),z)
    ]]></literal>
    <justification jstring="[para(803(a,1),23196(a,1,2))].">
      <j1 rule="para" parents="803 23196"/>
    </justification>
  </clause>

  <clause id="23497">
    <literal><![CDATA[
      (x * y) / ((L(x,z,u) * (y * (w * w))) / (w * w)) = T((L(x,z,u) * y) \ (x * y),w * w)
    ]]></literal>
    <justification jstring="[hyper(347,a,726,a(flip),b,23491,a),flip(a)].">
      <j1 rule="hyper" parents="347 726 23491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23498">
    <literal><![CDATA[
      (x * y) / ((L(x,z,u) * y) / ((w * w) / (w * w))) = T((L(x,z,u) * y) \ (x * y),w * w)
    ]]></literal>
    <justification jstring="[para(907(a,1),23497(a,1,2))].">
      <j1 rule="para" parents="907 23497"/>
    </justification>
  </clause>

  <clause id="23499">
    <literal><![CDATA[
      T((L(x,y,z) * u) \ (x * u),w * w) = (x * u) / ((L(x,y,z) * u) / 1)
    ]]></literal>
    <justification jstring="[para(77(a,1),23498(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="77 23498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23501">
    <literal><![CDATA[
      T((L(x,y,z) * u) \ (x * u),w * w) = (x * u) / (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(78(a,1),23499(a,2,2))].">
      <j1 rule="para" parents="78 23499"/>
    </justification>
  </clause>

  <clause id="23502">
    <literal><![CDATA[
      (x * y) / (L(x,z,u) * y) != w
    ]]></literal>
    <literal><![CDATA[
      (L(x,z,u) * y) \ (x * y) = w
    ]]></literal>
    <justification jstring="[para(23501(a,1),15534(a,1))].">
      <j1 rule="para" parents="23501 15534"/>
    </justification>
  </clause>

  <clause id="23503">
    <literal><![CDATA[
      R(x,(y * ((z * T(u,T(w,z))) \ T(u,T(w,z)))) * v5,v6) = R(x,(y * (T(z * u,K(z,w)) \ u)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,22497,a(flip),b,23492,a),flip(a)].">
      <j1 rule="hyper" parents="347 22497 23492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23504">
    <literal><![CDATA[
      a(x / (y * y),a(z,u,w),v5) = a(x,a(z,u,w),(y * y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(21150,a,23496,a),flip(a)].">
      <j1 rule="hyper" parents="21150 23496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23505">
    <literal><![CDATA[
      a(x / (y * y),a(z,u,w),v5) = a(x,a(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,14948,a(flip),b,23504,a),flip(a)].">
      <j1 rule="hyper" parents="347 14948 23504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23507">
    <literal><![CDATA[
      a(x \ 1,a(y,z,u),w) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(300(a,1),23505(a,1,1))].">
      <j1 rule="para" parents="300 23505"/>
    </justification>
  </clause>

  <clause id="23508">
    <literal><![CDATA[
      R(x,(y * ((z * T(u,T(w,z))) \ T(u,T(w,z)))) * v5,v6) = R(x,(y * ((u * z) \ T(u,T(z,w)))) * v5,v6)
    ]]></literal>
    <justification jstring="[para(21219(a,1),23503(a,2,2,1,2))].">
      <j1 rule="para" parents="21219 23503"/>
    </justification>
  </clause>

  <clause id="23509">
    <literal><![CDATA[
      R(x,(y * ((z * T(u,T(w,z))) \ T(u,T(w,z)))) * v5,v6) = R(x,(y * ((u * z) \ u)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,22498,a(flip),b,23508,a),flip(a)].">
      <j1 rule="hyper" parents="347 22498 23508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23511">
    <literal><![CDATA[
      R(x,(y * ((z * T(u,T(w,z))) \ T(u,T(w,z)))) * v5,v6) = R(x,(y * (u \ (u / z))) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,22554,a(flip),b,23509,a),flip(a)].">
      <j1 rule="hyper" parents="347 22554 23509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23512">
    <literal><![CDATA[
      R(x,(y * ((z * u) \ T(u,K(z,w)))) * v5,v6) = R(x,(y * (u \ (u / z))) * v5,v6)
    ]]></literal>
    <justification jstring="[para(21986(a,1),23511(a,1,2,1,2))].">
      <j1 rule="para" parents="21986 23511"/>
    </justification>
  </clause>

  <clause id="23513">
    <literal><![CDATA[
      R(x,(y * ((z * u) \ u)) * w,v5) = R(x,(y * (u \ (u / z))) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22498,a(flip),b,23512,a)].">
      <j1 rule="hyper" parents="63 22498 23512"/>
    </justification>
  </clause>

  <clause id="23515">
    <literal><![CDATA[
      T(K(x,y) * (z * L(x,u,w)),L(T(x,y),u,w)) = T(z,x) * L(R(T(x,y),z,x),u,w)
    ]]></literal>
    <justification jstring="[para(10953(a,1),21210(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10953 21210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23516">
    <literal><![CDATA[
      T(K(x,y) * (z * L(x,u,w)),T(x,y)) = T(z,x) * L(R(T(x,y),z,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(20487,a,23515,a)].">
      <j1 rule="hyper" parents="20487 23515"/>
    </justification>
  </clause>

  <clause id="23517">
    <literal><![CDATA[
      T(x,y) * L(R(T(y,z),x,y),u,w) = T((x * L(y,u,w)) * K(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(7798,a,23516,a),flip(a)].">
      <j1 rule="hyper" parents="7798 23516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23519">
    <literal><![CDATA[
      T(x,y) * L(R(T(y,z),x,y),u,w) = T(x * (L(y,u,w) * K(y,z)),y)
    ]]></literal>
    <justification jstring="[para(10087(a,1),23517(a,2,1))].">
      <j1 rule="para" parents="10087 23517"/>
    </justification>
  </clause>

  <clause id="23520">
    <literal><![CDATA[
      T(x,y) * L(R(T(y,z),x,y),u,w) = T(x * L(y * K(y,z),u,w),y)
    ]]></literal>
    <justification jstring="[para(21247(a,2),23519(a,2,1,2))].">
      <j1 rule="para" parents="21247 23519"/>
    </justification>
  </clause>

  <clause id="23521">
    <literal><![CDATA[
      T(x,y) * L(R(T(y,z),x,y),u,w) = T(x * L(T(y,z),u,w),y)
    ]]></literal>
    <justification jstring="[para(4929(a,2),23520(a,2,1,2,1))].">
      <j1 rule="para" parents="4929 23520"/>
    </justification>
  </clause>

  <clause id="23522">
    <literal><![CDATA[
      x * T(y * L(T(x,z),u,w),x) = (y * x) * L(T(x,z),u,w)
    ]]></literal>
    <justification jstring="[para(23521(a,1),10267(a,1,2))].">
      <j1 rule="para" parents="23521 10267"/>
    </justification>
  </clause>

  <clause id="23523">
    <literal><![CDATA[
      (x * L(T(y,z),u,w)) * y = (x * y) * L(T(y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(315,a,23522,a)].">
      <j1 rule="hyper" parents="315 23522"/>
    </justification>
  </clause>

  <clause id="23524">
    <literal><![CDATA[
      R(x,K(y,T(z,u)) / w,L(K(y,T(z,u)) / w,w,u)) = R(x,u \ (K(y,z) * (u / w)),w \ K(y,T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,20126,a(flip),b,21294,a),flip(a)].">
      <j1 rule="hyper" parents="347 20126 21294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23525">
    <literal><![CDATA[
      L(x,y,(z \ u) \ (L(w,(z \ T(u,v5)) \ v6,z \ T(u,v5)) * v6)) = L(x,y,((z \ T(u,v5)) \ v6) * w)
    ]]></literal>
    <justification jstring="[hyper(347,a,21466,a(flip),b,21554,a),flip(a)].">
      <j1 rule="hyper" parents="347 21466 21554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23527">
    <literal><![CDATA[
      L(x,y,(z \ u) \ (L(w,(z \ T(u,v5)) \ v6,z \ u) * v6)) = L(x,y,((z \ T(u,v5)) \ v6) * w)
    ]]></literal>
    <justification jstring="[para(21472(a,1),23525(a,1,3,2,1))].">
      <j1 rule="para" parents="21472 23525"/>
    </justification>
  </clause>

  <clause id="23529">
    <literal><![CDATA[
      L(x,y,(z \ u) \ (L(w,(z \ u) \ v5,z \ u) * v5)) = L(x,y,((z \ T(u,v6)) \ v5) * w)
    ]]></literal>
    <justification jstring="[para(21635(a,1),23527(a,1,3,2,1))].">
      <j1 rule="para" parents="21635 23527"/>
    </justification>
  </clause>

  <clause id="23530">
    <literal><![CDATA[
      L(x,y,((z \ T(u,w)) \ v5) * v6) = L(x,y,((z \ u) \ v5) * T(v6,v5))
    ]]></literal>
    <justification jstring="[para(874(a,1),23529(a,1,3)),flip(a)].">
      <j1 rule="para" parents="874 23529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23532">
    <literal><![CDATA[
      L(x,y,((z \ T(u,w)) \ v5) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y,((z \ u) \ v5) * v6) = v7
    ]]></literal>
    <justification jstring="[para(23530(a,2),21516(a,1))].">
      <j1 rule="para" parents="23530 21516"/>
    </justification>
  </clause>

  <clause id="23534">
    <literal><![CDATA[
      (R(x,y,z) / (x * x)) \ K(T(x \ (x \ R(x,y,z)),x),x * x) = (x \ (R(x,y,z) * (1 / x))) \ 1
    ]]></literal>
    <justification jstring="[para(3846(a,1),21943(a,2,1,2))].">
      <j1 rule="para" parents="3846 21943"/>
    </justification>
  </clause>

  <clause id="23535">
    <literal><![CDATA[
      (R(x,y,z) / (x * x)) \ K(T(x \ (x \ R(x,y,z)),x),x * x) = ((x \ R(x,y,z)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(1761(a,1),23534(a,2,1))].">
      <j1 rule="para" parents="1761 23534"/>
    </justification>
  </clause>

  <clause id="23536">
    <literal><![CDATA[
      (x \ (x \ R(x,y,z))) \ K(T(x \ (x \ R(x,y,z)),x),x * x) = ((x \ R(x,y,z)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(1777(a,1),23535(a,1,1))].">
      <j1 rule="para" parents="1777 23535"/>
    </justification>
  </clause>

  <clause id="23537">
    <literal><![CDATA[
      (x \ (x \ R(x,y,z))) \ K((x * x) \ R(x,y,z),x * x) = ((x \ R(x,y,z)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(3714(a,1),23536(a,1,2,1))].">
      <j1 rule="para" parents="3714 23536"/>
    </justification>
  </clause>

  <clause id="23538">
    <literal><![CDATA[
      (x \ (x \ R(x,y,z))) \ K(R(x,y,z),x * x) = ((x \ R(x,y,z)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(5540(a,1),23537(a,1,2))].">
      <j1 rule="para" parents="5540 23537"/>
    </justification>
  </clause>

  <clause id="23539">
    <literal><![CDATA[
      (x \ (x \ R(x,y,z))) \ K(x,x * x) = ((x \ R(x,y,z)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(20284(a,1),23538(a,1,2))].">
      <j1 rule="para" parents="20284 23538"/>
    </justification>
  </clause>

  <clause id="23540">
    <literal><![CDATA[
      (x * x) * (R(x,y,z) \ K(x,x * x)) = ((x \ R(x,y,z)) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,1779,a(flip),b,23539,a)].">
      <j1 rule="hyper" parents="63 1779 23539"/>
    </justification>
  </clause>

  <clause id="23542">
    <literal><![CDATA[
      L(x \ R(x,y,z \ ((u * w) * v5)),x,y * (z \ ((u * w) * v5))) = a(x,y,z \ ((u * T(w,v6)) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,21605,a(flip),b,22201,a)].">
      <j1 rule="hyper" parents="63 21605 22201"/>
    </justification>
  </clause>

  <clause id="23544">
    <literal><![CDATA[
      a(x,y,z \ ((u * T(w,v5)) * v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ ((u * w) * v6)) = v7
    ]]></literal>
    <justification jstring="[para(23542(a,1),14334(a,1))].">
      <j1 rule="para" parents="23542 14334"/>
    </justification>
  </clause>

  <clause id="23545">
    <literal><![CDATA[
      R(x,y,L(z,z,u \ ((u \ w) \ R(u,v5,u))) * (w \ u)) = R(x,y,(z \ 1) \ (u \ ((u \ w) \ R(u,v5,u))))
    ]]></literal>
    <justification jstring="[hyper(347,a,20126,a(flip),b,22294,a),flip(a)].">
      <j1 rule="hyper" parents="347 20126 22294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23546">
    <literal><![CDATA[
      R(x,K(y,T(z,u)) / w,L(K(y,T(z,u)) / w,w,u)) = R(x,u \ (K(y,z) * (u / w)),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,22086,a(flip),b,23524,a),flip(a)].">
      <j1 rule="hyper" parents="347 22086 23524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23548">
    <literal><![CDATA[
      R(x,K(y,T(z,u)) / w,L(K(y,T(z,u)) / w,w,u)) = R(x,u \ (u / w),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,22418,a(flip),b,23546,a),flip(a)].">
      <j1 rule="hyper" parents="347 22418 23546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23550">
    <literal><![CDATA[
      R(x,K(y,T(z,u)) / w,u \ (K(y,z) * (u / w))) = R(x,u \ (u / w),w)
    ]]></literal>
    <justification jstring="[para(21293(a,1),23548(a,1,3))].">
      <j1 rule="para" parents="21293 23548"/>
    </justification>
  </clause>

  <clause id="23551">
    <literal><![CDATA[
      R(x,K(y,T(z,u)) / w,u \ (u / w)) = R(x,u \ (u / w),w)
    ]]></literal>
    <justification jstring="[hyper(22095,a,23550,a)].">
      <j1 rule="hyper" parents="22095 23550"/>
    </justification>
  </clause>

  <clause id="23553">
    <literal><![CDATA[
      R(x,y \ K(z,T(u,w)),w \ (w / y)) = R(x,w \ (w / y),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,20555,a(flip),b,23551,a)].">
      <j1 rule="hyper" parents="63 20555 23551"/>
    </justification>
  </clause>

  <clause id="23555">
    <literal><![CDATA[
      R(x,y \ (y / z),z) = R(x,z,y \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(63,a,22436,a(flip),b,23553,a),flip(a)].">
      <j1 rule="hyper" parents="63 22436 23553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23557">
    <literal><![CDATA[
      R(x,y \ (z \ y),z) = R(x,z,y \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(22443,a,23555,a)].">
      <j1 rule="hyper" parents="22443 23555"/>
    </justification>
  </clause>

  <clause id="23558">
    <literal><![CDATA[
      R(x,y \ (z \ y),z) = R(x,z,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(347,a,22068,a(flip),b,23557,a),flip(a)].">
      <j1 rule="hyper" parents="347 22068 23557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23559">
    <literal><![CDATA[
      R(x,y,L(z,z,u \ ((u \ w) \ R(u,v5,u))) * (w \ u)) = R(x,y,z \ (u \ ((u \ w) \ R(u,v5,u))))
    ]]></literal>
    <justification jstring="[hyper(347,a,2241,a(flip),b,23545,a),flip(a)].">
      <j1 rule="hyper" parents="347 2241 23545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23560">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) * T(v5,T(u * T(w,v6),v7)))) = L(x,y,z \ (v5 * (u * T(w,v6))))
    ]]></literal>
    <justification jstring="[hyper(21517,a,21595,a),flip(a)].">
      <j1 rule="hyper" parents="21517 21595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23562">
    <literal><![CDATA[
      L(x,y,z \ (u * (w * T(v5,v6)))) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ ((w * v5) * u)) = v7
    ]]></literal>
    <justification jstring="[para(23560(a,1),21532(a,1))].">
      <j1 rule="para" parents="23560 21532"/>
    </justification>
  </clause>

  <clause id="23563">
    <literal><![CDATA[
      (K(x,y) * ((z * u) * w)) / (L(u,K(x,y),T(z,K(y,x))) * w) = R(K(x,y) * z,L(u,K(x,y),T(z,K(y,x))),w)
    ]]></literal>
    <justification jstring="[para(20008(a,1),21325(a,1,1))].">
      <j1 rule="para" parents="20008 21325"/>
    </justification>
  </clause>

  <clause id="23564">
    <literal><![CDATA[
      T(x,y \ L(y,z,u)) * ((L(y,z,u) * L(y \ 1,z,u)) \ w) = ((L(y,z,u) * L(y \ 1,z,u)) \ x) * w
    ]]></literal>
    <justification jstring="[para(1295(a,1),22938(a,1,1,2))].">
      <j1 rule="para" parents="1295 22938"/>
    </justification>
  </clause>

  <clause id="23566">
    <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="[para(20076(a,1),23564(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20076 23564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23567">
    <literal><![CDATA[
      x / (L(y,z,u) * L(y \ 1,z,u)) = (L(y,z,u) * L(y \ 1,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(131,a,188,a(flip),b,23566,a)].">
      <j1 rule="hyper" parents="131 188 23566"/>
    </justification>
  </clause>

  <clause id="23568">
    <literal><![CDATA[
      (x * ((L(y,z,u) * L(y \ 1,z,u)) \ w)) \ ((L(y,z,u) * L(y \ 1,z,u)) \ (x * w)) = a(L(y,z,u) * L(y \ 1,z,u),(L(y,z,u) * L(y \ 1,z,u)) \ x,w)
    ]]></literal>
    <justification jstring="[para(23566(a,1),14704(a,1,1))].">
      <j1 rule="para" parents="23566 14704"/>
    </justification>
  </clause>

  <clause id="23569">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) \ (u * w) = u * (w / (L(x,y,z) * L(x \ 1,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,12347,a(flip),b,23567,a),flip(a)].">
      <j1 rule="hyper" parents="63 12347 23567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23570">
    <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="[para(23567(a,1),23569(a,2,2))].">
      <j1 rule="para" parents="23567 23569"/>
    </justification>
  </clause>

  <clause id="23571">
    <literal><![CDATA[
      R(K(x,y) * z,L(u,K(x,y),T(z,K(y,x))),w) = (K(x,y) * ((z * u) * w)) / (u * w)
    ]]></literal>
    <justification jstring="[para(20075(a,1),23563(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20075 23563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23572">
    <literal><![CDATA[
      (K(x,y) * ((z * u) * w)) / (u * w) = R(K(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(20075(a,1),23571(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20075 23571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23573">
    <literal><![CDATA[
      K(x,y) * (((z * u) * w) / (u * w)) = R(K(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,20088,a(flip),b,23572,a)].">
      <j1 rule="hyper" parents="63 20088 23572"/>
    </justification>
  </clause>

  <clause id="23574">
    <literal><![CDATA[
      R(K(x,y) * z,u,w) = K(x,y) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),23573(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 23573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23576">
    <literal><![CDATA[
      x * R(K(x,y) * z,u,w) = T(x,y) * R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(134,a,23574,a,b,5157,a)].">
      <j1 rule="hyper" parents="134 23574 5157"/>
    </justification>
  </clause>

  <clause id="23577">
    <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(4149(a,2),23574(a,1,1))].">
      <j1 rule="para" parents="4149 23574"/>
    </justification>
  </clause>

  <clause id="23579">
    <literal><![CDATA[
      R(K(x,y) * z,u,w) \ v5 = R(z,u,w) \ (K(y,x) * v5)
    ]]></literal>
    <justification jstring="[para(23574(a,2),20003(a,1,1))].">
      <j1 rule="para" parents="23574 20003"/>
    </justification>
  </clause>

  <clause id="23580">
    <literal><![CDATA[
      (x \ 1) * R(K(y,z) * u,w,v5) = (x \ K(y,z)) * R(u,w,v5)
    ]]></literal>
    <justification jstring="[para(23574(a,2),20815(a,1,2))].">
      <j1 rule="para" parents="23574 20815"/>
    </justification>
  </clause>

  <clause id="23581">
    <literal><![CDATA[
      (x * (R(x,y,z) \ u)) * R(K(w,v5) * x,y,z) = u * (K(w,v5) * x)
    ]]></literal>
    <justification jstring="[para(23574(a,2),21426(a,1,2))].">
      <j1 rule="para" parents="23574 21426"/>
    </justification>
  </clause>

  <clause id="23582">
    <literal><![CDATA[
      ((x * (K(x,y) * z)) * (x \ 1)) * x = T(x,y) * R(z,x,x)
    ]]></literal>
    <justification jstring="[hyper(917,a,23576,a)].">
      <j1 rule="hyper" parents="917 23576"/>
    </justification>
  </clause>

  <clause id="23583">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ z,u,w) = x * R(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(5159(a,1),23576(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5159 23576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23584">
    <literal><![CDATA[
      ((K(x,y) * z) * (R(z,u,w) \ (K(y,x) * (v5 * (x * y))))) * R(K(x,y) * z,u,w) = (v5 * (T(x,y) * y)) * z
    ]]></literal>
    <justification jstring="[para(23579(a,1),21194(a,1,1,2))].">
      <j1 rule="para" parents="23579 21194"/>
    </justification>
  </clause>

  <clause id="23586">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (y * z),u,w) = y * (x * R(x \ z,u,w))
    ]]></literal>
    <justification jstring="[para(23583(a,1),1635(a,2,2))].">
      <j1 rule="para" parents="23583 1635"/>
    </justification>
  </clause>

  <clause id="23587">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = y * (x * R(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(23583(a,1),2153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23583 2153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23588">
    <literal><![CDATA[
      ((T(x,y) * z) * (x \ 1)) * x = T(x,y) * R(z,x,x)
    ]]></literal>
    <justification jstring="[para(4943(a,1),23582(a,1,1,1))].">
      <j1 rule="para" parents="4943 23582"/>
    </justification>
  </clause>

  <clause id="23589">
    <literal><![CDATA[
      R(x,y * (((T(z,u) * w) * (T(z,v5) \ 1)) * z),v6) = R(x,y * (T(z,u) * R(w,z,z)),v6)
    ]]></literal>
    <justification jstring="[para(23588(a,1),22466(a,2,2,2))].">
      <j1 rule="para" parents="23588 22466"/>
    </justification>
  </clause>

  <clause id="23590">
    <literal><![CDATA[
      (x \ K(y,z)) * R((u \ K(y,z)) \ w,v5,v6) = (x \ 1) * R((u \ 1) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(20833(a,1),23580(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20833 23580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23592">
    <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),23586(a,1,2,1,2))].">
      <j1 rule="para" parents="10 23586"/>
    </justification>
  </clause>

  <clause id="23595">
    <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(7355(a,1),23577(a,2,2,1))].">
      <j1 rule="para" parents="7355 23577"/>
    </justification>
  </clause>

  <clause id="23596">
    <literal><![CDATA[
      R(T(K(x,y),z) * z,u,w) = R(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,268,a(flip),b,23595,a),flip(a)].">
      <j1 rule="hyper" parents="347 268 23595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23597">
    <literal><![CDATA[
      R(x * K(y,z),u,w) = R(x,u,w) * K(y,z)
    ]]></literal>
    <justification jstring="[para(7358(a,1),23596(a,1,1))].">
      <j1 rule="para" parents="7358 23596"/>
    </justification>
  </clause>

  <clause id="23601">
    <literal><![CDATA[
      R(x * K(y,z),u,w) * v5 = R(x,u,w) * (K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(23597(a,2),20151(a,1,1))].">
      <j1 rule="para" parents="23597 20151"/>
    </justification>
  </clause>

  <clause id="23602">
    <literal><![CDATA[
      x \ R(y * K(z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      (x \ R(y,w,v5)) * K(z,u) = v6
    ]]></literal>
    <justification jstring="[para(23597(a,2),20112(a,1,2))].">
      <j1 rule="para" parents="23597 20112"/>
    </justification>
  </clause>

  <clause id="23603">
    <literal><![CDATA[
      K(x,y) * R(z * K(y,T(z,x)),u,w) = (y * R(z,u,w)) / T(y,x)
    ]]></literal>
    <justification jstring="[para(23597(a,2),20434(a,1,2))].">
      <j1 rule="para" parents="23597 20434"/>
    </justification>
  </clause>

  <clause id="23604">
    <literal><![CDATA[
      L(x,y,R(z * K(u,w),v5,v6)) = L(x,y,R(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(23597(a,2),21459(a,1,3))].">
      <j1 rule="para" parents="23597 21459"/>
    </justification>
  </clause>

  <clause id="23606">
    <literal><![CDATA[
      (x / y) * R(y * K(y,x),z,u) = (R(y,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(23597(a,2),22003(a,1,2))].">
      <j1 rule="para" parents="23597 22003"/>
    </justification>
  </clause>

  <clause id="23607">
    <literal><![CDATA[
      L(x,y * L(R(R(z,u,z) * K(w,v5),v6,v7),u,z),v8) = L(x,R(z,v6,v7) * y,v8)
    ]]></literal>
    <justification jstring="[para(23597(a,2),21972(a,1,2,2,1))].">
      <j1 rule="para" parents="23597 21972"/>
    </justification>
  </clause>

  <clause id="23608">
    <literal><![CDATA[
      R(x,y,R(z * K(u,w),v5,v6)) = R(x,y,R(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(23597(a,2),22056(a,1,3))].">
      <j1 rule="para" parents="23597 22056"/>
    </justification>
  </clause>

  <clause id="23609">
    <literal><![CDATA[
      L(x,y,(z * u) \ ((z * w) * u)) = L(x,y,R(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(20891,a,23604,a)].">
      <j1 rule="hyper" parents="20891 23604"/>
    </justification>
  </clause>

  <clause id="23611">
    <literal><![CDATA[
      R(x,y,(z * u) \ ((z * w) * u)) = R(x,y,R(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(20898,a,23608,a)].">
      <j1 rule="hyper" parents="20898 23608"/>
    </justification>
  </clause>

  <clause id="23612">
    <literal><![CDATA[
      L(x,y,(z * T(u,T(z * w,v5))) \ T(u * (z * w),K(z * w,v5))) = L(x,y,R(w,z,T(u,T(z * w,v5))))
    ]]></literal>
    <justification jstring="[para(6060(a,2),23609(a,1,3,2))].">
      <j1 rule="para" parents="6060 23609"/>
    </justification>
  </clause>

  <clause id="23613">
    <literal><![CDATA[
      R(x,y,R(z,u,w)) = R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,22242,a(flip),b,23611,a),flip(a)].">
      <j1 rule="hyper" parents="63 22242 23611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23614">
    <literal><![CDATA[
      R(x,y,(z * u) \ ((w * u) * z)) = R(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,22204,a,b,23613,a)].">
      <j1 rule="hyper" parents="63 22204 23613"/>
    </justification>
  </clause>

  <clause id="23615">
    <literal><![CDATA[
      R(x,y,R(L(z,u,w),v5,v6)) = R(x,y,L(L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),23613(a,2,3))].">
      <j1 rule="para" parents="30 23613"/>
    </justification>
  </clause>

  <clause id="23616">
    <literal><![CDATA[
      R(1 / x,x,L(y,z,u)) \ R(y,z,u) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(23613(a,1),420(a,1,1))].">
      <j1 rule="para" parents="23613 420"/>
    </justification>
  </clause>

  <clause id="23617">
    <literal><![CDATA[
      R(x,y,(z * u) * u) = R(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(2239,a,23614,a)].">
      <j1 rule="hyper" parents="2239 23614"/>
    </justification>
  </clause>

  <clause id="23618">
    <literal><![CDATA[
      (x / y) * R(T(y,x),z,u) = (R(y,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(4929(a,2),23606(a,1,2,1))].">
      <j1 rule="para" parents="4929 23606"/>
    </justification>
  </clause>

  <clause id="23619">
    <literal><![CDATA[
      (x \ R(x,y,z)) * R(T(x,R(x,y,z)),u,w) = (R(x,u,w) * R(x,y,z)) / x
    ]]></literal>
    <justification jstring="[para(3675(a,1),23618(a,1,1))].">
      <j1 rule="para" parents="3675 23618"/>
    </justification>
  </clause>

  <clause id="23620">
    <literal><![CDATA[
      R(x,y,L(R(z,u,w),v5,v6)) = R(x,y,L(L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(29(a,1),23615(a,1,3))].">
      <j1 rule="para" parents="29 23615"/>
    </justification>
  </clause>

  <clause id="23621">
    <literal><![CDATA[
      (x \ 1) \ R(x,y,z) = x * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3976(a,1),23616(a,1,1))].">
      <j1 rule="para" parents="3976 23616"/>
    </justification>
  </clause>

  <clause id="23622">
    <literal><![CDATA[
      a(x,y,L(z * R(z,u,u),w,v5)) = a(x,y,L(a(z,u,u),w,v5))
    ]]></literal>
    <justification jstring="[para(23621(a,1),15037(a,1,3,1))].">
      <j1 rule="para" parents="23621 15037"/>
    </justification>
  </clause>

  <clause id="23623">
    <literal><![CDATA[
      R(x,y \ R(y,z,u),w) = R(x,y * R(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(23621(a,1),20655(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23621 20655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23624">
    <literal><![CDATA[
      R(x,(y / z) * R(y / z,z,z),u) = R(x,(y / z) \ (y * (z \ 1)),u)
    ]]></literal>
    <justification jstring="[para(785(a,1),23623(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="785 23623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23625">
    <literal><![CDATA[
      R(x,y * R(y,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y * (z \ (y \ z)),u) = w
    ]]></literal>
    <justification jstring="[para(23623(a,1),22475(a,1))].">
      <j1 rule="para" parents="23623 22475"/>
    </justification>
  </clause>

  <clause id="23626">
    <literal><![CDATA[
      R(1 / x,x,L(L(y,z,u),w,v5)) \ R(R(y,z,u),w,v5) = x * R(R(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(23620(a,1),23616(a,1,1))].">
      <j1 rule="para" parents="23620 23616"/>
    </justification>
  </clause>

  <clause id="23627">
    <literal><![CDATA[
      ((x / y) \ R(x,y \ x,y \ x)) * K(y,z) = (T(y,z) * (x / y)) * (1 / (x / y))
    ]]></literal>
    <justification jstring="[hyper(23602,a,22757,a)].">
      <j1 rule="hyper" parents="23602 22757"/>
    </justification>
  </clause>

  <clause id="23628">
    <literal><![CDATA[
      R(K(x,y) * (z * K(y,T(z,x))),u,w) = (y * R(z,u,w)) / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,23574,a,b,23603,a)].">
      <j1 rule="hyper" parents="63 23574 23603"/>
    </justification>
  </clause>

  <clause id="23629">
    <literal><![CDATA[
      R((x * y) / T(x,z),u,w) = (x * R(y,u,w)) / T(x,z)
    ]]></literal>
    <justification jstring="[para(8141(a,1),23628(a,1,1))].">
      <j1 rule="para" parents="8141 23628"/>
    </justification>
  </clause>

  <clause id="23630">
    <literal><![CDATA[
      R(x,(y / z) * R(y / z,z,z),u) = R(x,(y / z) \ (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,2390,a(flip),b,23624,a),flip(a)].">
      <j1 rule="hyper" parents="347 2390 23624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23631">
    <literal><![CDATA[
      R(x,(y / z) * R(y / z,z,z),u) = R(x,(z \ y) \ (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,22422,a(flip),b,23630,a),flip(a)].">
      <j1 rule="hyper" parents="347 22422 23630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23632">
    <literal><![CDATA[
      R(x,(y / z) * (y * (z \ 1)),u) = R(x,(z \ y) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(785(a,1),23631(a,1,2,2))].">
      <j1 rule="para" parents="785 23631"/>
    </justification>
  </clause>

  <clause id="23633">
    <literal><![CDATA[
      R(x,(y \ z) \ (z * y),u) = R(x,(z / y) * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2381,a(flip),b,23632,a),flip(a)].">
      <j1 rule="hyper" parents="63 2381 23632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23634">
    <literal><![CDATA[
      R(x,(y \ z) \ (z * y),u) = R(x,(y \ z) * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,22411,a(flip),b,23633,a),flip(a)].">
      <j1 rule="hyper" parents="347 22411 23633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23635">
    <literal><![CDATA[
      R(x,(y \ z) \ (z * y),u) = R(x,a(z,y,y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,21302,a(flip),b,23634,a),flip(a)].">
      <j1 rule="hyper" parents="347 21302 23634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23636">
    <literal><![CDATA[
      R(x,(y \ z) \ (z * y),u) = L(x,a(z,y,y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,23225,a(flip),b,23635,a),flip(a)].">
      <j1 rule="hyper" parents="347 23225 23635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23637">
    <literal><![CDATA[
      R(x,(y \ z) \ (z * y),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,22774,a(flip),b,23636,a),flip(a)].">
      <j1 rule="hyper" parents="347 22774 23636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23638">
    <literal><![CDATA[
      (R(x,y,z) * R(x,u,w)) / x = (x \ R(x,u,w)) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(196(a,1),23619(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="196 23619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23639">
    <literal><![CDATA[
      (x \ R(x,y,z)) * R(x,u,w) = R(x,y,z) * (x \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,20692,a(flip),b,23638,a),flip(a)].">
      <j1 rule="hyper" parents="63 20692 23638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23640">
    <literal><![CDATA[
      (x \ K(y,z)) * R((x \ K(y,z)) \ u,w,v5) = x \ R(x * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,1461,a(flip),b,23590,a),flip(a)].">
      <j1 rule="hyper" parents="347 1461 23590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23641">
    <literal><![CDATA[
      (x / y) \ R((x / y) * z,u,w) = (y \ x) \ R((y \ x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11656,a(flip),b,23640,a),flip(a)].">
      <j1 rule="hyper" parents="63 11656 23640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23643">
    <literal><![CDATA[
      (x \ y) \ R((x \ y) * z,x \ y,x \ y) = (z * (y / x)) * (1 / (y / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,22756,a(flip),b,23641,a),flip(a)].">
      <j1 rule="hyper" parents="63 22756 23641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23644">
    <literal><![CDATA[
      (x \ y) \ R((x \ y) * x,z,u) = (y / x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),23641(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 23641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23645">
    <literal><![CDATA[
      R(x,y,z) / (u \ x) = (x / u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,3670,a(flip),b,23644,a)].">
      <j1 rule="hyper" parents="63 3670 23644"/>
    </justification>
  </clause>

  <clause id="23646">
    <literal><![CDATA[
      (x / y) \ R(x,y \ x,y \ x) = x * (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(2274,a,23645,a),flip(a)].">
      <j1 rule="hyper" parents="2274 23645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23647">
    <literal><![CDATA[
      ((x / y) \ R(x,z,u)) \ R(x,z,u) = y \ x
    ]]></literal>
    <justification jstring="[hyper(214,a,23645,a)].">
      <j1 rule="hyper" parents="214 23645"/>
    </justification>
  </clause>

  <clause id="23648">
    <literal><![CDATA[
      x \ R(y,z,u) != w \ y
    ]]></literal>
    <literal><![CDATA[
      (y / w) \ R(y,z,u) = x
    ]]></literal>
    <justification jstring="[para(23647(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="23647 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23649">
    <literal><![CDATA[
      (x * (y / z)) * (1 / (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      (x * (z \ y)) * (1 / (z \ y)) = u
    ]]></literal>
    <justification jstring="[para(23643(a,1),3672(a,1))].">
      <j1 rule="para" parents="23643 3672"/>
    </justification>
  </clause>

  <clause id="23650">
    <literal><![CDATA[
      L(x,y * L(R(R(z * K(u,w),v5,z),v6,v7),v5,z),v8) = L(x,R(z,v6,v7) * y,v8)
    ]]></literal>
    <justification jstring="[para(23597(a,2),23607(a,1,2,2,1,1))].">
      <j1 rule="para" parents="23597 23607"/>
    </justification>
  </clause>

  <clause id="23651">
    <literal><![CDATA[
      L(x,y * R(z * K(u,w),v5,v6),v7) = L(x,R(z,v5,v6) * y,v7)
    ]]></literal>
    <justification jstring="[para(22072(a,1),23650(a,1,2,2))].">
      <j1 rule="para" parents="22072 23650"/>
    </justification>
  </clause>

  <clause id="23652">
    <literal><![CDATA[
      L(x,y * R(z * T(z \ u,w),v5,v6),v7) = L(x,R(u,v5,v6) * y,v7)
    ]]></literal>
    <justification jstring="[para(1437(a,2),23651(a,1,2,2,1))].">
      <j1 rule="para" parents="1437 23651"/>
    </justification>
  </clause>

  <clause id="23653">
    <literal><![CDATA[
      (x \ 1) \ R(R(x,y,z),u,w) = x * R(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(10922(a,1),23626(a,1,1))].">
      <j1 rule="para" parents="10922 23626"/>
    </justification>
  </clause>

  <clause id="23654">
    <literal><![CDATA[
      (T(x,y) * (z / x)) * (1 / (z / x)) = (z * (1 / (x \ z))) * K(x,y)
    ]]></literal>
    <justification jstring="[para(23646(a,1),23627(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23646 23627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23655">
    <literal><![CDATA[
      (T(x,y) * (z / x)) * (1 / (z / x)) = z * ((1 / (x \ z)) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,20033,a(flip),b,23654,a),flip(a)].">
      <j1 rule="hyper" parents="347 20033 23654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23656">
    <literal><![CDATA[
      (T(x,y) * (z / x)) * (1 / (z / x)) = z * (1 / (T(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(20822(a,1),23655(a,2,2))].">
      <j1 rule="para" parents="20822 23655"/>
    </justification>
  </clause>

  <clause id="23657">
    <literal><![CDATA[
      (T(x,y) * (x \ z)) * (1 / (x \ z)) = z * (1 / (T(x,y) \ z))
    ]]></literal>
    <justification jstring="[hyper(23649,a,23656,a)].">
      <j1 rule="hyper" parents="23649 23656"/>
    </justification>
  </clause>

  <clause id="23658">
    <literal><![CDATA[
      (K(x,y) * z) * (1 / (x \ z)) = z * (1 / (T(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(4944(a,1),23657(a,1,1))].">
      <j1 rule="para" parents="4944 23657"/>
    </justification>
  </clause>

  <clause id="23659">
    <literal><![CDATA[
      x * (1 / (T(y,z) \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x * (1 / (y \ x))) = u
    ]]></literal>
    <justification jstring="[para(23658(a,1),20093(a,1))].">
      <j1 rule="para" parents="23658 20093"/>
    </justification>
  </clause>

  <clause id="23660">
    <literal><![CDATA[
      R(x,y * (((T(z,u) * w) * (T(z,v5) \ 1)) * z),v6) = R(x,y * (z * R(w,z,z)),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,22450,a(flip),b,23589,a),flip(a)].">
      <j1 rule="hyper" parents="347 22450 23589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23661">
    <literal><![CDATA[
      R(x,y * R(T(z,u) * w,z,z),v5) = R(x,y * (z * R(w,z,z)),v5)
    ]]></literal>
    <justification jstring="[hyper(22543,a,23660,a)].">
      <j1 rule="hyper" parents="22543 23660"/>
    </justification>
  </clause>

  <clause id="23663">
    <literal><![CDATA[
      L(x,y,(z * T(u,T(z * w,v5))) \ (u * (z * w))) = L(x,y,R(w,z,T(u,T(z * w,v5))))
    ]]></literal>
    <justification jstring="[hyper(21517,a,23612,a)].">
      <j1 rule="hyper" parents="21517 23612"/>
    </justification>
  </clause>

  <clause id="23664">
    <literal><![CDATA[
      L(x,y,R(z,u,T(w,T(u * z,v5)))) = L(x,y,(u * w) \ (w * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(21525,a,23663,a),flip(a)].">
      <j1 rule="hyper" parents="21525 23663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23667">
    <literal><![CDATA[
      L(x,y,R(z,u,T(w,T(u * z,v5)))) = L(x,y,L(K(w,u) * z,u,w))
    ]]></literal>
    <justification jstring="[para(10173(a,1),23664(a,2,3))].">
      <j1 rule="para" parents="10173 23664"/>
    </justification>
  </clause>

  <clause id="23668">
    <literal><![CDATA[
      L(x,y,R(z,u,T(w,T(u * z,v5)))) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,21482,a(flip),b,23667,a),flip(a)].">
      <j1 rule="hyper" parents="347 21482 23667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23670">
    <literal><![CDATA[
      L(x,y,R(z,u,w)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(20040(a,1),23668(a,1,3))].">
      <j1 rule="para" parents="20040 23668"/>
    </justification>
  </clause>

  <clause id="23671">
    <literal><![CDATA[
      L(x,y,(z * u) \ (u * (w * z))) = L(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(21589,a,23670,a)].">
      <j1 rule="hyper" parents="21589 23670"/>
    </justification>
  </clause>

  <clause id="23672">
    <literal><![CDATA[
      L(x,y,(z * u) * (z \ 1)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(20661,a,23670,a)].">
      <j1 rule="hyper" parents="20661 23670"/>
    </justification>
  </clause>

  <clause id="23673">
    <literal><![CDATA[
      (x * R(y,z,u)) \ (R(y,z,u) * (T(x,y) * w)) = L(w,T(x,y),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,20693,a,b,23670,a)].">
      <j1 rule="hyper" parents="63 20693 23670"/>
    </justification>
  </clause>

  <clause id="23674">
    <literal><![CDATA[
      L(1 / x,x,L(y,x,x)) = R(y,x,x) \ (y * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(63,a,3270,a(flip),b,23670,a),flip(a)].">
      <j1 rule="hyper" parents="63 3270 23670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23675">
    <literal><![CDATA[
      L(x \ y,x,L(1 / z,z,z \ x)) = (z \ x) \ (((z \ x) / x) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,895,a(flip),b,23670,a),flip(a)].">
      <j1 rule="hyper" parents="63 895 23670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23676">
    <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(134,a,23670,a(flip),b,98,a)].">
      <j1 rule="hyper" parents="134 23670 98"/>
    </justification>
  </clause>

  <clause id="23677">
    <literal><![CDATA[
      L(x,y,R(L(z,u,w),v5,v6)) = L(x,y,L(L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),23670(a,2,3))].">
      <j1 rule="para" parents="30 23670"/>
    </justification>
  </clause>

  <clause id="23678">
    <literal><![CDATA[
      L(x,y,L(z,u,w \ 1)) = L(x,y,R(z,u,w))
    ]]></literal>
    <justification jstring="[para(2190(a,1),23670(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2190 23670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23680">
    <literal><![CDATA[
      L(x,y,R(K(z,T(u,w)) / v5,v5,w)) = L(x,y,w \ (K(z,u) * (w / v5)))
    ]]></literal>
    <justification jstring="[para(21293(a,1),23670(a,2,3))].">
      <j1 rule="para" parents="21293 23670"/>
    </justification>
  </clause>

  <clause id="23681">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * L(1 / v5,v5,L(z,u,w))) = L(x,y,v5 \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(23670(a,1),22883(a,1,3,2))].">
      <j1 rule="para" parents="23670 22883"/>
    </justification>
  </clause>

  <clause id="23682">
    <literal><![CDATA[
      L(x,y,L(z,u,w \ 1)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,23670,a(flip),b,23678,a),flip(a)].">
      <j1 rule="hyper" parents="347 23670 23678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23683">
    <literal><![CDATA[
      a(x,y,L((z \ 1) * u,(z \ 1) * u,L(u \ 1,u,z))) = a(x,y,((z \ 1) * (((z \ 1) * u) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(23682(a,1),15013(a,1,3))].">
      <j1 rule="para" parents="23682 15013"/>
    </justification>
  </clause>

  <clause id="23684">
    <literal><![CDATA[
      L(x,y,L(z \ u,z,z)) = L(x,y,u * (z \ 1))
    ]]></literal>
    <justification jstring="[para(10(a,1),23672(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 23672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23685">
    <literal><![CDATA[
      L(1 / x,x,L(y,x,x)) = L(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,3516,a(flip),b,23674,a),flip(a)].">
      <j1 rule="hyper" parents="347 3516 23674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23686">
    <literal><![CDATA[
      L(x,y,L(R(z,u,w),v5,v6)) = L(x,y,L(L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(29(a,1),23677(a,1,3))].">
      <j1 rule="para" parents="29 23677"/>
    </justification>
  </clause>

  <clause id="23687">
    <literal><![CDATA[
      L(x \ y,x,L(z \ 1,z,z \ x)) = (z \ x) \ (((z \ x) / x) * y)
    ]]></literal>
    <justification jstring="[hyper(21590,a,23675,a)].">
      <j1 rule="hyper" parents="21590 23675"/>
    </justification>
  </clause>

  <clause id="23688">
    <literal><![CDATA[
      L(x \ y,x,L(1 / z,z,x)) = (z \ x) \ (((z \ x) / x) * y)
    ]]></literal>
    <justification jstring="[para(5506(a,1),23687(a,1,3))].">
      <j1 rule="para" parents="5506 23687"/>
    </justification>
  </clause>

  <clause id="23689">
    <literal><![CDATA[
      L(x \ y,x,L(z \ 1,z,x)) = (z \ x) \ (((z \ x) / x) * y)
    ]]></literal>
    <justification jstring="[hyper(21590,a,23688,a)].">
      <j1 rule="hyper" parents="21590 23688"/>
    </justification>
  </clause>

  <clause id="23690">
    <literal><![CDATA[
      L(x \ y,x,L(z \ 1,z,x)) = L(x \ y,x,z \ a(z,z,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,18989,a,b,23689,a),flip(a)].">
      <j1 rule="hyper" parents="347 18989 23689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23691">
    <literal><![CDATA[
      L(x,y,z / (u * (z * K(w,v5)))) = L(x,y,z \ (K(v5,w) * (z / u)))
    ]]></literal>
    <justification jstring="[para(21167(a,1),23680(a,1,3))].">
      <j1 rule="para" parents="21167 23680"/>
    </justification>
  </clause>

  <clause id="23692">
    <literal><![CDATA[
      L(x,y,(z * (u * K(w,v5))) \ u) = L(x,y,u \ (K(v5,w) * (u / z)))
    ]]></literal>
    <justification jstring="[hyper(20491,a,23691,a)].">
      <j1 rule="hyper" parents="20491 23691"/>
    </justification>
  </clause>

  <clause id="23693">
    <literal><![CDATA[
      L(x,y,z \ (K(u,w) * (z / v5))) = L(x,y,K(u,w) * ((v5 * z) \ z))
    ]]></literal>
    <justification jstring="[para(20837(a,1),23692(a,1,3)),flip(a)].">
      <j1 rule="para" parents="20837 23692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23694">
    <literal><![CDATA[
      L(x,y,z \ (K(u,w) * (z / v5))) = L(x,y,(v5 * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,21456,a(flip),b,23693,a),flip(a)].">
      <j1 rule="hyper" parents="347 21456 23693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23696">
    <literal><![CDATA[
      L(x,y,(z * u) \ u) = L(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[para(5027(a,1),23694(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5027 23694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23697">
    <literal><![CDATA[
      L(x,y,(z * u) \ z) = L(x,y,z \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(21521,a,23696,a)].">
      <j1 rule="hyper" parents="21521 23696"/>
    </justification>
  </clause>

  <clause id="23698">
    <literal><![CDATA[
      x \ (x * L(y,z,u \ (w \ u))) = L(y,z,(u * w) \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,9,a,b,23697,a)].">
      <j1 rule="hyper" parents="347 9 23697"/>
    </justification>
  </clause>

  <clause id="23699">
    <literal><![CDATA[
      L(x,y,(z * u) \ z) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ (u \ z)) = w
    ]]></literal>
    <justification jstring="[para(23698(a,1),356(a,1))].">
      <j1 rule="para" parents="23698 356"/>
    </justification>
  </clause>

  <clause id="23700">
    <literal><![CDATA[
      (x * R(y,z,u)) \ (R(y,z,u) * (T(x,y) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(w,x,L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(23673(a,2),21722(a,1))].">
      <j1 rule="para" parents="23673 21722"/>
    </justification>
  </clause>

  <clause id="23701">
    <literal><![CDATA[
      L(x,y,L(z,u,w) / v5) = L(x,y,v5 \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(3266(a,1),23681(a,1,3))].">
      <j1 rule="para" parents="3266 23681"/>
    </justification>
  </clause>

  <clause id="23702">
    <literal><![CDATA[
      L(x,y,z \ R(u,w,v5)) = L(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(20491,a,23701,a),flip(a)].">
      <j1 rule="hyper" parents="20491 23701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23703">
    <literal><![CDATA[
      L(x,y,x \ R(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,10541,a(flip),b,23702,a),flip(a)].">
      <j1 rule="hyper" parents="347 10541 23702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23705">
    <literal><![CDATA[
      L(x,y,z \ L(z,z,u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(18988(a,1),23702(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18988 23702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23706">
    <literal><![CDATA[
      L(x,y,y \ L(y,z,u)) * ((y \ R(y,z,u)) * y) = (y \ R(y,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[para(23702(a,1),22333(a,1,1))].">
      <j1 rule="para" parents="23702 22333"/>
    </justification>
  </clause>

  <clause id="23707">
    <literal><![CDATA[
      ((x \ R(x,y,z)) * u) * x = (x \ R(x,y,z)) * (u * x)
    ]]></literal>
    <justification jstring="[hyper(134,a,23703,a(flip),b,4048,a(flip))].">
      <j1 rule="hyper" parents="134 23703 4048"/>
    </justification>
  </clause>

  <clause id="23708">
    <literal><![CDATA[
      L(x,y,(z \ (u \ z)) * u) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(21585,a,23705,a)].">
      <j1 rule="hyper" parents="21585 23705"/>
    </justification>
  </clause>

  <clause id="23709">
    <literal><![CDATA[
      L((((x \ (y \ x)) * y) \ 1) \ z,a(y,y,x),a(y,y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (y \ x)) * y) * z = u
    ]]></literal>
    <justification jstring="[para(23708(a,1),21815(a,1))].">
      <j1 rule="para" parents="23708 21815"/>
    </justification>
  </clause>

  <clause id="23710">
    <literal><![CDATA[
      ((x \ R(x,y,z)) * L(x,u,x \ R(x,y,z))) * a(u,x \ R(x,y,z),L(x,u,x \ R(x,y,z))) = u \ (((x \ R(x,y,z)) * T(u,x \ R(x,y,z))) * x)
    ]]></literal>
    <justification jstring="[para(23707(a,2),14728(a,2,2))].">
      <j1 rule="para" parents="23707 14728"/>
    </justification>
  </clause>

  <clause id="23711">
    <literal><![CDATA[
      L(x,y,y \ L(y,z,u)) * R(y,z,u) = (y \ R(y,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[para(3678(a,1),23706(a,1,2))].">
      <j1 rule="para" parents="3678 23706"/>
    </justification>
  </clause>

  <clause id="23712">
    <literal><![CDATA[
      a(x,y,L((z \ 1) * u,u * z,L(u \ 1,u,z))) = a(x,y,((z \ 1) * (((z \ 1) * u) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(21695(a,1),23683(a,1,3))].">
      <j1 rule="para" parents="21695 23683"/>
    </justification>
  </clause>

  <clause id="23713">
    <literal><![CDATA[
      ((K(x,y) * z) * (R(z,u,w) \ T(v5 * (y * x),K(y,x)))) * R(K(x,y) * z,u,w) = (v5 * (T(x,y) * y)) * z
    ]]></literal>
    <justification jstring="[para(9590(a,2),23584(a,1,1,2,2))].">
      <j1 rule="para" parents="9590 23584"/>
    </justification>
  </clause>

  <clause id="23714">
    <literal><![CDATA[
      ((K(x,y) * z) * (R(z,u,w) \ T(v5 * (y * x),K(x,y)))) * R(K(x,y) * z,u,w) = (v5 * (T(x,y) * y)) * z
    ]]></literal>
    <justification jstring="[para(7330(a,1),23713(a,1,1,2,2))].">
      <j1 rule="para" parents="7330 23713"/>
    </justification>
  </clause>

  <clause id="23715">
    <literal><![CDATA[
      (K(x,y) * (z * (R(z,u,w) \ T(v5 * (y * x),K(x,y))))) * R(K(x,y) * z,u,w) = (v5 * (T(x,y) * y)) * z
    ]]></literal>
    <justification jstring="[para(20008(a,1),23714(a,1,1))].">
      <j1 rule="para" parents="20008 23714"/>
    </justification>
  </clause>

  <clause id="23716">
    <literal><![CDATA[
      K(x,y) * ((z * (R(z,u,w) \ T(v5 * (y * x),K(x,y)))) * R(K(x,y) * z,u,w)) = (v5 * (T(x,y) * y)) * z
    ]]></literal>
    <justification jstring="[hyper(20093,a,23715,a)].">
      <j1 rule="hyper" parents="20093 23715"/>
    </justification>
  </clause>

  <clause id="23717">
    <literal><![CDATA[
      K(x,y) * (T(z * (y * x),K(x,y)) * (K(x,y) * u)) = (z * (T(x,y) * y)) * u
    ]]></literal>
    <justification jstring="[para(23581(a,1),23716(a,1,2))].">
      <j1 rule="para" parents="23581 23716"/>
    </justification>
  </clause>

  <clause id="23718">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * ((z * (y * x)) * u)) = (z * (T(x,y) * y)) * u
    ]]></literal>
    <justification jstring="[para(21318(a,1),23717(a,1,2))].">
      <j1 rule="para" parents="21318 23717"/>
    </justification>
  </clause>

  <clause id="23719">
    <literal><![CDATA[
      x * (T(T(x,y),y) \ ((z * (x * y)) * u)) = (z * (T(y,x) * x)) * u
    ]]></literal>
    <justification jstring="[hyper(5897,a,23718,a)].">
      <j1 rule="hyper" parents="5897 23718"/>
    </justification>
  </clause>

  <clause id="23720">
    <literal><![CDATA[
      L(x,(T(T(y \ 1,z),z) \ ((u * ((y \ 1) * z)) * w)) * y,v5) = L(x,(u * (T(z,y \ 1) * (y \ 1))) * w,v5)
    ]]></literal>
    <justification jstring="[para(23719(a,1),21695(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23719 21695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23721">
    <literal><![CDATA[
      L(x,(T(T(y \ 1,z),z) \ ((u * ((y \ 1) * z)) * w)) * y,v5) = L(x,w * (u * (z * (y \ 1))),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,21877,a(flip),b,23720,a),flip(a)].">
      <j1 rule="hyper" parents="347 21877 23720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23723">
    <literal><![CDATA[
      L(x,(T(T(y \ 1,z),z) \ ((u * ((y \ 1) * z)) * w)) * y,v5) = L(x,w * (u * (z * y)),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,3332,a(flip),b,23721,a),flip(a)].">
      <j1 rule="hyper" parents="347 3332 23721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23724">
    <literal><![CDATA[
      L(x,y * (T(y \ 1,z) \ ((u * ((y \ 1) * z)) * w)),v5) = L(x,w * (u * (z * y)),v5)
    ]]></literal>
    <justification jstring="[hyper(21845,a,23723,a)].">
      <j1 rule="hyper" parents="21845 23723"/>
    </justification>
  </clause>

  <clause id="23725">
    <literal><![CDATA[
      L(x,y * ((y \ 1) \ ((z * ((y \ 1) * u)) * w)),v5) = L(x,w * (z * (u * y)),v5)
    ]]></literal>
    <justification jstring="[hyper(21737,a,23724,a)].">
      <j1 rule="hyper" parents="21737 23724"/>
    </justification>
  </clause>

  <clause id="23726">
    <literal><![CDATA[
      L(x,y * (y \ ((z * ((y \ 1) * u)) * w)),v5) = L(x,w * (z * (u * y)),v5)
    ]]></literal>
    <justification jstring="[hyper(3617,a,23725,a)].">
      <j1 rule="hyper" parents="3617 23725"/>
    </justification>
  </clause>

  <clause id="23727">
    <literal><![CDATA[
      L(x,(y * ((z \ 1) * u)) * w,v5) = L(x,w * (y * (u * z)),v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),23726(a,1,2))].">
      <j1 rule="para" parents="10 23726"/>
    </justification>
  </clause>

  <clause id="23729">
    <literal><![CDATA[
      L(x,y * (z * (u * z)),w) = L(x,L(u,z,z) * y,w)
    ]]></literal>
    <justification jstring="[para(3197(a,1),23727(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3197 23727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23730">
    <literal><![CDATA[
      L(x,L(a(y,y,z),L(z,y,y),L(z,y,y)) * u,w) = L(x,u * (L(z,y,y) * z),w)
    ]]></literal>
    <justification jstring="[para(14599(a,1),23729(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14599 23729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23731">
    <literal><![CDATA[
      L(x,L(a(y,y,z),L(z,y,y),L(z,y,y)) * u,w) = L(x,u * (z * L(z,y,y)),w)
    ]]></literal>
    <justification jstring="[para(274(a,1),23730(a,2,2,2))].">
      <j1 rule="para" parents="274 23730"/>
    </justification>
  </clause>

  <clause id="23732">
    <literal><![CDATA[
      L(x,y * (z * L(z,u,u)),w) = L(x,a(u,u,z) * y,w)
    ]]></literal>
    <justification jstring="[para(12369(a,1),23731(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12369 23731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23734">
    <literal><![CDATA[
      T(L(x \ y,z,u),T(x,y)) * ((x \ y) \ y) = L(x \ y,z,u) * ((x * L(x \ y,z,u)) / L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(7070(a,1),21193(a,1,1))].">
      <j1 rule="para" parents="7070 21193"/>
    </justification>
  </clause>

  <clause id="23735">
    <literal><![CDATA[
      L(T(x \ y,T(x,y)),z,u) * ((x \ y) \ y) = L(x \ y,z,u) * ((x * L(x \ y,z,u)) / L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),23734(a,1,1))].">
      <j1 rule="para" parents="25 23734"/>
    </justification>
  </clause>

  <clause id="23736">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x * L(x \ y,z,u)) / L(x \ y,z,u)) = L(T(x \ y,x),z,u) * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(4177(a,1),23735(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4177 23735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23737">
    <literal><![CDATA[
      L(T(x \ y,x),z,u) * ((x \ y) \ y) = L(x \ y,z,u) * x
    ]]></literal>
    <justification jstring="[para(11(a,1),23736(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 23736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23738">
    <literal><![CDATA[
      L(x,((y * z) \ ((u * z) * y)) \ (L(w,R(u,z,y) \ v5,L(u,z,y)) * v5),v6) = L(x,(R(u,z,y) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[para(23670(a,1),22014(a,1,2,2,1))].">
      <j1 rule="para" parents="23670 22014"/>
    </justification>
  </clause>

  <clause id="23739">
    <literal><![CDATA[
      L(x,(K(y,T(z,u)) / w) * L(K(y,T(z,u)) / w,w,u),v5) = L(x,(K(y,T(z,u)) / w) \ (u \ (u / w)),v5)
    ]]></literal>
    <justification jstring="[hyper(21830,a,21295,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="21830 21295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23740">
    <literal><![CDATA[
      L(x,(K(y,T(z,u)) / w) * L(K(y,T(z,u)) / w,w,u),v5) = L(x,(K(y,T(z,u)) / w) \ (u \ (w \ u)),v5)
    ]]></literal>
    <justification jstring="[hyper(21875,a,23739,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="21875 23739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23741">
    <literal><![CDATA[
      L(x,(K(y,T(z,u)) / w) * L(K(y,T(z,u)) / w,w,u),v5) = L(x,(w \ K(y,T(z,u))) \ (u \ (w \ u)),v5)
    ]]></literal>
    <justification jstring="[hyper(21727,a,23740,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="21727 23740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23742">
    <literal><![CDATA[
      L(x,(K(y,T(z,u)) / w) * L(K(y,T(z,u)) / w,w,u),v5) = L(x,w \ (u \ (w \ u)),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,21846,a(flip),b,23741,a),flip(a)].">
      <j1 rule="hyper" parents="347 21846 23741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23744">
    <literal><![CDATA[
      L(x,(K(y,T(z,u)) / w) * (u \ (K(y,z) * (u / w))),v5) = L(x,w \ (u \ (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(21293(a,1),23742(a,1,2,2))].">
      <j1 rule="para" parents="21293 23742"/>
    </justification>
  </clause>

  <clause id="23745">
    <literal><![CDATA[
      L(x,(K(y,T(z,u)) / w) * (u \ (u / w)),v5) = L(x,w \ (u \ (w \ u)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,21780,a(flip),b,23744,a)].">
      <j1 rule="hyper" parents="63 21780 23744"/>
    </justification>
  </clause>

  <clause id="23746">
    <literal><![CDATA[
      L(x,(y \ K(z,T(u,w))) * (w \ (w / y)),v5) = L(x,y \ (w \ (y \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(21728,a,23745,a)].">
      <j1 rule="hyper" parents="21728 23745"/>
    </justification>
  </clause>

  <clause id="23749">
    <literal><![CDATA[
      L(x,y \ (z \ (y \ z)),u) = L(x,(z \ (z / y)) * y,u)
    ]]></literal>
    <justification jstring="[hyper(21869,a,23746,a),flip(a)].">
      <j1 rule="hyper" parents="21869 23746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23751">
    <literal><![CDATA[
      L(x,y \ (z \ (y \ z)),u) = L(x,(z \ (y \ z)) * y,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,21825,a(flip),b,23749,a),flip(a)].">
      <j1 rule="hyper" parents="347 21825 23749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23752">
    <literal><![CDATA[
      L(x,y \ (z \ (y \ z)),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,21811,a(flip),b,23751,a),flip(a)].">
      <j1 rule="hyper" parents="347 21811 23751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23753">
    <literal><![CDATA[
      L((x \ (y \ (x \ y))) \ z,a(x,x,y),x) = (y \ (x \ y)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(651,a,23752,a),flip(a)].">
      <j1 rule="hyper" parents="651 23752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23754">
    <literal><![CDATA[
      a(L(T(x,y) \ z,x,u),u * T(x,y),w) = (L(w,u * T(x,y),(u * x) \ (u * z)) * (u * z)) \ (w * (u * z))
    ]]></literal>
    <justification jstring="[para(21480(a,1),21805(a,2,1,1))].">
      <j1 rule="para" parents="21480 21805"/>
    </justification>
  </clause>

  <clause id="23756">
    <literal><![CDATA[
      a(L(T(x,y) \ z,x,u),u * T(x,y),w) = (L(w,u * x,(u * x) \ (u * z)) * (u * z)) \ (w * (u * z))
    ]]></literal>
    <justification jstring="[para(21614(a,1),23754(a,2,1,1))].">
      <j1 rule="para" parents="21614 23754"/>
    </justification>
  </clause>

  <clause id="23757">
    <literal><![CDATA[
      a(L(T(x,y) \ z,x,u),u * T(x,y),w) = a((u * x) \ (u * z),u * x,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,14749,a(flip),b,23756,a),flip(a)].">
      <j1 rule="hyper" parents="347 14749 23756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23759">
    <literal><![CDATA[
      L(x,((T(y,T(z * u,w)) * u) \ (y * (z * u))) \ v5,v6) = L(x,R(z,u,T(y,T(z * u,w))) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(21740,a,22015,a)].">
      <j1 rule="hyper" parents="21740 22015"/>
    </justification>
  </clause>

  <clause id="23760">
    <literal><![CDATA[
      L(x,R(y,z,T(u,T(y * z,w))) \ v5,v6) = L(x,((u * z) \ (u * (y * z))) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(21832,a,23759,a),flip(a)].">
      <j1 rule="hyper" parents="21832 23759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23762">
    <literal><![CDATA[
      L(x,R(y,z,T(u,T(y * z,w))) \ v5,v6) = L(x,L(T(y,z),z,u) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(263(a,1),23760(a,2,2,1))].">
      <j1 rule="para" parents="263 23760"/>
    </justification>
  </clause>

  <clause id="23763">
    <literal><![CDATA[
      L(x,R(y,z,T(u,T(y * z,w))) \ v5,v6) = L(x,L(y,z,u) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(21731,a,23762,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="21731 23762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23764">
    <literal><![CDATA[
      L(x,R(y,z,u) \ w,v5) = L(x,L(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(20040(a,1),23763(a,1,2,1))].">
      <j1 rule="para" parents="20040 23763"/>
    </justification>
  </clause>

  <clause id="23766">
    <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(23764(a,1),23676(a,1,2))].">
      <j1 rule="para" parents="23764 23676"/>
    </justification>
  </clause>

  <clause id="23767">
    <literal><![CDATA[
      L(x,((y * z) \ ((u * z) * y)) \ (L(w,L(u,z,y) \ v5,L(u,z,y)) * v5),v6) = L(x,(R(u,z,y) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[para(23764(a,1),23738(a,1,2,2,1))].">
      <j1 rule="para" parents="23764 23738"/>
    </justification>
  </clause>

  <clause id="23768">
    <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(841,a,23766,a),flip(a)].">
      <j1 rule="hyper" parents="841 23766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23769">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) \ K(u,R(x,y,z) \ 1)) * u) = R(x,y,z) * (u * (R(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(5054(a,1),23768(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5054 23768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23770">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) \ K(u,x \ 1)) * u) = R(x,y,z) * (u * (R(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(20460(a,1),23769(a,1,2,1,2))].">
      <j1 rule="para" parents="20460 23769"/>
    </justification>
  </clause>

  <clause id="23772">
    <literal><![CDATA[
      R(x,y,z) * (u * (R(x,y,z) \ 1)) = L(x,y,z) * (u * (L(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(23488(a,1),23770(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23488 23770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23773">
    <literal><![CDATA[
      L(x,R(y,z,u) \ (L(w,L(y,z,u) \ v5,L(y,z,u)) * v5),v6) = L(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(22013,a,23767,a)].">
      <j1 rule="hyper" parents="22013 23767"/>
    </justification>
  </clause>

  <clause id="23774">
    <literal><![CDATA[
      L(x,L(y,z,u) \ (L(w,L(y,z,u) \ v5,L(y,z,u)) * v5),v6) = L(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,23764,a(flip),b,23773,a)].">
      <j1 rule="hyper" parents="63 23764 23773"/>
    </justification>
  </clause>

  <clause id="23775">
    <literal><![CDATA[
      L(x,(R(y,z,u) \ w) * T(v5,w),v6) = L(x,(L(y,z,u) \ w) * T(v5,w),v6)
    ]]></literal>
    <justification jstring="[para(874(a,1),23774(a,1,2)),flip(a)].">
      <j1 rule="para" parents="874 23774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23776">
    <literal><![CDATA[
      L(x,(R(y,z,u) \ w) * T(v5,w),v6) = L(x,(L(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,21614,a(flip),b,23775,a),flip(a)].">
      <j1 rule="hyper" parents="347 21614 23775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23777">
    <literal><![CDATA[
      L(x,(R(y,z,u) \ w) * v5,v6) = L(x,(L(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(21729,a,23776,a)].">
      <j1 rule="hyper" parents="21729 23776"/>
    </justification>
  </clause>

  <clause id="23779">
    <literal><![CDATA[
      L(x,(L(y,z,u) \ 1) * w,v5) = L(x,w * R(y,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(21703,a,23777,a),flip(a)].">
      <j1 rule="hyper" parents="21703 23777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23781">
    <literal><![CDATA[
      L(x,y * R(z,u,w),v5) = L(x,y * L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(21703,a,23779,a),flip(a)].">
      <j1 rule="hyper" parents="21703 23779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23782">
    <literal><![CDATA[
      L(x,y * R(z,u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y * L(z,u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(23779(a,1),21703(a,1))].">
      <j1 rule="para" parents="23779 21703"/>
    </justification>
  </clause>

  <clause id="23783">
    <literal><![CDATA[
      L(x,y * L(z * T(z \ u,w),v5,v6),v7) = L(x,R(u,v5,v6) * y,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,23652,a(flip),b,23781,a),flip(a)].">
      <j1 rule="hyper" parents="63 23652 23781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23784">
    <literal><![CDATA[
      L(x,R(y,z,u) * w,v5) = L(x,L(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,21970,a(flip),b,23783,a),flip(a)].">
      <j1 rule="hyper" parents="63 21970 23783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23785">
    <literal><![CDATA[
      L(x,R(R(y,z,u),w,v5) * (T(z,v6) * u),v7) = L(x,(L(y,w,v5) * T(z,v6)) * u,v7)
    ]]></literal>
    <justification jstring="[para(20561(a,1),23784(a,2,2))].">
      <j1 rule="para" parents="20561 23784"/>
    </justification>
  </clause>

  <clause id="23797">
    <literal><![CDATA[
      L(x,(R(y,z,u) * T(w,v5)) * v6,v7) = L(x,(L(y,z,u) * T(w,v5)) * v6,v7)
    ]]></literal>
    <justification jstring="[para(20560(a,1),23785(a,1,2))].">
      <j1 rule="para" parents="20560 23785"/>
    </justification>
  </clause>

  <clause id="23798">
    <literal><![CDATA[
      L(x,(L(y,z,u) * T(w,v5)) * v6,v7) = L(x,v6 * (R(y,z,u) * w),v7)
    ]]></literal>
    <justification jstring="[hyper(21848,a,23797,a),flip(a)].">
      <j1 rule="hyper" parents="21848 23797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23799">
    <literal><![CDATA[
      L(x,y * (R(z,u,w) * v5),v6) = L(x,y * (L(z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(21848,a,23798,a),flip(a)].">
      <j1 rule="hyper" parents="21848 23798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23801">
    <literal><![CDATA[
      L(x,y * (R(z,u,w) * v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y * (L(z,u,w) * v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(23798(a,1),21848(a,1))].">
      <j1 rule="para" parents="23798 21848"/>
    </justification>
  </clause>

  <clause id="23802">
    <literal><![CDATA[
      L(x,y * (L(z,u,w) * L(v5,v5,R(z,u,w))),v6) = L(x,y * (R(z,u,w) / (v5 \ 1)),v6)
    ]]></literal>
    <justification jstring="[para(2008(a,1),23799(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2008 23799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23803">
    <literal><![CDATA[
      L(x,y * (((z * u) * (z \ 1)) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y * (L(u,z,z) * w),v5) = v6
    ]]></literal>
    <justification jstring="[para(21824(a,2),23801(a,1))].">
      <j1 rule="para" parents="21824 23801"/>
    </justification>
  </clause>

  <clause id="23804">
    <literal><![CDATA[
      L(x,(((y * z) * y) * u) * w,v5) = L(x,w * (L(z,y,y) * u),v5)
    ]]></literal>
    <justification jstring="[hyper(23803,a,22741,a),flip(a)].">
      <j1 rule="hyper" parents="23803 22741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23805">
    <literal><![CDATA[
      L(x,a(y * z,y,z) * u,w) = L(x,u * (L(z,y,y) * z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21799,a(flip),b,23804,a)].">
      <j1 rule="hyper" parents="63 21799 23804"/>
    </justification>
  </clause>

  <clause id="23806">
    <literal><![CDATA[
      L(x,a(y * z,y,z) * u,w) = L(x,u * (z * L(z,y,y)),w)
    ]]></literal>
    <justification jstring="[para(274(a,1),23805(a,2,2,2))].">
      <j1 rule="para" parents="274 23805"/>
    </justification>
  </clause>

  <clause id="23807">
    <literal><![CDATA[
      L(x,a(y * z,y,z) * u,w) = L(x,a(y,y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,23732,a(flip),b,23806,a),flip(a)].">
      <j1 rule="hyper" parents="347 23732 23806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23808">
    <literal><![CDATA[
      L(x,y * (((z * u) * z) * u),w) = L(x,a(z,z,u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(21874,a,23807,a)].">
      <j1 rule="hyper" parents="21874 23807"/>
    </justification>
  </clause>

  <clause id="23809">
    <literal><![CDATA[
      L(x,L(R(y * z,y,z),y * z,y * z),u) = L(x,a(y,y,z) * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(21823,a,23808,a)].">
      <j1 rule="hyper" parents="21823 23808"/>
    </justification>
  </clause>

  <clause id="23810">
    <literal><![CDATA[
      L(x,L(R(y * z,y,z),y * z,y * z),u) = L(x,z * (a(y,y,z) * y),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,23127,a(flip),b,23809,a),flip(a)].">
      <j1 rule="hyper" parents="347 23127 23809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23811">
    <literal><![CDATA[
      L(x,R(1 / (1 / (y * z)),y,z),u) = L(x,z * (a(y,y,z) * y),u)
    ]]></literal>
    <justification jstring="[para(3198(a,2),23810(a,1,2))].">
      <j1 rule="para" parents="3198 23810"/>
    </justification>
  </clause>

  <clause id="23812">
    <literal><![CDATA[
      L(x,L(1 / (1 / (y * z)),y,z),u) = L(x,z * (a(y,y,z) * y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21974,a(flip),b,23811,a)].">
      <j1 rule="hyper" parents="63 21974 23811"/>
    </justification>
  </clause>

  <clause id="23813">
    <literal><![CDATA[
      L(x,L((1 / (y * z)) \ 1,y,z),u) = L(x,z * (a(y,y,z) * y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21659,a(flip),b,23812,a)].">
      <j1 rule="hyper" parents="63 21659 23812"/>
    </justification>
  </clause>

  <clause id="23814">
    <literal><![CDATA[
      L(x,y * (a(z,z,y) * z),u) = L(x,L(z * y,z,y),u)
    ]]></literal>
    <justification jstring="[para(83(a,1),23813(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 23813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23816">
    <literal><![CDATA[
      L(x,L(y * z,y,z),u) = L(x,z * R(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(18993(a,1),23814(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18993 23814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23817">
    <literal><![CDATA[
      L(x,L(y * z,y,z),u) = L(x,z * L(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,23781,a(flip),b,23816,a),flip(a)].">
      <j1 rule="hyper" parents="347 23781 23816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23818">
    <literal><![CDATA[
      L(x,L(y * z,y,z),u) = L(x,z / (y \ 1),u)
    ]]></literal>
    <justification jstring="[para(2008(a,1),23817(a,2,2))].">
      <j1 rule="para" parents="2008 23817"/>
    </justification>
  </clause>

  <clause id="23819">
    <literal><![CDATA[
      L(x,L(y * z,y,z),u) = L(x,(y \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,21619,a(flip),b,23818,a),flip(a)].">
      <j1 rule="hyper" parents="347 21619 23818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23820">
    <literal><![CDATA[
      L(x,L(y * z,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(23819(a,2),21751(a,1))].">
      <j1 rule="para" parents="23819 21751"/>
    </justification>
  </clause>

  <clause id="23821">
    <literal><![CDATA[
      L(x,y * (L(z,u,w) * L(v5,v5,R(z,u,w))),v6) = L(x,y * ((v5 \ 1) \ R(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,21681,a(flip),b,23802,a),flip(a)].">
      <j1 rule="hyper" parents="347 21681 23802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23822">
    <literal><![CDATA[
      L(x,y * (L(z,u,w) * L(v5,v5,R(z,u,w))),v6) = L(x,y * (v5 \ R(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,3600,a(flip),b,23821,a),flip(a)].">
      <j1 rule="hyper" parents="347 3600 23821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23823">
    <literal><![CDATA[
      L(x,y * (L(z,u,w) * L(v5,v5,L(z,u,w))),v6) = L(x,y * (v5 \ R(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[para(23670(a,1),23822(a,1,2,2,2))].">
      <j1 rule="para" parents="23670 23822"/>
    </justification>
  </clause>

  <clause id="23824">
    <literal><![CDATA[
      L(x,y * (L(z,u,w) / (v5 \ 1)),v6) = L(x,y * (v5 \ R(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[para(2008(a,1),23823(a,1,2,2))].">
      <j1 rule="para" parents="2008 23823"/>
    </justification>
  </clause>

  <clause id="23825">
    <literal><![CDATA[
      L(x,y * ((z \ 1) \ L(u,w,v5)),v6) = L(x,y * (z \ R(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(21759,a,23824,a)].">
      <j1 rule="hyper" parents="21759 23824"/>
    </justification>
  </clause>

  <clause id="23826">
    <literal><![CDATA[
      L(x,y * (z \ R(u,w,v5)),v6) = L(x,y * (z \ L(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(3617,a,23825,a),flip(a)].">
      <j1 rule="hyper" parents="3617 23825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23827">
    <literal><![CDATA[
      L(x,L(y,y,z \ R(u,w,v5)) * (z \ L(u,w,v5)),v6) = L(x,y \ (z \ R(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(21813,a,23826,a),flip(a)].">
      <j1 rule="hyper" parents="21813 23826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23828">
    <literal><![CDATA[
      L(x,L(y,y,z \ L(u,w,v5)) * (z \ L(u,w,v5)),v6) = L(x,y \ (z \ R(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(23702(a,1),23827(a,1,2,1))].">
      <j1 rule="para" parents="23702 23827"/>
    </justification>
  </clause>

  <clause id="23829">
    <literal><![CDATA[
      L(x,y \ (z \ R(u,w,v5)),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ (z \ L(u,w,v5)),v6) = v7
    ]]></literal>
    <justification jstring="[para(23828(a,1),21813(a,1))].">
      <j1 rule="para" parents="23828 21813"/>
    </justification>
  </clause>

  <clause id="23830">
    <literal><![CDATA[
      R(x,y,(z \ L(((u \ w) / v5) * K(u \ w,u),K(u,u \ w),K(u,u \ w))) * v6) = R(x,y,(z \ ((w / u) / v5)) * v6)
    ]]></literal>
    <justification jstring="[para(6117(a,1),22824(a,1,3,1,2,1))].">
      <j1 rule="para" parents="6117 22824"/>
    </justification>
  </clause>

  <clause id="23831">
    <literal><![CDATA[
      T((x \ 1) * ((a(y,z,u) * (x \ 1)) \ w),(w / ((x \ 1) * a(y,z,u))) / x) = (x \ 1) * ((a(y,z,u) * (x \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(23264(a,1),23266(a,1,1))].">
      <j1 rule="para" parents="23264 23266"/>
    </justification>
  </clause>

  <clause id="23832">
    <literal><![CDATA[
      R(x,y,(z \ (((u \ w) / v5) * K(u \ w,u))) * v6) = R(x,y,(z \ ((w / u) / v5)) * v6)
    ]]></literal>
    <justification jstring="[para(9930(a,1),23830(a,1,3,1,2))].">
      <j1 rule="para" parents="9930 23830"/>
    </justification>
  </clause>

  <clause id="23837">
    <literal><![CDATA[
      R(x,y,((z \ ((u \ w) / v5)) * K(u \ w,u)) * v6) = R(x,y,(z \ ((w / u) / v5)) * v6)
    ]]></literal>
    <justification jstring="[para(20109(a,1),23832(a,1,3,1))].">
      <j1 rule="para" parents="20109 23832"/>
    </justification>
  </clause>

  <clause id="23838">
    <literal><![CDATA[
      R(x,y,(z \ ((u \ w) / v5)) * (K(u \ w,u) * v6)) = R(x,y,(z \ ((w / u) / v5)) * v6)
    ]]></literal>
    <justification jstring="[para(20151(a,1),23837(a,1,3))].">
      <j1 rule="para" parents="20151 23837"/>
    </justification>
  </clause>

  <clause id="23839">
    <literal><![CDATA[
      R(x,y,(z \ ((u / w) / v5)) * v6) = R(x,y,(z \ ((w \ u) / v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(22097,a,23838,a),flip(a)].">
      <j1 rule="hyper" parents="22097 23838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23841">
    <literal><![CDATA[
      R(x,y,(z \ ((u / w) / v5)) * v6) = R(x,y,(z \ (v5 \ (w \ u))) * v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,22135,a(flip),b,23839,a),flip(a)].">
      <j1 rule="hyper" parents="347 22135 23839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23842">
    <literal><![CDATA[
      R(x,y,(z \ (u \ (w / v5))) * v6) = R(x,y,(z \ (u \ (v5 \ w))) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,22135,a(flip),b,23841,a)].">
      <j1 rule="hyper" parents="63 22135 23841"/>
    </justification>
  </clause>

  <clause id="23843">
    <literal><![CDATA[
      T(x * ((a(y,z,u) * x) \ w),(w / ((x \ 1) * a(y,z,u))) / x) = (x \ 1) * ((a(y,z,u) * (x \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(974(a,1),23831(a,1,1))].">
      <j1 rule="para" parents="974 23831"/>
    </justification>
  </clause>

  <clause id="23844">
    <literal><![CDATA[
      T(x * ((a(y,z,u) * x) \ w),w / (x * ((x \ 1) * a(y,z,u)))) = (x \ 1) * ((a(y,z,u) * (x \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(21056,a,23843,a)].">
      <j1 rule="hyper" parents="21056 23843"/>
    </justification>
  </clause>

  <clause id="23845">
    <literal><![CDATA[
      T(x * ((a(y,z,u) * x) \ w),w / L(a(y,z,u),x,x)) = (x \ 1) * ((a(y,z,u) * (x \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(3197(a,1),23844(a,1,2,2))].">
      <j1 rule="para" parents="3197 23844"/>
    </justification>
  </clause>

  <clause id="23850">
    <literal><![CDATA[
      ((L(x,y,z) * (x \ u)) \ u) \ K(u / (L(x,y,z) * (x \ u)),x \ L(x,y,z)) = 1 / ((L(x,y,z) * (x \ u)) \ u)
    ]]></literal>
    <justification jstring="[para(7388(a,1),22353(a,1,2))].">
      <j1 rule="para" parents="7388 22353"/>
    </justification>
  </clause>

  <clause id="23851">
    <literal><![CDATA[
      1 / ((L(x,y,z) * (x \ u)) \ u) = ((L(x,y,z) * (x \ u)) \ u) \ 1
    ]]></literal>
    <justification jstring="[para(20231(a,1),23850(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20231 23850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23853">
    <literal><![CDATA[
      1 / (((x / y) * L(y,z,u)) \ x) = ((L(y,z,u) * (y \ x)) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(20689(a,1),23851(a,1,2,1))].">
      <j1 rule="para" parents="20689 23851"/>
    </justification>
  </clause>

  <clause id="23854">
    <literal><![CDATA[
      x / L(y \ L(y,z,u),y,x) = x * (1 / (((L(y,z,u) * (y \ x)) \ x) \ 1))
    ]]></literal>
    <justification jstring="[para(23853(a,1),3971(a,2,2,2))].">
      <j1 rule="para" parents="23853 3971"/>
    </justification>
  </clause>

  <clause id="23855">
    <literal><![CDATA[
      x / L(y \ L(y,z,u),y,x) = x * ((L(y,z,u) * (y \ x)) \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,207,a(flip),b,23854,a),flip(a)].">
      <j1 rule="hyper" parents="347 207 23854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23857">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) \ u = u * ((L(x,y,z) * (x \ u)) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,20675,a(flip),b,23855,a)].">
      <j1 rule="hyper" parents="63 20675 23855"/>
    </justification>
  </clause>

  <clause id="23859">
    <literal><![CDATA[
      R(x,y * (T(z,u) * (T(T(z,w),v5) \ (T(T(z,w),v5) \ v6))),v7) = R(x,y * L(T(z,u) * v6,T(T(z,w),v5),T(T(z,w),v5)),v7)
    ]]></literal>
    <justification jstring="[para(22703(a,1),22704(a,1,2,2))].">
      <j1 rule="para" parents="22703 22704"/>
    </justification>
  </clause>

  <clause id="23860">
    <literal><![CDATA[
      R(x,y * (T(z,u) * (T(z,w) \ (T(T(T(z,w),v5),v5) \ v6))),v7) = R(x,y * L(T(z,u) * v6,T(T(z,w),v5),T(T(z,w),v5)),v7)
    ]]></literal>
    <justification jstring="[para(5580(a,1),23859(a,1,2,2,2))].">
      <j1 rule="para" parents="5580 23859"/>
    </justification>
  </clause>

  <clause id="23861">
    <literal><![CDATA[
      R(x,y * (K(z,u) * (K(w,z) * (T(T(T(z,w),v5),v5) \ v6))),v7) = R(x,y * L(T(z,u) * v6,T(T(z,w),v5),T(T(z,w),v5)),v7)
    ]]></literal>
    <justification jstring="[para(5244(a,2),23860(a,1,2,2))].">
      <j1 rule="para" parents="5244 23860"/>
    </justification>
  </clause>

  <clause id="23862">
    <literal><![CDATA[
      R(x,y * L(T(z,u) * w,T(T(z,v5),v6),T(T(z,v5),v6)),v7) = R(x,(K(z,u) * (T(T(T(z,v5),v6),v6) \ w)) * y,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,22496,a(flip),b,23861,a),flip(a)].">
      <j1 rule="hyper" parents="63 22496 23861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23864">
    <literal><![CDATA[
      R(x,y * L(T(z,u) * w,T(T(z,v5),v6),T(T(z,v5),v6)),v7) = R(x,K(z,u) * ((T(T(T(z,v5),v6),v6) \ w) * y),v7)
    ]]></literal>
    <justification jstring="[para(20008(a,1),23862(a,2,2))].">
      <j1 rule="para" parents="20008 23862"/>
    </justification>
  </clause>

  <clause id="23865">
    <literal><![CDATA[
      R(x,y * L(T(z,u) * w,T(T(z,v5),v6),T(T(z,v5),v6)),v7) = R(x,K(z,u) * (y * (T(T(z,v5),v6) \ w)),v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,22544,a(flip),b,23864,a),flip(a)].">
      <j1 rule="hyper" parents="347 22544 23864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23867">
    <literal><![CDATA[
      R(x,y * L(T(z,u) * w,T(T(z,v5),v6),T(T(z,v5),v6)),v7) = R(x,(y * (T(z,v5) \ w)) * K(z,u),v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,22505,a(flip),b,23865,a),flip(a)].">
      <j1 rule="hyper" parents="347 22505 23865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23869">
    <literal><![CDATA[
      R(x,y * L(T(z,u) * w,T(T(z,v5),v6),T(T(z,v5),v6)),v7) = R(x,y * (T(z,v5) \ w),v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,22396,a(flip),b,23867,a),flip(a)].">
      <j1 rule="hyper" parents="347 22396 23867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23871">
    <literal><![CDATA[
      R(x,y * L(T(z,u) * w,T(T(z,v5),v6),T(T(z,v5),v6)),v7) = R(x,y * (z \ w),v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,22426,a(flip),b,23869,a),flip(a)].">
      <j1 rule="hyper" parents="347 22426 23869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23873">
    <literal><![CDATA[
      R(x,y * L(T(z,u) * w,T(T(z,v5),v6),T(z,v5)),v7) = R(x,y * (z \ w),v7)
    ]]></literal>
    <justification jstring="[para(20041(a,1),23871(a,1,2,2))].">
      <j1 rule="para" parents="20041 23871"/>
    </justification>
  </clause>

  <clause id="23874">
    <literal><![CDATA[
      R(x,y * L(T(z,u) * w,T(T(z,v5),v6),z),v7) = R(x,y * (z \ w),v7)
    ]]></literal>
    <justification jstring="[para(20041(a,1),23873(a,1,2,2))].">
      <j1 rule="para" parents="20041 23873"/>
    </justification>
  </clause>

  <clause id="23876">
    <literal><![CDATA[
      R(x,y * L(T(z,u) * w,z,z),v5) = R(x,y * (z \ w),v5)
    ]]></literal>
    <justification jstring="[para(224(a,1),23874(a,1,2,2,2))].">
      <j1 rule="para" parents="224 23874"/>
    </justification>
  </clause>

  <clause id="23878">
    <literal><![CDATA[
      L(L(x \ 1,x,x \ y) \ z,K(x,u) * (y \ (y / T(x,u))),(y / T(x,u)) * x) = (y / T(x,u)) \ (((y / T(x,u)) * x) * z)
    ]]></literal>
    <justification jstring="[para(20166(a,1),21509(a,1,2))].">
      <j1 rule="para" parents="20166 21509"/>
    </justification>
  </clause>

  <clause id="23880">
    <literal><![CDATA[
      a(T(x,K(y,z)) * K(z,y),L(u,K(z,y),T(x,K(y,z))),w) = (K(z,y) * (x * (u * w))) \ ((K(z,y) * (x * u)) * w)
    ]]></literal>
    <justification jstring="[para(21322(a,1),22919(a,2,2,1))].">
      <j1 rule="para" parents="21322 22919"/>
    </justification>
  </clause>

  <clause id="23881">
    <literal><![CDATA[
      a(T(x,K(y,z)) * K(z,y),L(u,K(z,y),T(x,K(y,z))),w) = (K(z,y) * (x * (u * w))) \ (K(z,y) * ((x * u) * w))
    ]]></literal>
    <justification jstring="[para(20008(a,1),23880(a,2,2))].">
      <j1 rule="para" parents="20008 23880"/>
    </justification>
  </clause>

  <clause id="23882">
    <literal><![CDATA[
      a(K(x,y) * z,L(u,K(x,y),T(z,K(y,x))),w) = (K(x,y) * (z * (u * w))) \ (K(x,y) * ((z * u) * w))
    ]]></literal>
    <justification jstring="[para(6885(a,1),23881(a,1,1))].">
      <j1 rule="para" parents="6885 23881"/>
    </justification>
  </clause>

  <clause id="23883">
    <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(20075(a,1),23882(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20075 23882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23884">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),K(u,w)) = a(K(u,w) * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(944,a,23883,a)].">
      <j1 rule="hyper" parents="944 23883"/>
    </justification>
  </clause>

  <clause id="23885">
    <literal><![CDATA[
      a(K(x,y) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(20035,a,23884,a),flip(a)].">
      <j1 rule="hyper" parents="20035 23884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23886">
    <literal><![CDATA[
      a(K(x,y) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(23884(a,1),20035(a,1))].">
      <j1 rule="para" parents="23884 20035"/>
    </justification>
  </clause>

  <clause id="23887">
    <literal><![CDATA[
      a(x \ T(y,z),u,w) = a(x \ y,u,w)
    ]]></literal>
    <justification jstring="[hyper(17840,a,23885,a)].">
      <j1 rule="hyper" parents="17840 23885"/>
    </justification>
  </clause>

  <clause id="23888">
    <literal><![CDATA[
      a(x \ K(y,z),u,w) = a(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(17839,a,23885,a)].">
      <j1 rule="hyper" parents="17839 23885"/>
    </justification>
  </clause>

  <clause id="23891">
    <literal><![CDATA[
      a(x * K(y,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,17852,a(flip),b,23885,a)].">
      <j1 rule="hyper" parents="63 17852 23885"/>
    </justification>
  </clause>

  <clause id="23892">
    <literal><![CDATA[
      a((x / y) \ z,u,w) = a((y \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,11590,a(flip),b,23885,a)].">
      <j1 rule="hyper" parents="63 11590 23885"/>
    </justification>
  </clause>

  <clause id="23893">
    <literal><![CDATA[
      a(x / y,z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,11581,a(flip),b,23885,a)].">
      <j1 rule="hyper" parents="63 11581 23885"/>
    </justification>
  </clause>

  <clause id="23894">
    <literal><![CDATA[
      a(T(x,y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(1324(a,2),23885(a,1,1))].">
      <j1 rule="para" parents="1324 23885"/>
    </justification>
  </clause>

  <clause id="23895">
    <literal><![CDATA[
      a((x \ y) * x,z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(4898(a,1),23885(a,1,1))].">
      <j1 rule="para" parents="4898 23885"/>
    </justification>
  </clause>

  <clause id="23896">
    <literal><![CDATA[
      a(x * y,z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(4909(a,1),23885(a,1,1))].">
      <j1 rule="para" parents="4909 23885"/>
    </justification>
  </clause>

  <clause id="23898">
    <literal><![CDATA[
      a(T(x,y) * z,u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(4946(a,1),23885(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4946 23885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23899">
    <literal><![CDATA[
      a((x / y) * z,u,w) = a((y \ x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(5237(a,1),23885(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5237 23885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23900">
    <literal><![CDATA[
      a(L(T(x,y),z,u),w,v5) = a(L(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(5028(a,1),23885(a,1,1))].">
      <j1 rule="para" parents="5028 23885"/>
    </justification>
  </clause>

  <clause id="23901">
    <literal><![CDATA[
      a(x * T(y,z),u,w) = a(x * y,u,w)
    ]]></literal>
    <justification jstring="[para(5573(a,1),23885(a,1,1))].">
      <j1 rule="para" parents="5573 23885"/>
    </justification>
  </clause>

  <clause id="23902">
    <literal><![CDATA[
      a(x * (K(y,z) * u),w,v5) = a(x * u,w,v5)
    ]]></literal>
    <justification jstring="[para(5885(a,1),23885(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5885 23885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23903">
    <literal><![CDATA[
      a(x * (y * z),u,w) = a(x * (z * y),u,w)
    ]]></literal>
    <justification jstring="[para(9586(a,1),23885(a,1,1))].">
      <j1 rule="para" parents="9586 23885"/>
    </justification>
  </clause>

  <clause id="23904">
    <literal><![CDATA[
      a(((x \ y) * x) * z,u,w) = a(y * z,u,w)
    ]]></literal>
    <justification jstring="[para(10244(a,1),23885(a,1,1))].">
      <j1 rule="para" parents="10244 23885"/>
    </justification>
  </clause>

  <clause id="23905">
    <literal><![CDATA[
      a(((x \ y) * x) \ z,u,w) = a(y \ z,u,w)
    ]]></literal>
    <justification jstring="[para(10296(a,1),23885(a,1,1))].">
      <j1 rule="para" parents="10296 23885"/>
    </justification>
  </clause>

  <clause id="23906">
    <literal><![CDATA[
      a(x \ (K(y,z) * u),w,v5) = a(x \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(19540(a,1),23885(a,1,1))].">
      <j1 rule="para" parents="19540 23885"/>
    </justification>
  </clause>

  <clause id="23907">
    <literal><![CDATA[
      a(x * (T(y,z) \ u),w,v5) = a(x * (y \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(19545(a,1),23885(a,1,1))].">
      <j1 rule="para" parents="19545 23885"/>
    </justification>
  </clause>

  <clause id="23908">
    <literal><![CDATA[
      a((K(x,y) * z) \ u,w,v5) = a(z \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(20697(a,1),23885(a,1,1))].">
      <j1 rule="para" parents="20697 23885"/>
    </justification>
  </clause>

  <clause id="23909">
    <literal><![CDATA[
      a((x * T(y,z)) \ u,w,v5) = a((x * y) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(20828(a,1),23885(a,1,1))].">
      <j1 rule="para" parents="20828 23885"/>
    </justification>
  </clause>

  <clause id="23910">
    <literal><![CDATA[
      a((x \ K(y,z)) \ u,w,v5) = a((x \ 1) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(20832(a,1),23885(a,1,1))].">
      <j1 rule="para" parents="20832 23885"/>
    </justification>
  </clause>

  <clause id="23911">
    <literal><![CDATA[
      a((x \ T(y,z)) \ u,w,v5) = a((x \ y) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(20834(a,1),23885(a,1,1))].">
      <j1 rule="para" parents="20834 23885"/>
    </justification>
  </clause>

  <clause id="23912">
    <literal><![CDATA[
      a(((x * y) * z) * u,w,v5) = a(((y * x) * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(20724(a,1),23885(a,1,1))].">
      <j1 rule="para" parents="20724 23885"/>
    </justification>
  </clause>

  <clause id="23913">
    <literal><![CDATA[
      a((T(x,y) * z) \ u,w,v5) = a((x * z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(20829(a,1),23885(a,1,1))].">
      <j1 rule="para" parents="20829 23885"/>
    </justification>
  </clause>

  <clause id="23914">
    <literal><![CDATA[
      a(((x / y) \ z) * u,w,v5) = a(((y \ x) \ z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(20721(a,1),23885(a,1,1))].">
      <j1 rule="para" parents="20721 23885"/>
    </justification>
  </clause>

  <clause id="23915">
    <literal><![CDATA[
      a(((x \ 1) * T(y,K(z,u))) \ w,v5,v6) = a(((x \ K(z,u)) * y) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(21206(a,1),23885(a,1,1))].">
      <j1 rule="para" parents="21206 23885"/>
    </justification>
  </clause>

  <clause id="23922">
    <literal><![CDATA[
      a(L(x / y,z,u),w,v5) = a(L(y \ x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(278(a,1),23894(a,1,1)),flip(a)].">
      <j1 rule="para" parents="278 23894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23923">
    <literal><![CDATA[
      a((x \ y) * (x * x),z,u) = a((x \ 1) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(816(a,1),23894(a,1,1))].">
      <j1 rule="para" parents="816 23894"/>
    </justification>
  </clause>

  <clause id="23925">
    <literal><![CDATA[
      a(x * y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y * x,z,u) = w
    ]]></literal>
    <justification jstring="[para(23894(a,1),11584(a,1))].">
      <j1 rule="para" parents="23894 11584"/>
    </justification>
  </clause>

  <clause id="23934">
    <literal><![CDATA[
      a(x * (y / z),u,w) = a(x * (z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(5927(a,1),23891(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5927 23891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23935">
    <literal><![CDATA[
      a(x * (y * K(z,u)),w,v5) = a(x * y,w,v5)
    ]]></literal>
    <justification jstring="[para(7609(a,1),23891(a,1,1))].">
      <j1 rule="para" parents="7609 23891"/>
    </justification>
  </clause>

  <clause id="23936">
    <literal><![CDATA[
      a(x \ (y / z),u,w) = a(x \ (z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(13113(a,1),23891(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13113 23891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23937">
    <literal><![CDATA[
      a(x \ (y * T(z,u)),w,v5) = a(x \ (y * z),w,v5)
    ]]></literal>
    <justification jstring="[para(20791(a,1),23891(a,1,1))].">
      <j1 rule="para" parents="20791 23891"/>
    </justification>
  </clause>

  <clause id="23938">
    <literal><![CDATA[
      a(x \ (y \ T(z,u)),w,v5) = a(x \ (y \ z),w,v5)
    ]]></literal>
    <justification jstring="[para(20794(a,1),23891(a,1,1))].">
      <j1 rule="para" parents="20794 23891"/>
    </justification>
  </clause>

  <clause id="23939">
    <literal><![CDATA[
      a(L(x * K(y,z),u,w),v5,v6) = a(L(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(21247(a,2),23891(a,1,1))].">
      <j1 rule="para" parents="21247 23891"/>
    </justification>
  </clause>

  <clause id="23943">
    <literal><![CDATA[
      a((x * T(y,z * x)) \ (y * (z * x)),u,w) = a(R(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[para(13917(a,2),23893(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13917 23893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23944">
    <literal><![CDATA[
      a(x * ((y * y) * z),u,w) = a(z * (x * (y * y)),u,w)
    ]]></literal>
    <justification jstring="[para(117(a,1),23895(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="117 23895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23945">
    <literal><![CDATA[
      L(x,y,a((z * z) \ u,w,v5)) = L(x,y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(23895(a,1),23258(a,1,3)),flip(a)].">
      <j1 rule="para" parents="23895 23258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23947">
    <literal><![CDATA[
      a(((x * y) \ z) * T(x,y),u,w) = a(x * ((y * x) \ z),u,w)
    ]]></literal>
    <justification jstring="[para(10295(a,1),23896(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10295 23896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23948">
    <literal><![CDATA[
      a(K(x,y) * (L(z,u,w) * v5),v6,v7) = a(v5 * L(K(x,y) * z,u,w),v6,v7)
    ]]></literal>
    <justification jstring="[para(21271(a,1),23896(a,1,1))].">
      <j1 rule="para" parents="21271 23896"/>
    </justification>
  </clause>

  <clause id="23949">
    <literal><![CDATA[
      a(x \ ((y / z) / (1 / z)),u,w) = a(x \ (z \ (y / (z \ 1))),u,w)
    ]]></literal>
    <justification jstring="[para(2286(a,1),23887(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2286 23887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23950">
    <literal><![CDATA[
      a(((x * x) \ y) * z,u,w) = a(y * ((x * x) \ z),u,w)
    ]]></literal>
    <justification jstring="[para(829(a,1),23898(a,1,1))].">
      <j1 rule="para" parents="829 23898"/>
    </justification>
  </clause>

  <clause id="23951">
    <literal><![CDATA[
      a((x * (y * (x \ 1))) * z,u,w) = a(L(y,x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(3290(a,1),23898(a,1,1,1))].">
      <j1 rule="para" parents="3290 23898"/>
    </justification>
  </clause>

  <clause id="23953">
    <literal><![CDATA[
      a(T(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(1324(a,2),23886(a,1,1))].">
      <j1 rule="para" parents="1324 23886"/>
    </justification>
  </clause>

  <clause id="23954">
    <literal><![CDATA[
      a((x \ y) * x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(4898(a,1),23886(a,1,1))].">
      <j1 rule="para" parents="4898 23886"/>
    </justification>
  </clause>

  <clause id="23955">
    <literal><![CDATA[
      a(T(x,y) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(4974(a,1),23886(a,1,1))].">
      <j1 rule="para" parents="4974 23886"/>
    </justification>
  </clause>

  <clause id="23956">
    <literal><![CDATA[
      a(x / y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(5012(a,1),23886(a,1,1))].">
      <j1 rule="para" parents="5012 23886"/>
    </justification>
  </clause>

  <clause id="23957">
    <literal><![CDATA[
      a((x \ y) \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(5017(a,2),23886(a,1,1))].">
      <j1 rule="para" parents="5017 23886"/>
    </justification>
  </clause>

  <clause id="23959">
    <literal><![CDATA[
      a(T(x,y) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x \ z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(5209(a,1),23886(a,1,1))].">
      <j1 rule="para" parents="5209 23886"/>
    </justification>
  </clause>

  <clause id="23960">
    <literal><![CDATA[
      a(((x \ y) \ y) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x \ z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(5340(a,2),23886(a,1,1))].">
      <j1 rule="para" parents="5340 23886"/>
    </justification>
  </clause>

  <clause id="23961">
    <literal><![CDATA[
      a((x / y) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((y \ x) \ z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(5441(a,1),23886(a,1,1))].">
      <j1 rule="para" parents="5441 23886"/>
    </justification>
  </clause>

  <clause id="23962">
    <literal><![CDATA[
      a((x / y) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((y \ x) * z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(5479(a,1),23886(a,1,1))].">
      <j1 rule="para" parents="5479 23886"/>
    </justification>
  </clause>

  <clause id="23963">
    <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(5028(a,1),23886(a,1,1))].">
      <j1 rule="para" parents="5028 23886"/>
    </justification>
  </clause>

  <clause id="23964">
    <literal><![CDATA[
      a(x * T(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * y,u,w) = v5
    ]]></literal>
    <justification jstring="[para(5573(a,1),23886(a,1,1))].">
      <j1 rule="para" parents="5573 23886"/>
    </justification>
  </clause>

  <clause id="23966">
    <literal><![CDATA[
      a(x * K(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(7372(a,1),23886(a,1,1))].">
      <j1 rule="para" parents="7372 23886"/>
    </justification>
  </clause>

  <clause id="23967">
    <literal><![CDATA[
      a(x * (y * z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * (z * y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(9586(a,1),23886(a,1,1))].">
      <j1 rule="para" parents="9586 23886"/>
    </justification>
  </clause>

  <clause id="23968">
    <literal><![CDATA[
      a(((x \ y) * x) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y * z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(10244(a,1),23886(a,1,1))].">
      <j1 rule="para" parents="10244 23886"/>
    </justification>
  </clause>

  <clause id="23969">
    <literal><![CDATA[
      a((x * y) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((y * x) * z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(10281(a,1),23886(a,1,1))].">
      <j1 rule="para" parents="10281 23886"/>
    </justification>
  </clause>

  <clause id="23970">
    <literal><![CDATA[
      a(R(T(x,y),z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(R(x,z,u),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(14119(a,1),23886(a,1,1))].">
      <j1 rule="para" parents="14119 23886"/>
    </justification>
  </clause>

  <clause id="23971">
    <literal><![CDATA[
      a(x \ (K(y,z) * u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x \ u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(19540(a,1),23886(a,1,1))].">
      <j1 rule="para" parents="19540 23886"/>
    </justification>
  </clause>

  <clause id="23972">
    <literal><![CDATA[
      a((x \ y) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((T(x,v6) \ y) * z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(20718(a,1),23886(a,1,1))].">
      <j1 rule="para" parents="20718 23886"/>
    </justification>
  </clause>

  <clause id="23973">
    <literal><![CDATA[
      a((x * T(y,z)) \ u,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a((x * y) \ u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(20828(a,1),23886(a,1,1))].">
      <j1 rule="para" parents="20828 23886"/>
    </justification>
  </clause>

  <clause id="23974">
    <literal><![CDATA[
      a((x \ T(y,z)) \ u,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a((x \ y) \ u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(20834(a,1),23886(a,1,1))].">
      <j1 rule="para" parents="20834 23886"/>
    </justification>
  </clause>

  <clause id="23975">
    <literal><![CDATA[
      a((T(x,y) * z) \ u,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a((x * z) \ u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(20829(a,1),23886(a,1,1))].">
      <j1 rule="para" parents="20829 23886"/>
    </justification>
  </clause>

  <clause id="23976">
    <literal><![CDATA[
      a(L(K(x,y) * z,u,w),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(L(z,u,w),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(21250(a,2),23886(a,1,1))].">
      <j1 rule="para" parents="21250 23886"/>
    </justification>
  </clause>

  <clause id="23977">
    <literal><![CDATA[
      a((x \ y) * (x * x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a((x \ 1) \ y,z,u) = w
    ]]></literal>
    <justification jstring="[para(816(a,1),23953(a,1,1))].">
      <j1 rule="para" parents="816 23953"/>
    </justification>
  </clause>

  <clause id="23978">
    <literal><![CDATA[
      a((x * T(y,x * x)) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(((x * x) * z) * ((x \ 1) * y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(992(a,1),23925(a,1,1))].">
      <j1 rule="para" parents="992 23925"/>
    </justification>
  </clause>

  <clause id="23980">
    <literal><![CDATA[
      a(x * (y * (z * z)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y * ((z * z) * x),u,w) = v5
    ]]></literal>
    <justification jstring="[para(117(a,1),23954(a,1,1,1))].">
      <j1 rule="para" parents="117 23954"/>
    </justification>
  </clause>

  <clause id="23982">
    <literal><![CDATA[
      a(x * ((y \ z) \ z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * y,u,w) = v5
    ]]></literal>
    <justification jstring="[para(5954(a,1),23966(a,1,1))].">
      <j1 rule="para" parents="5954 23966"/>
    </justification>
  </clause>

  <clause id="23983">
    <literal><![CDATA[
      a(x * (y / z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * (z \ y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(6075(a,1),23966(a,1,1))].">
      <j1 rule="para" parents="6075 23966"/>
    </justification>
  </clause>

  <clause id="23984">
    <literal><![CDATA[
      a(x \ ((y \ z) \ z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x \ y,u,w) = v5
    ]]></literal>
    <justification jstring="[para(13103(a,2),23966(a,1,1))].">
      <j1 rule="para" parents="13103 23966"/>
    </justification>
  </clause>

  <clause id="23985">
    <literal><![CDATA[
      a(x \ (y / z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x \ (z \ y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(13354(a,1),23966(a,1,1))].">
      <j1 rule="para" parents="13354 23966"/>
    </justification>
  </clause>

  <clause id="23986">
    <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(20791(a,1),23966(a,1,1))].">
      <j1 rule="para" parents="20791 23966"/>
    </justification>
  </clause>

  <clause id="23987">
    <literal><![CDATA[
      a(x,K(y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(22920(a,1),23966(a,1))].">
      <j1 rule="para" parents="22920 23966"/>
    </justification>
  </clause>

  <clause id="23990">
    <literal><![CDATA[
      a(x,y * K(z,u),w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(23987,a,19081,a),flip(a)].">
      <j1 rule="hyper" parents="23987 19081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23991">
    <literal><![CDATA[
      a(x,T(y,z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(23987,a,14983,a)].">
      <j1 rule="hyper" parents="23987 14983"/>
    </justification>
  </clause>

  <clause id="23992">
    <literal><![CDATA[
      a(x,T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(1324(a,2),23987(a,1,2))].">
      <j1 rule="para" parents="1324 23987"/>
    </justification>
  </clause>

  <clause id="23993">
    <literal><![CDATA[
      a(x,(y \ z) * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(4898(a,1),23987(a,1,2))].">
      <j1 rule="para" parents="4898 23987"/>
    </justification>
  </clause>

  <clause id="23994">
    <literal><![CDATA[
      a(x,y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z * y,u) = w
    ]]></literal>
    <justification jstring="[para(4909(a,1),23987(a,1,2))].">
      <j1 rule="para" parents="4909 23987"/>
    </justification>
  </clause>

  <clause id="23995">
    <literal><![CDATA[
      a(x,T(y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y * u,w) = v5
    ]]></literal>
    <justification jstring="[para(4974(a,1),23987(a,1,2))].">
      <j1 rule="para" parents="4974 23987"/>
    </justification>
  </clause>

  <clause id="23996">
    <literal><![CDATA[
      a(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,K(w,v5) * y,z) = u
    ]]></literal>
    <justification jstring="[para(5261(a,1),23987(a,1,2))].">
      <j1 rule="para" parents="5261 23987"/>
    </justification>
  </clause>

  <clause id="23997">
    <literal><![CDATA[
      a(x,y / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,u) = w
    ]]></literal>
    <justification jstring="[para(5012(a,1),23987(a,1,2))].">
      <j1 rule="para" parents="5012 23987"/>
    </justification>
  </clause>

  <clause id="23998">
    <literal><![CDATA[
      a(x,(y \ z) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(5017(a,2),23987(a,1,2))].">
      <j1 rule="para" parents="5017 23987"/>
    </justification>
  </clause>

  <clause id="24001">
    <literal><![CDATA[
      a(x,(y / z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,(z \ y) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(5479(a,1),23987(a,1,2))].">
      <j1 rule="para" parents="5479 23987"/>
    </justification>
  </clause>

  <clause id="24002">
    <literal><![CDATA[
      a(x,y \ T(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ z,w) = v5
    ]]></literal>
    <justification jstring="[para(5570(a,1),23987(a,1,2))].">
      <j1 rule="para" parents="5570 23987"/>
    </justification>
  </clause>

  <clause id="24003">
    <literal><![CDATA[
      a(x,L(y,z,u) * (u * z),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u * (z * y),w) = v5
    ]]></literal>
    <justification jstring="[para(4911(a,1),23987(a,1,2))].">
      <j1 rule="para" parents="4911 23987"/>
    </justification>
  </clause>

  <clause id="24005">
    <literal><![CDATA[
      a(x,y * K(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(7372(a,1),23987(a,1,2))].">
      <j1 rule="para" parents="7372 23987"/>
    </justification>
  </clause>

  <clause id="24006">
    <literal><![CDATA[
      a(x,y * (z * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y * (u * z),w) = v5
    ]]></literal>
    <justification jstring="[para(9586(a,1),23987(a,1,2))].">
      <j1 rule="para" parents="9586 23987"/>
    </justification>
  </clause>

  <clause id="24007">
    <literal><![CDATA[
      a(x,(y * z) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,(z * y) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(10274(a,1),23987(a,1,2))].">
      <j1 rule="para" parents="10274 23987"/>
    </justification>
  </clause>

  <clause id="24008">
    <literal><![CDATA[
      a(x,(y * z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,(z * y) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(10281(a,1),23987(a,1,2))].">
      <j1 rule="para" parents="10281 23987"/>
    </justification>
  </clause>

  <clause id="24010">
    <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(19545(a,1),23987(a,1,2))].">
      <j1 rule="para" parents="19545 23987"/>
    </justification>
  </clause>

  <clause id="24012">
    <literal><![CDATA[
      a(x,L(y / z,u,w) \ v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,L(z \ y,u,w) \ v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(21279(a,1),23987(a,1,2))].">
      <j1 rule="para" parents="21279 23987"/>
    </justification>
  </clause>

  <clause id="24014">
    <literal><![CDATA[
      a(x,(y \ z) \ z,u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(14999,a,23991,a)].">
      <j1 rule="hyper" parents="14999 23991"/>
    </justification>
  </clause>

  <clause id="24022">
    <literal><![CDATA[
      a(x,L(T(y,z),u,w),v5) = a(x,L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(25(a,2),23991(a,1,2))].">
      <j1 rule="para" parents="25 23991"/>
    </justification>
  </clause>

  <clause id="24023">
    <literal><![CDATA[
      a(x,y / z,u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(113(a,1),23991(a,1,2)),flip(a)].">
      <j1 rule="para" parents="113 23991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24024">
    <literal><![CDATA[
      a(x,L(y / z,u,w),v5) = a(x,L(z \ y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(278(a,1),23991(a,1,2)),flip(a)].">
      <j1 rule="para" parents="278 23991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24036">
    <literal><![CDATA[
      a(x,y,K(z,u) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,22020,a(flip),b,23990,a)].">
      <j1 rule="hyper" parents="63 22020 23990"/>
    </justification>
  </clause>

  <clause id="24037">
    <literal><![CDATA[
      a(x,y * z,u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(91(a,1),23990(a,1,2))].">
      <j1 rule="para" parents="91 23990"/>
    </justification>
  </clause>

  <clause id="24038">
    <literal><![CDATA[
      a(x,(y \ z) * y,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(330(a,1),23990(a,1,2))].">
      <j1 rule="para" parents="330 23990"/>
    </justification>
  </clause>

  <clause id="24040">
    <literal><![CDATA[
      a(x,L(y,z,u) * (u * z),w) = a(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[para(537(a,1),23990(a,1,2))].">
      <j1 rule="para" parents="537 23990"/>
    </justification>
  </clause>

  <clause id="24042">
    <literal><![CDATA[
      a(x,T(y,z) * u,w) = a(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(5564(a,1),23990(a,1,2))].">
      <j1 rule="para" parents="5564 23990"/>
    </justification>
  </clause>

  <clause id="24043">
    <literal><![CDATA[
      a(x,y * (z / u),w) = a(x,y * (u \ z),w)
    ]]></literal>
    <justification jstring="[para(5927(a,1),23990(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5927 23990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24044">
    <literal><![CDATA[
      a(x,y \ R(T(z,u),w,v5),v6) = a(x,y \ R(z,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(5796(a,1),23990(a,1,2))].">
      <j1 rule="para" parents="5796 23990"/>
    </justification>
  </clause>

  <clause id="24045">
    <literal><![CDATA[
      a(x,y * (z * T(u,w)),v5) = a(x,y * (z * u),v5)
    ]]></literal>
    <justification jstring="[para(6975(a,1),23990(a,1,2))].">
      <j1 rule="para" parents="6975 23990"/>
    </justification>
  </clause>

  <clause id="24046">
    <literal><![CDATA[
      a(x,y * (z * u),w) = a(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[para(6977(a,1),23990(a,1,2))].">
      <j1 rule="para" parents="6977 23990"/>
    </justification>
  </clause>

  <clause id="24048">
    <literal><![CDATA[
      a(x,(y / z) * u,w) = a(x,(z \ y) * u,w)
    ]]></literal>
    <justification jstring="[para(7768(a,1),23990(a,1,2))].">
      <j1 rule="para" parents="7768 23990"/>
    </justification>
  </clause>

  <clause id="24049">
    <literal><![CDATA[
      a(x,y * (z * K(u,w)),v5) = a(x,y * z,v5)
    ]]></literal>
    <justification jstring="[para(7609(a,1),23990(a,1,2))].">
      <j1 rule="para" parents="7609 23990"/>
    </justification>
  </clause>

  <clause id="24051">
    <literal><![CDATA[
      a(x,y \ (z / u),w) = a(x,y \ (u \ z),w)
    ]]></literal>
    <justification jstring="[para(13113(a,1),23990(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13113 23990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24052">
    <literal><![CDATA[
      a(x,y \ (z * u),w) = a(x,y \ (u * z),w)
    ]]></literal>
    <justification jstring="[para(13432(a,1),23990(a,1,2))].">
      <j1 rule="para" parents="13432 23990"/>
    </justification>
  </clause>

  <clause id="24053">
    <literal><![CDATA[
      a(x,y \ (z * K(u,w)),v5) = a(x,y \ z,v5)
    ]]></literal>
    <justification jstring="[para(14549(a,1),23990(a,1,2))].">
      <j1 rule="para" parents="14549 23990"/>
    </justification>
  </clause>

  <clause id="24054">
    <literal><![CDATA[
      a(x,y \ (K(z,u) * w),v5) = a(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(20369(a,1),23990(a,1,2))].">
      <j1 rule="para" parents="20369 23990"/>
    </justification>
  </clause>

  <clause id="24055">
    <literal><![CDATA[
      a(x,L(y * K(z,u),w,v5),v6) = a(x,L(y,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(21247(a,2),23990(a,1,2))].">
      <j1 rule="para" parents="21247 23990"/>
    </justification>
  </clause>

  <clause id="24060">
    <literal><![CDATA[
      a(x,(y * y) \ z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14953,a(flip),b,24023,a),flip(a)].">
      <j1 rule="hyper" parents="63 14953 24023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24061">
    <literal><![CDATA[
      a(x,(y * z) / (u * (w * w)),v5) = a(x,u \ (y * (z / (w * w))),v5)
    ]]></literal>
    <justification jstring="[para(813(a,1),24023(a,1,2))].">
      <j1 rule="para" parents="813 24023"/>
    </justification>
  </clause>

  <clause id="24067">
    <literal><![CDATA[
      a(x,y,T(z,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(1324(a,2),24036(a,1,3))].">
      <j1 rule="para" parents="1324 24036"/>
    </justification>
  </clause>

  <clause id="24068">
    <literal><![CDATA[
      a(x,y,(z \ u) * z) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(4898(a,1),24036(a,1,3))].">
      <j1 rule="para" parents="4898 24036"/>
    </justification>
  </clause>

  <clause id="24069">
    <literal><![CDATA[
      a(x,y,z * u) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(4909(a,1),24036(a,1,3))].">
      <j1 rule="para" parents="4909 24036"/>
    </justification>
  </clause>

  <clause id="24070">
    <literal><![CDATA[
      a(x,y,T(z,u) * w) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(4946(a,1),24036(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4946 24036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24071">
    <literal><![CDATA[
      a(x,y,z / u) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(5012(a,1),24036(a,1,3))].">
      <j1 rule="para" parents="5012 24036"/>
    </justification>
  </clause>

  <clause id="24072">
    <literal><![CDATA[
      a(x,y,(z \ u) \ u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(5017(a,2),24036(a,1,3))].">
      <j1 rule="para" parents="5017 24036"/>
    </justification>
  </clause>

  <clause id="24073">
    <literal><![CDATA[
      a(x,y,T(z,u) \ w) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(5159(a,1),24036(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5159 24036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24074">
    <literal><![CDATA[
      a(x,y,(z / u) * w) = a(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[para(5237(a,1),24036(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5237 24036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24075">
    <literal><![CDATA[
      a(x,y,L(T(z,u),w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(5028(a,1),24036(a,1,3))].">
      <j1 rule="para" parents="5028 24036"/>
    </justification>
  </clause>

  <clause id="24076">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * (w * u)) = a(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[para(4911(a,1),24036(a,1,3))].">
      <j1 rule="para" parents="4911 24036"/>
    </justification>
  </clause>

  <clause id="24077">
    <literal><![CDATA[
      a(x,y,(T(z,u) * w) * v5) = a(x,y,(z * w) * v5)
    ]]></literal>
    <justification jstring="[para(5846(a,1),24036(a,1,3))].">
      <j1 rule="para" parents="5846 24036"/>
    </justification>
  </clause>

  <clause id="24078">
    <literal><![CDATA[
      a(x,y,z * (K(u,w) * v5)) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(5885(a,1),24036(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5885 24036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24080">
    <literal><![CDATA[
      a(x,y,z * K(u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(7372(a,1),24036(a,1,3))].">
      <j1 rule="para" parents="7372 24036"/>
    </justification>
  </clause>

  <clause id="24082">
    <literal><![CDATA[
      a(x,y,z * (u * w)) = a(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[para(9586(a,1),24036(a,1,3))].">
      <j1 rule="para" parents="9586 24036"/>
    </justification>
  </clause>

  <clause id="24083">
    <literal><![CDATA[
      a(x,y,(z * u) \ w) = a(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[para(10274(a,1),24036(a,1,3))].">
      <j1 rule="para" parents="10274 24036"/>
    </justification>
  </clause>

  <clause id="24084">
    <literal><![CDATA[
      a(x,y,(z * u) * w) = a(x,y,(u * z) * w)
    ]]></literal>
    <justification jstring="[para(10281(a,1),24036(a,1,3))].">
      <j1 rule="para" parents="10281 24036"/>
    </justification>
  </clause>

  <clause id="24086">
    <literal><![CDATA[
      a(x,y,(z * T(u,w)) \ v5) = a(x,y,(z * u) \ v5)
    ]]></literal>
    <justification jstring="[para(20828(a,1),24036(a,1,3))].">
      <j1 rule="para" parents="20828 24036"/>
    </justification>
  </clause>

  <clause id="24087">
    <literal><![CDATA[
      a(x,y,L(K(z,u) * w,v5,v6)) = a(x,y,L(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(21250(a,2),24036(a,1,3))].">
      <j1 rule="para" parents="21250 24036"/>
    </justification>
  </clause>

  <clause id="24088">
    <literal><![CDATA[
      a(x,y,L(z * u,w,v5) * v6) = a(x,y,L(u * z,w,v5) * v6)
    ]]></literal>
    <justification jstring="[para(21281(a,1),24036(a,1,3))].">
      <j1 rule="para" parents="21281 24036"/>
    </justification>
  </clause>

  <clause id="24104">
    <literal><![CDATA[
      a(x,(y * y) * z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(15005,a,24037,a),flip(a)].">
      <j1 rule="hyper" parents="15005 24037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24105">
    <literal><![CDATA[
      a(x,y * (z \ 1),u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,14970,a,b,24037,a)].">
      <j1 rule="hyper" parents="347 14970 24037"/>
    </justification>
  </clause>

  <clause id="24106">
    <literal><![CDATA[
      a(x,y * ((z * z) * u),w) = a(x,u * (y * (z * z)),w)
    ]]></literal>
    <justification jstring="[para(32(a,1),24037(a,1,2))].">
      <j1 rule="para" parents="32 24037"/>
    </justification>
  </clause>

  <clause id="24107">
    <literal><![CDATA[
      a(x,L(y,y,z) * z,u) = a(x,z / (y \ 1),u)
    ]]></literal>
    <justification jstring="[para(2008(a,1),24037(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2008 24037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24108">
    <literal><![CDATA[
      a(x,(1 / (1 / (y \ z))) * z,u) = a(x,z / (z \ y),u)
    ]]></literal>
    <justification jstring="[para(3397(a,1),24037(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3397 24037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24109">
    <literal><![CDATA[
      a(x,a(y,z,y) * (u * w),v5) = a(x,w * (a(y,z,y) * u),v5)
    ]]></literal>
    <justification jstring="[para(11372(a,1),24037(a,1,2))].">
      <j1 rule="para" parents="11372 24037"/>
    </justification>
  </clause>

  <clause id="24110">
    <literal><![CDATA[
      a(x,(y * y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(24037(a,1),15005(a,1))].">
      <j1 rule="para" parents="24037 15005"/>
    </justification>
  </clause>

  <clause id="24111">
    <literal><![CDATA[
      a(x,K(y,z) * (u * w),v5) = a(x,w * (K(y,z) * u),v5)
    ]]></literal>
    <justification jstring="[para(20008(a,1),24037(a,1,2))].">
      <j1 rule="para" parents="20008 24037"/>
    </justification>
  </clause>

  <clause id="24112">
    <literal><![CDATA[
      (x * (y * a(z,u * w,v5))) / T(x * a(z,u * w,v5),y) = L(y,a(z,w * u,v5),x)
    ]]></literal>
    <justification jstring="[para(24037(a,1),20610(a,2,2))].">
      <j1 rule="para" parents="24037 20610"/>
    </justification>
  </clause>

  <clause id="24113">
    <literal><![CDATA[
      a(x,(y * y) \ (z \ u),w) = a(x,z \ (u \ 1),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,14971,a,b,24060,a),flip(a)].">
      <j1 rule="hyper" parents="347 14971 24060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24114">
    <literal><![CDATA[
      a(x,y * (y * z),u) = a(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(18(a,2),24060(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 24060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24115">
    <literal><![CDATA[
      a(x,(y \ 1) \ z,u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(500(a,1),24060(a,1,2)),flip(a)].">
      <j1 rule="para" parents="500 24060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24116">
    <literal><![CDATA[
      a(x,L(y \ z,y,y),u) = a(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(99(a,2),24060(a,1,2))].">
      <j1 rule="para" parents="99 24060"/>
    </justification>
  </clause>

  <clause id="24117">
    <literal><![CDATA[
      a(x,(y * (z \ 1)) \ u,w) = a(x,(y * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(973(a,1),24060(a,1,2)),flip(a)].">
      <j1 rule="para" parents="973 24060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24118">
    <literal><![CDATA[
      a(x,L((y * y) \ z,u,w),v5) = a(x,L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(3181(a,2),24060(a,1,2))].">
      <j1 rule="para" parents="3181 24060"/>
    </justification>
  </clause>

  <clause id="24119">
    <literal><![CDATA[
      a(x,L((y \ 1) \ z,u,w),v5) = a(x,L(y \ z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(3183(a,1),24060(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3183 24060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24120">
    <literal><![CDATA[
      a(x,y,L(z * u,w,v5)) = a(x,y,L(u * z,w,v5))
    ]]></literal>
    <justification jstring="[para(3173(a,1),24068(a,1,3))].">
      <j1 rule="para" parents="3173 24068"/>
    </justification>
  </clause>

  <clause id="24123">
    <literal><![CDATA[
      a(x,y,z * u) \ (w * (u * z)) != v5
    ]]></literal>
    <literal><![CDATA[
      (a(x,y,u * z) \ w) * (u * z) = v5
    ]]></literal>
    <justification jstring="[para(24069(a,1),23131(a,1,1))].">
      <j1 rule="para" parents="24069 23131"/>
    </justification>
  </clause>

  <clause id="24126">
    <literal><![CDATA[
      a(x,y,(z * u) / (w * (v5 * v5))) = a(x,y,w \ (z * (u / (v5 * v5))))
    ]]></literal>
    <justification jstring="[para(813(a,1),24071(a,1,3))].">
      <j1 rule="para" parents="813 24071"/>
    </justification>
  </clause>

  <clause id="24127">
    <literal><![CDATA[
      (x \ a(x,x,y \ z)) * (z / y) = x \ (z / y)
    ]]></literal>
    <justification jstring="[para(24071(a,1),18983(a,1,1,2))].">
      <j1 rule="para" parents="24071 18983"/>
    </justification>
  </clause>

  <clause id="24128">
    <literal><![CDATA[
      x \ a(x,x,y \ (z \ ((z * x) * y))) = R(1 / x,x,a(z,x,y))
    ]]></literal>
    <justification jstring="[para(24071(a,1),23141(a,1,2))].">
      <j1 rule="para" parents="24071 23141"/>
    </justification>
  </clause>

  <clause id="24134">
    <literal><![CDATA[
      a(x,y,z * (u / w)) = a(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[para(5927(a,1),24080(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5927 24080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24135">
    <literal><![CDATA[
      a(x,y,z * (u * T(w,v5))) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(6975(a,1),24080(a,1,3))].">
      <j1 rule="para" parents="6975 24080"/>
    </justification>
  </clause>

  <clause id="24136">
    <literal><![CDATA[
      a(x,y,z * (u * K(w,v5))) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(7609(a,1),24080(a,1,3))].">
      <j1 rule="para" parents="7609 24080"/>
    </justification>
  </clause>

  <clause id="24137">
    <literal><![CDATA[
      a(x,y,z \ (u / w)) = a(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(13113(a,1),24080(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13113 24080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24138">
    <literal><![CDATA[
      a(x,y,z \ (u * w)) = a(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[para(13432(a,1),24080(a,1,3))].">
      <j1 rule="para" parents="13432 24080"/>
    </justification>
  </clause>

  <clause id="24139">
    <literal><![CDATA[
      a(x,y,z \ (u * K(w,v5))) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(14549(a,1),24080(a,1,3))].">
      <j1 rule="para" parents="14549 24080"/>
    </justification>
  </clause>

  <clause id="24140">
    <literal><![CDATA[
      a(x,y,z \ (u * T(w,v5))) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(20791(a,1),24080(a,1,3))].">
      <j1 rule="para" parents="20791 24080"/>
    </justification>
  </clause>

  <clause id="24141">
    <literal><![CDATA[
      a(x,y,z \ (u \ T(w,v5))) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(20794(a,1),24080(a,1,3))].">
      <j1 rule="para" parents="20794 24080"/>
    </justification>
  </clause>

  <clause id="24142">
    <literal><![CDATA[
      a(x,y,L(z * K(u,w),v5,v6)) = a(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(21247(a,2),24080(a,1,3))].">
      <j1 rule="para" parents="21247 24080"/>
    </justification>
  </clause>

  <clause id="24143">
    <literal><![CDATA[
      a(x,(y \ (z \ 1)) \ u,w) = a(x,(y \ z) \ u,w)
    ]]></literal>
    <justification jstring="[para(822(a,1),24104(a,1,2))].">
      <j1 rule="para" parents="822 24104"/>
    </justification>
  </clause>

  <clause id="24144">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),w) = a(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(3972(a,1),24104(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3972 24104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24145">
    <literal><![CDATA[
      a(x,y * a(z,z,y),u) = a(x,z \ (z \ y),u)
    ]]></literal>
    <justification jstring="[para(15292(a,1),24104(a,1,2))].">
      <j1 rule="para" parents="15292 24104"/>
    </justification>
  </clause>

  <clause id="24146">
    <literal><![CDATA[
      a(x,L((y \ z) \ z,u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,L(y,u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(342(a,1),23992(a,1,2))].">
      <j1 rule="para" parents="342 23992"/>
    </justification>
  </clause>

  <clause id="24147">
    <literal><![CDATA[
      a(x,y * T(z,u),w) = a(x,z * y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24037,a,b,24042,a)].">
      <j1 rule="hyper" parents="63 24037 24042"/>
    </justification>
  </clause>

  <clause id="24149">
    <literal><![CDATA[
      a(x,y,L(z \ 1,z,u) * w) = a(x,y,(u \ (u / z)) * w)
    ]]></literal>
    <justification jstring="[para(3262(a,1),24070(a,1,3,1))].">
      <j1 rule="para" parents="3262 24070"/>
    </justification>
  </clause>

  <clause id="24150">
    <literal><![CDATA[
      a(x,y,T(z,u) / (T(z,u) \ w)) = a(x,y,z * (1 / (1 / (w \ T(z,u)))))
    ]]></literal>
    <justification jstring="[para(3397(a,1),24070(a,1,3))].">
      <j1 rule="para" parents="3397 24070"/>
    </justification>
  </clause>

  <clause id="24151">
    <literal><![CDATA[
      a(x,(y \ 1) * z,u) = a(x,y * z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,24037,a,b,24105,a)].">
      <j1 rule="hyper" parents="63 24037 24105"/>
    </justification>
  </clause>

  <clause id="24152">
    <literal><![CDATA[
      a(x,y \ R(y,z,u),w) = a(x,y * R(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(1463(a,1),24105(a,1,2))].">
      <j1 rule="para" parents="1463 24105"/>
    </justification>
  </clause>

  <clause id="24153">
    <literal><![CDATA[
      a(x,y \ a(y,z,u),w) = a(x,y * a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(15268(a,1),24105(a,1,2))].">
      <j1 rule="para" parents="15268 24105"/>
    </justification>
  </clause>

  <clause id="24154">
    <literal><![CDATA[
      L(x,y \ z,(y \ 1) \ z) \ x = a((y \ 1) \ z,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,14607,a(flip),b,24115,a)].">
      <j1 rule="hyper" parents="63 14607 24115"/>
    </justification>
  </clause>

  <clause id="24156">
    <literal><![CDATA[
      a(x,y * ((z * z) \ u),(z * z) * w) = a(x,u * y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,2106,a,b,24147,a)].">
      <j1 rule="hyper" parents="63 2106 24147"/>
    </justification>
  </clause>

  <clause id="24157">
    <literal><![CDATA[
      a(L(T(x,y) \ z,x,u),x * u,w) = a((u * x) \ (u * z),u * x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,23757,a(flip),b,24147,a),flip(a)].">
      <j1 rule="hyper" parents="63 23757 24147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24158">
    <literal><![CDATA[
      a(x,y * ((z \ u) \ u),w) = a(x,z * y,w)
    ]]></literal>
    <justification jstring="[para(112(a,1),24147(a,1,2,2))].">
      <j1 rule="para" parents="112 24147"/>
    </justification>
  </clause>

  <clause id="24159">
    <literal><![CDATA[
      a(x,(y * y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(14955(a,1),23993(a,1))].">
      <j1 rule="para" parents="14955 23993"/>
    </justification>
  </clause>

  <clause id="24160">
    <literal><![CDATA[
      a(x,(y * z) * L(u,z,y),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,(z * u) * y,w) = v5
    ]]></literal>
    <justification jstring="[para(97(a,2),23994(a,1,2))].">
      <j1 rule="para" parents="97 23994"/>
    </justification>
  </clause>

  <clause id="24161">
    <literal><![CDATA[
      a(x,y * (z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z * y,u) = w
    ]]></literal>
    <justification jstring="[para(14970(a,2),23994(a,1))].">
      <j1 rule="para" parents="14970 23994"/>
    </justification>
  </clause>

  <clause id="24164">
    <literal><![CDATA[
      a(x,(y * T(z,u * y)) \ (z * (u * y)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,R(u,y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(13920(a,1),23998(a,1,2,1))].">
      <j1 rule="para" parents="13920 23998"/>
    </justification>
  </clause>

  <clause id="24165">
    <literal><![CDATA[
      a(x,y * (z / u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y * (u \ z),w) = v5
    ]]></literal>
    <justification jstring="[para(6075(a,1),24005(a,1,2))].">
      <j1 rule="para" parents="6075 24005"/>
    </justification>
  </clause>

  <clause id="24166">
    <literal><![CDATA[
      a(x,y * (z * K(u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y * z,v5) = v6
    ]]></literal>
    <justification jstring="[para(7609(a,1),24005(a,1,2))].">
      <j1 rule="para" parents="7609 24005"/>
    </justification>
  </clause>

  <clause id="24167">
    <literal><![CDATA[
      a(x,y \ (z \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ (u / z),w) = v5
    ]]></literal>
    <justification jstring="[para(13113(a,1),24005(a,1,2))].">
      <j1 rule="para" parents="13113 24005"/>
    </justification>
  </clause>

  <clause id="24168">
    <literal><![CDATA[
      a(x,y \ (z * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ (u * z),w) = v5
    ]]></literal>
    <justification jstring="[para(13432(a,1),24005(a,1,2))].">
      <j1 rule="para" parents="13432 24005"/>
    </justification>
  </clause>

  <clause id="24169">
    <literal><![CDATA[
      a(x,y,K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(22020(a,1),24005(a,1))].">
      <j1 rule="para" parents="22020 24005"/>
    </justification>
  </clause>

  <clause id="24172">
    <literal><![CDATA[
      a(x,(y \ 1) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(495(a,1),24110(a,1,2))].">
      <j1 rule="para" parents="495 24110"/>
    </justification>
  </clause>

  <clause id="24173">
    <literal><![CDATA[
      a(x,y * (y * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,L(z,y,y),u) = w
    ]]></literal>
    <justification jstring="[para(97(a,1),24110(a,1,2))].">
      <j1 rule="para" parents="97 24110"/>
    </justification>
  </clause>

  <clause id="24174">
    <literal><![CDATA[
      a(x,(y * (z \ 1)) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,(y * z) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(819(a,1),24110(a,1,2))].">
      <j1 rule="para" parents="819 24110"/>
    </justification>
  </clause>

  <clause id="24175">
    <literal><![CDATA[
      a(x,L(y \ 1,z,u) \ w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,L(y,z,u) \ w,v5) = v6
    ]]></literal>
    <justification jstring="[para(3325(a,1),24110(a,1,2))].">
      <j1 rule="para" parents="3325 24110"/>
    </justification>
  </clause>

  <clause id="24176">
    <literal><![CDATA[
      a(x,L(L(y \ z,u,w),y,y),v5) = a(x,L(y * z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(3336(a,1),24114(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3336 24114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24177">
    <literal><![CDATA[
      a(x,L(y \ z,y,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y * z,u) = w
    ]]></literal>
    <justification jstring="[para(99(a,2),24159(a,1,2))].">
      <j1 rule="para" parents="99 24159"/>
    </justification>
  </clause>

  <clause id="24178">
    <literal><![CDATA[
      a(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(1324(a,2),24169(a,1,3))].">
      <j1 rule="para" parents="1324 24169"/>
    </justification>
  </clause>

  <clause id="24179">
    <literal><![CDATA[
      a(x,y,(z \ u) * z) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(4898(a,1),24169(a,1,3))].">
      <j1 rule="para" parents="4898 24169"/>
    </justification>
  </clause>

  <clause id="24180">
    <literal><![CDATA[
      a(x,y,z * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(4909(a,1),24169(a,1,3))].">
      <j1 rule="para" parents="4909 24169"/>
    </justification>
  </clause>

  <clause id="24181">
    <literal><![CDATA[
      a(x,y,z / u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(5012(a,1),24169(a,1,3))].">
      <j1 rule="para" parents="5012 24169"/>
    </justification>
  </clause>

  <clause id="24182">
    <literal><![CDATA[
      a(x,y,(z \ u) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(5017(a,2),24169(a,1,3))].">
      <j1 rule="para" parents="5017 24169"/>
    </justification>
  </clause>

  <clause id="24183">
    <literal><![CDATA[
      a(x,y,((z \ u) \ u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ w) = v5
    ]]></literal>
    <justification jstring="[para(5340(a,2),24169(a,1,3))].">
      <j1 rule="para" parents="5340 24169"/>
    </justification>
  </clause>

  <clause id="24184">
    <literal><![CDATA[
      a(x,y,L(T(z,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(5028(a,1),24169(a,1,3))].">
      <j1 rule="para" parents="5028 24169"/>
    </justification>
  </clause>

  <clause id="24185">
    <literal><![CDATA[
      a(x,y,z * T(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * u) = v5
    ]]></literal>
    <justification jstring="[para(5573(a,1),24169(a,1,3))].">
      <j1 rule="para" parents="5573 24169"/>
    </justification>
  </clause>

  <clause id="24186">
    <literal><![CDATA[
      a(x,y,z \ T(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ u) = v5
    ]]></literal>
    <justification jstring="[para(5570(a,1),24169(a,1,3))].">
      <j1 rule="para" parents="5570 24169"/>
    </justification>
  </clause>

  <clause id="24188">
    <literal><![CDATA[
      a(x,y,z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(7372(a,1),24169(a,1,3))].">
      <j1 rule="para" parents="7372 24169"/>
    </justification>
  </clause>

  <clause id="24189">
    <literal><![CDATA[
      a(x,y,z * (K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * v5) = v6
    ]]></literal>
    <justification jstring="[para(9400(a,1),24169(a,1,3))].">
      <j1 rule="para" parents="9400 24169"/>
    </justification>
  </clause>

  <clause id="24190">
    <literal><![CDATA[
      a(x,y,z * (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (w * u)) = v5
    ]]></literal>
    <justification jstring="[para(9586(a,1),24169(a,1,3))].">
      <j1 rule="para" parents="9586 24169"/>
    </justification>
  </clause>

  <clause id="24191">
    <literal><![CDATA[
      a(x,y,(z * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u * z) \ w) = v5
    ]]></literal>
    <justification jstring="[para(10274(a,1),24169(a,1,3))].">
      <j1 rule="para" parents="10274 24169"/>
    </justification>
  </clause>

  <clause id="24192">
    <literal><![CDATA[
      a(x,y,(z * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u * z) * w) = v5
    ]]></literal>
    <justification jstring="[para(10281(a,1),24169(a,1,3))].">
      <j1 rule="para" parents="10281 24169"/>
    </justification>
  </clause>

  <clause id="24193">
    <literal><![CDATA[
      a(x,y,((z \ u) * z) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u \ w) = v5
    ]]></literal>
    <justification jstring="[para(10296(a,1),24169(a,1,3))].">
      <j1 rule="para" parents="10296 24169"/>
    </justification>
  </clause>

  <clause id="24194">
    <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(11712(a,1),24169(a,1,3))].">
      <j1 rule="para" parents="11712 24169"/>
    </justification>
  </clause>

  <clause id="24196">
    <literal><![CDATA[
      a(x,y,z \ (K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ v5) = v6
    ]]></literal>
    <justification jstring="[para(19540(a,1),24169(a,1,3))].">
      <j1 rule="para" parents="19540 24169"/>
    </justification>
  </clause>

  <clause id="24197">
    <literal><![CDATA[
      a(x,y,(K(z,u) * w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w \ v5) = v6
    ]]></literal>
    <justification jstring="[para(20697(a,1),24169(a,1,3))].">
      <j1 rule="para" parents="20697 24169"/>
    </justification>
  </clause>

  <clause id="24198">
    <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(20828(a,1),24169(a,1,3))].">
      <j1 rule="para" parents="20828 24169"/>
    </justification>
  </clause>

  <clause id="24199">
    <literal><![CDATA[
      a(x,y,((z * T(u,w)) \ v5) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,((z * u) \ v5) * v6) = v7
    ]]></literal>
    <justification jstring="[para(21047(a,1),24169(a,1,3))].">
      <j1 rule="para" parents="21047 24169"/>
    </justification>
  </clause>

  <clause id="24200">
    <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(21250(a,2),24169(a,1,3))].">
      <j1 rule="para" parents="21250 24169"/>
    </justification>
  </clause>

  <clause id="24204">
    <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(3173(a,1),24179(a,1,3))].">
      <j1 rule="para" parents="3173 24179"/>
    </justification>
  </clause>

  <clause id="24205">
    <literal><![CDATA[
      x * (y / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,x,y * x) = z
    ]]></literal>
    <justification jstring="[para(18991(a,1),24180(a,1))].">
      <j1 rule="para" parents="18991 24180"/>
    </justification>
  </clause>

  <clause id="24206">
    <literal><![CDATA[
      a(x,y,(z / u) * (w * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,((w * w) \ u) \ z) = v5
    ]]></literal>
    <justification jstring="[para(896(a,1),24181(a,1,3))].">
      <j1 rule="para" parents="896 24181"/>
    </justification>
  </clause>

  <clause id="24207">
    <literal><![CDATA[
      a(x,y,z * (u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (w / u)) = v5
    ]]></literal>
    <justification jstring="[para(5927(a,1),24188(a,1,3))].">
      <j1 rule="para" parents="5927 24188"/>
    </justification>
  </clause>

  <clause id="24208">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * u) = v5
    ]]></literal>
    <justification jstring="[para(5954(a,1),24188(a,1,3))].">
      <j1 rule="para" parents="5954 24188"/>
    </justification>
  </clause>

  <clause id="24209">
    <literal><![CDATA[
      a(x,y,z * (u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(6075(a,1),24188(a,1,3))].">
      <j1 rule="para" parents="6075 24188"/>
    </justification>
  </clause>

  <clause id="24210">
    <literal><![CDATA[
      a(x,y,z * (u * K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * u) = v6
    ]]></literal>
    <justification jstring="[para(7609(a,1),24188(a,1,3))].">
      <j1 rule="para" parents="7609 24188"/>
    </justification>
  </clause>

  <clause id="24211">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) * u)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * w) = v5
    ]]></literal>
    <justification jstring="[para(8171(a,1),24188(a,1,3))].">
      <j1 rule="para" parents="8171 24188"/>
    </justification>
  </clause>

  <clause id="24212">
    <literal><![CDATA[
      a(x,y,z \ ((u \ w) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ u) = v5
    ]]></literal>
    <justification jstring="[para(13103(a,2),24188(a,1,3))].">
      <j1 rule="para" parents="13103 24188"/>
    </justification>
  </clause>

  <clause id="24213">
    <literal><![CDATA[
      a(x,y,z \ (u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ (w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(13354(a,1),24188(a,1,3))].">
      <j1 rule="para" parents="13354 24188"/>
    </justification>
  </clause>

  <clause id="24214">
    <literal><![CDATA[
      a(x,y,z \ (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ (w * u)) = v5
    ]]></literal>
    <justification jstring="[para(13432(a,1),24188(a,1,3))].">
      <j1 rule="para" parents="13432 24188"/>
    </justification>
  </clause>

  <clause id="24215">
    <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(20791(a,1),24188(a,1,3))].">
      <j1 rule="para" parents="20791 24188"/>
    </justification>
  </clause>

  <clause id="24217">
    <literal><![CDATA[
      a(L(x \ y,x,z) \ u,w,v5) = a(((z * y) / (z * x)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(99(a,2),23892(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="99 23892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24218">
    <literal><![CDATA[
      a(((x / y) / (1 / y)) \ z,u,w) = a((y \ (x / (y \ 1))) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(2287(a,1),23892(a,1,1,1))].">
      <j1 rule="para" parents="2287 23892"/>
    </justification>
  </clause>

  <clause id="24219">
    <literal><![CDATA[
      a(((x \ 1) \ y) * x,z,u) = a(y * (x * x),z,u)
    ]]></literal>
    <justification jstring="[para(782(a,1),23899(a,1,1)),flip(a)].">
      <j1 rule="para" parents="782 23899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24220">
    <literal><![CDATA[
      a(L(T(L(x \ 1,x,y),z),y * x,u),w,v5) = a((u * (y * x)) \ (u * y),w,v5)
    ]]></literal>
    <justification jstring="[para(446(a,1),23900(a,2,1))].">
      <j1 rule="para" parents="446 23900"/>
    </justification>
  </clause>

  <clause id="24221">
    <literal><![CDATA[
      a(x * ((y / z) \ u),w,v5) = a(x * ((z \ y) \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(5441(a,1),23902(a,1,1,2))].">
      <j1 rule="para" parents="5441 23902"/>
    </justification>
  </clause>

  <clause id="24222">
    <literal><![CDATA[
      a(x * (y \ T(z,u)),w,v5) = a(x * (y \ z),w,v5)
    ]]></literal>
    <justification jstring="[para(5456(a,1),23902(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5456 23902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24223">
    <literal><![CDATA[
      a(x * (y \ (K(z,u) * w)),v5,v6) = a(x * (y \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(19540(a,1),23902(a,1,1,2))].">
      <j1 rule="para" parents="19540 23902"/>
    </justification>
  </clause>

  <clause id="24224">
    <literal><![CDATA[
      a((x * T(y,z)) * u,w,v5) = a((x * y) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(20808(a,1),23902(a,1,1))].">
      <j1 rule="para" parents="20808 23902"/>
    </justification>
  </clause>

  <clause id="24225">
    <literal><![CDATA[
      a(x * ((T(y,z) * u) \ w),v5,v6) = a(x * ((y * u) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(20829(a,1),23902(a,1,1,2))].">
      <j1 rule="para" parents="20829 23902"/>
    </justification>
  </clause>

  <clause id="24226">
    <literal><![CDATA[
      a((x \ (K(y,z) * u)) * w,v5,v6) = a((x \ u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(20967(a,1),23902(a,1,1))].">
      <j1 rule="para" parents="20967 23902"/>
    </justification>
  </clause>

  <clause id="24227">
    <literal><![CDATA[
      a(x * ((y \ (K(z,u) * w)) \ v5),v6,v7) = a(x * ((y \ w) \ v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(21227(a,1),23902(a,1,1,2))].">
      <j1 rule="para" parents="21227 23902"/>
    </justification>
  </clause>

  <clause id="24228">
    <literal><![CDATA[
      a((x * y) * z,u,w) = a(z * (y * x),u,w)
    ]]></literal>
    <justification jstring="[hyper(23925,a,23903,a)].">
      <j1 rule="hyper" parents="23925 23903"/>
    </justification>
  </clause>

  <clause id="24229">
    <literal><![CDATA[
      a(x * (y * z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((z * y) * x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(23903(a,1),23925(a,1))].">
      <j1 rule="para" parents="23903 23925"/>
    </justification>
  </clause>

  <clause id="24230">
    <literal><![CDATA[
      a((R(1 / x,x,y) * x) * z,u,w) = a(a(x,x,y * x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(19010(a,1),23904(a,1,1,1,1))].">
      <j1 rule="para" parents="19010 23904"/>
    </justification>
  </clause>

  <clause id="24231">
    <literal><![CDATA[
      a(x \ (y * (z * u)),w,v5) = a(x \ (y * (u * z)),w,v5)
    ]]></literal>
    <justification jstring="[para(9586(a,1),23906(a,1,1,2))].">
      <j1 rule="para" parents="9586 23906"/>
    </justification>
  </clause>

  <clause id="24232">
    <literal><![CDATA[
      a(x \ ((y / T(z,u)) \ w),v5,v6) = a(x \ ((y / z) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(20827(a,1),23906(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="20827 23906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24233">
    <literal><![CDATA[
      a(((x / y) \ z) \ u,w,v5) = a(((y \ x) \ z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(5441(a,1),23908(a,1,1,1))].">
      <j1 rule="para" parents="5441 23908"/>
    </justification>
  </clause>

  <clause id="24234">
    <literal><![CDATA[
      a(T(x * (y \ z),K(z,u)) \ w,v5,v6) = a((x * (y \ T(z,u))) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(21130(a,1),23908(a,1,1,1))].">
      <j1 rule="para" parents="21130 23908"/>
    </justification>
  </clause>

  <clause id="24235">
    <literal><![CDATA[
      a(x * (y * (z / u)),w,v5) = a(x * (y * (u \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(5927(a,1),23935(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5927 23935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24236">
    <literal><![CDATA[
      a(x * (y * ((z \ u) \ u)),w,v5) = a(x * (y * z),w,v5)
    ]]></literal>
    <justification jstring="[para(5954(a,1),23935(a,1,1,2))].">
      <j1 rule="para" parents="5954 23935"/>
    </justification>
  </clause>

  <clause id="24237">
    <literal><![CDATA[
      a(x * (y * (z * K(u,w))),v5,v6) = a(x * (y * z),v5,v6)
    ]]></literal>
    <justification jstring="[para(7609(a,1),23935(a,1,1,2))].">
      <j1 rule="para" parents="7609 23935"/>
    </justification>
  </clause>

  <clause id="24239">
    <literal><![CDATA[
      a(x \ ((y * z) / (u * K(w,v5))),v6,v7) = a(x \ (u \ (y * (z * K(v5,w)))),v6,v7)
    ]]></literal>
    <justification jstring="[para(20775(a,1),23936(a,1,1,2))].">
      <j1 rule="para" parents="20775 23936"/>
    </justification>
  </clause>

  <clause id="24241">
    <literal><![CDATA[
      a(x,y * ((z * z) \ (u * z)),w) = a(x,y * (u * (z \ 1)),w)
    ]]></literal>
    <justification jstring="[para(780(a,1),24043(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="780 24043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24242">
    <literal><![CDATA[
      a(x,y * ((z * z) \ (u \ z)),w) = a(x,y * (u \ (z \ 1)),w)
    ]]></literal>
    <justification jstring="[para(820(a,1),24043(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="820 24043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24243">
    <literal><![CDATA[
      a(x,(y * z) * u,w) = a(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[hyper(23994,a,24046,a)].">
      <j1 rule="hyper" parents="23994 24046"/>
    </justification>
  </clause>

  <clause id="24244">
    <literal><![CDATA[
      a(x,y * (z * y),u) = a(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,24114,a(flip),b,24046,a),flip(a)].">
      <j1 rule="hyper" parents="347 24114 24046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24245">
    <literal><![CDATA[
      a(x,y * (((z * z) \ u) * L(z,w,v5)),v6) = a(x,y * (L(z \ 1,w,v5) * u),v6)
    ]]></literal>
    <justification jstring="[para(3326(a,1),24046(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3326 24046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24246">
    <literal><![CDATA[
      a(x,y * (((z * u) * w) * T(u,z)),v5) = a(x,y * (u * ((u * z) * w)),v5)
    ]]></literal>
    <justification jstring="[para(10302(a,1),24046(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10302 24046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24247">
    <literal><![CDATA[
      a(x,y * (z * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,(u * z) * y,w) = v5
    ]]></literal>
    <justification jstring="[para(24046(a,1),23994(a,1))].">
      <j1 rule="para" parents="24046 23994"/>
    </justification>
  </clause>

  <clause id="24248">
    <literal><![CDATA[
      a(x,(y * z) * z,u) = a(x,L(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(23994,a,24244,a)].">
      <j1 rule="hyper" parents="23994 24244"/>
    </justification>
  </clause>

  <clause id="24249">
    <literal><![CDATA[
      a(x,y * (z * (u / w)),v5) = a(x,y * (z * (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(5927(a,1),24049(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5927 24049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24250">
    <literal><![CDATA[
      a(x,y * (z * (u * w)),v5) = a(x,y * (z * (w * u)),v5)
    ]]></literal>
    <justification jstring="[para(6977(a,1),24049(a,1,2,2))].">
      <j1 rule="para" parents="6977 24049"/>
    </justification>
  </clause>

  <clause id="24251">
    <literal><![CDATA[
      a(x,y * (T(z,u) \ w),v5) = a(x,y * (z \ w),v5)
    ]]></literal>
    <justification jstring="[para(8122(a,1),24049(a,1,2,2))].">
      <j1 rule="para" parents="8122 24049"/>
    </justification>
  </clause>

  <clause id="24252">
    <literal><![CDATA[
      a(x,y * ((z / u) * w),v5) = a(x,y * ((u \ z) * w),v5)
    ]]></literal>
    <justification jstring="[para(7768(a,1),24049(a,1,2,2))].">
      <j1 rule="para" parents="7768 24049"/>
    </justification>
  </clause>

  <clause id="24253">
    <literal><![CDATA[
      a(x,y * (z * (u * K(w,v5))),v6) = a(x,y * (z * u),v6)
    ]]></literal>
    <justification jstring="[para(7609(a,1),24049(a,1,2,2))].">
      <j1 rule="para" parents="7609 24049"/>
    </justification>
  </clause>

  <clause id="24254">
    <literal><![CDATA[
      a(x,y * (z \ K(u,w)),v5) = a(x,y * (z \ 1),v5)
    ]]></literal>
    <justification jstring="[para(12973(a,1),24049(a,1,2,2))].">
      <j1 rule="para" parents="12973 24049"/>
    </justification>
  </clause>

  <clause id="24255">
    <literal><![CDATA[
      a(x,y * (z \ (u / w)),v5) = a(x,y * (z \ (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(13113(a,1),24049(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13113 24049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24256">
    <literal><![CDATA[
      a(x,(y \ (z / u)) \ 1,w) = a(x,y \ (u \ z),w)
    ]]></literal>
    <justification jstring="[hyper(14959,a,24051,a)].">
      <j1 rule="hyper" parents="14959 24051"/>
    </justification>
  </clause>

  <clause id="24257">
    <literal><![CDATA[
      x / (y * ((y \ (x / z)) * z)) = a(y,y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[hyper(13425,a,24051,a)].">
      <j1 rule="hyper" parents="13425 24051"/>
    </justification>
  </clause>

  <clause id="24259">
    <literal><![CDATA[
      a(x,(y * z) \ ((z * u) * y),w) = a(x,L(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(18(a,2),24052(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 24052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24260">
    <literal><![CDATA[
      a(x,y \ K(z,u),w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(14992,a,24053,a),flip(a)].">
      <j1 rule="hyper" parents="14992 24053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24261">
    <literal><![CDATA[
      a(x,y \ (z * (u / w)),v5) = a(x,y \ (z * (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(5927(a,1),24053(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5927 24053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24262">
    <literal><![CDATA[
      a(x,y \ (z * (u * w)),v5) = a(x,y \ (z * (w * u)),v5)
    ]]></literal>
    <justification jstring="[para(6977(a,1),24053(a,1,2,2))].">
      <j1 rule="para" parents="6977 24053"/>
    </justification>
  </clause>

  <clause id="24264">
    <literal><![CDATA[
      a(x,y \ (z * (u * K(w,v5))),v6) = a(x,y \ (z * u),v6)
    ]]></literal>
    <justification jstring="[para(7609(a,1),24053(a,1,2,2))].">
      <j1 rule="para" parents="7609 24053"/>
    </justification>
  </clause>

  <clause id="24265">
    <literal><![CDATA[
      a(x,y \ (z \ (K(u,w) * v5)),v6) = a(x,y \ (z \ v5),v6)
    ]]></literal>
    <justification jstring="[para(20369(a,1),24053(a,1,2,2))].">
      <j1 rule="para" parents="20369 24053"/>
    </justification>
  </clause>

  <clause id="24266">
    <literal><![CDATA[
      a(x,y \ (z \ (u * T(w,v5))),v6) = a(x,y \ (z \ (u * w)),v6)
    ]]></literal>
    <justification jstring="[para(20791(a,1),24053(a,1,2,2))].">
      <j1 rule="para" parents="20791 24053"/>
    </justification>
  </clause>

  <clause id="24268">
    <literal><![CDATA[
      a(x,(y * z) \ u,w) = a(x,(z * y) \ u,w)
    ]]></literal>
    <justification jstring="[para(10299(a,1),24054(a,1,2))].">
      <j1 rule="para" parents="10299 24054"/>
    </justification>
  </clause>

  <clause id="24269">
    <literal><![CDATA[
      a(x,(K(y,z) * u) \ w,v5) = a(x,u \ w,v5)
    ]]></literal>
    <justification jstring="[para(20003(a,2),24054(a,1,2))].">
      <j1 rule="para" parents="20003 24054"/>
    </justification>
  </clause>

  <clause id="24270">
    <literal><![CDATA[
      a(x,(T(y,z) * u) \ w,v5) = a(x,(y * u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(20701(a,1),24054(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20701 24054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24271">
    <literal><![CDATA[
      a(x,y \ ((T(z,u) * w) \ v5),v6) = a(x,y \ ((z * w) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(20829(a,1),24054(a,1,2,2))].">
      <j1 rule="para" parents="20829 24054"/>
    </justification>
  </clause>

  <clause id="24272">
    <literal><![CDATA[
      a(x,y,((z * (u * u)) \ ((u * u) * w)) * v5) = a(x,y,(T(w,u \ (u \ 1)) / z) * v5)
    ]]></literal>
    <justification jstring="[para(1121(a,1),24074(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1121 24074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24273">
    <literal><![CDATA[
      a(x,y,R(z * K(u,z),u,w) * v5) = a(x,y,((u * w) \ ((u * z) * w)) * v5)
    ]]></literal>
    <justification jstring="[para(5061(a,2),24074(a,1,3,1))].">
      <j1 rule="para" parents="5061 24074"/>
    </justification>
  </clause>

  <clause id="24275">
    <literal><![CDATA[
      a(x,y,L(L(z / u,w,v5),v6,v7)) = a(x,y,L(L(u \ z,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(278(a,1),24075(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="278 24075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24276">
    <literal><![CDATA[
      a(x,y,L((z * z) \ (u * z),w,v5)) = a(x,y,L(u * (z \ 1),w,v5))
    ]]></literal>
    <justification jstring="[para(791(a,1),24075(a,1,3,1))].">
      <j1 rule="para" parents="791 24075"/>
    </justification>
  </clause>

  <clause id="24278">
    <literal><![CDATA[
      a(x,y,z * ((u / w) * v5)) = a(x,y,z * ((w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(5237(a,1),24078(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5237 24078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24279">
    <literal><![CDATA[
      a(x,y,z * (u \ T(w,v5))) = a(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[para(5456(a,1),24078(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5456 24078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24280">
    <literal><![CDATA[
      a(x,y,z * (u * (K(w,v5) * v6))) = a(x,y,z * (u * v6))
    ]]></literal>
    <justification jstring="[para(5885(a,1),24078(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5885 24078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24281">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * v5)) = a(x,y,z * ((w * u) * v5))
    ]]></literal>
    <justification jstring="[para(10281(a,1),24078(a,1,3,2))].">
      <j1 rule="para" parents="10281 24078"/>
    </justification>
  </clause>

  <clause id="24282">
    <literal><![CDATA[
      a(x,y,(z \ T(u,w)) * v5) = a(x,y,(z \ u) * v5)
    ]]></literal>
    <justification jstring="[para(20179(a,1),24078(a,1,3))].">
      <j1 rule="para" parents="20179 24078"/>
    </justification>
  </clause>

  <clause id="24283">
    <literal><![CDATA[
      a(x,y,(z * T(u,w)) * v5) = a(x,y,(z * u) * v5)
    ]]></literal>
    <justification jstring="[para(20808(a,1),24078(a,1,3))].">
      <j1 rule="para" parents="20808 24078"/>
    </justification>
  </clause>

  <clause id="24284">
    <literal><![CDATA[
      a(x,y,(z * u) * w) = a(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(24180,a,24082,a)].">
      <j1 rule="hyper" parents="24180 24082"/>
    </justification>
  </clause>

  <clause id="24285">
    <literal><![CDATA[
      a(x,y,z * ((u * u) * w)) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(14940,a,24082,a),flip(a)].">
      <j1 rule="hyper" parents="14940 24082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24286">
    <literal><![CDATA[
      a(x,y,z * (u * z)) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,14956,a(flip),b,24082,a),flip(a)].">
      <j1 rule="hyper" parents="347 14956 24082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24287">
    <literal><![CDATA[
      a(x,y,z * (((u * u) * w) * R(v5,u,u))) = a(x,y,z * (((v5 * u) * u) * w))
    ]]></literal>
    <justification jstring="[para(593(a,1),24082(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="593 24082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24288">
    <literal><![CDATA[
      a(x,y,z * ((u * u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * w) = v5
    ]]></literal>
    <justification jstring="[para(24082(a,1),14940(a,1))].">
      <j1 rule="para" parents="24082 14940"/>
    </justification>
  </clause>

  <clause id="24289">
    <literal><![CDATA[
      a(x,y,z * ((K(u,w) * v5) * (v6 \ 1))) = a(x,y,z * ((v6 \ K(u,w)) * v5))
    ]]></literal>
    <justification jstring="[para(20815(a,1),24082(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="20815 24082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24290">
    <literal><![CDATA[
      a(x,y,z * (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(w * u) * z) = v5
    ]]></literal>
    <justification jstring="[para(24082(a,1),24180(a,1))].">
      <j1 rule="para" parents="24082 24180"/>
    </justification>
  </clause>

  <clause id="24291">
    <literal><![CDATA[
      a(x,y,L(z,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * u) * u) = w
    ]]></literal>
    <justification jstring="[para(24286(a,1),24180(a,1))].">
      <j1 rule="para" parents="24286 24180"/>
    </justification>
  </clause>

  <clause id="24292">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) \ w) = a(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(15004,a,24083,a),flip(a)].">
      <j1 rule="hyper" parents="15004 24083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24293">
    <literal><![CDATA[
      a(x,y,((z * z) * u) \ w) = a(x,y,(z * z) \ (u \ w))
    ]]></literal>
    <justification jstring="[para(459(a,1),24083(a,1,3)),flip(a)].">
      <j1 rule="para" parents="459 24083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24294">
    <literal><![CDATA[
      a(x,y,(z * u) \ (u * (w * z))) = a(x,y,L(T(w,z),z,u))
    ]]></literal>
    <justification jstring="[para(263(a,1),24083(a,1,3)),flip(a)].">
      <j1 rule="para" parents="263 24083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24295">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u * z) \ w) = v5
    ]]></literal>
    <justification jstring="[para(24083(a,1),15004(a,1))].">
      <j1 rule="para" parents="24083 15004"/>
    </justification>
  </clause>

  <clause id="24296">
    <literal><![CDATA[
      a(x,y,(z * u) * (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(u,z,z \ u)) = w
    ]]></literal>
    <justification jstring="[para(24084(a,1),14943(a,1))].">
      <j1 rule="para" parents="24084 14943"/>
    </justification>
  </clause>

  <clause id="24297">
    <literal><![CDATA[
      a(x,y,(z * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w * (u * z)) = v5
    ]]></literal>
    <justification jstring="[para(24084(a,1),24180(a,1))].">
      <j1 rule="para" parents="24084 24180"/>
    </justification>
  </clause>

  <clause id="24299">
    <literal><![CDATA[
      a(x,y,z * ((u * u) \ (w \ u))) = a(x,y,z * (w \ (u \ 1)))
    ]]></literal>
    <justification jstring="[para(820(a,1),24134(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="820 24134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24300">
    <literal><![CDATA[
      a(x,y,z * (u \ (z \ u))) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(18986(a,1),24134(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18986 24134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24301">
    <literal><![CDATA[
      a(x,y,z * (u * (w / v5))) = a(x,y,z * (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(5927(a,1),24136(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5927 24136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24302">
    <literal><![CDATA[
      a(x,y,z * (u * L(T(w,v5),v6,v7))) = a(x,y,z * (u * L(w,v6,v7)))
    ]]></literal>
    <justification jstring="[para(11144(a,1),24136(a,1,3,2))].">
      <j1 rule="para" parents="11144 24136"/>
    </justification>
  </clause>

  <clause id="24303">
    <literal><![CDATA[
      a(x,y,z \ ((u * u) \ (w \ u))) = a(x,y,z \ (w \ (u \ 1)))
    ]]></literal>
    <justification jstring="[para(820(a,1),24137(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="820 24137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24304">
    <literal><![CDATA[
      a(x,y,L(z,z,u)) = a(x,y,u \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(2007(a,2),24137(a,1,3))].">
      <j1 rule="para" parents="2007 24137"/>
    </justification>
  </clause>

  <clause id="24305">
    <literal><![CDATA[
      a(x,y,L(z \ L(z,u,w),z,w * u)) = a(x,y,(w * u) \ (z \ (w * (u * z))))
    ]]></literal>
    <justification jstring="[para(3970(a,2),24137(a,1,3))].">
      <j1 rule="para" parents="3970 24137"/>
    </justification>
  </clause>

  <clause id="24307">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((w \ u) * (z * w))) = a(x,y,a(z,w,w \ u))
    ]]></literal>
    <justification jstring="[para(87(a,1),24138(a,1,3)),flip(a)].">
      <j1 rule="para" parents="87 24138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24308">
    <literal><![CDATA[
      a(x,y,z \ K(u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(14937,a,24139,a),flip(a)].">
      <j1 rule="hyper" parents="14937 24139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24309">
    <literal><![CDATA[
      a(x,y,z \ (u * (w / v5))) = a(x,y,z \ (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(5927(a,1),24139(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5927 24139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24310">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * K(v5,v6)))) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(7609(a,1),24139(a,1,3,2))].">
      <j1 rule="para" parents="7609 24139"/>
    </justification>
  </clause>

  <clause id="24311">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w / v5))) = a(x,y,z \ (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(13113(a,1),24139(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="13113 24139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24312">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * v5))) = a(x,y,z \ (u \ (v5 * w)))
    ]]></literal>
    <justification jstring="[para(13432(a,1),24139(a,1,3,2))].">
      <j1 rule="para" parents="13432 24139"/>
    </justification>
  </clause>

  <clause id="24313">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),u * L(x,y,z)) = x * (L(x,y,z) * (x \ (u / (L(x,y,z) * u))))
    ]]></literal>
    <justification jstring="[hyper(24205,a,1404,a(flip))].">
      <j1 rule="hyper" parents="24205 1404"/>
    </justification>
  </clause>

  <clause id="24314">
    <literal><![CDATA[
      a((x * x) * (y * z),u,w) = a(z * (y * (x * x)),u,w)
    ]]></literal>
    <justification jstring="[para(33(a,1),24228(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33 24228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24315">
    <literal><![CDATA[
      a(L(x,y,z) * (y * z),u,w) = a(z * (y * x),u,w)
    ]]></literal>
    <justification jstring="[para(97(a,1),24228(a,1,1)),flip(a)].">
      <j1 rule="para" parents="97 24228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24316">
    <literal><![CDATA[
      a((x * y) * R(R(z,y,x),u,w),v5,v6) = a((R(z,u,w) * y) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(469(a,1),24228(a,2,1))].">
      <j1 rule="para" parents="469 24228"/>
    </justification>
  </clause>

  <clause id="24317">
    <literal><![CDATA[
      a((x * y) * L(R(z,y,x),u,w),v5,v6) = a((L(z,u,w) * y) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(471(a,1),24228(a,2,1))].">
      <j1 rule="para" parents="471 24228"/>
    </justification>
  </clause>

  <clause id="24318">
    <literal><![CDATA[
      a(x,(y * z) * u,w) = a(x,(z * y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24037,a,b,24243,a)].">
      <j1 rule="hyper" parents="347 24037 24243"/>
    </justification>
  </clause>

  <clause id="24319">
    <literal><![CDATA[
      a(x,L(y,z,u) * (z * u),w) = a(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[para(97(a,1),24243(a,1,2)),flip(a)].">
      <j1 rule="para" parents="97 24243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24320">
    <literal><![CDATA[
      a(x,a(y,z,L(u,z,y)),w) = a(x,(L(u,z,y) * z) \ (z * u),w)
    ]]></literal>
    <justification jstring="[para(14707(a,2),24268(a,1,2))].">
      <j1 rule="para" parents="14707 24268"/>
    </justification>
  </clause>

  <clause id="24321">
    <literal><![CDATA[
      a(x,(y \ T(z,u)) \ w,v5) = a(x,(y \ z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(5456(a,1),24269(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5456 24269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24322">
    <literal><![CDATA[
      a(x,(y * T(z,u)) \ w,v5) = a(x,(y * z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(5573(a,1),24269(a,1,2,1))].">
      <j1 rule="para" parents="5573 24269"/>
    </justification>
  </clause>

  <clause id="24323">
    <literal><![CDATA[
      a(x,(y * (K(z,u) * w)) \ v5,v6) = a(x,(y * w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(5885(a,1),24269(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5885 24269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24324">
    <literal><![CDATA[
      a(x,(y * (z * u)) \ w,v5) = a(x,(y * (u * z)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(9586(a,1),24269(a,1,2,1))].">
      <j1 rule="para" parents="9586 24269"/>
    </justification>
  </clause>

  <clause id="24325">
    <literal><![CDATA[
      a(x,y,z * ((u * u) * w)) = a(x,y,w * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,24069,a,b,24285,a),flip(a)].">
      <j1 rule="hyper" parents="347 24069 24285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24326">
    <literal><![CDATA[
      a(x,y,z * ((u * u) \ w)) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),24285(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10 24285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24327">
    <literal><![CDATA[
      a(x,y,(z \ 1) * u) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(302(a,1),24285(a,1,3)),flip(a)].">
      <j1 rule="para" parents="302 24285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24328">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ w)) = a(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[para(495(a,1),24285(a,1,3,2))].">
      <j1 rule="para" parents="495 24285"/>
    </justification>
  </clause>

  <clause id="24329">
    <literal><![CDATA[
      a(x,y,z * R((z \ 1) \ (z \ u),w,v5)) = a(x,y,z \ R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(1479(a,1),24327(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1479 24327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24330">
    <literal><![CDATA[
      a(x,y,(z \ ((z * (u \ 1)) * w)) / w) = a(x,y,u * a(z,u \ 1,w))
    ]]></literal>
    <justification jstring="[para(23138(a,2),24327(a,1,3))].">
      <j1 rule="para" parents="23138 24327"/>
    </justification>
  </clause>

  <clause id="24331">
    <literal><![CDATA[
      a(x,(y * z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u * (z * y),w) = v5
    ]]></literal>
    <justification jstring="[para(24318(a,1),23994(a,1))].">
      <j1 rule="para" parents="24318 23994"/>
    </justification>
  </clause>

  <clause id="24332">
    <literal><![CDATA[
      a(x,y,((z * z) * u) * w) = a(x,y,u * w)
    ]]></literal>
    <justification jstring="[hyper(24180,a,24325,a)].">
      <j1 rule="hyper" parents="24180 24325"/>
    </justification>
  </clause>

  <clause id="24333">
    <literal><![CDATA[
      a(x,y,(z * (u \ 1)) * w) = a(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[para(828(a,1),24326(a,1,3))].">
      <j1 rule="para" parents="828 24326"/>
    </justification>
  </clause>

  <clause id="24334">
    <literal><![CDATA[
      a(x,y,(z \ (u \ 1)) * w) = a(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[para(831(a,1),24326(a,1,3))].">
      <j1 rule="para" parents="831 24326"/>
    </justification>
  </clause>

  <clause id="24335">
    <literal><![CDATA[
      a(x,y,z * L((u \ 1) \ w,v5,v6)) = a(x,y,z * L(u \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(3183(a,1),24326(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3183 24326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24336">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) * w) = a(x,y,u * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),24332(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 24332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24337">
    <literal><![CDATA[
      a(x,y,(z * a(u,u,z)) * w) = a(x,y,(u \ (u \ z)) * w)
    ]]></literal>
    <justification jstring="[para(15292(a,1),24332(a,1,3,1))].">
      <j1 rule="para" parents="15292 24332"/>
    </justification>
  </clause>

  <clause id="24339">
    <literal><![CDATA[
      a(x,y \ L(T(z,u),w,v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ L(z,w,v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(25(a,2),24002(a,1,2,2))].">
      <j1 rule="para" parents="25 24002"/>
    </justification>
  </clause>

  <clause id="24340">
    <literal><![CDATA[
      a(x,L(y,y,z) * z,u) = a(x,(y \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,24023,a(flip),b,24107,a),flip(a)].">
      <j1 rule="hyper" parents="347 24023 24107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24341">
    <literal><![CDATA[
      (a(x,y,z \ u) \ 1) * (u / z) = a(x,y,z \ u) \ (u / z)
    ]]></literal>
    <justification jstring="[para(23125(a,1),24127(a,1,1,2))].">
      <j1 rule="para" parents="23125 24127"/>
    </justification>
  </clause>

  <clause id="24342">
    <literal><![CDATA[
      a(x,y \ (y \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,L(z,y,y),u) = w
    ]]></literal>
    <justification jstring="[para(24145(a,1),15034(a,1))].">
      <j1 rule="para" parents="24145 15034"/>
    </justification>
  </clause>

  <clause id="24343">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y * L(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(1295(a,1),24161(a,1,2))].">
      <j1 rule="para" parents="1295 24161"/>
    </justification>
  </clause>

  <clause id="24344">
    <literal><![CDATA[
      a(x,(y \ 1) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y * z,u) = w
    ]]></literal>
    <justification jstring="[para(24037(a,1),24161(a,1))].">
      <j1 rule="para" parents="24037 24161"/>
    </justification>
  </clause>

  <clause id="24345">
    <literal><![CDATA[
      a(x,y,z \ L(T(u,w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ L(u,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(25(a,2),24186(a,1,3,2))].">
      <j1 rule="para" parents="25 24186"/>
    </justification>
  </clause>

  <clause id="24346">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) \ u)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ (u \ (u / w))) = v5
    ]]></literal>
    <justification jstring="[para(3257(a,1),24186(a,1,3,2))].">
      <j1 rule="para" parents="3257 24186"/>
    </justification>
  </clause>

  <clause id="24347">
    <literal><![CDATA[
      a(x,L(y,y,z) * z,u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,24115,a(flip),b,24340,a),flip(a)].">
      <j1 rule="hyper" parents="347 24115 24340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24348">
    <literal><![CDATA[
      a(x,L(y,y,z) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(24340(a,2),24172(a,1))].">
      <j1 rule="para" parents="24340 24172"/>
    </justification>
  </clause>

  <clause id="24349">
    <literal><![CDATA[
      a(x,R(L(y,R(y,z,u),w),z,u) * w,v5) = a(x,R(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(29(a,2),24347(a,1,2,1))].">
      <j1 rule="para" parents="29 24347"/>
    </justification>
  </clause>

  <clause id="24350">
    <literal><![CDATA[
      a(x * (y / T(z,u)),w,v5) = a(x * (z \ y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,23934,a,b,23907,a)].">
      <j1 rule="hyper" parents="63 23934 23907"/>
    </justification>
  </clause>

  <clause id="24351">
    <literal><![CDATA[
      a(x * (((y * z) \ y) \ u),w,v5) = a(x * ((y \ (y / z)) \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(3257(a,1),23907(a,1,1,2,1))].">
      <j1 rule="para" parents="3257 23907"/>
    </justification>
  </clause>

  <clause id="24352">
    <literal><![CDATA[
      a((x * (y / z)) \ u,w,v5) = a((x * (z \ y)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(113(a,1),23909(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="113 23909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24353">
    <literal><![CDATA[
      a((x \ (y / z)) \ u,w,v5) = a((x \ (z \ y)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(113(a,1),23911(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="113 23911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24354">
    <literal><![CDATA[
      a(R(T(x,T(y,z) * u),u,T(y,z)),w,v5) = a((y * u) \ ((x * u) * T(T(y,z),u)),w,v5)
    ]]></literal>
    <justification jstring="[para(9627(a,1),23913(a,1,1))].">
      <j1 rule="para" parents="9627 23913"/>
    </justification>
  </clause>

  <clause id="24355">
    <literal><![CDATA[
      L(x,a((y \ 1) \ z,u,w),v5) = L(x,a(y \ z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(23923(a,1),22768(a,1,2))].">
      <j1 rule="para" parents="23923 22768"/>
    </justification>
  </clause>

  <clause id="24356">
    <literal><![CDATA[
      a(x \ (y * (z / u)),w,v5) = a(x \ (y * (u \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(113(a,1),23937(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 23937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24357">
    <literal><![CDATA[
      a(x \ (y \ (z / u)),w,v5) = a(x \ (y \ (u \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(113(a,1),23938(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 23938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24359">
    <literal><![CDATA[
      a(L(x \ (K(y,z) * u),w,v5),v6,v7) = a(L(x \ u,w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(20369(a,1),23939(a,1,1,1))].">
      <j1 rule="para" parents="20369 23939"/>
    </justification>
  </clause>

  <clause id="24360">
    <literal><![CDATA[
      a(x,(y \ L(z \ u,w,v5)) * y,v6) = a(x,L(u / z,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,24038,a,b,24024,a)].">
      <j1 rule="hyper" parents="347 24038 24024"/>
    </justification>
  </clause>

  <clause id="24362">
    <literal><![CDATA[
      a(x,L(y * T(z,u),w,v5),v6) = a(x,L(y * z,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(1440(a,1),24055(a,1,2,1))].">
      <j1 rule="para" parents="1440 24055"/>
    </justification>
  </clause>

  <clause id="24363">
    <literal><![CDATA[
      a(x,L(y \ (z / u),w,v5),v6) = a(x,L(y \ (u \ z),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(13113(a,1),24055(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13113 24055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24364">
    <literal><![CDATA[
      a(x,L(L(y * K(z,u),w,v5),v6,v7),v8) = a(x,L(L(y,w,v5),v6,v7),v8)
    ]]></literal>
    <justification jstring="[para(21247(a,2),24055(a,1,2,1))].">
      <j1 rule="para" parents="21247 24055"/>
    </justification>
  </clause>

  <clause id="24365">
    <literal><![CDATA[
      a(x,y,z * (T(u,w) * v5)) = a(x,y,(u * v5) * z)
    ]]></literal>
    <justification jstring="[hyper(24180,a,24077,a)].">
      <j1 rule="hyper" parents="24180 24077"/>
    </justification>
  </clause>

  <clause id="24366">
    <literal><![CDATA[
      a(x,y,((z / u) * w) * v5) = a(x,y,((u \ z) * w) * v5)
    ]]></literal>
    <justification jstring="[para(113(a,1),24077(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="113 24077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24367">
    <literal><![CDATA[
      a(x,y,(z * ((u * u) * w)) \ v5) = a(x,y,(z * (w * (u * u))) \ v5)
    ]]></literal>
    <justification jstring="[para(253(a,1),24086(a,1,3,1,2))].">
      <j1 rule="para" parents="253 24086"/>
    </justification>
  </clause>

  <clause id="24368">
    <literal><![CDATA[
      a(x,y,((z * T(u,w)) * w) \ v5) = a(x,y,((z * u) * w) \ v5)
    ]]></literal>
    <justification jstring="[para(6115(a,1),24086(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="6115 24086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24369">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u \ w),v5,v6)) = a(x,y,L((w / u) \ ((u \ w) / (z \ 1)),v5,v6))
    ]]></literal>
    <justification jstring="[para(5606(a,1),24087(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5606 24087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24370">
    <literal><![CDATA[
      a(x,y,L(K(z,u) * w,v5,v6 * v7)) = a(x,y,L(w,v5,v7 * v6))
    ]]></literal>
    <justification jstring="[para(20042(a,1),24087(a,1,3))].">
      <j1 rule="para" parents="20042 24087"/>
    </justification>
  </clause>

  <clause id="24371">
    <literal><![CDATA[
      a(x,y \ (z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(24113(a,1),24159(a,1))].">
      <j1 rule="para" parents="24113 24159"/>
    </justification>
  </clause>

  <clause id="24372">
    <literal><![CDATA[
      a(x,((y \ 1) * z) \ u,w) = a(x,(z * y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24268,a,b,24117,a)].">
      <j1 rule="hyper" parents="63 24268 24117"/>
    </justification>
  </clause>

  <clause id="24373">
    <literal><![CDATA[
      a(x,((y \ 1) * ((z * z) \ 1)) \ u,w) = a(x,(y \ (z * z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(460(a,1),24117(a,2,2,1))].">
      <j1 rule="para" parents="460 24117"/>
    </justification>
  </clause>

  <clause id="24374">
    <literal><![CDATA[
      a(x,(L(y,z,u) \ y) \ w,v5) = a(x,(y * L(y,z,u)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(1409(a,1),24117(a,1,2,1))].">
      <j1 rule="para" parents="1409 24117"/>
    </justification>
  </clause>

  <clause id="24375">
    <literal><![CDATA[
      a(x,((y \ 1) * ((y * (z * (y \ 1))) \ 1)) \ u,w) = a(x,(L(z,y,y) * (y \ 1)) \ u,w)
    ]]></literal>
    <justification jstring="[para(3212(a,1),24117(a,2,2,1))].">
      <j1 rule="para" parents="3212 24117"/>
    </justification>
  </clause>

  <clause id="24376">
    <literal><![CDATA[
      a(x,((y * L(z \ 1,u,w)) * 1) \ v5,v6) = a(x,((y * L(z,u,w)) * (z * z)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(3327(a,1),24117(a,1,2,1))].">
      <j1 rule="para" parents="3327 24117"/>
    </justification>
  </clause>

  <clause id="24377">
    <literal><![CDATA[
      a(x,((y \ 1) * L(z,y,y)) \ u,w) = a(x,(y \ (z \ 1)) \ u,w)
    ]]></literal>
    <justification jstring="[para(15302(a,1),24117(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15302 24117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24378">
    <literal><![CDATA[
      a(x,y,z * (T(u,w) * v5)) = a(x,y,z * (v5 * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,24082,a,b,24135,a)].">
      <j1 rule="hyper" parents="63 24082 24135"/>
    </justification>
  </clause>

  <clause id="24379">
    <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(18785(a,1),24140(a,1,3))].">
      <j1 rule="para" parents="18785 24140"/>
    </justification>
  </clause>

  <clause id="24380">
    <literal><![CDATA[
      L(a(x,x,x \ (x \ y)),y,z) = (y * z) \ (z * ((x \ 1) \ (x \ T(y,z))))
    ]]></literal>
    <justification jstring="[para(24141(a,1),10210(a,1,1))].">
      <j1 rule="para" parents="24141 10210"/>
    </justification>
  </clause>

  <clause id="24382">
    <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),24142(a,2,3))].">
      <j1 rule="para" parents="30 24142"/>
    </justification>
  </clause>

  <clause id="24384">
    <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="[hyper(63,a,20958,a,b,24144,a)].">
      <j1 rule="hyper" parents="63 20958 24144"/>
    </justification>
  </clause>

  <clause id="24385">
    <literal><![CDATA[
      a(x \ L(x,y,z),x,u) = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14772,a,b,24144,a)].">
      <j1 rule="hyper" parents="63 14772 24144"/>
    </justification>
  </clause>

  <clause id="24386">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ (x \ (L(x,y,z) * u)) = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14704,a,b,24144,a)].">
      <j1 rule="hyper" parents="63 14704 24144"/>
    </justification>
  </clause>

  <clause id="24387">
    <literal><![CDATA[
      a(x,y * R(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(12648,a,24152,a),flip(a)].">
      <j1 rule="hyper" parents="12648 24152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24388">
    <literal><![CDATA[
      a(x,y * R(y,z,z),u) = a(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(13398(a,1),24152(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13398 24152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24389">
    <literal><![CDATA[
      (x \ y) \ (z \ ((z * (x \ a(x,x,y))) * y)) = a(z,x * a(x,x,y),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,19000,a,b,24153,a)].">
      <j1 rule="hyper" parents="63 19000 24153"/>
    </justification>
  </clause>

  <clause id="24390">
    <literal><![CDATA[
      a(x,y * L((z * z) * u,y,y),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,L((y \ (z * z)) * u,y,y),w) = v5
    ]]></literal>
    <justification jstring="[para(3222(a,1),24173(a,1,2,2))].">
      <j1 rule="para" parents="3222 24173"/>
    </justification>
  </clause>

  <clause id="24391">
    <literal><![CDATA[
      a(x,(y * z) * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,L(z,y,y),u) = w
    ]]></literal>
    <justification jstring="[para(24037(a,1),24173(a,1))].">
      <j1 rule="para" parents="24037 24173"/>
    </justification>
  </clause>

  <clause id="24392">
    <literal><![CDATA[
      a(x,y * (z * y),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,L(z,y,y),u) = w
    ]]></literal>
    <justification jstring="[para(24046(a,1),24173(a,1))].">
      <j1 rule="para" parents="24046 24173"/>
    </justification>
  </clause>

  <clause id="24396">
    <literal><![CDATA[
      a(T((x * y) * z,u),w,v5) = a((x * T(y,v6)) * z,w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,23894,a,b,24224,a)].">
      <j1 rule="hyper" parents="347 23894 24224"/>
    </justification>
  </clause>

  <clause id="24397">
    <literal><![CDATA[
      a(x,y * ((z / u) \ w),v5) = a(x,y * ((u \ z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(113(a,1),24251(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="113 24251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24398">
    <literal><![CDATA[
      a(x,y * (L(z / u,w,v5) \ v6),v7) = a(x,y * (L(u \ z,w,v5) \ v6),v7)
    ]]></literal>
    <justification jstring="[para(278(a,1),24251(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="278 24251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24399">
    <literal><![CDATA[
      a(x,y * (z \ K(u,w)),v5) = a(x,z * y,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24105,a(flip),b,24254,a),flip(a)].">
      <j1 rule="hyper" parents="347 24105 24254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24400">
    <literal><![CDATA[
      a(x,y * ((z \ 1) * (a(u,w,z) \ z)),v5) = a(x,a(u,w,z) * y,v5)
    ]]></literal>
    <justification jstring="[para(23354(a,1),24399(a,1,2,2))].">
      <j1 rule="para" parents="23354 24399"/>
    </justification>
  </clause>

  <clause id="24401">
    <literal><![CDATA[
      a(x,y,z * T(T(u,w) * (1 / v5),v5)) = a(x,y,z * (L(v5,v5,T(u,w)) \ u))
    ]]></literal>
    <justification jstring="[para(6354(a,2),24279(a,1,3,2))].">
      <j1 rule="para" parents="6354 24279"/>
    </justification>
  </clause>

  <clause id="24402">
    <literal><![CDATA[
      a(x,(y \ (z / u)) \ w,v5) = a(x,(y \ (u \ z)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(113(a,1),24321(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="113 24321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24403">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) \ (z * u)) = a(x,y,(z * u) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,15158,a,b,24328,a)].">
      <j1 rule="hyper" parents="63 15158 24328"/>
    </justification>
  </clause>

  <clause id="24404">
    <literal><![CDATA[
      a(x,y,(z * a(u,u,z)) * w) = a(x,y,L(z,u,u) * w)
    ]]></literal>
    <justification jstring="[para(14611(a,1),24333(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="14611 24333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24405">
    <literal><![CDATA[
      a(x * ((y \ z) \ y),u,w) = a(x * (y * (z \ y)),u,w)
    ]]></literal>
    <justification jstring="[para(3276(a,1),24350(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3276 24350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24406">
    <literal><![CDATA[
      a(x,y,z * (((u * w) \ v5) * u)) = a(x,y,z * (u * ((w * u) \ v5)))
    ]]></literal>
    <justification jstring="[para(10295(a,1),24378(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10295 24378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24407">
    <literal><![CDATA[
      a(x,y,z * (((u * w) * v5) * w)) = a(x,y,z * (w * ((w * u) * v5)))
    ]]></literal>
    <justification jstring="[para(10302(a,1),24378(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10302 24378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24408">
    <literal><![CDATA[
      a(x * a(y,z,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((x \ 1) \ a(y,z,x),u,w) = v5
    ]]></literal>
    <justification jstring="[para(14326(a,1),23961(a,1,1))].">
      <j1 rule="para" parents="14326 23961"/>
    </justification>
  </clause>

  <clause id="24409">
    <literal><![CDATA[
      a((x * y) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z * (y * x),u,w) = v5
    ]]></literal>
    <justification jstring="[para(23896(a,1),23967(a,1))].">
      <j1 rule="para" parents="23896 23967"/>
    </justification>
  </clause>

  <clause id="24410">
    <literal><![CDATA[
      a(x \ ((y / z) \ u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x \ ((z \ y) \ u),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(5441(a,1),23971(a,1,1,2))].">
      <j1 rule="para" parents="5441 23971"/>
    </justification>
  </clause>

  <clause id="24411">
    <literal><![CDATA[
      a(x,y * (a(z,u,z) * (w * v5)),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y * (v5 * (a(z,u,z) * w)),v6) = v7
    ]]></literal>
    <justification jstring="[para(11372(a,1),24006(a,1,2,2))].">
      <j1 rule="para" parents="11372 24006"/>
    </justification>
  </clause>

  <clause id="24412">
    <literal><![CDATA[
      a(x,y / (z * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,(u * z) \ y,w) = v5
    ]]></literal>
    <justification jstring="[para(24023(a,2),24007(a,1))].">
      <j1 rule="para" parents="24023 24007"/>
    </justification>
  </clause>

  <clause id="24413">
    <literal><![CDATA[
      a(x,((y \ 1) * z) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,(y * z) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(24372(a,2),24007(a,1))].">
      <j1 rule="para" parents="24372 24007"/>
    </justification>
  </clause>

  <clause id="24414">
    <literal><![CDATA[
      a(x,L(y,z * T(u,w * w),v5) * (v5 * (z * T(u,w * w))),v6) = a(x,v5 * ((z * ((w * w) \ u)) * ((w * w) * y)),v6)
    ]]></literal>
    <justification jstring="[para(1092(a,2),24040(a,2,2,2))].">
      <j1 rule="para" parents="1092 24040"/>
    </justification>
  </clause>

  <clause id="24415">
    <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(6075(a,1),24166(a,1,2,2))].">
      <j1 rule="para" parents="6075 24166"/>
    </justification>
  </clause>

  <clause id="24416">
    <literal><![CDATA[
      a(x,y * (z * (u * T(w,v5))),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y * (z * (u * w)),v6) = v7
    ]]></literal>
    <justification jstring="[para(6975(a,1),24166(a,1,2,2))].">
      <j1 rule="para" parents="6975 24166"/>
    </justification>
  </clause>

  <clause id="24417">
    <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(7768(a,1),24166(a,1,2,2))].">
      <j1 rule="para" parents="7768 24166"/>
    </justification>
  </clause>

  <clause id="24418">
    <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(13354(a,1),24166(a,1,2,2))].">
      <j1 rule="para" parents="13354 24166"/>
    </justification>
  </clause>

  <clause id="24419">
    <literal><![CDATA[
      a(x,y * (z \ (K(u,w) * v5)),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y * (z \ v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(20369(a,1),24166(a,1,2,2))].">
      <j1 rule="para" parents="20369 24166"/>
    </justification>
  </clause>

  <clause id="24420">
    <literal><![CDATA[
      a(x,L(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,(u * z) \ ((z * y) * u),w) = v5
    ]]></literal>
    <justification jstring="[para(18(a,2),24168(a,1,2))].">
      <j1 rule="para" parents="18 24168"/>
    </justification>
  </clause>

  <clause id="24421">
    <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(5479(a,1),24189(a,1,3,2))].">
      <j1 rule="para" parents="5479 24189"/>
    </justification>
  </clause>

  <clause id="24422">
    <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(5570(a,1),24189(a,1,3,2))].">
      <j1 rule="para" parents="5570 24189"/>
    </justification>
  </clause>

  <clause id="24423">
    <literal><![CDATA[
      a(x,y,z * (L(T(u,w),v5,v6) \ v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (L(u,v5,v6) \ v7)) = v8
    ]]></literal>
    <justification jstring="[para(5343(a,1),24189(a,1,3,2))].">
      <j1 rule="para" parents="5343 24189"/>
    </justification>
  </clause>

  <clause id="24424">
    <literal><![CDATA[
      a(x,y,z * ((T(u,w) * v5) * v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * ((u * v5) * v6)) = v7
    ]]></literal>
    <justification jstring="[para(5846(a,1),24189(a,1,3,2))].">
      <j1 rule="para" parents="5846 24189"/>
    </justification>
  </clause>

  <clause id="24425">
    <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(9586(a,1),24189(a,1,3,2))].">
      <j1 rule="para" parents="9586 24189"/>
    </justification>
  </clause>

  <clause id="24426">
    <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(10274(a,1),24189(a,1,3,2))].">
      <j1 rule="para" parents="10274 24189"/>
    </justification>
  </clause>

  <clause id="24427">
    <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(10281(a,1),24189(a,1,3,2))].">
      <j1 rule="para" parents="10281 24189"/>
    </justification>
  </clause>

  <clause id="24428">
    <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(20179(a,1),24189(a,1,3))].">
      <j1 rule="para" parents="20179 24189"/>
    </justification>
  </clause>

  <clause id="24429">
    <literal><![CDATA[
      a(x,y,(z \ (K(u,w) * v5)) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z \ v5) * v6) = v7
    ]]></literal>
    <justification jstring="[para(20967(a,1),24189(a,1,3))].">
      <j1 rule="para" parents="20967 24189"/>
    </justification>
  </clause>

  <clause id="24430">
    <literal><![CDATA[
      a(x,y,(z \ (u * T(w,v5))) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z \ (u * w)) * v6) = v7
    ]]></literal>
    <justification jstring="[para(21031(a,1),24189(a,1,3))].">
      <j1 rule="para" parents="21031 24189"/>
    </justification>
  </clause>

  <clause id="24431">
    <literal><![CDATA[
      a(x,y,z * ((u * T(w,u * u)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (((u * u) * v5) * ((u \ 1) * w))) = v6
    ]]></literal>
    <justification jstring="[para(992(a,1),24190(a,1,3,2))].">
      <j1 rule="para" parents="992 24190"/>
    </justification>
  </clause>

  <clause id="24432">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * ((L(w,u,u) \ 1) * (u \ 1))) = v5
    ]]></literal>
    <justification jstring="[para(15302(a,1),24190(a,1,3,2))].">
      <j1 rule="para" parents="15302 24190"/>
    </justification>
  </clause>

  <clause id="24434">
    <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(5441(a,1),24196(a,1,3,2))].">
      <j1 rule="para" parents="5441 24196"/>
    </justification>
  </clause>

  <clause id="24435">
    <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(20083(a,1),24196(a,1,3))].">
      <j1 rule="para" parents="20083 24196"/>
    </justification>
  </clause>

  <clause id="24436">
    <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(20707(a,1),24196(a,1,3))].">
      <j1 rule="para" parents="20707 24196"/>
    </justification>
  </clause>

  <clause id="24437">
    <literal><![CDATA[
      a(x,y,(((z \ u) * z) * w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u * w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(10244(a,1),24197(a,1,3,1))].">
      <j1 rule="para" parents="10244 24197"/>
    </justification>
  </clause>

  <clause id="24438">
    <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(13354(a,1),24210(a,1,3,2))].">
      <j1 rule="para" parents="13354 24210"/>
    </justification>
  </clause>

  <clause id="24439">
    <literal><![CDATA[
      a(x,y,z * (u * (w * (v5 * v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (w * ((v5 * v5) * u))) = v6
    ]]></literal>
    <justification jstring="[para(117(a,1),24211(a,1,3,2,1))].">
      <j1 rule="para" parents="117 24211"/>
    </justification>
  </clause>

  <clause id="24440">
    <literal><![CDATA[
      a(x,y,z * ((u * u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * w) = v5
    ]]></literal>
    <justification jstring="[para(14921(a,1),24211(a,1))].">
      <j1 rule="para" parents="14921 24211"/>
    </justification>
  </clause>

  <clause id="24441">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u \ (w \ (z \ ((z * u) * w)))) = v5
    ]]></literal>
    <justification jstring="[para(23139(a,2),24213(a,1,3))].">
      <j1 rule="para" parents="23139 24213"/>
    </justification>
  </clause>

  <clause id="24443">
    <literal><![CDATA[
      a(x,y * (z / (u \ 1)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,(L(u,u,z) * z) * y,w) = v5
    ]]></literal>
    <justification jstring="[para(2008(a,1),24247(a,1,2,2))].">
      <j1 rule="para" parents="2008 24247"/>
    </justification>
  </clause>

  <clause id="24444">
    <literal><![CDATA[
      a(x,(y * z) \ ((y * u) * z),w) = a(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(24007,a,24259,a)].">
      <j1 rule="hyper" parents="24007 24259"/>
    </justification>
  </clause>

  <clause id="24445">
    <literal><![CDATA[
      a(x,y,(z * T(u,w * w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * ((w * w) \ u)) * v5) = v6
    ]]></literal>
    <justification jstring="[para(1092(a,1),24288(a,1,3))].">
      <j1 rule="para" parents="1092 24288"/>
    </justification>
  </clause>

  <clause id="24446">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(w * u) * z) = v5
    ]]></literal>
    <justification jstring="[para(15035(a,2),24290(a,1))].">
      <j1 rule="para" parents="15035 24290"/>
    </justification>
  </clause>

  <clause id="24447">
    <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(24378(a,2),24290(a,1))].">
      <j1 rule="para" parents="24378 24290"/>
    </justification>
  </clause>

  <clause id="24448">
    <literal><![CDATA[
      L(x,a(y * (y * z),u,w),v5) = L(x,a(L(z,y,y),u,w),v5)
    ]]></literal>
    <justification jstring="[para(24315(a,1),22768(a,1,2))].">
      <j1 rule="para" parents="24315 22768"/>
    </justification>
  </clause>

  <clause id="24449">
    <literal><![CDATA[
      a(x,y,(z \ 1) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * u) = w
    ]]></literal>
    <justification jstring="[para(497(a,1),24440(a,1,3))].">
      <j1 rule="para" parents="497 24440"/>
    </justification>
  </clause>

  <clause id="24450">
    <literal><![CDATA[
      a(x,y,(z * (u \ 1)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * u) * w) = v5
    ]]></literal>
    <justification jstring="[para(828(a,1),24440(a,1,3))].">
      <j1 rule="para" parents="828 24440"/>
    </justification>
  </clause>

  <clause id="24451">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(3326(a,1),24440(a,1,3))].">
      <j1 rule="para" parents="3326 24440"/>
    </justification>
  </clause>

  <clause id="24452">
    <literal><![CDATA[
      a(x,y,(1 / z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * u) = w
    ]]></literal>
    <justification jstring="[para(4124(a,2),24449(a,1))].">
      <j1 rule="para" parents="4124 24449"/>
    </justification>
  </clause>

  <clause id="24453">
    <literal><![CDATA[
      a(x,y,z * L(z,z,u)) = a(x,y,z * ((u * (1 / (1 / z))) \ u))
    ]]></literal>
    <justification jstring="[hyper(24452,a,15171,a),flip(a)].">
      <j1 rule="hyper" parents="24452 15171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24456">
    <literal><![CDATA[
      a(((x * y) * T(x \ 1,x)) * z,u,w) = a(((y * (x \ 1)) * x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(986(a,1),23912(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="986 23912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24457">
    <literal><![CDATA[
      a((((x \ y) \ y) \ z) * u,w,v5) = a((x \ z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(80(a,1),23914(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="80 23914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24458">
    <literal><![CDATA[
      a((x \ y) * (z * (x * x)),u,w) = a(z * ((x \ 1) \ y),u,w)
    ]]></literal>
    <justification jstring="[para(495(a,1),23944(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="495 23944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24459">
    <literal><![CDATA[
      a(L((x * x) \ y,(x * x) \ y,((x * x) \ y) \ z) \ ((x * x) \ y),u,w) = a(((x * x) \ (L((x * x) \ y,(x * x) \ y,z) \ 1)) * y,u,w)
    ]]></literal>
    <justification jstring="[para(10202(a,2),23950(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10202 23950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24460">
    <literal><![CDATA[
      a(x,y * ((z * z) * u),w) = a(x,u * y,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,14974,a(flip),b,24106,a),flip(a)].">
      <j1 rule="hyper" parents="347 14974 24106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24462">
    <literal><![CDATA[
      a(x,y * L((z * z) * u,w,v5),v6) = a(x,L(u,w,v5) * y,v6)
    ]]></literal>
    <justification jstring="[para(3176(a,2),24460(a,1,2,2))].">
      <j1 rule="para" parents="3176 24460"/>
    </justification>
  </clause>

  <clause id="24463">
    <literal><![CDATA[
      a(x,L((y * y) \ z,u,w) * v5,v6) = a(x,v5 * L(z,u,w),v6)
    ]]></literal>
    <justification jstring="[para(3320(a,1),24460(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3320 24460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24464">
    <literal><![CDATA[
      a(x,y * (L(z \ 1,u,w) \ v5),v6) = a(x,(L(z,u,w) \ v5) * y,v6)
    ]]></literal>
    <justification jstring="[para(3325(a,1),24460(a,1,2,2))].">
      <j1 rule="para" parents="3325 24460"/>
    </justification>
  </clause>

  <clause id="24465">
    <literal><![CDATA[
      a(x,(1 / (1 / (y \ z))) * z,u) = a(x,(z \ y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,24023,a(flip),b,24108,a),flip(a)].">
      <j1 rule="hyper" parents="347 24023 24108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24466">
    <literal><![CDATA[
      a(x,y * (K(z,u) * w),v5) = a(x,w * y,v5)
    ]]></literal>
    <justification jstring="[hyper(23987,a,24111,a),flip(a)].">
      <j1 rule="hyper" parents="23987 24111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24467">
    <literal><![CDATA[
      a(x,y * (K(z,u) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,w * y,v5) = v6
    ]]></literal>
    <justification jstring="[para(24111(a,1),23987(a,1))].">
      <j1 rule="para" parents="24111 23987"/>
    </justification>
  </clause>

  <clause id="24469">
    <literal><![CDATA[
      a(x,y * (T(z,u) * w),v5) = a(x,(z * w) * y,v5)
    ]]></literal>
    <justification jstring="[para(4974(a,1),24466(a,1,2,2))].">
      <j1 rule="para" parents="4974 24466"/>
    </justification>
  </clause>

  <clause id="24470">
    <literal><![CDATA[
      a(x,((y * z) * u) * w,v5) = a(x,w * ((z * y) * u),v5)
    ]]></literal>
    <justification jstring="[para(10281(a,1),24466(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10281 24466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24471">
    <literal><![CDATA[
      a(x,((T(y,z) * u) * w) * v5,v6) = a(x,v5 * ((y * u) * w),v6)
    ]]></literal>
    <justification jstring="[para(20344(a,1),24466(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="20344 24466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24472">
    <literal><![CDATA[
      a(x,y * L(K(z,u) * w,v5,v6),v7) = a(x,L(w,v5,v6) * y,v7)
    ]]></literal>
    <justification jstring="[para(21250(a,2),24466(a,1,2,2))].">
      <j1 rule="para" parents="21250 24466"/>
    </justification>
  </clause>

  <clause id="24473">
    <literal><![CDATA[
      a(x,(T(y,z) * u) * w,v5) = a(x,(y * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(23994,a,24469,a)].">
      <j1 rule="hyper" parents="23994 24469"/>
    </justification>
  </clause>

  <clause id="24474">
    <literal><![CDATA[
      a(x,(y * (K(z,y) * u)) * w,v5) = a(x,(L(y,z,y) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(5702(a,1),24473(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5702 24473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24475">
    <literal><![CDATA[
      a(x,y * (T(z,u) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,(z * w) * y,v5) = v6
    ]]></literal>
    <justification jstring="[para(4974(a,1),24467(a,1,2,2))].">
      <j1 rule="para" parents="4974 24467"/>
    </justification>
  </clause>

  <clause id="24476">
    <literal><![CDATA[
      a(x,y * ((T(z,u) \ w) * v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,((z \ w) * v5) * y,v6) = v7
    ]]></literal>
    <justification jstring="[para(11712(a,1),24467(a,1,2,2))].">
      <j1 rule="para" parents="11712 24467"/>
    </justification>
  </clause>

  <clause id="24477">
    <literal><![CDATA[
      a(x,(y * T(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,w * (y * z),v5) = v6
    ]]></literal>
    <justification jstring="[para(20808(a,1),24467(a,1,2))].">
      <j1 rule="para" parents="20808 24467"/>
    </justification>
  </clause>

  <clause id="24478">
    <literal><![CDATA[
      a(x,(y * (K(z,u) * w)) * v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,v5 * (y * w),v6) = v7
    ]]></literal>
    <justification jstring="[para(21138(a,1),24467(a,1,2))].">
      <j1 rule="para" parents="21138 24467"/>
    </justification>
  </clause>

  <clause id="24479">
    <literal><![CDATA[
      a(x,L(y * a(z,z,y),u,w),v5) = a(x,L(z \ (z \ y),u,w),v5)
    ]]></literal>
    <justification jstring="[para(15286(a,1),24119(a,1,2,1))].">
      <j1 rule="para" parents="15286 24119"/>
    </justification>
  </clause>

  <clause id="24480">
    <literal><![CDATA[
      a(x,y * ((z * z) \ u),w) = a(x,u * y,w)
    ]]></literal>
    <justification jstring="[hyper(15002,a,24156,a)].">
      <j1 rule="hyper" parents="15002 24156"/>
    </justification>
  </clause>

  <clause id="24482">
    <literal><![CDATA[
      a(x,((y * y) \ z) * u,w) = a(x,z * u,w)
    ]]></literal>
    <justification jstring="[hyper(23994,a,24480,a)].">
      <j1 rule="hyper" parents="23994 24480"/>
    </justification>
  </clause>

  <clause id="24484">
    <literal><![CDATA[
      a(x,((y \ 1) \ z) * u,w) = a(x,u * (y \ z),w)
    ]]></literal>
    <justification jstring="[para(500(a,1),24480(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="500 24480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24485">
    <literal><![CDATA[
      a(x,y * L(z \ u,z,z),w) = a(x,(z * u) * y,w)
    ]]></literal>
    <justification jstring="[para(99(a,2),24480(a,1,2,2))].">
      <j1 rule="para" parents="99 24480"/>
    </justification>
  </clause>

  <clause id="24486">
    <literal><![CDATA[
      a(x,((y * z) * (z \ y)) * u,w) = a(x,a(y,z,z \ y) * u,w)
    ]]></literal>
    <justification jstring="[para(87(a,1),24482(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="87 24482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24487">
    <literal><![CDATA[
      a(x,y * ((z \ 1) \ u),w) = a(x,y * (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(23994,a,24484,a)].">
      <j1 rule="hyper" parents="23994 24484"/>
    </justification>
  </clause>

  <clause id="24488">
    <literal><![CDATA[
      a(x,y * L(z \ u,z,z),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y * (z * u),w) = v5
    ]]></literal>
    <justification jstring="[para(24485(a,2),23994(a,1))].">
      <j1 rule="para" parents="24485 23994"/>
    </justification>
  </clause>

  <clause id="24489">
    <literal><![CDATA[
      a(x * (y \ (T(z,u) * w)),v5,v6) = a(x * (y \ (z * w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(4946(a,1),24223(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4946 24223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24490">
    <literal><![CDATA[
      a((x \ (y / z)) * u,w,v5) = a((x \ (z \ y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(5012(a,1),24226(a,1,1,1,2))].">
      <j1 rule="para" parents="5012 24226"/>
    </justification>
  </clause>

  <clause id="24491">
    <literal><![CDATA[
      a(x \ (y * ((L(z,u,z) \ w) * z)),v5,v6) = a(x \ (y * (w * a(z,u,z))),v5,v6)
    ]]></literal>
    <justification jstring="[para(8508(a,1),24231(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8508 24231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24492">
    <literal><![CDATA[
      a(x * (y \ R(y,y,z)),u,w) = a(x * (y * (z \ (y \ z))),u,w)
    ]]></literal>
    <justification jstring="[para(2377(a,2),24235(a,1,1,2))].">
      <j1 rule="para" parents="2377 24235"/>
    </justification>
  </clause>

  <clause id="24493">
    <literal><![CDATA[
      a(x * (y * ((z * u) \ z)),w,v5) = a(x * (y * (z \ (z / u))),w,v5)
    ]]></literal>
    <justification jstring="[para(3256(a,1),24236(a,1,1,2,2))].">
      <j1 rule="para" parents="3256 24236"/>
    </justification>
  </clause>

  <clause id="24494">
    <literal><![CDATA[
      a(x * (y * (z \ (u / w))),v5,v6) = a(x * (y * (z \ (w \ u))),v5,v6)
    ]]></literal>
    <justification jstring="[para(13113(a,1),24237(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13113 24237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24495">
    <literal><![CDATA[
      a(x,y * ((K(z,u) * w) * (v5 \ v6)),v7) = a(x,y * (K(z,u) * (w * (v6 / v5))),v7)
    ]]></literal>
    <justification jstring="[para(20008(a,1),24249(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="20008 24249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24496">
    <literal><![CDATA[
      a(x,y * (z * ((u * u) * w)),v5) = a(x,y * (z * w),(u * u) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,2105,a(flip),b,24250,a),flip(a)].">
      <j1 rule="hyper" parents="347 2105 24250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24497">
    <literal><![CDATA[
      a(x,y * (z * (u \ K(w,v5))),v6) = a(x,y * (z * (u \ 1)),v6)
    ]]></literal>
    <justification jstring="[para(12973(a,1),24253(a,1,2,2,2))].">
      <j1 rule="para" parents="12973 24253"/>
    </justification>
  </clause>

  <clause id="24498">
    <literal><![CDATA[
      a(x,y \ (z * ((u * (w \ K(v5,v6))) \ K(v5,v6))),v7) = a(x,y \ (z * (1 / (u * (w \ 1)))),v7)
    ]]></literal>
    <justification jstring="[para(22144(a,1),24261(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="22144 24261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24499">
    <literal><![CDATA[
      a(x,y \ ((z * u) * w),v5) = a(x,y \ (w * (u * z)),v5)
    ]]></literal>
    <justification jstring="[hyper(24168,a,24262,a)].">
      <j1 rule="hyper" parents="24168 24262"/>
    </justification>
  </clause>

  <clause id="24500">
    <literal><![CDATA[
      a(x,y \ (z * (u * K(w,v5))),v6) = a(x,K(v7,v8) * (y \ (z * u)),v6)
    ]]></literal>
    <justification jstring="[hyper(23996,a,24264,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="23996 24264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24501">
    <literal><![CDATA[
      a(x,y \ (z * (u \ T(w,v5))),v6) = a(x,y \ (z * (u \ w)),v6)
    ]]></literal>
    <justification jstring="[para(1438(a,1),24264(a,1,2,2,2))].">
      <j1 rule="para" parents="1438 24264"/>
    </justification>
  </clause>

  <clause id="24502">
    <literal><![CDATA[
      a(x,y \ (z \ (T(u,w) * v5)),v6) = a(x,y \ (z \ (u * v5)),v6)
    ]]></literal>
    <justification jstring="[para(4946(a,1),24265(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4946 24265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24503">
    <literal><![CDATA[
      a(x,y,z * (((u * u) \ (w \ u)) * v5)) = a(x,y,z * ((w \ (u \ 1)) * v5))
    ]]></literal>
    <justification jstring="[para(820(a,1),24278(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="820 24278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24504">
    <literal><![CDATA[
      a(x,y,z * (u * ((w / v5) * v6))) = a(x,y,z * (u * ((v5 \ w) * v6)))
    ]]></literal>
    <justification jstring="[para(5237(a,1),24280(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="5237 24280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24505">
    <literal><![CDATA[
      a(x,y,z * ((u \ T(w,v5)) * v6)) = a(x,y,z * ((u \ w) * v6))
    ]]></literal>
    <justification jstring="[para(20179(a,1),24280(a,1,3,2))].">
      <j1 rule="para" parents="20179 24280"/>
    </justification>
  </clause>

  <clause id="24506">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) * v5) = a(x,y,v5 * ((w * u) * z))
    ]]></literal>
    <justification jstring="[hyper(24290,a,24281,a)].">
      <j1 rule="hyper" parents="24290 24281"/>
    </justification>
  </clause>

  <clause id="24507">
    <literal><![CDATA[
      a(x,y,z * ((u * ((w * w) * v5)) * v6)) = a(x,y,z * ((v5 * (u * (w * w))) * v6))
    ]]></literal>
    <justification jstring="[para(32(a,1),24281(a,1,3,2,1))].">
      <j1 rule="para" parents="32 24281"/>
    </justification>
  </clause>

  <clause id="24508">
    <literal><![CDATA[
      a(x,y,((z * z) * u) \ w) = a(x,y,u \ w)
    ]]></literal>
    <justification jstring="[hyper(347,a,14948,a(flip),b,24293,a),flip(a)].">
      <j1 rule="hyper" parents="347 14948 24293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24510">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) \ w) = a(x,y,(z \ u) \ w)
    ]]></literal>
    <justification jstring="[para(495(a,1),24508(a,1,3,1))].">
      <j1 rule="para" parents="495 24508"/>
    </justification>
  </clause>

  <clause id="24511">
    <literal><![CDATA[
      a(x,y,(z * (z * u)) \ w) = a(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[para(97(a,1),24508(a,1,3,1))].">
      <j1 rule="para" parents="97 24508"/>
    </justification>
  </clause>

  <clause id="24512">
    <literal><![CDATA[
      a(x,y,((z * u) * z) \ w) = a(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(24191,a,24511,a)].">
      <j1 rule="hyper" parents="24191 24511"/>
    </justification>
  </clause>

  <clause id="24513">
    <literal><![CDATA[
      a(x,y,z \ ((u * K(w,v5)) * v6)) = a(x,y,z \ (v6 * u))
    ]]></literal>
    <justification jstring="[hyper(24214,a,24310,a)].">
      <j1 rule="hyper" parents="24214 24310"/>
    </justification>
  </clause>

  <clause id="24514">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((w / z) \ (u * w))) = a(x,y,a(z \ w,z,u))
    ]]></literal>
    <justification jstring="[para(14708(a,1),24312(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14708 24312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24515">
    <literal><![CDATA[
      a(x,(y * ((z / u) * w)) \ v5,v6) = a(x,(y * ((u \ z) * w)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(5237(a,1),24323(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5237 24323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24516">
    <literal><![CDATA[
      a(x,((y * T(z,u)) * w) \ v5,v6) = a(x,((y * z) * w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(20808(a,1),24323(a,1,2,1))].">
      <j1 rule="para" parents="20808 24323"/>
    </justification>
  </clause>

  <clause id="24517">
    <literal><![CDATA[
      a(x,(y * ((z * z) * u)) \ w,v5) = a(x,(z * z) \ ((y * u) \ w),v5)
    ]]></literal>
    <justification jstring="[para(775(a,1),24324(a,1,2)),flip(a)].">
      <j1 rule="para" parents="775 24324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24518">
    <literal><![CDATA[
      a((x * ((y * y) \ z)) \ u,w,v5) = a((y * y) * ((x * z) \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(818(a,1),24352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="818 24352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24519">
    <literal><![CDATA[
      a(L(x \ y,x,y \ (z * (u / w))) \ (z * (w \ u)),v5,v6) = a(T(((z * (u / w)) / y) * x,x \ y),v5,v6)
    ]]></literal>
    <justification jstring="[para(13788(a,1),24356(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13788 24356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24520">
    <literal><![CDATA[
      a(x,y,((z / u) * w) * v5) = a(x,y,(w * (u \ z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24084,a,b,24366,a),flip(a)].">
      <j1 rule="hyper" parents="347 24084 24366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24521">
    <literal><![CDATA[
      a((x * T(y,z)) * u,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a((x * y) * u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(24396(a,1),17834(a,1))].">
      <j1 rule="para" parents="24396 17834"/>
    </justification>
  </clause>

  <clause id="24522">
    <literal><![CDATA[
      a((L(T(x,y),z,u) \ w) * v5,v6,v7) = a((L(x,z,u) \ w) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(9710(a,1),24457(a,1,1,1,1))].">
      <j1 rule="para" parents="9710 24457"/>
    </justification>
  </clause>

  <clause id="24523">
    <literal><![CDATA[
      a(x,((1 / (y \ z)) \ 1) * z,u) = a(x,(z \ y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(24001,a,24465,a)].">
      <j1 rule="hyper" parents="24001 24465"/>
    </justification>
  </clause>

  <clause id="24524">
    <literal><![CDATA[
      a(x,(y * (z * u)) * w,v5) = a(x,w * ((u * z) * y),v5)
    ]]></literal>
    <justification jstring="[hyper(24008,a,24470,a)].">
      <j1 rule="hyper" parents="24008 24470"/>
    </justification>
  </clause>

  <clause id="24525">
    <literal><![CDATA[
      a((x \ (y / z)) * u,w,v5) = a(u * (x \ (z \ y)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,23896,a,b,24490,a),flip(a)].">
      <j1 rule="hyper" parents="347 23896 24490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24526">
    <literal><![CDATA[
      a(x,(y * z) \ (z * (u * y)),w) = a(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24444,a(flip),b,24499,a),flip(a)].">
      <j1 rule="hyper" parents="63 24444 24499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24527">
    <literal><![CDATA[
      a(x,y \ (z * ((z \ 1) * (z * u))),w) = a(x,y \ (z * R(u,z,z)),w)
    ]]></literal>
    <justification jstring="[para(916(a,1),24499(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="916 24499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24528">
    <literal><![CDATA[
      a(x,(y * (z * u)) \ (z * (u * y)),w) = a(x,K(u,z) * a(y,u,z),w)
    ]]></literal>
    <justification jstring="[para(21241(a,1),24499(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21241 24499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24529">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) * v5)) = a(x,y,z \ (v5 * (w * u)))
    ]]></literal>
    <justification jstring="[para(91(a,1),24513(a,1,3,2,1))].">
      <j1 rule="para" parents="91 24513"/>
    </justification>
  </clause>

  <clause id="24530">
    <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(24520(a,1),24192(a,1))].">
      <j1 rule="para" parents="24520 24192"/>
    </justification>
  </clause>

  <clause id="24531">
    <literal><![CDATA[
      a(x,(y \ z) \ y,u) = a(x,(z \ y) * y,u)
    ]]></literal>
    <justification jstring="[para(83(a,1),24523(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="83 24523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24533">
    <literal><![CDATA[
      a(x,(y * ((z * ((1 / z) * u)) * z)) * w,v5) = a(x,w * (L(z * u,z,z \ 1) * y),v5)
    ]]></literal>
    <justification jstring="[para(3375(a,1),24524(a,2,2,2,1))].">
      <j1 rule="para" parents="3375 24524"/>
    </justification>
  </clause>

  <clause id="24534">
    <literal><![CDATA[
      a((x \ (y / z)) * u,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a((x \ (z \ y)) * u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(24525(a,2),23925(a,1))].">
      <j1 rule="para" parents="24525 23925"/>
    </justification>
  </clause>

  <clause id="24535">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) \ (w * (u * z))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(14(a,2),24529(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14 24529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24536">
    <literal><![CDATA[
      a(((x * (y \ 1)) * y) * z,u,w) = a(L(x,y,y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(23969,a,23951,a)].">
      <j1 rule="hyper" parents="23969 23951"/>
    </justification>
  </clause>

  <clause id="24537">
    <literal><![CDATA[
      a((x \ ((y \ z) \ z)) \ u,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a((x \ y) \ u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(112(a,1),23974(a,1,1,1,2))].">
      <j1 rule="para" parents="112 23974"/>
    </justification>
  </clause>

  <clause id="24538">
    <literal><![CDATA[
      a(L(T(x,y) \ z,u,w),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(L(x \ z,u,w),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(5209(a,1),23976(a,1,1,1))].">
      <j1 rule="para" parents="5209 23976"/>
    </justification>
  </clause>

  <clause id="24539">
    <literal><![CDATA[
      a(x,L((y * y) \ (z * y),u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,L(z * (y \ 1),u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(783(a,1),24146(a,1,2,1,1))].">
      <j1 rule="para" parents="783 24146"/>
    </justification>
  </clause>

  <clause id="24540">
    <literal><![CDATA[
      a(x,L(L(T(y,z),u,w),v5,v6),v7) != v8
    ]]></literal>
    <literal><![CDATA[
      a(x,L(L(y,u,w),v5,v6),v7) = v8
    ]]></literal>
    <justification jstring="[para(9710(a,1),24146(a,1,2,1))].">
      <j1 rule="para" parents="9710 24146"/>
    </justification>
  </clause>

  <clause id="24541">
    <literal><![CDATA[
      a(x,((y \ 1) * z) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,(z * y) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(24268(a,1),24174(a,1))].">
      <j1 rule="para" parents="24268 24174"/>
    </justification>
  </clause>

  <clause id="24542">
    <literal><![CDATA[
      a(x,y,L(T(z,u) * w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z * w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(4974(a,1),24200(a,1,3,1))].">
      <j1 rule="para" parents="4974 24200"/>
    </justification>
  </clause>

  <clause id="24543">
    <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(5012(a,1),24200(a,1,3,1))].">
      <j1 rule="para" parents="5012 24200"/>
    </justification>
  </clause>

  <clause id="24544">
    <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(10274(a,1),24200(a,1,3,1))].">
      <j1 rule="para" parents="10274 24200"/>
    </justification>
  </clause>

  <clause id="24545">
    <literal><![CDATA[
      a(x,y,L(z * (u * T(w,v5)),v6,v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z * (u * w),v6,v7)) = v8
    ]]></literal>
    <justification jstring="[para(22355(a,1),24200(a,1))].">
      <j1 rule="para" parents="22355 24200"/>
    </justification>
  </clause>

  <clause id="24546">
    <literal><![CDATA[
      a(x,y,(z * u) \ (u * (w * z))) = a(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,24075,a(flip),b,24294,a),flip(a)].">
      <j1 rule="hyper" parents="347 24075 24294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24547">
    <literal><![CDATA[
      a(x,y,(z * u) \ (u * (w * z))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(w,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(24294(a,2),24184(a,1))].">
      <j1 rule="para" parents="24294 24184"/>
    </justification>
  </clause>

  <clause id="24549">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((z * w) * u)) = a(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,24529,a,b,24546,a)].">
      <j1 rule="hyper" parents="63 24529 24546"/>
    </justification>
  </clause>

  <clause id="24550">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,w)) = a(x,y,(z * w) \ (u * w))
    ]]></literal>
    <justification jstring="[para(10(a,1),24549(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="10 24549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24551">
    <literal><![CDATA[
      a(x,y,L(z \ (u \ (w \ 1)),z,v5 * v5)) = a(x,y,(z * (v5 * v5)) \ (u \ (w \ (v5 * v5))))
    ]]></literal>
    <justification jstring="[para(727(a,1),24550(a,2,3,2))].">
      <j1 rule="para" parents="727 24550"/>
    </justification>
  </clause>

  <clause id="24552">
    <literal><![CDATA[
      a(x,y,L((L(z,u,w) \ v5) \ v6,L(z,u,w) \ v5,L(T(z,v7),u,w))) = a(x,y,((z \ v5) * T(z,v7)) \ (v6 * L(T(z,v7),u,w)))
    ]]></literal>
    <justification jstring="[para(21228(a,1),24550(a,2,3,1))].">
      <j1 rule="para" parents="21228 24550"/>
    </justification>
  </clause>

  <clause id="24553">
    <literal><![CDATA[
      a(x,y,(z \ (z \ u)) * w) = a(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24404,a(flip),b,24337,a),flip(a)].">
      <j1 rule="hyper" parents="63 24404 24337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24554">
    <literal><![CDATA[
      a(x,y,L(z,u,u) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(24553(a,1),24179(a,1))].">
      <j1 rule="para" parents="24553 24179"/>
    </justification>
  </clause>

  <clause id="24555">
    <literal><![CDATA[
      a(x,y,(T(z,u) \ w) \ v5) = a(x,y,(z \ w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(24435,a,xx),flip(a)].">
      <j1 rule="hyper" parents="24435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24556">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) * w)) = a(x,y,(u * w) * z)
    ]]></literal>
    <justification jstring="[hyper(24446,a,24082,a),flip(a)].">
      <j1 rule="hyper" parents="24446 24082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24557">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u * w) * z) = v5
    ]]></literal>
    <justification jstring="[para(24082(a,1),24446(a,1))].">
      <j1 rule="para" parents="24082 24446"/>
    </justification>
  </clause>

  <clause id="24558">
    <literal><![CDATA[
      a(x,y,(z * (u * u)) * w) = a(x,y,w * (z \ (u * u)))
    ]]></literal>
    <justification jstring="[para(460(a,1),24556(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="460 24556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24559">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * w))) = a(x,y,u * ((w * w) * z))
    ]]></literal>
    <justification jstring="[para(32(a,1),24558(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32 24558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24560">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * w))) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,24285,a(flip),b,24559,a),flip(a)].">
      <j1 rule="hyper" parents="347 24285 24559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24562">
    <literal><![CDATA[
      a(x,y,(z * (L(z,u,w) \ z)) * v5) = a(x,y,v5 * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(20988(a,1),24560(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="20988 24560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24563">
    <literal><![CDATA[
      a(((x * y) \ z) * x,u,w) = a(x * ((y * x) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(23964,a,23947,a)].">
      <j1 rule="hyper" parents="23964 23947"/>
    </justification>
  </clause>

  <clause id="24564">
    <literal><![CDATA[
      a((T(x * y,z) \ u) * x,w,v5) = a(x * ((y * x) \ u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(23972,a,24563,a)].">
      <j1 rule="hyper" parents="23972 24563"/>
    </justification>
  </clause>

  <clause id="24567">
    <literal><![CDATA[
      a(x,y,L(z * u,w,v5) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,v6 * L(u * z,w,v5)) = v7
    ]]></literal>
    <justification jstring="[para(24088(a,1),24180(a,1))].">
      <j1 rule="para" parents="24088 24180"/>
    </justification>
  </clause>

  <clause id="24568">
    <literal><![CDATA[
      a(x,y * (a(z,u,z) * w),v5) = a(x,w * y,v5)
    ]]></literal>
    <justification jstring="[hyper(12453,a,24109,a),flip(a)].">
      <j1 rule="hyper" parents="12453 24109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24570">
    <literal><![CDATA[
      a(x,y * (z * (u \ 1)),w) = a(x,(z * u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24480,a(flip),b,24241,a),flip(a)].">
      <j1 rule="hyper" parents="63 24480 24241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24572">
    <literal><![CDATA[
      a(x,y * ((z \ 1) * ((u * u) \ 1)),w) = a(x,(z \ (u * u)) * y,w)
    ]]></literal>
    <justification jstring="[para(460(a,1),24570(a,2,2,1))].">
      <j1 rule="para" parents="460 24570"/>
    </justification>
  </clause>

  <clause id="24573">
    <literal><![CDATA[
      a(x,y * (z * ((1 / (1 / (u \ z))) \ 1)),w) = a(x,(z / (z \ u)) * y,w)
    ]]></literal>
    <justification jstring="[para(3397(a,1),24570(a,2,2,1))].">
      <j1 rule="para" parents="3397 24570"/>
    </justification>
  </clause>

  <clause id="24574">
    <literal><![CDATA[
      a(x,y * (z \ (u \ 1)),w) = a(x,(z \ u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24480,a(flip),b,24242,a),flip(a)].">
      <j1 rule="hyper" parents="63 24480 24242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24576">
    <literal><![CDATA[
      a(x,y * (z \ (u \ 1)),w) = a(x,y * (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24037,a,b,24574,a),flip(a)].">
      <j1 rule="hyper" parents="347 24037 24574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24577">
    <literal><![CDATA[
      a(x,y * (z \ (u \ 1)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,(z \ u) * y,w) = v5
    ]]></literal>
    <justification jstring="[para(24576(a,2),23994(a,1))].">
      <j1 rule="para" parents="24576 23994"/>
    </justification>
  </clause>

  <clause id="24578">
    <literal><![CDATA[
      a(x,y \ R(T(z,T(u,w) * v5),v5,T(u,w)),v6) = a(x,y \ ((u * v5) \ ((z * v5) * T(T(u,w),v5))),v6)
    ]]></literal>
    <justification jstring="[para(9627(a,1),24271(a,1,2,2))].">
      <j1 rule="para" parents="9627 24271"/>
    </justification>
  </clause>

  <clause id="24579">
    <literal><![CDATA[
      a(x,y \ L(z * K(u * z,T(w,v5)),u,T(w,v5)),v6) = a(x,y \ ((w * u) \ ((u * z) * T(w,v5))),v6)
    ]]></literal>
    <justification jstring="[para(13232(a,2),24271(a,1,2,2))].">
      <j1 rule="para" parents="13232 24271"/>
    </justification>
  </clause>

  <clause id="24580">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ 1))) = a(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(24440,a,24299,a),flip(a)].">
      <j1 rule="hyper" parents="24440 24299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24581">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (u \ w)) = v5
    ]]></literal>
    <justification jstring="[para(24299(a,1),24440(a,1))].">
      <j1 rule="para" parents="24299 24440"/>
    </justification>
  </clause>

  <clause id="24583">
    <literal><![CDATA[
      a(x,y,z * (R(u / w,w,u \ (v5 \ 1)) \ v5)) = a(x,y,z * (w * (u \ (v5 \ 1))))
    ]]></literal>
    <justification jstring="[para(693(a,1),24580(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="693 24580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24584">
    <literal><![CDATA[
      a(L(K(x,y) * ((y * z) \ u),w,v5),v6,v7) = a(L((z * T(y,x)) \ u,w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(21039(a,1),24359(a,1,1,1))].">
      <j1 rule="para" parents="21039 24359"/>
    </justification>
  </clause>

  <clause id="24585">
    <literal><![CDATA[
      a(x,L(y / z,u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,L(z \ y,u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(24360(a,1),23993(a,1))].">
      <j1 rule="para" parents="24360 23993"/>
    </justification>
  </clause>

  <clause id="24587">
    <literal><![CDATA[
      a(x,y,L(z,u,w * v5)) = a(x,y,L(z,u,v5 * w))
    ]]></literal>
    <justification jstring="[hyper(24200,a,24370,a)].">
      <j1 rule="hyper" parents="24200 24370"/>
    </justification>
  </clause>

  <clause id="24588">
    <literal><![CDATA[
      a(x,y,L(z,u,w * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,v5 * w)) = v6
    ]]></literal>
    <justification jstring="[para(24370(a,1),24200(a,1))].">
      <j1 rule="para" parents="24370 24200"/>
    </justification>
  </clause>

  <clause id="24589">
    <literal><![CDATA[
      a(x,y,L(z,u,w * ((v5 * v5) * v6))) = a(x,y,L(z,u,v6 * (w * (v5 * v5))))
    ]]></literal>
    <justification jstring="[para(32(a,1),24587(a,1,3,3))].">
      <j1 rule="para" parents="32 24587"/>
    </justification>
  </clause>

  <clause id="24591">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (z * u)) = a(x,y,(z * u) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,24510,a(flip),b,24403,a)].">
      <j1 rule="hyper" parents="63 24510 24403"/>
    </justification>
  </clause>

  <clause id="24592">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (z * u)) = a(x,y,a(u,z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(24296,a,24591,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="24296 24591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24593">
    <literal><![CDATA[
      a((x * x) * (y * (x \ z)),u,w) = a(y * ((x \ 1) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24314,a,b,24458,a)].">
      <j1 rule="hyper" parents="63 24314 24458"/>
    </justification>
  </clause>

  <clause id="24594">
    <literal><![CDATA[
      a(x,L(y \ z,y,y) * u,w) = a(x,u * (y * z),w)
    ]]></literal>
    <justification jstring="[para(3179(a,1),24462(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3179 24462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24595">
    <literal><![CDATA[
      a(x,y * ((T(z,u) * w) * v5),v6) = a(x,y * ((z * w) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(23994,a,24471,a)].">
      <j1 rule="hyper" parents="23994 24471"/>
    </justification>
  </clause>

  <clause id="24596">
    <literal><![CDATA[
      a(x,((y * (y * z)) * u) * w,v5) = a(x,w * ((y * (z * y)) * u),v5)
    ]]></literal>
    <justification jstring="[para(1529(a,1),24471(a,1,2,1,1))].">
      <j1 rule="para" parents="1529 24471"/>
    </justification>
  </clause>

  <clause id="24597">
    <literal><![CDATA[
      a(x,y * L(K(z,u) * w,v5,v6),v7) = a(x,y * L(w,v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,24037,a,b,24472,a),flip(a)].">
      <j1 rule="hyper" parents="347 24037 24472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24598">
    <literal><![CDATA[
      a(x,y * (z * (u \ K(w,v5))),v6) = a(x,(z * u) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,24570,a(flip),b,24497,a),flip(a)].">
      <j1 rule="hyper" parents="347 24570 24497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24599">
    <literal><![CDATA[
      a(x,y,z * (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(u,z,z)) = w
    ]]></literal>
    <justification jstring="[para(14948(a,1),24547(a,1))].">
      <j1 rule="para" parents="14948 24547"/>
    </justification>
  </clause>

  <clause id="24600">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((z * w) * u)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(w,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(24529(a,2),24547(a,1))].">
      <j1 rule="para" parents="24529 24547"/>
    </justification>
  </clause>

  <clause id="24601">
    <literal><![CDATA[
      a(x,y,(z * u) * z) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(u,z,z)) = w
    ]]></literal>
    <justification jstring="[para(24284(a,2),24599(a,1))].">
      <j1 rule="para" parents="24284 24599"/>
    </justification>
  </clause>

  <clause id="24602">
    <literal><![CDATA[
      a(x,y * L(z * u,w,v5),v6) = a(x,y * L(u * z,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(4909(a,1),24597(a,1,2,2,1))].">
      <j1 rule="para" parents="4909 24597"/>
    </justification>
  </clause>

  <clause id="24603">
    <literal><![CDATA[
      a(x,y * L(z / u,w,v5),v6) = a(x,y * L(u \ z,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(5012(a,1),24597(a,1,2,2,1))].">
      <j1 rule="para" parents="5012 24597"/>
    </justification>
  </clause>

  <clause id="24604">
    <literal><![CDATA[
      a(x,y * L(z \ K(u,T(w,v5)),z,v5),v6) = a(x,y * (v5 \ (K(u,w) * (v5 / z))),v6)
    ]]></literal>
    <justification jstring="[para(21293(a,1),24603(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="21293 24603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24605">
    <literal><![CDATA[
      a(R(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((y * z) \ (z * (x * y)),u,w) = v5
    ]]></literal>
    <justification jstring="[para(23943(a,1),23973(a,1))].">
      <j1 rule="para" parents="23943 23973"/>
    </justification>
  </clause>

  <clause id="24606">
    <literal><![CDATA[
      a(((x * x) * y) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y * ((x * x) * z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(24228(a,2),23980(a,1))].">
      <j1 rule="para" parents="24228 23980"/>
    </justification>
  </clause>

  <clause id="24607">
    <literal><![CDATA[
      x \ a(x,x,y \ (z \ ((z * x) * y))) = L(1 / x,x,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,23247,a(flip),b,24128,a),flip(a)].">
      <j1 rule="hyper" parents="347 23247 24128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24609">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) \ w) = a(x,y,w / u)
    ]]></literal>
    <justification jstring="[hyper(24206,a,14918,a)].">
      <j1 rule="hyper" parents="24206 14918"/>
    </justification>
  </clause>

  <clause id="24611">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u \ w) = v5
    ]]></literal>
    <justification jstring="[para(24609(a,2),24181(a,1))].">
      <j1 rule="para" parents="24609 24181"/>
    </justification>
  </clause>

  <clause id="24613">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,z) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * u) \ w) = v5
    ]]></literal>
    <justification jstring="[para(99(a,2),24611(a,1,3,1))].">
      <j1 rule="para" parents="99 24611"/>
    </justification>
  </clause>

  <clause id="24614">
    <literal><![CDATA[
      a((x * x) * ((x * y) \ z),u,w) = a(L(x \ y,x,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(777(a,1),24217(a,2,1)),flip(a)].">
      <j1 rule="para" parents="777 24217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24615">
    <literal><![CDATA[
      a(x,y,K(z,u) * (w \ ((v5 \ K(u,z)) * (w * v5)))) = a(x,y,a(w,v5,v5 \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(20166(a,1),24307(a,1,3))].">
      <j1 rule="para" parents="20166 24307"/>
    </justification>
  </clause>

  <clause id="24616">
    <literal><![CDATA[
      a(x,y,z \ L(u,u,u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ L(u,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(10201(a,1),24345(a,1,3,2))].">
      <j1 rule="para" parents="10201 24345"/>
    </justification>
  </clause>

  <clause id="24617">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) \ u)) = a(x,y,z \ (u \ (u / w)))
    ]]></literal>
    <justification jstring="[hyper(24346,a,xx),flip(a)].">
      <j1 rule="hyper" parents="24346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24618">
    <literal><![CDATA[
      a(x,((y \ 1) * L(z,y,y)) \ u,w) = a(x,(y \ z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24143,a(flip),b,24377,a),flip(a)].">
      <j1 rule="hyper" parents="347 24143 24377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24619">
    <literal><![CDATA[
      a(x,(y * L(z,y,y)) \ u,w) = a(x,(y \ z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(24413,a,24618,a)].">
      <j1 rule="hyper" parents="24413 24618"/>
    </justification>
  </clause>

  <clause id="24620">
    <literal><![CDATA[
      a(x \ ((y / T(z,u)) \ w),v5,v6) = a(x \ ((z \ y) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(24410,a,24232,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="24410 24232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24621">
    <literal><![CDATA[
      a(x \ ((T(y,z) \ u) \ w),v5,v6) = a(x \ ((y \ u) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(24410,a,24620,a)].">
      <j1 rule="hyper" parents="24410 24620"/>
    </justification>
  </clause>

  <clause id="24622">
    <literal><![CDATA[
      a(x \ (((y / z) \ u) \ w),v5,v6) = a(x \ (((z \ y) \ u) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(113(a,1),24621(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="113 24621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24623">
    <literal><![CDATA[
      a(x,y,z * ((u * u) \ (w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (((u * u) * w) \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(459(a,1),24426(a,1,3,2))].">
      <j1 rule="para" parents="459 24426"/>
    </justification>
  </clause>

  <clause id="24624">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(T(x,v7),y,z * ((w * u) \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(23894(a,1),24426(a,1))].">
      <j1 rule="para" parents="23894 24426"/>
    </justification>
  </clause>

  <clause id="24625">
    <literal><![CDATA[
      a(x,y,z * (u * ((w * w) * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (((w * w) * u) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(32(a,1),24427(a,1,3,2))].">
      <j1 rule="para" parents="32 24427"/>
    </justification>
  </clause>

  <clause id="24626">
    <literal><![CDATA[
      a(x,y,z * (u * R(w,u,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (((u \ 1) * (u * w)) * u)) = v5
    ]]></literal>
    <justification jstring="[para(916(a,1),24427(a,1,3,2))].">
      <j1 rule="para" parents="916 24427"/>
    </justification>
  </clause>

  <clause id="24627">
    <literal><![CDATA[
      a(x,y,((z * u) * w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,v5 * ((u * z) * w)) = v6
    ]]></literal>
    <justification jstring="[para(24069(a,1),24427(a,1))].">
      <j1 rule="para" parents="24069 24427"/>
    </justification>
  </clause>

  <clause id="24628">
    <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(4909(a,1),24429(a,1,3,1,2))].">
      <j1 rule="para" parents="4909 24429"/>
    </justification>
  </clause>

  <clause id="24629">
    <literal><![CDATA[
      a(x,y,((z * u) * u) \ w) = a(x,y,L(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(24436,a,24512,a)].">
      <j1 rule="hyper" parents="24436 24512"/>
    </justification>
  </clause>

  <clause id="24630">
    <literal><![CDATA[
      a(x,y,(z * (u * z)) \ w) = a(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(24191,a,24629,a)].">
      <j1 rule="hyper" parents="24191 24629"/>
    </justification>
  </clause>

  <clause id="24631">
    <literal><![CDATA[
      a(x,y,L(z,z,u) * w) = a(x,y,(u \ (u / z)) * w)
    ]]></literal>
    <justification jstring="[hyper(24451,a,24149,a)].">
      <j1 rule="hyper" parents="24451 24149"/>
    </justification>
  </clause>

  <clause id="24632">
    <literal><![CDATA[
      a(x,y,L(z,z,u) * u) = a(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(347,a,24068,a(flip),b,24631,a),flip(a)].">
      <j1 rule="hyper" parents="347 24068 24631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24633">
    <literal><![CDATA[
      a(x,y,L(z,z,u) * u) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,24071,a(flip),b,24632,a),flip(a)].">
      <j1 rule="hyper" parents="347 24071 24632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24634">
    <literal><![CDATA[
      a(x,y,z * L(z,z,u)) = a(x,y,z * (u \ (u / ((1 / z) \ 1))))
    ]]></literal>
    <justification jstring="[para(3260(a,1),24453(a,2,3,2))].">
      <j1 rule="para" parents="3260 24453"/>
    </justification>
  </clause>

  <clause id="24635">
    <literal><![CDATA[
      a(x,K(y,z) * ((z * u) * w),v5) = a(x,(L(z,y,z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(20433(a,1),24474(a,1,2))].">
      <j1 rule="para" parents="20433 24474"/>
    </justification>
  </clause>

  <clause id="24636">
    <literal><![CDATA[
      a(x,((y \ 1) * z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u * ((y \ K(v6,v7)) * z),w) = v5
    ]]></literal>
    <justification jstring="[para(20816(a,1),24478(a,1,2,1))].">
      <j1 rule="para" parents="20816 24478"/>
    </justification>
  </clause>

  <clause id="24637">
    <literal><![CDATA[
      a(x,a(y,z,z \ y) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u * ((y * z) * (z \ y)),w) = v5
    ]]></literal>
    <justification jstring="[para(24486(a,1),23994(a,1))].">
      <j1 rule="para" parents="24486 23994"/>
    </justification>
  </clause>

  <clause id="24638">
    <literal><![CDATA[
      a(((x \ (y \ x)) * y) * z,u,w) = a(z * (y \ R(y,y,x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24228,a,b,24492,a)].">
      <j1 rule="hyper" parents="347 24228 24492"/>
    </justification>
  </clause>

  <clause id="24639">
    <literal><![CDATA[
      a(x,y,z \ L(u,u,u \ w)) = a(x,y,z \ L(u,u,w))
    ]]></literal>
    <justification jstring="[hyper(24616,a,xx),flip(a)].">
      <j1 rule="hyper" parents="24616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24640">
    <literal><![CDATA[
      a(x,y,z \ L(u,u,u * w)) = a(x,y,z \ L(u,u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),24639(a,1,3,2,3)),flip(a)].">
      <j1 rule="para" parents="9 24639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24641">
    <literal><![CDATA[
      a(x,y,z * ((z * u) * u)) = a(x,y,a(u * z,u,z))
    ]]></literal>
    <justification jstring="[hyper(24627,a,14928,a)].">
      <j1 rule="hyper" parents="24627 14928"/>
    </justification>
  </clause>

  <clause id="24642">
    <literal><![CDATA[
      a(x,y,(z \ (u * w)) * v5) = a(x,y,v5 * (z \ (w * u)))
    ]]></literal>
    <justification jstring="[hyper(24628,a,24069,a)].">
      <j1 rule="hyper" parents="24628 24069"/>
    </justification>
  </clause>

  <clause id="24643">
    <literal><![CDATA[
      a(x,y,(z \ (u * w)) * v5) = a(x,y,(z \ (w * u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(24628,a,xx)].">
      <j1 rule="hyper" parents="24628"/>
    </justification>
  </clause>

  <clause id="24644">
    <literal><![CDATA[
      a(x,y,(z \ (K(u,w) * (v5 * v6))) * v7) = a(x,y,v7 * (z \ (v6 * (K(u,w) * v5))))
    ]]></literal>
    <justification jstring="[para(20008(a,1),24642(a,1,3,1,2))].">
      <j1 rule="para" parents="20008 24642"/>
    </justification>
  </clause>

  <clause id="24645">
    <literal><![CDATA[
      a(x,y,z * L(z,z,u)) = a(x,y,z * (u \ (u / z)))
    ]]></literal>
    <justification jstring="[para(83(a,1),24634(a,2,3,2,2,2))].">
      <j1 rule="para" parents="83 24634"/>
    </justification>
  </clause>

  <clause id="24646">
    <literal><![CDATA[
      a(x,y,z * L(z,z,u)) = a(x,y,z * (u \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(24438,a,24645,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="24438 24645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24647">
    <literal><![CDATA[
      a(x,y,z * L(z,z,u)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,24300,a(flip),b,24646,a),flip(a)].">
      <j1 rule="hyper" parents="347 24300 24646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24648">
    <literal><![CDATA[
      a(x,(L(y,z,y) * u) * w,v5) = a(x,(y * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(23987,a,24635,a),flip(a)].">
      <j1 rule="hyper" parents="23987 24635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24649">
    <literal><![CDATA[
      a(x,(L(y,z,y) * u) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,(y * u) * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(24635(a,1),23987(a,1))].">
      <j1 rule="para" parents="24635 23987"/>
    </justification>
  </clause>

  <clause id="24651">
    <literal><![CDATA[
      a(x,((L(y,z,y) / u) * K(u \ 1,w)) * v5,v6) = a(x,(y * T(L(y,z,y) \ (L(y,z,y) / u),w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(5126(a,2),24648(a,1,2,1))].">
      <j1 rule="para" parents="5126 24648"/>
    </justification>
  </clause>

  <clause id="24652">
    <literal><![CDATA[
      a(((x \ (y \ x)) * y) * z,u,w) = a(z * a(y,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(18988(a,1),24638(a,2,1,2))].">
      <j1 rule="para" parents="18988 24638"/>
    </justification>
  </clause>

  <clause id="24653">
    <literal><![CDATA[
      a(x \ ((1 / y) \ (z / y)),u,w) = a(x \ (y \ (z / (y \ 1))),u,w)
    ]]></literal>
    <justification jstring="[hyper(23985,a,23949,a)].">
      <j1 rule="hyper" parents="23985 23949"/>
    </justification>
  </clause>

  <clause id="24654">
    <literal><![CDATA[
      a(x,(y * (z * z)) \ (u * w),v5) = a(x,y \ (u * (w / (z * z))),v5)
    ]]></literal>
    <justification jstring="[hyper(23997,a,24061,a)].">
      <j1 rule="hyper" parents="23997 24061"/>
    </justification>
  </clause>

  <clause id="24655">
    <literal><![CDATA[
      a(x,y,(z * (u * u)) \ (w * v5)) = a(x,y,z \ (w * (v5 / (u * u))))
    ]]></literal>
    <justification jstring="[hyper(24181,a,24126,a)].">
      <j1 rule="hyper" parents="24181 24126"/>
    </justification>
  </clause>

  <clause id="24656">
    <literal><![CDATA[
      a(((1 / x) \ (y / x)) \ z,u,w) = a((x \ (y / (x \ 1))) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(23961,a,24218,a)].">
      <j1 rule="hyper" parents="23961 24218"/>
    </justification>
  </clause>

  <clause id="24657">
    <literal><![CDATA[
      a(x * ((y \ (z / u)) \ w),v5,v6) = a(x * ((y \ (u \ z)) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(5012(a,1),24227(a,1,1,2,1,2))].">
      <j1 rule="para" parents="5012 24227"/>
    </justification>
  </clause>

  <clause id="24658">
    <literal><![CDATA[
      a((x * R(x \ 1,x,y)) * z,u,w) = a(a(x,x,y * x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(746(a,1),24230(a,1,1,1))].">
      <j1 rule="para" parents="746 24230"/>
    </justification>
  </clause>

  <clause id="24659">
    <literal><![CDATA[
      a(x,y,L(K(z,u) * L(w \ v5,v6,v7),v8,v9)) = a(x,y,L(L(v5 / w,v6,v7),v8,v9))
    ]]></literal>
    <justification jstring="[hyper(347,a,24087,a,b,24275,a)].">
      <j1 rule="hyper" parents="347 24087 24275"/>
    </justification>
  </clause>

  <clause id="24660">
    <literal><![CDATA[
      a(x,y,L(z * (u \ 1),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(24276(a,1),14995(a,1))].">
      <j1 rule="para" parents="24276 14995"/>
    </justification>
  </clause>

  <clause id="24662">
    <literal><![CDATA[
      a(x,y,L(R(z / u,u,z),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(u * z,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(15018(a,2),24660(a,1))].">
      <j1 rule="para" parents="15018 24660"/>
    </justification>
  </clause>

  <clause id="24663">
    <literal><![CDATA[
      a(x,R(L(y,L(y,z,u),w),z,u) * w,v5) = a(x,R(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(21974(a,1),24349(a,1,2,1,1))].">
      <j1 rule="para" parents="21974 24349"/>
    </justification>
  </clause>

  <clause id="24664">
    <literal><![CDATA[
      a(x,y,(z * ((u * u) * w)) \ v5) = a(x,y,(u * u) \ ((z * w) \ v5))
    ]]></literal>
    <justification jstring="[para(775(a,1),24367(a,2,3))].">
      <j1 rule="para" parents="775 24367"/>
    </justification>
  </clause>

  <clause id="24665">
    <literal><![CDATA[
      a(x,((y \ 1) / (z * z)) \ u,w) = a(x,(y \ (z * z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(665(a,1),24373(a,1,2,1))].">
      <j1 rule="para" parents="665 24373"/>
    </justification>
  </clause>

  <clause id="24666">
    <literal><![CDATA[
      a(x,(y * y) * ((z \ 1) \ u),w) = a(x,(z \ (y * y)) \ u,w)
    ]]></literal>
    <justification jstring="[para(777(a,1),24665(a,1,2))].">
      <j1 rule="para" parents="777 24665"/>
    </justification>
  </clause>

  <clause id="24667">
    <literal><![CDATA[
      a(x,(y \ (z * z)) \ u,w) = a(x,(z * z) * (y \ u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24487,a(flip),b,24666,a),flip(a)].">
      <j1 rule="hyper" parents="63 24487 24666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24668">
    <literal><![CDATA[
      a(x,(y \ (z * z)) \ u,w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24104,a(flip),b,24667,a),flip(a)].">
      <j1 rule="hyper" parents="347 24104 24667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24670">
    <literal><![CDATA[
      a(x,y,L(z * a(u,z,w),w,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(24379(a,2),24600(a,1))].">
      <j1 rule="para" parents="24379 24600"/>
    </justification>
  </clause>

  <clause id="24671">
    <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(21247(a,2),24382(a,1,3,1))].">
      <j1 rule="para" parents="21247 24382"/>
    </justification>
  </clause>

  <clause id="24672">
    <literal><![CDATA[
      a(x,y,L(z * (z * (z \ (u \ w))),z,u)) = a(x,y,z * (((z * u) \ w) * z))
    ]]></literal>
    <justification jstring="[para(3392(a,2),24406(a,2,3)),flip(a)].">
      <j1 rule="para" parents="3392 24406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24673">
    <literal><![CDATA[
      a(x,y,z * ((u * u) * (((u * u) * (w \ ((u * u) \ v5))) * v6))) = a(x,y,z * (((w \ T(v5,u * u)) * v6) * (u * u)))
    ]]></literal>
    <justification jstring="[para(815(a,1),24407(a,1,3,2,1,1)),flip(a)].">
      <j1 rule="para" parents="815 24407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24674">
    <literal><![CDATA[
      a(x,y * ((z \ 1) \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,(L(z,z,u) * u) * y,w) = v5
    ]]></literal>
    <justification jstring="[para(24043(a,1),24443(a,1))].">
      <j1 rule="para" parents="24043 24443"/>
    </justification>
  </clause>

  <clause id="24675">
    <literal><![CDATA[
      a(x * (y * ((z * u) \ z)),w,v5) = a(x * (y * (z \ (u \ z))),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24493,a,b,24494,a)].">
      <j1 rule="hyper" parents="63 24493 24494"/>
    </justification>
  </clause>

  <clause id="24676">
    <literal><![CDATA[
      a(x,y * (z * ((u * u) * w)),v5) = a(x,y * (z * w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,14954,a(flip),b,24496,a),flip(a)].">
      <j1 rule="hyper" parents="347 14954 24496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24677">
    <literal><![CDATA[
      a(x,y * (z * ((u * u) * w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y * (z * w),v5) = v6
    ]]></literal>
    <justification jstring="[para(24496(a,2),15002(a,1))].">
      <j1 rule="para" parents="24496 15002"/>
    </justification>
  </clause>

  <clause id="24679">
    <literal><![CDATA[
      a(x,y * (z * ((u * u) \ w)),v5) = a(x,y * (z * w),v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),24676(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 24676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24680">
    <literal><![CDATA[
      a(x,y * ((z \ 1) * u),w) = a(x,y * (z * u),w)
    ]]></literal>
    <justification jstring="[para(302(a,1),24676(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="302 24676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24681">
    <literal><![CDATA[
      a(x,y * (z * (u * (u * w))),v5) = a(x,y * (z * L(w,u,u)),v5)
    ]]></literal>
    <justification jstring="[para(97(a,1),24676(a,1,2,2,2))].">
      <j1 rule="para" parents="97 24676"/>
    </justification>
  </clause>

  <clause id="24682">
    <literal><![CDATA[
      a(x,y * (z * (L(u \ 1,w,v5) \ v6)),v7) = a(x,y * (z * (L(u,w,v5) \ v6)),v7)
    ]]></literal>
    <justification jstring="[para(3325(a,1),24676(a,1,2,2,2))].">
      <j1 rule="para" parents="3325 24676"/>
    </justification>
  </clause>

  <clause id="24683">
    <literal><![CDATA[
      a(x,(y * (z \ 1)) * u,w) = a(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[hyper(24247,a,24680,a)].">
      <j1 rule="hyper" parents="24247 24680"/>
    </justification>
  </clause>

  <clause id="24684">
    <literal><![CDATA[
      a(x,y * (z * (a(u,w,z) \ z)),v5) = a(x,a(u,w,z) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24400,a(flip),b,24680,a),flip(a)].">
      <j1 rule="hyper" parents="63 24400 24680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24685">
    <literal><![CDATA[
      a(x,y * (((z * z) / u) * w),v5) = a(x,y * ((u / (z * z)) * w),v5)
    ]]></literal>
    <justification jstring="[para(515(a,1),24680(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="515 24680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24686">
    <literal><![CDATA[
      a(x,y * ((z \ (u * u)) * w),v5) = a(x,y * (z * ((u * u) * w)),v5)
    ]]></literal>
    <justification jstring="[para(516(a,1),24680(a,1,2,2))].">
      <j1 rule="para" parents="516 24680"/>
    </justification>
  </clause>

  <clause id="24687">
    <literal><![CDATA[
      a(x,y * (z * (L(z,u,w) \ z)),v5) = a(x,y * (L(z,u,w) \ 1),v5)
    ]]></literal>
    <justification jstring="[para(10874(a,1),24680(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10874 24680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24688">
    <literal><![CDATA[
      a(x,y * ((z * (u \ 1)) * w),v5) = a(x,y * ((z * u) * w),v5)
    ]]></literal>
    <justification jstring="[para(828(a,1),24679(a,1,2,2))].">
      <j1 rule="para" parents="828 24679"/>
    </justification>
  </clause>

  <clause id="24689">
    <literal><![CDATA[
      a(x,y * (z * (a(u,w,u) \ v5)),v6) = a(x,y * (z * (a(u,w,u) * v5)),v6)
    ]]></literal>
    <justification jstring="[para(11405(a,1),24679(a,1,2,2,2))].">
      <j1 rule="para" parents="11405 24679"/>
    </justification>
  </clause>

  <clause id="24690">
    <literal><![CDATA[
      a(x,y * (z * L(z,u,u)),w) = a(x,a(u,u,z) * y,w)
    ]]></literal>
    <justification jstring="[para(14601(a,1),24684(a,1,2,2,2))].">
      <j1 rule="para" parents="14601 24684"/>
    </justification>
  </clause>

  <clause id="24691">
    <literal><![CDATA[
      a(x,y * ((L(z,u,u) \ 1) * w),v5) = a(x,y * ((a(u,u,z) * z) * w),v5)
    ]]></literal>
    <justification jstring="[para(14605(a,1),24688(a,1,2,2,1))].">
      <j1 rule="para" parents="14605 24688"/>
    </justification>
  </clause>

  <clause id="24692">
    <literal><![CDATA[
      a(x,((y * (y * z)) * u) * w,v5) = a(x,w * (u * L(z,y,y)),v5)
    ]]></literal>
    <justification jstring="[hyper(24247,a,24681,a)].">
      <j1 rule="hyper" parents="24247 24681"/>
    </justification>
  </clause>

  <clause id="24693">
    <literal><![CDATA[
      a(x,K(y,z) * (u \ (w * (v5 \ K(v6,v7)))),v8) = a(x,u \ (w * (v5 \ 1)),v8)
    ]]></literal>
    <justification jstring="[para(13009(a,1),24500(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13009 24500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24694">
    <literal><![CDATA[
      a(x,(y * ((z * z) * u)) \ w,v5) = a(x,(y * u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24060,a(flip),b,24517,a),flip(a)].">
      <j1 rule="hyper" parents="347 24060 24517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24696">
    <literal><![CDATA[
      a(x,(y * (z * (z * u))) \ w,v5) = a(x,(y * L(u,z,z)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(97(a,1),24694(a,1,2,1,2))].">
      <j1 rule="para" parents="97 24694"/>
    </justification>
  </clause>

  <clause id="24697">
    <literal><![CDATA[
      a(x,((y * T(z,y * y)) * u) \ w,v5) = a(x,(((y \ 1) * z) * u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(992(a,1),24694(a,1,2,1))].">
      <j1 rule="para" parents="992 24694"/>
    </justification>
  </clause>

  <clause id="24698">
    <literal><![CDATA[
      a(x,(T(y,z) * L(u,1 / T(y,z),1 / T(y,z))) \ w,v5) = a(x,(y * ((1 / y) * ((1 / T(y,z)) * u))) \ w,v5)
    ]]></literal>
    <justification jstring="[para(22310(a,1),24696(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="22310 24696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24699">
    <literal><![CDATA[
      a((x * x) * ((x * y) \ z),u,w) = a(((x \ 1) * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(497(a,1),24518(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="497 24518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24700">
    <literal><![CDATA[
      a(L(x \ y,x,x) \ z,u,w) = a(((x \ 1) * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24614,a(flip),b,24699,a)].">
      <j1 rule="hyper" parents="63 24614 24699"/>
    </justification>
  </clause>

  <clause id="24701">
    <literal><![CDATA[
      a(((x \ 1) * (x * y)) \ z,u,w) = a(L(y,x,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),24700(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 24700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24702">
    <literal><![CDATA[
      a(x,y * ((z \ 1) / (u * u)),w) = a(x,(z \ (u * u)) * y,w)
    ]]></literal>
    <justification jstring="[para(665(a,1),24572(a,1,2,2))].">
      <j1 rule="para" parents="665 24572"/>
    </justification>
  </clause>

  <clause id="24703">
    <literal><![CDATA[
      a(x,y * ((z * z) \ (u \ 1)),w) = a(x,(u \ (z * z)) * y,w)
    ]]></literal>
    <justification jstring="[hyper(24165,a,24702,a)].">
      <j1 rule="hyper" parents="24165 24702"/>
    </justification>
  </clause>

  <clause id="24704">
    <literal><![CDATA[
      a(x,((y * y) \ z) * u,w) = a(x,(z \ (y * y)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(24577,a,24703,a)].">
      <j1 rule="hyper" parents="24577 24703"/>
    </justification>
  </clause>

  <clause id="24705">
    <literal><![CDATA[
      a(x,(y \ (z * z)) * u,w) = a(x,y * u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24482,a(flip),b,24704,a),flip(a)].">
      <j1 rule="hyper" parents="63 24482 24704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24707">
    <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),24705(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14 24705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24708">
    <literal><![CDATA[
      a(x,y * ((z * (u * z)) * u),w) = a(x,a(u,z,u * z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(24331,a,24707,a)].">
      <j1 rule="hyper" parents="24331 24707"/>
    </justification>
  </clause>

  <clause id="24709">
    <literal><![CDATA[
      a(x,y * ((z * (u * z)) * w),v5) = a(x,y * (w * L(u,z,z)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24692,a(flip),b,24596,a),flip(a)].">
      <j1 rule="hyper" parents="63 24692 24596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24710">
    <literal><![CDATA[
      a(x,a(y,z,y * z) * u,w) = a(x,u * (y * L(y,z,z)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24708,a(flip),b,24709,a)].">
      <j1 rule="hyper" parents="63 24708 24709"/>
    </justification>
  </clause>

  <clause id="24711">
    <literal><![CDATA[
      a(x,a(y,z,y * z) * u,w) = a(x,a(z,z,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24690,a(flip),b,24710,a),flip(a)].">
      <j1 rule="hyper" parents="347 24690 24710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24712">
    <literal><![CDATA[
      a(x \ ((1 / y) \ (y \ z)),u,w) = a(x \ (y \ (z / (y \ 1))),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24357,a(flip),b,24653,a)].">
      <j1 rule="hyper" parents="63 24357 24653"/>
    </justification>
  </clause>

  <clause id="24713">
    <literal><![CDATA[
      a(x,(y * y) \ (z \ (u * w)),v5) = a(x,z \ (u * (w / (y * y))),v5)
    ]]></literal>
    <justification jstring="[para(459(a,1),24654(a,1,2))].">
      <j1 rule="para" parents="459 24654"/>
    </justification>
  </clause>

  <clause id="24714">
    <literal><![CDATA[
      a(x,y,(z * z) \ (u \ (w * v5))) = a(x,y,u \ (w * (v5 / (z * z))))
    ]]></literal>
    <justification jstring="[para(459(a,1),24655(a,1,3))].">
      <j1 rule="para" parents="459 24655"/>
    </justification>
  </clause>

  <clause id="24715">
    <literal><![CDATA[
      a(((x \ 1) \ (y / x)) \ z,u,w) = a((x \ (y / (x \ 1))) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24233,a(flip),b,24656,a)].">
      <j1 rule="hyper" parents="63 24233 24656"/>
    </justification>
  </clause>

  <clause id="24716">
    <literal><![CDATA[
      a(x * (((y * z) \ y) \ u),w,v5) = a(x * ((y \ (z \ y)) \ u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24351,a,b,24657,a)].">
      <j1 rule="hyper" parents="63 24351 24657"/>
    </justification>
  </clause>

  <clause id="24717">
    <literal><![CDATA[
      a(x,y,(z * ((u * u) * w)) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(24664(a,2),14949(a,1))].">
      <j1 rule="para" parents="24664 14949"/>
    </justification>
  </clause>

  <clause id="24718">
    <literal><![CDATA[
      a(x,(L(y,y,z) * z) * u,w) = a(x,u * (y \ z),w)
    ]]></literal>
    <justification jstring="[hyper(24674,a,24487,a)].">
      <j1 rule="hyper" parents="24674 24487"/>
    </justification>
  </clause>

  <clause id="24719">
    <literal><![CDATA[
      a(x * (y * L(z \ 1,z,u)),w,v5) = a(x * (y * (u \ (z \ u))),w,v5)
    ]]></literal>
    <justification jstring="[para(244(a,2),24675(a,1,1,2,2))].">
      <j1 rule="para" parents="244 24675"/>
    </justification>
  </clause>

  <clause id="24720">
    <literal><![CDATA[
      a(x,y * (((z * z) / u) * w),v5) = a(x,y * (((z * z) \ u) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24252,a(flip),b,24685,a),flip(a)].">
      <j1 rule="hyper" parents="347 24252 24685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24721">
    <literal><![CDATA[
      a(x,y * ((z \ (u * u)) * w),v5) = a(x,y * (z * w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24676,a(flip),b,24686,a),flip(a)].">
      <j1 rule="hyper" parents="347 24676 24686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24722">
    <literal><![CDATA[
      a(x,y * ((z \ (u * u)) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y * (z * w),v5) = v6
    ]]></literal>
    <justification jstring="[para(24686(a,2),24677(a,1))].">
      <j1 rule="para" parents="24686 24677"/>
    </justification>
  </clause>

  <clause id="24724">
    <literal><![CDATA[
      a(x,y * ((z \ 1) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y * (z * u),w) = v5
    ]]></literal>
    <justification jstring="[para(7(a,1),24722(a,1,2,2,1,2))].">
      <j1 rule="para" parents="7 24722"/>
    </justification>
  </clause>

  <clause id="24725">
    <literal><![CDATA[
      a(x,(y * (z \ 1)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u * (z * y),w) = v5
    ]]></literal>
    <justification jstring="[para(24243(a,2),24724(a,1))].">
      <j1 rule="para" parents="24243 24724"/>
    </justification>
  </clause>

  <clause id="24726">
    <literal><![CDATA[
      a(x,y * (z * (L(z,u,w) \ z)),v5) = a(x,L(z,u,w) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24105,a(flip),b,24687,a),flip(a)].">
      <j1 rule="hyper" parents="347 24105 24687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24727">
    <literal><![CDATA[
      a(x,y * (z * a(u,u,z)),w) = a(x,L(z,u,u) * y,w)
    ]]></literal>
    <justification jstring="[para(14600(a,1),24726(a,1,2,2,2))].">
      <j1 rule="para" parents="14600 24726"/>
    </justification>
  </clause>

  <clause id="24728">
    <literal><![CDATA[
      a(x \ ((y \ 1) \ (y \ z)),u,w) = a(x \ (y \ (z / (y \ 1))),u,w)
    ]]></literal>
    <justification jstring="[hyper(24410,a,24712,a)].">
      <j1 rule="hyper" parents="24410 24712"/>
    </justification>
  </clause>

  <clause id="24729">
    <literal><![CDATA[
      a(x,y \ (z * (u / (w * w))),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ (z * u),v5) = v6
    ]]></literal>
    <justification jstring="[para(24713(a,1),24159(a,1))].">
      <j1 rule="para" parents="24713 24159"/>
    </justification>
  </clause>

  <clause id="24730">
    <literal><![CDATA[
      a(x,y \ (z * ((u * u) \ w)),v5) = a(x,y \ (z * w),v5)
    ]]></literal>
    <justification jstring="[hyper(24729,a,24261,a),flip(a)].">
      <j1 rule="hyper" parents="24729 24261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24731">
    <literal><![CDATA[
      a(x,y \ (z * (u \ 1)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ (z * u),w) = v5
    ]]></literal>
    <justification jstring="[para(300(a,1),24729(a,1,2,2,2))].">
      <j1 rule="para" parents="300 24729"/>
    </justification>
  </clause>

  <clause id="24732">
    <literal><![CDATA[
      a(x,y \ (z * (u * (w \ 1))),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ (z * (u * w)),v5) = v6
    ]]></literal>
    <justification jstring="[para(780(a,1),24729(a,1,2,2,2))].">
      <j1 rule="para" parents="780 24729"/>
    </justification>
  </clause>

  <clause id="24733">
    <literal><![CDATA[
      a(x,y \ ((z * z) * u),w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),24730(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 24730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24734">
    <literal><![CDATA[
      a(x,y \ ((z \ 1) \ u),w) = a(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[para(495(a,1),24733(a,1,2,2))].">
      <j1 rule="para" parents="495 24733"/>
    </justification>
  </clause>

  <clause id="24735">
    <literal><![CDATA[
      a(x,R(y / z,z,y \ ((u * u) * w)) \ w,v5) = a(x,z * (y \ ((u * u) * w)),v5)
    ]]></literal>
    <justification jstring="[para(693(a,1),24733(a,1,2)),flip(a)].">
      <j1 rule="para" parents="693 24733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24736">
    <literal><![CDATA[
      a(x,y \ (z / (u \ 1)),w) = a(x,y \ (u \ z),w)
    ]]></literal>
    <justification jstring="[hyper(24167,a,24734,a)].">
      <j1 rule="hyper" parents="24167 24734"/>
    </justification>
  </clause>

  <clause id="24737">
    <literal><![CDATA[
      a(x,y \ (z \ (u * (z \ 1))),w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(11(a,1),24736(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 24736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24738">
    <literal><![CDATA[
      a(x,L(y,y,z),u) = a(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[para(2007(a,2),24736(a,1,2))].">
      <j1 rule="para" parents="2007 24736"/>
    </justification>
  </clause>

  <clause id="24739">
    <literal><![CDATA[
      a(x,L(y \ 1,y,z),u) = a(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,14972,a,b,24738,a)].">
      <j1 rule="hyper" parents="63 14972 24738"/>
    </justification>
  </clause>

  <clause id="24740">
    <literal><![CDATA[
      a(x,(y * z) \ y,u) = a(x,y \ (z \ y),u)
    ]]></literal>
    <justification jstring="[para(244(a,1),24739(a,1,2))].">
      <j1 rule="para" parents="244 24739"/>
    </justification>
  </clause>

  <clause id="24741">
    <literal><![CDATA[
      a(x,y \ (z \ y),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,L(z,z,y),u) = w
    ]]></literal>
    <justification jstring="[para(24739(a,1),15029(a,1))].">
      <j1 rule="para" parents="24739 15029"/>
    </justification>
  </clause>

  <clause id="24742">
    <literal><![CDATA[
      a(x,(y * z) \ z,u) = a(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(24007,a,24740,a)].">
      <j1 rule="hyper" parents="24007 24740"/>
    </justification>
  </clause>

  <clause id="24743">
    <literal><![CDATA[
      a(x * y,x \ (y \ x),z) * (((x * y) \ x) * z) = L(y \ z,y,x)
    ]]></literal>
    <justification jstring="[para(24740(a,1),14752(a,1,1))].">
      <j1 rule="para" parents="24740 14752"/>
    </justification>
  </clause>

  <clause id="24744">
    <literal><![CDATA[
      a(x,L(y * (z \ 1),z,z),u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(24342,a,24737,a)].">
      <j1 rule="hyper" parents="24342 24737"/>
    </justification>
  </clause>

  <clause id="24745">
    <literal><![CDATA[
      a(x,y \ (z * (u \ 1)),w) = a(x,y \ (z * u),w)
    ]]></literal>
    <justification jstring="[hyper(24731,a,xx),flip(a)].">
      <j1 rule="hyper" parents="24731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24746">
    <literal><![CDATA[
      a(x,y \ (z * a(u,u,z)),w) = a(x,y \ L(z,u,u),w)
    ]]></literal>
    <justification jstring="[para(14611(a,1),24745(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14611 24745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24747">
    <literal><![CDATA[
      a(x,y \ ((z \ 1) \ (z \ u)),w) = a(x,y \ L(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(15286(a,2),24746(a,1,2,2))].">
      <j1 rule="para" parents="15286 24746"/>
    </justification>
  </clause>

  <clause id="24748">
    <literal><![CDATA[
      a(x,y \ (z \ (z \ u)),w) = a(x,y \ L(u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24734,a(flip),b,24747,a)].">
      <j1 rule="hyper" parents="63 24734 24747"/>
    </justification>
  </clause>

  <clause id="24749">
    <literal><![CDATA[
      a(x,y \ L(z * u,z,z),w) = a(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[para(9(a,1),24748(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 24748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24750">
    <literal><![CDATA[
      a(x,y,z \ (u * (w / (v5 * v5)))) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[hyper(14949,a,24714,a),flip(a)].">
      <j1 rule="hyper" parents="14949 24714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24752">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * w) \ v5))) = a(x,y,z \ (u * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,24309,a(flip),b,24750,a)].">
      <j1 rule="hyper" parents="63 24309 24750"/>
    </justification>
  </clause>

  <clause id="24753">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * w) * v5))) = a(x,y,z \ (u * v5))
    ]]></literal>
    <justification jstring="[para(9(a,1),24752(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="9 24752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24754">
    <literal><![CDATA[
      a(x,y,z \ ((u * u) * w)) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(10(a,1),24752(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10 24752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24755">
    <literal><![CDATA[
      a(x,y,z \ ((u * (w \ 1)) * v5)) = a(x,y,z \ ((u * w) * v5))
    ]]></literal>
    <justification jstring="[para(828(a,1),24752(a,1,3,2))].">
      <j1 rule="para" parents="828 24752"/>
    </justification>
  </clause>

  <clause id="24756">
    <literal><![CDATA[
      a(x,y,z \ ((u * u) \ w)) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(10(a,1),24754(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10 24754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24757">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) \ w)) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(495(a,1),24754(a,1,3,2))].">
      <j1 rule="para" parents="495 24754"/>
    </justification>
  </clause>

  <clause id="24758">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w \ 1))) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,24303,a(flip),b,24756,a)].">
      <j1 rule="hyper" parents="63 24303 24756"/>
    </justification>
  </clause>

  <clause id="24759">
    <literal><![CDATA[
      a(x,y,z \ L(u \ w,u,u)) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(99(a,2),24756(a,1,3,2))].">
      <j1 rule="para" parents="99 24756"/>
    </justification>
  </clause>

  <clause id="24760">
    <literal><![CDATA[
      a(x,y,(z \ (u \ w)) * K(v5,v6)) = a(x,y,z \ ((u \ 1) \ w))
    ]]></literal>
    <justification jstring="[hyper(347,a,24080,a,b,24757,a)].">
      <j1 rule="hyper" parents="347 24080 24757"/>
    </justification>
  </clause>

  <clause id="24761">
    <literal><![CDATA[
      a(x,y,L(z,z,u)) = a(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,24304,a,b,24757,a)].">
      <j1 rule="hyper" parents="63 24304 24757"/>
    </justification>
  </clause>

  <clause id="24762">
    <literal><![CDATA[
      a(x,y,z \ ((R(u,w,w) \ u) \ v5)) = a(x,y,z \ (a(u,w,w) \ v5))
    ]]></literal>
    <justification jstring="[para(13401(a,1),24757(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="13401 24757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24763">
    <literal><![CDATA[
      a(x,y,L(z \ u,z \ u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(24761(a,2),24212(a,1))].">
      <j1 rule="para" parents="24761 24212"/>
    </justification>
  </clause>

  <clause id="24765">
    <literal><![CDATA[
      a(x,y,z \ ((u * ((w * w) * v5)) * T(((w * w) * v5) \ 1,(w * w) * v5))) = a(x,y,z \ ((u * (((w * w) * v5) \ 1)) * v5))
    ]]></literal>
    <justification jstring="[para(986(a,2),24753(a,1,3,2))].">
      <j1 rule="para" parents="986 24753"/>
    </justification>
  </clause>

  <clause id="24766">
    <literal><![CDATA[
      a(x,y,z \ ((u * T(w,v5 * v5)) * v6)) = a(x,y,z \ ((u * ((v5 * v5) \ w)) * v6))
    ]]></literal>
    <justification jstring="[para(1092(a,1),24753(a,1,3,2))].">
      <j1 rule="para" parents="1092 24753"/>
    </justification>
  </clause>

  <clause id="24767">
    <literal><![CDATA[
      a(x,y,z \ (R(T(u * K((w * w) * v5,u),v6),v7,v8) * v5)) = a(x,y,z \ (((w * w) * v5) * R(T(u,v6),v7,v8)))
    ]]></literal>
    <justification jstring="[para(5082(a,1),24753(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5082 24753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24768">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ (u \ w)) = v5
    ]]></literal>
    <justification jstring="[para(24760(a,1),4120(a,1))].">
      <j1 rule="para" parents="24760 4120"/>
    </justification>
  </clause>

  <clause id="24769">
    <literal><![CDATA[
      a(x,y,z \ (u * a(w,w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ (w \ (w \ u))) = v5
    ]]></literal>
    <justification jstring="[para(15286(a,1),24768(a,1,3,2))].">
      <j1 rule="para" parents="15286 24768"/>
    </justification>
  </clause>

  <clause id="24770">
    <literal><![CDATA[
      a(x,y,L(z,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u \ (z \ u)) = w
    ]]></literal>
    <justification jstring="[para(24304(a,2),24768(a,1))].">
      <j1 rule="para" parents="24304 24768"/>
    </justification>
  </clause>

  <clause id="24771">
    <literal><![CDATA[
      a(((x \ 1) \ (x \ y)) \ z,u,w) = a((x \ (y / (x \ 1))) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24353,a(flip),b,24715,a)].">
      <j1 rule="hyper" parents="63 24353 24715"/>
    </justification>
  </clause>

  <clause id="24772">
    <literal><![CDATA[
      a(x,y * (((z * z) \ u) * w),v5) = a(x,y * ((u \ (z * z)) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(24417,a,24720,a),flip(a)].">
      <j1 rule="hyper" parents="24417 24720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24773">
    <literal><![CDATA[
      a(x \ ((y \ 1) \ (y \ z)),u,w) = a(x \ (y \ ((y \ 1) \ z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24357,a(flip),b,24728,a),flip(a)].">
      <j1 rule="hyper" parents="347 24357 24728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24774">
    <literal><![CDATA[
      a(((x \ 1) \ (x \ y)) \ z,u,w) = a((x \ ((x \ 1) \ y)) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24353,a(flip),b,24771,a),flip(a)].">
      <j1 rule="hyper" parents="347 24353 24771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24775">
    <literal><![CDATA[
      a(x,y * (((z * z) \ u) * w),v5) = a(x,y * (u * w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24721,a(flip),b,24772,a),flip(a)].">
      <j1 rule="hyper" parents="347 24721 24772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24777">
    <literal><![CDATA[
      a(x \ (y \ ((y \ 1) \ z)),u,w) = a(x \ (z * a(y,y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(15286(a,1),24773(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="15286 24773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24778">
    <literal><![CDATA[
      a(L(x \ y,x,z),x * z,u) = a((z * x) \ (z * y),z * x,u)
    ]]></literal>
    <justification jstring="[hyper(24538,a,24157,a)].">
      <j1 rule="hyper" parents="24538 24157"/>
    </justification>
  </clause>

  <clause id="24780">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((u * (w \ 1)) * z))) = a(x,y,w * a(u,w \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(24181,a,24330,a)].">
      <j1 rule="hyper" parents="24181 24330"/>
    </justification>
  </clause>

  <clause id="24781">
    <literal><![CDATA[
      (x \ y) \ (z \ ((z * (x \ a(x,x,y))) * y)) = a(z,R(x,x,y),y)
    ]]></literal>
    <justification jstring="[para(18990(a,1),24389(a,2,2))].">
      <j1 rule="para" parents="18990 24389"/>
    </justification>
  </clause>

  <clause id="24782">
    <literal><![CDATA[
      a(x,y,z * ((u * T(w,v5)) * v6)) = a(x,y,z * ((w * u) * v6))
    ]]></literal>
    <justification jstring="[hyper(24424,a,24281,a),flip(a)].">
      <j1 rule="hyper" parents="24424 24281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24783">
    <literal><![CDATA[
      a(x,((y \ 1) * z) * u,w) = a(x,u * (T(y,v5) * z),w)
    ]]></literal>
    <justification jstring="[hyper(24476,a,24680,a)].">
      <j1 rule="hyper" parents="24476 24680"/>
    </justification>
  </clause>

  <clause id="24784">
    <literal><![CDATA[
      a(x,((y \ 1) * z) * u,w) = a(x,(y * z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24469,a(flip),b,24783,a),flip(a)].">
      <j1 rule="hyper" parents="347 24469 24783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24785">
    <literal><![CDATA[
      a(x,((y \ 1) * z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,(y * z) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(24783(a,2),24475(a,1))].">
      <j1 rule="para" parents="24783 24475"/>
    </justification>
  </clause>

  <clause id="24786">
    <literal><![CDATA[
      a(x,y \ L(z * u,z,z),w) = a(x,y \ (z * R(u,z,z)),w)
    ]]></literal>
    <justification jstring="[para(3197(a,1),24527(a,1,2,2))].">
      <j1 rule="para" parents="3197 24527"/>
    </justification>
  </clause>

  <clause id="24787">
    <literal><![CDATA[
      a(x,(y * (z * u)) \ (z * (u * y)),w) = a(x,a(y,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(23987,a,24528,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="23987 24528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24789">
    <literal><![CDATA[
      a(x,(y * z) \ (u \ (y * (z * u))),w) = a(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(22370(a,1),24787(a,1,2))].">
      <j1 rule="para" parents="22370 24787"/>
    </justification>
  </clause>

  <clause id="24790">
    <literal><![CDATA[
      a(x,y * ((z \ K(u,w)) * v5),v6) = a(x,(z * v5) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(24636,a,24784,a)].">
      <j1 rule="hyper" parents="24636 24784"/>
    </justification>
  </clause>

  <clause id="24791">
    <literal><![CDATA[
      a(x,y \ (z * ((u \ 1) * w)),v5) = a(x,y \ (z * (w * u)),v5)
    ]]></literal>
    <justification jstring="[hyper(24732,a,24262,a),flip(a)].">
      <j1 rule="hyper" parents="24732 24262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24792">
    <literal><![CDATA[
      a(x,y \ (z * (u * (w \ 1))),v5) = a(x,y \ (z * (u * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(24732,a,xx),flip(a)].">
      <j1 rule="hyper" parents="24732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24793">
    <literal><![CDATA[
      a(x,y \ (z * ((u \ 1) * w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ (z * (w * u)),v5) = v6
    ]]></literal>
    <justification jstring="[para(24262(a,1),24732(a,1))].">
      <j1 rule="para" parents="24262 24732"/>
    </justification>
  </clause>

  <clause id="24794">
    <literal><![CDATA[
      a(x,y \ (z * (u * (w \ 1))),v5) = a(x,y \ (z * (w * u)),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24262,a,b,24792,a),flip(a)].">
      <j1 rule="hyper" parents="347 24262 24792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24795">
    <literal><![CDATA[
      a(x,y \ (z * (u * (w * u))),v5) = a(x,y \ (z * R(w,u,u)),v5)
    ]]></literal>
    <justification jstring="[para(786(a,1),24794(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="786 24794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24796">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((u * (w \ 1)) * z))) = a(x,y,w * a(u,w,z))
    ]]></literal>
    <justification jstring="[para(14950(a,1),24780(a,2,3,2))].">
      <j1 rule="para" parents="14950 24780"/>
    </justification>
  </clause>

  <clause id="24797">
    <literal><![CDATA[
      a(((x \ K(y,z)) * u) \ w,v5,v6) = a(((x \ 1) * u) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(23973,a,23915,a),flip(a)].">
      <j1 rule="hyper" parents="23973 23915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24799">
    <literal><![CDATA[
      a(T(x * (y \ K(z,u)),K(y \ K(z,u),w)) \ v5,v6,v7) = a(((y \ 1) * T(x,T(y \ K(z,u),w))) \ v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(6060(a,2),24797(a,1,1,1))].">
      <j1 rule="para" parents="6060 24797"/>
    </justification>
  </clause>

  <clause id="24800">
    <literal><![CDATA[
      a(x * L(K(y,z) * u,w,v5),v6,v7) = a(L(u,w,v5) * x,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(23886,a,23948,a),flip(a)].">
      <j1 rule="hyper" parents="23886 23948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24802">
    <literal><![CDATA[
      a(L(x * y,z,u) * w,v5,v6) = a(w * L(y * x,z,u),v5,v6)
    ]]></literal>
    <justification jstring="[para(4909(a,1),24800(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4909 24800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24803">
    <literal><![CDATA[
      a(x,y,(T(z,u) \ w) \ T(z,u)) = a(x,y,z * (1 / (1 / (w \ T(z,u)))))
    ]]></literal>
    <justification jstring="[hyper(24181,a,24150,a)].">
      <j1 rule="hyper" parents="24181 24150"/>
    </justification>
  </clause>

  <clause id="24804">
    <literal><![CDATA[
      a(x,(y * z) \ (z * (u * y)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,R(u,y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(24322(a,1),24164(a,1))].">
      <j1 rule="para" parents="24322 24164"/>
    </justification>
  </clause>

  <clause id="24805">
    <literal><![CDATA[
      a(x,R(y,z,u),w) = a(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(24804,a,24526,a)].">
      <j1 rule="hyper" parents="24804 24526"/>
    </justification>
  </clause>

  <clause id="24807">
    <literal><![CDATA[
      (x \ y) \ (z \ ((z * (x \ a(x,x,y))) * y)) = a(z,L(x,x,y),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,24781,a,b,24805,a)].">
      <j1 rule="hyper" parents="63 24781 24805"/>
    </justification>
  </clause>

  <clause id="24811">
    <literal><![CDATA[
      a((x * (y \ T(z,u))) \ w,v5,v6) = a((x * (y \ z)) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(23959,a,24234,a),flip(a)].">
      <j1 rule="hyper" parents="23959 24234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24812">
    <literal><![CDATA[
      a((x * (y \ (z / u))) \ w,v5,v6) = a((x * (y \ (u \ z))) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(113(a,1),24811(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="113 24811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24813">
    <literal><![CDATA[
      a(x,y * (((z * u) * w) * u),v5) = a(x,y * (u * ((u * z) * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24045,a(flip),b,24246,a)].">
      <j1 rule="hyper" parents="63 24045 24246"/>
    </justification>
  </clause>

  <clause id="24815">
    <literal><![CDATA[
      a(x,y,z * (K(u,w) * (v5 * (v6 \ 1)))) = a(x,y,z * ((v6 \ K(u,w)) * v5))
    ]]></literal>
    <justification jstring="[para(20008(a,1),24289(a,1,3,2))].">
      <j1 rule="para" parents="20008 24289"/>
    </justification>
  </clause>

  <clause id="24816">
    <literal><![CDATA[
      L(a(x,x,x \ (x \ y)),y,z) = (y * z) \ (z * T((x \ 1) \ (x \ y),z))
    ]]></literal>
    <justification jstring="[para(1165(a,2),24380(a,2,2,2))].">
      <j1 rule="para" parents="1165 24380"/>
    </justification>
  </clause>

  <clause id="24818">
    <literal><![CDATA[
      ((x * (y \ L(y,z,u))) * y) \ (K(x * (y \ L(y,z,u)),y) * (L(y,z,u) * x)) = a(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(21081,a,24384,a)].">
      <j1 rule="hyper" parents="21081 24384"/>
    </justification>
  </clause>

  <clause id="24819">
    <literal><![CDATA[
      (x * (y * L(y \ (x \ y),z,u))) \ (L(x,z,u) * (x \ y)) = a(x,x * L(x,z,u),x \ y)
    ]]></literal>
    <justification jstring="[para(20955(a,1),24384(a,1,1,2))].">
      <j1 rule="para" parents="20955 24384"/>
    </justification>
  </clause>

  <clause id="24820">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ (L(x,y,z) * (x \ u)) = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(1402(a,1),24386(a,1,2))].">
      <j1 rule="para" parents="1402 24386"/>
    </justification>
  </clause>

  <clause id="24821">
    <literal><![CDATA[
      a(x,y * (L(1 / z,u,w) \ v5),v6) = a(x,(L(z,u,w) \ v5) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,24464,a(flip),b,24398,a),flip(a)].">
      <j1 rule="hyper" parents="347 24464 24398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24822">
    <literal><![CDATA[
      a(((x * y) * T(x \ 1,x)) * z,u,w) = a(L(y,x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24536,a(flip),b,24456,a),flip(a)].">
      <j1 rule="hyper" parents="347 24536 24456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24823">
    <literal><![CDATA[
      a(((x * y) * (x \ 1)) * z,u,w) = a(L(y,x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(24521,a,24822,a)].">
      <j1 rule="hyper" parents="24521 24822"/>
    </justification>
  </clause>

  <clause id="24825">
    <literal><![CDATA[
      a(x,y * (z * (1 / (u \ z))),w) = a(x,(z / (z \ u)) * y,w)
    ]]></literal>
    <justification jstring="[para(83(a,1),24573(a,1,2,2,2))].">
      <j1 rule="para" parents="83 24573"/>
    </justification>
  </clause>

  <clause id="24826">
    <literal><![CDATA[
      a(x,y * (z * ((u \ z) \ 1)),w) = a(x,(z / (z \ u)) * y,w)
    ]]></literal>
    <justification jstring="[hyper(24415,a,24825,a)].">
      <j1 rule="hyper" parents="24415 24825"/>
    </justification>
  </clause>

  <clause id="24828">
    <literal><![CDATA[
      a(x,(y / (y \ z)) * u,w) = a(x,(y * (z \ y)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24570,a(flip),b,24826,a),flip(a)].">
      <j1 rule="hyper" parents="63 24570 24826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24829">
    <literal><![CDATA[
      a(x,((y \ z) \ y) * u,w) = a(x,(y * (z \ y)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(24001,a,24828,a)].">
      <j1 rule="hyper" parents="24001 24828"/>
    </justification>
  </clause>

  <clause id="24830">
    <literal><![CDATA[
      a(x,y * ((a(z,z,u) * u) * w),v5) = a(x,y * (L(u,z,z) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(24724,a,24691,a),flip(a)].">
      <j1 rule="hyper" parents="24724 24691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24831">
    <literal><![CDATA[
      a(x,K(y,z) * (u \ (w * (v5 \ K(v6,v7)))),v8) = a(x,u \ (w * v5),v8)
    ]]></literal>
    <justification jstring="[hyper(347,a,24745,a(flip),b,24693,a),flip(a)].">
      <j1 rule="hyper" parents="347 24745 24693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24832">
    <literal><![CDATA[
      a(x,y \ (z * (u \ K(w,v5))),v6) = a(x,y \ (z * u),v6)
    ]]></literal>
    <justification jstring="[hyper(23987,a,24831,a)].">
      <j1 rule="hyper" parents="23987 24831"/>
    </justification>
  </clause>

  <clause id="24833">
    <literal><![CDATA[
      a(x,(((y \ 1) * z) * u) \ w,v5) = a(x,((y * z) * u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24516,a(flip),b,24697,a),flip(a)].">
      <j1 rule="hyper" parents="63 24516 24697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24834">
    <literal><![CDATA[
      a(x,(y * ((z \ 1) * u)) \ w,v5) = a(x,((z * u) * y) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(24007,a,24833,a)].">
      <j1 rule="hyper" parents="24007 24833"/>
    </justification>
  </clause>

  <clause id="24836">
    <literal><![CDATA[
      a(x,((y * z) * y) \ u,w) = a(x,L(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(3197(a,1),24834(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3197 24834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24837">
    <literal><![CDATA[
      a(x,(y * (y * z)) \ u,w) = a(x,L(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(24007,a,24836,a)].">
      <j1 rule="hyper" parents="24007 24836"/>
    </justification>
  </clause>

  <clause id="24838">
    <literal><![CDATA[
      a(x,y,z * (1 / (1 / (u \ T(z,w))))) = a(x,y,(T(z,w) \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(24186,a,24803,a),flip(a)].">
      <j1 rule="hyper" parents="24186 24803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24839">
    <literal><![CDATA[
      a(x,y,z * (1 / (1 / (u \ T(z,w))))) = a(x,y,(z \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,24555,a(flip),b,24838,a),flip(a)].">
      <j1 rule="hyper" parents="347 24555 24838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24840">
    <literal><![CDATA[
      a(x,y,z * ((1 / (u \ T(z,w))) \ 1)) = a(x,y,(z \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(24209,a,24839,a)].">
      <j1 rule="hyper" parents="24209 24839"/>
    </justification>
  </clause>

  <clause id="24842">
    <literal><![CDATA[
      a(x,y,z * (u \ T(z,w))) = a(x,y,(z \ u) \ z)
    ]]></literal>
    <justification jstring="[para(83(a,1),24840(a,1,3,2))].">
      <j1 rule="para" parents="83 24840"/>
    </justification>
  </clause>

  <clause id="24843">
    <literal><![CDATA[
      a(x,y,(z \ u) \ z) = a(x,y,z * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(24422,a,24842,a),flip(a)].">
      <j1 rule="hyper" parents="24422 24842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24845">
    <literal><![CDATA[
      a(x,y,(z \ u) * (u \ (z \ u))) = a(x,y,z \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(24183,a,24843,a),flip(a)].">
      <j1 rule="hyper" parents="24183 24843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24846">
    <literal><![CDATA[
      (x \ y) \ (x * L(x \ (x \ y),z,z)) = a(z,z,x * (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[para(24843(a,1),14616(a,2,1))].">
      <j1 rule="para" parents="24843 14616"/>
    </justification>
  </clause>

  <clause id="24847">
    <literal><![CDATA[
      a(x,x,y * (z \ y)) \ 1 = (y \ z) \ (y \ L(z,x,x))
    ]]></literal>
    <justification jstring="[para(3341(a,1),24846(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3341 24846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24848">
    <literal><![CDATA[
      a(x,y,z * ((u \ K(w,v5)) * v6)) = a(x,y,z * (v6 * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(24189,a,24815,a),flip(a)].">
      <j1 rule="hyper" parents="24189 24815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24851">
    <literal><![CDATA[
      a(x,y,z * ((u \ K(w,v5)) * v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u * v6) * z) = v7
    ]]></literal>
    <justification jstring="[para(24848(a,2),24446(a,1))].">
      <j1 rule="para" parents="24848 24446"/>
    </justification>
  </clause>

  <clause id="24852">
    <literal><![CDATA[
      L(a(x,x,x \ (x \ y)),y,z) = (y * z) \ (((x \ 1) \ (x \ y)) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,250,a(flip),b,24816,a),flip(a)].">
      <j1 rule="hyper" parents="347 250 24816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24853">
    <literal><![CDATA[
      L(a(x,x,x * (x \ y)),y,z) = (y * z) \ (((x \ 1) \ (x \ y)) * z)
    ]]></literal>
    <justification jstring="[para(15279(a,1),24852(a,1,1))].">
      <j1 rule="para" parents="15279 24852"/>
    </justification>
  </clause>

  <clause id="24854">
    <literal><![CDATA[
      (x * y) \ (((z \ 1) \ (z \ x)) * y) = L(a(z,z,x),x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),24853(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="10 24853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24855">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * (K(u,z) * v5)) = a(x,y,((u * w) \ ((u * z) * w)) * v5)
    ]]></literal>
    <justification jstring="[para(23601(a,1),24273(a,1,3))].">
      <j1 rule="para" parents="23601 24273"/>
    </justification>
  </clause>

  <clause id="24856">
    <literal><![CDATA[
      a(x,y,z * (L(u,u,T(w,v5)) \ w)) = a(x,y,z * (T(w,v5) * (1 / u)))
    ]]></literal>
    <justification jstring="[hyper(24185,a,24401,a),flip(a)].">
      <j1 rule="hyper" parents="24185 24401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24857">
    <literal><![CDATA[
      a(x,y,z * (L(u,u,T(w,v5)) \ w)) = a(x,y,z * (T(w,v5) * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(347,a,24301,a(flip),b,24856,a),flip(a)].">
      <j1 rule="hyper" parents="347 24301 24856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24858">
    <literal><![CDATA[
      a(x,y,z * (L(u,u,T(w,v5)) \ w)) = a(x,y,(w * (u \ 1)) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,24365,a(flip),b,24857,a),flip(a)].">
      <j1 rule="hyper" parents="347 24365 24857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24860">
    <literal><![CDATA[
      a(x,y,z * (L(u,u,w) \ w)) = a(x,y,(w * (u \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(110(a,1),24858(a,1,3,2,1,3))].">
      <j1 rule="para" parents="110 24858"/>
    </justification>
  </clause>

  <clause id="24861">
    <literal><![CDATA[
      a(x,y,z * (L(u,u,w) \ w)) = a(x,y,(w * u) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,24333,a(flip),b,24860,a),flip(a)].">
      <j1 rule="hyper" parents="347 24333 24860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24862">
    <literal><![CDATA[
      a(x,y,z * (u * ((w * w) * v5))) = a(x,y,z * (v5 * u))
    ]]></literal>
    <justification jstring="[hyper(24439,a,14945,a)].">
      <j1 rule="hyper" parents="24439 14945"/>
    </justification>
  </clause>

  <clause id="24863">
    <literal><![CDATA[
      a(x,y,(z * ((u * u) \ w)) * v5) = a(x,y,(z * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(24445,a,24283,a)].">
      <j1 rule="hyper" parents="24445 24283"/>
    </justification>
  </clause>

  <clause id="24864">
    <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(3326(a,1),24863(a,1,3,1))].">
      <j1 rule="para" parents="3326 24863"/>
    </justification>
  </clause>

  <clause id="24865">
    <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(83(a,1),24864(a,1,3,1,1,1)),flip(a)].">
      <j1 rule="para" parents="83 24864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24866">
    <literal><![CDATA[
      a(x,y,(z * L(1 / u,w,v5)) * v6) = a(x,y,(L(u,w,v5) * z) * v6)
    ]]></literal>
    <justification jstring="[hyper(24192,a,24865,a)].">
      <j1 rule="hyper" parents="24192 24865"/>
    </justification>
  </clause>

  <clause id="24867">
    <literal><![CDATA[
      a(x,L(y * (z \ 1),u,w),v5) = a(x,L(y * z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(24539,a,24118,a)].">
      <j1 rule="hyper" parents="24539 24118"/>
    </justification>
  </clause>

  <clause id="24868">
    <literal><![CDATA[
      a(x,L(y * z,z,z),u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,24744,a(flip),b,24867,a),flip(a)].">
      <j1 rule="hyper" parents="63 24744 24867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24869">
    <literal><![CDATA[
      a(x,L(T(y * K(z \ 1,y),u) * z,w,v5),v6) = a(x,L((z \ 1) * T(y,u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(5063(a,1),24867(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5063 24867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24870">
    <literal><![CDATA[
      a(x,L(y * a(z,z,y),u,w),v5) = a(x,L(L(y,z,z),u,w),v5)
    ]]></literal>
    <justification jstring="[para(14611(a,1),24867(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14611 24867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24871">
    <literal><![CDATA[
      a(x,L(y \ (y \ z),u,w),v5) = a(x,L(L(z,y,y),u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24479,a(flip),b,24870,a)].">
      <j1 rule="hyper" parents="63 24479 24870"/>
    </justification>
  </clause>

  <clause id="24872">
    <literal><![CDATA[
      a(x,y,z * (((u * u) * w) \ v5)) = a(x,y,z * (w \ v5))
    ]]></literal>
    <justification jstring="[hyper(24623,a,24326,a)].">
      <j1 rule="hyper" parents="24623 24326"/>
    </justification>
  </clause>

  <clause id="24873">
    <literal><![CDATA[
      a(x,y,z * (((u * u) \ w) \ v5)) = a(x,y,z * (w \ v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),24872(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="10 24872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24874">
    <literal><![CDATA[
      a(x,y,z * (L(T(u,w),w,w) \ v5)) = a(x,y,z * ((w * (u * w)) \ v5))
    ]]></literal>
    <justification jstring="[para(263(a,1),24873(a,1,3,2,1))].">
      <j1 rule="para" parents="263 24873"/>
    </justification>
  </clause>

  <clause id="24875">
    <literal><![CDATA[
      a(x,y,z * ((u * (w * u)) \ v5)) = a(x,y,z * (L(w,u,u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(24423,a,24874,a),flip(a)].">
      <j1 rule="hyper" parents="24423 24874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24876">
    <literal><![CDATA[
      a(x,y,z * (((u * w) * w) \ v5)) = a(x,y,z * (L(u,w,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(24426,a,24875,a)].">
      <j1 rule="hyper" parents="24426 24875"/>
    </justification>
  </clause>

  <clause id="24877">
    <literal><![CDATA[
      a(x,y,z * (((u * u) * w) * v5)) = a(x,y,z * (v5 * w))
    ]]></literal>
    <justification jstring="[hyper(24625,a,24862,a)].">
      <j1 rule="hyper" parents="24625 24862"/>
    </justification>
  </clause>

  <clause id="24878">
    <literal><![CDATA[
      a(x,y,z * (((u \ 1) \ w) * v5)) = a(x,y,z * (v5 * (u \ w)))
    ]]></literal>
    <justification jstring="[para(495(a,1),24877(a,1,3,2,1))].">
      <j1 rule="para" parents="495 24877"/>
    </justification>
  </clause>

  <clause id="24879">
    <literal><![CDATA[
      a(x,y,z * (u * ((w \ 1) \ v5))) = a(x,y,z * (u * (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(24190,a,24878,a)].">
      <j1 rule="hyper" parents="24190 24878"/>
    </justification>
  </clause>

  <clause id="24880">
    <literal><![CDATA[
      a(x,y,z * (u * ((w * w) * ((v5 \ (w * w)) \ v6)))) = a(x,y,z * (u * (v5 \ v6)))
    ]]></literal>
    <justification jstring="[para(778(a,2),24879(a,1,3,2,2))].">
      <j1 rule="para" parents="778 24879"/>
    </justification>
  </clause>

  <clause id="24881">
    <literal><![CDATA[
      a(x,y,L(z * (z * (z \ (u \ w))),z,u)) = a(x,y,L((z * u) \ w,z,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,24286,a(flip),b,24672,a),flip(a)].">
      <j1 rule="hyper" parents="347 24286 24672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24882">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,z,z)) = a(x,y,L(z * (u \ w),z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),24881(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="10 24881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24884">
    <literal><![CDATA[
      a(x,y,((z * u) \ ((z * w) * u)) * v5) = a(x,y,R(w,z,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(24189,a,24855,a),flip(a)].">
      <j1 rule="hyper" parents="24189 24855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24886">
    <literal><![CDATA[
      a(x,y,((z * u) \ ((z * w) * u)) * K(v5,v6)) = a(x,y,R(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,24080,a(flip),b,24884,a),flip(a)].">
      <j1 rule="hyper" parents="347 24080 24884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24887">
    <literal><![CDATA[
      a(x,y,((T(z,u) * T(w,z * v5)) \ (K(z,u) * (w * (z * v5)))) * v6) = a(x,y,R(v5,T(z,u),T(w,z * v5)) * v6)
    ]]></literal>
    <justification jstring="[para(21020(a,1),24884(a,1,3,1,2))].">
      <j1 rule="para" parents="21020 24884"/>
    </justification>
  </clause>

  <clause id="24888">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((z * w) * u)) = a(x,y,R(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(24188,a,24886,a)].">
      <j1 rule="hyper" parents="24188 24886"/>
    </justification>
  </clause>

  <clause id="24889">
    <literal><![CDATA[
      a(x,y,R(z,u,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(24600,a,24888,a),flip(a)].">
      <j1 rule="hyper" parents="24600 24888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24890">
    <literal><![CDATA[
      a(x,y,R(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(24888(a,1),24600(a,1))].">
      <j1 rule="para" parents="24888 24600"/>
    </justification>
  </clause>

  <clause id="24891">
    <literal><![CDATA[
      a(x,y,R(a(z,u,z) \ w,v5,v6)) = a(x,y,L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,12440,a,b,24889,a)].">
      <j1 rule="hyper" parents="63 12440 24889"/>
    </justification>
  </clause>

  <clause id="24892">
    <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),24889(a,2,3))].">
      <j1 rule="para" parents="30 24889"/>
    </justification>
  </clause>

  <clause id="24893">
    <literal><![CDATA[
      a(x,y,L(z,u,w * (v5 * v5))) = a(x,y,R(z,u,w))
    ]]></literal>
    <justification jstring="[para(2185(a,1),24889(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2185 24889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24894">
    <literal><![CDATA[
      a(x,y,L(z,u,w \ 1)) = a(x,y,R(z,u,w))
    ]]></literal>
    <justification jstring="[para(2190(a,1),24889(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2190 24889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24895">
    <literal><![CDATA[
      L(x,y,z * ((u \ a(u,u,L(w,v5,v6))) * L(w,v5,v6))) = L(x,y,z * (u \ R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(24889(a,1),22873(a,1,3,2,1,2))].">
      <j1 rule="para" parents="24889 22873"/>
    </justification>
  </clause>

  <clause id="24896">
    <literal><![CDATA[
      a(x,y,L(z,u,w \ 1)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(24894(a,2),24890(a,1))].">
      <j1 rule="para" parents="24894 24890"/>
    </justification>
  </clause>

  <clause id="24897">
    <literal><![CDATA[
      a(x,y,L(z,u,w * (v5 * v5))) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,24889,a(flip),b,24893,a),flip(a)].">
      <j1 rule="hyper" parents="347 24889 24893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24898">
    <literal><![CDATA[
      a(x,y,L(z,u,w * (v5 * (v6 * v6)))) = a(x,y,L(z,u,w * v5))
    ]]></literal>
    <justification jstring="[para(33(a,1),24897(a,1,3,3))].">
      <j1 rule="para" parents="33 24897"/>
    </justification>
  </clause>

  <clause id="24899">
    <literal><![CDATA[
      a(x,y,L(z,u,w * (w * v5))) = a(x,y,L(z,u,L(v5,w,w)))
    ]]></literal>
    <justification jstring="[para(21559(a,1),24897(a,1,3))].">
      <j1 rule="para" parents="21559 24897"/>
    </justification>
  </clause>

  <clause id="24900">
    <literal><![CDATA[
      a(x,y,R(z * (a(u,w,u) \ v5),v6,v7)) = a(x,y,L(z * v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(11881(a,1),24891(a,1,3,1))].">
      <j1 rule="para" parents="11881 24891"/>
    </justification>
  </clause>

  <clause id="24901">
    <literal><![CDATA[
      a(x,y,L(L((z \ 1) \ u,w,v5),z,z)) = a(x,y,L((z \ 1) * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(24896,a,15041,a)].">
      <j1 rule="hyper" parents="24896 15041"/>
    </justification>
  </clause>

  <clause id="24902">
    <literal><![CDATA[
      a(x,y,L(R(z,u,w),v5,v6)) = a(x,y,L(L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(29(a,1),24892(a,1,3))].">
      <j1 rule="para" parents="29 24892"/>
    </justification>
  </clause>

  <clause id="24903">
    <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(24662,a,24902,a),flip(a)].">
      <j1 rule="hyper" parents="24662 24902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24905">
    <literal><![CDATA[
      a(x,y,L(R(z,u,w),v5,z)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,12448,a(flip),b,24902,a),flip(a)].">
      <j1 rule="hyper" parents="347 12448 24902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24906">
    <literal><![CDATA[
      a(x,y,L(z,u,(w * v5) * w)) = a(x,y,L(z,u,L(v5,w,w)))
    ]]></literal>
    <justification jstring="[hyper(24588,a,24899,a)].">
      <j1 rule="hyper" parents="24588 24899"/>
    </justification>
  </clause>

  <clause id="24907">
    <literal><![CDATA[
      a(x,y,L(L(z \ u,z,u),w,v5)) = a(x,y,L(z * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,24275,a(flip),b,24903,a)].">
      <j1 rule="hyper" parents="63 24275 24903"/>
    </justification>
  </clause>

  <clause id="24908">
    <literal><![CDATA[
      a(x,y,L(z * u,z,u)) = a(x,y,L(z * u,z,z))
    ]]></literal>
    <justification jstring="[hyper(15040,a,24907,a)].">
      <j1 rule="hyper" parents="15040 24907"/>
    </justification>
  </clause>

  <clause id="24909">
    <literal><![CDATA[
      a(x,y,L(z * u,u,z)) = a(x,y,L(u * z,u,u))
    ]]></literal>
    <justification jstring="[hyper(24204,a,24908,a)].">
      <j1 rule="hyper" parents="24204 24908"/>
    </justification>
  </clause>

  <clause id="24910">
    <literal><![CDATA[
      a(x,y,L(z,u,w * ((v5 * v5) * v6))) = a(x,y,L(z,u,v6 * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,24589,a,b,24898,a)].">
      <j1 rule="hyper" parents="63 24589 24898"/>
    </justification>
  </clause>

  <clause id="24911">
    <literal><![CDATA[
      a(x,y,L(z,u,w * (v5 \ 1))) = a(x,y,L(z,u,w * v5))
    ]]></literal>
    <justification jstring="[para(240(a,1),24898(a,1,3,3,2)),flip(a)].">
      <j1 rule="para" parents="240 24898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24912">
    <literal><![CDATA[
      a(x,y,L(z,u,(w \ 1) * v5)) = a(x,y,L(z,u,v5 * w))
    ]]></literal>
    <justification jstring="[hyper(24588,a,24911,a)].">
      <j1 rule="hyper" parents="24588 24911"/>
    </justification>
  </clause>

  <clause id="24913">
    <literal><![CDATA[
      a(x,y,L(z,u,(w \ 1) * v5)) = a(x,y,L(z,u,w * v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,24587,a,b,24912,a),flip(a)].">
      <j1 rule="hyper" parents="347 24587 24912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24914">
    <literal><![CDATA[
      a(x,y,L(z,u,(w \ 1) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,v5 * w)) = v6
    ]]></literal>
    <justification jstring="[para(24913(a,2),24588(a,1))].">
      <j1 rule="para" parents="24913 24588"/>
    </justification>
  </clause>

  <clause id="24916">
    <literal><![CDATA[
      a(x,y,L(z,u,w * ((v5 \ 1) \ v6))) = a(x,y,L(z,u,(v5 \ v6) * w))
    ]]></literal>
    <justification jstring="[para(495(a,1),24910(a,1,3,3,2))].">
      <j1 rule="para" parents="495 24910"/>
    </justification>
  </clause>

  <clause id="24917">
    <literal><![CDATA[
      a(x,y,L(z * (a(u,w,u) \ v5),v6,v7)) = a(x,y,L(z * v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(24890,a,24900,a)].">
      <j1 rule="hyper" parents="24890 24900"/>
    </justification>
  </clause>

  <clause id="24918">
    <literal><![CDATA[
      a(x,y,L(z,u,w * ((v5 \ 1) \ v6))) = a(x,y,L(z,u,w * (v5 \ v6)))
    ]]></literal>
    <justification jstring="[hyper(347,a,24587,a,b,24916,a),flip(a)].">
      <j1 rule="hyper" parents="347 24587 24916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24919">
    <literal><![CDATA[
      a(x,y,L((z \ 1) * u,w,v5)) = a(x,y,L(z * u,w,v5))
    ]]></literal>
    <justification jstring="[para(3200(a,1),24901(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3200 24901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24920">
    <literal><![CDATA[
      a(L(L(x \ 1,x,y),y * x,z),u,w) = a((z * (y * x)) \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(23963,a,24220,a)].">
      <j1 rule="hyper" parents="23963 24220"/>
    </justification>
  </clause>

  <clause id="24921">
    <literal><![CDATA[
      a(x \ ((y * K(z,u)) \ (w * v5)),v6,v7) = a(x \ (y \ (w * (v5 * K(u,z)))),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(23985,a,24239,a)].">
      <j1 rule="hyper" parents="23985 24239"/>
    </justification>
  </clause>

  <clause id="24922">
    <literal><![CDATA[
      a(x,y * (L(z \ 1,u,w) * v5),v6) = a(x,y * (v5 * L(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,24775,a(flip),b,24245,a),flip(a)].">
      <j1 rule="hyper" parents="63 24775 24245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24923">
    <literal><![CDATA[
      a(x,y * (z * L(u \ 1,w,v5)),v6) = a(x,y * (z * L(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(24006,a,24922,a)].">
      <j1 rule="hyper" parents="24006 24922"/>
    </justification>
  </clause>

  <clause id="24925">
    <literal><![CDATA[
      a(x,y,(z * u) \ (w \ (z * (u * w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(w * L(w,u,z),w,z * u)) = v5
    ]]></literal>
    <justification jstring="[para(24305(a,1),15050(a,1))].">
      <j1 rule="para" parents="24305 15050"/>
    </justification>
  </clause>

  <clause id="24926">
    <literal><![CDATA[
      a(x,y,z * ((L(u,w,w) \ 1) * (w \ 1))) = a(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[hyper(24432,a,24580,a)].">
      <j1 rule="hyper" parents="24432 24580"/>
    </justification>
  </clause>

  <clause id="24927">
    <literal><![CDATA[
      a(x,y,(z * (L(u,z,z) \ 1)) * w) = a(x,y,w * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(24446,a,24926,a)].">
      <j1 rule="hyper" parents="24446 24926"/>
    </justification>
  </clause>

  <clause id="24928">
    <literal><![CDATA[
      a(x,y,(z * L(u,z,z)) * w) = a(x,y,w * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(24450,a,24927,a)].">
      <j1 rule="hyper" parents="24450 24927"/>
    </justification>
  </clause>

  <clause id="24929">
    <literal><![CDATA[
      a(x,y,z * (L(u,w,w) * w)) = a(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[hyper(24297,a,24928,a)].">
      <j1 rule="hyper" parents="24297 24928"/>
    </justification>
  </clause>

  <clause id="24930">
    <literal><![CDATA[
      a(x,y,(L(z,u,u) * u) * w) = a(x,y,w * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(24192,a,24928,a)].">
      <j1 rule="hyper" parents="24192 24928"/>
    </justification>
  </clause>

  <clause id="24931">
    <literal><![CDATA[
      a(x,y,z * (u * L(w,u,u))) = a(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(24180,a,24928,a)].">
      <j1 rule="hyper" parents="24180 24928"/>
    </justification>
  </clause>

  <clause id="24932">
    <literal><![CDATA[
      a(x \ (y * ((L(z,u,z) \ w) * z)),v5,v6) = a(a(z,u,z) * (x \ (y * w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(11888(a,1),24491(a,2,1))].">
      <j1 rule="para" parents="11888 24491"/>
    </justification>
  </clause>

  <clause id="24933">
    <literal><![CDATA[
      a(x,y * ((K(z,u) * w) * (v5 \ v6)),v7) = a(x,(w * (v6 / v5)) * y,v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,24466,a(flip),b,24495,a),flip(a)].">
      <j1 rule="hyper" parents="347 24466 24495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24935">
    <literal><![CDATA[
      a(x,y * (K(z,u) * (w * (v5 \ v6))),v7) = a(x,(w * (v6 / v5)) * y,v7)
    ]]></literal>
    <justification jstring="[para(14548(a,1),24933(a,1,2,2))].">
      <j1 rule="para" parents="14548 24933"/>
    </justification>
  </clause>

  <clause id="24936">
    <literal><![CDATA[
      a(x,(y * (z / u)) * w,v5) = a(x,(y * (u \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(24467,a,24935,a),flip(a)].">
      <j1 rule="hyper" parents="24467 24935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24937">
    <literal><![CDATA[
      a(x,y,z * ((u * ((w * w) * v5)) * v6)) = a(x,y,z * ((v5 * u) * ((w * w) * v6)))
    ]]></literal>
    <justification jstring="[para(125(a,1),24507(a,2,3,2))].">
      <j1 rule="para" parents="125 24507"/>
    </justification>
  </clause>

  <clause id="24938">
    <literal><![CDATA[
      a(L((x * T(y,z)) \ u,w,v5),v6,v7) != v8
    ]]></literal>
    <literal><![CDATA[
      a(L((y * x) \ u,w,v5),v6,v7) = v8
    ]]></literal>
    <justification jstring="[para(24584(a,1),23976(a,1))].">
      <j1 rule="para" parents="24584 23976"/>
    </justification>
  </clause>

  <clause id="24939">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * (K(v5,v6) * v7)))) = a(x,y,(u \ (v7 * w)) * z)
    ]]></literal>
    <justification jstring="[hyper(24429,a,24644,a),flip(a)].">
      <j1 rule="hyper" parents="24429 24644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24940">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * (K(v5,v6) * v7)))) != v8
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u \ (v7 * w)) * z) = v8
    ]]></literal>
    <justification jstring="[para(24644(a,1),24429(a,1))].">
      <j1 rule="para" parents="24644 24429"/>
    </justification>
  </clause>

  <clause id="24941">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w \ K(v5,v6)) * v7))) = a(x,y,(u \ (v7 * (w \ 1))) * z)
    ]]></literal>
    <justification jstring="[para(20815(a,1),24939(a,1,3,2,2))].">
      <j1 rule="para" parents="20815 24939"/>
    </justification>
  </clause>

  <clause id="24942">
    <literal><![CDATA[
      a(x,y,L(L(z / u,w,v5),v6,v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(L(u \ z,w,v5),v6,v7)) = v8
    ]]></literal>
    <justification jstring="[para(24659(a,1),24200(a,1))].">
      <j1 rule="para" parents="24659 24200"/>
    </justification>
  </clause>

  <clause id="24943">
    <literal><![CDATA[
      a(x,y * (z * (L(u \ 1,w,v5) \ K(v6,v7))),v8) = a(x,(z * L(u,w,v5)) * y,v8)
    ]]></literal>
    <justification jstring="[hyper(347,a,24598,a(flip),b,24682,a),flip(a)].">
      <j1 rule="hyper" parents="347 24598 24682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24944">
    <literal><![CDATA[
      a(x,y,z \ ((u * ((w * w) \ v5)) * v6)) = a(x,y,z \ ((u * v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(23544,a,24766,a),flip(a)].">
      <j1 rule="hyper" parents="23544 24766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24945">
    <literal><![CDATA[
      a(x,y,z \ ((u * ((w * w) * v5)) * v6)) = a(x,y,z \ ((u * v5) * v6))
    ]]></literal>
    <justification jstring="[para(9(a,1),24944(a,1,3,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 24944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24946">
    <literal><![CDATA[
      a(x,y,z \ (((u \ 1) * w) * v5)) = a(x,y,z \ ((u * w) * v5))
    ]]></literal>
    <justification jstring="[para(497(a,1),24944(a,1,3,2,1))].">
      <j1 rule="para" parents="497 24944"/>
    </justification>
  </clause>

  <clause id="24947">
    <literal><![CDATA[
      a(x,y,((z \ 1) * (u * w)) \ ((z * w) * u)) = a(x,y,K(w,u) * a(z \ 1,w,u))
    ]]></literal>
    <justification jstring="[para(21241(a,1),24946(a,1,3)),flip(a)].">
      <j1 rule="para" parents="21241 24946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24948">
    <literal><![CDATA[
      a(x,y,(z * ((u * u) * (w * v5))) \ ((z * w) * v5)) = a(x,y,a(z * (u * u),w,v5))
    ]]></literal>
    <justification jstring="[para(1982(a,1),24945(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1982 24945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24949">
    <literal><![CDATA[
      a(x,y,z * (((u \ (w * w)) \ v5) * v6)) = a(x,y,z * (v6 * (u \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,24862,a(flip),b,24880,a)].">
      <j1 rule="hyper" parents="63 24862 24880"/>
    </justification>
  </clause>

  <clause id="24951">
    <literal><![CDATA[
      a(x \ (y \ (z * (u * K(w,v5)))),v6,v7) = a(x \ (K(w,v5) * (y \ (z * u))),v6,v7)
    ]]></literal>
    <justification jstring="[para(20166(a,1),24921(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="20166 24921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24952">
    <literal><![CDATA[
      a(x \ (y * ((L(z,u,z) \ w) * z)),v5,v6) = a(x \ (y * w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,11563,a(flip),b,24932,a),flip(a)].">
      <j1 rule="hyper" parents="347 11563 24932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24954">
    <literal><![CDATA[
      a(x,y,z * ((u * ((w * w) * v5)) * v6)) = a(x,y,z * (v6 * (v5 * u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,24862,a(flip),b,24937,a),flip(a)].">
      <j1 rule="hyper" parents="347 24862 24937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24955">
    <literal><![CDATA[
      a(x,y,z * ((((u * u) * w) * v5) * v6)) = a(x,y,z * (v6 * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(24427,a,24954,a)].">
      <j1 rule="hyper" parents="24427 24954"/>
    </justification>
  </clause>

  <clause id="24957">
    <literal><![CDATA[
      a(x,y,z * (u * (((w * w) \ v5) * v6))) = a(x,y,z * ((v5 * v6) * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),24955(a,1,3,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 24955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24958">
    <literal><![CDATA[
      a(x,y,z * (((u * u) \ w) * v5)) = a(x,y,z * ((w * v5) * K(v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(24189,a,24957,a)].">
      <j1 rule="hyper" parents="24189 24957"/>
    </justification>
  </clause>

  <clause id="24959">
    <literal><![CDATA[
      a(x,y,z * (((u * u) \ w) * v5)) = a(x,y,z * (w * v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,24136,a(flip),b,24958,a),flip(a)].">
      <j1 rule="hyper" parents="347 24136 24958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24960">
    <literal><![CDATA[
      a(x,y,z * ((u \ (w \ 1)) * v5)) = a(x,y,z * ((u \ w) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,24503,a(flip),b,24959,a)].">
      <j1 rule="hyper" parents="63 24503 24959"/>
    </justification>
  </clause>

  <clause id="24962">
    <literal><![CDATA[
      a(x,(y * L(z \ 1,u,w)) * v5,v6) = a(x,(y * L(z,u,w)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,24598,a(flip),b,24943,a)].">
      <j1 rule="hyper" parents="63 24598 24943"/>
    </justification>
  </clause>

  <clause id="24963">
    <literal><![CDATA[
      a(x \ (y \ (z * (u * K(w,v5)))),v6,v7) != v8
    ]]></literal>
    <literal><![CDATA[
      a(x \ (y \ (z * u)),v6,v7) = v8
    ]]></literal>
    <justification jstring="[para(24951(a,2),23971(a,1))].">
      <j1 rule="para" parents="24951 23971"/>
    </justification>
  </clause>

  <clause id="24964">
    <literal><![CDATA[
      a(x \ (y \ (T(z,u) * w)),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x \ (y \ (z * w)),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(7088(a,1),24963(a,1,1,2,2))].">
      <j1 rule="para" parents="7088 24963"/>
    </justification>
  </clause>

  <clause id="24965">
    <literal><![CDATA[
      a(x \ (y \ (T(z,u) * w)),v5,v6) = a(x \ (y \ (z * w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(24964,a,xx),flip(a)].">
      <j1 rule="hyper" parents="24964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24966">
    <literal><![CDATA[
      a(x \ (y \ (z * (u * K(w,v5)))),v6,v7) != v8
    ]]></literal>
    <literal><![CDATA[
      a(x \ (y \ (T(z,v9) * u)),v6,v7) = v8
    ]]></literal>
    <justification jstring="[para(24965(a,1),24963(a,1))].">
      <j1 rule="para" parents="24965 24963"/>
    </justification>
  </clause>

  <clause id="24967">
    <literal><![CDATA[
      a(((x * x) * y) * ((x \ 1) * z),u,w) = a((x * z) * y,u,w)
    ]]></literal>
    <justification jstring="[hyper(23978,a,24224,a)].">
      <j1 rule="hyper" parents="23978 24224"/>
    </justification>
  </clause>

  <clause id="24968">
    <literal><![CDATA[
      a(x * ((y * y) * ((y \ 1) * z)),u,w) = a((y * z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(24606,a,24967,a)].">
      <j1 rule="hyper" parents="24606 24967"/>
    </justification>
  </clause>

  <clause id="24969">
    <literal><![CDATA[
      a(x * ((y \ 1) \ L(z,y,y)),u,w) = a((y * z) * x,u,w)
    ]]></literal>
    <justification jstring="[para(3219(a,1),24968(a,1,1,2))].">
      <j1 rule="para" parents="3219 24968"/>
    </justification>
  </clause>

  <clause id="24970">
    <literal><![CDATA[
      a((x * y) * (x \ 1),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),24969(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 24969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24971">
    <literal><![CDATA[
      a(L(x * ((T(x,y) \ 1) \ z),x,x),u,w) = a((x * z) * T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(22592(a,2),24969(a,1,1))].">
      <j1 rule="para" parents="22592 24969"/>
    </justification>
  </clause>

  <clause id="24972">
    <literal><![CDATA[
      a((x \ 1) * (x * y),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(23925,a,24970,a)].">
      <j1 rule="hyper" parents="23925 24970"/>
    </justification>
  </clause>

  <clause id="24973">
    <literal><![CDATA[
      a(L(x \ y,x,x),z,u) = a(y * (x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),24970(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 24970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24974">
    <literal><![CDATA[
      a(L((x \ 1) * y,x,x),z,u) = a((x \ 1) * L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(3197(a,1),24972(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3197 24972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24975">
    <literal><![CDATA[
      a(L(x * ((T(x,y) \ 1) \ z),x,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((x * z) * x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(24971(a,2),23964(a,1))].">
      <j1 rule="para" parents="24971 23964"/>
    </justification>
  </clause>

  <clause id="24976">
    <literal><![CDATA[
      a(x,y,L((z \ (u \ z)) * (u * u),w,v5)) = a(x,y,L(L(u,u,u \ z),w,v5))
    ]]></literal>
    <justification jstring="[para(21379(a,1),24369(a,2,3,1)),flip(a)].">
      <j1 rule="para" parents="21379 24369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24977">
    <literal><![CDATA[
      a(x,y,L(L(z,z,z \ u),w,v5)) = a(x,y,L(u \ (z \ u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(14942,a,24976,a),flip(a)].">
      <j1 rule="hyper" parents="14942 24976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24979">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u),w,v5)) = a(x,y,L(u \ (z \ u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,12454,a(flip),b,24977,a)].">
      <j1 rule="hyper" parents="63 12454 24977"/>
    </justification>
  </clause>

  <clause id="24980">
    <literal><![CDATA[
      a(x,L((y \ (z * z)) * u,y,y),w) = a(x,L(u,y,y) * y,w)
    ]]></literal>
    <justification jstring="[hyper(24390,a,24462,a)].">
      <j1 rule="hyper" parents="24390 24462"/>
    </justification>
  </clause>

  <clause id="24981">
    <literal><![CDATA[
      a(x,L(y * z,y,y),u) = a(x,L(z,y,y) * y,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),24980(a,1,2,1,1))].">
      <j1 rule="para" parents="9 24980"/>
    </justification>
  </clause>

  <clause id="24982">
    <literal><![CDATA[
      a(x,y * (z * (a(u,w,u) * v5)),v6) = a(x,(v5 * z) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(24411,a,24568,a)].">
      <j1 rule="hyper" parents="24411 24568"/>
    </justification>
  </clause>

  <clause id="24983">
    <literal><![CDATA[
      a(x,y * (z * (a(u,w,u) \ v5)),v6) = a(x,(v5 * z) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,24689,a,b,24982,a)].">
      <j1 rule="hyper" parents="63 24689 24982"/>
    </justification>
  </clause>

  <clause id="24985">
    <literal><![CDATA[
      a(x,y,z * (R(u / w,w,u \ v5) \ v5)) = a(x,y,z * (w * (u \ (v5 \ 1))))
    ]]></literal>
    <justification jstring="[para(2205(a,1),24583(a,1,3,2,1))].">
      <j1 rule="para" parents="2205 24583"/>
    </justification>
  </clause>

  <clause id="24986">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ (v5 \ 1)))) = a(x,y,z * (u * (w \ v5)))
    ]]></literal>
    <justification jstring="[para(693(a,1),24985(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="693 24985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24987">
    <literal><![CDATA[
      a(x,y * L(z \ K(u,T(w,v5)),z,v5),v6) = a(x,y * (v5 \ (v5 / z)),v6)
    ]]></literal>
    <justification jstring="[hyper(24419,a,24604,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="24419 24604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24988">
    <literal><![CDATA[
      a(x,y * L(z \ K(u,T(w,v5)),z,v5),v6) = a(x,y * (v5 \ (z \ v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,24255,a(flip),b,24987,a),flip(a)].">
      <j1 rule="hyper" parents="347 24255 24987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24991">
    <literal><![CDATA[
      a(x,y * ((z * u) \ (K(w,v5) * z)),v6) = a(x,y * (z \ (u \ z)),v6)
    ]]></literal>
    <justification jstring="[para(7114(a,1),24988(a,1,2,2))].">
      <j1 rule="para" parents="7114 24988"/>
    </justification>
  </clause>

  <clause id="24992">
    <literal><![CDATA[
      a(x,y * ((z * u) \ z),w) = a(x,y * (z \ (u \ z)),w)
    ]]></literal>
    <justification jstring="[hyper(24419,a,24991,a)].">
      <j1 rule="hyper" parents="24419 24991"/>
    </justification>
  </clause>

  <clause id="24993">
    <literal><![CDATA[
      a(x,R(y / z,z,y \ u) \ u,w) = a(x,z * (y \ ((v5 * v5) * u)),w)
    ]]></literal>
    <justification jstring="[para(22112(a,1),24735(a,1,2,1))].">
      <j1 rule="para" parents="22112 24735"/>
    </justification>
  </clause>

  <clause id="24994">
    <literal><![CDATA[
      a(x,y * (z \ ((u * u) * w)),v5) = a(x,y * (z \ w),v5)
    ]]></literal>
    <justification jstring="[para(693(a,1),24993(a,1,2)),flip(a)].">
      <j1 rule="para" parents="693 24993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24996">
    <literal><![CDATA[
      a(x,y * (z \ ((u \ 1) \ w)),v5) = a(x,y * (z \ (u \ w)),v5)
    ]]></literal>
    <justification jstring="[para(495(a,1),24994(a,1,2,2,2))].">
      <j1 rule="para" parents="495 24994"/>
    </justification>
  </clause>

  <clause id="24997">
    <literal><![CDATA[
      a(x,y * (z \ (u * a(w,w,u))),v5) = a(x,y * (z \ (w \ (w \ u))),v5)
    ]]></literal>
    <justification jstring="[para(15292(a,1),24994(a,1,2,2,2))].">
      <j1 rule="para" parents="15292 24994"/>
    </justification>
  </clause>

  <clause id="24998">
    <literal><![CDATA[
      a(x,y * (z \ ((a(u,u,w) \ 1) \ w)),v5) = a(x,y * (z \ L(w,u,u)),v5)
    ]]></literal>
    <justification jstring="[para(14601(a,1),24996(a,2,2,2,2))].">
      <j1 rule="para" parents="14601 24996"/>
    </justification>
  </clause>

  <clause id="24999">
    <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(21803(a,1),24998(a,1,2,2,2))].">
      <j1 rule="para" parents="21803 24998"/>
    </justification>
  </clause>

  <clause id="25000">
    <literal><![CDATA[
      a(x,y * (z \ (u \ (u \ w))),v5) = a(x,y * (z \ L(w,u,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24997,a(flip),b,24999,a)].">
      <j1 rule="hyper" parents="63 24997 24999"/>
    </justification>
  </clause>

  <clause id="25001">
    <literal><![CDATA[
      a(x,y,((z \ 1) * (u * w)) \ ((z * w) * u)) = a(x,y,a(z \ 1,w,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,24036,a(flip),b,24947,a),flip(a)].">
      <j1 rule="hyper" parents="347 24036 24947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25003">
    <literal><![CDATA[
      a(x,y,a(z * (u * u),w,v5)) = a(x,y,(z * (w * v5)) \ ((z * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(24717,a,24948,a),flip(a)].">
      <j1 rule="hyper" parents="24717 24948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25004">
    <literal><![CDATA[
      a(x,y,a(z * (u * u),w,v5)) = a(x,y,a(z,w,v5))
    ]]></literal>
    <justification jstring="[para(14(a,2),25003(a,2,3))].">
      <j1 rule="para" parents="14 25003"/>
    </justification>
  </clause>

  <clause id="25005">
    <literal><![CDATA[
      a(x,y,a(z * (u * (w * w)),v5,v6)) = a(x,y,a(z * u,v5,v6))
    ]]></literal>
    <justification jstring="[para(33(a,1),25004(a,1,3,1))].">
      <j1 rule="para" parents="33 25004"/>
    </justification>
  </clause>

  <clause id="25006">
    <literal><![CDATA[
      a(x,y,a(z \ 1,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(240(a,1),25004(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="240 25004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25007">
    <literal><![CDATA[
      a(x,y,a(z * (z * u),w,v5)) = a(x,y,a(L(u,z,z),w,v5))
    ]]></literal>
    <justification jstring="[para(24315(a,1),25004(a,1,3))].">
      <j1 rule="para" parents="24315 25004"/>
    </justification>
  </clause>

  <clause id="25008">
    <literal><![CDATA[
      a(x,y,K(z,u) * a(w,v5,v6)) = a(x,y,a(w \ 1,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,24036,a,b,25006,a)].">
      <j1 rule="hyper" parents="347 24036 25006"/>
    </justification>
  </clause>

  <clause id="25009">
    <literal><![CDATA[
      a(x,y,((z \ 1) * (u * w)) \ ((z * w) * u)) = a(x,y,a(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,25001,a,b,25006,a)].">
      <j1 rule="hyper" parents="63 25001 25006"/>
    </justification>
  </clause>

  <clause id="25010">
    <literal><![CDATA[
      a(x,y,a(z \ 1,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(25008(a,1),6429(a,1))].">
      <j1 rule="para" parents="25008 6429"/>
    </justification>
  </clause>

  <clause id="25011">
    <literal><![CDATA[
      a(x,y,a(z * (u \ 1),w,v5)) = a(x,y,a(z * u,w,v5))
    ]]></literal>
    <justification jstring="[para(240(a,1),25005(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="240 25005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25012">
    <literal><![CDATA[
      a(x,y,a(z * ((u \ 1) \ w),v5,v6)) = a(x,y,a((u \ w) * z,v5,v6))
    ]]></literal>
    <justification jstring="[para(24458(a,1),25005(a,1,3))].">
      <j1 rule="para" parents="24458 25005"/>
    </justification>
  </clause>

  <clause id="25013">
    <literal><![CDATA[
      a(x,y,((z * u) * w) \ ((w * u) * z)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(24295,a,25009,a)].">
      <j1 rule="hyper" parents="24295 25009"/>
    </justification>
  </clause>

  <clause id="25014">
    <literal><![CDATA[
      a(x,y,((z * T(u,w)) * w) \ ((u * w) * z)) = a(x,y,a(w,T(u,w),z))
    ]]></literal>
    <justification jstring="[para(111(a,1),25013(a,1,3,2,1))].">
      <j1 rule="para" parents="111 25013"/>
    </justification>
  </clause>

  <clause id="25015">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) \ (((z \ u) * z) * z)) = a(x,y,a(z \ u,z,z))
    ]]></literal>
    <justification jstring="[para(495(a,1),25013(a,1,3,1))].">
      <j1 rule="para" parents="495 25013"/>
    </justification>
  </clause>

  <clause id="25016">
    <literal><![CDATA[
      a(x,y,a(((z \ 1) \ u) * w,v5,v6)) = a(x,y,a((z \ u) * w,v5,v6))
    ]]></literal>
    <justification jstring="[para(23896(a,1),25012(a,1,3))].">
      <j1 rule="para" parents="23896 25012"/>
    </justification>
  </clause>

  <clause id="25017">
    <literal><![CDATA[
      a(x,y,((z * u) * w) \ ((u * w) * z)) = a(x,y,a(w,T(u,w),z))
    ]]></literal>
    <justification jstring="[hyper(63,a,24368,a(flip),b,25014,a)].">
      <j1 rule="hyper" parents="63 24368 25014"/>
    </justification>
  </clause>

  <clause id="25018">
    <literal><![CDATA[
      a(x,y,((z * u) * w) \ ((u * w) * z)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(18295(a,1),25017(a,2,3))].">
      <j1 rule="para" parents="18295 25017"/>
    </justification>
  </clause>

  <clause id="25019">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((w * u) * (w \ z))) = a(x,y,a(u,w,w \ z))
    ]]></literal>
    <justification jstring="[hyper(24437,a,25018,a)].">
      <j1 rule="hyper" parents="24437 25018"/>
    </justification>
  </clause>

  <clause id="25020">
    <literal><![CDATA[
      a(x,y,((z * u) * (w * K(v5,v6))) \ ((u * w) * (K(v5,v6) * z))) = a(x,y,a(w * K(v5,v6),u,z))
    ]]></literal>
    <justification jstring="[para(20819(a,1),25018(a,1,3,2))].">
      <j1 rule="para" parents="20819 25018"/>
    </justification>
  </clause>

  <clause id="25022">
    <literal><![CDATA[
      L(x,a(y,z * u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,u * z,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(24112(a,1),20611(a,1))].">
      <j1 rule="para" parents="24112 20611"/>
    </justification>
  </clause>

  <clause id="25023">
    <literal><![CDATA[
      a(x,y,((z * (u * u)) \ ((u * u) * w)) * v5) = a(x,y,(z \ T(w,u \ (u \ 1))) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24074,a(flip),b,24272,a),flip(a)].">
      <j1 rule="hyper" parents="347 24074 24272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25024">
    <literal><![CDATA[
      a(x,((y * L(z,u,w)) * (z * z)) \ v5,v6) = a(x,(y * L(z \ 1,u,w)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(8(a,1),24376(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8 24376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25025">
    <literal><![CDATA[
      a(x,(y * y) \ ((z * L(y,u,w)) \ v5),v6) = a(x,(z * L(y \ 1,u,w)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(459(a,1),25024(a,1,2))].">
      <j1 rule="para" parents="459 25024"/>
    </justification>
  </clause>

  <clause id="25026">
    <literal><![CDATA[
      a(x,(y * L(z \ 1,u,w)) \ v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,(y * L(z,u,w)) \ v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(25025(a,1),24159(a,1))].">
      <j1 rule="para" parents="25025 24159"/>
    </justification>
  </clause>

  <clause id="25027">
    <literal><![CDATA[
      a(x,L(T(y * K(z \ 1,y),u) * z,w,v5),v6) = a(x,L((z \ 1) * y,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,24362,a(flip),b,24869,a),flip(a)].">
      <j1 rule="hyper" parents="347 24362 24869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25029">
    <literal><![CDATA[
      a(x,L((y \ 1) * z,u,w),v5) = a(x,L(z * y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(5058(a,1),25027(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5058 25027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25030">
    <literal><![CDATA[
      L(x,y,z * (u \ R(w,v5,v6))) = L(x,y,z * (u \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(18983(a,1),24895(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="18983 24895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25031">
    <literal><![CDATA[
      L(x,y,z * (u \ L(u,u,w))) = L(x,y,z * a(u,u,w))
    ]]></literal>
    <justification jstring="[para(18988(a,1),25030(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="18988 25030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25032">
    <literal><![CDATA[
      a(x,y,((z * (u * u)) \ ((u * u) * w)) * v5) = a(x,y,(z \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24282,a(flip),b,25023,a),flip(a)].">
      <j1 rule="hyper" parents="347 24282 25023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25034">
    <literal><![CDATA[
      a(x,y,((z * z) \ (u \ ((z * z) * w))) * v5) = a(x,y,(u \ w) * v5)
    ]]></literal>
    <justification jstring="[para(459(a,1),25032(a,1,3,1))].">
      <j1 rule="para" parents="459 25032"/>
    </justification>
  </clause>

  <clause id="25035">
    <literal><![CDATA[
      a(x,y,(z \ ((u * u) * w)) * v5) = a(x,y,(z \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24336,a(flip),b,25034,a)].">
      <j1 rule="hyper" parents="63 24336 25034"/>
    </justification>
  </clause>

  <clause id="25036">
    <literal><![CDATA[
      a(x,y,(z \ (u * (w * w))) * v5) = a(x,y,(z \ u) * v5)
    ]]></literal>
    <justification jstring="[hyper(24628,a,25035,a)].">
      <j1 rule="hyper" parents="24628 25035"/>
    </justification>
  </clause>

  <clause id="25038">
    <literal><![CDATA[
      a(x,y,(z \ (u * T(w,u * u))) * v5) = a(x,y,(z \ ((u \ 1) * w)) * v5)
    ]]></literal>
    <justification jstring="[para(934(a,1),25036(a,1,3,1,2))].">
      <j1 rule="para" parents="934 25036"/>
    </justification>
  </clause>

  <clause id="25039">
    <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(25038(a,1),24430(a,1))].">
      <j1 rule="para" parents="25038 24430"/>
    </justification>
  </clause>

  <clause id="25040">
    <literal><![CDATA[
      a(x,y,(z \ (u * (w \ 1))) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z \ (w * u)) * v5) = v6
    ]]></literal>
    <justification jstring="[para(24643(a,1),25039(a,1))].">
      <j1 rule="para" parents="24643 25039"/>
    </justification>
  </clause>

  <clause id="25041">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w \ K(v5,v6)) * v7))) = a(x,y,(u \ (w * v7)) * z)
    ]]></literal>
    <justification jstring="[hyper(25040,a,24941,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="25040 24941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25042">
    <literal><![CDATA[
      a(x,y,(z \ (u * (z * u))) * K(w,v5)) = a(x,y,a(z,u,u \ K(v5,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,24615,a(flip),b,25041,a),flip(a)].">
      <j1 rule="hyper" parents="63 24615 25041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25043">
    <literal><![CDATA[
      a(x,y,a(z,u,u \ K(w,v5))) = a(x,y,z \ (u * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(24188,a,25042,a),flip(a)].">
      <j1 rule="hyper" parents="24188 25042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25046">
    <literal><![CDATA[
      a((x * y) \ ((z * y) * T(T(x,u),y)),w,v5) = a(R(T(z,T(x,u) * y),y,x),w,v5)
    ]]></literal>
    <justification jstring="[para(20040(a,1),24354(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20040 24354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25047">
    <literal><![CDATA[
      a((x * y) \ ((z * y) * T(T(x,u),y)),w,v5) = a(R(z,y,x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(23970,a,25046,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="23970 25046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25049">
    <literal><![CDATA[
      a((x * y) \ ((z * y) * T(x,u)),w,v5) = a(R(z,y,x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(23986,a,25047,a)].">
      <j1 rule="hyper" parents="23986 25047"/>
    </justification>
  </clause>

  <clause id="25050">
    <literal><![CDATA[
      a((x * y) \ ((z * y) * x),u,w) = a(R(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(23986,a,25049,a)].">
      <j1 rule="hyper" parents="23986 25049"/>
    </justification>
  </clause>

  <clause id="25053">
    <literal><![CDATA[
      a((T(x,T(y * z,u)) * z) \ T(x * (y * z),K(y * z,u)),w,v5) = a(R(y,z,T(x,T(y * z,u))),w,v5)
    ]]></literal>
    <justification jstring="[para(6060(a,2),25050(a,1,1,2))].">
      <j1 rule="para" parents="6060 25050"/>
    </justification>
  </clause>

  <clause id="25056">
    <literal><![CDATA[
      a(x,(y * ((y * (z * y)) \ 1)) \ u,w) = a(x,(L(z,y,y) * (y \ 1)) \ u,w)
    ]]></literal>
    <justification jstring="[para(2679(a,1),24375(a,1,2,1))].">
      <j1 rule="para" parents="2679 24375"/>
    </justification>
  </clause>

  <clause id="25057">
    <literal><![CDATA[
      a(x,(L(y,z,z) * (z \ 1)) \ u,w) = a(x,(z * (z * (y * z))) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(24174,a,25056,a),flip(a)].">
      <j1 rule="hyper" parents="24174 25056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25058">
    <literal><![CDATA[
      a(x,(L(y,z,z) * (z \ 1)) \ u,w) = a(x,L(y * z,z,z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24837,a(flip),b,25057,a),flip(a)].">
      <j1 rule="hyper" parents="347 24837 25057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25059">
    <literal><![CDATA[
      a(x,L(y * z,z,z) \ u,w) = a(x,(L(y,z,z) * z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(24174,a,25058,a),flip(a)].">
      <j1 rule="hyper" parents="24174 25058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25060">
    <literal><![CDATA[
      a(x,L(y * z,z,z) \ (z * y),u) = a(x,a(z,z,L(y,z,z)),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,24320,a,b,25059,a),flip(a)].">
      <j1 rule="hyper" parents="347 24320 25059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25061">
    <literal><![CDATA[
      a(x,K(y,z) * a(y,y,z * y),u) = a(x,a(y,y,L(z,y,y)),u)
    ]]></literal>
    <justification jstring="[para(14644(a,1),25060(a,1,2))].">
      <j1 rule="para" parents="14644 25060"/>
    </justification>
  </clause>

  <clause id="25062">
    <literal><![CDATA[
      a(x,a(y,y,L(z,y,y)),u) = a(x,a(y,y,z * y),u)
    ]]></literal>
    <justification jstring="[hyper(23987,a,25061,a),flip(a)].">
      <j1 rule="hyper" parents="23987 25061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25064">
    <literal><![CDATA[
      a(x,a(y,y,z * y),u) = a(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(15277(a,1),25062(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15277 25062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25065">
    <literal><![CDATA[
      a(x,a(y,y,y * z),u) = a(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(14642(a,1),25064(a,1,2))].">
      <j1 rule="para" parents="14642 25064"/>
    </justification>
  </clause>

  <clause id="25066">
    <literal><![CDATA[
      a(x,(y * L(z * u,u,u \ 1)) * w,v5) = a(x,w * (L(u * z,u,u \ 1) * y),v5)
    ]]></literal>
    <justification jstring="[para(3378(a,1),24533(a,1,2,1,2))].">
      <j1 rule="para" parents="3378 24533"/>
    </justification>
  </clause>

  <clause id="25067">
    <literal><![CDATA[
      a(x,y \ (z * ((u * (w \ K(v5,v6))) \ K(v5,v6))),v7) = a(x,y \ (z * ((u * (w \ 1)) \ 1)),v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,24261,a(flip),b,24498,a),flip(a)].">
      <j1 rule="hyper" parents="347 24261 24498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25068">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ (L(x,y,z) * (x \ u)) = a(x,x * L(x,y,z),x \ u)
    ]]></literal>
    <justification jstring="[para(3362(a,1),24819(a,1,1))].">
      <j1 rule="para" parents="3362 24819"/>
    </justification>
  </clause>

  <clause id="25069">
    <literal><![CDATA[
      a(x,x * L(x,y,z),x \ u) = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,24820,a(flip),b,25068,a),flip(a)].">
      <j1 rule="hyper" parents="63 24820 25068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25070">
    <literal><![CDATA[
      a(x,x * L(x,y,z),x * u) = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,12443,a(flip),b,25069,a),flip(a)].">
      <j1 rule="hyper" parents="63 12443 25069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25071">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u * x) = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(24180,a,25070,a)].">
      <j1 rule="hyper" parents="24180 25070"/>
    </justification>
  </clause>

  <clause id="25072">
    <literal><![CDATA[
      a(x,y \ (z * ((u * (w \ K(v5,v6))) \ K(v5,v6))),v7) = a(x,y \ (z * (u * (w \ 1))),v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,24745,a(flip),b,25067,a),flip(a)].">
      <j1 rule="hyper" parents="347 24745 25067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25073">
    <literal><![CDATA[
      a(x,y \ (z * ((u * (w \ K(v5,v6))) \ K(v5,v6))),v7) = a(x,y \ (z * (u * w)),v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,24792,a(flip),b,25072,a),flip(a)].">
      <j1 rule="hyper" parents="347 24792 25072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25074">
    <literal><![CDATA[
      a(x,y \ (z * (u * (w \ K(v5,v6)))),v7) = a(x,y \ (z * (u * w)),v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,24832,a(flip),b,25073,a)].">
      <j1 rule="hyper" parents="63 24832 25073"/>
    </justification>
  </clause>

  <clause id="25076">
    <literal><![CDATA[
      a(x,y \ (z * ((u \ 1) * (w * (u \ 1)))),v5) = a(x,y \ (z * (u * ((w * u) \ K(v6,v7)))),v5)
    ]]></literal>
    <justification jstring="[para(974(a,1),25074(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="974 25074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25077">
    <literal><![CDATA[
      a(x,y \ (z * ((u \ 1) * (w * (u \ 1)))),v5) = a(x,y \ (z * (u * (w * u))),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,25074,a(flip),b,25076,a),flip(a)].">
      <j1 rule="hyper" parents="347 25074 25076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25078">
    <literal><![CDATA[
      a(x,y,z * (((u * u) * w) * ((u \ 1) * v5))) = a(x,y,z * ((v5 * u) * w))
    ]]></literal>
    <justification jstring="[hyper(24431,a,24782,a)].">
      <j1 rule="hyper" parents="24431 24782"/>
    </justification>
  </clause>

  <clause id="25079">
    <literal><![CDATA[
      a(x,y,z * (((u \ 1) * w) * v5)) = a(x,y,z * ((w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,24877,a(flip),b,25078,a)].">
      <j1 rule="hyper" parents="63 24877 25078"/>
    </justification>
  </clause>

  <clause id="25080">
    <literal><![CDATA[
      a(x,y,z * ((u * (w \ 1)) * v5)) = a(x,y,z * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(24427,a,25079,a)].">
      <j1 rule="hyper" parents="24427 25079"/>
    </justification>
  </clause>

  <clause id="25082">
    <literal><![CDATA[
      a(x,y,z * (((u \ (w * w)) * v5) * v6)) = a(x,y,z * ((((w * w) * v5) * u) * v6))
    ]]></literal>
    <justification jstring="[para(516(a,1),25079(a,1,3,2,1))].">
      <j1 rule="para" parents="516 25079"/>
    </justification>
  </clause>

  <clause id="25083">
    <literal><![CDATA[
      a(x,y,z * (((u \ (w * w)) * v5) * v6)) = a(x,y,z * (v6 * (v5 * u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,24955,a(flip),b,25082,a),flip(a)].">
      <j1 rule="hyper" parents="347 24955 25082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25084">
    <literal><![CDATA[
      a(x,y,z * ((u * (w \ (v5 * v5))) * v6)) = a(x,y,z * (v6 * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(24427,a,25083,a)].">
      <j1 rule="hyper" parents="24427 25083"/>
    </justification>
  </clause>

  <clause id="25086">
    <literal><![CDATA[
      a(x,y,K(z,u) * (((w * v5) * v6) \ ((v5 * v6) * (K(u,z) * w)))) = a(x,y,a(v6 * K(u,z),v5,w))
    ]]></literal>
    <justification jstring="[para(20837(a,1),25020(a,1,3))].">
      <j1 rule="para" parents="20837 25020"/>
    </justification>
  </clause>

  <clause id="25087">
    <literal><![CDATA[
      a(x,y,(((z * u) * w) \ (z * (u * w))) * K(v5,v6)) = a(x,y,a(w * K(v6,v5),u,z))
    ]]></literal>
    <justification jstring="[hyper(24940,a,25086,a)].">
      <j1 rule="hyper" parents="24940 25086"/>
    </justification>
  </clause>

  <clause id="25089">
    <literal><![CDATA[
      a(x,y,((z * u) \ ((z * (u * w)) / w)) * K(v5,v6)) = a(x,y,a(w * K(v6,v5),u,z))
    ]]></literal>
    <justification jstring="[para(3980(a,1),25087(a,1,3,1))].">
      <j1 rule="para" parents="3980 25087"/>
    </justification>
  </clause>

  <clause id="25090">
    <literal><![CDATA[
      a(x,y,a(z * K(u,w),v5,v6)) = a(x,y,(v6 * v5) \ ((v6 * (v5 * z)) / z))
    ]]></literal>
    <justification jstring="[hyper(24188,a,25089,a),flip(a)].">
      <j1 rule="hyper" parents="24188 25089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25092">
    <literal><![CDATA[
      a(x,y,a(z * K(u,w),v5,v6)) = a(x,y,(v6 * v5) \ (z \ (v6 * (v5 * z))))
    ]]></literal>
    <justification jstring="[hyper(347,a,24137,a(flip),b,25090,a),flip(a)].">
      <j1 rule="hyper" parents="347 24137 25090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25093">
    <literal><![CDATA[
      a(x,y,(z * u) \ (w \ (z * (u * w)))) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(203(a,1),25092(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="203 25092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25094">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),z,w * u)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(24925,a,25093,a)].">
      <j1 rule="hyper" parents="24925 25093"/>
    </justification>
  </clause>

  <clause id="25095">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ ((w * u) * T(T(z,v5),u))),v6) = a(x,y \ R(T(w,T(z,v5) * u),u,z),v6)
    ]]></literal>
    <justification jstring="[para(20040(a,1),24578(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="20040 24578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25096">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ ((w * u) * T(T(z,v5),u))),v6) = a(x,y \ R(w,u,z),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,24044,a(flip),b,25095,a),flip(a)].">
      <j1 rule="hyper" parents="347 24044 25095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25099">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ ((w * u) * T(z,v5))),v6) = a(x,y \ R(w,u,z),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,24266,a(flip),b,25096,a)].">
      <j1 rule="hyper" parents="63 24266 25096"/>
    </justification>
  </clause>

  <clause id="25101">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ ((w * u) * z)),v5) = a(x,y \ R(w,u,z),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24266,a(flip),b,25099,a)].">
      <j1 rule="hyper" parents="63 24266 25099"/>
    </justification>
  </clause>

  <clause id="25102">
    <literal><![CDATA[
      a(x,y \ L(z * K(u * z,T(w,v5)),u,w),v6) = a(x,y \ ((w * u) \ ((u * z) * T(w,v5))),v6)
    ]]></literal>
    <justification jstring="[para(20041(a,1),24579(a,1,2,2))].">
      <j1 rule="para" parents="20041 24579"/>
    </justification>
  </clause>

  <clause id="25104">
    <literal><![CDATA[
      a(x,(y \ L(z,u,w)) * K(u * z,T(w,v5)),v6) = a(x,y \ ((w * u) \ ((u * z) * T(w,v5))),v6)
    ]]></literal>
    <justification jstring="[para(21258(a,1),25102(a,1,2))].">
      <j1 rule="para" parents="21258 25102"/>
    </justification>
  </clause>

  <clause id="25105">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ ((u * w) * T(z,v5))),v6) = a(x,y \ L(w,u,z),v6)
    ]]></literal>
    <justification jstring="[hyper(24005,a,25104,a),flip(a)].">
      <j1 rule="hyper" parents="24005 25104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25107">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ ((u * w) * z)),v5) = a(x,y \ L(w,u,z),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24266,a(flip),b,25105,a)].">
      <j1 rule="hyper" parents="63 24266 25105"/>
    </justification>
  </clause>

  <clause id="25108">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ (T(w * u,K(u,v5)) * z)),v6) = a(x,y \ L(T(w,T(u,v5)),u,z),v6)
    ]]></literal>
    <justification jstring="[para(6060(a,2),25107(a,1,2,2,2,1))].">
      <j1 rule="para" parents="6060 25107"/>
    </justification>
  </clause>

  <clause id="25109">
    <literal><![CDATA[
      a(x,y \ L(T(z,T(u,w)),u,v5),v6) = a(x,y \ ((v5 * u) \ ((z * u) * v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,24502,a(flip),b,25108,a),flip(a)].">
      <j1 rule="hyper" parents="63 24502 25108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25111">
    <literal><![CDATA[
      a(x,y \ L(T(z,T(u,w)),u,v5),v6) = a(x,y \ R(z,u,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,25101,a(flip),b,25109,a),flip(a)].">
      <j1 rule="hyper" parents="347 25101 25109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25112">
    <literal><![CDATA[
      a(x,y \ R(z,u,w),v5) = a(x,y \ L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(24339,a,25111,a),flip(a)].">
      <j1 rule="hyper" parents="24339 25111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25113">
    <literal><![CDATA[
      a(x,y \ R(z,u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ L(z,u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(25111(a,1),24339(a,1))].">
      <j1 rule="para" parents="25111 24339"/>
    </justification>
  </clause>

  <clause id="25115">
    <literal><![CDATA[
      a(x,T(y,z) * R(u,w,v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,R(1 / T(y,z),y,R(u,w,v5)) \ L(u,w,v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(20558(a,1),25113(a,1,2))].">
      <j1 rule="para" parents="20558 25113"/>
    </justification>
  </clause>

  <clause id="25116">
    <literal><![CDATA[
      a(x,R(1 / T(y,z),y,R(u,w,v5)) \ L(u,w,v5),v6) = a(x,y * R(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(25115,a,24042,a)].">
      <j1 rule="hyper" parents="25115 24042"/>
    </justification>
  </clause>

  <clause id="25117">
    <literal><![CDATA[
      a(x,R(1 / T(y,z),y,L(u,w,v5)) \ L(u,w,v5),v6) = a(x,y * R(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(23613(a,1),25116(a,1,2,1))].">
      <j1 rule="para" parents="23613 25116"/>
    </justification>
  </clause>

  <clause id="25118">
    <literal><![CDATA[
      a(x,T(y,z) * L(u,w,v5),v6) = a(x,y * R(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(20558(a,1),25117(a,1,2))].">
      <j1 rule="para" parents="20558 25117"/>
    </justification>
  </clause>

  <clause id="25119">
    <literal><![CDATA[
      a(x,y * R(z,u,w),v5) = a(x,y * L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(23995,a,25118,a),flip(a)].">
      <j1 rule="hyper" parents="23995 25118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25120">
    <literal><![CDATA[
      a(x,L(y,z,u) * w,v5) = a(x,w * R(y,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24037,a,b,25119,a)].">
      <j1 rule="hyper" parents="347 24037 25119"/>
    </justification>
  </clause>

  <clause id="25121">
    <literal><![CDATA[
      a(x,y * L(y,z,z),u) = a(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,24388,a(flip),b,25119,a),flip(a)].">
      <j1 rule="hyper" parents="63 24388 25119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25122">
    <literal><![CDATA[
      a(x,y * L(z,u,w * (v5 \ 1)),v6) = a(x,y * R(z,u,w * v5),v6)
    ]]></literal>
    <justification jstring="[para(2204(a,1),25119(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2204 25119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25123">
    <literal><![CDATA[
      a(x,a(y,z,z),u) = a(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,15026,a(flip),b,25121,a),flip(a)].">
      <j1 rule="hyper" parents="63 15026 25121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25124">
    <literal><![CDATA[
      a(x,a(y * z,z,z),u) = a(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,25064,a(flip),b,25123,a),flip(a)].">
      <j1 rule="hyper" parents="347 25064 25123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25125">
    <literal><![CDATA[
      a(x,R(y,z,u) * w,v5) = a(x,L(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24037,a,b,25120,a)].">
      <j1 rule="hyper" parents="347 24037 25120"/>
    </justification>
  </clause>

  <clause id="25126">
    <literal><![CDATA[
      a(x,R(L(y,z,u),w,v5) * v6,v7) = a(x,L(L(y,w,v5),z,u) * v6,v7)
    ]]></literal>
    <justification jstring="[para(30(a,1),25125(a,2,2,1))].">
      <j1 rule="para" parents="30 25125"/>
    </justification>
  </clause>

  <clause id="25127">
    <literal><![CDATA[
      a(x,L(R(y,z,u),w,v5) * (z * u),v6) = a(x,(R(y,w,v5) * z) * u,v6)
    ]]></literal>
    <justification jstring="[para(469(a,1),25125(a,1,2)),flip(a)].">
      <j1 rule="para" parents="469 25125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25128">
    <literal><![CDATA[
      a(x,y * L(z,u,w * (v5 \ 1)),v6) = a(x,y * L(z,u,w * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,25119,a(flip),b,25122,a),flip(a)].">
      <j1 rule="hyper" parents="347 25119 25122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25129">
    <literal><![CDATA[
      a(x,L(L(y,z,u),L(y,z,u),w) * w,v5) = a(x,R(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24663,a(flip),b,25126,a),flip(a)].">
      <j1 rule="hyper" parents="63 24663 25126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25130">
    <literal><![CDATA[
      a(x,R(y,z,u) \ w,v5) = a(x,L(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(24348,a,25129,a),flip(a)].">
      <j1 rule="hyper" parents="24348 25129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25131">
    <literal><![CDATA[
      a(x,(R(y,z,u) * w) * v5,v6) = a(x,(L(y,z,u) * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(471(a,1),25127(a,1,2)),flip(a)].">
      <j1 rule="para" parents="471 25127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25132">
    <literal><![CDATA[
      a(x,(L(y,z,u) * (w \ 1)) * v5,v6) = a(x,v5 * (w * R(y,z,u)),v6)
    ]]></literal>
    <justification jstring="[hyper(24725,a,25131,a),flip(a)].">
      <j1 rule="hyper" parents="24725 25131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25133">
    <literal><![CDATA[
      a(x,(L(y,z,u) * T(w,v5)) * v6,v7) = a(x,v6 * (R(y,z,u) * w),v7)
    ]]></literal>
    <justification jstring="[hyper(24477,a,25131,a),flip(a)].">
      <j1 rule="hyper" parents="24477 25131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25134">
    <literal><![CDATA[
      a(x,(L(y,z,u) * w) * L(v5,v5,R(y,z,u) * w),v6) = a(x,(R(y,z,u) * w) / (v5 \ 1),v6)
    ]]></literal>
    <justification jstring="[para(2008(a,1),25131(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2008 25131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25135">
    <literal><![CDATA[
      a(x,y * (z * R(u,w,v5)),v6) = a(x,y * (z * L(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(24725,a,25132,a),flip(a)].">
      <j1 rule="hyper" parents="24725 25132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25136">
    <literal><![CDATA[
      a(x,(L(y,z,u) * T(w,v5)) * v6,v7) = a(x,(w * R(y,z,u)) * v6,v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,24243,a,b,25133,a),flip(a)].">
      <j1 rule="hyper" parents="347 24243 25133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25137">
    <literal><![CDATA[
      a(x,y * (R(z,u,w) * v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y * (L(z,u,w) * v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(25133(a,1),24477(a,1))].">
      <j1 rule="para" parents="25133 24477"/>
    </justification>
  </clause>

  <clause id="25138">
    <literal><![CDATA[
      a(x,(y * R(z,u,w)) * v5,v6) = a(x,(y * L(z,u,w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(111(a,1),25136(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="111 25136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25139">
    <literal><![CDATA[
      a(x,(y * L(z,u,w \ 1)) * v5,v6) = a(x,(y * R(z,u,w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(2190(a,1),25138(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2190 25138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25140">
    <literal><![CDATA[
      a(x,(y * L(z,u,w \ 1)) * v5,v6) = a(x,(y * L(z,u,w)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,25138,a(flip),b,25139,a),flip(a)].">
      <j1 rule="hyper" parents="347 25138 25139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25141">
    <literal><![CDATA[
      a(x,y * (L(z * u,z,z \ 1) * w),v5) = a(x,(w * L(u * z,z,z)) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,25066,a(flip),b,25140,a)].">
      <j1 rule="hyper" parents="63 25066 25140"/>
    </justification>
  </clause>

  <clause id="25142">
    <literal><![CDATA[
      a(x,(L(y,z,u) * w) * L(v5,v5,R(y,z,u) * w),v6) = a(x,(v5 \ 1) \ (R(y,z,u) * w),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,24023,a(flip),b,25134,a),flip(a)].">
      <j1 rule="hyper" parents="347 24023 25134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25143">
    <literal><![CDATA[
      a(x,(L(y,z,u) * w) * L(v5,v5,R(y,z,u) * w),v6) = a(x,v5 \ (R(y,z,u) * w),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,24115,a(flip),b,25142,a),flip(a)].">
      <j1 rule="hyper" parents="347 24115 25142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25144">
    <literal><![CDATA[
      a(x,(L(y,z,u) * w) * L(v5,v5,L(y,z,u) * w),v6) = a(x,v5 \ (R(y,z,u) * w),v6)
    ]]></literal>
    <justification jstring="[para(22849(a,1),25143(a,1,2,2))].">
      <j1 rule="para" parents="22849 25143"/>
    </justification>
  </clause>

  <clause id="25145">
    <literal><![CDATA[
      a(x,(L(y,z,u) * w) / (v5 \ 1),v6) = a(x,v5 \ (R(y,z,u) * w),v6)
    ]]></literal>
    <justification jstring="[para(2008(a,1),25144(a,1,2))].">
      <j1 rule="para" parents="2008 25144"/>
    </justification>
  </clause>

  <clause id="25146">
    <literal><![CDATA[
      a(x,(y \ 1) \ (L(z,u,w) * v5),v6) = a(x,y \ (R(z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(23997,a,25145,a)].">
      <j1 rule="hyper" parents="23997 25145"/>
    </justification>
  </clause>

  <clause id="25147">
    <literal><![CDATA[
      a(x,y \ (R(z,u,w) * v5),v6) = a(x,y \ (L(z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(24172,a,25146,a),flip(a)].">
      <j1 rule="hyper" parents="24172 25146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25148">
    <literal><![CDATA[
      a(x,y \ (R(z,u,w) * v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ (L(z,u,w) * v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(25146(a,1),24172(a,1))].">
      <j1 rule="para" parents="25146 24172"/>
    </justification>
  </clause>

  <clause id="25149">
    <literal><![CDATA[
      a(x,y \ (L(z,u,w \ 1) * v5),v6) = a(x,y \ (R(z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[para(2190(a,1),25147(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2190 25147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25150">
    <literal><![CDATA[
      a(x,y \ T(z * R(u,w,v5),K(R(u,w,v5),v6)),v7) = a(x,y \ (L(u,w,v5) * T(z,T(R(u,w,v5),v6))),v7)
    ]]></literal>
    <justification jstring="[para(6060(a,2),25147(a,1,2,2))].">
      <j1 rule="para" parents="6060 25147"/>
    </justification>
  </clause>

  <clause id="25151">
    <literal><![CDATA[
      a(x,y \ (L(z,u,w \ 1) * v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ (L(z,u,w) * v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(25149(a,2),25148(a,1))].">
      <j1 rule="para" parents="25149 25148"/>
    </justification>
  </clause>

  <clause id="25152">
    <literal><![CDATA[
      a(x,y \ (L(z,u,w) * T(v5,T(R(z,u,w),v6))),v7) = a(x,y \ (v5 * R(z,u,w)),v7)
    ]]></literal>
    <justification jstring="[hyper(24002,a,25150,a),flip(a)].">
      <j1 rule="hyper" parents="24002 25150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25154">
    <literal><![CDATA[
      a(x,y \ (L(z,u,w) * T(v5,R(T(z,v6),u,w))),v7) = a(x,y \ (v5 * R(z,u,w)),v7)
    ]]></literal>
    <justification jstring="[para(27(a,2),25152(a,1,2,2,2,2))].">
      <j1 rule="para" parents="27 25152"/>
    </justification>
  </clause>

  <clause id="25155">
    <literal><![CDATA[
      a(x,y \ (L(z,u,w) * T(v5,T(z,v6))),v7) = a(x,y \ (v5 * R(z,u,w)),v7)
    ]]></literal>
    <justification jstring="[para(19951(a,1),25154(a,1,2,2,2))].">
      <j1 rule="para" parents="19951 25154"/>
    </justification>
  </clause>

  <clause id="25157">
    <literal><![CDATA[
      a(x,y \ T(z * L(u,w,v5),K(u,v6)),v7) = a(x,y \ (z * R(u,w,v5)),v7)
    ]]></literal>
    <justification jstring="[para(21356(a,2),25155(a,1,2,2))].">
      <j1 rule="para" parents="21356 25155"/>
    </justification>
  </clause>

  <clause id="25158">
    <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(25157(a,1),24002(a,1))].">
      <j1 rule="para" parents="25157 24002"/>
    </justification>
  </clause>

  <clause id="25159">
    <literal><![CDATA[
      a(x,y \ L(z * u,z,z),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ (z * L(u,z,z)),w) = v5
    ]]></literal>
    <justification jstring="[para(24786(a,2),25158(a,1))].">
      <j1 rule="para" parents="24786 25158"/>
    </justification>
  </clause>

  <clause id="25160">
    <literal><![CDATA[
      a(x,y \ (z * (u * (w * u))),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ (z * L(w,u,u)),v5) = v6
    ]]></literal>
    <justification jstring="[para(24795(a,2),25158(a,1))].">
      <j1 rule="para" parents="24795 25158"/>
    </justification>
  </clause>

  <clause id="25161">
    <literal><![CDATA[
      a(x,y \ (z * L(u,z,z)),w) = a(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(25159,a,24749,a)].">
      <j1 rule="hyper" parents="25159 24749"/>
    </justification>
  </clause>

  <clause id="25162">
    <literal><![CDATA[
      a(x,y \ (z * ((u \ 1) * (w * (u \ 1)))),v5) = a(x,y \ (z * L(w,u,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(25160,a,25077,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="25160 25077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25163">
    <literal><![CDATA[
      a(x,y \ (z * L(u,w \ 1,w \ 1)),v5) = a(x,y \ (z * L(u,w,w)),v5)
    ]]></literal>
    <justification jstring="[hyper(25160,a,25162,a)].">
      <j1 rule="hyper" parents="25160 25162"/>
    </justification>
  </clause>

  <clause id="25164">
    <literal><![CDATA[
      a(x,y \ (z * L(u,w,w \ 1)),v5) = a(x,y \ (z * L(u,w,w)),v5)
    ]]></literal>
    <justification jstring="[para(3188(a,1),25163(a,1,2,2,2))].">
      <j1 rule="para" parents="3188 25163"/>
    </justification>
  </clause>

  <clause id="25165">
    <literal><![CDATA[
      a(L(x \ y,x,y \ (z * (u / w))) \ (z * (w \ u)),v5,v6) = a(((z * (u / w)) / y) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,23894,a(flip),b,24519,a),flip(a)].">
      <j1 rule="hyper" parents="347 23894 24519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25167">
    <literal><![CDATA[
      a(L(x \ y,x,y \ (z * (u / w))) \ (z * (w \ u)),v5,v6) = a((y \ (z * (u / w))) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,23899,a(flip),b,25165,a),flip(a)].">
      <j1 rule="hyper" parents="347 23899 25165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25168">
    <literal><![CDATA[
      a(L(x \ y,x,y \ (z * (u \ w))) \ (z * (u \ w)),v5,v6) = a((y \ (z * (w / u))) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(21567(a,1),25167(a,1,1,1))].">
      <j1 rule="para" parents="21567 25167"/>
    </justification>
  </clause>

  <clause id="25169">
    <literal><![CDATA[
      a(T(((x * (y \ z)) / u) * w,w \ u),v5,v6) = a((u \ (x * (z / y))) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(13788(a,1),25168(a,1,1))].">
      <j1 rule="para" parents="13788 25168"/>
    </justification>
  </clause>

  <clause id="25170">
    <literal><![CDATA[
      a(((x * (y \ z)) / u) * w,v5,v6) = a((u \ (x * (z / y))) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(23953,a,25169,a)].">
      <j1 rule="hyper" parents="23953 25169"/>
    </justification>
  </clause>

  <clause id="25172">
    <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(25170(a,1),23962(a,1))].">
      <j1 rule="para" parents="25170 23962"/>
    </justification>
  </clause>

  <clause id="25173">
    <literal><![CDATA[
      a(x,(L(y,z,y) / u) * (K(u \ 1,w) * v5),v6) = a(x,(y * T(L(y,z,y) \ (L(y,z,y) / u),w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(20151(a,1),24651(a,1,2))].">
      <j1 rule="para" parents="20151 24651"/>
    </justification>
  </clause>

  <clause id="25174">
    <literal><![CDATA[
      ((x * y) * (y \ L(y,z,u))) \ (K(x * (y \ L(y,z,u)),y) * (L(y,z,u) * x)) = a(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(3625(a,1),24818(a,1,1))].">
      <j1 rule="para" parents="3625 24818"/>
    </justification>
  </clause>

  <clause id="25175">
    <literal><![CDATA[
      a((T(x,T(y * z,u)) * z) \ (x * (y * z)),w,v5) = a(R(y,z,T(x,T(y * z,u))),w,v5)
    ]]></literal>
    <justification jstring="[hyper(17833,a,25053,a)].">
      <j1 rule="hyper" parents="17833 25053"/>
    </justification>
  </clause>

  <clause id="25176">
    <literal><![CDATA[
      a(R(x,y,T(z,T(x * y,u))),w,v5) = a((z * y) \ (z * (x * y)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(23975,a,25175,a),flip(a)].">
      <j1 rule="hyper" parents="23975 25175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25179">
    <literal><![CDATA[
      a(R(x,y,T(z,T(x * y,u))),w,v5) = a(L(T(x,y),y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(263(a,1),25176(a,2,1))].">
      <j1 rule="para" parents="263 25176"/>
    </justification>
  </clause>

  <clause id="25180">
    <literal><![CDATA[
      a(R(x,y,T(z,T(x * y,u))),w,v5) = a(L(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,23900,a(flip),b,25179,a),flip(a)].">
      <j1 rule="hyper" parents="347 23900 25179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25182">
    <literal><![CDATA[
      a(R(x,y,z),u,w) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(20040(a,1),25180(a,1,1))].">
      <j1 rule="para" parents="20040 25180"/>
    </justification>
  </clause>

  <clause id="25183">
    <literal><![CDATA[
      a((x * y) \ (y * (z * x)),u,w) = a(L(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(24605,a,25182,a)].">
      <j1 rule="hyper" parents="24605 25182"/>
    </justification>
  </clause>

  <clause id="25184">
    <literal><![CDATA[
      a(R(K(x,y) * z,u,w),v5,v6) = a(L(z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(23976,a,25182,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="23976 25182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25185">
    <literal><![CDATA[
      a(L(x,y,z * (u \ 1)),w,v5) = a(R(x,y,z * u),w,v5)
    ]]></literal>
    <justification jstring="[para(2204(a,1),25182(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2204 25182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25186">
    <literal><![CDATA[
      a(L(x / y,y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a((y * (x \ 1)) \ 1,z,u) = w
    ]]></literal>
    <justification jstring="[para(25182(a,1),11588(a,1))].">
      <j1 rule="para" parents="25182 11588"/>
    </justification>
  </clause>

  <clause id="25188">
    <literal><![CDATA[
      a(R(K(x,y) * z,u,w),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(L(z,u,w),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(25182(a,2),23976(a,1))].">
      <j1 rule="para" parents="25182 23976"/>
    </justification>
  </clause>

  <clause id="25189">
    <literal><![CDATA[
      a(L(L(x,y,x) \ z,x,u),w,v5) = a((x * u) \ (u * z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24952,a(flip),b,25183,a),flip(a)].">
      <j1 rule="hyper" parents="63 24952 25183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25190">
    <literal><![CDATA[
      a((x * y) \ L(x,y,y),z,u) = a(L(y \ 1,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3197(a,1),25183(a,1,1,2))].">
      <j1 rule="para" parents="3197 25183"/>
    </justification>
  </clause>

  <clause id="25191">
    <literal><![CDATA[
      a((x * y) \ (y * ((1 / x) * x)),z,u) = a(y \ (y / x),z,u)
    ]]></literal>
    <justification jstring="[para(3264(a,1),25183(a,2,1))].">
      <j1 rule="para" parents="3264 25183"/>
    </justification>
  </clause>

  <clause id="25192">
    <literal><![CDATA[
      a(L(x,y,z * (u \ 1)),w,v5) = a(L(x,y,z * u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,25182,a(flip),b,25185,a),flip(a)].">
      <j1 rule="hyper" parents="347 25182 25185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25193">
    <literal><![CDATA[
      a((x * y) \ L(x,y,y),z,u) = a(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,11580,a(flip),b,25190,a),flip(a)].">
      <j1 rule="hyper" parents="347 11580 25190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25195">
    <literal><![CDATA[
      a(R(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(L(x,y,z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(202(a,1),25188(a,1,1,1))].">
      <j1 rule="para" parents="202 25188"/>
    </justification>
  </clause>

  <clause id="25196">
    <literal><![CDATA[
      a((x * (y \ 1)) * y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(L(x,y,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(3665(a,1),25188(a,1,1))].">
      <j1 rule="para" parents="3665 25188"/>
    </justification>
  </clause>

  <clause id="25197">
    <literal><![CDATA[
      a(L(x,y,y) * y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(L(y * x,y,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(24823(a,1),25196(a,1))].">
      <j1 rule="para" parents="24823 25196"/>
    </justification>
  </clause>

  <clause id="25198">
    <literal><![CDATA[
      a(L(x \ y,x,y),z,u) = a((x * (y \ 1)) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(25186,a,23922,a),flip(a)].">
      <j1 rule="hyper" parents="25186 23922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25199">
    <literal><![CDATA[
      a((x * y) \ y,z,u) = a(y \ (y / x),z,u)
    ]]></literal>
    <justification jstring="[para(82(a,1),25191(a,1,1,2))].">
      <j1 rule="para" parents="82 25191"/>
    </justification>
  </clause>

  <clause id="25200">
    <literal><![CDATA[
      a((x * y) \ y,z,u) = a(y \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,23936,a(flip),b,25199,a),flip(a)].">
      <j1 rule="hyper" parents="347 23936 25199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25201">
    <literal><![CDATA[
      a((((x * y) / x) * T(x,y)) \ T(x,y),z,u) = a(T(x,y) \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(1254(a,1),25200(a,2,1,2))].">
      <j1 rule="para" parents="1254 25200"/>
    </justification>
  </clause>

  <clause id="25202">
    <literal><![CDATA[
      a((T(x,y) * y) \ T(x,y),z,u) = a(T(x,y) \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(4779(a,1),25201(a,1,1,1))].">
      <j1 rule="para" parents="4779 25201"/>
    </justification>
  </clause>

  <clause id="25203">
    <literal><![CDATA[
      a(T(x,y) \ (y \ x),z,u) = a((x * y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(13195(a,1),25202(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13195 25202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25204">
    <literal><![CDATA[
      a((x * y) \ x,z,u) = a(x \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(23959,a,25203,a),flip(a)].">
      <j1 rule="hyper" parents="23959 25203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25208">
    <literal><![CDATA[
      L(x,a(L(y,y,z),u,w),v5) = L(x,a(z \ (y \ z),u,w),v5)
    ]]></literal>
    <justification jstring="[para(25204(a,1),22771(a,2,2))].">
      <j1 rule="para" parents="25204 22771"/>
    </justification>
  </clause>

  <clause id="25209">
    <literal><![CDATA[
      a(x,(y * T(L(y,z,y) \ (L(y,z,y) / u),w)) * v5,v6) = a(x,v5 * (L(y,z,y) / u),v6)
    ]]></literal>
    <justification jstring="[hyper(24467,a,25173,a),flip(a)].">
      <j1 rule="hyper" parents="24467 25173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25211">
    <literal><![CDATA[
      a(x,(y * T(L(y,z,y) \ (L(y,z,y) / u),w)) * v5,v6) = a(x,v5 * (u \ L(y,z,y)),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,24043,a(flip),b,25209,a),flip(a)].">
      <j1 rule="hyper" parents="347 24043 25209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25212">
    <literal><![CDATA[
      a(x,(y * T(y \ (y / z),u)) * w,v5) = a(x,w * (z \ L(y,v6,y)),v5)
    ]]></literal>
    <justification jstring="[para(11410(a,1),25211(a,1,2,1,2,1))].">
      <j1 rule="para" parents="11410 25211"/>
    </justification>
  </clause>

  <clause id="25213">
    <literal><![CDATA[
      a(x,y * (z \ L(u,w,u)),v5) = a(x,y * (u * (u \ (u / z))),v5)
    ]]></literal>
    <justification jstring="[hyper(24477,a,25212,a),flip(a)].">
      <j1 rule="hyper" parents="24477 25212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25215">
    <literal><![CDATA[
      a(x,y * (z \ L(u,w,u)),v5) = a(x,y * (u / z),v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),25213(a,2,2,2))].">
      <j1 rule="para" parents="10 25213"/>
    </justification>
  </clause>

  <clause id="25216">
    <literal><![CDATA[
      a(x,y * (z \ L(u,w,u)),v5) = a(x,y * (z \ u),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24043,a(flip),b,25215,a),flip(a)].">
      <j1 rule="hyper" parents="347 24043 25215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25218">
    <literal><![CDATA[
      ((x * y) * (y \ L(y,z,u))) \ (K(x,y) * (L(y,z,u) * x)) = a(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(11020(a,1),25174(a,1,2,1))].">
      <j1 rule="para" parents="11020 25174"/>
    </justification>
  </clause>

  <clause id="25220">
    <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(20345(a,1),25218(a,1,2))].">
      <j1 rule="para" parents="20345 25218"/>
    </justification>
  </clause>

  <clause id="25221">
    <literal><![CDATA[
      (x * y) \ ((x * L(y,z,u)) / (y \ L(y,z,u))) = a(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3983,a(flip),b,25220,a)].">
      <j1 rule="hyper" parents="63 3983 25220"/>
    </justification>
  </clause>

  <clause id="25222">
    <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(20250(a,1),25221(a,1,2))].">
      <j1 rule="para" parents="20250 25221"/>
    </justification>
  </clause>

  <clause id="25223">
    <literal><![CDATA[
      (x * y) \ R(x / (1 / y),y,L(y,z,u)) = a(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(21387(a,1),25222(a,1,2))].">
      <j1 rule="para" parents="21387 25222"/>
    </justification>
  </clause>

  <clause id="25224">
    <literal><![CDATA[
      ((x * (1 / y)) * y) \ R(x,y,L(y,z,u)) = a(y,y * L(y,z,u),x * (1 / y))
    ]]></literal>
    <justification jstring="[para(11(a,1),25223(a,1,2,1))].">
      <j1 rule="para" parents="11 25223"/>
    </justification>
  </clause>

  <clause id="25225">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u * (1 / x)) = R(u,x,x) \ R(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(2259(a,1),25224(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2259 25224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25226">
    <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(14941,a,25225,a),flip(a)].">
      <j1 rule="hyper" parents="14941 25225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25227">
    <literal><![CDATA[
      R(x,y,y) \ R(x,y,L(y,z,u)) = a(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,25071,a(flip),b,25226,a),flip(a)].">
      <j1 rule="hyper" parents="347 25071 25226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25228">
    <literal><![CDATA[
      a(((x \ 1) * T(y,T(x \ K(z,u),w))) \ v5,v6,v7) = a((y * (x \ K(z,u))) \ v5,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(23959,a,24799,a),flip(a)].">
      <j1 rule="hyper" parents="23959 24799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25229">
    <literal><![CDATA[
      a((x * (y \ K(z,u))) \ w,v5,v6) = a(((y \ 1) * x) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(23973,a,25228,a),flip(a)].">
      <j1 rule="hyper" parents="23973 25228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25231">
    <literal><![CDATA[
      a(((x \ 1) * (x * y)) \ z,u,w) = a(R(y,x,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(6541(a,1),25229(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6541 25229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25232">
    <literal><![CDATA[
      a(R(x,y,y) \ z,u,w) = a(L(x,y,y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24701,a(flip),b,25231,a),flip(a)].">
      <j1 rule="hyper" parents="63 24701 25231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25233">
    <literal><![CDATA[
      a(x,(T(y,z) * L(u,1 / T(y,z),1 / T(y,z))) \ w,v5) = a(x,(y * ((y \ 1) * ((1 / T(y,z)) * u))) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24515,a(flip),b,24698,a),flip(a)].">
      <j1 rule="hyper" parents="347 24515 24698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25234">
    <literal><![CDATA[
      a(x,y,R(z,T(u,w),T(v5,u * z)) * v6) = a(x,y,((u * T(v5,u * z)) \ (v5 * (u * z))) * v6)
    ]]></literal>
    <justification jstring="[para(20701(a,1),24887(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="20701 24887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25235">
    <literal><![CDATA[
      a(x,y,R(z,T(u,w),T(v5,u * z)) * v6) = a(x,y,((u * v5) \ (v5 * (u * z))) * v6)
    ]]></literal>
    <justification jstring="[hyper(24199,a,25234,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="24199 25234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25237">
    <literal><![CDATA[
      a(x,y,R(z,T(u,w),T(v5,u * z)) * v6) = a(x,y,L(K(v5,u) * z,u,v5) * v6)
    ]]></literal>
    <justification jstring="[para(10173(a,1),25235(a,2,3,1))].">
      <j1 rule="para" parents="10173 25235"/>
    </justification>
  </clause>

  <clause id="25238">
    <literal><![CDATA[
      a(x,y,R(z,T(u,w),T(v5,u * z)) * v6) = a(x,y,K(v5,u) * (L(z,u,v5) * v6))
    ]]></literal>
    <justification jstring="[para(21271(a,1),25237(a,2,3))].">
      <j1 rule="para" parents="21271 25237"/>
    </justification>
  </clause>

  <clause id="25239">
    <literal><![CDATA[
      a(x,y,R(z,T(u,w),T(v5,u * z)) * v6) = a(x,y,L(z,u,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,24036,a(flip),b,25238,a),flip(a)].">
      <j1 rule="hyper" parents="347 24036 25238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25241">
    <literal><![CDATA[
      a(x,y,R(z,T(u,w),v5) * v6) = a(x,y,L(z,u,v5) * v6)
    ]]></literal>
    <justification jstring="[para(20040(a,1),25239(a,1,3,1))].">
      <j1 rule="para" parents="20040 25239"/>
    </justification>
  </clause>

  <clause id="25242">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * v5) = a(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(110(a,1),25241(a,1,3,1,2))].">
      <j1 rule="para" parents="110 25241"/>
    </justification>
  </clause>

  <clause id="25244">
    <literal><![CDATA[
      a(x,y,L(z / u,u,u) * w) = a(x,y,(z * (u \ 1)) * w)
    ]]></literal>
    <justification jstring="[para(785(a,1),25242(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="785 25242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25245">
    <literal><![CDATA[
      a(x,y,L(R(z,u,w),v5,v6) * (u * w)) = a(x,y,(R(z,v5,v6) * u) * w)
    ]]></literal>
    <justification jstring="[para(469(a,1),25242(a,1,3)),flip(a)].">
      <j1 rule="para" parents="469 25242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25246">
    <literal><![CDATA[
      a(x,y,T(z * R(u,w,v5),K(R(u,w,v5),v6))) = a(x,y,L(u,w,v5) * T(z,T(R(u,w,v5),v6)))
    ]]></literal>
    <justification jstring="[para(6060(a,2),25242(a,1,3))].">
      <j1 rule="para" parents="6060 25242"/>
    </justification>
  </clause>

  <clause id="25247">
    <literal><![CDATA[
      a(x,y,L(z / u,u,u) * w) = a(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24333,a(flip),b,25244,a),flip(a)].">
      <j1 rule="hyper" parents="347 24333 25244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25248">
    <literal><![CDATA[
      a(x,y,((z * u) * u) * w) = a(x,y,L(z,u,u) * w)
    ]]></literal>
    <justification jstring="[para(11(a,1),25247(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="11 25247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25249">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * u)) = a(x,y,L(w,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(24627,a,25248,a)].">
      <j1 rule="hyper" parents="24627 25248"/>
    </justification>
  </clause>

  <clause id="25250">
    <literal><![CDATA[
      a(x,y,L(z,u * z,u * z)) = a(x,y,L(u,z,z) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(24601,a,25248,a)].">
      <j1 rule="hyper" parents="24601 25248"/>
    </justification>
  </clause>

  <clause id="25251">
    <literal><![CDATA[
      a(x,y,z * (u * (w * u))) = a(x,y,L(w,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(24297,a,25248,a)].">
      <j1 rule="hyper" parents="24297 25248"/>
    </justification>
  </clause>

  <clause id="25252">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * w)) = a(x,y,L(u,w,w) * z)
    ]]></literal>
    <justification jstring="[hyper(24180,a,25248,a)].">
      <j1 rule="hyper" parents="24180 25248"/>
    </justification>
  </clause>

  <clause id="25253">
    <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(25248(a,1),24180(a,1))].">
      <j1 rule="para" parents="25248 24180"/>
    </justification>
  </clause>

  <clause id="25254">
    <literal><![CDATA[
      a(x,y,L(z,u,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w * ((u * z) * u)) = v5
    ]]></literal>
    <justification jstring="[para(25248(a,1),24627(a,1))].">
      <j1 rule="para" parents="25248 24627"/>
    </justification>
  </clause>

  <clause id="25255">
    <literal><![CDATA[
      a(x,y,L(z * u,z,z)) = a(x,y,L(u,z,z) * z)
    ]]></literal>
    <justification jstring="[hyper(24599,a,25249,a)].">
      <j1 rule="hyper" parents="24599 25249"/>
    </justification>
  </clause>

  <clause id="25256">
    <literal><![CDATA[
      a(x,y,L(z * u,z,z)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(24554,a,25255,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="24554 25255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25257">
    <literal><![CDATA[
      a(x,y,L(z * u,z,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ u) = w
    ]]></literal>
    <justification jstring="[para(25255(a,2),24554(a,1))].">
      <j1 rule="para" parents="25255 24554"/>
    </justification>
  </clause>

  <clause id="25258">
    <literal><![CDATA[
      a(x,y,L(z * u,u,u)) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(24204,a,25256,a)].">
      <j1 rule="hyper" parents="24204 25256"/>
    </justification>
  </clause>

  <clause id="25259">
    <literal><![CDATA[
      a(x,y,L(z * u,u,z)) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,24909,a,b,25256,a)].">
      <j1 rule="hyper" parents="63 24909 25256"/>
    </justification>
  </clause>

  <clause id="25260">
    <literal><![CDATA[
      a(x,y,L(z * u,z,u)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,24908,a,b,25256,a)].">
      <j1 rule="hyper" parents="63 24908 25256"/>
    </justification>
  </clause>

  <clause id="25261">
    <literal><![CDATA[
      a(x,y,z \ (z \ u)) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),25256(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 25256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25262">
    <literal><![CDATA[
      x * a(y,z,L(u * w,w,w)) = x * a(y,z,w \ u)
    ]]></literal>
    <justification jstring="[hyper(134,a,25258,a,b,9,a)].">
      <j1 rule="hyper" parents="134 25258 9"/>
    </justification>
  </clause>

  <clause id="25263">
    <literal><![CDATA[
      a(x,y,z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z * u,z,u)) = w
    ]]></literal>
    <justification jstring="[para(25259(a,1),24204(a,1))].">
      <j1 rule="para" parents="25259 24204"/>
    </justification>
  </clause>

  <clause id="25264">
    <literal><![CDATA[
      a(x,y,L(z * u,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(24120(a,1),25257(a,1))].">
      <j1 rule="para" parents="24120 25257"/>
    </justification>
  </clause>

  <clause id="25265">
    <literal><![CDATA[
      a(x,y,L(z * u,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(24909(a,2),25257(a,1))].">
      <j1 rule="para" parents="24909 25257"/>
    </justification>
  </clause>

  <clause id="25266">
    <literal><![CDATA[
      a(x,y,a(z,u,z * u)) = a(x,y,L(z,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(14944,a,25251,a)].">
      <j1 rule="hyper" parents="14944 25251"/>
    </justification>
  </clause>

  <clause id="25267">
    <literal><![CDATA[
      a(x,y,a(z,u,z * u)) = a(x,y,z * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,24069,a,b,25266,a),flip(a)].">
      <j1 rule="hyper" parents="347 24069 25266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25268">
    <literal><![CDATA[
      a(x,y,a(z,u,z * u)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,15020,a(flip),b,25267,a),flip(a)].">
      <j1 rule="hyper" parents="347 15020 25267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25269">
    <literal><![CDATA[
      a(x,y,a(z,u,u * z)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(18773(a,1),25268(a,1,3))].">
      <j1 rule="para" parents="18773 25268"/>
    </justification>
  </clause>

  <clause id="25270">
    <literal><![CDATA[
      a(x,y,a(z,u * z,L(u,z,z))) = a(x,y,a(u * z,u * z,z))
    ]]></literal>
    <justification jstring="[para(24286(a,1),25268(a,1,3))].">
      <j1 rule="para" parents="24286 25268"/>
    </justification>
  </clause>

  <clause id="25271">
    <literal><![CDATA[
      a(x,y,a(z * u,z,u)) = a(x,y,L(u,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,24641,a(flip),b,25252,a)].">
      <j1 rule="hyper" parents="63 24641 25252"/>
    </justification>
  </clause>

  <clause id="25272">
    <literal><![CDATA[
      a(x,y,a(z * u,z,u)) = a(x,y,u * L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,24069,a,b,25271,a),flip(a)].">
      <j1 rule="hyper" parents="347 24069 25271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25273">
    <literal><![CDATA[
      a(x,y,a(z * u,z,u)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,15020,a(flip),b,25272,a),flip(a)].">
      <j1 rule="hyper" parents="347 15020 25272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25274">
    <literal><![CDATA[
      a(x,y,a(z * u,u,z)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(18294(a,2),25273(a,1,3))].">
      <j1 rule="para" parents="18294 25273"/>
    </justification>
  </clause>

  <clause id="25275">
    <literal><![CDATA[
      a(x,y,L(z,u * z,u * z)) = a(x,y,u * (L(u,z,z) * z))
    ]]></literal>
    <justification jstring="[para(1401(a,1),25250(a,2,3))].">
      <j1 rule="para" parents="1401 25250"/>
    </justification>
  </clause>

  <clause id="25276">
    <literal><![CDATA[
      a(x,y,L(z,u * z,u * z)) = a(x,y,u * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,24929,a(flip),b,25275,a),flip(a)].">
      <j1 rule="hyper" parents="347 24929 25275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25277">
    <literal><![CDATA[
      a(x,y,L(z,u * ((w * w) * z),u * ((w * w) * z))) = a(x,y,u * (((w * w) * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(15007,a,25276,a)].">
      <j1 rule="hyper" parents="15007 25276"/>
    </justification>
  </clause>

  <clause id="25278">
    <literal><![CDATA[
      x * (a(y,z,L(x,u * x,u * x)) * w) = a(y,z,u * (x \ u)) * (x * w)
    ]]></literal>
    <justification jstring="[para(25276(a,1),23262(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25276 23262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25279">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) * v5) * v6) = a(x,y,(L(z,u,w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(471(a,1),25245(a,1,3)),flip(a)].">
      <j1 rule="para" parents="471 25245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25280">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) * v5) * v6) = a(x,y,(v5 * L(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,24084,a,b,25279,a),flip(a)].">
      <j1 rule="hyper" parents="347 24084 25279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25281">
    <literal><![CDATA[
      a(x,y,(z * R(u,w,v5)) * v6) = a(x,y,(z * L(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(24192,a,25280,a)].">
      <j1 rule="hyper" parents="24192 25280"/>
    </justification>
  </clause>

  <clause id="25282">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) * v5) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * v5) * v6) = v7
    ]]></literal>
    <justification jstring="[para(25280(a,2),24192(a,1))].">
      <j1 rule="para" parents="25280 24192"/>
    </justification>
  </clause>

  <clause id="25283">
    <literal><![CDATA[
      a(x,y,z * (T(u,w) * L(v5,v6,v7))) = a(x,y,(u * R(v5,v6,v7)) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,24365,a,b,25281,a)].">
      <j1 rule="hyper" parents="347 24365 25281"/>
    </justification>
  </clause>

  <clause id="25284">
    <literal><![CDATA[
      a(x,y,(z * L(u,w,v5)) * L(v6,v6,z * R(u,w,v5))) = a(x,y,(z * R(u,w,v5)) / (v6 \ 1))
    ]]></literal>
    <justification jstring="[para(2008(a,1),25281(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2008 25281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25285">
    <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(25283(a,1),24447(a,1))].">
      <j1 rule="para" parents="25283 24447"/>
    </justification>
  </clause>

  <clause id="25286">
    <literal><![CDATA[
      a(x,y,z * (u \ z)) * (u * w) = u * (a(x,y,z * (u \ z)) * w)
    ]]></literal>
    <justification jstring="[para(25276(a,1),25278(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="25276 25278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25287">
    <literal><![CDATA[
      a(x,y,z * (u \ z)) * (u * w) != v5
    ]]></literal>
    <literal><![CDATA[
      u * (w * a(x,y,z * (u \ z))) = v5
    ]]></literal>
    <justification jstring="[para(25286(a,2),20023(a,1))].">
      <j1 rule="para" parents="25286 20023"/>
    </justification>
  </clause>

  <clause id="25288">
    <literal><![CDATA[
      a(x,y,L(z,z * u,u * ((w * w) * z))) = a(x,y,u * (((w * w) * z) \ u))
    ]]></literal>
    <justification jstring="[para(21697(a,1),25277(a,1,3))].">
      <j1 rule="para" parents="21697 25277"/>
    </justification>
  </clause>

  <clause id="25289">
    <literal><![CDATA[
      a(x,y,L(z,z * u,z * u)) = a(x,y,u * (((w * w) * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,24910,a(flip),b,25288,a)].">
      <j1 rule="hyper" parents="63 24910 25288"/>
    </justification>
  </clause>

  <clause id="25291">
    <literal><![CDATA[
      a(x,y,L(z,z * u,z * u)) = a(x,y,u * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,24872,a(flip),b,25289,a),flip(a)].">
      <j1 rule="hyper" parents="347 24872 25289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25293">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * T(v5,T(R(z,u,w),v6))) = a(x,y,v5 * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(24178,a,25246,a),flip(a)].">
      <j1 rule="hyper" parents="24178 25246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25295">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * T(v5,R(T(z,v6),u,w))) = a(x,y,v5 * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(27(a,2),25293(a,1,3,2,2))].">
      <j1 rule="para" parents="27 25293"/>
    </justification>
  </clause>

  <clause id="25296">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * T(v5,T(z,v6))) = a(x,y,v5 * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(19951(a,1),25295(a,1,3,2))].">
      <j1 rule="para" parents="19951 25295"/>
    </justification>
  </clause>

  <clause id="25298">
    <literal><![CDATA[
      a(x,y,T(z * L(u,w,v5),K(u,v6))) = a(x,y,z * R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(21356(a,2),25296(a,1,3))].">
      <j1 rule="para" parents="21356 25296"/>
    </justification>
  </clause>

  <clause id="25299">
    <literal><![CDATA[
      a(x,y,z * R(u,w,v5)) = a(x,y,z * L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(24178,a,25298,a),flip(a)].">
      <j1 rule="hyper" parents="24178 25298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25301">
    <literal><![CDATA[
      a(x,y,z * L((z \ 1) \ (z \ u),w,v5)) = a(x,y,z \ R(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,24329,a(flip),b,25299,a),flip(a)].">
      <j1 rule="hyper" parents="63 24329 25299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25302">
    <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),25299(a,2,3,2))].">
      <j1 rule="para" parents="30 25299"/>
    </justification>
  </clause>

  <clause id="25303">
    <literal><![CDATA[
      x * a(R(y,z,u),R(y,z,u),x * L(y,z,u)) = R(y,z,u) \ ((R(y,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(25299(a,1),19767(a,1,2))].">
      <j1 rule="para" parents="25299 19767"/>
    </justification>
  </clause>

  <clause id="25304">
    <literal><![CDATA[
      a(x,y,z * R(K(u,T(w,v5)) / v6,v6,v5)) = a(x,y,z * (v5 \ (K(u,w) * (v5 / v6))))
    ]]></literal>
    <justification jstring="[para(21293(a,1),25299(a,2,3,2))].">
      <j1 rule="para" parents="21293 25299"/>
    </justification>
  </clause>

  <clause id="25305">
    <literal><![CDATA[
      L(x,y,(z \ a(z,z,u * L(w,v5,v6))) * (u * L(w,v5,v6))) = L(x,y,z \ (u * R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(25299(a,1),22874(a,1,3,1,2))].">
      <j1 rule="para" parents="25299 22874"/>
    </justification>
  </clause>

  <clause id="25306">
    <literal><![CDATA[
      a(x,y,z * L(z \ (z \ u),w,v5)) = a(x,y,z \ R(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,24335,a(flip),b,25301,a)].">
      <j1 rule="hyper" parents="63 24335 25301"/>
    </justification>
  </clause>

  <clause id="25307">
    <literal><![CDATA[
      a(x,y,z \ R(u,w,v5)) = a(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(3341(a,1),25306(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3341 25306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25308">
    <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),25307(a,2,3,2))].">
      <j1 rule="para" parents="30 25307"/>
    </justification>
  </clause>

  <clause id="25309">
    <literal><![CDATA[
      a(x,y,z * L(R(u,w,v5),v6,v7)) = a(x,y,z * L(L(u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(29(a,1),25302(a,1,3,2))].">
      <j1 rule="para" parents="29 25302"/>
    </justification>
  </clause>

  <clause id="25310">
    <literal><![CDATA[
      a(x,y,z \ L(R(u,w,v5),v6,v7)) = a(x,y,z \ L(L(u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(29(a,1),25308(a,1,3,2))].">
      <j1 rule="para" parents="29 25308"/>
    </justification>
  </clause>

  <clause id="25311">
    <literal><![CDATA[
      a(x,y,(z * u) * L(R(w,v5,v6),u,z)) = a(x,y,z * (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(97(a,1),25309(a,2,3))].">
      <j1 rule="para" parents="97 25309"/>
    </justification>
  </clause>

  <clause id="25312">
    <literal><![CDATA[
      a(x,y,z * L(L(u,w,v5),R(u,w,v5),z)) = a(x,y,z / (R(u,w,v5) \ 1))
    ]]></literal>
    <justification jstring="[para(2008(a,1),25309(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2008 25309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25313">
    <literal><![CDATA[
      a(x,y,z * (u * R(w,v5,v6))) = a(x,y,z * (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(97(a,1),25311(a,1,3))].">
      <j1 rule="para" parents="97 25311"/>
    </justification>
  </clause>

  <clause id="25314">
    <literal><![CDATA[
      a(x,y,z * (((u \ 1) * (u * w)) * u)) = a(x,y,z * (u * L(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(24626,a,25313,a)].">
      <j1 rule="hyper" parents="24626 25313"/>
    </justification>
  </clause>

  <clause id="25315">
    <literal><![CDATA[
      a(x,y,L(z,u * R(w,v5,v6),u * R(w,v5,v6)) * (u * L(w,v5,v6))) = a(x,y,(u * R(w,v5,v6)) \ z)
    ]]></literal>
    <justification jstring="[hyper(24554,a,25313,a),flip(a)].">
      <j1 rule="hyper" parents="24554 25313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25316">
    <literal><![CDATA[
      a(x,y,z * (((u * u) * w) * L(v5,u,u))) = a(x,y,z * (((v5 * u) * u) * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,24287,a(flip),b,25313,a),flip(a)].">
      <j1 rule="hyper" parents="63 24287 25313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25317">
    <literal><![CDATA[
      a(x,y,z * L(u * w,w,w)) = a(x,y,z * (w * L(u,w,w)))
    ]]></literal>
    <justification jstring="[para(3217(a,1),25314(a,1,3,2))].">
      <j1 rule="para" parents="3217 25314"/>
    </justification>
  </clause>

  <clause id="25318">
    <literal><![CDATA[
      a(x,y,z * L(u * w,w,w)) = a(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,24931,a(flip),b,25317,a),flip(a)].">
      <j1 rule="hyper" parents="347 24931 25317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25319">
    <literal><![CDATA[
      a(x,y,z * L((u \ (z \ 1)) * u,u,u)) = a(x,y,(z * u) \ L(z * u,u,u))
    ]]></literal>
    <justification jstring="[para(3355(a,1),25317(a,2,3))].">
      <j1 rule="para" parents="3355 25317"/>
    </justification>
  </clause>

  <clause id="25320">
    <literal><![CDATA[
      a(x,y,L(z * u,u,u) * w) = a(x,y,w * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(24180,a,25318,a)].">
      <j1 rule="hyper" parents="24180 25318"/>
    </justification>
  </clause>

  <clause id="25321">
    <literal><![CDATA[
      a(x,y,z * L(u * w,u,u)) = a(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(24567,a,25320,a)].">
      <j1 rule="hyper" parents="24567 25320"/>
    </justification>
  </clause>

  <clause id="25322">
    <literal><![CDATA[
      a(x,y,z * L(L(u,w,v5),R(u,w,v5),z)) = a(x,y,(R(u,w,v5) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,24071,a(flip),b,25312,a),flip(a)].">
      <j1 rule="hyper" parents="347 24071 25312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25323">
    <literal><![CDATA[
      a(x,y,z * L(L(u,w,v5),R(u,w,v5),z)) = a(x,y,R(u,w,v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,14957,a(flip),b,25322,a),flip(a)].">
      <j1 rule="hyper" parents="347 14957 25322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25324">
    <literal><![CDATA[
      a(x,y,z * L(L(u,w,v5),L(u,w,v5),z)) = a(x,y,R(u,w,v5) \ z)
    ]]></literal>
    <justification jstring="[para(21974(a,1),25323(a,1,3,2))].">
      <j1 rule="para" parents="21974 25323"/>
    </justification>
  </clause>

  <clause id="25325">
    <literal><![CDATA[
      a(x,y,z / (L(u,w,v5) \ 1)) = a(x,y,R(u,w,v5) \ z)
    ]]></literal>
    <justification jstring="[para(2008(a,1),25324(a,1,3))].">
      <j1 rule="para" parents="2008 25324"/>
    </justification>
  </clause>

  <clause id="25326">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) \ 1) \ v5) = a(x,y,R(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(24181,a,25325,a)].">
      <j1 rule="hyper" parents="24181 25325"/>
    </justification>
  </clause>

  <clause id="25327">
    <literal><![CDATA[
      a(x,y,R(z,u,w) \ v5) = a(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(15003,a,25326,a),flip(a)].">
      <j1 rule="hyper" parents="15003 25326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25328">
    <literal><![CDATA[
      a(x,y,R(z,u,w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(25326(a,1),15003(a,1))].">
      <j1 rule="para" parents="25326 15003"/>
    </justification>
  </clause>

  <clause id="25329">
    <literal><![CDATA[
      a(x,y,L(z,u,w \ 1) \ v5) = a(x,y,R(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(2190(a,1),25327(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="2190 25327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25330">
    <literal><![CDATA[
      a(x,y,L(z,u,w \ 1) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(25329(a,2),25328(a,1))].">
      <j1 rule="para" parents="25329 25328"/>
    </justification>
  </clause>

  <clause id="25331">
    <literal><![CDATA[
      a(x,y,z * (((u * w) * w) * v5)) = a(x,y,z * (L(u,w,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,24877,a(flip),b,25316,a),flip(a)].">
      <j1 rule="hyper" parents="63 24877 25316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25333">
    <literal><![CDATA[
      a(x,y,z * (L(u / w,w,w) * v5)) = a(x,y,z * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[para(12(a,1),25331(a,1,3,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 25331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25334">
    <literal><![CDATA[
      a(x,y,z * L((u \ (z \ 1)) * u,u,u)) = a(x,y,a(u,u,u * z) \ 1)
    ]]></literal>
    <justification jstring="[para(14643(a,1),25319(a,2,3))].">
      <j1 rule="para" parents="14643 25319"/>
    </justification>
  </clause>

  <clause id="25335">
    <literal><![CDATA[
      a(x,y,z * L((u \ (z \ 1)) * u,u,u)) = a(x,y,a(u,u,u * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,14922,a(flip),b,25334,a),flip(a)].">
      <j1 rule="hyper" parents="347 14922 25334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25336">
    <literal><![CDATA[
      a(x,y,a(z,z,z * u)) = a(x,y,u * (((z \ 1) * (u \ 1)) * z))
    ]]></literal>
    <justification jstring="[para(3291(a,1),25335(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3291 25335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25337">
    <literal><![CDATA[
      a(x,y,a(z,z,z * u)) = a(x,y,u * (((z \ 1) * u) * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,25080,a(flip),b,25336,a),flip(a)].">
      <j1 rule="hyper" parents="347 25080 25336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25338">
    <literal><![CDATA[
      a(x,y,a(z,z,z * u)) = a(x,y,u * ((u * z) * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,25079,a(flip),b,25337,a),flip(a)].">
      <j1 rule="hyper" parents="347 25079 25337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25339">
    <literal><![CDATA[
      a(x,y,a(z,z,z * u)) = a(x,y,L(u,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,25252,a(flip),b,25338,a),flip(a)].">
      <j1 rule="hyper" parents="347 25252 25338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25340">
    <literal><![CDATA[
      a(x,y,a(z,z,z * u)) = a(x,y,u * L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,24069,a,b,25339,a),flip(a)].">
      <j1 rule="hyper" parents="347 24069 25339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25341">
    <literal><![CDATA[
      a(x,y,a(z,z,z * u)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,15020,a(flip),b,25340,a),flip(a)].">
      <j1 rule="hyper" parents="347 15020 25340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25342">
    <literal><![CDATA[
      a(x,y,a(z,z,u * z)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(14642(a,1),25341(a,1,3))].">
      <j1 rule="para" parents="14642 25341"/>
    </justification>
  </clause>

  <clause id="25343">
    <literal><![CDATA[
      a(x,y,z * (u / (w * (u * K(v5,v6))))) = a(x,y,z * (u \ (K(v6,v5) * (u / w))))
    ]]></literal>
    <justification jstring="[para(21167(a,1),25304(a,1,3,2))].">
      <j1 rule="para" parents="21167 25304"/>
    </justification>
  </clause>

  <clause id="25344">
    <literal><![CDATA[
      a(x,y,z * ((u * (w * K(v5,v6))) \ w)) = a(x,y,z * (w \ (K(v6,v5) * (w / u))))
    ]]></literal>
    <justification jstring="[hyper(24209,a,25343,a)].">
      <j1 rule="hyper" parents="24209 25343"/>
    </justification>
  </clause>

  <clause id="25345">
    <literal><![CDATA[
      a(x,y,z * (u \ (K(w,v5) * (u / v6)))) = a(x,y,z * (K(w,v5) * ((v6 * u) \ u)))
    ]]></literal>
    <justification jstring="[para(20837(a,1),25344(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="20837 25344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25346">
    <literal><![CDATA[
      a(x,y,z * (u \ (K(w,v5) * (u / v6)))) = a(x,y,z * ((v6 * u) \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,24078,a(flip),b,25345,a),flip(a)].">
      <j1 rule="hyper" parents="347 24078 25345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25347">
    <literal><![CDATA[
      a(x,y,z \ (K(u,w) * (z / v5))) = a(x,y,K(v6,v7) * ((v5 * z) \ z))
    ]]></literal>
    <justification jstring="[hyper(24169,a,25346,a)].">
      <j1 rule="hyper" parents="24169 25346"/>
    </justification>
  </clause>

  <clause id="25349">
    <literal><![CDATA[
      a(x,y,z \ (K(u,w) * (z / v5))) = a(x,y,(v5 * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,24036,a(flip),b,25347,a),flip(a)].">
      <j1 rule="hyper" parents="347 24036 25347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25350">
    <literal><![CDATA[
      a(x,y,(z * u) \ u) = a(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[para(5027(a,1),25349(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5027 25349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25351">
    <literal><![CDATA[
      a(x,y,(z * u) \ z) = a(x,y,z \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(24191,a,25350,a)].">
      <j1 rule="hyper" parents="24191 25350"/>
    </justification>
  </clause>

  <clause id="25352">
    <literal><![CDATA[
      a(x,y,((z * (u \ 1)) * z) \ z) = a(x,y,z \ L(u,u,u \ z))
    ]]></literal>
    <justification jstring="[para(10154(a,2),25350(a,2,3,2))].">
      <j1 rule="para" parents="10154 25350"/>
    </justification>
  </clause>

  <clause id="25353">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,u) \ u) = a(x,y,u \ L(z,z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,24512,a(flip),b,25352,a)].">
      <j1 rule="hyper" parents="63 24512 25352"/>
    </justification>
  </clause>

  <clause id="25354">
    <literal><![CDATA[
      a(x,y,L(z,u,u) \ u) = a(x,y,u \ L(z,z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(15008,a,25353,a)].">
      <j1 rule="hyper" parents="15008 25353"/>
    </justification>
  </clause>

  <clause id="25355">
    <literal><![CDATA[
      a(x,y,L(z,u,u) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u \ L(z,z,u)) = w
    ]]></literal>
    <justification jstring="[para(25354(a,2),24616(a,1))].">
      <j1 rule="para" parents="25354 24616"/>
    </justification>
  </clause>

  <clause id="25356">
    <literal><![CDATA[
      x * a(R(y,z,u),L(y,z,u),x * L(y,z,u)) = R(y,z,u) \ ((R(y,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(24805(a,1),25303(a,1,2))].">
      <j1 rule="para" parents="24805 25303"/>
    </justification>
  </clause>

  <clause id="25357">
    <literal><![CDATA[
      x * a(L(y,z,u),L(y,z,u),x * L(y,z,u)) = R(y,z,u) \ ((R(y,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(25182(a,1),25356(a,1,2))].">
      <j1 rule="para" parents="25182 25356"/>
    </justification>
  </clause>

  <clause id="25358">
    <literal><![CDATA[
      a(x,y,(z * L(u,w,v5)) * L(v6,v6,z * R(u,w,v5))) = a(x,y,(v6 \ 1) \ (z * R(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(347,a,24071,a(flip),b,25284,a),flip(a)].">
      <j1 rule="hyper" parents="347 24071 25284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25359">
    <literal><![CDATA[
      L(x,y,z \ (u * R(w,v5,v6))) = L(x,y,z \ (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(18983(a,1),25305(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18983 25305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25360">
    <literal><![CDATA[
      L(x,y,((z * u) * w) \ ((z * u) * L(w,z,u))) = L(x,y,a(w,z,u))
    ]]></literal>
    <justification jstring="[para(14246(a,2),25359(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14246 25359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25361">
    <literal><![CDATA[
      L(x,y,z \ ((u \ a(u,u,R(w,v5,v6))) * L(w,v5,v6))) = L(x,y,z \ (u \ R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(18983(a,1),25359(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="18983 25359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25362">
    <literal><![CDATA[
      L(x,y,((z * u) * w) \ (u * (T(z,u) * w))) = L(x,y,a(w,z,u))
    ]]></literal>
    <justification jstring="[para(10150(a,1),25360(a,1,3,2))].">
      <j1 rule="para" parents="10150 25360"/>
    </justification>
  </clause>

  <clause id="25363">
    <literal><![CDATA[
      L(x,y,(z * u) \ ((z * (u * w)) / w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(21393(a,1),25362(a,1,3))].">
      <j1 rule="para" parents="21393 25362"/>
    </justification>
  </clause>

  <clause id="25365">
    <literal><![CDATA[
      L(x,y,a(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,10546,a(flip),b,25363,a),flip(a)].">
      <j1 rule="hyper" parents="63 10546 25363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25366">
    <literal><![CDATA[
      R(x,y,a(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(23257,a,25365,a)].">
      <j1 rule="hyper" parents="23257 25365"/>
    </justification>
  </clause>

  <clause id="25367">
    <literal><![CDATA[
      L(x * y,z,a(x,y,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(63,a,23287,a(flip),b,25365,a)].">
      <j1 rule="hyper" parents="63 23287 25365"/>
    </justification>
  </clause>

  <clause id="25368">
    <literal><![CDATA[
      L(x \ 1,y,a(x,z,u)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,23259,a(flip),b,25365,a)].">
      <j1 rule="hyper" parents="63 23259 25365"/>
    </justification>
  </clause>

  <clause id="25369">
    <literal><![CDATA[
      (a(x,y,z) * u) * x = a(x,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[hyper(134,a,25365,a(flip),b,4048,a(flip))].">
      <j1 rule="hyper" parents="134 25365 4048"/>
    </justification>
  </clause>

  <clause id="25370">
    <literal><![CDATA[
      x / (a(x,y,z) \ 1) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,25365,a(flip),b,15418,a)].">
      <j1 rule="hyper" parents="131 25365 15418"/>
    </justification>
  </clause>

  <clause id="25371">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * x = a(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,25365,a(flip),b,3197,a),flip(a)].">
      <j1 rule="hyper" parents="128 25365 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25372">
    <literal><![CDATA[
      L(R(x,y,z),u,a(x,w,v5)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(25365(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25365 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25373">
    <literal><![CDATA[
      a(x,y,z) \ (u * x) = (a(x,y,z) \ u) * x
    ]]></literal>
    <justification jstring="[para(25365(a,1),538(a,1,2,2))].">
      <j1 rule="para" parents="25365 538"/>
    </justification>
  </clause>

  <clause id="25374">
    <literal><![CDATA[
      (a(x,y,z) * u) * L(x,w,v5) = a(x,y,z) * (u * L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(25365(a,1),474(a,1,2,1))].">
      <j1 rule="para" parents="25365 474"/>
    </justification>
  </clause>

  <clause id="25375">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,a(x,w,v5)) = x \ L(L(x,u,a(x,w,v5)),y,z)
    ]]></literal>
    <justification jstring="[para(25365(a,1),4638(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25365 4638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25376">
    <literal><![CDATA[
      (x * y) * a(x,z,u) = x * (a(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(25365(a,1),23239(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25365 23239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25377">
    <literal><![CDATA[
      a(x,y,z) * (x * u) = x * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(25365(a,1),23242(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25365 23242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25378">
    <literal><![CDATA[
      x \ (y * a(x,z,u)) = (x \ y) * a(x,z,u)
    ]]></literal>
    <justification jstring="[para(25365(a,1),23246(a,1,1))].">
      <j1 rule="para" parents="25365 23246"/>
    </justification>
  </clause>

  <clause id="25380">
    <literal><![CDATA[
      a(x,y,y) \ (z * (x * y)) != u
    ]]></literal>
    <literal><![CDATA[
      (a(x,y,y) \ z) * (x * y) = u
    ]]></literal>
    <justification jstring="[para(25367(a,1),876(a,1,2,2))].">
      <j1 rule="para" parents="25367 876"/>
    </justification>
  </clause>

  <clause id="25381">
    <literal><![CDATA[
      T(a(x,y,y) * (z / (x * y)),x * y) = (x * y) \ (a(x,y,y) * z)
    ]]></literal>
    <justification jstring="[para(25367(a,1),13764(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25367 13764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25383">
    <literal><![CDATA[
      L(L(x \ 1,y,z),u,a(x,w,v5)) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(25368(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25368 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25384">
    <literal><![CDATA[
      a(x,y,z) * ((x \ 1) * u) = (x \ 1) * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(25368(a,1),23242(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25368 23242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25385">
    <literal><![CDATA[
      (x \ 1) \ (y * a(x,z,u)) = ((x \ 1) \ y) * a(x,z,u)
    ]]></literal>
    <justification jstring="[para(25368(a,1),23246(a,1,1))].">
      <j1 rule="para" parents="25368 23246"/>
    </justification>
  </clause>

  <clause id="25386">
    <literal><![CDATA[
      x * (a(x,y,z) \ 1) = a(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(20232,a,25371,a)].">
      <j1 rule="hyper" parents="20232 25371"/>
    </justification>
  </clause>

  <clause id="25387">
    <literal><![CDATA[
      T(a(x,y,z) * (u / R(x,w,v5)),R(x,w,v5)) = R(x,w,v5) \ (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(25372(a,1),13764(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25372 13764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25388">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * a(x,u,w) = R(x,y,z) \ a(x,u,w)
    ]]></literal>
    <justification jstring="[para(25372(a,1),23153(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25372 23153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25389">
    <literal><![CDATA[
      R(x,y,(a(z,u,w) \ z) * v5) = R(x,y,(z * a(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(25386(a,1),22148(a,1,3,1))].">
      <j1 rule="para" parents="25386 22148"/>
    </justification>
  </clause>

  <clause id="25390">
    <literal><![CDATA[
      L(a(x,y,z),u,x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(23110,a,25369,a)].">
      <j1 rule="hyper" parents="23110 25369"/>
    </justification>
  </clause>

  <clause id="25391">
    <literal><![CDATA[
      L(L(x \ 1,x,y),y * x,a(x,z,u)) = ((a(x,z,u) * y) * x) \ (a(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(25369(a,2),446(a,2,1))].">
      <j1 rule="para" parents="25369 446"/>
    </justification>
  </clause>

  <clause id="25392">
    <literal><![CDATA[
      (a(x,y,z) * (u * x)) / (a(x,y,z) * x) = L(u,a(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(25369(a,1),23232(a,1,1))].">
      <j1 rule="para" parents="25369 23232"/>
    </justification>
  </clause>

  <clause id="25395">
    <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(25390(a,1),4625(a,1,2,2))].">
      <j1 rule="para" parents="25390 4625"/>
    </justification>
  </clause>

  <clause id="25397">
    <literal><![CDATA[
      a(x,y,z) \ (x \ u) = x \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(35,a,23296,a(flip),b,25373,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 23296 25373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25398">
    <literal><![CDATA[
      ((a(x,y,z) \ y) * x) * z = x * (T(y,x) * z)
    ]]></literal>
    <justification jstring="[para(25373(a,1),18309(a,1,1))].">
      <j1 rule="para" parents="25373 18309"/>
    </justification>
  </clause>

  <clause id="25399">
    <literal><![CDATA[
      (x * (a(x,y,z) \ u)) \ (x * u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,169,a(flip),b,25376,a)].">
      <j1 rule="hyper" parents="128 169 25376"/>
    </justification>
  </clause>

  <clause id="25400">
    <literal><![CDATA[
      a(x,y,z) * (x \ (a(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(675,a,25377,a),flip(a)].">
      <j1 rule="hyper" parents="675 25377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25401">
    <literal><![CDATA[
      (x * y) / (x * (a(x,z,u) \ y)) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(131,a,169,a(flip),b,25377,a)].">
      <j1 rule="hyper" parents="131 169 25377"/>
    </justification>
  </clause>

  <clause id="25402">
    <literal><![CDATA[
      a(x,y,z) \ (x * u) = x * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(128,a,169,a(flip),b,25377,a)].">
      <j1 rule="hyper" parents="128 169 25377"/>
    </justification>
  </clause>

  <clause id="25403">
    <literal><![CDATA[
      R(x,y,y) * L(z,x,a(x,y,y)) = x * (a(x,y,y) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,13408,a,b,25377,a)].">
      <j1 rule="hyper" parents="63 13408 25377"/>
    </justification>
  </clause>

  <clause id="25404">
    <literal><![CDATA[
      (x * (a(x,y,z) * x)) \ u = (x * x) \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(25377(a,1),459(a,1,1))].">
      <j1 rule="para" parents="25377 459"/>
    </justification>
  </clause>

  <clause id="25405">
    <literal><![CDATA[
      x \ (a(x,y,z) * u) = (x \ u) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(21188,a,25378,a)].">
      <j1 rule="hyper" parents="21188 25378"/>
    </justification>
  </clause>

  <clause id="25406">
    <literal><![CDATA[
      (x \ L(x,y,z)) * a(x,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) * (x \ a(x,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(25378(a,1),1426(a,1))].">
      <j1 rule="para" parents="25378 1426"/>
    </justification>
  </clause>

  <clause id="25407">
    <literal><![CDATA[
      (x \ R(x,y,z)) * a(x,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) * (x \ a(x,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(25378(a,1),1766(a,1))].">
      <j1 rule="para" parents="25378 1766"/>
    </justification>
  </clause>

  <clause id="25408">
    <literal><![CDATA[
      (x * a(y,z,u)) \ ((y \ 1) \ ((y \ x) * a(y,z,u))) = a(y,y,x * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(25378(a,1),15289(a,1,2,2))].">
      <j1 rule="para" parents="25378 15289"/>
    </justification>
  </clause>

  <clause id="25409">
    <literal><![CDATA[
      (x / (a(x,y,z) \ 1)) \ L(x,u,w) = x \ (a(x,y,z) \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,23374,a,b,25397,a)].">
      <j1 rule="hyper" parents="63 23374 25397"/>
    </justification>
  </clause>

  <clause id="25410">
    <literal><![CDATA[
      L(a(x,y,z),u,a(x,y,z)) = (x * w) / (x * (a(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(347,a,16636,a,b,25401,a)].">
      <j1 rule="hyper" parents="347 16636 25401"/>
    </justification>
  </clause>

  <clause id="25411">
    <literal><![CDATA[
      a(x,y,z) \ (x * u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (a(x,y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(25401(a,1),359(a,1,1))].">
      <j1 rule="para" parents="25401 359"/>
    </justification>
  </clause>

  <clause id="25412">
    <literal><![CDATA[
      (a(x,y,z) \ u) / x = a(x,y,z) \ (u / x)
    ]]></literal>
    <justification jstring="[hyper(23235,a,25402,a)].">
      <j1 rule="hyper" parents="23235 25402"/>
    </justification>
  </clause>

  <clause id="25413">
    <literal><![CDATA[
      (x * (y * z)) / z = x * (a(x,y,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,14628,a(flip),b,25402,a)].">
      <j1 rule="hyper" parents="63 14628 25402"/>
    </justification>
  </clause>

  <clause id="25414">
    <literal><![CDATA[
      (x * (a(x,y,z) \ y)) * z = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,25402,a(flip),b,14628,a(flip))].">
      <j1 rule="hyper" parents="133 25402 14628"/>
    </justification>
  </clause>

  <clause id="25415">
    <literal><![CDATA[
      a(x,y,z) \ y = x \ ((x * (y * z)) / z)
    ]]></literal>
    <justification jstring="[hyper(128,a,14628,a(flip),b,25402,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 14628 25402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25416">
    <literal><![CDATA[
      x * (a(x,y,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(25402(a,1),363(a,1))].">
      <j1 rule="para" parents="25402 363"/>
    </justification>
  </clause>

  <clause id="25417">
    <literal><![CDATA[
      x * (y * (a(y,z,x) \ z)) = L(x,z,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(25402(a,1),14623(a,1,2))].">
      <j1 rule="para" parents="25402 14623"/>
    </justification>
  </clause>

  <clause id="25418">
    <literal><![CDATA[
      a(x,y,z) * ((x * u) * R((x * u) \ (x * (a(x,y,z) \ u)),w,v5)) = (x * u) * (a(x,y,z) * R(a(x,y,z) \ 1,w,v5))
    ]]></literal>
    <justification jstring="[para(25402(a,1),23587(a,1,2,2,1,2))].">
      <j1 rule="para" parents="25402 23587"/>
    </justification>
  </clause>

  <clause id="25419">
    <literal><![CDATA[
      x * (a(x,y,y) \ y) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(800,a,25413,a),flip(a)].">
      <j1 rule="hyper" parents="800 25413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25420">
    <literal><![CDATA[
      (x * (a(x,y,z) \ y)) * (z \ 1) = x * (y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(133,a,25413,a(flip),b,966,a)].">
      <j1 rule="hyper" parents="133 25413 966"/>
    </justification>
  </clause>

  <clause id="25421">
    <literal><![CDATA[
      a(x,y,y) \ y = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,2004,a(flip),b,25413,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 2004 25413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25422">
    <literal><![CDATA[
      (x * ((y \ (z / u)) * w)) / w = x * (a(x,y \ (u \ z),w) \ (y \ (z / u)))
    ]]></literal>
    <justification jstring="[para(24051(a,1),25413(a,2,2,1))].">
      <j1 rule="para" parents="24051 25413"/>
    </justification>
  </clause>

  <clause id="25423">
    <literal><![CDATA[
      L(x,x,y) * a(y,x,x) = x
    ]]></literal>
    <justification jstring="[hyper(20014,a,25421,a)].">
      <j1 rule="hyper" parents="20014 25421"/>
    </justification>
  </clause>

  <clause id="25424">
    <literal><![CDATA[
      a(x,y,y) * L(y,y,x) = y
    ]]></literal>
    <justification jstring="[hyper(150,a,25421,a)].">
      <j1 rule="hyper" parents="150 25421"/>
    </justification>
  </clause>

  <clause id="25425">
    <literal><![CDATA[
      L(x,x,y) \ x = a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(39,a,3309,a,b,25421,a)].">
      <j1 rule="hyper" parents="39 3309 25421"/>
    </justification>
  </clause>

  <clause id="25426">
    <literal><![CDATA[
      a(x,y,y) \ 1 = y \ L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,25421,a(flip),b,12717,a),flip(a)].">
      <j1 rule="hyper" parents="128 25421 12717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25427">
    <literal><![CDATA[
      L(x,x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      a(y,x,x) = z
    ]]></literal>
    <justification jstring="[para(25421(a,1),20577(a,1,1))].">
      <j1 rule="para" parents="25421 20577"/>
    </justification>
  </clause>

  <clause id="25428">
    <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(25423(a,1),99(a,2,1))].">
      <j1 rule="para" parents="25423 99"/>
    </justification>
  </clause>

  <clause id="25429">
    <literal><![CDATA[
      x * (1 / L(x,x,y)) = a(y * x,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,22736,a(flip),b,25425,a)].">
      <j1 rule="hyper" parents="63 22736 25425"/>
    </justification>
  </clause>

  <clause id="25430">
    <literal><![CDATA[
      (L(x,x,y) \ 1) * x = a(x \ y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,10202,a(flip),b,25425,a)].">
      <j1 rule="hyper" parents="63 10202 25425"/>
    </justification>
  </clause>

  <clause id="25431">
    <literal><![CDATA[
      x \ ((y \ (y / x)) \ 1) = a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3642,a(flip),b,25425,a)].">
      <j1 rule="hyper" parents="63 3642 25425"/>
    </justification>
  </clause>

  <clause id="25432">
    <literal><![CDATA[
      (x \ (x / y)) \ 1 = y * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,25425,a(flip),b,3642,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 25425 3642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25433">
    <literal><![CDATA[
      a(x,y,y) / y = 1 / L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,25425,a(flip),b,3310,a)].">
      <j1 rule="hyper" parents="131 25425 3310"/>
    </justification>
  </clause>

  <clause id="25434">
    <literal><![CDATA[
      a(x \ y,x,x) / x = L(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(131,a,25425,a(flip),b,10202,a(flip))].">
      <j1 rule="hyper" parents="131 25425 10202"/>
    </justification>
  </clause>

  <clause id="25435">
    <literal><![CDATA[
      L(x,x,y) \ 1 = x \ a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,25425,a(flip),b,1409,a),flip(a)].">
      <j1 rule="hyper" parents="128 25425 1409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25436">
    <literal><![CDATA[
      L(1 / x,x,y) \ 1 = a(y,x,x) * x
    ]]></literal>
    <justification jstring="[para(25425(a,1),3645(a,2,1))].">
      <j1 rule="para" parents="25425 3645"/>
    </justification>
  </clause>

  <clause id="25437">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((y \ x) \ (x \ y)) = (x \ y) * a(x,x \ y,x \ y)
    ]]></literal>
    <justification jstring="[para(25425(a,1),3546(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25425 3546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25438">
    <literal><![CDATA[
      L(x,R(y,y,z) \ y,a(z,y,y)) / (((R(y,y,z) \ y) \ 1) * x) = a(y,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(25425(a,1),22385(a,1,1,3))].">
      <j1 rule="para" parents="25425 22385"/>
    </justification>
  </clause>

  <clause id="25439">
    <literal><![CDATA[
      a(x,(y * L(y,y,z)) \ u,w) = a(x,a(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(25425(a,1),24374(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="25425 24374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25440">
    <literal><![CDATA[
      (x \ (x / y)) * y = a(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,3350,a(flip),b,25426,a)].">
      <j1 rule="hyper" parents="347 3350 25426"/>
    </justification>
  </clause>

  <clause id="25441">
    <literal><![CDATA[
      x * ((y * x) \ y) = a(y,x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,3348,a(flip),b,25426,a)].">
      <j1 rule="hyper" parents="347 3348 25426"/>
    </justification>
  </clause>

  <clause id="25442">
    <literal><![CDATA[
      R(x,y,y) \ x = y \ L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,13405,a,b,25426,a)].">
      <j1 rule="hyper" parents="63 13405 25426"/>
    </justification>
  </clause>

  <clause id="25443">
    <literal><![CDATA[
      (a(x,y,y) \ 1) \ z = (y \ L(y,y,x)) \ z
    ]]></literal>
    <justification jstring="[hyper(61,a,25426,a)].">
      <j1 rule="hyper" parents="61 25426"/>
    </justification>
  </clause>

  <clause id="25444">
    <literal><![CDATA[
      x * (R(y,x,x) \ y) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,13405,a,b,25426,a(flip))].">
      <j1 rule="hyper" parents="134 13405 25426"/>
    </justification>
  </clause>

  <clause id="25445">
    <literal><![CDATA[
      (x \ L(x,x,y)) \ (a(y,x,x) * z) = (a(y,x,x) * a(y,x,x)) * z
    ]]></literal>
    <justification jstring="[para(25426(a,1),494(a,1,1))].">
      <j1 rule="para" parents="25426 494"/>
    </justification>
  </clause>

  <clause id="25446">
    <literal><![CDATA[
      (a(x,y \ z,y \ z) \ 1) * (z / y) = L(z / y,y \ z,x)
    ]]></literal>
    <justification jstring="[para(25426(a,2),21224(a,1,1))].">
      <j1 rule="para" parents="25426 21224"/>
    </justification>
  </clause>

  <clause id="25447">
    <literal><![CDATA[
      1 / (a(x,y,y) / y) = L(y,y,y * x)
    ]]></literal>
    <justification jstring="[hyper(220,a,25433,a,b,10205,a)].">
      <j1 rule="hyper" parents="220 25433 10205"/>
    </justification>
  </clause>

  <clause id="25448">
    <literal><![CDATA[
      x \ (R(y,x,x) \ y) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(128,a,25442,a,b,3343,a)].">
      <j1 rule="hyper" parents="128 25442 3343"/>
    </justification>
  </clause>

  <clause id="25449">
    <literal><![CDATA[
      R(x \ y,x,x) \ (x \ y) = x * (y \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(34,a,5513,a,b,25444,a),flip(a)].">
      <j1 rule="hyper" parents="34 5513 25444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25450">
    <literal><![CDATA[
      R(x,x \ y,R(z,y,y) \ z) = L(y,y,z) / ((x \ y) * (R(z,y,y) \ z))
    ]]></literal>
    <justification jstring="[para(25444(a,1),104(a,2,1))].">
      <j1 rule="para" parents="25444 104"/>
    </justification>
  </clause>

  <clause id="25451">
    <literal><![CDATA[
      x * (a(x,R(y,z,u),L(y,z,u)) \ R(y,z,u)) = x / (R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(24889(a,1),25419(a,1,2,1))].">
      <j1 rule="para" parents="24889 25419"/>
    </justification>
  </clause>

  <clause id="25452">
    <literal><![CDATA[
      a(x,y,y) \ ((x \ (x / y)) \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(39,a,19984,a,b,25431,a)].">
      <j1 rule="hyper" parents="39 19984 25431"/>
    </justification>
  </clause>

  <clause id="25453">
    <literal><![CDATA[
      T(x,y) * a(x * y,T(x,y),T(x,y)) = ((x * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(213(a,1),25432(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="213 25432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25454">
    <literal><![CDATA[
      (x * a(y,x,x)) * K(1 \ (y \ (y / x)),(y \ (y / x)) \ 1) = 1 / (1 / ((y \ (y / x)) \ 1))
    ]]></literal>
    <justification jstring="[para(25432(a,1),2400(a,1,1))].">
      <j1 rule="para" parents="25432 2400"/>
    </justification>
  </clause>

  <clause id="25455">
    <literal><![CDATA[
      L((x \ (x / y)) \ 1,y,x) = y
    ]]></literal>
    <justification jstring="[para(25432(a,2),14738(a,1,1))].">
      <j1 rule="para" parents="25432 14738"/>
    </justification>
  </clause>

  <clause id="25456">
    <literal><![CDATA[
      a(x,L(y \ (y / z),z,y),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(25455(a,1),14972(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25455 14972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25457">
    <literal><![CDATA[
      R(x,(y \ (z \ (z / y))) \ u,w) = R(x,(a(z,y,y) \ 1) \ u,w)
    ]]></literal>
    <justification jstring="[para(25440(a,1),21123(a,2,2,1))].">
      <j1 rule="para" parents="25440 21123"/>
    </justification>
  </clause>

  <clause id="25458">
    <literal><![CDATA[
      a(x,x \ y,x \ y) \ 1 = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(10(a,1),25441(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 25441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25459">
    <literal><![CDATA[
      L(((x * y) \ x) \ z,(x * y) \ x,y) = (a(x,y,y) \ 1) \ (y * z)
    ]]></literal>
    <justification jstring="[para(25441(a,1),99(a,2,1))].">
      <j1 rule="para" parents="25441 99"/>
    </justification>
  </clause>

  <clause id="25460">
    <literal><![CDATA[
      a(x \ y,x,x) \ 1 = x * L(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(5507(a,1),25441(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5507 25441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25461">
    <literal><![CDATA[
      a((x * (y \ z)) \ (y \ (z * x)),x * (y \ z),x * (y \ z)) \ 1 = (x * (y \ z)) * ((y \ (z * x)) \ ((x * (y \ z)) \ (y \ (z * x))))
    ]]></literal>
    <justification jstring="[para(21378(a,1),25441(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="21378 25441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25462">
    <literal><![CDATA[
      a(a(x,y,y) \ 1,y \ (((x * y) \ x) \ y),z) * (((y * ((x * y) \ x)) \ y) * z) = L(((x * y) \ x) \ z,(x * y) \ x,y)
    ]]></literal>
    <justification jstring="[para(25441(a,1),24743(a,1,1,1))].">
      <j1 rule="para" parents="25441 24743"/>
    </justification>
  </clause>

  <clause id="25463">
    <literal><![CDATA[
      (x * y) \ (x * ((x \ (x / y)) \ 1)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[para(25452(a,1),25399(a,1,1,2))].">
      <j1 rule="para" parents="25452 25399"/>
    </justification>
  </clause>

  <clause id="25464">
    <literal><![CDATA[
      a(x,a((y \ 1) \ z,y \ 1,y \ 1) \ u,w) = a(x,((L(y \ 1,y \ 1,z) \ 1) * y) \ u,w)
    ]]></literal>
    <justification jstring="[para(25430(a,1),24117(a,1,2,1))].">
      <j1 rule="para" parents="25430 24117"/>
    </justification>
  </clause>

  <clause id="25465">
    <literal><![CDATA[
      (x \ a(y,x,x)) * x = a(x \ y,x,x)
    ]]></literal>
    <justification jstring="[para(25435(a,1),25430(a,1,1))].">
      <j1 rule="para" parents="25435 25430"/>
    </justification>
  </clause>

  <clause id="25466">
    <literal><![CDATA[
      (1 / x) * (L(x \ 1,x \ 1,y) \ 1) = a((x \ 1) \ y,x \ 1,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,25434,a(flip),b,23107,a(flip))].">
      <j1 rule="hyper" parents="134 25434 23107"/>
    </justification>
  </clause>

  <clause id="25467">
    <literal><![CDATA[
      a(x,y * (L(1 / z,z,u) \ w),v5) = a(x,y * ((a(u,z,z) * z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(25436(a,1),24487(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="25436 24487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25468">
    <literal><![CDATA[
      1 / (a(L(x,y,z) \ u,x,x) / x) = L(x,x,(u / L(x,y,z)) * x)
    ]]></literal>
    <justification jstring="[para(20676(a,2),25447(a,2,3))].">
      <j1 rule="para" parents="20676 25447"/>
    </justification>
  </clause>

  <clause id="25469">
    <literal><![CDATA[
      L(L(x \ 1,x,y),x,R(y,x,x)) = (R(y,x,x) * x) \ y
    ]]></literal>
    <justification jstring="[para(25448(a,1),329(a,1,1))].">
      <j1 rule="para" parents="25448 329"/>
    </justification>
  </clause>

  <clause id="25470">
    <literal><![CDATA[
      a(L(x,y,z) \ u,L(x,y,z),L(x,y,z)) = (x \ a(u,L(x,y,z),L(x,y,z))) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,20680,a(flip),b,25465,a),flip(a)].">
      <j1 rule="hyper" parents="63 20680 25465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25471">
    <literal><![CDATA[
      T(x * (a(x,y,L(z,z,y)) \ y),L(z,z,y)) = L(z,z,y) \ (x * (y / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(462,a,2010,a(flip),b,25414,a)].">
      <j1 rule="hyper" parents="462 2010 25414"/>
    </justification>
  </clause>

  <clause id="25474">
    <literal><![CDATA[
      a(x,L(y \ (z \ y),z,y),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,24363,a(flip),b,25456,a)].">
      <j1 rule="hyper" parents="63 24363 25456"/>
    </justification>
  </clause>

  <clause id="25476">
    <literal><![CDATA[
      a(x,y,((a(z,u,L(w * v5,v5,v5)) \ u) * z) * (v5 \ w)) = a(x,y,z * (T(u,z) * L(w * v5,v5,v5)))
    ]]></literal>
    <justification jstring="[para(25398(a,1),25318(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25398 25318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25477">
    <literal><![CDATA[
      a(a(x,y,y) * (x * y),z,u) = a(x * ((x \ (x / y)) \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(25463(a,1),23895(a,1,1,1))].">
      <j1 rule="para" parents="25463 23895"/>
    </justification>
  </clause>

  <clause id="25479">
    <literal><![CDATA[
      (x * y) \ (L(x,z,y) * (y * z)) = L(a(y,z,x) \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,25417,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="128 25417 97"/>
    </justification>
  </clause>

  <clause id="25480">
    <literal><![CDATA[
      L(x,y \ a(y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      y * (a(y,z,u) \ ((y \ a(y,z,u)) * x)) = w
    ]]></literal>
    <justification jstring="[para(98(a,1),25411(a,1))].">
      <j1 rule="para" parents="98 25411"/>
    </justification>
  </clause>

  <clause id="25481">
    <literal><![CDATA[
      a(x,y,z) * (R(x,u,w) \ 1) = R(x,u,w) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(20479,a,25388,a)].">
      <j1 rule="hyper" parents="20479 25388"/>
    </justification>
  </clause>

  <clause id="25482">
    <literal><![CDATA[
      L(L(x \ 1,x,y),x,L(y,x,x)) = (R(y,x,x) * x) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,23670,a(flip),b,25469,a)].">
      <j1 rule="hyper" parents="63 23670 25469"/>
    </justification>
  </clause>

  <clause id="25483">
    <literal><![CDATA[
      L(x,y,(z * u) \ (L(z,T(w,v5),u) * (u * T(w,v5)))) = L(x,y,L(a(u,T(w,v5),z) \ w,u,z))
    ]]></literal>
    <justification jstring="[para(25479(a,2),21555(a,1,3))].">
      <j1 rule="para" parents="25479 21555"/>
    </justification>
  </clause>

  <clause id="25484">
    <literal><![CDATA[
      L(x,L(a(y,z,u) \ z,y,u),w) = L(x,(u * y) \ ((u * z) * y),w)
    ]]></literal>
    <justification jstring="[para(25479(a,1),22673(a,1,2))].">
      <j1 rule="para" parents="25479 22673"/>
    </justification>
  </clause>

  <clause id="25485">
    <literal><![CDATA[
      L(a(x,a(y,z,u),w) \ a(y,z,u),x,w) = (w * x) \ ((a(y,z,u) * w) * x)
    ]]></literal>
    <justification jstring="[para(23236(a,1),25479(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23236 25479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25487">
    <literal><![CDATA[
      L(a(x,y,z),u,L(x,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(23110,a,25374,a)].">
      <j1 rule="hyper" parents="23110 25374"/>
    </justification>
  </clause>

  <clause id="25488">
    <literal><![CDATA[
      R(a(x,y,z),u,L(x,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(12342,a,25374,a)].">
      <j1 rule="hyper" parents="12342 25374"/>
    </justification>
  </clause>

  <clause id="25489">
    <literal><![CDATA[
      a(a(x,y,z),u,L(x,w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,25374,a(flip),b,13372,a),flip(a)].">
      <j1 rule="hyper" parents="129 25374 13372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25490">
    <literal><![CDATA[
      (L(x,y,z) * ((L(x,y,z) \ u) / a(x,w,v5))) \ u = a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,9644,a(flip),b,25487,a)].">
      <j1 rule="hyper" parents="63 9644 25487"/>
    </justification>
  </clause>

  <clause id="25491">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) \ u) * a(x,w,v5)) = u * a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(134,a,25487,a(flip),b,98,a),flip(a)].">
      <j1 rule="hyper" parents="134 25487 98"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25492">
    <literal><![CDATA[
      R(x,y,T(a(z,u,w) \ z,v5) * v6) = R(x,y,(z * a(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(22090,a,25389,a)].">
      <j1 rule="hyper" parents="22090 25389"/>
    </justification>
  </clause>

  <clause id="25493">
    <literal><![CDATA[
      L(x,a(y,z,u),y) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(23260,a,25392,a),flip(a)].">
      <j1 rule="hyper" parents="23260 25392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25494">
    <literal><![CDATA[
      L(x,a(y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(25392(a,1),23260(a,1))].">
      <j1 rule="para" parents="25392 23260"/>
    </justification>
  </clause>

  <clause id="25495">
    <literal><![CDATA[
      L((x \ (y \ (x \ y))) \ z,x,a(x,x,y)) = (y \ (x \ y)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,23753,a(flip),b,25493,a),flip(a)].">
      <j1 rule="hyper" parents="63 23753 25493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25496">
    <literal><![CDATA[
      L(L(x,y \ (z \ y),z),z,a(z,z,y)) = L(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21919,a(flip),b,25493,a),flip(a)].">
      <j1 rule="hyper" parents="63 21919 25493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25497">
    <literal><![CDATA[
      (x \ a(x,y,z)) * L(u,x,a(x,y,z)) = (x \ 1) * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(25493(a,1),23238(a,1,2))].">
      <j1 rule="para" parents="25493 23238"/>
    </justification>
  </clause>

  <clause id="25498">
    <literal><![CDATA[
      L(a(x,y,z),u,a(x,y,z)) = (x * (w * z)) / (x * ((a(x,y,z) \ w) * z))
    ]]></literal>
    <justification jstring="[para(23121(a,1),25410(a,2,2,2))].">
      <j1 rule="para" parents="23121 25410"/>
    </justification>
  </clause>

  <clause id="25499">
    <literal><![CDATA[
      a(x,y \ z,y \ z) \ (z / y) = L(z / y,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,24341,a(flip),b,25446,a)].">
      <j1 rule="hyper" parents="63 24341 25446"/>
    </justification>
  </clause>

  <clause id="25500">
    <literal><![CDATA[
      (K(x,y) * (K(y,x) * a(z,u \ w,u \ w))) \ (w / u) = L(w / u,u \ w,z)
    ]]></literal>
    <justification jstring="[para(5261(a,2),25499(a,1,1))].">
      <j1 rule="para" parents="5261 25499"/>
    </justification>
  </clause>

  <clause id="25501">
    <literal><![CDATA[
      L((a(x,y \ z,y \ z) \ (z / y)) \ (z / y),u,w) * (w * u) = w * (u * (L(z / y,y \ z,x) \ (z / y)))
    ]]></literal>
    <justification jstring="[para(25499(a,2),20241(a,1,1,1,1))].">
      <j1 rule="para" parents="25499 20241"/>
    </justification>
  </clause>

  <clause id="25502">
    <literal><![CDATA[
      (L(x,y,z) * (a(x,u,w) \ (L(x,y,z) \ v5))) \ v5 = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(19977(a,1),25490(a,1,1,2))].">
      <j1 rule="para" parents="19977 25490"/>
    </justification>
  </clause>

  <clause id="25503">
    <literal><![CDATA[
      L(a(x,y,y) \ z,a(x,y,y),L(y,y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      L(y,y,x) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(25428(a,2),1426(a,1))].">
      <j1 rule="para" parents="25428 1426"/>
    </justification>
  </clause>

  <clause id="25504">
    <literal><![CDATA[
      a(R(x,y,y) * y,z,u) = a(x * ((x \ (x / y)) \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(23126(a,1),25477(a,1,1))].">
      <j1 rule="para" parents="23126 25477"/>
    </justification>
  </clause>

  <clause id="25505">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,a(x,w,v5)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(25365(a,1),25375(a,2,2,1))].">
      <j1 rule="para" parents="25365 25375"/>
    </justification>
  </clause>

  <clause id="25506">
    <literal><![CDATA[
      a(a(x,y,z),u,x \ L(x,w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(53,a,25505,a)].">
      <j1 rule="hyper" parents="53 25505"/>
    </justification>
  </clause>

  <clause id="25507">
    <literal><![CDATA[
      a(a(x,y,z),u,x * L(x,w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(15027,a,25506,a)].">
      <j1 rule="hyper" parents="15027 25506"/>
    </justification>
  </clause>

  <clause id="25508">
    <literal><![CDATA[
      a(a(x,y,z),u,a(x,x,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,24647,a(flip),b,25507,a)].">
      <j1 rule="hyper" parents="63 24647 25507"/>
    </justification>
  </clause>

  <clause id="25509">
    <literal><![CDATA[
      L(a(x,x,y),z,a(x,u,w)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(52,a,25508,a)].">
      <j1 rule="hyper" parents="52 25508"/>
    </justification>
  </clause>

  <clause id="25510">
    <literal><![CDATA[
      (x * y) \ (a(x,y,y) * z) = ((x * y) \ z) * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,23116,a(flip),b,25381,a),flip(a)].">
      <j1 rule="hyper" parents="63 23116 25381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25511">
    <literal><![CDATA[
      (x * a(x,y,z)) \ L(x,u,w) = x \ (a(x,y,z) \ L(x,u,w))
    ]]></literal>
    <justification jstring="[para(25370(a,1),25409(a,1,1))].">
      <j1 rule="para" parents="25370 25409"/>
    </justification>
  </clause>

  <clause id="25512">
    <literal><![CDATA[
      (a(x,y,y) \ 1) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(((x * y) \ x) \ z,x \ (y \ x),y) = u
    ]]></literal>
    <justification jstring="[para(25459(a,1),21916(a,1))].">
      <j1 rule="para" parents="25459 21916"/>
    </justification>
  </clause>

  <clause id="25514">
    <literal><![CDATA[
      L(x,L(a(y,z,u) \ z,y,u),w) = L(x,L(z,u,y),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,22647,a(flip),b,25484,a),flip(a)].">
      <j1 rule="hyper" parents="347 22647 25484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25516">
    <literal><![CDATA[
      a(x,y,z) * L(L(u,x,a(x,y,z)),x \ a(x,y,z),x) = x * ((x \ 1) * (a(x,y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(134,a,25497,a(flip),b,538,a),flip(a)].">
      <j1 rule="hyper" parents="134 25497 538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25517">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((y \ x) \ (x \ y)) = (x \ y) \ (x \ (y * (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(347,a,11654,a(flip),b,25437,a),flip(a)].">
      <j1 rule="hyper" parents="347 11654 25437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25518">
    <literal><![CDATA[
      (x \ y) * (1 / (y \ x)) = x \ (y * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(134,a,3661,a(flip),b,25517,a(flip))].">
      <j1 rule="hyper" parents="134 3661 25517"/>
    </justification>
  </clause>

  <clause id="25519">
    <literal><![CDATA[
      (x \ y) \ (y \ x) = y \ (x * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(15342,a,25518,a)].">
      <j1 rule="hyper" parents="15342 25518"/>
    </justification>
  </clause>

  <clause id="25520">
    <literal><![CDATA[
      R(x,((y \ z) / (z \ y)) * u,w) = R(x,(y \ (z * (y \ z))) * u,w)
    ]]></literal>
    <justification jstring="[para(25519(a,1),22411(a,2,2,1))].">
      <j1 rule="para" parents="25519 22411"/>
    </justification>
  </clause>

  <clause id="25521">
    <literal><![CDATA[
      x * (a(x,L(y,z,u),L(y,z,u)) \ R(y,z,u)) = x / (R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(24805(a,1),25451(a,1,2,1))].">
      <j1 rule="para" parents="24805 25451"/>
    </justification>
  </clause>

  <clause id="25522">
    <literal><![CDATA[
      R(x,x \ y,L(z,y,y) \ z) = L(y,y,z) / ((x \ y) * (R(z,y,y) \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,22262,a(flip),b,25450,a)].">
      <j1 rule="hyper" parents="63 22262 25450"/>
    </justification>
  </clause>

  <clause id="25523">
    <literal><![CDATA[
      a((x \ 1) \ y,x \ 1,x \ 1) = (1 / x) * (L(x \ 1,x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(3188(a,1),25466(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3188 25466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25524">
    <literal><![CDATA[
      a((x \ 1) \ y,x \ 1,x \ 1) = L(x \ 1,x,y) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(347,a,22028,a(flip),b,25523,a),flip(a)].">
      <j1 rule="hyper" parents="347 22028 25523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25525">
    <literal><![CDATA[
      a((x \ 1) \ y,x \ 1,x \ 1) = x * (1 / L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,21352,a(flip),b,25524,a),flip(a)].">
      <j1 rule="hyper" parents="347 21352 25524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25526">
    <literal><![CDATA[
      a((x \ 1) \ y,x \ 1,x \ 1) = a(y * x,x,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,25429,a(flip),b,25525,a),flip(a)].">
      <j1 rule="hyper" parents="347 25429 25525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25527">
    <literal><![CDATA[
      a(x,y * ((a(z,u,u) * u) \ w),v5) = a(x,(L(u,u,z) \ w) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24821,a(flip),b,25467,a),flip(a)].">
      <j1 rule="hyper" parents="63 24821 25467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25528">
    <literal><![CDATA[
      L(a(x,y,z),u,a(x,y,z)) = (x * ((x \ w) * z)) / (x * ((x \ (a(x,y,z) \ w)) * z))
    ]]></literal>
    <justification jstring="[para(25397(a,1),25498(a,2,2,2,1))].">
      <j1 rule="para" parents="25397 25498"/>
    </justification>
  </clause>

  <clause id="25529">
    <literal><![CDATA[
      R(x,x \ y,a(y,y,z)) = L(y,y,z) / ((x \ y) * (R(z,y,y) \ z))
    ]]></literal>
    <justification jstring="[para(14600(a,1),25522(a,1,3))].">
      <j1 rule="para" parents="14600 25522"/>
    </justification>
  </clause>

  <clause id="25530">
    <literal><![CDATA[
      L(x,x \ y,a(y,y,z)) = L(y,y,z) / ((x \ y) * (R(z,y,y) \ z))
    ]]></literal>
    <justification jstring="[hyper(23284,a,25529,a)].">
      <j1 rule="hyper" parents="23284 25529"/>
    </justification>
  </clause>

  <clause id="25531">
    <literal><![CDATA[
      R(x,y,z) \ (a(x,u,w) * v5) = (R(x,y,z) \ v5) * a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,23116,a(flip),b,25387,a),flip(a)].">
      <j1 rule="hyper" parents="63 23116 25387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25532">
    <literal><![CDATA[
      (x * ((x \ (y / z)) * u)) / u = x * (x \ (a(x,x \ (z \ y),u) \ (y / z)))
    ]]></literal>
    <justification jstring="[para(25397(a,1),25422(a,2,2))].">
      <j1 rule="para" parents="25397 25422"/>
    </justification>
  </clause>

  <clause id="25533">
    <literal><![CDATA[
      x * (a(x,y,z) \ ((x \ a(x,y,z)) * u)) = L(u,x * a(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(25480,a,15271,a)].">
      <j1 rule="hyper" parents="25480 15271"/>
    </justification>
  </clause>

  <clause id="25534">
    <literal><![CDATA[
      L(a(x,a(y,z,u),w) \ a(y,z,u),x,w) = R(T(a(y,z,u),w * x),w,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,744,a(flip),b,25485,a),flip(a)].">
      <j1 rule="hyper" parents="347 744 25485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25535">
    <literal><![CDATA[
      L(a(x,a(y,z,u),w) \ a(y,z,u),x,w) = R(a(y,z,u),w,x)
    ]]></literal>
    <justification jstring="[para(20005(a,1),25534(a,2,1))].">
      <j1 rule="para" parents="20005 25534"/>
    </justification>
  </clause>

  <clause id="25537">
    <literal><![CDATA[
      a(x,x \ (y \ z),u) \ (z / y) = (x * ((x \ (z / y)) * u)) / u
    ]]></literal>
    <justification jstring="[hyper(347,a,10,a(flip),b,25532,a)].">
      <j1 rule="hyper" parents="347 10 25532"/>
    </justification>
  </clause>

  <clause id="25539">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,z) = (z * y) \ ((z * y) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,833,a(flip),b,25395,a),flip(a)].">
      <j1 rule="hyper" parents="63 833 25395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25540">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,z) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,9,a(flip),b,25539,a),flip(a)].">
      <j1 rule="hyper" parents="347 9 25539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25541">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,z) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,9,a(flip),b,25539,a),flip(a)].">
      <j1 rule="hyper" parents="128 9 25539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25543">
    <literal><![CDATA[
      L(L(x,y,z) / x,u,z) = (x \ x) * (L(x,y,z) / x)
    ]]></literal>
    <justification jstring="[para(25540(a,1),21200(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="25540 21200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25544">
    <literal><![CDATA[
      L(L(x,y,z) / x,u,z) = 1 * (L(x,y,z) / x)
    ]]></literal>
    <justification jstring="[para(68(a,1),25543(a,2,1))].">
      <j1 rule="para" parents="68 25543"/>
    </justification>
  </clause>

  <clause id="25546">
    <literal><![CDATA[
      L(L(x,y,z) / x,u,z) = 1 * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(3161(a,1),25544(a,2,2))].">
      <j1 rule="para" parents="3161 25544"/>
    </justification>
  </clause>

  <clause id="25547">
    <literal><![CDATA[
      L(L(x,y,z) / x,u,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,7,a(flip),b,25546,a),flip(a)].">
      <j1 rule="hyper" parents="347 7 25546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25548">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3161(a,1),25547(a,1,1))].">
      <j1 rule="para" parents="3161 25547"/>
    </justification>
  </clause>

  <clause id="25549">
    <literal><![CDATA[
      L(x,y,z) * (x \ L(x,u,z)) = L(L(x,u,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,25548,a(flip),b,4640,a)].">
      <j1 rule="hyper" parents="134 25548 4640"/>
    </justification>
  </clause>

  <clause id="25550">
    <literal><![CDATA[
      (x * y) * (z \ L(z,u,x)) = x * (y * (z \ L(z,u,x)))
    ]]></literal>
    <justification jstring="[hyper(134,a,25548,a(flip),b,4048,a(flip))].">
      <j1 rule="hyper" parents="134 25548 4048"/>
    </justification>
  </clause>

  <clause id="25551">
    <literal><![CDATA[
      (x / y) * L(y,z,x) = x * (y \ L(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(134,a,25548,a(flip),b,3965,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 25548 3965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25552">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(x,u,z) = L(L(x,u,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,25548,a(flip),b,4642,a)].">
      <j1 rule="hyper" parents="133 25548 4642"/>
    </justification>
  </clause>

  <clause id="25553">
    <literal><![CDATA[
      L(x,y,z) \ ((x \ L(x,u,z)) \ 1) = L(L(x,y,z),u,z) \ 1
    ]]></literal>
    <justification jstring="[para(25548(a,1),10911(a,1,2,1))].">
      <j1 rule="para" parents="25548 10911"/>
    </justification>
  </clause>

  <clause id="25554">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ L(x,y,z),u,z)) \ w = (L(x,y,z) * L(x \ 1,y,z)) \ (x \ w)
    ]]></literal>
    <justification jstring="[para(25548(a,2),12344(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="25548 12344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25555">
    <literal><![CDATA[
      L(x \ (y * L(y \ x,z,u)),w,u) = (y / x) \ L(y / x,z,u)
    ]]></literal>
    <justification jstring="[para(20956(a,1),25548(a,1,1))].">
      <j1 rule="para" parents="20956 25548"/>
    </justification>
  </clause>

  <clause id="25556">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ z = z * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(25548(a,1),20945(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25548 20945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25557">
    <literal><![CDATA[
      (L(x,y,z) / u) \ L(L(x,y,z),w,z) = (x \ L(x,w,z)) / (u \ 1)
    ]]></literal>
    <justification jstring="[para(25548(a,1),23367(a,2,1))].">
      <j1 rule="para" parents="25548 23367"/>
    </justification>
  </clause>

  <clause id="25558">
    <literal><![CDATA[
      x \ ((x / y) * L(y,z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      y \ L(y,z,x) = u
    ]]></literal>
    <justification jstring="[para(25551(a,2),356(a,1,2))].">
      <j1 rule="para" parents="25551 356"/>
    </justification>
  </clause>

  <clause id="25559">
    <literal><![CDATA[
      (x \ L(x,y,z)) / ((L(x,y,z) \ x) \ z) = R(1 / z,z,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(220,a,25556,a,b,420,a)].">
      <j1 rule="hyper" parents="220 25556 420"/>
    </justification>
  </clause>

  <clause id="25560">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ 1) / (z * ((x \ L(x,y,z)) \ 1)) = (x \ L(x,y,z)) / ((L(x,y,z) \ x) \ z)
    ]]></literal>
    <justification jstring="[para(25556(a,2),823(a,2,2))].">
      <j1 rule="para" parents="25556 823"/>
    </justification>
  </clause>

  <clause id="25561">
    <literal><![CDATA[
      L(x,y,z) * L(x,u,z) = x * L(L(x,u,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,25549,a(flip),b,1402,a),flip(a)].">
      <j1 rule="hyper" parents="134 25549 1402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25562">
    <literal><![CDATA[
      L(x,y,z) * L(x \ 1,u,z) = x \ L(L(x,u,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,25549,a(flip),b,3358,a),flip(a)].">
      <j1 rule="hyper" parents="128 25549 3358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25563">
    <literal><![CDATA[
      L(x,y * L(L(z,u,w),u,w),v5) = L(x,y * z,v5)
    ]]></literal>
    <justification jstring="[para(25549(a,1),12298(a,1,2,2))].">
      <j1 rule="para" parents="25549 12298"/>
    </justification>
  </clause>

  <clause id="25564">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),u,w) \ v5) = a(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(25549(a,1),14962(a,1,3,1))].">
      <j1 rule="para" parents="25549 14962"/>
    </justification>
  </clause>

  <clause id="25565">
    <literal><![CDATA[
      R(x,y,z * L(L(u,w,v5),w,v5)) = R(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(25549(a,1),22752(a,1,3,2))].">
      <j1 rule="para" parents="25549 22752"/>
    </justification>
  </clause>

  <clause id="25566">
    <literal><![CDATA[
      a(x,y,z * L(L(u,w,v5),w,v5)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(25552(a,1),14947(a,1,3,2))].">
      <j1 rule="para" parents="25552 14947"/>
    </justification>
  </clause>

  <clause id="25567">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x \ L(x,u,z)) = x \ L(L(x,y,z),u,z)
    ]]></literal>
    <justification jstring="[para(25552(a,1),20954(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25552 20954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25568">
    <literal><![CDATA[
      R(x,y,y * y) * L(L(y,z,u),z,u) = (x * y) * (y \ L(L(y,z,u),z,u))
    ]]></literal>
    <justification jstring="[para(25565(a,1),10927(a,1,1))].">
      <j1 rule="para" parents="25565 10927"/>
    </justification>
  </clause>

  <clause id="25569">
    <literal><![CDATA[
      (x * y) * (z \ L(z,x,x \ L(x,u,w))) = x * (y * (z \ L(z,x * L(x,u,w),x)))
    ]]></literal>
    <justification jstring="[para(3653(a,1),25550(a,1,2,2))].">
      <j1 rule="para" parents="3653 25550"/>
    </justification>
  </clause>

  <clause id="25570">
    <literal><![CDATA[
      (x * y) * ((z \ L(z,u,w)) \ L(z \ L(z,u,w),z,x)) = x * (y * ((z \ L(z,u,w)) \ (x \ ((x / z) * L(z,u,w)))))
    ]]></literal>
    <justification jstring="[para(3965(a,1),25550(a,2,2,2,2))].">
      <j1 rule="para" parents="3965 25550"/>
    </justification>
  </clause>

  <clause id="25571">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,u,z) \ x) = L(L(x,y,z),u,z) \ 1
    ]]></literal>
    <justification jstring="[para(10882(a,1),25553(a,1,2))].">
      <j1 rule="para" parents="10882 25553"/>
    </justification>
  </clause>

  <clause id="25572">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ 1,y,z)) \ u = (x * (L(L(x,y,z),y,z) \ 1)) * u
    ]]></literal>
    <justification jstring="[para(25571(a,1),12350(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="25571 12350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25573">
    <literal><![CDATA[
      (x \ (y * (L(L(y,z,u),z,u) \ 1))) \ (x \ 1) = L(y,z,u) * L(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(25571(a,1),22811(a,1,1,2,2))].">
      <j1 rule="para" parents="25571 22811"/>
    </justification>
  </clause>

  <clause id="25574">
    <literal><![CDATA[
      a(x,y * (z \ L(u,L(u,w,v5),L(u,w,v5))),v6) = a(x,y * (z \ (L(L(u,w,v5),w,v5) \ 1)),v6)
    ]]></literal>
    <justification jstring="[para(25571(a,1),25000(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="25571 25000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25575">
    <literal><![CDATA[
      L(x,y,z) * ((x \ L(L(x,y,z),y,z)) \ u) = (x * ((x \ L(x,y,z)) \ 1)) * u
    ]]></literal>
    <justification jstring="[para(25567(a,1),984(a,1,2,1))].">
      <j1 rule="para" parents="25567 984"/>
    </justification>
  </clause>

  <clause id="25576">
    <literal><![CDATA[
      a(x,y,z * ((u \ L(L(u,w,v5),w,v5)) * v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * v6) = v7
    ]]></literal>
    <justification jstring="[para(25567(a,1),24288(a,1,3,2,1))].">
      <j1 rule="para" parents="25567 24288"/>
    </justification>
  </clause>

  <clause id="25577">
    <literal><![CDATA[
      L((x * y) \ (x * L(y,z,u)),w,u) = (x / (x * y)) \ L(x / (x * y),z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),25555(a,1,1,2,2,1))].">
      <j1 rule="para" parents="9 25555"/>
    </justification>
  </clause>

  <clause id="25578">
    <literal><![CDATA[
      (L(x,y,z) / u) \ L(L(x,y,z),w,z) = (x / u) \ L(x,w,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,23364,a(flip),b,25557,a),flip(a)].">
      <j1 rule="hyper" parents="347 23364 25557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25579">
    <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(2174(a,1),25572(a,2,1))].">
      <j1 rule="para" parents="2174 25572"/>
    </justification>
  </clause>

  <clause id="25580">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x,y,z) \ x) = L(L(x,y,z),y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(12349,a,25579,a)].">
      <j1 rule="hyper" parents="12349 25579"/>
    </justification>
  </clause>

  <clause id="25581">
    <literal><![CDATA[
      (x \ L(L(x,y,z),y,z)) \ u = (L(L(x,y,z),y,z) \ x) * u
    ]]></literal>
    <justification jstring="[para(25562(a,1),25579(a,1,1))].">
      <j1 rule="para" parents="25562 25579"/>
    </justification>
  </clause>

  <clause id="25582">
    <literal><![CDATA[
      a(x,y,(L(L(z,u,w),u,w) \ z) \ v5) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[para(25580(a,1),14948(a,1,3,1))].">
      <j1 rule="para" parents="25580 14948"/>
    </justification>
  </clause>

  <clause id="25583">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(24182,a,25582,a)].">
      <j1 rule="hyper" parents="24182 25582"/>
    </justification>
  </clause>

  <clause id="25584">
    <literal><![CDATA[
      a(x,y,L(z \ (u \ z),u,z)) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,24979,a(flip),b,25583,a)].">
      <j1 rule="hyper" parents="63 24979 25583"/>
    </justification>
  </clause>

  <clause id="25585">
    <literal><![CDATA[
      a(x,y,L(L(L(z,u,w),v5,v6),u,w)) = a(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(30(a,1),25583(a,1,3,1))].">
      <j1 rule="para" parents="30 25583"/>
    </justification>
  </clause>

  <clause id="25586">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,u,z)) = a(x,y,u \ (z \ w))
    ]]></literal>
    <justification jstring="[para(329(a,1),25583(a,1,3,1))].">
      <j1 rule="para" parents="329 25583"/>
    </justification>
  </clause>

  <clause id="25587">
    <literal><![CDATA[
      R(x,L(y \ (z \ y),z,y),L(y \ (z \ y),z,y)) = a(x,L(y \ (z \ y),z,y),z) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,25584,a(flip),b,13402,a),flip(a)].">
      <j1 rule="hyper" parents="133 25584 13402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25588">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,z,u)) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(24544,a,25586,a)].">
      <j1 rule="hyper" parents="24544 25586"/>
    </justification>
  </clause>

  <clause id="25589">
    <literal><![CDATA[
      a(x,y,z \ (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(u,z,z)) = w
    ]]></literal>
    <justification jstring="[para(25586(a,1),14995(a,1))].">
      <j1 rule="para" parents="25586 14995"/>
    </justification>
  </clause>

  <clause id="25590">
    <literal><![CDATA[
      a(x,y,(z \ u) * (u \ (z \ u))) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(u,z,z)) = w
    ]]></literal>
    <justification jstring="[para(24845(a,2),25589(a,1))].">
      <j1 rule="para" parents="24845 25589"/>
    </justification>
  </clause>

  <clause id="25591">
    <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(21652(a,1),25588(a,1,3,1))].">
      <j1 rule="para" parents="21652 25588"/>
    </justification>
  </clause>

  <clause id="25592">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) \ x) \ 1 = x \ L(L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(3977,a,25581,a)].">
      <j1 rule="hyper" parents="3977 25581"/>
    </justification>
  </clause>

  <clause id="25593">
    <literal><![CDATA[
      (x * y) * (y \ L(L(y,z,u),z,u)) = x * L(L(y,z,u),z,u)
    ]]></literal>
    <justification jstring="[para(586(a,1),25568(a,1,1)),flip(a)].">
      <j1 rule="para" parents="586 25568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25594">
    <literal><![CDATA[
      (((x * y) / x) * x) * (x \ L(L(x,z,u),z,u)) = L(L(x,z,u),z,u) * y
    ]]></literal>
    <justification jstring="[hyper(347,a,22024,a(flip),b,25593,a),flip(a)].">
      <j1 rule="hyper" parents="347 22024 25593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25595">
    <literal><![CDATA[
      ((x \ a(x,x,L(L(y,z,u),z,u))) * y) * (y \ L(L(y,z,u),z,u)) = x \ L(L(y,z,u),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,18983,a(flip),b,25593,a),flip(a)].">
      <j1 rule="hyper" parents="347 18983 25593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25596">
    <literal><![CDATA[
      (x * (y \ 1)) * (y * L(L(y,z,u),z,u)) = x * L(L(y,z,u),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,10924,a,b,25593,a)].">
      <j1 rule="hyper" parents="63 10924 25593"/>
    </justification>
  </clause>

  <clause id="25597">
    <literal><![CDATA[
      L(T((x * y) \ 1,y \ L(L(y,z,u),z,u)),y \ L(L(y,z,u),z,u),x * y) = (x * L(L(y,z,u),z,u)) \ L(y \ L(L(y,z,u),z,u),x * y,x * y)
    ]]></literal>
    <justification jstring="[para(25593(a,1),3221(a,2,1))].">
      <j1 rule="para" parents="25593 3221"/>
    </justification>
  </clause>

  <clause id="25598">
    <literal><![CDATA[
      a(x,y,L(z,u \ L(L(u,w,v5),w,v5),v6 * u) * (v6 * L(L(u,w,v5),w,v5))) = a(x,y,(v6 * u) * ((u \ L(L(u,w,v5),w,v5)) * z))
    ]]></literal>
    <justification jstring="[para(25593(a,1),24076(a,1,3,2))].">
      <j1 rule="para" parents="25593 24076"/>
    </justification>
  </clause>

  <clause id="25599">
    <literal><![CDATA[
      L(x,(L(y,z,u) * (y \ 1)) * (y * L(L(y,z,u),z,u)),L(y,z,u)) = L(x,L(y,z,u),L(y,z,u) \ L(L(y,z,u),z,u))
    ]]></literal>
    <justification jstring="[para(25596(a,2),3653(a,1,2))].">
      <j1 rule="para" parents="25596 3653"/>
    </justification>
  </clause>

  <clause id="25600">
    <literal><![CDATA[
      (x * y) * (x \ L(L(x,z,u),z,u)) = L(L(x,z,u),z,u) * y
    ]]></literal>
    <justification jstring="[hyper(353,a,25594,a)].">
      <j1 rule="hyper" parents="353 25594"/>
    </justification>
  </clause>

  <clause id="25602">
    <literal><![CDATA[
      x * ((L(x,y,z) * L(x,y,z)) \ (x \ L(L(x,y,z),y,z))) = L(L(x,y,z) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,3326,a(flip),b,25600,a),flip(a)].">
      <j1 rule="hyper" parents="35 3326 25600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25603">
    <literal><![CDATA[
      L(x \ ((x / y) * L(y,z,u)),w,u) = (x / (x * y)) \ L(x / (x * y),z,u)
    ]]></literal>
    <justification jstring="[para(3963(a,1),25577(a,1,1))].">
      <j1 rule="para" parents="3963 25577"/>
    </justification>
  </clause>

  <clause id="25604">
    <literal><![CDATA[
      L(x \ ((x / y) * L(y,z,u)),w,u) = (x * y) \ (x * L(x \ (x * y),z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,20956,a(flip),b,25603,a),flip(a)].">
      <j1 rule="hyper" parents="347 20956 25603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25605">
    <literal><![CDATA[
      L(x \ ((x / y) * L(y,z,u)),w,u) = (x * y) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),25604(a,2,2,2,1))].">
      <j1 rule="para" parents="9 25604"/>
    </justification>
  </clause>

  <clause id="25606">
    <literal><![CDATA[
      (x * a(y,z,u)) \ (((y \ 1) \ (y \ x)) * a(y,z,u)) = a(y,y,x * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(25385(a,1),25408(a,1,2))].">
      <j1 rule="para" parents="25385 25408"/>
    </justification>
  </clause>

  <clause id="25607">
    <literal><![CDATA[
      (x \ (L(L(y,z,u),z,u) \ y)) \ (x \ 1) = L(y,z,u) * L(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(2174(a,1),25573(a,1,1,2))].">
      <j1 rule="para" parents="2174 25573"/>
    </justification>
  </clause>

  <clause id="25608">
    <literal><![CDATA[
      (x \ (L(L(y,z,u),z,u) \ y)) \ (x \ 1) = y \ L(L(y,z,u),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,25562,a(flip),b,25607,a),flip(a)].">
      <j1 rule="hyper" parents="347 25562 25607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25609">
    <literal><![CDATA[
      L(a(x,x,(y \ (L(L(z,u,w),u,w) \ z)) \ (y \ 1)) * ((y \ (L(L(z,u,w),u,w) \ z)) \ (y \ 1)),x,x) = z \ L(L(z,u,w),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,15301,a,b,25608,a)].">
      <j1 rule="hyper" parents="63 15301 25608"/>
    </justification>
  </clause>

  <clause id="25610">
    <literal><![CDATA[
      ((a(x,y,z) * u) * x) \ (a(x,y,z) * u) = L(x \ 1,x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,25383,a(flip),b,25391,a),flip(a)].">
      <j1 rule="hyper" parents="63 25383 25391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25612">
    <literal><![CDATA[
      L(x,x,a(x,y,z) * u) = L(x \ 1,x,u) * (x * x)
    ]]></literal>
    <justification jstring="[para(25610(a,1),730(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25610 730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25613">
    <literal><![CDATA[
      L((x \ 1) * (x * x),x,y) = L(x,x,a(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,1390,a,b,25612,a)].">
      <j1 rule="hyper" parents="347 1390 25612"/>
    </justification>
  </clause>

  <clause id="25614">
    <literal><![CDATA[
      L(x,x,a(x,y,z) * u) = L(x,x,u)
    ]]></literal>
    <justification jstring="[para(240(a,1),25613(a,1,1)),flip(a)].">
      <j1 rule="para" parents="240 25613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25615">
    <literal><![CDATA[
      L(x,L(y,y,z) \ y,a(z,y,y)) / (((R(y,y,z) \ y) \ 1) * x) = a(y,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(23764(a,1),25438(a,1,1))].">
      <j1 rule="para" parents="23764 25438"/>
    </justification>
  </clause>

  <clause id="25616">
    <literal><![CDATA[
      L(x,a(y,z,z),a(y,z,z)) / (((R(z,z,y) \ z) \ 1) * x) = a(z,z,y) \ 1
    ]]></literal>
    <justification jstring="[para(25425(a,1),25615(a,1,1,2))].">
      <j1 rule="para" parents="25425 25615"/>
    </justification>
  </clause>

  <clause id="25617">
    <literal><![CDATA[
      L(x,a(y,z,z),a(y,z,z)) / ((z \ R(z,z,y)) * x) = a(z,z,y) \ 1
    ]]></literal>
    <justification jstring="[para(10763(a,1),25616(a,1,2,1))].">
      <j1 rule="para" parents="10763 25616"/>
    </justification>
  </clause>

  <clause id="25618">
    <literal><![CDATA[
      L(x,a(y,z,z),a(y,z,z)) / (a(z,z,y) * x) = a(z,z,y) \ 1
    ]]></literal>
    <justification jstring="[para(18988(a,1),25617(a,1,2,1))].">
      <j1 rule="para" parents="18988 25617"/>
    </justification>
  </clause>

  <clause id="25619">
    <literal><![CDATA[
      (a(x,x,y) * z) \ L(z,a(y,x,x),a(y,x,x)) = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,23290,a(flip),b,25618,a)].">
      <j1 rule="hyper" parents="63 23290 25618"/>
    </justification>
  </clause>

  <clause id="25620">
    <literal><![CDATA[
      L(x,y,z \ ((u \ a(u,u,L(w,v5,v6))) * L(w,v5,v6))) = L(x,y,z \ (u \ R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(24889(a,1),25361(a,1,3,2,1,2))].">
      <j1 rule="para" parents="24889 25361"/>
    </justification>
  </clause>

  <clause id="25621">
    <literal><![CDATA[
      L(a(x,x \ (y \ z),u),w,a(x,x \ (y \ z),u)) = (x * ((x \ (z / y)) * u)) / (x * ((x \ ((x * ((x \ (z / y)) * u)) / u)) * u))
    ]]></literal>
    <justification jstring="[para(25537(a,1),25528(a,2,2,2,1,2))].">
      <j1 rule="para" parents="25537 25528"/>
    </justification>
  </clause>

  <clause id="25622">
    <literal><![CDATA[
      x * ((x * L(L(x,y,z),y,z)) \ (x \ L(L(x,y,z),y,z))) = L(L(x,y,z) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(25561(a,1),25602(a,1,2,1))].">
      <j1 rule="para" parents="25561 25602"/>
    </justification>
  </clause>

  <clause id="25623">
    <literal><![CDATA[
      L(x,y,z \ (u \ R(w,v5,v6))) = L(x,y,z \ (u \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(18983(a,1),25620(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="18983 25620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25624">
    <literal><![CDATA[
      R(x,y,L(z,z,u \ ((u \ w) \ L(u,v5,u))) * (w \ u)) = R(x,y,z \ (u \ ((u \ w) \ R(u,v5,u))))
    ]]></literal>
    <justification jstring="[para(25623(a,1),23559(a,1,3,1))].">
      <j1 rule="para" parents="25623 23559"/>
    </justification>
  </clause>

  <clause id="25625">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ L(x,y,z),u,z)) \ w = (x \ L(L(x,y,z),y,z)) \ (x \ w)
    ]]></literal>
    <justification jstring="[para(25562(a,1),25554(a,2,1))].">
      <j1 rule="para" parents="25562 25554"/>
    </justification>
  </clause>

  <clause id="25626">
    <literal><![CDATA[
      (x \ L(L(x,y,z),y,z)) \ (x \ u) = L(L(x,y,z),y,z) \ u
    ]]></literal>
    <justification jstring="[para(4637(a,1),25625(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4637 25625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25627">
    <literal><![CDATA[
      x * ((x \ L(L(x,y,z),y,z)) * u) = L(L(x,y,z),y,z) * u
    ]]></literal>
    <justification jstring="[hyper(710,a,25626,a),flip(a)].">
      <j1 rule="hyper" parents="710 25626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25628">
    <literal><![CDATA[
      (L(L(x,y,z),y,z) \ x) * (x \ u) = L(L(x,y,z),y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,25581,a(flip),b,25626,a)].">
      <j1 rule="hyper" parents="63 25581 25626"/>
    </justification>
  </clause>

  <clause id="25629">
    <literal><![CDATA[
      (x \ L(L(x,y,z),y,z)) * (x * u) = L(L(x,y,z),y,z) * u
    ]]></literal>
    <justification jstring="[hyper(34,a,2173,a(flip),b,25627,a),flip(a)].">
      <j1 rule="hyper" parents="34 2173 25627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25630">
    <literal><![CDATA[
      (x \ L(L(x,y,z),y,z)) \ u = x * (L(L(x,y,z),y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(128,a,470,a(flip),b,25629,a)].">
      <j1 rule="hyper" parents="128 470 25629"/>
    </justification>
  </clause>

  <clause id="25631">
    <literal><![CDATA[
      L(x,y,z) * (x * (L(L(x,y,z),y,z) \ u)) = (x * ((x \ L(x,y,z)) \ 1)) * u
    ]]></literal>
    <justification jstring="[para(25630(a,1),25575(a,1,2))].">
      <j1 rule="para" parents="25630 25575"/>
    </justification>
  </clause>

  <clause id="25632">
    <literal><![CDATA[
      x * (L(x,y,z) * (L(L(x,y,z),y,z) \ u)) = (x * ((x \ L(x,y,z)) \ 1)) * u
    ]]></literal>
    <justification jstring="[hyper(1430,a,25631,a)].">
      <j1 rule="hyper" parents="1430 25631"/>
    </justification>
  </clause>

  <clause id="25633">
    <literal><![CDATA[
      R(x,L(y \ (z \ y),z,y),L(y \ (z \ y),z,y)) = a(x,z,z) * x
    ]]></literal>
    <justification jstring="[para(25474(a,1),25587(a,2,1))].">
      <j1 rule="para" parents="25474 25587"/>
    </justification>
  </clause>

  <clause id="25634">
    <literal><![CDATA[
      R(x,L(y \ (z \ y),z,y),L(y \ (z \ y),z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,z,z) = u
    ]]></literal>
    <justification jstring="[para(25633(a,2),13407(a,1))].">
      <j1 rule="para" parents="25633 13407"/>
    </justification>
  </clause>

  <clause id="25636">
    <literal><![CDATA[
      a(x,y,(z * L(u,w,v5)) * L(v6,v6,z * R(u,w,v5))) = a(x,y,v6 \ (z * R(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(347,a,14957,a(flip),b,25358,a),flip(a)].">
      <j1 rule="hyper" parents="347 14957 25358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25637">
    <literal><![CDATA[
      a(x,y,(z * L(u,w,v5)) * L(v6,v6,z * L(u,w,v5))) = a(x,y,v6 \ (z * R(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(22863(a,1),25636(a,1,3,2))].">
      <j1 rule="para" parents="22863 25636"/>
    </justification>
  </clause>

  <clause id="25638">
    <literal><![CDATA[
      a(x,y,(z * L(u,w,v5)) / (v6 \ 1)) = a(x,y,v6 \ (z * R(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(2008(a,1),25637(a,1,3))].">
      <j1 rule="para" parents="2008 25637"/>
    </justification>
  </clause>

  <clause id="25639">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ (u * L(w,v5,v6))) = a(x,y,z \ (u * R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(24181,a,25638,a)].">
      <j1 rule="hyper" parents="24181 25638"/>
    </justification>
  </clause>

  <clause id="25640">
    <literal><![CDATA[
      a(x,y,z \ (u * R(w,v5,v6))) = a(x,y,z \ (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(15003,a,25639,a),flip(a)].">
      <j1 rule="hyper" parents="15003 25639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25641">
    <literal><![CDATA[
      a(x,y,z \ (R(T(u * K((w * w) * v5,u),v6),v7,v8) * v5)) = a(x,y,z \ (((w * w) * v5) * L(T(u,v6),v7,v8)))
    ]]></literal>
    <justification jstring="[hyper(63,a,24767,a,b,25640,a)].">
      <j1 rule="hyper" parents="63 24767 25640"/>
    </justification>
  </clause>

  <clause id="25642">
    <literal><![CDATA[
      a(x,y,z) * L(L(u,x,a(x,y,z)),x * a(x,y,z),x) = x * ((x \ 1) * (a(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(15271(a,1),25516(a,1,2))].">
      <j1 rule="para" parents="15271 25516"/>
    </justification>
  </clause>

  <clause id="25643">
    <literal><![CDATA[
      (x * a(y,x,x)) * K(y \ (y / x),(y \ (y / x)) \ 1) = 1 / (1 / ((y \ (y / x)) \ 1))
    ]]></literal>
    <justification jstring="[para(66(a,1),25454(a,1,2,1))].">
      <j1 rule="para" parents="66 25454"/>
    </justification>
  </clause>

  <clause id="25644">
    <literal><![CDATA[
      (x * a(y,x,x)) * K(y \ (y / x),x) = 1 / (1 / ((y \ (y / x)) \ 1))
    ]]></literal>
    <justification jstring="[para(6262(a,1),25643(a,1,2))].">
      <j1 rule="para" parents="6262 25643"/>
    </justification>
  </clause>

  <clause id="25645">
    <literal><![CDATA[
      1 / (1 / ((x \ (x / y)) \ 1)) = (y * a(x,y,y)) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2397(a,1),25644(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2397 25644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25647">
    <literal><![CDATA[
      1 / (1 / ((x \ (x / y)) \ 1)) = y * (a(x,y,y) * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,20033,a(flip),b,25645,a),flip(a)].">
      <j1 rule="hyper" parents="347 20033 25645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25649">
    <literal><![CDATA[
      1 / (1 / ((x \ (x / y)) \ 1)) = y * ((y \ a(x,y,y)) * y)
    ]]></literal>
    <justification jstring="[para(23158(a,1),25647(a,2,2))].">
      <j1 rule="para" parents="23158 25647"/>
    </justification>
  </clause>

  <clause id="25650">
    <literal><![CDATA[
      1 / (1 / ((x \ (x / y)) \ 1)) = y * a(y \ x,y,y)
    ]]></literal>
    <justification jstring="[para(25465(a,1),25649(a,2,2))].">
      <j1 rule="para" parents="25465 25649"/>
    </justification>
  </clause>

  <clause id="25651">
    <literal><![CDATA[
      1 / (x \ (x / y)) = y * a(y \ x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,206,a(flip),b,25650,a)].">
      <j1 rule="hyper" parents="63 206 25650"/>
    </justification>
  </clause>

  <clause id="25653">
    <literal><![CDATA[
      ((x \ y) \ y) * a(T(x \ y,x),(x \ y) \ y,(x \ y) \ y) = 1 / (y \ (y / ((x \ y) \ y)))
    ]]></literal>
    <justification jstring="[para(4320(a,2),25651(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4320 25651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25654">
    <literal><![CDATA[
      L(x,y,(z * u) \ (L(z,w,u) * (u * T(w,v5)))) = L(x,y,L(a(u,T(w,v5),z) \ w,u,z))
    ]]></literal>
    <justification jstring="[para(21616(a,1),25483(a,1,3,2,1))].">
      <j1 rule="para" parents="21616 25483"/>
    </justification>
  </clause>

  <clause id="25655">
    <literal><![CDATA[
      L(x,y,L(a(z,T(u,w),v5) \ u,z,v5)) = L(x,y,(v5 * z) \ ((z * u) * L(v5,u,z)))
    ]]></literal>
    <justification jstring="[hyper(23562,a,25654,a),flip(a)].">
      <j1 rule="hyper" parents="23562 25654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25657">
    <literal><![CDATA[
      L(x,y,L(a(z,T(u,w),v5) \ u,z,v5)) = L(x,y,(v5 * z) \ (z * (u * v5)))
    ]]></literal>
    <justification jstring="[para(97(a,1),25655(a,2,3,2))].">
      <j1 rule="para" parents="97 25655"/>
    </justification>
  </clause>

  <clause id="25658">
    <literal><![CDATA[
      L(x,y,L(a(z,T(u,w),v5) \ u,z,v5)) = L(x,y,L(u,v5,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,23671,a(flip),b,25657,a),flip(a)].">
      <j1 rule="hyper" parents="347 23671 25657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25659">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w) \ u,z,w)) = L(x,y,L(u,w,z))
    ]]></literal>
    <justification jstring="[para(110(a,1),25658(a,1,3,1,1,2))].">
      <j1 rule="para" parents="110 25658"/>
    </justification>
  </clause>

  <clause id="25660">
    <literal><![CDATA[
      a(x,y * (z \ L(u,L(u,w,v5),L(u,w,v5))),v6) = a(x,(z \ L(L(u,w,v5),w,v5)) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,24574,a(flip),b,25574,a),flip(a)].">
      <j1 rule="hyper" parents="347 24574 25574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25661">
    <literal><![CDATA[
      a(x,(y \ L(L(z,u,w),u,w)) * v5,v6) = a(x,v5 * (y \ L(z,L(z,u,w),z)),v6)
    ]]></literal>
    <justification jstring="[para(10969(a,1),25660(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10969 25660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25662">
    <literal><![CDATA[
      a(x,(y \ L(L(z,u,w),u,w)) * v5,v6) = a(x,v5 * (y \ z),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,25216,a(flip),b,25661,a),flip(a)].">
      <j1 rule="hyper" parents="347 25216 25661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25664">
    <literal><![CDATA[
      a(x,y * (z \ L(L(u,w,v5),w,v5)),v6) = a(x,y * (z \ u),v6)
    ]]></literal>
    <justification jstring="[hyper(23994,a,25662,a)].">
      <j1 rule="hyper" parents="23994 25662"/>
    </justification>
  </clause>

  <clause id="25666">
    <literal><![CDATA[
      ((x \ a(x,x,y)) * y) * (y \ L(L(y,z,u),z,u)) = x \ L(L(y,z,u),z,u)
    ]]></literal>
    <justification jstring="[para(25583(a,1),25595(a,1,1,1,2))].">
      <j1 rule="para" parents="25583 25595"/>
    </justification>
  </clause>

  <clause id="25667">
    <literal><![CDATA[
      (x \ y) * (y \ L(L(y,z,u),z,u)) = x \ L(L(y,z,u),z,u)
    ]]></literal>
    <justification jstring="[para(18983(a,1),25666(a,1,1))].">
      <j1 rule="para" parents="18983 25666"/>
    </justification>
  </clause>

  <clause id="25669">
    <literal><![CDATA[
      ((x \ y) \ y) * a(T(x \ y,x),(x \ y) \ y,(x \ y) \ y) = 1 / (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(80(a,1),25653(a,2,2,2))].">
      <j1 rule="para" parents="80 25653"/>
    </justification>
  </clause>

  <clause id="25671">
    <literal><![CDATA[
      ((x \ y) \ y) * a(T(x \ y,x),(x \ y) \ y,x) = 1 / (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(24072(a,1),25669(a,1,2))].">
      <j1 rule="para" parents="24072 25669"/>
    </justification>
  </clause>

  <clause id="25672">
    <literal><![CDATA[
      ((x \ y) \ y) * a(T(x \ y,x),x,x) = 1 / (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(24014(a,1),25671(a,1,2))].">
      <j1 rule="para" parents="24014 25671"/>
    </justification>
  </clause>

  <clause id="25674">
    <literal><![CDATA[
      ((x \ y) \ y) * a(x \ y,x,x) = 1 / (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(15127(a,1),25672(a,1,2))].">
      <j1 rule="para" parents="15127 25672"/>
    </justification>
  </clause>

  <clause id="25677">
    <literal><![CDATA[
      x * (1 / (y \ (x \ y))) = (x \ y) \ (y * x)
    ]]></literal>
    <justification jstring="[para(25674(a,1),20983(a,1,2))].">
      <j1 rule="para" parents="25674 20983"/>
    </justification>
  </clause>

  <clause id="25678">
    <literal><![CDATA[
      L(x,y,((z \ T(u,w)) \ u) * a(z \ T(u,w),z,z)) = L(x,y,1 / (T(u,w) \ (z \ T(u,w))))
    ]]></literal>
    <justification jstring="[para(25674(a,1),21544(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25674 21544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25679">
    <literal><![CDATA[
      L(x,y,((z \ T(u,w)) \ u) * a(z \ T(u,w),z,z)) = L(x,y,(T(u,w) \ (z \ T(u,w))) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,20079,a(flip),b,25678,a),flip(a)].">
      <j1 rule="hyper" parents="347 20079 25678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25680">
    <literal><![CDATA[
      L(x,y,((z \ T(u,w)) \ u) * a(z \ T(u,w),z,z)) = L(x,y,(T(u,w) \ (z \ u)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,21901,a(flip),b,25679,a),flip(a)].">
      <j1 rule="hyper" parents="347 21901 25679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25682">
    <literal><![CDATA[
      L(x,y,((z \ T(u,w)) \ u) * a(z \ T(u,w),z,z)) = L(x,y,(u \ (z \ u)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,21548,a(flip),b,25680,a),flip(a)].">
      <j1 rule="hyper" parents="347 21548 25680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25684">
    <literal><![CDATA[
      L(x,y,((z \ T(u,w)) \ u) * a(z \ u,z,z)) = L(x,y,(u \ (z \ u)) \ 1)
    ]]></literal>
    <justification jstring="[para(15128(a,1),25682(a,1,3,2))].">
      <j1 rule="para" parents="15128 25682"/>
    </justification>
  </clause>

  <clause id="25686">
    <literal><![CDATA[
      a(x,((L(y \ 1,y \ 1,z) \ 1) * y) \ u,w) = a(x,a(z * y,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(25526(a,1),25464(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="25526 25464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25687">
    <literal><![CDATA[
      a(x,((L(y \ 1,y,z) \ 1) * y) \ u,w) = a(x,a(z * y,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(3188(a,1),25686(a,1,2,1,1,1))].">
      <j1 rule="para" parents="3188 25686"/>
    </justification>
  </clause>

  <clause id="25688">
    <literal><![CDATA[
      a(x,(y * L(y \ 1,y,z)) \ u,w) = a(x,a(z * y,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(24541,a,25687,a)].">
      <j1 rule="hyper" parents="24541 25687"/>
    </justification>
  </clause>

  <clause id="25689">
    <literal><![CDATA[
      a(x,a(y * z,z,z) \ u,w) = a(x,(z * L(z,z,y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(25026,a,25688,a),flip(a)].">
      <j1 rule="hyper" parents="25026 25688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25690">
    <literal><![CDATA[
      a(x,a(y * z,z,z) \ u,w) = a(x,a(y,z,z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,25439,a(flip),b,25689,a),flip(a)].">
      <j1 rule="hyper" parents="347 25439 25689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25691">
    <literal><![CDATA[
      (L(x,y,z) \ x) / (z * ((x \ L(x,y,z)) \ 1)) = (x \ L(x,y,z)) / ((L(x,y,z) \ x) \ z)
    ]]></literal>
    <justification jstring="[para(10882(a,1),25560(a,1,1))].">
      <j1 rule="para" parents="10882 25560"/>
    </justification>
  </clause>

  <clause id="25692">
    <literal><![CDATA[
      (L(x,y,z) \ x) / (z * (L(x,y,z) \ x)) = (x \ L(x,y,z)) / ((L(x,y,z) \ x) \ z)
    ]]></literal>
    <justification jstring="[para(10882(a,1),25691(a,1,2,2))].">
      <j1 rule="para" parents="10882 25691"/>
    </justification>
  </clause>

  <clause id="25693">
    <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(20041(a,1),25591(a,1,3))].">
      <j1 rule="para" parents="20041 25591"/>
    </justification>
  </clause>

  <clause id="25694">
    <literal><![CDATA[
      a(x,y,z \ (T(u,w) \ ((T(u,w) * w) * z))) = a(x,y,L(L(w,z,u),u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,24671,a(flip),b,25693,a),flip(a)].">
      <j1 rule="hyper" parents="63 24671 25693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25697">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((u * w) * z))) = a(x,y,L(L(w,z,u),u,z))
    ]]></literal>
    <justification jstring="[para(20965(a,1),25694(a,1,3,2))].">
      <j1 rule="para" parents="20965 25694"/>
    </justification>
  </clause>

  <clause id="25698">
    <literal><![CDATA[
      a(x,y,L(L(z \ 1,u,w),w,u)) = a(x,y,z * a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,24796,a(flip),b,25697,a),flip(a)].">
      <j1 rule="hyper" parents="63 24796 25697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25700">
    <literal><![CDATA[
      x \ a(x,x,L(L(x,y,z),z,y)) = L(1 / x,x,a(z,x,y))
    ]]></literal>
    <justification jstring="[para(25697(a,1),24607(a,1,2))].">
      <j1 rule="para" parents="25697 24607"/>
    </justification>
  </clause>

  <clause id="25701">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),w,u)) = a(x,y,z * a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(15053,a,25698,a)].">
      <j1 rule="hyper" parents="15053 25698"/>
    </justification>
  </clause>

  <clause id="25702">
    <literal><![CDATA[
      L(1 / x,x,a(y,x,z)) = x \ K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(21996(a,1),25700(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21996 25700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25703">
    <literal><![CDATA[
      L(1 / x,x,a(y,x,z)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(347,a,1925,a(flip),b,25702,a),flip(a)].">
      <j1 rule="hyper" parents="347 1925 25702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25705">
    <literal><![CDATA[
      (1 / x) \ a(y,x,z) = a(y,x,z) * x
    ]]></literal>
    <justification jstring="[para(25703(a,1),23243(a,1,1))].">
      <j1 rule="para" parents="25703 23243"/>
    </justification>
  </clause>

  <clause id="25706">
    <literal><![CDATA[
      a(x,y,L(z,u * R(w,v5,v6),u * L(w,v5,v6)) * (u * L(w,v5,v6))) = a(x,y,(u * R(w,v5,v6)) \ z)
    ]]></literal>
    <justification jstring="[para(22863(a,1),25315(a,1,3,1))].">
      <j1 rule="para" parents="22863 25315"/>
    </justification>
  </clause>

  <clause id="25707">
    <literal><![CDATA[
      a(x,y,((a(z,u,L(w * v5,v5,v5)) \ u) * z) * (v5 \ w)) = a(x,y,(u * L(w * v5,v5,v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,24365,a(flip),b,25476,a),flip(a)].">
      <j1 rule="hyper" parents="347 24365 25476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25709">
    <literal><![CDATA[
      a(x,y,((a(z,u,w \ v5) \ u) * z) * (w \ v5)) = a(x,y,(u * L(v5 * w,w,w)) * z)
    ]]></literal>
    <justification jstring="[para(25258(a,1),25707(a,1,3,1,1,1))].">
      <j1 rule="para" parents="25258 25707"/>
    </justification>
  </clause>

  <clause id="25710">
    <literal><![CDATA[
      a(x,y,(z * L(u * w,w,w)) * v5) = a(x,y,v5 * (T(z,v5) * (w \ u)))
    ]]></literal>
    <justification jstring="[para(25398(a,1),25709(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25398 25709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25711">
    <literal><![CDATA[
      a(x,y,(z * L(u * w,w,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * (w \ u)) * v5) = v6
    ]]></literal>
    <justification jstring="[para(25710(a,2),24447(a,1))].">
      <j1 rule="para" parents="25710 24447"/>
    </justification>
  </clause>

  <clause id="25712">
    <literal><![CDATA[
      R(x,y,z \ (u \ ((u \ w) \ R(u,v5,u)))) = R(x,y,L(z,z,u \ ((u \ w) \ u)) * (w \ u))
    ]]></literal>
    <justification jstring="[para(21600(a,1),25624(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="21600 25624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25714">
    <literal><![CDATA[
      a(x,y,L(z,u * L(w,v5,v6),u * L(w,v5,v6)) * (u * L(w,v5,v6))) = a(x,y,(u * R(w,v5,v6)) \ z)
    ]]></literal>
    <justification jstring="[para(23781(a,1),25706(a,1,3,1))].">
      <j1 rule="para" parents="23781 25706"/>
    </justification>
  </clause>

  <clause id="25715">
    <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(25714(a,1),24554(a,1))].">
      <j1 rule="para" parents="25714 24554"/>
    </justification>
  </clause>

  <clause id="25716">
    <literal><![CDATA[
      a(x,(T(y,z) * L(u,1 / T(y,z),1 / T(y,z))) \ w,v5) = a(x,L((1 / T(y,z)) * u,y,y) \ w,v5)
    ]]></literal>
    <justification jstring="[para(3197(a,1),25233(a,2,2,1))].">
      <j1 rule="para" parents="3197 25233"/>
    </justification>
  </clause>

  <clause id="25717">
    <literal><![CDATA[
      a(x,(T(y,z) * L(u,1 / T(y,z),T(y,z) \ 1)) \ w,v5) = a(x,L((1 / T(y,z)) * u,y,y) \ w,v5)
    ]]></literal>
    <justification jstring="[para(3936(a,1),25716(a,1,2,1,2))].">
      <j1 rule="para" parents="3936 25716"/>
    </justification>
  </clause>

  <clause id="25718">
    <literal><![CDATA[
      a(x,(T(y,z) * L(u,1 / T(y,z),y \ 1)) \ w,v5) = a(x,L((1 / T(y,z)) * u,y,y) \ w,v5)
    ]]></literal>
    <justification jstring="[para(21468(a,1),25717(a,1,2,1,2))].">
      <j1 rule="para" parents="21468 25717"/>
    </justification>
  </clause>

  <clause id="25719">
    <literal><![CDATA[
      a(x,(T(y,z) * L(u,T(y,z),y \ 1)) \ w,v5) = a(x,L((1 / T(y,z)) * u,y,y) \ w,v5)
    ]]></literal>
    <justification jstring="[para(3189(a,1),25718(a,1,2,1,2))].">
      <j1 rule="para" parents="3189 25718"/>
    </justification>
  </clause>

  <clause id="25721">
    <literal><![CDATA[
      a(x,L((1 / T(y,z)) * u,y,y) \ w,v5) = a(x,(T(y,z) * L(u,y,y \ 1)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(21616(a,1),25719(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="21616 25719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25723">
    <literal><![CDATA[
      L(a(x,y \ z,y \ z),u,w) * (w * u) = w * (u * (L(z / y,y \ z,x) \ (z / y)))
    ]]></literal>
    <justification jstring="[para(19984(a,1),25501(a,1,1,1))].">
      <j1 rule="para" parents="19984 25501"/>
    </justification>
  </clause>

  <clause id="25725">
    <literal><![CDATA[
      a(x,y,z * ((u * u) * (((u * u) * (w \ ((u * u) \ v5))) * v6))) = a(x,y,z * ((w \ T(v5,u * u)) * v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,14921,a(flip),b,24673,a),flip(a)].">
      <j1 rule="hyper" parents="347 14921 24673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25727">
    <literal><![CDATA[
      a(x,y,z * ((u * u) * (((u * u) * (w \ ((u * u) \ v5))) * v6))) = a(x,y,z * ((w \ v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,24505,a(flip),b,25725,a),flip(a)].">
      <j1 rule="hyper" parents="347 24505 25725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25728">
    <literal><![CDATA[
      a(x,y,z * (((u * u) * (w \ ((u * u) \ v5))) * v6)) = a(x,y,z * ((w \ v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(24288,a,25727,a)].">
      <j1 rule="hyper" parents="24288 25727"/>
    </justification>
  </clause>

  <clause id="25731">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ ((v5 * v5) \ v6)))) = a(x,y,z * ((w \ v6) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,24877,a(flip),b,25728,a)].">
      <j1 rule="hyper" parents="63 24877 25728"/>
    </justification>
  </clause>

  <clause id="25733">
    <literal><![CDATA[
      a(x,L(y,z * u,w) * (w * (z * T(u,v5 * v5))),v6) = a(x,w * ((z * ((v5 * v5) \ u)) * ((v5 * v5) * y)),v6)
    ]]></literal>
    <justification jstring="[para(21614(a,1),24414(a,1,2,1))].">
      <j1 rule="para" parents="21614 24414"/>
    </justification>
  </clause>

  <clause id="25734">
    <literal><![CDATA[
      a(x,L(y,z * u,w) * (w * (z * u)),v5) = a(x,w * ((z * ((v6 * v6) \ u)) * ((v6 * v6) * y)),v5)
    ]]></literal>
    <justification jstring="[hyper(24416,a,25733,a)].">
      <j1 rule="hyper" parents="24416 25733"/>
    </justification>
  </clause>

  <clause id="25736">
    <literal><![CDATA[
      a(x,y * ((z * ((u * u) \ w)) * ((u * u) * v5)),v6) = a(x,y * ((z * w) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(24003,a,25734,a),flip(a)].">
      <j1 rule="hyper" parents="24003 25734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25737">
    <literal><![CDATA[
      a(x,y * ((z * ((u * u) \ w)) * v5),v6) = a(x,y * ((z * w) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(24677,a,25736,a)].">
      <j1 rule="hyper" parents="24677 25736"/>
    </justification>
  </clause>

  <clause id="25739">
    <literal><![CDATA[
      a(x,y * (((z \ 1) * u) * w),v5) = a(x,y * ((z * u) * w),v5)
    ]]></literal>
    <justification jstring="[para(497(a,1),25737(a,1,2,2,1))].">
      <j1 rule="para" parents="497 25737"/>
    </justification>
  </clause>

  <clause id="25740">
    <literal><![CDATA[
      a(x,(y * ((z \ 1) * u)) * w,v5) = a(x,w * ((z * u) * y),v5)
    ]]></literal>
    <justification jstring="[hyper(24247,a,25739,a)].">
      <j1 rule="hyper" parents="24247 25739"/>
    </justification>
  </clause>

  <clause id="25741">
    <literal><![CDATA[
      a(x,y * (z * ((u \ 1) * w)),v5) = a(x,y * ((u * w) * z),v5)
    ]]></literal>
    <justification jstring="[hyper(24006,a,25739,a)].">
      <j1 rule="hyper" parents="24006 25739"/>
    </justification>
  </clause>

  <clause id="25742">
    <literal><![CDATA[
      (x * y) * (z \ (L(z,u,w) * L(L(z,u,w) \ z,z,x))) = x * (y * ((z \ L(z,u,w)) \ (x \ ((x / z) * L(z,u,w)))))
    ]]></literal>
    <justification jstring="[para(3354(a,1),25570(a,1,2))].">
      <j1 rule="para" parents="3354 25570"/>
    </justification>
  </clause>

  <clause id="25743">
    <literal><![CDATA[
      a(x,y,z \ ((u * ((w * w) * v5)) * (((w * w) * v5) \ 1))) = a(x,y,z \ ((u * (((w * w) * v5) \ 1)) * v5))
    ]]></literal>
    <justification jstring="[hyper(24215,a,24765,a)].">
      <j1 rule="hyper" parents="24215 24765"/>
    </justification>
  </clause>

  <clause id="25745">
    <literal><![CDATA[
      a(x,y,z \ R(u,(w * w) * v5,(w * w) * v5)) = a(x,y,z \ ((u * (((w * w) * v5) \ 1)) * v5))
    ]]></literal>
    <justification jstring="[para(786(a,1),25743(a,1,3,2))].">
      <j1 rule="para" parents="786 25743"/>
    </justification>
  </clause>

  <clause id="25746">
    <literal><![CDATA[
      a(x,y,z \ ((u * (((w * w) * v5) \ 1)) * v5)) = a(x,y,z \ R(u,(w * w) * v5,v5))
    ]]></literal>
    <justification jstring="[para(2240(a,1),25745(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2240 25745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25748">
    <literal><![CDATA[
      a(x,y,z \ ((u * (((w * w) * v5) \ 1)) * v5)) = a(x,y,z \ R(u,v5,v5))
    ]]></literal>
    <justification jstring="[para(20647(a,1),25746(a,2,3,2))].">
      <j1 rule="para" parents="20647 25746"/>
    </justification>
  </clause>

  <clause id="25749">
    <literal><![CDATA[
      a(x,y,z \ ((u * (((w * w) * v5) \ 1)) * v5)) = a(x,y,z \ L(u,v5,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,25307,a(flip),b,25748,a),flip(a)].">
      <j1 rule="hyper" parents="347 25307 25748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25751">
    <literal><![CDATA[
      a(x,y,z \ ((u * ((w * w) * v5)) * v5)) = a(x,y,z \ L(u,v5,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,24755,a(flip),b,25749,a)].">
      <j1 rule="hyper" parents="63 24755 25749"/>
    </justification>
  </clause>

  <clause id="25752">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) * w)) = a(x,y,z \ L(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,24945,a(flip),b,25751,a)].">
      <j1 rule="hyper" parents="63 24945 25751"/>
    </justification>
  </clause>

  <clause id="25753">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * u))) = a(x,y,z \ L(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(24214,a,25752,a)].">
      <j1 rule="hyper" parents="24214 25752"/>
    </justification>
  </clause>

  <clause id="25754">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) \ L(z \ u,z,z)) = a(x,y,a(z \ u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,25015,a(flip),b,25752,a),flip(a)].">
      <j1 rule="hyper" parents="63 25015 25752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25755">
    <literal><![CDATA[
      a(x,y,a(z,u,u \ K(w,v5))) = a(x,y,z \ L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,25043,a,b,25753,a)].">
      <j1 rule="hyper" parents="63 25043 25753"/>
    </justification>
  </clause>

  <clause id="25756">
    <literal><![CDATA[
      a(x,y,L(z \ L(z,u,u),w,v5)) = a(x,y,a(L(z,w,v5),u,u \ K(v6,v7)))
    ]]></literal>
    <justification jstring="[para(4638(a,1),25755(a,2,3)),flip(a)].">
      <j1 rule="para" parents="4638 25755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25757">
    <literal><![CDATA[
      a(x,y,a(z \ u,z,z)) = a(x,y,((z \ 1) \ u) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,24759,a(flip),b,25754,a),flip(a)].">
      <j1 rule="hyper" parents="63 24759 25754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25758">
    <literal><![CDATA[
      a(x,y,a(z \ u,z,z)) = a(x,y,(z \ u) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,24510,a(flip),b,25757,a),flip(a)].">
      <j1 rule="hyper" parents="347 24510 25757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25759">
    <literal><![CDATA[
      a(x,y,a(z \ u,z,z)) = a(x,y,a(u,z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,24592,a(flip),b,25758,a),flip(a)].">
      <j1 rule="hyper" parents="347 24592 25758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25760">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,u),w,v5)) = a(x,y,a(L(z,w,v5),u,u \ K(v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(15050,a,25756,a)].">
      <j1 rule="hyper" parents="15050 25756"/>
    </justification>
  </clause>

  <clause id="25761">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,u),w,v5)) = a(x,y,a(L(z,w,v5),u,u))
    ]]></literal>
    <justification jstring="[para(24308(a,1),25760(a,2,3))].">
      <j1 rule="para" parents="24308 25760"/>
    </justification>
  </clause>

  <clause id="25762">
    <literal><![CDATA[
      a(x,y,z) * (x * (u * R(u \ (a(x,y,z) \ u),w,v5))) = (x * u) * (a(x,y,z) * R(a(x,y,z) \ 1,w,v5))
    ]]></literal>
    <justification jstring="[para(1185(a,1),25418(a,1,2))].">
      <j1 rule="para" parents="1185 25418"/>
    </justification>
  </clause>

  <clause id="25763">
    <literal><![CDATA[
      x * (a(x,y,z) * (u * R(u \ (a(x,y,z) \ u),w,v5))) = (x * u) * (a(x,y,z) * R(a(x,y,z) \ 1,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,25377,a(flip),b,25762,a)].">
      <j1 rule="hyper" parents="63 25377 25762"/>
    </justification>
  </clause>

  <clause id="25764">
    <literal><![CDATA[
      (x * y) * (a(x,z,u) * R(a(x,z,u) \ 1,w,v5)) = x * (y * (a(x,z,u) * R(a(x,z,u) \ 1,w,v5)))
    ]]></literal>
    <justification jstring="[para(23587(a,1),25763(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23587 25763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25765">
    <literal><![CDATA[
      (x * y) * (a(x,z,u) * R(a(x,z,u) \ 1,w,v5)) = x * (y * (a(x,z,u) * L(a(x,z,u) \ 1,w,v5)))
    ]]></literal>
    <justification jstring="[para(23384(a,1),25764(a,2,2,2,2))].">
      <j1 rule="para" parents="23384 25764"/>
    </justification>
  </clause>

  <clause id="25766">
    <literal><![CDATA[
      (x * y) * (a(x,z,u) * R(a(x,z,u) \ 1,w,v5)) = x * (y * (a(x,z,u) \ L(a(x,z,u),w,v5)))
    ]]></literal>
    <justification jstring="[para(3343(a,1),25765(a,2,2,2))].">
      <j1 rule="para" parents="3343 25765"/>
    </justification>
  </clause>

  <clause id="25767">
    <literal><![CDATA[
      (x * y) * (a(x,z,u) * L(a(x,z,u) \ 1,w,v5)) = x * (y * (a(x,z,u) \ L(a(x,z,u),w,v5)))
    ]]></literal>
    <justification jstring="[para(23384(a,1),25766(a,1,2,2))].">
      <j1 rule="para" parents="23384 25766"/>
    </justification>
  </clause>

  <clause id="25768">
    <literal><![CDATA[
      (x * y) * (a(x,z,u) \ L(a(x,z,u),w,v5)) = x * (y * (a(x,z,u) \ L(a(x,z,u),w,v5)))
    ]]></literal>
    <justification jstring="[para(3343(a,1),25767(a,1,2))].">
      <j1 rule="para" parents="3343 25767"/>
    </justification>
  </clause>

  <clause id="25769">
    <literal><![CDATA[
      L(x,(y \ L(y,z,u)) * (y * L(L(y,z,u),z,u)),L(y,z,u)) = L(x,L(y,z,u),L(y,z,u) \ L(L(y,z,u),z,u))
    ]]></literal>
    <justification jstring="[para(1295(a,1),25599(a,1,2,1))].">
      <j1 rule="para" parents="1295 25599"/>
    </justification>
  </clause>

  <clause id="25770">
    <literal><![CDATA[
      L(x,y * (L(L(y,z,u),z,u) * (y \ L(y,z,u))),L(y,z,u)) = L(x,L(y,z,u),L(y,z,u) \ L(L(y,z,u),z,u))
    ]]></literal>
    <justification jstring="[para(20952(a,1),25769(a,1,2))].">
      <j1 rule="para" parents="20952 25769"/>
    </justification>
  </clause>

  <clause id="25771">
    <literal><![CDATA[
      a(x,y,L((L(z,u,w) \ v5) \ v6,L(z,u,w) \ v5,L(z,u,w))) = a(x,y,((z \ v5) * T(z,v7)) \ (v6 * L(T(z,v7),u,w)))
    ]]></literal>
    <justification jstring="[para(20531(a,1),24552(a,1,3))].">
      <j1 rule="para" parents="20531 24552"/>
    </justification>
  </clause>

  <clause id="25772">
    <literal><![CDATA[
      a(x,y,((z \ u) * T(z,w)) \ (v5 * L(T(z,w),v6,v7))) = a(x,y,u \ (L(z,v6,v7) * v5))
    ]]></literal>
    <justification jstring="[para(561(a,1),25771(a,1,3)),flip(a)].">
      <j1 rule="para" parents="561 25771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25774">
    <literal><![CDATA[
      a(x,y,((z \ u) * z) \ (w * L(T(z,v5),v6,v7))) = a(x,y,u \ (L(z,v6,v7) * w))
    ]]></literal>
    <justification jstring="[hyper(24198,a,25772,a)].">
      <j1 rule="hyper" parents="24198 25772"/>
    </justification>
  </clause>

  <clause id="25775">
    <literal><![CDATA[
      a(x,y,z \ (u * L(T(w,v5),v6,v7))) = a(x,y,z \ (L(w,v6,v7) * u))
    ]]></literal>
    <justification jstring="[hyper(24193,a,25774,a)].">
      <j1 rule="hyper" parents="24193 25774"/>
    </justification>
  </clause>

  <clause id="25777">
    <literal><![CDATA[
      a(x,y,z \ (R(T(u * K((w * w) * v5,u),v6),v7,v8) * v5)) = a(x,y,z \ (L(u,v7,v8) * ((w * w) * v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,25641,a,b,25775,a)].">
      <j1 rule="hyper" parents="63 25641 25775"/>
    </justification>
  </clause>

  <clause id="25780">
    <literal><![CDATA[
      a(x,y,z \ (R(T(u * K((w * w) * v5,u),v6),v7,v8) * v5)) = a(x,y,z \ (L(u,v7,v8) * v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,24753,a(flip),b,25777,a),flip(a)].">
      <j1 rule="hyper" parents="347 24753 25777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25782">
    <literal><![CDATA[
      a(x,y,z \ (R(u,w,v5) * v6)) = a(x,y,z \ (L(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(5058(a,1),25780(a,1,3,2,1,1))].">
      <j1 rule="para" parents="5058 25780"/>
    </justification>
  </clause>

  <clause id="25783">
    <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(2008(a,1),25782(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2008 25782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25784">
    <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(347,a,24137,a(flip),b,25783,a),flip(a)].">
      <j1 rule="hyper" parents="347 24137 25783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25785">
    <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(347,a,24757,a(flip),b,25784,a),flip(a)].">
      <j1 rule="hyper" parents="347 24757 25784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25786">
    <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(23670(a,1),25785(a,1,3,2,2))].">
      <j1 rule="para" parents="23670 25785"/>
    </justification>
  </clause>

  <clause id="25787">
    <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(2008(a,1),25786(a,1,3,2))].">
      <j1 rule="para" parents="2008 25786"/>
    </justification>
  </clause>

  <clause id="25788">
    <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(24213,a,25787,a)].">
      <j1 rule="hyper" parents="24213 25787"/>
    </justification>
  </clause>

  <clause id="25789">
    <literal><![CDATA[
      a(x,y,z \ (u \ R(w,v5,v6))) = a(x,y,z \ (u \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(24768,a,25788,a),flip(a)].">
      <j1 rule="hyper" parents="24768 25788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25790">
    <literal><![CDATA[
      a(a(x,y,y) \ 1,y \ ((x \ (x / y)) \ y),z) * (((y * ((x * y) \ x)) \ y) * z) = L(((x * y) \ x) \ z,(x * y) \ x,y)
    ]]></literal>
    <justification jstring="[para(19105(a,1),25462(a,1,1))].">
      <j1 rule="para" parents="19105 25462"/>
    </justification>
  </clause>

  <clause id="25791">
    <literal><![CDATA[
      a(a(x,y,y) \ 1,1 / (x \ (x / y)),z) * (((y * ((x * y) \ x)) \ y) * z) = L(((x * y) \ x) \ z,(x * y) \ x,y)
    ]]></literal>
    <justification jstring="[para(15347(a,1),25790(a,1,1,2))].">
      <j1 rule="para" parents="15347 25790"/>
    </justification>
  </clause>

  <clause id="25792">
    <literal><![CDATA[
      a(a(x,y,y) \ 1,(x \ (x / y)) \ 1,z) * (((y * ((x * y) \ x)) \ y) * z) = L(((x * y) \ x) \ z,(x * y) \ x,y)
    ]]></literal>
    <justification jstring="[para(4044(a,1),25791(a,1,1))].">
      <j1 rule="para" parents="4044 25791"/>
    </justification>
  </clause>

  <clause id="25793">
    <literal><![CDATA[
      a(a(x,y,y) \ 1,x \ (y \ x),z) * (((y * ((x * y) \ x)) \ y) * z) = L(((x * y) \ x) \ z,(x * y) \ x,y)
    ]]></literal>
    <justification jstring="[para(24256(a,1),25792(a,1,1))].">
      <j1 rule="para" parents="24256 25792"/>
    </justification>
  </clause>

  <clause id="25794">
    <literal><![CDATA[
      L(L(x \ 1,x,x \ y) \ z,T(y \ (y / x),K(x,u)),(y / T(x,u)) * x) = (y / T(x,u)) \ (((y / T(x,u)) * x) * z)
    ]]></literal>
    <justification jstring="[para(21032(a,1),23878(a,1,2))].">
      <j1 rule="para" parents="21032 23878"/>
    </justification>
  </clause>

  <clause id="25795">
    <literal><![CDATA[
      L(L(x \ 1,x,x \ y) \ z,y \ (y / x),(y / T(x,u)) * x) = (y / T(x,u)) \ (((y / T(x,u)) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(21722,a,25794,a)].">
      <j1 rule="hyper" parents="21722 25794"/>
    </justification>
  </clause>

  <clause id="25797">
    <literal><![CDATA[
      L(L(x \ 1,x,x \ y) \ z,y \ (y / x),y * K(u,x)) = (y / T(x,u)) \ (((y / T(x,u)) * x) * z)
    ]]></literal>
    <justification jstring="[para(6107(a,1),25795(a,1,3))].">
      <j1 rule="para" parents="6107 25795"/>
    </justification>
  </clause>

  <clause id="25798">
    <literal><![CDATA[
      L(L(x \ 1,x,x \ y) \ z,y \ (y / x),y) = (y / T(x,u)) \ (((y / T(x,u)) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(21520,a,25797,a)].">
      <j1 rule="hyper" parents="21520 25797"/>
    </justification>
  </clause>

  <clause id="25799">
    <literal><![CDATA[
      L(L(x \ 1,x,x \ y) \ z,y \ (x \ y),y) = (y / T(x,u)) \ (((y / T(x,u)) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(21763,a,25798,a)].">
      <j1 rule="hyper" parents="21763 25798"/>
    </justification>
  </clause>

  <clause id="25801">
    <literal><![CDATA[
      (x / T(y,z)) \ (((x / T(y,z)) * y) * u) = (x / y) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21856,a(flip),b,25799,a),flip(a)].">
      <j1 rule="hyper" parents="63 21856 25799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25802">
    <literal><![CDATA[
      (x / T(y,z)) \ ((x * K(z,y)) * u) = (x / y) \ (x * u)
    ]]></literal>
    <justification jstring="[para(6107(a,1),25801(a,1,2,1))].">
      <j1 rule="para" parents="6107 25801"/>
    </justification>
  </clause>

  <clause id="25803">
    <literal><![CDATA[
      (x / T(y,z)) \ (x * (K(z,y) * u)) = (x / y) \ (x * u)
    ]]></literal>
    <justification jstring="[para(20151(a,1),25802(a,1,2))].">
      <j1 rule="para" parents="20151 25802"/>
    </justification>
  </clause>

  <clause id="25804">
    <literal><![CDATA[
      (T(x,y) \ z) \ (((T(x,y) \ z) * x) * u) = (z / x) \ (z * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,21040,a,b,25803,a)].">
      <j1 rule="hyper" parents="63 21040 25803"/>
    </justification>
  </clause>

  <clause id="25806">
    <literal><![CDATA[
      (((T(x,y) \ z) * x) \ (T(x,y) \ z)) \ ((T(x,y) \ z) \ ((T(x,y) \ z) * x)) = (z / x) \ (z * ((T(x,y) \ z) \ ((T(x,y) \ z) * x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,25519,a,b,25804,a)].">
      <j1 rule="hyper" parents="63 25519 25804"/>
    </justification>
  </clause>

  <clause id="25807">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,L(T(x,x \ 1),y,z) \ (x \ 1),L(x,y,z)) = ((x \ 1) \ 1) \ (L(T(x,x \ 1),y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(20659,a,21196,a)].">
      <j1 rule="hyper" parents="20659 21196"/>
    </justification>
  </clause>

  <clause id="25808">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,L(T(x,x \ 1),y,z) \ x,L(x,y,z)) = ((x \ 1) \ 1) \ (L(T(x,x \ 1),y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(21771,a,25807,a)].">
      <j1 rule="hyper" parents="21771 25807"/>
    </justification>
  </clause>

  <clause id="25810">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,(L(x,y,z) \ 1) * x,L(x,y,z)) = ((x \ 1) \ 1) \ (L(T(x,x \ 1),y,z) * u)
    ]]></literal>
    <justification jstring="[para(9331(a,1),25808(a,1,2))].">
      <j1 rule="para" parents="9331 25808"/>
    </justification>
  </clause>

  <clause id="25811">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (L(T(x,x \ 1),y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,x * L(x,y,z),L(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(25810(a,1),21703(a,1))].">
      <j1 rule="para" parents="25810 21703"/>
    </justification>
  </clause>

  <clause id="25812">
    <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(25811,a,21392,a)].">
      <j1 rule="hyper" parents="25811 21392"/>
    </justification>
  </clause>

  <clause id="25813">
    <literal><![CDATA[
      a(x,y,L(z,u * L(L(u,w,v5),w,v5),v6 * u) * (v6 * L(L(u,w,v5),w,v5))) = a(x,y,(v6 * u) * ((u \ L(L(u,w,v5),w,v5)) * z))
    ]]></literal>
    <justification jstring="[para(10926(a,1),25598(a,1,3,1))].">
      <j1 rule="para" parents="10926 25598"/>
    </justification>
  </clause>

  <clause id="25814">
    <literal><![CDATA[
      L(a(x,x \ (y \ z),u),w,a(x,x \ (y \ z),u)) = a(x,x \ (u \ (x * ((x \ (z / y)) * u))),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,24257,a(flip),b,25621,a),flip(a)].">
      <j1 rule="hyper" parents="347 24257 25621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25815">
    <literal><![CDATA[
      a(x,y,L(z,u * u,w * u) * (w * L(L(u,v5,v6),v5,v6))) = a(x,y,(w * u) * ((u \ L(L(u,v5,v6),v5,v6)) * z))
    ]]></literal>
    <justification jstring="[para(25563(a,1),25813(a,1,3,1))].">
      <j1 rule="para" parents="25563 25813"/>
    </justification>
  </clause>

  <clause id="25816">
    <literal><![CDATA[
      a(x,y,(z * u) * ((u \ L(L(u,w,v5),w,v5)) * v6)) = a(x,y,v6 * (z * L(L(u,w,v5),w,v5)))
    ]]></literal>
    <justification jstring="[para(534(a,1),25815(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="534 25815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25818">
    <literal><![CDATA[
      a(x,y,z * (u * L(L(w,v5,v6),v5,v6))) = a(x,y,(u * w) * z)
    ]]></literal>
    <justification jstring="[hyper(25576,a,25816,a),flip(a)].">
      <j1 rule="hyper" parents="25576 25816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25819">
    <literal><![CDATA[
      (x * (y * (x \ L(x,z,u)))) * a(L(y,x,x \ L(x,z,u)),x * L(x,z,u),x) = (x \ L(x,z,u)) * (x * R(y,x \ L(x,z,u),x))
    ]]></literal>
    <justification jstring="[para(24144(a,1),21197(a,1,2))].">
      <j1 rule="para" parents="24144 21197"/>
    </justification>
  </clause>

  <clause id="25820">
    <literal><![CDATA[
      ((x / y) * L(T(y,z),(y \ x) * K(y,z),y)) \ ((y \ x) * K(y,z)) = L(T(y,x * K(y,z)) \ 1,y,(y \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[para(6761(a,1),21436(a,2,1,1,2))].">
      <j1 rule="para" parents="6761 21436"/>
    </justification>
  </clause>

  <clause id="25821">
    <literal><![CDATA[
      ((x / y) * L(T(y,z),(y \ x) * K(y,z),y)) \ ((y \ x) * K(y,z)) = L(T(y,x) \ 1,y,(y \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[para(7855(a,1),25820(a,2,1,1))].">
      <j1 rule="para" parents="7855 25820"/>
    </justification>
  </clause>

  <clause id="25822">
    <literal><![CDATA[
      ((x / y) * L(T(y,z),(y \ x) * K(y,z),y)) \ ((y \ x) * K(y,z)) = L(T(y,x) \ 1,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,21459,a(flip),b,25821,a),flip(a)].">
      <j1 rule="hyper" parents="347 21459 25821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25825">
    <literal><![CDATA[
      ((x / y) * L(T(y,z),(y \ x) * K(y,z),y)) \ ((y \ x) * K(y,z)) = x \ ((T(x,y) / y) * 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,12404,a(flip),b,25822,a),flip(a)].">
      <j1 rule="hyper" parents="347 12404 25822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25826">
    <literal><![CDATA[
      ((x / y) * L(T(y,z),(y \ x) * K(y,z),y)) \ ((y \ x) * K(y,z)) = x \ (T(x,y) / y)
    ]]></literal>
    <justification jstring="[hyper(347,a,175,a(flip),b,25825,a),flip(a)].">
      <j1 rule="hyper" parents="347 175 25825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25827">
    <literal><![CDATA[
      ((x / y) * L(T(y,z),y \ x,y)) \ ((y \ x) * K(y,z)) = x \ (T(x,y) / y)
    ]]></literal>
    <justification jstring="[para(11179(a,1),25826(a,1,1,2))].">
      <j1 rule="para" parents="11179 25826"/>
    </justification>
  </clause>

  <clause id="25829">
    <literal><![CDATA[
      ((x / y) * L(T(y,z),y * x,y)) \ ((y \ x) * K(y,z)) = x \ (T(x,y) / y)
    ]]></literal>
    <justification jstring="[para(12204(a,1),25827(a,1,1,2))].">
      <j1 rule="para" parents="12204 25827"/>
    </justification>
  </clause>

  <clause id="25831">
    <literal><![CDATA[
      (x * (y \ L(T(y,z),y * x,y))) \ ((y \ x) * K(y,z)) = x \ (T(x,y) / y)
    ]]></literal>
    <justification jstring="[para(23308(a,1),25829(a,1,1))].">
      <j1 rule="para" parents="23308 25829"/>
    </justification>
  </clause>

  <clause id="25832">
    <literal><![CDATA[
      ((x * ((x \ y) * T(x,z))) / x) \ ((x \ y) * K(x,z)) = y \ (T(y,x) / x)
    ]]></literal>
    <justification jstring="[para(21371(a,1),25831(a,1,1))].">
      <j1 rule="para" parents="21371 25831"/>
    </justification>
  </clause>

  <clause id="25833">
    <literal><![CDATA[
      (x \ y) \ (x \ (x \ y)) = y \ (T(y,x) / x)
    ]]></literal>
    <justification jstring="[hyper(63,a,22378,a(flip),b,25832,a)].">
      <j1 rule="hyper" parents="63 22378 25832"/>
    </justification>
  </clause>

  <clause id="25834">
    <literal><![CDATA[
      L(x,y \ (x \ T(y,x)),y) * (x \ T(y,x)) = y * (((x \ y) \ (x \ (x \ y))) * x)
    ]]></literal>
    <justification jstring="[para(25833(a,2),13709(a,2,2,1))].">
      <j1 rule="para" parents="25833 13709"/>
    </justification>
  </clause>

  <clause id="25835">
    <literal><![CDATA[
      L(x,y \ (x \ y),y) * (x \ T(y,x)) = y * (((x \ y) \ (x \ (x \ y))) * x)
    ]]></literal>
    <justification jstring="[para(21692(a,1),25834(a,1,1))].">
      <j1 rule="para" parents="21692 25834"/>
    </justification>
  </clause>

  <clause id="25836">
    <literal><![CDATA[
      x \ (y * L(x,y \ (x \ y),y)) = y * (((x \ y) \ (x \ (x \ y))) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,20688,a(flip),b,25835,a)].">
      <j1 rule="hyper" parents="63 20688 25835"/>
    </justification>
  </clause>

  <clause id="25838">
    <literal><![CDATA[
      x * (((y \ x) \ (y \ (y \ x))) * y) = T(x * ((x \ (x / y)) * y),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,21124,a(flip),b,25836,a),flip(a)].">
      <j1 rule="hyper" parents="63 21124 25836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25839">
    <literal><![CDATA[
      x * (((y \ x) \ (y \ (y \ x))) * y) = T(x * (y * ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[para(3261(a,1),25838(a,2,1,2))].">
      <j1 rule="para" parents="3261 25838"/>
    </justification>
  </clause>

  <clause id="25840">
    <literal><![CDATA[
      T(x * (y * ((x * y) \ x)),y) = x * ((x \ (T(x,y) / y)) * y)
    ]]></literal>
    <justification jstring="[para(25833(a,1),25839(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="25833 25839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25841">
    <literal><![CDATA[
      T(x * (y * ((x * y) \ x)),y) = x * (y * ((x * y) \ T(x,y)))
    ]]></literal>
    <justification jstring="[hyper(347,a,22539,a(flip),b,25840,a),flip(a)].">
      <j1 rule="hyper" parents="347 22539 25840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25842">
    <literal><![CDATA[
      T(x * (y * ((x * y) \ x)),y) = x * (y * ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(6347(a,1),25841(a,2,2,2))].">
      <j1 rule="para" parents="6347 25841"/>
    </justification>
  </clause>

  <clause id="25843">
    <literal><![CDATA[
      T(x * (a(x,y,y) \ 1),y) = x * (y * ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(25441(a,1),25842(a,1,1,2))].">
      <j1 rule="para" parents="25441 25842"/>
    </justification>
  </clause>

  <clause id="25844">
    <literal><![CDATA[
      T(a(x,y,y) \ x,y) = x * (y * ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(25386(a,1),25843(a,1,1))].">
      <j1 rule="para" parents="25386 25843"/>
    </justification>
  </clause>

  <clause id="25845">
    <literal><![CDATA[
      L(a(x,x,y \ L(L(y,z,u),z,u)) * ((w \ (L(L(y,z,u),z,u) \ y)) \ (w \ 1)),x,x) = y \ L(L(y,z,u),z,u)
    ]]></literal>
    <justification jstring="[para(25608(a,1),25609(a,1,1,1,3))].">
      <j1 rule="para" parents="25608 25609"/>
    </justification>
  </clause>

  <clause id="25846">
    <literal><![CDATA[
      L(a(x,x,y * L(L(y,z,u),z,u)) * ((w \ (L(L(y,z,u),z,u) \ y)) \ (w \ 1)),x,x) = y \ L(L(y,z,u),z,u)
    ]]></literal>
    <justification jstring="[para(14986(a,1),25845(a,1,1,1))].">
      <j1 rule="para" parents="14986 25845"/>
    </justification>
  </clause>

  <clause id="25848">
    <literal><![CDATA[
      L(a(x,x,y * y) * ((z \ (L(L(y,u,w),u,w) \ y)) \ (z \ 1)),x,x) = y \ L(L(y,u,w),u,w)
    ]]></literal>
    <justification jstring="[para(25566(a,1),25846(a,1,1,1))].">
      <j1 rule="para" parents="25566 25846"/>
    </justification>
  </clause>

  <clause id="25849">
    <literal><![CDATA[
      L(1 * ((x \ (L(L(y,z,u),z,u) \ y)) \ (x \ 1)),w,w) = y \ L(L(y,z,u),z,u)
    ]]></literal>
    <justification jstring="[para(553(a,1),25848(a,1,1,1))].">
      <j1 rule="para" parents="553 25848"/>
    </justification>
  </clause>

  <clause id="25852">
    <literal><![CDATA[
      L(1 * (x \ L(L(x,y,z),y,z)),u,u) = x \ L(L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(25608(a,1),25849(a,1,1,2))].">
      <j1 rule="para" parents="25608 25849"/>
    </justification>
  </clause>

  <clause id="25853">
    <literal><![CDATA[
      L(x \ L(L(x,y,z),y,z),u,u) = x \ L(L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),25852(a,1,1))].">
      <j1 rule="para" parents="7 25852"/>
    </justification>
  </clause>

  <clause id="25854">
    <literal><![CDATA[
      (((x \ y) * x) \ (x \ y)) \ ((T(x,z) \ y) \ ((T(x,z) \ y) * x)) = (y / x) \ (y * ((T(x,z) \ y) \ ((T(x,z) \ y) * x)))
    ]]></literal>
    <justification jstring="[para(22632(a,1),25806(a,1,1))].">
      <j1 rule="para" parents="22632 25806"/>
    </justification>
  </clause>

  <clause id="25855">
    <literal><![CDATA[
      (x \ (x / y)) \ ((T(y,z) \ x) \ ((T(y,z) \ x) * y)) = (x / y) \ (x * ((T(y,z) \ x) \ ((T(y,z) \ x) * y)))
    ]]></literal>
    <justification jstring="[para(5510(a,1),25854(a,1,1))].">
      <j1 rule="para" parents="5510 25854"/>
    </justification>
  </clause>

  <clause id="25857">
    <literal><![CDATA[
      (x / y) \ (x * ((T(y,z) \ x) \ ((T(y,z) \ x) * y))) = (x \ (x / y)) \ y
    ]]></literal>
    <justification jstring="[para(9(a,1),25855(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 25855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25858">
    <literal><![CDATA[
      (x \ (x / y)) \ y = (x / y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),25857(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 25857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25859">
    <literal><![CDATA[
      (x / (x \ y)) \ (x * (x \ y)) = (x \ y) / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,15349,a(flip),b,25858,a),flip(a)].">
      <j1 rule="hyper" parents="63 15349 25858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25861">
    <literal><![CDATA[
      R(x \ (x / y),(x / y) \ (x * y),z) \ (y * z) = ((x \ (x / y)) \ y) * z
    ]]></literal>
    <justification jstring="[para(25858(a,1),578(a,1,1,2))].">
      <j1 rule="para" parents="25858 578"/>
    </justification>
  </clause>

  <clause id="25862">
    <literal><![CDATA[
      (x \ y) / (y \ x) = (x / (x \ y)) \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),25859(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 25859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25863">
    <literal><![CDATA[
      R(x,((y / (y \ z)) \ z) * u,w) = R(x,(y \ (z * (y \ z))) * u,w)
    ]]></literal>
    <justification jstring="[para(25862(a,1),25520(a,1,2,1))].">
      <j1 rule="para" parents="25862 25520"/>
    </justification>
  </clause>

  <clause id="25864">
    <literal><![CDATA[
      R(x,(((y \ z) \ y) \ z) * u,w) = R(x,(y \ (z * (y \ z))) * u,w)
    ]]></literal>
    <justification jstring="[hyper(22448,a,25863,a)].">
      <j1 rule="hyper" parents="22448 25863"/>
    </justification>
  </clause>

  <clause id="25865">
    <literal><![CDATA[
      R(x \ (x / y),(y \ x) \ (x * y),z) \ (y * z) = ((x \ (x / y)) \ y) * z
    ]]></literal>
    <justification jstring="[para(22422(a,1),25861(a,1,1))].">
      <j1 rule="para" parents="22422 25861"/>
    </justification>
  </clause>

  <clause id="25866">
    <literal><![CDATA[
      L(x \ (x / y),a(y,y,x),z) \ (y * z) = ((x \ (x / y)) \ y) * z
    ]]></literal>
    <justification jstring="[para(23637(a,1),25865(a,1,1))].">
      <j1 rule="para" parents="23637 25865"/>
    </justification>
  </clause>

  <clause id="25867">
    <literal><![CDATA[
      L(x \ (x / y),a(y,y,x),z) \ (y * z) = ((x / y) \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(25858(a,1),25866(a,2,1))].">
      <j1 rule="para" parents="25858 25866"/>
    </justification>
  </clause>

  <clause id="25868">
    <literal><![CDATA[
      T(((x / a(y,z,u)) * w) / (a(y,z,u) * (x / a(y,z,u))),T(x,a(y,z,u))) = (w * (a(y,z,u) \ x)) / (a(y,z,u) * (x / a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(19977(a,1),23199(a,2,1,2))].">
      <j1 rule="para" parents="19977 23199"/>
    </justification>
  </clause>

  <clause id="25869">
    <literal><![CDATA[
      T(((x / a(y,z,u)) * w) / (a(y,z,u) * (x / a(y,z,u))),T(x,a(y,z,u))) = (w * (a(y,z,u) \ x)) / x
    ]]></literal>
    <justification jstring="[para(20007(a,1),25868(a,2,2))].">
      <j1 rule="para" parents="20007 25868"/>
    </justification>
  </clause>

  <clause id="25870">
    <literal><![CDATA[
      T(((a(x,y,z) \ u) * w) / (a(x,y,z) * (u / a(x,y,z))),T(u,a(x,y,z))) = (w * (a(x,y,z) \ u)) / u
    ]]></literal>
    <justification jstring="[para(19977(a,1),25869(a,1,1,1,1))].">
      <j1 rule="para" parents="19977 25869"/>
    </justification>
  </clause>

  <clause id="25871">
    <literal><![CDATA[
      T(((a(x,y,z) \ u) * w) / u,T(u,a(x,y,z))) = (w * (a(x,y,z) \ u)) / u
    ]]></literal>
    <justification jstring="[para(20007(a,1),25870(a,1,1,2))].">
      <j1 rule="para" parents="20007 25870"/>
    </justification>
  </clause>

  <clause id="25872">
    <literal><![CDATA[
      T(((a(x,y,z) \ u) * w) / u,u) = (w * (a(x,y,z) \ u)) / u
    ]]></literal>
    <justification jstring="[hyper(16872,a,25871,a)].">
      <j1 rule="hyper" parents="16872 25871"/>
    </justification>
  </clause>

  <clause id="25873">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) / w = w \ ((a(y,z,u) \ w) * x)
    ]]></literal>
    <justification jstring="[hyper(386,a,25872,a),flip(a)].">
      <j1 rule="hyper" parents="386 25872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25875">
    <literal><![CDATA[
      (((a(x,y,z) \ u) \ w) * (u / a(x,y,z))) \ (((a(x,y,z) \ u) \ w) * u) = ((w / (a(x,y,z) \ u)) * u) / w
    ]]></literal>
    <justification jstring="[para(19986(a,1),21230(a,2,1,2))].">
      <j1 rule="para" parents="19986 21230"/>
    </justification>
  </clause>

  <clause id="25876">
    <literal><![CDATA[
      (((a(x,y,z) \ u) \ w) * (a(x,y,z) \ u)) \ (((a(x,y,z) \ u) \ w) * u) = ((w / (a(x,y,z) \ u)) * u) / w
    ]]></literal>
    <justification jstring="[para(19977(a,1),25875(a,1,1,2))].">
      <j1 rule="para" parents="19977 25875"/>
    </justification>
  </clause>

  <clause id="25877">
    <literal><![CDATA[
      ((x / (a(y,z,u) \ w)) * w) / x = x \ ((x / (a(y,z,u) \ w)) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10191,a(flip),b,25876,a),flip(a)].">
      <j1 rule="hyper" parents="63 10191 25876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25878">
    <literal><![CDATA[
      (x * ((a(y,z,u) \ x) \ w)) / w = w \ ((w / (a(y,z,u) \ x)) * x)
    ]]></literal>
    <justification jstring="[para(23495(a,1),25877(a,1,1))].">
      <j1 rule="para" parents="23495 25877"/>
    </justification>
  </clause>

  <clause id="25879">
    <literal><![CDATA[
      (x * ((a(y,z,u) \ x) \ w)) / w = w \ (x * ((a(y,z,u) \ x) \ w))
    ]]></literal>
    <justification jstring="[para(23495(a,1),25878(a,2,2))].">
      <j1 rule="para" parents="23495 25878"/>
    </justification>
  </clause>

  <clause id="25880">
    <literal><![CDATA[
      1 * (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="[para(20388(a,1),22805(a,1,1))].">
      <j1 rule="para" parents="20388 22805"/>
    </justification>
  </clause>

  <clause id="25881">
    <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(135,a,25880,a)].">
      <j1 rule="hyper" parents="135 25880"/>
    </justification>
  </clause>

  <clause id="25883">
    <literal><![CDATA[
      (x / T(a(y,z,u) * (a(y,z,u) \ w),v5)) * T(w / a(y,z,u),v5) = T(w / a(y,z,u),v5) * ((a(y,z,u) * T(w / a(y,z,u),v5)) \ x)
    ]]></literal>
    <justification jstring="[para(23113(a,2),23267(a,1,1,2))].">
      <j1 rule="para" parents="23113 23267"/>
    </justification>
  </clause>

  <clause id="25884">
    <literal><![CDATA[
      T(x / a(y,z,u),w) * ((a(y,z,u) * T(x / a(y,z,u),w)) \ v5) = (v5 / T(x,w)) * T(x / a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(10(a,1),25883(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 25883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25885">
    <literal><![CDATA[
      T(x / a(y,z,u),w) * ((a(y,z,u) * T(x / a(y,z,u),w)) \ v5) = (v5 / T(x,w)) * T(a(y,z,u) \ x,w)
    ]]></literal>
    <justification jstring="[para(19977(a,1),25884(a,2,2,1))].">
      <j1 rule="para" parents="19977 25884"/>
    </justification>
  </clause>

  <clause id="25886">
    <literal><![CDATA[
      T(x / a(y,z,u),w) * ((a(y,z,u) * T(x / a(y,z,u),w)) \ v5) = (v5 / x) * (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,23180,a(flip),b,25885,a),flip(a)].">
      <j1 rule="hyper" parents="347 23180 25885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25888">
    <literal><![CDATA[
      T(a(x,y,z) \ u,w) * ((a(x,y,z) * T(u / a(x,y,z),w)) \ v5) = (v5 / u) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(19977(a,1),25886(a,1,1,1))].">
      <j1 rule="para" parents="19977 25886"/>
    </justification>
  </clause>

  <clause id="25889">
    <literal><![CDATA[
      T(a(x,y,z) \ u,w) * ((a(x,y,z) * T(a(x,y,z) \ u,w)) \ v5) = (v5 / u) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(19977(a,1),25888(a,1,2,1,2,1))].">
      <j1 rule="para" parents="19977 25888"/>
    </justification>
  </clause>

  <clause id="25890">
    <literal><![CDATA[
      T(a(x,y,z) \ u,w) * (T(a(x,y,z) * (a(x,y,z) \ u),w) \ v5) = (v5 / u) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(23113(a,2),25889(a,1,2,1))].">
      <j1 rule="para" parents="23113 25889"/>
    </justification>
  </clause>

  <clause id="25891">
    <literal><![CDATA[
      T(a(x,y,z) \ u,w) * (T(u,w) \ v5) = (v5 / u) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),25890(a,1,2,1,1))].">
      <j1 rule="para" parents="10 25890"/>
    </justification>
  </clause>

  <clause id="25892">
    <literal><![CDATA[
      R(x,y * ((z \ u) \ R(w,(z \ K(v5,v6)) \ u,(z \ K(v5,v6)) \ u)),v7) = R(x,y * (w * (1 / ((z \ K(v5,v6)) \ u))),v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,22404,a(flip),b,22573,a),flip(a)].">
      <j1 rule="hyper" parents="347 22404 22573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25894">
    <literal><![CDATA[
      R(x,y * ((z \ u) \ R(w,(z \ K(v5,v6)) \ u,(z \ K(v5,v6)) \ u)),v7) = R(x,y * (w * (((z \ K(v5,v6)) \ u) \ 1)),v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,22451,a(flip),b,25892,a),flip(a)].">
      <j1 rule="hyper" parents="347 22451 25892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25895">
    <literal><![CDATA[
      R(x,y * ((z \ u) \ R(w,(z \ K(v5,v6)) \ u,(z \ K(v5,v6)) \ u)),v7) = R(x,y * (w * (((z \ 1) \ u) \ K(v5,v6))),v7)
    ]]></literal>
    <justification jstring="[para(21050(a,1),25894(a,2,2,2,2))].">
      <j1 rule="para" parents="21050 25894"/>
    </justification>
  </clause>

  <clause id="25896">
    <literal><![CDATA[
      R(x,y * ((z \ u) \ R(w,(z \ K(v5,v6)) \ u,(z \ K(v5,v6)) \ u)),v7) = R(x,y * (w * ((z \ 1) \ u)),v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,22421,a(flip),b,25895,a),flip(a)].">
      <j1 rule="hyper" parents="347 22421 25895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25898">
    <literal><![CDATA[
      R(x,y * ((z \ u) \ R(w,(z \ K(v5,v6)) \ u,z \ u)),v7) = R(x,y * (w * ((z \ 1) \ u)),v7)
    ]]></literal>
    <justification jstring="[para(22133(a,1),25896(a,1,2,2,2))].">
      <j1 rule="para" parents="22133 25896"/>
    </justification>
  </clause>

  <clause id="25900">
    <literal><![CDATA[
      R(x,y * ((z \ u) \ R(w,z \ u,z \ u)),v5) = R(x,y * (w * ((z \ 1) \ u)),v5)
    ]]></literal>
    <justification jstring="[para(22470(a,1),25898(a,1,2,2,2))].">
      <j1 rule="para" parents="22470 25898"/>
    </justification>
  </clause>

  <clause id="25901">
    <literal><![CDATA[
      R(x,y * T(z * (1 / (u \ w)),u \ w),v5) = R(x,y * (z * ((u \ 1) \ w)),v5)
    ]]></literal>
    <justification jstring="[para(2263(a,2),25900(a,1,2,2))].">
      <j1 rule="para" parents="2263 25900"/>
    </justification>
  </clause>

  <clause id="25902">
    <literal><![CDATA[
      R(x,y * (z * (1 / (u \ w))),v5) = R(x,y * (z * ((u \ 1) \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(22438,a,25901,a)].">
      <j1 rule="hyper" parents="22438 25901"/>
    </justification>
  </clause>

  <clause id="25904">
    <literal><![CDATA[
      R(x,y * (z * ((u \ 1) \ w)),v5) = R(x,y * (z * ((u \ w) \ 1)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22451,a(flip),b,25902,a),flip(a)].">
      <j1 rule="hyper" parents="63 22451 25902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25905">
    <literal><![CDATA[
      R(x,y * (z * ((u \ 1) \ w)),v5) = R(x,y * (z * (u \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,2381,a(flip),b,25904,a),flip(a)].">
      <j1 rule="hyper" parents="347 2381 25904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25906">
    <literal><![CDATA[
      a(L((x * x) \ y,(x * x) \ y,((x * x) \ y) \ z) \ ((x * x) \ y),u,w) = a(((x * x) \ (L((x * x) \ y,y,z) \ 1)) * y,u,w)
    ]]></literal>
    <justification jstring="[para(3607(a,1),24459(a,2,1,1,2,1))].">
      <j1 rule="para" parents="3607 24459"/>
    </justification>
  </clause>

  <clause id="25907">
    <literal><![CDATA[
      a(L((x * x) \ y,(x * x) \ y,((x * x) \ y) \ z) \ ((x * x) \ y),u,w) = a((L(T(y,x * x),y,z) \ 1) * y,u,w)
    ]]></literal>
    <justification jstring="[para(1398(a,1),25906(a,2,1,1))].">
      <j1 rule="para" parents="1398 25906"/>
    </justification>
  </clause>

  <clause id="25909">
    <literal><![CDATA[
      a(L((x * x) \ y,(x * x) \ y,((x * x) \ y) \ z) \ ((x * x) \ y),u,w) = a((L(y,y,z) \ 1) * y,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24522,a(flip),b,25907,a),flip(a)].">
      <j1 rule="hyper" parents="347 24522 25907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25911">
    <literal><![CDATA[
      a(L((x * x) \ y,(x * x) \ y,((x * x) \ y) \ z) \ ((x * x) \ y),u,w) = a(L(y,y,z) \ y,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,4025,a(flip),b,25909,a),flip(a)].">
      <j1 rule="hyper" parents="347 4025 25909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25912">
    <literal><![CDATA[
      a(L((x * x) \ y,(x * x) \ y,(y \ z) * (x * x)) \ ((x * x) \ y),u,w) = a(L(y,y,z) \ y,u,w)
    ]]></literal>
    <justification jstring="[para(21534(a,1),25911(a,1,1,1))].">
      <j1 rule="para" parents="21534 25911"/>
    </justification>
  </clause>

  <clause id="25913">
    <literal><![CDATA[
      a(L((x * x) \ y,y,(y \ z) * (x * x)) \ ((x * x) \ y),u,w) = a(L(y,y,z) \ y,u,w)
    ]]></literal>
    <justification jstring="[para(3607(a,1),25912(a,1,1,1))].">
      <j1 rule="para" parents="3607 25912"/>
    </justification>
  </clause>

  <clause id="25915">
    <literal><![CDATA[
      a(L(x,x,(x \ y) * (z * z)) \ x,u,w) = a(L(x,x,y) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(21332(a,1),25913(a,1,1))].">
      <j1 rule="para" parents="21332 25913"/>
    </justification>
  </clause>

  <clause id="25917">
    <literal><![CDATA[
      (L(T(x \ y,x),z,u) * ((x \ y) \ y)) * ((x \ y) \ y) = (x * L(x \ y,z,u)) * ((L(x \ y,z,u) * x) / L(T(x \ y,x),z,u))
    ]]></literal>
    <justification jstring="[para(23737(a,1),21307(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23737 21307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25918">
    <literal><![CDATA[
      (L(T(x \ y,x),z,u) * ((x \ y) \ y)) * ((x \ y) \ y) = (x * L(x \ y,z,u)) * (L(x \ y,z,u) \ (L(x \ y,z,u) * x))
    ]]></literal>
    <justification jstring="[para(9724(a,1),25917(a,2,2))].">
      <j1 rule="para" parents="9724 25917"/>
    </justification>
  </clause>

  <clause id="25919">
    <literal><![CDATA[
      (L(T(x \ y,x),z,u) * ((x \ y) \ y)) * ((x \ y) \ y) = (x * L(x \ y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,170,a(flip),b,25918,a),flip(a)].">
      <j1 rule="hyper" parents="347 170 25918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25921">
    <literal><![CDATA[
      (L(T(x \ y,x),z,u) * ((x \ y) \ y)) * ((x \ y) \ y) = L(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,3338,a(flip),b,25919,a),flip(a)].">
      <j1 rule="hyper" parents="347 3338 25919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25922">
    <literal><![CDATA[
      (L(x \ y,z,u) * x) * ((x \ y) \ y) = L(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(23737(a,1),25921(a,1,1))].">
      <j1 rule="para" parents="23737 25921"/>
    </justification>
  </clause>

  <clause id="25923">
    <literal><![CDATA[
      ((x \ R(x,y,z)) * x) * a(u,x \ R(x,y,z),L(x,u,x \ R(x,y,z))) = u \ (((x \ R(x,y,z)) * T(u,x \ R(x,y,z))) * x)
    ]]></literal>
    <justification jstring="[para(23703(a,1),23710(a,1,1,2))].">
      <j1 rule="para" parents="23703 23710"/>
    </justification>
  </clause>

  <clause id="25924">
    <literal><![CDATA[
      R(x,y,z) * a(u,x \ R(x,y,z),L(x,u,x \ R(x,y,z))) = u \ (((x \ R(x,y,z)) * T(u,x \ R(x,y,z))) * x)
    ]]></literal>
    <justification jstring="[para(3678(a,1),25923(a,1,1))].">
      <j1 rule="para" parents="3678 25923"/>
    </justification>
  </clause>

  <clause id="25925">
    <literal><![CDATA[
      x \ (((y \ R(y,z,u)) * T(x,y \ R(y,z,u))) * y) = R(y,z,u) * a(x,y \ R(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(23703(a,1),25924(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="23703 25924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25926">
    <literal><![CDATA[
      x \ (((y \ R(y,z,u)) * T(x,y \ R(y,z,u))) * y) = R(y,z,u) * a(x,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(25112(a,1),25925(a,2,2))].">
      <j1 rule="para" parents="25112 25925"/>
    </justification>
  </clause>

  <clause id="25927">
    <literal><![CDATA[
      x \ (((y \ R(y,z,u)) * T(x,y \ R(y,z,u))) * y) = R(y,z,u) * a(x,y * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(24144(a,1),25926(a,2,2))].">
      <j1 rule="para" parents="24144 25926"/>
    </justification>
  </clause>

  <clause id="25928">
    <literal><![CDATA[
      (((L(x,y,z) \ x) * u) * T(w,w * ((x \ x) * u))) / (L(w,(L(x,y,z) \ x) * u,w) * u) = L(L(x,y,z) \ x,u,L(w,(L(x,y,z) \ x) * u,w))
    ]]></literal>
    <justification jstring="[para(23332(a,1),22351(a,1,1,2))].">
      <j1 rule="para" parents="23332 22351"/>
    </justification>
  </clause>

  <clause id="25929">
    <literal><![CDATA[
      (((L(x,y,z) \ x) * u) * T(w,w * u)) / (L(w,(L(x,y,z) \ x) * u,w) * u) = L(L(x,y,z) \ x,u,L(w,(L(x,y,z) \ x) * u,w))
    ]]></literal>
    <justification jstring="[para(187(a,1),25928(a,1,1,2,2,2))].">
      <j1 rule="para" parents="187 25928"/>
    </justification>
  </clause>

  <clause id="25931">
    <literal><![CDATA[
      (((L(x,y,z) \ x) * u) * T(w,u * w)) / (L(w,(L(x,y,z) \ x) * u,w) * u) = L(L(x,y,z) \ x,u,L(w,(L(x,y,z) \ x) * u,w))
    ]]></literal>
    <justification jstring="[para(4323(a,2),25929(a,1,1,2))].">
      <j1 rule="para" parents="4323 25929"/>
    </justification>
  </clause>

  <clause id="25932">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,L(w,(L(x,y,z) \ x) * u,w)) = (((L(x,y,z) \ x) * u) * T(w,u * w)) / (L(w,x * (x * u),w) * u)
    ]]></literal>
    <justification jstring="[para(23451(a,1),25931(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23451 25931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25933">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,L(w,(L(x,y,z) \ x) * u,w)) = (((L(x,y,z) \ x) * u) * T(w,u * w)) / (L(w,L(u,x,x),w) * u)
    ]]></literal>
    <justification jstring="[para(3609(a,1),25932(a,2,2,1))].">
      <j1 rule="para" parents="3609 25932"/>
    </justification>
  </clause>

  <clause id="25935">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,L(w,(L(x,y,z) \ x) * u,w)) = (((L(x,y,z) \ x) * u) * T(w,u * w)) / (L(w,u,w) * u)
    ]]></literal>
    <justification jstring="[para(12187(a,1),25933(a,2,2,1))].">
      <j1 rule="para" parents="12187 25933"/>
    </justification>
  </clause>

  <clause id="25936">
    <literal><![CDATA[
      R(((L(x,y,z) \ x) * u) / u,u,w) = L(L(x,y,z) \ x,u,L(w,(L(x,y,z) \ x) * u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,20513,a(flip),b,25935,a)].">
      <j1 rule="hyper" parents="347 20513 25935"/>
    </justification>
  </clause>

  <clause id="25938">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,L(w,(L(x,y,z) \ x) * u,w)) = R(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(11(a,1),25936(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 25936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25939">
    <literal><![CDATA[
      R(L(x,y,z) \ x,u,w) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(11451,a,25938,a),flip(a)].">
      <j1 rule="hyper" parents="11451 25938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25941">
    <literal><![CDATA[
      R(L(x,y,z) \ x,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(25938(a,1),11451(a,1))].">
      <j1 rule="para" parents="25938 11451"/>
    </justification>
  </clause>

  <clause id="25943">
    <literal><![CDATA[
      L(T((x * y) \ 1,y \ L(y,z,u)),y \ L(L(y,z,u),z,u),x * y) = (x * L(L(y,z,u),z,u)) \ L(y \ L(L(y,z,u),z,u),x * y,x * y)
    ]]></literal>
    <justification jstring="[para(22932(a,1),25597(a,1,1))].">
      <j1 rule="para" parents="22932 25597"/>
    </justification>
  </clause>

  <clause id="25944">
    <literal><![CDATA[
      (x * L(L(y,z,u),z,u)) \ L(y \ L(L(y,z,u),z,u),x * y,x * y) = L((x * y) \ 1,y \ L(L(y,z,u),z,u),x * y)
    ]]></literal>
    <justification jstring="[para(20076(a,1),25943(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20076 25943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25946">
    <literal><![CDATA[
      (x * L(L(y,z,u),z,u)) \ L(y \ L(L(y,z,u),z,u),x * y,x * y) = L((x * y) \ 1,y * L(L(y,z,u),z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,10926,a(flip),b,25944,a),flip(a)].">
      <j1 rule="hyper" parents="347 10926 25944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25948">
    <literal><![CDATA[
      (x * L(L(y,z,u),z,u)) \ L(y \ L(L(y,z,u),z,u),x * y,x * y) = L((x * y) \ 1,y * y,x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,25563,a(flip),b,25946,a),flip(a)].">
      <j1 rule="hyper" parents="347 25563 25946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25950">
    <literal><![CDATA[
      (x * L(L(y,z,u),z,u)) \ L(y \ L(L(y,z,u),z,u),x * y,x * y) = (x * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,534,a(flip),b,25948,a),flip(a)].">
      <j1 rule="hyper" parents="347 534 25948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25952">
    <literal><![CDATA[
      (x * L(L(y,z,u),z,u)) \ (y \ L(L(y,z,u),z,u)) = (x * y) \ 1
    ]]></literal>
    <justification jstring="[para(25853(a,1),25950(a,1,2))].">
      <j1 rule="para" parents="25853 25950"/>
    </justification>
  </clause>

  <clause id="25953">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,y,z) = x * ((x * x) \ 1)
    ]]></literal>
    <justification jstring="[para(25952(a,1),25622(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25952 25622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25955">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,y,z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(130,a,497,a(flip),b,25953,a),flip(a)].">
      <j1 rule="hyper" parents="130 497 25953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25956">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ 1 = u
    ]]></literal>
    <justification jstring="[para(25953(a,2),503(a,1))].">
      <j1 rule="para" parents="25953 503"/>
    </justification>
  </clause>

  <clause id="25958">
    <literal><![CDATA[
      L(x * y,y,x) \ 1 = y \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(623,a,25955,a),flip(a)].">
      <j1 rule="hyper" parents="623 25955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25959">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ 1,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,83,a(flip),b,25955,a),flip(a)].">
      <j1 rule="hyper" parents="347 83 25955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25960">
    <literal><![CDATA[
      L(L(L(x,y,z) \ 1,u,w),y,z) = L(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(25955(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25955 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25961">
    <literal><![CDATA[
      L(L(L(x,y,z),u,w) \ 1,y,z) = L(x,u,w) \ 1
    ]]></literal>
    <justification jstring="[para(30(a,1),25955(a,1,1,1))].">
      <j1 rule="para" parents="30 25955"/>
    </justification>
  </clause>

  <clause id="25962">
    <literal><![CDATA[
      L(((x * y) \ z) \ 1,y,x) = (y \ (x \ z)) \ 1
    ]]></literal>
    <justification jstring="[para(329(a,1),25955(a,1,1,1))].">
      <j1 rule="para" parents="329 25955"/>
    </justification>
  </clause>

  <clause id="25963">
    <literal><![CDATA[
      (x \ (y \ ((y * x) * z))) \ 1 = L(z \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(536(a,1),25955(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="536 25955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25964">
    <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(25955(a,1),3439(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="25955 3439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25965">
    <literal><![CDATA[
      L(((x * y) \ ((x * (y * z)) / z)) \ 1,z,x * y) = (z \ L(z,y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(3970(a,1),25955(a,1,1,1))].">
      <j1 rule="para" parents="3970 25955"/>
    </justification>
  </clause>

  <clause id="25966">
    <literal><![CDATA[
      L((L(x,y,z) \ 1) \ L(L(x,y,z) \ 1,u,w),y,z) = (x \ 1) \ L(L(L(x,y,z) \ 1,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(25955(a,1),4638(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25955 4638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25967">
    <literal><![CDATA[
      a(x,L(L(y,z,u),z,u),w) = a(x,y \ 1,w)
    ]]></literal>
    <justification jstring="[para(25955(a,1),14972(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25955 14972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25968">
    <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(25955(a,1),20687(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="25955 20687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25969">
    <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(25955(a,1),20689(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25955 20689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25970">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,x) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(25390(a,1),25955(a,1,1,1))].">
      <j1 rule="para" parents="25390 25955"/>
    </justification>
  </clause>

  <clause id="25971">
    <literal><![CDATA[
      x \ (y \ ((y * x) * z)) = L(1 / z,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(41,a,536,a,b,25959,a)].">
      <j1 rule="hyper" parents="41 536 25959"/>
    </justification>
  </clause>

  <clause id="25972">
    <literal><![CDATA[
      L(x * (L(x,y,z) \ x),y,z) = x
    ]]></literal>
    <justification jstring="[para(3638(a,1),25959(a,1,1))].">
      <j1 rule="para" parents="3638 25959"/>
    </justification>
  </clause>

  <clause id="25973">
    <literal><![CDATA[
      L(1 / L(x,y,z),y,z) = 1 / x
    ]]></literal>
    <justification jstring="[para(4658(a,1),25959(a,1,1))].">
      <j1 rule="para" parents="4658 25959"/>
    </justification>
  </clause>

  <clause id="25974">
    <literal><![CDATA[
      x \ (y \ ((y * x) * z)) = z * (L(z,x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(41,a,536,a,b,25972,a)].">
      <j1 rule="hyper" parents="41 536 25972"/>
    </justification>
  </clause>

  <clause id="25975">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * (L(x * (L(x,y,z) \ x),y,z) \ u) = (u * (x * (L(x,y,z) \ x))) / x
    ]]></literal>
    <justification jstring="[hyper(220,a,25972,a(flip),b,20988,a),flip(a)].">
      <j1 rule="hyper" parents="220 25972 20988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25976">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      u * (L(u,y,z) \ u) = x
    ]]></literal>
    <justification jstring="[para(25972(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="25972 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25977">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * (L(x * (L(x,y,z) \ x),y,z) \ u) = x \ ((x * (L(x,y,z) \ x)) * u)
    ]]></literal>
    <justification jstring="[para(25972(a,1),1407(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25972 1407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25978">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * (L(x * (L(x,y,z) \ x),y,z) \ u) = (u / x) * (x * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(25972(a,1),20676(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="25972 20676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25979">
    <literal><![CDATA[
      ((x * (L(x,y,z) \ x)) * u) / (x * u) != w
    ]]></literal>
    <literal><![CDATA[
      (L(x * (L(x,y,z) \ x),y,z) * u) \ ((x * (L(x,y,z) \ x)) * u) = w
    ]]></literal>
    <justification jstring="[para(25972(a,1),23502(a,1,2,1))].">
      <j1 rule="para" parents="25972 23502"/>
    </justification>
  </clause>

  <clause id="25981">
    <literal><![CDATA[
      L(1 / x,y,a(x,z,u)) = 1 / x
    ]]></literal>
    <justification jstring="[para(25365(a,1),25973(a,1,1,2))].">
      <j1 rule="para" parents="25365 25973"/>
    </justification>
  </clause>

  <clause id="25982">
    <literal><![CDATA[
      L(x * y,y,x) = 1 / (y \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(222,a,25958,a),flip(a)].">
      <j1 rule="hyper" parents="222 25958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25983">
    <literal><![CDATA[
      L(a(x,y,z) * u,u,a(x,y,z)) = ((a(x,y,z) \ 1) / u) \ 1
    ]]></literal>
    <justification jstring="[hyper(39,a,22288,a,b,25958,a),flip(a)].">
      <j1 rule="hyper" parents="39 22288 25958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25984">
    <literal><![CDATA[
      L(x,y \ x,y) \ 1 = (y \ x) \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),25958(a,1,1,1))].">
      <j1 rule="para" parents="10 25958"/>
    </justification>
  </clause>

  <clause id="25985">
    <literal><![CDATA[
      ((x * y) * (x * y)) * (y \ (x \ 1)) = L((x * y) \ 1,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(25958(a,1),3325(a,1,2))].">
      <j1 rule="para" parents="25958 3325"/>
    </justification>
  </clause>

  <clause id="25986">
    <literal><![CDATA[
      L(x,y,L(z * u,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(u \ (z \ 1)) \ 1) = w
    ]]></literal>
    <justification jstring="[para(25982(a,2),3951(a,1,3))].">
      <j1 rule="para" parents="25982 3951"/>
    </justification>
  </clause>

  <clause id="25987">
    <literal><![CDATA[
      a(x,x,L(y,z,x)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(14635,a,25970,a)].">
      <j1 rule="hyper" parents="14635 25970"/>
    </justification>
  </clause>

  <clause id="25989">
    <literal><![CDATA[
      x * ((x \ y) * (a(x,z,u) \ 1)) = y * (a(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,25970,a(flip),b,98,a),flip(a)].">
      <j1 rule="hyper" parents="134 25970 98"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25990">
    <literal><![CDATA[
      L(x,y,z) != a(z,u,w) \ 1
    ]]></literal>
    <literal><![CDATA[
      a(z,u,w) \ 1 = x
    ]]></literal>
    <justification jstring="[para(25970(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="25970 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25991">
    <literal><![CDATA[
      a(x,x,y \ x) = a(x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(25265,a,25987,a)].">
      <j1 rule="hyper" parents="25265 25987"/>
    </justification>
  </clause>

  <clause id="25992">
    <literal><![CDATA[
      R(x,x,L(y,z,x)) = x * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,25987,a(flip),b,18988,a),flip(a)].">
      <j1 rule="hyper" parents="134 25987 18988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25993">
    <literal><![CDATA[
      a(x,x,y * a(x,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,x,L(y,x,z)) = u
    ]]></literal>
    <justification jstring="[para(25987(a,1),24670(a,1))].">
      <j1 rule="para" parents="25987 24670"/>
    </justification>
  </clause>

  <clause id="25995">
    <literal><![CDATA[
      a(x,x,x * (y \ x)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(24182,a,25991,a),flip(a)].">
      <j1 rule="hyper" parents="24182 25991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25996">
    <literal><![CDATA[
      R(x,x,L(y,z,x)) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,18990,a(flip),b,25992,a),flip(a)].">
      <j1 rule="hyper" parents="347 18990 25992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25997">
    <literal><![CDATA[
      x \ a(y,y \ x,x) = (y \ x) \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,22838,a(flip),b,25984,a)].">
      <j1 rule="hyper" parents="63 22838 25984"/>
    </justification>
  </clause>

  <clause id="25998">
    <literal><![CDATA[
      a(x,L(L(y,z,u),z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(25967(a,2),14965(a,1))].">
      <j1 rule="para" parents="25967 14965"/>
    </justification>
  </clause>

  <clause id="25999">
    <literal><![CDATA[
      (1 / x) * (x * ((((x \ 1) * x) \ y) \ 1)) = (x \ ((x \ 1) \ y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(2974,a,25962,a)].">
      <j1 rule="hyper" parents="2974 25962"/>
    </justification>
  </clause>

  <clause id="26000">
    <literal><![CDATA[
      L(((x * y) \ (z \ ((z * x) * y))) \ 1,y,x) = (x \ (z \ ((z * x) * y))) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,11313,a(flip),b,25962,a),flip(a)].">
      <j1 rule="hyper" parents="347 11313 25962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26001">
    <literal><![CDATA[
      a(x,(y * z) \ (z * ((((z * y) \ u) \ 1) * y)),w) = a(x,(y \ (z \ u)) \ 1,w)
    ]]></literal>
    <justification jstring="[para(25962(a,1),24526(a,2,2))].">
      <j1 rule="para" parents="25962 24526"/>
    </justification>
  </clause>

  <clause id="26002">
    <literal><![CDATA[
      x \ (y \ ((y * x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(1 / z,x,y) \ 1 = u
    ]]></literal>
    <justification jstring="[para(25974(a,2),3640(a,1))].">
      <j1 rule="para" parents="25974 3640"/>
    </justification>
  </clause>

  <clause id="26003">
    <literal><![CDATA[
      L(x \ R(x,y,L(y,z,u) \ y),x,z \ (u \ ((u * z) * y))) = a(x,y,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(25974(a,2),14250(a,2,3)),flip(a)].">
      <j1 rule="para" parents="25974 14250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26004">
    <literal><![CDATA[
      a(x,L((y * z) \ u,z,y),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ (y \ u),w) = v5
    ]]></literal>
    <justification jstring="[para(329(a,1),25998(a,1,2,1))].">
      <j1 rule="para" parents="329 25998"/>
    </justification>
  </clause>

  <clause id="26005">
    <literal><![CDATA[
      a(x,L(y,z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(12431(a,1),25998(a,1))].">
      <j1 rule="para" parents="12431 25998"/>
    </justification>
  </clause>

  <clause id="26006">
    <literal><![CDATA[
      a(x,L(y * z,y,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(24176(a,1),25998(a,1))].">
      <j1 rule="para" parents="24176 25998"/>
    </justification>
  </clause>

  <clause id="26007">
    <literal><![CDATA[
      a(x,y \ (y * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(552(a,1),26005(a,1,2))].">
      <j1 rule="para" parents="552 26005"/>
    </justification>
  </clause>

  <clause id="26008">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ 1,u,w) = L(1 / L(x,u,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(25973(a,1),25961(a,1,1,1,1))].">
      <j1 rule="para" parents="25973 25961"/>
    </justification>
  </clause>

  <clause id="26009">
    <literal><![CDATA[
      a(x,L(y,z,z) * z,u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(26006,a,24981,a),flip(a)].">
      <j1 rule="hyper" parents="26006 24981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26010">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (a(x,u,w) \ 1) = ((a(x,u,w) \ 1) / x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,20930,a,b,25989,a),flip(a)].">
      <j1 rule="hyper" parents="34 20930 25989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26011">
    <literal><![CDATA[
      L(a(x,y,z) * (u * ((a(x,y,z) \ 1) * (a(x,y,z) \ 1))),u * ((a(x,y,z) \ 1) * (a(x,y,z) \ 1)),a(x,y,z)) = (((a(x,y,z) \ 1) \ 1) / u) \ 1
    ]]></literal>
    <justification jstring="[para(812(a,1),25983(a,2,1))].">
      <j1 rule="para" parents="812 25983"/>
    </justification>
  </clause>

  <clause id="26012">
    <literal><![CDATA[
      a(x,L(T(a(y,z,y) \ u,w * v5),v5,w),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,v5 \ (w \ (u * (a(y,z,y) \ (w * v5)))),v6) = v7
    ]]></literal>
    <justification jstring="[para(11884(a,1),26004(a,1,2,1))].">
      <j1 rule="para" parents="11884 26004"/>
    </justification>
  </clause>

  <clause id="26013">
    <literal><![CDATA[
      L((x * y) \ 1,y,x) \ 1 = (x \ ((x * y) \ 1)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,975,a(flip),b,25985,a),flip(a)].">
      <j1 rule="hyper" parents="63 975 25985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26014">
    <literal><![CDATA[
      L((x * y) \ 1,y,x) * ((L((x * y) \ 1,y,x) \ 1) * z) = (a(L((x * y) \ 1,y,x),(x \ ((x * y) \ 1)) \ (x \ 1),z) \ 1) * z
    ]]></literal>
    <justification jstring="[para(26013(a,1),14631(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="26013 14631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26015">
    <literal><![CDATA[
      (1 / x) * (x * ((K(x \ 1,x) \ y) \ 1)) = (x \ ((x \ 1) \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(290(a,2),25999(a,1,2,2,1,1))].">
      <j1 rule="para" parents="290 25999"/>
    </justification>
  </clause>

  <clause id="26016">
    <literal><![CDATA[
      (1 / x) * (x * (y \ K(x \ 1,x))) = (x \ ((x \ 1) \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(13129(a,1),26015(a,1,2,2))].">
      <j1 rule="para" parents="13129 26015"/>
    </justification>
  </clause>

  <clause id="26017">
    <literal><![CDATA[
      (1 / x) * (L(x,x,x) * (y \ 1)) = (x \ ((x \ 1) \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(3432(a,1),26016(a,1,2))].">
      <j1 rule="para" parents="3432 26016"/>
    </justification>
  </clause>

  <clause id="26018">
    <literal><![CDATA[
      (x \ ((x \ 1) \ y)) \ 1 = (x \ 1) * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,5711,a(flip),b,26017,a),flip(a)].">
      <j1 rule="hyper" parents="63 5711 26017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26019">
    <literal><![CDATA[
      (x \ ((x \ 1) \ (a(y,z,u) * x))) \ 1 = (x \ 1) * ((1 / (x * a(y,z,u))) * x)
    ]]></literal>
    <justification jstring="[para(23264(a,2),26018(a,2,2))].">
      <j1 rule="para" parents="23264 26018"/>
    </justification>
  </clause>

  <clause id="26020">
    <literal><![CDATA[
      x * ((L(x,y,z) \ 1) * ((x \ 1) \ u)) = (x * ((x \ L(x,y,z)) \ 1)) * u
    ]]></literal>
    <justification jstring="[para(25964(a,1),25632(a,1,2))].">
      <j1 rule="para" parents="25964 25632"/>
    </justification>
  </clause>

  <clause id="26021">
    <literal><![CDATA[
      L(((x * y) \ ((x * (y * z)) / z)) \ 1,z,x * y) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(347,a,10882,a(flip),b,25965,a),flip(a)].">
      <j1 rule="hyper" parents="347 10882 25965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26022">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) \ 1,x,a(z,u,w) * y) = L(x,y,a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(23274(a,1),26021(a,1,1,1))].">
      <j1 rule="para" parents="23274 26021"/>
    </justification>
  </clause>

  <clause id="26023">
    <literal><![CDATA[
      (a(x,y,z) \ (1 / x)) * R(x,u,w) = (x \ R(x,u,w)) * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(25412(a,1),26010(a,2,1)),flip(a)].">
      <j1 rule="para" parents="25412 26010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26024">
    <literal><![CDATA[
      x * ((L(x,y,z) \ 1) * ((x \ 1) \ u)) = (x * (L(x,y,z) \ x)) * u
    ]]></literal>
    <justification jstring="[para(10882(a,1),26020(a,2,1,2))].">
      <j1 rule="para" parents="10882 26020"/>
    </justification>
  </clause>

  <clause id="26025">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * ((x \ 1) * u) = x * ((L(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),26024(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 26024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26026">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * u != x * w
    ]]></literal>
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x \ 1) \ u) = w
    ]]></literal>
    <justification jstring="[para(26024(a,1),43(a,1))].">
      <j1 rule="para" parents="26024 43"/>
    </justification>
  </clause>

  <clause id="26027">
    <literal><![CDATA[
      (x \ (y \ ((y * x) * z))) \ z = L(a(y,x,z) \ 1,z,x)
    ]]></literal>
    <justification jstring="[para(14699(a,2),26000(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14699 26000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26028">
    <literal><![CDATA[
      L(a(x,y,L(L(z,u,w),u,w) \ z) \ 1,L(L(z,u,w),u,w) \ z,y) \ ((y \ (x \ ((x * y) * (L(L(z,u,w),u,w) \ z)))) \ 1) = z \ L(L(z,u,w),u,w)
    ]]></literal>
    <justification jstring="[para(26027(a,1),25608(a,1,1))].">
      <j1 rule="para" parents="26027 25608"/>
    </justification>
  </clause>

  <clause id="26029">
    <literal><![CDATA[
      a(x,(y * z) \ (z * (y * ((z * y) \ u))),w) = a(x,(y \ (z \ u)) \ 1,w)
    ]]></literal>
    <justification jstring="[hyper(24793,a,26001,a)].">
      <j1 rule="hyper" parents="24793 26001"/>
    </justification>
  </clause>

  <clause id="26030">
    <literal><![CDATA[
      a(x,L(K(y,z) * ((y * z) \ u),z,y),w) = a(x,(z \ (y \ u)) \ 1,w)
    ]]></literal>
    <justification jstring="[para(10173(a,1),26029(a,1,2))].">
      <j1 rule="para" parents="10173 26029"/>
    </justification>
  </clause>

  <clause id="26031">
    <literal><![CDATA[
      a(x,L((y * z) \ u,y,z),w) = a(x,(y \ (z \ u)) \ 1,w)
    ]]></literal>
    <justification jstring="[para(10274(a,1),26030(a,1,2,1))].">
      <j1 rule="para" parents="10274 26030"/>
    </justification>
  </clause>

  <clause id="26032">
    <literal><![CDATA[
      a(x,L((y * z) \ u,y,z),w) = a(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,14950,a(flip),b,26031,a),flip(a)].">
      <j1 rule="hyper" parents="347 14950 26031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26033">
    <literal><![CDATA[
      a(x,L((y * z) \ u,y,z),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ (z \ u),w) = v5
    ]]></literal>
    <justification jstring="[para(26031(a,2),14965(a,1))].">
      <j1 rule="para" parents="26031 14965"/>
    </justification>
  </clause>

  <clause id="26034">
    <literal><![CDATA[
      a(x,L(L(T(y,z),z,u),u,z),w) = a(x,u \ (z \ (u * (y * z))),w)
    ]]></literal>
    <justification jstring="[para(263(a,1),26032(a,1,2,1))].">
      <j1 rule="para" parents="263 26032"/>
    </justification>
  </clause>

  <clause id="26035">
    <literal><![CDATA[
      a(x,L(L(y * K(y * z,u),z,u),u,T(z,y)),w) = a(x,u \ (T(z,y) \ ((T(z,y) * y) * u)),w)
    ]]></literal>
    <justification jstring="[para(21652(a,1),26032(a,1,2,1))].">
      <j1 rule="para" parents="21652 26032"/>
    </justification>
  </clause>

  <clause id="26036">
    <literal><![CDATA[
      a(x,y \ (z \ (y * (u * z))),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,L(L(u,z,y),y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(26034(a,1),24540(a,1))].">
      <j1 rule="para" parents="26034 24540"/>
    </justification>
  </clause>

  <clause id="26037">
    <literal><![CDATA[
      L(a(x,x \ (y \ z),u),w,a(x,x \ (y \ z),u)) = a(x,L(L(x \ (z / y),u,x),x,u),u)
    ]]></literal>
    <justification jstring="[hyper(26036,a,25814,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="26036 25814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26038">
    <literal><![CDATA[
      (x \ 1) * ((1 / (x * a(y,z,u))) * x) = (x \ ((x * x) * a(y,z,u))) \ 1
    ]]></literal>
    <justification jstring="[para(20571(a,1),26019(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="20571 26019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26039">
    <literal><![CDATA[
      (x \ 1) * ((1 / (x * a(y,z,u))) * x) = ((x \ a(y,z,u)) * (x * x)) \ 1
    ]]></literal>
    <justification jstring="[para(20587(a,1),26038(a,2,1))].">
      <j1 rule="para" parents="20587 26038"/>
    </justification>
  </clause>

  <clause id="26040">
    <literal><![CDATA[
      (x \ 1) * ((1 / (x * a(y,z,u))) * x) = ((1 / x) \ a(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(23342(a,1),26039(a,2,1))].">
      <j1 rule="para" parents="23342 26039"/>
    </justification>
  </clause>

  <clause id="26041">
    <literal><![CDATA[
      (x \ 1) * (x * ((a(y,z,u) * x) \ 1)) = ((1 / x) \ a(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(23264(a,1),26040(a,1,2))].">
      <j1 rule="para" parents="23264 26040"/>
    </justification>
  </clause>

  <clause id="26042">
    <literal><![CDATA[
      (x * (y \ 1)) / (L(y,z,u) \ 1) = (y \ 1) * ((L(y,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(25955(a,1),25968(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25955 25968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26043">
    <literal><![CDATA[
      (x * (y \ 1)) / (L(y,z,u) \ 1) = y * ((L(1 / y,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3740,a(flip),b,26042,a),flip(a)].">
      <j1 rule="hyper" parents="347 3740 26042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26045">
    <literal><![CDATA[
      (1 / x) * (((L(1 / (a(y,z,y) / x),u,w) \ 1) \ v5) * a(y,z,y)) = (v5 * ((a(y,z,y) / x) \ 1)) / (L(a(y,z,y) / x,u,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,12112,a,b,26043,a)].">
      <j1 rule="hyper" parents="347 12112 26043"/>
    </justification>
  </clause>

  <clause id="26046">
    <literal><![CDATA[
      (x / (L(y,z,u) \ 1)) * (y \ 1) = (y \ 1) * ((L(y,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(25955(a,1),25969(a,1,2))].">
      <j1 rule="para" parents="25955 25969"/>
    </justification>
  </clause>

  <clause id="26047">
    <literal><![CDATA[
      (x / (L(y,z,u) \ 1)) * (y \ 1) = y * ((L(1 / y,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3740,a(flip),b,26046,a),flip(a)].">
      <j1 rule="hyper" parents="347 3740 26046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26049">
    <literal><![CDATA[
      a(x,L(L(x \ (y / z),u,x),x,u),u) = a(x,x \ (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(21178,a,26037,a),flip(a)].">
      <j1 rule="hyper" parents="21178 26037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26050">
    <literal><![CDATA[
      a(x,(y * x) \ ((x * L(x \ (z / u),y,x)) * y),y) = a(x,x \ (u \ z),y)
    ]]></literal>
    <justification jstring="[hyper(24420,a,26049,a)].">
      <j1 rule="hyper" parents="24420 26049"/>
    </justification>
  </clause>

  <clause id="26051">
    <literal><![CDATA[
      a(x,(y * x) \ (x * (y * L(y \ (x \ z),y,x))),y) = a(x,x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[para(2063(a,1),26050(a,1,2,2))].">
      <j1 rule="para" parents="2063 26050"/>
    </justification>
  </clause>

  <clause id="26052">
    <literal><![CDATA[
      a(x,(y * x) \ (x * (y * ((x * y) \ z))),y) = a(x,x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[para(329(a,1),26051(a,1,2,2,2,2))].">
      <j1 rule="para" parents="329 26051"/>
    </justification>
  </clause>

  <clause id="26053">
    <literal><![CDATA[
      a(x,L(K(x,y) * ((x * y) \ z),y,x),y) = a(x,x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[para(10173(a,1),26052(a,1,2))].">
      <j1 rule="para" parents="10173 26052"/>
    </justification>
  </clause>

  <clause id="26054">
    <literal><![CDATA[
      a(x,L((y * x) \ z,y,x),y) = a(x,x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[para(10274(a,1),26053(a,1,2,1))].">
      <j1 rule="para" parents="10274 26053"/>
    </justification>
  </clause>

  <clause id="26055">
    <literal><![CDATA[
      a(x,y \ (x \ z),y) = a(x,x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(26033,a,26054,a)].">
      <j1 rule="hyper" parents="26033 26054"/>
    </justification>
  </clause>

  <clause id="26056">
    <literal><![CDATA[
      a(x,x \ (y \ 1),y) = a(x,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(24371,a,26055,a),flip(a)].">
      <j1 rule="hyper" parents="24371 26055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26057">
    <literal><![CDATA[
      a(x,y \ x,y) = a(x,x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(24371,a,26056,a),flip(a)].">
      <j1 rule="hyper" parents="24371 26056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26058">
    <literal><![CDATA[
      ((x * (x \ y)) * y) * a(y,y \ x,x) = (x * (x \ y)) * R(y,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,26057,a(flip),b,18787,a(flip))].">
      <j1 rule="hyper" parents="134 26057 18787"/>
    </justification>
  </clause>

  <clause id="26059">
    <literal><![CDATA[
      x \ a(y,x \ y,x) = (y \ x) \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(26057(a,2),25997(a,1,2))].">
      <j1 rule="para" parents="26057 25997"/>
    </justification>
  </clause>

  <clause id="26060">
    <literal><![CDATA[
      T(x * ((x \ 1) / y),y) = (x \ y) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(14997,a,26059,a)].">
      <j1 rule="hyper" parents="14997 26059"/>
    </justification>
  </clause>

  <clause id="26061">
    <literal><![CDATA[
      L(x,y,((z \ u) \ (z \ 1)) \ w) = L(x,y,(z * ((z \ 1) / u)) \ w)
    ]]></literal>
    <justification jstring="[para(26060(a,1),21468(a,1,3,1))].">
      <j1 rule="para" parents="26060 21468"/>
    </justification>
  </clause>

  <clause id="26062">
    <literal><![CDATA[
      L(x,y,((z \ u) \ (z \ 1)) \ w) = L(x,y,(z * (u \ (z \ 1))) \ w)
    ]]></literal>
    <justification jstring="[hyper(347,a,21551,a(flip),b,26061,a),flip(a)].">
      <j1 rule="hyper" parents="347 21551 26061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26063">
    <literal><![CDATA[
      L(x,y,(z * ((z * u) \ (z \ 1))) \ w) = L(x,y,(u \ (z \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(9(a,1),26062(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="9 26062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26064">
    <literal><![CDATA[
      (x * (x \ y)) * R(y,x \ y,x) = (y * y) * a(y,y \ x,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),26058(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 26058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26065">
    <literal><![CDATA[
      (x * (x \ y)) * R(y,x \ y,x) = y * (a(y,y \ x,x) * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,25376,a(flip),b,26064,a),flip(a)].">
      <j1 rule="hyper" parents="347 25376 26064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26067">
    <literal><![CDATA[
      (x * (y * (L(y,z,u) \ y))) / y = (y * (L(y,z,u) \ y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(25972(a,1),25975(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="25972 25975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26068">
    <literal><![CDATA[
      x / y != (y * (L(y,z,u) \ y)) * (y \ w)
    ]]></literal>
    <literal><![CDATA[
      w * (y * (L(y,z,u) \ y)) = x
    ]]></literal>
    <justification jstring="[para(26067(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="26067 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26069">
    <literal><![CDATA[
      R(x / (1 / (y * (L(y,z,u) \ y))),y * (L(y,z,u) \ y),y * (L(y,z,u) \ y)) / y = (y * (L(y,z,u) \ y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(2262(a,2),26067(a,1,1))].">
      <j1 rule="para" parents="2262 26067"/>
    </justification>
  </clause>

  <clause id="26070">
    <literal><![CDATA[
      (x * ((L(y,z,u) \ y) * y)) / y = (y * (L(y,z,u) \ y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(3318(a,2),26067(a,1,1,2))].">
      <j1 rule="para" parents="3318 26067"/>
    </justification>
  </clause>

  <clause id="26071">
    <literal><![CDATA[
      x / y != (y * (L(y,z,u) \ y)) * (y \ w)
    ]]></literal>
    <literal><![CDATA[
      w * ((L(y,z,u) \ y) * y) = x
    ]]></literal>
    <justification jstring="[para(26070(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="26070 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26072">
    <literal><![CDATA[
      x \ ((x * (L(x,y,z) \ x)) * u) = (x * (L(x,y,z) \ x)) * (x \ u)
    ]]></literal>
    <justification jstring="[para(25972(a,1),25977(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="25972 25977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26073">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * (x * u) = x * ((x * (L(x,y,z) \ x)) * u)
    ]]></literal>
    <justification jstring="[hyper(1052,a,26072,a),flip(a)].">
      <j1 rule="hyper" parents="1052 26072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26074">
    <literal><![CDATA[
      ((K(x,K(y,z)) * u) * (K(x,K(y,z)) * (L(K(x,K(y,z)) * u,w,v5) \ u))) * ((K(x,K(y,z)) * u) * v6) = (K(x,K(y,z)) * u) * (((K(x,K(y,z)) * u) * (L(K(x,K(y,z)) * u,w,v5) \ (K(x,K(y,z)) * u))) * v6)
    ]]></literal>
    <justification jstring="[para(17000(a,1),26073(a,1,1,2))].">
      <j1 rule="para" parents="17000 26073"/>
    </justification>
  </clause>

  <clause id="26075">
    <literal><![CDATA[
      x \ ((y * (L(y,z,u) \ y)) * (L(y * (L(y,z,u) \ y),z,u) \ x)) = L(L(y,z,u) \ y,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(128,a,25978,a,b,10157,a)].">
      <j1 rule="hyper" parents="128 25978 10157"/>
    </justification>
  </clause>

  <clause id="26076">
    <literal><![CDATA[
      a(x,L(L(y * K(y * z,u),z,u),u,z),w) = a(x,u \ (T(z,y) \ ((T(z,y) * y) * u)),w)
    ]]></literal>
    <justification jstring="[para(20041(a,1),26035(a,1,2))].">
      <j1 rule="para" parents="20041 26035"/>
    </justification>
  </clause>

  <clause id="26077">
    <literal><![CDATA[
      a(x,y \ (T(z,u) \ ((T(z,u) * u) * y)),w) = a(x,L(L(u,z,y),y,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24364,a(flip),b,26076,a),flip(a)].">
      <j1 rule="hyper" parents="63 24364 26076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26080">
    <literal><![CDATA[
      a(x,y \ (z \ ((z * u) * y)),w) = a(x,L(L(u,z,y),y,z),w)
    ]]></literal>
    <justification jstring="[para(20965(a,1),26077(a,1,2,2))].">
      <j1 rule="para" parents="20965 26077"/>
    </justification>
  </clause>

  <clause id="26082">
    <literal><![CDATA[
      L((L(x,y,z) \ 1) \ L(L(x,y,z) \ 1,u,w),y,z) = (x \ 1) \ L(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(25955(a,1),25966(a,2,2,1))].">
      <j1 rule="para" parents="25955 25966"/>
    </justification>
  </clause>

  <clause id="26083">
    <literal><![CDATA[
      L((L(x,y,z) \ 1) \ L(L(x,y,z) \ 1,u,w),y,z) = x \ L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,3357,a(flip),b,26082,a),flip(a)].">
      <j1 rule="hyper" parents="347 3357 26082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26085">
    <literal><![CDATA[
      L(L(x,y,z) \ L(L(x,y,z),u,w),y,z) = x \ L(x,u,w)
    ]]></literal>
    <justification jstring="[para(3357(a,1),26083(a,1,1))].">
      <j1 rule="para" parents="3357 26083"/>
    </justification>
  </clause>

  <clause id="26086">
    <literal><![CDATA[
      L(L(x,y,z),y,z) * (x \ L(x,u,w)) = L(L(L(x,y,z),y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(134,a,26085,a(flip),b,4638,a)].">
      <j1 rule="hyper" parents="134 26085 4638"/>
    </justification>
  </clause>

  <clause id="26087">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),u,w) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4638(a,1),26085(a,1,1))].">
      <j1 rule="para" parents="4638 26085"/>
    </justification>
  </clause>

  <clause id="26088">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z))) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(25976,a,26087,a)].">
      <j1 rule="hyper" parents="25976 26087"/>
    </justification>
  </clause>

  <clause id="26089">
    <literal><![CDATA[
      x * (y * L(z \ L(z,u,w),y,x)) = (x * y) * (z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(134,a,26087,a(flip),b,18,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 26087 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26090">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * L(L(x \ L(x,y,z),u,w) \ 1,u,w) = L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,26087,a(flip),b,3337,a),flip(a)].">
      <j1 rule="hyper" parents="128 26087 3337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26091">
    <literal><![CDATA[
      L(x \ ((x / y) * L(y,z,u)),y,x) = y \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(3965(a,1),26087(a,1,1))].">
      <j1 rule="para" parents="3965 26087"/>
    </justification>
  </clause>

  <clause id="26092">
    <literal><![CDATA[
      ((L(x,y,z) / x) \ 1) * (L(L(L(x \ L(x,y,z),u,w),u,w),v5,v6) \ (x \ L(x,y,z))) = L(L(x,y,z) / x,v5,v6) \ 1
    ]]></literal>
    <justification jstring="[para(26087(a,2),21333(a,1,2,1,1))].">
      <j1 rule="para" parents="26087 21333"/>
    </justification>
  </clause>

  <clause id="26093">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),x,x) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(34,a,23027,a(flip),b,26089,a),flip(a)].">
      <j1 rule="hyper" parents="34 23027 26089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26094">
    <literal><![CDATA[
      x \ ((y / x) \ L(y,z,u)) = L(y \ L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(138,a,26093,a)].">
      <j1 rule="hyper" parents="138 26093"/>
    </justification>
  </clause>

  <clause id="26095">
    <literal><![CDATA[
      L(x,y * L(L(L(y,z,u),z,u),z,u),L(y,z,u)) = L(x,L(y,z,u),L(y,z,u) \ L(L(y,z,u),z,u))
    ]]></literal>
    <justification jstring="[para(26086(a,1),25770(a,1,2,2))].">
      <j1 rule="para" parents="26086 25770"/>
    </justification>
  </clause>

  <clause id="26096">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (L(x * L(x,y,z),u,w) \ (x * L(x,y,z))) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(2698(a,1),26088(a,1,2))].">
      <j1 rule="para" parents="2698 26088"/>
    </justification>
  </clause>

  <clause id="26097">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) \ 1 = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10890,a(flip),b,26096,a)].">
      <j1 rule="hyper" parents="63 10890 26096"/>
    </justification>
  </clause>

  <clause id="26098">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) != v5 \ 1
    ]]></literal>
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(26097(a,1),48(a,1))].">
      <j1 rule="para" parents="26097 48"/>
    </justification>
  </clause>

  <clause id="26099">
    <literal><![CDATA[
      x \ ((y * (L(y,z,u) \ y)) * (L(y * (L(y,z,u) \ y),z,u) \ x)) = L(L(y,z,u) \ y,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,22808,a(flip),b,26075,a),flip(a)].">
      <j1 rule="hyper" parents="347 22808 26075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26100">
    <literal><![CDATA[
      x \ ((y * (L(y,z,u) \ y)) * (y \ x)) = L(L(y,z,u) \ y,y,x)
    ]]></literal>
    <justification jstring="[para(25972(a,1),26099(a,1,2,2,1))].">
      <j1 rule="para" parents="25972 26099"/>
    </justification>
  </clause>

  <clause id="26101">
    <literal><![CDATA[
      a(x,L(a(y,z,y) \ u,w,v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,w \ (v5 \ (u * (a(y,z,y) \ (v5 * w)))),v6) = v7
    ]]></literal>
    <justification jstring="[para(24022(a,1),26012(a,1))].">
      <j1 rule="para" parents="24022 26012"/>
    </justification>
  </clause>

  <clause id="26103">
    <literal><![CDATA[
      L(x,L(y,z,u),L(y,z,u) \ L(L(y,z,u),z,u)) = L(x,y * L(y,z,u),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,25563,a(flip),b,26095,a),flip(a)].">
      <j1 rule="hyper" parents="63 25563 26095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26105">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * ((x \ L(x,y,z)) \ 1) = L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(25955(a,1),26090(a,1,2))].">
      <j1 rule="para" parents="25955 26090"/>
    </justification>
  </clause>

  <clause id="26106">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z)) = x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12346,a(flip),b,26105,a),flip(a)].">
      <j1 rule="hyper" parents="63 12346 26105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26108">
    <literal><![CDATA[
      (L(x * (L(x,y,z) \ x),y,z) * u) \ ((x * (L(x,y,z) \ x)) * u) = R(x / L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(25979,a,20997,a)].">
      <j1 rule="hyper" parents="25979 20997"/>
    </justification>
  </clause>

  <clause id="26109">
    <literal><![CDATA[
      (L(x * (L(x,y,z) \ x),y,z) * u) \ ((x * (L(x,y,z) \ x)) * u) = R(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[para(3308(a,1),26108(a,2,1))].">
      <j1 rule="para" parents="3308 26108"/>
    </justification>
  </clause>

  <clause id="26110">
    <literal><![CDATA[
      (L(x * (L(x,y,z) \ x),y,z) * u) \ ((x * (L(x,y,z) \ x)) * u) = L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,25939,a(flip),b,26109,a),flip(a)].">
      <j1 rule="hyper" parents="347 25939 26109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26111">
    <literal><![CDATA[
      a(x,y,z * (L(z,y,x) \ z)) = L(L(z,y,x) \ z,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(18302,a,26110,a)].">
      <j1 rule="hyper" parents="18302 26110"/>
    </justification>
  </clause>

  <clause id="26112">
    <literal><![CDATA[
      a(x,y,z * (z * L(z,y,x))) = L(L(z,y,x) \ z,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,15036,a(flip),b,26111,a)].">
      <j1 rule="hyper" parents="63 15036 26111"/>
    </justification>
  </clause>

  <clause id="26113">
    <literal><![CDATA[
      a(x,y,L(z * (z * z),y,x)) = L(L(z,y,x) \ z,z,y * x)
    ]]></literal>
    <justification jstring="[para(3372(a,2),26112(a,1,3))].">
      <j1 rule="para" parents="3372 26112"/>
    </justification>
  </clause>

  <clause id="26114">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(z,y,L(x,y,z)) = u
    ]]></literal>
    <justification jstring="[para(26113(a,1),14942(a,1))].">
      <j1 rule="para" parents="26113 14942"/>
    </justification>
  </clause>

  <clause id="26115">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,z * y) = a(z,y,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(26114,a,20042,a),flip(a)].">
      <j1 rule="hyper" parents="26114 20042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26116">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ 1) * (L(L(L(x \ L(x,y,z),u,w),u,w),v5,v6) \ (x \ L(x,y,z))) = L(L(x,y,z) / x,v5,v6) \ 1
    ]]></literal>
    <justification jstring="[para(3161(a,1),26092(a,1,1,1))].">
      <j1 rule="para" parents="3161 26092"/>
    </justification>
  </clause>

  <clause id="26117">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(L(L(x \ L(x,y,z),u,w),u,w),v5,v6) \ (x \ L(x,y,z))) = L(L(x,y,z) / x,v5,v6) \ 1
    ]]></literal>
    <justification jstring="[para(10882(a,1),26116(a,1,1))].">
      <j1 rule="para" parents="10882 26116"/>
    </justification>
  </clause>

  <clause id="26118">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x \ L(x,y,z),u,w) \ (x \ L(x,y,z))) = L(L(x,y,z) / x,u,w) \ 1
    ]]></literal>
    <justification jstring="[para(14380(a,1),26117(a,1,2,1,1))].">
      <j1 rule="para" parents="14380 26117"/>
    </justification>
  </clause>

  <clause id="26119">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x * (L(x,y,z) \ L(x \ L(x,y,z),u,w))) = L(L(x,y,z) / x,u,w) \ 1
    ]]></literal>
    <justification jstring="[para(26106(a,1),26118(a,1,2))].">
      <j1 rule="para" parents="26106 26118"/>
    </justification>
  </clause>

  <clause id="26120">
    <literal><![CDATA[
      L(L(x,y,z) / x,u,w) \ 1 = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,3534,a(flip),b,26119,a),flip(a)].">
      <j1 rule="hyper" parents="63 3534 26119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26121">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ 1 = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(3161(a,1),26120(a,1,1,1))].">
      <j1 rule="para" parents="3161 26120"/>
    </justification>
  </clause>

  <clause id="26122">
    <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(10904,a,26121,a)].">
      <j1 rule="hyper" parents="10904 26121"/>
    </justification>
  </clause>

  <clause id="26123">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) * L(L(x,y,z),u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,26121,a(flip),b,10910,a)].">
      <j1 rule="hyper" parents="133 26121 10910"/>
    </justification>
  </clause>

  <clause id="26124">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,z * y) = ((z * y) \ ((z * (y * x)) / x)) \ 1
    ]]></literal>
    <justification jstring="[para(3970(a,1),26121(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3970 26121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26125">
    <literal><![CDATA[
      ((x * y) \ ((x * (y * z)) / z)) \ 1 = a(x,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,26115,a(flip),b,26124,a),flip(a)].">
      <j1 rule="hyper" parents="63 26115 26124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26126">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,w),z,w * u)) = a(x,y,((w * u) \ ((w * (u * z)) / z)) \ 1)
    ]]></literal>
    <justification jstring="[para(26124(a,1),15039(a,1,3)),flip(a)].">
      <j1 rule="para" parents="26124 15039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26127">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) / z) = a(x,y,L(z,y,x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(39,a,19984,a,b,26125,a),flip(a)].">
      <j1 rule="hyper" parents="39 19984 26125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26128">
    <literal><![CDATA[
      L(x,a(y,z,L(u,z,y)),w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(26125(a,1),22667(a,1,2))].">
      <j1 rule="para" parents="26125 22667"/>
    </justification>
  </clause>

  <clause id="26129">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,a(y,z,u),x)) = a(w,a(y,z,u),x) \ 1
    ]]></literal>
    <justification jstring="[para(23272(a,1),26125(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23272 26125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26130">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),y,x)) = a(a(z,u,w),y,x) \ 1
    ]]></literal>
    <justification jstring="[para(23299(a,1),26125(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23299 26125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26131">
    <literal><![CDATA[
      a(x,(y * z) \ (u \ (y * (z * u))),w) = a(x,a(y,z,L(u,z,y)),w)
    ]]></literal>
    <justification jstring="[para(26125(a,1),24256(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26125 24256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26132">
    <literal><![CDATA[
      L(a(x,y,L(z,y,x)),z,x * y) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[para(26125(a,1),26021(a,1,1))].">
      <j1 rule="para" parents="26125 26021"/>
    </justification>
  </clause>

  <clause id="26133">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),y,x)) \ 1 = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(20593,a,26130,a)].">
      <j1 rule="hyper" parents="20593 26130"/>
    </justification>
  </clause>

  <clause id="26134">
    <literal><![CDATA[
      a(a(x,y,L(z,y,x)),z,x * y) = a(x * y,z,L(z,y,x) \ z) \ 1
    ]]></literal>
    <justification jstring="[para(26132(a,1),26133(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="26132 26133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26135">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (y * z)) = a(x,y,L(z,y,x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,3980,a,b,26127,a)].">
      <j1 rule="hyper" parents="63 3980 26127"/>
    </justification>
  </clause>

  <clause id="26136">
    <literal><![CDATA[
      (a(x,y,L(z,y,x)) \ 1) * ((x * y) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(26127(a,1),21447(a,1,1))].">
      <j1 rule="para" parents="26127 21447"/>
    </justification>
  </clause>

  <clause id="26138">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,u,z)) \ 1) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(26127(a,1),25363(a,1,3))].">
      <j1 rule="para" parents="26127 25363"/>
    </justification>
  </clause>

  <clause id="26139">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * L(z,y,x))) = a(x,y,L(L(z,y,x),y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(97(a,1),26135(a,1,1))].">
      <j1 rule="para" parents="97 26135"/>
    </justification>
  </clause>

  <clause id="26140">
    <literal><![CDATA[
      (a(a(x,y,z),z * y,L(x,z * y,a(x,y,z))) \ 1) * ((a(x,y,z) * (z * y)) * x) = (z * y) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,18793,a(flip),b,26136,a),flip(a)].">
      <j1 rule="hyper" parents="347 18793 26136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26142">
    <literal><![CDATA[
      a(x,a(y,z,L(u,z,y)),w) = a(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24789,a(flip),b,26131,a),flip(a)].">
      <j1 rule="hyper" parents="63 24789 26131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26143">
    <literal><![CDATA[
      a(x,a(y,z,L(L(u,w,w),z,y)),v5) = a(x,a(w * (w * u),z,y),v5)
    ]]></literal>
    <justification jstring="[para(15023(a,1),26142(a,1,2))].">
      <j1 rule="para" parents="15023 26142"/>
    </justification>
  </clause>

  <clause id="26144">
    <literal><![CDATA[
      a(x,a(L(y,y,z),u,w),v5) = a(x,a(w,u,L(z \ (y \ z),u,w)),v5)
    ]]></literal>
    <justification jstring="[para(24979(a,1),26142(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24979 26142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26145">
    <literal><![CDATA[
      a(x,a(y * (y * z),u,w),v5) = a(x,a(L(z,y,y),u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,26142,a(flip),b,26143,a),flip(a)].">
      <j1 rule="hyper" parents="63 26142 26143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26146">
    <literal><![CDATA[
      a(a(x,y,L(z,y,x)),z,x * y) = a(x * y,z,z * L(z,y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(14939(a,1),26134(a,2,1))].">
      <j1 rule="para" parents="14939 26134"/>
    </justification>
  </clause>

  <clause id="26147">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * L(z,y,x))) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(25583(a,1),26139(a,2,1))].">
      <j1 rule="para" parents="25583 26139"/>
    </justification>
  </clause>

  <clause id="26148">
    <literal><![CDATA[
      L((x * y) \ (x * L(y,x,z)),x * y,z) = a(z,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(686,a,26147,a)].">
      <j1 rule="hyper" parents="686 26147"/>
    </justification>
  </clause>

  <clause id="26149">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (x * (x \ u))) \ ((x \ L(x,y,z)) * (x * (L(x,y,z) \ ((x \ L(x,y,z)) * u)))) = a(x \ L(x,y,z),x,x \ u) \ 1
    ]]></literal>
    <justification jstring="[para(3168(a,1),26147(a,1,2,2,2))].">
      <j1 rule="para" parents="3168 26147"/>
    </justification>
  </clause>

  <clause id="26150">
    <literal><![CDATA[
      (x * ((y \ L(y,z,u)) * y)) \ (x * (L(y,z,u) * (y \ L(y,y \ L(y,z,u),x)))) = a(x,y \ L(y,z,u),y) \ 1
    ]]></literal>
    <justification jstring="[para(11236(a,1),26147(a,1,2,2))].">
      <j1 rule="para" parents="11236 26147"/>
    </justification>
  </clause>

  <clause id="26152">
    <literal><![CDATA[
      (x * (y * (z \ L(z,u,w)))) \ ((x * y) * (z \ L(z,u,w))) = a(x,y,z \ L(z,u,w)) \ 1
    ]]></literal>
    <justification jstring="[para(26089(a,1),26147(a,1,2))].">
      <j1 rule="para" parents="26089 26147"/>
    </justification>
  </clause>

  <clause id="26153">
    <literal><![CDATA[
      L(x \ ((x / y) * L(y,x,z)),x * y,z) = a(z,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(3963(a,1),26148(a,1,1))].">
      <j1 rule="para" parents="3963 26148"/>
    </justification>
  </clause>

  <clause id="26154">
    <literal><![CDATA[
      x \ ((x / y) * L(y,x,z)) = a(z,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(25990,a,26153,a),flip(a)].">
      <j1 rule="hyper" parents="25990 26153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26155">
    <literal><![CDATA[
      (x * y) * (a(z,x,y) \ 1) = x * L(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,26153,a(flip),b,25605,a(flip))].">
      <j1 rule="hyper" parents="134 26153 25605"/>
    </justification>
  </clause>

  <clause id="26156">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,y) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(3968,a,26154,a)].">
      <j1 rule="hyper" parents="3968 26154"/>
    </justification>
  </clause>

  <clause id="26157">
    <literal><![CDATA[
      (x / y) * L(y,x,z) = x * (a(z,x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(150,a,26154,a),flip(a)].">
      <j1 rule="hyper" parents="150 26154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26158">
    <literal><![CDATA[
      x \ (y * L(y \ x,x,z)) = a(z,x,y \ x) \ 1
    ]]></literal>
    <justification jstring="[para(80(a,1),26154(a,1,2,1))].">
      <j1 rule="para" parents="80 26154"/>
    </justification>
  </clause>

  <clause id="26159">
    <literal><![CDATA[
      a(x,y,L(z,y,x) \ 1) \ 1 = y \ ((y / (L(z,y,x) \ 1)) * (z \ 1))
    ]]></literal>
    <justification jstring="[para(25955(a,1),26154(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="25955 26154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26161">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,z,y) = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[para(26154(a,1),26091(a,1,1))].">
      <j1 rule="para" parents="26154 26091"/>
    </justification>
  </clause>

  <clause id="26162">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,z,y)
    ]]></literal>
    <justification jstring="[hyper(26098,a,26156,a),flip(a)].">
      <j1 rule="hyper" parents="26098 26156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26163">
    <literal><![CDATA[
      x \ (y * L(y \ x,y,z)) = a(z,y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(651,a,26156,a)].">
      <j1 rule="hyper" parents="651 26156"/>
    </justification>
  </clause>

  <clause id="26164">
    <literal><![CDATA[
      a(x,a(y,z,u),y) \ 1 = y \ L(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,25505,a(flip),b,26156,a),flip(a)].">
      <j1 rule="hyper" parents="63 25505 26156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26165">
    <literal><![CDATA[
      a(x,y,y \ z) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      z \ (y * L(y \ z,y,x)) = u
    ]]></literal>
    <justification jstring="[para(26156(a,1),651(a,1))].">
      <j1 rule="para" parents="26156 651"/>
    </justification>
  </clause>

  <clause id="26166">
    <literal><![CDATA[
      x * ((L(y,x,z) * (y \ x)) \ x) = x / (a(z,x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(26156(a,1),23855(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26156 23855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26167">
    <literal><![CDATA[
      (x * y) * (y \ L(y,x,z)) = x * (y * (a(z,x,y) \ 1))
    ]]></literal>
    <justification jstring="[para(26156(a,1),26089(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="26156 26089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26168">
    <literal><![CDATA[
      L(x,L(x,y,z),u) \ x = a(u,L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,22638,a(flip),b,26162,a)].">
      <j1 rule="hyper" parents="347 22638 26162"/>
    </justification>
  </clause>

  <clause id="26169">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ L(L(x,y,z) \ x,x,y) = a(z,y,x) * ((L(x,y,z) \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,26162,a,b,1296,a),flip(a)].">
      <j1 rule="hyper" parents="133 26162 1296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26170">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,y) = a(z,T(y,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,23991,a,b,26162,a),flip(a)].">
      <j1 rule="hyper" parents="63 23991 26162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26171">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z),z,y) \ a(x,y,z)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(25976,a,26162,a(flip))].">
      <j1 rule="hyper" parents="25976 26162"/>
    </justification>
  </clause>

  <clause id="26172">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),x,y) = L(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(26162(a,2),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26162 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26173">
    <literal><![CDATA[
      L(x,y,z) != a(u,z,y)
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) \ y = x
    ]]></literal>
    <justification jstring="[para(26162(a,2),50(a,1)),flip(a)].">
      <j1 rule="para" parents="26162 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26174">
    <literal><![CDATA[
      L(L(T(x,y),z,u) \ x,T(x,y),z) \ (L(T(x,y),z,u) \ x) = a(u,z,T(x,y)) \ (L(T(x,y),z,u) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(26162(a,2),22801(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26162 22801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26175">
    <literal><![CDATA[
      L(L(x,y,z * L(u,w,v5)) \ x,x,y) = a(z * R(u,w,v5),y,x)
    ]]></literal>
    <justification jstring="[para(22863(a,1),26162(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="22863 26162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26176">
    <literal><![CDATA[
      L(L(x,y,z * (u * L(w,v5,v6))) \ x,x,y) = a(z * (u * R(w,v5,v6)),y,x)
    ]]></literal>
    <justification jstring="[para(22871(a,1),26162(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="22871 26162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26177">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)) \ x,x,y) = a(a(z * (v5 * v5),u,w),y,x)
    ]]></literal>
    <justification jstring="[para(23258(a,1),26162(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="23258 26162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26179">
    <literal><![CDATA[
      L(a(x,y,L(y,x,z) \ y) \ y,x,L(y,x,z) \ y) = ((L(y,x,z) \ y) * x) \ (a(z,x,y) * (x * y))
    ]]></literal>
    <justification jstring="[para(26162(a,2),25479(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="26162 25479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26180">
    <literal><![CDATA[
      R(x,x,L(y,x,z) \ y) = R(x,x,a(z,x,y))
    ]]></literal>
    <justification jstring="[para(26162(a,2),25996(a,1,3)),flip(a)].">
      <j1 rule="para" parents="26162 25996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26181">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),z,y) = L(z \ L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(26161(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26161 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26182">
    <literal><![CDATA[
      L(a(x,y,z \ u) \ 1,L(z * u,z,u),y) = L(z * u,z,u) \ L(L(z * u,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(25260(a,1),26161(a,1,1,1))].">
      <j1 rule="para" parents="25260 26161"/>
    </justification>
  </clause>

  <clause id="26183">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w) \ 1,x,y) = L(a(z,y,x) \ 1,u,w) \ 1
    ]]></literal>
    <justification jstring="[para(26161(a,1),25961(a,1,1,1,1))].">
      <j1 rule="para" parents="26161 25961"/>
    </justification>
  </clause>

  <clause id="26184">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(26170(a,2),18300(a,1))].">
      <j1 rule="para" parents="26170 18300"/>
    </justification>
  </clause>

  <clause id="26185">
    <literal><![CDATA[
      (x * y) * z != x * L(y,x,u)
    ]]></literal>
    <literal><![CDATA[
      a(u,x,y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(26155(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="26155 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26186">
    <literal><![CDATA[
      L(x,y,z) * (x \ y) = y * (a(z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(21069,a,26157,a)].">
      <j1 rule="hyper" parents="21069 26157"/>
    </justification>
  </clause>

  <clause id="26187">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * y = (y / z) * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,20078,a,b,26157,a)].">
      <j1 rule="hyper" parents="347 20078 26157"/>
    </justification>
  </clause>

  <clause id="26188">
    <literal><![CDATA[
      L(x,L(x,y,z),u) \ x = a(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,14574,a(flip),b,26168,a),flip(a)].">
      <j1 rule="hyper" parents="347 14574 26168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26189">
    <literal><![CDATA[
      R(x,x,L(y,x,z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,x,a(z,x,y)) = u
    ]]></literal>
    <justification jstring="[para(26180(a,2),23284(a,1))].">
      <j1 rule="para" parents="26180 23284"/>
    </justification>
  </clause>

  <clause id="26190">
    <literal><![CDATA[
      (1 / x) * (L(y,x,z) * (y \ x)) = L(a(z,x,y) \ 1,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,26186,a,b,2946,a)].">
      <j1 rule="hyper" parents="134 26186 2946"/>
    </justification>
  </clause>

  <clause id="26191">
    <literal><![CDATA[
      ((x * y) / x) \ (L(z,y,u) * (z \ y)) = K(y,x) * (a(u,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,26186,a,b,5195,a)].">
      <j1 rule="hyper" parents="128 26186 5195"/>
    </justification>
  </clause>

  <clause id="26192">
    <literal><![CDATA[
      L(x * (y \ x),x,z) * (((x \ y) \ 1) \ 1) = x * (a(z,x,x * (y \ x)) \ 1)
    ]]></literal>
    <justification jstring="[para(3272(a,2),26186(a,1,2))].">
      <j1 rule="para" parents="3272 26186"/>
    </justification>
  </clause>

  <clause id="26193">
    <literal><![CDATA[
      R(x / y,L(y,x,z),L(y,x,z)) / (L(y,x,z) \ 1) = (a(z,x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,788,a,b,26187,a)].">
      <j1 rule="hyper" parents="347 788 26187"/>
    </justification>
  </clause>

  <clause id="26194">
    <literal><![CDATA[
      (T(x,y) \ z) \ ((x * y) \ (y * z)) = a(y,x,z \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,22602,a,b,26158,a)].">
      <j1 rule="hyper" parents="63 22602 26158"/>
    </justification>
  </clause>

  <clause id="26195">
    <literal><![CDATA[
      (x \ y) \ ((z * x) \ (z * y)) = a(z,x,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,3536,a,b,26158,a)].">
      <j1 rule="hyper" parents="63 3536 26158"/>
    </justification>
  </clause>

  <clause id="26196">
    <literal><![CDATA[
      L(a(x,y,z \ y) \ 1,y,y) = (z * y) \ L(z * y,y,x)
    ]]></literal>
    <justification jstring="[para(26158(a,1),21429(a,1,1))].">
      <j1 rule="para" parents="26158 21429"/>
    </justification>
  </clause>

  <clause id="26197">
    <literal><![CDATA[
      x \ (L(x,y,z) * L(L(x,y,z) \ x,x,u)) = a(x \ u,x,L(x,y,z) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(22808(a,1),26158(a,1,2,2))].">
      <j1 rule="para" parents="22808 26158"/>
    </justification>
  </clause>

  <clause id="26198">
    <literal><![CDATA[
      (x \ y) \ (z * ((x * z) \ y)) = a(x,z,z \ (x \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(329(a,1),26163(a,1,2,2))].">
      <j1 rule="para" parents="329 26163"/>
    </justification>
  </clause>

  <clause id="26199">
    <literal><![CDATA[
      L(a(x,a(y,z,u),y) \ 1,w,y) = y \ L(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(15046,a,26164,a)].">
      <j1 rule="hyper" parents="15046 26164"/>
    </justification>
  </clause>

  <clause id="26200">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,x,u),x,y) = L(a(z,y,x),x,x \ u)
    ]]></literal>
    <justification jstring="[para(22808(a,1),26172(a,1,1))].">
      <j1 rule="para" parents="22808 26172"/>
    </justification>
  </clause>

  <clause id="26201">
    <literal><![CDATA[
      ((x * y) \ (x * z)) \ (y \ z) = a(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(10936,a,26195,a)].">
      <j1 rule="hyper" parents="10936 26195"/>
    </justification>
  </clause>

  <clause id="26202">
    <literal><![CDATA[
      L(x \ 1,x,y) \ ((z * (y * x)) \ (z * y)) = a(z,y * x,y \ (y * x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(662,a,26195,a)].">
      <j1 rule="hyper" parents="662 26195"/>
    </justification>
  </clause>

  <clause id="26203">
    <literal><![CDATA[
      (x \ (x * (T(y,z) \ u))) \ ((w * x) \ (w * (x * (T(y,z) \ u)))) = a(w,x,((x * (y \ u)) \ x) * K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(21991(a,2),26195(a,2,1,3))].">
      <j1 rule="para" parents="21991 26195"/>
    </justification>
  </clause>

  <clause id="26204">
    <literal><![CDATA[
      L(x \ y,x,z) \ (x \ y) = a(z,x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(687,a,26201,a)].">
      <j1 rule="hyper" parents="687 26201"/>
    </justification>
  </clause>

  <clause id="26205">
    <literal><![CDATA[
      ((x * y) \ (x * (y * z))) \ (y \ (y * z)) = a(x,y,L(z \ 1,z,y))
    ]]></literal>
    <justification jstring="[para(244(a,2),26201(a,2,3))].">
      <j1 rule="para" parents="244 26201"/>
    </justification>
  </clause>

  <clause id="26206">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,u) \ (x \ (L(x,y,z) \ x)) = a(u,x,(L(x,y,z) \ x) \ x)
    ]]></literal>
    <justification jstring="[para(1419(a,1),26201(a,1,1))].">
      <j1 rule="para" parents="1419 26201"/>
    </justification>
  </clause>

  <clause id="26207">
    <literal><![CDATA[
      L(L(x \ (x \ y),z,u),x,w) \ (x \ (x \ L(y,z,u))) = a(w,x,(x \ L(y,z,u)) \ x)
    ]]></literal>
    <justification jstring="[para(3382(a,2),26204(a,1,1,1))].">
      <j1 rule="para" parents="3382 26204"/>
    </justification>
  </clause>

  <clause id="26208">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),y) = (L(z,y,x) * (z \ y)) \ y
    ]]></literal>
    <justification jstring="[hyper(34,a,2008,a,b,26166,a)].">
      <j1 rule="hyper" parents="34 2008 26166"/>
    </justification>
  </clause>

  <clause id="26209">
    <literal><![CDATA[
      (x * y) * (y \ L(y,x,z)) = x * (a(z,x,y) \ y)
    ]]></literal>
    <justification jstring="[para(12717(a,1),26167(a,2,2))].">
      <j1 rule="para" parents="12717 26167"/>
    </justification>
  </clause>

  <clause id="26210">
    <literal><![CDATA[
      a(x,y,y \ L(y,x,z)) * (y * (y \ L(y,x,z))) = a(z,x,y) \ y
    ]]></literal>
    <justification jstring="[hyper(14736,a,26209,a)].">
      <j1 rule="hyper" parents="14736 26209"/>
    </justification>
  </clause>

  <clause id="26211">
    <literal><![CDATA[
      L(a(x,y * z,z) \ 1,z,y) = z \ L(z,y * z,x)
    ]]></literal>
    <justification jstring="[hyper(41,a,10259,a,b,26181,a),flip(a)].">
      <j1 rule="hyper" parents="41 10259 26181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26212">
    <literal><![CDATA[
      (x \ y) \ L(x \ y,x * (x \ y),z) = L(a(z,y,x \ y) \ 1,x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),26211(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 26211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26213">
    <literal><![CDATA[
      L(a(x,(y * y) * z,R(y,y,z) * z) \ 1,R(y,y,z) * z,y) = (R(y,y,z) * z) \ L(R(y,y,z) * z,y * (R(y,y,z) * z),x)
    ]]></literal>
    <justification jstring="[para(1750(a,1),26211(a,1,1,1,2))].">
      <j1 rule="para" parents="1750 26211"/>
    </justification>
  </clause>

  <clause id="26214">
    <literal><![CDATA[
      L(a(x,y,z),z,z \ u) = L(a(x,y,z),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,26172,a(flip),b,26200,a),flip(a)].">
      <j1 rule="hyper" parents="63 26172 26200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26215">
    <literal><![CDATA[
      L(a(x,y,z),z,u * z) != w
    ]]></literal>
    <literal><![CDATA[
      L(a(x,y,z),z,u) = w
    ]]></literal>
    <justification jstring="[para(26214(a,1),10237(a,1))].">
      <j1 rule="para" parents="26214 10237"/>
    </justification>
  </clause>

  <clause id="26216">
    <literal><![CDATA[
      a(x * R(y,z,u),w,v5) = a(x * L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26184,a,26175,a),flip(a)].">
      <j1 rule="hyper" parents="26184 26175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26217">
    <literal><![CDATA[
      a(x * R(y,z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x * L(y,z,u),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(26175(a,1),26184(a,1))].">
      <j1 rule="para" parents="26175 26184"/>
    </justification>
  </clause>

  <clause id="26218">
    <literal><![CDATA[
      a((x * y) * R(R(z,y,x),u,w),v5,v6) = a((L(z,u,w) * y) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,24317,a(flip),b,26216,a),flip(a)].">
      <j1 rule="hyper" parents="347 24317 26216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26219">
    <literal><![CDATA[
      a(a(x * (y * y),z,u),w,v5) = a(a(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26184,a,26177,a),flip(a)].">
      <j1 rule="hyper" parents="26184 26177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26220">
    <literal><![CDATA[
      a(a((x \ 1) \ y,z,u),w,v5) = a(a(x \ y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(23923(a,1),26219(a,1,1))].">
      <j1 rule="para" parents="23923 26219"/>
    </justification>
  </clause>

  <clause id="26221">
    <literal><![CDATA[
      (1 / x) * (L(y,x,z) * (y \ x)) = L(a(z,x,y) \ 1,x,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,23388,a(flip),b,26190,a),flip(a)].">
      <j1 rule="hyper" parents="347 23388 26190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26222">
    <literal><![CDATA[
      ((x * y) / x) \ (L(z,y,u) * (z \ y)) = a(u,y,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,16907,a(flip),b,26191,a),flip(a)].">
      <j1 rule="hyper" parents="347 16907 26191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26223">
    <literal><![CDATA[
      L(x,y,z) \ (y \ (y * x)) = a(z,y,L(x \ 1,x,y))
    ]]></literal>
    <justification jstring="[para(18(a,2),26205(a,1,1))].">
      <j1 rule="para" parents="18 26205"/>
    </justification>
  </clause>

  <clause id="26224">
    <literal><![CDATA[
      a(x,y,L(z \ 1,z,y)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[para(9(a,1),26223(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 26223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26225">
    <literal><![CDATA[
      a(x,y,L(z,z,y)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(15032,a,26224,a)].">
      <j1 rule="hyper" parents="15032 26224"/>
    </justification>
  </clause>

  <clause id="26226">
    <literal><![CDATA[
      a(x,y,y \ (z \ y)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(24770,a,26225,a)].">
      <j1 rule="hyper" parents="24770 26225"/>
    </justification>
  </clause>

  <clause id="26227">
    <literal><![CDATA[
      L(x \ y,y,z) \ (x \ y) = a(z,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(24763,a,26225,a),flip(a)].">
      <j1 rule="hyper" parents="24763 26225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26228">
    <literal><![CDATA[
      a(x,y,L(L(z,L(z,u,w),y),u,w)) = L(L(z,u,w),y,x) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[para(30(a,1),26225(a,1,3))].">
      <j1 rule="para" parents="30 26225"/>
    </justification>
  </clause>

  <clause id="26229">
    <literal><![CDATA[
      a(x,L(y,z,u),L(L(y,L(y,w,v5),y),w,v5)) = L(L(y,w,v5),L(y,z,u),x) \ L(y,w,v5)
    ]]></literal>
    <justification jstring="[para(10970(a,1),26225(a,1,3))].">
      <j1 rule="para" parents="10970 26225"/>
    </justification>
  </clause>

  <clause id="26230">
    <literal><![CDATA[
      L(a(x,y,z),z,u) \ a(x,y,z) = a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(12360(a,1),26225(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12360 26225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26231">
    <literal><![CDATA[
      L(x,a(y,z,L(u,u,z)),w) = R(x,L(u,z,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(26225(a,1),23225(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26225 23225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26232">
    <literal><![CDATA[
      R(x,y,L(z,u,w) \ z) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(w,u,L(z,z,u))) = v5
    ]]></literal>
    <justification jstring="[para(26225(a,1),23284(a,1,3))].">
      <j1 rule="para" parents="26225 23284"/>
    </justification>
  </clause>

  <clause id="26233">
    <literal><![CDATA[
      L(x \ y,y,z) \ (x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      a(z,y,y \ x) = u
    ]]></literal>
    <justification jstring="[para(26225(a,1),24763(a,1))].">
      <j1 rule="para" parents="26225 24763"/>
    </justification>
  </clause>

  <clause id="26234">
    <literal><![CDATA[
      L(a(x,y,z),x,u) \ a(x,y,z) = a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(25390(a,1),26225(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25390 26225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26235">
    <literal><![CDATA[
      T(x * ((L(y,z,x) \ y) \ z),L(y,y,z)) = L(y,y,z) \ (x * (z / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(26225(a,1),25471(a,1,1,2,1))].">
      <j1 rule="para" parents="26225 25471"/>
    </justification>
  </clause>

  <clause id="26236">
    <literal><![CDATA[
      a(x * y,z,L(L(z,y,x) \ z,L(z,y,x) \ z,z)) = a(x,y,L(z,y,x)) \ (L(z,y,x) \ z)
    ]]></literal>
    <justification jstring="[para(26115(a,1),26225(a,2,1))].">
      <j1 rule="para" parents="26115 26225"/>
    </justification>
  </clause>

  <clause id="26237">
    <literal><![CDATA[
      a(x,L(y,z,u) \ y,L(w,a(u,z,L(y,y,z)),x)) = a(w,a(u,z,L(y,y,z)),x) \ 1
    ]]></literal>
    <justification jstring="[para(26225(a,1),26129(a,1,2))].">
      <j1 rule="para" parents="26225 26129"/>
    </justification>
  </clause>

  <clause id="26238">
    <literal><![CDATA[
      L(x,y,z) = a(z,y,y \ (x \ y)) \ x
    ]]></literal>
    <justification jstring="[hyper(20593,a,26226,a),flip(a)].">
      <j1 rule="hyper" parents="20593 26226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26240">
    <literal><![CDATA[
      L(1 \ L(1 / L(x,y,z),u,w),L(1 / L(x,y,z),u,w),v5) \ (1 \ L(1 / L(x,y,z),u,w)) = a(v5,L(1 / L(x,y,z),u,w),L(L(1 / x,u,w) \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(26008(a,2),26227(a,2,3))].">
      <j1 rule="para" parents="26008 26227"/>
    </justification>
  </clause>

  <clause id="26241">
    <literal><![CDATA[
      a(x,y,z) * a(y,z,a(x,y,z)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[para(26230(a,1),26171(a,1,2))].">
      <j1 rule="para" parents="26230 26171"/>
    </justification>
  </clause>

  <clause id="26242">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) \ (L(y,x,z) \ y) = a(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(20594,a,26241,a)].">
      <j1 rule="hyper" parents="20594 26241"/>
    </justification>
  </clause>

  <clause id="26243">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * a(y,x,a(z,y,x))) * (a(y,x,a(z,y,x)) \ (L(x,y,z) \ x)) = (L(x,y,z) \ x) * R(L(x,y,z) \ x,a(y,x,a(z,y,x)),a(z,y,x))
    ]]></literal>
    <justification jstring="[para(26242(a,1),862(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="26242 862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26244">
    <literal><![CDATA[
      L(x,a(y,z,L(u,u,z)),w) = R(x,u * L(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,2285,a(flip),b,26231,a),flip(a)].">
      <j1 rule="hyper" parents="347 2285 26231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26245">
    <literal><![CDATA[
      R(x,y * L(y,z,u),w) = L(x,L(y,z,u) \ y,w)
    ]]></literal>
    <justification jstring="[para(26225(a,1),26244(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26225 26244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26246">
    <literal><![CDATA[
      R(x,y * L(y,z,u),w) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,3251,a(flip),b,26245,a),flip(a)].">
      <j1 rule="hyper" parents="347 3251 26245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26247">
    <literal><![CDATA[
      R(x,y * L(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * L(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(26245(a,2),3529(a,1))].">
      <j1 rule="para" parents="26245 3529"/>
    </justification>
  </clause>

  <clause id="26248">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),w) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,10905,a,b,26246,a)].">
      <j1 rule="hyper" parents="63 10905 26246"/>
    </justification>
  </clause>

  <clause id="26249">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,w) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,2285,a,b,26246,a)].">
      <j1 rule="hyper" parents="63 2285 26246"/>
    </justification>
  </clause>

  <clause id="26250">
    <literal><![CDATA[
      L(x,y * L(y,z,u),w \ a(v5,v6,v5)) = R(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,12266,a(flip),b,26246,a),flip(a)].">
      <j1 rule="hyper" parents="63 12266 26246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26251">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * L(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(2285(a,2),26247(a,1))].">
      <j1 rule="para" parents="2285 26247"/>
    </justification>
  </clause>

  <clause id="26252">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y * L(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(10905(a,2),26247(a,1))].">
      <j1 rule="para" parents="10905 26247"/>
    </justification>
  </clause>

  <clause id="26253">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,w,u))) = R(x,y,w * L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(26232,a,2213,a)].">
      <j1 rule="hyper" parents="26232 2213"/>
    </justification>
  </clause>

  <clause id="26254">
    <literal><![CDATA[
      L(x,y * L(y,z,u),w \ a(v5,v6,v5)) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,26246,a(flip),b,26250,a),flip(a)].">
      <j1 rule="hyper" parents="347 26246 26250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26255">
    <literal><![CDATA[
      L(x,y * L(y,z,u),w \ 1) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(11848,a,26254,a)].">
      <j1 rule="hyper" parents="11848 26254"/>
    </justification>
  </clause>

  <clause id="26256">
    <literal><![CDATA[
      a(x,y,y * L(y,x,z)) * (y * (y \ L(y,x,z))) = a(z,x,y) \ y
    ]]></literal>
    <justification jstring="[para(14977(a,1),26210(a,1,1))].">
      <j1 rule="para" parents="14977 26210"/>
    </justification>
  </clause>

  <clause id="26257">
    <literal><![CDATA[
      a(x,y,L(z,y,x) \ 1) \ 1 = y \ (z * ((L(1 / z,y,x) \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(26047(a,1),26159(a,2,2))].">
      <j1 rule="para" parents="26047 26159"/>
    </justification>
  </clause>

  <clause id="26258">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),x,y) = L(a(z,y,x) \ 1,u,w) \ 1
    ]]></literal>
    <justification jstring="[para(26121(a,1),26183(a,1,1))].">
      <j1 rule="para" parents="26121 26183"/>
    </justification>
  </clause>

  <clause id="26259">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) \ 1 = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,26172,a(flip),b,26258,a),flip(a)].">
      <j1 rule="hyper" parents="63 26172 26258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26260">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) = L(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(14636,a,26259,a)].">
      <j1 rule="hyper" parents="14636 26259"/>
    </justification>
  </clause>

  <clause id="26261">
    <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(63,a,12599,a,b,26259,a)].">
      <j1 rule="hyper" parents="63 12599 26259"/>
    </justification>
  </clause>

  <clause id="26262">
    <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(128,a,26259,a(flip),b,12599,a),flip(a)].">
      <j1 rule="hyper" parents="128 26259 12599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26263">
    <literal><![CDATA[
      L(a(x,x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(26259(a,1),14636(a,1))].">
      <j1 rule="para" parents="26259 14636"/>
    </justification>
  </clause>

  <clause id="26264">
    <literal><![CDATA[
      x \ (R(y,y,z) * (y \ x)) = a(y,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,21170,a,b,26260,a)].">
      <j1 rule="hyper" parents="347 21170 26260"/>
    </justification>
  </clause>

  <clause id="26265">
    <literal><![CDATA[
      a(x,x,L(y,z,a(x,u,w))) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,25509,a(flip),b,26260,a),flip(a)].">
      <j1 rule="hyper" parents="347 25509 26260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26266">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ L(L(a(x,x,y),z,u),w,v5) = L(a(x,x,y) \ L(a(x,x,y),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(26260(a,2),4638(a,1,1))].">
      <j1 rule="para" parents="26260 4638"/>
    </justification>
  </clause>

  <clause id="26267">
    <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(26260(a,2),14634(a,1,1))].">
      <j1 rule="para" parents="26260 14634"/>
    </justification>
  </clause>

  <clause id="26268">
    <literal><![CDATA[
      ((x \ 1) * y) \ ((x \ y) * L((x \ y) \ ((x \ 1) * y),z,u)) = a(x,x,y) \ a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(26260(a,2),15364(a,2,2))].">
      <j1 rule="para" parents="26260 15364"/>
    </justification>
  </clause>

  <clause id="26269">
    <literal><![CDATA[
      (x * y) \ (((z \ 1) \ (z \ x)) * y) != u
    ]]></literal>
    <literal><![CDATA[
      a(z,z,L(x,x,y)) = u
    ]]></literal>
    <justification jstring="[para(24854(a,2),26263(a,1))].">
      <j1 rule="para" parents="24854 26263"/>
    </justification>
  </clause>

  <clause id="26270">
    <literal><![CDATA[
      a(x,x,L(y,x,z)) * z = R(x,x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(38,a,19974,a,b,26264,a)].">
      <j1 rule="hyper" parents="38 19974 26264"/>
    </justification>
  </clause>

  <clause id="26271">
    <literal><![CDATA[
      a(x,x,L(y,y,a(x,z,u))) = a(x,x,y * a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(26269,a,25606,a)].">
      <j1 rule="hyper" parents="26269 25606"/>
    </justification>
  </clause>

  <clause id="26272">
    <literal><![CDATA[
      a(x,x,y * a(x,z,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,26265,a(flip),b,26271,a),flip(a)].">
      <j1 rule="hyper" parents="63 26265 26271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26273">
    <literal><![CDATA[
      a(x,x,L(y,x,z)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(25993,a,26272,a)].">
      <j1 rule="hyper" parents="25993 26272"/>
    </justification>
  </clause>

  <clause id="26274">
    <literal><![CDATA[
      a(x,x,a(x,y,z) * u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(24180,a,26272,a)].">
      <j1 rule="hyper" parents="24180 26272"/>
    </justification>
  </clause>

  <clause id="26276">
    <literal><![CDATA[
      a(x,x,y * L(z,y,x)) = a(x,x,y * z)
    ]]></literal>
    <justification jstring="[para(14720(a,1),26272(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14720 26272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26278">
    <literal><![CDATA[
      R(x,x,y) * (x \ z) = a(x,x,y) * z
    ]]></literal>
    <justification jstring="[para(26273(a,1),26270(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26273 26270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26279">
    <literal><![CDATA[
      R(x,x,L(y,x,z)) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,26270,a(flip),b,26278,a),flip(a)].">
      <j1 rule="hyper" parents="35 26270 26278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26280">
    <literal><![CDATA[
      x * (a(x,x,y) * z) = R(x,x,y) * z
    ]]></literal>
    <justification jstring="[hyper(134,a,26278,a(flip),b,1746,a)].">
      <j1 rule="hyper" parents="134 26278 1746"/>
    </justification>
  </clause>

  <clause id="26281">
    <literal><![CDATA[
      (a(x,x,y) * z) \ (a(x,x,y) * z) = a(x,a(x,x,y),z)
    ]]></literal>
    <justification jstring="[para(26278(a,1),19015(a,1,2))].">
      <j1 rule="para" parents="26278 19015"/>
    </justification>
  </clause>

  <clause id="26282">
    <literal><![CDATA[
      R(x,y,(((z \ u) \ 1) * R(z,z,w)) \ v5) = R(x,y,(a(z,z,w) * u) \ v5)
    ]]></literal>
    <justification jstring="[para(26278(a,1),22120(a,2,3,1))].">
      <j1 rule="para" parents="26278 22120"/>
    </justification>
  </clause>

  <clause id="26284">
    <literal><![CDATA[
      x * (y * (a(x,x,y) * z)) = R(x,x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(12713(a,1),26280(a,1,2))].">
      <j1 rule="para" parents="12713 26280"/>
    </justification>
  </clause>

  <clause id="26285">
    <literal><![CDATA[
      a(x,a(x,x,y),z) = 1
    ]]></literal>
    <justification jstring="[hyper(236,a,26281,a),flip(a)].">
      <j1 rule="hyper" parents="236 26281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26286">
    <literal><![CDATA[
      a(x,a(x,x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(26281(a,1),236(a,1))].">
      <j1 rule="para" parents="26281 236"/>
    </justification>
  </clause>

  <clause id="26288">
    <literal><![CDATA[
      L(a(x,y,z),z,y) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,26171,a(flip),b,26261,a),flip(a)].">
      <j1 rule="hyper" parents="63 26171 26261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26289">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ 1,u,w) = L(a(x,y,z),u,w) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,3337,a,b,26261,a)].">
      <j1 rule="hyper" parents="34 3337 26261"/>
    </justification>
  </clause>

  <clause id="26290">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) = L(a(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(26261(a,1),4670(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26261 4670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26291">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),u,w) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(26261(a,1),25972(a,1,1))].">
      <j1 rule="para" parents="26261 25972"/>
    </justification>
  </clause>

  <clause id="26292">
    <literal><![CDATA[
      a(x,y,z) * a(u,x,a(x,y,z)) = L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(26234(a,1),26261(a,1,2))].">
      <j1 rule="para" parents="26234 26261"/>
    </justification>
  </clause>

  <clause id="26293">
    <literal><![CDATA[
      L(a(x,y,z * R(u,w,v5)),z * L(u,w,v5),y) = L(z * R(u,w,v5),y,x) \ (z * R(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(23782,a,26288,a)].">
      <j1 rule="hyper" parents="23782 26288"/>
    </justification>
  </clause>

  <clause id="26294">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (y * x) = y * (x * a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(133,a,26288,a(flip),b,20006,a)].">
      <j1 rule="hyper" parents="133 26288 20006"/>
    </justification>
  </clause>

  <clause id="26295">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),z,y) = L(L(z,y,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(26288(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26288 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26296">
    <literal><![CDATA[
      ((x * y) * a(z,x,y)) \ (x * (y * a(z,x,y))) = a(x,y,L(y,x,z) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(26288(a,1),26135(a,2,1,3))].">
      <j1 rule="para" parents="26288 26135"/>
    </justification>
  </clause>

  <clause id="26297">
    <literal><![CDATA[
      L(a(x,y,z),x,z * y) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(18790,a,26291,a),flip(a)].">
      <j1 rule="hyper" parents="18790 26291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26298">
    <literal><![CDATA[
      L(a(x,y,z),x,y * z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(14253,a,26291,a),flip(a)].">
      <j1 rule="hyper" parents="14253 26291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26299">
    <literal><![CDATA[
      L(L(a(x,y,y),z,u),z,u) = L(y,y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,25425,a,b,26291,a),flip(a)].">
      <j1 rule="hyper" parents="347 25425 26291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26300">
    <literal><![CDATA[
      x * (y * L(a(z,u,w),y,x)) = (x * y) * a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(134,a,26291,a(flip),b,18,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 26291 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26301">
    <literal><![CDATA[
      a(x,y,z) * R(u,u,L(a(x,y,z),u,u)) = L(a(x,y,z),u,u) * u
    ]]></literal>
    <justification jstring="[para(26291(a,1),9729(a,1,1))].">
      <j1 rule="para" parents="26291 9729"/>
    </justification>
  </clause>

  <clause id="26302">
    <literal><![CDATA[
      x \ (L(a(y,z,u),w,v5) \ (x * L(L(a(y,z,u),w,v5),w,v5))) = (L(a(y,z,u),w,v5) * x) \ (x * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(26291(a,1),22368(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="26291 22368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26303">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),x,z * y) = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(26297(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26297 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26304">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ a(x,y,z) = a(y * z,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(26298(a,1),26234(a,1,1))].">
      <j1 rule="para" parents="26298 26234"/>
    </justification>
  </clause>

  <clause id="26305">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,a(x,y,z) * u) = u * ((a(x,y,z) * u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(22925,a,26290,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="22925 26290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26306">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),u,w) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(26290(a,2),25955(a,1,1))].">
      <j1 rule="para" parents="26290 25955"/>
    </justification>
  </clause>

  <clause id="26307">
    <literal><![CDATA[
      L(x,y,z) != a(u,w,v5) \ 1
    ]]></literal>
    <literal><![CDATA[
      L(a(u,w,v5) \ 1,y,z) = x
    ]]></literal>
    <justification jstring="[para(26306(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="26306 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26308">
    <literal><![CDATA[
      (x * a(y,z,u)) * a(w,x,a(y,z,u)) = x * L(a(y,z,u),x,w)
    ]]></literal>
    <justification jstring="[hyper(34,a,14706,a,b,26300,a)].">
      <j1 rule="hyper" parents="34 14706 26300"/>
    </justification>
  </clause>

  <clause id="26309">
    <literal><![CDATA[
      x * (L(a(y,z,u),w,x) * w) = (x * w) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(20224(a,2),26300(a,1,2))].">
      <j1 rule="para" parents="20224 26300"/>
    </justification>
  </clause>

  <clause id="26310">
    <literal><![CDATA[
      x \ ((x * y) * a(z,u,w)) = L(a(z,u,w),y,x) * y
    ]]></literal>
    <justification jstring="[hyper(138,a,26309,a)].">
      <j1 rule="hyper" parents="138 26309"/>
    </justification>
  </clause>

  <clause id="26311">
    <literal><![CDATA[
      x \ ((x * y) * a(z,z,u)) = a(z,z,L(u,y,x)) * y
    ]]></literal>
    <justification jstring="[para(26260(a,2),26310(a,2,1))].">
      <j1 rule="para" parents="26260 26310"/>
    </justification>
  </clause>

  <clause id="26312">
    <literal><![CDATA[
      x \ ((x * y) * a(y,y,z)) = R(y,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,18993,a(flip),b,26311,a),flip(a)].">
      <j1 rule="hyper" parents="347 18993 26311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26313">
    <literal><![CDATA[
      (x * y) * a(y,y,z) = x * R(y,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,26279,a(flip),b,26312,a),flip(a)].">
      <j1 rule="hyper" parents="134 26279 26312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26314">
    <literal><![CDATA[
      a(x,x,y) * (z * x) = z * R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(20479,a,26313,a)].">
      <j1 rule="hyper" parents="20479 26313"/>
    </justification>
  </clause>

  <clause id="26315">
    <literal><![CDATA[
      (x / y) * R(y,y,z) = x * a(y,y,z)
    ]]></literal>
    <justification jstring="[hyper(353,a,26313,a),flip(a)].">
      <j1 rule="hyper" parents="353 26313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26316">
    <literal><![CDATA[
      L(x,y,a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(23263,a,26314,a)].">
      <j1 rule="hyper" parents="23263 26314"/>
    </justification>
  </clause>

  <clause id="26317">
    <literal><![CDATA[
      (x * R(y,y,z)) \ (a(y,y,z) * (y * (T(x,y) * u))) = L(L(u,x,y),x * y,a(y,y,z))
    ]]></literal>
    <justification jstring="[para(26314(a,1),10171(a,1,1))].">
      <j1 rule="para" parents="26314 10171"/>
    </justification>
  </clause>

  <clause id="26318">
    <literal><![CDATA[
      L(x,y \ (z \ y),z) = L(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,25496,a(flip),b,26316,a),flip(a)].">
      <j1 rule="hyper" parents="63 25496 26316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26319">
    <literal><![CDATA[
      (x \ (y \ (x \ y))) \ z = (y \ (x \ y)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,25495,a(flip),b,26316,a),flip(a)].">
      <j1 rule="hyper" parents="63 25495 26316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26320">
    <literal><![CDATA[
      L(x,y,a(y,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(26316(a,1),50(a,2))].">
      <j1 rule="para" parents="26316 50"/>
    </justification>
  </clause>

  <clause id="26321">
    <literal><![CDATA[
      (x \ 1) * (a(x,x,y) * z) = (x \ a(x,x,y)) * z
    ]]></literal>
    <justification jstring="[para(26316(a,1),25497(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26316 25497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26322">
    <literal><![CDATA[
      L(x,y \ z,(z / y) * (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(19003(a,1),26320(a,1,3))].">
      <j1 rule="para" parents="19003 26320"/>
    </justification>
  </clause>

  <clause id="26324">
    <literal><![CDATA[
      x / L(y \ (x \ y),x,x) = x * (1 / (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(220,a,26318,a(flip),b,3280,a(flip))].">
      <j1 rule="hyper" parents="220 26318 3280"/>
    </justification>
  </clause>

  <clause id="26326">
    <literal><![CDATA[
      (x \ 1) * (y * a(x,x,z)) = (x \ a(x,x,z)) * y
    ]]></literal>
    <justification jstring="[hyper(20023,a,26321,a)].">
      <j1 rule="hyper" parents="20023 26321"/>
    </justification>
  </clause>

  <clause id="26327">
    <literal><![CDATA[
      a(x,x,y) * ((x \ 1) * z) = (x \ a(x,x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,25384,a,b,26321,a)].">
      <j1 rule="hyper" parents="63 25384 26321"/>
    </justification>
  </clause>

  <clause id="26328">
    <literal><![CDATA[
      (x \ 1) * (y * a(x,x,z)) = y * T(x \ a(x,x,z),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,111,a,b,26326,a),flip(a)].">
      <j1 rule="hyper" parents="347 111 26326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26329">
    <literal><![CDATA[
      x / T(y \ (x \ y),x) = x * (1 / (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[para(22317(a,1),26324(a,1,2))].">
      <j1 rule="para" parents="22317 26324"/>
    </justification>
  </clause>

  <clause id="26330">
    <literal><![CDATA[
      x * (1 / (y \ (x \ y))) = (y \ (x \ y)) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,21982,a(flip),b,26329,a),flip(a)].">
      <j1 rule="hyper" parents="63 21982 26329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26331">
    <literal><![CDATA[
      (x \ R(x,y,z)) * a(z * y,x,a(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,23896,a,b,26304,a)].">
      <j1 rule="hyper" parents="134 23896 26304"/>
    </justification>
  </clause>

  <clause id="26332">
    <literal><![CDATA[
      (x \ 1) * (y * a(x,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ a(x,x,z)) * y = u
    ]]></literal>
    <justification jstring="[para(26328(a,2),315(a,1))].">
      <j1 rule="para" parents="26328 315"/>
    </justification>
  </clause>

  <clause id="26333">
    <literal><![CDATA[
      (x \ R(x,y,z)) * u != a(x,y,z)
    ]]></literal>
    <literal><![CDATA[
      a(z * y,x,a(x,y,z)) = u
    ]]></literal>
    <justification jstring="[para(26331(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="26331 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26334">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ 1 = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(26185,a,26308,a)].">
      <j1 rule="hyper" parents="26185 26308"/>
    </justification>
  </clause>

  <clause id="26335">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ 1 != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(26334(a,1),12597(a,1,1))].">
      <j1 rule="para" parents="26334 12597"/>
    </justification>
  </clause>

  <clause id="26336">
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) \ 1 = a(x,y,a(u * z,w,v5))
    ]]></literal>
    <justification jstring="[para(23896(a,1),26334(a,1,1,3))].">
      <j1 rule="para" parents="23896 26334"/>
    </justification>
  </clause>

  <clause id="26337">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ x = x * a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(26334(a,1),25386(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26334 25386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26338">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)),x,a(z,u,w) * y) = L(x,y,a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(26334(a,1),26022(a,1,1))].">
      <j1 rule="para" parents="26334 26022"/>
    </justification>
  </clause>

  <clause id="26339">
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) = a(x,y,a(u * z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(26335,a,26336,a)].">
      <j1 rule="hyper" parents="26335 26336"/>
    </justification>
  </clause>

  <clause id="26340">
    <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(26336(a,1),26335(a,1))].">
      <j1 rule="para" parents="26336 26335"/>
    </justification>
  </clause>

  <clause id="26341">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z * (w * u),v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(24228(a,1),26340(a,1,3))].">
      <j1 rule="para" parents="24228 26340"/>
    </justification>
  </clause>

  <clause id="26342">
    <literal><![CDATA[
      L(a(x,y,z),u,u) * u = a(x,y,z) * R(u,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(3387(a,1),26301(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3387 26301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26343">
    <literal><![CDATA[
      L(a(x,y,z),u,u) * u = a(x,y,z) * L(u,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(23247(a,1),26342(a,2,2))].">
      <j1 rule="para" parents="23247 26342"/>
    </justification>
  </clause>

  <clause id="26346">
    <literal><![CDATA[
      L(a(x,y,z),u,u) * u = a(x,y,z) / (u \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,2008,a(flip),b,26343,a),flip(a)].">
      <j1 rule="hyper" parents="347 2008 26343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26347">
    <literal><![CDATA[
      L(a(x,y,z),u,u) * u = (1 / u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,23107,a(flip),b,26346,a),flip(a)].">
      <j1 rule="hyper" parents="347 23107 26346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26348">
    <literal><![CDATA[
      x * L(a(y,z,u),x,x) = (1 / x) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(21075,a,26347,a)].">
      <j1 rule="hyper" parents="21075 26347"/>
    </justification>
  </clause>

  <clause id="26349">
    <literal><![CDATA[
      L(a(x,y,z),y,y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,25705,a(flip),b,26347,a),flip(a)].">
      <j1 rule="hyper" parents="35 25705 26347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26350">
    <literal><![CDATA[
      a(x,x,a(y,x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,26349,a,b,14599,a),flip(a)].">
      <j1 rule="hyper" parents="129 26349 14599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26351">
    <literal><![CDATA[
      (1 / x) * a(y,x,z) = a(y,x,z) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,26349,a(flip),b,22044,a),flip(a)].">
      <j1 rule="hyper" parents="131 26349 22044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26352">
    <literal><![CDATA[
      (x \ 1) * a(y,x,z) = x \ a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,26349,a(flip),b,3197,a),flip(a)].">
      <j1 rule="hyper" parents="128 26349 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26353">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,y,y) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(26349(a,1),25955(a,1,1,1))].">
      <j1 rule="para" parents="26349 25955"/>
    </justification>
  </clause>

  <clause id="26354">
    <literal><![CDATA[
      x * a(y,y,a(z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(26350(a,2),142(a,1,2))].">
      <j1 rule="para" parents="26350 142"/>
    </justification>
  </clause>

  <clause id="26355">
    <literal><![CDATA[
      L(x,x,a(y,x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(23184,a,26352,a(flip))].">
      <j1 rule="hyper" parents="23184 26352"/>
    </justification>
  </clause>

  <clause id="26356">
    <literal><![CDATA[
      L(x,y \ a(z,y,u),w) = L(x,y * a(z,y,u),w)
    ]]></literal>
    <justification jstring="[para(26352(a,1),3599(a,1,2))].">
      <j1 rule="para" parents="26352 3599"/>
    </justification>
  </clause>

  <clause id="26357">
    <literal><![CDATA[
      R(x,y \ a(z,y,u),a(z,y,u)) * R(y \ 1,a(z,y,u),a(z,y,u)) = (x * ((y \ 1) * a(z,y,u))) * (a(z,y,u) \ 1)
    ]]></literal>
    <justification jstring="[para(26352(a,1),20565(a,1,1,2))].">
      <j1 rule="para" parents="26352 20565"/>
    </justification>
  </clause>

  <clause id="26358">
    <literal><![CDATA[
      a(a(x,y,z),y,y) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,26355,a,b,25424,a),flip(a)].">
      <j1 rule="hyper" parents="129 26355 25424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26359">
    <literal><![CDATA[
      L(x,x,x * a(y,x,z)) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(26358(a,1),25447(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="26358 25447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26360">
    <literal><![CDATA[
      (x * y) \ L(x * y,y,z) = a(z,y,x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,26196,a(flip),b,26353,a)].">
      <j1 rule="hyper" parents="63 26196 26353"/>
    </justification>
  </clause>

  <clause id="26361">
    <literal><![CDATA[
      L(x * ((a(y,z,u) \ 1) / x),z,z) = x * ((a(y,z,u) \ 1) / x)
    ]]></literal>
    <justification jstring="[para(26353(a,1),3159(a,2,2,1))].">
      <j1 rule="para" parents="26353 3159"/>
    </justification>
  </clause>

  <clause id="26362">
    <literal><![CDATA[
      a(x,y,x \ y) = a(x,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(13948,a,26360,a),flip(a)].">
      <j1 rule="hyper" parents="13948 26360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26363">
    <literal><![CDATA[
      a(x,y * x,x \ (y * x)) = a(x,y * x,L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,24286,a(flip),b,26362,a),flip(a)].">
      <j1 rule="hyper" parents="347 24286 26362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26364">
    <literal><![CDATA[
      a(x,y * x,L(y,x,x)) = a(x,y * x,T(y,x))
    ]]></literal>
    <justification jstring="[para(22(a,2),26363(a,1,3)),flip(a)].">
      <j1 rule="para" parents="22 26363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26365">
    <literal><![CDATA[
      a(x,y * x,L(y,x,x)) = a(x,y * x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,24067,a(flip),b,26364,a),flip(a)].">
      <j1 rule="hyper" parents="347 24067 26364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26367">
    <literal><![CDATA[
      a(x,y,a(z * u,z * u,u)) = a(x,y,a(u,z * u,z))
    ]]></literal>
    <justification jstring="[para(26365(a,1),25270(a,1,3)),flip(a)].">
      <j1 rule="para" parents="26365 25270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26368">
    <literal><![CDATA[
      a(x,y,a(T(z * u,K(u,w)),u * T(z,T(u,w)),T(z,T(u,w)))) = a(x,y,a(T(z,T(u,w)),u * T(z,T(u,w)),u))
    ]]></literal>
    <justification jstring="[para(6060(a,2),26367(a,1,3,1))].">
      <j1 rule="para" parents="6060 26367"/>
    </justification>
  </clause>

  <clause id="26369">
    <literal><![CDATA[
      L(x * ((a(y,z,u) \ 1) / x),z,z) != x * w
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,u) \ 1) / x = w
    ]]></literal>
    <justification jstring="[para(26361(a,2),43(a,1))].">
      <j1 rule="para" parents="26361 43"/>
    </justification>
  </clause>

  <clause id="26370">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ x = x \ R(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,26297,a(flip),b,26338,a),flip(a)].">
      <j1 rule="hyper" parents="63 26297 26338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26371">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ x = x \ L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(23247(a,1),26370(a,2,2))].">
      <j1 rule="para" parents="23247 26370"/>
    </justification>
  </clause>

  <clause id="26372">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ x) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(134,a,26371,a,b,xx)].">
      <j1 rule="hyper" parents="134 26371"/>
    </justification>
  </clause>

  <clause id="26373">
    <literal><![CDATA[
      L(x \ 1,y,a(z,u,w)) = L(x,y,a(z,u,w)) \ 1
    ]]></literal>
    <justification jstring="[hyper(39,a,4619,a,b,26371,a),flip(a)].">
      <j1 rule="hyper" parents="39 4619 26371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26374">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) * u) * w) = u * L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,26372,a(flip),b,25974,a),flip(a)].">
      <j1 rule="hyper" parents="134 26372 25974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26375">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[para(26372(a,1),25972(a,1,1))].">
      <j1 rule="para" parents="26372 25972"/>
    </justification>
  </clause>

  <clause id="26376">
    <literal><![CDATA[
      L(x / (y * a(z,u,w)),y,a(z,u,w)) = (a(z,u,w) \ x) / y
    ]]></literal>
    <justification jstring="[hyper(23265,a,26375,a),flip(a)].">
      <j1 rule="hyper" parents="23265 26375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26377">
    <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="[hyper(21375,a,26375,a),flip(a)].">
      <j1 rule="hyper" parents="21375 26375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26378">
    <literal><![CDATA[
      L((a(x,y,z) * u) \ w,u,a(x,y,z)) = u \ (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(623,a,26375,a),flip(a)].">
      <j1 rule="hyper" parents="623 26375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26379">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z),a(x,y,z)) = (a(x,y,z) \ 1) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,3200,a(flip),b,26375,a)].">
      <j1 rule="hyper" parents="63 3200 26375"/>
    </justification>
  </clause>

  <clause id="26380">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(v5,y,a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[para(26375(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="26375 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26381">
    <literal><![CDATA[
      (L(x,y,a(z,u,w)) * y) * a(z,u,w) = x * (a(z,u,w) * y)
    ]]></literal>
    <justification jstring="[para(26375(a,1),23239(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26375 23239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26382">
    <literal><![CDATA[
      L(x \ 1,y,a(z,u,w)) != v5 \ 1
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(26373(a,2),48(a,1))].">
      <j1 rule="para" parents="26373 48"/>
    </justification>
  </clause>

  <clause id="26383">
    <literal><![CDATA[
      (x * L(y,x,a(z,u,w))) * a(z,u,w) = (a(z,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(20014,a,26374,a)].">
      <j1 rule="hyper" parents="20014 26374"/>
    </justification>
  </clause>

  <clause id="26384">
    <literal><![CDATA[
      L((x \ 1) \ y,x,a(x,z,u) * x) = x * L(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(15135,a,26374,a)].">
      <j1 rule="hyper" parents="15135 26374"/>
    </justification>
  </clause>

  <clause id="26385">
    <literal><![CDATA[
      (x * y) * a(a(z,u,w),x,y) = x * L(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(14729,a,26374,a)].">
      <j1 rule="hyper" parents="14729 26374"/>
    </justification>
  </clause>

  <clause id="26386">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ 1 = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(26185,a,26385,a)].">
      <j1 rule="hyper" parents="26185 26385"/>
    </justification>
  </clause>

  <clause id="26387">
    <literal><![CDATA[
      a(a(x,y,L(z,y,x)),z,x * y) = a(x * y,z,z * L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(39,a,26146,a(flip),b,26386,a),flip(a)].">
      <j1 rule="hyper" parents="39 26146 26386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26388">
    <literal><![CDATA[
      L((x * a(y,z,u)) \ w,x,a(y,z,u)) = x \ (a(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(19985(a,1),26378(a,1,1,1))].">
      <j1 rule="para" parents="19985 26378"/>
    </justification>
  </clause>

  <clause id="26389">
    <literal><![CDATA[
      x \ (a(y,z,u) \ (x * (w * a(y,z,u)))) = L(L(w,a(y,z,u),x),x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(21148(a,1),26378(a,1,1)),flip(a)].">
      <j1 rule="para" parents="21148 26378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26390">
    <literal><![CDATA[
      x \ (a(y,z,u) \ ((x * a(y,z,u)) * w)) = L(w,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),26388(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 26388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26391">
    <literal><![CDATA[
      a(x,y,z) * L(u,x,a(x,y,z)) = x \ ((x * a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(134,a,26390,a(flip),b,25397,a)].">
      <j1 rule="hyper" parents="134 26390 25397"/>
    </justification>
  </clause>

  <clause id="26392">
    <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(20078(a,1),26377(a,1,1))].">
      <j1 rule="para" parents="20078 26377"/>
    </justification>
  </clause>

  <clause id="26393">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u)) * (a(y,z,u) \ 1) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(21373,a,26392,a)].">
      <j1 rule="hyper" parents="21373 26392"/>
    </justification>
  </clause>

  <clause id="26394">
    <literal><![CDATA[
      R(x,y,z) * (a(x,u,w) \ 1) = a(x,u,w) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(25372(a,1),26393(a,1,1))].">
      <j1 rule="para" parents="25372 26393"/>
    </justification>
  </clause>

  <clause id="26395">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (a(x,u,w) \ 1) = x \ (a(x,u,w) \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,26394,a(flip),b,25989,a),flip(a)].">
      <j1 rule="hyper" parents="128 26394 25989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26396">
    <literal><![CDATA[
      (a(x,y,z) \ (1 / x)) * R(x,u,w) = x \ (a(x,y,z) \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,26023,a,b,26395,a)].">
      <j1 rule="hyper" parents="63 26023 26395"/>
    </justification>
  </clause>

  <clause id="26397">
    <literal><![CDATA[
      a((R(x,y,z) * u) * w,v5,v6) = a((L(x,y,z) * u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,24316,a(flip),b,26218,a)].">
      <j1 rule="hyper" parents="63 24316 26218"/>
    </justification>
  </clause>

  <clause id="26398">
    <literal><![CDATA[
      a((L(x,y,z) * u) * T(w,R(x,y,z) * u),v5,v6) = a(w * (R(x,y,z) * u),v5,v6)
    ]]></literal>
    <justification jstring="[para(111(a,1),26397(a,1,1)),flip(a)].">
      <j1 rule="para" parents="111 26397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26399">
    <literal><![CDATA[
      a((L(x,y,z) * u) * L(1 / w,w,R(x,y,z) * u),v5,v6) = a((R(x,y,z) * u) / w,v5,v6)
    ]]></literal>
    <justification jstring="[para(3266(a,1),26397(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3266 26397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26400">
    <literal><![CDATA[
      a(T(x * R(y,z,u),K(R(y,z,u),w)) * v5,v6,v7) = a((L(y,z,u) * T(x,T(R(y,z,u),w))) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(6060(a,2),26397(a,1,1,1))].">
      <j1 rule="para" parents="6060 26397"/>
    </justification>
  </clause>

  <clause id="26401">
    <literal><![CDATA[
      a(x,y,L(L(z,L(z,u,w),y),u,w)) = L(L(z,y,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,26122,a(flip),b,26228,a),flip(a)].">
      <j1 rule="hyper" parents="347 26122 26228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26402">
    <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(23120(a,1),26401(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="23120 26401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26403">
    <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(25390(a,1),26401(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="25390 26401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26404">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) \ 1 = y \ (z * ((L(1 / z,y,x) \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(14922(a,1),26257(a,1,1))].">
      <j1 rule="para" parents="14922 26257"/>
    </justification>
  </clause>

  <clause id="26405">
    <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(26234(a,1),26403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26234 26403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26407">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ a(x,y,z) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(26289(a,1),3366(a,1))].">
      <j1 rule="para" parents="26289 3366"/>
    </justification>
  </clause>

  <clause id="26408">
    <literal><![CDATA[
      a(x * (y * R(z,u,w)),v5,v6) = a(x * (y * L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26184,a,26176,a),flip(a)].">
      <j1 rule="hyper" parents="26184 26176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26409">
    <literal><![CDATA[
      a(x * (y * R(z,u,w)),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x * (y * L(z,u,w)),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(26176(a,1),26184(a,1))].">
      <j1 rule="para" parents="26176 26184"/>
    </justification>
  </clause>

  <clause id="26410">
    <literal><![CDATA[
      L(a(x,y,z \ y) \ 1,z \ y,z) = (z \ y) \ L(z \ y,y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),26212(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 26212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26411">
    <literal><![CDATA[
      L(a(x,y,z \ y) \ 1,z \ y,z) = z \ (y * L(y \ z,y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,3354,a(flip),b,26410,a),flip(a)].">
      <j1 rule="hyper" parents="347 3354 26410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26412">
    <literal><![CDATA[
      L(a(x,y,z \ y) \ 1,z \ y,z) = a(x,y,y \ z) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,26163,a(flip),b,26411,a),flip(a)].">
      <j1 rule="hyper" parents="347 26163 26411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26413">
    <literal><![CDATA[
      T(x * ((L(y,z,x) \ y) \ z),y) = L(y,y,z) \ (x * (z / (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(20487,a,26235,a)].">
      <j1 rule="hyper" parents="20487 26235"/>
    </justification>
  </clause>

  <clause id="26415">
    <literal><![CDATA[
      (x / y) \ L(x,y,z) = y * (a(z,y,y * (x \ y)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(23025,a,26192,a)].">
      <j1 rule="hyper" parents="23025 26192"/>
    </justification>
  </clause>

  <clause id="26416">
    <literal><![CDATA[
      L(x \ 1,x,y) \ ((z * (y * x)) \ (z * y)) = a(z,y * x,x) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),26202(a,2,1,3))].">
      <j1 rule="para" parents="9 26202"/>
    </justification>
  </clause>

  <clause id="26418">
    <literal><![CDATA[
      a(x,y,L(a(z,x,y),y,x)) \ 1 = a(x,y,L(y,x,z) \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,26135,a(flip),b,26296,a)].">
      <j1 rule="hyper" parents="63 26135 26296"/>
    </justification>
  </clause>

  <clause id="26419">
    <literal><![CDATA[
      a(x,y,L(y,x,z) \ y) \ 1 = (a(a(z,x,y),y,x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(26130(a,1),26418(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26130 26418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26420">
    <literal><![CDATA[
      a(x,y,L(y,x,z) \ y) \ 1 = (a(y,a(z,x,y),x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(22007(a,1),26419(a,2,1,1))].">
      <j1 rule="para" parents="22007 26419"/>
    </justification>
  </clause>

  <clause id="26421">
    <literal><![CDATA[
      a(x,y,L(y,x,z) \ y) \ 1 = a(y,a(z,x,y),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,19984,a(flip),b,26420,a),flip(a)].">
      <j1 rule="hyper" parents="347 19984 26420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26423">
    <literal><![CDATA[
      a(x,y,y * L(y,x,z)) \ 1 = a(y,a(z,x,y),x)
    ]]></literal>
    <justification jstring="[para(14939(a,1),26421(a,1,1))].">
      <j1 rule="para" parents="14939 26421"/>
    </justification>
  </clause>

  <clause id="26424">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ L(L(x,y,z) \ x,x,y) = a(z,y,x) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(10888(a,1),26169(a,2,2))].">
      <j1 rule="para" parents="10888 26169"/>
    </justification>
  </clause>

  <clause id="26425">
    <literal><![CDATA[
      L(x,y,z) \ (x * L(x \ L(x,y,z),x,y)) = a(z,y,x) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(3365,a,26424,a)].">
      <j1 rule="hyper" parents="3365 26424"/>
    </justification>
  </clause>

  <clause id="26426">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ a(z,y,x) = a(z,y,x) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(26162(a,2),26424(a,1,2))].">
      <j1 rule="para" parents="26162 26424"/>
    </justification>
  </clause>

  <clause id="26427">
    <literal><![CDATA[
      L(x,y,z) \ (x * (a(z,y,x) \ 1)) = a(z,y,x) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(26156(a,1),26425(a,1,2,2))].">
      <j1 rule="para" parents="26156 26425"/>
    </justification>
  </clause>

  <clause id="26428">
    <literal><![CDATA[
      L(x,y,z) \ (a(z,y,x) \ x) = a(z,y,x) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(12717(a,1),26427(a,1,2))].">
      <j1 rule="para" parents="12717 26427"/>
    </justification>
  </clause>

  <clause id="26429">
    <literal><![CDATA[
      a(x,y,z) \ (L(z,y,x) \ z) = a(x,y,z) * (z \ L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,23297,a(flip),b,26428,a)].">
      <j1 rule="hyper" parents="63 23297 26428"/>
    </justification>
  </clause>

  <clause id="26430">
    <literal><![CDATA[
      a(x \ y,x,L(x,z,u) \ x) \ 1 = a(y,x,L(x,z,u) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,26158,a(flip),b,26197,a),flip(a)].">
      <j1 rule="hyper" parents="63 26158 26197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26431">
    <literal><![CDATA[
      a(x \ y,x,L(x,z,u) \ x) \ 1 = a(y,x,x * L(x,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(14939(a,1),26430(a,2,1))].">
      <j1 rule="para" parents="14939 26430"/>
    </justification>
  </clause>

  <clause id="26432">
    <literal><![CDATA[
      a(x,y,(L(y,z,u) \ y) \ y) = L(L(y,z,u) \ 1,y,x) \ (L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(1415(a,1),26206(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1415 26206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26433">
    <literal><![CDATA[
      a(x,y,(L(y,z,u) \ y) \ y) = L(L(y,z,u),y,x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,10875,a(flip),b,26432,a),flip(a)].">
      <j1 rule="hyper" parents="347 10875 26432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26434">
    <literal><![CDATA[
      a(x,y,(L(y,z,u) \ y) \ y) = L(L(y,y,x) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,26122,a(flip),b,26433,a),flip(a)].">
      <j1 rule="hyper" parents="347 26122 26433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26435">
    <literal><![CDATA[
      a(x,y,(L(y,z,u) \ y) \ y) = L(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[para(25425(a,1),26434(a,2,1))].">
      <j1 rule="para" parents="25425 26434"/>
    </justification>
  </clause>

  <clause id="26436">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) = L(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(24182,a,26435,a)].">
      <j1 rule="hyper" parents="24182 26435"/>
    </justification>
  </clause>

  <clause id="26437">
    <literal><![CDATA[
      a(x,y,L(y,z,x)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,25390,a(flip),b,26436,a),flip(a)].">
      <j1 rule="hyper" parents="347 25390 26436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26438">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) * (u * z) = u * (z * a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(133,a,26436,a,b,20006,a)].">
      <j1 rule="hyper" parents="133 26436 20006"/>
    </justification>
  </clause>

  <clause id="26439">
    <literal><![CDATA[
      a(x,L(y,z,u),L(R(y,z,u),w,v5)) = L(a(x,L(y,z,u),L(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24902,a,b,26436,a)].">
      <j1 rule="hyper" parents="63 24902 26436"/>
    </justification>
  </clause>

  <clause id="26441">
    <literal><![CDATA[
      a(x,y,L(y,z,z)) \ z = a(x,y,y) \ R(z,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(26436(a,2),9728(a,1,1))].">
      <j1 rule="para" parents="26436 9728"/>
    </justification>
  </clause>

  <clause id="26442">
    <literal><![CDATA[
      a(x,L(L(y \ z,u,w),y,y),L(L(L(y \ z,u,w),y,y),v5,v6)) = L(a(x,L(L(y \ z,u,w),y,y),L(y * z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(14996(a,1),26436(a,2,1))].">
      <j1 rule="para" parents="14996 26436"/>
    </justification>
  </clause>

  <clause id="26443">
    <literal><![CDATA[
      a(x,y,L(z * R(z,u,u),w,v5)) = a(x,y,a(z,u,L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(26436(a,2),23622(a,2,3))].">
      <j1 rule="para" parents="26436 23622"/>
    </justification>
  </clause>

  <clause id="26444">
    <literal><![CDATA[
      a(x,y \ z,L(y \ z,u,w)) * (w * u) = w * (u * (L(z / y,y \ z,x) \ (z / y)))
    ]]></literal>
    <justification jstring="[para(26436(a,2),25723(a,1,1))].">
      <j1 rule="para" parents="26436 25723"/>
    </justification>
  </clause>

  <clause id="26445">
    <literal><![CDATA[
      L(a(x,y,L(y,z,u)),z,u) = L(y,y,x) \ y
    ]]></literal>
    <justification jstring="[para(26436(a,2),26299(a,1,1))].">
      <j1 rule="para" parents="26436 26299"/>
    </justification>
  </clause>

  <clause id="26447">
    <literal><![CDATA[
      a(L(x,y,z),a(z,x,L(x,y,z)),u) = a(a(z,x,x),L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(26437(a,1),22007(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26437 22007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26448">
    <literal><![CDATA[
      a(x,y,L(y,z,z)) \ z = a(x,y,y) \ L(z,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(23247(a,1),26441(a,2,2))].">
      <j1 rule="para" parents="23247 26441"/>
    </justification>
  </clause>

  <clause id="26449">
    <literal><![CDATA[
      a(L(x,y,z),a(z,x,x),u) = a(a(z,x,x),L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(26437(a,1),26447(a,1,2))].">
      <j1 rule="para" parents="26437 26447"/>
    </justification>
  </clause>

  <clause id="26451">
    <literal><![CDATA[
      a(x,y,((z * u) \ ((z * (u * w)) / w)) \ 1) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,25094,a(flip),b,26126,a),flip(a)].">
      <j1 rule="hyper" parents="63 25094 26126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26452">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,u,z))) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(26125(a,1),26451(a,1,3))].">
      <j1 rule="para" parents="26125 26451"/>
    </justification>
  </clause>

  <clause id="26453">
    <literal><![CDATA[
      a(x,L(y,z,u) \ y,L(w,L(y,z,u) \ y,x)) = a(w,a(u,z,L(y,y,z)),x) \ 1
    ]]></literal>
    <justification jstring="[para(26225(a,1),26237(a,1,3,2))].">
      <j1 rule="para" parents="26225 26237"/>
    </justification>
  </clause>

  <clause id="26454">
    <literal><![CDATA[
      a(x,L(y,z,u) \ y,L(w,y * L(y,z,u),x)) = a(w,a(u,z,L(y,y,z)),x) \ 1
    ]]></literal>
    <justification jstring="[para(3251(a,1),26453(a,1,3))].">
      <j1 rule="para" parents="3251 26453"/>
    </justification>
  </clause>

  <clause id="26455">
    <literal><![CDATA[
      a(x,y * L(y,z,u),L(w,y * L(y,z,u),x)) = a(w,a(u,z,L(y,y,z)),x) \ 1
    ]]></literal>
    <justification jstring="[hyper(15028,a,26454,a)].">
      <j1 rule="hyper" parents="15028 26454"/>
    </justification>
  </clause>

  <clause id="26456">
    <literal><![CDATA[
      a(x,y * L(y,z,u),L(w,y * L(y,z,u),x)) = a(w,L(y,z,u) \ y,x) \ 1
    ]]></literal>
    <justification jstring="[para(26225(a,1),26455(a,2,1,2))].">
      <j1 rule="para" parents="26225 26455"/>
    </justification>
  </clause>

  <clause id="26457">
    <literal><![CDATA[
      a(x,y * L(y,z,u),L(w,y * L(y,z,u),x)) = a(w,y * L(y,z,u),x) \ 1
    ]]></literal>
    <justification jstring="[para(14988(a,1),26456(a,2,1))].">
      <j1 rule="para" parents="14988 26456"/>
    </justification>
  </clause>

  <clause id="26458">
    <literal><![CDATA[
      L(L(x \ (x \ y),z,u),x,w) \ L(x \ (x \ y),z,u) = a(w,x,(x \ L(y,z,u)) \ x)
    ]]></literal>
    <justification jstring="[para(3382(a,2),26207(a,1,2))].">
      <j1 rule="para" parents="3382 26207"/>
    </justification>
  </clause>

  <clause id="26459">
    <literal><![CDATA[
      L(L(x,y,z),L(x,u,w),v5) \ L(x,y,z) = a(v5,L(x,u,w),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,12441,a(flip),b,26229,a),flip(a)].">
      <j1 rule="hyper" parents="63 12441 26229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26461">
    <literal><![CDATA[
      L(L(x,L(x,y,z),u) \ x,w,v5) = a(u,L(x,y,z),L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,26122,a(flip),b,26459,a)].">
      <j1 rule="hyper" parents="63 26122 26459"/>
    </justification>
  </clause>

  <clause id="26462">
    <literal><![CDATA[
      a(x,L(y,z,u),L(y,w,v5)) = L(a(x,y,L(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(26188(a,1),26461(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26188 26461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26463">
    <literal><![CDATA[
      a(x,L(y,z,u),L(y,z,u)) = L(y,y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,26445,a(flip),b,26462,a),flip(a)].">
      <j1 rule="hyper" parents="347 26445 26462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26464">
    <literal><![CDATA[
      a(x,L(y,z,u),L(y,z,u)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,25425,a(flip),b,26463,a),flip(a)].">
      <j1 rule="hyper" parents="347 25425 26463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26466">
    <literal><![CDATA[
      (x \ a(y,L(x,z,u),L(x,z,u))) * x = a(L(x,z,u) \ y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,25470,a(flip),b,26464,a)].">
      <j1 rule="hyper" parents="63 25470 26464"/>
    </justification>
  </clause>

  <clause id="26467">
    <literal><![CDATA[
      a(x,y,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      R(x,L(y,u,w),L(y,u,w)) = z
    ]]></literal>
    <justification jstring="[para(26464(a,1),13407(a,1,1))].">
      <j1 rule="para" parents="26464 13407"/>
    </justification>
  </clause>

  <clause id="26468">
    <literal><![CDATA[
      x * (a(x,y,y) \ L(y,z,u)) = x / (L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(26464(a,1),25419(a,1,2,1))].">
      <j1 rule="para" parents="26464 25419"/>
    </justification>
  </clause>

  <clause id="26469">
    <literal><![CDATA[
      x * (a(x,y,y) \ R(y,z,u)) = x / (R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(26464(a,1),25521(a,1,2,1))].">
      <j1 rule="para" parents="26464 25521"/>
    </justification>
  </clause>

  <clause id="26470">
    <literal><![CDATA[
      a(x,L(y,z,u),L(R(y,z,u),w,v5)) = L(a(x,y,y),w,v5)
    ]]></literal>
    <justification jstring="[para(26464(a,1),26439(a,2,1))].">
      <j1 rule="para" parents="26464 26439"/>
    </justification>
  </clause>

  <clause id="26471">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y,z,u)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(26467,a,13403,a)].">
      <j1 rule="hyper" parents="26467 13403"/>
    </justification>
  </clause>

  <clause id="26472">
    <literal><![CDATA[
      R(x / L(y,z,u),y,y) = x * (L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(796,a,26471,a),flip(a)].">
      <j1 rule="hyper" parents="796 26471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26473">
    <literal><![CDATA[
      R(x,y \ (z \ y),y \ (z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,z,z) = u
    ]]></literal>
    <justification jstring="[para(26471(a,1),25634(a,1))].">
      <j1 rule="para" parents="26471 25634"/>
    </justification>
  </clause>

  <clause id="26474">
    <literal><![CDATA[
      R(x / y,y,y) / (L(y,x,z) \ 1) = (a(z,x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(26471(a,1),26193(a,1,1))].">
      <j1 rule="para" parents="26471 26193"/>
    </justification>
  </clause>

  <clause id="26475">
    <literal><![CDATA[
      R(x * (L(x,y,z) \ u),x,x) = (u * x) * (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(20673(a,1),26472(a,1,1))].">
      <j1 rule="para" parents="20673 26472"/>
    </justification>
  </clause>

  <clause id="26476">
    <literal><![CDATA[
      R(L(x \ L(x,y,z),u,w) \ v5,x \ L(x,y,z),x \ L(x,y,z)) = v5 * (L(x \ L(x,y,z),u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(20675(a,1),26472(a,1,1))].">
      <j1 rule="para" parents="20675 26472"/>
    </justification>
  </clause>

  <clause id="26477">
    <literal><![CDATA[
      ((R(x,y,z) \ 1) \ 1) * (u * (((R(x,y,z) \ 1) \ 1) \ 1)) = (1 * (a(1,x,x) \ R(x,y,z))) * (u * (R(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(26469(a,2),2929(a,2,1))].">
      <j1 rule="para" parents="26469 2929"/>
    </justification>
  </clause>

  <clause id="26479">
    <literal><![CDATA[
      R(x / (y \ (z \ y)),z,z) = x * ((y \ (z \ y)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(26473,a,785,a)].">
      <j1 rule="hyper" parents="26473 785"/>
    </justification>
  </clause>

  <clause id="26481">
    <literal><![CDATA[
      a(x,L(y,z,u),L(R(y,z,u),w,v5)) = a(x,y,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,26436,a,b,26470,a),flip(a)].">
      <j1 rule="hyper" parents="347 26436 26470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26483">
    <literal><![CDATA[
      a(x,L(y,z,u),L(L(y,z,u),w,v5)) = a(x,y,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,24902,a(flip),b,26481,a)].">
      <j1 rule="hyper" parents="63 24902 26481"/>
    </justification>
  </clause>

  <clause id="26484">
    <literal><![CDATA[
      (x * (y \ 1)) / (L(y,x,z) \ 1) = (a(z,x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(785(a,1),26474(a,1,1))].">
      <j1 rule="para" parents="785 26474"/>
    </justification>
  </clause>

  <clause id="26486">
    <literal><![CDATA[
      x * ((L(1 / x,y,z) \ 1) \ y) = (a(z,y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,26043,a(flip),b,26484,a)].">
      <j1 rule="hyper" parents="63 26043 26484"/>
    </justification>
  </clause>

  <clause id="26487">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) \ 1 = y \ ((a(x,y,z) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(26486(a,1),26404(a,2,2))].">
      <j1 rule="para" parents="26486 26404"/>
    </justification>
  </clause>

  <clause id="26488">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) \ 1 = T(a(x,y,z) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,22,a,b,26487,a),flip(a)].">
      <j1 rule="hyper" parents="347 22 26487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26489">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(39,a,20087,a(flip),b,26488,a),flip(a)].">
      <j1 rule="hyper" parents="39 20087 26488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26490">
    <literal><![CDATA[
      a(x,y * L(y,z,u),w) \ 1 = a(w,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,26457,a(flip),b,26489,a)].">
      <j1 rule="hyper" parents="63 26457 26489"/>
    </justification>
  </clause>

  <clause id="26491">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ 1 = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,26129,a(flip),b,26489,a)].">
      <j1 rule="hyper" parents="63 26129 26489"/>
    </justification>
  </clause>

  <clause id="26492">
    <literal><![CDATA[
      a(x,y,(x * y) \ z) = a(x,y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,25586,a(flip),b,26489,a),flip(a)].">
      <j1 rule="hyper" parents="63 25586 26489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26493">
    <literal><![CDATA[
      a(x,y,z) * (y * L(z,y,x)) = y * z
    ]]></literal>
    <justification jstring="[para(26489(a,1),14730(a,1,1))].">
      <j1 rule="para" parents="26489 14730"/>
    </justification>
  </clause>

  <clause id="26494">
    <literal><![CDATA[
      a(x,y,z) \ (y * z) = y * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(26489(a,1),14733(a,1,1))].">
      <j1 rule="para" parents="26489 14733"/>
    </justification>
  </clause>

  <clause id="26496">
    <literal><![CDATA[
      x * (L(x,y,z) \ y) = a(z,y,x) * y
    ]]></literal>
    <justification jstring="[para(26489(a,1),23151(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26489 23151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26497">
    <literal><![CDATA[
      L(x,a(y,z,u),w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(26489(a,1),26128(a,1,2))].">
      <j1 rule="para" parents="26489 26128"/>
    </justification>
  </clause>

  <clause id="26499">
    <literal><![CDATA[
      a(x,a(y,z,u),w) = a(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(26489(a,1),26142(a,1,2))].">
      <j1 rule="para" parents="26489 26142"/>
    </justification>
  </clause>

  <clause id="26500">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),y,x)) \ 1 != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(26489(a,2),26335(a,1,1))].">
      <j1 rule="para" parents="26489 26335"/>
    </justification>
  </clause>

  <clause id="26501">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(26489(a,1),26452(a,1,3))].">
      <j1 rule="para" parents="26489 26452"/>
    </justification>
  </clause>

  <clause id="26502">
    <literal><![CDATA[
      L(x,y,z) = (a(z,y,x) * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(128,a,26493,a(flip),b,23112,a),flip(a)].">
      <j1 rule="hyper" parents="128 26493 23112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26503">
    <literal><![CDATA[
      L(x \ (y * L(z,y,u)),x,a(u,y,z)) = (x * a(u,y,z)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(26493(a,1),20025(a,2,2))].">
      <j1 rule="para" parents="26493 20025"/>
    </justification>
  </clause>

  <clause id="26504">
    <literal><![CDATA[
      a(a(x,y,z),u,(u * a(x,y,z)) \ w) * (u * (u \ (a(x,y,z) \ w))) = u * ((u * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(26388(a,1),26493(a,1,2,2))].">
      <j1 rule="para" parents="26388 26493"/>
    </justification>
  </clause>

  <clause id="26505">
    <literal><![CDATA[
      (a(x,y,z) \ y) * z = y * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(23131,a,26494,a)].">
      <j1 rule="hyper" parents="23131 26494"/>
    </justification>
  </clause>

  <clause id="26506">
    <literal><![CDATA[
      (x \ ((x * y) * z)) \ (y * z) = (y * z) \ (y * L(z,y,x))
    ]]></literal>
    <justification jstring="[para(26494(a,1),21797(a,2,2))].">
      <j1 rule="para" parents="26494 21797"/>
    </justification>
  </clause>

  <clause id="26507">
    <literal><![CDATA[
      L(x / y,y,z) \ x = a(z,y,y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(21412,a,26496,a)].">
      <j1 rule="hyper" parents="21412 26496"/>
    </justification>
  </clause>

  <clause id="26508">
    <literal><![CDATA[
      x \ (y * a(z,y,x)) = L(x,y,z) \ y
    ]]></literal>
    <justification jstring="[hyper(128,a,19985,a(flip),b,26496,a)].">
      <j1 rule="hyper" parents="128 19985 26496"/>
    </justification>
  </clause>

  <clause id="26509">
    <literal><![CDATA[
      T(a(x,y,z) * y,z) = L(z,y,x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(26496(a,1),11225(a,1,1))].">
      <j1 rule="para" parents="26496 11225"/>
    </justification>
  </clause>

  <clause id="26510">
    <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(347,a,23358,a(flip),b,26497,a),flip(a)].">
      <j1 rule="hyper" parents="347 23358 26497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26511">
    <literal><![CDATA[
      L(x,a(y \ z,y,z),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,22774,a(flip),b,26497,a),flip(a)].">
      <j1 rule="hyper" parents="347 22774 26497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26512">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * a(v5,v6,v7) = a(v5,v6,v7) * L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(134,a,26497,a,b,19988,a),flip(a)].">
      <j1 rule="hyper" parents="134 26497 19988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26513">
    <literal><![CDATA[
      (x * a(y,z,u)) * L(w,a(u,z,y),x) = x * (a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(134,a,26497,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="134 26497 18"/>
    </justification>
  </clause>

  <clause id="26514">
    <literal><![CDATA[
      L(x,a(y,z,u),w * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,a(u,z,y),v5 * w) = v6
    ]]></literal>
    <justification jstring="[para(26497(a,1),20105(a,1))].">
      <j1 rule="para" parents="26497 20105"/>
    </justification>
  </clause>

  <clause id="26515">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (w * a(u,z,y)) = (a(u,z,y) * x) * w
    ]]></literal>
    <justification jstring="[para(26497(a,1),23236(a,1,1))].">
      <j1 rule="para" parents="26497 23236"/>
    </justification>
  </clause>

  <clause id="26516">
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) = a(x,y,a(v5,w,u * z))
    ]]></literal>
    <justification jstring="[hyper(26340,a,26501,a)].">
      <j1 rule="hyper" parents="26340 26501"/>
    </justification>
  </clause>

  <clause id="26517">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w \ ((w * z) * u)))) = a(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(24441,a,26501,a)].">
      <j1 rule="hyper" parents="24441 26501"/>
    </justification>
  </clause>

  <clause id="26518">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ 1 = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,26334,a,b,26501,a)].">
      <j1 rule="hyper" parents="347 26334 26501"/>
    </justification>
  </clause>

  <clause id="26519">
    <literal><![CDATA[
      x \ (a(y,z,a(u,w,v5)) * x) = a(y,z,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,19974,a,b,26501,a)].">
      <j1 rule="hyper" parents="347 19974 26501"/>
    </justification>
  </clause>

  <clause id="26520">
    <literal><![CDATA[
      a(x,y,a(z * u,u,u)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,25342,a(flip),b,26501,a),flip(a)].">
      <j1 rule="hyper" parents="347 25342 26501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26521">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,26501,a,b,19974,a),flip(a)].">
      <j1 rule="hyper" parents="134 26501 19974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26522">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) = x * a(y,z,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,26501,a,b,9,a)].">
      <j1 rule="hyper" parents="134 26501 9"/>
    </justification>
  </clause>

  <clause id="26523">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ v5 = a(x,y,a(w,u,z)) \ v5
    ]]></literal>
    <justification jstring="[hyper(61,a,26501,a)].">
      <j1 rule="hyper" parents="61 26501"/>
    </justification>
  </clause>

  <clause id="26524">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * ((y * a(w,u,z)) * x) = (y * a(w,u,z)) * R(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(26501(a,1),14244(a,1,1))].">
      <j1 rule="para" parents="26501 14244"/>
    </justification>
  </clause>

  <clause id="26526">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(y,z,a(v5,w,u)) * x = v6
    ]]></literal>
    <justification jstring="[para(26501(a,1),20479(a,1,2))].">
      <j1 rule="para" parents="26501 20479"/>
    </justification>
  </clause>

  <clause id="26528">
    <literal><![CDATA[
      a(x,y,a(z,u,w * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(v5 * w,u,z)) = v6
    ]]></literal>
    <justification jstring="[para(26501(a,1),26340(a,1))].">
      <j1 rule="para" parents="26501 26340"/>
    </justification>
  </clause>

  <clause id="26529">
    <literal><![CDATA[
      a(x,y,L(a(y,z,u),w,v5)) = L(a(x,y,a(u,z,y)),w,v5)
    ]]></literal>
    <justification jstring="[para(26501(a,1),26405(a,2,1))].">
      <j1 rule="para" parents="26501 26405"/>
    </justification>
  </clause>

  <clause id="26530">
    <literal><![CDATA[
      a(x,(a(y,z,z) * z) \ u,w) = a(x,L(z,z,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(26502(a,2),24668(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="26502 24668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26531">
    <literal><![CDATA[
      ((a(x,a(y,y,z),z \ (z / y)) * a(y,y,z)) \ (a(y,y,z) * (z \ (z / y)))) \ (y * x) = ((z / y) \ (z * y)) * x
    ]]></literal>
    <justification jstring="[para(26502(a,1),25867(a,1,1))].">
      <j1 rule="para" parents="26502 25867"/>
    </justification>
  </clause>

  <clause id="26532">
    <literal><![CDATA[
      L(x,y,z) * (x \ y) = a(z,y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(35,a,20681,a,b,26505,a)].">
      <j1 rule="hyper" parents="35 20681 26505"/>
    </justification>
  </clause>

  <clause id="26533">
    <literal><![CDATA[
      x * L(y,x,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(a(z,x,y) \ x,y) = y \ u
    ]]></literal>
    <justification jstring="[para(26505(a,1),309(a,1))].">
      <j1 rule="para" parents="26505 309"/>
    </justification>
  </clause>

  <clause id="26534">
    <literal><![CDATA[
      (a(x,x,K(x,x \ 1) * y) \ x) * (K(x,x \ 1) * y) = x * (x * ((1 / x) * y))
    ]]></literal>
    <justification jstring="[para(3216(a,1),26505(a,2,2))].">
      <j1 rule="para" parents="3216 26505"/>
    </justification>
  </clause>

  <clause id="26535">
    <literal><![CDATA[
      (x \ y) * a(z,x \ y,x) = L(x,x \ y,z) \ y
    ]]></literal>
    <justification jstring="[hyper(38,a,1423,a(flip),b,26508,a),flip(a)].">
      <j1 rule="hyper" parents="38 1423 26508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26536">
    <literal><![CDATA[
      x * (a(y,x,z) \ 1) = a(y,x,z) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,26186,a(flip),b,26532,a)].">
      <j1 rule="hyper" parents="63 26186 26532"/>
    </justification>
  </clause>

  <clause id="26537">
    <literal><![CDATA[
      x * (a(y,z,x) \ z) = L(x,z,y) * z
    ]]></literal>
    <justification jstring="[hyper(134,a,26532,a(flip),b,1402,a)].">
      <j1 rule="hyper" parents="134 26532 1402"/>
    </justification>
  </clause>

  <clause id="26538">
    <literal><![CDATA[
      x \ (a(y,x,z) \ x) = a(y,x,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,26532,a(flip),b,26186,a(flip))].">
      <j1 rule="hyper" parents="128 26532 26186"/>
    </justification>
  </clause>

  <clause id="26539">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),y) = (a(x,y,z) \ y) \ y
    ]]></literal>
    <justification jstring="[para(26532(a,1),26208(a,2,1))].">
      <j1 rule="para" parents="26532 26208"/>
    </justification>
  </clause>

  <clause id="26540">
    <literal><![CDATA[
      (1 / x) * (a(y,x,z) \ x) = L(a(y,x,z) \ 1,x,x)
    ]]></literal>
    <justification jstring="[para(26532(a,1),26221(a,1,2))].">
      <j1 rule="para" parents="26532 26221"/>
    </justification>
  </clause>

  <clause id="26541">
    <literal><![CDATA[
      ((x * y) / x) \ (a(z,y,u) \ y) = a(z,y,u) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(26532(a,1),26222(a,1,2))].">
      <j1 rule="para" parents="26532 26222"/>
    </justification>
  </clause>

  <clause id="26542">
    <literal><![CDATA[
      a(x,y,y * (z \ y)) \ y = (z / y) \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,26415,a,b,26536,a),flip(a)].">
      <j1 rule="hyper" parents="63 26415 26536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26543">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * y = a(x,y,z) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,20078,a,b,26536,a)].">
      <j1 rule="hyper" parents="63 20078 26536"/>
    </justification>
  </clause>

  <clause id="26544">
    <literal><![CDATA[
      L(K(x,x \ 1) * (a(y,1 / x,z) \ 1),x,x) = x * (a(y,1 / x,z) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(26536(a,1),3216(a,2,2))].">
      <j1 rule="para" parents="26536 3216"/>
    </justification>
  </clause>

  <clause id="26545">
    <literal><![CDATA[
      L(x,a(y,z,u) \ z,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,z * a(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(26536(a,1),3528(a,1,2))].">
      <j1 rule="para" parents="26536 3528"/>
    </justification>
  </clause>

  <clause id="26548">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ u = u * a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(26386(a,1),26536(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26386 26536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26549">
    <literal><![CDATA[
      R(x,y,L(z * u,u,z)) = R(x,y,L(z,u,u) * u)
    ]]></literal>
    <justification jstring="[para(26537(a,1),22255(a,1,3)),flip(a)].">
      <j1 rule="para" parents="26537 22255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26550">
    <literal><![CDATA[
      a(x \ y,x,L(x,z,u) \ x) \ x = L(x,z,u) * L(L(x,z,u) \ x,x,y)
    ]]></literal>
    <justification jstring="[hyper(38,a,26197,a,b,26538,a),flip(a)].">
      <j1 rule="hyper" parents="38 26197 26538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26551">
    <literal><![CDATA[
      x * (a(y,x,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,x,z) \ x = u
    ]]></literal>
    <justification jstring="[para(26538(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="26538 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26552">
    <literal><![CDATA[
      (a(x,y,z) \ y) \ (((a(x,y,z) \ y) / y) * u) = L(y \ u,y,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(26538(a,1),10156(a,1,3)),flip(a)].">
      <j1 rule="para" parents="26538 10156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26553">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ y = y * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(26538(a,1),21798(a,1,1))].">
      <j1 rule="para" parents="26538 21798"/>
    </justification>
  </clause>

  <clause id="26554">
    <literal><![CDATA[
      L(x,x,x \ (a(y,x \ 1,z) \ 1)) = (a(y,x \ 1,z) \ (x \ 1)) \ (a(y,x \ 1,z) \ 1)
    ]]></literal>
    <justification jstring="[para(26543(a,1),10154(a,2,1))].">
      <j1 rule="para" parents="26543 10154"/>
    </justification>
  </clause>

  <clause id="26555">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ 1 = a(w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,26499,a,b,26491,a),flip(a)].">
      <j1 rule="hyper" parents="347 26499 26491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26556">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ 1 != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,a(y,z,u),x) = v5
    ]]></literal>
    <justification jstring="[para(26491(a,1),12597(a,1,1))].">
      <j1 rule="para" parents="26491 12597"/>
    </justification>
  </clause>

  <clause id="26557">
    <literal><![CDATA[
      a(x,a(y,z,u),w * v5) \ 1 != v6
    ]]></literal>
    <literal><![CDATA[
      a(v5 * w,a(y,z,u),x) = v6
    ]]></literal>
    <justification jstring="[para(26491(a,2),23925(a,1))].">
      <j1 rule="para" parents="26491 23925"/>
    </justification>
  </clause>

  <clause id="26558">
    <literal><![CDATA[
      (x * ((y * x) \ z)) \ (y \ z) = a(y,x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,14705,a,b,26492,a)].">
      <j1 rule="hyper" parents="63 14705 26492"/>
    </justification>
  </clause>

  <clause id="26559">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ a(w,u,z) = a(w,u,z) * a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(26518(a,1),21803(a,1,1))].">
      <j1 rule="para" parents="26518 21803"/>
    </justification>
  </clause>

  <clause id="26560">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(w,u,z)) = v5
    ]]></literal>
    <justification jstring="[para(26518(a,1),26335(a,1))].">
      <j1 rule="para" parents="26518 26335"/>
    </justification>
  </clause>

  <clause id="26561">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ x != v5
    ]]></literal>
    <literal><![CDATA[
      x * a(w,a(u,z,y),x) = v5
    ]]></literal>
    <justification jstring="[para(26555(a,1),23134(a,1,1))].">
      <j1 rule="para" parents="26555 23134"/>
    </justification>
  </clause>

  <clause id="26562">
    <literal><![CDATA[
      L(x,y,z) * (x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      a(z,y,x) \ y = u
    ]]></literal>
    <justification jstring="[para(26186(a,2),26551(a,1))].">
      <j1 rule="para" parents="26186 26551"/>
    </justification>
  </clause>

  <clause id="26563">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(v6,v5,z * (w * u))) = v7
    ]]></literal>
    <justification jstring="[para(23903(a,1),26560(a,1,3))].">
      <j1 rule="para" parents="23903 26560"/>
    </justification>
  </clause>

  <clause id="26564">
    <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(26516(a,1),26560(a,1))].">
      <j1 rule="para" parents="26516 26560"/>
    </justification>
  </clause>

  <clause id="26565">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      x * a(y,z,a(v5,w,u)) = v6
    ]]></literal>
    <justification jstring="[para(26519(a,1),620(a,1,2))].">
      <j1 rule="para" parents="26519 620"/>
    </justification>
  </clause>

  <clause id="26566">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ (a(x,y,a(w,u,z)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      v5 = v6
    ]]></literal>
    <justification jstring="[para(26521(a,2),20015(a,1,2))].">
      <j1 rule="para" parents="26521 20015"/>
    </justification>
  </clause>

  <clause id="26567">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),y,x)) \ v5 = a(x,y,a(w,u,z)) \ v5
    ]]></literal>
    <justification jstring="[para(26489(a,2),26523(a,1,1))].">
      <j1 rule="para" parents="26489 26523"/>
    </justification>
  </clause>

  <clause id="26568">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,19984,a(flip),b,26539,a),flip(a)].">
      <j1 rule="hyper" parents="347 19984 26539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26570">
    <literal><![CDATA[
      (x / y) \ L(x,y,z) != u \ y
    ]]></literal>
    <literal><![CDATA[
      a(z,y,y * (x \ y)) = u
    ]]></literal>
    <justification jstring="[para(26542(a,1),48(a,1))].">
      <j1 rule="para" parents="26542 48"/>
    </justification>
  </clause>

  <clause id="26571">
    <literal><![CDATA[
      x * (y * a(a(z,u,w),y,x)) = L(x,y,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(26548(a,1),26537(a,1,2))].">
      <j1 rule="para" parents="26548 26537"/>
    </justification>
  </clause>

  <clause id="26572">
    <literal><![CDATA[
      R(x,y,L(z * u,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(26549(a,2),22240(a,1))].">
      <j1 rule="para" parents="26549 22240"/>
    </justification>
  </clause>

  <clause id="26573">
    <literal><![CDATA[
      x * (a(y,x,z) \ (x \ 1)) = L(a(y,x,z) \ 1,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,23278,a(flip),b,26540,a)].">
      <j1 rule="hyper" parents="63 23278 26540"/>
    </justification>
  </clause>

  <clause id="26574">
    <literal><![CDATA[
      a(x,a(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,a(u,z,y),w) = v5
    ]]></literal>
    <justification jstring="[para(26555(a,1),26556(a,1))].">
      <j1 rule="para" parents="26555 26556"/>
    </justification>
  </clause>

  <clause id="26575">
    <literal><![CDATA[
      a(x,a(y,z,L(u,z,y)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,a(u,z,y),w) = v5
    ]]></literal>
    <justification jstring="[para(26489(a,2),26574(a,1,2))].">
      <j1 rule="para" parents="26489 26574"/>
    </justification>
  </clause>

  <clause id="26576">
    <literal><![CDATA[
      a(x,y,z) \ (y \ 1) = y \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,26353,a(flip),b,26573,a),flip(a)].">
      <j1 rule="hyper" parents="128 26353 26573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26577">
    <literal><![CDATA[
      (a(x,y,z) \ (y \ 1)) \ L(a(x,y,z) \ 1,y,y) = T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(128,a,26573,a(flip),b,23050,a)].">
      <j1 rule="hyper" parents="128 26573 23050"/>
    </justification>
  </clause>

  <clause id="26578">
    <literal><![CDATA[
      a(x,y * L(y,z,u),w) != v5 \ 1
    ]]></literal>
    <literal><![CDATA[
      a(w,y * L(y,z,u),x) = v5
    ]]></literal>
    <justification jstring="[para(26490(a,1),48(a,1))].">
      <j1 rule="para" parents="26490 48"/>
    </justification>
  </clause>

  <clause id="26579">
    <literal><![CDATA[
      a(x,y * L(y,z,u),w) \ 1 != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,y * L(y,z,u),x) = v5
    ]]></literal>
    <justification jstring="[para(26490(a,1),12597(a,1,1))].">
      <j1 rule="para" parents="26490 12597"/>
    </justification>
  </clause>

  <clause id="26580">
    <literal><![CDATA[
      x \ T(a(y,x,z) \ x,u) = a(y,x,z) \ K(x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,23178,a(flip),b,26541,a)].">
      <j1 rule="hyper" parents="63 23178 26541"/>
    </justification>
  </clause>

  <clause id="26581">
    <literal><![CDATA[
      ((x \ ((x * y) * z)) / z) \ T(y,u) = a(x,y,z) \ K(y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,23188,a,b,26580,a)].">
      <j1 rule="hyper" parents="63 23188 26580"/>
    </justification>
  </clause>

  <clause id="26582">
    <literal><![CDATA[
      a(x,a(L(y,y,z),u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,a(z \ (y \ z),u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(26144(a,2),26575(a,1))].">
      <j1 rule="para" parents="26144 26575"/>
    </justification>
  </clause>

  <clause id="26583">
    <literal><![CDATA[
      (x \ ((x * y) * z)) \ (y * z) = y \ ((y / z) * L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,3963,a(flip),b,26506,a),flip(a)].">
      <j1 rule="hyper" parents="347 3963 26506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26584">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (w \ (z \ (u * w)))) = a(x,y,a(w,z \ u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),26517(a,1,3,2,2,2,1))].">
      <j1 rule="para" parents="10 26517"/>
    </justification>
  </clause>

  <clause id="26585">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ v5 != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(w,u,z)) \ v5 = v6
    ]]></literal>
    <justification jstring="[para(10(a,1),26566(a,1,2))].">
      <j1 rule="para" parents="10 26566"/>
    </justification>
  </clause>

  <clause id="26586">
    <literal><![CDATA[
      a(x,y,a(z,u,L(u,y,x))) \ w = a(x,y,a(u,u,z)) \ w
    ]]></literal>
    <justification jstring="[para(26436(a,2),26567(a,1,1,3))].">
      <j1 rule="para" parents="26436 26567"/>
    </justification>
  </clause>

  <clause id="26587">
    <literal><![CDATA[
      ((a(x,y,z) \ K(y,u)) \ T(y,u)) * a(((x \ ((x * y) * z)) / z) \ T(y,u),(x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z) = 1 / (T(y,u) \ (((x \ ((x * y) * z)) / z) \ T(y,u)))
    ]]></literal>
    <justification jstring="[para(26581(a,1),25674(a,1,1,1))].">
      <j1 rule="para" parents="26581 25674"/>
    </justification>
  </clause>

  <clause id="26588">
    <literal><![CDATA[
      (x \ ((x * y) * z)) \ (y * z) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,26154,a(flip),b,26583,a),flip(a)].">
      <j1 rule="hyper" parents="347 26154 26583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26589">
    <literal><![CDATA[
      ((x * y) * (x * y)) * (a(x,y,x * y) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) \ (y * (x * y)) = z
    ]]></literal>
    <justification jstring="[para(26588(a,1),965(a,1,2))].">
      <j1 rule="para" parents="26588 965"/>
    </justification>
  </clause>

  <clause id="26590">
    <literal><![CDATA[
      a(x,y,a(z,u,L(u,y,x))) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(313,a,26586,a),flip(a)].">
      <j1 rule="hyper" parents="313 26586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26591">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(26500,a,26133,a),flip(a)].">
      <j1 rule="hyper" parents="26500 26133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26592">
    <literal><![CDATA[
      a(x,a(y,z,x),u) = a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(22008,a,26591,a)].">
      <j1 rule="hyper" parents="22008 26591"/>
    </justification>
  </clause>

  <clause id="26593">
    <literal><![CDATA[
      a(x * (y \ 1),z,a(u,w,v5)) = a(a(u,w,v5),z,x * y)
    ]]></literal>
    <justification jstring="[hyper(15021,a,26591,a),flip(a)].">
      <j1 rule="hyper" parents="15021 26591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26594">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,26501,a,b,26591,a),flip(a)].">
      <j1 rule="hyper" parents="347 26501 26591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26595">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,26591,a,b,19974,a),flip(a)].">
      <j1 rule="hyper" parents="134 26591 19974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26596">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * v5 = v5 * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,26591,a,b,19982,a)].">
      <j1 rule="hyper" parents="133 26591 19982"/>
    </justification>
  </clause>

  <clause id="26597">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) != 1
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[para(26591(a,1),52(a,1))].">
      <j1 rule="para" parents="26591 52"/>
    </justification>
  </clause>

  <clause id="26598">
    <literal><![CDATA[
      a(a(x,y,z),u,w * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(v5 * w,u,a(x,y,z)) = v6
    ]]></literal>
    <justification jstring="[para(26591(a,2),23925(a,1))].">
      <j1 rule="para" parents="26591 23925"/>
    </justification>
  </clause>

  <clause id="26599">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ 1 != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(26591(a,2),26335(a,1,1))].">
      <j1 rule="para" parents="26591 26335"/>
    </justification>
  </clause>

  <clause id="26600">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * y) \ (y * x) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(26591(a,1),26502(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="26591 26502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26601">
    <literal><![CDATA[
      a(x,a(x,y,z),u) = a(u,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(26574,a,26592,a)].">
      <j1 rule="hyper" parents="26574 26592"/>
    </justification>
  </clause>

  <clause id="26602">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) \ 1 = a(y,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,26518,a,b,26592,a)].">
      <j1 rule="hyper" parents="347 26518 26592"/>
    </justification>
  </clause>

  <clause id="26603">
    <literal><![CDATA[
      a(x,a(y,z,x),u) = a(u,x,a(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,26501,a,b,26592,a),flip(a)].">
      <j1 rule="hyper" parents="347 26501 26592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26604">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) \ 1 = a(y,a(z,u,y),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,26334,a,b,26592,a)].">
      <j1 rule="hyper" parents="347 26334 26592"/>
    </justification>
  </clause>

  <clause id="26605">
    <literal><![CDATA[
      a(x,y * z,a(y,y,y * z)) = a(y * z,a(y,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,25065,a(flip),b,26592,a),flip(a)].">
      <j1 rule="hyper" parents="63 25065 26592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26606">
    <literal><![CDATA[
      a(x,a(y,z,x),u) \ 1 = a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(26592(a,2),26334(a,1,1))].">
      <j1 rule="para" parents="26592 26334"/>
    </justification>
  </clause>

  <clause id="26607">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,26591,a,b,26594,a)].">
      <j1 rule="hyper" parents="347 26591 26594"/>
    </justification>
  </clause>

  <clause id="26608">
    <literal><![CDATA[
      a(x,y,a(z,y,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(26286,a,26601,a),flip(a)].">
      <j1 rule="hyper" parents="26286 26601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26609">
    <literal><![CDATA[
      a(a(x,y,z),x,u) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,26594,a,b,26601,a)].">
      <j1 rule="hyper" parents="347 26594 26601"/>
    </justification>
  </clause>

  <clause id="26610">
    <literal><![CDATA[
      a(x,a(x,y,z),u) = a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,26501,a,b,26601,a),flip(a)].">
      <j1 rule="hyper" parents="347 26501 26601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26611">
    <literal><![CDATA[
      L(a(x,y,z),z,u) \ a(x,y,z) = a(z,a(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,26230,a,b,26601,a)].">
      <j1 rule="hyper" parents="347 26230 26601"/>
    </justification>
  </clause>

  <clause id="26612">
    <literal><![CDATA[
      a(x,y,a(y,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(26560,a,26608,a)].">
      <j1 rule="hyper" parents="26560 26608"/>
    </justification>
  </clause>

  <clause id="26613">
    <literal><![CDATA[
      (x * y) * a(z,y,y) = x * (y * a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(1093,a,26608,a)].">
      <j1 rule="hyper" parents="1093 26608"/>
    </justification>
  </clause>

  <clause id="26614">
    <literal><![CDATA[
      (x / y) \ (x * a(z,y,y)) = (y * a(z,y,y)) * 1
    ]]></literal>
    <justification jstring="[hyper(134,a,26608,a(flip),b,14708,a),flip(a)].">
      <j1 rule="hyper" parents="134 26608 14708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26615">
    <literal><![CDATA[
      a(x,a(x,x,y),z) = a(u,w,a(w,w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,26285,a,b,26612,a)].">
      <j1 rule="hyper" parents="347 26285 26612"/>
    </justification>
  </clause>

  <clause id="26616">
    <literal><![CDATA[
      a(L(x,x,y) \ x,z,u) = a(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(25425(a,2),26607(a,1,1))].">
      <j1 rule="para" parents="25425 26607"/>
    </justification>
  </clause>

  <clause id="26617">
    <literal><![CDATA[
      a(a(x,y,L(z,y,x)),u,w) = a(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(26489(a,2),26607(a,1,1))].">
      <j1 rule="para" parents="26489 26607"/>
    </justification>
  </clause>

  <clause id="26618">
    <literal><![CDATA[
      a(x,a(a(y,z,u),w,v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,a(v5,w,a(u,z,y)),v6) = v7
    ]]></literal>
    <justification jstring="[para(26607(a,1),26574(a,1,2))].">
      <j1 rule="para" parents="26607 26574"/>
    </justification>
  </clause>

  <clause id="26619">
    <literal><![CDATA[
      a(x,y,z) \ ((x \ a(x,y,z)) * u) = a(x,a(x,y,z),u) * ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(26609(a,1),15308(a,2,1))].">
      <j1 rule="para" parents="26609 15308"/>
    </justification>
  </clause>

  <clause id="26620">
    <literal><![CDATA[
      a(x,a(x,y,z),u * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w * u,x,a(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(26610(a,2),23925(a,1))].">
      <j1 rule="para" parents="26610 23925"/>
    </justification>
  </clause>

  <clause id="26621">
    <literal><![CDATA[
      a(x,a(y,x,x),z) = a(u,w,a(w,w,v5))
    ]]></literal>
    <justification jstring="[hyper(26575,a,26615,a)].">
      <j1 rule="hyper" parents="26575 26615"/>
    </justification>
  </clause>

  <clause id="26622">
    <literal><![CDATA[
      a(x,a(y,z,u),y) = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(39,a,26555,a,b,26602,a)].">
      <j1 rule="hyper" parents="39 26555 26602"/>
    </justification>
  </clause>

  <clause id="26623">
    <literal><![CDATA[
      L(a(x,y,a(y,z,u)) \ 1,w,y) = y \ L(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(26622(a,1),26199(a,1,1,1))].">
      <j1 rule="para" parents="26622 26199"/>
    </justification>
  </clause>

  <clause id="26624">
    <literal><![CDATA[
      a(x,a(y,z,u),u) = a(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(39,a,26491,a,b,26604,a)].">
      <j1 rule="hyper" parents="39 26491 26604"/>
    </justification>
  </clause>

  <clause id="26625">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) / u) * L(u,a(x,y,z),z)) = (a(u,z,a(x,y,z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(26604(a,2),26154(a,2,1))].">
      <j1 rule="para" parents="26604 26154"/>
    </justification>
  </clause>

  <clause id="26626">
    <literal><![CDATA[
      a(x,a(y,z,x),u) \ x = x * a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(26604(a,1),26553(a,1,1))].">
      <j1 rule="para" parents="26604 26553"/>
    </justification>
  </clause>

  <clause id="26627">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) != 1
    ]]></literal>
    <literal><![CDATA[
      L(y,a(z,u,y),x) = y
    ]]></literal>
    <justification jstring="[para(26624(a,1),52(a,1))].">
      <j1 rule="para" parents="26624 52"/>
    </justification>
  </clause>

  <clause id="26628">
    <literal><![CDATA[
      a(x,y,y) * (z * y) = z * (y * a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(20479,a,26613,a)].">
      <j1 rule="hyper" parents="20479 26613"/>
    </justification>
  </clause>

  <clause id="26629">
    <literal><![CDATA[
      a(a(x,x,(x \ y) * (z * z)),u,w) = a(L(x,x,y) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,25915,a(flip),b,26616,a),flip(a)].">
      <j1 rule="hyper" parents="63 25915 26616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26630">
    <literal><![CDATA[
      a(x,y,y) * ((z \ a(z,z,a(x,y,y) * y)) * y) = z \ (y * a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,18999,a(flip),b,26628,a),flip(a)].">
      <j1 rule="hyper" parents="347 18999 26628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26631">
    <literal><![CDATA[
      a(x,y,L(y,y,z)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,26438,a,b,26628,a)].">
      <j1 rule="hyper" parents="35 26438 26628"/>
    </justification>
  </clause>

  <clause id="26632">
    <literal><![CDATA[
      a(x,y,L(y,y,z)) = L(y,y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,25425,a,b,26631,a),flip(a)].">
      <j1 rule="hyper" parents="347 25425 26631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26633">
    <literal><![CDATA[
      (x * (a(x,y,y) \ y)) * L(y,y,z) = x * (y * L(y,y,z))
    ]]></literal>
    <justification jstring="[para(26631(a,1),25414(a,1,1,2,1))].">
      <j1 rule="para" parents="26631 25414"/>
    </justification>
  </clause>

  <clause id="26634">
    <literal><![CDATA[
      a(x,y,z \ (y \ z)) = L(y,y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(24770,a,26632,a)].">
      <j1 rule="hyper" parents="24770 26632"/>
    </justification>
  </clause>

  <clause id="26635">
    <literal><![CDATA[
      a(x \ (y \ x),z,L(y,y,u) \ y) = 1
    ]]></literal>
    <justification jstring="[para(26634(a,1),12361(a,1,3))].">
      <j1 rule="para" parents="26634 12361"/>
    </justification>
  </clause>

  <clause id="26636">
    <literal><![CDATA[
      a(x \ (y \ x),z,y * L(y,y,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(15022,a,26635,a)].">
      <j1 rule="hyper" parents="15022 26635"/>
    </justification>
  </clause>

  <clause id="26637">
    <literal><![CDATA[
      a(x \ (y \ x),z,a(y,y,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,24647,a(flip),b,26636,a)].">
      <j1 rule="hyper" parents="63 24647 26636"/>
    </justification>
  </clause>

  <clause id="26638">
    <literal><![CDATA[
      a(x * y,z,z * L(z,y,x)) = a(a(z,y,x),z,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,26387,a(flip),b,26617,a)].">
      <j1 rule="hyper" parents="63 26387 26617"/>
    </justification>
  </clause>

  <clause id="26639">
    <literal><![CDATA[
      x * (y * a(a(z,u,w),x,x)) = R(x,x,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(26595(a,1),26280(a,1,2))].">
      <j1 rule="para" parents="26595 26280"/>
    </justification>
  </clause>

  <clause id="26640">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      x * a(a(u,w,v5),z,y) = v6
    ]]></literal>
    <justification jstring="[para(26596(a,1),20016(a,1))].">
      <j1 rule="para" parents="26596 20016"/>
    </justification>
  </clause>

  <clause id="26641">
    <literal><![CDATA[
      (x / y) \ R(x,y,y) = (y * a(x,y,y)) * 1
    ]]></literal>
    <justification jstring="[para(13399(a,1),26614(a,1,2))].">
      <j1 rule="para" parents="13399 26614"/>
    </justification>
  </clause>

  <clause id="26642">
    <literal><![CDATA[
      (x / y) \ R(x,y,y) = y * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,8,a(flip),b,26641,a),flip(a)].">
      <j1 rule="hyper" parents="347 8 26641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26643">
    <literal><![CDATA[
      T(x,y) * a(x * y,T(x,y),T(x,y)) = y \ R(x * y,T(x,y),T(x,y))
    ]]></literal>
    <justification jstring="[para(213(a,1),26642(a,1,1)),flip(a)].">
      <j1 rule="para" parents="213 26642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26644">
    <literal><![CDATA[
      L(a(x,y,z),z,u \ a(w,v5,u)) \ a(x,y,z) = a(z,a(z,y,x),u * a(w,v5,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,14991,a(flip),b,26611,a),flip(a)].">
      <j1 rule="hyper" parents="347 14991 26611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26645">
    <literal><![CDATA[
      a(x * y,z,z * L(z,y,x)) = a(z,a(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,26609,a(flip),b,26638,a),flip(a)].">
      <j1 rule="hyper" parents="347 26609 26638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26646">
    <literal><![CDATA[
      x * (y * a(a(z,u,w),x,x)) = L(x,x,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(23247(a,1),26639(a,2,1))].">
      <j1 rule="para" parents="23247 26639"/>
    </justification>
  </clause>

  <clause id="26647">
    <literal><![CDATA[
      a(x * (y \ 1),z,a(u,w,v5)) = a(y * x,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(26598,a,26593,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="26598 26593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26648">
    <literal><![CDATA[
      a(x * (x * y),z,a(u,w,v5)) = a(L(y,x,x),z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,24970,a(flip),b,26647,a),flip(a)].">
      <j1 rule="hyper" parents="63 24970 26647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26649">
    <literal><![CDATA[
      L(a(x,y,a(y,z,u)),w,y) = y \ L(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(26334(a,1),26623(a,1,1))].">
      <j1 rule="para" parents="26334 26623"/>
    </justification>
  </clause>

  <clause id="26650">
    <literal><![CDATA[
      x \ L(x,a(x,y,z),u) = a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(20172,a,26649,a),flip(a)].">
      <j1 rule="hyper" parents="20172 26649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26651">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) * y = L(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(38,a,19974,a,b,26650,a)].">
      <j1 rule="hyper" parents="38 19974 26650"/>
    </justification>
  </clause>

  <clause id="26652">
    <literal><![CDATA[
      x \ L(x,a(y,z,x),u) = a(u,x,a(x,z,y))
    ]]></literal>
    <justification jstring="[para(26497(a,1),26650(a,1,2))].">
      <j1 rule="para" parents="26497 26650"/>
    </justification>
  </clause>

  <clause id="26653">
    <literal><![CDATA[
      x \ L(x,a(y,z,x),u) = a(x,a(y,z,x),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,26603,a,b,26652,a),flip(a)].">
      <j1 rule="hyper" parents="347 26603 26652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26654">
    <literal><![CDATA[
      x * a(x,a(y,z,x),u) = L(x,a(y,z,x),u)
    ]]></literal>
    <justification jstring="[hyper(134,a,26603,a,b,26652,a)].">
      <j1 rule="hyper" parents="134 26603 26652"/>
    </justification>
  </clause>

  <clause id="26655">
    <literal><![CDATA[
      x * a(y,x,a(z,u,x)) = L(x,a(z,u,x),y)
    ]]></literal>
    <justification jstring="[hyper(134,a,26501,a,b,26652,a)].">
      <j1 rule="hyper" parents="134 26501 26652"/>
    </justification>
  </clause>

  <clause id="26656">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * y = L(y,a(z,u,y),x)
    ]]></literal>
    <justification jstring="[hyper(38,a,26519,a,b,26652,a)].">
      <j1 rule="hyper" parents="38 26519 26652"/>
    </justification>
  </clause>

  <clause id="26657">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * x = L(x,a(y,z,x),u)
    ]]></literal>
    <justification jstring="[hyper(38,a,19974,a,b,26653,a)].">
      <j1 rule="hyper" parents="38 19974 26653"/>
    </justification>
  </clause>

  <clause id="26658">
    <literal><![CDATA[
      L(T(x,x \ 1),a(y,z,x),u) = (x \ 1) \ a(x,a(y,z,x),u)
    ]]></literal>
    <justification jstring="[hyper(128,a,26653,a(flip),b,1297,a),flip(a)].">
      <j1 rule="hyper" parents="128 26653 1297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26659">
    <literal><![CDATA[
      L(x,a(y,z,x),u) \ x = a(x,a(y,z,x),u) \ 1
    ]]></literal>
    <justification jstring="[para(26653(a,1),10882(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26653 10882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26660">
    <literal><![CDATA[
      L(x,a(y,z,x),u) \ x = a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,26606,a(flip),b,26659,a),flip(a)].">
      <j1 rule="hyper" parents="347 26606 26659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26661">
    <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(26660(a,1),26402(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26660 26402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26662">
    <literal><![CDATA[
      a(x,a(y,z,u),L(u,w,v5)) = a(x,u,L(a(u,z,y),w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,26529,a,b,26661,a),flip(a)].">
      <j1 rule="hyper" parents="347 26529 26661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26663">
    <literal><![CDATA[
      a(x,a(y,z,u),L(u,w,y)) = a(x,u,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(12360(a,1),26662(a,2,3))].">
      <j1 rule="para" parents="12360 26662"/>
    </justification>
  </clause>

  <clause id="26664">
    <literal><![CDATA[
      a(x,a(y,z,u),L(y,w,u)) = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(26574,a,26663,a)].">
      <j1 rule="hyper" parents="26574 26663"/>
    </justification>
  </clause>

  <clause id="26665">
    <literal><![CDATA[
      a(x,a(y,z,u),u \ (y \ u)) = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(24770,a,26664,a)].">
      <j1 rule="hyper" parents="24770 26664"/>
    </justification>
  </clause>

  <clause id="26666">
    <literal><![CDATA[
      a(x,a(y,y,z),z \ (y \ z)) = 1
    ]]></literal>
    <justification jstring="[hyper(347,a,26612,a(flip),b,26665,a),flip(a)].">
      <j1 rule="hyper" parents="347 26612 26665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26667">
    <literal><![CDATA[
      (x / (y \ 1)) * L(y,y,z) = x * (y * L(y,y,z))
    ]]></literal>
    <justification jstring="[para(25419(a,1),26633(a,1,1))].">
      <j1 rule="para" parents="25419 26633"/>
    </justification>
  </clause>

  <clause id="26668">
    <literal><![CDATA[
      a(x,((y / ((z \ 1) \ 1)) * L(z,z \ 1,u)) * w,v5) = a(x,(y * ((z \ 1) * L(z \ 1,z \ 1,u))) * w,v5)
    ]]></literal>
    <justification jstring="[para(26667(a,1),24962(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="26667 24962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26669">
    <literal><![CDATA[
      a((x * y) * x,z,a(u,w,v5)) = a(L(y,x,x),z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(23925,a,26648,a)].">
      <j1 rule="hyper" parents="23925 26648"/>
    </justification>
  </clause>

  <clause id="26670">
    <literal><![CDATA[
      a(a(x,x,x \ y),z,u) = a(L(x,x,y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(65(a,1),26629(a,1,1,3))].">
      <j1 rule="para" parents="65 26629"/>
    </justification>
  </clause>

  <clause id="26671">
    <literal><![CDATA[
      a(a(x,x,x \ y),z,u) = a(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,26616,a(flip),b,26670,a),flip(a)].">
      <j1 rule="hyper" parents="347 26616 26670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26672">
    <literal><![CDATA[
      a(a(x,x,x * y),z,u) = a(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),26671(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="9 26671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26673">
    <literal><![CDATA[
      a(x * y,a(x,x,x * y),z) = a(a(x,x,y),x * y,z)
    ]]></literal>
    <justification jstring="[hyper(22008,a,26672,a)].">
      <j1 rule="hyper" parents="22008 26672"/>
    </justification>
  </clause>

  <clause id="26674">
    <literal><![CDATA[
      a(a(x,x,y),x * y,z) = a(x * y,a(x,x,y),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,25065,a(flip),b,26673,a),flip(a)].">
      <j1 rule="hyper" parents="63 25065 26673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26676">
    <literal><![CDATA[
      a(L(x,y,z) \ u,x,x) = (x \ a(u,x,x)) * x
    ]]></literal>
    <justification jstring="[para(26464(a,1),26466(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="26464 26466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26677">
    <literal><![CDATA[
      a(L(x,y,z) \ u,x,x) = a(x \ u,x,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,25465,a(flip),b,26676,a),flip(a)].">
      <j1 rule="hyper" parents="347 25465 26676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26679">
    <literal><![CDATA[
      L(x,x,(y / L(x,z,u)) * x) = 1 / (a(x \ y,x,x) / x)
    ]]></literal>
    <justification jstring="[para(26677(a,1),25468(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="26677 25468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26680">
    <literal><![CDATA[
      L(x,x,(y / L(x,z,u)) * x) = 1 / (L(x,x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(25434(a,1),26679(a,2,2))].">
      <j1 rule="para" parents="25434 26679"/>
    </justification>
  </clause>

  <clause id="26682">
    <literal><![CDATA[
      L(x,x,(y / L(x,z,u)) * x) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,80,a(flip),b,26680,a),flip(a)].">
      <j1 rule="hyper" parents="347 80 26680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26684">
    <literal><![CDATA[
      L(x,x,x * (L(x,y,z) \ u)) = L(x,x,u)
    ]]></literal>
    <justification jstring="[para(20676(a,1),26682(a,1,3))].">
      <j1 rule="para" parents="20676 26682"/>
    </justification>
  </clause>

  <clause id="26685">
    <literal><![CDATA[
      L(x,x,L(x,y,z) * u) = L(x,x,x * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),26684(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="9 26684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26686">
    <literal><![CDATA[
      L(x,x,L(x,y,z) \ u) = L(x,x,x \ u)
    ]]></literal>
    <justification jstring="[para(1408(a,1),26684(a,1,3))].">
      <j1 rule="para" parents="1408 26684"/>
    </justification>
  </clause>

  <clause id="26687">
    <literal><![CDATA[
      L(x,x,y * L(x,z,u)) = L(x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(20105,a,26685,a)].">
      <j1 rule="hyper" parents="20105 26685"/>
    </justification>
  </clause>

  <clause id="26688">
    <literal><![CDATA[
      L(1 / x,1 / x,L(1 / x,y,z) * (x * u)) = L(1 / x,1 / x,L(u,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(2939(a,1),26685(a,2,3))].">
      <j1 rule="para" parents="2939 26685"/>
    </justification>
  </clause>

  <clause id="26689">
    <literal><![CDATA[
      L(x,x,x \ y) * R(L(x,z,u) \ y,x,x) = x * (L(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(26686(a,1),11764(a,1,1))].">
      <j1 rule="para" parents="26686 11764"/>
    </justification>
  </clause>

  <clause id="26690">
    <literal><![CDATA[
      (a(x,y,z) \ (y \ 1)) \ (a(x,y,z) \ 1) = T(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(26353(a,1),26577(a,1,2))].">
      <j1 rule="para" parents="26353 26577"/>
    </justification>
  </clause>

  <clause id="26694">
    <literal><![CDATA[
      a(x,y,z) \ ((x \ a(x,y,z)) * u) = (x \ 1) * (a(x,a(x,y,z),u) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,25384,a(flip),b,26619,a),flip(a)].">
      <j1 rule="hyper" parents="347 25384 26619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26695">
    <literal><![CDATA[
      T(x,y) * a(x * y,T(x,y),T(x,y)) = y \ R(x * y,T(x,y),x)
    ]]></literal>
    <justification jstring="[para(20040(a,1),26643(a,2,2))].">
      <j1 rule="para" parents="20040 26643"/>
    </justification>
  </clause>

  <clause id="26697">
    <literal><![CDATA[
      T(x,y) * a(x * y,T(x,y),T(x,y)) = y \ R(x * y,x,x)
    ]]></literal>
    <justification jstring="[para(20496(a,1),26695(a,2,2))].">
      <j1 rule="para" parents="20496 26695"/>
    </justification>
  </clause>

  <clause id="26698">
    <literal><![CDATA[
      x \ R(y * x,y,y) = ((y * x) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,25453,a(flip),b,26697,a),flip(a)].">
      <j1 rule="hyper" parents="63 25453 26697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26700">
    <literal><![CDATA[
      a(R(x * y,x,x) \ z,u,w) = a(((((x * y) \ y) \ 1) * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(26698(a,1),23905(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="26698 23905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26701">
    <literal><![CDATA[
      a(L(x * y,x,x) \ z,u,w) = a(((((x * y) \ y) \ 1) * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,25232,a(flip),b,26700,a)].">
      <j1 rule="hyper" parents="63 25232 26700"/>
    </justification>
  </clause>

  <clause id="26702">
    <literal><![CDATA[
      a(x \ y,x,x * L(x,z,u)) \ x = L(x,z,u) * L(L(x,z,u) \ x,x,y)
    ]]></literal>
    <justification jstring="[para(14939(a,1),26550(a,1,1))].">
      <j1 rule="para" parents="14939 26550"/>
    </justification>
  </clause>

  <clause id="26703">
    <literal><![CDATA[
      (a(x,x,y) \ x) * (K(x,x \ 1) * y) = x * (x * ((1 / x) * y))
    ]]></literal>
    <justification jstring="[para(4123(a,1),26534(a,1,1,1))].">
      <j1 rule="para" parents="4123 26534"/>
    </justification>
  </clause>

  <clause id="26704">
    <literal><![CDATA[
      (a(x,x,y) \ T(x,x \ 1)) * y = x * (x * ((1 / x) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,20179,a(flip),b,26703,a)].">
      <j1 rule="hyper" parents="63 20179 26703"/>
    </justification>
  </clause>

  <clause id="26707">
    <literal><![CDATA[
      T(a(x,x,y) \ x,x \ 1) * y = x * (x * ((1 / x) * y))
    ]]></literal>
    <justification jstring="[para(23175(a,2),26704(a,1,1))].">
      <j1 rule="para" parents="23175 26704"/>
    </justification>
  </clause>

  <clause id="26708">
    <literal><![CDATA[
      L(K(x,x \ 1) * (a(y,x,z) \ 1),x,x) = x * (a(y,1 / x,z) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(14964(a,1),26544(a,1,1,2,1))].">
      <j1 rule="para" parents="14964 26544"/>
    </justification>
  </clause>

  <clause id="26709">
    <literal><![CDATA[
      L(x * ((a(y,x,z) \ 1) / x),x,x) = x * (a(y,1 / x,z) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(23218(a,1),26708(a,1,1))].">
      <j1 rule="para" parents="23218 26708"/>
    </justification>
  </clause>

  <clause id="26710">
    <literal><![CDATA[
      L(x * ((a(y,x,z) \ 1) / x),x,x) = x * (a(y,x,z) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(14964(a,1),26709(a,2,2,1))].">
      <j1 rule="para" parents="14964 26709"/>
    </justification>
  </clause>

  <clause id="26711">
    <literal><![CDATA[
      (a(x,y,z) \ 1) / y = a(x,y,z) \ (1 / y)
    ]]></literal>
    <justification jstring="[hyper(26369,a,26710,a)].">
      <j1 rule="hyper" parents="26369 26710"/>
    </justification>
  </clause>

  <clause id="26712">
    <literal><![CDATA[
      L(a(x,y,z),z,a(u,w,z)) \ a(x,y,z) = a(z,a(z,y,x),z * a(u,w,z))
    ]]></literal>
    <justification jstring="[para(26214(a,1),26644(a,1,1))].">
      <j1 rule="para" parents="26214 26644"/>
    </justification>
  </clause>

  <clause id="26713">
    <literal><![CDATA[
      a(x,a(x,y,z),x * a(z,y,x)) = a(z,y,x) \ a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(21180,a,26712,a),flip(a)].">
      <j1 rule="hyper" parents="21180 26712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26714">
    <literal><![CDATA[
      a(x,a(x,y,z),x * a(z,y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(347,a,68,a(flip),b,26713,a),flip(a)].">
      <j1 rule="hyper" parents="347 68 26713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26715">
    <literal><![CDATA[
      a(x,a(x,y,z),a(z,y,x) * x) = 1
    ]]></literal>
    <justification jstring="[hyper(24180,a,26714,a)].">
      <j1 rule="hyper" parents="24180 26714"/>
    </justification>
  </clause>

  <clause id="26720">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * ((y * a(w,u,z)) * x) = (y * a(w,u,z)) * L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(23247(a,1),26524(a,2,2))].">
      <j1 rule="para" parents="23247 26524"/>
    </justification>
  </clause>

  <clause id="26721">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) / u) * L(u,z,a(x,y,z))) = (a(u,z,a(x,y,z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(23359(a,1),26625(a,1,2,2))].">
      <j1 rule="para" parents="23359 26625"/>
    </justification>
  </clause>

  <clause id="26722">
    <literal><![CDATA[
      L(1 / x,1 / x,(1 / x) * (L(x,y,z) * u)) = L(1 / x,1 / x,L(u,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(22794(a,1),26688(a,1,3))].">
      <j1 rule="para" parents="22794 26688"/>
    </justification>
  </clause>

  <clause id="26723">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * ((y * a(w,u,z)) * x) = a(w,u,z) * (T(y,a(w,u,z)) * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,10150,a(flip),b,26720,a),flip(a)].">
      <j1 rule="hyper" parents="347 10150 26720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26724">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * ((y * a(w,u,z)) * x) = a(w,u,z) * (y * x)
    ]]></literal>
    <justification jstring="[para(19939(a,1),26723(a,2,2,1))].">
      <j1 rule="para" parents="19939 26723"/>
    </justification>
  </clause>

  <clause id="26725">
    <literal><![CDATA[
      (a(x,y,a(z,u,y)) \ 1) \ 1 = x \ L(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(25558,a,26721,a),flip(a)].">
      <j1 rule="hyper" parents="25558 26721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26726">
    <literal><![CDATA[
      x * a(x,y,a(z,u,y)) = L(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(20579,a,26725,a)].">
      <j1 rule="hyper" parents="20579 26725"/>
    </justification>
  </clause>

  <clause id="26727">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,y)) = a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(20577,a,26725,a),flip(a)].">
      <j1 rule="hyper" parents="20577 26725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26728">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,y)),w,v5) = a(L(x,w,v5),y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(34,a,4637,a,b,26726,a)].">
      <j1 rule="hyper" parents="34 4637 26726"/>
    </justification>
  </clause>

  <clause id="26730">
    <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(26727(a,1),26728(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26727 26728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26731">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,u)) = a(x,a(w,v5,u),L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,26661,a,b,26730,a),flip(a)].">
      <j1 rule="hyper" parents="347 26661 26730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26732">
    <literal><![CDATA[
      a(x,a(y,z,u),L(u,w,v5)) \ 1 = a(u,a(y,z,u),L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(26731(a,1),26604(a,1,1))].">
      <j1 rule="para" parents="26731 26604"/>
    </justification>
  </clause>

  <clause id="26733">
    <literal><![CDATA[
      a(L(x,y,z),a(u,w,x),v5) = a(x,a(u,w,x),L(v5,y,z))
    ]]></literal>
    <justification jstring="[hyper(26556,a,26732,a)].">
      <j1 rule="hyper" parents="26556 26732"/>
    </justification>
  </clause>

  <clause id="26734">
    <literal><![CDATA[
      a(a(x,y,y),L(y,z,x),u) = a(y,a(x,y,y),L(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,26449,a(flip),b,26733,a)].">
      <j1 rule="hyper" parents="63 26449 26733"/>
    </justification>
  </clause>

  <clause id="26735">
    <literal><![CDATA[
      a(a(x,y,y),L(y,z,x),u) = a(w,v5,a(v5,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,26621,a(flip),b,26734,a),flip(a)].">
      <j1 rule="hyper" parents="347 26621 26734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26737">
    <literal><![CDATA[
      a(a(x,y,y),x \ (y \ x),z) = a(u,w,a(w,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,24738,a(flip),b,26735,a)].">
      <j1 rule="hyper" parents="63 24738 26735"/>
    </justification>
  </clause>

  <clause id="26738">
    <literal><![CDATA[
      L(1 / x,1 / x,(x \ 1) * (L(x,y,z) * u)) = L(1 / x,1 / x,L(u,x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(21515,a,26722,a)].">
      <j1 rule="hyper" parents="21515 26722"/>
    </justification>
  </clause>

  <clause id="26739">
    <literal><![CDATA[
      L(1 / x,x,(x \ 1) * (L(x,y,z) * u)) = L(1 / x,1 / x,L(u,x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(3520,a,26738,a)].">
      <j1 rule="hyper" parents="3520 26738"/>
    </justification>
  </clause>

  <clause id="26740">
    <literal><![CDATA[
      L(1 / x,1 / x,L(y,x,x \ 1)) = L(1 / x,x,x \ (L(x,z,u) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,21603,a(flip),b,26739,a),flip(a)].">
      <j1 rule="hyper" parents="63 21603 26739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26741">
    <literal><![CDATA[
      (x * R(y,y,z)) \ (y * (a(y,y,z) * (T(x,y) * u))) = L(L(u,x,y),x * y,a(y,y,z))
    ]]></literal>
    <justification jstring="[para(25377(a,1),26317(a,1,2))].">
      <j1 rule="para" parents="25377 26317"/>
    </justification>
  </clause>

  <clause id="26742">
    <literal><![CDATA[
      L(L(x \ (x \ y),x,z) \ (x \ (x \ y)),u,w) = a(z,x,(x \ L(y,u,w)) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,26122,a(flip),b,26458,a)].">
      <j1 rule="hyper" parents="63 26122 26458"/>
    </justification>
  </clause>

  <clause id="26743">
    <literal><![CDATA[
      a(x,y,(y \ L(z,u,w)) \ y) = L(a(x,y,(y \ z) \ y),u,w)
    ]]></literal>
    <justification jstring="[para(26204(a,1),26742(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26204 26742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26744">
    <literal><![CDATA[
      a(x,y,(y \ L(z,u,w)) \ y) = L(a(x,y,y * (z \ y)),u,w)
    ]]></literal>
    <justification jstring="[para(24843(a,1),26743(a,2,1))].">
      <j1 rule="para" parents="24843 26743"/>
    </justification>
  </clause>

  <clause id="26745">
    <literal><![CDATA[
      a(x,y,y * (L(z,u,w) \ y)) = L(a(x,y,y * (z \ y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24843,a(flip),b,26744,a)].">
      <j1 rule="hyper" parents="63 24843 26744"/>
    </justification>
  </clause>

  <clause id="26746">
    <literal><![CDATA[
      (x * R(y,y,z)) \ (R(y,y,z) * (T(x,y) * u)) = L(L(u,x,y),x * y,a(y,y,z))
    ]]></literal>
    <justification jstring="[para(26280(a,1),26741(a,1,2))].">
      <j1 rule="para" parents="26280 26741"/>
    </justification>
  </clause>

  <clause id="26747">
    <literal><![CDATA[
      L(L(x,y,z),y * z,a(z,z,u)) = L(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(23700,a,26746,a),flip(a)].">
      <j1 rule="hyper" parents="23700 26746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26748">
    <literal><![CDATA[
      L(x,y,L(z,z,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,23130,a(flip),b,26747,a),flip(a)].">
      <j1 rule="hyper" parents="63 23130 26747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26749">
    <literal><![CDATA[
      a(x,y,z \ L(z,u,w)) \ 1 = a(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(836,a,26152,a),flip(a)].">
      <j1 rule="hyper" parents="836 26152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26750">
    <literal><![CDATA[
      a(x,y,z \ L(z,u,w)) \ 1 = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,14977,a(flip),b,26749,a),flip(a)].">
      <j1 rule="hyper" parents="347 14977 26749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26751">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) \ 1 = a(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(14977(a,1),26750(a,1,1))].">
      <j1 rule="para" parents="14977 26750"/>
    </justification>
  </clause>

  <clause id="26752">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) * a(x,y,z * L(z,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(20014,a,26751,a)].">
      <j1 rule="hyper" parents="20014 26751"/>
    </justification>
  </clause>

  <clause id="26753">
    <literal><![CDATA[
      a(x \ y,x,L(x,z,u) \ x) \ 1 = a(y,x,x * L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,26431,a,b,26751,a)].">
      <j1 rule="hyper" parents="63 26431 26751"/>
    </justification>
  </clause>

  <clause id="26754">
    <literal><![CDATA[
      a(x,y,y * L(y,x,z)) = a(y,a(z,x,y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,26423,a(flip),b,26751,a),flip(a)].">
      <j1 rule="hyper" parents="63 26423 26751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26756">
    <literal><![CDATA[
      a(x,y * L(y,z,u),w * L(w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(w * L(w,v5,v6),y * L(y,z,u),x) = v7
    ]]></literal>
    <justification jstring="[para(26751(a,1),26579(a,1))].">
      <j1 rule="para" parents="26751 26579"/>
    </justification>
  </clause>

  <clause id="26757">
    <literal><![CDATA[
      a(x,a(y,z,x),z) * (x * (x \ L(x,z,y))) = a(y,z,x) \ x
    ]]></literal>
    <justification jstring="[para(26754(a,1),26256(a,1,1))].">
      <j1 rule="para" parents="26754 26256"/>
    </justification>
  </clause>

  <clause id="26758">
    <literal><![CDATA[
      a(x \ y,x,x * L(x,z,u)) \ 1 = a(y,x,x * L(x,z,u))
    ]]></literal>
    <justification jstring="[para(14939(a,1),26753(a,1,1))].">
      <j1 rule="para" parents="14939 26753"/>
    </justification>
  </clause>

  <clause id="26759">
    <literal><![CDATA[
      a(x,a(y,z,x),z) * L(x,z,y) = a(y,z,x) \ x
    ]]></literal>
    <justification jstring="[hyper(357,a,26757,a)].">
      <j1 rule="hyper" parents="357 26757"/>
    </justification>
  </clause>

  <clause id="26761">
    <literal><![CDATA[
      (a(x,a(y,z,x),z) * x) * L(x,z,y) = (a(y,z,x) \ x) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,26759,a(flip),b,2001,a),flip(a)].">
      <j1 rule="hyper" parents="133 26759 2001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26762">
    <literal><![CDATA[
      x \ (a(y,z,x) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,z,y) * (x \ a(x,a(y,z,x),z)) = u
    ]]></literal>
    <justification jstring="[para(26759(a,1),20606(a,1,2))].">
      <j1 rule="para" parents="26759 20606"/>
    </justification>
  </clause>

  <clause id="26763">
    <literal><![CDATA[
      a(x,y,a(y,x,z)) * L(y,x,z) = a(z,x,y) \ y
    ]]></literal>
    <justification jstring="[para(26603(a,1),26759(a,1,1))].">
      <j1 rule="para" parents="26603 26759"/>
    </justification>
  </clause>

  <clause id="26764">
    <literal><![CDATA[
      a(x \ y,x,x * L(x,z,u)) = a(y,x,x * L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,26751,a(flip),b,26758,a)].">
      <j1 rule="hyper" parents="63 26751 26758"/>
    </justification>
  </clause>

  <clause id="26765">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,x,u) = a(u,x,x * L(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[para(26764(a,1),26702(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26764 26702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26766">
    <literal><![CDATA[
      (a(x,a(y,z,x),z) * x) * L(x,z,y) = x * (a(y,z,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,23087,a(flip),b,26761,a),flip(a)].">
      <j1 rule="hyper" parents="347 23087 26761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26767">
    <literal><![CDATA[
      L(x,a(y,z,x),z) * L(x,z,y) = x * (a(y,z,x) \ x)
    ]]></literal>
    <justification jstring="[para(26657(a,1),26766(a,1,1))].">
      <j1 rule="para" parents="26657 26766"/>
    </justification>
  </clause>

  <clause id="26768">
    <literal><![CDATA[
      L(x,y,z) * (x \ a(x,a(z,y,x),y)) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(26762,a,12720,a)].">
      <j1 rule="hyper" parents="26762 12720"/>
    </justification>
  </clause>

  <clause id="26769">
    <literal><![CDATA[
      L(a(x,y,z \ u) \ 1,z \ u,y) = L(z * u,z,u) \ L(L(z * u,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(23820,a,26182,a)].">
      <j1 rule="hyper" parents="23820 26182"/>
    </justification>
  </clause>

  <clause id="26770">
    <literal><![CDATA[
      L(x * y,x,y) \ L(L(x * y,x,y),z,u) = (x \ y) \ L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,26161,a(flip),b,26769,a),flip(a)].">
      <j1 rule="hyper" parents="63 26161 26769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26771">
    <literal><![CDATA[
      L(x * y,x,y) \ L(L(x * y,x,y),z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,3354,a(flip),b,26770,a),flip(a)].">
      <j1 rule="hyper" parents="347 3354 26770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26772">
    <literal><![CDATA[
      L((x * y) \ L(x * y,z,u),x,y) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(4639,a,26771,a)].">
      <j1 rule="hyper" parents="4639 26771"/>
    </justification>
  </clause>

  <clause id="26773">
    <literal><![CDATA[
      (x / y) * (y * ((y * (y \ x)) \ L(y * (y \ x),z,u))) = x * (y \ ((y \ x) * L((y \ x) \ y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(134,a,26772,a(flip),b,10192,a),flip(a)].">
      <j1 rule="hyper" parents="134 26772 10192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26774">
    <literal><![CDATA[
      a((L(x,y,z) * u) * L(1 / w,w,R(x,y,z) * u),v5,v6) = a(w \ (R(x,y,z) * u),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,23893,a(flip),b,26399,a),flip(a)].">
      <j1 rule="hyper" parents="347 23893 26399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26775">
    <literal><![CDATA[
      L(x,x,x \ (a(y,x,z) \ 1)) = (a(y,x \ 1,z) \ (x \ 1)) \ (a(y,x \ 1,z) \ 1)
    ]]></literal>
    <justification jstring="[para(14950(a,1),26554(a,1,3,2,1))].">
      <j1 rule="para" parents="14950 26554"/>
    </justification>
  </clause>

  <clause id="26776">
    <literal><![CDATA[
      a((L(x,y,z) * u) * L(1 / w,w,L(x,y,z) * u),v5,v6) = a(w \ (R(x,y,z) * u),v5,v6)
    ]]></literal>
    <justification jstring="[para(22849(a,1),26774(a,1,1,2))].">
      <j1 rule="para" parents="22849 26774"/>
    </justification>
  </clause>

  <clause id="26777">
    <literal><![CDATA[
      a((L(x,y,z) * u) / w,v5,v6) = a(w \ (R(x,y,z) * u),v5,v6)
    ]]></literal>
    <justification jstring="[para(3266(a,1),26776(a,1,1))].">
      <j1 rule="para" parents="3266 26776"/>
    </justification>
  </clause>

  <clause id="26778">
    <literal><![CDATA[
      a(x \ (R(y,z,u) * w),v5,v6) = a(x \ (L(y,z,u) * w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(23956,a,26777,a),flip(a)].">
      <j1 rule="hyper" parents="23956 26777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26779">
    <literal><![CDATA[
      a(x \ (R(y,z,u) * w),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x \ (L(y,z,u) * w),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(26777(a,1),23956(a,1))].">
      <j1 rule="para" parents="26777 23956"/>
    </justification>
  </clause>

  <clause id="26780">
    <literal><![CDATA[
      a(x \ (L(y,z,u \ 1) * w),v5,v6) = a(x \ (R(y,z,u) * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(2190(a,1),26778(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2190 26778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26781">
    <literal><![CDATA[
      a(x \ (L(y,z,u \ 1) * w),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x \ (L(y,z,u) * w),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(26780(a,2),26779(a,1))].">
      <j1 rule="para" parents="26780 26779"/>
    </justification>
  </clause>

  <clause id="26783">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) \ (L(z,y,x) \ z) = a(x * y,z,L(z,y,x) \ z)
    ]]></literal>
    <justification jstring="[para(12354(a,1),26236(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12354 26236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26784">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) \ (L(z,y,x) \ z) = a(x * y,z,z * L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,14939,a(flip),b,26783,a),flip(a)].">
      <j1 rule="hyper" parents="347 14939 26783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26786">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) \ (L(z,y,x) \ z) = a(z,a(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,26645,a(flip),b,26784,a),flip(a)].">
      <j1 rule="hyper" parents="347 26645 26784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26787">
    <literal><![CDATA[
      a(x,a(x,y,z),z * y) \ (L(x,y,z) \ x) = a(z,y,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(39,a,19984,a,b,26786,a)].">
      <j1 rule="hyper" parents="39 19984 26786"/>
    </justification>
  </clause>

  <clause id="26788">
    <literal><![CDATA[
      (L(x,y,z) * a(z,y,L(x,y,z))) \ x = a(x,a(x,y,z),z * y)
    ]]></literal>
    <justification jstring="[para(26787(a,1),25502(a,1,1,2))].">
      <j1 rule="para" parents="26787 25502"/>
    </justification>
  </clause>

  <clause id="26789">
    <literal><![CDATA[
      (L(x,y,z) * a(z,y,x)) \ x = a(x,a(x,y,z),z * y)
    ]]></literal>
    <justification jstring="[para(26489(a,1),26788(a,1,1,2))].">
      <j1 rule="para" parents="26489 26788"/>
    </justification>
  </clause>

  <clause id="26790">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ L(a(x,x,L(y,z,u)),w,v5) = L(a(x,x,y) \ L(a(x,x,y),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(26260(a,2),26266(a,1,2,1))].">
      <j1 rule="para" parents="26260 26266"/>
    </justification>
  </clause>

  <clause id="26791">
    <literal><![CDATA[
      L(a(x,y,z * L(u,w,v5)),z * L(u,w,v5),y) = L(z * R(u,w,v5),y,x) \ (z * R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(25299(a,1),26293(a,1,1))].">
      <j1 rule="para" parents="25299 26293"/>
    </justification>
  </clause>

  <clause id="26792">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ a(x,x,L(L(y,z,u),w,v5)) = L(a(x,x,y) \ L(a(x,x,y),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(26260(a,2),26790(a,1,2))].">
      <j1 rule="para" parents="26260 26790"/>
    </justification>
  </clause>

  <clause id="26793">
    <literal><![CDATA[
      L(x * R(y,z,u),w,v5) \ (x * R(y,z,u)) = L(x * L(y,z,u),w,v5) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,26288,a(flip),b,26791,a),flip(a)].">
      <j1 rule="hyper" parents="63 26288 26791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26794">
    <literal><![CDATA[
      a(x,(L(y * L(z,u,w),v5,v6) \ (y * L(z,u,w))) \ (y * R(z,u,w)),v7) = a(x,L(y * R(z,u,w),v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(26793(a,1),24014(a,1,2,1))].">
      <j1 rule="para" parents="26793 24014"/>
    </justification>
  </clause>

  <clause id="26795">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ a(x,x,L(L(y,z,u),w,v5)) = L(a(x,x,y) \ a(x,x,L(y,w,v5)),z,u)
    ]]></literal>
    <justification jstring="[para(26260(a,2),26792(a,2,1,2))].">
      <j1 rule="para" parents="26260 26792"/>
    </justification>
  </clause>

  <clause id="26796">
    <literal><![CDATA[
      L(a(x,y,y * L(y,x,z)) \ y,x,L(y,x,z) \ y) = ((L(y,x,z) \ y) * x) \ (a(z,x,y) * (x * y))
    ]]></literal>
    <justification jstring="[para(14939(a,1),26179(a,1,1,1))].">
      <j1 rule="para" parents="14939 26179"/>
    </justification>
  </clause>

  <clause id="26797">
    <literal><![CDATA[
      a((L(x,y,z) * T(u,T(R(x,y,z),w))) * v5,v6,v7) = a((u * R(x,y,z)) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(23955,a,26400,a),flip(a)].">
      <j1 rule="hyper" parents="23955 26400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26799">
    <literal><![CDATA[
      a((L(x,y,z) * T(u,R(T(x,w),y,z))) * v5,v6,v7) = a((u * R(x,y,z)) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(27(a,2),26797(a,1,1,1,2,2))].">
      <j1 rule="para" parents="27 26797"/>
    </justification>
  </clause>

  <clause id="26800">
    <literal><![CDATA[
      a((L(x,y,z) * T(u,T(x,w))) * v5,v6,v7) = a((u * R(x,y,z)) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(19951(a,1),26799(a,1,1,1,2))].">
      <j1 rule="para" parents="19951 26799"/>
    </justification>
  </clause>

  <clause id="26802">
    <literal><![CDATA[
      a(T(x * L(y,z,u),K(y,w)) * v5,v6,v7) = a((x * R(y,z,u)) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(21356(a,2),26800(a,1,1,1))].">
      <j1 rule="para" parents="21356 26800"/>
    </justification>
  </clause>

  <clause id="26803">
    <literal><![CDATA[
      a((x * R(y,z,u)) * w,v5,v6) = a((x * L(y,z,u)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(23955,a,26802,a),flip(a)].">
      <j1 rule="hyper" parents="23955 26802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26804">
    <literal><![CDATA[
      a(((R(x,y,z) \ u) * L(x,y,z)) * w,v5,v6) = a(u * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(23968,a,26803,a),flip(a)].">
      <j1 rule="hyper" parents="23968 26803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26806">
    <literal><![CDATA[
      a(R(x,y,z) * u,w,v5) = a(L(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(187(a,1),26804(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="187 26804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26807">
    <literal><![CDATA[
      a(L(x,y,y) * y,z,u) = a(x * ((x \ (x / y)) \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,25504,a(flip),b,26806,a),flip(a)].">
      <j1 rule="hyper" parents="63 25504 26806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26808">
    <literal><![CDATA[
      a(R(L(x,y,z),u,w) * T(v5,x),v6,v7) = a(v5 * L(L(x,u,w),y,z),v6,v7)
    ]]></literal>
    <justification jstring="[para(22025(a,1),26806(a,2,1))].">
      <j1 rule="para" parents="22025 26806"/>
    </justification>
  </clause>

  <clause id="26809">
    <literal><![CDATA[
      a(L(x * y,x,x),z,u) = a(y * ((y \ (y / x)) \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(25197,a,26807,a)].">
      <j1 rule="hyper" parents="25197 26807"/>
    </justification>
  </clause>

  <clause id="26810">
    <literal><![CDATA[
      a(L(x * y,x,x),z,u) = a(y * ((y \ (x \ y)) \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,24657,a(flip),b,26809,a),flip(a)].">
      <j1 rule="hyper" parents="347 24657 26809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26811">
    <literal><![CDATA[
      a(L(R(x,y,z),u,w) * T(v5,x),v6,v7) = a(v5 * L(L(x,y,z),u,w),v6,v7)
    ]]></literal>
    <justification jstring="[para(29(a,1),26808(a,1,1,1))].">
      <j1 rule="para" parents="29 26808"/>
    </justification>
  </clause>

  <clause id="26812">
    <literal><![CDATA[
      a(x * L(R(y,z,u),w,v5),v6,v7) = a(x * L(L(y,z,u),w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(20691(a,1),26811(a,1,1))].">
      <j1 rule="para" parents="20691 26811"/>
    </justification>
  </clause>

  <clause id="26813">
    <literal><![CDATA[
      (x / y) * (y * ((y * (y \ x)) \ L(y * (y \ x),z,u))) = x * (y \ ((x / y) \ L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(22984(a,1),26773(a,2,2,2))].">
      <j1 rule="para" parents="22984 26773"/>
    </justification>
  </clause>

  <clause id="26814">
    <literal><![CDATA[
      (x / y) * (y * ((y * (y \ x)) \ L(y * (y \ x),z,u))) = x * L(x \ L(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[para(26094(a,1),26813(a,2,2))].">
      <j1 rule="para" parents="26094 26813"/>
    </justification>
  </clause>

  <clause id="26815">
    <literal><![CDATA[
      (x / y) * (y * (x \ L(y * (y \ x),z,u))) = x * L(x \ L(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),26814(a,1,2,2,1))].">
      <j1 rule="para" parents="10 26814"/>
    </justification>
  </clause>

  <clause id="26816">
    <literal><![CDATA[
      (x / y) * (y * (x \ L(x,z,u))) = x * L(x \ L(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),26815(a,1,2,2,2,1))].">
      <j1 rule="para" parents="10 26815"/>
    </justification>
  </clause>

  <clause id="26818">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * T(y / x,x) = y * L(y \ L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,23317,a,b,26816,a)].">
      <j1 rule="hyper" parents="63 23317 26816"/>
    </justification>
  </clause>

  <clause id="26819">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * (x \ y) = y * L(y \ L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(113(a,1),26818(a,1,2))].">
      <j1 rule="para" parents="113 26818"/>
    </justification>
  </clause>

  <clause id="26820">
    <literal><![CDATA[
      L(x,y,y) * L(L(x,y,y) \ L(L(x,y,y),z,u),y,y) = (y * (L(x,y,y) \ L(L(x,y,y),z,u))) * ((y \ 1) * x)
    ]]></literal>
    <justification jstring="[para(3202(a,1),26819(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3202 26819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26821">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w) \ v5,x * L(x,y,z),x \ L(x,y,z)) = v5 * (L(x \ L(x,y,z),u,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(26252,a,26476,a)].">
      <j1 rule="hyper" parents="26252 26476"/>
    </justification>
  </clause>

  <clause id="26822">
    <literal><![CDATA[
      (1 \ 1) * ((a(x,y,z) * (z * y)) * x) = (z * y) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(25489(a,1),26140(a,1,1,1))].">
      <j1 rule="para" parents="25489 26140"/>
    </justification>
  </clause>

  <clause id="26823">
    <literal><![CDATA[
      1 * ((a(x,y,z) * (z * y)) * x) = (z * y) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(66(a,1),26822(a,1,1))].">
      <j1 rule="para" parents="66 26822"/>
    </justification>
  </clause>

  <clause id="26826">
    <literal><![CDATA[
      1 * ((x * (y * a(z,y,x))) * z) = (x * y) * R(z,y,x)
    ]]></literal>
    <justification jstring="[para(20597(a,1),26823(a,1,2,1))].">
      <j1 rule="para" parents="20597 26823"/>
    </justification>
  </clause>

  <clause id="26827">
    <literal><![CDATA[
      (x * (y * a(z,y,x))) * z = (x * y) * R(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(135,a,26826,a)].">
      <j1 rule="hyper" parents="135 26826"/>
    </justification>
  </clause>

  <clause id="26828">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * v5) \ (v5 * a(x,y,z)) = v5 \ (L(a(x,y,z),u,w) \ (v5 * a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(26291(a,1),26302(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="26291 26302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26829">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * v5) \ (v5 * a(x,y,z)) = v5 \ (a(x,y,z) * (L(a(x,y,z),u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(19976(a,1),26828(a,2,2))].">
      <j1 rule="para" parents="19976 26828"/>
    </justification>
  </clause>

  <clause id="26831">
    <literal><![CDATA[
      a(x,((y / ((z \ 1) \ 1)) * L(z,z \ 1,u)) * w,v5) = a(x,(y * ((z \ 1) * L(z \ 1,z,u))) * w,v5)
    ]]></literal>
    <justification jstring="[para(3188(a,1),26668(a,2,2,1,2,2))].">
      <j1 rule="para" parents="3188 26668"/>
    </justification>
  </clause>

  <clause id="26832">
    <literal><![CDATA[
      a(x,((y / ((z \ 1) \ 1)) * L(z,z \ 1,u)) * w,v5) = a(x,w * ((z * L(z \ 1,z,u)) * y),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,25740,a(flip),b,26831,a),flip(a)].">
      <j1 rule="hyper" parents="347 25740 26831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26833">
    <literal><![CDATA[
      a(x,((y / ((z \ 1) \ 1)) * L(z,z \ 1,u)) * w,v5) = a(x,w * ((z \ L(z,z,u)) * y),v5)
    ]]></literal>
    <justification jstring="[para(3343(a,1),26832(a,2,2,2,1))].">
      <j1 rule="para" parents="3343 26832"/>
    </justification>
  </clause>

  <clause id="26834">
    <literal><![CDATA[
      a(x,(L(y * L(z,u,w),v5,v6) \ (y * L(z,u,w))) \ (y * L(z,u,w)),v7) = a(x,L(y * R(z,u,w),v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(25158,a,26794,a)].">
      <j1 rule="hyper" parents="25158 26794"/>
    </justification>
  </clause>

  <clause id="26835">
    <literal><![CDATA[
      a(x,L(y * R(z,u,w),v5,v6),v7) != v8
    ]]></literal>
    <literal><![CDATA[
      a(x,L(y * L(z,u,w),v5,v6),v7) = v8
    ]]></literal>
    <justification jstring="[para(26834(a,1),23998(a,1))].">
      <j1 rule="para" parents="26834 23998"/>
    </justification>
  </clause>

  <clause id="26836">
    <literal><![CDATA[
      a(x,L((y \ 1) * L(z,u,w),v5,v6),v7) = a(x,L(R(z,u,w) * y,v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(26835,a,25029,a)].">
      <j1 rule="hyper" parents="26835 25029"/>
    </justification>
  </clause>

  <clause id="26837">
    <literal><![CDATA[
      L(L(T(x,y),z,u) \ x,T(x,y),z) \ (L(T(x,y),z,u) \ x) = a(u,z,x) \ (L(T(x,y),z,u) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(24067(a,1),26174(a,2,1))].">
      <j1 rule="para" parents="24067 26174"/>
    </justification>
  </clause>

  <clause id="26838">
    <literal><![CDATA[
      L(L(T(x,y),z,u) \ x,T(x,y),z) \ (L(T(x,y),z,u) \ x) = a(u,z,x) \ (L(x,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(19964(a,1),26837(a,2,2))].">
      <j1 rule="para" parents="19964 26837"/>
    </justification>
  </clause>

  <clause id="26840">
    <literal><![CDATA[
      L(L(T(x,y),z,u) \ x,T(x,y),z) \ (L(T(x,y),z,u) \ x) = a(u,z,x) * (x \ L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,26429,a(flip),b,26838,a),flip(a)].">
      <j1 rule="hyper" parents="347 26429 26838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26842">
    <literal><![CDATA[
      L(L(T(x,y),z,u) \ x,x,z) \ (L(T(x,y),z,u) \ x) = a(u,z,x) * (x \ L(x,z,u))
    ]]></literal>
    <justification jstring="[para(21616(a,1),26840(a,1,1))].">
      <j1 rule="para" parents="21616 26840"/>
    </justification>
  </clause>

  <clause id="26843">
    <literal><![CDATA[
      a(x,y,y \ L(T(y,z),x,u)) = a(u,x,y) * (y \ L(y,x,u))
    ]]></literal>
    <justification jstring="[hyper(26233,a,26842,a)].">
      <j1 rule="hyper" parents="26233 26842"/>
    </justification>
  </clause>

  <clause id="26845">
    <literal><![CDATA[
      a(x,y,z) * (z \ L(z,y,x)) = a(y,z,z \ L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(24345,a,26843,a),flip(a)].">
      <j1 rule="hyper" parents="24345 26843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26846">
    <literal><![CDATA[
      a(x,y,z) * (z \ L(z,y,x)) = a(y,z,z * L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,14977,a(flip),b,26845,a),flip(a)].">
      <j1 rule="hyper" parents="347 14977 26845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26847">
    <literal><![CDATA[
      L(x,y,z) * (x \ a(z,y,x)) = a(y,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(21438,a,26846,a)].">
      <j1 rule="hyper" parents="21438 26846"/>
    </justification>
  </clause>

  <clause id="26848">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ a(z,y,x) = a(y,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,26426,a,b,26846,a)].">
      <j1 rule="hyper" parents="63 26426 26846"/>
    </justification>
  </clause>

  <clause id="26849">
    <literal><![CDATA[
      L(x,y,z) * (x \ a(z,y,x)) = a(x,a(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,26754,a(flip),b,26847,a),flip(a)].">
      <j1 rule="hyper" parents="347 26754 26847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26850">
    <literal><![CDATA[
      x * a(x,a(y,z,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,z,y) * a(y,z,x) = u
    ]]></literal>
    <justification jstring="[para(26849(a,1),1413(a,1,2))].">
      <j1 rule="para" parents="26849 1413"/>
    </justification>
  </clause>

  <clause id="26851">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ a(z,y,x) = a(x,a(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,26754,a(flip),b,26848,a),flip(a)].">
      <j1 rule="hyper" parents="347 26754 26848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26852">
    <literal><![CDATA[
      (L(x,y,z) \ x) * a(y,x,a(z,y,x)) = a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,26592,a(flip),b,26851,a)].">
      <j1 rule="hyper" parents="134 26592 26851"/>
    </justification>
  </clause>

  <clause id="26853">
    <literal><![CDATA[
      L(x,y,z) * a(z,y,x) = L(x,a(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(26850,a,26654,a)].">
      <j1 rule="hyper" parents="26850 26654"/>
    </justification>
  </clause>

  <clause id="26854">
    <literal><![CDATA[
      a(x,a(x,y,z),z * y) = L(x,a(z,y,x),y) \ x
    ]]></literal>
    <justification jstring="[para(26853(a,1),26789(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26853 26789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26855">
    <literal><![CDATA[
      a(x,a(x,y,z),z * y) = a(y,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,26660,a(flip),b,26854,a),flip(a)].">
      <j1 rule="hyper" parents="347 26660 26854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26856">
    <literal><![CDATA[
      a(x * y,z,a(z,x,y)) = a(x,z,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(26620,a,26855,a)].">
      <j1 rule="hyper" parents="26620 26855"/>
    </justification>
  </clause>

  <clause id="26857">
    <literal><![CDATA[
      ((x * y) * z) \ (L(x * y,a(z,y,x),z) * (z * a(z,y,x))) = L(a(y,z,a(x,y,z)) \ a(z,y,x),z,x * y)
    ]]></literal>
    <justification jstring="[para(26855(a,1),25479(a,2,1,1))].">
      <j1 rule="para" parents="26855 25479"/>
    </justification>
  </clause>

  <clause id="26858">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ a(x,y,z) = a(y,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,26304,a,b,26856,a)].">
      <j1 rule="hyper" parents="63 26304 26856"/>
    </justification>
  </clause>

  <clause id="26859">
    <literal><![CDATA[
      (x \ R(x,y,z)) * a(x,a(z,y,x),y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,26592,a,b,26858,a)].">
      <j1 rule="hyper" parents="134 26592 26858"/>
    </justification>
  </clause>

  <clause id="26860">
    <literal><![CDATA[
      a(x * y,z,a(z,y,x)) = a(z,a(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(26333,a,26859,a)].">
      <j1 rule="hyper" parents="26333 26859"/>
    </justification>
  </clause>

  <clause id="26861">
    <literal><![CDATA[
      R(x,y,z) * (x \ a(x,a(z,y,x),y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(25407,a,26859,a)].">
      <j1 rule="hyper" parents="25407 26859"/>
    </justification>
  </clause>

  <clause id="26862">
    <literal><![CDATA[
      (x * y) \ (((x * y) * z) * a(z,y,x)) = a(z,a(x,y,z),y) * (z * a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(133,a,26860,a(flip),b,14723,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 26860 14723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26863">
    <literal><![CDATA[
      a((x * y) \ L(x,y,y),z,u) = R(y \ 1,z,u) * ((y \ 1) \ a(y \ 1,a(u,z,y \ 1),z))
    ]]></literal>
    <justification jstring="[hyper(347,a,25193,a,b,26861,a)].">
      <j1 rule="hyper" parents="347 25193 26861"/>
    </justification>
  </clause>

  <clause id="26864">
    <literal><![CDATA[
      R(x,y,z) = (a(x,a(z,y,x),y) / x) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,26861,a(flip),b,20110,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 26861 20110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26865">
    <literal><![CDATA[
      R(x,y,L(z \ a(z,a(u,w,z),w),R(z,w,u),v5) * (v5 * R(z,w,u))) = R(x,y,v5 * a(z,w,u))
    ]]></literal>
    <justification jstring="[para(26861(a,1),20639(a,2,3,2))].">
      <j1 rule="para" parents="26861 20639"/>
    </justification>
  </clause>

  <clause id="26866">
    <literal><![CDATA[
      L(x,y,z * (L(u,w,v5) * (u \ a(u,a(v5,w,u),w)))) = L(x,y,z * a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(26861(a,1),22875(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="26861 22875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26867">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * (z \ a(z,a(w,u,z),u))) * v5) = a(x,y,a(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(26861(a,1),25279(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="26861 25279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26868">
    <literal><![CDATA[
      (a(x,a(y,z * (((u * w) * v5) * w),x),z * (w * ((w * u) * v5))) / x) \ a(x,z * (((u * w) * v5) * w),y) = R(x,z * (((u * w) * v5) * w),y)
    ]]></literal>
    <justification jstring="[para(24407(a,1),26864(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="24407 26864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26869">
    <literal><![CDATA[
      (x * y) \ ((x * y) * R(z,y,x)) = a(z,a(x,y,z),y) * (z * a(z,y,x))
    ]]></literal>
    <justification jstring="[para(18788(a,1),26862(a,1,2))].">
      <j1 rule="para" parents="18788 26862"/>
    </justification>
  </clause>

  <clause id="26870">
    <literal><![CDATA[
      R(x,y,z) = a(x,a(z,y,x),y) * (x * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(358,a,26869,a),flip(a)].">
      <j1 rule="hyper" parents="358 26869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26872">
    <literal><![CDATA[
      L(x,y,z * (a(u,w,v5) \ 1)) = L(x,y,z * a(v5,w,u))
    ]]></literal>
    <justification jstring="[para(26768(a,1),26866(a,1,3,2))].">
      <j1 rule="para" parents="26768 26866"/>
    </justification>
  </clause>

  <clause id="26873">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) \ 1) * v5) = a(x,y,a(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[para(26768(a,1),26867(a,1,3,1))].">
      <j1 rule="para" parents="26768 26867"/>
    </justification>
  </clause>

  <clause id="26874">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(w,u,z) * v5) = v6
    ]]></literal>
    <justification jstring="[para(26873(a,1),24449(a,1))].">
      <j1 rule="para" parents="26873 24449"/>
    </justification>
  </clause>

  <clause id="26875">
    <literal><![CDATA[
      a(x,x,a(y,z,x) * u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(26874,a,26274,a)].">
      <j1 rule="hyper" parents="26874 26274"/>
    </justification>
  </clause>

  <clause id="26876">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * v5) = a(x,y,v5 * a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(26874,a,24069,a)].">
      <j1 rule="hyper" parents="26874 24069"/>
    </justification>
  </clause>

  <clause id="26877">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * (a(w,u,z) \ v5)) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24068,a(flip),b,26876,a),flip(a)].">
      <j1 rule="hyper" parents="347 24068 26876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26878">
    <literal><![CDATA[
      a(x,a(x,y,z),x * a(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,26715,a(flip),b,26876,a),flip(a)].">
      <j1 rule="hyper" parents="63 26715 26876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26880">
    <literal><![CDATA[
      a(x,y,y) * ((z \ a(z,z,y * a(y,y,x))) * y) = z \ (y * a(x,y,y))
    ]]></literal>
    <justification jstring="[para(26876(a,1),26630(a,1,2,1,2))].">
      <j1 rule="para" parents="26876 26630"/>
    </justification>
  </clause>

  <clause id="26882">
    <literal><![CDATA[
      a(x,y,y) * ((z \ a(z,z,R(y,y,x))) * y) = z \ (y * a(x,y,y))
    ]]></literal>
    <justification jstring="[para(18990(a,1),26880(a,1,2,1,2,3))].">
      <j1 rule="para" parents="18990 26880"/>
    </justification>
  </clause>

  <clause id="26883">
    <literal><![CDATA[
      a(x,y,y) * ((z \ a(z,z,L(y,y,x))) * y) = z \ (y * a(x,y,y))
    ]]></literal>
    <justification jstring="[para(24889(a,1),26882(a,1,2,1,2))].">
      <j1 rule="para" parents="24889 26882"/>
    </justification>
  </clause>

  <clause id="26884">
    <literal><![CDATA[
      a((x * y) \ L(x,y,y),z,u) = R(y \ 1,z,u) * ((y \ 1) \ a(y \ 1,a(u,z,y),z))
    ]]></literal>
    <justification jstring="[para(14922(a,1),26863(a,2,2,2,2))].">
      <j1 rule="para" parents="14922 26863"/>
    </justification>
  </clause>

  <clause id="26885">
    <literal><![CDATA[
      a((x * y) \ L(x,y,y),z,u) = R(y \ 1,z,u) * ((y \ 1) \ a(y,a(u,z,y),z))
    ]]></literal>
    <justification jstring="[para(23507(a,1),26884(a,2,2,2))].">
      <j1 rule="para" parents="23507 26884"/>
    </justification>
  </clause>

  <clause id="26886">
    <literal><![CDATA[
      a((x * y) \ L(x,y,y),z,u) = R(y \ 1,z,u) * L(T(y,y \ 1),a(u,z,y),z)
    ]]></literal>
    <justification jstring="[para(26658(a,2),26885(a,2,2))].">
      <j1 rule="para" parents="26658 26885"/>
    </justification>
  </clause>

  <clause id="26887">
    <literal><![CDATA[
      a((x * y) \ L(x,y,y),z,u) = L(y,a(u,z,y),z) * R(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,20190,a(flip),b,26886,a),flip(a)].">
      <j1 rule="hyper" parents="347 20190 26886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26888">
    <literal><![CDATA[
      L(x,a(y,z,x),z) * R(x \ 1,z,y) = a(x \ 1,z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,25193,a(flip),b,26887,a),flip(a)].">
      <j1 rule="hyper" parents="63 25193 26887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26889">
    <literal><![CDATA[
      x * R(x \ 1,x,y) = a(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(12630(a,1),26888(a,1,1))].">
      <j1 rule="para" parents="12630 26888"/>
    </justification>
  </clause>

  <clause id="26891">
    <literal><![CDATA[
      a(x,y * (L(z,a(u,w,z),w) * L(z \ 1,w,u)),v5) = a(x,y * a(z \ 1,w,u),v5)
    ]]></literal>
    <justification jstring="[para(26888(a,1),25135(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="26888 25135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26892">
    <literal><![CDATA[
      (x / (y * x)) * y = a(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(869,a,26889,a)].">
      <j1 rule="hyper" parents="869 26889"/>
    </justification>
  </clause>

  <clause id="26893">
    <literal><![CDATA[
      a(x \ 1,x,y) / x = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,26889,a(flip),b,746,a)].">
      <j1 rule="hyper" parents="131 26889 746"/>
    </justification>
  </clause>

  <clause id="26894">
    <literal><![CDATA[
      (x / (y * x)) \ a(y \ 1,y,x) = y
    ]]></literal>
    <justification jstring="[hyper(128,a,26889,a(flip),b,867,a)].">
      <j1 rule="hyper" parents="128 26889 867"/>
    </justification>
  </clause>

  <clause id="26895">
    <literal><![CDATA[
      a(a(x \ 1,x,y) * z,u,w) = a(a(x,x,y * x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(26889(a,1),24658(a,1,1,1))].">
      <j1 rule="para" parents="26889 24658"/>
    </justification>
  </clause>

  <clause id="26896">
    <literal><![CDATA[
      L(x,y,z) * (x \ (u / (L(x,y,z) * u))) = a(L(x,y,z) \ 1,L(x,y,z),u) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,26892,a(flip),b,20681,a),flip(a)].">
      <j1 rule="hyper" parents="131 26892 20681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26897">
    <literal><![CDATA[
      R(x,(((y * z) \ z) * y) \ u,w) = R(x,a(y \ 1,y,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(26892(a,1),22471(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="26892 22471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26898">
    <literal><![CDATA[
      a(x \ 1,x,y) * a(y / (x * y),y / (x * y),a(x \ 1,x,y)) = ((y / (x * y)) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(128,a,26894,a(flip),b,15291,a),flip(a)].">
      <j1 rule="hyper" parents="128 26894 15291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26899">
    <literal><![CDATA[
      a(x,y * (L(z,a(u,w,z),w) * L(z,w,u)),v5) = a(x,y * a(z \ 1,w,u),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24923,a(flip),b,26891,a)].">
      <j1 rule="hyper" parents="63 24923 26891"/>
    </justification>
  </clause>

  <clause id="26900">
    <literal><![CDATA[
      a(x,y * (z * (a(u,w,z) \ z)),v5) = a(x,y * a(z \ 1,w,u),v5)
    ]]></literal>
    <justification jstring="[para(26767(a,1),26899(a,1,2,2))].">
      <j1 rule="para" parents="26767 26899"/>
    </justification>
  </clause>

  <clause id="26901">
    <literal><![CDATA[
      a(x,y * a(z \ 1,u,w),v5) = a(x,a(w,u,z) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24684,a(flip),b,26900,a),flip(a)].">
      <j1 rule="hyper" parents="63 24684 26900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26907">
    <literal><![CDATA[
      a(x \ 1,x,y) * a(y / (x * y),y / (x * y),a(x,x,y)) = ((y / (x * y)) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(25006(a,1),26898(a,1,2))].">
      <j1 rule="para" parents="25006 26898"/>
    </justification>
  </clause>

  <clause id="26908">
    <literal><![CDATA[
      a(x \ 1,x,y) * a(y / (x * y),(x * y) \ y,a(x,x,y)) = ((y / (x * y)) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(24023(a,1),26907(a,1,2))].">
      <j1 rule="para" parents="24023 26907"/>
    </justification>
  </clause>

  <clause id="26909">
    <literal><![CDATA[
      a(x \ 1,x,y) * a(y / (x * y),y \ (x \ y),a(x,x,y)) = ((y / (x * y)) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(24742(a,1),26908(a,1,2))].">
      <j1 rule="para" parents="24742 26908"/>
    </justification>
  </clause>

  <clause id="26910">
    <literal><![CDATA[
      a(x \ 1,x,y) * a((x * y) \ y,y \ (x \ y),a(x,x,y)) = ((y / (x * y)) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(23893(a,1),26909(a,1,2))].">
      <j1 rule="para" parents="23893 26909"/>
    </justification>
  </clause>

  <clause id="26911">
    <literal><![CDATA[
      a(x \ 1,x,y) * a(y \ (x \ y),y \ (x \ y),a(x,x,y)) = ((y / (x * y)) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(25200(a,1),26910(a,1,2))].">
      <j1 rule="para" parents="25200 26910"/>
    </justification>
  </clause>

  <clause id="26912">
    <literal><![CDATA[
      ((x / (y * x)) \ 1) \ y = a(y \ 1,y,x) * 1
    ]]></literal>
    <justification jstring="[para(26637(a,1),26911(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26637 26911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26913">
    <literal><![CDATA[
      ((x / (y * x)) \ 1) \ y = a(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,8,a(flip),b,26912,a),flip(a)].">
      <j1 rule="hyper" parents="347 8 26912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26915">
    <literal><![CDATA[
      R(x,y,L(z \ a(z,a(u,w,z),w),L(z,w,u),v5) * (v5 * R(z,w,u))) = R(x,y,v5 * a(z,w,u))
    ]]></literal>
    <justification jstring="[para(21974(a,1),26865(a,1,3,1))].">
      <j1 rule="para" parents="21974 26865"/>
    </justification>
  </clause>

  <clause id="26916">
    <literal><![CDATA[
      a(x,y,((y * (z \ u)) \ y) * K(z,w)) \ 1 = (T(z,w) \ u) \ ((x * y) \ (x * (y * (T(z,w) \ u))))
    ]]></literal>
    <justification jstring="[para(9(a,1),26203(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 26203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26918">
    <literal><![CDATA[
      a(x,y,((y * (z \ u)) \ y) * K(z,w)) \ 1 = (T(z,w) \ u) \ L(T(z,w) \ u,y,x)
    ]]></literal>
    <justification jstring="[para(18(a,2),26916(a,2,2))].">
      <j1 rule="para" parents="18 26916"/>
    </justification>
  </clause>

  <clause id="26919">
    <literal><![CDATA[
      T(x,y) \ (z * L(z \ T(x,y),u,w)) = a(w,u,((u * (x \ z)) \ u) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,3354,a(flip),b,26918,a)].">
      <j1 rule="hyper" parents="347 3354 26918"/>
    </justification>
  </clause>

  <clause id="26920">
    <literal><![CDATA[
      a(x,y,((y * (z \ u)) \ y) * K(z,w)) \ 1 = z \ (u * L(u \ z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,22789,a(flip),b,26919,a),flip(a)].">
      <j1 rule="hyper" parents="63 22789 26919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26922">
    <literal><![CDATA[
      a(x,y,(y * (T(z,u) \ w)) \ y) \ 1 = z \ (w * L(w \ z,y,x))
    ]]></literal>
    <justification jstring="[para(21991(a,1),26920(a,1,1,3))].">
      <j1 rule="para" parents="21991 26920"/>
    </justification>
  </clause>

  <clause id="26923">
    <literal><![CDATA[
      a(x,y,y \ ((T(z,u) \ w) \ y)) \ 1 = z \ (w * L(w \ z,y,x))
    ]]></literal>
    <justification jstring="[para(25351(a,1),26922(a,1,1))].">
      <j1 rule="para" parents="25351 26922"/>
    </justification>
  </clause>

  <clause id="26924">
    <literal><![CDATA[
      a(x,y,y \ ((z \ u) \ y)) \ 1 = z \ (u * L(u \ z,y,x))
    ]]></literal>
    <justification jstring="[para(110(a,1),26923(a,1,1,3,2,1,1))].">
      <j1 rule="para" parents="110 26923"/>
    </justification>
  </clause>

  <clause id="26925">
    <literal><![CDATA[
      R(x,y,y) \ (x * L(a(x,y,y),z,u)) = a(u,z,z \ ((R(x,y,y) \ x) \ z)) \ 1
    ]]></literal>
    <justification jstring="[para(13398(a,1),26924(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="13398 26924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26926">
    <literal><![CDATA[
      a(x,y,y \ (a(z,z,u) \ y)) \ 1 = ((z \ 1) * u) \ ((z \ u) * L((z \ u) \ ((z \ 1) * u),y,x))
    ]]></literal>
    <justification jstring="[para(14713(a,1),26924(a,1,1,3,2,1))].">
      <j1 rule="para" parents="14713 26924"/>
    </justification>
  </clause>

  <clause id="26927">
    <literal><![CDATA[
      R(x,y,y) \ (x * L(a(x,y,y),z,u)) = a(u,z,z \ (a(x,y,y) \ z)) \ 1
    ]]></literal>
    <justification jstring="[para(24762(a,1),26925(a,2,1))].">
      <j1 rule="para" parents="24762 26925"/>
    </justification>
  </clause>

  <clause id="26928">
    <literal><![CDATA[
      R(x,y,y) \ (x * a(x,y,L(y,z,u))) = a(u,z,z \ (a(x,y,y) \ z)) \ 1
    ]]></literal>
    <justification jstring="[para(26436(a,2),26927(a,1,2,2))].">
      <j1 rule="para" parents="26436 26927"/>
    </justification>
  </clause>

  <clause id="26929">
    <literal><![CDATA[
      ((x * y) * z) \ (L(x * y,z,a(z,y,x)) * (z * a(z,y,x))) = L(a(y,z,a(x,y,z)) \ a(z,y,x),z,x * y)
    ]]></literal>
    <justification jstring="[para(25493(a,1),26857(a,1,2,1))].">
      <j1 rule="para" parents="25493 26857"/>
    </justification>
  </clause>

  <clause id="26930">
    <literal><![CDATA[
      L(a(x,y,a(z,x,y)) \ a(y,x,z),y,z * x) = ((z * x) * y) \ (((z * x) * y) * a(y,x,z))
    ]]></literal>
    <justification jstring="[para(23241(a,1),26929(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23241 26929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26931">
    <literal><![CDATA[
      L(a(x,y,a(z,x,y)) \ a(y,x,z),y,z * x) = a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,9,a(flip),b,26930,a),flip(a)].">
      <j1 rule="hyper" parents="347 9 26930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26933">
    <literal><![CDATA[
      L(a(x,y,z) * a(y,x,a(x,y,z)),x,z * y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(26559(a,1),26931(a,1,1))].">
      <j1 rule="para" parents="26559 26931"/>
    </justification>
  </clause>

  <clause id="26934">
    <literal><![CDATA[
      L(L(a(x,y,z),x,y),x,z * y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(26292(a,1),26933(a,1,1))].">
      <j1 rule="para" parents="26292 26933"/>
    </justification>
  </clause>

  <clause id="26935">
    <literal><![CDATA[
      L(a(x,y,z),x,y) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(18790,a,26934,a),flip(a)].">
      <j1 rule="hyper" parents="18790 26934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26936">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,26303,a(flip),b,26934,a),flip(a)].">
      <j1 rule="hyper" parents="63 26303 26934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26937">
    <literal><![CDATA[
      x \ (y * R(y \ x,y,z)) = a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,561,a(flip),b,26936,a)].">
      <j1 rule="hyper" parents="347 561 26936"/>
    </justification>
  </clause>

  <clause id="26938">
    <literal><![CDATA[
      (x / y) * R(y,x,z) = x * a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,26936,a,b,4072,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 26936 4072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26939">
    <literal><![CDATA[
      (x * y) * a(y,x,z) = x * R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,26936,a,b,99,a(flip))].">
      <j1 rule="hyper" parents="134 26936 99"/>
    </justification>
  </clause>

  <clause id="26941">
    <literal><![CDATA[
      (x * (1 / y)) * R(L(y,y,x),x,z) = x * a(L(y,y,x),x,z)
    ]]></literal>
    <justification jstring="[para(3282(a,1),26938(a,1,1))].">
      <j1 rule="para" parents="3282 26938"/>
    </justification>
  </clause>

  <clause id="26942">
    <literal><![CDATA[
      x * (y * a(x,y,z)) = R(x,y,z) * y
    ]]></literal>
    <justification jstring="[para(26938(a,1),20930(a,1,2))].">
      <j1 rule="para" parents="26938 20930"/>
    </justification>
  </clause>

  <clause id="26943">
    <literal><![CDATA[
      a(x,y,z) * (y * x) = y * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(20479,a,26939,a)].">
      <j1 rule="hyper" parents="20479 26939"/>
    </justification>
  </clause>

  <clause id="26944">
    <literal><![CDATA[
      (x * y) * a(y,x,z) != x * u
    ]]></literal>
    <literal><![CDATA[
      R(y,x,z) = u
    ]]></literal>
    <justification jstring="[para(26939(a,2),43(a,1))].">
      <j1 rule="para" parents="26939 43"/>
    </justification>
  </clause>

  <clause id="26945">
    <literal><![CDATA[
      x * (a(x,y,z) * y) = R(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(20480,a,26942,a)].">
      <j1 rule="hyper" parents="20480 26942"/>
    </justification>
  </clause>

  <clause id="26946">
    <literal><![CDATA[
      x * (y * (L(y,z,u) \ a(x,L(y,z,u) \ y,y))) = R(x,L(y,z,u) \ y,y) * (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(12372(a,1),26942(a,1,2))].">
      <j1 rule="para" parents="12372 26942"/>
    </justification>
  </clause>

  <clause id="26947">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * (x \ a(L(x,y,z) \ x,x,u)) = (x * R(L(x,y,z) \ x,x,u)) / x
    ]]></literal>
    <justification jstring="[para(26943(a,1),26067(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26943 26067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26948">
    <literal><![CDATA[
      (x * (1 / y)) * L(R(y,x,z),y,x) = x * a(L(y,y,x),x,z)
    ]]></literal>
    <justification jstring="[para(29(a,1),26941(a,1,2))].">
      <j1 rule="para" parents="29 26941"/>
    </justification>
  </clause>

  <clause id="26949">
    <literal><![CDATA[
      x * a(L(y,y,x),x,z) = x * ((1 / y) * R(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(3208,a,26948,a),flip(a)].">
      <j1 rule="hyper" parents="3208 26948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26950">
    <literal><![CDATA[
      x * a(L(y,y,x),x,z) = x * (y \ R(y,x,z))
    ]]></literal>
    <justification jstring="[para(3681(a,1),26949(a,2,2))].">
      <j1 rule="para" parents="3681 26949"/>
    </justification>
  </clause>

  <clause id="26951">
    <literal><![CDATA[
      a(L(x,x,y),y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(626,a,26950,a),flip(a)].">
      <j1 rule="hyper" parents="626 26950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26953">
    <literal><![CDATA[
      T(x,y * (z \ R(z,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(26951(a,1),23047(a,1,2,2))].">
      <j1 rule="para" parents="26951 23047"/>
    </justification>
  </clause>

  <clause id="26954">
    <literal><![CDATA[
      ((x \ R(x,y,z)) * y) \ (y * z) = L(z,y,L(x,x,y))
    ]]></literal>
    <justification jstring="[para(26951(a,1),26502(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="26951 26502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26955">
    <literal><![CDATA[
      T(x,R(y,z,u) * (y \ w)) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,20935,a,b,26953,a)].">
      <j1 rule="hyper" parents="63 20935 26953"/>
    </justification>
  </clause>

  <clause id="26957">
    <literal><![CDATA[
      T(x,R(y,z,u) * w) = T(x,y * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),26955(a,1,2,2))].">
      <j1 rule="para" parents="9 26955"/>
    </justification>
  </clause>

  <clause id="26961">
    <literal><![CDATA[
      a((L(x,y,z) * u) * T(w,x * u),v5,v6) = a(w * (R(x,y,z) * u),v5,v6)
    ]]></literal>
    <justification jstring="[para(26957(a,1),26398(a,1,1,2))].">
      <j1 rule="para" parents="26957 26398"/>
    </justification>
  </clause>

  <clause id="26962">
    <literal><![CDATA[
      ((x \ R(x,x \ L(x,y,z),u)) * (x \ L(x,y,z))) \ ((x \ L(x,y,z)) * u) = L(u,x \ L(x,y,z),L(x,x * L(x,y,z),x))
    ]]></literal>
    <justification jstring="[para(3653(a,2),26954(a,2,3))].">
      <j1 rule="para" parents="3653 26954"/>
    </justification>
  </clause>

  <clause id="26963">
    <literal><![CDATA[
      a(x * (R(y,z,u) * w),v5,v6) = a(x * (L(y,z,u) * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(22945(a,1),26961(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22945 26961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26965">
    <literal><![CDATA[
      a(x * (L(y,z,u) * (y \ a(y,a(u,z,y),z))),w,v5) = a(x * a(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(26861(a,1),26963(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="26861 26963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26966">
    <literal><![CDATA[
      a(x * (a(y,z,u) \ 1),w,v5) = a(x * a(u,z,y),w,v5)
    ]]></literal>
    <justification jstring="[para(26768(a,1),26965(a,1,1,2))].">
      <j1 rule="para" parents="26768 26965"/>
    </justification>
  </clause>

  <clause id="26967">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * (x \ a(L(x,y,z) \ x,x,u)) = (x * L(L(x,y,z) \ x,x,u)) / x
    ]]></literal>
    <justification jstring="[para(25939(a,1),26947(a,2,1,2))].">
      <j1 rule="para" parents="25939 26947"/>
    </justification>
  </clause>

  <clause id="26968">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * (x \ a(L(x,y,z) \ x,x,u)) = L((x * (L(x,y,z) \ x)) / x,x,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,949,a,b,26967,a),flip(a)].">
      <j1 rule="hyper" parents="347 949 26967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26969">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * (x \ a(L(x,y,z) \ x,x,u)) = L(x / L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(20674(a,1),26968(a,2,1))].">
      <j1 rule="para" parents="20674 26968"/>
    </justification>
  </clause>

  <clause id="26970">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * (x \ a(L(x,y,z) \ x,x,u)) = L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[para(3308(a,1),26969(a,2,1))].">
      <j1 rule="para" parents="3308 26969"/>
    </justification>
  </clause>

  <clause id="26971">
    <literal><![CDATA[
      x * (y * (L(y,z,u) \ a(x,y * L(y,z,u),y))) = R(x,L(y,z,u) \ y,y) * (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(14988(a,1),26946(a,1,2,2,2))].">
      <j1 rule="para" parents="14988 26946"/>
    </justification>
  </clause>

  <clause id="26972">
    <literal><![CDATA[
      (x * L(y,z,u)) \ (x * (L(y,z,u) * (y \ L(y,y \ L(y,z,u),x)))) = a(x,y \ L(y,z,u),y) \ 1
    ]]></literal>
    <justification jstring="[para(3163(a,1),26150(a,1,1,2))].">
      <j1 rule="para" parents="3163 26150"/>
    </justification>
  </clause>

  <clause id="26973">
    <literal><![CDATA[
      (x * L(y,z,u)) \ (x * (L(y,z,u) * (y \ L(y,y * L(y,z,u),x)))) = a(x,y \ L(y,z,u),y) \ 1
    ]]></literal>
    <justification jstring="[para(3603(a,1),26972(a,1,2,2,2,2))].">
      <j1 rule="para" parents="3603 26972"/>
    </justification>
  </clause>

  <clause id="26974">
    <literal><![CDATA[
      L(x \ L(x,x * L(x,y,z),u),L(x,y,z),u) = a(u,x \ L(x,y,z),x) \ 1
    ]]></literal>
    <justification jstring="[hyper(545,a,26973,a)].">
      <j1 rule="hyper" parents="545 26973"/>
    </justification>
  </clause>

  <clause id="26975">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),y) \ 1 = y \ L(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(25990,a,26974,a)].">
      <j1 rule="hyper" parents="25990 26974"/>
    </justification>
  </clause>

  <clause id="26977">
    <literal><![CDATA[
      a(x,y * L(y,z,u),y) \ 1 = y \ L(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(24144(a,1),26975(a,1,1))].">
      <j1 rule="para" parents="24144 26975"/>
    </justification>
  </clause>

  <clause id="26978">
    <literal><![CDATA[
      x \ L(x,x * L(x,y,z),u) = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(26579,a,26977,a),flip(a)].">
      <j1 rule="hyper" parents="26579 26977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26979">
    <literal><![CDATA[
      a(x,y,a(T(z * u,K(u,w)),T(z * u,K(u,w)),T(z,T(u,w)))) = a(x,y,a(T(z,T(u,w)),u * T(z,T(u,w)),u))
    ]]></literal>
    <justification jstring="[para(6060(a,2),26368(a,1,3,2))].">
      <j1 rule="para" parents="6060 26368"/>
    </justification>
  </clause>

  <clause id="26980">
    <literal><![CDATA[
      ((a(x,a(y,y,z),z \ (y \ z)) * a(y,y,z)) \ (a(y,y,z) * (z \ (z / y)))) \ (y * x) = ((z / y) \ (z * y)) * x
    ]]></literal>
    <justification jstring="[para(24137(a,1),26531(a,1,1,1,1))].">
      <j1 rule="para" parents="24137 26531"/>
    </justification>
  </clause>

  <clause id="26981">
    <literal><![CDATA[
      L(x,y,y) * L(L(x,y,y) \ L(L(x,y,y),z,u),y,y) = (y * L(x \ L(x,z,u),y,y)) * ((y \ 1) * x)
    ]]></literal>
    <justification jstring="[para(4638(a,1),26820(a,2,1,2))].">
      <j1 rule="para" parents="4638 26820"/>
    </justification>
  </clause>

  <clause id="26982">
    <literal><![CDATA[
      L(x,y,y) * L(L(x,y,y) \ L(L(x,y,y),z,u),y,y) = ((x / y) \ L(x,z,u)) * ((y \ 1) * x)
    ]]></literal>
    <justification jstring="[para(26093(a,1),26981(a,2,1))].">
      <j1 rule="para" parents="26093 26981"/>
    </justification>
  </clause>

  <clause id="26983">
    <literal><![CDATA[
      ((x / y) \ L(x,z,u)) * ((y \ 1) * x) = L(x,y,y) * (x \ L(x,z,u))
    ]]></literal>
    <justification jstring="[para(26085(a,1),26982(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26085 26982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26985">
    <literal><![CDATA[
      a(x,y,a(T(z * u,K(u,w)),T(z * u,K(u,w)),z)) = a(x,y,a(T(z,T(u,w)),u * T(z,T(u,w)),u))
    ]]></literal>
    <justification jstring="[para(14641(a,1),26979(a,1,3))].">
      <j1 rule="para" parents="14641 26979"/>
    </justification>
  </clause>

  <clause id="26987">
    <literal><![CDATA[
      a(x,y,a(T(z * u,K(u,w)),z * u,z)) = a(x,y,a(T(z,T(u,w)),u * T(z,T(u,w)),u))
    ]]></literal>
    <justification jstring="[para(19080(a,1),26985(a,1,3))].">
      <j1 rule="para" parents="19080 26985"/>
    </justification>
  </clause>

  <clause id="26988">
    <literal><![CDATA[
      a(x,y,a(T(z,T(u,w)),u * T(z,T(u,w)),u)) = a(x,y,a(z * u,z * u,z))
    ]]></literal>
    <justification jstring="[para(17838(a,1),26987(a,1,3)),flip(a)].">
      <j1 rule="para" parents="17838 26987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26993">
    <literal><![CDATA[
      a(x,y,a(T(z,T(u,w)),z * u,u)) = a(x,y,a(z * u,z * u,z))
    ]]></literal>
    <justification jstring="[para(24147(a,1),26988(a,1,3))].">
      <j1 rule="para" parents="24147 26988"/>
    </justification>
  </clause>

  <clause id="26994">
    <literal><![CDATA[
      a(x,y,a(z * u,z * u,z)) = a(x,y,a(z,z * u,u))
    ]]></literal>
    <justification jstring="[para(23894(a,1),26993(a,1,3)),flip(a)].">
      <j1 rule="para" parents="23894 26993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26997">
    <literal><![CDATA[
      ((1 * a(x,x,y)) \ (a(x,x,y) * (y \ (y / x)))) \ (x * z) = ((y / x) \ (y * x)) * z
    ]]></literal>
    <justification jstring="[para(26666(a,1),26980(a,1,1,1,1))].">
      <j1 rule="para" parents="26666 26980"/>
    </justification>
  </clause>

  <clause id="26998">
    <literal><![CDATA[
      (a(x,x,y) \ (a(x,x,y) * (y \ (y / x)))) \ (x * z) = ((y / x) \ (y * x)) * z
    ]]></literal>
    <justification jstring="[para(7(a,1),26997(a,1,1,1))].">
      <j1 rule="para" parents="7 26997"/>
    </justification>
  </clause>

  <clause id="27000">
    <literal><![CDATA[
      (x \ (x / y)) \ (y * z) = ((x / y) \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(9(a,1),26998(a,1,1))].">
      <j1 rule="para" parents="9 26998"/>
    </justification>
  </clause>

  <clause id="27001">
    <literal><![CDATA[
      L((x \ (y \ (y / x))) \ z,x \ (y \ (y / x)),x) = ((y / x) \ (y * x)) * z
    ]]></literal>
    <justification jstring="[hyper(946,a,27000,a)].">
      <j1 rule="hyper" parents="946 27000"/>
    </justification>
  </clause>

  <clause id="27003">
    <literal><![CDATA[
      ((x / (y \ x)) \ (x * (y \ x))) * z = (x \ y) \ ((y \ x) * z)
    ]]></literal>
    <justification jstring="[para(80(a,1),27000(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="80 27000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27004">
    <literal><![CDATA[
      (x \ y) \ ((y \ x) * z) = (y \ (x * (y \ x))) * z
    ]]></literal>
    <justification jstring="[para(80(a,1),27003(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="80 27003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27005">
    <literal><![CDATA[
      L((x \ (y \ (y / x))) \ z,x \ (y \ (x \ y)),x) = ((y / x) \ (y * x)) * z
    ]]></literal>
    <justification jstring="[hyper(21875,a,27001,a)].">
      <j1 rule="hyper" parents="21875 27001"/>
    </justification>
  </clause>

  <clause id="27006">
    <literal><![CDATA[
      L((x \ (y \ (y / x))) \ z,a(x,x,y),x) = ((y / x) \ (y * x)) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,23752,a(flip),b,27005,a)].">
      <j1 rule="hyper" parents="63 23752 27005"/>
    </justification>
  </clause>

  <clause id="27007">
    <literal><![CDATA[
      L((x \ (y \ (y / x))) \ z,x,a(x,x,y)) = ((y / x) \ (y * x)) * z
    ]]></literal>
    <justification jstring="[hyper(25494,a,27006,a)].">
      <j1 rule="hyper" parents="25494 27006"/>
    </justification>
  </clause>

  <clause id="27008">
    <literal><![CDATA[
      (x \ (y \ (y / x))) \ z = ((y / x) \ (y * x)) * z
    ]]></literal>
    <justification jstring="[hyper(26320,a,27007,a)].">
      <j1 rule="hyper" parents="26320 27007"/>
    </justification>
  </clause>

  <clause id="27009">
    <literal><![CDATA[
      ((x / y) \ (x * y)) \ z = (y \ (x \ (x / y))) * z
    ]]></literal>
    <justification jstring="[hyper(355,a,27008,a),flip(a)].">
      <j1 rule="hyper" parents="355 27008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27011">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) * (u * (((R(x,y,z) \ 1) \ 1) \ 1)) = (1 * (a(1,x,x) \ R(x,y,z))) * (u * (R(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(4725(a,2),26477(a,1,1))].">
      <j1 rule="para" parents="4725 26477"/>
    </justification>
  </clause>

  <clause id="27012">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) * (u * (R((x \ 1) \ 1,y,z) \ 1)) = (1 * (a(1,x,x) \ R(x,y,z))) * (u * (R(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(4725(a,2),27011(a,1,2,2,1))].">
      <j1 rule="para" parents="4725 27011"/>
    </justification>
  </clause>

  <clause id="27013">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) * (u * (L((x \ 1) \ 1,y,z) \ 1)) = (1 * (a(1,x,x) \ R(x,y,z))) * (u * (R(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,23772,a(flip),b,27012,a)].">
      <j1 rule="hyper" parents="63 23772 27012"/>
    </justification>
  </clause>

  <clause id="27014">
    <literal><![CDATA[
      L(x,y \ a(z,y,u),a(z,y,u)) * R(y \ 1,a(z,y,u),a(z,y,u)) = (x * ((y \ 1) * a(z,y,u))) * (a(z,y,u) \ 1)
    ]]></literal>
    <justification jstring="[para(23247(a,1),26357(a,1,1))].">
      <j1 rule="para" parents="23247 26357"/>
    </justification>
  </clause>

  <clause id="27015">
    <literal><![CDATA[
      R(x / L(1 / y,z,u),y * (L(y,z,u) \ y),y * (L(y,z,u) \ y)) / y = (y * (L(y,z,u) \ y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(3646(a,1),26069(a,1,1,1,2))].">
      <j1 rule="para" parents="3646 26069"/>
    </justification>
  </clause>

  <clause id="27016">
    <literal><![CDATA[
      a(x,L(L(y \ z,u,w),y,y),L(L(L(y \ z,u,w),y,y),v5,v6)) = L(a(x,L(y * z,u,w),L(y * z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(24176(a,1),26442(a,2,1))].">
      <j1 rule="para" parents="24176 26442"/>
    </justification>
  </clause>

  <clause id="27017">
    <literal><![CDATA[
      a(x,L(L(y \ z,u,w),y,y),L(L(L(y \ z,u,w),y,y),v5,v6)) = L(a(x,y * z,y * z),v5,v6)
    ]]></literal>
    <justification jstring="[para(26464(a,1),27016(a,2,1))].">
      <j1 rule="para" parents="26464 27016"/>
    </justification>
  </clause>

  <clause id="27018">
    <literal><![CDATA[
      a(x,L(L(y \ z,u,w),y,y),L(L(L(y \ z,u,w),y,y),v5,v6)) = a(x,y * z,L(y * z,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,26436,a,b,27017,a),flip(a)].">
      <j1 rule="hyper" parents="347 26436 27017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27020">
    <literal><![CDATA[
      a(x,L(y \ z,u,w),L(L(y \ z,u,w),v5,v6)) = a(x,y * z,L(y * z,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,26483,a(flip),b,27018,a)].">
      <j1 rule="hyper" parents="63 26483 27018"/>
    </justification>
  </clause>

  <clause id="27022">
    <literal><![CDATA[
      a(x,y \ z,L(y \ z,u,w)) = a(x,y * z,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,26483,a(flip),b,27020,a)].">
      <j1 rule="hyper" parents="63 26483 27020"/>
    </justification>
  </clause>

  <clause id="27023">
    <literal><![CDATA[
      a(x,y * z,L(y * z,u,w)) * (w * u) = w * (u * (L(z / y,y \ z,x) \ (z / y)))
    ]]></literal>
    <justification jstring="[para(27022(a,1),26444(a,1,1))].">
      <j1 rule="para" parents="27022 26444"/>
    </justification>
  </clause>

  <clause id="27024">
    <literal><![CDATA[
      x * (y * (L(z / u,u \ z,w) \ (z / u))) = x * (y * a(w,u * z,u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,26438,a(flip),b,27023,a),flip(a)].">
      <j1 rule="hyper" parents="63 26438 27023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27025">
    <literal><![CDATA[
      x * (y * (L(z \ u,z \ u,w) \ (z \ u))) = x * (y * a(w,z * u,z * u))
    ]]></literal>
    <justification jstring="[para(21331(a,1),27024(a,1,2,2))].">
      <j1 rule="para" parents="21331 27024"/>
    </justification>
  </clause>

  <clause id="27026">
    <literal><![CDATA[
      x * (y * a(z,u \ w,u \ w)) = x * (y * a(z,u * w,u * w))
    ]]></literal>
    <justification jstring="[para(25425(a,1),27025(a,1,2,2))].">
      <j1 rule="para" parents="25425 27025"/>
    </justification>
  </clause>

  <clause id="27027">
    <literal><![CDATA[
      (K(x,y) * (K(y,x) * a(z,u * w,u * w))) \ (w / u) = L(w / u,u \ w,z)
    ]]></literal>
    <justification jstring="[para(27026(a,1),25500(a,1,1))].">
      <j1 rule="para" parents="27026 25500"/>
    </justification>
  </clause>

  <clause id="27028">
    <literal><![CDATA[
      a(x,y * z,y * z) \ (z / y) = L(z / y,y \ z,x)
    ]]></literal>
    <justification jstring="[para(2784(a,1),27027(a,1,1))].">
      <j1 rule="para" parents="2784 27027"/>
    </justification>
  </clause>

  <clause id="27029">
    <literal><![CDATA[
      a(x,y \ z,y \ z) = a(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(39,a,25499,a,b,27028,a)].">
      <j1 rule="hyper" parents="39 25499 27028"/>
    </justification>
  </clause>

  <clause id="27030">
    <literal><![CDATA[
      a(x,y * z,y * z) * x = R(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(133,a,27029,a(flip),b,13402,a)].">
      <j1 rule="hyper" parents="133 27029 13402"/>
    </justification>
  </clause>

  <clause id="27031">
    <literal><![CDATA[
      a(x,(y * z) * (((y * z) / y) * u),(y * z) * (((y * z) / y) * u)) = a(x,L(y \ u,y,z),(y * z) \ (((y * z) / y) * u))
    ]]></literal>
    <justification jstring="[para(10193(a,1),27029(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10193 27029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27032">
    <literal><![CDATA[
      a(x,((y \ K(y,z)) * u) * (T(y,z) * w),((y \ K(y,z)) * u) * (T(y,z) * w)) = a(x,((y \ 1) * u) \ (y * w),((y \ K(y,z)) * u) \ (T(y,z) * w))
    ]]></literal>
    <justification jstring="[para(21397(a,1),27029(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21397 27029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27034">
    <literal><![CDATA[
      a(x,x * y,x * y) \ 1 = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(27029(a,1),25458(a,1,1))].">
      <j1 rule="para" parents="27029 25458"/>
    </justification>
  </clause>

  <clause id="27035">
    <literal><![CDATA[
      a(x,(y * (z * u)) * (y * (z * L(u,z,y))),(y * (z * u)) * (y * (z * L(u,z,y)))) = a(x,a(y,z,u) \ 1,(y * (z * u)) \ (y * (z * L(u,z,y))))
    ]]></literal>
    <justification jstring="[para(26147(a,1),27029(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26147 27029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27037">
    <literal><![CDATA[
      R(x,y \ z,y \ z) = R(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(13407,a,27030,a),flip(a)].">
      <j1 rule="hyper" parents="13407 27030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27038">
    <literal><![CDATA[
      a(x,y * L(y,z,u),y * L(y,z,u)) * x = L(x,y * L(y,z,u),y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,26248,a(flip),b,27030,a),flip(a)].">
      <j1 rule="hyper" parents="347 26248 27030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27039">
    <literal><![CDATA[
      R(x,y * (z \ y),y * (z \ y)) = R(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(26473,a,27037,a),flip(a)].">
      <j1 rule="hyper" parents="26473 27037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27040">
    <literal><![CDATA[
      a(R(K(x,y) * z,u * w,u * w),v5,v6) = a(L(z,u \ w,u \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(27037(a,1),25184(a,1,1))].">
      <j1 rule="para" parents="27037 25184"/>
    </justification>
  </clause>

  <clause id="27041">
    <literal><![CDATA[
      R(x / L(1 / y,z,u),L(y,z,u),L(y,z,u)) / y = (y * (L(y,z,u) \ y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(27039(a,1),27015(a,1,1))].">
      <j1 rule="para" parents="27039 27015"/>
    </justification>
  </clause>

  <clause id="27044">
    <literal><![CDATA[
      a(L(x,y \ z,y \ z),u,w) = a(L(x,y * z,y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(25188,a,27040,a),flip(a)].">
      <j1 rule="hyper" parents="25188 27040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27045">
    <literal><![CDATA[
      R(x / L(1 / y,z,u),y,y) / y = (y * (L(y,z,u) \ y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(26471(a,1),27041(a,1,1))].">
      <j1 rule="para" parents="26471 27041"/>
    </justification>
  </clause>

  <clause id="27047">
    <literal><![CDATA[
      (x * (L(x,y,z) \ (u * x))) / x = (x * (L(x,y,z) \ x)) * (x \ u)
    ]]></literal>
    <justification jstring="[para(21453(a,1),27045(a,1,1))].">
      <j1 rule="para" parents="21453 27045"/>
    </justification>
  </clause>

  <clause id="27049">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * x)) = u * ((L(x,y,z) \ x) * x)
    ]]></literal>
    <justification jstring="[hyper(26071,a,27047,a),flip(a)].">
      <j1 rule="hyper" parents="26071 27047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27050">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * x)) = u * (x * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[hyper(26068,a,27047,a),flip(a)].">
      <j1 rule="hyper" parents="26068 27047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27051">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * (x \ u) = (u * x) / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(20677,a,27047,a),flip(a)].">
      <j1 rule="hyper" parents="20677 27047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27052">
    <literal><![CDATA[
      ((x * (L(x,y,z) \ x)) \ 1) * (u * (((x * (L(x,y,z) \ x)) \ 1) \ 1)) = (1 / (x * (L(x,y,z) \ x))) * (x * (L(x,y,z) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(27050(a,2),2929(a,2,2))].">
      <j1 rule="para" parents="27050 2929"/>
    </justification>
  </clause>

  <clause id="27053">
    <literal><![CDATA[
      L(x * (a(y,z,u) * (L(a(y,z,u),w,v5) \ a(y,z,u))),a(y,z,u),a(y,z,u)) = (a(y,z,u) \ 1) \ (L(a(y,z,u),w,v5) \ (x * a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(27050(a,1),26379(a,1,1))].">
      <j1 rule="para" parents="27050 26379"/>
    </justification>
  </clause>

  <clause id="27054">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * (x \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,20673,a(flip),b,27051,a),flip(a)].">
      <j1 rule="hyper" parents="347 20673 27051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27055">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * (x \ u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (L(x,y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(27051(a,2),21064(a,1))].">
      <j1 rule="para" parents="27051 21064"/>
    </justification>
  </clause>

  <clause id="27056">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * u = x * (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(134,a,27054,a(flip),b,26072,a),flip(a)].">
      <j1 rule="hyper" parents="134 27054 26072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27057">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * (x \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(3638(a,2),27054(a,1,1))].">
      <j1 rule="para" parents="3638 27054"/>
    </justification>
  </clause>

  <clause id="27058">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * ((x \ u) * K(x * (L(x,y,z) \ u),w)) = T((x * (L(x,y,z) \ x)) * (x \ u),w)
    ]]></literal>
    <justification jstring="[para(27054(a,1),13038(a,1,2,2,1))].">
      <j1 rule="para" parents="27054 13038"/>
    </justification>
  </clause>

  <clause id="27059">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (x \ v5) = x * (L(x,y,a(z,u,w)) \ v5)
    ]]></literal>
    <justification jstring="[para(26372(a,1),27054(a,1,1))].">
      <j1 rule="para" parents="26372 27054"/>
    </justification>
  </clause>

  <clause id="27060">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x \ 1) \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(26026,a,27056,a)].">
      <j1 rule="hyper" parents="26026 27056"/>
    </justification>
  </clause>

  <clause id="27061">
    <literal><![CDATA[
      x * (x * (L(x,y,z) \ ((x \ 1) * u))) = x * ((L(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,26025,a(flip),b,27056,a),flip(a)].">
      <j1 rule="hyper" parents="63 26025 27056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27062">
    <literal><![CDATA[
      L(x,((y \ 1) * (L(y \ 1,z,u) \ (y \ 1))) \ y,(y \ 1) * (L(y \ 1,z,u) \ (y \ 1))) = (y \ 1) * (L(y \ 1,z,u) \ ((((y \ 1) * (L(y \ 1,z,u) \ (y \ 1))) \ (y \ 1)) * x))
    ]]></literal>
    <justification jstring="[hyper(3514,a,27056,a(flip))].">
      <j1 rule="hyper" parents="3514 27056"/>
    </justification>
  </clause>

  <clause id="27063">
    <literal><![CDATA[
      (1 / (x * (L(x,y,z) \ x))) * (x * (x * (L(x,y,z) \ u))) = L(u,x * (L(x,y,z) \ x),(x * (L(x,y,z) \ x)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,27056,a(flip),b,2946,a)].">
      <j1 rule="hyper" parents="134 27056 2946"/>
    </justification>
  </clause>

  <clause id="27064">
    <literal><![CDATA[
      a(x,y,z * (z * (L(z,u,w) \ v5))) = a(x,y,v5 * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(27056(a,1),24562(a,1,3))].">
      <j1 rule="para" parents="27056 24562"/>
    </justification>
  </clause>

  <clause id="27065">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x \ 1) \ u) = (x * (L(x,y,z) \ x)) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,27054,a,b,27060,a),flip(a)].">
      <j1 rule="hyper" parents="347 27054 27060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27066">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ (L(x,y,z) \ u) = (x \ 1) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(128,a,1408,a(flip),b,27060,a)].">
      <j1 rule="hyper" parents="128 1408 27060"/>
    </justification>
  </clause>

  <clause id="27067">
    <literal><![CDATA[
      L(x,y,z) * (L(L(x,y,z),y,z) \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,25964,a,b,27060,a)].">
      <j1 rule="hyper" parents="63 25964 27060"/>
    </justification>
  </clause>

  <clause id="27068">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),u) * u = (x \ 1) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(15295,a,27066,a)].">
      <j1 rule="hyper" parents="15295 27066"/>
    </justification>
  </clause>

  <clause id="27069">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(35,a,15290,a(flip),b,27068,a),flip(a)].">
      <j1 rule="hyper" parents="35 15290 27068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27070">
    <literal><![CDATA[
      (x / y) * L(y,z,a(u,w,v5)) = y * (L(y,z,a(u,w,v5)) \ x)
    ]]></literal>
    <justification jstring="[hyper(21010,a,27059,a)].">
      <j1 rule="hyper" parents="21010 27059"/>
    </justification>
  </clause>

  <clause id="27071">
    <literal><![CDATA[
      L(x * (L(x,y,z) \ u),x,x) = x * ((L(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(3754,a,27061,a)].">
      <j1 rule="hyper" parents="3754 27061"/>
    </justification>
  </clause>

  <clause id="27072">
    <literal><![CDATA[
      x * (L(x,y,z) \ L(u,x,x)) = x * ((L(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(3218(a,1),27061(a,1,2))].">
      <j1 rule="para" parents="3218 27061"/>
    </justification>
  </clause>

  <clause id="27073">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w) \ v5,a(x,y,z),a(x,y,z)) = (L(a(x,y,z),u,w) \ 1) * v5
    ]]></literal>
    <justification jstring="[hyper(22371,a,27071,a)].">
      <j1 rule="hyper" parents="22371 27071"/>
    </justification>
  </clause>

  <clause id="27074">
    <literal><![CDATA[
      L(x,y,z) \ L(u,x,x) = (L(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(626,a,27072,a),flip(a)].">
      <j1 rule="hyper" parents="626 27072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27075">
    <literal><![CDATA[
      L(x,L(y,z,u),L(y,z,u)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(3225,a,27074,a)].">
      <j1 rule="hyper" parents="3225 27074"/>
    </justification>
  </clause>

  <clause id="27077">
    <literal><![CDATA[
      L(x,L(a(y,z,u) \ z,y,u),L(z,u,y)) = L(x,a(y,z,u) \ z,a(y,z,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,25659,a(flip),b,27075,a)].">
      <j1 rule="hyper" parents="63 25659 27075"/>
    </justification>
  </clause>

  <clause id="27078">
    <literal><![CDATA[
      L(x,(1 / y) * z,L(y \ z,y,y \ 1)) = L(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[para(2938(a,1),27075(a,1,2))].">
      <j1 rule="para" parents="2938 27075"/>
    </justification>
  </clause>

  <clause id="27079">
    <literal><![CDATA[
      R(x,y,L(z * L(u,w,v5),u,u)) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y,L(u,w,v5) \ z) = v6
    ]]></literal>
    <justification jstring="[para(27075(a,1),22241(a,1,3))].">
      <j1 rule="para" parents="27075 22241"/>
    </justification>
  </clause>

  <clause id="27081">
    <literal><![CDATA[
      L(x,(1 / y) * z,(1 / y) * z) = L(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[para(2938(a,1),27078(a,1,3))].">
      <j1 rule="para" parents="2938 27078"/>
    </justification>
  </clause>

  <clause id="27082">
    <literal><![CDATA[
      L(x,(1 / y) * z,(y \ 1) * z) = L(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(21515,a,27081,a)].">
      <j1 rule="hyper" parents="21515 27081"/>
    </justification>
  </clause>

  <clause id="27083">
    <literal><![CDATA[
      L(x,(y \ 1) * z,(y \ 1) * z) = L(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(21728,a,27082,a)].">
      <j1 rule="hyper" parents="21728 27082"/>
    </justification>
  </clause>

  <clause id="27084">
    <literal><![CDATA[
      L(x,y * z,(z \ 1) * y) = L(x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(21703,a,27083,a)].">
      <j1 rule="hyper" parents="21703 27083"/>
    </justification>
  </clause>

  <clause id="27085">
    <literal><![CDATA[
      L(x,y * z,y * (z \ 1)) = L(x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(20105,a,27084,a)].">
      <j1 rule="hyper" parents="20105 27084"/>
    </justification>
  </clause>

  <clause id="27086">
    <literal><![CDATA[
      L(x,y * z,z * (y \ 1)) = L(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(21666,a,27085,a)].">
      <j1 rule="hyper" parents="21666 27085"/>
    </justification>
  </clause>

  <clause id="27087">
    <literal><![CDATA[
      L(x,(y \ 1) * z,z * ((y \ 1) \ 1)) = L(x,y \ z,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,3608,a(flip),b,27086,a),flip(a)].">
      <j1 rule="hyper" parents="347 3608 27086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27088">
    <literal><![CDATA[
      (((x \ 1) \ (L(x,y,z) \ 1)) * (x \ 1)) * ((x \ 1) \ u) = u * T(u \ ((x * (L(x,y,z) \ x)) * (x \ u)),x \ 1)
    ]]></literal>
    <justification jstring="[para(27065(a,1),1374(a,2,2,1,2))].">
      <j1 rule="para" parents="27065 1374"/>
    </justification>
  </clause>

  <clause id="27089">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x \ 1) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (L(x,y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(27065(a,2),27055(a,1))].">
      <j1 rule="para" parents="27065 27055"/>
    </justification>
  </clause>

  <clause id="27090">
    <literal><![CDATA[
      L(x,(y \ 1) * z,z * y) = L(x,y \ z,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(21530,a,27087,a)].">
      <j1 rule="hyper" parents="21530 27087"/>
    </justification>
  </clause>

  <clause id="27091">
    <literal><![CDATA[
      L(x,y \ z,(y \ 1) \ z) = L(x,z * y,z * y)
    ]]></literal>
    <justification jstring="[hyper(21703,a,27090,a),flip(a)].">
      <j1 rule="hyper" parents="21703 27090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27092">
    <literal><![CDATA[
      a((x \ 1) \ y,x \ y,z) = L(z,y * x,y * x) \ z
    ]]></literal>
    <justification jstring="[para(27091(a,1),24154(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27091 24154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27093">
    <literal><![CDATA[
      a((x \ 1) \ y,x \ y,z) = a(y * x,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,14600,a(flip),b,27092,a),flip(a)].">
      <j1 rule="hyper" parents="347 14600 27092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27094">
    <literal><![CDATA[
      a(a(x \ y,x \ y,z),u,w) = a(a(y * x,y * x,z),u,w)
    ]]></literal>
    <justification jstring="[para(27093(a,1),26220(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27093 26220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27095">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w) \ v5,a(x,y,z),a(x,y,z)) = L(a(x,y,z) \ 1,u,w) * v5
    ]]></literal>
    <justification jstring="[para(26290(a,2),27073(a,2,1))].">
      <j1 rule="para" parents="26290 27073"/>
    </justification>
  </clause>

  <clause id="27096">
    <literal><![CDATA[
      L(x,a(y,z,u) \ z,a(y,z,u) \ z) = L(x,L(z,u,y),L(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,25514,a(flip),b,27077,a),flip(a)].">
      <j1 rule="hyper" parents="63 25514 27077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27097">
    <literal><![CDATA[
      L(x,a(y,z,u) \ z,a(y,z,u) \ z) = L(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,27075,a(flip),b,27096,a),flip(a)].">
      <j1 rule="hyper" parents="347 27075 27096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27104">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * ((x \ u) * K(u,w)) = T((x * (L(x,y,z) \ x)) * (x \ u),w)
    ]]></literal>
    <justification jstring="[para(23415(a,1),27058(a,1,2,2))].">
      <j1 rule="para" parents="23415 27058"/>
    </justification>
  </clause>

  <clause id="27105">
    <literal><![CDATA[
      T((x * (L(x,y,z) \ x)) * (x \ u),w) = (x * (L(x,y,z) \ x)) * (x \ T(u,w))
    ]]></literal>
    <justification jstring="[para(13045(a,1),27104(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13045 27104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27107">
    <literal><![CDATA[
      T((x * (L(x,y,z) \ x)) * (x \ u),w) = x * (L(x,y,z) \ T(u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,27054,a(flip),b,27105,a),flip(a)].">
      <j1 rule="hyper" parents="347 27054 27105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27108">
    <literal><![CDATA[
      T(x * (L(x,y,z) \ u),w) = x * (L(x,y,z) \ T(u,w))
    ]]></literal>
    <justification jstring="[para(27054(a,1),27107(a,1,1))].">
      <j1 rule="para" parents="27054 27107"/>
    </justification>
  </clause>

  <clause id="27109">
    <literal><![CDATA[
      T(x * (L(x,x,y) \ x),y * x) = 1 / ((L(x,y,x) * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,22643,a,b,27108,a),flip(a)].">
      <j1 rule="hyper" parents="347 22643 27108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27111">
    <literal><![CDATA[
      T(T(x * (L(x,y,z) \ u),w),T(x,u)) = L(x,y,z) \ (T(u,w) * x)
    ]]></literal>
    <justification jstring="[para(27108(a,2),13614(a,1,1))].">
      <j1 rule="para" parents="27108 13614"/>
    </justification>
  </clause>

  <clause id="27112">
    <literal><![CDATA[
      T(x * (L(x,x,y) \ x),y * x) = 1 / (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(21744(a,1),27109(a,2,2))].">
      <j1 rule="para" parents="21744 27109"/>
    </justification>
  </clause>

  <clause id="27113">
    <literal><![CDATA[
      T(x * a(y,x,x),y * x) = 1 / (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(25425(a,1),27112(a,1,1,2))].">
      <j1 rule="para" parents="25425 27112"/>
    </justification>
  </clause>

  <clause id="27114">
    <literal><![CDATA[
      x * (1 / (y \ (x \ y))) = y \ (x * (y * x))
    ]]></literal>
    <justification jstring="[para(27113(a,1),14739(a,1,2))].">
      <j1 rule="para" parents="27113 14739"/>
    </justification>
  </clause>

  <clause id="27115">
    <literal><![CDATA[
      (x \ (y \ x)) \ y = x \ (y * (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,26330,a(flip),b,27114,a)].">
      <j1 rule="hyper" parents="63 26330 27114"/>
    </justification>
  </clause>

  <clause id="27116">
    <literal><![CDATA[
      (x \ y) \ (y * x) = y \ (x * (y * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,25677,a(flip),b,27114,a)].">
      <j1 rule="hyper" parents="63 25677 27114"/>
    </justification>
  </clause>

  <clause id="27117">
    <literal><![CDATA[
      x \ ((x \ y) * (x * (x \ y))) = ((x \ y) \ x) \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),27116(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 27116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27118">
    <literal><![CDATA[
      R(x,((y \ 1) \ (z * (y * z))) \ u,w) = R(x,((z \ y) \ (y * z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(27116(a,2),21192(a,2,2,1))].">
      <j1 rule="para" parents="27116 21192"/>
    </justification>
  </clause>

  <clause id="27119">
    <literal><![CDATA[
      ((x \ y) \ x) \ y = x \ ((x \ y) * y)
    ]]></literal>
    <justification jstring="[para(10(a,1),27117(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 27117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27121">
    <literal><![CDATA[
      R(x,(y \ ((y \ z) * z)) * u,w) = R(x,(y \ (z * (y \ z))) * u,w)
    ]]></literal>
    <justification jstring="[para(27119(a,1),25864(a,1,2,1))].">
      <j1 rule="para" parents="27119 25864"/>
    </justification>
  </clause>

  <clause id="27122">
    <literal><![CDATA[
      T(L(x,y,z) \ (u * x),w) = L(x,y,z) \ (T(u,w) * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,11311,a(flip),b,27111,a)].">
      <j1 rule="hyper" parents="63 11311 27111"/>
    </justification>
  </clause>

  <clause id="27123">
    <literal><![CDATA[
      T(L(x / T(y,z),y,z) \ (y * (x / T(y,z))),z) = ((y * z) \ (z * x)) \ x
    ]]></literal>
    <justification jstring="[hyper(347,a,21346,a(flip),b,27122,a),flip(a)].">
      <j1 rule="hyper" parents="347 21346 27122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27124">
    <literal><![CDATA[
      T(T(a(x,y,z / T(y,x)) * y,z / T(y,x)),x) = ((y * x) \ (x * z)) \ z
    ]]></literal>
    <justification jstring="[para(26509(a,2),27123(a,1,1))].">
      <j1 rule="para" parents="26509 27123"/>
    </justification>
  </clause>

  <clause id="27125">
    <literal><![CDATA[
      T(T(a(x,y,T(y,x) \ z) * y,z / T(y,x)),x) = ((y * x) \ (x * z)) \ z
    ]]></literal>
    <justification jstring="[para(24071(a,1),27124(a,1,1,1,1))].">
      <j1 rule="para" parents="24071 27124"/>
    </justification>
  </clause>

  <clause id="27126">
    <literal><![CDATA[
      T(T(a(x,y,y \ z) * y,z / T(y,x)),x) = ((y * x) \ (x * z)) \ z
    ]]></literal>
    <justification jstring="[para(24073(a,1),27125(a,1,1,1,1))].">
      <j1 rule="para" parents="24073 27125"/>
    </justification>
  </clause>

  <clause id="27128">
    <literal><![CDATA[
      x * T(x \ ((y * (L(y,z,u) \ y)) * (y \ x)),y \ 1) = ((L(y,z,u) \ y) * (y \ 1)) * ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(10873(a,1),27088(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10873 27088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27129">
    <literal><![CDATA[
      x * T(x \ ((y * (L(y,z,u) \ y)) * (y \ x)),y \ 1) = (L(y,z,u) \ 1) * ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(10254(a,1),27128(a,2,1))].">
      <j1 rule="para" parents="10254 27128"/>
    </justification>
  </clause>

  <clause id="27130">
    <literal><![CDATA[
      x * T(L(L(y,z,u) \ y,y,x),y \ 1) = (L(y,z,u) \ 1) * ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(26100(a,1),27129(a,1,2,1))].">
      <j1 rule="para" parents="26100 27129"/>
    </justification>
  </clause>

  <clause id="27131">
    <literal><![CDATA[
      x * L(T(L(y,z,u) \ y,y \ 1),y,x) = (L(y,z,u) \ 1) * ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(25(a,2),27130(a,1,2))].">
      <j1 rule="para" parents="25 27130"/>
    </justification>
  </clause>

  <clause id="27132">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x \ 1) \ u) = u * L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[para(10878(a,1),27131(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10878 27131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27133">
    <literal><![CDATA[
      x * L(L(y,z,u) \ y,y,x) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(27089,a,27132,a),flip(a)].">
      <j1 rule="hyper" parents="27089 27132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27135">
    <literal><![CDATA[
      x * (L(y,z,x) \ y) = y * (L(y,z,x) \ x)
    ]]></literal>
    <justification jstring="[para(25541(a,1),27133(a,1,2))].">
      <j1 rule="para" parents="25541 27133"/>
    </justification>
  </clause>

  <clause id="27136">
    <literal><![CDATA[
      (x * (L(x,y,z) \ z)) * (z * ((L(x,y,z) \ x) / (z * (L(x,y,z) \ x)))) = (z \ 1) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(27135(a,1),19008(a,1,1))].">
      <j1 rule="para" parents="27135 19008"/>
    </justification>
  </clause>

  <clause id="27137">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ y),(y * (L(y,z,u) \ y)) \ 1) = L(1 / y,z,u) * (y * (y * (L(y,z,u) \ x)))
    ]]></literal>
    <justification jstring="[para(3646(a,1),27063(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3646 27063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27138">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ y),(y * (L(y,z,u) \ y)) \ 1) = (1 / y) * (L(y,z,u) * (y * (L(y,z,u) \ x)))
    ]]></literal>
    <justification jstring="[hyper(347,a,22794,a(flip),b,27137,a),flip(a)].">
      <j1 rule="hyper" parents="347 22794 27137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27139">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ y),(y * (L(y,z,u) \ y)) \ 1) = (1 / y) * (y * x)
    ]]></literal>
    <justification jstring="[para(1405(a,1),27138(a,2,2))].">
      <j1 rule="para" parents="1405 27138"/>
    </justification>
  </clause>

  <clause id="27140">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ y),(y * (L(y,z,u) \ y)) \ 1) = L(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,2939,a(flip),b,27139,a),flip(a)].">
      <j1 rule="hyper" parents="347 2939 27139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27142">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ y),L(y \ 1,z,u)) = L(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(4670(a,1),27140(a,1,3))].">
      <j1 rule="para" parents="4670 27140"/>
    </justification>
  </clause>

  <clause id="27143">
    <literal><![CDATA[
      L(x,y * (y * L(y,z,u)),L(y \ 1,z,u)) = L(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(21854,a,27142,a)].">
      <j1 rule="hyper" parents="21854 27142"/>
    </justification>
  </clause>

  <clause id="27144">
    <literal><![CDATA[
      L(x,L(y * (y * y),z,u),L(y \ 1,z,u)) = L(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3372(a,2),27143(a,1,2))].">
      <j1 rule="para" parents="3372 27143"/>
    </justification>
  </clause>

  <clause id="27145">
    <literal><![CDATA[
      L(x,L(y,z,u),L(y \ 1,z,u)) = L(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3522,a,27144,a)].">
      <j1 rule="hyper" parents="3522 27144"/>
    </justification>
  </clause>

  <clause id="27160">
    <literal><![CDATA[
      a(x,(y * z) * (((y * z) / y) * u),(y * z) * (((y * z) / y) * u)) = a(x,L(y \ u,y,z),L(y \ u,y,z))
    ]]></literal>
    <justification jstring="[para(10193(a,1),27031(a,2,3))].">
      <j1 rule="para" parents="10193 27031"/>
    </justification>
  </clause>

  <clause id="27161">
    <literal><![CDATA[
      a(x,(y * z) * (((y * z) / y) * u),(y * z) * (((y * z) / y) * u)) = a(x,y \ u,y \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,26464,a(flip),b,27160,a),flip(a)].">
      <j1 rule="hyper" parents="347 26464 27160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27163">
    <literal><![CDATA[
      a(x,(y * z) * (((y * z) / y) * u),(y * z) * (((y * z) / y) * u)) = a(x,y * u,y * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,27029,a(flip),b,27161,a),flip(a)].">
      <j1 rule="hyper" parents="347 27029 27161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27164">
    <literal><![CDATA[
      a(x,(y * z) * (((y * z) / y) * u),(y * z) * ((y \ (y * z)) * u)) = a(x,y * u,y * u)
    ]]></literal>
    <justification jstring="[hyper(24421,a,27163,a)].">
      <j1 rule="hyper" parents="24421 27163"/>
    </justification>
  </clause>

  <clause id="27165">
    <literal><![CDATA[
      a(x,(y * z) * (((y * z) / y) * u),(y * z) * (z * u)) = a(x,y * u,y * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),27164(a,1,3,2,1))].">
      <j1 rule="para" parents="9 27164"/>
    </justification>
  </clause>

  <clause id="27166">
    <literal><![CDATA[
      a(x,(y * z) * ((y \ (y * z)) * u),(y * z) * (z * u)) = a(x,y * u,y * u)
    ]]></literal>
    <justification jstring="[hyper(24417,a,27165,a)].">
      <j1 rule="hyper" parents="24417 27165"/>
    </justification>
  </clause>

  <clause id="27167">
    <literal><![CDATA[
      a(x,(y * z) * (z * u),(y * z) * (z * u)) = a(x,y * u,y * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),27166(a,1,2,2,1))].">
      <j1 rule="para" parents="9 27166"/>
    </justification>
  </clause>

  <clause id="27168">
    <literal><![CDATA[
      ((x \ L(x,x * L(x,y,z),u)) * (x \ L(x,y,z))) \ ((x \ L(x,y,z)) * u) = L(u,x \ L(x,y,z),L(x,x * L(x,y,z),x))
    ]]></literal>
    <justification jstring="[para(26248(a,1),26962(a,1,1,1,2))].">
      <j1 rule="para" parents="26248 26962"/>
    </justification>
  </clause>

  <clause id="27169">
    <literal><![CDATA[
      L((x * y) \ 1,y,x) * ((L((x * y) \ 1,y,x) \ 1) * z) = (a(L((x * y) \ 1,y,x),(x \ ((x * y) \ 1)) \ x,z) \ 1) * z
    ]]></literal>
    <justification jstring="[para(14971(a,1),26014(a,2,1,1))].">
      <j1 rule="para" parents="14971 26014"/>
    </justification>
  </clause>

  <clause id="27170">
    <literal><![CDATA[
      L((x * y) \ 1,y,x) * ((L((x * y) \ 1,y,x) \ 1) * z) = (a(L((x * y) \ 1,y,x),(((x * y) \ 1) \ x) * x,z) \ 1) * z
    ]]></literal>
    <justification jstring="[para(24531(a,1),27169(a,2,1,1))].">
      <j1 rule="para" parents="24531 27169"/>
    </justification>
  </clause>

  <clause id="27171">
    <literal><![CDATA[
      L((x * y) \ 1,y,x) * ((L((x * y) \ 1,y,x) \ 1) * z) = (a(L((x * y) \ 1,y,x),x * ((x * y) \ x),z) \ 1) * z
    ]]></literal>
    <justification jstring="[para(24484(a,1),27170(a,2,1,1))].">
      <j1 rule="para" parents="24484 27170"/>
    </justification>
  </clause>

  <clause id="27172">
    <literal><![CDATA[
      L((x * y) \ 1,y,x) * ((L((x * y) \ 1,y,x) \ 1) * z) = (a(L((x * y) \ 1,y,x),x * (x \ (y \ x)),z) \ 1) * z
    ]]></literal>
    <justification jstring="[para(24992(a,1),27171(a,2,1,1))].">
      <j1 rule="para" parents="24992 27171"/>
    </justification>
  </clause>

  <clause id="27173">
    <literal><![CDATA[
      L((x * y) \ 1,y,x) * ((L((x * y) \ 1,y,x) \ 1) * z) = (a(L((x * y) \ 1,y,x),y \ x,z) \ 1) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),27172(a,2,1,1,2))].">
      <j1 rule="para" parents="10 27172"/>
    </justification>
  </clause>

  <clause id="27175">
    <literal><![CDATA[
      (1 / x) * (((L(1 / (a(y,z,y) / x),u,w) \ 1) \ v5) * a(y,z,y)) = (v5 * (a(y,z,y) \ x)) / (L(a(y,z,y) / x,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(11849(a,1),26045(a,2,1,2))].">
      <j1 rule="para" parents="11849 26045"/>
    </justification>
  </clause>

  <clause id="27176">
    <literal><![CDATA[
      (1 / x) * (((L(1 / (a(y,z,y) / x),u,w) \ 1) \ v5) * a(y,z,y)) = a(y,z,y) \ ((v5 * x) / (L(a(y,z,y) / x,u,w) \ 1))
    ]]></literal>
    <justification jstring="[hyper(347,a,11909,a(flip),b,27175,a),flip(a)].">
      <j1 rule="hyper" parents="347 11909 27175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27177">
    <literal><![CDATA[
      (1 / x) * (((L(1 / (a(y,z,y) / x),u,w) \ 1) \ v5) * a(y,z,y)) = (v5 * x) / (L(a(y,z,y) / x,u,w) \ a(y,z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,11919,a(flip),b,27176,a),flip(a)].">
      <j1 rule="hyper" parents="347 11919 27176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27178">
    <literal><![CDATA[
      (1 / x) * (((L(1 / (a(y,z,y) / x),u,w) \ 1) \ v5) * a(y,z,y)) = (v5 * x) / (L(1 / x,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(12459(a,1),27177(a,2,2))].">
      <j1 rule="para" parents="12459 27177"/>
    </justification>
  </clause>

  <clause id="27179">
    <literal><![CDATA[
      (1 / x) * (((a(y,z,y) / L(x,u,w)) \ v5) * a(y,z,y)) = (v5 * x) / (L(1 / x,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(12309(a,1),27178(a,1,2,1,1))].">
      <j1 rule="para" parents="12309 27178"/>
    </justification>
  </clause>

  <clause id="27181">
    <literal><![CDATA[
      (x * y) / (L(1 / y,z,u) \ 1) = (1 / y) * ((1 / L(y,z,u)) \ x)
    ]]></literal>
    <justification jstring="[para(11896(a,1),27179(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11896 27179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27182">
    <literal><![CDATA[
      (x * y) / (L(1 / y,z,u) \ 1) = y * ((1 / L(y \ 1,z,u)) \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,22023,a(flip),b,27181,a),flip(a)].">
      <j1 rule="hyper" parents="347 22023 27181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27183">
    <literal><![CDATA[
      (x * y) / (L(1 / y,z,u) \ 1) = y * ((L(1 / y,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(4660(a,1),27182(a,2,2,1))].">
      <j1 rule="para" parents="4660 27182"/>
    </justification>
  </clause>

  <clause id="27184">
    <literal><![CDATA[
      L(a(x,(y * y) * z,L(y,y,z) * z) \ 1,R(y,y,z) * z,y) = (R(y,y,z) * z) \ L(R(y,y,z) * z,y * (R(y,y,z) * z),x)
    ]]></literal>
    <justification jstring="[para(25242(a,1),26213(a,1,1,1))].">
      <j1 rule="para" parents="25242 26213"/>
    </justification>
  </clause>

  <clause id="27185">
    <literal><![CDATA[
      L(x \ 1,y,z) * (u * (((x * (L(x,y,z) \ x)) \ 1) \ 1)) = (1 / (x * (L(x,y,z) \ x))) * (x * (L(x,y,z) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(4670(a,1),27052(a,1,1))].">
      <j1 rule="para" parents="4670 27052"/>
    </justification>
  </clause>

  <clause id="27186">
    <literal><![CDATA[
      (1 / (x * (L(x,y,z) \ x))) * (x * (L(x,y,z) \ (u * x))) = L(x \ 1,y,z) * (u * (L(x \ 1,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(4670(a,1),27185(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4670 27185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27187">
    <literal><![CDATA[
      L(x \ 1,y,z) * (u * (L(x \ 1,y,z) \ 1)) = L(1 / x,y,z) * (x * (L(x,y,z) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(3646(a,1),27186(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3646 27186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27188">
    <literal><![CDATA[
      L(x \ 1,y,z) * (u * (L(x \ 1,y,z) \ 1)) = (1 / x) * (L(x,y,z) * (L(x,y,z) \ (u * x)))
    ]]></literal>
    <justification jstring="[hyper(347,a,22794,a(flip),b,27187,a),flip(a)].">
      <j1 rule="hyper" parents="347 22794 27187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27189">
    <literal><![CDATA[
      L(x \ 1,y,z) * (u * (L(x \ 1,y,z) \ 1)) = (1 / x) * (u * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,169,a(flip),b,27188,a),flip(a)].">
      <j1 rule="hyper" parents="347 169 27188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27191">
    <literal><![CDATA[
      (1 * (a(1,x,x) \ R(x,y,z))) * (u * (R(x,y,z) \ 1)) = (1 / (x \ 1)) * (u * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,27013,a(flip),b,27189,a)].">
      <j1 rule="hyper" parents="63 27013 27189"/>
    </justification>
  </clause>

  <clause id="27193">
    <literal><![CDATA[
      (1 * (a(1,x,x) \ R(x,y,z))) * (u * (R(x,y,z) \ 1)) = x * (u * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(347,a,208,a(flip),b,27191,a),flip(a)].">
      <j1 rule="hyper" parents="347 208 27191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27195">
    <literal><![CDATA[
      (1 * (1 \ R(x,y,z))) * (u * (R(x,y,z) \ 1)) = x * (u * (x \ 1))
    ]]></literal>
    <justification jstring="[para(400(a,1),27193(a,1,1,2,1))].">
      <j1 rule="para" parents="400 27193"/>
    </justification>
  </clause>

  <clause id="27196">
    <literal><![CDATA[
      R(x,y,z) * (u * (R(x,y,z) \ 1)) = x * (u * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(628,a,27195,a)].">
      <j1 rule="hyper" parents="628 27195"/>
    </justification>
  </clause>

  <clause id="27199">
    <literal><![CDATA[
      L(x,y,z) * (u * (L(x,y,z) \ 1)) = x * (u * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,23772,a(flip),b,27196,a)].">
      <j1 rule="hyper" parents="63 23772 27196"/>
    </justification>
  </clause>

  <clause id="27201">
    <literal><![CDATA[
      (R(x,x,y) * y) \ L(R(x,x,y) * y,x * (R(x,x,y) * y),z) = L(a(z,(x * x) * y,x \ y) \ 1,R(x,x,y) * y,x)
    ]]></literal>
    <justification jstring="[para(24633(a,1),27184(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="24633 27184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27202">
    <literal><![CDATA[
      (R(x,x,y) * y) \ L(R(x,x,y) * y,x * (R(x,x,y) * y),z) = L(a(z,y,x \ y) \ 1,R(x,x,y) * y,x)
    ]]></literal>
    <justification jstring="[para(24104(a,1),27201(a,2,1,1))].">
      <j1 rule="para" parents="24104 27201"/>
    </justification>
  </clause>

  <clause id="27203">
    <literal><![CDATA[
      (R(x,x,y) * y) \ L(R(x,x,y) * y,x * (R(x,x,y) * y),z) = L(a(z,y,x \ y) \ 1,L(x,x,y) * y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,23784,a(flip),b,27202,a),flip(a)].">
      <j1 rule="hyper" parents="347 23784 27202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27205">
    <literal><![CDATA[
      (R(x,x,y) * y) \ L(R(x,x,y) * y,x * (R(x,x,y) * y),z) = L(a(z,y,x \ y) \ 1,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,21812,a(flip),b,27203,a),flip(a)].">
      <j1 rule="hyper" parents="347 21812 27203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27206">
    <literal><![CDATA[
      (R(x,x,y) * y) \ L(R(x,x,y) * y,x * (R(x,x,y) * y),z) = a(z,y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,26412,a(flip),b,27205,a),flip(a)].">
      <j1 rule="hyper" parents="347 26412 27205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27207">
    <literal><![CDATA[
      (R(x,x,y) * y) \ L(R(x,x,y) * y,(x * x) * y,z) = a(z,y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[para(1750(a,1),27206(a,1,2,2))].">
      <j1 rule="para" parents="1750 27206"/>
    </justification>
  </clause>

  <clause id="27208">
    <literal><![CDATA[
      (R(x,x,y) * y) \ L(R(x,x,y) * y,y,z) = a(z,y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[para(3604(a,1),27207(a,1,2))].">
      <j1 rule="para" parents="3604 27207"/>
    </justification>
  </clause>

  <clause id="27209">
    <literal><![CDATA[
      a(x,y,R(z,z,y) \ y) \ 1 = a(x,y,y \ z) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,26360,a(flip),b,27208,a)].">
      <j1 rule="hyper" parents="63 26360 27208"/>
    </justification>
  </clause>

  <clause id="27211">
    <literal><![CDATA[
      a(x,y,(z \ 1) * y) \ 1 = a(x,y,y \ z) \ 1
    ]]></literal>
    <justification jstring="[para(2257(a,1),27209(a,1,1,3))].">
      <j1 rule="para" parents="2257 27209"/>
    </justification>
  </clause>

  <clause id="27212">
    <literal><![CDATA[
      a(x,y,y \ z) \ 1 = a(x,y,z * y) \ 1
    ]]></literal>
    <justification jstring="[para(24327(a,1),27211(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24327 27211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27213">
    <literal><![CDATA[
      x \ (y * L(y \ x,y,z)) = a(z,y,x * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(26165,a,27212,a)].">
      <j1 rule="hyper" parents="26165 27212"/>
    </justification>
  </clause>

  <clause id="27214">
    <literal><![CDATA[
      a(x,y,y \ z) = a(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(313,a,27212,a),flip(a)].">
      <j1 rule="hyper" parents="313 27212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27215">
    <literal><![CDATA[
      a(x,y,((z \ u) \ y) * y) \ 1 = z \ (u * L(u \ z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,26924,a(flip),b,27212,a),flip(a)].">
      <j1 rule="hyper" parents="63 26924 27212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27217">
    <literal><![CDATA[
      L(x \ y,y,z) \ (x \ y) = a(z,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,26227,a,b,27214,a)].">
      <j1 rule="hyper" parents="63 26227 27214"/>
    </justification>
  </clause>

  <clause id="27218">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / (x * z) = a(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,13383,a,b,27214,a)].">
      <j1 rule="hyper" parents="63 13383 27214"/>
    </justification>
  </clause>

  <clause id="27219">
    <literal><![CDATA[
      a(x,y,(y * z) * y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12443,a(flip),b,27214,a),flip(a)].">
      <j1 rule="hyper" parents="63 12443 27214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27221">
    <literal><![CDATA[
      x \ ((x * y) * (y \ z)) = z * a(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,27214,a(flip),b,14701,a),flip(a)].">
      <j1 rule="hyper" parents="134 27214 14701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27222">
    <literal><![CDATA[
      R(x * y,z,a(u,y,y \ x)) = x * y
    ]]></literal>
    <justification jstring="[para(27214(a,2),12364(a,1,3))].">
      <j1 rule="para" parents="27214 12364"/>
    </justification>
  </clause>

  <clause id="27225">
    <literal><![CDATA[
      a(x,a(y,z,z \ y) * u,w) = a(x,a(z,z,y) * u,w)
    ]]></literal>
    <justification jstring="[para(27214(a,2),24711(a,1,2,1))].">
      <j1 rule="para" parents="27214 24711"/>
    </justification>
  </clause>

  <clause id="27226">
    <literal><![CDATA[
      a(x,y,a(z,u,u \ z)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(27214(a,2),25268(a,1,3))].">
      <j1 rule="para" parents="27214 25268"/>
    </justification>
  </clause>

  <clause id="27227">
    <literal><![CDATA[
      L(x,y,z) = a(z,y,(x \ y) * y) \ x
    ]]></literal>
    <justification jstring="[para(27214(a,1),26238(a,2,1))].">
      <j1 rule="para" parents="27214 26238"/>
    </justification>
  </clause>

  <clause id="27228">
    <literal><![CDATA[
      L(x / y,y,z) \ x = a(z,y,x * y) * y
    ]]></literal>
    <justification jstring="[para(27214(a,1),26507(a,2,1))].">
      <j1 rule="para" parents="27214 26507"/>
    </justification>
  </clause>

  <clause id="27229">
    <literal><![CDATA[
      (x * y) * a(y,x,z * x) = x * R(y,x,x \ z)
    ]]></literal>
    <justification jstring="[para(27214(a,1),26939(a,1,2))].">
      <j1 rule="para" parents="27214 26939"/>
    </justification>
  </clause>

  <clause id="27230">
    <literal><![CDATA[
      T(T(a(x,y,z * y) * y,z / T(y,x)),x) = ((y * x) \ (x * z)) \ z
    ]]></literal>
    <justification jstring="[para(27214(a,1),27126(a,1,1,1,1))].">
      <j1 rule="para" parents="27214 27126"/>
    </justification>
  </clause>

  <clause id="27231">
    <literal><![CDATA[
      a(x,y,L(z,y,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(24601,a,27219,a)].">
      <j1 rule="hyper" parents="24601 27219"/>
    </justification>
  </clause>

  <clause id="27232">
    <literal><![CDATA[
      a(x,y,y * (L(z,z,y) \ y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,24861,a,b,27219,a)].">
      <j1 rule="hyper" parents="63 24861 27219"/>
    </justification>
  </clause>

  <clause id="27233">
    <literal><![CDATA[
      a(x,y,L(z,y,y)) \ u = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(61,a,27231,a)].">
      <j1 rule="hyper" parents="61 27231"/>
    </justification>
  </clause>

  <clause id="27235">
    <literal><![CDATA[
      (x \ (y \ 1)) * (a(y,x,x \ y) \ 1) = (y * x) \ 1
    ]]></literal>
    <justification jstring="[para(27222(a,1),15014(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27222 15014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27236">
    <literal><![CDATA[
      a(x \ y,x,((x \ L(x,z,u)) \ x) * x) \ (x \ L(x,z,u)) = L(x \ L(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[hyper(10195,a,27227,a),flip(a)].">
      <j1 rule="hyper" parents="10195 27227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27237">
    <literal><![CDATA[
      L(x,y,((z \ a(u,w,u)) \ v5) \ v6) = a(((z \ 1) \ v5) \ v6,y,(x \ y) * y) \ x
    ]]></literal>
    <justification jstring="[para(12177(a,1),27227(a,2,1))].">
      <j1 rule="para" parents="12177 27227"/>
    </justification>
  </clause>

  <clause id="27238">
    <literal><![CDATA[
      L(a(x,y,y * (z \ y)),z,y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,26745,a(flip),b,27232,a)].">
      <j1 rule="hyper" parents="63 26745 27232"/>
    </justification>
  </clause>

  <clause id="27239">
    <literal><![CDATA[
      a(x,y,y * (z \ y)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(26173,a,27238,a),flip(a)].">
      <j1 rule="hyper" parents="26173 27238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27240">
    <literal><![CDATA[
      L(x \ a(x,y,z),a(x,y,z),x) = x \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(189,a,27217,a,b,26878,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="189 27217 26878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27241">
    <literal><![CDATA[
      a(x,y,a(z \ u,z,u)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(26560,a,27226,a)].">
      <j1 rule="hyper" parents="26560 27226"/>
    </justification>
  </clause>

  <clause id="27242">
    <literal><![CDATA[
      a(x,y,a(z \ u,z,z)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,25759,a,b,27226,a)].">
      <j1 rule="hyper" parents="63 25759 27226"/>
    </justification>
  </clause>

  <clause id="27243">
    <literal><![CDATA[
      a(x \ y,z,a(x,x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,12361,a(flip),b,27226,a),flip(a)].">
      <j1 rule="hyper" parents="63 12361 27226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27244">
    <literal><![CDATA[
      L(x \ y,z,a(x,x,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(26597,a,27243,a)].">
      <j1 rule="hyper" parents="26597 27243"/>
    </justification>
  </clause>

  <clause id="27245">
    <literal><![CDATA[
      L(x / y,y,a(z,u,w)) \ x = y * a(x * y,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,26596,a(flip),b,27228,a),flip(a)].">
      <j1 rule="hyper" parents="347 26596 27228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27246">
    <literal><![CDATA[
      L(x / y,y,z) \ a(L(x / y,y,z),L(x / y,y,z),x) = (a(z,y,x * y) * y) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,27228,a(flip),b,18983,a),flip(a)].">
      <j1 rule="hyper" parents="131 27228 18983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27247">
    <literal><![CDATA[
      a(x,y \ z,a(y,y,z)) * (y \ z) = L(y \ z,a(y \ z,y,z),x)
    ]]></literal>
    <justification jstring="[para(27241(a,1),26651(a,1,1))].">
      <j1 rule="para" parents="27241 26651"/>
    </justification>
  </clause>

  <clause id="27248">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,w)) = y * a(a(z,u,w),x,y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,26374,a(flip),b,27221,a)].">
      <j1 rule="hyper" parents="63 26374 27221"/>
    </justification>
  </clause>

  <clause id="27249">
    <literal><![CDATA[
      R(x,y,y \ z) = R(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(26944,a,27229,a),flip(a)].">
      <j1 rule="hyper" parents="26944 27229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27250">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,u,w * u) = L(a(x,y,z) \ 1,u,u \ w)
    ]]></literal>
    <justification jstring="[hyper(23390,a,27249,a),flip(a)].">
      <j1 rule="hyper" parents="23390 27249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27251">
    <literal><![CDATA[
      x \ ((y * z) * (z \ x)) = R(T(y,x),z,x * z)
    ]]></literal>
    <justification jstring="[hyper(1376,a,27249,a)].">
      <j1 rule="hyper" parents="1376 27249"/>
    </justification>
  </clause>

  <clause id="27252">
    <literal><![CDATA[
      R(x,y,y \ z) = R(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,20497,a,b,27249,a),flip(a)].">
      <j1 rule="hyper" parents="347 20497 27249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27253">
    <literal><![CDATA[
      ((x * a(y,z,u)) * (x \ w)) / w = R(a(y,z,u),x,w * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,20588,a,b,27249,a)].">
      <j1 rule="hyper" parents="63 20588 27249"/>
    </justification>
  </clause>

  <clause id="27254">
    <literal><![CDATA[
      T((x * (y \ z)) / z,y) = R(y \ x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,1036,a,b,27249,a)].">
      <j1 rule="hyper" parents="63 1036 27249"/>
    </justification>
  </clause>

  <clause id="27255">
    <literal><![CDATA[
      R(x,x \ y,z * (x \ y)) = (y * ((x \ y) \ z)) / z
    ]]></literal>
    <justification jstring="[hyper(63,a,843,a(flip),b,27249,a),flip(a)].">
      <j1 rule="hyper" parents="63 843 27249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27256">
    <literal><![CDATA[
      R(x,y,z * y) * z = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(133,a,27249,a(flip),b,106,a)].">
      <j1 rule="hyper" parents="133 27249 106"/>
    </justification>
  </clause>

  <clause id="27257">
    <literal><![CDATA[
      ((x * (y \ z)) / z) * y = y * R(y \ x,y,z * y)
    ]]></literal>
    <justification jstring="[para(27249(a,1),954(a,2,2))].">
      <j1 rule="para" parents="27249 954"/>
    </justification>
  </clause>

  <clause id="27258">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y,z,u) \ (y * (L(y,z,u) \ w))) = R(x,L(y,z,u),w * y)
    ]]></literal>
    <justification jstring="[para(20989(a,1),27249(a,2,3))].">
      <j1 rule="para" parents="20989 27249"/>
    </justification>
  </clause>

  <clause id="27259">
    <literal><![CDATA[
      R(x,y,R(z,u,w * u)) = R(x,y,L(z,u,u \ w))
    ]]></literal>
    <justification jstring="[para(27249(a,1),23613(a,1,3))].">
      <j1 rule="para" parents="27249 23613"/>
    </justification>
  </clause>

  <clause id="27260">
    <literal><![CDATA[
      a(x,y,R(z,u,w * u)) = a(x,y,L(z,u,u \ w))
    ]]></literal>
    <justification jstring="[para(27249(a,1),24889(a,1,3))].">
      <j1 rule="para" parents="27249 24889"/>
    </justification>
  </clause>

  <clause id="27263">
    <literal><![CDATA[
      R(x,y,z * R(z \ 1,z,z * u)) = R(x,y,z * (u \ (z \ u)))
    ]]></literal>
    <justification jstring="[para(27252(a,1),22328(a,1,3,2))].">
      <j1 rule="para" parents="27252 22328"/>
    </justification>
  </clause>

  <clause id="27264">
    <literal><![CDATA[
      (x / y) * R(y,z,(y \ x) * z) = (y * z) * (z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(20111,a,27256,a)].">
      <j1 rule="hyper" parents="20111 27256"/>
    </justification>
  </clause>

  <clause id="27265">
    <literal><![CDATA[
      ((x * y) * R(z,y,x)) / T(x * y,z) = R(z,y,T(x * y,z) * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,22620,a,b,27256,a)].">
      <j1 rule="hyper" parents="131 22620 27256"/>
    </justification>
  </clause>

  <clause id="27266">
    <literal><![CDATA[
      a(x * R(y,z,x * z),u,w) = a((y * z) * (z \ x),u,w)
    ]]></literal>
    <justification jstring="[para(27256(a,1),23896(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27256 23896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27267">
    <literal><![CDATA[
      x * R(x \ y,x,z * x) != u
    ]]></literal>
    <literal><![CDATA[
      ((y * (x \ z)) / z) * x = u
    ]]></literal>
    <justification jstring="[para(27254(a,1),315(a,1,2))].">
      <j1 rule="para" parents="27254 315"/>
    </justification>
  </clause>

  <clause id="27268">
    <literal><![CDATA[
      R((L(x,y,z) \ x) \ u,L(x,y,z) \ x,(L(1 / x,y,z) \ 1) * (L(x,y,z) \ x)) = T((u * x) / (L(1 / x,y,z) \ 1),L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(3647(a,1),27254(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3647 27254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27269">
    <literal><![CDATA[
      T(x \ (y * ((a(z,u,w) \ y) \ x)),a(z,u,w) \ y) = R((a(z,u,w) \ y) \ y,a(z,u,w) \ y,x * (a(z,u,w) \ y))
    ]]></literal>
    <justification jstring="[para(25879(a,1),27254(a,1,1))].">
      <j1 rule="para" parents="25879 27254"/>
    </justification>
  </clause>

  <clause id="27270">
    <literal><![CDATA[
      L(x \ a(x,y,z),x,a(x,y,z)) = x \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(25494,a,27240,a)].">
      <j1 rule="hyper" parents="25494 27240"/>
    </justification>
  </clause>

  <clause id="27271">
    <literal><![CDATA[
      R(x,y,L(z,u,u \ w)) = R(x,y,L(z,u,w * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,23613,a(flip),b,27259,a),flip(a)].">
      <j1 rule="hyper" parents="63 23613 27259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27272">
    <literal><![CDATA[
      a(x,y,L(z,u,u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,w * u)) = v5
    ]]></literal>
    <justification jstring="[para(27260(a,1),24890(a,1))].">
      <j1 rule="para" parents="27260 24890"/>
    </justification>
  </clause>

  <clause id="27274">
    <literal><![CDATA[
      a(x,y,z) \ (a(x,y,z) * R(a(x,y,z) \ u,a(x,y,z),w * a(x,y,z))) = (u * (a(x,y,z) \ w)) / w
    ]]></literal>
    <justification jstring="[hyper(20594,a,27257,a)].">
      <j1 rule="hyper" parents="20594 27257"/>
    </justification>
  </clause>

  <clause id="27275">
    <literal><![CDATA[
      a(x,y * ((z * u) * (u \ z)),w) = a(x,a(u,u,z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(24637,a,27225,a)].">
      <j1 rule="hyper" parents="24637 27225"/>
    </justification>
  </clause>

  <clause id="27276">
    <literal><![CDATA[
      ((x * a(y,z,u)) * (x \ w)) / w = L(a(y,z,u),x,w * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,23097,a(flip),b,27253,a),flip(a)].">
      <j1 rule="hyper" parents="347 23097 27253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27277">
    <literal><![CDATA[
      a(x * L(y,z,x * z),u,w) = a((y * z) * (z \ x),u,w)
    ]]></literal>
    <justification jstring="[hyper(26217,a,27266,a)].">
      <j1 rule="hyper" parents="26217 27266"/>
    </justification>
  </clause>

  <clause id="27278">
    <literal><![CDATA[
      L(a(x,y,z),u,u \ w) = L(a(x,y,z),u,w * u)
    ]]></literal>
    <justification jstring="[hyper(23106,a,27276,a)].">
      <j1 rule="hyper" parents="23106 27276"/>
    </justification>
  </clause>

  <clause id="27279">
    <literal><![CDATA[
      x * L(a(y,z,u),w,x * w) = (x / w) * (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,27278,a(flip),b,10192,a)].">
      <j1 rule="hyper" parents="134 27278 10192"/>
    </justification>
  </clause>

  <clause id="27280">
    <literal><![CDATA[
      a(x * L(y,z,z * x),u,w) = a((y * z) * (z \ x),u,w)
    ]]></literal>
    <justification jstring="[para(11447(a,1),27277(a,1,1,2))].">
      <j1 rule="para" parents="11447 27277"/>
    </justification>
  </clause>

  <clause id="27281">
    <literal><![CDATA[
      a(x * L(R(y,z,u) \ w,R(y,z,u),R(y,z,u) * x),v5,v6) = a(((y \ w) * y) * (R(y,z,u) \ x),v5,v6)
    ]]></literal>
    <justification jstring="[para(21017(a,1),27280(a,2,1,1))].">
      <j1 rule="para" parents="21017 27280"/>
    </justification>
  </clause>

  <clause id="27282">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,u \ w) = L(a(x,y,z) \ 1,u,w * u)
    ]]></literal>
    <justification jstring="[hyper(23390,a,27250,a),flip(a)].">
      <j1 rule="hyper" parents="23390 27250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27287">
    <literal><![CDATA[
      R(x,y,(z \ (u \ z)) * u) = R(x,y,u * R(u \ 1,u,u * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,20497,a,b,27263,a)].">
      <j1 rule="hyper" parents="347 20497 27263"/>
    </justification>
  </clause>

  <clause id="27289">
    <literal><![CDATA[
      R(x,y,a(z \ 1,z,z * u)) = R(x,y,(u \ (z \ u)) * z)
    ]]></literal>
    <justification jstring="[para(26889(a,1),27287(a,2,3)),flip(a)].">
      <j1 rule="para" parents="26889 27287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27290">
    <literal><![CDATA[
      R(x,y,(z \ (u \ z)) * u) = L(x,y,a(u \ 1,u,u * z))
    ]]></literal>
    <justification jstring="[hyper(23284,a,27289,a),flip(a)].">
      <j1 rule="hyper" parents="23284 27289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27291">
    <literal><![CDATA[
      R(x,y,(z \ (u \ z)) * u) = L(x,y,a(u,u,u * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,23259,a(flip),b,27290,a),flip(a)].">
      <j1 rule="hyper" parents="347 23259 27290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27292">
    <literal><![CDATA[
      R(x,y,z * (u \ (z \ u))) = L(x,y,a(z,z,z * u))
    ]]></literal>
    <justification jstring="[hyper(20517,a,27291,a)].">
      <j1 rule="hyper" parents="20517 27291"/>
    </justification>
  </clause>

  <clause id="27293">
    <literal><![CDATA[
      a(x,y \ z,a(y,y,z)) * (y \ z) = L(y \ z,a(y,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,26511,a(flip),b,27247,a),flip(a)].">
      <j1 rule="hyper" parents="347 26511 27247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27294">
    <literal><![CDATA[
      ((x * y) * R(z,y,x)) / T(x * y,z) = R(z,y,(x * y) * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,22062,a(flip),b,27265,a),flip(a)].">
      <j1 rule="hyper" parents="347 22062 27265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27296">
    <literal><![CDATA[
      ((x * y) * R(z,y,x)) / T(x * y,z) = R(z,y,L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,23617,a(flip),b,27294,a),flip(a)].">
      <j1 rule="hyper" parents="347 23617 27294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27297">
    <literal><![CDATA[
      R(((x * y) * z) / T(x * y,z),y,x) = R(z,y,L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,23629,a,b,27296,a)].">
      <j1 rule="hyper" parents="63 23629 27296"/>
    </justification>
  </clause>

  <clause id="27298">
    <literal><![CDATA[
      R(x,y,L(z,y,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(213(a,1),27297(a,1,1)),flip(a)].">
      <j1 rule="para" parents="213 27297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27299">
    <literal><![CDATA[
      R(x,y,L(y,z,u) \ w) = R(x,y,w * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(27079,a,27298,a)].">
      <j1 rule="hyper" parents="27079 27298"/>
    </justification>
  </clause>

  <clause id="27300">
    <literal><![CDATA[
      a(R(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(L(x,y,L(z,y,y)),u,w) = v5
    ]]></literal>
    <justification jstring="[para(27298(a,1),25195(a,1,1))].">
      <j1 rule="para" parents="27298 25195"/>
    </justification>
  </clause>

  <clause id="27301">
    <literal><![CDATA[
      a(L(x,y,L(z,y,y)),u,w) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(27300,a,25182,a)].">
      <j1 rule="hyper" parents="27300 25182"/>
    </justification>
  </clause>

  <clause id="27302">
    <literal><![CDATA[
      a(L(x,y,L(z \ u,y,y)),w,v5) = a(L(x,y,T(z,v6) \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(21468(a,2),27301(a,2,1))].">
      <j1 rule="para" parents="21468 27301"/>
    </justification>
  </clause>

  <clause id="27303">
    <literal><![CDATA[
      a(L(x,y,T(y,z) \ u),w,v5) = a(L(x,y,u * (y \ 1)),w,v5)
    ]]></literal>
    <justification jstring="[para(23684(a,1),27302(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23684 27302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27304">
    <literal><![CDATA[
      a(L(x,y,T(y,z) \ u),w,v5) = a(L(x,y,u * y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,25192,a(flip),b,27303,a),flip(a)].">
      <j1 rule="hyper" parents="347 25192 27303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27305">
    <literal><![CDATA[
      a(L(x,y,y \ z),u,w) = a(L(x,y,z * y),u,w)
    ]]></literal>
    <justification jstring="[para(110(a,1),27304(a,1,1,3,1))].">
      <j1 rule="para" parents="110 27304"/>
    </justification>
  </clause>

  <clause id="27306">
    <literal><![CDATA[
      T(T(x * a(y,x,z * x),x \ z),y) = ((x * y) \ (y * z)) \ z
    ]]></literal>
    <justification jstring="[para(21962(a,1),27230(a,1,1))].">
      <j1 rule="para" parents="21962 27230"/>
    </justification>
  </clause>

  <clause id="27308">
    <literal><![CDATA[
      R(x,L(y,z,u),y * (L(y,z,u) \ (L(y,z,u) \ w))) = R(x,L(y,z,u),w * y)
    ]]></literal>
    <justification jstring="[para(1407(a,1),27258(a,1,3))].">
      <j1 rule="para" parents="1407 27258"/>
    </justification>
  </clause>

  <clause id="27309">
    <literal><![CDATA[
      R(x,L(y,z,u),L(w,L(y,z,u),L(y,z,u)) * y) = R(x,L(y,z,u),w * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,22239,a(flip),b,27308,a)].">
      <j1 rule="hyper" parents="63 22239 27308"/>
    </justification>
  </clause>

  <clause id="27310">
    <literal><![CDATA[
      R(x,L(y,z,u),L(w,y,y) * y) = R(x,L(y,z,u),w * y)
    ]]></literal>
    <justification jstring="[para(27075(a,1),27309(a,1,3,1))].">
      <j1 rule="para" parents="27075 27309"/>
    </justification>
  </clause>

  <clause id="27311">
    <literal><![CDATA[
      R(x,L(y,z,u),y \ w) = R(x,L(y,z,u),w * y)
    ]]></literal>
    <justification jstring="[hyper(22240,a,27310,a)].">
      <j1 rule="hyper" parents="22240 27310"/>
    </justification>
  </clause>

  <clause id="27313">
    <literal><![CDATA[
      R(L(x,y,z) \ x,L(x,y,z),u * x) = u / ((u / (x * K(w,v5))) * L(x * K(w,v5),y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,22827,a(flip),b,27311,a),flip(a)].">
      <j1 rule="hyper" parents="63 22827 27311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27314">
    <literal><![CDATA[
      L(x,y,((z \ a(u,w,u)) \ v5) \ v6) = L(x,y,((z \ 1) \ v5) \ v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,27227,a,b,27237,a),flip(a)].">
      <j1 rule="hyper" parents="347 27227 27237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27315">
    <literal><![CDATA[
      a(x \ y,x,((L(x,z,u) \ x) * x) * x) \ (x \ L(x,z,u)) = L(x \ L(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[para(10937(a,1),27236(a,1,1,3,1))].">
      <j1 rule="para" parents="10937 27236"/>
    </justification>
  </clause>

  <clause id="27316">
    <literal><![CDATA[
      L(x / y,y,z) \ a(L(x / y,y,z),L(y \ x,y,z),x) = (a(z,y,x * y) * y) / x
    ]]></literal>
    <justification jstring="[para(24024(a,1),27246(a,1,2))].">
      <j1 rule="para" parents="24024 27246"/>
    </justification>
  </clause>

  <clause id="27317">
    <literal><![CDATA[
      a(x \ y,x,x * (x * (L(x,z,u) \ x))) \ (x \ L(x,z,u)) = L(x \ L(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[para(24284(a,1),27315(a,1,1))].">
      <j1 rule="para" parents="24284 27315"/>
    </justification>
  </clause>

  <clause id="27318">
    <literal><![CDATA[
      a(x \ y,x,x * L(x,z,u)) \ (x \ L(x,z,u)) = L(x \ L(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[para(27064(a,1),27317(a,1,1))].">
      <j1 rule="para" parents="27064 27317"/>
    </justification>
  </clause>

  <clause id="27319">
    <literal><![CDATA[
      L(L(x,y,z) \ x,L(x,y,z),u * x) = u / ((u / (x * K(w,v5))) * L(x * K(w,v5),y,z))
    ]]></literal>
    <justification jstring="[hyper(25941,a,27313,a)].">
      <j1 rule="hyper" parents="25941 27313"/>
    </justification>
  </clause>

  <clause id="27320">
    <literal><![CDATA[
      L(L(x,y,z) \ x,L(x,y,z),u * x) = u / (L(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[para(22826(a,1),27319(a,2,2))].">
      <j1 rule="para" parents="22826 27319"/>
    </justification>
  </clause>

  <clause id="27321">
    <literal><![CDATA[
      a(x,y,z) \ (a(x,y,z) * L(a(x,y,z) \ u,a(x,y,z),w * a(x,y,z))) = (u * (a(x,y,z) \ w)) / w
    ]]></literal>
    <justification jstring="[para(23225(a,1),27274(a,1,2,2))].">
      <j1 rule="para" parents="23225 27274"/>
    </justification>
  </clause>

  <clause id="27322">
    <literal><![CDATA[
      a(x * L(R(y,z,u) \ w,R(y,z,u),L(y,z,u) * x),v5,v6) = a(((y \ w) * y) * (R(y,z,u) \ x),v5,v6)
    ]]></literal>
    <justification jstring="[para(22849(a,1),27281(a,1,1,2))].">
      <j1 rule="para" parents="22849 27281"/>
    </justification>
  </clause>

  <clause id="27323">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) / w != v5
    ]]></literal>
    <literal><![CDATA[
      L(a(y,z,u) \ x,a(y,z,u),w * a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(27321(a,1),356(a,1))].">
      <j1 rule="para" parents="27321 356"/>
    </justification>
  </clause>

  <clause id="27324">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),w * a(x,y,z)) = w \ ((a(x,y,z) \ w) * u)
    ]]></literal>
    <justification jstring="[hyper(27323,a,25873,a)].">
      <j1 rule="hyper" parents="27323 25873"/>
    </justification>
  </clause>

  <clause id="27325">
    <literal><![CDATA[
      a(x,y,z) * L(a(u,w,v5) \ v6,a(u,w,v5),v7 * a(u,w,v5)) = (v7 \ ((a(u,w,v5) \ v7) * v6)) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,27324,a,b,19988,a)].">
      <j1 rule="hyper" parents="134 27324 19988"/>
    </justification>
  </clause>

  <clause id="27326">
    <literal><![CDATA[
      a(x * L(R(y,z,u) \ w,L(y,z,u),L(y,z,u) * x),v5,v6) = a(((y \ w) * y) * (R(y,z,u) \ x),v5,v6)
    ]]></literal>
    <justification jstring="[para(21974(a,1),27322(a,1,1,2))].">
      <j1 rule="para" parents="21974 27322"/>
    </justification>
  </clause>

  <clause id="27327">
    <literal><![CDATA[
      a(((R(x,y,z) \ u) * L(x,y,z)) * (L(x,y,z) \ w),v5,v6) = a(((x \ u) * x) * (R(x,y,z) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,27280,a(flip),b,27326,a)].">
      <j1 rule="hyper" parents="63 27280 27326"/>
    </justification>
  </clause>

  <clause id="27328">
    <literal><![CDATA[
      a(((R(x,y,z) \ u) * L(x,y,z)) * (L(x,y,z) \ w),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(u * (R(x,y,z) \ w),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(27327(a,2),23968(a,1))].">
      <j1 rule="para" parents="27327 23968"/>
    </justification>
  </clause>

  <clause id="27329">
    <literal><![CDATA[
      a(x * (R(y,z,u) \ w),v5,v6) = a(x * (L(y,z,u) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(27328,a,26804,a)].">
      <j1 rule="hyper" parents="27328 26804"/>
    </justification>
  </clause>

  <clause id="27330">
    <literal><![CDATA[
      a(x * (R(K(y,T(z,u)) / w,w,u) \ v5),v6,v7) = a(x * ((u \ (K(y,z) * (u / w))) \ v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(21293(a,1),27329(a,2,1,2,1))].">
      <j1 rule="para" parents="21293 27329"/>
    </justification>
  </clause>

  <clause id="27331">
    <literal><![CDATA[
      a(x * ((y / (z * (y * K(u,w)))) \ v5),v6,v7) = a(x * ((y \ (K(w,u) * (y / z))) \ v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(21167(a,1),27330(a,1,1,2,1))].">
      <j1 rule="para" parents="21167 27330"/>
    </justification>
  </clause>

  <clause id="27332">
    <literal><![CDATA[
      a(x * (((y * (z * K(u,w))) \ z) \ v5),v6,v7) = a(x * ((z \ (K(w,u) * (z / y))) \ v5),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,24221,a(flip),b,27331,a)].">
      <j1 rule="hyper" parents="63 24221 27331"/>
    </justification>
  </clause>

  <clause id="27333">
    <literal><![CDATA[
      a(x * ((y \ (K(z,u) * (y / w))) \ v5),v6,v7) = a(x * ((K(z,u) * ((w * y) \ y)) \ v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(20837(a,1),27332(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20837 27332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27334">
    <literal><![CDATA[
      a(x * ((y \ (K(z,u) * (y / w))) \ v5),v6,v7) = a(x * (((w * y) \ y) \ (K(u,z) * v5)),v6,v7)
    ]]></literal>
    <justification jstring="[para(20003(a,1),27333(a,2,1,2))].">
      <j1 rule="para" parents="20003 27333"/>
    </justification>
  </clause>

  <clause id="27335">
    <literal><![CDATA[
      a(x * ((y \ (K(z,u) * (y / w))) \ v5),v6,v7) = a(x * (((w * y) \ y) \ v5),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,24223,a(flip),b,27334,a),flip(a)].">
      <j1 rule="hyper" parents="347 24223 27334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27337">
    <literal><![CDATA[
      a(x * (((y * z) \ z) \ u),w,v5) = a(x * ((z \ (z / y)) \ u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24227,a(flip),b,27335,a),flip(a)].">
      <j1 rule="hyper" parents="63 24227 27335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27338">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ ((x \ L(x,y,z)) * (x * (L(x,y,z) \ ((x \ L(x,y,z)) * u)))) = a(x \ L(x,y,z),x,x \ u) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),26149(a,1,1,2))].">
      <j1 rule="para" parents="10 26149"/>
    </justification>
  </clause>

  <clause id="27340">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ ((x \ L(x,y,z)) * L(u,x,x \ L(x,y,z))) = a(x \ L(x,y,z),x,x \ u) \ 1
    ]]></literal>
    <justification jstring="[para(3651(a,1),27338(a,1,2,2))].">
      <j1 rule="para" parents="3651 27338"/>
    </justification>
  </clause>

  <clause id="27341">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (((x \ L(x,y,z)) / u) * L(u,x,x \ L(x,y,z))) = a(x \ L(x,y,z),x,x \ u) \ 1
    ]]></literal>
    <justification jstring="[hyper(3973,a,27340,a)].">
      <j1 rule="hyper" parents="3973 27340"/>
    </justification>
  </clause>

  <clause id="27342">
    <literal><![CDATA[
      a(x \ L(x,y,z),x,x \ u) \ 1 = u \ L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(25558,a,27341,a),flip(a)].">
      <j1 rule="hyper" parents="25558 27341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27343">
    <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(24385(a,1),27342(a,1,1))].">
      <j1 rule="para" parents="24385 27342"/>
    </justification>
  </clause>

  <clause id="27344">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u) \ 1 = u \ L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(25069(a,1),27343(a,1,1))].">
      <j1 rule="para" parents="25069 27343"/>
    </justification>
  </clause>

  <clause id="27345">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (L(a(x,y,z),u,w) \ (v5 * a(x,y,z))) = L(v5 * L(a(x,y,z),u,w),a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(26261(a,1),27053(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="26261 27053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27346">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (a(x,y,z) * (L(a(x,y,z),u,w) \ v5)) = L(v5 * L(a(x,y,z),u,w),a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(19976(a,1),27345(a,1,2))].">
      <j1 rule="para" parents="19976 27345"/>
    </justification>
  </clause>

  <clause id="27347">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * (L(a(x,y,z),u,w) \ v5) = L(v5 * L(a(x,y,z),u,w),a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(502,a,27346,a)].">
      <j1 rule="hyper" parents="502 27346"/>
    </justification>
  </clause>

  <clause id="27348">
    <literal><![CDATA[
      L(x * L(a(y,z,u),w,v5),a(y,z,u),a(y,z,u)) = L(a(y,z,u) \ 1,w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,3325,a(flip),b,27347,a),flip(a)].">
      <j1 rule="hyper" parents="63 3325 27347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27349">
    <literal><![CDATA[
      R((L(x,y,z) \ x) \ u,L(x,y,z) \ x,(L(1 / x,y,z) \ 1) * (L(x,y,z) \ x)) = T(x * ((L(1 / x,y,z) \ 1) \ u),L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(27183(a,1),27268(a,2,1))].">
      <j1 rule="para" parents="27183 27268"/>
    </justification>
  </clause>

  <clause id="27350">
    <literal><![CDATA[
      R((L(x,y,z) \ x) \ u,L(x,y,z) \ x,(L(1 / x,y,z) \ 1) * (L(x,y,z) \ x)) = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,20002,a(flip),b,27349,a),flip(a)].">
      <j1 rule="hyper" parents="347 20002 27349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27352">
    <literal><![CDATA[
      R((L(x,y,z) \ x) \ u,L(x,y,z) \ x,(L(1 / x,y,z) \ 1) * (x * L(x,y,z))) = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,2311,a(flip),b,27350,a)].">
      <j1 rule="hyper" parents="63 2311 27350"/>
    </justification>
  </clause>

  <clause id="27353">
    <literal><![CDATA[
      (a(x,a(y,z * (u * ((u * w) * v5)),x),z * (u * ((u * w) * v5))) / x) \ a(x,z * (((w * u) * v5) * u),y) = R(x,z * (((w * u) * v5) * u),y)
    ]]></literal>
    <justification jstring="[para(24813(a,1),26868(a,1,1,1,2))].">
      <j1 rule="para" parents="24813 26868"/>
    </justification>
  </clause>

  <clause id="27354">
    <literal><![CDATA[
      (a(x,a(y,z * (u * ((u * w) * v5)),x),z * (u * ((u * w) * v5))) / x) \ a(x,z * (u * ((u * w) * v5)),y) = R(x,z * (((w * u) * v5) * u),y)
    ]]></literal>
    <justification jstring="[para(24813(a,1),27353(a,1,2))].">
      <j1 rule="para" parents="24813 27353"/>
    </justification>
  </clause>

  <clause id="27355">
    <literal><![CDATA[
      R(x,y * (((z * u) * w) * u),v5) = R(x,y * (u * ((u * z) * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,26864,a,b,27354,a),flip(a)].">
      <j1 rule="hyper" parents="63 26864 27354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27356">
    <literal><![CDATA[
      R(x,y * (z * ((z * u) * u)),w) = R(x,y * a(u * z,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(21168,a,27355,a),flip(a)].">
      <j1 rule="hyper" parents="21168 27355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27357">
    <literal><![CDATA[
      R(x,y * a(z * u,z,u),w) = R(x,y * a(u,z,u * z),w)
    ]]></literal>
    <justification jstring="[hyper(22571,a,27356,a),flip(a)].">
      <j1 rule="hyper" parents="22571 27356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27358">
    <literal><![CDATA[
      L(a(x,y,z) * (u * ((a(x,y,z) * a(x,y,z)) \ 1)),u * ((a(x,y,z) \ 1) * (a(x,y,z) \ 1)),a(x,y,z)) = (((a(x,y,z) \ 1) \ 1) / u) \ 1
    ]]></literal>
    <justification jstring="[para(21374(a,1),26011(a,1,1,2,2))].">
      <j1 rule="para" parents="21374 26011"/>
    </justification>
  </clause>

  <clause id="27359">
    <literal><![CDATA[
      L(a(x,y,z) * (u / (a(x,y,z) * a(x,y,z))),u * ((a(x,y,z) \ 1) * (a(x,y,z) \ 1)),a(x,y,z)) = (((a(x,y,z) \ 1) \ 1) / u) \ 1
    ]]></literal>
    <justification jstring="[para(665(a,1),27358(a,1,1,2))].">
      <j1 rule="para" parents="665 27358"/>
    </justification>
  </clause>

  <clause id="27360">
    <literal><![CDATA[
      L(a(x,y,z) * ((a(x,y,z) * a(x,y,z)) \ u),u * ((a(x,y,z) \ 1) * (a(x,y,z) \ 1)),a(x,y,z)) = (((a(x,y,z) \ 1) \ 1) / u) \ 1
    ]]></literal>
    <justification jstring="[para(23191(a,1),27359(a,1,1,2))].">
      <j1 rule="para" parents="23191 27359"/>
    </justification>
  </clause>

  <clause id="27361">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) * u,u * ((a(x,y,z) \ 1) * (a(x,y,z) \ 1)),a(x,y,z)) = (((a(x,y,z) \ 1) \ 1) / u) \ 1
    ]]></literal>
    <justification jstring="[para(497(a,1),27360(a,1,1))].">
      <j1 rule="para" parents="497 27360"/>
    </justification>
  </clause>

  <clause id="27362">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) * u,u,a(x,y,z)) = (((a(x,y,z) \ 1) \ 1) / u) \ 1
    ]]></literal>
    <justification jstring="[hyper(3518,a,27361,a)].">
      <j1 rule="hyper" parents="3518 27361"/>
    </justification>
  </clause>

  <clause id="27364">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) * u,u,a(x,y,z)) = (a(x,y,z) / u) \ 1
    ]]></literal>
    <justification jstring="[para(12592(a,1),27362(a,2,1,1))].">
      <j1 rule="para" parents="12592 27362"/>
    </justification>
  </clause>

  <clause id="27366">
    <literal><![CDATA[
      a(x,((y \ K(y,z)) * u) * (T(y,z) * w),((y \ K(y,z)) * u) * (T(y,z) * w)) = a(x,((y \ 1) * u) \ (y * w),((y \ 1) * u) \ (y * w))
    ]]></literal>
    <justification jstring="[para(21397(a,1),27032(a,2,3))].">
      <j1 rule="para" parents="21397 27032"/>
    </justification>
  </clause>

  <clause id="27367">
    <literal><![CDATA[
      a(x,((y \ K(y,z)) * u) * (T(y,z) * w),((y \ K(y,z)) * u) * (T(y,z) * w)) = a(x,((y \ 1) * u) \ (y * w),(u * y) \ (y * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,24292,a(flip),b,27366,a),flip(a)].">
      <j1 rule="hyper" parents="347 24292 27366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27369">
    <literal><![CDATA[
      a(x,((y \ K(y,z)) * u) * (T(y,z) * w),((y \ K(y,z)) * u) * (T(y,z) * w)) = a(x,(u * y) \ (y * w),(u * y) \ (y * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,24372,a(flip),b,27367,a),flip(a)].">
      <j1 rule="hyper" parents="347 24372 27367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27370">
    <literal><![CDATA[
      a(x,((y \ K(y,z)) * u) * (T(y,z) * w),((y \ K(y,z)) * u) * (T(y,z) * w)) = a(x,(u * y) * (y * w),(u * y) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,27029,a(flip),b,27369,a),flip(a)].">
      <j1 rule="hyper" parents="347 27029 27369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27371">
    <literal><![CDATA[
      a(x,((y \ K(y,z)) * u) * (T(y,z) * w),((y \ K(y,z)) * u) * (T(y,z) * w)) = a(x,u * w,u * w)
    ]]></literal>
    <justification jstring="[hyper(347,a,27167,a(flip),b,27370,a),flip(a)].">
      <j1 rule="hyper" parents="347 27167 27370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27372">
    <literal><![CDATA[
      a(x,((y \ K(y,z)) * u) * (T(y,z) * w),(y * w) * ((y \ K(y,z)) * u)) = a(x,u * w,u * w)
    ]]></literal>
    <justification jstring="[hyper(24447,a,27371,a)].">
      <j1 rule="hyper" parents="24447 27371"/>
    </justification>
  </clause>

  <clause id="27374">
    <literal><![CDATA[
      a(x,((y \ K(y,z)) * u) * (T(y,z) * w),(y * u) * (y * w)) = a(x,u * w,u * w)
    ]]></literal>
    <justification jstring="[hyper(24851,a,27372,a)].">
      <j1 rule="hyper" parents="24851 27372"/>
    </justification>
  </clause>

  <clause id="27376">
    <literal><![CDATA[
      a(x,(y * z) * ((y \ K(y,u)) * w),(y * w) * (y * z)) = a(x,w * z,w * z)
    ]]></literal>
    <justification jstring="[hyper(24475,a,27374,a)].">
      <j1 rule="hyper" parents="24475 27374"/>
    </justification>
  </clause>

  <clause id="27378">
    <literal><![CDATA[
      a(x,(y * z) * (y * u),(y * z) * (y * u)) = a(x,z * u,z * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,24790,a(flip),b,27376,a)].">
      <j1 rule="hyper" parents="63 24790 27376"/>
    </justification>
  </clause>

  <clause id="27380">
    <literal><![CDATA[
      a(x,(y * (z * u)) * (y * (z * L(u,z,y))),(y * (z * u)) * (y * (z * L(u,z,y)))) = a(x,a(y,z,u) \ 1,a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(26147(a,1),27035(a,2,3))].">
      <j1 rule="para" parents="26147 27035"/>
    </justification>
  </clause>

  <clause id="27381">
    <literal><![CDATA[
      a(x,(y * (z * u)) * (y * (z * L(u,z,y))),(y * (z * u)) * (y * (z * L(u,z,y)))) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,a(y,z,u),a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(27380(a,2),14967(a,1))].">
      <j1 rule="para" parents="27380 14967"/>
    </justification>
  </clause>

  <clause id="27382">
    <literal><![CDATA[
      a(x,(y * z) * (y * L(z,y,u)),(y * z) * (y * L(z,y,u))) = a(x,a(u,y,z),a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(27381,a,27378,a),flip(a)].">
      <j1 rule="hyper" parents="27381 27378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27383">
    <literal><![CDATA[
      a(x,y * L(y,z,u),y * L(y,z,u)) = a(x,a(u,z,y),a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,27378,a(flip),b,27382,a)].">
      <j1 rule="hyper" parents="63 27378 27382"/>
    </justification>
  </clause>

  <clause id="27384">
    <literal><![CDATA[
      a(x * L(x,y,z),x * L(x,y,z),u) = a(u,a(z,y,x),a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(26756,a,27383,a)].">
      <j1 rule="hyper" parents="26756 27383"/>
    </justification>
  </clause>

  <clause id="27386">
    <literal><![CDATA[
      L(x,y * L(y,z,u),y \ L(y,z,u)) = a(x,a(u,z,y),a(u,z,y)) * x
    ]]></literal>
    <justification jstring="[para(27383(a,1),27038(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27383 27038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27387">
    <literal><![CDATA[
      L(x,y * L(y,z,u),y \ L(y,z,u)) = R(x,a(u,z,y),a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,13403,a(flip),b,27386,a),flip(a)].">
      <j1 rule="hyper" parents="347 13403 27386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27388">
    <literal><![CDATA[
      L(x,y * L(y,z,u),y \ L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,a(u,z,y),a(u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(27387(a,2),23226(a,1))].">
      <j1 rule="para" parents="27387 23226"/>
    </justification>
  </clause>

  <clause id="27389">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w) \ v5,a(z,y,x),a(z,y,x)) = v5 * (L(x \ L(x,y,z),u,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(27388,a,26821,a)].">
      <j1 rule="hyper" parents="27388 26821"/>
    </justification>
  </clause>

  <clause id="27390">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w) \ v5,a(z,y,x),a(z,y,x)) = v5 * L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(26121(a,1),27389(a,2,2))].">
      <j1 rule="para" parents="26121 27389"/>
    </justification>
  </clause>

  <clause id="27391">
    <literal><![CDATA[
      L(a(x,y,z \ z) \ 1,L(L(z,u,w),u,w) \ z,y) \ ((y \ (x \ ((x * y) * (L(L(z,u,w),u,w) \ z)))) \ 1) = z \ L(L(z,u,w),u,w)
    ]]></literal>
    <justification jstring="[para(25564(a,1),26028(a,1,1,1,1))].">
      <j1 rule="para" parents="25564 26028"/>
    </justification>
  </clause>

  <clause id="27392">
    <literal><![CDATA[
      L(a(x,y,1) \ 1,L(L(z,u,w),u,w) \ z,y) \ ((y \ (x \ ((x * y) * (L(L(z,u,w),u,w) \ z)))) \ 1) = z \ L(L(z,u,w),u,w)
    ]]></literal>
    <justification jstring="[para(68(a,1),27391(a,1,1,1,1,3))].">
      <j1 rule="para" parents="68 27391"/>
    </justification>
  </clause>

  <clause id="27395">
    <literal><![CDATA[
      L(1 \ 1,L(L(x,y,z),y,z) \ x,u) \ ((u \ (w \ ((w * u) * (L(L(x,y,z),y,z) \ x)))) \ 1) = x \ L(L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(555(a,1),27392(a,1,1,1,1))].">
      <j1 rule="para" parents="555 27392"/>
    </justification>
  </clause>

  <clause id="27396">
    <literal><![CDATA[
      L(1,L(L(x,y,z),y,z) \ x,u) \ ((u \ (w \ ((w * u) * (L(L(x,y,z),y,z) \ x)))) \ 1) = x \ L(L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(66(a,1),27395(a,1,1,1))].">
      <j1 rule="para" parents="66 27395"/>
    </justification>
  </clause>

  <clause id="27399">
    <literal><![CDATA[
      1 \ ((x \ (y \ ((y * x) * (L(L(z,u,w),u,w) \ z)))) \ 1) = z \ L(L(z,u,w),u,w)
    ]]></literal>
    <justification jstring="[para(556(a,1),27396(a,1,1))].">
      <j1 rule="para" parents="556 27396"/>
    </justification>
  </clause>

  <clause id="27401">
    <literal><![CDATA[
      1 \ L((L(L(x,y,z),y,z) \ x) \ 1,u,w) = x \ L(L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(25963(a,1),27399(a,1,2))].">
      <j1 rule="para" parents="25963 27399"/>
    </justification>
  </clause>

  <clause id="27402">
    <literal><![CDATA[
      1 \ L(x \ L(L(x,y,z),y,z),u,w) = x \ L(L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(25592(a,1),27401(a,1,2,1))].">
      <j1 rule="para" parents="25592 27401"/>
    </justification>
  </clause>

  <clause id="27403">
    <literal><![CDATA[
      L(x \ L(L(x,y,z),y,z),u,w) = x \ L(L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(185,a,27402,a)].">
      <j1 rule="hyper" parents="185 27402"/>
    </justification>
  </clause>

  <clause id="27406">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * a(y,x,a(z,y,x))) * (a(y,x,a(z,y,x)) \ (L(x,y,z) \ x)) = (L(x,y,z) \ x) * L(L(x,y,z) \ x,a(y,x,a(z,y,x)),a(z,y,x))
    ]]></literal>
    <justification jstring="[para(23225(a,1),26243(a,2,2))].">
      <j1 rule="para" parents="23225 26243"/>
    </justification>
  </clause>

  <clause id="27407">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * a(y,x,a(z,y,x))) * (a(y,x,a(z,y,x)) \ (L(x,y,z) \ x)) = (L(x,y,z) \ x) * L(L(x,y,z) \ x,a(z,y,x),a(y,x,a(z,y,x)))
    ]]></literal>
    <justification jstring="[para(23359(a,1),27406(a,2,2))].">
      <j1 rule="para" parents="23359 27406"/>
    </justification>
  </clause>

  <clause id="27408">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * a(y,x,a(z,y,x))) * (a(y,x,a(z,y,x)) \ (L(x,y,z) \ x)) = (L(x,y,z) \ x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(23135(a,1),27407(a,2,2))].">
      <j1 rule="para" parents="23135 27407"/>
    </justification>
  </clause>

  <clause id="27409">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * a(y,x,a(z,y,x))) * (a(y,x,a(z,y,x)) \ (L(x,y,z) \ x)) = L(L(x,y,z),y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(347,a,25580,a(flip),b,27408,a),flip(a)].">
      <j1 rule="hyper" parents="347 25580 27408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27411">
    <literal><![CDATA[
      a(x,y,z) * (a(y,z,a(x,y,z)) \ (L(z,y,x) \ z)) = L(L(z,y,x),y,x) \ z
    ]]></literal>
    <justification jstring="[para(26852(a,1),27409(a,1,1))].">
      <j1 rule="para" parents="26852 27409"/>
    </justification>
  </clause>

  <clause id="27412">
    <literal><![CDATA[
      L(L(x,y,z),y,z) \ x = a(z,y,x) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(26242(a,1),27411(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26242 27411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27413">
    <literal><![CDATA[
      L(L(L(x,y,z),y,z),u,w) \ L(x,u,w) = a(z,y,L(x,u,w)) * a(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(116(a,2),27412(a,1,1))].">
      <j1 rule="para" parents="116 27412"/>
    </justification>
  </clause>

  <clause id="27414">
    <literal><![CDATA[
      (x \ L(L(x,y,z),y,z)) \ u = (a(z,y,x) * a(z,y,x)) * u
    ]]></literal>
    <justification jstring="[para(27412(a,1),25581(a,2,1))].">
      <j1 rule="para" parents="27412 25581"/>
    </justification>
  </clause>

  <clause id="27415">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * (z \ u) = L(L(z,y,x),y,x) \ u
    ]]></literal>
    <justification jstring="[para(27412(a,1),25628(a,1,1))].">
      <j1 rule="para" parents="27412 25628"/>
    </justification>
  </clause>

  <clause id="27416">
    <literal><![CDATA[
      L(x,y,z) * (a(z,y,x) * a(z,y,x)) = x * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(27412(a,1),27067(a,1,2))].">
      <j1 rule="para" parents="27412 27067"/>
    </justification>
  </clause>

  <clause id="27417">
    <literal><![CDATA[
      a(x,y,z) \ (a(x,y,z) \ 1) = z \ L(L(z,y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(980,a,27414,a)].">
      <j1 rule="hyper" parents="980 27414"/>
    </justification>
  </clause>

  <clause id="27418">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ u = (z \ L(L(z,y,x),y,x)) * u
    ]]></literal>
    <justification jstring="[hyper(355,a,27414,a),flip(a)].">
      <j1 rule="hyper" parents="355 27414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27419">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * u = z * (L(L(z,y,x),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,25630,a(flip),b,27414,a),flip(a)].">
      <j1 rule="hyper" parents="63 25630 27414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27420">
    <literal><![CDATA[
      a(x,y,z) * (z \ L(L(z,y,x),y,x)) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(150,a,27417,a)].">
      <j1 rule="hyper" parents="150 27417"/>
    </justification>
  </clause>

  <clause id="27421">
    <literal><![CDATA[
      (x * a(y,z,u)) * (u \ L(L(u,z,y),z,y)) = x * (a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,27417,a(flip),b,790,a)].">
      <j1 rule="hyper" parents="134 27417 790"/>
    </justification>
  </clause>

  <clause id="27422">
    <literal><![CDATA[
      (((x * (a(y,z,u) \ 1)) / (x * a(y,z,u))) * x) * a(y,z,u) = x * (a(y,z,u) * R(u \ L(L(u,z,y),z,y),x,a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(27417(a,1),1684(a,2,2,2,1))].">
      <j1 rule="para" parents="27417 1684"/>
    </justification>
  </clause>

  <clause id="27423">
    <literal><![CDATA[
      (x \ y) * (a(z,u,x) * a(z,u,x)) = L(L(x,u,z),u,z) \ y
    ]]></literal>
    <justification jstring="[hyper(23078,a,27415,a)].">
      <j1 rule="hyper" parents="23078 27415"/>
    </justification>
  </clause>

  <clause id="27424">
    <literal><![CDATA[
      R(x,y,z * (L(L(u,w,v5),w,v5) \ v6)) = R(x,y,z * (u \ v6))
    ]]></literal>
    <justification jstring="[para(27415(a,1),22146(a,1,3,2))].">
      <j1 rule="para" parents="27415 22146"/>
    </justification>
  </clause>

  <clause id="27425">
    <literal><![CDATA[
      R(x,y * (L(L(z,u,w),u,w) \ v5),v6) = R(x,y * (z \ v5),v6)
    ]]></literal>
    <justification jstring="[para(27415(a,1),22476(a,1,2,2))].">
      <j1 rule="para" parents="27415 22476"/>
    </justification>
  </clause>

  <clause id="27426">
    <literal><![CDATA[
      a(x,y,z * (L(L(u,w,v5),w,v5) \ v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (u \ v6)) = v7
    ]]></literal>
    <justification jstring="[para(27415(a,1),24288(a,1,3,2))].">
      <j1 rule="para" parents="27415 24288"/>
    </justification>
  </clause>

  <clause id="27427">
    <literal><![CDATA[
      L(x * (a(y,z,x) * a(y,z,x)),z,y) = x * (L(x,z,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(1391,a,27416,a)].">
      <j1 rule="hyper" parents="1391 27416"/>
    </justification>
  </clause>

  <clause id="27428">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (a(x,y,z) \ 1) = (z \ L(L(z,y,x),y,x)) * u
    ]]></literal>
    <justification jstring="[hyper(21417,a,27418,a)].">
      <j1 rule="hyper" parents="21417 27418"/>
    </justification>
  </clause>

  <clause id="27429">
    <literal><![CDATA[
      x * (L(L(x,y,z),y,z) \ u) = u * (a(z,y,x) * a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(23078,a,27419,a),flip(a)].">
      <j1 rule="hyper" parents="23078 27419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27430">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (u * a(x,y,z)) = z * (L(L(z,y,x),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(20617,a,27419,a)].">
      <j1 rule="hyper" parents="20617 27419"/>
    </justification>
  </clause>

  <clause id="27431">
    <literal><![CDATA[
      x * (T(a(y,z,u) * a(y,z,u),x) * L(w,x,a(y,z,u) * a(y,z,u))) = u * (L(L(u,z,y),z,y) \ (x * L(w,a(y,z,u) * a(y,z,u),x)))
    ]]></literal>
    <justification jstring="[hyper(10229,a,27419,a)].">
      <j1 rule="hyper" parents="10229 27419"/>
    </justification>
  </clause>

  <clause id="27432">
    <literal><![CDATA[
      (x \ L(x,x,y)) \ (a(y,x,x) * z) = x * (L(L(x,x,y),x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,25445,a,b,27419,a)].">
      <j1 rule="hyper" parents="63 25445 27419"/>
    </justification>
  </clause>

  <clause id="27433">
    <literal><![CDATA[
      (x \ ((L(x,y,z) \ L(L(x,y,z),y,z)) * u)) * (a(z,y,x) * a(z,y,x)) = L(L(x,y,z) \ u,L(x,y,z),L(x,y,z) \ L(L(x,y,z),y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,3168,a,b,27423,a),flip(a)].">
      <j1 rule="hyper" parents="347 3168 27423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27434">
    <literal><![CDATA[
      R(x,y * (L(L(z,u,w),u,w) \ v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      R(x,y * (z \ v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(27423(a,1),20903(a,1,2,2))].">
      <j1 rule="para" parents="27423 20903"/>
    </justification>
  </clause>

  <clause id="27435">
    <literal><![CDATA[
      a(x,(T(y \ z,u) * (a(w,v5,y) * a(w,v5,y))) \ v6,v7) = a(x,(L(L(y,v5,w),v5,w) \ z) \ v6,v7)
    ]]></literal>
    <justification jstring="[para(27423(a,1),24270(a,2,2,1))].">
      <j1 rule="para" parents="27423 24270"/>
    </justification>
  </clause>

  <clause id="27436">
    <literal><![CDATA[
      R(x,y,z * (L(u * w,u,u) \ v5)) = R(x,y,z * (((u \ 1) \ w) \ v5))
    ]]></literal>
    <justification jstring="[para(3192(a,1),27424(a,1,3,2,1,1))].">
      <j1 rule="para" parents="3192 27424"/>
    </justification>
  </clause>

  <clause id="27437">
    <literal><![CDATA[
      L(x * (R(x,y,z) \ (a(u,w,R(x,y,z) \ x) * a(u,w,R(x,y,z) \ x))),w,u) = (R(x,y,z) \ x) * (L(R(x,y,z) \ x,w,u) \ (R(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(1769(a,1),27427(a,1,1))].">
      <j1 rule="para" parents="1769 27427"/>
    </justification>
  </clause>

  <clause id="27438">
    <literal><![CDATA[
      a(x,y,L((z * R(u,w,v5)) * (a(v6,v7,z * R(u,w,v5)) * a(v6,v7,z * R(u,w,v5))),v7,v6)) = a(x,y,(z * L(u,w,v5)) * (L(z * R(u,w,v5),v7,v6) \ (z * R(u,w,v5))))
    ]]></literal>
    <justification jstring="[para(27427(a,2),25281(a,1,3))].">
      <j1 rule="para" parents="27427 25281"/>
    </justification>
  </clause>

  <clause id="27439">
    <literal><![CDATA[
      x \ ((x / L(L(y,z,u),z,u)) * y) = a(u,z,y) * a(u,z,y)
    ]]></literal>
    <justification jstring="[hyper(21313,a,27429,a)].">
      <j1 rule="hyper" parents="21313 27429"/>
    </justification>
  </clause>

  <clause id="27440">
    <literal><![CDATA[
      L(L(L(x,y,z),y,z),u,w) \ (L(L(x,y,z) \ L(L(x,y,z),u,w),y,z) * x) = a(z,y,x) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(4642(a,1),27439(a,1,2,1))].">
      <j1 rule="para" parents="4642 27439"/>
    </justification>
  </clause>

  <clause id="27441">
    <literal><![CDATA[
      (a(x,y,z) * u) * (z \ L(L(z,y,x),y,x)) = u * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(20248,a,27421,a)].">
      <j1 rule="hyper" parents="20248 27421"/>
    </justification>
  </clause>

  <clause id="27442">
    <literal><![CDATA[
      x / ((((a(y,z,u) \ 1) * a(y,z,u)) * (u \ L(L(u,z,y),z,y))) \ w) = (x / w) * ((a(y,z,u) \ 1) * (a(y,z,u) \ 1))
    ]]></literal>
    <justification jstring="[para(27421(a,2),896(a,1,2,1))].">
      <j1 rule="para" parents="27421 896"/>
    </justification>
  </clause>

  <clause id="27443">
    <literal><![CDATA[
      L(L(x,y,(a(z,u,w) * (a(z,u,w) \ 1)) * (w \ L(L(w,u,z),u,z))),y,v5) = L(x,y,v5 * ((a(z,u,w) \ 1) * (a(z,u,w) \ 1)))
    ]]></literal>
    <justification jstring="[para(27441(a,2),3606(a,1,1,3))].">
      <j1 rule="para" parents="27441 3606"/>
    </justification>
  </clause>

  <clause id="27444">
    <literal><![CDATA[
      R(x,y,z * (L(u * w,u,u) \ v5)) = R(x,y,z * ((u \ w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,22203,a(flip),b,27436,a),flip(a)].">
      <j1 rule="hyper" parents="347 22203 27436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27445">
    <literal><![CDATA[
      a(x,(a(y,z,u) * a(y,z,u)) \ (T(u \ w,v5) \ v6),v7) = a(x,(L(L(u,z,y),z,y) \ w) \ v6,v7)
    ]]></literal>
    <justification jstring="[para(459(a,1),27435(a,1,2))].">
      <j1 rule="para" parents="459 27435"/>
    </justification>
  </clause>

  <clause id="27446">
    <literal><![CDATA[
      a(x,(y \ L(L(y,z,u),z,u)) * (T(y \ w,v5) \ v6),v7) = a(x,(L(L(y,z,u),z,u) \ w) \ v6,v7)
    ]]></literal>
    <justification jstring="[para(27418(a,1),27445(a,1,2))].">
      <j1 rule="para" parents="27418 27445"/>
    </justification>
  </clause>

  <clause id="27447">
    <literal><![CDATA[
      a(x,(y \ L(L(y,z,u),z,u)) * ((y \ w) \ v5),v6) = a(x,(L(L(y,z,u),z,u) \ w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(24010,a,27446,a)].">
      <j1 rule="hyper" parents="24010 27446"/>
    </justification>
  </clause>

  <clause id="27448">
    <literal><![CDATA[
      a(x,(L(L(y,z,u),z,u) \ w) \ v5,v6) = a(x,((y \ w) \ v5) * (y \ y),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,25662,a(flip),b,27447,a),flip(a)].">
      <j1 rule="hyper" parents="63 25662 27447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27450">
    <literal><![CDATA[
      a(x,(L(L(y,z,u),z,u) \ w) \ v5,v6) = a(x,(y \ w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(188(a,1),27448(a,2,2))].">
      <j1 rule="para" parents="188 27448"/>
    </justification>
  </clause>

  <clause id="27452">
    <literal><![CDATA[
      L(L(L(x,y,z),y,z),u,w) \ ((x \ L(x,u,w)) * x) = a(z,y,x) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(26085(a,1),27440(a,1,2,1))].">
      <j1 rule="para" parents="26085 27440"/>
    </justification>
  </clause>

  <clause id="27453">
    <literal><![CDATA[
      L(L(L(x,y,z),y,z),u,w) \ L(x,u,w) = a(z,y,x) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(3163(a,1),27452(a,1,2))].">
      <j1 rule="para" parents="3163 27452"/>
    </justification>
  </clause>

  <clause id="27455">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * a(x,y,L(z,u,w)) = a(x,y,z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,27413,a(flip),b,27453,a)].">
      <j1 rule="hyper" parents="63 27413 27453"/>
    </justification>
  </clause>

  <clause id="27457">
    <literal><![CDATA[
      (x / y) * ((a(z,u,w) \ 1) * (a(z,u,w) \ 1)) = x / ((1 * (w \ L(L(w,u,z),u,z))) \ y)
    ]]></literal>
    <justification jstring="[para(19986(a,1),27442(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="19986 27442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27458">
    <literal><![CDATA[
      (x / y) * ((a(z,u,w) \ 1) * (a(z,u,w) \ 1)) = x / ((w \ L(L(w,u,z),u,z)) \ y)
    ]]></literal>
    <justification jstring="[para(7(a,1),27457(a,2,2,1))].">
      <j1 rule="para" parents="7 27457"/>
    </justification>
  </clause>

  <clause id="27460">
    <literal><![CDATA[
      (x / y) * ((a(z,u,w) \ 1) * (a(z,u,w) \ 1)) = x / (w * (L(L(w,u,z),u,z) \ y))
    ]]></literal>
    <justification jstring="[para(25630(a,1),27458(a,2,2))].">
      <j1 rule="para" parents="25630 27458"/>
    </justification>
  </clause>

  <clause id="27461">
    <literal><![CDATA[
      (x / y) * ((z \ L(L(z,u,w),u,w)) * 1) = x / (z * (L(L(z,u,w),u,w) \ y))
    ]]></literal>
    <justification jstring="[para(27428(a,1),27460(a,1,2))].">
      <j1 rule="para" parents="27428 27460"/>
    </justification>
  </clause>

  <clause id="27462">
    <literal><![CDATA[
      x / (y * (L(L(y,z,u),z,u) \ w)) = (x / w) * (y \ L(L(y,z,u),z,u))
    ]]></literal>
    <justification jstring="[hyper(640,a,27461,a),flip(a)].">
      <j1 rule="hyper" parents="640 27461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27463">
    <literal><![CDATA[
      (x * ((a(y,z,u) * x) \ (x * (a(y,z,u) \ 1)))) * a(y,z,u) = x * (a(y,z,u) * R(u \ L(L(u,z,y),z,y),x,a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(23264(a,1),27422(a,1,1))].">
      <j1 rule="para" parents="23264 27422"/>
    </justification>
  </clause>

  <clause id="27464">
    <literal><![CDATA[
      x * (a(y,z,u) * R(u \ L(L(u,z,y),z,y),x,a(y,z,u))) = (x * (a(y,z,u) \ (T(a(y,z,u),x) \ 1))) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(10317(a,1),27463(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10317 27463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27465">
    <literal><![CDATA[
      x * (a(y,z,u) * R(u \ L(L(u,z,y),z,y),x,a(y,z,u))) = (x * (a(y,z,u) \ (a(y,z,u) \ 1))) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(20005(a,1),27464(a,2,1,2,2,1))].">
      <j1 rule="para" parents="20005 27464"/>
    </justification>
  </clause>

  <clause id="27467">
    <literal><![CDATA[
      x * (a(y,z,u) * R(u \ L(L(u,z,y),z,y),x,a(y,z,u))) = (x * (u \ L(L(u,z,y),z,y))) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(27417(a,1),27465(a,2,1,2))].">
      <j1 rule="para" parents="27417 27465"/>
    </justification>
  </clause>

  <clause id="27468">
    <literal><![CDATA[
      x * (a(y,z,u) * L(u \ L(L(u,z,y),z,y),x,a(y,z,u))) = (x * (u \ L(L(u,z,y),z,y))) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(23247(a,1),27467(a,1,2,2))].">
      <j1 rule="para" parents="23247 27467"/>
    </justification>
  </clause>

  <clause id="27469">
    <literal><![CDATA[
      (x * (y \ L(L(y,z,u),z,u))) * a(u,z,y) = x * (a(u,z,y) * (y \ L(L(y,z,u),z,u)))
    ]]></literal>
    <justification jstring="[para(27403(a,1),27468(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="27403 27468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27471">
    <literal><![CDATA[
      (x * (y \ L(L(y,z,u),z,u))) * a(u,z,y) = x * (a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(27420(a,1),27469(a,2,2))].">
      <j1 rule="para" parents="27420 27469"/>
    </justification>
  </clause>

  <clause id="27472">
    <literal><![CDATA[
      L(L(x,y,z \ L(L(z,u,w),u,w)),y,v5) = L(x,y,v5 * ((a(w,u,z) \ 1) * (a(w,u,z) \ 1)))
    ]]></literal>
    <justification jstring="[para(71(a,1),27443(a,1,1,3))].">
      <j1 rule="para" parents="71 27443"/>
    </justification>
  </clause>

  <clause id="27474">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),L(x,y,z) \ L(L(x,y,z),y,z)) = (x \ (L(x \ L(x,y,z),y,z) * u)) * (a(z,y,x) * a(z,y,x))
    ]]></literal>
    <justification jstring="[para(4638(a,1),27433(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4638 27433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27475">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),L(x,y,z) \ L(L(x,y,z),y,z)) = (x \ ((x \ L(x,y,z)) * u)) * (a(z,y,x) * a(z,y,x))
    ]]></literal>
    <justification jstring="[para(25548(a,1),27474(a,2,1,2,1))].">
      <j1 rule="para" parents="25548 27474"/>
    </justification>
  </clause>

  <clause id="27476">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),L(x,y,z) \ L(L(x,y,z),y,z)) = ((x \ u) * (x \ L(x,y,z))) * (a(z,y,x) * a(z,y,x))
    ]]></literal>
    <justification jstring="[para(20954(a,1),27475(a,2,1))].">
      <j1 rule="para" parents="20954 27475"/>
    </justification>
  </clause>

  <clause id="27478">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),L(x,y,z) \ L(L(x,y,z),y,z)) = (x \ u) * ((x \ L(x,y,z)) * (a(z,y,x) * a(z,y,x)))
    ]]></literal>
    <justification jstring="[hyper(347,a,33,a(flip),b,27476,a),flip(a)].">
      <j1 rule="hyper" parents="347 33 27476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27479">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),L(x,y,z) \ L(L(x,y,z),y,z)) = (x \ u) * (L(L(x,y,z),y,z) \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(27423(a,1),27478(a,2,2))].">
      <j1 rule="para" parents="27423 27478"/>
    </justification>
  </clause>

  <clause id="27480">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),L(x,y,z) \ L(L(x,y,z),y,z)) = (x \ u) * L(L(x,y,z) \ x,y,z)
    ]]></literal>
    <justification jstring="[para(26122(a,1),27479(a,2,2))].">
      <j1 rule="para" parents="26122 27479"/>
    </justification>
  </clause>

  <clause id="27481">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),L(x,y,z) \ L(L(x,y,z),y,z)) = (x \ u) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(25541(a,1),27480(a,2,2))].">
      <j1 rule="para" parents="25541 27480"/>
    </justification>
  </clause>

  <clause id="27483">
    <literal><![CDATA[
      x * (L(L(x,y,z),y,z) \ (u * L(w,a(z,y,x) * a(z,y,x),u))) = u * ((a(z,y,x) * a(z,y,x)) * L(w,u,a(z,y,x) * a(z,y,x)))
    ]]></literal>
    <justification jstring="[para(23077(a,1),27431(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23077 27431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27485">
    <literal><![CDATA[
      L(x * (R(x,y,z) \ (a(u,w,L(x,y,z) \ x) * a(u,w,R(x,y,z) \ x))),w,u) = (R(x,y,z) \ x) * (L(R(x,y,z) \ x,w,u) \ (R(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(25327(a,1),27437(a,1,1,2,2,1))].">
      <j1 rule="para" parents="25327 27437"/>
    </justification>
  </clause>

  <clause id="27486">
    <literal><![CDATA[
      L(x * (R(x,y,z) \ (a(u,w,x * L(x,y,z)) * a(u,w,R(x,y,z) \ x))),w,u) = (R(x,y,z) \ x) * (L(R(x,y,z) \ x,w,u) \ (R(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(14939(a,1),27485(a,1,1,2,2,1))].">
      <j1 rule="para" parents="14939 27485"/>
    </justification>
  </clause>

  <clause id="27487">
    <literal><![CDATA[
      L(x * (R(x,y,z) \ (a(u,w,x * L(x,y,z)) * a(u,w,L(x,y,z) \ x))),w,u) = (R(x,y,z) \ x) * (L(R(x,y,z) \ x,w,u) \ (R(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(25327(a,1),27486(a,1,1,2,2,2))].">
      <j1 rule="para" parents="25327 27486"/>
    </justification>
  </clause>

  <clause id="27488">
    <literal><![CDATA[
      L(x * (R(x,y,z) \ (a(u,w,x * L(x,y,z)) * a(u,w,x * L(x,y,z)))),w,u) = (R(x,y,z) \ x) * (L(R(x,y,z) \ x,w,u) \ (R(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(14939(a,1),27487(a,1,1,2,2,2))].">
      <j1 rule="para" parents="14939 27487"/>
    </justification>
  </clause>

  <clause id="27489">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (L(R(x,y,z) \ x,u,w) \ (R(x,y,z) \ x)) = L(x * (R(x,y,z) \ 1),u,w)
    ]]></literal>
    <justification jstring="[para(26752(a,1),27488(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="26752 27488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27490">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (L(R(x,y,z) \ x,u,w) \ (R(x,y,z) \ x)) = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(1755(a,1),27489(a,2,1))].">
      <j1 rule="para" parents="1755 27489"/>
    </justification>
  </clause>

  <clause id="27492">
    <literal><![CDATA[
      L(1 / (R(x,y,z) \ x),u,w) \ 1 = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(3640,a,27490,a)].">
      <j1 rule="hyper" parents="3640 27490"/>
    </justification>
  </clause>

  <clause id="27493">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) \ 1 = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(4743(a,1),27492(a,1,1,1))].">
      <j1 rule="para" parents="4743 27492"/>
    </justification>
  </clause>

  <clause id="27494">
    <literal><![CDATA[
      L(R(x,y,z) \ x,x,z * y) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(18786(a,2),27493(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18786 27493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27495">
    <literal><![CDATA[
      L(R(x,y \ z,y) \ x,x,z) = a(x,y \ z,y) \ 1
    ]]></literal>
    <justification jstring="[para(18789(a,1),27493(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18789 27493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27496">
    <literal><![CDATA[
      L(R(x,y,z) \ x,x,y) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(26936(a,2),27493(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26936 27493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27497">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,z * y) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(26307,a,27494,a)].">
      <j1 rule="hyper" parents="26307 27494"/>
    </justification>
  </clause>

  <clause id="27498">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,y * z) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(20105,a,27497,a)].">
      <j1 rule="hyper" parents="20105 27497"/>
    </justification>
  </clause>

  <clause id="27499">
    <literal><![CDATA[
      L(a(R(x,y,z),u,w) \ 1,L(x,y,z),u * w) = R(R(x,y,z),u,w) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21974,a(flip),b,27498,a)].">
      <j1 rule="hyper" parents="63 21974 27498"/>
    </justification>
  </clause>

  <clause id="27500">
    <literal><![CDATA[
      L(R(a(x,y,z) \ 1,u,w),x,y * z) = R(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(27498(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27498 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27501">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),x,y * z) = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(27498(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27498 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27502">
    <literal><![CDATA[
      R(x,(y \ (y \ (R(y,z \ y,z) \ y))) * u,w) = R(x,u * (a(y,z \ y,z) \ 1),w)
    ]]></literal>
    <justification jstring="[para(27495(a,1),22491(a,2,2,2))].">
      <j1 rule="para" parents="27495 22491"/>
    </justification>
  </clause>

  <clause id="27503">
    <literal><![CDATA[
      L(L(x,a(y,z,u) \ w,a(y,z,u)) \ x,x,w) = a(x,a(y,z,u) \ w,a(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(23247(a,1),27495(a,1,1,1))].">
      <j1 rule="para" parents="23247 27495"/>
    </justification>
  </clause>

  <clause id="27504">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),x,y * z) = R(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(23384(a,1),27500(a,1,1))].">
      <j1 rule="para" parents="23384 27500"/>
    </justification>
  </clause>

  <clause id="27505">
    <literal><![CDATA[
      R(R(x,y,z) \ x,u,w) = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,27501,a(flip),b,27504,a),flip(a)].">
      <j1 rule="hyper" parents="63 27501 27504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27506">
    <literal><![CDATA[
      L(a(L(x,y,z),u,w) \ 1,L(x,y,z),u * w) = R(R(x,y,z),u,w) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(25182(a,1),27499(a,1,1,1))].">
      <j1 rule="para" parents="25182 27499"/>
    </justification>
  </clause>

  <clause id="27507">
    <literal><![CDATA[
      R(R(x,y,z),u,w) \ R(x,y,z) = R(L(x,y,z),u,w) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,27498,a(flip),b,27506,a),flip(a)].">
      <j1 rule="hyper" parents="63 27498 27506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27508">
    <literal><![CDATA[
      R(R(x,y,z),u,w) \ R(x,y,z) = L(R(x,u,w),y,z) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(29(a,1),27507(a,2,1))].">
      <j1 rule="para" parents="29 27507"/>
    </justification>
  </clause>

  <clause id="27509">
    <literal><![CDATA[
      L(L(1 / L(x,y,z),u,w),L(1 / L(x,y,z),u,w),v5) \ (1 \ L(1 / L(x,y,z),u,w)) = a(v5,L(1 / L(x,y,z),u,w),L(L(1 / x,u,w) \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(66(a,1),26240(a,1,1,1))].">
      <j1 rule="para" parents="66 26240"/>
    </justification>
  </clause>

  <clause id="27510">
    <literal><![CDATA[
      L(L(1 / L(x,y,z),u,w),L(L(x,y,z),u,w),v5) \ (1 \ L(1 / L(x,y,z),u,w)) = a(v5,L(1 / L(x,y,z),u,w),L(L(1 / x,u,w) \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(3370(a,1),27509(a,1,1))].">
      <j1 rule="para" parents="3370 27509"/>
    </justification>
  </clause>

  <clause id="27511">
    <literal><![CDATA[
      L(L(1 / L(x,y,z),u,w),L(L(x,y,z),u,w),v5) \ L(1 / L(x,y,z),u,w) = a(v5,L(1 / L(x,y,z),u,w),L(L(1 / x,u,w) \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(66(a,1),27510(a,1,2))].">
      <j1 rule="para" parents="66 27510"/>
    </justification>
  </clause>

  <clause id="27512">
    <literal><![CDATA[
      L(L(1 / L(x,y,z),L(L(x,y,z),u,w),v5) \ (1 / L(x,y,z)),u,w) = a(v5,L(1 / L(x,y,z),u,w),L(L(1 / x,u,w) \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,26122,a(flip),b,27511,a)].">
      <j1 rule="hyper" parents="63 26122 27511"/>
    </justification>
  </clause>

  <clause id="27513">
    <literal><![CDATA[
      L(L(L(x,y,z) \ 1,L(L(x,y,z),u,w),v5) \ (L(x,y,z) \ 1),u,w) = a(v5,L(1 / L(x,y,z),u,w),L(L(1 / x,u,w) \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(3504(a,1),27512(a,1,1))].">
      <j1 rule="para" parents="3504 27512"/>
    </justification>
  </clause>

  <clause id="27514">
    <literal><![CDATA[
      L(L(L(x,y,z),L(L(x,y,z),u,w),v5) \ L(x,y,z),u,w) = a(v5,L(1 / L(x,y,z),u,w),L(L(1 / x,u,w) \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(10875(a,1),27513(a,1,1))].">
      <j1 rule="para" parents="10875 27513"/>
    </justification>
  </clause>

  <clause id="27515">
    <literal><![CDATA[
      a(x,L(1 / L(y,z,u),w,v5),L(L(1 / y,w,v5) \ 1,z,u)) = a(x,L(L(y,z,u),w,v5),L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,26461,a(flip),b,27514,a),flip(a)].">
      <j1 rule="hyper" parents="63 26461 27514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27516">
    <literal><![CDATA[
      a(x,L(1 / L(y,z,u),w,v5),L(L(1 / y,w,v5) \ 1,z,u)) = a(x,L(y,z,u),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,26464,a(flip),b,27515,a),flip(a)].">
      <j1 rule="hyper" parents="347 26464 27515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27518">
    <literal><![CDATA[
      a(x,L(1 / L(y,z,u),w,v5),L(L(1 / y,w,v5) \ 1,z,u)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,26464,a(flip),b,27516,a),flip(a)].">
      <j1 rule="hyper" parents="347 26464 27516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27519">
    <literal><![CDATA[
      a(x,L(1 / L(y,z,u),w,v5),L(L(1 / y,w,v5),z,u)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(15032,a,27518,a)].">
      <j1 rule="hyper" parents="15032 27518"/>
    </justification>
  </clause>

  <clause id="27521">
    <literal><![CDATA[
      a(x,L(1 / L(y,z,u),w,v5),L(L(y \ 1,w,v5),z,u)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(24942,a,27519,a)].">
      <j1 rule="hyper" parents="24942 27519"/>
    </justification>
  </clause>

  <clause id="27522">
    <literal><![CDATA[
      a(x,L(1 / L(y,z,u),w,v5),L(L(y,w,v5),z,u)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(15053,a,27521,a)].">
      <j1 rule="hyper" parents="15053 27521"/>
    </justification>
  </clause>

  <clause id="27523">
    <literal><![CDATA[
      a(x,L(L(y,z,u) \ 1,w,v5),L(L(y,w,v5),z,u)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(24585,a,27522,a)].">
      <j1 rule="hyper" parents="24585 27522"/>
    </justification>
  </clause>

  <clause id="27524">
    <literal><![CDATA[
      a(x,L(L(y,z,u),w,v5),L(L(y,w,v5),z,u)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(15029,a,27523,a)].">
      <j1 rule="hyper" parents="15029 27523"/>
    </justification>
  </clause>

  <clause id="27525">
    <literal><![CDATA[
      (x * ((L(y,z,u) * L(y \ 1,z,u)) \ w)) \ (x * ((L(y,z,u) * L(y \ 1,z,u)) \ w)) = a(L(y,z,u) * L(y \ 1,z,u),(L(y,z,u) * L(y \ 1,z,u)) \ x,w)
    ]]></literal>
    <justification jstring="[para(23570(a,1),23568(a,1,2))].">
      <j1 rule="para" parents="23570 23568"/>
    </justification>
  </clause>

  <clause id="27526">
    <literal><![CDATA[
      a(L(x,y,z) * L(x \ 1,y,z),(L(x,y,z) * L(x \ 1,y,z)) \ u,w) = 1
    ]]></literal>
    <justification jstring="[hyper(236,a,27525,a),flip(a)].">
      <j1 rule="hyper" parents="236 27525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27527">
    <literal><![CDATA[
      a(L(x,y,z) * L(x \ 1,y,z),u,w) = 1
    ]]></literal>
    <justification jstring="[hyper(26007,a,27526,a)].">
      <j1 rule="hyper" parents="26007 27526"/>
    </justification>
  </clause>

  <clause id="27530">
    <literal><![CDATA[
      a(x \ L(L(x,y,z),y,z),u,w) = 1
    ]]></literal>
    <justification jstring="[para(25562(a,1),27527(a,1,1))].">
      <j1 rule="para" parents="25562 27527"/>
    </justification>
  </clause>

  <clause id="27531">
    <literal><![CDATA[
      L(x,y,z \ L(L(z,u,w),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,27530,a)].">
      <j1 rule="hyper" parents="52 27530"/>
    </justification>
  </clause>

  <clause id="27532">
    <literal><![CDATA[
      L(L(x,y,z \ L(L(z,u,w),u,w)),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(27531(a,1),161(a,2))].">
      <j1 rule="para" parents="27531 161"/>
    </justification>
  </clause>

  <clause id="27533">
    <literal><![CDATA[
      L(x,y,z * ((a(u,w,v5) \ 1) * (a(u,w,v5) \ 1))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(27531(a,1),27472(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27531 27472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27535">
    <literal><![CDATA[
      L(x,y,z * ((u \ L(L(u,w,v5),w,v5)) * 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(27428(a,1),27533(a,1,3,2))].">
      <j1 rule="para" parents="27428 27533"/>
    </justification>
  </clause>

  <clause id="27536">
    <literal><![CDATA[
      L(x,y,z * (u \ L(L(u,w,v5),w,v5))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),27535(a,1,3,2))].">
      <j1 rule="para" parents="8 27535"/>
    </justification>
  </clause>

  <clause id="27537">
    <literal><![CDATA[
      L(x,y,L(L(z,u,w),u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),27536(a,1,3))].">
      <j1 rule="para" parents="10 27536"/>
    </justification>
  </clause>

  <clause id="27538">
    <literal><![CDATA[
      L(x,y,z * L(L(u,w,v5),w,v5)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(25593(a,1),27536(a,1,3))].">
      <j1 rule="para" parents="25593 27536"/>
    </justification>
  </clause>

  <clause id="27539">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ 1) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(27420(a,1),27536(a,1,3))].">
      <j1 rule="para" parents="27420 27536"/>
    </justification>
  </clause>

  <clause id="27540">
    <literal><![CDATA[
      L(x,y,z * (a(u,w,v5) \ 1)) = L(x,y,z * a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(27421(a,1),27536(a,1,3))].">
      <j1 rule="para" parents="27421 27536"/>
    </justification>
  </clause>

  <clause id="27541">
    <literal><![CDATA[
      L(L(x,y,z \ L(L(z,u,w),u,w)),v5,v6) = L(x,v5,L(L(v6,v7,v8),v7,v8))
    ]]></literal>
    <justification jstring="[hyper(27532,a,27537,a),flip(a)].">
      <j1 rule="hyper" parents="27532 27537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27542">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),v5,z) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,12369,a(flip),b,27537,a),flip(a)].">
      <j1 rule="hyper" parents="63 12369 27537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27543">
    <literal><![CDATA[
      L(x,y,L(z \ 1,u,w)) = L(x,y,L(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(25955(a,1),27537(a,1,3,1))].">
      <j1 rule="para" parents="25955 27537"/>
    </justification>
  </clause>

  <clause id="27544">
    <literal><![CDATA[
      (a(x,y,z) \ y) \ (((a(x,y,z) \ y) / y) * u) = L(y \ u,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,26552,a,b,27539,a)].">
      <j1 rule="hyper" parents="63 26552 27539"/>
    </justification>
  </clause>

  <clause id="27546">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,u,z))) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,26138,a(flip),b,27539,a),flip(a)].">
      <j1 rule="hyper" parents="63 26138 27539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27547">
    <literal><![CDATA[
      L(x \ y,x,a(z,z,y)) = ((y \ L(y,z,z)) * x) \ L(y,z,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,14647,a(flip),b,27539,a),flip(a)].">
      <j1 rule="hyper" parents="63 14647 27539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27548">
    <literal><![CDATA[
      L(x \ ((a(y,z,u) \ 1) \ w),x,a(y,z,u)) = ((a(y,z,u) \ 1) * x) \ w
    ]]></literal>
    <justification jstring="[hyper(63,a,329,a(flip),b,27539,a),flip(a)].">
      <j1 rule="hyper" parents="63 329 27539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27549">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,w,u))) = L(x,y,(L(w,u,z) \ w) \ 1)
    ]]></literal>
    <justification jstring="[para(26225(a,1),27539(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="26225 27539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27551">
    <literal><![CDATA[
      x * a(x,y,L(y,z,u)) = R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,27542,a(flip),b,26935,a(flip))].">
      <j1 rule="hyper" parents="134 27542 26935"/>
    </justification>
  </clause>

  <clause id="27552">
    <literal><![CDATA[
      R(x,y,y) \ R(x,y,L(y,z,u)) = a(u,z,z \ (a(x,y,y) \ z)) \ 1
    ]]></literal>
    <justification jstring="[para(27551(a,1),26928(a,1,2))].">
      <j1 rule="para" parents="27551 26928"/>
    </justification>
  </clause>

  <clause id="27553">
    <literal><![CDATA[
      L(x,y,a(z,u,u)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(15277(a,1),27546(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15277 27546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27554">
    <literal><![CDATA[
      L(x,y,a(z,y,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(27546(a,1),26320(a,1))].">
      <j1 rule="para" parents="27546 26320"/>
    </justification>
  </clause>

  <clause id="27555">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(26489(a,1),27546(a,1,3))].">
      <j1 rule="para" parents="26489 27546"/>
    </justification>
  </clause>

  <clause id="27556">
    <literal><![CDATA[
      (a(x,y,y) * y) \ z = y \ (a(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(27554,a,26378,a)].">
      <j1 rule="hyper" parents="27554 26378"/>
    </justification>
  </clause>

  <clause id="27557">
    <literal><![CDATA[
      L(x * y,z,a(y,x,x)) = x * y
    ]]></literal>
    <justification jstring="[hyper(347,a,23254,a(flip),b,27553,a),flip(a)].">
      <j1 rule="hyper" parents="347 23254 27553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27558">
    <literal><![CDATA[
      (x * y) \ (z * a(y,x,x)) = ((x * y) \ z) * a(y,x,x)
    ]]></literal>
    <justification jstring="[para(27557(a,1),23246(a,1,1))].">
      <j1 rule="para" parents="27557 23246"/>
    </justification>
  </clause>

  <clause id="27559">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,a(w,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(26380,a,27555,a)].">
      <j1 rule="hyper" parents="26380 27555"/>
    </justification>
  </clause>

  <clause id="27560">
    <literal><![CDATA[
      L(a(x,y,z),u,a(z,y,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(21178,a,27555,a),flip(a)].">
      <j1 rule="hyper" parents="21178 27555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27561">
    <literal><![CDATA[
      L((a(x,y,z) * u) \ w,u,a(z,y,x)) = u \ (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(347,a,26378,a(flip),b,27555,a),flip(a)].">
      <j1 rule="hyper" parents="347 26378 27555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27563">
    <literal><![CDATA[
      (a(x,y,z) * u) / L(w,w \ u,a(z,y,x)) = a(x,y,z) * (u / w)
    ]]></literal>
    <justification jstring="[hyper(220,a,27555,a,b,9645,a(flip))].">
      <j1 rule="hyper" parents="220 27555 9645"/>
    </justification>
  </clause>

  <clause id="27564">
    <literal><![CDATA[
      a(x,y,z) * L(1 / u,u,a(z,y,x)) = a(x,y,z) / u
    ]]></literal>
    <justification jstring="[hyper(134,a,27555,a,b,3264,a(flip))].">
      <j1 rule="hyper" parents="134 27555 3264"/>
    </justification>
  </clause>

  <clause id="27565">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ a(u,z,y) = (x \ 1) * a(u,z,y)
    ]]></literal>
    <justification jstring="[para(27555(a,1),23153(a,1,1))].">
      <j1 rule="para" parents="27555 23153"/>
    </justification>
  </clause>

  <clause id="27566">
    <literal><![CDATA[
      L(x,y,a(z * u,w,v5)) = L(x,y,a(v5,w,u * z))
    ]]></literal>
    <justification jstring="[para(23896(a,1),27555(a,1,3))].">
      <j1 rule="para" parents="23896 27555"/>
    </justification>
  </clause>

  <clause id="27567">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(v5,y,a(w,u,z)) = x
    ]]></literal>
    <justification jstring="[para(27555(a,1),26380(a,1))].">
      <j1 rule="para" parents="27555 26380"/>
    </justification>
  </clause>

  <clause id="27568">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (x \ v5) = x * (L(x,y,a(w,u,z)) \ v5)
    ]]></literal>
    <justification jstring="[para(27555(a,1),27059(a,1,1))].">
      <j1 rule="para" parents="27555 27059"/>
    </justification>
  </clause>

  <clause id="27569">
    <literal><![CDATA[
      T(x,a(y,z,u)) = L(L(x,w,a(v5,v6,v7)),w,a(v7,v6,v5))
    ]]></literal>
    <justification jstring="[hyper(20031,a,27559,a)].">
      <j1 rule="hyper" parents="20031 27559"/>
    </justification>
  </clause>

  <clause id="27570">
    <literal><![CDATA[
      a(x,y,z) * (L(u,w,a(z,y,x)) * w) = u * (a(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(27559(a,1),23242(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27559 23242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27571">
    <literal><![CDATA[
      R(x,y,z) \ (a(u,R(x,y,z),R(x,y,z)) \ (R(x,y,z) * (T(a(u,R(x,y,z),R(x,y,z)),x) * w))) = L(w,a(u,R(x,y,z),R(x,y,z)),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(23700,a,27556,a),flip(a)].">
      <j1 rule="hyper" parents="23700 27556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27572">
    <literal><![CDATA[
      a(x,y * (z \ (a(u,z,z) \ w)),v5) = a(x,(L(z,z,u) \ w) * y,v5)
    ]]></literal>
    <justification jstring="[para(27556(a,1),25527(a,1,2,2))].">
      <j1 rule="para" parents="27556 25527"/>
    </justification>
  </clause>

  <clause id="27573">
    <literal><![CDATA[
      L(x,y,L(z \ 1,u,w) \ 1) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(27543(a,1),20662(a,1))].">
      <j1 rule="para" parents="27543 20662"/>
    </justification>
  </clause>

  <clause id="27574">
    <literal><![CDATA[
      a(x,y,L(z,u,L(w \ 1,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,L(w,v5,v6))) = v7
    ]]></literal>
    <justification jstring="[para(27543(a,2),24896(a,1,3))].">
      <j1 rule="para" parents="27543 24896"/>
    </justification>
  </clause>

  <clause id="27575">
    <literal><![CDATA[
      L(x,y,a(z,u,w * v5)) = L(x,y,a(z,u,v5 * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,27555,a,b,27566,a)].">
      <j1 rule="hyper" parents="63 27555 27566"/>
    </justification>
  </clause>

  <clause id="27576">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,a(w,u,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(27569(a,1),12667(a,1))].">
      <j1 rule="para" parents="27569 12667"/>
    </justification>
  </clause>

  <clause id="27578">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(w,u,z)) = v5
    ]]></literal>
    <justification jstring="[para(26375(a,1),27576(a,1,1))].">
      <j1 rule="para" parents="26375 27576"/>
    </justification>
  </clause>

  <clause id="27579">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(27555(a,1),27576(a,1,1))].">
      <j1 rule="para" parents="27555 27576"/>
    </justification>
  </clause>

  <clause id="27581">
    <literal><![CDATA[
      L(x,y,a(z,u * w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(v5,w * u,z)) = v6
    ]]></literal>
    <justification jstring="[para(24037(a,1),27578(a,1,3))].">
      <j1 rule="para" parents="24037 27578"/>
    </justification>
  </clause>

  <clause id="27582">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ 1) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(w,u,z)) = v5
    ]]></literal>
    <justification jstring="[para(27539(a,2),27578(a,1))].">
      <j1 rule="para" parents="27539 27578"/>
    </justification>
  </clause>

  <clause id="27583">
    <literal><![CDATA[
      L(x,y,a(z * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(u * z,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(27566(a,2),27578(a,1))].">
      <j1 rule="para" parents="27566 27578"/>
    </justification>
  </clause>

  <clause id="27584">
    <literal><![CDATA[
      L((a(x,y,z) * u) \ w,u,a(x,y,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      u \ (a(x,y,z) \ w) = v5
    ]]></literal>
    <justification jstring="[para(329(a,1),27579(a,1,1))].">
      <j1 rule="para" parents="329 27579"/>
    </justification>
  </clause>

  <clause id="27585">
    <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(21366(a,1),27579(a,1,1))].">
      <j1 rule="para" parents="21366 27579"/>
    </justification>
  </clause>

  <clause id="27586">
    <literal><![CDATA[
      L(L(x,y,z),u,a(w,v5,x)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(23130(a,1),27579(a,1,1))].">
      <j1 rule="para" parents="23130 27579"/>
    </justification>
  </clause>

  <clause id="27587">
    <literal><![CDATA[
      L(L(L(x,y,z),u,w),v5,a(v6,v7,x)) != v8
    ]]></literal>
    <literal><![CDATA[
      L(L(x,y,z),u,w) = v8
    ]]></literal>
    <justification jstring="[para(23133(a,1),27579(a,1,1))].">
      <j1 rule="para" parents="23133 27579"/>
    </justification>
  </clause>

  <clause id="27588">
    <literal><![CDATA[
      L(L(x,y,a(z,a(u,w,v5),v6)),y,a(z,a(v5,w,u),v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(26499(a,1),27579(a,1,1,3))].">
      <j1 rule="para" parents="26499 27579"/>
    </justification>
  </clause>

  <clause id="27589">
    <literal><![CDATA[
      L(x,y,z \ L(z,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,z,u)) = w
    ]]></literal>
    <justification jstring="[para(25426(a,1),27582(a,1,3))].">
      <j1 rule="para" parents="25426 27582"/>
    </justification>
  </clause>

  <clause id="27590">
    <literal><![CDATA[
      L(x,y,z * a(u,w,v5)) = L(x,y,z * a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,26872,a(flip),b,27540,a)].">
      <j1 rule="hyper" parents="63 26872 27540"/>
    </justification>
  </clause>

  <clause id="27591">
    <literal><![CDATA[
      L(x,y,z * (u * L(1 / u,u,w))) = L(x,y,z * a(u \ w,u,u))
    ]]></literal>
    <justification jstring="[para(25460(a,1),27540(a,1,3,2))].">
      <j1 rule="para" parents="25460 27540"/>
    </justification>
  </clause>

  <clause id="27592">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ u) = L(x,y,u * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(26536(a,1),27540(a,1,3))].">
      <j1 rule="para" parents="26536 27540"/>
    </justification>
  </clause>

  <clause id="27593">
    <literal><![CDATA[
      L(x,y,z * a(L(u,u,w),w,v5)) = L(x,y,z * ((u \ R(u,w,v5)) \ 1))
    ]]></literal>
    <justification jstring="[para(26951(a,1),27540(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="26951 27540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27594">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * v5) = L(x,y,v5 * a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(20105,a,27590,a)].">
      <j1 rule="hyper" parents="20105 27590"/>
    </justification>
  </clause>

  <clause id="27595">
    <literal><![CDATA[
      L(x,a(y,z,u) \ z,z * a(y,z,u)) = L(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,27097,a(flip),b,27592,a),flip(a)].">
      <j1 rule="hyper" parents="63 27097 27592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27596">
    <literal><![CDATA[
      L(x,x,y * a(z,u,x)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,25614,a(flip),b,27594,a),flip(a)].">
      <j1 rule="hyper" parents="63 25614 27594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27597">
    <literal><![CDATA[
      L(x,x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      a(y * a(u,w,x),x,x) = z
    ]]></literal>
    <justification jstring="[para(27596(a,1),25427(a,1,1))].">
      <j1 rule="para" parents="27596 25427"/>
    </justification>
  </clause>

  <clause id="27598">
    <literal><![CDATA[
      L(x,y * a(z,y,u),y * a(z,y,u)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(26545,a,27595,a)].">
      <j1 rule="hyper" parents="26545 27595"/>
    </justification>
  </clause>

  <clause id="27599">
    <literal><![CDATA[
      a(x * a(y,z,u),u,u) = a(x,u,u)
    ]]></literal>
    <justification jstring="[hyper(27597,a,25425,a)].">
      <j1 rule="hyper" parents="27597 25425"/>
    </justification>
  </clause>

  <clause id="27600">
    <literal><![CDATA[
      (x * y) * (((x * y) \ z) * a(y,x,x)) != u
    ]]></literal>
    <literal><![CDATA[
      z * a(y,x,x) = u
    ]]></literal>
    <justification jstring="[para(27558(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="27558 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27601">
    <literal><![CDATA[
      a(x,y,z) * (a(z,y,x) \ (a(z,y,x) / u)) = a(x,y,z) / u
    ]]></literal>
    <justification jstring="[para(3264(a,1),27564(a,1,2))].">
      <j1 rule="para" parents="3264 27564"/>
    </justification>
  </clause>

  <clause id="27602">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,w,u))) = L(x,y,w \ L(w,u,z))
    ]]></literal>
    <justification jstring="[para(10888(a,1),27549(a,2,3))].">
      <j1 rule="para" parents="10888 27549"/>
    </justification>
  </clause>

  <clause id="27603">
    <literal><![CDATA[
      L(L(x,y,z \ L(z,u,w)),y,a(w,u,L(z,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(26380,a,27602,a)].">
      <j1 rule="hyper" parents="26380 27602"/>
    </justification>
  </clause>

  <clause id="27604">
    <literal><![CDATA[
      R(x,y,z * L(z,u,w)) = L(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,26253,a(flip),b,27602,a)].">
      <j1 rule="hyper" parents="63 26253 27602"/>
    </justification>
  </clause>

  <clause id="27605">
    <literal><![CDATA[
      L(1 / x,y,z \ L(z,u,x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(63,a,25981,a(flip),b,27602,a),flip(a)].">
      <j1 rule="hyper" parents="63 25981 27602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27606">
    <literal><![CDATA[
      L(x,y,z \ L(z,u,x)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,25365,a(flip),b,27602,a),flip(a)].">
      <j1 rule="hyper" parents="63 25365 27602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27608">
    <literal><![CDATA[
      L(x,y,L(z,u,w) \ z) = L(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(26225(a,1),27602(a,1,3))].">
      <j1 rule="para" parents="26225 27602"/>
    </justification>
  </clause>

  <clause id="27609">
    <literal><![CDATA[
      (x \ L(x,y,z)) / (z \ 1) = (x \ L(x,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(134,a,27606,a(flip),b,3194,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="134 27606 3194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27610">
    <literal><![CDATA[
      R(x,y,z * (u \ (z \ u))) = L(x,y,z \ L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(22191,a,27604,a)].">
      <j1 rule="hyper" parents="22191 27604"/>
    </justification>
  </clause>

  <clause id="27611">
    <literal><![CDATA[
      R(x,y,L(z,u,w) \ z) = L(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(21423,a,27604,a)].">
      <j1 rule="hyper" parents="21423 27604"/>
    </justification>
  </clause>

  <clause id="27612">
    <literal><![CDATA[
      R(x,y,z \ L(z,u,w)) = L(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(3978,a,27604,a)].">
      <j1 rule="hyper" parents="3978 27604"/>
    </justification>
  </clause>

  <clause id="27613">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),y * L(y,z,u)) \ x = a(y \ L(y,z,u),y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(27604(a,2),14600(a,1,1))].">
      <j1 rule="para" parents="27604 14600"/>
    </justification>
  </clause>

  <clause id="27614">
    <literal><![CDATA[
      L(x,y,(K(z,u) * (T(w,v5) \ v6)) \ L(K(z,u) * (T(w,v5) \ v6),w,v5)) = R(x,y,(K(z,u) * (T(w,v5) \ v6)) * (K(z,u) * ((w * v5) \ (v5 * v6))))
    ]]></literal>
    <justification jstring="[para(21268(a,1),27604(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="21268 27604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27615">
    <literal><![CDATA[
      L(x,x,y \ L(y,z,u)) * (y \ L(y,z,u)) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(27604(a,1),22992(a,1,1))].">
      <j1 rule="para" parents="27604 22992"/>
    </justification>
  </clause>

  <clause id="27616">
    <literal><![CDATA[
      L(a(x,y,y * L(y,x,z)) \ y,x,y \ L(y,x,z)) = ((L(y,x,z) \ y) * x) \ (a(z,x,y) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,26796,a(flip),b,27608,a),flip(a)].">
      <j1 rule="hyper" parents="63 26796 27608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27617">
    <literal><![CDATA[
      (x \ L(x,y,z)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (x / z) \ L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(27609(a,1),23365(a,1))].">
      <j1 rule="para" parents="27609 23365"/>
    </justification>
  </clause>

  <clause id="27618">
    <literal><![CDATA[
      L(x,x,y \ L(y,x,z)) = L(x,x,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(26189,a,27611,a),flip(a)].">
      <j1 rule="hyper" parents="26189 27611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27619">
    <literal><![CDATA[
      L(x \ L(x,y,y \ L(y,z,u)),x,z \ (u \ ((u * z) * y))) = a(x,y,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(27611(a,1),26003(a,1,1,2))].">
      <j1 rule="para" parents="27611 26003"/>
    </justification>
  </clause>

  <clause id="27620">
    <literal><![CDATA[
      (x \ L(x,y,z)) / ((L(x,y,z) \ x) \ z) = L(1 / z,z,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,25559,a,b,27612,a)].">
      <j1 rule="hyper" parents="63 25559 27612"/>
    </justification>
  </clause>

  <clause id="27621">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,w \ L(w,u,z)) = v5
    ]]></literal>
    <justification jstring="[para(27603(a,1),27579(a,1,1))].">
      <j1 rule="para" parents="27603 27579"/>
    </justification>
  </clause>

  <clause id="27622">
    <literal><![CDATA[
      R(x,y,z * (u \ (z \ u))) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,z,u)) = w
    ]]></literal>
    <justification jstring="[para(27610(a,2),27589(a,1))].">
      <j1 rule="para" parents="27610 27589"/>
    </justification>
  </clause>

  <clause id="27623">
    <literal><![CDATA[
      L(x,y,a(z,z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,z,u)) = w
    ]]></literal>
    <justification jstring="[para(27292(a,1),27622(a,1))].">
      <j1 rule="para" parents="27292 27622"/>
    </justification>
  </clause>

  <clause id="27624">
    <literal><![CDATA[
      L(x,y,L(z,u,w) \ z) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(26225(a,1),27621(a,1,3))].">
      <j1 rule="para" parents="26225 27621"/>
    </justification>
  </clause>

  <clause id="27625">
    <literal><![CDATA[
      L(x,y,z * a(u \ w,u,u)) = L(x,y,z * (u \ L(u,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,21604,a(flip),b,27591,a),flip(a)].">
      <j1 rule="hyper" parents="63 21604 27591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27626">
    <literal><![CDATA[
      L(x,y,z * a(u \ w,u,u)) = L(x,y,z * a(u,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,25031,a(flip),b,27625,a),flip(a)].">
      <j1 rule="hyper" parents="347 25031 27625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27627">
    <literal><![CDATA[
      L(x,y,((z \ T(u,w)) \ u) * a(z,z,u)) = L(x,y,(u \ (z \ u)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,25684,a(flip),b,27626,a),flip(a)].">
      <j1 rule="hyper" parents="63 25684 27626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27628">
    <literal><![CDATA[
      L(x,x,y \ L(y,x,z)) * (y \ L(y,x,z)) = a(z,x,x * (y \ x)) \ x
    ]]></literal>
    <justification jstring="[hyper(347,a,26542,a,b,27615,a),flip(a)].">
      <j1 rule="hyper" parents="347 26542 27615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27629">
    <literal><![CDATA[
      L(x,x,a(y,z,z) \ 1) * (z \ L(z,z,y)) = (z / x) \ L(z,z,y)
    ]]></literal>
    <justification jstring="[para(25426(a,2),27615(a,1,1,3))].">
      <j1 rule="para" parents="25426 27615"/>
    </justification>
  </clause>

  <clause id="27630">
    <literal><![CDATA[
      L(x,x,a(y,z,z)) * (z \ L(z,z,y)) = (z / x) \ L(z,z,y)
    ]]></literal>
    <justification jstring="[para(27539(a,1),27629(a,1,1))].">
      <j1 rule="para" parents="27539 27629"/>
    </justification>
  </clause>

  <clause id="27631">
    <literal><![CDATA[
      L(x,y,L(L(z,u,w),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(27541(a,1),27532(a,1))].">
      <j1 rule="para" parents="27541 27532"/>
    </justification>
  </clause>

  <clause id="27632">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u) = a(z,y,y \ (a(u,x,x) \ y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,25227,a(flip),b,27552,a)].">
      <j1 rule="hyper" parents="63 25227 27552"/>
    </justification>
  </clause>

  <clause id="27633">
    <literal><![CDATA[
      a(x,y,L((z \ 1) * u,u * z,L(u,u,z))) = a(x,y,((z \ 1) * (((z \ 1) * u) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(27574,a,23712,a)].">
      <j1 rule="hyper" parents="27574 23712"/>
    </justification>
  </clause>

  <clause id="27634">
    <literal><![CDATA[
      a(x,y,L(z * (a(u,w,u) \ v5),v5 * z,L(v5,v5,z))) = a(x,y,((a(u,w,u) \ z) * (((a(u,w,u) \ z) * v5) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(27574,a,21861,a)].">
      <j1 rule="hyper" parents="27574 21861"/>
    </justification>
  </clause>

  <clause id="27635">
    <literal><![CDATA[
      L(x,y,z * a(L(u,u,w),w,v5)) = L(x,y,z * (R(u,w,v5) \ u))
    ]]></literal>
    <justification jstring="[para(4742(a,1),27593(a,2,3,2))].">
      <j1 rule="para" parents="4742 27593"/>
    </justification>
  </clause>

  <clause id="27636">
    <literal><![CDATA[
      L(x,y,z * (R(u,w,v5) \ u)) = L(x,y,z * (u \ R(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(26951(a,1),27635(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="26951 27635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27637">
    <literal><![CDATA[
      L(x,y,z * (R(u,w,v5) \ u)) = L(x,y,z * (u \ L(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(347,a,25030,a(flip),b,27636,a),flip(a)].">
      <j1 rule="hyper" parents="347 25030 27636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27638">
    <literal><![CDATA[
      L(x,y,((z \ u) \ u) * a(z,z,u)) = L(x,y,(u \ (z \ u)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(23532,a,27627,a)].">
      <j1 rule="hyper" parents="23532 27627"/>
    </justification>
  </clause>

  <clause id="27639">
    <literal><![CDATA[
      L(x,y,R(T(z,z \ u),z,u)) = L(x,y,(u \ (z \ u)) \ 1)
    ]]></literal>
    <justification jstring="[para(20855(a,1),27638(a,1,3))].">
      <j1 rule="para" parents="20855 27638"/>
    </justification>
  </clause>

  <clause id="27640">
    <literal><![CDATA[
      L(x,y,(z \ (u \ z)) \ 1) = L(x,y,((u \ 1) * z) \ z)
    ]]></literal>
    <justification jstring="[para(10500(a,1),27639(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10500 27639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27641">
    <literal><![CDATA[
      L(x,y,(z \ (u \ z)) \ 1) = L(x,y,z \ ((u \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,23696,a(flip),b,27640,a),flip(a)].">
      <j1 rule="hyper" parents="347 23696 27640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27642">
    <literal><![CDATA[
      (a(x,y,z) \ y) \ ((y \ (a(x,y,z) \ y)) * u) = L(y \ u,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(20230(a,1),27544(a,1,2,1))].">
      <j1 rule="para" parents="20230 27544"/>
    </justification>
  </clause>

  <clause id="27643">
    <literal><![CDATA[
      L(x \ a(y,z,u),x,a(y,z,u)) = ((a(y,z,u) \ 1) * x) \ 1
    ]]></literal>
    <justification jstring="[para(12592(a,1),27548(a,1,1,2))].">
      <j1 rule="para" parents="12592 27548"/>
    </justification>
  </clause>

  <clause id="27644">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * x) \ 1 = x \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,27270,a(flip),b,27643,a),flip(a)].">
      <j1 rule="hyper" parents="63 27270 27643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27645">
    <literal><![CDATA[
      (a(x,y,z) \ x) \ 1 = x \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(25371(a,1),27644(a,1,1))].">
      <j1 rule="para" parents="25371 27644"/>
    </justification>
  </clause>

  <clause id="27646">
    <literal><![CDATA[
      T(a(x,y,z) \ x,(a(x,y,z) \ x) \ 1) = (x \ a(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(27645(a,1),112(a,2,1))].">
      <j1 rule="para" parents="27645 112"/>
    </justification>
  </clause>

  <clause id="27647">
    <literal><![CDATA[
      T(a(x,y,z) \ x,x \ 1) = (x \ a(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(23038,a,27646,a)].">
      <j1 rule="hyper" parents="23038 27646"/>
    </justification>
  </clause>

  <clause id="27648">
    <literal><![CDATA[
      R(x,y,((z \ a(z,u,w)) \ 1) * v5) = R(x,y,(z * a(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(27646(a,1),25492(a,1,3,1))].">
      <j1 rule="para" parents="27646 25492"/>
    </justification>
  </clause>

  <clause id="27649">
    <literal><![CDATA[
      ((x \ a(x,x,y)) \ 1) * y = x * (x * ((1 / x) * y))
    ]]></literal>
    <justification jstring="[para(27647(a,1),26707(a,1,1))].">
      <j1 rule="para" parents="27647 26707"/>
    </justification>
  </clause>

  <clause id="27650">
    <literal><![CDATA[
      ((x \ a(x,x,y)) \ 1) * y = L(x * y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,3375,a(flip),b,27649,a),flip(a)].">
      <j1 rule="hyper" parents="347 3375 27649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27651">
    <literal><![CDATA[
      K(x,(y \ a(y,y,x)) \ 1) * (L(y * x,y,y \ 1) * z) = (x * ((y \ a(y,y,x)) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(27650(a,1),10281(a,1,2,1))].">
      <j1 rule="para" parents="27650 10281"/>
    </justification>
  </clause>

  <clause id="27652">
    <literal><![CDATA[
      a(x,y \ ((z * ((u \ a(u,u,z)) \ 1)) * w),v5) = a(x,y \ (w * L(u * z,u,u \ 1)),v5)
    ]]></literal>
    <justification jstring="[para(27650(a,1),24499(a,2,2,2,2))].">
      <j1 rule="para" parents="27650 24499"/>
    </justification>
  </clause>

  <clause id="27653">
    <literal><![CDATA[
      a(x,y \ (z * L(u * w,u,u \ 1)),v5) = a(x,y \ (z * (w * (u \ a(u,u,w)))),v5)
    ]]></literal>
    <justification jstring="[para(27650(a,1),24791(a,1,2,2,2))].">
      <j1 rule="para" parents="27650 24791"/>
    </justification>
  </clause>

  <clause id="27654">
    <literal><![CDATA[
      a(x,y * (L(z * u,z,z \ 1) * w),v5) = a(x,y * (((z \ a(z,z,u)) * u) * w),v5)
    ]]></literal>
    <justification jstring="[para(27650(a,1),25739(a,1,2,2,1))].">
      <j1 rule="para" parents="27650 25739"/>
    </justification>
  </clause>

  <clause id="27655">
    <literal><![CDATA[
      R(x,y,(z \ a(z,u,w)) * v5) = R(x,y,(z * a(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(21089,a,27648,a)].">
      <j1 rule="hyper" parents="21089 27648"/>
    </justification>
  </clause>

  <clause id="27656">
    <literal><![CDATA[
      L((x \ L(x,y,y)) * z,a(y,y,x),a(y,y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(14610(a,1),27585(a,1,1,1))].">
      <j1 rule="para" parents="14610 27585"/>
    </justification>
  </clause>

  <clause id="27657">
    <literal><![CDATA[
      (x \ L(x,y,z)) / ((L(x,y,z) \ x) \ z) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(347,a,27605,a(flip),b,27620,a),flip(a)].">
      <j1 rule="hyper" parents="347 27605 27620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27659">
    <literal><![CDATA[
      (L(x,y,z) \ x) / (z * (L(x,y,z) \ x)) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(63,a,25692,a,b,27657,a)].">
      <j1 rule="hyper" parents="63 25692 27657"/>
    </justification>
  </clause>

  <clause id="27661">
    <literal><![CDATA[
      (x * (L(x,y,z) \ z)) * (z * (1 / z)) = (z \ 1) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(27659(a,1),27136(a,1,2,2))].">
      <j1 rule="para" parents="27659 27136"/>
    </justification>
  </clause>

  <clause id="27662">
    <literal><![CDATA[
      (x * (L(x,y,z) \ z)) * K(z,z \ 1) = (z \ 1) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(1936,a,27661,a)].">
      <j1 rule="hyper" parents="1936 27661"/>
    </justification>
  </clause>

  <clause id="27664">
    <literal><![CDATA[
      x * ((L(x,y,z) \ z) * K(z,z \ 1)) = (z \ 1) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(20359,a,27662,a)].">
      <j1 rule="hyper" parents="20359 27662"/>
    </justification>
  </clause>

  <clause id="27665">
    <literal><![CDATA[
      x * (L(x,y,z) \ T(z,z \ 1)) = (z \ 1) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(2335(a,1),27664(a,1,2))].">
      <j1 rule="para" parents="2335 27664"/>
    </justification>
  </clause>

  <clause id="27666">
    <literal><![CDATA[
      ((x \ 1) \ (L(y,z,x) \ y)) \ (T(x,x \ 1) * y) = L(y,z,x)
    ]]></literal>
    <justification jstring="[para(27665(a,1),20988(a,1,1))].">
      <j1 rule="para" parents="27665 20988"/>
    </justification>
  </clause>

  <clause id="27667">
    <literal><![CDATA[
      L(x,x,a(y,x,z)) * (z \ L(z,x,y)) = a(y,x,x * (z \ x)) \ x
    ]]></literal>
    <justification jstring="[para(27618(a,1),27628(a,1,1))].">
      <j1 rule="para" parents="27618 27628"/>
    </justification>
  </clause>

  <clause id="27668">
    <literal><![CDATA[
      a(x,y,y * (z \ y)) \ y = y * (z \ L(z,y,x))
    ]]></literal>
    <justification jstring="[para(26355(a,1),27667(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26355 27667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27669">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ y = y * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(27239(a,1),27668(a,1,1))].">
      <j1 rule="para" parents="27239 27668"/>
    </justification>
  </clause>

  <clause id="27670">
    <literal><![CDATA[
      T(x * (y * (z \ L(z,y,x))),z) = L(z,z,y) \ (x * (y / (z \ 1)))
    ]]></literal>
    <justification jstring="[para(27669(a,1),26413(a,1,1,2))].">
      <j1 rule="para" parents="27669 26413"/>
    </justification>
  </clause>

  <clause id="27671">
    <literal><![CDATA[
      L(x,x,y) * T(z * (y * (x \ L(x,y,z))),x) = z * (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(134,a,27670,a,b,xx)].">
      <j1 rule="hyper" parents="134 27670"/>
    </justification>
  </clause>

  <clause id="27672">
    <literal><![CDATA[
      (x * (y * (z \ L(z,y,x)))) * L(z,z,y) = x * (y / (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(19956,a,27671,a)].">
      <j1 rule="hyper" parents="19956 27671"/>
    </justification>
  </clause>

  <clause id="27673">
    <literal><![CDATA[
      (a(x,y,z) \ y) \ ((a(x,y,z) \ 1) * u) = L(y \ u,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(26538(a,1),27642(a,1,2,1))].">
      <j1 rule="para" parents="26538 27642"/>
    </justification>
  </clause>

  <clause id="27680">
    <literal><![CDATA[
      L(x,y * L(y,z,u),y * L(y,z,u)) \ x = a(y \ L(y,z,u),y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(26248(a,1),27613(a,1,1))].">
      <j1 rule="para" parents="26248 27613"/>
    </justification>
  </clause>

  <clause id="27681">
    <literal><![CDATA[
      a(x,y \ (z * (u * (w \ a(w,w,u)))),v5) = a(x,y \ (z * L(w * u,w,w)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,25164,a(flip),b,27653,a),flip(a)].">
      <j1 rule="hyper" parents="63 25164 27653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27682">
    <literal><![CDATA[
      a(x,y \ (z * L(u * w,u,u)),v5) = a(x,y \ (z * (u \ T(w,u \ 1))),v5)
    ]]></literal>
    <justification jstring="[para(18987(a,1),27681(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="18987 27681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27683">
    <literal><![CDATA[
      a(x,y \ (z * L(u * w,u,u)),v5) = a(x,y \ (z * (u \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24501,a(flip),b,27682,a),flip(a)].">
      <j1 rule="hyper" parents="347 24501 27682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27685">
    <literal><![CDATA[
      a(x,y * (L(z * u,z,z \ 1) * w),v5) = a(x,y * ((z \ u) * w),v5)
    ]]></literal>
    <justification jstring="[para(18983(a,1),27654(a,2,2,2,1))].">
      <j1 rule="para" parents="18983 27654"/>
    </justification>
  </clause>

  <clause id="27686">
    <literal><![CDATA[
      a(x,(y * L(z * u,u,u)) * w,v5) = a(x,w * ((u \ z) * y),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,25141,a(flip),b,27685,a)].">
      <j1 rule="hyper" parents="63 25141 27685"/>
    </justification>
  </clause>

  <clause id="27687">
    <literal><![CDATA[
      a(x \ L(x,y,z),x \ L(x,y,z),u) = a(x * L(x,y,z),x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(14615,a,27680,a),flip(a)].">
      <j1 rule="hyper" parents="14615 27680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27688">
    <literal><![CDATA[
      a(x * L(x,y,z),x * L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x \ L(x,y,z),x * L(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(27687(a,1),24343(a,1))].">
      <j1 rule="para" parents="27687 24343"/>
    </justification>
  </clause>

  <clause id="27689">
    <literal><![CDATA[
      a(x \ L(x,y,z),x * L(x,y,z),u) = a(u,a(z,y,x),a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(27688,a,27384,a)].">
      <j1 rule="hyper" parents="27688 27384"/>
    </justification>
  </clause>

  <clause id="27690">
    <literal><![CDATA[
      a(x,y,L(z * u,u * z,L(u,u,z))) = a(x,y,((z \ 1) * (((z \ 1) * u) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,24919,a(flip),b,27633,a)].">
      <j1 rule="hyper" parents="63 24919 27633"/>
    </justification>
  </clause>

  <clause id="27691">
    <literal><![CDATA[
      K(x,a(y,y,x) \ y) * (L(y * x,y,y \ 1) * z) = (x * ((y \ a(y,y,x)) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(6250(a,1),27651(a,1,1))].">
      <j1 rule="para" parents="6250 27651"/>
    </justification>
  </clause>

  <clause id="27692">
    <literal><![CDATA[
      K(x,y) * (L(y * x,y,y \ 1) * z) = (x * ((y \ a(y,y,x)) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(23208(a,1),27691(a,1,1))].">
      <j1 rule="para" parents="23208 27691"/>
    </justification>
  </clause>

  <clause id="27693">
    <literal><![CDATA[
      (x * ((y \ a(y,y,x)) \ 1)) * z = L(x * y,y,y \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(21290,a,27692,a),flip(a)].">
      <j1 rule="hyper" parents="21290 27692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27695">
    <literal><![CDATA[
      a(x,y \ (L(z * u,u,u \ 1) * w),v5) = a(x,y \ (w * L(u * z,u,u \ 1)),v5)
    ]]></literal>
    <justification jstring="[para(27693(a,1),27652(a,1,2,2))].">
      <j1 rule="para" parents="27693 27652"/>
    </justification>
  </clause>

  <clause id="27696">
    <literal><![CDATA[
      a(x,y \ (z * L(u * w,u,u \ 1)),v5) = a(x,y \ (L(w * u,u,u) * z),v5)
    ]]></literal>
    <justification jstring="[hyper(25151,a,27695,a),flip(a)].">
      <j1 rule="hyper" parents="25151 27695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27697">
    <literal><![CDATA[
      a(x,y \ (L(z * u,u,u) * w),v5) = a(x,y \ (w * L(u * z,u,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,25164,a(flip),b,27696,a),flip(a)].">
      <j1 rule="hyper" parents="63 25164 27696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27698">
    <literal><![CDATA[
      a(x,y \ (L(z * u,u,u) * w),v5) = a(x,y \ (w * (u \ z)),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,27683,a(flip),b,27697,a),flip(a)].">
      <j1 rule="hyper" parents="347 27683 27697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27699">
    <literal><![CDATA[
      L(a(x,a(y,z,x),z) \ x,z,x \ L(x,z,y)) = ((L(x,z,y) \ x) * z) \ (a(y,z,x) * (z * x))
    ]]></literal>
    <justification jstring="[para(26754(a,1),27616(a,1,1,1))].">
      <j1 rule="para" parents="26754 27616"/>
    </justification>
  </clause>

  <clause id="27700">
    <literal><![CDATA[
      L(x * a(y,x,a(z,y,x)),y,x \ L(x,y,z)) = ((L(x,y,z) \ x) * y) \ (a(z,y,x) * (y * x))
    ]]></literal>
    <justification jstring="[para(26626(a,1),27699(a,1,1))].">
      <j1 rule="para" parents="26626 27699"/>
    </justification>
  </clause>

  <clause id="27701">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * y) \ (a(z,y,x) * (y * x)) = L(L(x,a(z,y,x),y),y,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(26655(a,1),27700(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26655 27700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27702">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * y) \ (a(z,y,x) * (y * x)) = L(x,a(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,10543,a(flip),b,27701,a),flip(a)].">
      <j1 rule="hyper" parents="347 10543 27701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27704">
    <literal><![CDATA[
      (((x \ R(x,y,z)) \ a(x,y,z)) * x) \ (a(z * y,x,a(x,y,z)) * (x * a(x,y,z))) = L(a(x,y,z),a(z * y,x,a(x,y,z)),x)
    ]]></literal>
    <justification jstring="[para(26297(a,1),27702(a,1,1,1,1))].">
      <j1 rule="para" parents="26297 27702"/>
    </justification>
  </clause>

  <clause id="27705">
    <literal><![CDATA[
      a(x,y,L(z * u,u * z,L(u,u,z))) = a(x,y,((a(w,v5,w) \ z) * (((a(w,v5,w) \ z) * u) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,24917,a(flip),b,27634,a)].">
      <j1 rule="hyper" parents="63 24917 27634"/>
    </justification>
  </clause>

  <clause id="27707">
    <literal><![CDATA[
      a(x,y,L(z * u,u * z,L(u,u,z))) = a(x,y,((a(w,v5,w) \ z) * ((z * (a(w,v5,w) \ u)) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(11883(a,1),27705(a,2,3,1,2,1))].">
      <j1 rule="para" parents="11883 27705"/>
    </justification>
  </clause>

  <clause id="27708">
    <literal><![CDATA[
      a(x,y,L(z * u,u * z,L(u,u,z))) = a(x,y,((a(w,v5,w) \ z) * (a(w,v5,w) * ((z * u) \ 1))) \ z)
    ]]></literal>
    <justification jstring="[para(11918(a,1),27707(a,2,3,1,2))].">
      <j1 rule="para" parents="11918 27707"/>
    </justification>
  </clause>

  <clause id="27709">
    <literal><![CDATA[
      a(x,y,L(z * u,u * z,L(u,u,z))) = a(x,y,(z * ((z * u) \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(11880(a,1),27708(a,2,3,1))].">
      <j1 rule="para" parents="11880 27708"/>
    </justification>
  </clause>

  <clause id="27710">
    <literal><![CDATA[
      a(x,y,L(z * u,u * z,L(u,u,z))) = a(x,y,z \ (((z * u) \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,25351,a(flip),b,27709,a),flip(a)].">
      <j1 rule="hyper" parents="347 25351 27709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27711">
    <literal><![CDATA[
      a(x,y,L(z * u,u * z,L(u,u,z))) = a(x,y,z \ ((z * u) \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,24757,a(flip),b,27710,a),flip(a)].">
      <j1 rule="hyper" parents="347 24757 27710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27712">
    <literal><![CDATA[
      a(x,y,L(z * u,u * z,L(u,u,z))) = a(x,y,z \ (z \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,24617,a(flip),b,27711,a),flip(a)].">
      <j1 rule="hyper" parents="347 24617 27711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27713">
    <literal><![CDATA[
      a(x,y,L(z * u,u * z,L(u,u,z))) = a(x,y,z \ (z \ (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,24311,a(flip),b,27712,a),flip(a)].">
      <j1 rule="hyper" parents="347 24311 27712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27714">
    <literal><![CDATA[
      a(x,y,((z \ 1) * (((z \ 1) * u) \ 1)) \ z) = a(x,y,z \ (z \ (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,27690,a(flip),b,27713,a)].">
      <j1 rule="hyper" parents="63 27690 27713"/>
    </justification>
  </clause>

  <clause id="27715">
    <literal><![CDATA[
      a(x,y,((z \ 1) * ((z \ 1) * u)) \ z) = a(x,y,z \ (z \ (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(15004,a,27714,a)].">
      <j1 rule="hyper" parents="15004 27714"/>
    </justification>
  </clause>

  <clause id="27716">
    <literal><![CDATA[
      a(x,y,L(z,u \ 1,u \ 1) \ u) = a(x,y,u \ (u \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,24511,a(flip),b,27715,a)].">
      <j1 rule="hyper" parents="63 24511 27715"/>
    </justification>
  </clause>

  <clause id="27717">
    <literal><![CDATA[
      a(x,y,L(z,u,u \ 1) \ u) = a(x,y,u \ (u \ (z \ u)))
    ]]></literal>
    <justification jstring="[para(3188(a,1),27716(a,1,3,1))].">
      <j1 rule="para" parents="3188 27716"/>
    </justification>
  </clause>

  <clause id="27718">
    <literal><![CDATA[
      a(x,y,z \ (z \ (u \ z))) = a(x,y,L(u,z,z) \ z)
    ]]></literal>
    <justification jstring="[hyper(25330,a,27717,a),flip(a)].">
      <j1 rule="hyper" parents="25330 27717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27719">
    <literal><![CDATA[
      a(x,y,L(z \ u,u,u)) = a(x,y,L(z,u,u) \ u)
    ]]></literal>
    <justification jstring="[hyper(25589,a,27718,a)].">
      <j1 rule="hyper" parents="25589 27718"/>
    </justification>
  </clause>

  <clause id="27720">
    <literal><![CDATA[
      a(x,y,L(z \ u,u,u)) = a(x,y,u \ L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(25355,a,27719,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="25355 27719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27721">
    <literal><![CDATA[
      a(x,y,L(z,u * z,u * z)) = a(x,y,(u * z) \ L(u,u,u * z))
    ]]></literal>
    <justification jstring="[para(9(a,1),27720(a,1,3,1))].">
      <j1 rule="para" parents="9 27720"/>
    </justification>
  </clause>

  <clause id="27722">
    <literal><![CDATA[
      a(x,y,(z * u) \ L(z,z,z * u)) = a(x,y,z * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,25276,a(flip),b,27721,a),flip(a)].">
      <j1 rule="hyper" parents="63 25276 27721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27723">
    <literal><![CDATA[
      a(x,y,(z * u) \ L(z,z,u)) = a(x,y,z * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,24640,a(flip),b,27722,a)].">
      <j1 rule="hyper" parents="63 24640 27722"/>
    </justification>
  </clause>

  <clause id="27724">
    <literal><![CDATA[
      a(x,y,L((z * u) * L(z,z,u),z * u,L(z,z,u))) = a(x,y,z * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(25263,a,27723,a)].">
      <j1 rule="hyper" parents="25263 27723"/>
    </justification>
  </clause>

  <clause id="27725">
    <literal><![CDATA[
      a(x,y,L(z * (T(u,z) * u),u * z,L(u,u,z))) = a(x,y,u * (z \ u))
    ]]></literal>
    <justification jstring="[para(10150(a,1),27724(a,1,3,1))].">
      <j1 rule="para" parents="10150 27724"/>
    </justification>
  </clause>

  <clause id="27726">
    <literal><![CDATA[
      a(x,y,L(z * (u * T(u,z)),u * z,L(u,u,z))) = a(x,y,u * (z \ u))
    ]]></literal>
    <justification jstring="[para(272(a,1),27725(a,1,3,1,2))].">
      <j1 rule="para" parents="272 27725"/>
    </justification>
  </clause>

  <clause id="27727">
    <literal><![CDATA[
      a(x,y,L(z * (u * u),u * z,L(u,u,z))) = a(x,y,u * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(24545,a,27726,a)].">
      <j1 rule="hyper" parents="24545 27726"/>
    </justification>
  </clause>

  <clause id="27728">
    <literal><![CDATA[
      a(x,y,L(z,u * z,L(u,u,z))) = a(x,y,u * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(14942,a,27727,a)].">
      <j1 rule="hyper" parents="14942 27727"/>
    </justification>
  </clause>

  <clause id="27730">
    <literal><![CDATA[
      a(x,y,L(z,u * z,u)) = a(x,y,u * (z \ u))
    ]]></literal>
    <justification jstring="[para(26748(a,1),27728(a,1,3))].">
      <j1 rule="para" parents="26748 27728"/>
    </justification>
  </clause>

  <clause id="27731">
    <literal><![CDATA[
      (((x \ R(x,y,z)) \ a(x,y,z)) * x) \ (a(x,a(z,y,x),y) * (x * a(x,y,z))) = L(a(x,y,z),a(z * y,x,a(x,y,z)),x)
    ]]></literal>
    <justification jstring="[para(26860(a,1),27704(a,1,2,1))].">
      <j1 rule="para" parents="26860 27704"/>
    </justification>
  </clause>

  <clause id="27732">
    <literal><![CDATA[
      (a(x,y,a(z,x,y)) * y) \ (a(y,a(z,x,y),x) * (y * a(y,x,z))) = L(a(y,x,z),a(z * x,y,a(y,x,z)),y)
    ]]></literal>
    <justification jstring="[para(26858(a,1),27731(a,1,1,1))].">
      <j1 rule="para" parents="26858 27731"/>
    </justification>
  </clause>

  <clause id="27733">
    <literal><![CDATA[
      L(x,a(y,z,x),z) \ (a(x,a(y,z,x),z) * (x * a(x,z,y))) = L(a(x,z,y),a(y * z,x,a(x,z,y)),x)
    ]]></literal>
    <justification jstring="[para(26656(a,1),27732(a,1,1))].">
      <j1 rule="para" parents="26656 27732"/>
    </justification>
  </clause>

  <clause id="27734">
    <literal><![CDATA[
      L(a(x,y,z),a(z * y,x,a(x,y,z)),x) = L(x,a(z,y,x),y) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(26870(a,2),27733(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26870 27733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27735">
    <literal><![CDATA[
      L(x,a(y,z,x),z) \ R(x,z,y) = a(x,z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,25390,a(flip),b,27734,a),flip(a)].">
      <j1 rule="hyper" parents="63 25390 27734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27737">
    <literal><![CDATA[
      a(x,y,z) \ R(x,y,z) = L(x,a(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(39,a,19984,a,b,27735,a)].">
      <j1 rule="hyper" parents="39 19984 27735"/>
    </justification>
  </clause>

  <clause id="27738">
    <literal><![CDATA[
      R(x,y,z) = a(x,y,z) * L(x,a(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(38,a,19974,a,b,27735,a),flip(a)].">
      <j1 rule="hyper" parents="38 19974 27735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27739">
    <literal><![CDATA[
      a(x,R(y,z,u),w) * L(x,a(w,R(y,z,u),x),L(y,z,u)) = R(x,R(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(134,a,23670,a(flip),b,27737,a)].">
      <j1 rule="hyper" parents="134 23670 27737"/>
    </justification>
  </clause>

  <clause id="27740">
    <literal><![CDATA[
      a(x,y * (z * R(u,w,v5)),v6) * L(x,a(v6,y * (z * R(u,w,v5)),x),y * (z * L(u,w,v5))) = R(x,y * (z * R(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(134,a,22871,a(flip),b,27737,a)].">
      <j1 rule="hyper" parents="134 22871 27737"/>
    </justification>
  </clause>

  <clause id="27741">
    <literal><![CDATA[
      a(x,y * R(z,u,w),v5) * L(x,a(v5,y * R(z,u,w),x),y * L(z,u,w)) = R(x,y * R(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(134,a,22863,a(flip),b,27737,a)].">
      <j1 rule="hyper" parents="134 22863 27737"/>
    </justification>
  </clause>

  <clause id="27742">
    <literal><![CDATA[
      a(x,y,z) * L(x,a(z,y,x),y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(27737(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="27737 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27743">
    <literal><![CDATA[
      a(x,(y \ (z \ u)) \ w,v5) * L(x,a(v5,(y \ (u / z)) \ w,x),(y \ (u / z)) \ w) = R(x,(y \ (u / z)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(24402(a,1),27738(a,2,1)),flip(a)].">
      <j1 rule="para" parents="24402 27738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27744">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * v5) * L(x,a(R(z,u,w) * v5,y,x),y) = R(x,y,R(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(25242(a,1),27738(a,2,1)),flip(a)].">
      <j1 rule="para" parents="25242 27738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27745">
    <literal><![CDATA[
      a(x,y,z * (u * L(w,v5,v6))) * L(x,a(z * (u * R(w,v5,v6)),y,x),y) = R(x,y,z * (u * R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(25313(a,1),27738(a,2,1)),flip(a)].">
      <j1 rule="para" parents="25313 27738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27746">
    <literal><![CDATA[
      a(x,L(y,z,u),w) * L(x,a(w,R(y,z,u),x),L(y,z,u)) = R(x,R(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(24805(a,1),27739(a,1,1))].">
      <j1 rule="para" parents="24805 27739"/>
    </justification>
  </clause>

  <clause id="27747">
    <literal><![CDATA[
      a(x,L(y,z,u),w) * L(x,a(w,L(y,z,u),x),L(y,z,u)) = R(x,R(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(24805(a,1),27746(a,1,2,2))].">
      <j1 rule="para" parents="24805 27746"/>
    </justification>
  </clause>

  <clause id="27748">
    <literal><![CDATA[
      R(x,R(y,z,u),w) = R(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(27742,a,27747,a),flip(a)].">
      <j1 rule="hyper" parents="27742 27747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27749">
    <literal><![CDATA[
      R(x,L(1 / y,y,z),u * w) * (R(1 / y,y,z) * (w * u)) = (x * (z / (y * z))) * (w * u)
    ]]></literal>
    <justification jstring="[para(27748(a,1),21164(a,1,1))].">
      <j1 rule="para" parents="27748 21164"/>
    </justification>
  </clause>

  <clause id="27750">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * v5) * L(x,a(L(z,u,w) * v5,y,x),y) = R(x,y,R(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(26806(a,1),27744(a,1,2,2))].">
      <j1 rule="para" parents="26806 27744"/>
    </justification>
  </clause>

  <clause id="27751">
    <literal><![CDATA[
      R(x,y,R(z,u,w) * v5) = R(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(27742,a,27750,a),flip(a)].">
      <j1 rule="hyper" parents="27742 27750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27752">
    <literal><![CDATA[
      R(x,y,R(z,u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y,L(z,u,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(27750(a,1),27742(a,1))].">
      <j1 rule="para" parents="27750 27742"/>
    </justification>
  </clause>

  <clause id="27753">
    <literal><![CDATA[
      R(x,L(y \ 1,y,z),u * w) * (R(1 / y,y,z) * (w * u)) = (x * (z / (y * z))) * (w * u)
    ]]></literal>
    <justification jstring="[para(20559(a,1),27749(a,1,1))].">
      <j1 rule="para" parents="20559 27749"/>
    </justification>
  </clause>

  <clause id="27754">
    <literal><![CDATA[
      R(x,L(y,y,z),u * w) * (R(1 / y,y,z) * (w * u)) = (x * (z / (y * z))) * (w * u)
    ]]></literal>
    <justification jstring="[para(2364(a,1),27753(a,1,1))].">
      <j1 rule="para" parents="2364 27753"/>
    </justification>
  </clause>

  <clause id="27755">
    <literal><![CDATA[
      R(x,L(y,y,z),z * y) * (((1 / y) * y) * z) = (x * (z / (y * z))) * (y * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),27754(a,1,2))].">
      <j1 rule="para" parents="107 27754"/>
    </justification>
  </clause>

  <clause id="27756">
    <literal><![CDATA[
      R(x,L(y,y,z),z * y) * z = (x * (z / (y * z))) * (y * z)
    ]]></literal>
    <justification jstring="[para(81(a,1),27755(a,1,2))].">
      <j1 rule="para" parents="81 27755"/>
    </justification>
  </clause>

  <clause id="27757">
    <literal><![CDATA[
      (((x * L(y,y,z)) * (z * y)) / (L(y,y,z) * (z * y))) * z = (x * (z / (y * z))) * (y * z)
    ]]></literal>
    <justification jstring="[para(20(a,1),27756(a,1,1))].">
      <j1 rule="para" parents="20 27756"/>
    </justification>
  </clause>

  <clause id="27758">
    <literal><![CDATA[
      a(x,y * L(z,u,w),v5) * L(x,a(v5,y * R(z,u,w),x),y * L(z,u,w)) = R(x,y * R(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(25119(a,1),27741(a,1,1))].">
      <j1 rule="para" parents="25119 27741"/>
    </justification>
  </clause>

  <clause id="27759">
    <literal><![CDATA[
      a(x,y * L(z,u,w),v5) * L(x,a(v5,y * L(z,u,w),x),y * L(z,u,w)) = R(x,y * R(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(25119(a,1),27758(a,1,2,2))].">
      <j1 rule="para" parents="25119 27758"/>
    </justification>
  </clause>

  <clause id="27760">
    <literal><![CDATA[
      R(x,y * R(z,u,w),v5) = R(x,y * L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(27742,a,27759,a),flip(a)].">
      <j1 rule="hyper" parents="27742 27759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27761">
    <literal><![CDATA[
      R(x,y * R(y,z,u),w) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,26246,a(flip),b,27760,a),flip(a)].">
      <j1 rule="hyper" parents="347 26246 27760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27762">
    <literal><![CDATA[
      R(x,y * L(T(z,u) * w,z,z),v5) = R(x,y * (z * R(w,z,z)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,23661,a(flip),b,27760,a),flip(a)].">
      <j1 rule="hyper" parents="63 23661 27760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27763">
    <literal><![CDATA[
      R(x,y * (z \ (y \ z)),u) = L(x,y * L(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(23625,a,27761,a)].">
      <j1 rule="hyper" parents="23625 27761"/>
    </justification>
  </clause>

  <clause id="27764">
    <literal><![CDATA[
      L(R(x,y,z),x * L(x,y,z),u) \ (x * u) = (R(x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[para(27761(a,1),2367(a,1,1))].">
      <j1 rule="para" parents="27761 2367"/>
    </justification>
  </clause>

  <clause id="27765">
    <literal><![CDATA[
      R(x,y * (z \ (y \ z)),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,21839,a(flip),b,27763,a),flip(a)].">
      <j1 rule="hyper" parents="347 21839 27763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27766">
    <literal><![CDATA[
      L(R(x,y,z \ (y \ z)),a(y,y,z),y) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,22730,a(flip),b,27765,a),flip(a)].">
      <j1 rule="hyper" parents="63 22730 27765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27767">
    <literal><![CDATA[
      L(R(x,y,z \ (y \ z)),y,a(y,y,z)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(25494,a,27766,a)].">
      <j1 rule="hyper" parents="25494 27766"/>
    </justification>
  </clause>

  <clause id="27768">
    <literal><![CDATA[
      R(x,y,z \ (y \ z)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(26320,a,27767,a)].">
      <j1 rule="hyper" parents="26320 27767"/>
    </justification>
  </clause>

  <clause id="27770">
    <literal><![CDATA[
      R(x,y \ (z \ y),z) = R(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,23558,a,b,27768,a)].">
      <j1 rule="hyper" parents="63 23558 27768"/>
    </justification>
  </clause>

  <clause id="27772">
    <literal><![CDATA[
      (L(R(x,y,z),x * L(x,y,z),u) \ (x * u)) \ (R(x,y,z) \ (x * u)) = (R(x,y,z) * ((R(x,y,z) \ x) * u)) \ (x * u)
    ]]></literal>
    <justification jstring="[para(27764(a,1),22576(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="27764 22576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27773">
    <literal><![CDATA[
      a(x,y,z * (u * L(w,v5,v6))) * L(x,a(z * (u * L(w,v5,v6)),y,x),y) = R(x,y,z * (u * R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(26408(a,1),27745(a,1,2,2))].">
      <j1 rule="para" parents="26408 27745"/>
    </justification>
  </clause>

  <clause id="27774">
    <literal><![CDATA[
      R(x,y,z * (u * R(w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z * (u * L(w,v5,v6))) = v7
    ]]></literal>
    <justification jstring="[para(27773(a,1),27742(a,1))].">
      <j1 rule="para" parents="27773 27742"/>
    </justification>
  </clause>

  <clause id="27775">
    <literal><![CDATA[
      R(x,y,L(z \ a(z,a(u,w,z),w),L(z,w,u),v5) * (v5 * L(z,w,u))) = R(x,y,v5 * a(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(27774,a,26915,a)].">
      <j1 rule="hyper" parents="27774 26915"/>
    </justification>
  </clause>

  <clause id="27776">
    <literal><![CDATA[
      R(x,y,L(z,u * R(w,v5,v6),u * R(w,v5,v6)) * (u * L(w,v5,v6))) = R(x,y,(u * R(w,v5,v6)) \ z)
    ]]></literal>
    <justification jstring="[hyper(27774,a,22238,a)].">
      <j1 rule="hyper" parents="27774 22238"/>
    </justification>
  </clause>

  <clause id="27777">
    <literal><![CDATA[
      R(x,y,z * (u * L(T(w,v5),v6,v7))) = R(x,y,(u * R(w,v6,v7)) * z)
    ]]></literal>
    <justification jstring="[hyper(27774,a,22140,a)].">
      <j1 rule="hyper" parents="27774 22140"/>
    </justification>
  </clause>

  <clause id="27778">
    <literal><![CDATA[
      R(x,y,(z * R(u,w,v5)) * v6) = R(x,y,(z * L(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(22295,a,27777,a),flip(a)].">
      <j1 rule="hyper" parents="22295 27777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27779">
    <literal><![CDATA[
      R(x,y,z * (u * ((w * v5) * w))) = R(x,y,(u * L(v5,w,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(22250,a,27778,a)].">
      <j1 rule="hyper" parents="22250 27778"/>
    </justification>
  </clause>

  <clause id="27780">
    <literal><![CDATA[
      R(x,y,z * (L(u,w,v5) * (u \ a(u,a(v5,w,u),w)))) = R(x,y,z * a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(22088,a,27775,a)].">
      <j1 rule="hyper" parents="22088 27775"/>
    </justification>
  </clause>

  <clause id="27781">
    <literal><![CDATA[
      R(x,y,z * (a(u,w,v5) \ 1)) = R(x,y,z * a(v5,w,u))
    ]]></literal>
    <justification jstring="[para(26768(a,1),27780(a,1,3,2))].">
      <j1 rule="para" parents="26768 27780"/>
    </justification>
  </clause>

  <clause id="27782">
    <literal><![CDATA[
      R(x,y,a(z,u,w) * v5) = R(x,y,v5 * a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(20896,a,27781,a)].">
      <j1 rule="hyper" parents="20896 27781"/>
    </justification>
  </clause>

  <clause id="27783">
    <literal><![CDATA[
      R(x,y,z * a(u \ 1,w,v5)) = R(x,y,a(v5,w,u) * z)
    ]]></literal>
    <justification jstring="[para(14922(a,1),27782(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="14922 27782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27784">
    <literal><![CDATA[
      R(x,y,L(z,u * R(w,v5,v6),u * L(w,v5,v6)) * (u * L(w,v5,v6))) = R(x,y,(u * R(w,v5,v6)) \ z)
    ]]></literal>
    <justification jstring="[para(22863(a,1),27776(a,1,3,1))].">
      <j1 rule="para" parents="22863 27776"/>
    </justification>
  </clause>

  <clause id="27785">
    <literal><![CDATA[
      R(x,y,L(z,u * L(w,v5,v6),u * L(w,v5,v6)) * (u * L(w,v5,v6))) = R(x,y,(u * R(w,v5,v6)) \ z)
    ]]></literal>
    <justification jstring="[para(23781(a,1),27784(a,1,3,1))].">
      <j1 rule="para" parents="23781 27784"/>
    </justification>
  </clause>

  <clause id="27786">
    <literal><![CDATA[
      R(x,y,(z * R(u,w,v5)) \ v6) != v7
    ]]></literal>
    <literal><![CDATA[
      R(x,y,(z * L(u,w,v5)) \ v6) = v7
    ]]></literal>
    <justification jstring="[para(27785(a,1),22240(a,1))].">
      <j1 rule="para" parents="27785 22240"/>
    </justification>
  </clause>

  <clause id="27787">
    <literal><![CDATA[
      R(x,y,(((z \ u) \ 1) * L(z,z,w)) \ v5) = R(x,y,(a(z,z,w) * u) \ v5)
    ]]></literal>
    <justification jstring="[hyper(27786,a,26282,a)].">
      <j1 rule="hyper" parents="27786 26282"/>
    </justification>
  </clause>

  <clause id="27788">
    <literal><![CDATA[
      R(x,y,(L(z,z,u) * (z \ w)) \ v5) = R(x,y,(a(z,z,u) * w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(22121,a,27787,a)].">
      <j1 rule="hyper" parents="22121 27787"/>
    </justification>
  </clause>

  <clause id="27789">
    <literal><![CDATA[
      a(x,(y \ (z \ u)) \ w,v5) * L(x,a(v5,(y \ (z \ u)) \ w,x),(y \ (u / z)) \ w) = R(x,(y \ (u / z)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(24402(a,1),27743(a,1,2,2))].">
      <j1 rule="para" parents="24402 27743"/>
    </justification>
  </clause>

  <clause id="27790">
    <literal><![CDATA[
      a(x,(y \ (z \ u)) \ w,v5) * L(x,a(v5,(y \ (z \ u)) \ w,x),(y \ (z \ u)) \ w) = R(x,(y \ (u / z)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(21553(a,1),27789(a,1,2))].">
      <j1 rule="para" parents="21553 27789"/>
    </justification>
  </clause>

  <clause id="27791">
    <literal><![CDATA[
      R(x,(y \ (z / u)) \ w,v5) = R(x,(y \ (u \ z)) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(27742,a,27790,a),flip(a)].">
      <j1 rule="hyper" parents="27742 27790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27792">
    <literal><![CDATA[
      R(x,(y \ (z \ (y \ z))) \ u,w) = R(x,((z \ (y \ z)) * y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,22503,a(flip),b,27791,a),flip(a)].">
      <j1 rule="hyper" parents="63 22503 27791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27793">
    <literal><![CDATA[
      R(x,(y \ (z \ y)) \ (z * u),w) = R(x,((y / z) \ (y * z)) * u,w)
    ]]></literal>
    <justification jstring="[para(27000(a,1),27791(a,1,2)),flip(a)].">
      <j1 rule="para" parents="27000 27791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27794">
    <literal><![CDATA[
      R(x,((y \ (z \ y)) * z) \ u,w) = R(x,(y \ (z \ y)) \ (z * u),w)
    ]]></literal>
    <justification jstring="[para(26319(a,1),27792(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26319 27792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27795">
    <literal><![CDATA[
      (L(R(x,y,z),x * L(x,y,z),u) \ (x * u)) \ (R(x,y,z) \ (x * u)) = (L(x,y,z) * ((L(x,y,z) \ x) * u)) \ (x * u)
    ]]></literal>
    <justification jstring="[para(23768(a,1),27772(a,2,1))].">
      <j1 rule="para" parents="23768 27772"/>
    </justification>
  </clause>

  <clause id="27796">
    <literal><![CDATA[
      (L(R(x,y,z),x * L(x,y,z),u) \ (x * u)) \ (R(x,y,z) \ (x * u)) = a(L(x,y,z),L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,88,a(flip),b,27795,a),flip(a)].">
      <j1 rule="hyper" parents="347 88 27795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27797">
    <literal><![CDATA[
      (L(R(x,y,z),x * L(x,y,z),u) \ (x * u)) \ (R(x,y,z) \ (x * u)) = a(L(x,y,z),x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,14988,a(flip),b,27796,a),flip(a)].">
      <j1 rule="hyper" parents="347 14988 27796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27798">
    <literal><![CDATA[
      a(x,y * (z * L(u,w,v5)),v6) * L(x,a(v6,y * (z * R(u,w,v5)),x),y * (z * L(u,w,v5))) = R(x,y * (z * R(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(25135(a,1),27740(a,1,1))].">
      <j1 rule="para" parents="25135 27740"/>
    </justification>
  </clause>

  <clause id="27799">
    <literal><![CDATA[
      a(x,y * (z * L(u,w,v5)),v6) * L(x,a(v6,y * (z * L(u,w,v5)),x),y * (z * L(u,w,v5))) = R(x,y * (z * R(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(25135(a,1),27798(a,1,2,2))].">
      <j1 rule="para" parents="25135 27798"/>
    </justification>
  </clause>

  <clause id="27800">
    <literal><![CDATA[
      R(x,y * (z * R(u,w,v5)),v6) = R(x,y * (z * L(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(27742,a,27799,a),flip(a)].">
      <j1 rule="hyper" parents="27742 27799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27801">
    <literal><![CDATA[
      R(x,y * (z * R(u,w,v5)),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      R(x,y * (z * L(u,w,v5)),v6) = v7
    ]]></literal>
    <justification jstring="[para(27799(a,1),27742(a,1))].">
      <j1 rule="para" parents="27799 27742"/>
    </justification>
  </clause>

  <clause id="27802">
    <literal><![CDATA[
      R(x,y * (L(z,a(u,w,z),w) * L(z \ 1,w,u)),v5) = R(x,y * a(z \ 1,w,u),v5)
    ]]></literal>
    <justification jstring="[para(26888(a,1),27800(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="26888 27800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27803">
    <literal><![CDATA[
      R(x,y * L(T(z,u) * w,z,z),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y * (z * L(w,z,z)),v5) = v6
    ]]></literal>
    <justification jstring="[para(27762(a,2),27801(a,1))].">
      <j1 rule="para" parents="27762 27801"/>
    </justification>
  </clause>

  <clause id="27804">
    <literal><![CDATA[
      R(x,y * (z * L(u,z,z)),w) = R(x,y * (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(27803,a,23876,a)].">
      <j1 rule="hyper" parents="27803 23876"/>
    </justification>
  </clause>

  <clause id="27805">
    <literal><![CDATA[
      R(x,(L(y,a(z,u,y),u) * L(y,u,z)) * w,v5) = R(x,w * a(y \ 1,u,z),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22515,a(flip),b,27802,a)].">
      <j1 rule="hyper" parents="63 22515 27802"/>
    </justification>
  </clause>

  <clause id="27806">
    <literal><![CDATA[
      L(x,y,(K(z,u) * (T(w,v5) \ v6)) \ L(K(z,u) * (T(w,v5) \ v6),w,v5)) = R(x,y,K(z,u) * ((T(w,v5) \ v6) * (K(z,u) * ((w * v5) \ (v5 * v6)))))
    ]]></literal>
    <justification jstring="[para(20008(a,1),27614(a,2,3))].">
      <j1 rule="para" parents="20008 27614"/>
    </justification>
  </clause>

  <clause id="27807">
    <literal><![CDATA[
      L(x,y,(K(z,u) * (T(w,v5) \ v6)) \ L(K(z,u) * (T(w,v5) \ v6),w,v5)) = R(x,y,K(z,u) * ((T(w,v5) \ v6) * ((w * v5) \ (v5 * v6))))
    ]]></literal>
    <justification jstring="[hyper(347,a,22102,a(flip),b,27806,a),flip(a)].">
      <j1 rule="hyper" parents="347 22102 27806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27809">
    <literal><![CDATA[
      L(x,y,(K(z,u) * (T(w,v5) \ v6)) \ L(K(z,u) * (T(w,v5) \ v6),w,v5)) = R(x,y,(((w * v5) \ (v5 * v6)) * (w \ v6)) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,22269,a(flip),b,27807,a),flip(a)].">
      <j1 rule="hyper" parents="347 22269 27807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27811">
    <literal><![CDATA[
      L(x,y,(K(z,u) * (T(w,v5) \ v6)) \ L(K(z,u) * (T(w,v5) \ v6),w,v5)) = R(x,y,((w * v5) \ (v5 * v6)) * (w \ v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,22056,a(flip),b,27809,a),flip(a)].">
      <j1 rule="hyper" parents="347 22056 27809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27813">
    <literal><![CDATA[
      L(x,y,(K(z,u) * (T(w,v5) \ v6)) \ (K(z,u) * ((w * v5) \ (v5 * v6)))) = R(x,y,((w * v5) \ (v5 * v6)) * (w \ v6))
    ]]></literal>
    <justification jstring="[para(21268(a,1),27811(a,1,3,2))].">
      <j1 rule="para" parents="21268 27811"/>
    </justification>
  </clause>

  <clause id="27814">
    <literal><![CDATA[
      L(x,y,(T(z,u) \ w) \ ((z * u) \ (u * w))) = R(x,y,((z * u) \ (u * w)) * (z \ w))
    ]]></literal>
    <justification jstring="[para(3455(a,1),27813(a,1,3))].">
      <j1 rule="para" parents="3455 27813"/>
    </justification>
  </clause>

  <clause id="27815">
    <literal><![CDATA[
      R(x,y,((z * u) \ (u * w)) * (z \ w)) = L(x,y,a(u,z,w \ z) \ 1)
    ]]></literal>
    <justification jstring="[para(26194(a,1),27814(a,1,3)),flip(a)].">
      <j1 rule="para" parents="26194 27814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27816">
    <literal><![CDATA[
      R(x,y,((z * u) \ (u * w)) * (z \ w)) = L(x,y,a(u,z,w \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,27539,a(flip),b,27815,a),flip(a)].">
      <j1 rule="hyper" parents="347 27539 27815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27817">
    <literal><![CDATA[
      R(x,y,z) \ (a(u,R(x,y,z),R(x,y,z)) \ (R(x,y,z) * (T(a(u,R(x,y,z),R(x,y,z)),x) * w))) = L(w,a(u,R(x,y,z),L(x,y,z)),L(x,y,z))
    ]]></literal>
    <justification jstring="[para(24889(a,1),27571(a,2,2))].">
      <j1 rule="para" parents="24889 27571"/>
    </justification>
  </clause>

  <clause id="27818">
    <literal><![CDATA[
      R(x,y,z) \ (a(u,R(x,y,z),R(x,y,z)) \ (R(x,y,z) * (T(a(u,R(x,y,z),R(x,y,z)),x) * w))) = L(w,a(u,L(x,y,z),L(x,y,z)),L(x,y,z))
    ]]></literal>
    <justification jstring="[para(24805(a,1),27817(a,2,2))].">
      <j1 rule="para" parents="24805 27817"/>
    </justification>
  </clause>

  <clause id="27819">
    <literal><![CDATA[
      R(x,y,z) \ (a(u,R(x,y,z),R(x,y,z)) \ (R(x,y,z) * (T(a(u,R(x,y,z),R(x,y,z)),x) * w))) = L(w,a(u,x,x),L(x,y,z))
    ]]></literal>
    <justification jstring="[para(26464(a,1),27818(a,2,2))].">
      <j1 rule="para" parents="26464 27818"/>
    </justification>
  </clause>

  <clause id="27820">
    <literal><![CDATA[
      R(x,y,z) \ (a(u,R(x,y,z),L(x,y,z)) \ (R(x,y,z) * (T(a(u,R(x,y,z),R(x,y,z)),x) * w))) = L(w,a(u,x,x),L(x,y,z))
    ]]></literal>
    <justification jstring="[para(24889(a,1),27819(a,1,2,1))].">
      <j1 rule="para" parents="24889 27819"/>
    </justification>
  </clause>

  <clause id="27822">
    <literal><![CDATA[
      R(x,y,z) \ (a(u,L(x,y,z),L(x,y,z)) \ (R(x,y,z) * (T(a(u,R(x,y,z),R(x,y,z)),x) * w))) = L(w,a(u,x,x),L(x,y,z))
    ]]></literal>
    <justification jstring="[para(24805(a,1),27820(a,1,2,1))].">
      <j1 rule="para" parents="24805 27820"/>
    </justification>
  </clause>

  <clause id="27823">
    <literal><![CDATA[
      R(x,y,z) \ (a(u,x,x) \ (R(x,y,z) * (T(a(u,R(x,y,z),R(x,y,z)),x) * w))) = L(w,a(u,x,x),L(x,y,z))
    ]]></literal>
    <justification jstring="[para(26464(a,1),27822(a,1,2,1))].">
      <j1 rule="para" parents="26464 27822"/>
    </justification>
  </clause>

  <clause id="27824">
    <literal><![CDATA[
      R(x,y,z) \ (a(u,x,x) \ (R(x,y,z) * (T(a(u,R(x,y,z),L(x,y,z)),x) * w))) = L(w,a(u,x,x),L(x,y,z))
    ]]></literal>
    <justification jstring="[para(24889(a,1),27823(a,1,2,2,2,1,1))].">
      <j1 rule="para" parents="24889 27823"/>
    </justification>
  </clause>

  <clause id="27826">
    <literal><![CDATA[
      R(x,y,z) \ (a(u,x,x) \ (R(x,y,z) * (T(a(u,L(x,y,z),L(x,y,z)),x) * w))) = L(w,a(u,x,x),L(x,y,z))
    ]]></literal>
    <justification jstring="[para(24805(a,1),27824(a,1,2,2,2,1,1))].">
      <j1 rule="para" parents="24805 27824"/>
    </justification>
  </clause>

  <clause id="27827">
    <literal><![CDATA[
      R(x,y,z) \ (a(u,x,x) \ (R(x,y,z) * (T(a(u,x,x),x) * w))) = L(w,a(u,x,x),L(x,y,z))
    ]]></literal>
    <justification jstring="[para(26464(a,1),27826(a,1,2,2,2,1,1))].">
      <j1 rule="para" parents="26464 27826"/>
    </justification>
  </clause>

  <clause id="27828">
    <literal><![CDATA[
      R(x,y,z) \ (a(u,x,x) \ (R(x,y,z) * (a(u,x,x) * w))) = L(w,a(u,x,x),L(x,y,z))
    ]]></literal>
    <justification jstring="[para(11789(a,1),27827(a,1,2,2,2,1))].">
      <j1 rule="para" parents="11789 27827"/>
    </justification>
  </clause>

  <clause id="27831">
    <literal><![CDATA[
      R(x,y,z) \ (R(x,y,z) * (a(u,x,x) \ (a(u,x,x) * w))) = L(w,a(u,x,x),L(x,y,z))
    ]]></literal>
    <justification jstring="[para(23269(a,1),27828(a,1,2))].">
      <j1 rule="para" parents="23269 27828"/>
    </justification>
  </clause>

  <clause id="27832">
    <literal><![CDATA[
      L(x,a(y,z,z),L(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(366,a,27831,a)].">
      <j1 rule="hyper" parents="366 27831"/>
    </justification>
  </clause>

  <clause id="27833">
    <literal><![CDATA[
      L(x,x,y) * (x \ z) = a(y,x,x) \ z
    ]]></literal>
    <justification jstring="[hyper(25503,a,27832,a)].">
      <j1 rule="hyper" parents="25503 27832"/>
    </justification>
  </clause>

  <clause id="27835">
    <literal><![CDATA[
      x * (a(y,x,x) \ z) = L(x,x,y) * z
    ]]></literal>
    <justification jstring="[hyper(134,a,27832,a(flip),b,25428,a(flip))].">
      <j1 rule="hyper" parents="134 27832 25428"/>
    </justification>
  </clause>

  <clause id="27836">
    <literal><![CDATA[
      (x / y) * L(y,y,z) = a(z,y,y) \ x
    ]]></literal>
    <justification jstring="[hyper(21010,a,27833,a)].">
      <j1 rule="hyper" parents="21010 27833"/>
    </justification>
  </clause>

  <clause id="27837">
    <literal><![CDATA[
      L(x,x,y) * (((x \ 1) \ 1) \ z) = a(y * x,x,x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,22373,a(flip),b,27833,a)].">
      <j1 rule="hyper" parents="63 22373 27833"/>
    </justification>
  </clause>

  <clause id="27838">
    <literal><![CDATA[
      (a(x,y,y) \ z) * y = z * L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,27833,a(flip),b,20687,a)].">
      <j1 rule="hyper" parents="133 27833 20687"/>
    </justification>
  </clause>

  <clause id="27839">
    <literal><![CDATA[
      R(x,y,(a(z,u,u) \ w) \ v5) = R(x,y,(a(u,u,z) * w) \ v5)
    ]]></literal>
    <justification jstring="[para(27833(a,1),27788(a,1,3,1))].">
      <j1 rule="para" parents="27833 27788"/>
    </justification>
  </clause>

  <clause id="27840">
    <literal><![CDATA[
      a(x,y,y) \ ((1 / y) * z) = L(1 / y,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(34,a,21338,a(flip),b,27835,a),flip(a)].">
      <j1 rule="hyper" parents="34 21338 27835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27841">
    <literal><![CDATA[
      (x * (a(x,y,z) \ y)) * L(z,z,u) = a(u,z,z) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[para(25413(a,1),27836(a,1,1))].">
      <j1 rule="para" parents="25413 27836"/>
    </justification>
  </clause>

  <clause id="27842">
    <literal><![CDATA[
      T(a(x,y,y) \ x,y) = y \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(462,a,2008,a(flip),b,27838,a)].">
      <j1 rule="hyper" parents="462 2008 27838"/>
    </justification>
  </clause>

  <clause id="27843">
    <literal><![CDATA[
      x * (y * ((y * x) \ x)) = y \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,25844,a(flip),b,27842,a)].">
      <j1 rule="hyper" parents="63 25844 27842"/>
    </justification>
  </clause>

  <clause id="27844">
    <literal><![CDATA[
      a(x,y,y) \ x = (x / y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(40,a,2286,a,b,27842,a),flip(a)].">
      <j1 rule="hyper" parents="40 2286 27842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27845">
    <literal><![CDATA[
      R(x,y,z) * (x \ (u / (x \ 1))) = (a(u,x,x) \ u) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(27842(a,1),19966(a,1,2))].">
      <j1 rule="para" parents="27842 19966"/>
    </justification>
  </clause>

  <clause id="27846">
    <literal><![CDATA[
      (x / y) * L(z,1 / y,(1 / y) \ (x / y)) = (a(x,y,y) \ x) * ((1 / y) * z)
    ]]></literal>
    <justification jstring="[para(27844(a,2),10157(a,2,1))].">
      <j1 rule="para" parents="27844 10157"/>
    </justification>
  </clause>

  <clause id="27847">
    <literal><![CDATA[
      a(x,y,y) \ (x * L(y,z,u)) = ((x / y) / (1 / y)) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(27844(a,1),23137(a,2,1))].">
      <j1 rule="para" parents="27844 23137"/>
    </justification>
  </clause>

  <clause id="27848">
    <literal><![CDATA[
      R(x,(y * ((y * ((z \ 1) \ u)) \ ((z \ 1) \ u))) * (z \ u),w) = R(x,y \ (((z \ 1) \ u) / (y \ 1)),w)
    ]]></literal>
    <justification jstring="[para(27843(a,1),22483(a,1,2)),flip(a)].">
      <j1 rule="para" parents="27843 22483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27849">
    <literal><![CDATA[
      (x / ((y \ 1) \ 1)) * L(y,y,z) = a(z * y,y,y) \ x
    ]]></literal>
    <justification jstring="[hyper(21074,a,27837,a)].">
      <j1 rule="hyper" parents="21074 27837"/>
    </justification>
  </clause>

  <clause id="27850">
    <literal><![CDATA[
      ((x / y) / (1 / y)) * L(y,z,u) = x * (a(x,y,y) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(25411,a,27847,a),flip(a)].">
      <j1 rule="hyper" parents="25411 27847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27851">
    <literal><![CDATA[
      ((x / y) / (1 / y)) * L(y,z,u) = x / (L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,26468,a(flip),b,27850,a),flip(a)].">
      <j1 rule="hyper" parents="347 26468 27850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27852">
    <literal><![CDATA[
      L(x,y,z) * (x \ (u / (x \ 1))) = u / (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(21174,a,27851,a)].">
      <j1 rule="hyper" parents="21174 27851"/>
    </justification>
  </clause>

  <clause id="27853">
    <literal><![CDATA[
      (x / y) * L(z,1 / y,(1 / y) \ (y \ x)) = (a(x,y,y) \ x) * ((1 / y) * z)
    ]]></literal>
    <justification jstring="[para(21498(a,1),27846(a,1,2))].">
      <j1 rule="para" parents="21498 27846"/>
    </justification>
  </clause>

  <clause id="27854">
    <literal><![CDATA[
      (x / y) * L(z,1 / y,(y \ 1) \ (y \ x)) = (a(x,y,y) \ x) * ((1 / y) * z)
    ]]></literal>
    <justification jstring="[para(3943(a,1),27853(a,1,2))].">
      <j1 rule="para" parents="3943 27853"/>
    </justification>
  </clause>

  <clause id="27855">
    <literal><![CDATA[
      R(x,(y * ((y * ((z \ 1) \ u)) \ ((z \ 1) \ u))) * (z \ u),w) = R(x,y \ ((y \ 1) \ ((z \ 1) \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,22417,a(flip),b,27848,a),flip(a)].">
      <j1 rule="hyper" parents="347 22417 27848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27856">
    <literal><![CDATA[
      R(x,(y * ((y * ((z \ 1) \ u)) \ ((z \ 1) \ u))) * (z \ u),w) = R(x,y \ ((y \ 1) \ (z \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,22567,a(flip),b,27855,a),flip(a)].">
      <j1 rule="hyper" parents="347 22567 27855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27857">
    <literal><![CDATA[
      R(x,(y * ((y * ((z \ 1) \ u)) \ ((z \ 1) \ u))) * (z \ u),w) = R(x,y \ (y \ (z \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,22529,a(flip),b,27856,a),flip(a)].">
      <j1 rule="hyper" parents="347 22529 27856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27858">
    <literal><![CDATA[
      R(x,(y * ((y * ((z \ 1) \ u)) \ ((z \ 1) \ u))) * (z \ u),w) = R(x,L(z \ u,y,y),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,20870,a(flip),b,27857,a),flip(a)].">
      <j1 rule="hyper" parents="347 20870 27857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27859">
    <literal><![CDATA[
      a(x,y,(z * L(u,w,v5)) * (L(z * R(u,w,v5),v6,v7) \ (z * R(u,w,v5)))) = a(x,y,L(z * R(u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(14942,a,27438,a),flip(a)].">
      <j1 rule="hyper" parents="14942 27438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27861">
    <literal><![CDATA[
      a(x,y,(z * L(u,w,v5)) * (L(z * L(u,w,v5),v6,v7) \ (z * L(u,w,v5)))) = a(x,y,L(z * R(u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(26793(a,1),27859(a,1,3,2))].">
      <j1 rule="para" parents="26793 27859"/>
    </justification>
  </clause>

  <clause id="27862">
    <literal><![CDATA[
      a(x,y,L(1 / (z * L(u,w,v5)),v6,v7) \ 1) = a(x,y,L(z * R(u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(3638(a,2),27861(a,1,3))].">
      <j1 rule="para" parents="3638 27861"/>
    </justification>
  </clause>

  <clause id="27863">
    <literal><![CDATA[
      a(x,y,L(1 / (z * L(u,w,v5)),v6,v7)) = a(x,y,L(z * R(u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(14931,a,27862,a)].">
      <j1 rule="hyper" parents="14931 27862"/>
    </justification>
  </clause>

  <clause id="27864">
    <literal><![CDATA[
      a(x,y,L((z * L(u,w,v5)) \ 1,v6,v7)) = a(x,y,L(z * R(u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(24543,a,27863,a)].">
      <j1 rule="hyper" parents="24543 27863"/>
    </justification>
  </clause>

  <clause id="27865">
    <literal><![CDATA[
      a(x,y,L(z * R(u,w,v5),v6,v7)) = a(x,y,L(z * L(u,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(15032,a,27864,a),flip(a)].">
      <j1 rule="hyper" parents="15032 27864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27866">
    <literal><![CDATA[
      a(x,y,L(z * L(z,u,u),w,v5)) = a(x,y,a(z,u,L(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,26443,a(flip),b,27865,a),flip(a)].">
      <j1 rule="hyper" parents="63 26443 27865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27867">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),v5,v5)) = a(x,y,a(z,v5,L(v5,u,w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,25761,a(flip),b,27866,a)].">
      <j1 rule="hyper" parents="63 25761 27866"/>
    </justification>
  </clause>

  <clause id="27868">
    <literal><![CDATA[
      x \ ((a(y,z,u) \ 1) \ ((x * (T(a(y,z,u) * a(y,z,u),x) \ w)) * a(y,z,u))) = (a(y,z,u) * a(y,z,u)) * L((a(y,z,u) * a(y,z,u)) \ w,x,a(y,z,u) * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(10209(a,1),21381(a,1,2,2,1,2))].">
      <j1 rule="para" parents="10209 21381"/>
    </justification>
  </clause>

  <clause id="27869">
    <literal><![CDATA[
      x \ ((a(y,z,u) \ 1) \ ((x * ((a(y,z,u) * a(y,z,u)) \ w)) * a(y,z,u))) = (a(y,z,u) * a(y,z,u)) * L((a(y,z,u) * a(y,z,u)) \ w,x,a(y,z,u) * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(23077(a,1),27868(a,1,2,2,1,2,1))].">
      <j1 rule="para" parents="23077 27868"/>
    </justification>
  </clause>

  <clause id="27871">
    <literal><![CDATA[
      x \ ((a(y,z,u) \ 1) \ ((x * w) * ((a(y,z,u) * a(y,z,u)) \ a(y,z,u)))) = (a(y,z,u) * a(y,z,u)) * L((a(y,z,u) * a(y,z,u)) \ w,x,a(y,z,u) * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(23222(a,1),27869(a,1,2,2))].">
      <j1 rule="para" parents="23222 27869"/>
    </justification>
  </clause>

  <clause id="27872">
    <literal><![CDATA[
      x \ ((a(y,z,u) \ 1) \ ((x * w) * T(a(y,z,u) \ 1,a(y,z,u)))) = (a(y,z,u) * a(y,z,u)) * L((a(y,z,u) * a(y,z,u)) \ w,x,a(y,z,u) * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(518(a,2),27871(a,1,2,2,2))].">
      <j1 rule="para" parents="518 27871"/>
    </justification>
  </clause>

  <clause id="27873">
    <literal><![CDATA[
      x \ ((a(y,z,u) \ 1) \ ((x * w) * (a(y,z,u) \ 1))) = (a(y,z,u) * a(y,z,u)) * L((a(y,z,u) * a(y,z,u)) \ w,x,a(y,z,u) * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(19939(a,1),27872(a,1,2,2,2))].">
      <j1 rule="para" parents="19939 27872"/>
    </justification>
  </clause>

  <clause id="27874">
    <literal><![CDATA[
      x \ T(x * y,a(z,u,w) \ 1) = (a(z,u,w) * a(z,u,w)) * L((a(z,u,w) * a(z,u,w)) \ y,x,a(z,u,w) * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(22(a,2),27873(a,1,2))].">
      <j1 rule="para" parents="22 27873"/>
    </justification>
  </clause>

  <clause id="27877">
    <literal><![CDATA[
      x \ (x * y) = (a(z,u,w) * a(z,u,w)) * L((a(z,u,w) * a(z,u,w)) \ y,x,a(z,u,w) * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(20000(a,1),27874(a,1,2))].">
      <j1 rule="para" parents="20000 27874"/>
    </justification>
  </clause>

  <clause id="27878">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * L((a(x,y,z) * a(x,y,z)) \ u,w,a(x,y,z) * a(x,y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(358,a,27877,a)].">
      <j1 rule="hyper" parents="358 27877"/>
    </justification>
  </clause>

  <clause id="27880">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(3331,a,27878,a)].">
      <j1 rule="hyper" parents="3331 27878"/>
    </justification>
  </clause>

  <clause id="27883">
    <literal><![CDATA[
      x \ ((a(y,z,u) * a(y,z,u)) * w) = (a(y,z,u) * a(y,z,u)) * (x \ w)
    ]]></literal>
    <justification jstring="[hyper(23289,a,27880,a)].">
      <j1 rule="hyper" parents="23289 27880"/>
    </justification>
  </clause>

  <clause id="27886">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(27880(a,1),50(a,2))].">
      <j1 rule="para" parents="27880 50"/>
    </justification>
  </clause>

  <clause id="27888">
    <literal><![CDATA[
      L(x,y,z * (a(u,w,v5) * a(u,w,v5))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(27880(a,1),3606(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27880 3606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27889">
    <literal><![CDATA[
      x * (L(L(x,y,z),y,z) \ (u * L(w,a(z,y,x) * a(z,y,x),u))) = u * ((a(z,y,x) * a(z,y,x)) * w)
    ]]></literal>
    <justification jstring="[para(27880(a,1),27483(a,2,2,2))].">
      <j1 rule="para" parents="27880 27483"/>
    </justification>
  </clause>

  <clause id="27890">
    <literal><![CDATA[
      L(x,y,(a(z,u,w) * a(z,u,w)) \ v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(20492,a,27888,a),flip(a)].">
      <j1 rule="hyper" parents="20492 27888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27891">
    <literal><![CDATA[
      (L(x,y,z) * (y * (z * (a(u,w,v5) * a(u,w,v5))))) \ (x * (y * (z * (a(u,w,v5) * a(u,w,v5))))) = a(z * (a(u,w,v5) * a(u,w,v5)),y,x)
    ]]></literal>
    <justification jstring="[para(27888(a,1),18298(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="27888 18298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27892">
    <literal><![CDATA[
      L(x,y,(a(z,u,w) * a(z,u,w)) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,v5) = v6
    ]]></literal>
    <justification jstring="[para(27888(a,1),20492(a,1))].">
      <j1 rule="para" parents="27888 20492"/>
    </justification>
  </clause>

  <clause id="27893">
    <literal><![CDATA[
      L(x,y,L(L(z,u,w),u,w) \ v5) = L(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(27423(a,1),27888(a,1,3))].">
      <j1 rule="para" parents="27423 27888"/>
    </justification>
  </clause>

  <clause id="27894">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ (z \ u)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(23076(a,1),27890(a,1,3)),flip(a)].">
      <j1 rule="para" parents="23076 27890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27895">
    <literal><![CDATA[
      L(x,a(y,z,u),w \ (w \ v5)) = L(x,a(y,z,u),L(v5,w,w))
    ]]></literal>
    <justification jstring="[hyper(23230,a,27894,a)].">
      <j1 rule="hyper" parents="23230 27894"/>
    </justification>
  </clause>

  <clause id="27896">
    <literal><![CDATA[
      (x / y) * L(z,1 / y,L(x,y,y)) = (a(x,y,y) \ x) * ((1 / y) * z)
    ]]></literal>
    <justification jstring="[para(27894(a,1),27854(a,1,2))].">
      <j1 rule="para" parents="27894 27854"/>
    </justification>
  </clause>

  <clause id="27897">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * (L(L(z,u,w),u,w) \ v5)) = L(x,y,z \ (L(z,u,w) * v5))
    ]]></literal>
    <justification jstring="[para(1407(a,1),27893(a,1,3))].">
      <j1 rule="para" parents="1407 27893"/>
    </justification>
  </clause>

  <clause id="27898">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ 1) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(3946(a,1),27892(a,1))].">
      <j1 rule="para" parents="3946 27892"/>
    </justification>
  </clause>

  <clause id="27899">
    <literal><![CDATA[
      L(x,y,z \ (a(u,w,v5) \ 1)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ a(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(16644(a,1),27892(a,1,3))].">
      <j1 rule="para" parents="16644 27892"/>
    </justification>
  </clause>

  <clause id="27900">
    <literal><![CDATA[
      L(x,x,x \ a(y,x,z)) = (a(y,x \ 1,z) \ (x \ 1)) \ (a(y,x \ 1,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(27899,a,26775,a)].">
      <j1 rule="hyper" parents="27899 26775"/>
    </justification>
  </clause>

  <clause id="27901">
    <literal><![CDATA[
      (a(x,y,y) \ x) * ((1 / y) * z) = (x / y) * L(z,y,L(x,y,y))
    ]]></literal>
    <justification jstring="[para(3189(a,1),27896(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3189 27896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27902">
    <literal><![CDATA[
      x \ (y * (L(L(y,z,u),z,u) \ w)) = (a(u,z,y) * a(u,z,y)) * (x \ w)
    ]]></literal>
    <justification jstring="[para(27419(a,1),27883(a,1,2))].">
      <j1 rule="para" parents="27419 27883"/>
    </justification>
  </clause>

  <clause id="27903">
    <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(347,a,27419,a(flip),b,27902,a),flip(a)].">
      <j1 rule="hyper" parents="347 27419 27902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27904">
    <literal><![CDATA[
      L(x,y,z \ (L(z,u,w) * v5)) = L(x,y,z * (L(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(27067(a,1),27897(a,1,3)),flip(a)].">
      <j1 rule="para" parents="27067 27897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27905">
    <literal><![CDATA[
      L(1 / x,1 / x,L(y,x,x \ 1)) = L(1 / x,x,x * (L(x,z,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,26740,a,b,27904,a)].">
      <j1 rule="hyper" parents="63 26740 27904"/>
    </justification>
  </clause>

  <clause id="27906">
    <literal><![CDATA[
      L(x \ 1,x,L(x,y,z) \ u) = L(1 / x,1 / x,L(u,x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(347,a,5505,a(flip),b,27905,a)].">
      <j1 rule="hyper" parents="347 5505 27905"/>
    </justification>
  </clause>

  <clause id="27907">
    <literal><![CDATA[
      L(x \ 1,x,L(x,y,z) \ u) = L(1 / x,1 / x,L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,23682,a(flip),b,27906,a),flip(a)].">
      <j1 rule="hyper" parents="347 23682 27906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27908">
    <literal><![CDATA[
      L(x \ 1,x,L(x,y,z) \ u) = L(1 / x,x,L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,3189,a(flip),b,27907,a),flip(a)].">
      <j1 rule="hyper" parents="347 3189 27907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27909">
    <literal><![CDATA[
      L(x \ 1,x,L(x,y,z) \ u) = L(1 / x,x,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,23685,a(flip),b,27908,a),flip(a)].">
      <j1 rule="hyper" parents="347 23685 27908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27910">
    <literal><![CDATA[
      ((L(x,y,z) \ u) * x) \ (L(x,y,z) \ u) = L(1 / x,x,u)
    ]]></literal>
    <justification jstring="[hyper(572,a,27909,a)].">
      <j1 rule="hyper" parents="572 27909"/>
    </justification>
  </clause>

  <clause id="27911">
    <literal><![CDATA[
      L(1 / x,x,y) \ L(L(x \ 1,x,L(x,z,u) \ y),w,v5) = L(x \ L(x,w,v5),x,L(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(27910(a,1),4643(a,1,1))].">
      <j1 rule="para" parents="27910 4643"/>
    </justification>
  </clause>

  <clause id="27912">
    <literal><![CDATA[
      L(x,x,x \ a(y,x,z)) = (a(y,x,z) \ (x \ 1)) \ (a(y,x \ 1,z) \ 1)
    ]]></literal>
    <justification jstring="[para(14950(a,1),27900(a,2,1,1))].">
      <j1 rule="para" parents="14950 27900"/>
    </justification>
  </clause>

  <clause id="27913">
    <literal><![CDATA[
      L(x,x,x \ a(y,x,z)) = (a(y,x,z) \ (x \ 1)) \ (a(y,x,z) \ 1)
    ]]></literal>
    <justification jstring="[para(14950(a,1),27912(a,2,2,1))].">
      <j1 rule="para" parents="14950 27912"/>
    </justification>
  </clause>

  <clause id="27914">
    <literal><![CDATA[
      L(x,x,x \ a(y,x,z)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,26690,a(flip),b,27913,a),flip(a)].">
      <j1 rule="hyper" parents="347 26690 27913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27916">
    <literal><![CDATA[
      T(x,x \ 1) * R(L(x,y,z) \ a(u,x,w),x,x) = x * (L(x,y,z) \ a(u,x,w))
    ]]></literal>
    <justification jstring="[para(27914(a,1),26689(a,1,1))].">
      <j1 rule="para" parents="27914 26689"/>
    </justification>
  </clause>

  <clause id="27917">
    <literal><![CDATA[
      R(x * (L(x,y,z) \ a(u,x,w)),x,x) = x * (L(x,y,z) \ a(u,x,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,2987,a(flip),b,27916,a)].">
      <j1 rule="hyper" parents="63 2987 27916"/>
    </justification>
  </clause>

  <clause id="27918">
    <literal><![CDATA[
      (a(x,y,z) * y) * (L(y,u,w) \ 1) = y * (L(y,u,w) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,26475,a(flip),b,27917,a)].">
      <j1 rule="hyper" parents="63 26475 27917"/>
    </justification>
  </clause>

  <clause id="27919">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,L(x,u,w) \ v5) = L(1 / x,x,v5) \ L(L(1 / x,x,v5),y,z)
    ]]></literal>
    <justification jstring="[para(27909(a,1),27911(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="27909 27911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27920">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,L(x,u,w) \ v5) = L((1 / x) \ L(1 / x,y,z),x,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,4638,a(flip),b,27919,a),flip(a)].">
      <j1 rule="hyper" parents="347 4638 27919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27922">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,L(x,u,w) \ v5) = L(x \ L(x,y,z),x,v5)
    ]]></literal>
    <justification jstring="[para(3356(a,1),27920(a,2,1))].">
      <j1 rule="para" parents="3356 27920"/>
    </justification>
  </clause>

  <clause id="27923">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) \ u = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(27922(a,1),23326(a,1,1))].">
      <j1 rule="para" parents="27922 23326"/>
    </justification>
  </clause>

  <clause id="27924">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) \ u = u \ (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(128,a,27923,a(flip),b,23857,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="128 27923 23857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27926">
    <literal><![CDATA[
      x / (L(y,z,u) * (y \ x)) = x \ (y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,21939,a,b,27924,a)].">
      <j1 rule="hyper" parents="63 21939 27924"/>
    </justification>
  </clause>

  <clause id="27927">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) \ x = x \ (y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(20689(a,1),27924(a,1,1))].">
      <j1 rule="para" parents="20689 27924"/>
    </justification>
  </clause>

  <clause id="27928">
    <literal><![CDATA[
      x \ ((y \ x) * (L(y \ x,z,u) \ x)) = (y * L(y \ x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(20684(a,1),27924(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20684 27924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27929">
    <literal><![CDATA[
      x / (x * (x \ (y * (L(y,z,u) \ x)))) = x \ (L(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[para(27924(a,1),22890(a,1,2,2))].">
      <j1 rule="para" parents="27924 22890"/>
    </justification>
  </clause>

  <clause id="27930">
    <literal><![CDATA[
      L(L(x,y,z) \ x,L(x,y,z),u * x) = u \ (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,27320,a,b,27926,a)].">
      <j1 rule="hyper" parents="63 27320 27926"/>
    </justification>
  </clause>

  <clause id="27931">
    <literal><![CDATA[
      x \ (y * (L(y,y,y \ x) \ x)) = ((x / y) / (y \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(13710(a,1),27927(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13710 27927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27932">
    <literal><![CDATA[
      x \ (y * T(x * (y \ 1),y)) = ((x / y) / (y \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(10164(a,1),27931(a,1,2,2))].">
      <j1 rule="para" parents="10164 27931"/>
    </justification>
  </clause>

  <clause id="27933">
    <literal><![CDATA[
      ((x / y) / (y \ 1)) \ x = x \ ((x * (y \ 1)) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,250,a(flip),b,27932,a),flip(a)].">
      <j1 rule="hyper" parents="63 250 27932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27934">
    <literal><![CDATA[
      x / (y * (L(y,z,u) \ x)) = x \ (L(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[para(10(a,1),27929(a,1,2))].">
      <j1 rule="para" parents="10 27929"/>
    </justification>
  </clause>

  <clause id="27935">
    <literal><![CDATA[
      (L(x,y,z) \ u) \ (x \ u) = u \ (L(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,22609,a(flip),b,27934,a)].">
      <j1 rule="hyper" parents="63 22609 27934"/>
    </justification>
  </clause>

  <clause id="27937">
    <literal><![CDATA[
      (x * (x * (L(x,y,z) \ u))) \ (x * u) = u \ (L(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,22582,a,b,27935,a)].">
      <j1 rule="hyper" parents="63 22582 27935"/>
    </justification>
  </clause>

  <clause id="27938">
    <literal><![CDATA[
      (x \ (L(y,z,u) * (y \ x))) \ (y \ x) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(39,a,22047,a,b,27935,a)].">
      <j1 rule="hyper" parents="39 22047 27935"/>
    </justification>
  </clause>

  <clause id="27939">
    <literal><![CDATA[
      (x \ ((x / y) * L(y,z,u))) \ (y \ x) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(20689(a,1),27938(a,1,1,2))].">
      <j1 rule="para" parents="20689 27938"/>
    </justification>
  </clause>

  <clause id="27940">
    <literal><![CDATA[
      (L(x,y,z) \ u) \ (x \ u) != w
    ]]></literal>
    <literal><![CDATA[
      u \ (L(x,y,z) * (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(27938(a,1),22048(a,1,1))].">
      <j1 rule="para" parents="27938 22048"/>
    </justification>
  </clause>

  <clause id="27941">
    <literal><![CDATA[
      x * (L(L(x,y,z),y,z) \ (u * L(w,a(z,y,x) * a(z,y,x),u))) = u * (x * (L(L(x,y,z),y,z) \ w))
    ]]></literal>
    <justification jstring="[para(27419(a,1),27889(a,2,2))].">
      <j1 rule="para" parents="27419 27889"/>
    </justification>
  </clause>

  <clause id="27942">
    <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(534(a,1),27941(a,1,2,2,2))].">
      <j1 rule="para" parents="534 27941"/>
    </justification>
  </clause>

  <clause id="27943">
    <literal><![CDATA[
      ((L(x,y,z) * (y * (z * (a(u,w,v5) * a(u,w,v5))))) \ (x * (y * z))) * (a(u,w,v5) * a(u,w,v5)) = a(z * (a(u,w,v5) * a(u,w,v5)),y,x)
    ]]></literal>
    <justification jstring="[hyper(1371,a,27891,a)].">
      <j1 rule="hyper" parents="1371 27891"/>
    </justification>
  </clause>

  <clause id="27944">
    <literal><![CDATA[
      ((a(x,y,z) * a(x,y,z)) \ ((L(u,w,v5) * (w * v5)) \ (u * (w * v5)))) * (a(x,y,z) * a(x,y,z)) = a(v5 * (a(x,y,z) * a(x,y,z)),w,u)
    ]]></literal>
    <justification jstring="[para(1102(a,1),27943(a,1,1))].">
      <j1 rule="para" parents="1102 27943"/>
    </justification>
  </clause>

  <clause id="27945">
    <literal><![CDATA[
      ((a(x,y,z) * a(x,y,z)) \ a(u,w,v5)) * (a(x,y,z) * a(x,y,z)) = a(u * (a(x,y,z) * a(x,y,z)),w,v5)
    ]]></literal>
    <justification jstring="[para(18298(a,2),27944(a,1,1,2))].">
      <j1 rule="para" parents="18298 27944"/>
    </justification>
  </clause>

  <clause id="27946">
    <literal><![CDATA[
      a(x * (a(y,z,u) * a(y,z,u)),w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,23075,a(flip),b,27945,a),flip(a)].">
      <j1 rule="hyper" parents="63 23075 27945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27947">
    <literal><![CDATA[
      a((a(x,y,z) * a(x,y,z)) * u,w,v5) = a(u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(24229,a,27946,a)].">
      <j1 rule="hyper" parents="24229 27946"/>
    </justification>
  </clause>

  <clause id="27948">
    <literal><![CDATA[
      a((a(x,y,z) \ 1) \ u,w,v5) = a(a(x,y,z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(23977,a,27946,a)].">
      <j1 rule="hyper" parents="23977 27946"/>
    </justification>
  </clause>

  <clause id="27949">
    <literal><![CDATA[
      a((a(x,y,z) * a(x,y,z)) \ u,w,v5) = a(u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(23954,a,27946,a),flip(a)].">
      <j1 rule="hyper" parents="23954 27946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27951">
    <literal><![CDATA[
      a(a(x,y,z) \ 1,u,w) = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(240(a,1),27946(a,1,1)),flip(a)].">
      <j1 rule="para" parents="240 27946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27952">
    <literal><![CDATA[
      a(L(L(x,y,z),y,z) \ u,w,v5) = a(x \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(27423(a,1),27946(a,1,1))].">
      <j1 rule="para" parents="27423 27946"/>
    </justification>
  </clause>

  <clause id="27953">
    <literal><![CDATA[
      a(a(x,y,z),z * a(x,y,z),u) * (((a(x,y,z) \ 1) \ z) * u) = (a(x,y,z) \ 1) \ (z * u)
    ]]></literal>
    <justification jstring="[para(27951(a,1),21804(a,1,1))].">
      <j1 rule="para" parents="27951 21804"/>
    </justification>
  </clause>

  <clause id="27954">
    <literal><![CDATA[
      a(a(x,y,y),x \ (y \ x),z) * (((y * ((x * y) \ x)) \ y) * z) = L(((x * y) \ x) \ z,(x * y) \ x,y)
    ]]></literal>
    <justification jstring="[para(27951(a,1),25793(a,1,1))].">
      <j1 rule="para" parents="27951 25793"/>
    </justification>
  </clause>

  <clause id="27955">
    <literal><![CDATA[
      a(a(x,y,L(z,z,y)),u,w) = a((L(z,y,x) \ z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(26225(a,1),27951(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="26225 27951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27956">
    <literal><![CDATA[
      a(x * ((a(y,z,u) \ 1) \ w),v5,v6) = a(x * (a(y,z,u) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,24593,a(flip),b,27947,a)].">
      <j1 rule="hyper" parents="63 24593 27947"/>
    </justification>
  </clause>

  <clause id="27957">
    <literal><![CDATA[
      a(x * (y * (a(z,u,w) * a(z,u,w))),v5,v6) = a(y * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,24314,a(flip),b,27947,a)].">
      <j1 rule="hyper" parents="63 24314 27947"/>
    </justification>
  </clause>

  <clause id="27958">
    <literal><![CDATA[
      a((x \ 1) \ (x \ y),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(23076(a,1),27949(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23076 27949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27959">
    <literal><![CDATA[
      a((x \ L(L(x,y,z),y,z)) * u,w,v5) = a(u,w,v5)
    ]]></literal>
    <justification jstring="[para(27418(a,1),27949(a,1,1))].">
      <j1 rule="para" parents="27418 27949"/>
    </justification>
  </clause>

  <clause id="27960">
    <literal><![CDATA[
      a(L(x * y,x,x),z,u) = a((x \ 1) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),27958(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 27958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27961">
    <literal><![CDATA[
      a(L(x,y \ x,y \ x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(((y \ x) \ 1) \ y,z,u) = w
    ]]></literal>
    <justification jstring="[para(27958(a,1),23984(a,1))].">
      <j1 rule="para" parents="27958 23984"/>
    </justification>
  </clause>

  <clause id="27962">
    <literal><![CDATA[
      a((x \ 1) \ ((T(x,y) \ 1) \ z),u,w) = a((x * z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(24975,a,27960,a),flip(a)].">
      <j1 rule="hyper" parents="24975 27960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27963">
    <literal><![CDATA[
      a(x * ((x \ (y \ x)) \ 1),z,u) = a((y \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,26810,a(flip),b,27960,a)].">
      <j1 rule="hyper" parents="63 26810 27960"/>
    </justification>
  </clause>

  <clause id="27964">
    <literal><![CDATA[
      a(L(T(x * y,K(y,z)),y,y),u,w) = a((y \ 1) \ T(x,T(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(6060(a,2),27960(a,1,1,1))].">
      <j1 rule="para" parents="6060 27960"/>
    </justification>
  </clause>

  <clause id="27965">
    <literal><![CDATA[
      a(L(x * y,x,x) \ z,u,w) = a(((x \ 1) \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(3192(a,1),27952(a,1,1,1,1))].">
      <j1 rule="para" parents="3192 27952"/>
    </justification>
  </clause>

  <clause id="27966">
    <literal><![CDATA[
      a(L(x \ 1,y,z) \ u,w,v5) = a((L(x,y,z) \ 1) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(25955(a,1),27952(a,1,1,1,1))].">
      <j1 rule="para" parents="25955 27952"/>
    </justification>
  </clause>

  <clause id="27967">
    <literal><![CDATA[
      a(L(L(x,y,z),y,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(23954,a,27959,a)].">
      <j1 rule="hyper" parents="23954 27959"/>
    </justification>
  </clause>

  <clause id="27968">
    <literal><![CDATA[
      a(x * (y \ L(L(y,z,u),z,u)),w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(23925,a,27959,a)].">
      <j1 rule="hyper" parents="23925 27959"/>
    </justification>
  </clause>

  <clause id="27969">
    <literal><![CDATA[
      a(L(L(x,y,z),y,z) * u,w,v5) = a(x * u,w,v5)
    ]]></literal>
    <justification jstring="[para(25629(a,1),27959(a,1,1))].">
      <j1 rule="para" parents="25629 27959"/>
    </justification>
  </clause>

  <clause id="27970">
    <literal><![CDATA[
      a(L((x * y) \ z,y,x),u,w) = a(y \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[para(329(a,1),27967(a,1,1,1))].">
      <j1 rule="para" parents="329 27967"/>
    </justification>
  </clause>

  <clause id="27971">
    <literal><![CDATA[
      a(L((x * T(y,z)) \ u,y,x),w,v5) = a(T(y,z) \ (x \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(21654(a,1),27967(a,1,1,1))].">
      <j1 rule="para" parents="21654 27967"/>
    </justification>
  </clause>

  <clause id="27972">
    <literal><![CDATA[
      a(L(x \ 1,y,z),u,w) = a(L(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(25955(a,1),27967(a,1,1,1))].">
      <j1 rule="para" parents="25955 27967"/>
    </justification>
  </clause>

  <clause id="27973">
    <literal><![CDATA[
      a(x * L(L(y,z,u),z,u),w,v5) = a(x * y,w,v5)
    ]]></literal>
    <justification jstring="[para(25593(a,1),27968(a,1,1))].">
      <j1 rule="para" parents="25593 27968"/>
    </justification>
  </clause>

  <clause id="27974">
    <literal><![CDATA[
      a(x \ L(L(y,z,u),z,u),w,v5) = a(x \ y,w,v5)
    ]]></literal>
    <justification jstring="[para(25667(a,1),27968(a,1,1))].">
      <j1 rule="para" parents="25667 27968"/>
    </justification>
  </clause>

  <clause id="27975">
    <literal><![CDATA[
      a(L(x * y,x,x) * z,u,w) = a(((x \ 1) \ y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(3192(a,1),27969(a,1,1,1,1))].">
      <j1 rule="para" parents="3192 27969"/>
    </justification>
  </clause>

  <clause id="27976">
    <literal><![CDATA[
      L(x,y,z) * (x \ (u / (L(x,y,z) * u))) = a(L(x \ 1,y,z),L(x,y,z),u) / x
    ]]></literal>
    <justification jstring="[para(27972(a,2),26896(a,2,1))].">
      <j1 rule="para" parents="27972 26896"/>
    </justification>
  </clause>

  <clause id="27978">
    <literal><![CDATA[
      a((x \ 1) * L(y,x,x),z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(3202(a,1),27974(a,1,1))].">
      <j1 rule="para" parents="3202 27974"/>
    </justification>
  </clause>

  <clause id="27979">
    <literal><![CDATA[
      a(x \ (y * a(z,z,y)),u,w) = a(x \ L(y,z,z),u,w)
    ]]></literal>
    <justification jstring="[para(15300(a,1),27974(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15300 27974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27980">
    <literal><![CDATA[
      a((L(x,y,z) / u) \ x,w,v5) = a((x / u) \ L(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(25578(a,1),27974(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25578 27974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27981">
    <literal><![CDATA[
      a(L((x \ 1) * y,x,x),z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,24974,a,b,27978,a)].">
      <j1 rule="hyper" parents="63 24974 27978"/>
    </justification>
  </clause>

  <clause id="27982">
    <literal><![CDATA[
      L((x * y) \ 1,y,x) * ((L((x * y) \ 1,y,x) \ 1) * z) = (a(y \ (x \ 1),y \ x,z) \ 1) * z
    ]]></literal>
    <justification jstring="[para(27970(a,1),27173(a,2,1,1))].">
      <j1 rule="para" parents="27970 27173"/>
    </justification>
  </clause>

  <clause id="27986">
    <literal><![CDATA[
      a(x \ (y \ ((y \ 1) \ z)),u,w) = a(x \ L(z,y,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24777,a,b,27979,a)].">
      <j1 rule="hyper" parents="63 24777 27979"/>
    </justification>
  </clause>

  <clause id="27987">
    <literal><![CDATA[
      a(a(x,y,L(z,z,y)),u,w) = a(z \ L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(10888(a,1),27955(a,2,1))].">
      <j1 rule="para" parents="10888 27955"/>
    </justification>
  </clause>

  <clause id="27988">
    <literal><![CDATA[
      a(L(x,y,z) \ x,u,w) = a(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(26225(a,1),27987(a,1,1))].">
      <j1 rule="para" parents="26225 27987"/>
    </justification>
  </clause>

  <clause id="27989">
    <literal><![CDATA[
      a(x \ L(x,y,z),x * L(x,y,z),u) * u = (x \ L(x,y,z)) \ ((L(x,y,z) \ x) \ u)
    ]]></literal>
    <justification jstring="[para(27988(a,1),15309(a,1,1))].">
      <j1 rule="para" parents="27988 15309"/>
    </justification>
  </clause>

  <clause id="27990">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * (x \ a(x \ L(x,y,z),x,u)) = L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[para(27988(a,1),26970(a,1,2,2))].">
      <j1 rule="para" parents="27988 26970"/>
    </justification>
  </clause>

  <clause id="27991">
    <literal><![CDATA[
      a(((((x * y) \ y) \ 1) * y) \ z,u,w) = a(((x \ 1) \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,26701,a(flip),b,27965,a)].">
      <j1 rule="hyper" parents="63 26701 27965"/>
    </justification>
  </clause>

  <clause id="27992">
    <literal><![CDATA[
      a(((x \ 1) \ (x \ y)) \ z,u,w) = a(L(y,x,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),27965(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 27965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27993">
    <literal><![CDATA[
      a(x * L(y * z,z,z),u,w) = a(((z \ 1) \ y) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24802,a(flip),b,27975,a)].">
      <j1 rule="hyper" parents="63 24802 27975"/>
    </justification>
  </clause>

  <clause id="27994">
    <literal><![CDATA[
      a(x \ L((y \ 1) * z,y,y),u,w) = a(x \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),27986(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 27986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27995">
    <literal><![CDATA[
      a((x \ ((x \ 1) \ y)) \ z,u,w) = a(L(y,x,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24774,a(flip),b,27992,a)].">
      <j1 rule="hyper" parents="63 24774 27992"/>
    </justification>
  </clause>

  <clause id="27996">
    <literal><![CDATA[
      a(((x \ 1) \ (x \ (y * x))) \ z,u,w) = a((((x \ 1) * (x * y)) * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(3217(a,2),27992(a,2,1,1))].">
      <j1 rule="para" parents="3217 27992"/>
    </justification>
  </clause>

  <clause id="27997">
    <literal><![CDATA[
      a(L(x * y,y,y) * z,u,w) = a(((y \ 1) \ x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(23925,a,27993,a)].">
      <j1 rule="hyper" parents="23925 27993"/>
    </justification>
  </clause>

  <clause id="27998">
    <literal><![CDATA[
      a((x \ L((y \ 1) * z,y,y)) \ (y \ z),u,w) = a((x \ ((y \ 1) * z)) \ ((y \ 1) * z),u,w)
    ]]></literal>
    <justification jstring="[para(22971(a,1),27994(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22971 27994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27999">
    <literal><![CDATA[
      a((x \ L((y \ 1) * z,y,y)) \ (y \ z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(27994(a,1),23957(a,1))].">
      <j1 rule="para" parents="27994 23957"/>
    </justification>
  </clause>

  <clause id="28000">
    <literal><![CDATA[
      a(L((x \ 1) * y,x,x) \ z,u,w) = a((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),27995(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 27995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28001">
    <literal><![CDATA[
      a(x * ((a(y,z,u) * a(y,z,u)) * w),v5,v6) = a(x * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(23980,a,27957,a)].">
      <j1 rule="hyper" parents="23980 27957"/>
    </justification>
  </clause>

  <clause id="28002">
    <literal><![CDATA[
      a(x * (L(L(y,z,u),z,u) \ w),v5,v6) = a((y \ w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(27423(a,1),27957(a,1,1,2))].">
      <j1 rule="para" parents="27423 27957"/>
    </justification>
  </clause>

  <clause id="28003">
    <literal><![CDATA[
      a((x \ 1) \ ((x \ 1) \ y),z,u) = a((x * y) * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,24621,a(flip),b,27962,a)].">
      <j1 rule="hyper" parents="63 24621 27962"/>
    </justification>
  </clause>

  <clause id="28004">
    <literal><![CDATA[
      a(L(x \ 1,y,z) \ 1,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(L(x,y,z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(27966(a,2),11586(a,1))].">
      <j1 rule="para" parents="27966 11586"/>
    </justification>
  </clause>

  <clause id="28005">
    <literal><![CDATA[
      a((L(x,y,z) / u) \ x,w,v5) = a((u \ x) \ L(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,23892,a(flip),b,27980,a),flip(a)].">
      <j1 rule="hyper" parents="347 23892 27980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28006">
    <literal><![CDATA[
      a(x * ((a(y,z,u) * a(y,z,u)) \ w),v5,v6) = a(x * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(10(a,1),28001(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 28001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28007">
    <literal><![CDATA[
      a((x \ y) * L(x,z,u),w,v5) = a(x * (L(x,z,u) \ y),w,v5)
    ]]></literal>
    <justification jstring="[para(27067(a,1),28002(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27067 28002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28008">
    <literal><![CDATA[
      a((x \ L(y,z,u)) \ y,w,v5) = a((x \ y) \ L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(23961,a,28005,a)].">
      <j1 rule="hyper" parents="23961 28005"/>
    </justification>
  </clause>

  <clause id="28009">
    <literal><![CDATA[
      a(x * ((y \ L(L(y,z,u),z,u)) * w),v5,v6) = a(x * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(27418(a,1),28006(a,1,1,2))].">
      <j1 rule="para" parents="27418 28006"/>
    </justification>
  </clause>

  <clause id="28010">
    <literal><![CDATA[
      a(x * (L(L(y,z,u),z,u) * w),v5,v6) = a(x * (y * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(25629(a,1),28009(a,1,1,2))].">
      <j1 rule="para" parents="25629 28009"/>
    </justification>
  </clause>

  <clause id="28011">
    <literal><![CDATA[
      a(L((x * y) \ z,x,y),u,w) = a(T(x,v5) \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(24938,a,27971,a)].">
      <j1 rule="hyper" parents="24938 27971"/>
    </justification>
  </clause>

  <clause id="28012">
    <literal><![CDATA[
      a(L((x * y) \ z,x,y),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x \ (y \ z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(28011(a,2),17837(a,1))].">
      <j1 rule="para" parents="28011 17837"/>
    </justification>
  </clause>

  <clause id="28013">
    <literal><![CDATA[
      a(x * (a(y,z,u) \ 1),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x * a(y,z,u),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(27956(a,1),23982(a,1))].">
      <j1 rule="para" parents="27956 23982"/>
    </justification>
  </clause>

  <clause id="28014">
    <literal><![CDATA[
      a(x * a(y,z,u),w,v5) = a(x * a(u,z,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(28013,a,26966,a)].">
      <j1 rule="hyper" parents="28013 26966"/>
    </justification>
  </clause>

  <clause id="28015">
    <literal><![CDATA[
      a(x * a(y,z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x * a(u,z,y),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(26966(a,1),28013(a,1))].">
      <j1 rule="para" parents="26966 28013"/>
    </justification>
  </clause>

  <clause id="28016">
    <literal><![CDATA[
      a(a(x,y,z) * u,w,v5) = a(u * a(z,y,x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(23925,a,28014,a)].">
      <j1 rule="hyper" parents="23925 28014"/>
    </justification>
  </clause>

  <clause id="28017">
    <literal><![CDATA[
      a(x * a(y,z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(a(u,z,y) * x,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(28014(a,1),23925(a,1))].">
      <j1 rule="para" parents="28014 23925"/>
    </justification>
  </clause>

  <clause id="28018">
    <literal><![CDATA[
      a(x * a(y * (z \ y),y,y),u,w) = a(x * a(y,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(25995(a,1),28014(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="25995 28014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28019">
    <literal><![CDATA[
      a(a(x,y,z) * u,x,x) = a(u,x,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,27599,a(flip),b,28016,a),flip(a)].">
      <j1 rule="hyper" parents="347 27599 28016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28020">
    <literal><![CDATA[
      a(a(x \ 1,y,z) * u,w,v5) = a(u * a(z,y,x),w,v5)
    ]]></literal>
    <justification jstring="[para(14922(a,1),28016(a,2,1,2))].">
      <j1 rule="para" parents="14922 28016"/>
    </justification>
  </clause>

  <clause id="28021">
    <literal><![CDATA[
      a(a(x,y,z) * (u * (w * a(a(z,y,x),w,u))),v5,v6) = a((u * w) * R(a(z,y,x),w,u),v5,v6)
    ]]></literal>
    <justification jstring="[para(26827(a,1),28016(a,2,1))].">
      <j1 rule="para" parents="26827 28016"/>
    </justification>
  </clause>

  <clause id="28022">
    <literal><![CDATA[
      a(a(x,x,y * x) * z,u,w) = a(z * a(y,x,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,26895,a(flip),b,28020,a)].">
      <j1 rule="hyper" parents="63 26895 28020"/>
    </justification>
  </clause>

  <clause id="28023">
    <literal><![CDATA[
      a(x * a(y * z,y,y),u,w) = a(a(y,y,z) * x,u,w)
    ]]></literal>
    <justification jstring="[para(27219(a,1),28022(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="27219 28022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28024">
    <literal><![CDATA[
      a(a(x,x,y \ x) * z,u,w) = a(z * a(x,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,28023,a(flip),b,28018,a)].">
      <j1 rule="hyper" parents="63 28023 28018"/>
    </justification>
  </clause>

  <clause id="28025">
    <literal><![CDATA[
      a(a(x,x,x * y) * z,u,w) = a(z * a(x,x,y),u,w)
    ]]></literal>
    <justification jstring="[para(25991(a,1),28024(a,1,1,1))].">
      <j1 rule="para" parents="25991 28024"/>
    </justification>
  </clause>

  <clause id="28026">
    <literal><![CDATA[
      a(L(x,y * x,y * x),z,u) = a(((y \ x) \ 1) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(27961,a,27044,a),flip(a)].">
      <j1 rule="hyper" parents="27961 27044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28027">
    <literal><![CDATA[
      a((x \ 1) \ T(y,T(x,z)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(L(y * x,x,x),u,w) = v5
    ]]></literal>
    <justification jstring="[para(27964(a,1),23963(a,1))].">
      <j1 rule="para" parents="27964 23963"/>
    </justification>
  </clause>

  <clause id="28028">
    <literal><![CDATA[
      a(L(x * y,y,y),z,u) = a((y \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(28027,a,23887,a)].">
      <j1 rule="hyper" parents="28027 23887"/>
    </justification>
  </clause>

  <clause id="28029">
    <literal><![CDATA[
      a((((x \ 1) * (x * y)) * x) \ z,u,w) = a(((x \ 1) \ T(y,x)) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(22(a,2),27996(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="22 27996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28030">
    <literal><![CDATA[
      a((((x \ 1) * (x * y)) * x) \ z,u,w) = a(((x \ 1) \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,23911,a(flip),b,28029,a),flip(a)].">
      <j1 rule="hyper" parents="347 23911 28029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28032">
    <literal><![CDATA[
      a(L(x * y,y,y) \ z,u,w) = a(((y \ 1) \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(3217(a,1),28030(a,1,1,1))].">
      <j1 rule="para" parents="3217 28030"/>
    </justification>
  </clause>

  <clause id="28033">
    <literal><![CDATA[
      a(((x \ 1) \ y) \ ((y * x) * (L(y * x,x,x) * z)),u,w) = a((y * x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(1406(a,1),28032(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1406 28032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28034">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ ((L(x,y,z) \ x) \ u) = a(u,a(z,y,x),a(z,y,x)) * u
    ]]></literal>
    <justification jstring="[para(27689(a,1),27989(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27689 27989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28035">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ ((L(x,y,z) \ x) \ u) = R(u,a(z,y,x),a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,13403,a(flip),b,28034,a),flip(a)].">
      <j1 rule="hyper" parents="347 13403 28034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28036">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ ((L(x,y,z) \ x) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,a(z,y,x),a(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(28035(a,2),23226(a,1))].">
      <j1 rule="para" parents="28035 23226"/>
    </justification>
  </clause>

  <clause id="28037">
    <literal><![CDATA[
      a(a(x,y,z),z * a(x,y,z),u) * ((z * a(x,y,z)) * u) = (a(x,y,z) \ 1) \ (z * u)
    ]]></literal>
    <justification jstring="[para(21803(a,1),27953(a,1,2,1))].">
      <j1 rule="para" parents="21803 27953"/>
    </justification>
  </clause>

  <clause id="28038">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) * (z * a(x,y,z))) * u) = (a(x,y,z) \ 1) \ (z * u)
    ]]></literal>
    <justification jstring="[hyper(14737,a,28037,a)].">
      <j1 rule="hyper" parents="14737 28037"/>
    </justification>
  </clause>

  <clause id="28039">
    <literal><![CDATA[
      a(x,y,z) \ ((z * (a(x,y,z) * a(x,y,z))) * u) = (a(x,y,z) \ 1) \ (z * u)
    ]]></literal>
    <justification jstring="[para(12713(a,1),28038(a,1,2,1))].">
      <j1 rule="para" parents="12713 28038"/>
    </justification>
  </clause>

  <clause id="28040">
    <literal><![CDATA[
      a(x,y,z) \ (z * ((a(x,y,z) * a(x,y,z)) * u)) = (a(x,y,z) \ 1) \ (z * u)
    ]]></literal>
    <justification jstring="[para(32(a,1),28039(a,1,2))].">
      <j1 rule="para" parents="32 28039"/>
    </justification>
  </clause>

  <clause id="28041">
    <literal><![CDATA[
      x * (a(y,z,x) \ ((a(y,z,x) * a(y,z,x)) * u)) = (a(y,z,x) \ 1) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(13853,a,28040,a)].">
      <j1 rule="hyper" parents="13853 28040"/>
    </justification>
  </clause>

  <clause id="28042">
    <literal><![CDATA[
      x * ((a(y,z,x) * a(y,z,x)) * (a(y,z,x) \ u)) = (a(y,z,x) \ 1) \ (x * u)
    ]]></literal>
    <justification jstring="[para(27883(a,1),28041(a,1,2))].">
      <j1 rule="para" parents="27883 28041"/>
    </justification>
  </clause>

  <clause id="28043">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (z * u) = z * ((a(x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(495(a,1),28042(a,1,2)),flip(a)].">
      <j1 rule="para" parents="495 28042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28044">
    <literal><![CDATA[
      L(((x * y) \ x) \ z,x \ (y \ x),y) = y * ((a(x,y,y) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(25512,a,28043,a)].">
      <j1 rule="hyper" parents="25512 28043"/>
    </justification>
  </clause>

  <clause id="28045">
    <literal><![CDATA[
      L(((x * y) \ x) \ z,x \ (y \ x),y) != y * u
    ]]></literal>
    <literal><![CDATA[
      (a(x,y,y) \ 1) \ z = u
    ]]></literal>
    <justification jstring="[para(28044(a,2),43(a,1))].">
      <j1 rule="para" parents="28044 43"/>
    </justification>
  </clause>

  <clause id="28046">
    <literal><![CDATA[
      a(a(x,y,z) * (L(u,w,a(z,y,x)) * w),v5,v6) = a((u * w) * R(a(z,y,x),w,u),v5,v6)
    ]]></literal>
    <justification jstring="[para(26571(a,1),28021(a,1,1,2))].">
      <j1 rule="para" parents="26571 28021"/>
    </justification>
  </clause>

  <clause id="28047">
    <literal><![CDATA[
      a((x * y) * R(a(z,u,w),y,x),v5,v6) = a(x * (a(w,u,z) * y),v5,v6)
    ]]></literal>
    <justification jstring="[para(27570(a,1),28046(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27570 28046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28048">
    <literal><![CDATA[
      a((x * y) * L(a(z,u,w),y,x),v5,v6) = a(x * (a(w,u,z) * y),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26217,a,28047,a)].">
      <j1 rule="hyper" parents="26217 28047"/>
    </justification>
  </clause>

  <clause id="28049">
    <literal><![CDATA[
      a(x * (a(y,z,u) * w),v5,v6) = a(x * (w * a(u,z,y)),v5,v6)
    ]]></literal>
    <justification jstring="[para(97(a,1),28048(a,1,1)),flip(a)].">
      <j1 rule="para" parents="97 28048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28050">
    <literal><![CDATA[
      a((a(x,y,z) * u) * w,v5,v6) = a(w * (a(z,y,x) * u),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,24228,a,b,28049,a)].">
      <j1 rule="hyper" parents="347 24228 28049"/>
    </justification>
  </clause>

  <clause id="28051">
    <literal><![CDATA[
      a(((a(x,y,z) / u) * K(u \ 1,w)) * v5,v6,v7) = a(v5 * (a(z,y,x) * T(a(x,y,z) \ (a(x,y,z) / u),w)),v6,v7)
    ]]></literal>
    <justification jstring="[para(5126(a,2),28050(a,1,1,1))].">
      <j1 rule="para" parents="5126 28050"/>
    </justification>
  </clause>

  <clause id="28052">
    <literal><![CDATA[
      L(((x * y) \ x) \ z,(x * y) \ x,y) = a(u,w,a(w,w,v5)) * (((y * ((x * y) \ x)) \ y) * z)
    ]]></literal>
    <justification jstring="[para(26737(a,1),27954(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26737 27954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28053">
    <literal><![CDATA[
      L(((x * y) \ x) \ z,(x * y) \ x,y) = a(u,w,a(w,w,v5)) * (((a(x,y,y) \ 1) \ y) * z)
    ]]></literal>
    <justification jstring="[para(25441(a,1),28052(a,2,2,1,1))].">
      <j1 rule="para" parents="25441 28052"/>
    </justification>
  </clause>

  <clause id="28055">
    <literal><![CDATA[
      L(((x * y) \ x) \ z,(x * y) \ x,y) = a(u,w,a(w,w,v5)) * ((y * a(x,y,y)) * z)
    ]]></literal>
    <justification jstring="[para(21803(a,1),28053(a,2,2,1))].">
      <j1 rule="para" parents="21803 28053"/>
    </justification>
  </clause>

  <clause id="28056">
    <literal><![CDATA[
      L(((x * y) \ x) \ z,(x * y) \ x,y) = a(x,y,y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,26724,a(flip),b,28055,a),flip(a)].">
      <j1 rule="hyper" parents="347 26724 28055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28057">
    <literal><![CDATA[
      L(((x * y) \ x) \ z,(x * y) \ x,y) = y * (z * a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,20597,a(flip),b,28056,a),flip(a)].">
      <j1 rule="hyper" parents="347 20597 28056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28058">
    <literal><![CDATA[
      L(((x * y) \ x) \ z,x \ (y \ x),y) = y * (z * a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(21916,a,28057,a)].">
      <j1 rule="hyper" parents="21916 28057"/>
    </justification>
  </clause>

  <clause id="28059">
    <literal><![CDATA[
      (a(x,y,y) \ 1) \ z = z * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(28045,a,28058,a)].">
      <j1 rule="hyper" parents="28045 28058"/>
    </justification>
  </clause>

  <clause id="28060">
    <literal><![CDATA[
      x \ (a(y,z,z) \ x) = a(y,z,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(21802,a,28059,a)].">
      <j1 rule="hyper" parents="21802 28059"/>
    </justification>
  </clause>

  <clause id="28061">
    <literal><![CDATA[
      L(x,a(y,z,z),a(y,z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(21367,a,28059,a)].">
      <j1 rule="hyper" parents="21367 28059"/>
    </justification>
  </clause>

  <clause id="28062">
    <literal><![CDATA[
      (a(x,y,y) \ 1) * z = a(x,y,y) \ z
    ]]></literal>
    <justification jstring="[hyper(20578,a,28059,a)].">
      <j1 rule="hyper" parents="20578 28059"/>
    </justification>
  </clause>

  <clause id="28063">
    <literal><![CDATA[
      (x \ L(x,x,y)) \ z = z * a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,25443,a(flip),b,28059,a)].">
      <j1 rule="hyper" parents="63 25443 28059"/>
    </justification>
  </clause>

  <clause id="28064">
    <literal><![CDATA[
      L(x,a(y,z,z) \ u,w) = L(x,u * a(y,z,z),w)
    ]]></literal>
    <justification jstring="[para(28059(a,1),3608(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28059 3608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28065">
    <literal><![CDATA[
      (R(x,y,y) \ x) \ z = z * a(x,y,y)
    ]]></literal>
    <justification jstring="[para(13405(a,2),28059(a,1,1))].">
      <j1 rule="para" parents="13405 28059"/>
    </justification>
  </clause>

  <clause id="28066">
    <literal><![CDATA[
      (a(x,y,y) \ K(z,u)) \ w = K(u,z) * (w * a(x,y,y))
    ]]></literal>
    <justification jstring="[para(28059(a,1),20832(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28059 20832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28067">
    <literal><![CDATA[
      a(x,y * (a(z,u,u) \ w),v5) = a(x,y * (w * a(z,u,u)),v5)
    ]]></literal>
    <justification jstring="[para(28059(a,1),24487(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28059 24487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28068">
    <literal><![CDATA[
      R(x,(y \ (z \ (z / y))) \ u,w) = R(x,u * a(z,y,y),w)
    ]]></literal>
    <justification jstring="[para(28059(a,1),25457(a,2,2))].">
      <j1 rule="para" parents="28059 25457"/>
    </justification>
  </clause>

  <clause id="28069">
    <literal><![CDATA[
      x * (a(y,z,z) \ 1) = a(y,z,z) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,26392,a(flip),b,28061,a),flip(a)].">
      <j1 rule="hyper" parents="63 26392 28061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28070">
    <literal><![CDATA[
      (a(x,x,y) * z) \ z = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(28061(a,1),25619(a,1,2))].">
      <j1 rule="para" parents="28061 25619"/>
    </justification>
  </clause>

  <clause id="28071">
    <literal><![CDATA[
      x * (R(y,z,z) \ y) = a(y,z,z) \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,13405,a,b,28060,a)].">
      <j1 rule="hyper" parents="134 13405 28060"/>
    </justification>
  </clause>

  <clause id="28072">
    <literal><![CDATA[
      x * (y \ L(y,y,z)) = a(z,y,y) \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,25426,a(flip),b,28060,a)].">
      <j1 rule="hyper" parents="134 25426 28060"/>
    </justification>
  </clause>

  <clause id="28073">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u) = a(z,y,a(u,x,x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(28060(a,1),27632(a,2,1,3))].">
      <j1 rule="para" parents="28060 27632"/>
    </justification>
  </clause>

  <clause id="28074">
    <literal><![CDATA[
      (R(x,y,y) \ x) * z = a(x,y,y) \ z
    ]]></literal>
    <justification jstring="[para(13405(a,2),28062(a,1,1))].">
      <j1 rule="para" parents="13405 28062"/>
    </justification>
  </clause>

  <clause id="28075">
    <literal><![CDATA[
      a(x,(a(y,z,z) \ u) * w,v5) = a(x,(a(y,z,z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(28062(a,1),24784(a,1,2,1))].">
      <j1 rule="para" parents="28062 24784"/>
    </justification>
  </clause>

  <clause id="28076">
    <literal><![CDATA[
      a(x,(a(y,z,z) \ u) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,(a(y,z,z) * u) * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(28062(a,1),24785(a,1,2,1))].">
      <j1 rule="para" parents="28062 24785"/>
    </justification>
  </clause>

  <clause id="28077">
    <literal><![CDATA[
      (x \ L(x,x,y)) * z = a(y,x,x) \ z
    ]]></literal>
    <justification jstring="[para(25426(a,1),28062(a,1,1))].">
      <j1 rule="para" parents="25426 28062"/>
    </justification>
  </clause>

  <clause id="28078">
    <literal><![CDATA[
      a(x,x \ y,x \ y) \ z = ((x \ y) * (y \ x)) * z
    ]]></literal>
    <justification jstring="[para(25458(a,1),28062(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25458 28062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28079">
    <literal><![CDATA[
      a(x,x * y,x * y) \ z = ((x \ y) * (y \ x)) * z
    ]]></literal>
    <justification jstring="[para(27034(a,1),28062(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27034 28062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28080">
    <literal><![CDATA[
      (a(x,y,y) * z) * a(x,y,y) = y * (L(L(y,y,x),y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,27432,a(flip),b,28063,a),flip(a)].">
      <j1 rule="hyper" parents="63 27432 28063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28081">
    <literal><![CDATA[
      R(x,y,(z * ((u \ (u / z)) \ 1)) \ w) = R(x,y,w * a(u,z,z))
    ]]></literal>
    <justification jstring="[para(28063(a,1),3727(a,1,3)),flip(a)].">
      <j1 rule="para" parents="28063 3727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28082">
    <literal><![CDATA[
      L(R(x,y,y) \ x,z,u) \ (R(x,y,y) \ x) = (L(1 / (R(x,y,y) \ x),z,u) \ 1) * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(3649,a,28065,a)].">
      <j1 rule="hyper" parents="3649 28065"/>
    </justification>
  </clause>

  <clause id="28083">
    <literal><![CDATA[
      L(a(R(x,y,y) \ x,z,u),R(x,y,y) \ x,z) = R(R(x,y,y) \ x,z,u) * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,26935,a,b,28065,a)].">
      <j1 rule="hyper" parents="63 26935 28065"/>
    </justification>
  </clause>

  <clause id="28084">
    <literal><![CDATA[
      x * ((y * ((y \ z) * (y \ z))) \ (z * (y \ z))) = (R(y,y \ z,y \ z) \ y) \ x
    ]]></literal>
    <justification jstring="[para(88(a,2),28065(a,2,2)),flip(a)].">
      <j1 rule="para" parents="88 28065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28085">
    <literal><![CDATA[
      x * L(L(R(y,z,z) \ y,u,w) * a(y,z,z),(R(y,z,z) \ y) * L(R(y,z,z) \ y,u,w),x) = (L(R(y,z,z) \ y,u,w) \ (R(y,z,z) \ y)) \ x
    ]]></literal>
    <justification jstring="[para(28065(a,1),20945(a,1,2,1))].">
      <j1 rule="para" parents="28065 20945"/>
    </justification>
  </clause>

  <clause id="28086">
    <literal><![CDATA[
      (x * (y \ L(L(y,y,z),y,z))) * a(z,y,y) = a(z,y,y) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,27471,a,b,28069,a)].">
      <j1 rule="hyper" parents="63 27471 28069"/>
    </justification>
  </clause>

  <clause id="28087">
    <literal><![CDATA[
      x \ (a(y,y,z) \ x) = a(y,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(374,a,28070,a)].">
      <j1 rule="hyper" parents="374 28070"/>
    </justification>
  </clause>

  <clause id="28088">
    <literal><![CDATA[
      x * (a(y,y,z) \ 1) = a(y,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,28070,a(flip),b,21746,a(flip))].">
      <j1 rule="hyper" parents="134 28070 21746"/>
    </justification>
  </clause>

  <clause id="28089">
    <literal><![CDATA[
      (a(x,x,y) \ 1) \ z = z * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(28070(a,1),21359(a,1,1))].">
      <j1 rule="para" parents="28070 21359"/>
    </justification>
  </clause>

  <clause id="28090">
    <literal><![CDATA[
      L(x,x \ y,a(y,y,z)) = L(y,y,z) / (a(z,y,y) \ (x \ y))
    ]]></literal>
    <justification jstring="[para(28071(a,1),25530(a,2,2))].">
      <j1 rule="para" parents="28071 25530"/>
    </justification>
  </clause>

  <clause id="28091">
    <literal><![CDATA[
      a(x,y,y) \ L(z,z,a(x,y,y)) = (y / z) \ L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,27630,a(flip),b,28072,a),flip(a)].">
      <j1 rule="hyper" parents="63 27630 28072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28092">
    <literal><![CDATA[
      (x \ (y * R(y \ x,y,y))) \ z = (R(y \ x,y,y) \ (y \ x)) * z
    ]]></literal>
    <justification jstring="[para(26937(a,2),28074(a,2,1)),flip(a)].">
      <j1 rule="para" parents="26937 28074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28093">
    <literal><![CDATA[
      a(x,((y / ((z \ 1) \ 1)) * L(z,z \ 1,u)) * w,v5) = a(x,w * (a(u,z,z) \ y),v5)
    ]]></literal>
    <justification jstring="[para(28077(a,1),26833(a,2,2,2))].">
      <j1 rule="para" parents="28077 26833"/>
    </justification>
  </clause>

  <clause id="28094">
    <literal><![CDATA[
      x * L(a(y,y,z) \ 1,u,w) = a(y,y,L(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,14633,a,b,28087,a)].">
      <j1 rule="hyper" parents="134 14633 28087"/>
    </justification>
  </clause>

  <clause id="28095">
    <literal><![CDATA[
      ((x \ 1) * y) \ ((x \ y) * L((x \ y) \ ((x \ 1) * y),z,u)) = a(u,z,a(x,x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(28087(a,1),26926(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="28087 26926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28096">
    <literal><![CDATA[
      L(x,a(y,y,z),a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,26393,a,b,28088,a)].">
      <j1 rule="hyper" parents="35 26393 28088"/>
    </justification>
  </clause>

  <clause id="28097">
    <literal><![CDATA[
      (x \ L(x,y,y)) * z = a(y,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(27656,a,28096,a),flip(a)].">
      <j1 rule="hyper" parents="27656 28096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28098">
    <literal><![CDATA[
      (((x \ (y \ x)) * y) \ 1) \ z = ((x \ (y \ x)) * y) * z
    ]]></literal>
    <justification jstring="[hyper(23709,a,28096,a),flip(a)].">
      <j1 rule="hyper" parents="23709 28096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28099">
    <literal><![CDATA[
      a(x,y,a(z,z,u) \ w) = a(x,y,a(z,z,u) * w)
    ]]></literal>
    <justification jstring="[para(28096(a,1),14958(a,1,3))].">
      <j1 rule="para" parents="28096 14958"/>
    </justification>
  </clause>

  <clause id="28100">
    <literal><![CDATA[
      (R(x,x,y) \ x) \ z = z * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(18995(a,2),28089(a,1,1))].">
      <j1 rule="para" parents="18995 28089"/>
    </justification>
  </clause>

  <clause id="28101">
    <literal><![CDATA[
      L(x \ y,x,a(z,z,y)) = (a(z,z,y) \ x) \ L(y,z,z)
    ]]></literal>
    <justification jstring="[para(28097(a,1),27547(a,2,1))].">
      <j1 rule="para" parents="28097 27547"/>
    </justification>
  </clause>

  <clause id="28102">
    <literal><![CDATA[
      (R(x,x,y) \ x) * z = a(x,x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(20578,a,28100,a)].">
      <j1 rule="hyper" parents="20578 28100"/>
    </justification>
  </clause>

  <clause id="28103">
    <literal><![CDATA[
      a(x,x,y) \ (z * R(z \ ((R(x,x,y) \ x) \ z),u,w)) = z * ((R(x,x,y) \ x) * R((R(x,x,y) \ x) \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,23587,a(flip),b,28102,a),flip(a)].">
      <j1 rule="hyper" parents="63 23587 28102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28104">
    <literal><![CDATA[
      (x * a(y,y,z)) * L((R(y,y,z) \ y) * 1,u,w) = (x * (1 / a(y,y,z))) * L(a(y,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(28102(a,2),22339(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="28102 22339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28105">
    <literal><![CDATA[
      ((x * (y \ x)) / (y * ((y \ x) * (y \ x)))) \ z = ((y \ x) * (x \ y)) * z
    ]]></literal>
    <justification jstring="[para(13382(a,2),28078(a,1,1))].">
      <j1 rule="para" parents="13382 28078"/>
    </justification>
  </clause>

  <clause id="28106">
    <literal><![CDATA[
      a(x,x * y,x * y) * z = ((x \ y) * (y \ x)) \ z
    ]]></literal>
    <justification jstring="[hyper(355,a,28079,a)].">
      <j1 rule="hyper" parents="355 28079"/>
    </justification>
  </clause>

  <clause id="28107">
    <literal><![CDATA[
      a(x,y,y \ (K(z,u) * (y * a(w,v5,v5)))) \ 1 = a(w,v5,v5) \ (K(u,z) * L(K(u,z) \ a(w,v5,v5),y,x))
    ]]></literal>
    <justification jstring="[para(28066(a,1),26924(a,1,1,3,2))].">
      <j1 rule="para" parents="28066 26924"/>
    </justification>
  </clause>

  <clause id="28108">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u) = a(z,y,a(u,x,x)) \ 1
    ]]></literal>
    <justification jstring="[para(14922(a,1),28073(a,2,1))].">
      <j1 rule="para" parents="14922 28073"/>
    </justification>
  </clause>

  <clause id="28110">
    <literal><![CDATA[
      a(x,y * L(y,z,u),y) = a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(26578,a,28108,a)].">
      <j1 rule="hyper" parents="26578 28108"/>
    </justification>
  </clause>

  <clause id="28111">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u) = a(z,y,a(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,26334,a(flip),b,28108,a),flip(a)].">
      <j1 rule="hyper" parents="347 26334 28108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28112">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,a(u,x,x)) = w
    ]]></literal>
    <justification jstring="[para(28108(a,2),26335(a,1))].">
      <j1 rule="para" parents="28108 26335"/>
    </justification>
  </clause>

  <clause id="28113">
    <literal><![CDATA[
      (x * (y * (x \ L(x,z,u)))) * a(u,z,a(L(y,x,x \ L(x,z,u)),x,x)) = (x \ L(x,z,u)) * (x * R(y,x \ L(x,z,u),x))
    ]]></literal>
    <justification jstring="[para(28110(a,1),25819(a,1,2))].">
      <j1 rule="para" parents="28110 25819"/>
    </justification>
  </clause>

  <clause id="28114">
    <literal><![CDATA[
      x \ (((y \ R(y,z,u)) * T(x,y \ R(y,z,u))) * y) = R(y,z,u) * a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(28110(a,1),25927(a,2,2))].">
      <j1 rule="para" parents="28110 25927"/>
    </justification>
  </clause>

  <clause id="28115">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,y) * (L(y,z,u) \ y) = x * (y * (L(y,z,u) \ a(u,z,a(x,y,y))))
    ]]></literal>
    <justification jstring="[para(28110(a,1),26971(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="28110 26971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28116">
    <literal><![CDATA[
      x \ L(x,x * L(x,y,z),u) = a(z,y,a(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,26978,a,b,28111,a)].">
      <j1 rule="hyper" parents="63 26978 28111"/>
    </justification>
  </clause>

  <clause id="28117">
    <literal><![CDATA[
      a(x \ L(x,y,z),x,u) = a(z,y,a(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,24385,a,b,28111,a)].">
      <j1 rule="hyper" parents="63 24385 28111"/>
    </justification>
  </clause>

  <clause id="28118">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) * a(z,y,a(u,x,x)) = x \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(134,a,28111,a(flip),b,24386,a)].">
      <j1 rule="hyper" parents="134 28111 24386"/>
    </justification>
  </clause>

  <clause id="28119">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u) \ 1 = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(28111(a,2),28108(a,2,1)),flip(a)].">
      <j1 rule="para" parents="28111 28108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28120">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * (x \ a(z,y,a(u,x,x))) = L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[para(28117(a,1),27990(a,1,2,2))].">
      <j1 rule="para" parents="28117 27990"/>
    </justification>
  </clause>

  <clause id="28121">
    <literal><![CDATA[
      (a(x,y,a(z,u,u)) * (u \ L(u,y,x))) \ ((u \ L(u,y,x)) * z) = L(z,u \ L(u,y,x),L(u,u * L(u,y,x),u))
    ]]></literal>
    <justification jstring="[para(28116(a,1),27168(a,1,1,1))].">
      <j1 rule="para" parents="28116 27168"/>
    </justification>
  </clause>

  <clause id="28122">
    <literal><![CDATA[
      a(x,y,L(y,z,z)) \ z = (y / z) \ L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,26448,a,b,28091,a)].">
      <j1 rule="hyper" parents="63 26448 28091"/>
    </justification>
  </clause>

  <clause id="28123">
    <literal><![CDATA[
      x * L(R(y,y,z) \ y,u,w) = a(y,y,L(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(18995(a,2),28094(a,1,2,1))].">
      <j1 rule="para" parents="18995 28094"/>
    </justification>
  </clause>

  <clause id="28124">
    <literal><![CDATA[
      1 / ((x \ (y \ x)) * y) = ((x \ (y \ x)) * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(14327,a,28098,a)].">
      <j1 rule="hyper" parents="14327 28098"/>
    </justification>
  </clause>

  <clause id="28125">
    <literal><![CDATA[
      L(((x \ (y \ x)) * y) \ 1,a(y,y,x),y) = y \ R(1 / (x \ (y \ x)),x \ (y \ x),y)
    ]]></literal>
    <justification jstring="[para(28124(a,1),21814(a,1,1))].">
      <j1 rule="para" parents="28124 21814"/>
    </justification>
  </clause>

  <clause id="28126">
    <literal><![CDATA[
      L(x \ y,x,a(y,z,z)) = (a(z,z,y) \ x) \ L(y,z,z)
    ]]></literal>
    <justification jstring="[hyper(27578,a,28101,a)].">
      <j1 rule="hyper" parents="27578 28101"/>
    </justification>
  </clause>

  <clause id="28127">
    <literal><![CDATA[
      (a(x,x,y) \ z) \ L(y,x,x) != u
    ]]></literal>
    <literal><![CDATA[
      L(z \ y,z,a(y,x,x)) = u
    ]]></literal>
    <justification jstring="[para(28101(a,1),27578(a,1))].">
      <j1 rule="para" parents="28101 27578"/>
    </justification>
  </clause>

  <clause id="28128">
    <literal><![CDATA[
      x * (a(x,x * L(x,y,z),u) \ 1) = L(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(134,a,28119,a,b,26978,a)].">
      <j1 rule="hyper" parents="134 28119 26978"/>
    </justification>
  </clause>

  <clause id="28129">
    <literal><![CDATA[
      x \ L(x,y,y \ L(y,z,u)) = a(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,27344,a(flip),b,28119,a)].">
      <j1 rule="hyper" parents="63 27344 28119"/>
    </justification>
  </clause>

  <clause id="28130">
    <literal><![CDATA[
      L(R(x,x,y) \ x,z,u) = w \ (a(x,x,L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(138,a,28123,a),flip(a)].">
      <j1 rule="hyper" parents="138 28123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28131">
    <literal><![CDATA[
      (a(x,x,y) \ z) \ L(y,x,x) != u
    ]]></literal>
    <literal><![CDATA[
      L(z \ y,z,a(x,x,y)) = u
    ]]></literal>
    <justification jstring="[para(28126(a,1),27578(a,1))].">
      <j1 rule="para" parents="28126 27578"/>
    </justification>
  </clause>

  <clause id="28132">
    <literal><![CDATA[
      x \ L(x,y,y \ L(y,z,u)) = a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,28111,a(flip),b,28129,a),flip(a)].">
      <j1 rule="hyper" parents="347 28111 28129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28133">
    <literal><![CDATA[
      L(a(x,x * L(x,y,z),u),u,y \ (z \ ((z * y) * x))) = a(u,x,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(28129(a,1),27619(a,1,1))].">
      <j1 rule="para" parents="28129 27619"/>
    </justification>
  </clause>

  <clause id="28134">
    <literal><![CDATA[
      x * (y * (z \ L(z,x * L(x,u,w),x))) = (x * y) * a(w,u,a(z,x,x))
    ]]></literal>
    <justification jstring="[para(28132(a,1),25569(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28132 25569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28135">
    <literal><![CDATA[
      x * L(R(y,y,z) \ y,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y,y,L(z,u,w)) \ x = v5
    ]]></literal>
    <justification jstring="[para(28130(a,2),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="28130 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28136">
    <literal><![CDATA[
      R(x,((y / z) \ (y * z)) * u,w) = R(x,u * a(y,z,z),w)
    ]]></literal>
    <justification jstring="[para(27008(a,1),28068(a,1,2))].">
      <j1 rule="para" parents="27008 28068"/>
    </justification>
  </clause>

  <clause id="28137">
    <literal><![CDATA[
      R(x,(y \ (z \ y)) \ (z * u),w) = R(x,u * a(y,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,27793,a,b,28136,a)].">
      <j1 rule="hyper" parents="63 27793 28136"/>
    </justification>
  </clause>

  <clause id="28138">
    <literal><![CDATA[
      R(x,((y \ (z \ y)) * z) \ u,w) = R(x,u * a(y,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,27794,a,b,28137,a)].">
      <j1 rule="hyper" parents="63 27794 28137"/>
    </justification>
  </clause>

  <clause id="28139">
    <literal><![CDATA[
      R(x,(((y * z) \ z) * y) \ u,w) = R(x,u * a(y * z,y,y),w)
    ]]></literal>
    <justification jstring="[para(9(a,1),28138(a,1,2,1,1,2))].">
      <j1 rule="para" parents="9 28138"/>
    </justification>
  </clause>

  <clause id="28140">
    <literal><![CDATA[
      R(x,(R(1 / (y \ (z \ y)),y \ (z \ y),z) \ z) \ u,w) = R(x,u * a(y,z,z),w)
    ]]></literal>
    <justification jstring="[para(420(a,2),28138(a,1,2,1))].">
      <j1 rule="para" parents="420 28138"/>
    </justification>
  </clause>

  <clause id="28141">
    <literal><![CDATA[
      R(x,((((y \ z) * (y * y)) \ (u \ ((y \ z) * (y * y)))) * u) \ w,v5) = R(x,w * a((y \ 1) \ z,u,u),v5)
    ]]></literal>
    <justification jstring="[para(23923(a,1),28138(a,2,2,2))].">
      <j1 rule="para" parents="23923 28138"/>
    </justification>
  </clause>

  <clause id="28142">
    <literal><![CDATA[
      a(x,y,y) * (a(x,y,y) * z) = y * (L(L(y,y,x),y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(20479,a,28080,a)].">
      <j1 rule="hyper" parents="20479 28080"/>
    </justification>
  </clause>

  <clause id="28143">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u) \ x = L(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(25416,a,28128,a)].">
      <j1 rule="hyper" parents="25416 28128"/>
    </justification>
  </clause>

  <clause id="28144">
    <literal><![CDATA[
      R(x,y,(z * (u \ (u / z))) \ w) = R(x,y,w * a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(20901,a,28081,a)].">
      <j1 rule="hyper" parents="20901 28081"/>
    </justification>
  </clause>

  <clause id="28145">
    <literal><![CDATA[
      (x \ (y * R(y \ x,y,y))) \ z = (y * (x \ (x / y))) * z
    ]]></literal>
    <justification jstring="[para(25449(a,1),28092(a,2,1))].">
      <j1 rule="para" parents="25449 28092"/>
    </justification>
  </clause>

  <clause id="28146">
    <literal><![CDATA[
      (x \ ((x * (y \ 1)) * y)) \ z = (y * (x \ (x / y))) * z
    ]]></literal>
    <justification jstring="[para(922(a,1),28145(a,1,1,2))].">
      <j1 rule="para" parents="922 28145"/>
    </justification>
  </clause>

  <clause id="28147">
    <literal><![CDATA[
      (x \ ((x * (y \ 1)) * y)) * z = (y * (x \ (x / y))) \ z
    ]]></literal>
    <justification jstring="[hyper(355,a,28146,a)].">
      <j1 rule="hyper" parents="355 28146"/>
    </justification>
  </clause>

  <clause id="28148">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) * a(z,y,a(x,x,u)) = x \ (L(x,y,z) * (u * x))
    ]]></literal>
    <justification jstring="[para(26520(a,1),28118(a,1,2))].">
      <j1 rule="para" parents="26520 28118"/>
    </justification>
  </clause>

  <clause id="28149">
    <literal><![CDATA[
      ((x * ((y \ x) \ 1)) / y) \ z = ((y \ x) * (x \ y)) * z
    ]]></literal>
    <justification jstring="[para(814(a,1),28105(a,1,1))].">
      <j1 rule="para" parents="814 28105"/>
    </justification>
  </clause>

  <clause id="28150">
    <literal><![CDATA[
      (x \ (y * ((x \ y) \ 1))) \ z = ((x \ y) * (y \ x)) * z
    ]]></literal>
    <justification jstring="[para(12693(a,1),28149(a,1,1))].">
      <j1 rule="para" parents="12693 28149"/>
    </justification>
  </clause>

  <clause id="28151">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ 1 = x \ (y * ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(3977,a,28150,a)].">
      <j1 rule="hyper" parents="3977 28150"/>
    </justification>
  </clause>

  <clause id="28152">
    <literal><![CDATA[
      (x \ y) \ ((y \ x) \ 1) = y \ (x * ((y \ x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,10909,a(flip),b,28151,a)].">
      <j1 rule="hyper" parents="63 10909 28151"/>
    </justification>
  </clause>

  <clause id="28153">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((y \ x) \ 1) = x \ (y * ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,10907,a,b,28152,a)].">
      <j1 rule="hyper" parents="63 10907 28152"/>
    </justification>
  </clause>

  <clause id="28154">
    <literal><![CDATA[
      ((x \ y) \ 1) \ (x \ (y * ((x \ y) \ 1))) = (y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,28152,a(flip),b,10907,a)].">
      <j1 rule="hyper" parents="128 28152 10907"/>
    </justification>
  </clause>

  <clause id="28155">
    <literal><![CDATA[
      (x * T(x \ y,(x \ y) \ 1)) * ((x \ y) \ 1) = x * (((y \ x) \ 1) * ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[para(28154(a,1),1621(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="28154 1621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28156">
    <literal><![CDATA[
      x * (y * (z \ L(z,x,x \ L(x,u,w)))) = (x * y) * a(w,u,a(z,x,x))
    ]]></literal>
    <justification jstring="[para(3653(a,1),28134(a,1,2,2,2))].">
      <j1 rule="para" parents="3653 28134"/>
    </justification>
  </clause>

  <clause id="28157">
    <literal><![CDATA[
      (x * y) * a(z,u,a(w,x,x)) = x * (y * a(z,u,a(w,x,x)))
    ]]></literal>
    <justification jstring="[para(28132(a,1),28156(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28132 28156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28158">
    <literal><![CDATA[
      x * (L(x,y,z) \ a(z,y,a(u,x,x))) = L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[hyper(27055,a,28120,a)].">
      <j1 rule="hyper" parents="27055 28120"/>
    </justification>
  </clause>

  <clause id="28159">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) * a(z,y,a(x,x,u)) = x \ (x * (u * L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(20686(a,1),28148(a,2,2))].">
      <j1 rule="para" parents="20686 28148"/>
    </justification>
  </clause>

  <clause id="28160">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) * a(z,y,a(x,x,u)) = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,9,a(flip),b,28159,a),flip(a)].">
      <j1 rule="hyper" parents="347 9 28159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28162">
    <literal><![CDATA[
      x * ((y * ((y \ z) * (y \ z))) \ (z * (y \ z))) = ((z * ((y \ z) \ 1)) \ y) \ x
    ]]></literal>
    <justification jstring="[para(794(a,1),28084(a,2,1,1))].">
      <j1 rule="para" parents="794 28084"/>
    </justification>
  </clause>

  <clause id="28163">
    <literal><![CDATA[
      L(a(x,x * L(x,y,z),u),u,L(1 / x,y,z) \ 1) = a(u,x,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(25971(a,1),28133(a,1,3))].">
      <j1 rule="para" parents="25971 28133"/>
    </justification>
  </clause>

  <clause id="28164">
    <literal><![CDATA[
      L(a(x,x * L(x,y,z),u),u,L(x \ 1,y,z) \ 1) = a(u,x,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(21527,a,28163,a)].">
      <j1 rule="hyper" parents="21527 28163"/>
    </justification>
  </clause>

  <clause id="28165">
    <literal><![CDATA[
      L(a(x,x * L(x,y,z),u),u,L(x,y,z)) = a(u,x,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(27573,a,28164,a)].">
      <j1 rule="hyper" parents="27573 28164"/>
    </justification>
  </clause>

  <clause id="28166">
    <literal><![CDATA[
      L(a(x,x * L(x,y,z),u),u,L(x,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,x,x * L(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(28165(a,2),15022(a,1))].">
      <j1 rule="para" parents="28165 15022"/>
    </justification>
  </clause>

  <clause id="28167">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u) = a(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(28166,a,25487,a),flip(a)].">
      <j1 rule="hyper" parents="28166 25487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28168">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) = a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(28112,a,28167,a),flip(a)].">
      <j1 rule="hyper" parents="28112 28167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28169">
    <literal><![CDATA[
      a(x,y,y * L(y,z,u)) \ y = L(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(28167(a,1),28143(a,1,1))].">
      <j1 rule="para" parents="28167 28143"/>
    </justification>
  </clause>

  <clause id="28170">
    <literal><![CDATA[
      a(x,y,a(z \ u,z,z)) \ (z \ L(z,y,x)) = L(z \ L(z,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(28168(a,1),27318(a,1,1))].">
      <j1 rule="para" parents="28168 27318"/>
    </justification>
  </clause>

  <clause id="28171">
    <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(63,a,26765,a,b,28169,a)].">
      <j1 rule="hyper" parents="63 26765 28169"/>
    </justification>
  </clause>

  <clause id="28172">
    <literal><![CDATA[
      x * (y * ((z \ L(z,u,w)) \ (x \ ((x / z) * L(z,u,w))))) = (x * y) * (z \ L(z,z * L(z,u,w),x))
    ]]></literal>
    <justification jstring="[para(28171(a,1),25742(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28171 25742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28173">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) \ (z \ L(z,y,x)) = L(z \ L(z,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(27242(a,1),28170(a,1,1))].">
      <j1 rule="para" parents="27242 28170"/>
    </justification>
  </clause>

  <clause id="28174">
    <literal><![CDATA[
      a(x,((y / ((z \ 1) \ 1)) * L(z,z \ 1,u)) * w,v5) = a(x,w * (y * a(u,z,z)),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,28067,a(flip),b,28093,a),flip(a)].">
      <j1 rule="hyper" parents="347 28067 28093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28175">
    <literal><![CDATA[
      R(x,(R(1 / (y \ (z \ y)),z,z) \ z) \ u,w) = R(x,u * a(y,z,z),w)
    ]]></literal>
    <justification jstring="[para(27770(a,1),28140(a,1,2,1,1))].">
      <j1 rule="para" parents="27770 28140"/>
    </justification>
  </clause>

  <clause id="28176">
    <literal><![CDATA[
      R(x,((1 * ((y \ (z \ y)) \ 1)) \ z) \ u,w) = R(x,u * a(y,z,z),w)
    ]]></literal>
    <justification jstring="[para(26479(a,1),28175(a,1,2,1,1))].">
      <j1 rule="para" parents="26479 28175"/>
    </justification>
  </clause>

  <clause id="28178">
    <literal><![CDATA[
      R(x,(((y \ (z \ y)) \ 1) \ z) \ u,w) = R(x,u * a(y,z,z),w)
    ]]></literal>
    <justification jstring="[para(7(a,1),28176(a,1,2,1,1))].">
      <j1 rule="para" parents="7 28176"/>
    </justification>
  </clause>

  <clause id="28179">
    <literal><![CDATA[
      R(x,((y \ (z \ y)) \ z) \ u,w) = R(x,u * a(y,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21192,a(flip),b,28178,a)].">
      <j1 rule="hyper" parents="63 21192 28178"/>
    </justification>
  </clause>

  <clause id="28180">
    <literal><![CDATA[
      R(x,(y \ (z * (y * z))) \ u,w) = R(x,u * a(y,z,z),w)
    ]]></literal>
    <justification jstring="[para(27115(a,1),28179(a,1,2,1))].">
      <j1 rule="para" parents="27115 28179"/>
    </justification>
  </clause>

  <clause id="28181">
    <literal><![CDATA[
      (x * T(x \ y,(x \ y) \ 1)) * ((x \ y) \ 1) = x * (y \ (x * ((y \ x) \ 1)))
    ]]></literal>
    <justification jstring="[para(28153(a,1),28155(a,2,2))].">
      <j1 rule="para" parents="28153 28155"/>
    </justification>
  </clause>

  <clause id="28182">
    <literal><![CDATA[
      a(x,((y / ((z \ 1) \ 1)) * L(z,z,u)) * w,v5) = a(x,w * (y * a(u,z,z)),v5)
    ]]></literal>
    <justification jstring="[para(3188(a,1),28174(a,1,2,1,2))].">
      <j1 rule="para" parents="3188 28174"/>
    </justification>
  </clause>

  <clause id="28183">
    <literal><![CDATA[
      a(x,(a(y * z,z,z) \ u) * w,v5) = a(x,w * (u * a(y,z,z)),v5)
    ]]></literal>
    <justification jstring="[para(27849(a,1),28182(a,1,2,1))].">
      <j1 rule="para" parents="27849 28182"/>
    </justification>
  </clause>

  <clause id="28184">
    <literal><![CDATA[
      a(x,(a(y * z,z,z) * u) * w,v5) = a(x,w * (u * a(y,z,z)),v5)
    ]]></literal>
    <justification jstring="[hyper(28076,a,28183,a)].">
      <j1 rule="hyper" parents="28076 28183"/>
    </justification>
  </clause>

  <clause id="28185">
    <literal><![CDATA[
      L(a(L(x,y,y) \ x,z,u),R(x,y,y) \ x,z) = R(R(x,y,y) \ x,z,u) * a(x,y,y)
    ]]></literal>
    <justification jstring="[para(25232(a,1),28083(a,1,1))].">
      <j1 rule="para" parents="25232 28083"/>
    </justification>
  </clause>

  <clause id="28186">
    <literal><![CDATA[
      x \ (((y \ R(y,z,u)) * x) * y) = R(y,z,u) * a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(19975(a,1),28114(a,1,2,1,2))].">
      <j1 rule="para" parents="19975 28114"/>
    </justification>
  </clause>

  <clause id="28187">
    <literal><![CDATA[
      x \ ((y \ R(y,z,u)) * (x * y)) = R(y,z,u) * a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(23707(a,1),28186(a,1,2))].">
      <j1 rule="para" parents="23707 28186"/>
    </justification>
  </clause>

  <clause id="28188">
    <literal><![CDATA[
      x \ ((x * y) * (y \ R(y,z,u))) = R(y,z,u) * a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(20202(a,1),28187(a,1,2))].">
      <j1 rule="para" parents="20202 28187"/>
    </justification>
  </clause>

  <clause id="28189">
    <literal><![CDATA[
      L(((x \ (y \ x)) * y) \ 1,y,a(y,y,x)) = y \ R(1 / (x \ (y \ x)),x \ (y \ x),y)
    ]]></literal>
    <justification jstring="[hyper(25494,a,28125,a)].">
      <j1 rule="hyper" parents="25494 28125"/>
    </justification>
  </clause>

  <clause id="28190">
    <literal><![CDATA[
      L(a(a(x,x,y),z,u),R(y,x,x) \ y,z) = R(R(y,x,x) \ y,z,u) * a(y,x,x)
    ]]></literal>
    <justification jstring="[para(14600(a,1),28185(a,1,1,1))].">
      <j1 rule="para" parents="14600 28185"/>
    </justification>
  </clause>

  <clause id="28191">
    <literal><![CDATA[
      L(a(a(x,x,y),z,u),L(y,x,x) \ y,z) = R(R(y,x,x) \ y,z,u) * a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,23764,a(flip),b,28190,a)].">
      <j1 rule="hyper" parents="63 23764 28190"/>
    </justification>
  </clause>

  <clause id="28192">
    <literal><![CDATA[
      L(a(a(x,x,y),z,u),a(x,x,y),z) = R(R(y,x,x) \ y,z,u) * a(y,x,x)
    ]]></literal>
    <justification jstring="[para(14600(a,1),28191(a,1,2))].">
      <j1 rule="para" parents="14600 28191"/>
    </justification>
  </clause>

  <clause id="28193">
    <literal><![CDATA[
      R(R(x,y,y) \ x,z,u) * a(x,y,y) = a(y,y,x) \ R(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,26935,a(flip),b,28192,a),flip(a)].">
      <j1 rule="hyper" parents="63 26935 28192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28194">
    <literal><![CDATA[
      R(R(x,y,y) \ x,z,u) * a(x,y,y) = a(y,y,x) \ L(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(23097(a,1),28193(a,2,2))].">
      <j1 rule="para" parents="23097 28193"/>
    </justification>
  </clause>

  <clause id="28195">
    <literal><![CDATA[
      R(R(x,y,y) \ x,z,u) * a(x,y,y) = a(y,y,x) \ a(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(26260(a,2),28194(a,2,2))].">
      <j1 rule="para" parents="26260 28194"/>
    </justification>
  </clause>

  <clause id="28196">
    <literal><![CDATA[
      x \ R(1 / (y \ (x \ y)),y \ (x \ y),x) = ((y \ (x \ y)) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(26320,a,28189,a),flip(a)].">
      <j1 rule="hyper" parents="26320 28189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28198">
    <literal><![CDATA[
      x \ R(1 / (y \ (x \ y)),x,x) = ((y \ (x \ y)) * x) \ 1
    ]]></literal>
    <justification jstring="[para(27770(a,1),28196(a,1,2))].">
      <j1 rule="para" parents="27770 28196"/>
    </justification>
  </clause>

  <clause id="28199">
    <literal><![CDATA[
      x \ (1 * ((y \ (x \ y)) \ 1)) = ((y \ (x \ y)) * x) \ 1
    ]]></literal>
    <justification jstring="[para(26479(a,1),28198(a,1,2))].">
      <j1 rule="para" parents="26479 28198"/>
    </justification>
  </clause>

  <clause id="28201">
    <literal><![CDATA[
      ((x \ (y \ x)) * y) \ 1 = y \ ((x \ (y \ x)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(364,a,28199,a),flip(a)].">
      <j1 rule="hyper" parents="364 28199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28202">
    <literal><![CDATA[
      (x \ ((y \ (x \ y)) \ 1)) \ z = ((y \ (x \ y)) * x) * z
    ]]></literal>
    <justification jstring="[para(28201(a,1),28098(a,1,1))].">
      <j1 rule="para" parents="28201 28098"/>
    </justification>
  </clause>

  <clause id="28203">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,y) * (L(y,z,u) \ y) = x * L(L(y,z,u) \ y,y,x)
    ]]></literal>
    <justification jstring="[para(28158(a,1),28115(a,2,2))].">
      <j1 rule="para" parents="28158 28115"/>
    </justification>
  </clause>

  <clause id="28204">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,y) * (L(y,z,u) \ y) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,27133,a(flip),b,28203,a),flip(a)].">
      <j1 rule="hyper" parents="347 27133 28203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28205">
    <literal><![CDATA[
      L(x,y * L(y,z,u),y) * (L(y,z,u) \ y) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(26249(a,1),28204(a,1,1))].">
      <j1 rule="para" parents="26249 28204"/>
    </justification>
  </clause>

  <clause id="28206">
    <literal><![CDATA[
      L(x,y,y \ L(y,z,u)) * (L(y,z,u) \ y) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(3653(a,1),28205(a,1,1))].">
      <j1 rule="para" parents="3653 28205"/>
    </justification>
  </clause>

  <clause id="28208">
    <literal><![CDATA[
      ((x \ 1) * y) \ ((x \ y) * L((x \ y) \ ((x \ 1) * y),z,u)) = a(u,z,a(x,x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(14922(a,1),28095(a,2,1))].">
      <j1 rule="para" parents="14922 28095"/>
    </justification>
  </clause>

  <clause id="28210">
    <literal><![CDATA[
      ((x \ 1) * y) \ ((x \ y) * L((x \ y) \ ((x \ 1) * y),z,u)) = a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,26334,a(flip),b,28208,a),flip(a)].">
      <j1 rule="hyper" parents="347 26334 28208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28211">
    <literal><![CDATA[
      a(x,x,y) \ a(x,x,L(y,z,u)) = a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,26268,a(flip),b,28210,a)].">
      <j1 rule="hyper" parents="63 26268 28210"/>
    </justification>
  </clause>

  <clause id="28212">
    <literal><![CDATA[
      R(R(x,y,y) \ x,z,u) * a(x,y,y) = a(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,28195,a,b,28211,a)].">
      <j1 rule="hyper" parents="63 28195 28211"/>
    </justification>
  </clause>

  <clause id="28213">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ a(x,x,y) = a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,26267,a,b,28211,a)].">
      <j1 rule="hyper" parents="63 26267 28211"/>
    </justification>
  </clause>

  <clause id="28214">
    <literal><![CDATA[
      L(a(x,x,y) \ a(x,x,L(y,z,u)),w,v5) = a(u,z,a(x,x,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,26795,a(flip),b,28211,a)].">
      <j1 rule="hyper" parents="63 26795 28211"/>
    </justification>
  </clause>

  <clause id="28215">
    <literal><![CDATA[
      a(x,x,y) \ a(z,u,a(x,x,y)) = L(R(x,x,y) \ x,u,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,28213,a(flip),b,28123,a)].">
      <j1 rule="hyper" parents="128 28213 28123"/>
    </justification>
  </clause>

  <clause id="28216">
    <literal><![CDATA[
      L(R(x,y,y) \ x,z,u) * a(x,y,y) = a(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(27505(a,1),28212(a,1,1))].">
      <j1 rule="para" parents="27505 28212"/>
    </justification>
  </clause>

  <clause id="28217">
    <literal><![CDATA[
      (x * L(R(y,y,z) \ y,u,w)) \ ((x * (a(y,y,z) \ 1)) * a(w,u,a(y,y,z))) = a(x,a(y,y,z),a(w,u,a(y,y,z)))
    ]]></literal>
    <justification jstring="[para(28215(a,1),14963(a,1,1,2))].">
      <j1 rule="para" parents="28215 14963"/>
    </justification>
  </clause>

  <clause id="28218">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u,w,v5))) = L(a(x,y,a(z,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(28211(a,1),28214(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28211 28214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28219">
    <literal><![CDATA[
      L(R(x,y,y) \ x,z,u) \ (R(x,y,y) \ x) = (L((R(x,y,y) \ x) \ 1,z,u) \ 1) * a(x,y,y)
    ]]></literal>
    <justification jstring="[para(23006(a,1),28082(a,2,1,1,1))].">
      <j1 rule="para" parents="23006 28082"/>
    </justification>
  </clause>

  <clause id="28220">
    <literal><![CDATA[
      (x * a(y,y,z)) * L((R(y,y,z) \ y) * 1,u,w) = (x * (a(y,y,z) \ 1)) * L(a(y,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(12593(a,1),28104(a,2,1,2))].">
      <j1 rule="para" parents="12593 28104"/>
    </justification>
  </clause>

  <clause id="28221">
    <literal><![CDATA[
      L(R(x,y,y) \ x,z,u) \ (R(x,y,y) \ x) = (L(a(x,y,y),z,u) \ 1) * a(x,y,y)
    ]]></literal>
    <justification jstring="[para(13401(a,1),28219(a,2,1,1,1))].">
      <j1 rule="para" parents="13401 28219"/>
    </justification>
  </clause>

  <clause id="28222">
    <literal><![CDATA[
      L(R(x,y,y) \ x,z,u) \ (R(x,y,y) \ x) = L(a(x,y,y) \ 1,z,u) * a(x,y,y)
    ]]></literal>
    <justification jstring="[para(26290(a,2),28221(a,2,1))].">
      <j1 rule="para" parents="26290 28221"/>
    </justification>
  </clause>

  <clause id="28223">
    <literal><![CDATA[
      L(R(x,y,y) \ x,z,u) \ (R(x,y,y) \ x) = (a(x,y,y) \ 1) * L(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,3557,a(flip),b,28222,a),flip(a)].">
      <j1 rule="hyper" parents="347 3557 28222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28224">
    <literal><![CDATA[
      L(R(x,y,y) \ x,z,u) \ (R(x,y,y) \ x) = (a(x,y,y) \ 1) * a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(26436(a,2),28223(a,2,2))].">
      <j1 rule="para" parents="26436 28223"/>
    </justification>
  </clause>

  <clause id="28225">
    <literal><![CDATA[
      L(R(x,y,y) \ x,z,u) \ (R(x,y,y) \ x) = a(x,y,y) \ a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,28062,a(flip),b,28224,a),flip(a)].">
      <j1 rule="hyper" parents="347 28062 28224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28226">
    <literal><![CDATA[
      (x * a(y,y,z)) * L((R(y,y,z) \ y) * 1,u,w) = (a(y,y,z) \ x) * L(a(y,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(28088(a,1),28220(a,2,1))].">
      <j1 rule="para" parents="28088 28220"/>
    </justification>
  </clause>

  <clause id="28227">
    <literal><![CDATA[
      (x * a(y,y,z)) * L((R(y,y,z) \ y) * 1,u,w) = (a(y,y,z) \ x) * a(y,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(26260(a,2),28226(a,2,2))].">
      <j1 rule="para" parents="26260 28226"/>
    </justification>
  </clause>

  <clause id="28228">
    <literal><![CDATA[
      x * (y * ((z \ L(z,u,w)) \ (x \ ((x / z) * L(z,u,w))))) = (x * y) * a(w,u,a(x,z,z))
    ]]></literal>
    <justification jstring="[para(28116(a,1),28172(a,2,2))].">
      <j1 rule="para" parents="28116 28172"/>
    </justification>
  </clause>

  <clause id="28229">
    <literal><![CDATA[
      a(x,y,K(z,T(u,y)) * a(w,v5,v5)) \ 1 = a(w,v5,v5) \ (K(u,z) * L(K(u,z) \ a(w,v5,v5),y,x))
    ]]></literal>
    <justification jstring="[para(19539(a,1),28107(a,1,1,3))].">
      <j1 rule="para" parents="19539 28107"/>
    </justification>
  </clause>

  <clause id="28230">
    <literal><![CDATA[
      a(x,y,y) \ (K(z,u) * L(K(z,u) \ a(x,y,y),w,v5)) = a(v5,w,a(x,y,y)) \ 1
    ]]></literal>
    <justification jstring="[para(24036(a,1),28229(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24036 28229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28231">
    <literal><![CDATA[
      a(x,y,y) \ (K(z,u) * L(K(z,u) \ a(x,y,y),w,v5)) = a(v5,w,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,26334,a(flip),b,28230,a),flip(a)].">
      <j1 rule="hyper" parents="347 26334 28230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28233">
    <literal><![CDATA[
      a(x,y,y) \ (K(z,u) * L(K(u,z) * a(x,y,y),w,v5)) = a(v5,w,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(5256(a,1),28231(a,1,2,2,1))].">
      <j1 rule="para" parents="5256 28231"/>
    </justification>
  </clause>

  <clause id="28234">
    <literal><![CDATA[
      a(x,y,y) \ L(K(z,u) * (K(u,z) * a(x,y,y)),w,v5) = a(v5,w,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(21250(a,2),28233(a,1,2))].">
      <j1 rule="para" parents="21250 28233"/>
    </justification>
  </clause>

  <clause id="28235">
    <literal><![CDATA[
      a(x,y,y) \ L(a(x,y,y),z,u) = a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(2784(a,1),28234(a,1,2,1))].">
      <j1 rule="para" parents="2784 28234"/>
    </justification>
  </clause>

  <clause id="28236">
    <literal><![CDATA[
      a(x,y,y) \ a(x,y,L(y,z,u)) = a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(26436(a,2),28235(a,1,2))].">
      <j1 rule="para" parents="26436 28235"/>
    </justification>
  </clause>

  <clause id="28237">
    <literal><![CDATA[
      L(R(x,y,y) \ x,z,u) \ (R(x,y,y) \ x) = a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,28225,a,b,28236,a)].">
      <j1 rule="hyper" parents="63 28225 28236"/>
    </justification>
  </clause>

  <clause id="28238">
    <literal><![CDATA[
      R(x,((((y \ z) * (y * y)) \ ((u \ (y \ z)) * (y * y))) * u) \ w,v5) = R(x,w * a((y \ 1) \ z,u,u),v5)
    ]]></literal>
    <justification jstring="[para(456(a,1),28141(a,1,2,1,1,2))].">
      <j1 rule="para" parents="456 28141"/>
    </justification>
  </clause>

  <clause id="28239">
    <literal><![CDATA[
      R(x,(((((y \ z) * (y * y)) \ (u \ (y \ z))) * (y * y)) * u) \ w,v5) = R(x,w * a((y \ 1) \ z,u,u),v5)
    ]]></literal>
    <justification jstring="[para(456(a,1),28238(a,1,2,1,1))].">
      <j1 rule="para" parents="456 28238"/>
    </justification>
  </clause>

  <clause id="28240">
    <literal><![CDATA[
      R(x,((((y * y) \ ((y \ z) \ (u \ (y \ z)))) * (y * y)) * u) \ w,v5) = R(x,w * a((y \ 1) \ z,u,u),v5)
    ]]></literal>
    <justification jstring="[para(459(a,1),28239(a,1,2,1,1,1))].">
      <j1 rule="para" parents="459 28239"/>
    </justification>
  </clause>

  <clause id="28241">
    <literal><![CDATA[
      R(x,(T((y \ z) \ (u \ (y \ z)),y * y) * u) \ w,v5) = R(x,w * a((y \ 1) \ z,u,u),v5)
    ]]></literal>
    <justification jstring="[para(726(a,1),28240(a,1,2,1,1))].">
      <j1 rule="para" parents="726 28240"/>
    </justification>
  </clause>

  <clause id="28242">
    <literal><![CDATA[
      R(x,(((y \ z) \ (u \ (y \ z))) * u) \ w,v5) = R(x,w * a((y \ 1) \ z,u,u),v5)
    ]]></literal>
    <justification jstring="[hyper(22447,a,28241,a)].">
      <j1 rule="hyper" parents="22447 28241"/>
    </justification>
  </clause>

  <clause id="28244">
    <literal><![CDATA[
      R(x,y * a((z \ 1) \ u,w,w),v5) = R(x,y * a(z \ u,w,w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,28138,a(flip),b,28242,a),flip(a)].">
      <j1 rule="hyper" parents="63 28138 28242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28245">
    <literal><![CDATA[
      a(x * (a(y,z,u) * T(a(u,z,y) \ (a(u,z,y) / w),v5)),v6,v7) = a(T(a(u,z,y) / w,v5) * x,v6,v7)
    ]]></literal>
    <justification jstring="[para(23177(a,1),28051(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="23177 28051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28246">
    <literal><![CDATA[
      a(x * (a(y,z,u) * T(a(u,z,y) \ (a(u,z,y) / w),v5)),v6,v7) = a((a(u,z,y) / w) * x,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,23898,a(flip),b,28245,a),flip(a)].">
      <j1 rule="hyper" parents="347 23898 28245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28248">
    <literal><![CDATA[
      a(x * (a(y,z,u) * T(a(u,z,y) \ (a(u,z,y) / w),v5)),v6,v7) = a((w \ a(u,z,y)) * x,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,23899,a(flip),b,28246,a),flip(a)].">
      <j1 rule="hyper" parents="347 23899 28246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28249">
    <literal><![CDATA[
      a(x * T(a(y,z,u) * (a(u,z,y) \ (a(u,z,y) / w)),v5),v6,v7) = a((w \ a(u,z,y)) * x,v6,v7)
    ]]></literal>
    <justification jstring="[para(23113(a,2),28248(a,1,1,2))].">
      <j1 rule="para" parents="23113 28248"/>
    </justification>
  </clause>

  <clause id="28250">
    <literal><![CDATA[
      a(x * T(a(y,z,u) / w,v5),v6,v7) = a((w \ a(u,z,y)) * x,v6,v7)
    ]]></literal>
    <justification jstring="[para(27601(a,1),28249(a,1,1,2,1))].">
      <j1 rule="para" parents="27601 28249"/>
    </justification>
  </clause>

  <clause id="28251">
    <literal><![CDATA[
      a((x \ a(y,z,u)) * w,v5,v6) = a(w * (x \ a(u,z,y)),v5,v6)
    ]]></literal>
    <justification jstring="[para(113(a,1),28250(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="113 28250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28252">
    <literal><![CDATA[
      a(x * ((y / (z * y)) \ a(y,z,z \ 1)),u,w) = a(z * x,u,w)
    ]]></literal>
    <justification jstring="[para(26894(a,1),28251(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="26894 28251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28253">
    <literal><![CDATA[
      a(x * ((y / (z * y)) \ a(y,z,z)),u,w) = a(z * x,u,w)
    ]]></literal>
    <justification jstring="[para(14922(a,1),28252(a,1,1,2,2))].">
      <j1 rule="para" parents="14922 28252"/>
    </justification>
  </clause>

  <clause id="28254">
    <literal><![CDATA[
      a(x * (((y * z) \ z) \ a(z,y,y)),u,w) = a(y * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24221,a(flip),b,28253,a)].">
      <j1 rule="hyper" parents="63 24221 28253"/>
    </justification>
  </clause>

  <clause id="28255">
    <literal><![CDATA[
      a(x * ((y \ (y / z)) \ a(y,z,z)),u,w) = a(z * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,27337,a(flip),b,28254,a)].">
      <j1 rule="hyper" parents="63 27337 28254"/>
    </justification>
  </clause>

  <clause id="28256">
    <literal><![CDATA[
      a(x * ((y \ (z \ y)) \ a(y,z,z)),u,w) = a(z * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24657,a(flip),b,28255,a)].">
      <j1 rule="hyper" parents="63 24657 28255"/>
    </justification>
  </clause>

  <clause id="28257">
    <literal><![CDATA[
      a(x,x,y) \ (z * R(z \ ((R(x,x,y) \ x) \ z),u,w)) = z * ((R(x,x,y) \ x) * R(1 * a(x,x,y),u,w))
    ]]></literal>
    <justification jstring="[para(28100(a,1),28103(a,2,2,2,1))].">
      <j1 rule="para" parents="28100 28103"/>
    </justification>
  </clause>

  <clause id="28258">
    <literal><![CDATA[
      a(x,x,y) \ (z * R(z \ ((R(x,x,y) \ x) \ z),u,w)) = z * ((R(x,x,y) \ x) * R(a(x,x,y),u,w))
    ]]></literal>
    <justification jstring="[para(7(a,1),28257(a,2,2,2,1))].">
      <j1 rule="para" parents="7 28257"/>
    </justification>
  </clause>

  <clause id="28259">
    <literal><![CDATA[
      a(x,x,y) \ (z * R(z \ ((R(x,x,y) \ x) \ z),u,w)) = z * ((R(x,x,y) \ x) * L(a(x,x,y),u,w))
    ]]></literal>
    <justification jstring="[para(23097(a,1),28258(a,2,2,2))].">
      <j1 rule="para" parents="23097 28258"/>
    </justification>
  </clause>

  <clause id="28260">
    <literal><![CDATA[
      a(x,x,y) \ (z * R(z \ ((R(x,x,y) \ x) \ z),u,w)) = z * ((R(x,x,y) \ x) * a(x,x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(26260(a,2),28259(a,2,2,2))].">
      <j1 rule="para" parents="26260 28259"/>
    </justification>
  </clause>

  <clause id="28261">
    <literal><![CDATA[
      a(x,x,y) \ (z * R(z \ ((R(x,x,y) \ x) \ z),u,w)) = z * (a(x,x,y) \ a(x,x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(28102(a,1),28260(a,2,2))].">
      <j1 rule="para" parents="28102 28260"/>
    </justification>
  </clause>

  <clause id="28262">
    <literal><![CDATA[
      a(x,x,y) \ (z * R(z \ ((R(x,x,y) \ x) \ z),u,w)) = z * a(w,u,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(28211(a,1),28261(a,2,2))].">
      <j1 rule="para" parents="28211 28261"/>
    </justification>
  </clause>

  <clause id="28263">
    <literal><![CDATA[
      a(x,x,y) \ (z * R(z \ (z * a(x,x,y)),u,w)) = z * a(w,u,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(28100(a,1),28262(a,1,2,2,1,2))].">
      <j1 rule="para" parents="28100 28262"/>
    </justification>
  </clause>

  <clause id="28264">
    <literal><![CDATA[
      a(x,x,y) \ (z * R(a(x,x,y),u,w)) = z * a(w,u,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),28263(a,1,2,2,1))].">
      <j1 rule="para" parents="9 28263"/>
    </justification>
  </clause>

  <clause id="28266">
    <literal><![CDATA[
      a(x,x,y) \ (z * L(a(x,x,y),u,w)) = z * a(w,u,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(23097(a,1),28264(a,1,2,2))].">
      <j1 rule="para" parents="23097 28264"/>
    </justification>
  </clause>

  <clause id="28267">
    <literal><![CDATA[
      a(x,x,y) \ (z * a(x,x,L(y,u,w))) = z * a(w,u,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(26260(a,2),28266(a,1,2,2))].">
      <j1 rule="para" parents="26260 28266"/>
    </justification>
  </clause>

  <clause id="28268">
    <literal><![CDATA[
      (a(x,x,y) \ z) * a(x,x,L(y,u,w)) = z * a(w,u,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(12367,a,28267,a),flip(a)].">
      <j1 rule="hyper" parents="12367 28267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28269">
    <literal><![CDATA[
      (x * a(y,y,z)) * L((R(y,y,z) \ y) * 1,u,w) = x * a(w,u,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,28227,a,b,28268,a)].">
      <j1 rule="hyper" parents="63 28227 28268"/>
    </justification>
  </clause>

  <clause id="28270">
    <literal><![CDATA[
      (x * a(y,y,z)) * L(R(y,y,z) \ y,u,w) = x * a(w,u,a(y,y,z))
    ]]></literal>
    <justification jstring="[para(8(a,1),28269(a,1,2,1))].">
      <j1 rule="para" parents="8 28269"/>
    </justification>
  </clause>

  <clause id="28271">
    <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(28135,a,28270,a)].">
      <j1 rule="hyper" parents="28135 28270"/>
    </justification>
  </clause>

  <clause id="28272">
    <literal><![CDATA[
      (a(x,x,y) \ z) * a(u,w,a(x,x,y)) = a(x,x,L(y,w,u)) \ z
    ]]></literal>
    <justification jstring="[para(19986(a,1),28271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19986 28271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28273">
    <literal><![CDATA[
      (a(x,x,L(y,z,u)) \ w) \ ((w * (a(x,x,y) \ 1)) * a(u,z,a(x,x,y))) = a(w,a(x,x,y),a(u,z,a(x,x,y)))
    ]]></literal>
    <justification jstring="[para(28123(a,1),28217(a,1,1))].">
      <j1 rule="para" parents="28123 28217"/>
    </justification>
  </clause>

  <clause id="28274">
    <literal><![CDATA[
      (a(x,x,L(y,z,u)) \ w) \ ((a(x,x,y) \ w) * a(u,z,a(x,x,y))) = a(w,a(x,x,y),a(u,z,a(x,x,y)))
    ]]></literal>
    <justification jstring="[para(28088(a,1),28273(a,1,2,1))].">
      <j1 rule="para" parents="28088 28273"/>
    </justification>
  </clause>

  <clause id="28275">
    <literal><![CDATA[
      (a(x,x,L(y,z,u)) \ w) \ (a(x,x,L(y,z,u)) \ w) = a(w,a(x,x,y),a(u,z,a(x,x,y)))
    ]]></literal>
    <justification jstring="[para(28272(a,1),28274(a,1,2))].">
      <j1 rule="para" parents="28272 28274"/>
    </justification>
  </clause>

  <clause id="28276">
    <literal><![CDATA[
      a(x,a(y,y,z),a(u,w,a(y,y,z))) = 1
    ]]></literal>
    <justification jstring="[hyper(236,a,28275,a),flip(a)].">
      <j1 rule="hyper" parents="236 28275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28277">
    <literal><![CDATA[
      L(a(x,x,y),a(z,u,a(x,x,y)),w) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(26627,a,28276,a)].">
      <j1 rule="hyper" parents="26627 28276"/>
    </justification>
  </clause>

  <clause id="28279">
    <literal><![CDATA[
      a(x,x,L(y,a(z,u,a(x,x,y)),w)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(26263,a,28277,a)].">
      <j1 rule="hyper" parents="26263 28277"/>
    </justification>
  </clause>

  <clause id="28280">
    <literal><![CDATA[
      (x * (y * (x \ L(x,z,u)))) * a(u,z,a(L(y,x,L(x,z,u) * x),x,x)) = (x \ L(x,z,u)) * (x * R(y,x \ L(x,z,u),x))
    ]]></literal>
    <justification jstring="[para(27305(a,1),28113(a,1,2,3))].">
      <j1 rule="para" parents="27305 28113"/>
    </justification>
  </clause>

  <clause id="28281">
    <literal><![CDATA[
      (x * (y * (x \ L(x,z,u)))) * a(u,z,a(L(y,x,x * L(x,z,u)),x,x)) = (x \ L(x,z,u)) * (x * R(y,x \ L(x,z,u),x))
    ]]></literal>
    <justification jstring="[para(274(a,1),28280(a,1,2,3,1,3))].">
      <j1 rule="para" parents="274 28280"/>
    </justification>
  </clause>

  <clause id="28282">
    <literal><![CDATA[
      (x * (y * (x \ L(x,z,u)))) * a(u,z,a(y,x,L(x,x,x * L(x,z,u)))) = (x \ L(x,z,u)) * (x * R(y,x \ L(x,z,u),x))
    ]]></literal>
    <justification jstring="[para(27867(a,1),28281(a,1,2))].">
      <j1 rule="para" parents="27867 28281"/>
    </justification>
  </clause>

  <clause id="28283">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * R(u,x \ L(x,y,z),x)) = (x * (u * (x \ L(x,y,z)))) * a(z,y,a(u,x,x))
    ]]></literal>
    <justification jstring="[para(26631(a,1),28282(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="26631 28282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28284">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * R(u,x \ L(x,y,z),x)) = x * ((u * (x \ L(x,y,z))) * a(z,y,a(u,x,x)))
    ]]></literal>
    <justification jstring="[hyper(347,a,28157,a(flip),b,28283,a),flip(a)].">
      <j1 rule="hyper" parents="347 28157 28283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28286">
    <literal><![CDATA[
      x * L(a(y,z,a(u,u,w)),(R(w,u,u) \ w) * L(R(w,u,u) \ w,z,y),x) = (L(R(w,u,u) \ w,z,y) \ (R(w,u,u) \ w)) \ x
    ]]></literal>
    <justification jstring="[para(28216(a,1),28085(a,1,2,1))].">
      <j1 rule="para" parents="28216 28085"/>
    </justification>
  </clause>

  <clause id="28287">
    <literal><![CDATA[
      x * L(a(y,z,a(u,u,w)),a(w,u,u) \ L(R(w,u,u) \ w,z,y),x) = (L(R(w,u,u) \ w,z,y) \ (R(w,u,u) \ w)) \ x
    ]]></literal>
    <justification jstring="[para(28074(a,1),28286(a,1,2,2))].">
      <j1 rule="para" parents="28074 28286"/>
    </justification>
  </clause>

  <clause id="28288">
    <literal><![CDATA[
      x * L(a(y,z,a(u,u,w)),L(R(w,u,u) \ w,z,y) * a(w,u,u),x) = (L(R(w,u,u) \ w,z,y) \ (R(w,u,u) \ w)) \ x
    ]]></literal>
    <justification jstring="[para(28064(a,1),28287(a,1,2))].">
      <j1 rule="para" parents="28064 28287"/>
    </justification>
  </clause>

  <clause id="28289">
    <literal><![CDATA[
      (L(R(x,y,y) \ x,z,u) \ (R(x,y,y) \ x)) \ w = w * L(a(u,z,a(y,y,x)),a(u,z,a(y,y,x)),w)
    ]]></literal>
    <justification jstring="[para(28216(a,1),28288(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28216 28288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28290">
    <literal><![CDATA[
      (L(R(x,y,y) \ x,z,u) \ (R(x,y,y) \ x)) \ w = w * a(u,z,a(y,y,L(x,a(u,z,a(y,y,x)),w)))
    ]]></literal>
    <justification jstring="[para(28218(a,2),28289(a,2,2))].">
      <j1 rule="para" parents="28218 28289"/>
    </justification>
  </clause>

  <clause id="28291">
    <literal><![CDATA[
      (L(R(x,y,y) \ x,z,u) \ (R(x,y,y) \ x)) \ w = w * a(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(28279(a,1),28290(a,2,2,3))].">
      <j1 rule="para" parents="28279 28290"/>
    </justification>
  </clause>

  <clause id="28292">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) \ w = w * a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(28237(a,1),28291(a,1,1))].">
      <j1 rule="para" parents="28237 28291"/>
    </justification>
  </clause>

  <clause id="28294">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) \ w = w * a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(26585,a,28292,a)].">
      <j1 rule="hyper" parents="26585 28292"/>
    </justification>
  </clause>

  <clause id="28295">
    <literal><![CDATA[
      (x \ L(x,y,z)) * a(z,y,a(x,x,u)) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,28173,a(flip),b,28294,a),flip(a)].">
      <j1 rule="hyper" parents="63 28173 28294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28296">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) * (u \ L(u,y,x)) = L(u \ L(u,y,x),u,z)
    ]]></literal>
    <justification jstring="[hyper(26526,a,28295,a)].">
      <j1 rule="hyper" parents="26526 28295"/>
    </justification>
  </clause>

  <clause id="28297">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (u \ ((u / x) * L(x,y,z))) = a(z,y,a(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(128,a,3965,a(flip),b,28295,a)].">
      <j1 rule="hyper" parents="128 3965 28295"/>
    </justification>
  </clause>

  <clause id="28298">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),L(y,y * L(y,z,u),y)) = L(y \ L(y,z,u),y,x) \ ((y \ L(y,z,u)) * x)
    ]]></literal>
    <justification jstring="[para(28296(a,1),28121(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28296 28121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28299">
    <literal><![CDATA[
      (x * y) * a(z,u,a(x,w,w)) = x * (y * a(z,u,a(w,w,x)))
    ]]></literal>
    <justification jstring="[para(28297(a,1),28228(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28297 28228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28300">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * R(u,x \ L(x,y,z),x)) = x * (u * ((x \ L(x,y,z)) * a(z,y,a(x,x,u))))
    ]]></literal>
    <justification jstring="[para(28299(a,1),28284(a,2,2))].">
      <j1 rule="para" parents="28299 28284"/>
    </justification>
  </clause>

  <clause id="28301">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),L(y,y * L(y,z,u),y)) = (y \ L(y,z,u)) * (L(y \ L(y,z,u),y,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,1407,a(flip),b,28298,a),flip(a)].">
      <j1 rule="hyper" parents="347 1407 28298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28302">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),L(y,y * L(y,z,u),y)) = (y \ L(y,z,u)) * (y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(27923(a,1),28301(a,2,2))].">
      <j1 rule="para" parents="27923 28301"/>
    </justification>
  </clause>

  <clause id="28303">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),L(y,y * L(y,z,u),y)) = y * ((L(y,z,u) \ x) * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,20952,a(flip),b,28302,a),flip(a)].">
      <j1 rule="hyper" parents="347 20952 28302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28304">
    <literal><![CDATA[
      x * ((L(x,y,z) \ u) * (x \ L(x,y,z))) = L(u,x \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(11451,a,28303,a),flip(a)].">
      <j1 rule="hyper" parents="11451 28303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28306">
    <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(347,a,3652,a(flip),b,28304,a),flip(a)].">
      <j1 rule="hyper" parents="347 3652 28304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28307">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * R(u,x \ L(x,y,z),x)) = x * (u * L(x \ L(x,y,z),x,u))
    ]]></literal>
    <justification jstring="[para(28295(a,1),28300(a,2,2,2))].">
      <j1 rule="para" parents="28295 28300"/>
    </justification>
  </clause>

  <clause id="28308">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * R(u,x \ L(x,y,z),x)) = x * ((u / x) * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(3964(a,1),28307(a,2,2))].">
      <j1 rule="para" parents="3964 28307"/>
    </justification>
  </clause>

  <clause id="28309">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * R(u,x \ L(x,y,z),x)) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(347,a,21007,a(flip),b,28308,a),flip(a)].">
      <j1 rule="hyper" parents="347 21007 28308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28310">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * L(u,x,x \ L(x,y,z))) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[para(21388(a,1),28309(a,1,2,2))].">
      <j1 rule="para" parents="21388 28309"/>
    </justification>
  </clause>

  <clause id="28311">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(x * u,x,x \ L(x,y,z)) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[para(3655(a,2),28310(a,1,2))].">
      <j1 rule="para" parents="3655 28310"/>
    </justification>
  </clause>

  <clause id="28312">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(u,x,x \ L(x,y,z)) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),28311(a,1,2,1))].">
      <j1 rule="para" parents="10 28311"/>
    </justification>
  </clause>

  <clause id="28313">
    <literal><![CDATA[
      L(x,y,z) * (x \ ((x \ L(x,y,z)) \ (u * ((x \ L(x,y,z)) \ 1)))) = L(u,x,x \ L(x,y,z)) * ((x \ L(x,y,z)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(3539,a,28312,a),flip(a)].">
      <j1 rule="hyper" parents="3539 28312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28314">
    <literal><![CDATA[
      x \ y != (z \ L(z,u,w)) * L(z * v5,z,z \ L(z,u,w))
    ]]></literal>
    <literal><![CDATA[
      x * (L(z,u,w) * v5) = y
    ]]></literal>
    <justification jstring="[para(28312(a,2),1052(a,2))].">
      <j1 rule="para" parents="28312 1052"/>
    </justification>
  </clause>

  <clause id="28315">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * (L(x,y,z) \ u)) = L(x,y,z) * (x \ ((x \ L(x,y,z)) \ u))
    ]]></literal>
    <justification jstring="[para(3654(a,1),28312(a,1,2))].">
      <j1 rule="para" parents="3654 28312"/>
    </justification>
  </clause>

  <clause id="28316">
    <literal><![CDATA[
      L(x,y,z) * (x \ ((x \ L(x,y,z)) \ u)) = x * ((L(x,y,z) \ u) * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(20961,a,28315,a),flip(a)].">
      <j1 rule="hyper" parents="20961 28315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28317">
    <literal><![CDATA[
      L(x,y,z) * (x \ ((x \ L(x,y,z)) \ u)) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,28306,a(flip),b,28316,a),flip(a)].">
      <j1 rule="hyper" parents="347 28306 28316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28318">
    <literal><![CDATA[
      L(x,y,z) * (x \ ((x \ L(x,y,z)) \ (u * ((x \ L(x,y,z)) \ 1)))) = L(u,x,x \ L(x,y,z)) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(10882(a,1),28313(a,2,2))].">
      <j1 rule="para" parents="10882 28313"/>
    </justification>
  </clause>

  <clause id="28319">
    <literal><![CDATA[
      L(x,y,z) * (x \ ((x \ L(x,y,z)) \ (u * ((x \ L(x,y,z)) \ 1)))) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,28206,a(flip),b,28318,a),flip(a)].">
      <j1 rule="hyper" parents="347 28206 28318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28320">
    <literal><![CDATA[
      L(x,y,z) * (x \ ((x \ L(x,y,z)) \ (u * (L(x,y,z) \ x)))) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(10882(a,1),28319(a,1,2,2,2,2))].">
      <j1 rule="para" parents="10882 28319"/>
    </justification>
  </clause>

  <clause id="28321">
    <literal><![CDATA[
      L(x * (L(y,z,u) \ y),y,y \ L(y,z,u)) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,28317,a(flip),b,28320,a)].">
      <j1 rule="hyper" parents="63 28317 28320"/>
    </justification>
  </clause>

  <clause id="28323">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ ((x * (L(x,y,z) \ u)) * ((x \ L(x,y,z)) * x)) = x * T(u * (L(x,y,z) \ x),(x \ L(x,y,z)) * x)
    ]]></literal>
    <justification jstring="[para(28321(a,1),735(a,1,2,1))].">
      <j1 rule="para" parents="28321 735"/>
    </justification>
  </clause>

  <clause id="28324">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ ((x * (L(x,y,z) \ u)) * L(x,y,z)) = x * T(u * (L(x,y,z) \ x),(x \ L(x,y,z)) * x)
    ]]></literal>
    <justification jstring="[para(3163(a,1),28323(a,1,2,2))].">
      <j1 rule="para" parents="3163 28323"/>
    </justification>
  </clause>

  <clause id="28325">
    <literal><![CDATA[
      x * T(y * (L(x,z,u) \ x),(x \ L(x,z,u)) * x) = (x \ L(x,z,u)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(20989(a,1),28324(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20989 28324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28326">
    <literal><![CDATA[
      x * T(y * (L(x,z,u) \ x),(x \ L(x,z,u)) * x) = ((x \ L(x,z,u)) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,10544,a(flip),b,28325,a),flip(a)].">
      <j1 rule="hyper" parents="347 10544 28325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28328">
    <literal><![CDATA[
      x * T(y * (L(x,z,u) \ x),L(x,z,u)) = ((x \ L(x,z,u)) \ y) * x
    ]]></literal>
    <justification jstring="[para(3163(a,1),28326(a,1,2,2))].">
      <j1 rule="para" parents="3163 28326"/>
    </justification>
  </clause>

  <clause id="28329">
    <literal><![CDATA[
      x * T(y * (L(x,z,u) \ x),x) = ((x \ L(x,z,u)) \ y) * x
    ]]></literal>
    <justification jstring="[para(19937(a,1),28328(a,1,2))].">
      <j1 rule="para" parents="19937 28328"/>
    </justification>
  </clause>

  <clause id="28330">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ u) * x = (u * (L(x,y,z) \ x)) * x
    ]]></literal>
    <justification jstring="[hyper(315,a,28329,a),flip(a)].">
      <j1 rule="hyper" parents="315 28329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28332">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(35,a,20237,a,b,28330,a),flip(a)].">
      <j1 rule="hyper" parents="35 20237 28330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28333">
    <literal><![CDATA[
      (L(x,y,z) \ x) * ((L(x,y,z) \ x) \ u) = L(u,a(z,y,x),a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(28036,a,28332,a),flip(a)].">
      <j1 rule="hyper" parents="28036 28332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28335">
    <literal><![CDATA[
      (x * x) \ ((L(x,y,z) \ x) * u) = (x * L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(128,a,28332,a(flip),b,3729,a)].">
      <j1 rule="hyper" parents="128 28332 3729"/>
    </justification>
  </clause>

  <clause id="28337">
    <literal><![CDATA[
      (L(x,y,z) \ x) * ((x * x) \ u) = (x * L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,23338,a(flip),b,28335,a)].">
      <j1 rule="hyper" parents="63 23338 28335"/>
    </justification>
  </clause>

  <clause id="28338">
    <literal><![CDATA[
      a(x,(y * L(y,z,u)) \ w,v5) = a(x,w * (L(y,z,u) \ y),v5)
    ]]></literal>
    <justification jstring="[para(28337(a,1),24480(a,1,2))].">
      <j1 rule="para" parents="28337 24480"/>
    </justification>
  </clause>

  <clause id="28339">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(287,a,28333,a),flip(a)].">
      <j1 rule="hyper" parents="287 28333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28340">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(28333(a,1),287(a,1))].">
      <j1 rule="para" parents="28333 287"/>
    </justification>
  </clause>

  <clause id="28341">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * u = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(27585,a,28339,a),flip(a)].">
      <j1 rule="hyper" parents="27585 28339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28342">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ u = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(3204,a,28339,a),flip(a)].">
      <j1 rule="hyper" parents="3204 28339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28345">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ v5 = v5 * L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,27390,a(flip),b,28339,a),flip(a)].">
      <j1 rule="hyper" parents="63 27390 28339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28346">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) \ v5 = v5 * L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,27348,a(flip),b,28339,a)].">
      <j1 rule="hyper" parents="63 27348 28339"/>
    </justification>
  </clause>

  <clause id="28347">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) * v5 = L(a(x,y,z),u,w) \ v5
    ]]></literal>
    <justification jstring="[hyper(63,a,27095,a(flip),b,28339,a)].">
      <j1 rule="hyper" parents="63 27095 28339"/>
    </justification>
  </clause>

  <clause id="28348">
    <literal><![CDATA[
      x * (a(y,z,u) \ 1) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,26392,a(flip),b,28339,a),flip(a)].">
      <j1 rule="hyper" parents="63 26392 28339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28350">
    <literal><![CDATA[
      x \ (a(y,z,u) \ x) = a(y,z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,26392,a(flip),b,28339,a(flip))].">
      <j1 rule="hyper" parents="128 26392 28339"/>
    </justification>
  </clause>

  <clause id="28351">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ u = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,28339,a(flip),b,20920,a)].">
      <j1 rule="hyper" parents="128 28339 20920"/>
    </justification>
  </clause>

  <clause id="28352">
    <literal><![CDATA[
      (x * a(y,z,u)) \ x = a(y,z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,28339,a(flip),b,15418,a)].">
      <j1 rule="hyper" parents="128 28339 15418"/>
    </justification>
  </clause>

  <clause id="28353">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ u != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) * u = w
    ]]></literal>
    <justification jstring="[para(28339(a,1),3204(a,1))].">
      <j1 rule="para" parents="28339 3204"/>
    </justification>
  </clause>

  <clause id="28354">
    <literal><![CDATA[
      L(x,a(y,z,u) \ w,v5) = L(x,a(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(28339(a,1),3613(a,1,2))].">
      <j1 rule="para" parents="28339 3613"/>
    </justification>
  </clause>

  <clause id="28355">
    <literal><![CDATA[
      x \ (a(y,z,u) \ (((a(y,z,u) \ 1) \ x) * w)) = L(w,(a(y,z,u) \ 1) \ x,a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(28339(a,1),3227(a,1,2,2))].">
      <j1 rule="para" parents="28339 3227"/>
    </justification>
  </clause>

  <clause id="28357">
    <literal><![CDATA[
      a(x,y,a(z,u,w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(28339(a,1),14994(a,1,3))].">
      <j1 rule="para" parents="28339 14994"/>
    </justification>
  </clause>

  <clause id="28359">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * u != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) \ u = w
    ]]></literal>
    <justification jstring="[para(28339(a,1),21375(a,1)),flip(a)].">
      <j1 rule="para" parents="28339 21375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28360">
    <literal><![CDATA[
      R(x,a(y,z,u) \ w,v5) = R(x,w * a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[para(28339(a,1),22488(a,1,2))].">
      <j1 rule="para" parents="28339 22488"/>
    </justification>
  </clause>

  <clause id="28361">
    <literal><![CDATA[
      a(x,a(y,z,u) \ w,v5) = a(x,a(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(28339(a,1),24116(a,1,2))].">
      <j1 rule="para" parents="28339 24116"/>
    </justification>
  </clause>

  <clause id="28362">
    <literal><![CDATA[
      a(x,a(y,z,u) \ w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,a(y,z,u) * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(28339(a,1),24177(a,1,2))].">
      <j1 rule="para" parents="28339 24177"/>
    </justification>
  </clause>

  <clause id="28363">
    <literal><![CDATA[
      a(x,L(a(y,z,u) \ w,v5,v6),v7) = a(x,L(a(y,z,u) * w,v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(28339(a,1),24176(a,1,2))].">
      <j1 rule="para" parents="28339 24176"/>
    </justification>
  </clause>

  <clause id="28364">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,v5) \ v6)) = a(x,y,z * (a(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(28339(a,1),24931(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="28339 24931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28365">
    <literal><![CDATA[
      (a(x,y,z) * a(z,y,x)) * u = a(x,y,z) * (a(z,y,x) * u)
    ]]></literal>
    <justification jstring="[para(28339(a,1),26513(a,1,2))].">
      <j1 rule="para" parents="28339 26513"/>
    </justification>
  </clause>

  <clause id="28366">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) * v5 != v6
    ]]></literal>
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ v5 = v6
    ]]></literal>
    <justification jstring="[para(27095(a,1),28340(a,1))].">
      <j1 rule="para" parents="27095 28340"/>
    </justification>
  </clause>

  <clause id="28367">
    <literal><![CDATA[
      a(x,y,z) \ (a(z,y,x) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      (a(z,y,x) * a(x,y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(27561(a,1),28340(a,1))].">
      <j1 rule="para" parents="27561 28340"/>
    </justification>
  </clause>

  <clause id="28371">
    <literal><![CDATA[
      a(x \ (y \ 1),x \ y,z) \ z = L((y * x) \ 1,x,y) * ((L((y * x) \ 1,x,y) \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,27982,a,b,28341,a),flip(a)].">
      <j1 rule="hyper" parents="63 27982 28341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28372">
    <literal><![CDATA[
      a(x,y,z) \ ((u * w) * a(a(x,y,z) \ 1,u,w)) = ((a(x,y,z) \ 1) * u) * w
    ]]></literal>
    <justification jstring="[hyper(63,a,14706,a(flip),b,28341,a),flip(a)].">
      <j1 rule="hyper" parents="63 14706 28341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28373">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) \ ((x * (a(y,z,u) \ 1)) * w) = a(x,a(y,z,u) \ 1,w)
    ]]></literal>
    <justification jstring="[para(28341(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="28341 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28374">
    <literal><![CDATA[
      (x / y) \ ((a(z,u,w) \ (((a(z,u,w) \ 1) \ x) * y)) / y) = L(y,(a(z,u,w) \ 1) \ x,a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(28341(a,1),2020(a,1,2,1))].">
      <j1 rule="para" parents="28341 2020"/>
    </justification>
  </clause>

  <clause id="28376">
    <literal><![CDATA[
      (x * y) / (a(z,u,w) \ T(x,y)) = (y * x) / ((a(z,u,w) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(28341(a,1),13912(a,1,2))].">
      <j1 rule="para" parents="28341 13912"/>
    </justification>
  </clause>

  <clause id="28377">
    <literal><![CDATA[
      (L(a(x,y,z) \ 1,u,u \ w) * w) \ (a(x,y,z) \ w) = a(u \ w,u,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(28341(a,1),14749(a,1,2))].">
      <j1 rule="para" parents="28341 14749"/>
    </justification>
  </clause>

  <clause id="28380">
    <literal><![CDATA[
      R(x,y,(a(z,u,w) \ v5) \ v6) = R(x,y,(v5 * a(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[para(28341(a,1),22120(a,1,3,1))].">
      <j1 rule="para" parents="28341 22120"/>
    </justification>
  </clause>

  <clause id="28381">
    <literal><![CDATA[
      x \ (((a(y,z,u) \ 1) \ ((a(y,z,u) \ x) * w)) / w) = a(a(y,z,u) \ 1,x,w)
    ]]></literal>
    <justification jstring="[para(28341(a,1),23139(a,2,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="28341 23139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28382">
    <literal><![CDATA[
      a(x,y,z) \ (u * (w * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      u * (a(x,y,z) \ (w * w)) = v5
    ]]></literal>
    <justification jstring="[para(28341(a,1),23189(a,1))].">
      <j1 rule="para" parents="28341 23189"/>
    </justification>
  </clause>

  <clause id="28383">
    <literal><![CDATA[
      a(x,(a(y,z,u) \ w) \ v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,(w * a(y,z,u)) \ v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(28341(a,1),24541(a,1,2,1))].">
      <j1 rule="para" parents="28341 24541"/>
    </justification>
  </clause>

  <clause id="28387">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ v5 = a(x,y,a(z,u,w)) * v5
    ]]></literal>
    <justification jstring="[para(26334(a,1),28341(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26334 28341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28388">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ v5 = a(w,a(y,z,u),x) * v5
    ]]></literal>
    <justification jstring="[para(26491(a,1),28341(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26491 28341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28390">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,u,w * u) * w = (a(x,y,z) \ u) * (u \ w)
    ]]></literal>
    <justification jstring="[para(28341(a,1),27256(a,2,1))].">
      <j1 rule="para" parents="28341 27256"/>
    </justification>
  </clause>

  <clause id="28391">
    <literal><![CDATA[
      L(a(x,y,z) \ u,u,a(x,y,z)) = (a(x,y,z) / u) \ 1
    ]]></literal>
    <justification jstring="[para(28341(a,1),27364(a,1,1))].">
      <j1 rule="para" parents="28341 27364"/>
    </justification>
  </clause>

  <clause id="28392">
    <literal><![CDATA[
      (a(x,y,z) \ y) \ (a(x,y,z) \ u) = L(y \ u,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(28341(a,1),27673(a,1,2))].">
      <j1 rule="para" parents="28341 27673"/>
    </justification>
  </clause>

  <clause id="28394">
    <literal><![CDATA[
      x / (a(y,z,u) \ 1) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,20226,a,b,28342,a)].">
      <j1 rule="hyper" parents="63 20226 28342"/>
    </justification>
  </clause>

  <clause id="28395">
    <literal><![CDATA[
      a(x,y,z) * (u * a(x,y,z)) = z * (L(L(z,y,x),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,27430,a(flip),b,28342,a),flip(a)].">
      <j1 rule="hyper" parents="63 27430 28342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28396">
    <literal><![CDATA[
      (a(x,y,z) \ K(u,w)) \ v5 = a(x,y,z) * (K(w,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,20709,a(flip),b,28342,a)].">
      <j1 rule="hyper" parents="63 20709 28342"/>
    </justification>
  </clause>

  <clause id="28398">
    <literal><![CDATA[
      a(a(x,y,z) \ u,w,v5) = a(a(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(28342(a,1),27948(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28342 27948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28399">
    <literal><![CDATA[
      a(x * (a(y,z,u) \ w),v5,v6) = a(x * (a(y,z,u) * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(28342(a,1),27956(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="28342 27956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28402">
    <literal><![CDATA[
      x * (y * (a(z,u,w) \ 1)) = x * (a(z,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(134,a,28348,a,b,9,a)].">
      <j1 rule="hyper" parents="134 28348 9"/>
    </justification>
  </clause>

  <clause id="28403">
    <literal><![CDATA[
      (a(x,y,z) * u) \ u = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,9,a(flip),b,28348,a)].">
      <j1 rule="hyper" parents="128 9 28348"/>
    </justification>
  </clause>

  <clause id="28406">
    <literal><![CDATA[
      a(x,y,y \ x) * ((x * y) \ 1) = y \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,27235,a(flip),b,28348,a(flip))].">
      <j1 rule="hyper" parents="134 27235 28348"/>
    </justification>
  </clause>

  <clause id="28409">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,z) * ((u * a(x,y,z)) \ w)) = L((a(x,y,z) \ u) \ w,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(28348(a,1),3223(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="28348 3223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28410">
    <literal><![CDATA[
      (x \ (y * a(z,u,w))) * (a(z,u,w) \ 1) = (x \ (a(z,u,w) \ y)) * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(28348(a,1),12860(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="28348 12860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28413">
    <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(28348(a,1),22719(a,1,2,2))].">
      <j1 rule="para" parents="28348 22719"/>
    </justification>
  </clause>

  <clause id="28416">
    <literal><![CDATA[
      x * (a(y,z,u * w) \ 1) = a(y,z,w * u) \ x
    ]]></literal>
    <justification jstring="[para(24069(a,1),28348(a,1,2,1))].">
      <j1 rule="para" parents="24069 28348"/>
    </justification>
  </clause>

  <clause id="28421">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ v5) = L(x,y,v5 * a(w,u,z))
    ]]></literal>
    <justification jstring="[para(28348(a,1),26872(a,1,3))].">
      <j1 rule="para" parents="28348 26872"/>
    </justification>
  </clause>

  <clause id="28424">
    <literal><![CDATA[
      x * (a(y,z,u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(28350(a,1),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="28350 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28427">
    <literal><![CDATA[
      L(a(x,y,z),u,u) \ (u \ 1) = u \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(28350(a,1),22332(a,2,2))].">
      <j1 rule="para" parents="28350 22332"/>
    </justification>
  </clause>

  <clause id="28428">
    <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(28350(a,1),25881(a,1,1,1))].">
      <j1 rule="para" parents="28350 25881"/>
    </justification>
  </clause>

  <clause id="28430">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,a(x,y,z),u) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(443,a,28352,a)].">
      <j1 rule="hyper" parents="443 28352"/>
    </justification>
  </clause>

  <clause id="28433">
    <literal><![CDATA[
      ((a(x,y,z) * u) \ w) * ((1 / a(v5,v6,v7)) \ a(v5,v6,v7)) = a(v5,v6,v7) * (a(v5,v6,v7) * ((u * a(x,y,z)) \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,21927,a(flip),b,28394,a)].">
      <j1 rule="hyper" parents="63 21927 28394"/>
    </justification>
  </clause>

  <clause id="28435">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,a(x,y,z) * u,w) = (w * (a(x,y,z) * u)) \ (w * u)
    ]]></literal>
    <justification jstring="[para(28403(a,1),99(a,1,1))].">
      <j1 rule="para" parents="28403 99"/>
    </justification>
  </clause>

  <clause id="28437">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ v5 != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v6
    ]]></literal>
    <justification jstring="[para(26334(a,1),28353(a,1,1))].">
      <j1 rule="para" parents="26334 28353"/>
    </justification>
  </clause>

  <clause id="28438">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ v5 != v6
    ]]></literal>
    <literal><![CDATA[
      a(a(x,y,z),u,w) * v5 = v6
    ]]></literal>
    <justification jstring="[para(26386(a,1),28353(a,1,1))].">
      <j1 rule="para" parents="26386 28353"/>
    </justification>
  </clause>

  <clause id="28440">
    <literal><![CDATA[
      a(x,y,z) \ (a(u,w,v5) \ 1) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u,w,v5) \ (a(x,y,z) \ 1) = v6
    ]]></literal>
    <justification jstring="[para(28348(a,1),28359(a,1))].">
      <j1 rule="para" parents="28348 28359"/>
    </justification>
  </clause>

  <clause id="28441">
    <literal><![CDATA[
      a(x,y \ x,y) * ((x * (y \ x)) \ 1) = (y \ x) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(18778(a,1),28406(a,1,1))].">
      <j1 rule="para" parents="18778 28406"/>
    </justification>
  </clause>

  <clause id="28443">
    <literal><![CDATA[
      R(x,(((y * z) \ z) * y) \ u,w) = R(x,u * a(y \ 1,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,26897,a,b,28360,a)].">
      <j1 rule="hyper" parents="63 26897 28360"/>
    </justification>
  </clause>

  <clause id="28444">
    <literal><![CDATA[
      R(x,(y * (z * (y * z))) \ u,w) = R(x,u * a(y,z,y * z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,21899,a,b,28360,a)].">
      <j1 rule="hyper" parents="63 21899 28360"/>
    </justification>
  </clause>

  <clause id="28445">
    <literal><![CDATA[
      R(x,a(y,z,u) \ w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,a(y,z,u) * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(28360(a,2),22117(a,1))].">
      <j1 rule="para" parents="28360 22117"/>
    </justification>
  </clause>

  <clause id="28446">
    <literal><![CDATA[
      a(x,a(y * z,z,z) * u,w) = a(x,a(y,z,z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,25690,a(flip),b,28361,a),flip(a)].">
      <j1 rule="hyper" parents="63 25690 28361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28447">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(x,y,a(w,u,z)) * v5) = v5
    ]]></literal>
    <justification jstring="[hyper(26566,a,28387,a),flip(a)].">
      <j1 rule="hyper" parents="26566 28387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28448">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * a(x,y,a(w,u,z))) = v5
    ]]></literal>
    <justification jstring="[hyper(134,a,26521,a(flip),b,28387,a)].">
      <j1 rule="hyper" parents="134 26521 28387"/>
    </justification>
  </clause>

  <clause id="28449">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,a(x,y,z),u) \ ((w * (u * a(x,y,z))) \ (w * u)) = a(w,u * a(x,y,z),a(x,y,z)) * 1
    ]]></literal>
    <justification jstring="[hyper(63,a,26416,a,b,28387,a)].">
      <j1 rule="hyper" parents="63 26416 28387"/>
    </justification>
  </clause>

  <clause id="28450">
    <literal><![CDATA[
      ((x / y) * (y * a(z,u,w))) / a(z,u,w) = a(y \ x,y,a(z,u,w)) * x
    ]]></literal>
    <justification jstring="[hyper(63,a,23150,a(flip),b,28387,a)].">
      <j1 rule="hyper" parents="63 23150 28387"/>
    </justification>
  </clause>

  <clause id="28451">
    <literal><![CDATA[
      (x * (a(x,y,a(z,u,w)) * y)) * (a(z,u,w) \ 1) = x * (y * (a(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(28387(a,1),25420(a,1,1,2))].">
      <j1 rule="para" parents="28387 25420"/>
    </justification>
  </clause>

  <clause id="28452">
    <literal><![CDATA[
      a(x,y,y * x) \ ((x * y) * (x * y)) = (x \ 1) \ (y * (x * y))
    ]]></literal>
    <justification jstring="[hyper(26589,a,28416,a),flip(a)].">
      <j1 rule="hyper" parents="26589 28416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28453">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(39,a,26290,a(flip),b,28430,a(flip))].">
      <j1 rule="hyper" parents="39 26290 28430"/>
    </justification>
  </clause>

  <clause id="28455">
    <literal><![CDATA[
      L(a(x,y,z),a(z,y,x),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,26497,a,b,28453,a)].">
      <j1 rule="hyper" parents="63 26497 28453"/>
    </justification>
  </clause>

  <clause id="28456">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ a(x,y,z) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(28453(a,1),26225(a,1,3)),flip(a)].">
      <j1 rule="para" parents="28453 26225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28458">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),a(z,y,x),v5) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(28455(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28455 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28460">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u,w) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(26407,a,28456,a)].">
      <j1 rule="hyper" parents="26407 28456"/>
    </justification>
  </clause>

  <clause id="28461">
    <literal><![CDATA[
      a(x,y,z) * a(u,w,a(x,y,z)) = L(a(x,y,z),w,u)
    ]]></literal>
    <justification jstring="[hyper(134,a,28456,a(flip),b,26262,a(flip))].">
      <j1 rule="hyper" parents="134 28456 26262"/>
    </justification>
  </clause>

  <clause id="28462">
    <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(128,a,28456,a(flip),b,26289,a)].">
      <j1 rule="hyper" parents="128 28456 26289"/>
    </justification>
  </clause>

  <clause id="28463">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,u,z) = L(a(w,u,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(38,a,26519,a,b,28460,a)].">
      <j1 rule="hyper" parents="38 26519 28460"/>
    </justification>
  </clause>

  <clause id="28465">
    <literal><![CDATA[
      x * (y * (a(x,z,u) \ L(a(x,z,u),w,v5))) = (x * y) * a(v5,w,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(28460(a,1),25768(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28460 25768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28466">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(28461(a,1),356(a,1,2))].">
      <j1 rule="para" parents="28461 356"/>
    </justification>
  </clause>

  <clause id="28467">
    <literal><![CDATA[
      L(a(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(x,y,z)) * a(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(28461(a,1),11791(a,1))].">
      <j1 rule="para" parents="28461 11791"/>
    </justification>
  </clause>

  <clause id="28468">
    <literal><![CDATA[
      (x \ a(y,z,a(x,u,w))) * a(x,u,w) = x \ L(a(x,u,w),z,y)
    ]]></literal>
    <justification jstring="[para(28461(a,1),25405(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28461 25405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28470">
    <literal><![CDATA[
      a(x,a(x,y,z),u) * a(x,y,z) = L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(26601(a,2),28463(a,1,1))].">
      <j1 rule="para" parents="26601 28463"/>
    </justification>
  </clause>

  <clause id="28471">
    <literal><![CDATA[
      x / L(a(y,z,u) \ 1,w,v5) = x * L(a(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(21073,a,28346,a)].">
      <j1 rule="hyper" parents="21073 28346"/>
    </justification>
  </clause>

  <clause id="28473">
    <literal><![CDATA[
      x * L(a(y,z,u) \ 1,w,v5) = L(a(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(21076,a,28347,a)].">
      <j1 rule="hyper" parents="21076 28347"/>
    </justification>
  </clause>

  <clause id="28475">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ (u * w) = ((a(x,y,z) \ 1) * u) * w
    ]]></literal>
    <justification jstring="[hyper(63,a,23386,a(flip),b,28347,a),flip(a)].">
      <j1 rule="hyper" parents="63 23386 28347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28476">
    <literal><![CDATA[
      L((a(x,y,z) / u) \ 1,u,a(x,y,z)) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(26380,a,28391,a)].">
      <j1 rule="hyper" parents="26380 28391"/>
    </justification>
  </clause>

  <clause id="28477">
    <literal><![CDATA[
      (a(x,y,z) \ K(u,w)) * v5 = K(u,w) * (a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(134,a,5272,a(flip),b,28396,a)].">
      <j1 rule="hyper" parents="134 5272 28396"/>
    </justification>
  </clause>

  <clause id="28478">
    <literal><![CDATA[
      (x * L(a(y,z,u),w,v5)) \ x = L(a(y,z,u) \ 1,w,v5)
    ]]></literal>
    <justification jstring="[hyper(214,a,28471,a)].">
      <j1 rule="hyper" parents="214 28471"/>
    </justification>
  </clause>

  <clause id="28479">
    <literal><![CDATA[
      L((a(x,y,z) / (1 / u)) \ 1,u,a(x,y,z)) = a(x,y,z) \ (1 / u)
    ]]></literal>
    <justification jstring="[hyper(3520,a,28476,a)].">
      <j1 rule="hyper" parents="3520 28476"/>
    </justification>
  </clause>

  <clause id="28480">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ R((a(z,u,w) \ K(x,y)) \ v5,a(z,u,w) \ K(x,y),v6 * (a(z,u,w) \ K(x,y)))) = ((v5 * ((a(z,u,w) \ K(x,y)) \ v6)) / v6) * (a(z,u,w) \ K(x,y))
    ]]></literal>
    <justification jstring="[hyper(27267,a,28477,a),flip(a)].">
      <j1 rule="hyper" parents="27267 28477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28481">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ (x * y) = L(a(z,u,w) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(97(a,1),28478(a,1,1))].">
      <j1 rule="para" parents="97 28478"/>
    </justification>
  </clause>

  <clause id="28482">
    <literal><![CDATA[
      a(x,a(y * z,z,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,a(y,z,z) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(28446(a,2),28362(a,1))].">
      <j1 rule="para" parents="28446 28362"/>
    </justification>
  </clause>

  <clause id="28483">
    <literal><![CDATA[
      a(x,R(x,y,z) \ x,x) * ((x * (R(x,y,z) \ x)) \ 1) = (R(x,y,z) \ x) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(11254(a,1),28441(a,1,1))].">
      <j1 rule="para" parents="11254 28441"/>
    </justification>
  </clause>

  <clause id="28486">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ (u * w) = (a(x,y,z) \ u) * w
    ]]></literal>
    <justification jstring="[para(28341(a,1),28475(a,2,1))].">
      <j1 rule="para" parents="28341 28475"/>
    </justification>
  </clause>

  <clause id="28487">
    <literal><![CDATA[
      ((x * a(y,z,u)) * w) \ (x * w) = L(a(y,z,u) \ 1,x,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,23348,a,b,28481,a)].">
      <j1 rule="hyper" parents="63 23348 28481"/>
    </justification>
  </clause>

  <clause id="28488">
    <literal><![CDATA[
      L(L(a(x,y,z),a(x,y,z),u),u * a(x,y,z),w) = L(a(x,y,z) \ 1,u,w) * (a(x,y,z) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(28481(a,1),1381(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28481 1381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28489">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) \ (x * w) = L(a(y,z,u) \ 1,w,x)
    ]]></literal>
    <justification jstring="[para(19985(a,2),28481(a,1,1,2))].">
      <j1 rule="para" parents="19985 28481"/>
    </justification>
  </clause>

  <clause id="28490">
    <literal><![CDATA[
      ((a(x,y,z) * u) * w) \ (u * w) = L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(19985(a,2),28487(a,1,1,1))].">
      <j1 rule="para" parents="19985 28487"/>
    </justification>
  </clause>

  <clause id="28492">
    <literal><![CDATA[
      (x \ ((x / y) * L(y,z,u))) \ w = w * L(L(y,z,u) \ y,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3969,a(flip),b,28345,a)].">
      <j1 rule="hyper" parents="63 3969 28345"/>
    </justification>
  </clause>

  <clause id="28493">
    <literal><![CDATA[
      R(x,y,(a(z,z,u) * w) \ v5) = R(x,y,(w * a(u,z,z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,27839,a(flip),b,28380,a)].">
      <j1 rule="hyper" parents="63 27839 28380"/>
    </justification>
  </clause>

  <clause id="28494">
    <literal><![CDATA[
      L((a(x,y \ 1,z) \ (y \ 1)) \ (a(x,y \ 1,z) \ u),y,y) = L(y * u,y \ 1,a(x,y \ 1,z))
    ]]></literal>
    <justification jstring="[para(28392(a,2),3200(a,1,1))].">
      <j1 rule="para" parents="28392 3200"/>
    </justification>
  </clause>

  <clause id="28495">
    <literal><![CDATA[
      (a(x,y,z) * u) * a(x,y,z) = z * (L(L(z,y,x),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(20918,a,28395,a)].">
      <j1 rule="hyper" parents="20918 28395"/>
    </justification>
  </clause>

  <clause id="28496">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,z) * u) = z * (L(L(z,y,x),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(20480,a,28395,a)].">
      <j1 rule="hyper" parents="20480 28395"/>
    </justification>
  </clause>

  <clause id="28497">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ a(x,y,z) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(26262(a,2),28466(a,1))].">
      <j1 rule="para" parents="26262 28466"/>
    </justification>
  </clause>

  <clause id="28498">
    <literal><![CDATA[
      (x * a(y,z,u)) \ (x * L(u * (L(L(u,z,y),z,y) \ w),v5,v6)) = L(a(y,z,u) * L(w,v5,v6),a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(28496(a,1),3391(a,1,2,2,1))].">
      <j1 rule="para" parents="28496 3391"/>
    </justification>
  </clause>

  <clause id="28499">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w * u) * w = (a(x,y,z) \ u) * (u \ w)
    ]]></literal>
    <justification jstring="[para(23384(a,1),28390(a,1,1))].">
      <j1 rule="para" parents="23384 28390"/>
    </justification>
  </clause>

  <clause id="28500">
    <literal><![CDATA[
      (a(x,y,x * y) \ (x * y)) * (x * y) = (x \ 1) \ (y * (x * y))
    ]]></literal>
    <justification jstring="[hyper(24123,a,28452,a)].">
      <j1 rule="hyper" parents="24123 28452"/>
    </justification>
  </clause>

  <clause id="28501">
    <literal><![CDATA[
      L(a(x,y,z),u,w * u) \ w = (a(x,y,z) \ u) * (u \ w)
    ]]></literal>
    <justification jstring="[hyper(28366,a,28499,a)].">
      <j1 rule="hyper" parents="28366 28499"/>
    </justification>
  </clause>

  <clause id="28502">
    <literal><![CDATA[
      (a(x,y,z * u) \ u) * (u \ z) = a(x,y,z * u) \ z
    ]]></literal>
    <justification jstring="[para(12360(a,1),28501(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12360 28501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28503">
    <literal><![CDATA[
      (x \ 1) \ (y * (x * y)) = x * (y * (x * y))
    ]]></literal>
    <justification jstring="[hyper(14630,a,28500,a),flip(a)].">
      <j1 rule="hyper" parents="14630 28500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28504">
    <literal><![CDATA[
      R(x,((y \ z) \ (z * y)) \ u,w) = R(x,(z * (y * (z * y))) \ u,w)
    ]]></literal>
    <justification jstring="[para(28503(a,1),27118(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="28503 27118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28505">
    <literal><![CDATA[
      a(x,L(a(y,z,y) * u,w,v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,w \ (v5 \ (u * (a(y,z,y) \ (v5 * w)))),v6) = v7
    ]]></literal>
    <justification jstring="[para(28363(a,1),26101(a,1))].">
      <j1 rule="para" parents="28363 26101"/>
    </justification>
  </clause>

  <clause id="28506">
    <literal><![CDATA[
      (x * y) / T(a(z,u,w) \ x,y) = (y * x) / ((a(z,u,w) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(23175(a,2),28376(a,1,2))].">
      <j1 rule="para" parents="23175 28376"/>
    </justification>
  </clause>

  <clause id="28507">
    <literal><![CDATA[
      R(x,((y \ z) \ (z * y)) \ u,w) = R(x,u * a(z,y,z * y),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,28444,a(flip),b,28504,a),flip(a)].">
      <j1 rule="hyper" parents="347 28444 28504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28508">
    <literal><![CDATA[
      R(x,(y \ (z * (y * z))) \ u,w) = R(x,u * a(y,z,y * z),w)
    ]]></literal>
    <justification jstring="[para(27116(a,1),28507(a,1,2,1))].">
      <j1 rule="para" parents="27116 28507"/>
    </justification>
  </clause>

  <clause id="28509">
    <literal><![CDATA[
      R(x,y * a(z,u,z * u),w) = R(x,y * a(z,u,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,28180,a(flip),b,28508,a),flip(a)].">
      <j1 rule="hyper" parents="63 28180 28508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28510">
    <literal><![CDATA[
      R(x,y * a(z * u,z,u),w) = R(x,y * a(u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,27357,a,b,28509,a)].">
      <j1 rule="hyper" parents="63 27357 28509"/>
    </justification>
  </clause>

  <clause id="28511">
    <literal><![CDATA[
      R(x,y * a(z * u,u,z),w) = R(x,y * a(z,u,u),w)
    ]]></literal>
    <justification jstring="[para(18294(a,2),28510(a,1,2,2))].">
      <j1 rule="para" parents="18294 28510"/>
    </justification>
  </clause>

  <clause id="28512">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,a(x,y,z) * u,w) = L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,28489,a(flip),b,28435,a),flip(a)].">
      <j1 rule="hyper" parents="347 28489 28435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28513">
    <literal><![CDATA[
      a(x,y,z) \ ((u / w) * (w * a(x,y,z))) = a(w \ u,w,a(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(20018,a,28450,a)].">
      <j1 rule="hyper" parents="20018 28450"/>
    </justification>
  </clause>

  <clause id="28514">
    <literal><![CDATA[
      (x * y) * a(z,u,a(x,w,v5)) = x * (y * a(z,u,a(x,w,v5)))
    ]]></literal>
    <justification jstring="[para(28460(a,1),28465(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28460 28465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28515">
    <literal><![CDATA[
      (x \ 1) * a(y,z,a(x,u,w)) = x \ a(y,z,a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(431,a,28514,a),flip(a)].">
      <j1 rule="hyper" parents="431 28514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28516">
    <literal><![CDATA[
      a(x,y,a(z,u,a(x,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,28514,a(flip),b,13372,a),flip(a)].">
      <j1 rule="hyper" parents="129 28514 13372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28518">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * ((z \ 1) * a(z,u,w)) = (z \ a(x,y,a(z,u,w))) * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(28515(a,1),23119(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28515 23119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28519">
    <literal><![CDATA[
      a(x,y,z) \ ((u * w) * a(a(x,y,z) \ 1,u,w)) = (a(x,y,z) \ u) * w
    ]]></literal>
    <justification jstring="[para(28341(a,1),28372(a,2,1))].">
      <j1 rule="para" parents="28341 28372"/>
    </justification>
  </clause>

  <clause id="28520">
    <literal><![CDATA[
      a(x,y,z) \ ((u * w) * a(a(x,y,z),u,w)) = (a(x,y,z) \ u) * w
    ]]></literal>
    <justification jstring="[para(27951(a,1),28519(a,1,2,2))].">
      <j1 rule="para" parents="27951 28519"/>
    </justification>
  </clause>

  <clause id="28521">
    <literal><![CDATA[
      a(x,y,z) \ (u * L(w,u,a(x,y,z))) = (a(x,y,z) \ u) * w
    ]]></literal>
    <justification jstring="[para(26385(a,1),28520(a,1,2))].">
      <j1 rule="para" parents="26385 28520"/>
    </justification>
  </clause>

  <clause id="28522">
    <literal><![CDATA[
      L((a(x,y,z) \ u) \ w,u,a(x,y,z)) = u \ (a(x,y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(1674,a,28521,a)].">
      <j1 rule="hyper" parents="1674 28521"/>
    </justification>
  </clause>

  <clause id="28523">
    <literal><![CDATA[
      L(x \ (a(y,z,u) * w),x,a(y,z,u)) = (a(y,z,u) \ x) \ w
    ]]></literal>
    <justification jstring="[hyper(26380,a,28522,a)].">
      <j1 rule="hyper" parents="26380 28522"/>
    </justification>
  </clause>

  <clause id="28524">
    <literal><![CDATA[
      L(x \ (a(y,z,u) * w),x,a(y,z,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,u) \ x) \ w = v5
    ]]></literal>
    <justification jstring="[para(28522(a,1),27579(a,1,1))].">
      <j1 rule="para" parents="28522 27579"/>
    </justification>
  </clause>

  <clause id="28526">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) \ ((a(y,z,u) \ x) * w) = a(x,a(y,z,u) \ 1,w)
    ]]></literal>
    <justification jstring="[para(28348(a,1),28373(a,1,2,1))].">
      <j1 rule="para" parents="28348 28373"/>
    </justification>
  </clause>

  <clause id="28527">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) \ ((a(y,z,u) \ x) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,a(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(28526(a,2),14965(a,1))].">
      <j1 rule="para" parents="28526 14965"/>
    </justification>
  </clause>

  <clause id="28528">
    <literal><![CDATA[
      x \ (((x / a(y,z,u)) * w) / (a(y,z,u) \ w)) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(28527,a,20581,a),flip(a)].">
      <j1 rule="hyper" parents="28527 20581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28529">
    <literal><![CDATA[
      x \ (((a(y,z,u) \ x) * w) / (a(y,z,u) \ w)) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(19977(a,1),28528(a,1,2,1,1))].">
      <j1 rule="para" parents="19977 28528"/>
    </justification>
  </clause>

  <clause id="28530">
    <literal><![CDATA[
      x \ ((a(y,z,u) * ((a(y,z,u) \ x) * w)) / w) = a(a(y,z,u) \ 1,x,w)
    ]]></literal>
    <justification jstring="[para(28342(a,1),28381(a,1,2,1))].">
      <j1 rule="para" parents="28342 28381"/>
    </justification>
  </clause>

  <clause id="28531">
    <literal><![CDATA[
      x \ (y \ ((y * (a(z,u,w) \ x)) * a(z,u,w))) = a(a(z,u,w) \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(23244(a,1),28530(a,1,2))].">
      <j1 rule="para" parents="23244 28530"/>
    </justification>
  </clause>

  <clause id="28532">
    <literal><![CDATA[
      x \ (y \ (a(z,u,w) * (y * (a(z,u,w) \ x)))) = a(a(z,u,w) \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(19985(a,2),28531(a,1,2,2))].">
      <j1 rule="para" parents="19985 28531"/>
    </justification>
  </clause>

  <clause id="28533">
    <literal><![CDATA[
      (x \ (y * a(z,u,w))) * (a(z,u,w) \ 1) = a(z,u,w) * (x \ (a(z,u,w) \ y))
    ]]></literal>
    <justification jstring="[hyper(347,a,19985,a,b,28410,a),flip(a)].">
      <j1 rule="hyper" parents="347 19985 28410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28534">
    <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(28353,a,28413,a),flip(a)].">
      <j1 rule="hyper" parents="28353 28413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28535">
    <literal><![CDATA[
      a(x \ y,x,a(z,u,w)) * y = a(z,u,w) * ((y / x) * (a(z,u,w) \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,28513,a(flip),b,28534,a)].">
      <j1 rule="hyper" parents="63 28513 28534"/>
    </justification>
  </clause>

  <clause id="28536">
    <literal><![CDATA[
      x \ (a(y,z,u) * (x * (a(y,z,u) \ w))) = L(L(w,a(y,z,u),x),x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(28534(a,1),26389(a,1,2))].">
      <j1 rule="para" parents="28534 26389"/>
    </justification>
  </clause>

  <clause id="28537">
    <literal><![CDATA[
      (R(x,y,a(z,u,w)) * y) * (a(z,u,w) \ 1) = x * (y * (a(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(26945(a,1),28451(a,1,1))].">
      <j1 rule="para" parents="26945 28451"/>
    </justification>
  </clause>

  <clause id="28538">
    <literal><![CDATA[
      (L(x,y,a(z,u,w)) * y) * (a(z,u,w) \ 1) = x * (y * (a(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(23247(a,1),28537(a,1,1,1))].">
      <j1 rule="para" parents="23247 28537"/>
    </justification>
  </clause>

  <clause id="28539">
    <literal><![CDATA[
      x * (y * (a(z,u,w) \ 1)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,w) \ (L(x,y,a(z,u,w)) * y) = v5
    ]]></literal>
    <justification jstring="[para(28538(a,1),28424(a,1))].">
      <j1 rule="para" parents="28538 28424"/>
    </justification>
  </clause>

  <clause id="28540">
    <literal><![CDATA[
      a(x,y,z) \ (L(u,w,a(x,y,z)) * w) = u * (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(28539,a,28402,a)].">
      <j1 rule="hyper" parents="28539 28402"/>
    </justification>
  </clause>

  <clause id="28541">
    <literal><![CDATA[
      a(x,x,y) \ ((x \ y) * z) = (x \ y) * (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(27244(a,1),28540(a,1,2,1))].">
      <j1 rule="para" parents="27244 28540"/>
    </justification>
  </clause>

  <clause id="28542">
    <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(28424,a,28533,a)].">
      <j1 rule="hyper" parents="28424 28533"/>
    </justification>
  </clause>

  <clause id="28543">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) * (v5 \ (a(z,u,w) \ v6))) * a(z,u,w)) = a(x,y,v5 \ (v6 * a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(28542(a,1),24068(a,1,3,1))].">
      <j1 rule="para" parents="28542 24068"/>
    </justification>
  </clause>

  <clause id="28544">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (u * (a(x,y,z) \ w)) = L(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(41,a,28522,a,b,28536,a(flip))].">
      <j1 rule="hyper" parents="41 28522 28536"/>
    </justification>
  </clause>

  <clause id="28545">
    <literal><![CDATA[
      (x / y) \ L(L(x,a(z,u,w),y),y,a(z,u,w)) = L(y,a(z,u,w) \ x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(28536(a,1),23391(a,1,2))].">
      <j1 rule="para" parents="28536 23391"/>
    </justification>
  </clause>

  <clause id="28546">
    <literal><![CDATA[
      x \ L(L(x,a(y,z,u),w),w,a(y,z,u)) = a(a(y,z,u) \ 1,x,w)
    ]]></literal>
    <justification jstring="[para(28536(a,1),28532(a,1,2))].">
      <j1 rule="para" parents="28536 28532"/>
    </justification>
  </clause>

  <clause id="28547">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(w,a(x,y,z),u) = u * (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(150,a,28544,a)].">
      <j1 rule="hyper" parents="150 28544"/>
    </justification>
  </clause>

  <clause id="28548">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z),w) = (a(x,y,z) \ w) \ (w * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),28544(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 28544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28549">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (u * (a(x,y,z) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(w,a(x,y,z),u) = v5
    ]]></literal>
    <justification jstring="[para(28547(a,1),356(a,1,2))].">
      <j1 rule="para" parents="28547 356"/>
    </justification>
  </clause>

  <clause id="28550">
    <literal><![CDATA[
      L(a(x,y,z) * L(u \ (a(x,y,z) \ u),w,v5),a(x,y,z),u) = a(v5,w,(((a(x,y,z) \ u) \ u) \ w) * w) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,27215,a,b,28548,a),flip(a)].">
      <j1 rule="hyper" parents="347 27215 28548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28551">
    <literal><![CDATA[
      L(a(x,y,z) * T(u,w),a(x,y,z),w) = (a(x,y,z) \ w) \ (u * w)
    ]]></literal>
    <justification jstring="[hyper(347,a,250,a(flip),b,28548,a),flip(a)].">
      <j1 rule="hyper" parents="347 250 28548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28552">
    <literal><![CDATA[
      L(a(x,y,z) * u,z,a(x,y,z)) = (a(x,y,z) \ z) \ (z * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,23359,a(flip),b,28548,a)].">
      <j1 rule="hyper" parents="63 23359 28548"/>
    </justification>
  </clause>

  <clause id="28553">
    <literal><![CDATA[
      (x * y) / T(a(z,u,w) \ x,L(a(z,u,w) * y,a(z,u,w),x)) = (a(z,u,w) \ x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(28548(a,2),296(a,1,2,2))].">
      <j1 rule="para" parents="28548 296"/>
    </justification>
  </clause>

  <clause id="28554">
    <literal><![CDATA[
      (x * (a(y,z,u) \ 1)) * L(a(y,z,u) * w,a(y,z,u),1) = (x * a(y,z,u)) * (a(y,z,u) \ (1 * w))
    ]]></literal>
    <justification jstring="[para(28548(a,2),987(a,1,2))].">
      <j1 rule="para" parents="28548 987"/>
    </justification>
  </clause>

  <clause id="28555">
    <literal><![CDATA[
      x \ L(L(x,a(y,z,u),w),w,a(y,z,u)) = a(a(y,z,u),x,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,27951,a(flip),b,28546,a),flip(a)].">
      <j1 rule="hyper" parents="347 27951 28546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28556">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),w,a(y,z,u)) = x * a(w,x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(134,a,26594,a(flip),b,28555,a),flip(a)].">
      <j1 rule="hyper" parents="134 26594 28555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28557">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),w,a(y,z,u)) = a(a(y,z,u),x,w) * x
    ]]></literal>
    <justification jstring="[hyper(38,a,19974,a,b,28555,a),flip(a)].">
      <j1 rule="hyper" parents="38 19974 28555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28558">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),a(z,u,w),y) = x * a(y,x,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(1094,a,28556,a)].">
      <j1 rule="hyper" parents="1094 28556"/>
    </justification>
  </clause>

  <clause id="28559">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) \ 1,a(x,y,a(z,u,w)),y) \ ((v5 * (y * a(x,y,a(z,u,w)))) \ (v5 * y)) = a(v5,L(L(y,a(w,u,z),x),x,a(w,u,z)),a(x,y,a(z,u,w))) \ 1
    ]]></literal>
    <justification jstring="[para(28556(a,2),26416(a,2,1,2))].">
      <j1 rule="para" parents="28556 26416"/>
    </justification>
  </clause>

  <clause id="28560">
    <literal><![CDATA[
      L(a(a(x,y,z),u,w) * u,w,a(x,y,z)) = L(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(26380,a,28557,a)].">
      <j1 rule="hyper" parents="26380 28557"/>
    </justification>
  </clause>

  <clause id="28561">
    <literal><![CDATA[
      x \ (a(y,z,u) * (x * (a(y,z,u) \ w))) = a(a(y,z,u),w,x) * w
    ]]></literal>
    <justification jstring="[hyper(63,a,28536,a,b,28557,a)].">
      <j1 rule="hyper" parents="63 28536 28557"/>
    </justification>
  </clause>

  <clause id="28562">
    <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(12674(a,1),28560(a,1,1))].">
      <j1 rule="para" parents="12674 28560"/>
    </justification>
  </clause>

  <clause id="28563">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),w,a(u,z,y)) = x * a(a(y,z,u),x,w)
    ]]></literal>
    <justification jstring="[hyper(27567,a,28562,a)].">
      <j1 rule="hyper" parents="27567 28562"/>
    </justification>
  </clause>

  <clause id="28564">
    <literal><![CDATA[
      L(x * a(a(y,z,u),x,w),w,a(y,z,u)) \ v5 = L(x,a(y,z,u),w) \ v5
    ]]></literal>
    <justification jstring="[hyper(61,a,28562,a)].">
      <j1 rule="hyper" parents="61 28562"/>
    </justification>
  </clause>

  <clause id="28565">
    <literal><![CDATA[
      L(x * a(a(y,z,u),x,w),w,a(y,z,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(28563(a,1),27576(a,1,1))].">
      <j1 rule="para" parents="28563 27576"/>
    </justification>
  </clause>

  <clause id="28566">
    <literal><![CDATA[
      L(T(a(x,y,z) * u,w),a(x,y,z),w) = (a(x,y,z) \ w) \ (u * w)
    ]]></literal>
    <justification jstring="[para(23113(a,2),28551(a,1,1))].">
      <j1 rule="para" parents="23113 28551"/>
    </justification>
  </clause>

  <clause id="28567">
    <literal><![CDATA[
      x \ ((x * (a(y,z,u) \ w)) * a(y,z,u)) = a(a(y,z,u),w,x) * w
    ]]></literal>
    <justification jstring="[hyper(20942,a,28561,a)].">
      <j1 rule="hyper" parents="20942 28561"/>
    </justification>
  </clause>

  <clause id="28568">
    <literal><![CDATA[
      (a(x,y,z) * ((a(x,y,z) \ u) * w)) / w = a(a(x,y,z),u,w) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,23244,a,b,28567,a)].">
      <j1 rule="hyper" parents="63 23244 28567"/>
    </justification>
  </clause>

  <clause id="28569">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) * u) * w) = a(x,y,z) * ((a(x,y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(23140,a,28568,a)].">
      <j1 rule="hyper" parents="23140 28568"/>
    </justification>
  </clause>

  <clause id="28570">
    <literal><![CDATA[
      x \ ((x * a(y,z,u)) * (a(y,z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(w,a(y,z,u),x * a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(19988(a,1),28549(a,1,1))].">
      <j1 rule="para" parents="19988 28549"/>
    </justification>
  </clause>

  <clause id="28571">
    <literal><![CDATA[
      L((1 / x) * a(a(y,z,u),x,w),w,a(y,z,u)) \ v5 = L(1 / x,a(y,z,u),w) \ v5
    ]]></literal>
    <justification jstring="[para(14964(a,1),28564(a,1,1,1,2))].">
      <j1 rule="para" parents="14964 28564"/>
    </justification>
  </clause>

  <clause id="28572">
    <literal><![CDATA[
      R(x,(a(y,z,u) * ((a(y,z,u) \ w) * v5)) * a(y,z,u),v6) = R(x,(a(y,z,u) * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(28569(a,1),20552(a,1,2,1))].">
      <j1 rule="para" parents="28569 20552"/>
    </justification>
  </clause>

  <clause id="28573">
    <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(63,a,21006,a(flip),b,28428,a)].">
      <j1 rule="hyper" parents="63 21006 28428"/>
    </justification>
  </clause>

  <clause id="28575">
    <literal><![CDATA[
      a(x,x * R(x,y,z),x) * ((x * (R(x,y,z) \ x)) \ 1) = (R(x,y,z) \ x) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(14987(a,1),28483(a,1,1))].">
      <j1 rule="para" parents="14987 28483"/>
    </justification>
  </clause>

  <clause id="28576">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * ((z \ 1) * a(z,u,w)) = z \ L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,28468,a(flip),b,28518,a),flip(a)].">
      <j1 rule="hyper" parents="347 28468 28518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28577">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (z \ a(z,u,w)) = z \ L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(15264(a,1),28576(a,1,2))].">
      <j1 rule="para" parents="15264 28576"/>
    </justification>
  </clause>

  <clause id="28578">
    <literal><![CDATA[
      x * a(y,a(z,u,w),x * a(z,u,w)) = L(x,a(z,u,w),y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(28570,a,27221,a),flip(a)].">
      <j1 rule="hyper" parents="28570 27221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28579">
    <literal><![CDATA[
      L(a(a(x,y,z),u,w) / u,w,a(x,y,z)) \ v5 = L(1 / u,a(x,y,z),w) \ v5
    ]]></literal>
    <justification jstring="[para(26351(a,1),28571(a,1,1,1))].">
      <j1 rule="para" parents="26351 28571"/>
    </justification>
  </clause>

  <clause id="28580">
    <literal><![CDATA[
      L((a(a(x,y,z),u,w) / u) \ 1,w,a(x,y,z)) = L(1 / u,a(x,y,z),w) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,26373,a,b,28579,a)].">
      <j1 rule="hyper" parents="63 26373 28579"/>
    </justification>
  </clause>

  <clause id="28581">
    <literal><![CDATA[
      a(x,y,z) \ (u * L(a(x,y,z),w,v5)) = u * (a(x,y,z) \ L(a(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(28359,a,28573,a)].">
      <j1 rule="hyper" parents="28359 28573"/>
    </justification>
  </clause>

  <clause id="28582">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (a(x,y,z) \ v5) = v5 * (a(x,y,z) \ L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(21002,a,28581,a)].">
      <j1 rule="hyper" parents="21002 28581"/>
    </justification>
  </clause>

  <clause id="28584">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (a(x,y,z) \ v5) = v5 * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(28460(a,1),28582(a,2,2))].">
      <j1 rule="para" parents="28460 28582"/>
    </justification>
  </clause>

  <clause id="28586">
    <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(134,a,28584,a(flip),b,1402,a)].">
      <j1 rule="hyper" parents="134 28584 1402"/>
    </justification>
  </clause>

  <clause id="28587">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * a(z,u,w)) = L(a(z,u,w),y,x) * v5
    ]]></literal>
    <justification jstring="[hyper(21161,a,28586,a)].">
      <j1 rule="hyper" parents="21161 28586"/>
    </justification>
  </clause>

  <clause id="28588">
    <literal><![CDATA[
      1 * ((x * (R(x,y,z) \ x)) \ 1) = (R(x,y,z) \ x) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(24387(a,1),28575(a,1,1))].">
      <j1 rule="para" parents="24387 28575"/>
    </justification>
  </clause>

  <clause id="28589">
    <literal><![CDATA[
      (x * (R(x,y,z) \ x)) \ 1 = x \ (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(126,a,28588,a,b,3712,a(flip))].">
      <j1 rule="hyper" parents="126 28588 3712"/>
    </justification>
  </clause>

  <clause id="28591">
    <literal><![CDATA[
      (L(a(x,y,z) \ 1,u,w * u) * w) \ (a(x,y,z) \ w) = a(u \ w,u,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(27282(a,1),28377(a,1,1,1))].">
      <j1 rule="para" parents="27282 28377"/>
    </justification>
  </clause>

  <clause id="28592">
    <literal><![CDATA[
      (L(a(x,y,z),u,w * u) \ w) \ (a(x,y,z) \ w) = a(u \ w,u,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(28347(a,1),28591(a,1,1))].">
      <j1 rule="para" parents="28347 28591"/>
    </justification>
  </clause>

  <clause id="28593">
    <literal><![CDATA[
      x \ (L(a(y,z,u),w,x * w) * (a(y,z,u) \ x)) = a(w \ x,w,a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(27940,a,28592,a)].">
      <j1 rule="hyper" parents="27940 28592"/>
    </justification>
  </clause>

  <clause id="28594">
    <literal><![CDATA[
      x \ (x * a(x * y,y,a(z,u,w))) = a(y \ x,y,a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(28584(a,1),28593(a,1,2))].">
      <j1 rule="para" parents="28584 28593"/>
    </justification>
  </clause>

  <clause id="28595">
    <literal><![CDATA[
      a(x \ y,x,a(z,u,w) \ 1) = a(y * x,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(358,a,28594,a)].">
      <j1 rule="hyper" parents="358 28594"/>
    </justification>
  </clause>

  <clause id="28596">
    <literal><![CDATA[
      a(x \ y,x,a(z,u,w)) = a(y * x,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(14931,a,28595,a)].">
      <j1 rule="hyper" parents="14931 28595"/>
    </justification>
  </clause>

  <clause id="28598">
    <literal><![CDATA[
      a(x * y,y,a(z,u,w)) * x = a(z,u,w) * ((x / y) * (a(z,u,w) \ y))
    ]]></literal>
    <justification jstring="[para(28596(a,1),28535(a,1,1))].">
      <j1 rule="para" parents="28596 28535"/>
    </justification>
  </clause>

  <clause id="28599">
    <literal><![CDATA[
      a(x * y,x,a(z,u,w)) * y = a(z,u,w) * ((y / x) * (a(z,u,w) \ x))
    ]]></literal>
    <justification jstring="[para(18294(a,1),28598(a,1,1))].">
      <j1 rule="para" parents="18294 28598"/>
    </justification>
  </clause>

  <clause id="28600">
    <literal><![CDATA[
      a(x,y \ (z \ (u * (a(w,v5,w) \ (z * y)))),v6) = a(x,L(u,y,z),v6)
    ]]></literal>
    <justification jstring="[hyper(28505,a,12432,a)].">
      <j1 rule="hyper" parents="28505 12432"/>
    </justification>
  </clause>

  <clause id="28601">
    <literal><![CDATA[
      a(x,y \ (z \ (u * (z * (a(w,v5,w) \ y)))),v6) = a(x,L(u,y,z),v6)
    ]]></literal>
    <justification jstring="[para(11881(a,1),28600(a,1,2,2,2,2))].">
      <j1 rule="para" parents="11881 28600"/>
    </justification>
  </clause>

  <clause id="28602">
    <literal><![CDATA[
      a(x,y,z * (L(L(z,u,w),u,w) \ (v5 \ (a(w,u,z) \ v6)))) = a(x,y,v5 \ (v6 * a(w,u,z)))
    ]]></literal>
    <justification jstring="[para(28495(a,1),28543(a,1,3))].">
      <j1 rule="para" parents="28495 28543"/>
    </justification>
  </clause>

  <clause id="28603">
    <literal><![CDATA[
      R(x,y * (L(L(y,z,u),z,u) \ ((a(u,z,y) \ w) * v5)),v6) = R(x,(a(u,z,y) * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(28495(a,1),28572(a,1,2))].">
      <j1 rule="para" parents="28495 28572"/>
    </justification>
  </clause>

  <clause id="28604">
    <literal><![CDATA[
      a(x,y,z * (z \ (u \ (a(w,v5,z) \ v6)))) = a(x,y,u \ (v6 * a(w,v5,z)))
    ]]></literal>
    <justification jstring="[hyper(27426,a,28602,a)].">
      <j1 rule="hyper" parents="27426 28602"/>
    </justification>
  </clause>

  <clause id="28605">
    <literal><![CDATA[
      a(x,y,z \ (a(u,w,v5) \ v6)) = a(x,y,z \ (v6 * a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(10(a,1),28604(a,1,3))].">
      <j1 rule="para" parents="10 28604"/>
    </justification>
  </clause>

  <clause id="28607">
    <literal><![CDATA[
      a(x,y,z \ (u * a(w,w,u))) = a(x,y,z \ L(u,w,w))
    ]]></literal>
    <justification jstring="[para(14601(a,1),28605(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="14601 28605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28608">
    <literal><![CDATA[
      a(x,y,z \ (u \ (u \ w))) = a(x,y,z \ L(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(24769,a,28607,a)].">
      <j1 rule="hyper" parents="24769 28607"/>
    </justification>
  </clause>

  <clause id="28609">
    <literal><![CDATA[
      R(x,y * (y \ ((a(z,u,y) \ w) * v5)),v6) = R(x,(a(z,u,y) * w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(27434,a,28603,a)].">
      <j1 rule="hyper" parents="27434 28603"/>
    </justification>
  </clause>

  <clause id="28611">
    <literal><![CDATA[
      R(x,(a(y,z,u) \ w) * v5,v6) = R(x,(a(y,z,u) * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(10(a,1),28609(a,1,2))].">
      <j1 rule="para" parents="10 28609"/>
    </justification>
  </clause>

  <clause id="28613">
    <literal><![CDATA[
      L(x,(a(y,z,u) \ 1) \ w,a(y,z,u) \ 1) = w \ (a(y,z,u) \ ((a(y,z,u) * w) * x))
    ]]></literal>
    <justification jstring="[para(28342(a,1),28355(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="28342 28355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28614">
    <literal><![CDATA[
      L(x,(a(y,z,u) \ 1) \ w,a(y,z,u) \ 1) = L(1 / x,w,a(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,25971,a(flip),b,28613,a),flip(a)].">
      <j1 rule="hyper" parents="347 25971 28613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28615">
    <literal><![CDATA[
      L(x,(a(y,z,u) \ 1) \ w,a(y,z,u) \ 1) = L((1 / x) \ 1,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,26373,a,b,28614,a),flip(a)].">
      <j1 rule="hyper" parents="347 26373 28614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28616">
    <literal><![CDATA[
      L(x,(a(y,z,u) \ 1) \ w,a(y,z,u) \ 1) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(83(a,1),28615(a,2,1))].">
      <j1 rule="para" parents="83 28615"/>
    </justification>
  </clause>

  <clause id="28617">
    <literal><![CDATA[
      (x * y) / T(a(z,u,w) \ x,a(z,u,w) * y) = (a(z,u,w) \ x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(19937(a,1),28553(a,1,2))].">
      <j1 rule="para" parents="19937 28553"/>
    </justification>
  </clause>

  <clause id="28619">
    <literal><![CDATA[
      (x * y) / T(a(z,u,w) \ x,y) = (a(z,u,w) \ x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(23048(a,1),28617(a,1,2))].">
      <j1 rule="para" parents="23048 28617"/>
    </justification>
  </clause>

  <clause id="28620">
    <literal><![CDATA[
      (x * y) / ((a(z,u,w) \ 1) * y) = (a(z,u,w) \ y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,28506,a(flip),b,28619,a)].">
      <j1 rule="hyper" parents="63 28506 28619"/>
    </justification>
  </clause>

  <clause id="28622">
    <literal><![CDATA[
      (x * y) / (a(z,u,w) \ y) = (a(z,u,w) \ y) \ (y * x)
    ]]></literal>
    <justification jstring="[para(28341(a,1),28620(a,1,2))].">
      <j1 rule="para" parents="28341 28620"/>
    </justification>
  </clause>

  <clause id="28623">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (a(y,z,u) \ w) = (a(y,z,u) \ x) * w
    ]]></literal>
    <justification jstring="[hyper(133,a,28544,a(flip),b,28622,a)].">
      <j1 rule="hyper" parents="133 28544 28622"/>
    </justification>
  </clause>

  <clause id="28624">
    <literal><![CDATA[
      x \ ((a(y,z,u) \ w) \ (w * (a(y,z,u) \ x))) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(28622(a,1),28529(a,1,2))].">
      <j1 rule="para" parents="28622 28529"/>
    </justification>
  </clause>

  <clause id="28625">
    <literal><![CDATA[
      x \ L(x,a(y,z,u),w) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(28544(a,1),28624(a,1,2))].">
      <j1 rule="para" parents="28544 28624"/>
    </justification>
  </clause>

  <clause id="28627">
    <literal><![CDATA[
      x * a(x,a(y,z,u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(150,a,28625,a)].">
      <j1 rule="hyper" parents="150 28625"/>
    </justification>
  </clause>

  <clause id="28631">
    <literal><![CDATA[
      x \ L(x,a(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,a(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(28627(a,1),356(a,1,2))].">
      <j1 rule="para" parents="28627 356"/>
    </justification>
  </clause>

  <clause id="28632">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,z) * ((u * a(x,y,z)) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      (a(x,y,z) \ u) \ w = v5
    ]]></literal>
    <justification jstring="[para(28409(a,2),28340(a,1))].">
      <j1 rule="para" parents="28409 28340"/>
    </justification>
  </clause>

  <clause id="28633">
    <literal><![CDATA[
      x * (L(L(x,y,z),y,z) \ ((u * a(z,y,x)) \ w)) = (a(z,y,x) \ u) \ w
    ]]></literal>
    <justification jstring="[hyper(28632,a,28496,a),flip(a)].">
      <j1 rule="hyper" parents="28632 28496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28634">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z),w) != v5
    ]]></literal>
    <literal><![CDATA[
      (a(x,y,z) \ w) \ (w * u) = v5
    ]]></literal>
    <justification jstring="[para(3373(a,1),28632(a,1))].">
      <j1 rule="para" parents="3373 28632"/>
    </justification>
  </clause>

  <clause id="28635">
    <literal><![CDATA[
      L((a(x,y,z) \ (y \ 1)) \ (a(x,y \ 1,z) \ u),y,y) = L(y * u,y \ 1,a(x,y \ 1,z))
    ]]></literal>
    <justification jstring="[para(14950(a,1),28494(a,1,1,1,1))].">
      <j1 rule="para" parents="14950 28494"/>
    </justification>
  </clause>

  <clause id="28636">
    <literal><![CDATA[
      L((x \ (a(y,x,z) \ 1)) \ (a(y,x \ 1,z) \ u),x,x) = L(x * u,x \ 1,a(y,x \ 1,z))
    ]]></literal>
    <justification jstring="[para(26576(a,1),28635(a,1,1,1))].">
      <j1 rule="para" parents="26576 28635"/>
    </justification>
  </clause>

  <clause id="28637">
    <literal><![CDATA[
      L((x \ (a(y,x,z) \ 1)) \ (a(y,x,z) \ u),x,x) = L(x * u,x \ 1,a(y,x \ 1,z))
    ]]></literal>
    <justification jstring="[para(14950(a,1),28636(a,1,1,2,1))].">
      <j1 rule="para" parents="14950 28636"/>
    </justification>
  </clause>

  <clause id="28638">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(a(x,y,z) * w,a(x,y,z),1) = (u * a(x,y,z)) * (a(x,y,z) \ (1 * w))
    ]]></literal>
    <justification jstring="[para(28348(a,1),28554(a,1,1))].">
      <j1 rule="para" parents="28348 28554"/>
    </justification>
  </clause>

  <clause id="28639">
    <literal><![CDATA[
      (x * a(y,z,u)) * (a(y,z,u) \ (1 * w)) = (a(y,z,u) \ x) * (a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[para(398(a,1),28638(a,1,2)),flip(a)].">
      <j1 rule="para" parents="398 28638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28640">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (a(x,y,z) * w) = (u * a(x,y,z)) * (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(7(a,1),28639(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 28639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28642">
    <literal><![CDATA[
      (x / y) \ ((a(z,u,w) \ ((a(z,u,w) * x) * y)) / y) = L(y,(a(z,u,w) \ 1) \ x,a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(28342(a,1),28374(a,1,2,1,2,1))].">
      <j1 rule="para" parents="28342 28374"/>
    </justification>
  </clause>

  <clause id="28643">
    <literal><![CDATA[
      (x / y) \ ((a(z,u,w) * ((a(z,u,w) \ x) * y)) / y) = L(y,(a(z,u,w) \ 1) \ x,a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(28569(a,1),28642(a,1,2,1))].">
      <j1 rule="para" parents="28569 28642"/>
    </justification>
  </clause>

  <clause id="28644">
    <literal><![CDATA[
      (x / y) \ (y \ ((y * (a(z,u,w) \ x)) * a(z,u,w))) = L(y,(a(z,u,w) \ 1) \ x,a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(23244(a,1),28643(a,1,2))].">
      <j1 rule="para" parents="23244 28643"/>
    </justification>
  </clause>

  <clause id="28645">
    <literal><![CDATA[
      (x / y) \ (y \ (a(z,u,w) * (y * (a(z,u,w) \ x)))) = L(y,(a(z,u,w) \ 1) \ x,a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(19985(a,2),28644(a,1,2,2))].">
      <j1 rule="para" parents="19985 28644"/>
    </justification>
  </clause>

  <clause id="28646">
    <literal><![CDATA[
      (x / y) \ L(L(x,a(z,u,w),y),y,a(z,u,w)) = L(y,(a(z,u,w) \ 1) \ x,a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(28536(a,1),28645(a,1,2))].">
      <j1 rule="para" parents="28536 28645"/>
    </justification>
  </clause>

  <clause id="28647">
    <literal><![CDATA[
      (x / y) \ L(L(x,a(z,u,w),y),y,a(z,u,w)) = L(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,28616,a(flip),b,28646,a),flip(a)].">
      <j1 rule="hyper" parents="347 28616 28646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28648">
    <literal><![CDATA[
      L(x,a(y,z,u) \ w,a(y,z,u)) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,28545,a(flip),b,28647,a)].">
      <j1 rule="hyper" parents="63 28545 28647"/>
    </justification>
  </clause>

  <clause id="28650">
    <literal><![CDATA[
      L(x,y * a(z,u,w),a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(28648(a,1),10234(a,1))].">
      <j1 rule="para" parents="28648 10234"/>
    </justification>
  </clause>

  <clause id="28651">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)) \ x,x,y) = a(x,a(z,u,w) \ y,a(z,u,w)) \ 1
    ]]></literal>
    <justification jstring="[para(28648(a,1),27503(a,1,1,1))].">
      <j1 rule="para" parents="28648 27503"/>
    </justification>
  </clause>

  <clause id="28652">
    <literal><![CDATA[
      a(x,a(y,z,u) \ w,a(y,z,u)) \ 1 = a(a(y,z,u),w,x)
    ]]></literal>
    <justification jstring="[hyper(26184,a,28651,a),flip(a)].">
      <j1 rule="hyper" parents="26184 28651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28653">
    <literal><![CDATA[
      a(x,a(y,z,u) * w,a(y,z,u)) \ 1 = a(a(y,z,u),w,x)
    ]]></literal>
    <justification jstring="[para(28361(a,1),28652(a,1,1))].">
      <j1 rule="para" parents="28361 28652"/>
    </justification>
  </clause>

  <clause id="28654">
    <literal><![CDATA[
      a(x,a(y,z,u) * w,a(y,z,u)) = a(a(y,z,u),w,x)
    ]]></literal>
    <justification jstring="[hyper(26335,a,28653,a)].">
      <j1 rule="hyper" parents="26335 28653"/>
    </justification>
  </clause>

  <clause id="28655">
    <literal><![CDATA[
      L(L(a(x,y,z),a(x,y,z),u),u * a(x,y,z),w) = L((a(x,y,z) \ 1) * (a(x,y,z) * a(x,y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,1390,a,b,28488,a),flip(a)].">
      <j1 rule="hyper" parents="347 1390 28488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28656">
    <literal><![CDATA[
      L(L(a(x,y,z),a(x,y,z),u),u * a(x,y,z),w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(240(a,1),28655(a,2,1))].">
      <j1 rule="para" parents="240 28655"/>
    </justification>
  </clause>

  <clause id="28657">
    <literal><![CDATA[
      L(a(x,y,z),u * a(x,y,z),w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(28453(a,1),28656(a,1,1))].">
      <j1 rule="para" parents="28453 28656"/>
    </justification>
  </clause>

  <clause id="28659">
    <literal><![CDATA[
      ((a(x,y,z) * u) \ w) * ((1 / a(x,y,z)) \ a(x,y,z)) = (a(x,y,z) \ u) \ w
    ]]></literal>
    <justification jstring="[hyper(28632,a,28433,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="28632 28433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28660">
    <literal><![CDATA[
      ((a(x,y,z) * u) \ w) * ((a(x,y,z) \ 1) \ a(x,y,z)) = (a(x,y,z) \ u) \ w
    ]]></literal>
    <justification jstring="[para(12593(a,1),28659(a,1,2,1))].">
      <j1 rule="para" parents="12593 28659"/>
    </justification>
  </clause>

  <clause id="28661">
    <literal><![CDATA[
      ((a(x,y,z) * u) \ w) * (a(x,y,z) * a(x,y,z)) = (a(x,y,z) \ u) \ w
    ]]></literal>
    <justification jstring="[para(301(a,1),28660(a,1,2))].">
      <j1 rule="para" parents="301 28660"/>
    </justification>
  </clause>

  <clause id="28662">
    <literal><![CDATA[
      L(x,y,(a(z,u,w) \ v5) \ v6) = L(x,y,(a(z,u,w) * v5) \ v6)
    ]]></literal>
    <justification jstring="[para(28661(a,1),27888(a,1,3))].">
      <j1 rule="para" parents="28661 27888"/>
    </justification>
  </clause>

  <clause id="28663">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ ((u * (w * a(x,y,z))) \ (u * w)) = a(u,w * a(x,y,z),a(x,y,z)) * 1
    ]]></literal>
    <justification jstring="[para(28430(a,1),28449(a,1,1))].">
      <j1 rule="para" parents="28430 28449"/>
    </justification>
  </clause>

  <clause id="28665">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ L(a(x,y,z) \ 1,u,w) = a(w,u * a(x,y,z),a(x,y,z)) * 1
    ]]></literal>
    <justification jstring="[para(28481(a,1),28663(a,1,2))].">
      <j1 rule="para" parents="28481 28663"/>
    </justification>
  </clause>

  <clause id="28666">
    <literal><![CDATA[
      a(x,y * a(z,u,w),a(z,u,w)) * 1 = a(z,u,w) \ L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(3385,a,28665,a),flip(a)].">
      <j1 rule="hyper" parents="3385 28665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28667">
    <literal><![CDATA[
      a(x,y * a(z,u,w),a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(130,a,28666,a,b,28460,a(flip))].">
      <j1 rule="hyper" parents="130 28666 28460"/>
    </justification>
  </clause>

  <clause id="28668">
    <literal><![CDATA[
      L(a(x,y,z) * L(u \ (a(x,y,z) \ u),w,v5),a(x,y,z),u) = a(v5,w,(a(x,y,z) \ w) * w) \ 1
    ]]></literal>
    <justification jstring="[para(19984(a,1),28550(a,2,1,3,1,1))].">
      <j1 rule="para" parents="19984 28550"/>
    </justification>
  </clause>

  <clause id="28669">
    <literal><![CDATA[
      L(a(x,y,z) * L(u \ (a(x,y,z) \ u),w,v5),a(x,y,z),u) = a(v5,w,w * (a(x,y,z) \ w)) \ 1
    ]]></literal>
    <justification jstring="[hyper(126,a,28416,a,b,28668,a),flip(a)].">
      <j1 rule="hyper" parents="126 28416 28668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28671">
    <literal><![CDATA[
      L(a(x,y,z) * L(u \ (a(x,y,z) \ u),w,v5),a(x,y,z),u) = a(v5,w,w * (a(x,y,z) * w)) \ 1
    ]]></literal>
    <justification jstring="[para(28364(a,1),28669(a,2,1))].">
      <j1 rule="para" parents="28364 28669"/>
    </justification>
  </clause>

  <clause id="28672">
    <literal><![CDATA[
      L(a(x,y,z) * L(u \ (a(x,y,z) \ u),w,v5),a(x,y,z),u) = a(v5,w,L(a(x,y,z),w,w)) \ 1
    ]]></literal>
    <justification jstring="[para(24286(a,1),28671(a,2,1))].">
      <j1 rule="para" parents="24286 28671"/>
    </justification>
  </clause>

  <clause id="28673">
    <literal><![CDATA[
      L(a(x,y,z) * L(u \ (a(x,y,z) \ u),w,v5),a(x,y,z),u) = a(v5,w,a(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,27233,a(flip),b,28672,a),flip(a)].">
      <j1 rule="hyper" parents="347 27233 28672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28674">
    <literal><![CDATA[
      L(a(x,y,z) * L(u \ (a(x,y,z) \ u),w,v5),a(x,y,z),u) = a(v5,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,26334,a(flip),b,28673,a),flip(a)].">
      <j1 rule="hyper" parents="347 26334 28673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28675">
    <literal><![CDATA[
      L(a(x,y,z) * L(a(x,y,z) \ 1,u,w),a(x,y,z),v5) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(28350(a,1),28674(a,1,1,2,1))].">
      <j1 rule="para" parents="28350 28674"/>
    </justification>
  </clause>

  <clause id="28676">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w) \ a(x,y,z),a(x,y,z),v5) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(26289(a,1),28675(a,1,1))].">
      <j1 rule="para" parents="26289 28675"/>
    </justification>
  </clause>

  <clause id="28678">
    <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(28676(a,1),27133(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28676 27133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28679">
    <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(1424,a,28678,a),flip(a)].">
      <j1 rule="hyper" parents="1424 28678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28680">
    <literal><![CDATA[
      a(x,y,z) \ (a(u,w,a(x,y,z)) * v5) = L(a(x,y,z),w,u) \ v5
    ]]></literal>
    <justification jstring="[hyper(128,a,19985,a,b,28678,a)].">
      <j1 rule="hyper" parents="128 19985 28678"/>
    </justification>
  </clause>

  <clause id="28681">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * v5) \ (v5 * a(x,y,z)) = v5 \ (v5 * a(w,u,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(28678(a,1),26829(a,2,2))].">
      <j1 rule="para" parents="28678 26829"/>
    </justification>
  </clause>

  <clause id="28682">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(a(x,y,z),w,v5) = L(a(x,y,z),w,v5) \ u
    ]]></literal>
    <justification jstring="[hyper(26640,a,28679,a)].">
      <j1 rule="hyper" parents="26640 28679"/>
    </justification>
  </clause>

  <clause id="28683">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ a(z,y,x) = a(x,y,z) \ L(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(28463(a,1),28680(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28463 28680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28684">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * v5) \ (v5 * a(x,y,z)) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,9,a(flip),b,28681,a),flip(a)].">
      <j1 rule="hyper" parents="347 9 28681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28686">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)),a(x,y,a(z,u,w)),y) \ ((v5 * (y * a(x,y,a(z,u,w)))) \ (v5 * y)) = a(v5,L(L(y,a(w,u,z),x),x,a(w,u,z)),a(x,y,a(z,u,w))) \ 1
    ]]></literal>
    <justification jstring="[para(26334(a,1),28559(a,1,1,1))].">
      <j1 rule="para" parents="26334 28559"/>
    </justification>
  </clause>

  <clause id="28687">
    <literal><![CDATA[
      a(x,L(L(y,a(z,u,w),v5),v5,a(z,u,w)),a(v5,y,a(w,u,z))) \ 1 = a(v5,y,a(w,u,z)) \ ((x * (y * a(v5,y,a(w,u,z)))) \ (x * y))
    ]]></literal>
    <justification jstring="[para(26568(a,1),28686(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26568 28686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28689">
    <literal><![CDATA[
      a(x,L(L(y,a(z,u,w),v5),v5,a(z,u,w)),a(v5,y,a(w,u,z))) \ 1 = a(v5,y,a(w,u,z)) \ L(a(v5,y,a(w,u,z)) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(28481(a,1),28687(a,2,2))].">
      <j1 rule="para" parents="28481 28687"/>
    </justification>
  </clause>

  <clause id="28690">
    <literal><![CDATA[
      a(x,L(L(y,a(z,u,w),v5),v5,a(z,u,w)),a(v5,y,a(w,u,z))) \ 1 = a(v5,y,a(w,u,z)) \ L(a(v5,y,a(w,u,z)),y,x)
    ]]></literal>
    <justification jstring="[para(26334(a,1),28689(a,2,2,1))].">
      <j1 rule="para" parents="26334 28689"/>
    </justification>
  </clause>

  <clause id="28691">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ R((a(z,u,w) \ K(x,y)) \ v5,a(z,u,w) \ K(x,y),v6 * (a(z,u,w) \ K(x,y)))) = ((v5 * (a(z,u,w) * (K(y,x) * v6))) / v6) * (a(z,u,w) \ K(x,y))
    ]]></literal>
    <justification jstring="[para(28396(a,1),28480(a,2,1,1,2))].">
      <j1 rule="para" parents="28396 28480"/>
    </justification>
  </clause>

  <clause id="28692">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ R((a(z,u,w) \ K(x,y)) \ v5,a(z,u,w) \ K(x,y),v6 * (a(z,u,w) \ K(x,y)))) = (((v5 * (a(z,u,w) * v6)) / v6) * K(y,x)) * (a(z,u,w) \ K(x,y))
    ]]></literal>
    <justification jstring="[para(22916(a,1),28691(a,2,1))].">
      <j1 rule="para" parents="22916 28691"/>
    </justification>
  </clause>

  <clause id="28693">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ R((a(z,u,w) \ K(x,y)) \ v5,a(z,u,w) \ K(x,y),v6 * (a(z,u,w) \ K(x,y)))) = ((v6 \ ((v6 * a(z,u,w)) * v5)) * K(y,x)) * (a(z,u,w) \ K(x,y))
    ]]></literal>
    <justification jstring="[para(23293(a,1),28692(a,2,1,1))].">
      <j1 rule="para" parents="23293 28692"/>
    </justification>
  </clause>

  <clause id="28694">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ R((a(z,u,w) \ K(x,y)) \ v5,a(z,u,w) \ K(x,y),v6 * (a(z,u,w) \ K(x,y)))) = (v6 \ ((v6 * a(z,u,w)) * v5)) * (K(y,x) * (a(z,u,w) \ K(x,y)))
    ]]></literal>
    <justification jstring="[hyper(347,a,20151,a(flip),b,28693,a),flip(a)].">
      <j1 rule="hyper" parents="347 20151 28693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28695">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ R((a(z,u,w) \ K(x,y)) \ v5,a(z,u,w) \ K(x,y),v6 * (a(z,u,w) \ K(x,y)))) = (v6 \ ((v6 * a(z,u,w)) * v5)) * T(a(z,u,w) \ 1,K(x,y))
    ]]></literal>
    <justification jstring="[para(13012(a,1),28694(a,2,2))].">
      <j1 rule="para" parents="13012 28694"/>
    </justification>
  </clause>

  <clause id="28696">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ R((a(z,u,w) \ K(x,y)) \ v5,a(z,u,w) \ K(x,y),v6 * (a(z,u,w) \ K(x,y)))) = (v6 \ ((v6 * a(z,u,w)) * v5)) * (a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(20087(a,1),28695(a,2,2))].">
      <j1 rule="para" parents="20087 28695"/>
    </justification>
  </clause>

  <clause id="28697">
    <literal><![CDATA[
      a(x,y,z) \ (u \ ((u * a(x,y,z)) * w)) = K(v5,v6) * (a(x,y,z) \ R((a(x,y,z) \ K(v5,v6)) \ w,a(x,y,z) \ K(v5,v6),u * (a(x,y,z) \ K(v5,v6))))
    ]]></literal>
    <justification jstring="[hyper(347,a,28348,a(flip),b,28696,a)].">
      <j1 rule="hyper" parents="347 28348 28696"/>
    </justification>
  </clause>

  <clause id="28699">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ R((a(z,u,w) \ K(x,y)) \ v5,a(z,u,w) \ K(x,y),v6 * (a(z,u,w) \ K(x,y)))) = L(1 / v5,a(z,u,w),v6) \ 1
    ]]></literal>
    <justification jstring="[hyper(26002,a,28697,a),flip(a)].">
      <j1 rule="hyper" parents="26002 28697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28700">
    <literal><![CDATA[
      L(x,((y \ 1) * ((y \ 1) \ (L(y,z,u) \ 1))) \ y,(y \ 1) * (L(y \ 1,z,u) \ (y \ 1))) = (y \ 1) * (L(y \ 1,z,u) \ ((((y \ 1) * (L(y \ 1,z,u) \ (y \ 1))) \ (y \ 1)) * x))
    ]]></literal>
    <justification jstring="[para(3544(a,1),27062(a,1,2,1,2))].">
      <j1 rule="para" parents="3544 27062"/>
    </justification>
  </clause>

  <clause id="28701">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ ((((x \ 1) * (L(x \ 1,y,z) \ (x \ 1))) \ (x \ 1)) * u)) = L(u,(L(x,y,z) \ 1) \ x,(x \ 1) * (L(x \ 1,y,z) \ (x \ 1)))
    ]]></literal>
    <justification jstring="[para(10(a,1),28700(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 28700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28703">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ ((((x \ 1) * (L(x \ 1,y,z) \ (x \ 1))) \ (x \ 1)) * u)) = L(u,x * L(x,y,z),(x \ 1) * (L(x \ 1,y,z) \ (x \ 1)))
    ]]></literal>
    <justification jstring="[para(21419(a,1),28701(a,2,2))].">
      <j1 rule="para" parents="21419 28701"/>
    </justification>
  </clause>

  <clause id="28704">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ ((((x \ 1) * (L(x \ 1,y,z) \ (x \ 1))) \ (x \ 1)) * u)) = L(u,x * L(x,y,z),(x \ 1) * ((x \ 1) \ (L(x,y,z) \ 1)))
    ]]></literal>
    <justification jstring="[para(3544(a,1),28703(a,2,3,2))].">
      <j1 rule="para" parents="3544 28703"/>
    </justification>
  </clause>

  <clause id="28705">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ ((((x \ 1) * (L(x \ 1,y,z) \ (x \ 1))) \ (x \ 1)) * u)) = L(u,x * L(x,y,z),L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),28704(a,2,3))].">
      <j1 rule="para" parents="10 28704"/>
    </justification>
  </clause>

  <clause id="28706">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ ((((x \ 1) * (L(x \ 1,y,z) \ (x \ 1))) \ (x \ 1)) * u)) = L(u,x * L(x,y,z),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,26255,a(flip),b,28705,a),flip(a)].">
      <j1 rule="hyper" parents="347 26255 28705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28708">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ ((((x \ 1) * ((x \ 1) \ (L(x,y,z) \ 1))) \ (x \ 1)) * u)) = L(u,x * L(x,y,z),L(x,y,z))
    ]]></literal>
    <justification jstring="[para(3544(a,1),28706(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="3544 28706"/>
    </justification>
  </clause>

  <clause id="28709">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ (((L(x,y,z) \ 1) \ (x \ 1)) * u)) = L(u,x * L(x,y,z),L(x,y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),28708(a,1,2,2,1,1))].">
      <j1 rule="para" parents="10 28708"/>
    </justification>
  </clause>

  <clause id="28711">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) \ ((x \ L(x,y,z)) * u)) = L(u,x * L(x,y,z),L(x,y,z))
    ]]></literal>
    <justification jstring="[para(4617(a,1),28709(a,1,2,2,1))].">
      <j1 rule="para" parents="4617 28709"/>
    </justification>
  </clause>

  <clause id="28712">
    <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(63,a,3439,a(flip),b,28711,a)].">
      <j1 rule="hyper" parents="63 3439 28711"/>
    </justification>
  </clause>

  <clause id="28713">
    <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(63,a,3651,a(flip),b,28712,a),flip(a)].">
      <j1 rule="hyper" parents="63 3651 28712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28714">
    <literal><![CDATA[
      L(x,L(y,z,u),L(y,z,u) \ L(L(y,z,u),z,u)) = L(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,26103,a,b,28713,a)].">
      <j1 rule="hyper" parents="63 26103 28713"/>
    </justification>
  </clause>

  <clause id="28715">
    <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(63,a,25812,a(flip),b,28713,a),flip(a)].">
      <j1 rule="hyper" parents="63 25812 28713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28716">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) \ (x * u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,22744,a(flip),b,28715,a)].">
      <j1 rule="hyper" parents="63 22744 28715"/>
    </justification>
  </clause>

  <clause id="28717">
    <literal><![CDATA[
      L(L(x,y,z) \ u,x,x \ L(x,y,z)) = (x \ u) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,27481,a(flip),b,28714,a),flip(a)].">
      <j1 rule="hyper" parents="63 27481 28714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28718">
    <literal><![CDATA[
      1 / (T(x,y) \ (((z \ ((z * x) * u)) / u) \ T(x,y))) = ((a(z,x,u) \ 1) \ x) * a(((z \ ((z * x) * u)) / u) \ T(x,y),(z \ ((z * x) * u)) / u,(z \ ((z * x) * u)) / u)
    ]]></literal>
    <justification jstring="[para(16990(a,1),26587(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16990 26587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28720">
    <literal><![CDATA[
      1 / (T(x,y) \ (((z \ ((z * x) * u)) / u) \ T(x,y))) = (x * a(z,x,u)) * a(((z \ ((z * x) * u)) / u) \ T(x,y),(z \ ((z * x) * u)) / u,(z \ ((z * x) * u)) / u)
    ]]></literal>
    <justification jstring="[para(26553(a,1),28718(a,2,1))].">
      <j1 rule="para" parents="26553 28718"/>
    </justification>
  </clause>

  <clause id="28721">
    <literal><![CDATA[
      1 / (T(x,y) \ (((z \ ((z * x) * u)) / u) \ T(x,y))) = (x * a(z,x,u)) * a(a(z,x,u) \ K(x,y),(z \ ((z * x) * u)) / u,(z \ ((z * x) * u)) / u)
    ]]></literal>
    <justification jstring="[para(26581(a,1),28720(a,2,2,1))].">
      <j1 rule="para" parents="26581 28720"/>
    </justification>
  </clause>

  <clause id="28722">
    <literal><![CDATA[
      1 / (T(x,y) \ (((z \ ((z * x) * u)) / u) \ T(x,y))) = (x * a(z,x,u)) * a(a(z,x,u) \ K(x,y),(z \ ((z * x) * u)) / u,u \ (z \ ((z * x) * u)))
    ]]></literal>
    <justification jstring="[para(24071(a,1),28721(a,2,2))].">
      <j1 rule="para" parents="24071 28721"/>
    </justification>
  </clause>

  <clause id="28723">
    <literal><![CDATA[
      1 / (T(x,y) \ (((z \ ((z * x) * u)) / u) \ T(x,y))) = (x * a(z,x,u)) * a(a(z,x,u) \ K(x,y),(z \ ((z * x) * u)) / u,L(L(x,u,z),z,u))
    ]]></literal>
    <justification jstring="[para(25697(a,1),28722(a,2,2))].">
      <j1 rule="para" parents="25697 28722"/>
    </justification>
  </clause>

  <clause id="28724">
    <literal><![CDATA[
      1 / (T(x,y) \ (((z \ ((z * x) * u)) / u) \ T(x,y))) = (x * a(z,x,u)) * a(a(z,x,u) \ K(x,y),u \ (z \ ((z * x) * u)),L(L(x,u,z),z,u))
    ]]></literal>
    <justification jstring="[para(24023(a,1),28723(a,2,2))].">
      <j1 rule="para" parents="24023 28723"/>
    </justification>
  </clause>

  <clause id="28725">
    <literal><![CDATA[
      1 / (T(x,y) \ (((z \ ((z * x) * u)) / u) \ T(x,y))) = (x * a(z,x,u)) * a(a(z,x,u) \ K(x,y),L(L(x,z,u),u,z),L(L(x,u,z),z,u))
    ]]></literal>
    <justification jstring="[para(26080(a,1),28724(a,2,2))].">
      <j1 rule="para" parents="26080 28724"/>
    </justification>
  </clause>

  <clause id="28726">
    <literal><![CDATA[
      1 / (T(x,y) \ (((z \ ((z * x) * u)) / u) \ T(x,y))) = (x * a(z,x,u)) * a(a(z,x,u) \ K(x,y),x,x)
    ]]></literal>
    <justification jstring="[para(27524(a,1),28725(a,2,2))].">
      <j1 rule="para" parents="27524 28725"/>
    </justification>
  </clause>

  <clause id="28727">
    <literal><![CDATA[
      1 / (T(x,y) \ (((z \ ((z * x) * u)) / u) \ T(x,y))) = (x * a(z,x,u)) * a(a(z,x,u) \ 1,x,x)
    ]]></literal>
    <justification jstring="[para(23888(a,1),28726(a,2,2))].">
      <j1 rule="para" parents="23888 28726"/>
    </justification>
  </clause>

  <clause id="28730">
    <literal><![CDATA[
      1 / (T(x,y) \ (((z \ ((z * x) * u)) / u) \ T(x,y))) = (x * a(z,x,u)) * a(a(z,x,u),x,x)
    ]]></literal>
    <justification jstring="[para(27951(a,1),28727(a,2,2))].">
      <j1 rule="para" parents="27951 28727"/>
    </justification>
  </clause>

  <clause id="28731">
    <literal><![CDATA[
      1 / (T(x,y) \ (((z \ ((z * x) * u)) / u) \ T(x,y))) = (x * a(z,x,u)) * 1
    ]]></literal>
    <justification jstring="[para(26358(a,1),28730(a,2,2))].">
      <j1 rule="para" parents="26358 28730"/>
    </justification>
  </clause>

  <clause id="28732">
    <literal><![CDATA[
      1 / (T(x,y) \ (((z \ ((z * x) * u)) / u) \ T(x,y))) = x * a(z,x,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,8,a(flip),b,28731,a),flip(a)].">
      <j1 rule="hyper" parents="347 8 28731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28734">
    <literal><![CDATA[
      1 / (T(x,y) \ (a(z,x,u) \ K(x,y))) = x * a(z,x,u)
    ]]></literal>
    <justification jstring="[para(26581(a,1),28732(a,1,2,2))].">
      <j1 rule="para" parents="26581 28732"/>
    </justification>
  </clause>

  <clause id="28735">
    <literal><![CDATA[
      1 / (x \ (a(y,x,z) \ 1)) = x * a(y,x,z)
    ]]></literal>
    <justification jstring="[para(16989(a,1),28734(a,1,2))].">
      <j1 rule="para" parents="16989 28734"/>
    </justification>
  </clause>

  <clause id="28736">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) / y) \ 1 = y * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(22289,a,28735,a)].">
      <j1 rule="hyper" parents="22289 28735"/>
    </justification>
  </clause>

  <clause id="28737">
    <literal><![CDATA[
      (x * a(y,x,z)) \ 1 = x \ (a(y,x,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(214,a,28735,a)].">
      <j1 rule="hyper" parents="214 28735"/>
    </justification>
  </clause>

  <clause id="28738">
    <literal><![CDATA[
      (a(x,y,z) \ (1 / y)) \ 1 = y * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(26711(a,1),28736(a,1,1))].">
      <j1 rule="para" parents="26711 28736"/>
    </justification>
  </clause>

  <clause id="28739">
    <literal><![CDATA[
      L(x,x,a(y,x \ 1,z)) \ a(z,x \ 1,y) = (a(z,x \ 1,y) \ (1 / (x \ 1))) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,27565,a,b,28738,a)].">
      <j1 rule="hyper" parents="347 27565 28738"/>
    </justification>
  </clause>

  <clause id="28740">
    <literal><![CDATA[
      L(((x * a(y,x,z)) \ 1) \ u,a(y,x,z) \ (1 / x),(a(y,x,z) \ (1 / x)) \ 1) = 1 \ (((a(y,x,z) \ (1 / x)) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(28738(a,1),10212(a,1,1,1,1))].">
      <j1 rule="para" parents="28738 10212"/>
    </justification>
  </clause>

  <clause id="28741">
    <literal><![CDATA[
      L(x,x,a(y,x \ 1,z)) \ a(z,x \ 1,y) = (a(z,x,y) \ (1 / (x \ 1))) \ 1
    ]]></literal>
    <justification jstring="[para(14950(a,1),28739(a,2,1,1))].">
      <j1 rule="para" parents="14950 28739"/>
    </justification>
  </clause>

  <clause id="28742">
    <literal><![CDATA[
      L(x,x,a(y,x \ 1,z)) \ a(z,x \ 1,y) = (a(z,x,y) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(80(a,1),28741(a,2,1,2))].">
      <j1 rule="para" parents="80 28741"/>
    </justification>
  </clause>

  <clause id="28743">
    <literal><![CDATA[
      L(x,x,a(y,x,z)) \ a(z,x \ 1,y) = (a(z,x,y) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(14950(a,1),28742(a,1,1,3))].">
      <j1 rule="para" parents="14950 28742"/>
    </justification>
  </clause>

  <clause id="28744">
    <literal><![CDATA[
      (a(x,y,z) \ y) \ 1 = y \ a(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(26355(a,1),28743(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26355 28743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28745">
    <literal><![CDATA[
      (a(x,y,z) \ y) \ 1 = y \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(14950(a,1),28744(a,2,2))].">
      <j1 rule="para" parents="14950 28744"/>
    </justification>
  </clause>

  <clause id="28746">
    <literal><![CDATA[
      (a(x,y,z) / y) \ 1 = a(x,y,z) \ y
    ]]></literal>
    <justification jstring="[hyper(39,a,21966,a,b,28745,a)].">
      <j1 rule="hyper" parents="39 21966 28745"/>
    </justification>
  </clause>

  <clause id="28750">
    <literal><![CDATA[
      L(a(a(x,y,z),u,w) \ u,w,a(x,y,z)) = L(1 / u,a(x,y,z),w) \ 1
    ]]></literal>
    <justification jstring="[para(28746(a,1),28580(a,1,1))].">
      <j1 rule="para" parents="28746 28580"/>
    </justification>
  </clause>

  <clause id="28751">
    <literal><![CDATA[
      L(x * a(a(y,z,u),x,w),w,a(y,z,u)) = L(1 / x,a(y,z,u),w) \ 1
    ]]></literal>
    <justification jstring="[para(26548(a,1),28750(a,1,1))].">
      <j1 rule="para" parents="26548 28750"/>
    </justification>
  </clause>

  <clause id="28752">
    <literal><![CDATA[
      L(1 / x,a(y,z,u),w) \ 1 = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(28565,a,28751,a),flip(a)].">
      <j1 rule="hyper" parents="28565 28751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28753">
    <literal><![CDATA[
      L(1 / x,a(y,z,u),w) \ 1 != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(28751(a,1),28565(a,1))].">
      <j1 rule="para" parents="28751 28565"/>
    </justification>
  </clause>

  <clause id="28754">
    <literal><![CDATA[
      L(1 / x,a(y,z,u),w) \ 1 = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,26497,a,b,28752,a),flip(a)].">
      <j1 rule="hyper" parents="347 26497 28752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28755">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),a(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[para(28752(a,1),25959(a,1,1))].">
      <j1 rule="para" parents="28752 25959"/>
    </justification>
  </clause>

  <clause id="28756">
    <literal><![CDATA[
      L((x * (a(y,z,u) \ 1)) \ w,a(y,z,u),x) = (a(y,z,u) \ 1) \ (x \ w)
    ]]></literal>
    <justification jstring="[hyper(3203,a,28755,a),flip(a)].">
      <j1 rule="hyper" parents="3203 28755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28757">
    <literal><![CDATA[
      L((x * a(y,z,u)) \ w,a(y,z,u),x) = a(y,z,u) \ (x \ w)
    ]]></literal>
    <justification jstring="[hyper(623,a,28755,a),flip(a)].">
      <j1 rule="hyper" parents="623 28755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28758">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),a(u,z,y),w) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,26497,a,b,28755,a)].">
      <j1 rule="hyper" parents="63 26497 28755"/>
    </justification>
  </clause>

  <clause id="28759">
    <literal><![CDATA[
      a(x,y,L(z,a(u,w,v5),v6)) = a(x,y,L(z,a(v5,w,u),v6))
    ]]></literal>
    <justification jstring="[para(28758(a,1),25583(a,1,3,1))].">
      <j1 rule="para" parents="28758 25583"/>
    </justification>
  </clause>

  <clause id="28760">
    <literal><![CDATA[
      (a(x,y,z) \ L(u,a(z,y,x),w)) * w = u * (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(28758(a,1),28623(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28758 28623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28761">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ R((a(z,u,w) \ K(x,y)) \ v5,a(z,u,w) \ K(x,y),v6 * (a(z,u,w) \ K(x,y)))) = L(v5,a(w,u,z),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,28699,a,b,28754,a)].">
      <j1 rule="hyper" parents="63 28699 28754"/>
    </justification>
  </clause>

  <clause id="28762">
    <literal><![CDATA[
      x \ L(x,a(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(u,z,y),w) \ x = v5
    ]]></literal>
    <justification jstring="[para(28754(a,1),3649(a,1,2))].">
      <j1 rule="para" parents="28754 3649"/>
    </justification>
  </clause>

  <clause id="28763">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (x \ v5) = x * (L(x,a(u,z,y),w) \ v5)
    ]]></literal>
    <justification jstring="[para(28754(a,1),27057(a,1,1))].">
      <j1 rule="para" parents="28754 27057"/>
    </justification>
  </clause>

  <clause id="28764">
    <literal><![CDATA[
      L(x,a(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(u,z,y),w) = v5
    ]]></literal>
    <justification jstring="[para(28754(a,1),28753(a,1))].">
      <j1 rule="para" parents="28754 28753"/>
    </justification>
  </clause>

  <clause id="28765">
    <literal><![CDATA[
      L(x,a(y * z,u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,a(w,u,z * y),v5) = v6
    ]]></literal>
    <justification jstring="[para(23896(a,1),28764(a,1,2))].">
      <j1 rule="para" parents="23896 28764"/>
    </justification>
  </clause>

  <clause id="28766">
    <literal><![CDATA[
      L(x,a(y,z,u),w) \ x = a(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(28762,a,28625,a)].">
      <j1 rule="hyper" parents="28762 28625"/>
    </justification>
  </clause>

  <clause id="28767">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ x = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(39,a,19984,a,b,28766,a)].">
      <j1 rule="hyper" parents="39 19984 28766"/>
    </justification>
  </clause>

  <clause id="28768">
    <literal><![CDATA[
      x * a(y,a(z,u,w),x) = L(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(26561,a,28767,a)].">
      <j1 rule="hyper" parents="26561 28767"/>
    </justification>
  </clause>

  <clause id="28769">
    <literal><![CDATA[
      a(x,a(y,z,u),w) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(34,a,28627,a,b,28768,a)].">
      <j1 rule="hyper" parents="34 28627 28768"/>
    </justification>
  </clause>

  <clause id="28770">
    <literal><![CDATA[
      a(x * a(y,z,u),a(y,z,u),w) = a(x,a(y,z,u),w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(34,a,28578,a,b,28768,a),flip(a)].">
      <j1 rule="hyper" parents="34 28578 28768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28771">
    <literal><![CDATA[
      L(x,y,z) * a(u,x,a(x,w,z)) = L(L(x,y,z),a(x,w,z),u)
    ]]></literal>
    <justification jstring="[para(26664(a,1),28768(a,1,2))].">
      <j1 rule="para" parents="26664 28768"/>
    </justification>
  </clause>

  <clause id="28772">
    <literal><![CDATA[
      a(x,a(y,z,u),w) = a(w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(26574,a,28769,a)].">
      <j1 rule="hyper" parents="26574 28769"/>
    </justification>
  </clause>

  <clause id="28773">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * v5 = v5 * a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(134,a,28769,a,b,19974,a),flip(a)].">
      <j1 rule="hyper" parents="134 28769 19974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28775">
    <literal><![CDATA[
      a(x,a(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,a(y,z,u),x) = v5
    ]]></literal>
    <justification jstring="[para(28772(a,1),26574(a,1))].">
      <j1 rule="para" parents="28772 26574"/>
    </justification>
  </clause>

  <clause id="28776">
    <literal><![CDATA[
      a(x,a(y,z,L(u,u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(v5,a(w \ (u \ w),z,y),x) = v6
    ]]></literal>
    <justification jstring="[para(28772(a,1),26582(a,1))].">
      <j1 rule="para" parents="28772 26582"/>
    </justification>
  </clause>

  <clause id="28777">
    <literal><![CDATA[
      (a(x,y,z) \ (a(z,y,x) \ 1)) * u = (a(z,y,x) \ 1) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(28430(a,1),28760(a,1,1,2))].">
      <j1 rule="para" parents="28430 28760"/>
    </justification>
  </clause>

  <clause id="28778">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) * L(y,w,u) = L(L(y,w,u),a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(20479,a,28771,a)].">
      <j1 rule="hyper" parents="20479 28771"/>
    </justification>
  </clause>

  <clause id="28779">
    <literal><![CDATA[
      L(L(x,y,z),a(x,y,z),y) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,26763,a(flip),b,28778,a),flip(a)].">
      <j1 rule="hyper" parents="63 26763 28778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28780">
    <literal><![CDATA[
      L(L(x,y,z),a(z,y,x),y) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(28764,a,28779,a)].">
      <j1 rule="hyper" parents="28764 28779"/>
    </justification>
  </clause>

  <clause id="28781">
    <literal><![CDATA[
      (a(x,y,z) \ z) * (L(a(x,y,z) \ z,a(x,y,z),y) \ (a(x,y,z) \ z)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(25976,a,28780,a)].">
      <j1 rule="hyper" parents="25976 28780"/>
    </justification>
  </clause>

  <clause id="28782">
    <literal><![CDATA[
      a(x * a(y,z,u),a(u,z,y),w) = a(x,a(y,z,u),w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(26574,a,28770,a)].">
      <j1 rule="hyper" parents="26574 28770"/>
    </justification>
  </clause>

  <clause id="28783">
    <literal><![CDATA[
      a(L(L(x,a(y,z,u),w),w,a(y,z,u)),a(a(u,z,y),x,w),v5) = a(x,a(w,x,a(u,z,y)),v5 * a(w,x,a(u,z,y)))
    ]]></literal>
    <justification jstring="[para(28556(a,2),28782(a,1,1))].">
      <j1 rule="para" parents="28556 28782"/>
    </justification>
  </clause>

  <clause id="28784">
    <literal><![CDATA[
      L((a(x,y,z) \ u) \ w,a(x,y,z),u) = (a(x,y,z) \ 1) \ (u \ w)
    ]]></literal>
    <justification jstring="[para(28348(a,1),28756(a,1,1,1))].">
      <j1 rule="para" parents="28348 28756"/>
    </justification>
  </clause>

  <clause id="28785">
    <literal><![CDATA[
      L((a(x,y,z) \ u) \ w,a(x,y,z),u) = a(x,y,z) * (u \ w)
    ]]></literal>
    <justification jstring="[hyper(347,a,28342,a(flip),b,28784,a),flip(a)].">
      <j1 rule="hyper" parents="347 28342 28784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28786">
    <literal><![CDATA[
      L((a(x,y,z) \ u) \ w,a(x,y,z),u) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) * (u \ w) = v5
    ]]></literal>
    <justification jstring="[para(28784(a,2),28353(a,1))].">
      <j1 rule="para" parents="28784 28353"/>
    </justification>
  </clause>

  <clause id="28787">
    <literal><![CDATA[
      L((a(x,y,z) \ u) \ w,a(z,y,x),u) = a(x,y,z) * (u \ w)
    ]]></literal>
    <justification jstring="[hyper(28764,a,28785,a)].">
      <j1 rule="hyper" parents="28764 28785"/>
    </justification>
  </clause>

  <clause id="28788">
    <literal><![CDATA[
      (a(x,y,z) \ a(z,y,x)) \ u = a(x,y,z) * (a(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(28340,a,28787,a)].">
      <j1 rule="hyper" parents="28340 28787"/>
    </justification>
  </clause>

  <clause id="28789">
    <literal><![CDATA[
      a(x,y,L((z * (a(u,w,v5) \ a(v5,w,u))) \ v6,a(u,w,v5) \ a(v5,w,u),z)) = a(x,y,a(u,w,v5) * (a(v5,w,u) \ (z \ v6)))
    ]]></literal>
    <justification jstring="[para(28788(a,1),25586(a,2,3))].">
      <j1 rule="para" parents="28788 25586"/>
    </justification>
  </clause>

  <clause id="28790">
    <literal><![CDATA[
      a(x,y,L((z * (a(u,w,v5) \ a(v5,w,u))) \ v6,z,a(u,w,v5) \ a(v5,w,u))) = a(x,y,z \ (a(u,w,v5) * (a(v5,w,u) \ v6)))
    ]]></literal>
    <justification jstring="[para(28788(a,1),25588(a,2,3,2))].">
      <j1 rule="para" parents="28788 25588"/>
    </justification>
  </clause>

  <clause id="28791">
    <literal><![CDATA[
      L(x,y,z) = (a(z,y,x) \ x) * a(y,a(z,y,x),x \ a(z,y,x))
    ]]></literal>
    <justification jstring="[para(26204(a,1),28781(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26204 28781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28792">
    <literal><![CDATA[
      L(x,y,z) = (a(z,y,x) \ x) * a(y,a(z,y,x),x * a(z,y,x))
    ]]></literal>
    <justification jstring="[para(14991(a,1),28791(a,2,2))].">
      <j1 rule="para" parents="14991 28791"/>
    </justification>
  </clause>

  <clause id="28810">
    <literal><![CDATA[
      L((x \ (a(y,x,z) \ 1)) \ u,a(y,x,z) \ (1 / x),(a(y,x,z) \ (1 / x)) \ 1) = 1 \ (((a(y,x,z) \ (1 / x)) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(28737(a,1),28740(a,1,1,1))].">
      <j1 rule="para" parents="28737 28740"/>
    </justification>
  </clause>

  <clause id="28811">
    <literal><![CDATA[
      a(x,y,L((z * (a(u,w,v5) \ a(v5,w,u))) \ v6,a(u,w,v5) * a(v5,w,u),z)) = a(x,y,a(u,w,v5) * (a(v5,w,u) \ (z \ v6)))
    ]]></literal>
    <justification jstring="[para(28354(a,1),28789(a,1,3))].">
      <j1 rule="para" parents="28354 28789"/>
    </justification>
  </clause>

  <clause id="28812">
    <literal><![CDATA[
      a(x,y,L((z * (a(u,w,v5) \ a(v5,w,u))) \ v6,z,a(v5,w,u) * a(v5,w,u))) = a(x,y,z \ (a(u,w,v5) * (a(v5,w,u) \ v6)))
    ]]></literal>
    <justification jstring="[para(28421(a,1),28790(a,1,3))].">
      <j1 rule="para" parents="28421 28790"/>
    </justification>
  </clause>

  <clause id="28813">
    <literal><![CDATA[
      L((x \ (a(y,x,z) \ 1)) \ u,a(y,x,z) \ (1 / x),x * a(y,x,z)) = 1 \ (((a(y,x,z) \ (1 / x)) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(28738(a,1),28810(a,1,3))].">
      <j1 rule="para" parents="28738 28810"/>
    </justification>
  </clause>

  <clause id="28814">
    <literal><![CDATA[
      L((x \ (a(y,x,z) \ 1)) \ u,a(y,x,z) \ (x \ 1),x * a(y,x,z)) = 1 \ (((a(y,x,z) \ (1 / x)) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(21763,a,28813,a)].">
      <j1 rule="hyper" parents="21763 28813"/>
    </justification>
  </clause>

  <clause id="28815">
    <literal><![CDATA[
      L((x \ (a(y,x,z) \ 1)) \ u,x \ (a(y,x,z) \ 1),x * a(y,x,z)) = 1 \ (((a(y,x,z) \ (1 / x)) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(26576(a,1),28814(a,1,2))].">
      <j1 rule="para" parents="26576 28814"/>
    </justification>
  </clause>

  <clause id="28816">
    <literal><![CDATA[
      L((x \ (a(y,x,z) \ 1)) \ u,x \ a(y,x,z),x * a(y,x,z)) = 1 \ (((a(y,x,z) \ (1 / x)) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(21771,a,28815,a)].">
      <j1 rule="hyper" parents="21771 28815"/>
    </justification>
  </clause>

  <clause id="28817">
    <literal><![CDATA[
      L((x \ (a(y,x,z) \ 1)) \ u,x * a(y,x,z),x * a(y,x,z)) = 1 \ (((a(y,x,z) \ (1 / x)) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,26356,a(flip),b,28816,a)].">
      <j1 rule="hyper" parents="63 26356 28816"/>
    </justification>
  </clause>

  <clause id="28818">
    <literal><![CDATA[
      L((x \ (a(y,x,z) \ 1)) \ u,x,x) = 1 \ (((a(y,x,z) \ (1 / x)) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,27598,a(flip),b,28817,a)].">
      <j1 rule="hyper" parents="63 27598 28817"/>
    </justification>
  </clause>

  <clause id="28820">
    <literal><![CDATA[
      L((x \ (a(y,x,z) \ 1)) \ u,x,x) = 1 \ ((x * a(y,x,z)) * u)
    ]]></literal>
    <justification jstring="[para(28738(a,1),28818(a,2,2,1))].">
      <j1 rule="para" parents="28738 28818"/>
    </justification>
  </clause>

  <clause id="28821">
    <literal><![CDATA[
      L((x \ (a(y,x,z) \ 1)) \ u,x,x) != w
    ]]></literal>
    <literal><![CDATA[
      (x * a(y,x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(28820(a,2),185(a,1))].">
      <j1 rule="para" parents="28820 185"/>
    </justification>
  </clause>

  <clause id="28822">
    <literal><![CDATA[
      L(x * y,x \ 1,a(z,x \ 1,u)) = (x * a(z,x,u)) * (a(z,x,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(28821,a,28637,a),flip(a)].">
      <j1 rule="hyper" parents="28821 28637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28823">
    <literal><![CDATA[
      (x * a(y,x,z)) * (a(y,x,z) \ u) = L(x * u,x \ 1,a(y,x,z))
    ]]></literal>
    <justification jstring="[para(14950(a,1),28822(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14950 28822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28824">
    <literal><![CDATA[
      (x * a(y,x,z)) * (a(y,x,z) \ u) = L(x * u,x,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,3188,a(flip),b,28823,a),flip(a)].">
      <j1 rule="hyper" parents="347 3188 28823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28825">
    <literal><![CDATA[
      a(x,a(y,x,z),a(y,x,z) \ u) = u \ (x \ L(x * u,x,a(y,x,z)))
    ]]></literal>
    <justification jstring="[para(28824(a,1),14701(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28824 14701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28826">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ ((y * a(x,y,z)) \ (L(y * a(a(x,y,z),a(x,y,z),u),y,a(x,y,z)) * u)) = a(y * a(x,y,z),L(a(x,y,z),a(x,y,z),u),u)
    ]]></literal>
    <justification jstring="[para(28824(a,1),24807(a,1,2,2,1))].">
      <j1 rule="para" parents="28824 24807"/>
    </justification>
  </clause>

  <clause id="28827">
    <literal><![CDATA[
      x \ L(x * y,x,a(z,x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,a(z,x,u),x * a(z,x,u)) = w
    ]]></literal>
    <justification jstring="[para(28824(a,1),28570(a,1,2))].">
      <j1 rule="para" parents="28824 28570"/>
    </justification>
  </clause>

  <clause id="28828">
    <literal><![CDATA[
      a(x,a(y,x,z),a(y,x,z) \ u) = u \ (x * L(x \ u,x,a(y,x,z)))
    ]]></literal>
    <justification jstring="[para(3342(a,1),28825(a,2,2))].">
      <j1 rule="para" parents="3342 28825"/>
    </justification>
  </clause>

  <clause id="28829">
    <literal><![CDATA[
      a(x,a(y,x,z),a(y,x,z) \ u) = a(a(y,x,z),x,u * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,27213,a(flip),b,28828,a),flip(a)].">
      <j1 rule="hyper" parents="347 27213 28828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28830">
    <literal><![CDATA[
      a(x,a(y,x,z),a(y,x,z) \ u) = a(a(y,x,z),x,u * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,26386,a(flip),b,28829,a),flip(a)].">
      <j1 rule="hyper" parents="347 26386 28829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28831">
    <literal><![CDATA[
      a(x,a(y,x,z),u * a(y,x,z)) = a(a(y,x,z),x,u * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,27214,a(flip),b,28830,a)].">
      <j1 rule="hyper" parents="63 27214 28830"/>
    </justification>
  </clause>

  <clause id="28832">
    <literal><![CDATA[
      L(x,y,z) = (a(z,y,x) \ x) * a(a(z,y,x),y,x * y)
    ]]></literal>
    <justification jstring="[para(28831(a,1),28792(a,2,2))].">
      <j1 rule="para" parents="28831 28792"/>
    </justification>
  </clause>

  <clause id="28833">
    <literal><![CDATA[
      L(a(x,y,z),y,z * y) \ z = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,28682,a(flip),b,28832,a)].">
      <j1 rule="hyper" parents="347 28682 28832"/>
    </justification>
  </clause>

  <clause id="28834">
    <literal><![CDATA[
      L(x,y,z) / (y \ x) = a(z,y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(131,a,28833,a(flip),b,28501,a(flip))].">
      <j1 rule="hyper" parents="131 28833 28501"/>
    </justification>
  </clause>

  <clause id="28835">
    <literal><![CDATA[
      (x / y) \ L(x,y,z) = a(z,y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(22972,a,28834,a)].">
      <j1 rule="hyper" parents="22972 28834"/>
    </justification>
  </clause>

  <clause id="28836">
    <literal><![CDATA[
      a(x,y,y * (z \ y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(26570,a,28835,a)].">
      <j1 rule="hyper" parents="26570 28835"/>
    </justification>
  </clause>

  <clause id="28838">
    <literal><![CDATA[
      a(x,y,z) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,27239,a(flip),b,28836,a),flip(a)].">
      <j1 rule="hyper" parents="63 27239 28836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28839">
    <literal><![CDATA[
      L(x,y,z) * a(z,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(134,a,28836,a(flip),b,27239,a(flip))].">
      <j1 rule="hyper" parents="134 28836 27239"/>
    </justification>
  </clause>

  <clause id="28841">
    <literal><![CDATA[
      L(x,y,z) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(20593,a,28838,a),flip(a)].">
      <j1 rule="hyper" parents="20593 28838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28844">
    <literal><![CDATA[
      a(x,y,z \ y) = a(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,27217,a(flip),b,28838,a),flip(a)].">
      <j1 rule="hyper" parents="347 27217 28838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28845">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w)) = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,26371,a(flip),b,28838,a)].">
      <j1 rule="hyper" parents="347 26371 28838"/>
    </justification>
  </clause>

  <clause id="28846">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) = a(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,26122,a(flip),b,28838,a)].">
      <j1 rule="hyper" parents="347 26122 28838"/>
    </justification>
  </clause>

  <clause id="28850">
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 = x * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,28838,a,b,3637,a),flip(a)].">
      <j1 rule="hyper" parents="134 28838 3637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28852">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * L(L(z,y,x),u,w) = L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(133,a,28838,a,b,3311,a)].">
      <j1 rule="hyper" parents="133 28838 3311"/>
    </justification>
  </clause>

  <clause id="28853">
    <literal><![CDATA[
      a(x,y,z) * L(z,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(133,a,28838,a,b,3308,a)].">
      <j1 rule="hyper" parents="133 28838 3308"/>
    </justification>
  </clause>

  <clause id="28855">
    <literal><![CDATA[
      L(x,y,z) \ 1 = x \ a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(128,a,28838,a,b,1409,a),flip(a)].">
      <j1 rule="hyper" parents="128 28838 1409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28856">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(127,a,28838,a,b,26241,a),flip(a)].">
      <j1 rule="hyper" parents="127 28838 26241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28866">
    <literal><![CDATA[
      a(x,y,z) \ z != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(28838(a,2),3314(a,1,1))].">
      <j1 rule="para" parents="28838 3314"/>
    </justification>
  </clause>

  <clause id="28867">
    <literal><![CDATA[
      L(1 / x,y,z) \ 1 = a(z,y,x) * x
    ]]></literal>
    <justification jstring="[para(28838(a,2),3645(a,2,1))].">
      <j1 rule="para" parents="28838 3645"/>
    </justification>
  </clause>

  <clause id="28870">
    <literal><![CDATA[
      a(x,y,z) \ 1 = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[para(28838(a,2),10888(a,1,1))].">
      <j1 rule="para" parents="28838 10888"/>
    </justification>
  </clause>

  <clause id="28871">
    <literal><![CDATA[
      R(x,y * (z * a(u,w,z)),v5) = R(x,y * L(z,w,u),v5)
    ]]></literal>
    <justification jstring="[para(28838(a,2),10902(a,1,2,2,2))].">
      <j1 rule="para" parents="28838 10902"/>
    </justification>
  </clause>

  <clause id="28873">
    <literal><![CDATA[
      a(x,y,z * L(z,u,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(28838(a,2),14939(a,1,3)),flip(a)].">
      <j1 rule="para" parents="28838 14939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28876">
    <literal><![CDATA[
      R(x,y,(z * L(z,u,w)) * v5) = R(x,y,a(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[para(28838(a,2),22154(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="28838 22154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28877">
    <literal><![CDATA[
      R(x,(y * L(y,z,u)) * w,v5) = R(x,a(u,z,y) * w,v5)
    ]]></literal>
    <justification jstring="[para(28838(a,2),22542(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="28838 22542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28878">
    <literal><![CDATA[
      a(x,y,z) * L(L(z,y,x),u,w) = z * L(z \ L(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(28838(a,2),22575(a,1,1))].">
      <j1 rule="para" parents="28838 22575"/>
    </justification>
  </clause>

  <clause id="28880">
    <literal><![CDATA[
      R(x,y,z) * ((R(x,y,z) \ x) * u) = L(x,y,z) * (a(z,y,x) * u)
    ]]></literal>
    <justification jstring="[para(28838(a,2),23768(a,2,2,1))].">
      <j1 rule="para" parents="28838 23768"/>
    </justification>
  </clause>

  <clause id="28881">
    <literal><![CDATA[
      L(x,(L(y,z,u) \ w) * v5,v6) \ x = a(v6,(R(y,z,u) \ w) * v5,x)
    ]]></literal>
    <justification jstring="[para(23777(a,1),28838(a,2,1)),flip(a)].">
      <j1 rule="para" parents="23777 28838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28884">
    <literal><![CDATA[
      L(x,y,z) * (a(z,y,x) * a(x,u,w)) = x * a(x,u,w)
    ]]></literal>
    <justification jstring="[para(28838(a,2),25491(a,1,2,1))].">
      <j1 rule="para" parents="28838 25491"/>
    </justification>
  </clause>

  <clause id="28885">
    <literal><![CDATA[
      L(x * a(y,z,x),z,y) = x
    ]]></literal>
    <justification jstring="[para(28838(a,2),25972(a,1,1,2))].">
      <j1 rule="para" parents="28838 25972"/>
    </justification>
  </clause>

  <clause id="28887">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * L(L(z,y,x),u,w) = L(z,u,w)
    ]]></literal>
    <justification jstring="[para(28838(a,2),26123(a,1,1,1))].">
      <j1 rule="para" parents="28838 26123"/>
    </justification>
  </clause>

  <clause id="28888">
    <literal><![CDATA[
      a(x,y,z) * (y * z) = y * (z * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(28838(a,2),26294(a,1,1))].">
      <j1 rule="para" parents="28838 26294"/>
    </justification>
  </clause>

  <clause id="28891">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * x)) = u * (a(z,y,x) * x)
    ]]></literal>
    <justification jstring="[para(28838(a,2),27049(a,2,2,1))].">
      <j1 rule="para" parents="28838 27049"/>
    </justification>
  </clause>

  <clause id="28892">
    <literal><![CDATA[
      a(L(x \ 1,y,z),L(x,y,z),u) = L(u,x,x \ 1) \ u
    ]]></literal>
    <justification jstring="[para(27145(a,1),28838(a,2,1))].">
      <j1 rule="para" parents="27145 28838"/>
    </justification>
  </clause>

  <clause id="28893">
    <literal><![CDATA[
      L(x * (a(y,z,x) * a(y,z,x)),z,y) = x * a(y,z,x)
    ]]></literal>
    <justification jstring="[para(28838(a,2),27427(a,2,2))].">
      <j1 rule="para" parents="28838 27427"/>
    </justification>
  </clause>

  <clause id="28895">
    <literal><![CDATA[
      L(x,y,z \ L(z,u,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(28838(a,2),27608(a,1,3)),flip(a)].">
      <j1 rule="para" parents="28838 27608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28896">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,w \ L(w,u,z)) = v5
    ]]></literal>
    <justification jstring="[para(28838(a,2),27624(a,1,3))].">
      <j1 rule="para" parents="28838 27624"/>
    </justification>
  </clause>

  <clause id="28897">
    <literal><![CDATA[
      L(x,y,z) = ((z \ 1) \ a(z,y,x)) \ (T(z,z \ 1) * x)
    ]]></literal>
    <justification jstring="[para(28838(a,2),27666(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="28838 27666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28898">
    <literal><![CDATA[
      L(a(x,y,z),L(z,y,x),u * z) = u \ (z * (L(z,y,x) \ u))
    ]]></literal>
    <justification jstring="[para(28838(a,2),27930(a,1,1))].">
      <j1 rule="para" parents="28838 27930"/>
    </justification>
  </clause>

  <clause id="28899">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ u = a(z,y,x) * u
    ]]></literal>
    <justification jstring="[para(28838(a,2),28332(a,2,1))].">
      <j1 rule="para" parents="28838 28332"/>
    </justification>
  </clause>

  <clause id="28900">
    <literal><![CDATA[
      a(x,(y * L(y,z,u)) \ w,v5) = a(x,w * a(u,z,y),v5)
    ]]></literal>
    <justification jstring="[para(28838(a,2),28338(a,2,2,2))].">
      <j1 rule="para" parents="28838 28338"/>
    </justification>
  </clause>

  <clause id="28901">
    <literal><![CDATA[
      (x \ ((x / y) * L(y,z,u))) \ w = w * L(a(u,z,y),y,x)
    ]]></literal>
    <justification jstring="[para(28838(a,2),28492(a,2,2,1))].">
      <j1 rule="para" parents="28838 28492"/>
    </justification>
  </clause>

  <clause id="28902">
    <literal><![CDATA[
      L(L(x,y,z) \ u,x,x \ L(x,y,z)) = (x \ u) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(28838(a,2),28717(a,2,2))].">
      <j1 rule="para" parents="28838 28717"/>
    </justification>
  </clause>

  <clause id="28903">
    <literal><![CDATA[
      L(x,a(y,z,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(26627,a,28856,a)].">
      <j1 rule="hyper" parents="26627 28856"/>
    </justification>
  </clause>

  <clause id="28904">
    <literal><![CDATA[
      L(x,y,a(z,x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(26597,a,28856,a)].">
      <j1 rule="hyper" parents="26597 28856"/>
    </justification>
  </clause>

  <clause id="28905">
    <literal><![CDATA[
      a(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(189,a,26858,a,b,28856,a(flip))].">
      <j1 rule="hyper" parents="189 26858 28856"/>
    </justification>
  </clause>

  <clause id="28907">
    <literal><![CDATA[
      a(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(220,a,28903,a(flip),b,27737,a),flip(a)].">
      <j1 rule="hyper" parents="220 28903 27737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28908">
    <literal><![CDATA[
      R(x,y,z) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(134,a,28903,a(flip),b,27737,a),flip(a)].">
      <j1 rule="hyper" parents="134 28903 27737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28909">
    <literal><![CDATA[
      x * R(x \ 1,y,z) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(28903(a,1),26888(a,1,1))].">
      <j1 rule="para" parents="28903 26888"/>
    </justification>
  </clause>

  <clause id="28910">
    <literal><![CDATA[
      a(x,y,z) * x != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(28903(a,1),27742(a,1,2))].">
      <j1 rule="para" parents="28903 27742"/>
    </justification>
  </clause>

  <clause id="28911">
    <literal><![CDATA[
      R(x,(y * L(y,z,u)) * w,v5) = R(x,w * a(y \ 1,z,u),v5)
    ]]></literal>
    <justification jstring="[para(28903(a,1),27805(a,1,2,1,1))].">
      <j1 rule="para" parents="28903 27805"/>
    </justification>
  </clause>

  <clause id="28912">
    <literal><![CDATA[
      L(x,y,a(y,x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(27578,a,28904,a)].">
      <j1 rule="hyper" parents="27578 28904"/>
    </justification>
  </clause>

  <clause id="28913">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) != w \ (w * z)
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(28912(a,1),158(a,2,2,2))].">
      <j1 rule="para" parents="28912 158"/>
    </justification>
  </clause>

  <clause id="28916">
    <literal><![CDATA[
      L(x,y,z) \ x != u
    ]]></literal>
    <literal><![CDATA[
      a(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(28839(a,1),356(a,1,2))].">
      <j1 rule="para" parents="28839 356"/>
    </justification>
  </clause>

  <clause id="28919">
    <literal><![CDATA[
      L(a(x,y,z),L(z,y,x),u) = L(a(x,y,z),z,u)
    ]]></literal>
    <justification jstring="[para(28839(a,1),28657(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28839 28657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28920">
    <literal><![CDATA[
      L((x * y) \ 1,y,x) * ((L((x * y) \ 1,y,x) \ 1) * z) = L(z,y \ x,y \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(347,a,28371,a(flip),b,28841,a)].">
      <j1 rule="hyper" parents="347 28371 28841"/>
    </justification>
  </clause>

  <clause id="28922">
    <literal><![CDATA[
      (x * y) \ L(x * y,z,u) = a(u,z,y * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,28841,a,b,28416,a)].">
      <j1 rule="hyper" parents="128 28841 28416"/>
    </justification>
  </clause>

  <clause id="28929">
    <literal><![CDATA[
      a(x,y,z) * (a(a(x,y,z),x,u) \ u) = x \ ((x * a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(28841(a,1),26391(a,1,2))].">
      <j1 rule="para" parents="28841 26391"/>
    </justification>
  </clause>

  <clause id="28932">
    <literal><![CDATA[
      a(x,a(y,z,u) * u,w) = a(x,L(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(28841(a,2),28361(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28841 28361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28933">
    <literal><![CDATA[
      a(a(x,y,z) * z,u,w) = a(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(28841(a,2),28398(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28841 28398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28934">
    <literal><![CDATA[
      L(a(x,y,z) * u,z,a(x,y,z)) = L(z,y,x) \ (z * u)
    ]]></literal>
    <justification jstring="[para(28841(a,2),28552(a,2,1))].">
      <j1 rule="para" parents="28841 28552"/>
    </justification>
  </clause>

  <clause id="28941">
    <literal><![CDATA[
      L(a(x,y,z) * z,y,x) = z
    ]]></literal>
    <justification jstring="[para(11788(a,2),28885(a,1,1))].">
      <j1 rule="para" parents="11788 28885"/>
    </justification>
  </clause>

  <clause id="28942">
    <literal><![CDATA[
      a(x,y * (z \ (u * a(w,v5,u))),v6) = a(x,y * (z \ L(u,v5,w)),v6)
    ]]></literal>
    <justification jstring="[para(28885(a,1),25664(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="28885 25664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28943">
    <literal><![CDATA[
      R(x,y * ((z * a(u,w,z)) \ v5),v6) = R(x,y * (L(z,w,u) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(28885(a,1),27425(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="28885 27425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28944">
    <literal><![CDATA[
      L(x,y,z * a(u,w,z)) = L(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[para(28885(a,1),27537(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="28885 27537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28945">
    <literal><![CDATA[
      L(x,y,(z * a(u,w,z)) \ v5) = L(x,y,L(z,w,u) \ v5)
    ]]></literal>
    <justification jstring="[para(28885(a,1),27893(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="28885 27893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28946">
    <literal><![CDATA[
      a(x * a(y,z,x),u,w) = a(L(x,z,y),u,w)
    ]]></literal>
    <justification jstring="[para(28885(a,1),27967(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="28885 27967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28948">
    <literal><![CDATA[
      a(x \ (y * a(z,u,y)),w,v5) = a(x \ L(y,u,z),w,v5)
    ]]></literal>
    <justification jstring="[para(28885(a,1),27974(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="28885 27974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28958">
    <literal><![CDATA[
      R(x,y,z) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,28905,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="134 28905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28959">
    <literal><![CDATA[
      x \ (a(x,y,z) \ R(x,u,w)) = a(x,y,z) \ a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(128,a,28905,a,b,25400,a),flip(a)].">
      <j1 rule="hyper" parents="128 28905 25400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28960">
    <literal><![CDATA[
      R(T(x,x \ 1),y,z) = (x \ 1) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,28905,a,b,1464,a),flip(a)].">
      <j1 rule="hyper" parents="128 28905 1464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28961">
    <literal><![CDATA[
      R(x,y,z) \ a(x,y,z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,28905,a,b,1463,a)].">
      <j1 rule="hyper" parents="128 28905 1463"/>
    </justification>
  </clause>

  <clause id="28969">
    <literal><![CDATA[
      a(x,y,z) != x \ u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(28905(a,2),47(a,1))].">
      <j1 rule="para" parents="28905 47"/>
    </justification>
  </clause>

  <clause id="28970">
    <literal><![CDATA[
      x * a(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(28905(a,2),286(a,1,2)),flip(b)].">
      <j1 rule="para" parents="28905 286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28972">
    <literal><![CDATA[
      R(x,y,z) / (x * x) = x \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(28905(a,2),1777(a,2,2))].">
      <j1 rule="para" parents="28905 1777"/>
    </justification>
  </clause>

  <clause id="28974">
    <literal><![CDATA[
      a(x \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * R(x \ 1,y,z) = u
    ]]></literal>
    <justification jstring="[para(28905(a,2),3695(a,1))].">
      <j1 rule="para" parents="28905 3695"/>
    </justification>
  </clause>

  <clause id="28975">
    <literal><![CDATA[
      x \ ((x / y) * R(y,z,u)) = L(a(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(28905(a,2),4072(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28905 4072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28976">
    <literal><![CDATA[
      R(x,y,z) \ x = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(28905(a,2),4742(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28905 4742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28982">
    <literal><![CDATA[
      x * L(a(y,z,u),y,x) = R(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[para(28905(a,2),20928(a,1,2,1))].">
      <j1 rule="para" parents="28905 20928"/>
    </justification>
  </clause>

  <clause id="28983">
    <literal><![CDATA[
      x \ (R(y,z,u) * (y \ x)) = L(a(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(28905(a,2),20929(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28905 20929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28984">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(23247(a,1),28905(a,2,2)),flip(a)].">
      <j1 rule="para" parents="23247 28905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28985">
    <literal><![CDATA[
      R(x,y,z) * (x \ R(x,u,w)) = a(x,y,z) * R(x,u,w)
    ]]></literal>
    <justification jstring="[para(28905(a,2),23639(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28905 23639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28991">
    <literal><![CDATA[
      x \ ((x * y) * a(y,z,u)) = R(y,z,u) * a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(28905(a,2),28188(a,1,2,2))].">
      <j1 rule="para" parents="28905 28188"/>
    </justification>
  </clause>

  <clause id="28994">
    <literal><![CDATA[
      R(x,y,(z * (u * w)) \ (w * (u * z))) = a(x,y,a(z,u,w)) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,24535,a(flip),b,28907,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 24535 28907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28997">
    <literal><![CDATA[
      a(x,y,z) \ (1 / x) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(28907(a,2),4732(a,1,1))].">
      <j1 rule="para" parents="28907 4732"/>
    </justification>
  </clause>

  <clause id="29002">
    <literal><![CDATA[
      x \ R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(28908(a,2),20017(a,1,2))].">
      <j1 rule="para" parents="28908 20017"/>
    </justification>
  </clause>

  <clause id="29004">
    <literal><![CDATA[
      L(1 / x,y,z) * R(x,u,w) = L(x,y,z) * (x \ a(x,u,w))
    ]]></literal>
    <justification jstring="[para(28908(a,2),21410(a,1,2))].">
      <j1 rule="para" parents="28908 21410"/>
    </justification>
  </clause>

  <clause id="29007">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * x != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(28908(a,1),23284(a,1))].">
      <j1 rule="para" parents="28908 23284"/>
    </justification>
  </clause>

  <clause id="29008">
    <literal><![CDATA[
      (x * x) \ (a(x,y,z) \ u) = (x * R(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(28908(a,2),25404(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="28908 25404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29009">
    <literal><![CDATA[
      (x * (x \ y)) * R(y,x \ y,x) = y * R(y,y \ x,x)
    ]]></literal>
    <justification jstring="[para(28908(a,2),26065(a,2,2))].">
      <j1 rule="para" parents="28908 26065"/>
    </justification>
  </clause>

  <clause id="29010">
    <literal><![CDATA[
      L((x \ 1) \ y,x,R(x,z,u)) = x * L(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(28908(a,2),26384(a,1,3))].">
      <j1 rule="para" parents="28908 26384"/>
    </justification>
  </clause>

  <clause id="29011">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * w = L(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(27567,a,28941,a),flip(a)].">
      <j1 rule="hyper" parents="27567 28941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29013">
    <literal><![CDATA[
      L(a(x,y,z) * z,y,L(x,x,u)) = L(z,y * x,a(x,x,u))
    ]]></literal>
    <justification jstring="[para(28941(a,1),26747(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28941 26747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29014">
    <literal><![CDATA[
      a(x * ((a(y,z,u) * u) * w),v5,v6) = a(x * (L(u,z,y) * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(28941(a,1),28010(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="28941 28010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29019">
    <literal><![CDATA[
      R(x,a(x,y,z),a(x,y,z)) * ((a(x,y,z) * a(x,y,z)) * u) = (R(x,y,z) * a(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(28958(a,2),593(a,2,1,1))].">
      <j1 rule="para" parents="28958 593"/>
    </justification>
  </clause>

  <clause id="29021">
    <literal><![CDATA[
      a(x,y,z) * (x * L(x \ u,a(x,y,z),x)) = x * (a(x,y,z) * (R(x,y,z) \ (a(x,y,z) * u)))
    ]]></literal>
    <justification jstring="[para(28958(a,2),10435(a,2,2,2,1))].">
      <j1 rule="para" parents="28958 10435"/>
    </justification>
  </clause>

  <clause id="29025">
    <literal><![CDATA[
      x \ (a(x,y,z) \ L(x,u,w)) = R(x,y,z) \ L(x,u,w)
    ]]></literal>
    <justification jstring="[para(28958(a,2),25511(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28958 25511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29026">
    <literal><![CDATA[
      R(x,y,(z \ a(z,u,w)) * v5) = R(x,y,R(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(28958(a,2),27655(a,2,3,1))].">
      <j1 rule="para" parents="28958 27655"/>
    </justification>
  </clause>

  <clause id="29028">
    <literal><![CDATA[
      x * (L(L(x,y,z),y,z) \ (R(z,y,x) \ u)) = (a(z,y,x) \ z) \ u
    ]]></literal>
    <justification jstring="[para(28958(a,2),28633(a,1,2,2,1))].">
      <j1 rule="para" parents="28958 28633"/>
    </justification>
  </clause>

  <clause id="29030">
    <literal><![CDATA[
      ((x * y) \ (x * z)) \ (y \ z) = a(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,26201,a,b,28844,a)].">
      <j1 rule="hyper" parents="63 26201 28844"/>
    </justification>
  </clause>

  <clause id="29032">
    <literal><![CDATA[
      a(x,y * a(z \ 1,u,w * u),v5) = a(x,a(w \ u,u,z) * y,v5)
    ]]></literal>
    <justification jstring="[para(28844(a,1),26901(a,1,2,2))].">
      <j1 rule="para" parents="28844 26901"/>
    </justification>
  </clause>

  <clause id="29033">
    <literal><![CDATA[
      R(x,y,((z * u) \ (u * w)) * (z \ w)) = L(x,y,a(u,z,w * z))
    ]]></literal>
    <justification jstring="[para(28844(a,1),27816(a,2,3))].">
      <j1 rule="para" parents="28844 27816"/>
    </justification>
  </clause>

  <clause id="29034">
    <literal><![CDATA[
      T(x \ a(y,z,x),u \ L(R(u,w,v5),v6,v7)) = L(x,z,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,22953,a,b,28855,a)].">
      <j1 rule="hyper" parents="347 22953 28855"/>
    </justification>
  </clause>

  <clause id="29037">
    <literal><![CDATA[
      x \ (y * L(y \ x,z,u)) = a(u,z,x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,3354,a(flip),b,28870,a)].">
      <j1 rule="hyper" parents="347 3354 28870"/>
    </justification>
  </clause>

  <clause id="29038">
    <literal><![CDATA[
      a(x,y,z) \ (a(u,w,x) \ 1) = x \ (a(x,y,z) \ L(x,w,u))
    ]]></literal>
    <justification jstring="[hyper(128,a,28870,a,b,25400,a)].">
      <j1 rule="hyper" parents="128 28870 25400"/>
    </justification>
  </clause>

  <clause id="29040">
    <literal><![CDATA[
      x * (y \ L(y,z,u)) = a(u,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,28870,a(flip),b,28350,a)].">
      <j1 rule="hyper" parents="134 28870 28350"/>
    </justification>
  </clause>

  <clause id="29043">
    <literal><![CDATA[
      (x * y) \ (x * L(y,z,u)) = L(a(u,z,y) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(28870(a,2),99(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28870 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29046">
    <literal><![CDATA[
      R(x,y,z) \ L(R(x,y,z),u,x) = a(x,u,x) \ 1
    ]]></literal>
    <justification jstring="[para(11254(a,1),28870(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11254 28870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29050">
    <literal><![CDATA[
      1 / (x \ (y \ L(y,z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      ((a(u,z,y) \ 1) / x) \ 1 = w
    ]]></literal>
    <justification jstring="[para(28870(a,1),22289(a,1,2,2))].">
      <j1 rule="para" parents="28870 22289"/>
    </justification>
  </clause>

  <clause id="29054">
    <literal><![CDATA[
      L(x,y,z \ L(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(w,u,z)) = v5
    ]]></literal>
    <justification jstring="[para(28870(a,1),27898(a,1,3))].">
      <j1 rule="para" parents="28870 27898"/>
    </justification>
  </clause>

  <clause id="29055">
    <literal><![CDATA[
      (x \ L(x,y,z)) * u = a(z,y,x) \ u
    ]]></literal>
    <justification jstring="[para(28870(a,1),28341(a,1,1))].">
      <j1 rule="para" parents="28870 28341"/>
    </justification>
  </clause>

  <clause id="29056">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),w,v5) = L(a(u,z,y),w,v5) \ x
    ]]></literal>
    <justification jstring="[para(28870(a,1),28473(a,1,2,1))].">
      <j1 rule="para" parents="28870 28473"/>
    </justification>
  </clause>

  <clause id="29058">
    <literal><![CDATA[
      x * (R(y,z,u) \ y) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,28976,a,b,28350,a)].">
      <j1 rule="hyper" parents="134 28976 28350"/>
    </justification>
  </clause>

  <clause id="29064">
    <literal><![CDATA[
      (R(x,y,z) \ x) * u = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(28976(a,2),28341(a,1,1))].">
      <j1 rule="para" parents="28976 28341"/>
    </justification>
  </clause>

  <clause id="29065">
    <literal><![CDATA[
      (R(x,y,z) \ x) * u != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) \ u = w
    ]]></literal>
    <justification jstring="[para(28976(a,2),28359(a,1,1))].">
      <j1 rule="para" parents="28976 28359"/>
    </justification>
  </clause>

  <clause id="29068">
    <literal><![CDATA[
      x * R(x \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x \ 1,y,z) = u
    ]]></literal>
    <justification jstring="[para(3682(a,1),29002(a,1))].">
      <j1 rule="para" parents="3682 29002"/>
    </justification>
  </clause>

  <clause id="29069">
    <literal><![CDATA[
      x \ (y * R(y \ x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a((x \ y) \ 1,z,u) = w
    ]]></literal>
    <justification jstring="[para(3708(a,1),29002(a,1))].">
      <j1 rule="para" parents="3708 29002"/>
    </justification>
  </clause>

  <clause id="29072">
    <literal><![CDATA[
      x * a(y,a(z,u,w),x) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(z,u,w),y) = v5
    ]]></literal>
    <justification jstring="[para(28850(a,1),28753(a,1))].">
      <j1 rule="para" parents="28850 28753"/>
    </justification>
  </clause>

  <clause id="29073">
    <literal><![CDATA[
      a(x,y,(z * L(1 / u,w,v5)) * v6) = a(x,y,(z * (a(v5,w,u) * u)) * v6)
    ]]></literal>
    <justification jstring="[para(28867(a,1),24333(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="28867 24333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29075">
    <literal><![CDATA[
      (a(x,y,z) * z) \ (z * u) = L(z,y,x) * (z \ u)
    ]]></literal>
    <justification jstring="[para(28867(a,1),28716(a,1,1))].">
      <j1 rule="para" parents="28867 28716"/>
    </justification>
  </clause>

  <clause id="29079">
    <literal><![CDATA[
      L((x \ 1) \ y,x,L(x,z,u)) = L(x,z,u) * (a(u,z,x) * y)
    ]]></literal>
    <justification jstring="[para(28899(a,1),22722(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28899 22722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29080">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * R((y * z) \ y,u,w))) = a(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,4603,a,b,28909,a)].">
      <j1 rule="hyper" parents="63 4603 28909"/>
    </justification>
  </clause>

  <clause id="29082">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = y * a(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(28909(a,1),23587(a,2,2))].">
      <j1 rule="para" parents="28909 23587"/>
    </justification>
  </clause>

  <clause id="29083">
    <literal><![CDATA[
      x \ (a(x,y,z) \ R(x,u,w)) = (1 / R(x,y,z)) * R(x,u,w)
    ]]></literal>
    <justification jstring="[para(28997(a,1),26396(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28997 26396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29085">
    <literal><![CDATA[
      (x * (y \ x)) * L(((x \ y) \ 1) \ 1,z,u) = a(u,z,y \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,3830,a,b,29040,a)].">
      <j1 rule="hyper" parents="63 3830 29040"/>
    </justification>
  </clause>

  <clause id="29089">
    <literal><![CDATA[
      (x * (a(x,y,z) \ y)) * L(z,z,y) = x * (y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(29040(a,1),27672(a,1,1,2))].">
      <j1 rule="para" parents="29040 27672"/>
    </justification>
  </clause>

  <clause id="29092">
    <literal><![CDATA[
      (x / y) \ L(x,z,y) = a(y,z,x) \ y
    ]]></literal>
    <justification jstring="[hyper(27617,a,29055,a)].">
      <j1 rule="hyper" parents="27617 29055"/>
    </justification>
  </clause>

  <clause id="29093">
    <literal><![CDATA[
      L(x,y,z) * (x \ a(x,u,w)) = a(z,y,x) \ a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(25406,a,29055,a)].">
      <j1 rule="hyper" parents="25406 29055"/>
    </justification>
  </clause>

  <clause id="29094">
    <literal><![CDATA[
      L(x * y,x,x \ L(x,z,u)) = a(u,z,x) * (L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(28314,a,29055,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="28314 29055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29095">
    <literal><![CDATA[
      L(x,x \ y,z \ L(z,u,w)) = (a(w,u,z) \ (y / x)) \ ((z \ L(z,u,w)) * y)
    ]]></literal>
    <justification jstring="[para(29055(a,1),9645(a,2,1))].">
      <j1 rule="para" parents="29055 9645"/>
    </justification>
  </clause>

  <clause id="29099">
    <literal><![CDATA[
      (a(x,y,z) \ (u * z)) * a(x,y,a(z,z,u)) = u * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(29055(a,1),28160(a,1,1))].">
      <j1 rule="para" parents="29055 28160"/>
    </justification>
  </clause>

  <clause id="29101">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ u = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,19988,a(flip),b,29064,a)].">
      <j1 rule="hyper" parents="128 19988 29064"/>
    </justification>
  </clause>

  <clause id="29113">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(28838(a,2),28846(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28838 28846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29114">
    <literal><![CDATA[
      a(x,y,z) * a(u,w,a(x,y,z)) = a(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,28461,a,b,29113,a)].">
      <j1 rule="hyper" parents="347 28461 29113"/>
    </justification>
  </clause>

  <clause id="29117">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) = R(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,23097,a,b,29113,a),flip(a)].">
      <j1 rule="hyper" parents="347 23097 29113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29118">
    <literal><![CDATA[
      a(x,y,L(z,u,L(x,w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,25487,a(flip),b,29113,a),flip(a)].">
      <j1 rule="hyper" parents="347 25487 29113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29119">
    <literal><![CDATA[
      a(x,y,L(z,u,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,25390,a(flip),b,29113,a),flip(a)].">
      <j1 rule="hyper" parents="347 25390 29113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29120">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * (w * u) = w * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(133,a,29113,a,b,20006,a)].">
      <j1 rule="hyper" parents="133 29113 20006"/>
    </justification>
  </clause>

  <clause id="29125">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,u,w) = a(z,u,L(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(28467,a,29113,a(flip))].">
      <j1 rule="hyper" parents="28467 29113"/>
    </justification>
  </clause>

  <clause id="29128">
    <literal><![CDATA[
      a(x,y,L(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(29113(a,2),12368(a,1))].">
      <j1 rule="para" parents="29113 12368"/>
    </justification>
  </clause>

  <clause id="29131">
    <literal><![CDATA[
      a(x,y,L(z,u,u)) / T(u,u \ 1) = a(x,y,z) * (u \ 1)
    ]]></literal>
    <justification jstring="[para(29113(a,2),22043(a,1,1))].">
      <j1 rule="para" parents="29113 22043"/>
    </justification>
  </clause>

  <clause id="29132">
    <literal><![CDATA[
      R(x,a(y \ z,y,L(u,y * u,y * u)),w) = R(x,((z / y) \ (z * u)) * (y * u),w)
    ]]></literal>
    <justification jstring="[para(29113(a,2),22490(a,1,2))].">
      <j1 rule="para" parents="29113 22490"/>
    </justification>
  </clause>

  <clause id="29134">
    <literal><![CDATA[
      T(x * ((a(y,z,u) * x) \ w),w / a(y,z,L(u,x,x))) = (x \ 1) * ((a(y,z,u) * (x \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(29113(a,2),23845(a,1,2,2))].">
      <j1 rule="para" parents="29113 23845"/>
    </justification>
  </clause>

  <clause id="29136">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) = a(x,y,L(z,u,w)) \ 1
    ]]></literal>
    <justification jstring="[para(29113(a,2),26290(a,2,1))].">
      <j1 rule="para" parents="29113 26290"/>
    </justification>
  </clause>

  <clause id="29137">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),z,y) = L(L(z,y,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(29113(a,2),26295(a,1,1))].">
      <j1 rule="para" parents="29113 26295"/>
    </justification>
  </clause>

  <clause id="29140">
    <literal><![CDATA[
      a(x,y,L(z,u,u)) * u = (1 / u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(29113(a,2),26347(a,1,1))].">
      <j1 rule="para" parents="29113 26347"/>
    </justification>
  </clause>

  <clause id="29141">
    <literal><![CDATA[
      x * a(y,z,L(u,x,x)) = (1 / x) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[para(29113(a,2),26348(a,1,2))].">
      <j1 rule="para" parents="29113 26348"/>
    </justification>
  </clause>

  <clause id="29143">
    <literal><![CDATA[
      L(a(x,a(y,z,u),w) \ 1,v5,v6) = a(w,a(y,z,u),L(x,v5,v6))
    ]]></literal>
    <justification jstring="[para(26491(a,2),29113(a,2,1)),flip(a)].">
      <j1 rule="para" parents="26491 29113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29145">
    <literal><![CDATA[
      x * a(y,z,L(u,w,x * w)) = (x / w) * (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(29113(a,2),27279(a,1,2))].">
      <j1 rule="para" parents="29113 27279"/>
    </justification>
  </clause>

  <clause id="29146">
    <literal><![CDATA[
      a(x,y,L(z,u,u)) \ (u \ 1) = u \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(29113(a,2),28427(a,1,1))].">
      <j1 rule="para" parents="29113 28427"/>
    </justification>
  </clause>

  <clause id="29147">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(x,y,z) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(29113(a,2),28456(a,1,1))].">
      <j1 rule="para" parents="29113 28456"/>
    </justification>
  </clause>

  <clause id="29148">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),a(z,y,x),v5) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29113(a,2),28458(a,1,1))].">
      <j1 rule="para" parents="29113 28458"/>
    </justification>
  </clause>

  <clause id="29150">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ (u * w) = (a(x,y,z) \ u) * w
    ]]></literal>
    <justification jstring="[para(29113(a,2),28486(a,1,1))].">
      <j1 rule="para" parents="29113 28486"/>
    </justification>
  </clause>

  <clause id="29151">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(x,y,z) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(29113(a,2),28497(a,1,1))].">
      <j1 rule="para" parents="29113 28497"/>
    </justification>
  </clause>

  <clause id="29152">
    <literal><![CDATA[
      a(x,y,L(z,u,w * u)) \ w = (a(x,y,z) \ u) * (u \ w)
    ]]></literal>
    <justification jstring="[para(29113(a,2),28501(a,1,1))].">
      <j1 rule="para" parents="29113 28501"/>
    </justification>
  </clause>

  <clause id="29153">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (z \ a(z,u,w)) = z \ a(z,u,L(w,y,x))
    ]]></literal>
    <justification jstring="[para(29113(a,2),28577(a,2,2))].">
      <j1 rule="para" parents="29113 28577"/>
    </justification>
  </clause>

  <clause id="29154">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * a(z,u,w)) = a(z,u,L(w,y,x)) * v5
    ]]></literal>
    <justification jstring="[para(29113(a,2),28587(a,2,1))].">
      <j1 rule="para" parents="29113 28587"/>
    </justification>
  </clause>

  <clause id="29155">
    <literal><![CDATA[
      L(x \ L(x,a(y,z,u),w),v5,v6) = a(x,a(y,z,u),L(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(28625(a,2),29113(a,2,1)),flip(a)].">
      <j1 rule="para" parents="28625 29113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29156">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(w,v5,a(x,y,z)) = a(x,y,L(z,v5,w)) \ u
    ]]></literal>
    <justification jstring="[para(29113(a,2),28679(a,2,1))].">
      <j1 rule="para" parents="29113 28679"/>
    </justification>
  </clause>

  <clause id="29157">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(z,y,x) = a(x,y,z) \ L(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(29113(a,2),28683(a,1,1))].">
      <j1 rule="para" parents="29113 28683"/>
    </justification>
  </clause>

  <clause id="29158">
    <literal><![CDATA[
      a(x,L(L(y,a(z,u,w),v5),v5,a(z,u,w)),a(v5,y,a(w,u,z))) \ 1 = a(v5,y,a(w,u,z)) \ a(v5,y,L(a(w,u,z),y,x))
    ]]></literal>
    <justification jstring="[para(29113(a,2),28690(a,2,2))].">
      <j1 rule="para" parents="29113 28690"/>
    </justification>
  </clause>

  <clause id="29161">
    <literal><![CDATA[
      a(x,y,z \ x) = a(x,y,x * z)
    ]]></literal>
    <justification jstring="[hyper(25265,a,29119,a)].">
      <j1 rule="hyper" parents="25265 29119"/>
    </justification>
  </clause>

  <clause id="29163">
    <literal><![CDATA[
      a(x,y,z * a(x,z,u)) = a(x,y,L(z,x,u))
    ]]></literal>
    <justification jstring="[hyper(24670,a,29119,a),flip(a)].">
      <j1 rule="hyper" parents="24670 29119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29167">
    <literal><![CDATA[
      a(x,y,L(z,u,x)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,28905,a(flip),b,29119,a),flip(a)].">
      <j1 rule="hyper" parents="347 28905 29119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29169">
    <literal><![CDATA[
      a(x,y,(z * x) \ u) = a(x,y,z \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,25588,a(flip),b,29119,a),flip(a)].">
      <j1 rule="hyper" parents="63 25588 29119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29173">
    <literal><![CDATA[
      a(x,y,(x \ z) \ u) = a(x,y,z \ (x * u))
    ]]></literal>
    <justification jstring="[para(561(a,1),29119(a,1,3)),flip(a)].">
      <j1 rule="para" parents="561 29119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29174">
    <literal><![CDATA[
      a(x,y,x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x * z) = u
    ]]></literal>
    <justification jstring="[para(29119(a,1),14994(a,1))].">
      <j1 rule="para" parents="29119 14994"/>
    </justification>
  </clause>

  <clause id="29192">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,x))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(29113(a,2),29119(a,1,3))].">
      <j1 rule="para" parents="29113 29119"/>
    </justification>
  </clause>

  <clause id="29193">
    <literal><![CDATA[
      R(x,y,L(z,u,x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(28969,a,29167,a)].">
      <j1 rule="hyper" parents="28969 29167"/>
    </justification>
  </clause>

  <clause id="29194">
    <literal><![CDATA[
      a(x,y,L(z,u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(29167(a,2),29002(a,1))].">
      <j1 rule="para" parents="29167 29002"/>
    </justification>
  </clause>

  <clause id="29195">
    <literal><![CDATA[
      R(x,y,x \ z) = R(x,y,x * z)
    ]]></literal>
    <justification jstring="[hyper(2290,a,29193,a),flip(a)].">
      <j1 rule="hyper" parents="2290 29193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29198">
    <literal><![CDATA[
      L(a(x,a(y,z,u),w) \ a(y,z,u),x,w) = a(y,z,L(u,w,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,25535,a,b,29117,a)].">
      <j1 rule="hyper" parents="347 25535 29117"/>
    </justification>
  </clause>

  <clause id="29199">
    <literal><![CDATA[
      a(x,y,L(z,u,w * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(29117(a,2),598(a,1))].">
      <j1 rule="para" parents="29117 598"/>
    </justification>
  </clause>

  <clause id="29200">
    <literal><![CDATA[
      a(x,y,L(x,z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(x,z,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(29118(a,1),14994(a,1))].">
      <j1 rule="para" parents="29118 14994"/>
    </justification>
  </clause>

  <clause id="29201">
    <literal><![CDATA[
      a(x,y,(x * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(329(a,1),29194(a,1,3))].">
      <j1 rule="para" parents="329 29194"/>
    </justification>
  </clause>

  <clause id="29202">
    <literal><![CDATA[
      a(x,y,L((x * z) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z \ (x \ u),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(622(a,1),29194(a,1,3))].">
      <j1 rule="para" parents="622 29194"/>
    </justification>
  </clause>

  <clause id="29203">
    <literal><![CDATA[
      a(x \ y,z,L(x,x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x \ y,z,x) = u
    ]]></literal>
    <justification jstring="[para(12449(a,1),29194(a,1))].">
      <j1 rule="para" parents="12449 29194"/>
    </justification>
  </clause>

  <clause id="29204">
    <literal><![CDATA[
      a(x * y,z,y * (x \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x * y,z,x) = u
    ]]></literal>
    <justification jstring="[para(25291(a,1),29194(a,1))].">
      <j1 rule="para" parents="25291 29194"/>
    </justification>
  </clause>

  <clause id="29205">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,x))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = v6
    ]]></literal>
    <justification jstring="[para(29113(a,2),29194(a,1,3))].">
      <j1 rule="para" parents="29113 29194"/>
    </justification>
  </clause>

  <clause id="29206">
    <literal><![CDATA[
      a(x,y,(x \ z) * a(u,w,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x * (z * a(u,w,x))) = v5
    ]]></literal>
    <justification jstring="[para(12363(a,1),29174(a,1,3))].">
      <j1 rule="para" parents="12363 29174"/>
    </justification>
  </clause>

  <clause id="29211">
    <literal><![CDATA[
      a(x \ y,x,a(z,u,y)) = a(x,x,y * L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,23347,a(flip),b,28873,a),flip(a)].">
      <j1 rule="hyper" parents="63 23347 28873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29212">
    <literal><![CDATA[
      a(x,y,(z \ T(u,w)) * ((w * z) \ (u * w))) = a(x,y,a(w,z,z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(480(a,1),28873(a,1,3,2))].">
      <j1 rule="para" parents="480 28873"/>
    </justification>
  </clause>

  <clause id="29213">
    <literal><![CDATA[
      a(x,y,(T(z,u) \ w) * ((z * u) \ (u * w))) = a(x,y,a(u,z,T(z,u) \ w))
    ]]></literal>
    <justification jstring="[para(10169(a,1),28873(a,1,3,2))].">
      <j1 rule="para" parents="10169 28873"/>
    </justification>
  </clause>

  <clause id="29215">
    <literal><![CDATA[
      (x / y) \ (x * z) = y * (z * a(y \ x,y,z))
    ]]></literal>
    <justification jstring="[hyper(14735,a,28888,a)].">
      <j1 rule="hyper" parents="14735 28888"/>
    </justification>
  </clause>

  <clause id="29217">
    <literal><![CDATA[
      L(x / y,y,y \ L(y,z,u)) = L(x,y,a(u,z,y)) / y
    ]]></literal>
    <justification jstring="[para(28895(a,1),3656(a,2,1))].">
      <j1 rule="para" parents="28895 3656"/>
    </justification>
  </clause>

  <clause id="29218">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) * R(y,u,z) = (y \ R(y,u,z)) * (x * y)
    ]]></literal>
    <justification jstring="[para(28895(a,1),23711(a,1,1))].">
      <j1 rule="para" parents="28895 23711"/>
    </justification>
  </clause>

  <clause id="29220">
    <literal><![CDATA[
      a((x \ 1) \ a(y,z,x),u,w) = a(L(x,z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(24408,a,28946,a)].">
      <j1 rule="hyper" parents="24408 28946"/>
    </justification>
  </clause>

  <clause id="29222">
    <literal><![CDATA[
      x * L(x \ 1,y,a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(3345,a,28984,a)].">
      <j1 rule="hyper" parents="3345 28984"/>
    </justification>
  </clause>

  <clause id="29224">
    <literal><![CDATA[
      a(x,a(x,y,z),u) * u = L(u,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(26609(a,1),29011(a,1,1))].">
      <j1 rule="para" parents="26609 29011"/>
    </justification>
  </clause>

  <clause id="29225">
    <literal><![CDATA[
      a(a(x,y,z),u,u \ (a(x,y,z) \ w)) * (u * (u \ (a(x,y,z) \ w))) = u * ((u * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(29169(a,1),26504(a,1,1))].">
      <j1 rule="para" parents="29169 26504"/>
    </justification>
  </clause>

  <clause id="29226">
    <literal><![CDATA[
      a(x,y,(z * (u * u)) \ (w \ (v5 \ (u * u)))) = a(x,y,z \ (w \ (v5 \ 1)))
    ]]></literal>
    <justification jstring="[hyper(29199,a,24551,a),flip(a)].">
      <j1 rule="hyper" parents="29199 24551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29227">
    <literal><![CDATA[
      a(x,y,z) \ ((x \ a(x,y,z)) * u) = (x \ 1) * L(u,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(29224(a,1),26694(a,2,2))].">
      <j1 rule="para" parents="29224 26694"/>
    </justification>
  </clause>

  <clause id="29228">
    <literal><![CDATA[
      x \ ((x / y) * R(y,z,u)) = a(y,z,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,29113,a,b,28975,a),flip(a)].">
      <j1 rule="hyper" parents="347 29113 28975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29230">
    <literal><![CDATA[
      R(x,(y \ z) * ((u * y) \ (u * z)),w) = R(x,a(u,y,z * y),w)
    ]]></literal>
    <justification jstring="[para(29030(a,1),22054(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29030 22054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29231">
    <literal><![CDATA[
      a(x,y,z * (u \ z)) * (u * z) = (1 / (u * z)) \ a(x,y,u)
    ]]></literal>
    <justification jstring="[para(25291(a,1),29140(a,1,1))].">
      <j1 rule="para" parents="25291 29140"/>
    </justification>
  </clause>

  <clause id="29234">
    <literal><![CDATA[
      ((x \ 1) * y) * (z * a(a(x,x,y),(x \ 1) * y,z)) = ((x \ y) / ((x \ 1) * y)) \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(14713(a,1),29215(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14713 29215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29235">
    <literal><![CDATA[
      (a(x,y,z) / (z \ 1)) \ (a(x,y,z) * u) = (z \ 1) * (u * a(((z \ 1) \ 1) * a(x,y,z),z \ 1,u))
    ]]></literal>
    <justification jstring="[para(15052(a,2),29215(a,2,2,2,1))].">
      <j1 rule="para" parents="15052 29215"/>
    </justification>
  </clause>

  <clause id="29236">
    <literal><![CDATA[
      (x / y) \ (x * a(z,u,w)) = y * (a(z,u,w) * a(x * y,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(28596(a,1),29215(a,2,2,2))].">
      <j1 rule="para" parents="28596 29215"/>
    </justification>
  </clause>

  <clause id="29237">
    <literal><![CDATA[
      a(x,y,L(z,x,x * u)) = u \ (R(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,21169,a(flip),b,29228,a),flip(a)].">
      <j1 rule="hyper" parents="63 21169 29228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29238">
    <literal><![CDATA[
      x \ ((x / x) * R(x,y,L(z \ u,z,z \ (x \ 1)))) = a(x,y,x * (((x \ 1) / z) * u))
    ]]></literal>
    <justification jstring="[para(10194(a,1),29228(a,2,3))].">
      <j1 rule="para" parents="10194 29228"/>
    </justification>
  </clause>

  <clause id="29239">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * x = u * (a(z,y,x) * x)
    ]]></literal>
    <justification jstring="[hyper(11227,a,28891,a)].">
      <j1 rule="hyper" parents="11227 28891"/>
    </justification>
  </clause>

  <clause id="29241">
    <literal><![CDATA[
      a(x,(y * (R(y,z,u) \ 1)) \ w,v5) = a(x,(y * y) \ (a(y,z,u) \ w),v5)
    ]]></literal>
    <justification jstring="[para(29008(a,2),24117(a,2,2))].">
      <j1 rule="para" parents="29008 24117"/>
    </justification>
  </clause>

  <clause id="29242">
    <literal><![CDATA[
      x \ ((a(y,z,u \ x) \ 1) * u) = L(x \ u,z,y)
    ]]></literal>
    <justification jstring="[para(29037(a,1),20393(a,1,2,1))].">
      <j1 rule="para" parents="29037 20393"/>
    </justification>
  </clause>

  <clause id="29245">
    <literal><![CDATA[
      (a(x,x,x) \ 1) * ((x \ (x \ R(x,y,z))) \ 1) = (x \ R(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[para(29046(a,1),22924(a,1,1))].">
      <j1 rule="para" parents="29046 22924"/>
    </justification>
  </clause>

  <clause id="29246">
    <literal><![CDATA[
      x * (x * (L(x,y,z) \ u)) = (a(z,y,x) * x) * u
    ]]></literal>
    <justification jstring="[hyper(634,a,29075,a),flip(a)].">
      <j1 rule="hyper" parents="634 29075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29250">
    <literal><![CDATA[
      x * L(a(y,z,u) \ 1,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(y,z,L(u,w,v5)) \ x = v6
    ]]></literal>
    <justification jstring="[para(29136(a,2),28424(a,1,2))].">
      <j1 rule="para" parents="29136 28424"/>
    </justification>
  </clause>

  <clause id="29251">
    <literal><![CDATA[
      a(x * y,y,a(z,u,x)) = a(y,y,x * L(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,28596,a(flip),b,29211,a)].">
      <j1 rule="hyper" parents="63 28596 29211"/>
    </justification>
  </clause>

  <clause id="29252">
    <literal><![CDATA[
      L(x \ 1,y,a(z,u,w)) = x \ a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(128,a,26501,a,b,29222,a),flip(a)].">
      <j1 rule="hyper" parents="128 26501 29222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29253">
    <literal><![CDATA[
      x * R(x \ 1,y,a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(23247(a,2),29222(a,1,2))].">
      <j1 rule="para" parents="23247 29222"/>
    </justification>
  </clause>

  <clause id="29254">
    <literal><![CDATA[
      x \ (a(y,z,u \ x) \ u) = L(x \ u,z,y)
    ]]></literal>
    <justification jstring="[para(28341(a,1),29242(a,1,2))].">
      <j1 rule="para" parents="28341 29242"/>
    </justification>
  </clause>

  <clause id="29255">
    <literal><![CDATA[
      x \ (a(x,y,x * z) \ z) = L(x \ z,y,x)
    ]]></literal>
    <justification jstring="[para(29161(a,1),29254(a,1,2,1))].">
      <j1 rule="para" parents="29161 29254"/>
    </justification>
  </clause>

  <clause id="29256">
    <literal><![CDATA[
      x \ (a(x,y,z * x) \ z) = L(x \ z,y,x)
    ]]></literal>
    <justification jstring="[para(24069(a,1),29255(a,1,2,1))].">
      <j1 rule="para" parents="24069 29255"/>
    </justification>
  </clause>

  <clause id="29257">
    <literal><![CDATA[
      ((a(x,y,z) * z) * u) \ (z * u) = u \ (L(z,y,x) * (z \ u))
    ]]></literal>
    <justification jstring="[para(29246(a,1),27937(a,1,1))].">
      <j1 rule="para" parents="29246 27937"/>
    </justification>
  </clause>

  <clause id="29258">
    <literal><![CDATA[
      a(x * y,y,a(z,u,x)) = a(y,y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,28873,a(flip),b,29251,a),flip(a)].">
      <j1 rule="hyper" parents="347 28873 29251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29259">
    <literal><![CDATA[
      a(x \ 1,y,a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(29068,a,29253,a)].">
      <j1 rule="hyper" parents="29068 29253"/>
    </justification>
  </clause>

  <clause id="29260">
    <literal><![CDATA[
      a(x \ 1,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(29259(a,1),11586(a,1))].">
      <j1 rule="para" parents="29259 11586"/>
    </justification>
  </clause>

  <clause id="29261">
    <literal><![CDATA[
      (a(x,y,L(z,u,w)) * a(x,y,L(z,u,w))) * L(L(z,y,x),u,w) = (a(x,y,L(z,u,w)) \ 1) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(128,a,28852,a(flip),b,302,a),flip(a)].">
      <j1 rule="hyper" parents="128 28852 302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29262">
    <literal><![CDATA[
      L(x,y,z) \ (L(L(x,u,w),y,z) * a(w,u,x)) = a(z,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[para(28887(a,1),28684(a,1,1))].">
      <j1 rule="para" parents="28887 28684"/>
    </justification>
  </clause>

  <clause id="29264">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,L(z,u,w)) = a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(128,a,29114,a(flip),b,26522,a)].">
      <j1 rule="hyper" parents="128 29114 26522"/>
    </justification>
  </clause>

  <clause id="29265">
    <literal><![CDATA[
      a(x,y,L(z,y,y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(29114(a,1),26354(a,1))].">
      <j1 rule="para" parents="29114 26354"/>
    </justification>
  </clause>

  <clause id="29266">
    <literal><![CDATA[
      a(x,y,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * y) = u
    ]]></literal>
    <justification jstring="[para(25258(a,1),29265(a,1))].">
      <j1 rule="para" parents="25258 29265"/>
    </justification>
  </clause>

  <clause id="29267">
    <literal><![CDATA[
      a(x,L(y,z,u),L(w,y,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,L(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(27075(a,1),29265(a,1,3))].">
      <j1 rule="para" parents="27075 29265"/>
    </justification>
  </clause>

  <clause id="29268">
    <literal><![CDATA[
      a(a(x,y,z),y,u * y) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,a(x,y,z),u * a(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(28830(a,1),29266(a,1))].">
      <j1 rule="para" parents="28830 29266"/>
    </justification>
  </clause>

  <clause id="29275">
    <literal><![CDATA[
      a(x,y,(z * x) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(24083(a,1),29201(a,1))].">
      <j1 rule="para" parents="24083 29201"/>
    </justification>
  </clause>

  <clause id="29276">
    <literal><![CDATA[
      a(x,y,L(z,x,x * u)) = L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,28983,a(flip),b,29237,a),flip(a)].">
      <j1 rule="hyper" parents="347 28983 29237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29277">
    <literal><![CDATA[
      a(x,y,L(z,x,x * u)) = a(x,y,L(z,x,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,29113,a,b,29276,a),flip(a)].">
      <j1 rule="hyper" parents="347 29113 29276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29278">
    <literal><![CDATA[
      a(x,y,L(z,x,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(189,a,29264,a,b,28856,a(flip))].">
      <j1 rule="hyper" parents="189 29264 28856"/>
    </justification>
  </clause>

  <clause id="29279">
    <literal><![CDATA[
      R(x,(y * z) * (L(u,z,y) * a(w,v5,L(u,z,y))),v6) = R(x,y * (z * L(u,v5,w)),v6)
    ]]></literal>
    <justification jstring="[para(474(a,1),28871(a,2,2))].">
      <j1 rule="para" parents="474 28871"/>
    </justification>
  </clause>

  <clause id="29280">
    <literal><![CDATA[
      R(x,y,(T(z,z \ u) \ (u \ (z \ u))) * w) = R(x,y,a(u,z,T(z,z * u) \ 1) * w)
    ]]></literal>
    <justification jstring="[para(22754(a,1),28876(a,1,3,1))].">
      <j1 rule="para" parents="22754 28876"/>
    </justification>
  </clause>

  <clause id="29281">
    <literal><![CDATA[
      L(x,y,z) * (a(z,y,x) * a(x,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(28884(a,2),28970(a,1))].">
      <j1 rule="para" parents="28884 28970"/>
    </justification>
  </clause>

  <clause id="29282">
    <literal><![CDATA[
      a(L(x \ 1,y,z),L(x,y,z),u) = a(x \ 1,x,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,28838,a,b,28892,a),flip(a)].">
      <j1 rule="hyper" parents="347 28838 28892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29283">
    <literal><![CDATA[
      L(x,y,z) * (x \ (u / (L(x,y,z) * u))) = a(x \ 1,x,u) / x
    ]]></literal>
    <justification jstring="[para(29282(a,1),27976(a,2,1))].">
      <j1 rule="para" parents="29282 27976"/>
    </justification>
  </clause>

  <clause id="29285">
    <literal><![CDATA[
      L(x,y,z) = R(T(z,z \ 1),y,x) \ (T(z,z \ 1) * x)
    ]]></literal>
    <justification jstring="[para(28960(a,2),28897(a,2,1))].">
      <j1 rule="para" parents="28960 28897"/>
    </justification>
  </clause>

  <clause id="29286">
    <literal><![CDATA[
      L(a(x,y,z) * u,z,a(x,y,z)) = z * (L(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,1407,a(flip),b,28934,a),flip(a)].">
      <j1 rule="hyper" parents="347 1407 28934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29287">
    <literal><![CDATA[
      L(a(x,y,z) * u,z,a(x,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      z * (L(z,y,x) \ u) = w
    ]]></literal>
    <justification jstring="[para(28934(a,2),1429(a,1))].">
      <j1 rule="para" parents="28934 1429"/>
    </justification>
  </clause>

  <clause id="29289">
    <literal><![CDATA[
      a(x,y,z) * R(x,u,w) = R(x,y,z) * a(x,u,w)
    ]]></literal>
    <justification jstring="[para(28905(a,2),28985(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28905 28985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29290">
    <literal><![CDATA[
      R(x,y \ x,y) = R(x,x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(349,a,29009,a)].">
      <j1 rule="hyper" parents="349 29009"/>
    </justification>
  </clause>

  <clause id="29291">
    <literal><![CDATA[
      L((x \ 1) \ y,x,L(x,z,u)) = x * L(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,23670,a(flip),b,29010,a)].">
      <j1 rule="hyper" parents="63 23670 29010"/>
    </justification>
  </clause>

  <clause id="29292">
    <literal><![CDATA[
      R(x,y,(z \ a(z,u,w)) * v5) = R(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,27751,a(flip),b,29026,a),flip(a)].">
      <j1 rule="hyper" parents="347 27751 29026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29293">
    <literal><![CDATA[
      R(x,y,(z \ a(z,u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y,L(z,u,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(29026(a,2),27752(a,1))].">
      <j1 rule="para" parents="29026 27752"/>
    </justification>
  </clause>

  <clause id="29294">
    <literal><![CDATA[
      a(x,y,y) \ (z * (x * y)) = z * (x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,27841,a(flip),b,29089,a)].">
      <j1 rule="hyper" parents="63 27841 29089"/>
    </justification>
  </clause>

  <clause id="29295">
    <literal><![CDATA[
      (a(x,y,y) \ z) * (x * y) = z * (x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(25380,a,29294,a)].">
      <j1 rule="hyper" parents="25380 29294"/>
    </justification>
  </clause>

  <clause id="29296">
    <literal><![CDATA[
      ((a(x,y,y) \ z) * y) * (x * y) = (z * y) * (x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(23121(a,1),29295(a,1,1))].">
      <j1 rule="para" parents="23121 29295"/>
    </justification>
  </clause>

  <clause id="29297">
    <literal><![CDATA[
      L(a(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(29148(a,1),401(a,1)),flip(b)].">
      <j1 rule="para" parents="29148 401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29298">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,y,L(L(x,u,w),x,y)) = v5
    ]]></literal>
    <justification jstring="[para(29137(a,1),29297(a,1))].">
      <j1 rule="para" parents="29137 29297"/>
    </justification>
  </clause>

  <clause id="29299">
    <literal><![CDATA[
      a(x,y,a(z,u,(x * w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w \ (x \ v5))) = v6
    ]]></literal>
    <justification jstring="[para(329(a,1),29205(a,1,3,3))].">
      <j1 rule="para" parents="329 29205"/>
    </justification>
  </clause>

  <clause id="29300">
    <literal><![CDATA[
      L(x / y,y,a(z,u,y)) = L(x,y,a(z,u,y)) / y
    ]]></literal>
    <justification jstring="[hyper(29054,a,29217,a)].">
      <j1 rule="hyper" parents="29054 29217"/>
    </justification>
  </clause>

  <clause id="29302">
    <literal><![CDATA[
      L(x,y,z) = T(z,z \ 1) * (R(T(z,z \ 1),y,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,1753,a(flip),b,29285,a),flip(a)].">
      <j1 rule="hyper" parents="347 1753 29285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29303">
    <literal><![CDATA[
      R(x,y,z) * L(z,y,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(134,a,29285,a,b,22357,a(flip))].">
      <j1 rule="hyper" parents="134 29285 22357"/>
    </justification>
  </clause>

  <clause id="29309">
    <literal><![CDATA[
      L(a(x,y,z) * u,z,a(z,y,x)) = z * (L(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(27578,a,29286,a)].">
      <j1 rule="hyper" parents="27578 29286"/>
    </justification>
  </clause>

  <clause id="29311">
    <literal><![CDATA[
      a(x,y,z) * ((x * (L(x,y,z) \ u)) * x) = (a(z,y,x) * u) * (a(x,y,z) * x)
    ]]></literal>
    <justification jstring="[para(29286(a,1),27570(a,1,2,1))].">
      <j1 rule="para" parents="29286 27570"/>
    </justification>
  </clause>

  <clause id="29312">
    <literal><![CDATA[
      R(x,y,(z \ a(z,z,u \ ((u \ w) \ R(u,v5,u)))) * (w \ u)) = R(x,y,z \ (u \ ((u \ w) \ R(u,v5,u))))
    ]]></literal>
    <justification jstring="[hyper(347,a,23559,a(flip),b,29292,a),flip(a)].">
      <j1 rule="hyper" parents="347 23559 29292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29313">
    <literal><![CDATA[
      L(x,y,z) = z * (R(z,y,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,21117,a(flip),b,29302,a),flip(a)].">
      <j1 rule="hyper" parents="347 21117 29302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29316">
    <literal><![CDATA[
      L(x,y,z) * R(z,y,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(133,a,29313,a,b,21071,a)].">
      <j1 rule="hyper" parents="133 29313 21071"/>
    </justification>
  </clause>

  <clause id="29317">
    <literal><![CDATA[
      (L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u) = a(L(x,y,z),R(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(29316(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="29316 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29319">
    <literal><![CDATA[
      (x \ y) * L(a(z,u,x),x,y) = L(x,u,z) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,27939,a(flip),b,28901,a),flip(a)].">
      <j1 rule="hyper" parents="63 27939 28901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29320">
    <literal><![CDATA[
      (x \ y) * a(z,u,L(x,x,y)) = L(x,u,z) \ y
    ]]></literal>
    <justification jstring="[para(29113(a,2),29319(a,1,2))].">
      <j1 rule="para" parents="29113 29319"/>
    </justification>
  </clause>

  <clause id="29321">
    <literal><![CDATA[
      a(x,y,z) \ a(u,w,L(R(x,y,z),R(x,y,z),x)) = L(R(x,y,z),w,u) \ x
    ]]></literal>
    <justification jstring="[hyper(29065,a,29320,a)].">
      <j1 rule="hyper" parents="29065 29320"/>
    </justification>
  </clause>

  <clause id="29322">
    <literal><![CDATA[
      x \ a(y,z,L(u,x,x)) = a(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(23043,a,29131,a)].">
      <j1 rule="hyper" parents="23043 29131"/>
    </justification>
  </clause>

  <clause id="29323">
    <literal><![CDATA[
      x / ((a(y,z,u) \ w) * (w \ x)) = a(y,z,L(u,w,x * w))
    ]]></literal>
    <justification jstring="[hyper(222,a,29152,a)].">
      <j1 rule="hyper" parents="222 29152"/>
    </justification>
  </clause>

  <clause id="29324">
    <literal><![CDATA[
      a(x,y,L(z,T(u,T(w,v5)),T(u * w,K(w,v5)))) \ w = (a(x,y,z) \ T(u,T(w,v5))) * (T(u,T(w,v5)) \ w)
    ]]></literal>
    <justification jstring="[para(6060(a,2),29152(a,1,1,3,3))].">
      <j1 rule="para" parents="6060 29152"/>
    </justification>
  </clause>

  <clause id="29325">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * (u \ w)) \ w = a(x,y,L(z,u,w * u))
    ]]></literal>
    <justification jstring="[para(29152(a,1),19984(a,1,1))].">
      <j1 rule="para" parents="29152 19984"/>
    </justification>
  </clause>

  <clause id="29326">
    <literal><![CDATA[
      (x * L(y,y,z)) * (z * y) = (x * y) * (z / (y \ 1))
    ]]></literal>
    <justification jstring="[para(27838(a,1),29296(a,1,1))].">
      <j1 rule="para" parents="27838 29296"/>
    </justification>
  </clause>

  <clause id="29327">
    <literal><![CDATA[
      (((x * y) * (z / (y \ 1))) / (L(y,y,z) * (z * y))) * z = (x * (z / (y * z))) * (y * z)
    ]]></literal>
    <justification jstring="[para(29326(a,1),27757(a,1,1,1))].">
      <j1 rule="para" parents="29326 27757"/>
    </justification>
  </clause>

  <clause id="29328">
    <literal><![CDATA[
      a(x,y,L(z,u,w * u)) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      (a(x,y,z) \ u) * (u \ w) = v5
    ]]></literal>
    <justification jstring="[para(29323(a,1),359(a,1,1))].">
      <j1 rule="para" parents="29323 359"/>
    </justification>
  </clause>

  <clause id="29329">
    <literal><![CDATA[
      L(a(x,y,z),z,u * z) = u \ (z * (L(z,y,x) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,28919,a(flip),b,28898,a)].">
      <j1 rule="hyper" parents="63 28919 28898"/>
    </justification>
  </clause>

  <clause id="29330">
    <literal><![CDATA[
      x \ (y * (L(y,z,u) \ x)) = L(a(u,z,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(26215,a,29329,a),flip(a)].">
      <j1 rule="hyper" parents="26215 29329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29331">
    <literal><![CDATA[
      L(a(x,y,z \ u),z \ u,u) = (z * L(z \ u,y,x)) \ u
    ]]></literal>
    <justification jstring="[hyper(63,a,27928,a(flip),b,29330,a),flip(a)].">
      <j1 rule="hyper" parents="63 27928 29330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29332">
    <literal><![CDATA[
      a(x,y,L(z \ u,z \ u,u)) = (z * L(z \ u,y,x)) \ u
    ]]></literal>
    <justification jstring="[hyper(29297,a,29331,a)].">
      <j1 rule="hyper" parents="29297 29331"/>
    </justification>
  </clause>

  <clause id="29333">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) \ y = a(u,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(24763,a,29332,a),flip(a)].">
      <j1 rule="hyper" parents="24763 29332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29334">
    <literal><![CDATA[
      L(L(x,y,z) \ u,x,a(z,y,x)) = (x \ u) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(29054,a,28902,a)].">
      <j1 rule="hyper" parents="29054 28902"/>
    </justification>
  </clause>

  <clause id="29335">
    <literal><![CDATA[
      R(x,y * a(z \ 1,u,w),v5) = R(x,a(w,u,z) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,28877,a(flip),b,28911,a),flip(a)].">
      <j1 rule="hyper" parents="63 28877 28911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29336">
    <literal><![CDATA[
      R(x,(((y * z) \ z) * y) \ u,w) = R(x,a(z,y,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,28443,a,b,29335,a)].">
      <j1 rule="hyper" parents="63 28443 29335"/>
    </justification>
  </clause>

  <clause id="29337">
    <literal><![CDATA[
      R(x,y * a(z * u,z,z),w) = R(x,a(u,z,z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,28139,a(flip),b,29336,a)].">
      <j1 rule="hyper" parents="63 28139 29336"/>
    </justification>
  </clause>

  <clause id="29338">
    <literal><![CDATA[
      L(1 / x,y,z) * R(x,u,w) = a(z,y,x) \ a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,29093,a(flip),b,29004,a),flip(a)].">
      <j1 rule="hyper" parents="347 29093 29004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29339">
    <literal><![CDATA[
      T((x \ L(R(y,z,u),w,v5)) \ a(v6,v7,x \ L(L(y,z,u),w,v5)),v8 \ L(R(v8,v9,v10),v11,v12)) = L(x \ L(R(y,z,u),w,v5),v7,v6) \ 1
    ]]></literal>
    <justification jstring="[para(25310(a,1),29034(a,1,1,2))].">
      <j1 rule="para" parents="25310 29034"/>
    </justification>
  </clause>

  <clause id="29340">
    <literal><![CDATA[
      a(x,y,z) \ (a(u,w,x) \ 1) = R(x,y,z) \ L(x,w,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,29025,a(flip),b,29038,a),flip(a)].">
      <j1 rule="hyper" parents="347 29025 29038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29341">
    <literal><![CDATA[
      a(x,y,z) \ (a(z,u,w) \ 1) = R(z,u,w) \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(28440,a,29340,a)].">
      <j1 rule="hyper" parents="28440 29340"/>
    </justification>
  </clause>

  <clause id="29342">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (a(z,y,x) \ u) = (R(x,y,z) \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(29341(a,1),28777(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29341 28777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29343">
    <literal><![CDATA[
      L(x,y,z) * (a(z,y,x) * u) = x * L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,29291,a(flip),b,29079,a),flip(a)].">
      <j1 rule="hyper" parents="63 29291 29079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29344">
    <literal><![CDATA[
      x \ (a(x,y,z) \ R(x,u,w)) = R(x,y,z) \ R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,21441,a(flip),b,29083,a),flip(a)].">
      <j1 rule="hyper" parents="347 21441 29083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29345">
    <literal><![CDATA[
      a(x,y,z) \ a(x,u,w) = R(x,y,z) \ R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,28959,a(flip),b,29344,a)].">
      <j1 rule="hyper" parents="63 28959 29344"/>
    </justification>
  </clause>

  <clause id="29346">
    <literal><![CDATA[
      L(x * y,x,a(z,u,x)) = a(z,u,x) * (L(x,u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(29054,a,29094,a)].">
      <j1 rule="hyper" parents="29054 29094"/>
    </justification>
  </clause>

  <clause id="29347">
    <literal><![CDATA[
      L(x * y,x,a(z,u,x)) = L(x,u,z) * (a(z,u,x) * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,21177,a,b,29346,a),flip(a)].">
      <j1 rule="hyper" parents="347 21177 29346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29348">
    <literal><![CDATA[
      L(x * y,x,a(z,u,x)) = x * L(y,x,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,29343,a(flip),b,29347,a),flip(a)].">
      <j1 rule="hyper" parents="347 29343 29347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29349">
    <literal><![CDATA[
      L(x * (y * z),x,a(y,u,x)) = L(x,u,y) * (y * (a(y,u,x) * z))
    ]]></literal>
    <justification jstring="[para(25377(a,1),29347(a,2,2))].">
      <j1 rule="para" parents="25377 29347"/>
    </justification>
  </clause>

  <clause id="29350">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(127,a,26494,a,b,29099,a),flip(a)].">
      <j1 rule="hyper" parents="127 26494 29099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29351">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * z) * a(x,y,a(z,z,u)) = u * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(23121(a,1),29099(a,1,1))].">
      <j1 rule="para" parents="23121 29099"/>
    </justification>
  </clause>

  <clause id="29352">
    <literal><![CDATA[
      L(x,y,a(z,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(26597,a,29350,a)].">
      <j1 rule="hyper" parents="26597 29350"/>
    </justification>
  </clause>

  <clause id="29353">
    <literal><![CDATA[
      (x * y) * a(z,z,y) = x * (y * a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(1093,a,29350,a)].">
      <j1 rule="hyper" parents="1093 29350"/>
    </justification>
  </clause>

  <clause id="29354">
    <literal><![CDATA[
      a(x * y,a(x,x,y),z) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,26605,a(flip),b,29350,a)].">
      <j1 rule="hyper" parents="63 26605 29350"/>
    </justification>
  </clause>

  <clause id="29355">
    <literal><![CDATA[
      a(x,y,a(y,z * y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,26367,a(flip),b,29350,a)].">
      <j1 rule="hyper" parents="63 26367 29350"/>
    </justification>
  </clause>

  <clause id="29356">
    <literal><![CDATA[
      a(x,y * z,a(z,z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,25342,a(flip),b,29350,a)].">
      <j1 rule="hyper" parents="63 25342 29350"/>
    </justification>
  </clause>

  <clause id="29357">
    <literal><![CDATA[
      a(x,y * z,a(y,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,25341,a(flip),b,29350,a)].">
      <j1 rule="hyper" parents="63 25341 29350"/>
    </justification>
  </clause>

  <clause id="29358">
    <literal><![CDATA[
      a(x,x,L(y,y,z)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(189,a,29147,a,b,29350,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="189 29147 29350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29359">
    <literal><![CDATA[
      L(x,y * z,a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(27623,a,29352,a)].">
      <j1 rule="hyper" parents="27623 29352"/>
    </justification>
  </clause>

  <clause id="29360">
    <literal><![CDATA[
      L(x,y,a(y,z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(27578,a,29352,a)].">
      <j1 rule="hyper" parents="27578 29352"/>
    </justification>
  </clause>

  <clause id="29361">
    <literal><![CDATA[
      (a(x,x,y) * y) * z = a(x,x,y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1362,a,29352,a),flip(a)].">
      <j1 rule="hyper" parents="1362 29352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29362">
    <literal><![CDATA[
      a(x,x,y) * (L(y,x,x) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(63,a,29346,a(flip),b,29352,a)].">
      <j1 rule="hyper" parents="63 29346 29352"/>
    </justification>
  </clause>

  <clause id="29363">
    <literal><![CDATA[
      (x \ y) * a(z,z,x) = L(x,z,z) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,29334,a(flip),b,29352,a)].">
      <j1 rule="hyper" parents="63 29334 29352"/>
    </justification>
  </clause>

  <clause id="29364">
    <literal><![CDATA[
      x * (L(x,y,y) \ z) = a(y,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(63,a,29286,a(flip),b,29352,a)].">
      <j1 rule="hyper" parents="63 29286 29352"/>
    </justification>
  </clause>

  <clause id="29365">
    <literal><![CDATA[
      L(x,y,a(z,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(29352(a,1),50(a,2))].">
      <j1 rule="para" parents="29352 50"/>
    </justification>
  </clause>

  <clause id="29367">
    <literal><![CDATA[
      x * (a(x,y,y) * z) = R(x,y,y) * z
    ]]></literal>
    <justification jstring="[para(29360(a,1),25403(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29360 25403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29368">
    <literal><![CDATA[
      a(x * y,a(y,x,x),z) = 1
    ]]></literal>
    <justification jstring="[hyper(26574,a,29354,a)].">
      <j1 rule="hyper" parents="26574 29354"/>
    </justification>
  </clause>

  <clause id="29370">
    <literal><![CDATA[
      L(x,a(y,y,z),y * z) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,29354,a)].">
      <j1 rule="hyper" parents="52 29354"/>
    </justification>
  </clause>

  <clause id="29371">
    <literal><![CDATA[
      L(x,y,a(y,z * y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(26597,a,29355,a)].">
      <j1 rule="hyper" parents="26597 29355"/>
    </justification>
  </clause>

  <clause id="29373">
    <literal><![CDATA[
      a(x,y * z,a(y,z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(26560,a,29356,a)].">
      <j1 rule="hyper" parents="26560 29356"/>
    </justification>
  </clause>

  <clause id="29374">
    <literal><![CDATA[
      (x * (y * z)) * T(a(z,z,y),y * z) = x * (a(z,z,y) * (y * z))
    ]]></literal>
    <justification jstring="[hyper(189,a,18772,a(flip),b,29356,a(flip))].">
      <j1 rule="hyper" parents="189 18772 29356"/>
    </justification>
  </clause>

  <clause id="29375">
    <literal><![CDATA[
      (x * y) * (a(x,x,y) * z) = (R(x,x,y) * y) * z
    ]]></literal>
    <justification jstring="[para(29359(a,1),22189(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29359 22189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29376">
    <literal><![CDATA[
      ((x * y) * a(y,x,x)) * T(z,a(y,x,x)) = (x * y) * (z * a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(193,a,13385,a,b,29368,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="193 13385 29368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29377">
    <literal><![CDATA[
      L(x,a(y,y,z),y * z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(29370(a,1),50(a,2))].">
      <j1 rule="para" parents="29370 50"/>
    </justification>
  </clause>

  <clause id="29378">
    <literal><![CDATA[
      L(x,y,a(y,z * y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(29371(a,1),50(a,2))].">
      <j1 rule="para" parents="29371 50"/>
    </justification>
  </clause>

  <clause id="29379">
    <literal><![CDATA[
      L(x,y * z,a(y,z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(26597,a,29373,a)].">
      <j1 rule="hyper" parents="26597 29373"/>
    </justification>
  </clause>

  <clause id="29380">
    <literal><![CDATA[
      (x * (y * z)) * T(a(y,z,z),y * z) = x * (a(y,z,z) * (y * z))
    ]]></literal>
    <justification jstring="[hyper(189,a,18772,a(flip),b,29373,a(flip))].">
      <j1 rule="hyper" parents="189 18772 29373"/>
    </justification>
  </clause>

  <clause id="29381">
    <literal><![CDATA[
      (a(x,y,y) \ (x * y)) \ z = (x * y) \ (a(x,y,y) * z)
    ]]></literal>
    <justification jstring="[hyper(28524,a,29379,a)].">
      <j1 rule="hyper" parents="28524 29379"/>
    </justification>
  </clause>

  <clause id="29383">
    <literal><![CDATA[
      a(x,y,y) * ((z \ a(z,z,y)) * y) = z \ (y * a(x,y,y))
    ]]></literal>
    <justification jstring="[para(29358(a,1),26883(a,1,2,1,2))].">
      <j1 rule="para" parents="29358 26883"/>
    </justification>
  </clause>

  <clause id="29384">
    <literal><![CDATA[
      L(x,a(y,y,z),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(20042(a,1),29377(a,1))].">
      <j1 rule="para" parents="20042 29377"/>
    </justification>
  </clause>

  <clause id="29385">
    <literal><![CDATA[
      L(x,y,a(y,y * z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(24037(a,1),29378(a,1,3))].">
      <j1 rule="para" parents="24037 29378"/>
    </justification>
  </clause>

  <clause id="29386">
    <literal><![CDATA[
      L(x,y,y) * (x \ z) = a(y,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(128,a,10,a(flip),b,29362,a),flip(a)].">
      <j1 rule="hyper" parents="128 10 29362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29387">
    <literal><![CDATA[
      a(x,x,y) \ (L(y,x,x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(20594,a,29363,a)].">
      <j1 rule="hyper" parents="20594 29363"/>
    </justification>
  </clause>

  <clause id="29388">
    <literal><![CDATA[
      a(x,x,y) * (y \ z) = L(y,x,x) \ z
    ]]></literal>
    <justification jstring="[hyper(20479,a,29363,a)].">
      <j1 rule="hyper" parents="20479 29363"/>
    </justification>
  </clause>

  <clause id="29389">
    <literal><![CDATA[
      (L(x,y,z) \ u) * a(y,y,x) = L(L(x,y,z),y,y) \ u
    ]]></literal>
    <justification jstring="[para(26273(a,1),29363(a,1,2))].">
      <j1 rule="para" parents="26273 29363"/>
    </justification>
  </clause>

  <clause id="29390">
    <literal><![CDATA[
      a(x,y,y) * (R(x,y,y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(128,a,10,a(flip),b,29367,a),flip(a)].">
      <j1 rule="hyper" parents="128 10 29367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29391">
    <literal><![CDATA[
      (x / y) * R(y,z,z) = a(y,z,z) * x
    ]]></literal>
    <justification jstring="[hyper(34,a,20930,a,b,29367,a)].">
      <j1 rule="hyper" parents="34 20930 29367"/>
    </justification>
  </clause>

  <clause id="29392">
    <literal><![CDATA[
      a(x,y * (a((z * z) \ y,u,u) * w),v5) = a(x,R((z * z) \ y,u,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(29367(a,1),24482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29367 24482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29393">
    <literal><![CDATA[
      ((x / y) \ L(x,z,u)) * ((y \ 1) * x) = a(y,y,x) \ L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,26983,a,b,29386,a)].">
      <j1 rule="hyper" parents="63 26983 29386"/>
    </justification>
  </clause>

  <clause id="29394">
    <literal><![CDATA[
      a(x,x,y) * (z * L(y,x,x)) = z * y
    ]]></literal>
    <justification jstring="[hyper(134,a,20683,a(flip),b,29386,a(flip))].">
      <j1 rule="hyper" parents="134 20683 29386"/>
    </justification>
  </clause>

  <clause id="29395">
    <literal><![CDATA[
      (a(x,x,y) \ z) * y = z * L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,29386,a(flip),b,20687,a)].">
      <j1 rule="hyper" parents="133 29386 20687"/>
    </justification>
  </clause>

  <clause id="29396">
    <literal><![CDATA[
      R(x,(a(y,y,z) \ u) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,w * ((z \ u) * L(z,y,y)),v5) = v6
    ]]></literal>
    <justification jstring="[para(29386(a,1),22477(a,1,2,1))].">
      <j1 rule="para" parents="29386 22477"/>
    </justification>
  </clause>

  <clause id="29397">
    <literal><![CDATA[
      a(x,y,y) * (z * x) = z * R(x,y,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),29391(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 29391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29398">
    <literal><![CDATA[
      R(x,y * ((z \ u) * R(z,w,w)),v5) = R(x,y * (a(z,w,w) * u),v5)
    ]]></literal>
    <justification jstring="[para(29391(a,1),22452(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="29391 22452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29400">
    <literal><![CDATA[
      (a(a(x,y,z) * u,a(x,y,z) * u,a(x,y,z) \ 1) \ w) * (a(x,y,z) \ 1) = w * L(a(x,y,z) \ 1,u,a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(28512(a,1),29395(a,2,2))].">
      <j1 rule="para" parents="28512 29395"/>
    </justification>
  </clause>

  <clause id="29401">
    <literal><![CDATA[
      a(x,y,y) * (z * (a(y,u,w) * x)) = z * R(a(y,u,w) * x,y,y)
    ]]></literal>
    <justification jstring="[para(28019(a,1),29397(a,1,1))].">
      <j1 rule="para" parents="28019 29397"/>
    </justification>
  </clause>

  <clause id="29402">
    <literal><![CDATA[
      a(x,((y \ z) \ y) * a(u,u,z \ y),w) = a(x,y * ((z \ y) * a(u,u,z \ y)),w)
    ]]></literal>
    <justification jstring="[para(29353(a,1),24829(a,2,2))].">
      <j1 rule="para" parents="29353 24829"/>
    </justification>
  </clause>

  <clause id="29403">
    <literal><![CDATA[
      (a(x,x,y) * y) * z = y * (z * a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,20597,a(flip),b,29361,a),flip(a)].">
      <j1 rule="hyper" parents="347 20597 29361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29404">
    <literal><![CDATA[
      (x * a(y,y,x)) * z = x * (z * a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(20022,a,29403,a)].">
      <j1 rule="hyper" parents="20022 29403"/>
    </justification>
  </clause>

  <clause id="29405">
    <literal><![CDATA[
      a(x,y * (z * (u * a(w,w,z))),v5) = a(x,y * (L(z,w,w) * u),v5)
    ]]></literal>
    <justification jstring="[para(29403(a,1),24830(a,1,2,2))].">
      <j1 rule="para" parents="29403 24830"/>
    </justification>
  </clause>

  <clause id="29406">
    <literal><![CDATA[
      R(x,((y * a(z,z,u)) * u) * w,v5) = R(x,w * ((u * a(z,z,u)) * y),v5)
    ]]></literal>
    <justification jstring="[para(29404(a,2),22473(a,2,2,2))].">
      <j1 rule="para" parents="29404 22473"/>
    </justification>
  </clause>

  <clause id="29407">
    <literal><![CDATA[
      (x * y) * (z * a(x,x,y)) = (R(x,x,y) * y) * z
    ]]></literal>
    <justification jstring="[hyper(20023,a,29375,a)].">
      <j1 rule="hyper" parents="20023 29375"/>
    </justification>
  </clause>

  <clause id="29408">
    <literal><![CDATA[
      (x * (y * (a(x,x,y) * z))) \ ((R(x,x,y) * y) * z) = a(x,y,a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(128,a,29375,a(flip),b,86,a)].">
      <j1 rule="hyper" parents="128 29375 86"/>
    </justification>
  </clause>

  <clause id="29409">
    <literal><![CDATA[
      (x * (a(x,y,y) \ y)) \ z = (x * y) \ (a(x,y,y) * z)
    ]]></literal>
    <justification jstring="[para(25402(a,1),29381(a,1,1))].">
      <j1 rule="para" parents="25402 29381"/>
    </justification>
  </clause>

  <clause id="29410">
    <literal><![CDATA[
      (x * y) \ (a(x,y,y) * z) = (x / (y \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(25419(a,1),29409(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25419 29409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29411">
    <literal><![CDATA[
      ((x * y) \ z) * a(x,y,y) = (x / (y \ 1)) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,25510,a(flip),b,29410,a)].">
      <j1 rule="hyper" parents="63 25510 29410"/>
    </justification>
  </clause>

  <clause id="29412">
    <literal><![CDATA[
      a(x,y,y) \ ((x / (y \ 1)) \ z) = (x * y) \ z
    ]]></literal>
    <justification jstring="[hyper(20594,a,29411,a)].">
      <j1 rule="hyper" parents="20594 29411"/>
    </justification>
  </clause>

  <clause id="29413">
    <literal><![CDATA[
      a(x,y,y) * ((x * y) \ z) = (x / (y \ 1)) \ z
    ]]></literal>
    <justification jstring="[hyper(20479,a,29411,a)].">
      <j1 rule="hyper" parents="20479 29411"/>
    </justification>
  </clause>

  <clause id="29415">
    <literal><![CDATA[
      L(x,x,y) * ((y / (x \ 1)) \ z) = x * ((y * x) \ z)
    ]]></literal>
    <justification jstring="[para(29412(a,1),27835(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29412 27835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29416">
    <literal><![CDATA[
      a(x,1 / y,1 / y) * ((x * (1 / y)) \ z) = (x / y) \ z
    ]]></literal>
    <justification jstring="[para(83(a,1),29413(a,2,1,2))].">
      <j1 rule="para" parents="83 29413"/>
    </justification>
  </clause>

  <clause id="29417">
    <literal><![CDATA[
      (x \ (y \ x)) * ((y \ x) \ z) = y * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,22718,a(flip),b,29415,a)].">
      <j1 rule="hyper" parents="63 22718 29415"/>
    </justification>
  </clause>

  <clause id="29418">
    <literal><![CDATA[
      x \ (y * a(z,y,y)) = a(z,y,y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(18983(a,1),29383(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18983 29383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29420">
    <literal><![CDATA[
      x \ (a(y,z,z) * z) = a(y,z,z) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(21188,a,29418,a)].">
      <j1 rule="hyper" parents="21188 29418"/>
    </justification>
  </clause>

  <clause id="29421">
    <literal><![CDATA[
      L(x \ y,a(z,y,y),a(z,y,y) \ u) * u = (x \ y) * (((u / a(z,y,y)) * (x \ (a(z,y,y) * y))) / (x \ y))
    ]]></literal>
    <justification jstring="[para(29420(a,2),13870(a,2,2,1,2))].">
      <j1 rule="para" parents="29420 13870"/>
    </justification>
  </clause>

  <clause id="29422">
    <literal><![CDATA[
      a(x,1 / y,y) * ((x * (1 / y)) \ z) = (x / y) \ z
    ]]></literal>
    <justification jstring="[para(14923(a,1),29416(a,1,1))].">
      <j1 rule="para" parents="14923 29416"/>
    </justification>
  </clause>

  <clause id="29423">
    <literal><![CDATA[
      a(x,y,y) * ((x * (1 / y)) \ z) = (x / y) \ z
    ]]></literal>
    <justification jstring="[para(14964(a,1),29422(a,1,1))].">
      <j1 rule="para" parents="14964 29422"/>
    </justification>
  </clause>

  <clause id="29424">
    <literal><![CDATA[
      R(x,L((y * (1 / z)) \ u,a(y,z,z),a(y,z,z)),w) = R(x,((y / z) \ u) * a(y,z,z),w)
    ]]></literal>
    <justification jstring="[para(29423(a,1),22489(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="29423 22489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29426">
    <literal><![CDATA[
      (x * y) * a(z,u,L(w,x,y)) = (a(z,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,29198,a(flip),b,25485,a(flip))].">
      <j1 rule="hyper" parents="134 29198 25485"/>
    </justification>
  </clause>

  <clause id="29427">
    <literal><![CDATA[
      L(a(x,a(y,z,u),w) * a(y,z,u),w,x) = a(y,z,L(u,x,w))
    ]]></literal>
    <justification jstring="[para(28388(a,1),29198(a,1,1))].">
      <j1 rule="para" parents="28388 29198"/>
    </justification>
  </clause>

  <clause id="29428">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) * z = (v5 * z) * a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(25390(a,1),29426(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="25390 29426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29429">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) * R(y,u,z) = a(y,u,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(28905(a,2),29218(a,2,1))].">
      <j1 rule="para" parents="28905 29218"/>
    </justification>
  </clause>

  <clause id="29430">
    <literal><![CDATA[
      x * (y * a(z,u,y * (x \ y))) = (1 / (x * y)) \ a(z,u,x)
    ]]></literal>
    <justification jstring="[hyper(25287,a,29231,a)].">
      <j1 rule="hyper" parents="25287 29231"/>
    </justification>
  </clause>

  <clause id="29431">
    <literal><![CDATA[
      x \ (L(y,z,u) * (y \ x)) = L(a(u,z,y) \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,28490,a(flip),b,29257,a),flip(a)].">
      <j1 rule="hyper" parents="63 28490 29257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29432">
    <literal><![CDATA[
      x \ (y * (L(y,a(z,u,w),v5) \ x)) = L(a(v5,a(w,u,z),y) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(28763(a,1),29431(a,1,2))].">
      <j1 rule="para" parents="28763 29431"/>
    </justification>
  </clause>

  <clause id="29433">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),z,y)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(29298,a,28846,a)].">
      <j1 rule="hyper" parents="29298 28846"/>
    </justification>
  </clause>

  <clause id="29434">
    <literal><![CDATA[
      a(x,y,L(z \ ((z / u) * (w * u)),T(w,u),y)) = a(x,y,L(T(w,u),u,u \ z))
    ]]></literal>
    <justification jstring="[para(10155(a,1),29433(a,1,3,1))].">
      <j1 rule="para" parents="10155 29433"/>
    </justification>
  </clause>

  <clause id="29435">
    <literal><![CDATA[
      a(x,x,a(y,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(127,a,29395,a,b,29351,a),flip(a)].">
      <j1 rule="hyper" parents="127 29395 29351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29436">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(26597,a,29435,a)].">
      <j1 rule="hyper" parents="26597 29435"/>
    </justification>
  </clause>

  <clause id="29437">
    <literal><![CDATA[
      a(x,y,L(y,z,z)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(189,a,29264,a,b,29435,a(flip))].">
      <j1 rule="hyper" parents="189 29264 29435"/>
    </justification>
  </clause>

  <clause id="29438">
    <literal><![CDATA[
      a(x,x,L(y,z,z)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(189,a,29147,a,b,29435,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="189 29147 29435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29440">
    <literal><![CDATA[
      a(x,y * z,y \ z) = a(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(25257,a,29437,a)].">
      <j1 rule="hyper" parents="25257 29437"/>
    </justification>
  </clause>

  <clause id="29441">
    <literal><![CDATA[
      (x / y) \ L(x,x,z) = a(z,x,x) \ y
    ]]></literal>
    <justification jstring="[para(29437(a,1),28122(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29437 28122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29442">
    <literal><![CDATA[
      a(x,y,y) * (z \ 1) = z \ a(x,y,y)
    ]]></literal>
    <justification jstring="[para(29437(a,1),29322(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29437 29322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29444">
    <literal><![CDATA[
      a(x,x,y \ z) = a(x,x,y * z)
    ]]></literal>
    <justification jstring="[hyper(25257,a,29438,a)].">
      <j1 rule="hyper" parents="25257 29438"/>
    </justification>
  </clause>

  <clause id="29445">
    <literal><![CDATA[
      a(x,x,y * (z \ y)) = a(x,x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,25291,a(flip),b,29438,a)].">
      <j1 rule="hyper" parents="63 25291 29438"/>
    </justification>
  </clause>

  <clause id="29446">
    <literal><![CDATA[
      R(x,x,L(y,z,z)) = x * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,29438,a(flip),b,18988,a),flip(a)].">
      <j1 rule="hyper" parents="134 29438 18988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29449">
    <literal><![CDATA[
      x * a(y,y,z \ u) = x * a(y,y,u * z)
    ]]></literal>
    <justification jstring="[para(29438(a,1),25262(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29438 25262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29450">
    <literal><![CDATA[
      a(x,x,y) * (L(y,z,z) \ u) = L(L(y,z,z),x,x) \ u
    ]]></literal>
    <justification jstring="[para(29438(a,1),29388(a,1,1))].">
      <j1 rule="para" parents="29438 29388"/>
    </justification>
  </clause>

  <clause id="29451">
    <literal><![CDATA[
      (x \ y) \ (x \ L(y,z,z)) = a(z,z,y) \ 1
    ]]></literal>
    <justification jstring="[para(29445(a,1),24847(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29445 24847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29453">
    <literal><![CDATA[
      R(x,x,L(y,z,z)) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,28958,a,b,29446,a),flip(a)].">
      <j1 rule="hyper" parents="347 28958 29446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29456">
    <literal><![CDATA[
      R(x * y,x * y,y) = (((x * y) \ 1) \ T(x,z)) / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21158,a(flip),b,29453,a),flip(a)].">
      <j1 rule="hyper" parents="63 21158 29453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29457">
    <literal><![CDATA[
      a(x,y,y) \ (z \ y) = z \ L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(646,a,29441,a),flip(a)].">
      <j1 rule="hyper" parents="646 29441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29459">
    <literal><![CDATA[
      a(x,y,y) \ (z \ a(x,y,y)) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(138,a,29442,a)].">
      <j1 rule="hyper" parents="138 29442"/>
    </justification>
  </clause>

  <clause id="29460">
    <literal><![CDATA[
      x * (a(y,z,z) * (R(x,u,a(y,z,z)) \ 1)) = L(a(y,z,z),u,x)
    ]]></literal>
    <justification jstring="[para(29442(a,2),29313(a,2,2)),flip(a)].">
      <j1 rule="para" parents="29442 29313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29461">
    <literal><![CDATA[
      (x \ y) \ ((a(z,y,y) \ (x \ y)) * u) = (u * (x \ L(y,y,z))) / (x \ y)
    ]]></literal>
    <justification jstring="[para(29457(a,1),25873(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="29457 25873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29462">
    <literal><![CDATA[
      L(x,x \ y,a(y,y,z)) = L(y,y,z) / (x \ L(y,y,z))
    ]]></literal>
    <justification jstring="[para(29457(a,1),28090(a,2,2))].">
      <j1 rule="para" parents="29457 28090"/>
    </justification>
  </clause>

  <clause id="29463">
    <literal><![CDATA[
      ((x \ y) \ z) * a(u,u,y * x) = L(x \ y,u,u) \ z
    ]]></literal>
    <justification jstring="[hyper(63,a,29363,a(flip),b,29449,a),flip(a)].">
      <j1 rule="hyper" parents="63 29363 29449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29464">
    <literal><![CDATA[
      a(x,x,y) \ (z \ y) = z \ L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(38,a,28350,a,b,29451,a)].">
      <j1 rule="hyper" parents="38 28350 29451"/>
    </justification>
  </clause>

  <clause id="29466">
    <literal><![CDATA[
      L(x,y,y) \ (z \ L(x,y,y)) = x \ (z \ x)
    ]]></literal>
    <justification jstring="[hyper(128,a,29464,a(flip),b,29386,a)].">
      <j1 rule="hyper" parents="128 29464 29386"/>
    </justification>
  </clause>

  <clause id="29467">
    <literal><![CDATA[
      (x / y) \ L(x,z,z) = a(z,z,x) \ y
    ]]></literal>
    <justification jstring="[para(83(a,1),29464(a,1,2)),flip(a)].">
      <j1 rule="para" parents="83 29464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29468">
    <literal><![CDATA[
      a(x,y,z * (a(u,u,w) * (v5 \ w))) = a(x,y,z * (v5 \ L(w,u,u)))
    ]]></literal>
    <justification jstring="[para(29464(a,1),28364(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="29464 28364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29469">
    <literal><![CDATA[
      (a(x,x,y) \ z) \ L(y,x,x) = z \ y
    ]]></literal>
    <justification jstring="[para(29467(a,1),22970(a,1,1))].">
      <j1 rule="para" parents="29467 22970"/>
    </justification>
  </clause>

  <clause id="29470">
    <literal><![CDATA[
      a(x,y,z \ ((u / w) \ R(u,v5,v5))) = a(x,y,z \ (a(v5,v5,u) \ w))
    ]]></literal>
    <justification jstring="[para(29467(a,1),25789(a,2,3,2))].">
      <j1 rule="para" parents="29467 25789"/>
    </justification>
  </clause>

  <clause id="29471">
    <literal><![CDATA[
      a(a(x,x,(x \ 1) * y) \ z,u,w) = a((((x \ 1) * y) / z) \ (x \ y),u,w)
    ]]></literal>
    <justification jstring="[para(29467(a,1),27994(a,1,1))].">
      <j1 rule="para" parents="29467 27994"/>
    </justification>
  </clause>

  <clause id="29472">
    <literal><![CDATA[
      L(x \ y,x,a(z,z,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(28131,a,29469,a)].">
      <j1 rule="hyper" parents="28131 29469"/>
    </justification>
  </clause>

  <clause id="29473">
    <literal><![CDATA[
      L(x \ y,x,a(y,z,z)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(28127,a,29469,a)].">
      <j1 rule="hyper" parents="28127 29469"/>
    </justification>
  </clause>

  <clause id="29474">
    <literal><![CDATA[
      (a(x,x,y) * z) \ y = z \ L(y,x,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),29469(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 29469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29475">
    <literal><![CDATA[
      (L(x,y,y) \ z) \ x = (x \ z) \ L(x,y,y)
    ]]></literal>
    <justification jstring="[para(29387(a,1),29469(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29387 29469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29477">
    <literal><![CDATA[
      L(x \ (y * L(z,y,u)),x,a(u,u,y * z)) = x \ (y * L(z,y,u))
    ]]></literal>
    <justification jstring="[para(26276(a,1),29472(a,1,3))].">
      <j1 rule="para" parents="26276 29472"/>
    </justification>
  </clause>

  <clause id="29479">
    <literal><![CDATA[
      (x * a(y,z,z)) \ R(y,z,z) = x \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,21297,a(flip),b,29473,a)].">
      <j1 rule="hyper" parents="63 21297 29473"/>
    </justification>
  </clause>

  <clause id="29480">
    <literal><![CDATA[
      (x * L(y,z,z)) \ L(y,z,z) = (x * y) \ y
    ]]></literal>
    <justification jstring="[para(29394(a,1),29474(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29394 29474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29481">
    <literal><![CDATA[
      (x / y) \ R(x,z,z) = y * a(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(23648,a,29479,a)].">
      <j1 rule="hyper" parents="23648 29479"/>
    </justification>
  </clause>

  <clause id="29485">
    <literal><![CDATA[
      ((x \ L(y,z,z)) * x) \ (u \ L(y,z,z)) = K(x,x \ L(y,z,z)) * (y \ (u \ y))
    ]]></literal>
    <justification jstring="[para(29466(a,1),10296(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29466 10296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29486">
    <literal><![CDATA[
      a(((L((x \ 1) * y,z,z) \ u) \ L((x \ 1) * y,x,x)) \ (x \ y),w,v5) = a(((((x \ 1) * y) \ u) \ L((x \ 1) * y,z,z)) \ ((x \ 1) * y),w,v5)
    ]]></literal>
    <justification jstring="[para(29475(a,1),27998(a,2,1,1))].">
      <j1 rule="para" parents="29475 27998"/>
    </justification>
  </clause>

  <clause id="29487">
    <literal><![CDATA[
      R(T(x \ 1,y * (x \ z)),x,y \ z) = (x * (y * z)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,22300,a,b,29480,a)].">
      <j1 rule="hyper" parents="63 22300 29480"/>
    </justification>
  </clause>

  <clause id="29488">
    <literal><![CDATA[
      L(L(x,y,y),z,z) \ (a(z,z,x) \ u) = L(x,y,y) \ u
    ]]></literal>
    <justification jstring="[hyper(23298,a,29450,a),flip(a)].">
      <j1 rule="hyper" parents="23298 29450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29489">
    <literal><![CDATA[
      L(x,x \ y,a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,80,a(flip),b,29462,a),flip(a)].">
      <j1 rule="hyper" parents="347 80 29462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29491">
    <literal><![CDATA[
      (x \ y) * a(y,y,z) = x \ R(y,y,z)
    ]]></literal>
    <justification jstring="[para(29489(a,1),23273(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29489 23273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29492">
    <literal><![CDATA[
      R(x * y,x * y,y) = (((x * y) \ 1) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(347,a,13110,a(flip),b,29456,a),flip(a)].">
      <j1 rule="hyper" parents="347 13110 29456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29494">
    <literal><![CDATA[
      L(L(x \ 1,y * x,y * x),x,y) = R(y * x,y * x,x) \ y
    ]]></literal>
    <justification jstring="[para(29492(a,2),3292(a,2,1))].">
      <j1 rule="para" parents="29492 3292"/>
    </justification>
  </clause>

  <clause id="29495">
    <literal><![CDATA[
      a(x,y,z) * L(L(z,y,x),u,w) = L(a(w,u,z),y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(347,a,29056,a(flip),b,28878,a),flip(a)].">
      <j1 rule="hyper" parents="347 29056 28878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29496">
    <literal><![CDATA[
      a(x,y,z) * L(L(z,y,x),u,w) = a(w,u,L(z,y,x)) \ z
    ]]></literal>
    <justification jstring="[para(29113(a,2),29495(a,2,1))].">
      <j1 rule="para" parents="29113 29495"/>
    </justification>
  </clause>

  <clause id="29497">
    <literal><![CDATA[
      R(x,y,(z * (u * w)) \ (w * (u * z))) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(29007,a,28994,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="29007 28994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29498">
    <literal><![CDATA[
      R(x,y,(((z * z) \ u) * (w * v5)) \ ((w * u) * v5)) = L(x,y,a((z * z) \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(22897,a,29497,a)].">
      <j1 rule="hyper" parents="22897 29497"/>
    </justification>
  </clause>

  <clause id="29499">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) / u) \ 1 = ((z \ L(z,y,x)) / u) \ 1
    ]]></literal>
    <justification jstring="[hyper(29050,a,23490,a)].">
      <j1 rule="hyper" parents="29050 23490"/>
    </justification>
  </clause>

  <clause id="29501">
    <literal><![CDATA[
      a(x,y,L(z,y,y)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) \ u = w
    ]]></literal>
    <justification jstring="[para(29156(a,1),26354(a,1))].">
      <j1 rule="para" parents="29156 26354"/>
    </justification>
  </clause>

  <clause id="29502">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,a(z,y,x)) = a(z,y,L(x,w,u)) \ x
    ]]></literal>
    <justification jstring="[para(28841(a,2),29156(a,1,1))].">
      <j1 rule="para" parents="28841 29156"/>
    </justification>
  </clause>

  <clause id="29503">
    <literal><![CDATA[
      a(x,y,y \ z) \ u != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * y) \ u = w
    ]]></literal>
    <justification jstring="[para(25258(a,1),29501(a,1,1))].">
      <j1 rule="para" parents="25258 29501"/>
    </justification>
  </clause>

  <clause id="29504">
    <literal><![CDATA[
      R(x,(y \ z) * ((u * y) \ (u * z)),w) = L(x,a(u,y,z * y),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,23225,a(flip),b,29230,a),flip(a)].">
      <j1 rule="hyper" parents="347 23225 29230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29506">
    <literal><![CDATA[
      L(x,y,z) * (x \ (u / (L(x,y,z) * u))) = R(1 / x,x,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,26893,a(flip),b,29283,a),flip(a)].">
      <j1 rule="hyper" parents="347 26893 29283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29508">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),u * L(x,y,z)) = x * R(1 / x,x,u)
    ]]></literal>
    <justification jstring="[para(29506(a,1),24313(a,2,2))].">
      <j1 rule="para" parents="29506 24313"/>
    </justification>
  </clause>

  <clause id="29509">
    <literal><![CDATA[
      L(x * a(y,z,u),u,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      u * (L(u,z,y) \ x) = w
    ]]></literal>
    <justification jstring="[para(19985(a,1),29287(a,1,1))].">
      <j1 rule="para" parents="19985 29287"/>
    </justification>
  </clause>

  <clause id="29510">
    <literal><![CDATA[
      L(a(x,y,z) * u,z,a(z,y,x)) != w
    ]]></literal>
    <literal><![CDATA[
      z * (L(z,y,x) \ u) = w
    ]]></literal>
    <justification jstring="[para(27555(a,1),29287(a,1))].">
      <j1 rule="para" parents="27555 29287"/>
    </justification>
  </clause>

  <clause id="29511">
    <literal><![CDATA[
      (a(x,x,y) \ L(y,z,u)) \ L(y,z,u) = a((y / x) \ L(y,z,u),1 / x,y)
    ]]></literal>
    <justification jstring="[para(29393(a,1),23397(a,1,1))].">
      <j1 rule="para" parents="29393 23397"/>
    </justification>
  </clause>

  <clause id="29512">
    <literal><![CDATA[
      x * (a(y,z,z) * (L(x,u,a(y,z,z)) \ 1)) = L(a(y,z,z),u,x)
    ]]></literal>
    <justification jstring="[para(23247(a,1),29460(a,1,2,2,1))].">
      <j1 rule="para" parents="23247 29460"/>
    </justification>
  </clause>

  <clause id="29514">
    <literal><![CDATA[
      (x * ((y \ 1) \ z)) \ ((y \ 1) \ z) = (x * (y * z)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21999,a(flip),b,29487,a)].">
      <j1 rule="hyper" parents="63 21999 29487"/>
    </justification>
  </clause>

  <clause id="29515">
    <literal><![CDATA[
      R(x,(y * ((y * (z * u)) \ (z * u))) * (z \ u),w) = R(x,L(z \ u,y,y),w)
    ]]></literal>
    <justification jstring="[para(29514(a,1),27858(a,1,2,1,2))].">
      <j1 rule="para" parents="29514 27858"/>
    </justification>
  </clause>

  <clause id="29516">
    <literal><![CDATA[
      R(x,(((y * T(z,u)) \ (y * w)) \ 1) \ (z \ w),v5) = L(x,a(y,z,w * z),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22911,a,b,29504,a)].">
      <j1 rule="hyper" parents="63 22911 29504"/>
    </justification>
  </clause>

  <clause id="29517">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),u * L(x,y,z)) = a(x,x,x * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,19006,a(flip),b,29508,a),flip(a)].">
      <j1 rule="hyper" parents="347 19006 29508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29519">
    <literal><![CDATA[
      R(x,y,z) \ ((R(x,y,z) \ 1) \ u) = u * a(x,x,x * u)
    ]]></literal>
    <justification jstring="[para(29517(a,1),25357(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29517 25357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29520">
    <literal><![CDATA[
      R(x,y,z) \ ((R(x,y,z) \ 1) \ u) = x \ ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,19765,a(flip),b,29519,a),flip(a)].">
      <j1 rule="hyper" parents="347 19765 29519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29522">
    <literal><![CDATA[
      R(x,y,z) \ (((R(x,y,z) \ 1) \ 1) * (L(u,R(x,y,z) \ 1,R(x,y,z) \ 1) \ 1)) = x \ ((x \ 1) \ (u \ 1))
    ]]></literal>
    <justification jstring="[para(15302(a,2),29520(a,1,2))].">
      <j1 rule="para" parents="15302 29520"/>
    </justification>
  </clause>

  <clause id="29523">
    <literal><![CDATA[
      x * (a(y,z,z) * L(x \ 1,u,a(y,z,z))) = L(a(y,z,z),u,x)
    ]]></literal>
    <justification jstring="[para(26373(a,2),29512(a,1,2,2))].">
      <j1 rule="para" parents="26373 29512"/>
    </justification>
  </clause>

  <clause id="29524">
    <literal><![CDATA[
      R(x,y,z) * (a(x,y,z) \ u) = L(x,y,z) * (a(z,y,x) * u)
    ]]></literal>
    <justification jstring="[para(29064(a,1),28880(a,1,2))].">
      <j1 rule="para" parents="29064 28880"/>
    </justification>
  </clause>

  <clause id="29525">
    <literal><![CDATA[
      L(x,y,z) * (a(z,y,x) * R(a(x,y,z),u,w)) = R(x,y,z) * a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(28905(a,2),29524(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28905 29524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29526">
    <literal><![CDATA[
      a(x,(R(y,z,u) \ w) * v5,v6) = a(x,(L(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(28916,a,28881,a),flip(a)].">
      <j1 rule="hyper" parents="28916 28881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29527">
    <literal><![CDATA[
      (a(x,y,z) * u) * a(x,a(x,y,z),u) = a(x,y,z) * (a(a(x,y,z),x,u) \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,14702,a(flip),b,28929,a)].">
      <j1 rule="hyper" parents="347 14702 28929"/>
    </justification>
  </clause>

  <clause id="29528">
    <literal><![CDATA[
      R(x,y * ((z \ (z \ u)) \ w),v5) = R(x,y * (L(u,z,z) \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22552,a(flip),b,28943,a)].">
      <j1 rule="hyper" parents="63 22552 28943"/>
    </justification>
  </clause>

  <clause id="29529">
    <literal><![CDATA[
      a(x * ((y \ 1) * (y * (z * (y \ 1)))),u,w) = a(x * ((a(y,y,z) * z) * (y \ 1)),u,w)
    ]]></literal>
    <justification jstring="[para(3212(a,2),29014(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3212 29014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29530">
    <literal><![CDATA[
      a(x,a(y \ z,z,u) * w,v5) = a(x,a(y * z,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,26901,a(flip),b,29032,a),flip(a)].">
      <j1 rule="hyper" parents="63 26901 29032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29531">
    <literal><![CDATA[
      T(a(x,y,z \ u) \ u,K(u,w)) = L(((u \ z) \ 1) \ 1,y,x) * ((((u \ z) \ 1) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(29085(a,1),22039(a,1,1))].">
      <j1 rule="para" parents="29085 22039"/>
    </justification>
  </clause>

  <clause id="29532">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(z,y,x) = a(x,y,z) \ a(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(29113(a,2),29157(a,2,2))].">
      <j1 rule="para" parents="29113 29157"/>
    </justification>
  </clause>

  <clause id="29533">
    <literal><![CDATA[
      x * ((x \ 1) * L(y,x,a(z,u,x))) = L(y,x * a(x,u,z),x)
    ]]></literal>
    <justification jstring="[para(29227(a,1),25533(a,1,2))].">
      <j1 rule="para" parents="29227 25533"/>
    </justification>
  </clause>

  <clause id="29534">
    <literal><![CDATA[
      L(L(x,y,a(z,u,y)),y,y) = L(x,y * a(y,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(3226,a,29533,a)].">
      <j1 rule="hyper" parents="3226 29533"/>
    </justification>
  </clause>

  <clause id="29535">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)),y * a(y,z,u),y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(27559(a,1),29534(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27559 29534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29536">
    <literal><![CDATA[
      x * ((x \ 1) * (a(x,y,z) * u)) = a(x,y,z) * L(u,x,x)
    ]]></literal>
    <justification jstring="[para(29535(a,1),25642(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29535 25642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29537">
    <literal><![CDATA[
      a(x,y,z) * L(u,x,x) != w
    ]]></literal>
    <literal><![CDATA[
      L(a(x,y,z) * u,x,x) = w
    ]]></literal>
    <justification jstring="[para(29536(a,1),3226(a,1))].">
      <j1 rule="para" parents="29536 3226"/>
    </justification>
  </clause>

  <clause id="29539">
    <literal><![CDATA[
      a(x,y,z) \ (a(z,y,x) \ u) = (R(x,y,z) \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(28359,a,29342,a)].">
      <j1 rule="hyper" parents="28359 29342"/>
    </justification>
  </clause>

  <clause id="29540">
    <literal><![CDATA[
      (a(x,y,z) * a(z,y,x)) \ u = (R(z,y,x) \ L(z,y,x)) * u
    ]]></literal>
    <justification jstring="[hyper(28367,a,29539,a)].">
      <j1 rule="hyper" parents="28367 29539"/>
    </justification>
  </clause>

  <clause id="29541">
    <literal><![CDATA[
      L(x,y,y) * (y * (a(y,y,x) * z)) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(29365,a,29349,a),flip(a)].">
      <j1 rule="hyper" parents="29365 29349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29542">
    <literal><![CDATA[
      L(x * (y * z),x,a(x,u,y)) = L(x,u,y) * (y * (a(y,u,x) * z))
    ]]></literal>
    <justification jstring="[hyper(27578,a,29349,a)].">
      <j1 rule="hyper" parents="27578 29349"/>
    </justification>
  </clause>

  <clause id="29543">
    <literal><![CDATA[
      L(x,x,y) * (y * (a(y,x,x) * z)) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(27554,a,29349,a),flip(a)].">
      <j1 rule="hyper" parents="27554 29349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29544">
    <literal><![CDATA[
      L(x,y,y) * (R(y,y,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(26280(a,1),29541(a,1,2))].">
      <j1 rule="para" parents="26280 29541"/>
    </justification>
  </clause>

  <clause id="29545">
    <literal><![CDATA[
      L(x,x,y) * (R(y,x,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(29367(a,1),29543(a,1,2))].">
      <j1 rule="para" parents="29367 29543"/>
    </justification>
  </clause>

  <clause id="29546">
    <literal><![CDATA[
      (x * (y * z)) * T(a(z,z,y),y * z) = x * (y * R(z,z,y))
    ]]></literal>
    <justification jstring="[para(26314(a,1),29374(a,2,2))].">
      <j1 rule="para" parents="26314 29374"/>
    </justification>
  </clause>

  <clause id="29547">
    <literal><![CDATA[
      (x * (y * z)) * a(z,z,y) = x * (y * R(z,z,y))
    ]]></literal>
    <justification jstring="[para(12965(a,1),29546(a,1,2))].">
      <j1 rule="para" parents="12965 29546"/>
    </justification>
  </clause>

  <clause id="29549">
    <literal><![CDATA[
      (x * (y * z)) * T(a(y,z,z),y * z) = x * (R(y,z,z) * z)
    ]]></literal>
    <justification jstring="[para(23126(a,1),29380(a,2,2))].">
      <j1 rule="para" parents="23126 29380"/>
    </justification>
  </clause>

  <clause id="29550">
    <literal><![CDATA[
      a(x,y,y) * (z * (x * y)) = z * (R(x,y,y) * y)
    ]]></literal>
    <justification jstring="[hyper(20889,a,29549,a)].">
      <j1 rule="hyper" parents="20889 29549"/>
    </justification>
  </clause>

  <clause id="29552">
    <literal><![CDATA[
      (a(x,y,y) * (z * x)) \ (z * (R(x,y,y) * y)) = L(L(y,x,z),z * x,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(29550(a,1),542(a,1,2))].">
      <j1 rule="para" parents="29550 542"/>
    </justification>
  </clause>

  <clause id="29553">
    <literal><![CDATA[
      L(x,y,(z * (u * w)) * a(w,w,u)) = L(x,y,z * (R(u,w,w) * w))
    ]]></literal>
    <justification jstring="[para(29550(a,1),27594(a,1,3)),flip(a)].">
      <j1 rule="para" parents="29550 27594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29554">
    <literal><![CDATA[
      R(x,y * ((z \ u) * L(z,w,w)),v5) = R(x,y * (a(z,w,w) * u),v5)
    ]]></literal>
    <justification jstring="[hyper(27801,a,29398,a)].">
      <j1 rule="hyper" parents="27801 29398"/>
    </justification>
  </clause>

  <clause id="29555">
    <literal><![CDATA[
      a(x,y * ((z * a(u,u,w)) * w),v5) = a(x,y * (L(w,u,u) * z),v5)
    ]]></literal>
    <justification jstring="[hyper(24006,a,29405,a)].">
      <j1 rule="hyper" parents="24006 29405"/>
    </justification>
  </clause>

  <clause id="29556">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) * a(v5,v5,w))) = a(x,y,z * (u \ L(w,v5,v5)))
    ]]></literal>
    <justification jstring="[hyper(24190,a,29468,a)].">
      <j1 rule="hyper" parents="24190 29468"/>
    </justification>
  </clause>

  <clause id="29557">
    <literal><![CDATA[
      a(x,y,z * (a(u,u,((u * u) \ w) \ 1) * (v5 \ (((u * u) \ w) \ 1)))) = a(x,y,z * (v5 \ ((u \ (u \ w)) \ 1)))
    ]]></literal>
    <justification jstring="[para(25962(a,1),29468(a,2,3,2,2))].">
      <j1 rule="para" parents="25962 29468"/>
    </justification>
  </clause>

  <clause id="29558">
    <literal><![CDATA[
      a(x,y,z \ (a(u,u,w) \ v5)) = a(x,y,z \ (v5 * a(w,u,u)))
    ]]></literal>
    <justification jstring="[para(29481(a,1),29470(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="29481 29470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29559">
    <literal><![CDATA[
      a(x,y,z \ ((L(u,w,w) \ v5) * a(u,w,w))) = a(x,y,z \ (u \ v5))
    ]]></literal>
    <justification jstring="[para(29387(a,1),29558(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="29387 29558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29560">
    <literal><![CDATA[
      L(x \ (y * L(z,y,y)),x,a(y,y,z)) = x \ (y * L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(27623,a,29477,a)].">
      <j1 rule="hyper" parents="27623 29477"/>
    </justification>
  </clause>

  <clause id="29561">
    <literal><![CDATA[
      (x * a(y,y,z)) \ (y * z) = x \ (y * L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,26503,a(flip),b,29560,a)].">
      <j1 rule="hyper" parents="63 26503 29560"/>
    </justification>
  </clause>

  <clause id="29562">
    <literal><![CDATA[
      L(x,y,(z * (u * w)) * a(w,w,u)) = L(x,y,z * (L(u,w,w) * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,22875,a(flip),b,29553,a),flip(a)].">
      <j1 rule="hyper" parents="347 22875 29553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29563">
    <literal><![CDATA[
      a(x,y * (a(z,z,u) * (w * u)),v5) = a(x,y * (L(u,z,z) * w),v5)
    ]]></literal>
    <justification jstring="[para(23119(a,1),29555(a,1,2,2))].">
      <j1 rule="para" parents="23119 29555"/>
    </justification>
  </clause>

  <clause id="29564">
    <literal><![CDATA[
      a(x,y,z \ (a(u,w,w) * (L(u,w,w) \ v5))) = a(x,y,z \ (u \ v5))
    ]]></literal>
    <justification jstring="[hyper(24214,a,29559,a)].">
      <j1 rule="hyper" parents="24214 29559"/>
    </justification>
  </clause>

  <clause id="29565">
    <literal><![CDATA[
      L(x,y,z * (L(u,w,w) * w)) = L(x,y,z * (u * R(w,w,u)))
    ]]></literal>
    <justification jstring="[para(29547(a,1),29562(a,1,3)),flip(a)].">
      <j1 rule="para" parents="29547 29562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29566">
    <literal><![CDATA[
      L(x,y,z * (L(u,w,w) * w)) = L(x,y,z * (u * L(w,w,u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,22871,a(flip),b,29565,a),flip(a)].">
      <j1 rule="hyper" parents="347 22871 29565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29567">
    <literal><![CDATA[
      L(x,y,z * (L(u,w,w) * w)) = L(x,y,z * (u / (w \ 1)))
    ]]></literal>
    <justification jstring="[para(2008(a,1),29566(a,2,3,2))].">
      <j1 rule="para" parents="2008 29566"/>
    </justification>
  </clause>

  <clause id="29568">
    <literal><![CDATA[
      L(x,y,z * (L(u,w,w) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * ((w \ 1) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(29567(a,2),21523(a,1))].">
      <j1 rule="para" parents="29567 21523"/>
    </justification>
  </clause>

  <clause id="29569">
    <literal><![CDATA[
      R(x,y,z \ (a(u,w,w) * (L(u,w,w) \ v5))) = a(x,y,z \ (u \ v5)) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,29564,a(flip),b,28907,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 29564 28907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29572">
    <literal><![CDATA[
      a(x,y,L(z \ (x \ u),x,z)) = a(x,y,x \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(29202,a,25588,a)].">
      <j1 rule="hyper" parents="29202 25588"/>
    </justification>
  </clause>

  <clause id="29573">
    <literal><![CDATA[
      a(x,y,L(z \ (x \ u),x,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x * (z \ u)) = w
    ]]></literal>
    <justification jstring="[para(29572(a,2),29174(a,1))].">
      <j1 rule="para" parents="29572 29174"/>
    </justification>
  </clause>

  <clause id="29574">
    <literal><![CDATA[
      a(x,y,y \ (x \ z)) = a(x,y,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(29573,a,29278,a),flip(a)].">
      <j1 rule="hyper" parents="29573 29278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29575">
    <literal><![CDATA[
      a(x,y,L((x * z) \ (x \ u),x,z)) = a(x,y,x * ((x * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(29573,a,29277,a),flip(a)].">
      <j1 rule="hyper" parents="29573 29277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29576">
    <literal><![CDATA[
      a(x,y,y \ (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x * (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(29278(a,1),29573(a,1))].">
      <j1 rule="para" parents="29278 29573"/>
    </justification>
  </clause>

  <clause id="29577">
    <literal><![CDATA[
      a(x,y,(x \ z) * y) = a(x,y,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(29266,a,29574,a)].">
      <j1 rule="hyper" parents="29266 29574"/>
    </justification>
  </clause>

  <clause id="29578">
    <literal><![CDATA[
      (x \ y) \ (z * ((x * z) \ y)) = a(x,z,x * (z \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(29574(a,1),26198(a,2,1))].">
      <j1 rule="para" parents="29574 26198"/>
    </justification>
  </clause>

  <clause id="29579">
    <literal><![CDATA[
      a(x,y,x * (y \ z)) * x = R(x,y,(x \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,29577,a(flip),b,28907,a(flip))].">
      <j1 rule="hyper" parents="133 29577 28907"/>
    </justification>
  </clause>

  <clause id="29580">
    <literal><![CDATA[
      a(x,y,x * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y * (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(29577(a,1),24180(a,1))].">
      <j1 rule="para" parents="29577 24180"/>
    </justification>
  </clause>

  <clause id="29581">
    <literal><![CDATA[
      R(x,y,(x \ z) * y) = R(x,y,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(28910,a,29579,a),flip(a)].">
      <j1 rule="hyper" parents="28910 29579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29582">
    <literal><![CDATA[
      (x / y) * R(y,z,y * (z \ x)) = (y * z) * (z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(29581(a,1),27264(a,1,2))].">
      <j1 rule="para" parents="29581 27264"/>
    </justification>
  </clause>

  <clause id="29583">
    <literal><![CDATA[
      (x * ((y * x) \ z)) \ (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,x,y * (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(26558(a,2),29576(a,1))].">
      <j1 rule="para" parents="26558 29576"/>
    </justification>
  </clause>

  <clause id="29584">
    <literal><![CDATA[
      a(x,y,(y \ z) * x) = a(x,y,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(29580,a,24069,a),flip(a)].">
      <j1 rule="hyper" parents="29580 24069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29585">
    <literal><![CDATA[
      a(x,y,y * (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x * (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(29584(a,1),24180(a,1))].">
      <j1 rule="para" parents="29584 24180"/>
    </justification>
  </clause>

  <clause id="29586">
    <literal><![CDATA[
      a(x,y,y * ((x \ 1) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x * (y \ L(z,x,x))) = u
    ]]></literal>
    <justification jstring="[para(3202(a,1),29585(a,1,3,2))].">
      <j1 rule="para" parents="3202 29585"/>
    </justification>
  </clause>

  <clause id="29587">
    <literal><![CDATA[
      ((x * (y / x)) / x) * R(y / (y / x),z,(y / (y / x)) * (z \ y)) = ((y / (y / x)) * z) * (z \ ((y / (y / x)) \ y))
    ]]></literal>
    <justification jstring="[para(4396(a,2),29582(a,1,1))].">
      <j1 rule="para" parents="4396 29582"/>
    </justification>
  </clause>

  <clause id="29588">
    <literal><![CDATA[
      a(x,y,L(z \ (x \ (x \ u)),x,z)) = a(x,y,x * ((x * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(29202,a,29575,a)].">
      <j1 rule="hyper" parents="29202 29575"/>
    </justification>
  </clause>

  <clause id="29589">
    <literal><![CDATA[
      a(x,y,x * ((x * z) \ u)) = a(x,y,x * (z \ (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(29573,a,29588,a),flip(a)].">
      <j1 rule="hyper" parents="29573 29588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29590">
    <literal><![CDATA[
      a(x,y,x * ((z * x) \ u)) = a(x,y,x * (z \ (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(24426,a,29589,a)].">
      <j1 rule="hyper" parents="24426 29589"/>
    </justification>
  </clause>

  <clause id="29591">
    <literal><![CDATA[
      a(x,y,x * (z \ (x \ u))) != w
    ]]></literal>
    <literal><![CDATA[
      a(T(x,v5),y,x * ((z * x) \ u)) = w
    ]]></literal>
    <justification jstring="[para(29589(a,1),24624(a,1))].">
      <j1 rule="para" parents="29589 24624"/>
    </justification>
  </clause>

  <clause id="29592">
    <literal><![CDATA[
      a(x,y,(x * z) * y) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x * (y \ L(z,x,x))) = u
    ]]></literal>
    <justification jstring="[para(24556(a,1),29586(a,1))].">
      <j1 rule="para" parents="24556 29586"/>
    </justification>
  </clause>

  <clause id="29593">
    <literal><![CDATA[
      K(x,x * x) * ((x \ (x \ R(x,y,z))) \ 1) = (x \ R(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[para(5184(a,1),29245(a,1,1))].">
      <j1 rule="para" parents="5184 29245"/>
    </justification>
  </clause>

  <clause id="29595">
    <literal><![CDATA[
      K(x,x * x) * ((x * x) * (R(x,y,z) \ 1)) = (x \ R(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[para(1779(a,1),29593(a,1,2))].">
      <j1 rule="para" parents="1779 29593"/>
    </justification>
  </clause>

  <clause id="29596">
    <literal><![CDATA[
      (x * x) * (K(x,x * x) * (R(x,y,z) \ 1)) = (x \ R(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(5519,a,29595,a)].">
      <j1 rule="hyper" parents="5519 29595"/>
    </justification>
  </clause>

  <clause id="29597">
    <literal><![CDATA[
      (x * x) * (R(x,y,z) \ K(x,x * x)) = (x \ R(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[para(5892(a,1),29596(a,1,2))].">
      <j1 rule="para" parents="5892 29596"/>
    </justification>
  </clause>

  <clause id="29598">
    <literal><![CDATA[
      ((x \ R(x,y,z)) / x) \ 1 = (x \ R(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,23540,a(flip),b,29597,a)].">
      <j1 rule="hyper" parents="63 23540 29597"/>
    </justification>
  </clause>

  <clause id="29599">
    <literal><![CDATA[
      ((x \ R(x,y,z)) / x) \ 1 = x * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,20941,a(flip),b,29598,a),flip(a)].">
      <j1 rule="hyper" parents="347 20941 29598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29600">
    <literal><![CDATA[
      L(((x * (R(x,y,z) \ x)) \ 1) \ u,(x \ R(x,y,z)) / x,((x \ R(x,y,z)) / x) \ 1) = 1 \ ((((x \ R(x,y,z)) / x) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(29599(a,1),10212(a,1,1,1,1))].">
      <j1 rule="para" parents="29599 10212"/>
    </justification>
  </clause>

  <clause id="29603">
    <literal><![CDATA[
      a(x,y,a(z,u,(w * x) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w \ (x \ v5))) = v6
    ]]></literal>
    <justification jstring="[para(24083(a,1),29299(a,1,3))].">
      <j1 rule="para" parents="24083 29299"/>
    </justification>
  </clause>

  <clause id="29604">
    <literal><![CDATA[
      (x * R(y,x,x)) * T(z,a(y,x,x)) = (x * y) * (z * a(y,x,x))
    ]]></literal>
    <justification jstring="[para(26939(a,1),29376(a,1,1))].">
      <j1 rule="para" parents="26939 29376"/>
    </justification>
  </clause>

  <clause id="29605">
    <literal><![CDATA[
      (x * y) * (z * a(y,x,x)) = (x * R(y,x,x)) * z
    ]]></literal>
    <justification jstring="[para(12665(a,1),29604(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12665 29604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29606">
    <literal><![CDATA[
      (x * R(y,x,x)) * ((x * y) \ z) = z * a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(27600,a,29605,a),flip(a)].">
      <j1 rule="hyper" parents="27600 29605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29607">
    <literal><![CDATA[
      ((x \ K(y,x \ 1)) * R(y,x \ K(y,x \ 1),x \ K(y,x \ 1))) * z = (y * (x \ 1)) * (z * a(y,x \ K(y,x \ 1),x \ K(y,x \ 1)))
    ]]></literal>
    <justification jstring="[para(5054(a,1),29605(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5054 29605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29608">
    <literal><![CDATA[
      L(x,y,((z * u) \ w) * (R(u,z,z) * z)) = L(x,y,w * a(u,z,z))
    ]]></literal>
    <justification jstring="[para(29606(a,1),22855(a,1,3)),flip(a)].">
      <j1 rule="para" parents="29606 22855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29609">
    <literal><![CDATA[
      L(x,y,((z * u) \ w) * (L(u,z,z) * z)) = L(x,y,w * a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,22875,a(flip),b,29608,a)].">
      <j1 rule="hyper" parents="63 22875 29608"/>
    </justification>
  </clause>

  <clause id="29610">
    <literal><![CDATA[
      L(x,y,((z * u) \ w) * ((z \ 1) \ u)) = L(x,y,w * a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(29568,a,29609,a)].">
      <j1 rule="hyper" parents="29568 29609"/>
    </justification>
  </clause>

  <clause id="29611">
    <literal><![CDATA[
      L(x,y,(((z \ 1) \ u) \ w) * a(u,z,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z * u) \ w) = v5
    ]]></literal>
    <justification jstring="[para(29610(a,1),20894(a,1))].">
      <j1 rule="para" parents="29610 20894"/>
    </justification>
  </clause>

  <clause id="29612">
    <literal><![CDATA[
      a(T(x,y),z,x * (((u * x) * x) \ w)) = a(x,z,x * (u \ (x \ (x \ w))))
    ]]></literal>
    <justification jstring="[hyper(29591,a,29590,a)].">
      <j1 rule="hyper" parents="29591 29590"/>
    </justification>
  </clause>

  <clause id="29613">
    <literal><![CDATA[
      L(x,a(y,z,u),z * a(y,z,u)) = z * L(z \ x,z,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(28827,a,3342,a)].">
      <j1 rule="hyper" parents="28827 3342"/>
    </justification>
  </clause>

  <clause id="29614">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,a(z,x,u),x * a(z,x,u)) = w
    ]]></literal>
    <justification jstring="[para(3342(a,1),28827(a,1))].">
      <j1 rule="para" parents="3342 28827"/>
    </justification>
  </clause>

  <clause id="29615">
    <literal><![CDATA[
      (a(x,y,z) \ (y * a(x,y,z))) \ ((y * a(x,y,z)) * u) = y * L(y \ (a(x,y,z) * u),y,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(28634,a,29613,a)].">
      <j1 rule="hyper" parents="28634 29613"/>
    </justification>
  </clause>

  <clause id="29616">
    <literal><![CDATA[
      a(x,y,z) * L(u,a(x,y,z),y * a(x,y,z)) = (a(x,y,z) * y) * (y \ u)
    ]]></literal>
    <justification jstring="[hyper(134,a,29613,a,b,26374,a)].">
      <j1 rule="hyper" parents="134 29613 26374"/>
    </justification>
  </clause>

  <clause id="29617">
    <literal><![CDATA[
      (a(x,y,z) * (y * (y \ u))) \ (a(x,y,z) * L(u,a(x,y,z),y * a(x,y,z))) = a(a(x,y,z),y,y \ u) \ 1
    ]]></literal>
    <justification jstring="[para(29613(a,2),26147(a,1,2,2))].">
      <j1 rule="para" parents="29613 26147"/>
    </justification>
  </clause>

  <clause id="29618">
    <literal><![CDATA[
      a(x,y,(z * (a(u,w,v5) * v5)) * v6) = a(x,y,(L(v5,w,u) * z) * v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,24866,a(flip),b,29073,a),flip(a)].">
      <j1 rule="hyper" parents="63 24866 29073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29619">
    <literal><![CDATA[
      a(x,y,z * (u * (a(w,v5,v6) * v6))) = a(x,y,(L(v6,v5,w) * u) * z)
    ]]></literal>
    <justification jstring="[hyper(24180,a,29618,a)].">
      <j1 rule="hyper" parents="24180 29618"/>
    </justification>
  </clause>

  <clause id="29620">
    <literal><![CDATA[
      a(x,y,z * (u * (w * a(v5,v6,w)))) = a(x,y,(L(w,v6,v5) * u) * z)
    ]]></literal>
    <justification jstring="[hyper(24425,a,29619,a)].">
      <j1 rule="hyper" parents="24425 29619"/>
    </justification>
  </clause>

  <clause id="29621">
    <literal><![CDATA[
      a(x,y,(z * (u * u)) \ (w \ (v5 \ (u * u)))) = a(x,y,z \ (w \ v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,24758,a(flip),b,29226,a),flip(a)].">
      <j1 rule="hyper" parents="347 24758 29226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29622">
    <literal><![CDATA[
      a(x,y,(z * z) \ (u \ (w \ (v5 \ (z * z))))) = a(x,y,u \ (w \ v5))
    ]]></literal>
    <justification jstring="[para(459(a,1),29621(a,1,3))].">
      <j1 rule="para" parents="459 29621"/>
    </justification>
  </clause>

  <clause id="29623">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w \ (v5 * v5)))) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(14949,a,29622,a)].">
      <j1 rule="hyper" parents="14949 29622"/>
    </justification>
  </clause>

  <clause id="29625">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (u \ z)) = a(x,y,a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,26584,a(flip),b,29623,a),flip(a)].">
      <j1 rule="hyper" parents="63 26584 29623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29626">
    <literal><![CDATA[
      a(x,y,a(z,u \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z \ u) * (u \ z)) = w
    ]]></literal>
    <justification jstring="[para(29625(a,1),15047(a,1))].">
      <j1 rule="para" parents="29625 15047"/>
    </justification>
  </clause>

  <clause id="29627">
    <literal><![CDATA[
      (x / y) \ (x * a(z,u,x)) = y * (a(z,u,x) * a(y,y,a(z,u,x)))
    ]]></literal>
    <justification jstring="[para(29258(a,1),29236(a,2,2,2))].">
      <j1 rule="para" parents="29258 29236"/>
    </justification>
  </clause>

  <clause id="29628">
    <literal><![CDATA[
      (x / y) \ (x * a(z,u,x)) = y * a(z,u,L(x,y,y))
    ]]></literal>
    <justification jstring="[para(29114(a,1),29627(a,2,2))].">
      <j1 rule="para" parents="29114 29627"/>
    </justification>
  </clause>

  <clause id="29629">
    <literal><![CDATA[
      (x / y) \ (x * a(z,u,x)) = (1 / y) \ a(z,u,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,29141,a(flip),b,29628,a),flip(a)].">
      <j1 rule="hyper" parents="347 29141 29628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29630">
    <literal><![CDATA[
      a((x \ y) \ (y * a(z,u,y)),w,v5) = a((1 / x) \ a(z,u,y),w,v5)
    ]]></literal>
    <justification jstring="[para(29629(a,1),23892(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29629 23892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29631">
    <literal><![CDATA[
      a(x,y * (T(z / u,w) \ (z * a(v5,v6,z))),v7) = a(x,y * ((1 / u) \ a(v5,v6,z)),v7)
    ]]></literal>
    <justification jstring="[para(29629(a,1),24251(a,2,2,2))].">
      <j1 rule="para" parents="29629 24251"/>
    </justification>
  </clause>

  <clause id="29632">
    <literal><![CDATA[
      a((x \ y) \ L(y,z,u),w,v5) = a((1 / x) \ a(u,z,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,28948,a(flip),b,29630,a)].">
      <j1 rule="hyper" parents="63 28948 29630"/>
    </justification>
  </clause>

  <clause id="29633">
    <literal><![CDATA[
      a((x \ 1) \ a(y,z,u),w,v5) = a((x \ u) \ L(u,z,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,23892,a(flip),b,29632,a)].">
      <j1 rule="hyper" parents="347 23892 29632"/>
    </justification>
  </clause>

  <clause id="29634">
    <literal><![CDATA[
      a(x,(y * y) \ (a(y,z,u) \ w),v5) = a(x,(R(y,z,u) \ y) \ w,v5)
    ]]></literal>
    <justification jstring="[para(1755(a,1),29241(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1755 29241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29635">
    <literal><![CDATA[
      a(x,(y * y) \ (a(y,z,u) \ w),v5) = a(x,w * a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[para(29101(a,1),29634(a,2,2))].">
      <j1 rule="para" parents="29101 29634"/>
    </justification>
  </clause>

  <clause id="29636">
    <literal><![CDATA[
      a(x,(y * R(y,z,u)) \ w,v5) = a(x,w * a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[para(29008(a,1),29635(a,1,2))].">
      <j1 rule="para" parents="29008 29635"/>
    </justification>
  </clause>

  <clause id="29637">
    <literal><![CDATA[
      R(x,(a(y,y,z) * (u * z)) * w,v5) = R(x,w * ((z * a(y,y,z)) * u),v5)
    ]]></literal>
    <justification jstring="[para(23119(a,1),29406(a,1,2,1))].">
      <j1 rule="para" parents="23119 29406"/>
    </justification>
  </clause>

  <clause id="29638">
    <literal><![CDATA[
      (x * (y \ L(z,z,u))) / (y \ z) = (y \ z) \ ((y \ L(z,z,u)) * x)
    ]]></literal>
    <justification jstring="[para(29457(a,1),29461(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="29457 29461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29639">
    <literal><![CDATA[
      R(x,y,z \ (a(u,w,w) * (L(u,w,w) \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z \ (u \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(29569(a,2),28910(a,1))].">
      <j1 rule="para" parents="29569 28910"/>
    </justification>
  </clause>

  <clause id="29642">
    <literal><![CDATA[
      a(T(x,y),z,x * (L(u,x,x) \ w)) = a(x,z,x * (u \ (x \ (x \ w))))
    ]]></literal>
    <justification jstring="[hyper(63,a,24876,a(flip),b,29612,a)].">
      <j1 rule="hyper" parents="63 24876 29612"/>
    </justification>
  </clause>

  <clause id="29643">
    <literal><![CDATA[
      a(x,y,x * (z \ (x \ (x \ u)))) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x * (L(z,x,x) \ u)) = w
    ]]></literal>
    <justification jstring="[para(29642(a,1),17834(a,1))].">
      <j1 rule="para" parents="29642 17834"/>
    </justification>
  </clause>

  <clause id="29644">
    <literal><![CDATA[
      (x * y) \ (x * (z * (y * R(y \ (z \ y),u,w)))) = a(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(23592(a,1),29080(a,1,2,2))].">
      <j1 rule="para" parents="23592 29080"/>
    </justification>
  </clause>

  <clause id="29645">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((w * z) \ (u * w))) = a(x,y,a(w,z,z \ T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(24428,a,29212,a)].">
      <j1 rule="hyper" parents="24428 29212"/>
    </justification>
  </clause>

  <clause id="29647">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((w * z) \ (u * w))) = a(x,y,a(w,z,T(u,w) * z))
    ]]></literal>
    <justification jstring="[para(27214(a,1),29645(a,2,3))].">
      <j1 rule="para" parents="27214 29645"/>
    </justification>
  </clause>

  <clause id="29648">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((w * z) \ (u * w))) = a(x,y,a(w,z,u * z))
    ]]></literal>
    <justification jstring="[para(24070(a,1),29647(a,2,3))].">
      <j1 rule="para" parents="24070 29647"/>
    </justification>
  </clause>

  <clause id="29650">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((z * w) \ (w * u))) = a(x,y,a(w,z,T(z,w) \ u))
    ]]></literal>
    <justification jstring="[hyper(24194,a,29213,a)].">
      <j1 rule="hyper" parents="24194 29213"/>
    </justification>
  </clause>

  <clause id="29651">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((z * w) \ (w * u))) = a(x,y,a(w,z,z \ u))
    ]]></literal>
    <justification jstring="[para(24073(a,1),29650(a,2,3))].">
      <j1 rule="para" parents="24073 29650"/>
    </justification>
  </clause>

  <clause id="29653">
    <literal><![CDATA[
      (L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u) = a(L(x,y,z),L(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,24805,a(flip),b,29317,a),flip(a)].">
      <j1 rule="hyper" parents="347 24805 29317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29654">
    <literal><![CDATA[
      a(x,y,z) \ a(u,w,L(x,y,z)) = L(R(x,y,z),w,u) \ x
    ]]></literal>
    <justification jstring="[para(24905(a,1),29321(a,1,2))].">
      <j1 rule="para" parents="24905 29321"/>
    </justification>
  </clause>

  <clause id="29656">
    <literal><![CDATA[
      L(R(x,y,z),u,z) \ x = a(x,y,z) \ a(z,u,x)
    ]]></literal>
    <justification jstring="[para(29119(a,1),29654(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29119 29654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29657">
    <literal><![CDATA[
      R(x,y * ((z \ u) * L(z,w,w)),v5) = R(x,(a(w,w,z) * u) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(29396,a,28611,a)].">
      <j1 rule="hyper" parents="29396 28611"/>
    </justification>
  </clause>

  <clause id="29658">
    <literal><![CDATA[
      R(x,(a(y,y,z) * u) * w,v5) = R(x,w * (a(z,y,y) * u),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,29554,a(flip),b,29657,a),flip(a)].">
      <j1 rule="hyper" parents="63 29554 29657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29659">
    <literal><![CDATA[
      a(a(x,x,x * y) \ z,u,w) = a((((x \ 1) * y) / z) \ (x \ y),u,w)
    ]]></literal>
    <justification jstring="[para(24327(a,1),29471(a,1,1,1))].">
      <j1 rule="para" parents="24327 29471"/>
    </justification>
  </clause>

  <clause id="29660">
    <literal><![CDATA[
      a((((x \ 1) * y) / z) \ (x \ y),u,w) = a(a(x,x,x * y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,28398,a(flip),b,29659,a),flip(a)].">
      <j1 rule="hyper" parents="63 28398 29659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29661">
    <literal><![CDATA[
      a((((x \ 1) * y) / z) \ (x \ y),u,w) = a(z * a(x,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,28025,a(flip),b,29660,a),flip(a)].">
      <j1 rule="hyper" parents="347 28025 29660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29662">
    <literal><![CDATA[
      a((x \ ((y \ 1) * z)) \ (y \ z),u,w) = a(x * a(y,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(23961,a,29661,a)].">
      <j1 rule="hyper" parents="23961 29661"/>
    </justification>
  </clause>

  <clause id="29663">
    <literal><![CDATA[
      a((x / y) \ L(x,z,u),1 / y,x) = a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(20577,a,29511,a),flip(a)].">
      <j1 rule="hyper" parents="20577 29511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29664">
    <literal><![CDATA[
      a((x / y) \ L(x,z,u),y,x) = a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(14985,a,29663,a)].">
      <j1 rule="hyper" parents="14985 29663"/>
    </justification>
  </clause>

  <clause id="29666">
    <literal><![CDATA[
      a((x \ y) \ L(y,z,u),x,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(23961,a,29664,a)].">
      <j1 rule="hyper" parents="23961 29664"/>
    </justification>
  </clause>

  <clause id="29667">
    <literal><![CDATA[
      R(x,(y * ((z * u) \ ((z * u) / y))) * (z \ u),w) = R(x,L(z \ u,y,y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,23513,a(flip),b,29515,a)].">
      <j1 rule="hyper" parents="63 23513 29515"/>
    </justification>
  </clause>

  <clause id="29668">
    <literal><![CDATA[
      R(x,((y * T(z,u)) \ (y * w)) \ (z \ w),v5) = L(x,a(y,z,w * z),v5)
    ]]></literal>
    <justification jstring="[hyper(20908,a,29516,a)].">
      <j1 rule="hyper" parents="20908 29516"/>
    </justification>
  </clause>

  <clause id="29669">
    <literal><![CDATA[
      R(x,((y * z) \ (z * u)) \ (y \ u),w) = L(x,a(z,y,u * y),w)
    ]]></literal>
    <justification jstring="[hyper(22589,a,29668,a)].">
      <j1 rule="hyper" parents="22589 29668"/>
    </justification>
  </clause>

  <clause id="29670">
    <literal><![CDATA[
      T(a(x * a(y,x,z),a(y,x,z),u) \ a(y,x,z),u) = u \ ((a(y,x,z) * x) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(26533,a,29616,a)].">
      <j1 rule="hyper" parents="26533 29616"/>
    </justification>
  </clause>

  <clause id="29671">
    <literal><![CDATA[
      (x * y) \ (x * (y * a(z \ 1,u,w))) = a(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(29082(a,1),29644(a,1,2,2))].">
      <j1 rule="para" parents="29082 29644"/>
    </justification>
  </clause>

  <clause id="29672">
    <literal><![CDATA[
      a(L(x,y,z) \ 1,u,w) = L(a(x \ 1,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(545,a,29671,a),flip(a)].">
      <j1 rule="hyper" parents="545 29671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29673">
    <literal><![CDATA[
      a(L(x,y,z) \ 1,u,w) = a(x \ 1,u,L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,29113,a,b,29672,a),flip(a)].">
      <j1 rule="hyper" parents="347 29113 29672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29674">
    <literal><![CDATA[
      a((x \ 1) \ 1,y,L(z,u,w)) = a(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(28004,a,29673,a),flip(a)].">
      <j1 rule="hyper" parents="28004 29673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29675">
    <literal><![CDATA[
      a(L(x,y,z),u,w) = a(x,u,L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(23957,a,29674,a),flip(a)].">
      <j1 rule="hyper" parents="23957 29674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29676">
    <literal><![CDATA[
      a(L(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,L(w,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(29674(a,1),11586(a,1))].">
      <j1 rule="para" parents="29674 11586"/>
    </justification>
  </clause>

  <clause id="29677">
    <literal><![CDATA[
      a((x * y) \ z,u,L(w,x,y)) = a(x \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(28012,a,29675,a),flip(a)].">
      <j1 rule="hyper" parents="28012 29675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29678">
    <literal><![CDATA[
      a(x,L(x,y,z),u) = a(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(1682,a,29675,a)].">
      <j1 rule="hyper" parents="1682 29675"/>
    </justification>
  </clause>

  <clause id="29680">
    <literal><![CDATA[
      a(L(x,y,z),x * L(x,u,w),v5) = a(w,u,a(L(v5,y,z),x,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,28111,a(flip),b,29675,a),flip(a)].">
      <j1 rule="hyper" parents="347 28111 29675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29682">
    <literal><![CDATA[
      a(a(x,y,z) * z,u,w) = a(z,u,L(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,28933,a,b,29675,a)].">
      <j1 rule="hyper" parents="63 28933 29675"/>
    </justification>
  </clause>

  <clause id="29683">
    <literal><![CDATA[
      a((x * y) * x,z,a(u,w,v5)) = a(y,z,L(a(u,w,v5),x,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,26669,a,b,29675,a)].">
      <j1 rule="hyper" parents="63 26669 29675"/>
    </justification>
  </clause>

  <clause id="29684">
    <literal><![CDATA[
      a(R(x,y,z),u,w) = a(x,u,L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,25182,a,b,29675,a)].">
      <j1 rule="hyper" parents="63 25182 29675"/>
    </justification>
  </clause>

  <clause id="29686">
    <literal><![CDATA[
      a(x * y,z,L(u,y,y)) = a((y \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,28028,a(flip),b,29675,a),flip(a)].">
      <j1 rule="hyper" parents="63 28028 29675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29687">
    <literal><![CDATA[
      a((x \ 1) * y,z,L(u,x,x)) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,27981,a(flip),b,29675,a),flip(a)].">
      <j1 rule="hyper" parents="63 27981 29675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29688">
    <literal><![CDATA[
      a((x * y) \ z,u,L(w,y,x)) = a(y \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,27970,a(flip),b,29675,a),flip(a)].">
      <j1 rule="hyper" parents="63 27970 29675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29689">
    <literal><![CDATA[
      a(x * y,z,L(u,x,x)) = a((x \ 1) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,27960,a(flip),b,29675,a),flip(a)].">
      <j1 rule="hyper" parents="63 27960 29675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29690">
    <literal><![CDATA[
      a(L(x,y,x) \ z,u,L(w,x,v5)) = a((x * v5) \ (v5 * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,25189,a(flip),b,29675,a),flip(a)].">
      <j1 rule="hyper" parents="63 25189 29675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29691">
    <literal><![CDATA[
      a(x \ y,z,L(u,x,x)) = a(y * (x \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,24973,a(flip),b,29675,a),flip(a)].">
      <j1 rule="hyper" parents="63 24973 29675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29692">
    <literal><![CDATA[
      a(L(x \ 1,x,y),z,L(u,y * x,w)) = a((w * (y * x)) \ (w * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,24920,a(flip),b,29675,a),flip(a)].">
      <j1 rule="hyper" parents="63 24920 29675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29693">
    <literal><![CDATA[
      a((x * y) \ (x * z),x * y,u) = a(y \ z,y * x,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,24778,a(flip),b,29675,a)].">
      <j1 rule="hyper" parents="63 24778 29675"/>
    </justification>
  </clause>

  <clause id="29694">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * L(x,u,w) = R(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,29675,a(flip),b,28907,a(flip))].">
      <j1 rule="hyper" parents="133 29675 28907"/>
    </justification>
  </clause>

  <clause id="29695">
    <literal><![CDATA[
      a((x * x) * y,z,L(u,x,x)) = a(x * (x * y),z,u)
    ]]></literal>
    <justification jstring="[para(3180(a,1),29675(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3180 29675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29696">
    <literal><![CDATA[
      a(x,y,L(z,u,a(w,v5,x))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(23120(a,1),29675(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23120 29675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29697">
    <literal><![CDATA[
      a(x,y,a(z * (z * u),w,v5)) = a(x,y,a(u,w,L(v5,z,z)))
    ]]></literal>
    <justification jstring="[para(29675(a,1),25007(a,2,3))].">
      <j1 rule="para" parents="29675 25007"/>
    </justification>
  </clause>

  <clause id="29698">
    <literal><![CDATA[
      a(x,y,L(z,u,a(x,w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(25365(a,1),29675(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25365 29675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29699">
    <literal><![CDATA[
      L(x / y,y,z) \ a(x / y,L(y \ x,y,z),L(x,y,z)) = (a(z,y,x * y) * y) / x
    ]]></literal>
    <justification jstring="[para(29675(a,1),27316(a,1,2))].">
      <j1 rule="para" parents="29675 27316"/>
    </justification>
  </clause>

  <clause id="29700">
    <literal><![CDATA[
      a((x * y) \ z,u,L(w,x,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x \ (y \ z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(29675(a,1),28012(a,1))].">
      <j1 rule="para" parents="29675 28012"/>
    </justification>
  </clause>

  <clause id="29701">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ z = L(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(29675(a,1),28841(a,2,1)),flip(a)].">
      <j1 rule="para" parents="29675 28841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29702">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ z != v5
    ]]></literal>
    <literal><![CDATA[
      L(z,y,L(x,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(29675(a,1),28866(a,1,1))].">
      <j1 rule="para" parents="29675 28866"/>
    </justification>
  </clause>

  <clause id="29708">
    <literal><![CDATA[
      a(R(x,y,z),u,z) = a(x,u,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,12438,a(flip),b,29684,a),flip(a)].">
      <j1 rule="hyper" parents="347 12438 29684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29709">
    <literal><![CDATA[
      R(x,y,z) * a(x,u,z) = R(R(x,y,z),u,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,29708,a(flip),b,28905,a(flip))].">
      <j1 rule="hyper" parents="134 29708 28905"/>
    </justification>
  </clause>

  <clause id="29710">
    <literal><![CDATA[
      a(x,y,z) * R(x,u,z) = R(R(x,u,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,29708,a(flip),b,28907,a(flip))].">
      <j1 rule="hyper" parents="133 29708 28907"/>
    </justification>
  </clause>

  <clause id="29713">
    <literal><![CDATA[
      a(x,y,(x \ z) * a(u,w,x)) = a(x,y,L(x,w,u) \ z)
    ]]></literal>
    <justification jstring="[para(29334(a,1),29696(a,1,3))].">
      <j1 rule="para" parents="29334 29696"/>
    </justification>
  </clause>

  <clause id="29716">
    <literal><![CDATA[
      a(x,y,z) \ (u * a(x,w,v5)) = (a(x,y,z) \ u) * a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(29698(a,1),29150(a,1,1))].">
      <j1 rule="para" parents="29698 29150"/>
    </justification>
  </clause>

  <clause id="29717">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,a(z,y,x)) = L(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,29502,a,b,29701,a)].">
      <j1 rule="hyper" parents="63 29502 29701"/>
    </justification>
  </clause>

  <clause id="29718">
    <literal><![CDATA[
      a(x,y,z) * L(L(z,y,x),u,w) = L(z,u,L(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,29496,a,b,29701,a)].">
      <j1 rule="hyper" parents="63 29496 29701"/>
    </justification>
  </clause>

  <clause id="29720">
    <literal><![CDATA[
      (a(x,y,z) * (R(x,u,z) \ 1)) \ R(R(x,u,z),y,z) = R(x,u,z) * R(x,u,z)
    ]]></literal>
    <justification jstring="[para(29710(a,1),783(a,1,2))].">
      <j1 rule="para" parents="29710 783"/>
    </justification>
  </clause>

  <clause id="29721">
    <literal><![CDATA[
      a(R(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,L(w,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(25182(a,2),29676(a,1))].">
      <j1 rule="para" parents="25182 29676"/>
    </justification>
  </clause>

  <clause id="29722">
    <literal><![CDATA[
      a((x * (y \ 1)) \ 1,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x \ y,z,L(u,x,y)) = w
    ]]></literal>
    <justification jstring="[para(25198(a,1),29676(a,1))].">
      <j1 rule="para" parents="25198 29676"/>
    </justification>
  </clause>

  <clause id="29723">
    <literal><![CDATA[
      a((x \ 1) \ y,x,z) = a(x * y,x,z)
    ]]></literal>
    <justification jstring="[hyper(29265,a,29689,a),flip(a)].">
      <j1 rule="hyper" parents="29265 29689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29724">
    <literal><![CDATA[
      a((x \ 1) \ y,z,z) = a(x * y,z,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,29437,a(flip),b,29689,a),flip(a)].">
      <j1 rule="hyper" parents="63 29437 29689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29725">
    <literal><![CDATA[
      L(x,a(y \ z,y,u),w) = L(x,a(y * z,y,u),w)
    ]]></literal>
    <justification jstring="[para(29723(a,1),24355(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29723 24355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29726">
    <literal><![CDATA[
      R(x,y * a(z \ u,w,w),v5) = R(x,y * a(z * u,w,w),v5)
    ]]></literal>
    <justification jstring="[para(29724(a,1),28244(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="29724 28244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29727">
    <literal><![CDATA[
      a(x * (y \ 1),y,z) = a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29265,a,29691,a),flip(a)].">
      <j1 rule="hyper" parents="29265 29691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29728">
    <literal><![CDATA[
      a(x * (y \ 1),z,y) = a(y \ x,z,y)
    ]]></literal>
    <justification jstring="[hyper(29128,a,29691,a),flip(a)].">
      <j1 rule="hyper" parents="29128 29691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29729">
    <literal><![CDATA[
      a(x,y,a(z \ u,z,w)) = a(x,y,a(u * z,z,w))
    ]]></literal>
    <justification jstring="[para(29727(a,1),25011(a,1,3))].">
      <j1 rule="para" parents="29727 25011"/>
    </justification>
  </clause>

  <clause id="29730">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((w / z) \ (u * w))) = a(x,y,a(w * z,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,24514,a,b,29729,a)].">
      <j1 rule="hyper" parents="63 24514 29729"/>
    </justification>
  </clause>

  <clause id="29731">
    <literal><![CDATA[
      a((x * y) \ z,u,y) = a(x \ (y \ z),u,y)
    ]]></literal>
    <justification jstring="[hyper(29128,a,29677,a)].">
      <j1 rule="hyper" parents="29128 29677"/>
    </justification>
  </clause>

  <clause id="29732">
    <literal><![CDATA[
      a((x * x) \ y,z,z) = a(x \ (x \ y),z,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,29437,a(flip),b,29677,a)].">
      <j1 rule="hyper" parents="63 29437 29677"/>
    </justification>
  </clause>

  <clause id="29733">
    <literal><![CDATA[
      a(x \ y,z,L(u,w \ x,w)) = a((w \ x) \ (w \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,23905,a(flip),b,29677,a)].">
      <j1 rule="hyper" parents="63 23905 29677"/>
    </justification>
  </clause>

  <clause id="29734">
    <literal><![CDATA[
      a(x \ (y \ (z * (x * y))),u,w) = a(T(z,x * y),u,L(w,x,y))
    ]]></literal>
    <justification jstring="[para(22(a,2),29677(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22 29677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29735">
    <literal><![CDATA[
      a((x * (y \ (z / u))) \ w,v5,L(v6,x,y \ (u \ z))) = a(x \ ((y \ (z / u)) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(21498(a,1),29677(a,1,3))].">
      <j1 rule="para" parents="21498 29677"/>
    </justification>
  </clause>

  <clause id="29736">
    <literal><![CDATA[
      a((x * y) \ ((z \ (z / y)) \ 1),u,L(w,x,y)) = a(x \ a(z,y,y),u,w)
    ]]></literal>
    <justification jstring="[para(25431(a,1),29677(a,2,1,2))].">
      <j1 rule="para" parents="25431 29677"/>
    </justification>
  </clause>

  <clause id="29737">
    <literal><![CDATA[
      a(x \ (y \ z),u,y) != w
    ]]></literal>
    <literal><![CDATA[
      a((x * y) \ z,u,y) = w
    ]]></literal>
    <justification jstring="[para(29677(a,1),29128(a,1))].">
      <j1 rule="para" parents="29677 29128"/>
    </justification>
  </clause>

  <clause id="29738">
    <literal><![CDATA[
      a(x \ (y \ z),u,y) \ y = L(y,u,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(29731(a,1),28841(a,2,1)),flip(a)].">
      <j1 rule="para" parents="29731 28841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29739">
    <literal><![CDATA[
      L(x,y,(z * x) \ u) = L(x,y,z \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(28866,a,29738,a),flip(a)].">
      <j1 rule="hyper" parents="28866 29738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29740">
    <literal><![CDATA[
      x / L(y,z,z \ (y \ x)) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(220,a,29739,a(flip),b,13465,a(flip))].">
      <j1 rule="hyper" parents="220 29739 13465"/>
    </justification>
  </clause>

  <clause id="29741">
    <literal><![CDATA[
      L(x,y,y \ (x \ z)) \ z = T((z / (y * x)) * y,x)
    ]]></literal>
    <justification jstring="[para(29740(a,1),19941(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29740 19941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29742">
    <literal><![CDATA[
      a((x * y) \ z,u,x) = a(y \ (x \ z),u,x)
    ]]></literal>
    <justification jstring="[hyper(29128,a,29688,a)].">
      <j1 rule="hyper" parents="29128 29688"/>
    </justification>
  </clause>

  <clause id="29743">
    <literal><![CDATA[
      a((x * y) \ z,u,L(x,w,v5)) = a(y \ (x \ z),u,L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,12448,a(flip),b,29688,a)].">
      <j1 rule="hyper" parents="63 12448 29688"/>
    </justification>
  </clause>

  <clause id="29744">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * L(x,u,w) = L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,29,a(flip),b,29694,a),flip(a)].">
      <j1 rule="hyper" parents="347 29 29694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29745">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,a(z,y,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(z,w,u)) = v5
    ]]></literal>
    <justification jstring="[para(29502(a,2),29702(a,1))].">
      <j1 rule="para" parents="29502 29702"/>
    </justification>
  </clause>

  <clause id="29746">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,a(x,y,z)) = L(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(26565,a,29717,a)].">
      <j1 rule="hyper" parents="26565 29717"/>
    </justification>
  </clause>

  <clause id="29747">
    <literal><![CDATA[
      L(x,y,L(z,y,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(26354,a,29717,a),flip(a)].">
      <j1 rule="hyper" parents="26354 29717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29748">
    <literal><![CDATA[
      L(x,y,z) \ L(x,y,L(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(z,y,x)) = v5
    ]]></literal>
    <justification jstring="[para(29717(a,1),356(a,1,2))].">
      <j1 rule="para" parents="29717 356"/>
    </justification>
  </clause>

  <clause id="29749">
    <literal><![CDATA[
      L(L(x \ 1,x,y),x,y) = (R(y,x,x) * x) \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,25482,a(flip),b,29747,a),flip(a)].">
      <j1 rule="hyper" parents="63 25482 29747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29750">
    <literal><![CDATA[
      a(x,L(y,x,x),L(z,x,y)) = a(x,L(y,x,x),z)
    ]]></literal>
    <justification jstring="[para(29747(a,1),29278(a,1,3))].">
      <j1 rule="para" parents="29747 29278"/>
    </justification>
  </clause>

  <clause id="29751">
    <literal><![CDATA[
      a(x,y,z * (u * ((R(w,v5,v5) * v5) \ w))) = a(x,y,(u * (v5 \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(29749(a,1),25818(a,1,3,2,2))].">
      <j1 rule="para" parents="29749 25818"/>
    </justification>
  </clause>

  <clause id="29752">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * a(z,y,x) = L(x,u,L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(20016,a,29718,a)].">
      <j1 rule="hyper" parents="20016 29718"/>
    </justification>
  </clause>

  <clause id="29753">
    <literal><![CDATA[
      L(x,y,L(z,u,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(11871,a,29718,a),flip(a)].">
      <j1 rule="hyper" parents="11871 29718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29754">
    <literal><![CDATA[
      a(x,y,z) * L(L(z,u,w),y,x) = L(z,u,L(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,166,a,b,29718,a)].">
      <j1 rule="hyper" parents="63 166 29718"/>
    </justification>
  </clause>

  <clause id="29756">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,v5,x))) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(29113(a,2),29753(a,1,3))].">
      <j1 rule="para" parents="29113 29753"/>
    </justification>
  </clause>

  <clause id="29757">
    <literal><![CDATA[
      L(x,y,a(z,u,(x * w) \ v5)) = L(x,y,a(z,u,w \ (x \ v5)))
    ]]></literal>
    <justification jstring="[para(329(a,1),29756(a,1,3,3))].">
      <j1 rule="para" parents="329 29756"/>
    </justification>
  </clause>

  <clause id="29758">
    <literal><![CDATA[
      L(x,y,a(z,u,x \ w)) = L(x,y,a(z,u,w * x))
    ]]></literal>
    <justification jstring="[para(25258(a,1),29756(a,1,3))].">
      <j1 rule="para" parents="25258 29756"/>
    </justification>
  </clause>

  <clause id="29759">
    <literal><![CDATA[
      R(x,y,a(z,u,x \ w)) = L(x,y,a(z,u,w * x))
    ]]></literal>
    <justification jstring="[hyper(23257,a,29758,a)].">
      <j1 rule="hyper" parents="23257 29758"/>
    </justification>
  </clause>

  <clause id="29760">
    <literal><![CDATA[
      a(x,y,z) * L(x,u,a(w,v5,z)) = L(R(x,y,z),u,a(w,v5,z))
    ]]></literal>
    <justification jstring="[para(23120(a,1),29744(a,1,1,3))].">
      <j1 rule="para" parents="23120 29744"/>
    </justification>
  </clause>

  <clause id="29761">
    <literal><![CDATA[
      L(R(x,y,z),u,w) \ L(x,u,w) = a(x,y,L(z,u,w)) \ 1
    ]]></literal>
    <justification jstring="[para(29744(a,1),28403(a,1,1))].">
      <j1 rule="para" parents="29744 28403"/>
    </justification>
  </clause>

  <clause id="29762">
    <literal><![CDATA[
      x * a(y,z,a(a(u,w,x) * x,w,u)) = L(a(u,w,x) * x,w,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(28941(a,1),29746(a,1,1))].">
      <j1 rule="para" parents="28941 29746"/>
    </justification>
  </clause>

  <clause id="29763">
    <literal><![CDATA[
      L(x,y,z) \ L(x,y,L(z,u,w)) = a(z,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[para(29752(a,1),29262(a,1,2))].">
      <j1 rule="para" parents="29752 29262"/>
    </justification>
  </clause>

  <clause id="29764">
    <literal><![CDATA[
      L(a(x,x,y) * L(y,z,u),x,x) = L(y,z,L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(29537,a,29754,a)].">
      <j1 rule="hyper" parents="29537 29754"/>
    </justification>
  </clause>

  <clause id="29765">
    <literal><![CDATA[
      L(x,y,L(y,z,z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(189,a,29763,a,b,29435,a(flip))].">
      <j1 rule="hyper" parents="189 29763 29435"/>
    </justification>
  </clause>

  <clause id="29766">
    <literal><![CDATA[
      L(x,x,L(y,y,z)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(189,a,29763,a,b,28856,a(flip))].">
      <j1 rule="hyper" parents="189 29763 28856"/>
    </justification>
  </clause>

  <clause id="29767">
    <literal><![CDATA[
      L(x,x,(y * z) \ y) = L(x,x,z \ 1)
    ]]></literal>
    <justification jstring="[para(3196(a,1),29766(a,1,3))].">
      <j1 rule="para" parents="3196 29766"/>
    </justification>
  </clause>

  <clause id="29768">
    <literal><![CDATA[
      L(x,x,y \ (z \ y)) = L(x,x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(23699,a,29767,a)].">
      <j1 rule="hyper" parents="23699 29767"/>
    </justification>
  </clause>

  <clause id="29769">
    <literal><![CDATA[
      L(x,x,(y \ z) \ 1) = L(x,x,z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),29767(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 29767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29770">
    <literal><![CDATA[
      R(x,y,z \ (u \ ((u \ w) \ R(u,v5,u)))) = R(x,y,L(z,z,(u \ w) \ 1) * (w \ u))
    ]]></literal>
    <justification jstring="[para(29768(a,1),25712(a,2,3,1))].">
      <j1 rule="para" parents="29768 25712"/>
    </justification>
  </clause>

  <clause id="29771">
    <literal><![CDATA[
      L(L(x,y,z) * a(u,u,x),u,u) = L(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[para(11790(a,2),29764(a,1,1))].">
      <j1 rule="para" parents="11790 29764"/>
    </justification>
  </clause>

  <clause id="29772">
    <literal><![CDATA[
      (x \ 1) * (L(y,z,u) * a(x,x,y)) = x \ L(y,z,L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(128,a,29771,a(flip),b,3197,a),flip(a)].">
      <j1 rule="hyper" parents="128 29771 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29773">
    <literal><![CDATA[
      a(x,y,x * (z * a(u,w,x))) = a(x,y,L(x,w,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(29206,a,29713,a)].">
      <j1 rule="hyper" parents="29206 29713"/>
    </justification>
  </clause>

  <clause id="29775">
    <literal><![CDATA[
      a(x,y,x * (z * a(u,w,x))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(x,w,u) * z) = v5
    ]]></literal>
    <justification jstring="[para(29773(a,2),29200(a,1))].">
      <j1 rule="para" parents="29773 29200"/>
    </justification>
  </clause>

  <clause id="29776">
    <literal><![CDATA[
      a((x * y) * x,z,a(u,w,v5)) = a(y,z,a(u,w,L(v5,x,x)))
    ]]></literal>
    <justification jstring="[para(29113(a,2),29683(a,2,3))].">
      <j1 rule="para" parents="29113 29683"/>
    </justification>
  </clause>

  <clause id="29777">
    <literal><![CDATA[
      L(R(x,y,z),u,w) \ L(x,u,w) = L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,29136,a,b,29761,a),flip(a)].">
      <j1 rule="hyper" parents="347 29136 29761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29778">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(v5 * (v5 * x),y,a(z,u,w)) = v6
    ]]></literal>
    <justification jstring="[para(29776(a,1),23925(a,1))].">
      <j1 rule="para" parents="29776 23925"/>
    </justification>
  </clause>

  <clause id="29779">
    <literal><![CDATA[
      R(R(x,y,z),u,w) \ R(x,y,z) = L(a(x,u,w) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,27508,a,b,29777,a)].">
      <j1 rule="hyper" parents="63 27508 29777"/>
    </justification>
  </clause>

  <clause id="29780">
    <literal><![CDATA[
      a(L(x,y,z),x * L(x,u,w),v5) = a(w,u,a(v5,x,L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,27867,a(flip),b,29680,a),flip(a)].">
      <j1 rule="hyper" parents="347 27867 29680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29781">
    <literal><![CDATA[
      a((x * y) \ (y * z),u,w) = a(x \ z,u,L(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(11583,a,29690,a),flip(a)].">
      <j1 rule="hyper" parents="11583 29690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29782">
    <literal><![CDATA[
      a((x \ 1) \ (y \ 1),z,y) = a(y \ x,z,L(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(29722,a,29742,a),flip(a)].">
      <j1 rule="hyper" parents="29722 29742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29783">
    <literal><![CDATA[
      a((x \ 1) \ (y \ 1),z,y) = a(y \ x,z,y)
    ]]></literal>
    <justification jstring="[hyper(29203,a,29782,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="29203 29782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29784">
    <literal><![CDATA[
      a(x \ (y \ 1),z,y) = a(y \ (x \ 1),z,y)
    ]]></literal>
    <justification jstring="[hyper(23960,a,29783,a)].">
      <j1 rule="hyper" parents="23960 29783"/>
    </justification>
  </clause>

  <clause id="29785">
    <literal><![CDATA[
      a(x \ (y \ z),u,L(y,y,x)) = a(y \ (x \ z),u,y)
    ]]></literal>
    <justification jstring="[hyper(29700,a,29743,a),flip(a)].">
      <j1 rule="hyper" parents="29700 29743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29786">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[hyper(29748,a,29763,a)].">
      <j1 rule="hyper" parents="29748 29763"/>
    </justification>
  </clause>

  <clause id="29787">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,a(x,y,w)) = v5
    ]]></literal>
    <justification jstring="[para(29763(a,1),29748(a,1))].">
      <j1 rule="para" parents="29763 29748"/>
    </justification>
  </clause>

  <clause id="29788">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(26560,a,29786,a)].">
      <j1 rule="hyper" parents="26560 29786"/>
    </justification>
  </clause>

  <clause id="29790">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,26591,a,b,29786,a)].">
      <j1 rule="hyper" parents="347 26591 29786"/>
    </justification>
  </clause>

  <clause id="29791">
    <literal><![CDATA[
      a(x,y,a(z,u,y * x)) = a(z,u,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,25269,a(flip),b,29786,a),flip(a)].">
      <j1 rule="hyper" parents="347 25269 29786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29792">
    <literal><![CDATA[
      a(x,y,z) * a(z,y,a(u,w,x)) = a(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,29786,a,b,29264,a)].">
      <j1 rule="hyper" parents="134 29786 29264"/>
    </justification>
  </clause>

  <clause id="29793">
    <literal><![CDATA[
      x * a(y,z,a(x,u,w)) = L(x,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(134,a,29786,a,b,28984,a)].">
      <j1 rule="hyper" parents="134 29786 28984"/>
    </justification>
  </clause>

  <clause id="29794">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 != v6
    ]]></literal>
    <literal><![CDATA[
      v5 * a(z,u,a(x,y,w)) = v6
    ]]></literal>
    <justification jstring="[para(29786(a,1),20016(a,1,1))].">
      <j1 rule="para" parents="29786 20016"/>
    </justification>
  </clause>

  <clause id="29795">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u,w,a(y,z,v5)) * x = v6
    ]]></literal>
    <justification jstring="[para(29786(a,1),20479(a,1,2))].">
      <j1 rule="para" parents="29786 20479"/>
    </justification>
  </clause>

  <clause id="29796">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,a(w,y,x)) = v5
    ]]></literal>
    <justification jstring="[para(29786(a,1),26560(a,1))].">
      <j1 rule="para" parents="29786 26560"/>
    </justification>
  </clause>

  <clause id="29797">
    <literal><![CDATA[
      L(x / y,y,a(z,u,w)) \ x = y * a(z,u,a(x * y,y,w))
    ]]></literal>
    <justification jstring="[para(29786(a,1),27245(a,2,2))].">
      <j1 rule="para" parents="29786 27245"/>
    </justification>
  </clause>

  <clause id="29798">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * a(w,u,a(x,y,z))) = v5
    ]]></literal>
    <justification jstring="[para(29786(a,1),28448(a,1,2,2))].">
      <j1 rule="para" parents="29786 28448"/>
    </justification>
  </clause>

  <clause id="29799">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * z != v5
    ]]></literal>
    <literal><![CDATA[
      L(z,u,a(x,y,w)) = v5
    ]]></literal>
    <justification jstring="[para(29786(a,1),29007(a,1,1))].">
      <j1 rule="para" parents="29786 29007"/>
    </justification>
  </clause>

  <clause id="29800">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,y,w) = a(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[para(29786(a,1),29125(a,1,1))].">
      <j1 rule="para" parents="29786 29125"/>
    </justification>
  </clause>

  <clause id="29801">
    <literal><![CDATA[
      a(x,a(y,z,x),u) = a(y,z,a(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,26592,a,b,29788,a)].">
      <j1 rule="hyper" parents="347 26592 29788"/>
    </justification>
  </clause>

  <clause id="29802">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,26591,a,b,29788,a)].">
      <j1 rule="hyper" parents="347 26591 29788"/>
    </justification>
  </clause>

  <clause id="29803">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,29788,a(flip),b,29788,a)].">
      <j1 rule="hyper" parents="347 29788 29788"/>
    </justification>
  </clause>

  <clause id="29804">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) = a(v5,w,a(u,z,y * x))
    ]]></literal>
    <justification jstring="[hyper(347,a,26516,a(flip),b,29788,a),flip(a)].">
      <j1 rule="hyper" parents="347 26516 29788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29805">
    <literal><![CDATA[
      a(x,y,z) * a(z,y,a(x,u,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(134,a,29788,a,b,29264,a)].">
      <j1 rule="hyper" parents="134 29788 29264"/>
    </justification>
  </clause>

  <clause id="29806">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * a(x,y,a(z,u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,29788,a,b,29147,a)].">
      <j1 rule="hyper" parents="134 29788 29147"/>
    </justification>
  </clause>

  <clause id="29807">
    <literal><![CDATA[
      x * a(y,z,a(u,w,x)) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,29788,a,b,28984,a)].">
      <j1 rule="hyper" parents="134 29788 28984"/>
    </justification>
  </clause>

  <clause id="29808">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,29786,a,b,29788,a)].">
      <j1 rule="hyper" parents="63 29786 29788"/>
    </justification>
  </clause>

  <clause id="29809">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),a(y,z,u),w) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(29788(a,2),23358(a,1,1,2))].">
      <j1 rule="para" parents="29788 23358"/>
    </justification>
  </clause>

  <clause id="29810">
    <literal><![CDATA[
      a(x,y,a(z,u * w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(v5,w * u,a(x,y,z)) = v6
    ]]></literal>
    <justification jstring="[para(29788(a,2),23994(a,1))].">
      <j1 rule="para" parents="29788 23994"/>
    </justification>
  </clause>

  <clause id="29811">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(z,y,x)) = v5
    ]]></literal>
    <justification jstring="[para(29788(a,2),26560(a,1))].">
      <j1 rule="para" parents="29788 26560"/>
    </justification>
  </clause>

  <clause id="29812">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(v5,w,a(u,z,y)) * x = v6
    ]]></literal>
    <justification jstring="[para(29788(a,2),26526(a,1,2))].">
      <j1 rule="para" parents="29788 26526"/>
    </justification>
  </clause>

  <clause id="29813">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(z,u,a(x,y,w)) * v5) = v5
    ]]></literal>
    <justification jstring="[para(29788(a,1),28447(a,1,1))].">
      <j1 rule="para" parents="29788 28447"/>
    </justification>
  </clause>

  <clause id="29814">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),w,a(y,z,u)) = x * a(u,z,a(y,x,w))
    ]]></literal>
    <justification jstring="[para(29788(a,2),28556(a,2,2))].">
      <j1 rule="para" parents="29788 28556"/>
    </justification>
  </clause>

  <clause id="29815">
    <literal><![CDATA[
      (x \ y) * a(z,u,a(y,y,w)) = x \ R(y,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(29788(a,1),29491(a,1,2))].">
      <j1 rule="para" parents="29788 29491"/>
    </justification>
  </clause>

  <clause id="29816">
    <literal><![CDATA[
      a((x * y) \ z,u,a(x,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,w,a(v5,u,y \ (x \ z))) = v6
    ]]></literal>
    <justification jstring="[para(29788(a,1),29299(a,1))].">
      <j1 rule="para" parents="29788 29299"/>
    </justification>
  </clause>

  <clause id="29817">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) = a(w,u,a(x,y,L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(29675(a,1),29788(a,1,3))].">
      <j1 rule="para" parents="29675 29788"/>
    </justification>
  </clause>

  <clause id="29818">
    <literal><![CDATA[
      a(x,a(y,z,u) * w,a(y,z,u)) = a(y,z,a(x,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,28654,a,b,29790,a)].">
      <j1 rule="hyper" parents="63 28654 29790"/>
    </justification>
  </clause>

  <clause id="29819">
    <literal><![CDATA[
      x \ L(L(x,a(y,z,u),w),w,a(y,z,u)) = a(y,z,a(w,x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,28555,a,b,29790,a)].">
      <j1 rule="hyper" parents="63 28555 29790"/>
    </justification>
  </clause>

  <clause id="29820">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ x = a(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,28838,a(flip),b,29790,a)].">
      <j1 rule="hyper" parents="63 28838 29790"/>
    </justification>
  </clause>

  <clause id="29821">
    <literal><![CDATA[
      x * (y * a(z,u,a(x,x,w))) = L(x,x,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(29790(a,1),26646(a,1,2,2))].">
      <j1 rule="para" parents="29790 26646"/>
    </justification>
  </clause>

  <clause id="29822">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,w)) = y * a(z,u,a(y * x,x,w))
    ]]></literal>
    <justification jstring="[para(29790(a,1),27248(a,2,2))].">
      <j1 rule="para" parents="29790 27248"/>
    </justification>
  </clause>

  <clause id="29823">
    <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(29790(a,1),28562(a,1,1,2))].">
      <j1 rule="para" parents="29790 28562"/>
    </justification>
  </clause>

  <clause id="29824">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),w,a(u,z,y)) = x * a(y,z,a(w,x,u))
    ]]></literal>
    <justification jstring="[para(29790(a,1),28563(a,2,2))].">
      <j1 rule="para" parents="29790 28563"/>
    </justification>
  </clause>

  <clause id="29825">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),u,a(y,z,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,w),u) = v5
    ]]></literal>
    <justification jstring="[para(29790(a,1),28565(a,1,1,2))].">
      <j1 rule="para" parents="29790 28565"/>
    </justification>
  </clause>

  <clause id="29826">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) \ L(v5,a(z,u,a(x,y,w)),v6)) * v6 = v5 * (a(a(x,y,w),u,z) \ v6)
    ]]></literal>
    <justification jstring="[para(29790(a,1),28760(a,1,1,1))].">
      <j1 rule="para" parents="29790 28760"/>
    </justification>
  </clause>

  <clause id="29827">
    <literal><![CDATA[
      a(L(L(x,a(y,z,u),w),w,a(y,z,u)),a(u,z,a(w,x,y)),v5) = a(x,a(w,x,a(u,z,y)),v5 * a(w,x,a(u,z,y)))
    ]]></literal>
    <justification jstring="[para(29790(a,1),28783(a,1,2))].">
      <j1 rule="para" parents="29790 28783"/>
    </justification>
  </clause>

  <clause id="29828">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ z = L(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[para(29790(a,1),28841(a,2,1)),flip(a)].">
      <j1 rule="para" parents="29790 28841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29829">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ z != v5
    ]]></literal>
    <literal><![CDATA[
      L(z,u,a(x,y,w)) = v5
    ]]></literal>
    <justification jstring="[para(29790(a,1),28866(a,1,1))].">
      <j1 rule="para" parents="29790 28866"/>
    </justification>
  </clause>

  <clause id="29830">
    <literal><![CDATA[
      a(x,y,a(z * y,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,a(x,y,u),z * a(x,y,u)) = w
    ]]></literal>
    <justification jstring="[para(29790(a,1),29268(a,1))].">
      <j1 rule="para" parents="29790 29268"/>
    </justification>
  </clause>

  <clause id="29831">
    <literal><![CDATA[
      a(a(x,x,y),z,u) = a(x,a(u,z,x),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,26591,a,b,29801,a)].">
      <j1 rule="hyper" parents="347 26591 29801"/>
    </justification>
  </clause>

  <clause id="29832">
    <literal><![CDATA[
      a(x * y,a(z,u,x * y),y) = a(z,u,a(y,x * y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,26367,a(flip),b,29801,a),flip(a)].">
      <j1 rule="hyper" parents="347 26367 29801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29833">
    <literal><![CDATA[
      a(a(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(w,u,z)) = v5
    ]]></literal>
    <justification jstring="[para(29802(a,2),26560(a,1))].">
      <j1 rule="para" parents="29802 26560"/>
    </justification>
  </clause>

  <clause id="29834">
    <literal><![CDATA[
      a(x,a(y,z,a(u,w,v5)),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,a(v5,w,a(y,z,u)),v6) = v7
    ]]></literal>
    <justification jstring="[para(29802(a,1),26574(a,1,2))].">
      <j1 rule="para" parents="29802 26574"/>
    </justification>
  </clause>

  <clause id="29835">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),w,a(y,z,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(29802(a,1),28565(a,1,1,2))].">
      <j1 rule="para" parents="29802 28565"/>
    </justification>
  </clause>

  <clause id="29836">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * w = L(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(29802(a,1),29011(a,1,1))].">
      <j1 rule="para" parents="29802 29011"/>
    </justification>
  </clause>

  <clause id="29837">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(z,y,a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(26560,a,29803,a)].">
      <j1 rule="hyper" parents="26560 29803"/>
    </justification>
  </clause>

  <clause id="29838">
    <literal><![CDATA[
      a(x,y,a(z,u,w \ 1)) = a(z,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(25010,a,29803,a),flip(a)].">
      <j1 rule="hyper" parents="25010 29803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29839">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,29788,a,b,29803,a)].">
      <j1 rule="hyper" parents="347 29788 29803"/>
    </justification>
  </clause>

  <clause id="29840">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,29786,a,b,29803,a)].">
      <j1 rule="hyper" parents="347 29786 29803"/>
    </justification>
  </clause>

  <clause id="29841">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,x))) = a(z,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,29192,a,b,29803,a)].">
      <j1 rule="hyper" parents="347 29192 29803"/>
    </justification>
  </clause>

  <clause id="29842">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) = a(v5,z,a(u,w,y * x))
    ]]></literal>
    <justification jstring="[hyper(347,a,26516,a(flip),b,29803,a),flip(a)].">
      <j1 rule="hyper" parents="347 26516 29803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29843">
    <literal><![CDATA[
      a(x * y,z,a(y,x * y,u)) = a(u,z,a(y,x * y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,26367,a(flip),b,29803,a),flip(a)].">
      <j1 rule="hyper" parents="347 26367 29803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29844">
    <literal><![CDATA[
      a(x,y,a(z * x,z,u)) = a(u,y,a(z,z,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,25269,a(flip),b,29803,a),flip(a)].">
      <j1 rule="hyper" parents="347 25269 29803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29845">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(z,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(134,a,29803,a,b,19974,a),flip(a)].">
      <j1 rule="hyper" parents="134 29803 19974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29846">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) = x * a(v5,z,a(y,w,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,29803,a,b,9,a)].">
      <j1 rule="hyper" parents="134 29803 9"/>
    </justification>
  </clause>

  <clause id="29847">
    <literal><![CDATA[
      a(x,y,z) * a(x,u,a(w,y,z)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(134,a,29803,a(flip),b,29264,a)].">
      <j1 rule="hyper" parents="134 29803 29264"/>
    </justification>
  </clause>

  <clause id="29848">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 != v6
    ]]></literal>
    <literal><![CDATA[
      v5 * a(w,y,a(x,u,z)) = v6
    ]]></literal>
    <justification jstring="[para(29803(a,2),20016(a,1,1))].">
      <j1 rule="para" parents="29803 20016"/>
    </justification>
  </clause>

  <clause id="29849">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u,z,a(v5,w,y)) * x = v6
    ]]></literal>
    <justification jstring="[para(29803(a,1),20479(a,1,2))].">
      <j1 rule="para" parents="29803 20479"/>
    </justification>
  </clause>

  <clause id="29850">
    <literal><![CDATA[
      a(x,y,a(z,u,w * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(v5 * w,y,a(x,u,z)) = v6
    ]]></literal>
    <justification jstring="[para(29803(a,2),23925(a,1))].">
      <j1 rule="para" parents="29803 23925"/>
    </justification>
  </clause>

  <clause id="29851">
    <literal><![CDATA[
      a(x,y,a(z,u * w,v5)) = a(v5,y,a(x,w * u,z))
    ]]></literal>
    <justification jstring="[para(24037(a,1),29803(a,1,3))].">
      <j1 rule="para" parents="24037 29803"/>
    </justification>
  </clause>

  <clause id="29852">
    <literal><![CDATA[
      a(x,y * z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u,z * y,a(v5,w,x)) = v6
    ]]></literal>
    <justification jstring="[para(29803(a,1),23994(a,1))].">
      <j1 rule="para" parents="29803 23994"/>
    </justification>
  </clause>

  <clause id="29853">
    <literal><![CDATA[
      a(x,y * z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(v5,z * y,a(x,w,u)) = v6
    ]]></literal>
    <justification jstring="[para(29803(a,2),23994(a,1))].">
      <j1 rule="para" parents="29803 23994"/>
    </justification>
  </clause>

  <clause id="29854">
    <literal><![CDATA[
      a(x,y,a(z,u,(w * v5) * v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(v6 * (v5 * w),y,a(x,u,z)) = v7
    ]]></literal>
    <justification jstring="[para(29803(a,2),24409(a,1))].">
      <j1 rule="para" parents="29803 24409"/>
    </justification>
  </clause>

  <clause id="29855">
    <literal><![CDATA[
      a(x,y,a(z,u,w * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(z,y,a(v5 * w,u,x)) = v6
    ]]></literal>
    <justification jstring="[para(29803(a,1),26340(a,1))].">
      <j1 rule="para" parents="29803 26340"/>
    </justification>
  </clause>

  <clause id="29856">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(v5,z,a(y * x,w,u)) = v6
    ]]></literal>
    <justification jstring="[para(29803(a,2),26340(a,1))].">
      <j1 rule="para" parents="29803 26340"/>
    </justification>
  </clause>

  <clause id="29857">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,y,a(x,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(29803(a,1),26560(a,1))].">
      <j1 rule="para" parents="29803 26560"/>
    </justification>
  </clause>

  <clause id="29858">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,y,a(z,u,x)) = v5
    ]]></literal>
    <justification jstring="[para(29803(a,2),26560(a,1))].">
      <j1 rule="para" parents="29803 26560"/>
    </justification>
  </clause>

  <clause id="29859">
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(v5,y,a(x,w,u * z)) = v6
    ]]></literal>
    <justification jstring="[para(29803(a,2),26564(a,1))].">
      <j1 rule="para" parents="29803 26564"/>
    </justification>
  </clause>

  <clause id="29860">
    <literal><![CDATA[
      a(x,y,z) \ a(z,u,a(w,y,x)) = L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(29803(a,1),28462(a,1,2))].">
      <j1 rule="para" parents="29803 28462"/>
    </justification>
  </clause>

  <clause id="29861">
    <literal><![CDATA[
      a(x,y,z) * a(z,u,a(w,y,x)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(29803(a,1),29114(a,1,2))].">
      <j1 rule="para" parents="29803 29114"/>
    </justification>
  </clause>

  <clause id="29862">
    <literal><![CDATA[
      a(x \ (y \ x),z,a(u,w,v5)) = a(v5,z,a(u,w,L(y,y,x)))
    ]]></literal>
    <justification jstring="[para(24761(a,2),29808(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24761 29808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29863">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,y,a(x,u,z)) = v5
    ]]></literal>
    <justification jstring="[para(29808(a,1),26560(a,1))].">
      <j1 rule="para" parents="29808 26560"/>
    </justification>
  </clause>

  <clause id="29864">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      L(w,y,a(z,u,x)) = v5
    ]]></literal>
    <justification jstring="[para(29808(a,1),29007(a,1,1))].">
      <j1 rule="para" parents="29808 29007"/>
    </justification>
  </clause>

  <clause id="29865">
    <literal><![CDATA[
      a(a(x * y,x * y,z),u,w) = a(y \ x,a(w,u,y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,27094,a(flip),b,29831,a)].">
      <j1 rule="hyper" parents="63 27094 29831"/>
    </justification>
  </clause>

  <clause id="29866">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w)) = a(z,y,a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,28984,a,b,29837,a)].">
      <j1 rule="hyper" parents="347 28984 29837"/>
    </justification>
  </clause>

  <clause id="29867">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,y,a(w,u,x)) = v5
    ]]></literal>
    <justification jstring="[para(29837(a,1),26560(a,1))].">
      <j1 rule="para" parents="29837 26560"/>
    </justification>
  </clause>

  <clause id="29868">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) != 1
    ]]></literal>
    <literal><![CDATA[
      L(z,y,a(x,u,w)) = z
    ]]></literal>
    <justification jstring="[para(29837(a,1),26597(a,1))].">
      <j1 rule="para" parents="29837 26597"/>
    </justification>
  </clause>

  <clause id="29869">
    <literal><![CDATA[
      a(x,y,a(z,u,y * z)) = a(x,u,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,25269,a(flip),b,29839,a),flip(a)].">
      <j1 rule="hyper" parents="347 25269 29839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29870">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) = x * a(y,w,a(v5,z,u))
    ]]></literal>
    <justification jstring="[para(29839(a,1),26522(a,1,2))].">
      <j1 rule="para" parents="29839 26522"/>
    </justification>
  </clause>

  <clause id="29871">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),a(z,u,w),y) = x * a(y,u,a(w,x,z))
    ]]></literal>
    <justification jstring="[para(29839(a,1),28558(a,2,2))].">
      <j1 rule="para" parents="29839 28558"/>
    </justification>
  </clause>

  <clause id="29873">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) \ v6 = (v5 * a(x,u,a(w,y,z))) \ v6
    ]]></literal>
    <justification jstring="[para(29840(a,1),20119(a,1,1,1))].">
      <j1 rule="para" parents="29840 20119"/>
    </justification>
  </clause>

  <clause id="29874">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) \ v6 != v7
    ]]></literal>
    <literal><![CDATA[
      (v5 * a(x,u,a(w,y,z))) \ v6 = v7
    ]]></literal>
    <justification jstring="[para(29840(a,1),20024(a,1,1,1))].">
      <j1 rule="para" parents="29840 20024"/>
    </justification>
  </clause>

  <clause id="29875">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,a(z,y,w)) = v5
    ]]></literal>
    <justification jstring="[para(29840(a,1),26560(a,1))].">
      <j1 rule="para" parents="29840 26560"/>
    </justification>
  </clause>

  <clause id="29876">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      x * a(y,w,a(u,z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(29840(a,1),26565(a,1,2))].">
      <j1 rule="para" parents="29840 26565"/>
    </justification>
  </clause>

  <clause id="29877">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * z = L(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[hyper(20479,a,29793,a)].">
      <j1 rule="hyper" parents="20479 29793"/>
    </justification>
  </clause>

  <clause id="29879">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) != x * v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,a(x,y,w)) = v5
    ]]></literal>
    <justification jstring="[para(29793(a,1),43(a,1))].">
      <j1 rule="para" parents="29793 43"/>
    </justification>
  </clause>

  <clause id="29880">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,a(x,y,w)) = v5
    ]]></literal>
    <justification jstring="[para(29793(a,1),356(a,1,2))].">
      <j1 rule="para" parents="29793 356"/>
    </justification>
  </clause>

  <clause id="29881">
    <literal><![CDATA[
      (((x * L(y,z,a(u,w,v5))) / (x * y)) * x) * y = x * (y * R(a(u,w,a(v5,z,y)),x,y))
    ]]></literal>
    <justification jstring="[para(29807(a,1),1686(a,1,1,1,1,2))].">
      <j1 rule="para" parents="29807 1686"/>
    </justification>
  </clause>

  <clause id="29882">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,a(z,v5,x)) = L(L(x,y,z),v5,a(u,w,z))
    ]]></literal>
    <justification jstring="[para(29119(a,1),29807(a,1,2,3))].">
      <j1 rule="para" parents="29119 29807"/>
    </justification>
  </clause>

  <clause id="29883">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ x != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,a(x,y,w)) = v5
    ]]></literal>
    <justification jstring="[para(29828(a,1),20577(a,1,1))].">
      <j1 rule="para" parents="29828 20577"/>
    </justification>
  </clause>

  <clause id="29884">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * w = L(w,y,a(z,u,x))
    ]]></literal>
    <justification jstring="[para(29839(a,1),29836(a,1,1))].">
      <j1 rule="para" parents="29839 29836"/>
    </justification>
  </clause>

  <clause id="29885">
    <literal><![CDATA[
      L(x,y,a(z * u,z,w) * a(w,v5,a(z,z,u))) = L(x,y,L(a(z * u,z,w),v5,u))
    ]]></literal>
    <justification jstring="[para(29844(a,1),28944(a,1,3,2))].">
      <j1 rule="para" parents="29844 28944"/>
    </justification>
  </clause>

  <clause id="29888">
    <literal><![CDATA[
      L(x,y,a(z,u,u * x)) = a(z,y,a(u,u,x)) * x
    ]]></literal>
    <justification jstring="[para(29869(a,1),29877(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29869 29877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29890">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = L(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,29836,a(flip),b,29884,a)].">
      <j1 rule="hyper" parents="63 29836 29884"/>
    </justification>
  </clause>

  <clause id="29891">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) != v5 * x
    ]]></literal>
    <literal><![CDATA[
      a(w,y,a(z,u,x)) = v5
    ]]></literal>
    <justification jstring="[para(29884(a,1),44(a,1))].">
      <j1 rule="para" parents="29884 44"/>
    </justification>
  </clause>

  <clause id="29892">
    <literal><![CDATA[
      L(x,y,a(z * x,z * x,u)) = a(u,y,a(x,z * x,z)) * x
    ]]></literal>
    <justification jstring="[para(26367(a,1),29884(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26367 29884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29894">
    <literal><![CDATA[
      L(x,y * z,a(u,w,v5)) = L(x,w,a(v5,z * y,u))
    ]]></literal>
    <justification jstring="[hyper(27581,a,29890,a),flip(a)].">
      <j1 rule="hyper" parents="27581 29890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29895">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = L(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(27578,a,29890,a)].">
      <j1 rule="hyper" parents="27578 29890"/>
    </justification>
  </clause>

  <clause id="29896">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),u,a(w,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(27576,a,29890,a),flip(a)].">
      <j1 rule="hyper" parents="27576 29890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29897">
    <literal><![CDATA[
      L(x,y * z,a(u,w,v5)) = L(x,w,a(u,z * y,v5))
    ]]></literal>
    <justification jstring="[hyper(21666,a,29890,a)].">
      <j1 rule="hyper" parents="21666 29890"/>
    </justification>
  </clause>

  <clause id="29898">
    <literal><![CDATA[
      x * L(y,z,a(u,w,v5)) = x * L(y,w,a(u,z,v5))
    ]]></literal>
    <justification jstring="[hyper(134,a,29890,a,b,9,a)].">
      <j1 rule="hyper" parents="134 29890 9"/>
    </justification>
  </clause>

  <clause id="29899">
    <literal><![CDATA[
      L(x,y,a(z,u * w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,w * u,a(z,y,v5)) = v6
    ]]></literal>
    <justification jstring="[para(29890(a,1),21666(a,1))].">
      <j1 rule="para" parents="29890 21666"/>
    </justification>
  </clause>

  <clause id="29900">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u,a(w,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(29890(a,1),27578(a,1))].">
      <j1 rule="para" parents="29890 27578"/>
    </justification>
  </clause>

  <clause id="29901">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),u,a(z,y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(29890(a,1),27579(a,1,1))].">
      <j1 rule="para" parents="29890 27579"/>
    </justification>
  </clause>

  <clause id="29902">
    <literal><![CDATA[
      a(x,y,z) \ (u * L(w,y,a(x,u,z))) = (a(x,y,z) \ u) * w
    ]]></literal>
    <justification jstring="[para(29890(a,1),28521(a,1,2,2))].">
      <j1 rule="para" parents="29890 28521"/>
    </justification>
  </clause>

  <clause id="29903">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u,a(z,y,w)) = v5
    ]]></literal>
    <justification jstring="[para(29895(a,1),27578(a,1))].">
      <j1 rule="para" parents="29895 27578"/>
    </justification>
  </clause>

  <clause id="29904">
    <literal><![CDATA[
      L(x,y * z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,w,a(u,z * y,v5)) = v6
    ]]></literal>
    <justification jstring="[para(29895(a,1),27581(a,1))].">
      <j1 rule="para" parents="29895 27581"/>
    </justification>
  </clause>

  <clause id="29905">
    <literal><![CDATA[
      L(x * y,x,a(z,u,x)) = x * L(y,u,a(z,x,x))
    ]]></literal>
    <justification jstring="[para(29895(a,1),29348(a,2,2))].">
      <j1 rule="para" parents="29895 29348"/>
    </justification>
  </clause>

  <clause id="29907">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(w,y,z) \ u) = a(w,y,z) \ (x * u)
    ]]></literal>
    <justification jstring="[para(29896(a,1),28540(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="29896 28540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29908">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(26501(a,1),29787(a,1))].">
      <j1 rule="para" parents="26501 29787"/>
    </justification>
  </clause>

  <clause id="29909">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(z,u,a(w,y,L(x,v5,v6))) = v7
    ]]></literal>
    <justification jstring="[para(29675(a,1),29796(a,1))].">
      <j1 rule="para" parents="29675 29796"/>
    </justification>
  </clause>

  <clause id="29910">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,u,a(w,y,a(z,v5,v6))) = v7
    ]]></literal>
    <justification jstring="[para(29837(a,1),29903(a,1,3))].">
      <j1 rule="para" parents="29837 29903"/>
    </justification>
  </clause>

  <clause id="29911">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) * L(v6,a(z,y,a(w,u,x)),v5) = v5 * (a(z,y,a(w,u,x)) * v6)
    ]]></literal>
    <justification jstring="[hyper(133,a,29845,a,b,212,a)].">
      <j1 rule="hyper" parents="133 29845 212"/>
    </justification>
  </clause>

  <clause id="29912">
    <literal><![CDATA[
      (x * a(y,x,a(z,u,w))) \ (x * w) = L(w,x,a(y,u,z))
    ]]></literal>
    <justification jstring="[para(29845(a,1),26600(a,1,1))].">
      <j1 rule="para" parents="29845 26600"/>
    </justification>
  </clause>

  <clause id="29913">
    <literal><![CDATA[
      L(x,y,a(z,u,u * x)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,29884,a(flip),b,29888,a),flip(a)].">
      <j1 rule="hyper" parents="347 29884 29888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29914">
    <literal><![CDATA[
      ((x * y) / x) * L(x,z,a(u,u,w)) = L(x,z,a(w,u,u * x)) * y
    ]]></literal>
    <justification jstring="[para(29913(a,1),20690(a,1,2))].">
      <j1 rule="para" parents="29913 20690"/>
    </justification>
  </clause>

  <clause id="29915">
    <literal><![CDATA[
      L(x,y,a(z,a(z,y,u) * w,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,w,a(z,y,u)) = v5
    ]]></literal>
    <justification jstring="[para(29897(a,1),28650(a,1))].">
      <j1 rule="para" parents="29897 28650"/>
    </justification>
  </clause>

  <clause id="29916">
    <literal><![CDATA[
      a(L(x,y,a(z,u,w)) * v5,v6,v7) = a(v5 * L(x,u,a(z,y,w)),v6,v7)
    ]]></literal>
    <justification jstring="[para(29898(a,1),23896(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29898 23896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29917">
    <literal><![CDATA[
      ((x * L(y,z,a(u,R(x,w,v5),R(x,w,v5)))) / x) * R(x,w,v5) = L(R(x,w,v5) * y,R(x,w,v5),a(u,z,R(x,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(21077,a,29905,a(flip))].">
      <j1 rule="hyper" parents="21077 29905"/>
    </justification>
  </clause>

  <clause id="29918">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (a(z,y,a(w,v5,x)) * u) = L(T(a(x,y,L(z,v5,w)),u),a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(29792(a,1),28566(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="29792 28566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29919">
    <literal><![CDATA[
      a(x \ 1,y,z) * a(u,y,a(x,w,z)) = a(x \ 1,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[para(29838(a,1),29792(a,1,2))].">
      <j1 rule="para" parents="29838 29792"/>
    </justification>
  </clause>

  <clause id="29920">
    <literal><![CDATA[
      x * a(y,z,a(x,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u,a(y,z,w)) = v5
    ]]></literal>
    <justification jstring="[para(19985(a,1),29799(a,1))].">
      <j1 rule="para" parents="19985 29799"/>
    </justification>
  </clause>

  <clause id="29921">
    <literal><![CDATA[
      x * a(y,z,a(u,w,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,w,a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(26521(a,1),29799(a,1))].">
      <j1 rule="para" parents="26521 29799"/>
    </justification>
  </clause>

  <clause id="29922">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) * a(x,y,a(a(z,u,w),v5,v6)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(29113(a,2),29806(a,1,1,3))].">
      <j1 rule="para" parents="29113 29806"/>
    </justification>
  </clause>

  <clause id="29923">
    <literal><![CDATA[
      a(x,a(x,y,z) * u,a(w,y,z)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(29857,a,29818,a)].">
      <j1 rule="hyper" parents="29857 29818"/>
    </justification>
  </clause>

  <clause id="29924">
    <literal><![CDATA[
      a(x * y,z,u) * a(x * y,y,a(y,z,u)) = a((y \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,29686,a(flip),b,29847,a),flip(a)].">
      <j1 rule="hyper" parents="347 29686 29847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29925">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,a(z,y,w)) * a(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(29847(a,1),26526(a,1))].">
      <j1 rule="para" parents="29847 26526"/>
    </justification>
  </clause>

  <clause id="29926">
    <literal><![CDATA[
      a(x,y,z) * a(z,u * w,a(v5,y,x)) = a(x,y,L(z,w * u,v5))
    ]]></literal>
    <justification jstring="[para(21617(a,1),29861(a,2,3))].">
      <j1 rule="para" parents="21617 29861"/>
    </justification>
  </clause>

  <clause id="29927">
    <literal><![CDATA[
      a(x * y,x,z) * a(z,u,a(x,x,y)) = a(x * y,x,L(z,u,x))
    ]]></literal>
    <justification jstring="[para(25341(a,1),29861(a,1,2))].">
      <j1 rule="para" parents="25341 29861"/>
    </justification>
  </clause>

  <clause id="29928">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * (a(w,v5,z) * u) != v6
    ]]></literal>
    <literal><![CDATA[
      L(a(w,v5,z) * u,y,a(z,z,x)) = v6
    ]]></literal>
    <justification jstring="[para(26875(a,1),29864(a,1,1,3))].">
      <j1 rule="para" parents="26875 29864"/>
    </justification>
  </clause>

  <clause id="29929">
    <literal><![CDATA[
      (x \ y) * a(z,u,a(y,y,w)) = x \ L(y,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(23247(a,1),29815(a,2,2))].">
      <j1 rule="para" parents="23247 29815"/>
    </justification>
  </clause>

  <clause id="29930">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),v5,v6)) = a(x,y,a(z,v5,L(v6,u,w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,29788,a,b,29817,a)].">
      <j1 rule="hyper" parents="347 29788 29817"/>
    </justification>
  </clause>

  <clause id="29931">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) * w = L(w,y,a(z,u,L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[para(29817(a,1),29877(a,1,1))].">
      <j1 rule="para" parents="29817 29877"/>
    </justification>
  </clause>

  <clause id="29932">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,u,a(w,y,L(z,v5,v6))) = v7
    ]]></literal>
    <justification jstring="[para(29817(a,2),29857(a,1))].">
      <j1 rule="para" parents="29817 29857"/>
    </justification>
  </clause>

  <clause id="29933">
    <literal><![CDATA[
      x * a(y,z,a(u,w,L(x,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,z,a(u,w,L(y,v5,v6))) = v7
    ]]></literal>
    <justification jstring="[para(29817(a,1),29920(a,1,2))].">
      <j1 rule="para" parents="29817 29920"/>
    </justification>
  </clause>

  <clause id="29934">
    <literal><![CDATA[
      (x * y) * a(z,u,a(y,y,w)) = x * L(y,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(34,a,20686,a(flip),b,29821,a),flip(a)].">
      <j1 rule="hyper" parents="34 20686 29821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29935">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(z,z,a(x,y,u)) = u * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,29351,a(flip),b,29934,a),flip(a)].">
      <j1 rule="hyper" parents="63 29351 29934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29936">
    <literal><![CDATA[
      a(x,y,z) * ((u / w) * (a(x,y,z) \ w)) = u * a(x,y,a(u * w,w,z))
    ]]></literal>
    <justification jstring="[hyper(29794,a,28598,a),flip(a)].">
      <j1 rule="hyper" parents="29794 28598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29937">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      x * a(v5,w,a(y,z,u)) = v6
    ]]></literal>
    <justification jstring="[para(26521(a,1),29794(a,1))].">
      <j1 rule="para" parents="26521 29794"/>
    </justification>
  </clause>

  <clause id="29938">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(x,y,w) \ v5) = a(x,y,L(w,u,z)) \ v5
    ]]></literal>
    <justification jstring="[hyper(29795,a,29156,a)].">
      <j1 rule="hyper" parents="29795 29156"/>
    </justification>
  </clause>

  <clause id="29939">
    <literal><![CDATA[
      a(x,y * z,a(z * y,u,y)) = a(x,u,a(y,z * y,z))
    ]]></literal>
    <justification jstring="[hyper(29810,a,29843,a)].">
      <j1 rule="hyper" parents="29810 29843"/>
    </justification>
  </clause>

  <clause id="29940">
    <literal><![CDATA[
      L(1 / x,y,z) * R(x,u,a(w,y,z)) = L(a(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,29338,a,b,29860,a)].">
      <j1 rule="hyper" parents="63 29338 29860"/>
    </justification>
  </clause>

  <clause id="29941">
    <literal><![CDATA[
      a(x \ (y \ x),z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(v5,w,a(u,z,L(y,y,x))) = v6
    ]]></literal>
    <justification jstring="[para(29862(a,2),29875(a,1))].">
      <j1 rule="para" parents="29862 29875"/>
    </justification>
  </clause>

  <clause id="29942">
    <literal><![CDATA[
      T(L(R(x,y,z),u,a(w,v5,z)),L(x,u,a(w,v5,z))) / (L(x,u,a(w,v5,z)) * L(x,u,a(w,v5,z))) = L(x,u,a(w,v5,z)) \ R(a(x,y,z),L(x,u,a(w,v5,z)),L(x,u,a(w,v5,z)))
    ]]></literal>
    <justification jstring="[para(29760(a,1),1312(a,1,1,1))].">
      <j1 rule="para" parents="29760 1312"/>
    </justification>
  </clause>

  <clause id="29943">
    <literal><![CDATA[
      (x \ a(x,x,y)) * L(y,z,u) = x \ L(y,z,L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(26332,a,29772,a)].">
      <j1 rule="hyper" parents="26332 29772"/>
    </justification>
  </clause>

  <clause id="29944">
    <literal><![CDATA[
      x * (y \ L(x,z,L(u,y,y))) = L(x,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[para(29943(a,1),21009(a,1,2))].">
      <j1 rule="para" parents="29943 21009"/>
    </justification>
  </clause>

  <clause id="29945">
    <literal><![CDATA[
      a(x,y * ((z \ y) \ L(y,u,L(w,z \ y,z \ y))),v5) = a(x,z * L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(29944(a,2),24158(a,1,2))].">
      <j1 rule="para" parents="29944 24158"/>
    </justification>
  </clause>

  <clause id="29946">
    <literal><![CDATA[
      (L(R(x,y,z),x * L(x,y,z),u) \ (x * u)) \ (R(x,y,z) \ (x * u)) = a(z,y,a(u,x,L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,27797,a,b,29780,a)].">
      <j1 rule="hyper" parents="63 27797 29780"/>
    </justification>
  </clause>

  <clause id="29947">
    <literal><![CDATA[
      L(L(a(x,y,z),a(x,u,w),v5),v5,a(x,u,w)) = a(x,y,z) * a(w,u,a(v5,x,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(26610(a,1),29814(a,2,2,3))].">
      <j1 rule="para" parents="26610 29814"/>
    </justification>
  </clause>

  <clause id="29948">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),w,a(u,z,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(u,z,y),w) = v5
    ]]></literal>
    <justification jstring="[para(29814(a,1),27579(a,1,1))].">
      <j1 rule="para" parents="29814 27579"/>
    </justification>
  </clause>

  <clause id="29949">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),z,a(u,w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(u,z,y),w) = v5
    ]]></literal>
    <justification jstring="[para(29814(a,1),29901(a,1,1))].">
      <j1 rule="para" parents="29814 29901"/>
    </justification>
  </clause>

  <clause id="29950">
    <literal><![CDATA[
      L(x \ L(L(x,a(y,z,u),w),w,a(y,z,u)),v5,v6) = a(y,z,a(w,L(x,v5,v6),u))
    ]]></literal>
    <justification jstring="[hyper(16602,a,29819,a)].">
      <j1 rule="hyper" parents="16602 29819"/>
    </justification>
  </clause>

  <clause id="29951">
    <literal><![CDATA[
      (x * a(y,z,a(x * u,u,w))) / u = L(x / u,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(131,a,29822,a(flip),b,740,a)].">
      <j1 rule="hyper" parents="131 29822 740"/>
    </justification>
  </clause>

  <clause id="29952">
    <literal><![CDATA[
      ((x \ y) \ x) * L(((x \ y) \ x) \ z,(y \ x) * x,a(u,w,v5)) = z * a(u,w,a(z * ((x \ y) \ x),(x \ y) \ x,v5))
    ]]></literal>
    <justification jstring="[para(21843(a,1),29822(a,1,2))].">
      <j1 rule="para" parents="21843 29822"/>
    </justification>
  </clause>

  <clause id="29953">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),z,a(y,u,w)) = L(x,a(y,z,w),u)
    ]]></literal>
    <justification jstring="[hyper(29903,a,29823,a)].">
      <j1 rule="hyper" parents="29903 29823"/>
    </justification>
  </clause>

  <clause id="29954">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),w,a(z,u,y)) = L(x,a(z,u,y),w)
    ]]></literal>
    <justification jstring="[para(29788(a,1),29823(a,1,1,2))].">
      <j1 rule="para" parents="29788 29823"/>
    </justification>
  </clause>

  <clause id="29955">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),w,a(y,u,z)) = L(x,a(y,u,z),w)
    ]]></literal>
    <justification jstring="[para(29840(a,1),29823(a,1,1,2))].">
      <j1 rule="para" parents="29840 29823"/>
    </justification>
  </clause>

  <clause id="29956">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),a(w,u,z),y) = x * a(w,u,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(1094,a,29824,a)].">
      <j1 rule="hyper" parents="1094 29824"/>
    </justification>
  </clause>

  <clause id="29957">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),z,a(w,u,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,w),u) = v5
    ]]></literal>
    <justification jstring="[para(29824(a,1),29901(a,1,1))].">
      <j1 rule="para" parents="29824 29901"/>
    </justification>
  </clause>

  <clause id="29958">
    <literal><![CDATA[
      a(x \ y,a(z,u,x \ y),w) = a(y * x,a(z,u,y * x),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,29831,a(flip),b,29865,a),flip(a)].">
      <j1 rule="hyper" parents="63 29831 29865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29959">
    <literal><![CDATA[
      T(a(x,a(y,z,u),L(w,x,a(y,z,u))) * a(y,z,u),L(w,x,a(y,z,u))) = (w * a(x,z,a(u,w,y))) \ (a(y,z,u) * L(w,x,a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(29871(a,1),26509(a,2,1))].">
      <j1 rule="para" parents="29871 26509"/>
    </justification>
  </clause>

  <clause id="29960">
    <literal><![CDATA[
      (x \ (a(y,z,u) * w)) * a(x,z,a(u,x \ (a(y,z,u) * w),y)) = L((a(y,z,u) \ x) \ w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(28523(a,1),29871(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28523 29871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29961">
    <literal><![CDATA[
      L(L(x,y,z),y,a(u,w,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(z,w,u)) = v5
    ]]></literal>
    <justification jstring="[para(29882(a,1),29745(a,1))].">
      <j1 rule="para" parents="29882 29745"/>
    </justification>
  </clause>

  <clause id="29962">
    <literal><![CDATA[
      L(x,y,L(z,z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29961,a,29360,a)].">
      <j1 rule="hyper" parents="29961 29360"/>
    </justification>
  </clause>

  <clause id="29963">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,w) = L(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(29961,a,30,a),flip(a)].">
      <j1 rule="hyper" parents="29961 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29964">
    <literal><![CDATA[
      L(x,y,L(z \ 1,z,y)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(3188(a,1),29962(a,1,3))].">
      <j1 rule="para" parents="3188 29962"/>
    </justification>
  </clause>

  <clause id="29965">
    <literal><![CDATA[
      L(x \ y,x,z \ a(z,z,x)) = L(x \ y,x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,23690,a(flip),b,29964,a)].">
      <j1 rule="hyper" parents="63 23690 29964"/>
    </justification>
  </clause>

  <clause id="29968">
    <literal><![CDATA[
      L(L(x,y,L(z,u,w)) \ 1,y,z) = L(x,y,a(w,u,z)) \ 1
    ]]></literal>
    <justification jstring="[para(29963(a,1),25955(a,1,1,1))].">
      <j1 rule="para" parents="29963 25955"/>
    </justification>
  </clause>

  <clause id="29970">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),u,w) = L(x,u,L(w,y,z))
    ]]></literal>
    <justification jstring="[para(29890(a,1),29963(a,1,1))].">
      <j1 rule="para" parents="29890 29963"/>
    </justification>
  </clause>

  <clause id="29971">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),u,z) = L(x,u,L(z,y,w))
    ]]></literal>
    <justification jstring="[para(29895(a,1),29963(a,1,1))].">
      <j1 rule="para" parents="29895 29963"/>
    </justification>
  </clause>

  <clause id="29972">
    <literal><![CDATA[
      L(x \ (x * y),x,z \ 1) = L(y,x,z \ a(z,z,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),29965(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 29965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29973">
    <literal><![CDATA[
      L(x,y,z \ a(z,z,y)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),29972(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 29972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29975">
    <literal><![CDATA[
      (x \ a(x,x,y)) * (y * z) = (x \ y) * L(z,y,x \ 1)
    ]]></literal>
    <justification jstring="[para(29973(a,1),18998(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29973 18998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29976">
    <literal><![CDATA[
      L(L(x,y,L(z,u,w)) \ 1,y,z) = L(x \ 1,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,26373,a,b,29968,a),flip(a)].">
      <j1 rule="hyper" parents="347 26373 29968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29977">
    <literal><![CDATA[
      L(L(x,y,L(a(z * u,z,w),v5,u)) \ 1,y,a(z * u,z,w)) = L(x \ 1,y,a(w,v5,a(z,z,u)))
    ]]></literal>
    <justification jstring="[para(29844(a,1),29976(a,2,3))].">
      <j1 rule="para" parents="29844 29976"/>
    </justification>
  </clause>

  <clause id="29978">
    <literal><![CDATA[
      L(x,y,a(z * x,z * x,u)) = L(x,z * x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,29877,a(flip),b,29892,a),flip(a)].">
      <j1 rule="hyper" parents="347 29877 29892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29979">
    <literal><![CDATA[
      L(L(x,y * x,a(z,u,y)),u,z) = L(x,u,L(z,y * x,y * x))
    ]]></literal>
    <justification jstring="[para(29978(a,1),29963(a,1,1))].">
      <j1 rule="para" parents="29978 29963"/>
    </justification>
  </clause>

  <clause id="29980">
    <literal><![CDATA[
      L(x,x,y) * (z * L(u,x,a(y,z,x))) = x * ((a(y,x,x) \ z) * u)
    ]]></literal>
    <justification jstring="[para(29902(a,1),27835(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29902 27835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29982">
    <literal><![CDATA[
      a(x,y,a(L(z,u,y),w,u)) * a(x,w,L(z,u,y)) = a(x,w,z * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(29925,a,25701,a)].">
      <j1 rule="hyper" parents="29925 25701"/>
    </justification>
  </clause>

  <clause id="29983">
    <literal><![CDATA[
      L(L(x,y,z) * a(u,w,a(v5,x,L(x,y,z))),w,a(u,v5,x)) = L(L(x,y,z),a(u,w,x),v5)
    ]]></literal>
    <justification jstring="[para(14574(a,1),29953(a,1,1,2,3))].">
      <j1 rule="para" parents="14574 29953"/>
    </justification>
  </clause>

  <clause id="29984">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),u,a(z,y,w)) = L(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(29786(a,1),29953(a,1,1,2))].">
      <j1 rule="para" parents="29786 29953"/>
    </justification>
  </clause>

  <clause id="29985">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),z,a(u,w,y)) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(29803(a,1),29953(a,1,1,2))].">
      <j1 rule="para" parents="29803 29953"/>
    </justification>
  </clause>

  <clause id="29986">
    <literal><![CDATA[
      L(x * a(y,x,a(z,z,u)),u * z,a(z,z,y)) = L(x,a(z,z,y),u * z)
    ]]></literal>
    <justification jstring="[para(25342(a,1),29954(a,1,1,2))].">
      <j1 rule="para" parents="25342 29954"/>
    </justification>
  </clause>

  <clause id="29987">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),z,a(w,u,y)) = L(x,a(w,u,y),z)
    ]]></literal>
    <justification jstring="[para(26501(a,1),29954(a,1,1,2))].">
      <j1 rule="para" parents="26501 29954"/>
    </justification>
  </clause>

  <clause id="29988">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),u,a(z,w,y)) = L(x,a(y,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(29900,a,29955,a)].">
      <j1 rule="hyper" parents="29900 29955"/>
    </justification>
  </clause>

  <clause id="29989">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),a(z,y,w),u) = x * a(z,y,a(u,x,w))
    ]]></literal>
    <justification jstring="[para(29895(a,1),29956(a,1,1))].">
      <j1 rule="para" parents="29895 29956"/>
    </justification>
  </clause>

  <clause id="29990">
    <literal><![CDATA[
      a(x \ y,a(x \ y,z,u),w) = a(y * x,a(u,z,y * x),w)
    ]]></literal>
    <justification jstring="[hyper(26574,a,29958,a)].">
      <j1 rule="hyper" parents="26574 29958"/>
    </justification>
  </clause>

  <clause id="29991">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),u,a(w,z,y)) = L(x,a(w,u,y),z)
    ]]></literal>
    <justification jstring="[para(29803(a,1),29984(a,1,1,2))].">
      <j1 rule="para" parents="29803 29984"/>
    </justification>
  </clause>

  <clause id="29992">
    <literal><![CDATA[
      L(x,a(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x * a(u,z,a(y,x,w)),w,a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(29985(a,1),29903(a,1))].">
      <j1 rule="para" parents="29985 29903"/>
    </justification>
  </clause>

  <clause id="29993">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),u,a(y,z,w)) = L(x,a(w,u,y),z)
    ]]></literal>
    <justification jstring="[hyper(29900,a,29987,a)].">
      <j1 rule="hyper" parents="29900 29987"/>
    </justification>
  </clause>

  <clause id="29994">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),z,a(u,w,y)) = x * a(u,x,a(w,z,y))
    ]]></literal>
    <justification jstring="[hyper(41,a,29896,a,b,29987,a)].">
      <j1 rule="hyper" parents="41 29896 29987"/>
    </justification>
  </clause>

  <clause id="29995">
    <literal><![CDATA[
      L(x \ L(y,y,a(z,x \ y,u)),y,a(y,z,u)) = L(x \ y,a(u,y,y),z)
    ]]></literal>
    <justification jstring="[para(29929(a,1),29988(a,1,1))].">
      <j1 rule="para" parents="29929 29988"/>
    </justification>
  </clause>

  <clause id="29996">
    <literal><![CDATA[
      x \ L(L(x,a(y,z,u),w),z,a(u,w,y)) = a(u,x,a(w,z,y))
    ]]></literal>
    <justification jstring="[hyper(128,a,29994,a,b,xx)].">
      <j1 rule="hyper" parents="128 29994"/>
    </justification>
  </clause>

  <clause id="29997">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ (x * a(z,x,a(u,y,w))) = L(x \ L(x,a(w,y,z),u),y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(29994(a,1),4640(a,1,2))].">
      <j1 rule="para" parents="29994 4640"/>
    </justification>
  </clause>

  <clause id="29998">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),z,a(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(w,u,y),z) = v5
    ]]></literal>
    <justification jstring="[para(29994(a,1),29901(a,1,1))].">
      <j1 rule="para" parents="29994 29901"/>
    </justification>
  </clause>

  <clause id="29999">
    <literal><![CDATA[
      L(x \ L(L(x,a(y,z,u),w),z,a(u,w,y)),v5,v6) = a(u,L(x,v5,v6),a(w,z,y))
    ]]></literal>
    <justification jstring="[hyper(16602,a,29996,a)].">
      <j1 rule="hyper" parents="16602 29996"/>
    </justification>
  </clause>

  <clause id="30000">
    <literal><![CDATA[
      a(T(x \ (y \ 1),z) \ u,T(x \ (y \ 1),z) * x,L(w,T(x \ (y \ 1),z),x)) = a((y \ K(x \ (y \ 1),z)) \ (x * u),x * T(x \ (y \ 1),z),w)
    ]]></literal>
    <justification jstring="[para(13010(a,2),29693(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13010 29693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30011">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((z \ w) \ (u * w))) = a(x,y,a(w * z,z,u))
    ]]></literal>
    <justification jstring="[hyper(24434,a,29730,a)].">
      <j1 rule="hyper" parents="24434 29730"/>
    </justification>
  </clause>

  <clause id="30012">
    <literal><![CDATA[
      a(x \ (y \ (z * (x * y))),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,L(w,x,y)) = v5
    ]]></literal>
    <justification jstring="[para(29734(a,2),23953(a,1))].">
      <j1 rule="para" parents="29734 23953"/>
    </justification>
  </clause>

  <clause id="30014">
    <literal><![CDATA[
      a(x \ 1,y,L(z,u,w)) * a(w,y,a(x,u,L(z,u,w))) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,25583,a(flip),b,29919,a),flip(a)].">
      <j1 rule="hyper" parents="347 25583 29919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30015">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,v5,L(v6,u,w))) = v7
    ]]></literal>
    <justification jstring="[para(29840(a,1),29932(a,1))].">
      <j1 rule="para" parents="29840 29932"/>
    </justification>
  </clause>

  <clause id="30016">
    <literal><![CDATA[
      L(1 / x,y,z) * L(x,u,a(w,y,z)) = L(a(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(23247(a,1),29940(a,1,2))].">
      <j1 rule="para" parents="23247 29940"/>
    </justification>
  </clause>

  <clause id="30017">
    <literal><![CDATA[
      L(x,y,L(z,u * x,u * x)) = L(x,y,L(z,u * x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,29971,a(flip),b,29979,a),flip(a)].">
      <j1 rule="hyper" parents="63 29971 29979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30018">
    <literal><![CDATA[
      L(x,y,L(z,x * u,u * x)) = L(x,y,L(z,u * x,u))
    ]]></literal>
    <justification jstring="[para(21617(a,1),30017(a,1,3))].">
      <j1 rule="para" parents="21617 30017"/>
    </justification>
  </clause>

  <clause id="30019">
    <literal><![CDATA[
      L(x,y,z) * L(x \ 1,u,a(w,y,z)) = L(a(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,22393,a(flip),b,30016,a)].">
      <j1 rule="hyper" parents="63 22393 30016"/>
    </justification>
  </clause>

  <clause id="30020">
    <literal><![CDATA[
      x * (L(x,y,a(z,z,u)) \ (x * w)) = L(x,y,a(u,z,z * x)) * w
    ]]></literal>
    <justification jstring="[hyper(63,a,27070,a(flip),b,29914,a)].">
      <j1 rule="hyper" parents="63 27070 29914"/>
    </justification>
  </clause>

  <clause id="30021">
    <literal><![CDATA[
      x * (x * (L(x,y,a(z,z,u)) \ w)) = L(x,y,a(u,z,z * x)) * w
    ]]></literal>
    <justification jstring="[para(1407(a,1),30020(a,1,2))].">
      <j1 rule="para" parents="1407 30020"/>
    </justification>
  </clause>

  <clause id="30022">
    <literal><![CDATA[
      a(x,y,z * (u * ((R(w,v5,v5) * v5) \ w))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u * v5) * z) = v6
    ]]></literal>
    <justification jstring="[para(29751(a,2),24450(a,1))].">
      <j1 rule="para" parents="29751 24450"/>
    </justification>
  </clause>

  <clause id="30023">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),w,a(y,u,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,u,z),w) = v5
    ]]></literal>
    <justification jstring="[para(29840(a,1),29825(a,1,1,2))].">
      <j1 rule="para" parents="29840 29825"/>
    </justification>
  </clause>

  <clause id="30024">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),z,a(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,w),u) = v5
    ]]></literal>
    <justification jstring="[para(29890(a,1),29825(a,1))].">
      <j1 rule="para" parents="29890 29825"/>
    </justification>
  </clause>

  <clause id="30025">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),z,a(w,u,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(w,u,y),z) = v5
    ]]></literal>
    <justification jstring="[para(29788(a,2),29835(a,1,1,2))].">
      <j1 rule="para" parents="29788 29835"/>
    </justification>
  </clause>

  <clause id="30026">
    <literal><![CDATA[
      (x * a(y,z,a(u,w,v5))) \ v6 != v7
    ]]></literal>
    <literal><![CDATA[
      (x * a(v5,w,a(u,z,y))) \ v6 = v7
    ]]></literal>
    <justification jstring="[para(29845(a,1),29874(a,1,1))].">
      <j1 rule="para" parents="29845 29874"/>
    </justification>
  </clause>

  <clause id="30027">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,(w \ (v5 \ 1)) * v6)),(w \ v5) * v6,a(u,z,y)) = L(x,a(u,z,y),(w \ (v5 \ 1)) * v6)
    ]]></literal>
    <justification jstring="[hyper(29948,a,3605,a),flip(a)].">
      <j1 rule="hyper" parents="29948 3605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30028">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,L(w,v5,v6))),L(z,v5,v6),a(y,u,w)) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,u,w),L(z,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(29817(a,2),29948(a,1,1,2))].">
      <j1 rule="para" parents="29817 29948"/>
    </justification>
  </clause>

  <clause id="30029">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,z * a(u,z,y))),z * a(u,z,y),a(u,z,y)) = z * L(z \ x,z,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(29992,a,29613,a)].">
      <j1 rule="hyper" parents="29992 29613"/>
    </justification>
  </clause>

  <clause id="30030">
    <literal><![CDATA[
      a((x * (y * z)) \ (x * y),u,w) = a(z \ 1,u,L(L(w,y * z,x),z,y))
    ]]></literal>
    <justification jstring="[hyper(29676,a,29692,a),flip(a)].">
      <j1 rule="hyper" parents="29676 29692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30031">
    <literal><![CDATA[
      L(a(x,y,z) * z,y,L(x,u,w)) = z * a(w,u,a(z,y,L(x,y,x)))
    ]]></literal>
    <justification jstring="[para(29682(a,1),29762(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="29682 29762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30032">
    <literal><![CDATA[
      L(a(x,y,z) * z,y,L(x,u,w)) = z * a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(12438(a,1),30031(a,2,2,3))].">
      <j1 rule="para" parents="12438 30031"/>
    </justification>
  </clause>

  <clause id="30033">
    <literal><![CDATA[
      L(x,y * z,a(z,z,u)) = x * a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,29013,a(flip),b,30032,a)].">
      <j1 rule="hyper" parents="63 29013 30032"/>
    </justification>
  </clause>

  <clause id="30035">
    <literal><![CDATA[
      L(x,y * z,a(z,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(u,z,z)) = w
    ]]></literal>
    <justification jstring="[para(30033(a,2),29920(a,1))].">
      <j1 rule="para" parents="30033 29920"/>
    </justification>
  </clause>

  <clause id="30036">
    <literal><![CDATA[
      L(x,y,a(z,y * u,y)) = L(x,u,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(30035,a,29894,a),flip(a)].">
      <j1 rule="hyper" parents="30035 29894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30037">
    <literal><![CDATA[
      L(x * a(y,x,a(z,z,u)),u,a(y,z,z)) = L(x,a(z,z,y),u * z)
    ]]></literal>
    <justification jstring="[hyper(30035,a,29986,a)].">
      <j1 rule="hyper" parents="30035 29986"/>
    </justification>
  </clause>

  <clause id="30038">
    <literal><![CDATA[
      L(x,a(y,y,z),u * y) = L(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(30023,a,30037,a),flip(a)].">
      <j1 rule="hyper" parents="30023 30037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30040">
    <literal><![CDATA[
      L(x,a(y,z,z),z * u) = L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(26514,a,30038,a)].">
      <j1 rule="hyper" parents="26514 30038"/>
    </justification>
  </clause>

  <clause id="30042">
    <literal><![CDATA[
      L(x,a(y,L(z,u,w),L(z,u,w)),v5) = L(x,a(z,z,y),v5 * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(27069(a,1),30038(a,1,2)),flip(a)].">
      <j1 rule="para" parents="27069 30038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30043">
    <literal><![CDATA[
      L(x,a(y,y,z),u * L(y,w,v5)) = L(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(26464(a,1),30042(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26464 30042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30044">
    <literal><![CDATA[
      L(x,a(y,L(z,z,a(u,w,v5)),L(z,z,a(u,w,v5))),a(u,w,z) \ v5) = L(x,a(z,z,y),v5 * L(z,w,u))
    ]]></literal>
    <justification jstring="[para(29935(a,1),30042(a,2,3))].">
      <j1 rule="para" parents="29935 30042"/>
    </justification>
  </clause>

  <clause id="30047">
    <literal><![CDATA[
      a(x \ 1,y,L(z,u,w)) * a(w,y,a(x,u,z)) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(29192(a,1),30014(a,1,2))].">
      <j1 rule="para" parents="29192 30014"/>
    </justification>
  </clause>

  <clause id="30049">
    <literal><![CDATA[
      a((x * y) \ (y * 1),z,u) * a(y,z,a(x,x,u)) = a(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(29781(a,2),30047(a,1,1))].">
      <j1 rule="para" parents="29781 30047"/>
    </justification>
  </clause>

  <clause id="30050">
    <literal><![CDATA[
      a((x * y) \ y,z,u) * a(y,z,a(x,x,u)) = a(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(8(a,1),30049(a,1,1,1,2))].">
      <j1 rule="para" parents="8 30049"/>
    </justification>
  </clause>

  <clause id="30051">
    <literal><![CDATA[
      a(x \ (y \ x),z,u) * a(x,z,a(y,y,u)) = a(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(25200(a,1),30050(a,1,1))].">
      <j1 rule="para" parents="25200 30050"/>
    </justification>
  </clause>

  <clause id="30052">
    <literal><![CDATA[
      a(x \ (y \ x),z,u) * a(x,y,a(y,z,u)) = a(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(29876,a,30051,a)].">
      <j1 rule="hyper" parents="29876 30051"/>
    </justification>
  </clause>

  <clause id="30053">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) * a(u \ (y \ u),z,x) = a(y \ 1,z,x)
    ]]></literal>
    <justification jstring="[hyper(29812,a,30051,a)].">
      <j1 rule="hyper" parents="29812 30051"/>
    </justification>
  </clause>

  <clause id="30054">
    <literal><![CDATA[
      a(x \ (L(y,y,y) \ x),z,u) * a(x,L(y,y,y),a(L(y,y,y),z,u)) = a(1 / y,z,u)
    ]]></literal>
    <justification jstring="[para(3205(a,1),30052(a,2,1))].">
      <j1 rule="para" parents="3205 30052"/>
    </justification>
  </clause>

  <clause id="30055">
    <literal><![CDATA[
      (L(x,y,z) * (R(z,y,x) * u)) \ ((x * z) * u) = a(x,L(z,y,x),L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,29675,a(flip),b,29653,a),flip(a)].">
      <j1 rule="hyper" parents="347 29675 29653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30056">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,w,y))) * a(x,u,L(z,w,y)) = a(x,u,z * a(y,z,w))
    ]]></literal>
    <justification jstring="[para(29675(a,1),29982(a,1,1,3))].">
      <j1 rule="para" parents="29675 29982"/>
    </justification>
  </clause>

  <clause id="30057">
    <literal><![CDATA[
      (L(x,y,y) * (R(y,y,x) * z)) \ ((x * y) * z) = a(x,L(y,y,x),y \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,25261,a,b,30055,a),flip(a)].">
      <j1 rule="hyper" parents="347 25261 30055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30058">
    <literal><![CDATA[
      (L(x,x,y) * (R(y,x,x) * z)) \ ((x * y) * z) = a(x,x * (y * x),L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,24244,a,b,30055,a),flip(a)].">
      <j1 rule="hyper" parents="347 24244 30055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30059">
    <literal><![CDATA[
      L(x,x \ y,a(z,u,w)) = (a(z,u,w) \ (y / x)) \ ((w \ L(w,u,z)) * y)
    ]]></literal>
    <justification jstring="[hyper(29054,a,29095,a)].">
      <j1 rule="hyper" parents="29054 29095"/>
    </justification>
  </clause>

  <clause id="30060">
    <literal><![CDATA[
      L(x,x \ y,a(z,u,w)) = (a(z,u,w) \ (y / x)) \ (a(z,u,w) \ y)
    ]]></literal>
    <justification jstring="[para(29055(a,1),30059(a,2,2))].">
      <j1 rule="para" parents="29055 30059"/>
    </justification>
  </clause>

  <clause id="30061">
    <literal><![CDATA[
      (a(x,y,z) * u) * (a(z,y,x) * z) = a(z,y,x) * (u * (a(x,y,z) * z))
    ]]></literal>
    <justification jstring="[para(29239(a,1),29311(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29239 29311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30062">
    <literal><![CDATA[
      a(x,y,z) * (u * (a(z,y,x) * x)) = (a(z,y,x) * u) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(28908(a,2),30061(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28908 30061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30063">
    <literal><![CDATA[
      a(x,y,z) * (u * (a(z,y,x) * x)) = a(z,y,x) * (u * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,23132,a(flip),b,30062,a),flip(a)].">
      <j1 rule="hyper" parents="347 23132 30062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30064">
    <literal><![CDATA[
      a(x,y * (a((z * z) \ y,u,u) * w),v5) = a(x,L((z * z) \ y,u,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,25125,a(flip),b,29392,a),flip(a)].">
      <j1 rule="hyper" parents="347 25125 29392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30065">
    <literal><![CDATA[
      (R(x,x,y) * (y * z)) \ ((R(x,x,y) * y) * z) = a(x,y,a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[para(26284(a,1),29408(a,1,1))].">
      <j1 rule="para" parents="26284 29408"/>
    </justification>
  </clause>

  <clause id="30066">
    <literal><![CDATA[
      a(x,y,a(x,x,y) * z) = a(R(x,x,y),y,z)
    ]]></literal>
    <justification jstring="[hyper(836,a,30065,a),flip(a)].">
      <j1 rule="hyper" parents="836 30065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30067">
    <literal><![CDATA[
      a(x,y,a(x,x,y) * z) = a(x,y,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,29684,a(flip),b,30066,a),flip(a)].">
      <j1 rule="hyper" parents="347 29684 30066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30068">
    <literal><![CDATA[
      a(x,y,a(x,x,y) * z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,29278,a(flip),b,30067,a),flip(a)].">
      <j1 rule="hyper" parents="347 29278 30067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30069">
    <literal><![CDATA[
      a(x,y,a(a(x,x,z) * u,z,w)) = a(w,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(30068(a,1),29803(a,2,3))].">
      <j1 rule="para" parents="30068 29803"/>
    </justification>
  </clause>

  <clause id="30070">
    <literal><![CDATA[
      a(x,y,a(z * a(u,x,x),u * x,w)) = a(w,y,a(x,u * x,z))
    ]]></literal>
    <justification jstring="[para(28022(a,1),30069(a,1,3))].">
      <j1 rule="para" parents="28022 30069"/>
    </justification>
  </clause>

  <clause id="30071">
    <literal><![CDATA[
      x * a(x,y,a(z,u * z,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u * z,a(z,y,w * a(u,z,z))) = v5
    ]]></literal>
    <justification jstring="[para(30070(a,1),29921(a,1,2))].">
      <j1 rule="para" parents="30070 29921"/>
    </justification>
  </clause>

  <clause id="30072">
    <literal><![CDATA[
      a(x,y,L(T(z,u),u,u \ w)) = a(x,y,L(w \ ((w / u) * (z * u)),z,y))
    ]]></literal>
    <justification jstring="[para(21616(a,1),29434(a,1,3)),flip(a)].">
      <j1 rule="para" parents="21616 29434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30073">
    <literal><![CDATA[
      a(x,y,L(T(z,u),u,w * u)) = a(x,y,L(w \ ((w / u) * (z * u)),z,y))
    ]]></literal>
    <justification jstring="[hyper(27272,a,30072,a)].">
      <j1 rule="hyper" parents="27272 30072"/>
    </justification>
  </clause>

  <clause id="30075">
    <literal><![CDATA[
      a(x,y,L(z \ ((z / u) * (w * u)),w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(w,u,z * u)) = v5
    ]]></literal>
    <justification jstring="[para(30073(a,1),24184(a,1))].">
      <j1 rule="para" parents="30073 24184"/>
    </justification>
  </clause>

  <clause id="30076">
    <literal><![CDATA[
      a(x,y,z) * (a(a(x,y,z),x,u) \ u) = u * (a(x,a(x,y,z),u) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,21329,a(flip),b,29527,a),flip(a)].">
      <j1 rule="hyper" parents="63 21329 29527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30077">
    <literal><![CDATA[
      (R(x,y,z) \ a(x,u,z)) \ R(R(x,y,z),u,z) = R(x,y,z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(25481(a,1),29720(a,1,1))].">
      <j1 rule="para" parents="25481 29720"/>
    </justification>
  </clause>

  <clause id="30078">
    <literal><![CDATA[
      (x \ 1) \ R(R(x,y,z),y,z) = R(x,y,z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(28961(a,1),30077(a,1,1))].">
      <j1 rule="para" parents="28961 30077"/>
    </justification>
  </clause>

  <clause id="30079">
    <literal><![CDATA[
      R(x,y,z) * R(x,y,z) = x * R(R(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,23653,a(flip),b,30078,a),flip(a)].">
      <j1 rule="hyper" parents="63 23653 30078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30080">
    <literal><![CDATA[
      ((R(R(x,y,z),y,z) / x) * (R(x,y,z) * R(x,y,z))) / R(R(x,y,z),y,z) = L(R(R(x,y,z),y,z),x,x \ R(R(x,y,z),y,z))
    ]]></literal>
    <justification jstring="[para(30079(a,2),10199(a,1,1,2))].">
      <j1 rule="para" parents="30079 10199"/>
    </justification>
  </clause>

  <clause id="30081">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,v5),v6)) = L(a(x,y,a(z,u,v6)),w,v5)
    ]]></literal>
    <justification jstring="[para(29819(a,1),29950(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29819 29950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30082">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,v5),v6)) = a(x,y,L(a(z,u,v6),w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,29113,a,b,30081,a),flip(a)].">
      <j1 rule="hyper" parents="347 29113 30081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30083">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,v5),v6)) = a(x,y,a(z,u,L(v6,w,v5)))
    ]]></literal>
    <justification jstring="[para(29113(a,2),30082(a,2,3))].">
      <j1 rule="para" parents="29113 30082"/>
    </justification>
  </clause>

  <clause id="30084">
    <literal><![CDATA[
      a(x,y,a(z,u * w,L(v5,w,w))) = a(x,y,a(z,w \ u,v5))
    ]]></literal>
    <justification jstring="[para(24868(a,1),30083(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24868 30083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30086">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,v5,v6)) = L(a(x,y,a(w,v5,v6)),z,u)
    ]]></literal>
    <justification jstring="[para(29996(a,1),29999(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29996 29999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30087">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,v5,v6)) = a(x,y,L(a(w,v5,v6),z,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,29113,a,b,30086,a),flip(a)].">
      <j1 rule="hyper" parents="347 29113 30086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30088">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,v5,v6)) = a(x,y,a(w,v5,L(v6,z,u)))
    ]]></literal>
    <justification jstring="[para(29113(a,2),30087(a,2,3))].">
      <j1 rule="para" parents="29113 30087"/>
    </justification>
  </clause>

  <clause id="30089">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,y))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(26005,a,30088,a),flip(a)].">
      <j1 rule="hyper" parents="26005 30088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30091">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) * x = R(x,L(y,v5,v6),a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(133,a,30088,a(flip),b,28907,a(flip))].">
      <j1 rule="hyper" parents="133 30088 28907"/>
    </justification>
  </clause>

  <clause id="30092">
    <literal><![CDATA[
      a(x,y \ z,a(u,w,L(v5,y,y))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y * z,a(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(30088(a,1),24177(a,1))].">
      <j1 rule="para" parents="30088 24177"/>
    </justification>
  </clause>

  <clause id="30093">
    <literal><![CDATA[
      a(x,y * z,a(u,w,L(v5,y,y))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ z,a(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(30088(a,1),26006(a,1))].">
      <j1 rule="para" parents="30088 26006"/>
    </justification>
  </clause>

  <clause id="30094">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) * z = L(z,u,a(x,L(y,v5,v6),w))
    ]]></literal>
    <justification jstring="[para(30088(a,1),29877(a,1,1))].">
      <j1 rule="para" parents="30088 29877"/>
    </justification>
  </clause>

  <clause id="30095">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,L(w,v5,v6))),L(z,v5,v6),a(y,u,w)) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,L(z,v5,v6),w),u) = v7
    ]]></literal>
    <justification jstring="[para(30088(a,1),30024(a,1,1,2))].">
      <j1 rule="para" parents="30088 30024"/>
    </justification>
  </clause>

  <clause id="30096">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,u,L(z,w,y)) = a(x,u,z * a(y,z,w))
    ]]></literal>
    <justification jstring="[para(30089(a,1),30056(a,1,1))].">
      <j1 rule="para" parents="30089 30056"/>
    </justification>
  </clause>

  <clause id="30098">
    <literal><![CDATA[
      R(x,L(y,z,u),a(w,v5,v6)) = L(x,y,a(w,v5,L(v6,z,u)))
    ]]></literal>
    <justification jstring="[hyper(29007,a,30091,a),flip(a)].">
      <j1 rule="hyper" parents="29007 30091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30099">
    <literal><![CDATA[
      L(x,L(y,z,u),a(w,v5,v6)) = L(x,y,a(w,v5,L(v6,z,u)))
    ]]></literal>
    <justification jstring="[hyper(23284,a,30098,a)].">
      <j1 rule="hyper" parents="23284 30098"/>
    </justification>
  </clause>

  <clause id="30100">
    <literal><![CDATA[
      L(x,y \ z,a(u,w,L(v5,y,y))) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,a(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(30099(a,1),21768(a,1))].">
      <j1 rule="para" parents="30099 21768"/>
    </justification>
  </clause>

  <clause id="30101">
    <literal><![CDATA[
      L(x,L(y,z,u),a(w,v5,L(v6,z,u))) = L(x,y,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(25583(a,1),30099(a,2,3))].">
      <j1 rule="para" parents="25583 30099"/>
    </justification>
  </clause>

  <clause id="30102">
    <literal><![CDATA[
      L(x,y,a(z,L(u,w,v5),v6)) = L(x,y,a(z,u,L(v6,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(29799,a,30094,a),flip(a)].">
      <j1 rule="hyper" parents="29799 30094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30103">
    <literal><![CDATA[
      L(x,y,a(z,L(u,w,v5),v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,u,L(v6,w,v5))) = v7
    ]]></literal>
    <justification jstring="[para(30094(a,1),29799(a,1))].">
      <j1 rule="para" parents="30094 29799"/>
    </justification>
  </clause>

  <clause id="30104">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,v5,u))) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(12430(a,1),30102(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12430 30102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30105">
    <literal><![CDATA[
      L(x,y,a(z,u * w,L(v5,w,w))) = L(x,y,a(z,w \ u,v5))
    ]]></literal>
    <justification jstring="[para(24868(a,1),30102(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24868 30102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30110">
    <literal><![CDATA[
      a(x,L(y,y,x),y \ (y \ z)) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(29544(a,1),30057(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29544 30057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30111">
    <literal><![CDATA[
      a(x,L(y,y,x),y \ (y \ z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,14,a,b,30110,a),flip(a)].">
      <j1 rule="hyper" parents="347 14 30110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30112">
    <literal><![CDATA[
      a(x,L(y,y,x),L(z,y,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(25589,a,30111,a)].">
      <j1 rule="hyper" parents="25589 30111"/>
    </justification>
  </clause>

  <clause id="30113">
    <literal><![CDATA[
      a(x,L(y,y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29267,a,30112,a)].">
      <j1 rule="hyper" parents="29267 30112"/>
    </justification>
  </clause>

  <clause id="30115">
    <literal><![CDATA[
      a(x,x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(30113(a,1),15006(a,1))].">
      <j1 rule="para" parents="30113 15006"/>
    </justification>
  </clause>

  <clause id="30117">
    <literal><![CDATA[
      a(x,x * (y * x),L(z,x,y)) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(29545(a,1),30058(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29545 30058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30118">
    <literal><![CDATA[
      a(x,x * (y * x),L(z,x,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,14,a,b,30117,a),flip(a)].">
      <j1 rule="hyper" parents="347 14 30117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30119">
    <literal><![CDATA[
      a(x,L(y,x,x),L(z,x,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(24392,a,30118,a)].">
      <j1 rule="hyper" parents="24392 30118"/>
    </justification>
  </clause>

  <clause id="30120">
    <literal><![CDATA[
      a(x,L(y,x,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,29750,a(flip),b,30119,a)].">
      <j1 rule="hyper" parents="63 29750 30119"/>
    </justification>
  </clause>

  <clause id="30121">
    <literal><![CDATA[
      a(x,x \ y,z) = a(x,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(26006,a,30120,a)].">
      <j1 rule="hyper" parents="26006 30120"/>
    </justification>
  </clause>

  <clause id="30122">
    <literal><![CDATA[
      a(x,x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,x * y,z) = u
    ]]></literal>
    <justification jstring="[para(30120(a,1),24177(a,1))].">
      <j1 rule="para" parents="30120 24177"/>
    </justification>
  </clause>

  <clause id="30123">
    <literal><![CDATA[
      a(x,L(y,x,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(30120(a,1),25998(a,1))].">
      <j1 rule="para" parents="30120 25998"/>
    </justification>
  </clause>

  <clause id="30124">
    <literal><![CDATA[
      a(x,x * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(30120(a,1),26006(a,1))].">
      <j1 rule="para" parents="30120 26006"/>
    </justification>
  </clause>

  <clause id="30125">
    <literal><![CDATA[
      a(x,y,z) \ z != u
    ]]></literal>
    <literal><![CDATA[
      L(z,L(y,x,x),x) = u
    ]]></literal>
    <justification jstring="[para(30120(a,1),28866(a,1,1))].">
      <j1 rule="para" parents="30120 28866"/>
    </justification>
  </clause>

  <clause id="30126">
    <literal><![CDATA[
      a(x,y,z) * x != u
    ]]></literal>
    <literal><![CDATA[
      R(x,L(y,x,x),z) = u
    ]]></literal>
    <justification jstring="[para(30120(a,1),28910(a,1,1))].">
      <j1 rule="para" parents="30120 28910"/>
    </justification>
  </clause>

  <clause id="30127">
    <literal><![CDATA[
      a(x,y \ x,z) = a(x,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(30115,a,30121,a)].">
      <j1 rule="hyper" parents="30115 30121"/>
    </justification>
  </clause>

  <clause id="30128">
    <literal><![CDATA[
      a(x \ y,(x \ y) * y,z) = a(x \ y,x,z)
    ]]></literal>
    <justification jstring="[hyper(23998,a,30121,a),flip(a)].">
      <j1 rule="hyper" parents="23998 30121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30130">
    <literal><![CDATA[
      (x * ((x \ y) * z)) \ (y * z) = a(x,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,88,a,b,30121,a)].">
      <j1 rule="hyper" parents="63 88 30121"/>
    </justification>
  </clause>

  <clause id="30131">
    <literal><![CDATA[
      (x \ (y * z)) / z = (x \ y) * a(x,x * y,z)
    ]]></literal>
    <justification jstring="[para(30121(a,1),23143(a,2,2))].">
      <j1 rule="para" parents="30121 23143"/>
    </justification>
  </clause>

  <clause id="30132">
    <literal><![CDATA[
      a(x,y \ (x \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,x * (y \ z),y) = u
    ]]></literal>
    <justification jstring="[para(26055(a,2),30122(a,1))].">
      <j1 rule="para" parents="26055 30122"/>
    </justification>
  </clause>

  <clause id="30133">
    <literal><![CDATA[
      L(x,L(y,z,z),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(30125,a,28841,a(flip))].">
      <j1 rule="hyper" parents="30125 28841"/>
    </justification>
  </clause>

  <clause id="30134">
    <literal><![CDATA[
      L(x,y \ (z \ y),z * y) = L(x,L(z,y,y),z * y)
    ]]></literal>
    <justification jstring="[hyper(21917,a,30133,a)].">
      <j1 rule="hyper" parents="21917 30133"/>
    </justification>
  </clause>

  <clause id="30135">
    <literal><![CDATA[
      L(x,y \ z,y) = L(x,y * z,y)
    ]]></literal>
    <justification jstring="[hyper(21810,a,30133,a)].">
      <j1 rule="hyper" parents="21810 30133"/>
    </justification>
  </clause>

  <clause id="30137">
    <literal><![CDATA[
      L((x \ y) \ z,x * y,x) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(651,a,30135,a),flip(a)].">
      <j1 rule="hyper" parents="651 30135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30138">
    <literal><![CDATA[
      (x / y) \ (x * (L(1 / y,y,x) * z)) = L(z,x * (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,21865,a,b,30135,a)].">
      <j1 rule="hyper" parents="63 21865 30135"/>
    </justification>
  </clause>

  <clause id="30139">
    <literal><![CDATA[
      a(x,L(y \ z,y * z,y),u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(30135(a,1),14975(a,1,2))].">
      <j1 rule="para" parents="30135 14975"/>
    </justification>
  </clause>

  <clause id="30140">
    <literal><![CDATA[
      a(x \ y,z,L(u,w * x,w)) = a((w \ x) \ (w \ y),z,u)
    ]]></literal>
    <justification jstring="[para(30135(a,1),29733(a,1,3))].">
      <j1 rule="para" parents="30135 29733"/>
    </justification>
  </clause>

  <clause id="30141">
    <literal><![CDATA[
      L((x \ y) \ z,y * x,x) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(21666,a,30137,a)].">
      <j1 rule="hyper" parents="21666 30137"/>
    </justification>
  </clause>

  <clause id="30142">
    <literal><![CDATA[
      L((x \ (y * (x \ y))) \ z,a(x,x \ y,y),x) = (y * (x \ y)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,21873,a(flip),b,30137,a)].">
      <j1 rule="hyper" parents="63 21873 30137"/>
    </justification>
  </clause>

  <clause id="30143">
    <literal><![CDATA[
      L(((x \ y) \ (y \ x)) \ z,(1 / (x \ y)) \ (1 / (1 / (y \ x))),x \ y) = (y \ x) \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(3398(a,2),30137(a,1,2))].">
      <j1 rule="para" parents="3398 30137"/>
    </justification>
  </clause>

  <clause id="30144">
    <literal><![CDATA[
      L((x \ (y \ (y / x))) * z,(y / x) * (y * x),y / x) = (y * x) \ ((y / x) * z)
    ]]></literal>
    <justification jstring="[para(27009(a,1),30137(a,1,1))].">
      <j1 rule="para" parents="27009 30137"/>
    </justification>
  </clause>

  <clause id="30145">
    <literal><![CDATA[
      L(((x \ y) * (y \ x)) * z,x * (y * ((x \ y) \ 1)),x) = (y * ((x \ y) \ 1)) \ (x * z)
    ]]></literal>
    <justification jstring="[para(28150(a,1),30137(a,1,1))].">
      <j1 rule="para" parents="28150 30137"/>
    </justification>
  </clause>

  <clause id="30146">
    <literal><![CDATA[
      L((x * (y / (y * x))) \ z,((x \ 1) \ y) * (y * x),y * x) = ((x \ 1) \ y) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(19014(a,1),30141(a,1,1,1))].">
      <j1 rule="para" parents="19014 30141"/>
    </justification>
  </clause>

  <clause id="30147">
    <literal><![CDATA[
      R(x,L(y,x,x),z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(30126,a,28908,a(flip))].">
      <j1 rule="hyper" parents="30126 28908"/>
    </justification>
  </clause>

  <clause id="30148">
    <literal><![CDATA[
      R(x,x \ y,z) = R(x,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(21090,a,30147,a)].">
      <j1 rule="hyper" parents="21090 30147"/>
    </justification>
  </clause>

  <clause id="30149">
    <literal><![CDATA[
      R(x,y \ x,y) = R(x,x * y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,29290,a,b,30148,a)].">
      <j1 rule="hyper" parents="63 29290 30148"/>
    </justification>
  </clause>

  <clause id="30150">
    <literal><![CDATA[
      R(x,x * y,z) \ (y * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[para(30148(a,1),578(a,1,1))].">
      <j1 rule="para" parents="30148 578"/>
    </justification>
  </clause>

  <clause id="30151">
    <literal><![CDATA[
      R(x,x * y,y) \ 1 = (x \ y) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(30148(a,1),2197(a,1,1))].">
      <j1 rule="para" parents="30148 2197"/>
    </justification>
  </clause>

  <clause id="30152">
    <literal><![CDATA[
      R(x,(y \ (y \ (R(y,y * z,z) \ y))) * u,w) = R(x,u * (a(y,z \ y,z) \ 1),w)
    ]]></literal>
    <justification jstring="[para(30149(a,1),27502(a,1,2,1,2,2,1))].">
      <j1 rule="para" parents="30149 27502"/>
    </justification>
  </clause>

  <clause id="30153">
    <literal><![CDATA[
      R(x,x * y,a(z,u,w)) = (a(z,u,w) * y) / ((x \ y) * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(220,a,30150,a(flip),b,20020,a),flip(a)].">
      <j1 rule="hyper" parents="220 30150 20020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30155">
    <literal><![CDATA[
      L(x,y,(z * (u \ w)) \ (u \ (w * z))) = L(x,y,a(u,u * w,z))
    ]]></literal>
    <justification jstring="[para(30130(a,1),21577(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30130 21577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30156">
    <literal><![CDATA[
      a(x,L(L(y \ 1,z * y,z * y),y,z),u) = a(x,L(z \ ((((z * y) \ 1) \ z) / z),z * ((((z * y) \ 1) \ z) / z),z),u)
    ]]></literal>
    <justification jstring="[para(3292(a,2),30139(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3292 30139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30157">
    <literal><![CDATA[
      a(x \ y,z,L(u,x * w,w)) = a((w \ x) \ (w \ y),z,u)
    ]]></literal>
    <justification jstring="[para(12390(a,2),30140(a,1,3))].">
      <j1 rule="para" parents="12390 30140"/>
    </justification>
  </clause>

  <clause id="30158">
    <literal><![CDATA[
      a(x \ y,z,L(u,x * ((w / (x * w)) \ 1),(w / (x * w)) \ 1)) = a(a(x \ 1,x,w) \ (((w / (x * w)) \ 1) \ y),z,u)
    ]]></literal>
    <justification jstring="[para(26913(a,1),30157(a,2,1,1))].">
      <j1 rule="para" parents="26913 30157"/>
    </justification>
  </clause>

  <clause id="30159">
    <literal><![CDATA[
      L(x,y,a(z,z * u,w)) \ x != v5
    ]]></literal>
    <literal><![CDATA[
      a((w * (z \ u)) \ (z \ (u * w)),y,x) = v5
    ]]></literal>
    <justification jstring="[para(30155(a,1),28916(a,1,1))].">
      <j1 rule="para" parents="30155 28916"/>
    </justification>
  </clause>

  <clause id="30160">
    <literal><![CDATA[
      L(x,x * y,a(z,u,w)) = (a(z,u,w) * y) / ((x \ y) * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(23284,a,30153,a)].">
      <j1 rule="hyper" parents="23284 30153"/>
    </justification>
  </clause>

  <clause id="30161">
    <literal><![CDATA[
      L(x,y,a(z,u * x,w)) = (a(w,y,z) * u) / ((x \ u) * a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,29894,a(flip),b,30160,a)].">
      <j1 rule="hyper" parents="63 29894 30160"/>
    </justification>
  </clause>

  <clause id="30162">
    <literal><![CDATA[
      L((x \ (y * (x \ y))) \ z,x,a(x,x \ y,y)) = (y * (x \ y)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(25494,a,30142,a)].">
      <j1 rule="hyper" parents="25494 30142"/>
    </justification>
  </clause>

  <clause id="30163">
    <literal><![CDATA[
      L((x \ (y * (x \ y))) \ z,x,a(x,x * y,y)) = (y * (x \ y)) \ (x * z)
    ]]></literal>
    <justification jstring="[para(30121(a,1),30162(a,1,3))].">
      <j1 rule="para" parents="30121 30162"/>
    </justification>
  </clause>

  <clause id="30164">
    <literal><![CDATA[
      (x \ (y * (x \ y))) \ z = (y * (x \ y)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(29385,a,30163,a)].">
      <j1 rule="hyper" parents="29385 30163"/>
    </justification>
  </clause>

  <clause id="30165">
    <literal><![CDATA[
      a(x,y * (a((z * z) \ y,u,u) * w),v5) = a(x,w * L(y,u,u),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24463,a(flip),b,30064,a),flip(a)].">
      <j1 rule="hyper" parents="347 24463 30064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30167">
    <literal><![CDATA[
      a(x,y * (a(z \ (z \ y),u,u) * w),v5) = a(x,w * L(y,u,u),v5)
    ]]></literal>
    <justification jstring="[para(29732(a,1),30165(a,1,2,2,1))].">
      <j1 rule="para" parents="29732 30165"/>
    </justification>
  </clause>

  <clause id="30168">
    <literal><![CDATA[
      L(x,y * z,a(z,u,w * a(y,z,z))) = R(x,u,a(z,y * z,w))
    ]]></literal>
    <justification jstring="[hyper(30071,a,28958,a(flip))].">
      <j1 rule="hyper" parents="30071 28958"/>
    </justification>
  </clause>

  <clause id="30169">
    <literal><![CDATA[
      L(x,y * z,a(z,u,w * a(y,z,z))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u,a(z,y * z,w)) = v5
    ]]></literal>
    <justification jstring="[para(30168(a,2),23284(a,1))].">
      <j1 rule="para" parents="30168 23284"/>
    </justification>
  </clause>

  <clause id="30170">
    <literal><![CDATA[
      a(x,y,z) * (a(u,x,a(z,y,x)) \ u) = u * (a(x,a(x,y,z),u) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(26594(a,1),30076(a,1,2,1))].">
      <j1 rule="para" parents="26594 30076"/>
    </justification>
  </clause>

  <clause id="30171">
    <literal><![CDATA[
      a((x * (y \ z)) \ (y \ (z * x)),u,w) = a(y,y * z,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(30159,a,29820,a)].">
      <j1 rule="hyper" parents="30159 29820"/>
    </justification>
  </clause>

  <clause id="30172">
    <literal><![CDATA[
      a(((x * K(y,z)) * (u \ w)) \ (u \ (T(w,v5) * x)),v6,v7) = a(u,u * w,a(v7,v6,x * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(24966,a,30171,a)].">
      <j1 rule="hyper" parents="24966 30171"/>
    </justification>
  </clause>

  <clause id="30173">
    <literal><![CDATA[
      (x * (y \ z)) * ((y \ (z * x)) \ ((x * (y \ z)) \ (y \ (z * x)))) = a(y,y * z,a(x * (y \ z),x * (y \ z),x)) \ 1
    ]]></literal>
    <justification jstring="[para(30171(a,1),25461(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30171 25461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30174">
    <literal><![CDATA[
      a(x,y,z) * (a(u,x,a(z,y,x)) \ u) = u * L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(28470(a,1),30170(a,2,2))].">
      <j1 rule="para" parents="28470 30170"/>
    </justification>
  </clause>

  <clause id="30175">
    <literal><![CDATA[
      a(x,y,z) * (u * a(u,x,a(z,y,x))) = u * L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(26337(a,1),30174(a,1,2))].">
      <j1 rule="para" parents="26337 30174"/>
    </justification>
  </clause>

  <clause id="30176">
    <literal><![CDATA[
      a(x,y,z) * L(u,x,a(z,y,x)) = u * L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(26726(a,1),30175(a,1,2))].">
      <j1 rule="para" parents="26726 30175"/>
    </justification>
  </clause>

  <clause id="30177">
    <literal><![CDATA[
      a(x,y,z) * L(u,x,a(z,y,x)) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,28982,a(flip),b,30176,a),flip(a)].">
      <j1 rule="hyper" parents="347 28982 30176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30178">
    <literal><![CDATA[
      ((x \ L(y,z,z)) * x) \ (u \ L(y,z,z)) = K(x,x \ y) * (y \ (u \ y))
    ]]></literal>
    <justification jstring="[para(23462(a,1),29485(a,2,1))].">
      <j1 rule="para" parents="23462 29485"/>
    </justification>
  </clause>

  <clause id="30179">
    <literal><![CDATA[
      ((x \ L(y,z,z)) * x) \ (u \ L(y,z,z)) = ((x \ y) * x) \ (u \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,10296,a(flip),b,30178,a),flip(a)].">
      <j1 rule="hyper" parents="347 10296 30178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30181">
    <literal><![CDATA[
      L(x,y,y) \ (L(x,y,y) / z) = ((z \ x) * z) \ (z \ x)
    ]]></literal>
    <justification jstring="[hyper(5515,a,30179,a)].">
      <j1 rule="hyper" parents="5515 30179"/>
    </justification>
  </clause>

  <clause id="30182">
    <literal><![CDATA[
      L(x,y,y) \ (L(x,y,y) / z) = x \ (x / z)
    ]]></literal>
    <justification jstring="[hyper(347,a,5510,a(flip),b,30181,a),flip(a)].">
      <j1 rule="hyper" parents="347 5510 30181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30183">
    <literal><![CDATA[
      R(x,y,(((z * z) \ u) * ((w \ K(v5,v6)) * v7)) \ (v7 * (u * w))) = L(x,y,a((z * z) \ u,w \ K(v5,v6),v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,22265,a(flip),b,29498,a)].">
      <j1 rule="hyper" parents="63 22265 29498"/>
    </justification>
  </clause>

  <clause id="30184">
    <literal><![CDATA[
      L(x,y,z) * (a(z,y,x) * a(x,y,L(z,u,w))) = R(x,y,z) * a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29117(a,2),29525(a,1,2,2))].">
      <j1 rule="para" parents="29117 29525"/>
    </justification>
  </clause>

  <clause id="30185">
    <literal><![CDATA[
      L(L(x,y,z),z * y,a(y,x,x)) = (z * R(y,x,x)) \ (z * (R(y,x,x) * x))
    ]]></literal>
    <justification jstring="[para(29397(a,1),29552(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29397 29552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30186">
    <literal><![CDATA[
      L(L(x,y,z),z * y,a(y,x,x)) = L(x,R(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,18,a,b,30185,a),flip(a)].">
      <j1 rule="hyper" parents="347 18 30185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30187">
    <literal><![CDATA[
      L(L(x,y,z),z * y,a(y,x,x)) = L(x,L(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,21974,a(flip),b,30186,a),flip(a)].">
      <j1 rule="hyper" parents="347 21974 30186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30188">
    <literal><![CDATA[
      L(x,L(y,x,x),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(27586,a,30187,a),flip(a)].">
      <j1 rule="hyper" parents="27586 30187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30189">
    <literal><![CDATA[
      L(x,x \ y,z) = L(x,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(21810,a,30188,a)].">
      <j1 rule="hyper" parents="21810 30188"/>
    </justification>
  </clause>

  <clause id="30191">
    <literal><![CDATA[
      L(x,x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,x * y,z) = u
    ]]></literal>
    <justification jstring="[para(30188(a,1),21768(a,1))].">
      <j1 rule="para" parents="30188 21768"/>
    </justification>
  </clause>

  <clause id="30192">
    <literal><![CDATA[
      a(x,L(y,z,z),z) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[para(30188(a,1),28838(a,2,1))].">
      <j1 rule="para" parents="30188 28838"/>
    </justification>
  </clause>

  <clause id="30193">
    <literal><![CDATA[
      L(x \ y,(x \ y) * y,z) = L(x \ y,x,z)
    ]]></literal>
    <justification jstring="[hyper(21726,a,30189,a),flip(a)].">
      <j1 rule="hyper" parents="21726 30189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30194">
    <literal><![CDATA[
      L(x,x * y,a(z,u,w)) = (a(z,u,w) \ (y / x)) \ (a(z,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(63,a,30060,a(flip),b,30189,a),flip(a)].">
      <j1 rule="hyper" parents="63 30060 30189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30195">
    <literal><![CDATA[
      L(x,x * y,z) = (z * (y / x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,9645,a(flip),b,30189,a),flip(a)].">
      <j1 rule="hyper" parents="63 9645 30189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30196">
    <literal><![CDATA[
      (a(x,y,z) * u) / L(w,w * u,a(z,y,x)) = a(x,y,z) * (u / w)
    ]]></literal>
    <justification jstring="[para(30189(a,1),27563(a,1,2))].">
      <j1 rule="para" parents="30189 27563"/>
    </justification>
  </clause>

  <clause id="30198">
    <literal><![CDATA[
      a(x,L(y,z,z),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,28838,a,b,30192,a),flip(a)].">
      <j1 rule="hyper" parents="347 28838 30192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30199">
    <literal><![CDATA[
      a(x,y \ z,y) = a(x,y * z,y)
    ]]></literal>
    <justification jstring="[hyper(26006,a,30198,a)].">
      <j1 rule="hyper" parents="26006 30198"/>
    </justification>
  </clause>

  <clause id="30200">
    <literal><![CDATA[
      a(x,y \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y * z,y) = u
    ]]></literal>
    <justification jstring="[para(30198(a,1),24177(a,1))].">
      <j1 rule="para" parents="30198 24177"/>
    </justification>
  </clause>

  <clause id="30201">
    <literal><![CDATA[
      a(x,y * (x \ z),y) = a(x,x * (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(30132,a,30199,a),flip(a)].">
      <j1 rule="hyper" parents="30132 30199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30202">
    <literal><![CDATA[
      (x * y) \ ((x * (y / z)) * z) = a(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,18781,a,b,30199,a)].">
      <j1 rule="hyper" parents="63 18781 30199"/>
    </justification>
  </clause>

  <clause id="30203">
    <literal><![CDATA[
      (x \ y) * a(z,x * y,x) = L(x,x \ y,z) \ y
    ]]></literal>
    <justification jstring="[para(30199(a,1),26535(a,1,2))].">
      <j1 rule="para" parents="30199 26535"/>
    </justification>
  </clause>

  <clause id="30204">
    <literal><![CDATA[
      L(x / y,(y \ x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x / y,(x / y) * T(y,y \ x),z) = u
    ]]></literal>
    <justification jstring="[para(1251(a,1),30191(a,1,2))].">
      <j1 rule="para" parents="1251 30191"/>
    </justification>
  </clause>

  <clause id="30205">
    <literal><![CDATA[
      L(x,y,a(z,u * x,w)) = (a(z,y,w) * (u / x)) \ (a(z,y,w) * u)
    ]]></literal>
    <justification jstring="[hyper(29904,a,30195,a)].">
      <j1 rule="hyper" parents="29904 30195"/>
    </justification>
  </clause>

  <clause id="30206">
    <literal><![CDATA[
      L(x,y * x,z) = (z * (y / x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(21666,a,30195,a)].">
      <j1 rule="hyper" parents="21666 30195"/>
    </justification>
  </clause>

  <clause id="30207">
    <literal><![CDATA[
      a(x,y,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,(y \ z) * z,y \ z) = u
    ]]></literal>
    <justification jstring="[para(24014(a,1),30200(a,1))].">
      <j1 rule="para" parents="24014 30200"/>
    </justification>
  </clause>

  <clause id="30208">
    <literal><![CDATA[
      a(x,x * (y \ (a(z,x,x) \ u)),y) = a(x,(L(x,x,z) \ u) * y,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,27572,a(flip),b,30201,a),flip(a)].">
      <j1 rule="hyper" parents="63 27572 30201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30209">
    <literal><![CDATA[
      a(x,R(1 / y,y,z),y * z) = a(x,(y * z) * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,1008,a,b,30202,a)].">
      <j1 rule="hyper" parents="63 1008 30202"/>
    </justification>
  </clause>

  <clause id="30210">
    <literal><![CDATA[
      (x \ y) * a(z,x * y,x) = L(x,x * y,z) \ y
    ]]></literal>
    <justification jstring="[para(30189(a,1),30203(a,2,1))].">
      <j1 rule="para" parents="30189 30203"/>
    </justification>
  </clause>

  <clause id="30211">
    <literal><![CDATA[
      T(((x / y) \ x) * a(z,(x / y) * x,x / y),y \ x) = L(y \ x,(x / y) * x,z) \ x
    ]]></literal>
    <justification jstring="[para(30210(a,2),20678(a,1,1))].">
      <j1 rule="para" parents="30210 20678"/>
    </justification>
  </clause>

  <clause id="30212">
    <literal><![CDATA[
      a(x,(y \ z) * z,y \ z) = a(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(30207,a,27214,a)].">
      <j1 rule="hyper" parents="30207 27214"/>
    </justification>
  </clause>

  <clause id="30213">
    <literal><![CDATA[
      a(x,R(1 / y,y,z),y * z) = a(x,L(y,z,z),y * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,24248,a(flip),b,30209,a),flip(a)].">
      <j1 rule="hyper" parents="347 24248 30209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30214">
    <literal><![CDATA[
      a(x,L(1 / y,y,z),y * z) = a(x,L(y,z,z),y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,24805,a(flip),b,30213,a)].">
      <j1 rule="hyper" parents="63 24805 30213"/>
    </justification>
  </clause>

  <clause id="30215">
    <literal><![CDATA[
      a(x,L(y \ 1,y,z),y * z) = a(x,L(y,z,z),y * z)
    ]]></literal>
    <justification jstring="[hyper(24585,a,30214,a)].">
      <j1 rule="hyper" parents="24585 30214"/>
    </justification>
  </clause>

  <clause id="30216">
    <literal><![CDATA[
      a(x,L(y,z,z),y * z) = a(x,L(y,y,z),y * z)
    ]]></literal>
    <justification jstring="[hyper(15029,a,30215,a),flip(a)].">
      <j1 rule="hyper" parents="15029 30215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30217">
    <literal><![CDATA[
      L(x,y,a(z,u * x,w)) = (a(z,y,w) \ (u / x)) \ (a(z,y,w) \ u)
    ]]></literal>
    <justification jstring="[hyper(29904,a,30194,a)].">
      <j1 rule="hyper" parents="29904 30194"/>
    </justification>
  </clause>

  <clause id="30218">
    <literal><![CDATA[
      L(x,y,a(z,(a(z,y,u) * (w * x)) * x,u)) = (a(a(z,y,u),w,x) \ w) \ (a(z,y,u) \ (a(z,y,u) * (w * x)))
    ]]></literal>
    <justification jstring="[para(25415(a,2),30217(a,2,1))].">
      <j1 rule="para" parents="25415 30217"/>
    </justification>
  </clause>

  <clause id="30219">
    <literal><![CDATA[
      L(x / y,(x / y) * T(y,y \ x),z) = L(x / y,(x \ y) * y,z)
    ]]></literal>
    <justification jstring="[hyper(30204,a,21843,a)].">
      <j1 rule="hyper" parents="30204 21843"/>
    </justification>
  </clause>

  <clause id="30220">
    <literal><![CDATA[
      L(x / y,x * K(y,y \ x),z) = L(x / y,(x \ y) * y,z)
    ]]></literal>
    <justification jstring="[para(5925(a,1),30219(a,1,2))].">
      <j1 rule="para" parents="5925 30219"/>
    </justification>
  </clause>

  <clause id="30221">
    <literal><![CDATA[
      L(x / y,(x \ y) * y,z) = L(x / y,x,z)
    ]]></literal>
    <justification jstring="[hyper(21734,a,30220,a),flip(a)].">
      <j1 rule="hyper" parents="21734 30220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30223">
    <literal><![CDATA[
      L(x,y,L(a(z * u,z,w),v5,u)) = L(x,y,a(z * u,z,L(w,v5,z)))
    ]]></literal>
    <justification jstring="[para(29927(a,1),29885(a,1,3)),flip(a)].">
      <j1 rule="para" parents="29927 29885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30224">
    <literal><![CDATA[
      L(x,y,L(a(z * u,z,w),v5,u)) = L(x,y,a(z * u,z,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,30104,a(flip),b,30223,a),flip(a)].">
      <j1 rule="hyper" parents="347 30104 30223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30226">
    <literal><![CDATA[
      L((x \ (y \ (y / x))) * z,(y / x) * (y * x),x \ y) = (y * x) \ ((y / x) * z)
    ]]></literal>
    <justification jstring="[hyper(20491,a,30144,a)].">
      <j1 rule="hyper" parents="20491 30144"/>
    </justification>
  </clause>

  <clause id="30227">
    <literal><![CDATA[
      R(x,y,z) * a(a(x,y,z),u,w) = R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(29281,a,30184,a),flip(a)].">
      <j1 rule="hyper" parents="29281 30184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30228">
    <literal><![CDATA[
      R(x,y,z) * a(x,y,a(u,w,z)) = R(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[para(29790(a,1),30227(a,1,2))].">
      <j1 rule="para" parents="29790 30227"/>
    </justification>
  </clause>

  <clause id="30229">
    <literal><![CDATA[
      a(x,y,z) * R(x,y,a(u,w,z)) = R(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,29289,a,b,30228,a)].">
      <j1 rule="hyper" parents="63 29289 30228"/>
    </justification>
  </clause>

  <clause id="30230">
    <literal><![CDATA[
      R(x,y,z) * a(z,y,a(u,w,x)) = R(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[para(29808(a,1),30228(a,1,2))].">
      <j1 rule="para" parents="29808 30228"/>
    </justification>
  </clause>

  <clause id="30231">
    <literal><![CDATA[
      a(x,y,z) * L(x,y,a(u,w,z)) = R(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[para(23247(a,1),30229(a,1,2))].">
      <j1 rule="para" parents="23247 30229"/>
    </justification>
  </clause>

  <clause id="30232">
    <literal><![CDATA[
      x \ ((x * y) * a(y,z,u)) = R(y,z,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,28991,a,b,30230,a)].">
      <j1 rule="hyper" parents="63 28991 30230"/>
    </justification>
  </clause>

  <clause id="30233">
    <literal><![CDATA[
      R(x,a(y,z,u),L(w * x,x,w)) = w \ L(w * x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(28768(a,1),30232(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28768 30232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30234">
    <literal><![CDATA[
      R(x,y,L(a(z,u,w * x),x,w)) = w \ L(w * x,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(29807(a,1),30232(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29807 30232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30235">
    <literal><![CDATA[
      L(R(x,y,z),y,a(u,w,z)) = R(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,29760,a(flip),b,30231,a)].">
      <j1 rule="hyper" parents="63 29760 30231"/>
    </justification>
  </clause>

  <clause id="30236">
    <literal><![CDATA[
      L(R(x,y,z),u,a(w,y,z)) = R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(29903,a,30235,a)].">
      <j1 rule="hyper" parents="29903 30235"/>
    </justification>
  </clause>

  <clause id="30237">
    <literal><![CDATA[
      R(x,a(y,z,u),L(w * x,x,w)) = w * L(w \ x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,3342,a(flip),b,30233,a),flip(a)].">
      <j1 rule="hyper" parents="347 3342 30233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30238">
    <literal><![CDATA[
      R(x,y,L(a(z,u,w * x),x,w)) = w * L(w \ x,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,3342,a(flip),b,30234,a),flip(a)].">
      <j1 rule="hyper" parents="347 3342 30234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30239">
    <literal><![CDATA[
      x * L(x \ y,a(z,u,w),y) = R(y,a(z,u,w),y \ x)
    ]]></literal>
    <justification jstring="[hyper(26572,a,30237,a),flip(a)].">
      <j1 rule="hyper" parents="26572 30237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30240">
    <literal><![CDATA[
      x * L(x \ y,a(z,u,w),y) = R(y,a(z,u,w),y * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,29195,a(flip),b,30239,a),flip(a)].">
      <j1 rule="hyper" parents="347 29195 30239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30241">
    <literal><![CDATA[
      x * L(x \ y,a(z,u,w),y) != v5
    ]]></literal>
    <literal><![CDATA[
      L(y,a(z,u,w),y * x) = v5
    ]]></literal>
    <justification jstring="[para(30240(a,2),23226(a,1))].">
      <j1 rule="para" parents="30240 23226"/>
    </justification>
  </clause>

  <clause id="30242">
    <literal><![CDATA[
      R(x,y,a(z,u,L(w * x,x,w))) = w * L(w \ x,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(29113(a,2),30238(a,1,3))].">
      <j1 rule="para" parents="29113 30238"/>
    </justification>
  </clause>

  <clause id="30243">
    <literal><![CDATA[
      x * L(x \ y,z,a(y,u,w)) = R(y,u,a(w,z,y \ x))
    ]]></literal>
    <justification jstring="[para(25259(a,1),30242(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25259 30242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30244">
    <literal><![CDATA[
      x * L(x \ y,z,a(y,u,w)) = L(y,u,a(w,z,x * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,29759,a(flip),b,30243,a),flip(a)].">
      <j1 rule="hyper" parents="347 29759 30243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30245">
    <literal><![CDATA[
      a(x,y,z) * L(x,y,a(z,u,u * x)) = (a(x,y,z) * u) * (u \ x)
    ]]></literal>
    <justification jstring="[hyper(134,a,30244,a(flip),b,26374,a)].">
      <j1 rule="hyper" parents="134 30244 26374"/>
    </justification>
  </clause>

  <clause id="30246">
    <literal><![CDATA[
      a(x,y,z) * L(x,y,a(u,u,z)) = (a(x,y,z) * u) * (u \ x)
    ]]></literal>
    <justification jstring="[para(29913(a,1),30245(a,1,2))].">
      <j1 rule="para" parents="29913 30245"/>
    </justification>
  </clause>

  <clause id="30247">
    <literal><![CDATA[
      (a(x,y,z) * u) * (u \ x) = R(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,30231,a(flip),b,30246,a),flip(a)].">
      <j1 rule="hyper" parents="63 30231 30246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30248">
    <literal><![CDATA[
      L((x \ (y \ (y / x))) * z,(x \ y) * (y * x),x \ y) = (y * x) \ ((y / x) * z)
    ]]></literal>
    <justification jstring="[hyper(21728,a,30226,a)].">
      <j1 rule="hyper" parents="21728 30226"/>
    </justification>
  </clause>

  <clause id="30249">
    <literal><![CDATA[
      L((x \ (y \ (y / x))) * z,a(x,x,y),x \ y) = (y * x) \ ((y / x) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,22776,a(flip),b,30248,a)].">
      <j1 rule="hyper" parents="63 22776 30248"/>
    </justification>
  </clause>

  <clause id="30250">
    <literal><![CDATA[
      R(x,a(y \ z,y,y * (u \ y)),w) = R(x,((z / y) \ (z * u)) * (y * u),w)
    ]]></literal>
    <justification jstring="[para(25276(a,1),29132(a,1,2))].">
      <j1 rule="para" parents="25276 29132"/>
    </justification>
  </clause>

  <clause id="30251">
    <literal><![CDATA[
      R(x,((y / z) \ (y * u)) * (z * u),w) = R(x,a(z \ y,z,u),w)
    ]]></literal>
    <justification jstring="[para(28836(a,1),30250(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28836 30250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30252">
    <literal><![CDATA[
      R(x,((y / z) \ (y * u)) * (z * u),w) = L(x,a(z \ y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,23225,a(flip),b,30251,a),flip(a)].">
      <j1 rule="hyper" parents="347 23225 30251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30253">
    <literal><![CDATA[
      R(x,((y / z) \ (y * u)) * (z * u),w) = L(x,a(z * y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,29725,a(flip),b,30252,a),flip(a)].">
      <j1 rule="hyper" parents="347 29725 30252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30254">
    <literal><![CDATA[
      R(x,((y \ z) \ (z * u)) * (y * u),w) = L(x,a(y * z,y,u),w)
    ]]></literal>
    <justification jstring="[hyper(22448,a,30253,a)].">
      <j1 rule="hyper" parents="22448 30253"/>
    </justification>
  </clause>

  <clause id="30255">
    <literal><![CDATA[
      a(x,((y \ z) \ y) * a(u,u,z * y),w) = a(x,y * ((z \ y) * a(u,u,z \ y)),w)
    ]]></literal>
    <justification jstring="[para(29444(a,1),29402(a,1,2,2))].">
      <j1 rule="para" parents="29444 29402"/>
    </justification>
  </clause>

  <clause id="30256">
    <literal><![CDATA[
      a(x,y * (T(z / u,w) \ L(z,v5,v6)),v7) = a(x,y * ((1 / u) \ a(v6,v5,z)),v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,28942,a(flip),b,29631,a)].">
      <j1 rule="hyper" parents="63 28942 29631"/>
    </justification>
  </clause>

  <clause id="30257">
    <literal><![CDATA[
      a(x,y * ((z \ u) \ L(u,w,v5)),v6) = a(x,y * ((1 / z) \ a(v5,w,u)),v6)
    ]]></literal>
    <justification jstring="[para(113(a,1),30256(a,1,2,2,1))].">
      <j1 rule="para" parents="113 30256"/>
    </justification>
  </clause>

  <clause id="30258">
    <literal><![CDATA[
      a(x,y * ((z \ 1) \ a(u,w,v5)),v6) = a(x,y * ((z \ v5) \ L(v5,w,u)),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,24397,a(flip),b,30257,a)].">
      <j1 rule="hyper" parents="347 24397 30257"/>
    </justification>
  </clause>

  <clause id="30259">
    <literal><![CDATA[
      a(x,y * ((z \ u) \ L(u,w,v5)),v6) = a(x,y * (z \ a(v5,w,u)),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,24487,a(flip),b,30258,a),flip(a)].">
      <j1 rule="hyper" parents="63 24487 30258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30261">
    <literal><![CDATA[
      R(x,y,z \ (u \ ((u \ w) \ R(u,v5,u)))) = R(x,y,L(z,z,w \ u) * (w \ u))
    ]]></literal>
    <justification jstring="[para(29769(a,1),29770(a,2,3,1))].">
      <j1 rule="para" parents="29769 29770"/>
    </justification>
  </clause>

  <clause id="30262">
    <literal><![CDATA[
      R(x,y,z \ (u \ ((u \ w) \ R(u,v5,u)))) = R(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,21220,a(flip),b,30261,a),flip(a)].">
      <j1 rule="hyper" parents="347 21220 30261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30263">
    <literal><![CDATA[
      R(x,(y \ (R(y,y * z,z) \ 1)) * u,w) = R(x,u * (a(y,z \ y,z) \ 1),w)
    ]]></literal>
    <justification jstring="[para(1758(a,1),30152(a,1,2,1,2))].">
      <j1 rule="para" parents="1758 30152"/>
    </justification>
  </clause>

  <clause id="30264">
    <literal><![CDATA[
      R(x,(y \ ((y \ z) * (z \ 1))) * u,w) = R(x,u * (a(y,z \ y,z) \ 1),w)
    ]]></literal>
    <justification jstring="[para(30151(a,1),30263(a,1,2,1,2))].">
      <j1 rule="para" parents="30151 30263"/>
    </justification>
  </clause>

  <clause id="30265">
    <literal><![CDATA[
      R(x,y * (a(z,u \ z,u) \ 1),w) = R(x,(z \ ((z \ u) * u)) * y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,22482,a(flip),b,30264,a),flip(a)].">
      <j1 rule="hyper" parents="63 22482 30264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30266">
    <literal><![CDATA[
      a(x,y * ((z \ y) * a(u,u,z \ y)),w) = a(x,L(y \ z,u,u) \ y,w)
    ]]></literal>
    <justification jstring="[para(29463(a,1),30255(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29463 30255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30267">
    <literal><![CDATA[
      a(x,L(y \ z,u,u) \ y,w) = a(x,L(z \ y,u,u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24727,a(flip),b,30266,a),flip(a)].">
      <j1 rule="hyper" parents="63 24727 30266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30268">
    <literal><![CDATA[
      L(x,L((y * z) \ 1,z,y),L((y * z) \ 1,z,y)) = L(x,z \ y,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(3226,a,28920,a)].">
      <j1 rule="hyper" parents="3226 28920"/>
    </justification>
  </clause>

  <clause id="30269">
    <literal><![CDATA[
      L(x,L(y * z,z,y),L((y * z) \ 1,z,y)) = L(x,z \ y,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(3527,a,30268,a)].">
      <j1 rule="hyper" parents="3527 30268"/>
    </justification>
  </clause>

  <clause id="30270">
    <literal><![CDATA[
      L(x,y \ z,y \ (z \ 1)) = L(x,z * y,(z * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,27145,a(flip),b,30269,a),flip(a)].">
      <j1 rule="hyper" parents="63 27145 30269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30272">
    <literal><![CDATA[
      L(x,T(y * z,z \ 1),((y * z) \ y) \ (y \ 1)) = L(x,y * ((y * z) \ y),(y * ((y * z) \ y)) \ 1)
    ]]></literal>
    <justification jstring="[para(6289(a,2),30270(a,1,2))].">
      <j1 rule="para" parents="6289 30270"/>
    </justification>
  </clause>

  <clause id="30273">
    <literal><![CDATA[
      x \ (1 * R(x,y,L(z \ u,z,z \ (x \ 1)))) = a(x,y,x * (((x \ 1) / z) * u))
    ]]></literal>
    <justification jstring="[para(77(a,1),29238(a,1,2,1))].">
      <j1 rule="para" parents="77 29238"/>
    </justification>
  </clause>

  <clause id="30275">
    <literal><![CDATA[
      x \ (1 * R(x,y,L(z \ u,z,(x \ 1) * z))) = a(x,y,x * (((x \ 1) / z) * u))
    ]]></literal>
    <justification jstring="[para(27271(a,1),30273(a,1,2,2))].">
      <j1 rule="para" parents="27271 30273"/>
    </justification>
  </clause>

  <clause id="30276">
    <literal><![CDATA[
      x \ R(x,y,L(z \ u,z,(x \ 1) * z)) = a(x,y,x * (((x \ 1) / z) * u))
    ]]></literal>
    <justification jstring="[hyper(364,a,30275,a)].">
      <j1 rule="hyper" parents="364 30275"/>
    </justification>
  </clause>

  <clause id="30277">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,(x \ 1) * z)) = a(x,y,x * (((x \ 1) / z) * u))
    ]]></literal>
    <justification jstring="[hyper(29002,a,30276,a)].">
      <j1 rule="hyper" parents="29002 30276"/>
    </justification>
  </clause>

  <clause id="30278">
    <literal><![CDATA[
      a(x,y,x * (((x \ 1) / z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z \ u,z,z * x)) = w
    ]]></literal>
    <justification jstring="[para(30277(a,1),24914(a,1))].">
      <j1 rule="para" parents="30277 24914"/>
    </justification>
  </clause>

  <clause id="30279">
    <literal><![CDATA[
      a(x,y,x * ((z \ (x \ 1)) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z \ u,z,z * x)) = w
    ]]></literal>
    <justification jstring="[para(24278(a,1),30278(a,1))].">
      <j1 rule="para" parents="24278 30278"/>
    </justification>
  </clause>

  <clause id="30280">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,z * x)) = a(x,y,x * ((z \ x) * u))
    ]]></literal>
    <justification jstring="[hyper(30279,a,24960,a)].">
      <j1 rule="hyper" parents="30279 24960"/>
    </justification>
  </clause>

  <clause id="30281">
    <literal><![CDATA[
      R(x,y,a(z,u,T(u,u * z) \ 1) * w) = R(x,y,(u \ (z \ (u \ z))) * w)
    ]]></literal>
    <justification jstring="[hyper(22099,a,29280,a),flip(a)].">
      <j1 rule="hyper" parents="22099 29280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30283">
    <literal><![CDATA[
      R(x,y,a(z,u,T(u,u * z)) * w) = R(x,y,(u \ (z \ (u \ z))) * w)
    ]]></literal>
    <justification jstring="[para(14922(a,1),30281(a,1,3,1))].">
      <j1 rule="para" parents="14922 30281"/>
    </justification>
  </clause>

  <clause id="30284">
    <literal><![CDATA[
      R(x,y,(z \ (u \ (z \ u))) * w) = R(x,y,a(u,z,z) * w)
    ]]></literal>
    <justification jstring="[para(19096(a,1),30283(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="19096 30283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30286">
    <literal><![CDATA[
      (((x * y) * (z / (y \ 1))) / (y * (z * L(y,y,z)))) * z = (x * (z / (y * z))) * (y * z)
    ]]></literal>
    <justification jstring="[para(7667(a,1),29327(a,1,1,2))].">
      <j1 rule="para" parents="7667 29327"/>
    </justification>
  </clause>

  <clause id="30287">
    <literal><![CDATA[
      a(x * ((y \ 1) * (y * (z * (y \ 1)))),u,w) = a(x * (z * ((y \ 1) * a(y,y,z))),u,w)
    ]]></literal>
    <justification jstring="[para(29403(a,1),29529(a,2,1,2))].">
      <j1 rule="para" parents="29403 29529"/>
    </justification>
  </clause>

  <clause id="30289">
    <literal><![CDATA[
      T(a(x * a(y,x,z),a(y,x,z),u) \ a(y,x,z),u) = R(T(a(y,x,z),u),x,u * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,27251,a(flip),b,29670,a),flip(a)].">
      <j1 rule="hyper" parents="347 27251 29670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30290">
    <literal><![CDATA[
      T(a(x * a(y,x,z),a(y,x,z),u) \ a(y,x,z),u) = R(a(y,x,z),x,u * x)
    ]]></literal>
    <justification jstring="[para(20005(a,1),30289(a,2,1))].">
      <j1 rule="para" parents="20005 30289"/>
    </justification>
  </clause>

  <clause id="30291">
    <literal><![CDATA[
      T(a(x * a(y,x,z),a(y,x,z),u) \ a(y,x,z),u) = a(y,x,L(z,x,u * x))
    ]]></literal>
    <justification jstring="[hyper(347,a,29117,a,b,30290,a),flip(a)].">
      <j1 rule="hyper" parents="347 29117 30290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30293">
    <literal><![CDATA[
      T(a(x,a(y,z,u),z * a(y,z,u)) * a(y,z,u),x) = a(y,z,L(u,z,x * z))
    ]]></literal>
    <justification jstring="[para(28388(a,1),30291(a,1,1))].">
      <j1 rule="para" parents="28388 30291"/>
    </justification>
  </clause>

  <clause id="30294">
    <literal><![CDATA[
      L(x / y,y,z) \ a(y \ x,L(y \ x,y,z),L(x,y,z)) = (a(z,y,x * y) * y) / x
    ]]></literal>
    <justification jstring="[para(23893(a,1),29699(a,1,2))].">
      <j1 rule="para" parents="23893 29699"/>
    </justification>
  </clause>

  <clause id="30295">
    <literal><![CDATA[
      a((x * (y \ (z \ u))) \ w,v5,L(v6,x,y \ (z \ u))) = a(x \ ((y \ (u / z)) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,24812,a(flip),b,29735,a)].">
      <j1 rule="hyper" parents="63 24812 29735"/>
    </justification>
  </clause>

  <clause id="30296">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (a(z,y,a(w,v5,x)) * u) = L(a(x,y,L(z,v5,w)),a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(20005(a,1),29918(a,2,1))].">
      <j1 rule="para" parents="20005 29918"/>
    </justification>
  </clause>

  <clause id="30297">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (a(z,y,a(w,v5,x)) * u) = a(x,y,L(L(z,v5,w),a(x,y,z),u))
    ]]></literal>
    <justification jstring="[hyper(347,a,29113,a,b,30296,a),flip(a)].">
      <j1 rule="hyper" parents="347 29113 30296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30299">
    <literal><![CDATA[
      L(a(x,y,L(z,a(x,u,w),v5)),v5,a(x,u,w)) = a(x,y,z) * a(w,u,a(v5,x,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(29113(a,2),29947(a,1,1))].">
      <j1 rule="para" parents="29113 29947"/>
    </justification>
  </clause>

  <clause id="30300">
    <literal><![CDATA[
      L(L(L(x,y,z),x,a(u,w,v5)),w,a(u,v5,x)) = L(L(x,y,z),a(u,w,x),v5)
    ]]></literal>
    <justification jstring="[para(29807(a,1),29983(a,1,1))].">
      <j1 rule="para" parents="29807 29983"/>
    </justification>
  </clause>

  <clause id="30301">
    <literal><![CDATA[
      L(L(x,y,z),a(u,w,x),v5) = L(L(x,y,z),x,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(27587,a,30300,a),flip(a)].">
      <j1 rule="hyper" parents="27587 30300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30303">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (a(z,y,a(w,v5,x)) * u) = a(x,y,L(L(z,v5,w),z,a(x,y,u)))
    ]]></literal>
    <justification jstring="[para(30301(a,1),30297(a,2,3))].">
      <j1 rule="para" parents="30301 30297"/>
    </justification>
  </clause>

  <clause id="30304">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (a(z,y,a(w,v5,x)) * u) = a(x,y,L(z,v5,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,29698,a(flip),b,30303,a),flip(a)].">
      <j1 rule="hyper" parents="347 29698 30303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30306">
    <literal><![CDATA[
      a(T(a(x,x,y) / x,y),z,u) * a(y,L(x,x,x),a(L(x,x,x),z,u)) = a(1 / x,z,u)
    ]]></literal>
    <justification jstring="[para(19009(a,2),30054(a,1,1,1))].">
      <j1 rule="para" parents="19009 30054"/>
    </justification>
  </clause>

  <clause id="30307">
    <literal><![CDATA[
      L(((x \ y) * (y \ x)) * z,x * (y * (x \ y)),x) = (y * ((x \ y) \ 1)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(21774,a,30145,a)].">
      <j1 rule="hyper" parents="21774 30145"/>
    </justification>
  </clause>

  <clause id="30308">
    <literal><![CDATA[
      (((x * y) * (z / (y \ 1))) / (y * (z / (y \ 1)))) * z = (x * (z / (y * z))) * (y * z)
    ]]></literal>
    <justification jstring="[para(2008(a,1),30286(a,1,1,2,2))].">
      <j1 rule="para" parents="2008 30286"/>
    </justification>
  </clause>

  <clause id="30309">
    <literal><![CDATA[
      (x * (y / (z * y))) * (z * y) = R(x,z,y / (z \ 1)) * y
    ]]></literal>
    <justification jstring="[para(20(a,2),30308(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20 30308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30310">
    <literal><![CDATA[
      (x * (y / (z * y))) * (z * y) = R(x,z,(z \ 1) \ y) * y
    ]]></literal>
    <justification jstring="[para(20126(a,1),30309(a,2,1))].">
      <j1 rule="para" parents="20126 30309"/>
    </justification>
  </clause>

  <clause id="30311">
    <literal><![CDATA[
      (x * (y / (z * y))) * (z * y) = R(x,z,z \ y) * y
    ]]></literal>
    <justification jstring="[para(2241(a,1),30310(a,2,1))].">
      <j1 rule="para" parents="2241 30310"/>
    </justification>
  </clause>

  <clause id="30312">
    <literal><![CDATA[
      (x * (y / (z * y))) * (z * y) = (x * z) * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,392,a(flip),b,30311,a),flip(a)].">
      <j1 rule="hyper" parents="347 392 30311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30313">
    <literal><![CDATA[
      a(x,y / (z * y),z * y) = ((x * z) * (z \ y)) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,30312,a(flip),b,13396,a),flip(a)].">
      <j1 rule="hyper" parents="131 30312 13396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30314">
    <literal><![CDATA[
      a(x,y / (z * y),z * y) = a(x,z,y * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,27218,a(flip),b,30313,a),flip(a)].">
      <j1 rule="hyper" parents="347 27218 30313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30315">
    <literal><![CDATA[
      a(x,(y * z) \ z,y * z) = a(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(23997,a,30314,a)].">
      <j1 rule="hyper" parents="23997 30314"/>
    </justification>
  </clause>

  <clause id="30316">
    <literal><![CDATA[
      a(x,y \ (z \ y),z * y) = a(x,z,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,24742,a(flip),b,30315,a)].">
      <j1 rule="hyper" parents="63 24742 30315"/>
    </justification>
  </clause>

  <clause id="30317">
    <literal><![CDATA[
      a(x,L(y,y,z),y * z) = a(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(24741,a,30316,a)].">
      <j1 rule="hyper" parents="24741 30316"/>
    </justification>
  </clause>

  <clause id="30318">
    <literal><![CDATA[
      a(x,L(y \ z,y \ z,y),z) = a(x,y \ z,y * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(24179,a,30317,a)].">
      <j1 rule="hyper" parents="24179 30317"/>
    </justification>
  </clause>

  <clause id="30319">
    <literal><![CDATA[
      a(x,L(y,z,z),y * z) = a(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,30216,a,b,30317,a)].">
      <j1 rule="hyper" parents="63 30216 30317"/>
    </justification>
  </clause>

  <clause id="30320">
    <literal><![CDATA[
      a(x,y \ z,y * (y \ z)) = a(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(15006,a,30318,a),flip(a)].">
      <j1 rule="hyper" parents="15006 30318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30321">
    <literal><![CDATA[
      a(x,y \ z,y * (y \ z)) = a(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,30199,a(flip),b,30320,a),flip(a)].">
      <j1 rule="hyper" parents="347 30199 30320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30323">
    <literal><![CDATA[
      a(x,y \ z,z) = a(x,z * y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),30321(a,1,3))].">
      <j1 rule="para" parents="10 30321"/>
    </justification>
  </clause>

  <clause id="30324">
    <literal><![CDATA[
      a(x \ y,y * x,y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(19004,a,30323,a),flip(a)].">
      <j1 rule="hyper" parents="19004 30323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30325">
    <literal><![CDATA[
      a(x,(y * a(z,z,u)) \ (z * u),z * u) = a(x,(R(z,z,u) * u) * y,z * u)
    ]]></literal>
    <justification jstring="[para(29407(a,1),30323(a,2,2))].">
      <j1 rule="para" parents="29407 30323"/>
    </justification>
  </clause>

  <clause id="30326">
    <literal><![CDATA[
      L(a(x,x * y,y \ x) * z,y \ x,(x / y) * (y / x)) = (y \ x) * (L(y \ x,x * y,x) \ z)
    ]]></literal>
    <justification jstring="[para(30324(a,1),29309(a,1,3))].">
      <j1 rule="para" parents="30324 29309"/>
    </justification>
  </clause>

  <clause id="30327">
    <literal><![CDATA[
      a(x,y * z,y) * a(x,u,(y / z) * (z / y)) = a(x,y * z,L(y,u,z \ y))
    ]]></literal>
    <justification jstring="[para(30324(a,1),29847(a,1,2,3))].">
      <j1 rule="para" parents="30324 29847"/>
    </justification>
  </clause>

  <clause id="30328">
    <literal><![CDATA[
      a(x,y \ (z * L(u,z,z)),z * u) = a(x,(R(z,z,u) * u) * y,z * u)
    ]]></literal>
    <justification jstring="[para(29561(a,1),30325(a,1,2))].">
      <j1 rule="para" parents="29561 30325"/>
    </justification>
  </clause>

  <clause id="30329">
    <literal><![CDATA[
      a(x,(R(y,y,z) * z) * u,y * z) = a(x,u \ (y \ z),y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,25161,a(flip),b,30328,a),flip(a)].">
      <j1 rule="hyper" parents="63 25161 30328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30330">
    <literal><![CDATA[
      a(x,(L(y,y,z) * z) * u,y * z) = a(x,u \ (y \ z),y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,25131,a(flip),b,30329,a)].">
      <j1 rule="hyper" parents="63 25131 30329"/>
    </justification>
  </clause>

  <clause id="30331">
    <literal><![CDATA[
      a(x,y \ (z \ u),z * u) = a(x,y * (z \ u),z * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,24718,a(flip),b,30330,a),flip(a)].">
      <j1 rule="hyper" parents="63 24718 30330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30332">
    <literal><![CDATA[
      a(x,y * (z \ y),z * y) = a(x,z,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,30316,a(flip),b,30331,a),flip(a)].">
      <j1 rule="hyper" parents="63 30316 30331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30333">
    <literal><![CDATA[
      a(x,y * z,y) * a(x,u,(y / z) * (y \ z)) = a(x,y * z,L(y,u,z \ y))
    ]]></literal>
    <justification jstring="[para(24134(a,1),30327(a,1,2))].">
      <j1 rule="para" parents="24134 30327"/>
    </justification>
  </clause>

  <clause id="30334">
    <literal><![CDATA[
      a(x,y * z,y) * a(x,u,(z \ y) * (y \ z)) = a(x,y * z,L(y,u,z \ y))
    ]]></literal>
    <justification jstring="[para(24074(a,1),30333(a,1,2))].">
      <j1 rule="para" parents="24074 30333"/>
    </justification>
  </clause>

  <clause id="30335">
    <literal><![CDATA[
      a(x * ((y \ 1) * (y * (z * (y \ 1)))),u,w) = a(x * (z * (y \ a(y,y,z))),u,w)
    ]]></literal>
    <justification jstring="[para(15264(a,1),30287(a,2,1,2,2))].">
      <j1 rule="para" parents="15264 30287"/>
    </justification>
  </clause>

  <clause id="30336">
    <literal><![CDATA[
      a(x * ((y \ 1) * (y * (z * (y \ 1)))),u,w) = a(x * (y \ T(z,y \ 1)),u,w)
    ]]></literal>
    <justification jstring="[para(18987(a,1),30335(a,2,1,2))].">
      <j1 rule="para" parents="18987 30335"/>
    </justification>
  </clause>

  <clause id="30337">
    <literal><![CDATA[
      a(x * ((y \ 1) * (y * (z * (y \ 1)))),u,w) = a(x * (y \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24222,a(flip),b,30336,a),flip(a)].">
      <j1 rule="hyper" parents="347 24222 30336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30339">
    <literal><![CDATA[
      a(x * (L(y,z,z) * (z \ 1)),u,w) = a(x * (z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(3212(a,1),30337(a,1,1,2))].">
      <j1 rule="para" parents="3212 30337"/>
    </justification>
  </clause>

  <clause id="30340">
    <literal><![CDATA[
      a(x * (R(y,z,z) * (z \ 1)),u,w) = a(x * (z \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,26963,a,b,30339,a)].">
      <j1 rule="hyper" parents="63 26963 30339"/>
    </justification>
  </clause>

  <clause id="30341">
    <literal><![CDATA[
      a(x * R(y * (1 / z),z,z),u,w) = a(x * (z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(2273(a,2),30340(a,1,1,2))].">
      <j1 rule="para" parents="2273 30340"/>
    </justification>
  </clause>

  <clause id="30342">
    <literal><![CDATA[
      a(x * L(y * (1 / z),z,z),u,w) = a(x * (z \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(26217,a,30341,a)].">
      <j1 rule="hyper" parents="26217 30341"/>
    </justification>
  </clause>

  <clause id="30343">
    <literal><![CDATA[
      a(L(x * (1 / y),y,y) * z,u,w) = a(z * (y \ x),u,w)
    ]]></literal>
    <justification jstring="[hyper(23925,a,30342,a)].">
      <j1 rule="hyper" parents="23925 30342"/>
    </justification>
  </clause>

  <clause id="30344">
    <literal><![CDATA[
      a(x \ L(y * (1 / z),z,z),u,w) = a((x \ 1) * (z \ y),u,L(w,x,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,29687,a(flip),b,30342,a)].">
      <j1 rule="hyper" parents="63 29687 30342"/>
    </justification>
  </clause>

  <clause id="30345">
    <literal><![CDATA[
      a((x * (1 / y)) * (L(x * (1 / y),y,y) \ z),u,w) = a(((x * (1 / y)) \ z) * (y \ x),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,28007,a(flip),b,30342,a)].">
      <j1 rule="hyper" parents="63 28007 30342"/>
    </justification>
  </clause>

  <clause id="30346">
    <literal><![CDATA[
      a(T(L(x * (1 / y),y,y) \ (L(x * (1 / y),y,y) / z),u) * (y \ x),w,v5) = a((L(x * (1 / y),y,y) / z) * K(z \ 1,u),w,v5)
    ]]></literal>
    <justification jstring="[para(5126(a,2),30343(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5126 30343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30347">
    <literal><![CDATA[
      a(x \ L(y * (1 / z),z,z),u,w) = a(x \ (z \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,29687,a(flip),b,30344,a),flip(a)].">
      <j1 rule="hyper" parents="347 29687 30344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30348">
    <literal><![CDATA[
      L(x / y,y,z) \ a(y \ x,y \ x,L(L(x,y,z),y,z)) = (a(z,y,x * y) * y) / x
    ]]></literal>
    <justification jstring="[para(29678(a,1),30294(a,1,2))].">
      <j1 rule="para" parents="29678 30294"/>
    </justification>
  </clause>

  <clause id="30349">
    <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(30295(a,1),29700(a,1))].">
      <j1 rule="para" parents="30295 29700"/>
    </justification>
  </clause>

  <clause id="30350">
    <literal><![CDATA[
      a((x * y) \ ((z \ (y \ z)) \ 1),u,L(w,x,y)) = a(x \ a(z,y,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(30349,a,29736,a)].">
      <j1 rule="hyper" parents="30349 29736"/>
    </justification>
  </clause>

  <clause id="30351">
    <literal><![CDATA[
      a(x \ (y \ ((z \ (y \ z)) \ 1)),u,w) = a(x \ a(z,y,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(29700,a,30350,a)].">
      <j1 rule="hyper" parents="29700 30350"/>
    </justification>
  </clause>

  <clause id="30352">
    <literal><![CDATA[
      a((x \ (y \ ((z \ (y \ z)) \ 1))) \ a(z,y,y),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(30351(a,1),23957(a,1))].">
      <j1 rule="para" parents="30351 23957"/>
    </justification>
  </clause>

  <clause id="30353">
    <literal><![CDATA[
      a(x,y,L(L(z,a(x,u,w),v5),v5,a(x,u,w))) = a(x,y,z) * a(w,u,a(v5,x,a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(29297,a,30299,a)].">
      <j1 rule="hyper" parents="29297 30299"/>
    </justification>
  </clause>

  <clause id="30354">
    <literal><![CDATA[
      a(a(x,x,y) / x,z,u) * a(y,L(x,x,x),a(L(x,x,x),z,u)) = a(1 / x,z,u)
    ]]></literal>
    <justification jstring="[para(23894(a,1),30306(a,1,1))].">
      <j1 rule="para" parents="23894 30306"/>
    </justification>
  </clause>

  <clause id="30356">
    <literal><![CDATA[
      a(x \ a(x,x,y),z,u) * a(y,L(x,x,x),a(L(x,x,x),z,u)) = a(1 / x,z,u)
    ]]></literal>
    <justification jstring="[para(23893(a,1),30354(a,1,1))].">
      <j1 rule="para" parents="23893 30354"/>
    </justification>
  </clause>

  <clause id="30357">
    <literal><![CDATA[
      a(x \ a(x,x,y),z,u) * a(y,L(x,x,x),a(x,z,u)) = a(1 / x,z,u)
    ]]></literal>
    <justification jstring="[para(11569(a,1),30356(a,1,2,3))].">
      <j1 rule="para" parents="11569 30356"/>
    </justification>
  </clause>

  <clause id="30359">
    <literal><![CDATA[
      a(x \ a(x,x,y),z,u) * a(y,x,a(x,z,u)) = a(1 / x,z,u)
    ]]></literal>
    <justification jstring="[para(12430(a,1),30357(a,1,2))].">
      <j1 rule="para" parents="12430 30357"/>
    </justification>
  </clause>

  <clause id="30360">
    <literal><![CDATA[
      a(x \ a(x,x,y),z,u) * a(y,x,a(x,z,u)) = a(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,23893,a(flip),b,30359,a),flip(a)].">
      <j1 rule="hyper" parents="347 23893 30359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30362">
    <literal><![CDATA[
      L(x / y,y,z) \ a(y \ x,y \ x,x) = (a(z,y,x * y) * y) / x
    ]]></literal>
    <justification jstring="[para(25583(a,1),30348(a,1,2))].">
      <j1 rule="para" parents="25583 30348"/>
    </justification>
  </clause>

  <clause id="30363">
    <literal><![CDATA[
      L(x / y,y,z) \ ((x / y) * (y / x)) = (a(z,y,x * y) * y) / x
    ]]></literal>
    <justification jstring="[para(19003(a,1),30362(a,1,2))].">
      <j1 rule="para" parents="19003 30362"/>
    </justification>
  </clause>

  <clause id="30365">
    <literal><![CDATA[
      (x / y) * (L(x / y,y,z) \ (y / x)) = (a(z,y,x * y) * y) / x
    ]]></literal>
    <justification jstring="[hyper(1429,a,30363,a)].">
      <j1 rule="hyper" parents="1429 30363"/>
    </justification>
  </clause>

  <clause id="30366">
    <literal><![CDATA[
      a(x,y,z) * a(u,w,a(v5,x,a(x,y,z))) = a(x,y,L(z,a(x,w,u),v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,29698,a(flip),b,30353,a),flip(a)].">
      <j1 rule="hyper" parents="63 29698 30353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30367">
    <literal><![CDATA[
      a(x,y,L(z,a(x,u,w),v5)) = L(a(x,y,z),x,a(w,u,v5))
    ]]></literal>
    <justification jstring="[hyper(29921,a,30366,a),flip(a)].">
      <j1 rule="hyper" parents="29921 30366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30369">
    <literal><![CDATA[
      a(x,y,L(z,a(x,u,w),v5)) = a(x,y,L(z,x,a(w,u,v5)))
    ]]></literal>
    <justification jstring="[hyper(347,a,29113,a,b,30367,a),flip(a)].">
      <j1 rule="hyper" parents="347 29113 30367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30370">
    <literal><![CDATA[
      a(x,y,L(z,a(u,w,x),v5)) = a(x,y,L(z,x,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,28759,a,b,30369,a)].">
      <j1 rule="hyper" parents="63 28759 30369"/>
    </justification>
  </clause>

  <clause id="30371">
    <literal><![CDATA[
      R(x,L((y * (1 / z)) \ u,a(y,z,z),a(y,z,z)),w) = R(x,((z \ y) \ u) * a(y,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,22430,a(flip),b,29424,a),flip(a)].">
      <j1 rule="hyper" parents="347 22430 29424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30372">
    <literal><![CDATA[
      L(((x \ y) \ 1) \ 1,z,u) * ((((x \ y) \ 1) \ 1) \ x) = a(u,z,y \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(16871,a,29531,a),flip(a)].">
      <j1 rule="hyper" parents="16871 29531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30373">
    <literal><![CDATA[
      L((x \ y) \ 1,z,u) * (((x \ y) \ 1) \ x) = a(u,z,y \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,3438,a(flip),b,30372,a)].">
      <j1 rule="hyper" parents="63 3438 30372"/>
    </justification>
  </clause>

  <clause id="30374">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ x) = a(u,z,y \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,3438,a(flip),b,30373,a)].">
      <j1 rule="hyper" parents="63 3438 30373"/>
    </justification>
  </clause>

  <clause id="30375">
    <literal><![CDATA[
      (a(x,y,z \ u) \ u) * (u \ z) = u * L(u \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,30374,a(flip),b,20687,a)].">
      <j1 rule="hyper" parents="133 30374 20687"/>
    </justification>
  </clause>

  <clause id="30376">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ a(z,x,a(u,y,w))) = L(x \ L(x,a(w,y,z),u),y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(1429,a,29997,a)].">
      <j1 rule="hyper" parents="1429 29997"/>
    </justification>
  </clause>

  <clause id="30377">
    <literal><![CDATA[
      T(x * a(y,(z / x) * z,z / x),x \ z) = L(x \ z,(z / x) * z,y) \ z
    ]]></literal>
    <justification jstring="[para(83(a,1),30211(a,1,1,1))].">
      <j1 rule="para" parents="83 30211"/>
    </justification>
  </clause>

  <clause id="30379">
    <literal><![CDATA[
      T(x * a(y,(z / x) * z,x \ z),x \ z) = L(x \ z,(z / x) * z,y) \ z
    ]]></literal>
    <justification jstring="[para(24071(a,1),30377(a,1,1,2))].">
      <j1 rule="para" parents="24071 30377"/>
    </justification>
  </clause>

  <clause id="30380">
    <literal><![CDATA[
      T(x * a(y,(x \ z) * z,x \ z),x \ z) = L(x \ z,(z / x) * z,y) \ z
    ]]></literal>
    <justification jstring="[para(24048(a,1),30379(a,1,1,2))].">
      <j1 rule="para" parents="24048 30379"/>
    </justification>
  </clause>

  <clause id="30381">
    <literal><![CDATA[
      T(x * a(y,x,z * x),x \ z) = L(x \ z,(z / x) * z,y) \ z
    ]]></literal>
    <justification jstring="[para(30212(a,1),30380(a,1,1,2))].">
      <j1 rule="para" parents="30212 30380"/>
    </justification>
  </clause>

  <clause id="30382">
    <literal><![CDATA[
      T(x * a(y,x,z * x),x \ z) = L(x \ z,(x \ z) * z,y) \ z
    ]]></literal>
    <justification jstring="[para(21622(a,1),30381(a,2,1))].">
      <j1 rule="para" parents="21622 30381"/>
    </justification>
  </clause>

  <clause id="30383">
    <literal><![CDATA[
      T(x * a(y,x,z * x),x \ z) = L(x \ z,x,y) \ z
    ]]></literal>
    <justification jstring="[para(30193(a,1),30382(a,2,1))].">
      <j1 rule="para" parents="30193 30382"/>
    </justification>
  </clause>

  <clause id="30384">
    <literal><![CDATA[
      T(L(x \ y,x,z) \ y,z) = ((x * z) \ (z * y)) \ y
    ]]></literal>
    <justification jstring="[para(30383(a,1),27306(a,1,1))].">
      <j1 rule="para" parents="30383 27306"/>
    </justification>
  </clause>

  <clause id="30385">
    <literal><![CDATA[
      R(x,((y \ z) \ u) * a(z,y,y),w) = R(x,(z * (1 / y)) \ u,w)
    ]]></literal>
    <justification jstring="[para(28061(a,1),30371(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28061 30371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30386">
    <literal><![CDATA[
      R(x,((y \ z) \ u) * a(z,y,y),w) = R(x,(z * (y \ 1)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,22469,a(flip),b,30385,a),flip(a)].">
      <j1 rule="hyper" parents="347 22469 30385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30389">
    <literal><![CDATA[
      R(x,((y \ z) \ u) * a(z,y,y),w) = R(x,(z * y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,20656,a(flip),b,30386,a),flip(a)].">
      <j1 rule="hyper" parents="347 20656 30386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30390">
    <literal><![CDATA[
      R(x,((y \ (y \ (z \ 1))) \ u) * a(z \ (y \ 1),y,y),w) = R(x,((y \ (z \ 1)) * y) \ u,w)
    ]]></literal>
    <justification jstring="[para(29784(a,2),30389(a,1,2,2))].">
      <j1 rule="para" parents="29784 30389"/>
    </justification>
  </clause>

  <clause id="30391">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ a(z,x,a(u,y,w))) = a(x,a(w,y,z),L(u,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,29155,a(flip),b,30376,a),flip(a)].">
      <j1 rule="hyper" parents="347 29155 30376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30392">
    <literal><![CDATA[
      x * ((a(x,y,z) * a(x,y,z)) * u) = (R(x,y,z) * a(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(25366(a,1),29019(a,1,1))].">
      <j1 rule="para" parents="25366 29019"/>
    </justification>
  </clause>

  <clause id="30393">
    <literal><![CDATA[
      x * (y * (L(L(y,z,x),z,x) \ u)) = (R(x,z,y) * a(x,z,y)) * u
    ]]></literal>
    <justification jstring="[para(27419(a,1),30392(a,1,2))].">
      <j1 rule="para" parents="27419 30392"/>
    </justification>
  </clause>

  <clause id="30394">
    <literal><![CDATA[
      x * (y * (L(L(y,z,x),z,x) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      (a(x,z,y) * R(x,z,y)) * u = w
    ]]></literal>
    <justification jstring="[para(30393(a,2),20248(a,1))].">
      <j1 rule="para" parents="30393 20248"/>
    </justification>
  </clause>

  <clause id="30395">
    <literal><![CDATA[
      x * (L(L(x,y,z),y,z) \ (z * u)) = (a(z,y,x) * R(z,y,x)) * u
    ]]></literal>
    <justification jstring="[hyper(30394,a,27942,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="30394 27942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30396">
    <literal><![CDATA[
      x * (L(L(x,y,z),y,z) \ (z * u)) = R(R(z,y,x),y,x) * u
    ]]></literal>
    <justification jstring="[para(29710(a,1),30395(a,2,1))].">
      <j1 rule="para" parents="29710 30395"/>
    </justification>
  </clause>

  <clause id="30397">
    <literal><![CDATA[
      L((x * (y / (y * x))) \ z,(y * x) * (x \ y),y * x) = ((x \ 1) \ y) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[hyper(21704,a,30146,a)].">
      <j1 rule="hyper" parents="21704 30146"/>
    </justification>
  </clause>

  <clause id="30398">
    <literal><![CDATA[
      L((x * (y / (y * x))) \ z,a(x,x,y),y * x) = ((x \ 1) \ y) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,22775,a(flip),b,30397,a)].">
      <j1 rule="hyper" parents="63 22775 30397"/>
    </justification>
  </clause>

  <clause id="30399">
    <literal><![CDATA[
      ((x \ 1) \ y) \ ((y * x) * z) = (x * (y / (y * x))) \ z
    ]]></literal>
    <justification jstring="[hyper(29384,a,30398,a),flip(a)].">
      <j1 rule="hyper" parents="29384 30398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30400">
    <literal><![CDATA[
      a((x * (y / (y * x))) \ (L(y * x,x,x) * z),u,w) = a((y * x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(30399(a,1),28033(a,1,1))].">
      <j1 rule="para" parents="30399 28033"/>
    </justification>
  </clause>

  <clause id="30401">
    <literal><![CDATA[
      a((x * ((y * x) \ y)) \ (L(y * x,x,x) * z),u,w) = a((y * x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24352,a(flip),b,30400,a)].">
      <j1 rule="hyper" parents="63 24352 30400"/>
    </justification>
  </clause>

  <clause id="30402">
    <literal><![CDATA[
      a((a(x,y,y) \ 1) \ (L(x * y,y,y) * z),u,w) = a((x * y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(25441(a,1),30401(a,1,1,1))].">
      <j1 rule="para" parents="25441 30401"/>
    </justification>
  </clause>

  <clause id="30403">
    <literal><![CDATA[
      a(a(x,y,y) * (L(x * y,y,y) * z),u,w) = a((x * y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(28342(a,1),30402(a,1,1))].">
      <j1 rule="para" parents="28342 30402"/>
    </justification>
  </clause>

  <clause id="30404">
    <literal><![CDATA[
      a((x * (K(y,z) * (u \ w))) \ (u \ (T(w,v5) * x)),v6,v7) = a(u,u * w,a(v7,v6,x * K(y,z)))
    ]]></literal>
    <justification jstring="[para(20151(a,1),30172(a,1,1,1))].">
      <j1 rule="para" parents="20151 30172"/>
    </justification>
  </clause>

  <clause id="30405">
    <literal><![CDATA[
      a(a(x,x,y * (1 / x)) * z,u,w) = a(((y * (1 / x)) \ z) * (x \ y),u,w)
    ]]></literal>
    <justification jstring="[para(29364(a,1),30345(a,1,1))].">
      <j1 rule="para" parents="29364 30345"/>
    </justification>
  </clause>

  <clause id="30406">
    <literal><![CDATA[
      a(a(x,x,y * x) * z,u,w) = a(((y * (1 / x)) \ z) * (x \ y),u,w)
    ]]></literal>
    <justification jstring="[para(14925(a,1),30405(a,1,1,1))].">
      <j1 rule="para" parents="14925 30405"/>
    </justification>
  </clause>

  <clause id="30407">
    <literal><![CDATA[
      a(((x * (1 / y)) \ z) * (y \ x),u,w) = a(z * a(x,y,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,28022,a(flip),b,30406,a),flip(a)].">
      <j1 rule="hyper" parents="63 28022 30406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30408">
    <literal><![CDATA[
      R(x,((y \ (y \ (z \ 1))) \ u) * a(z * (y \ 1),y,y),w) = R(x,((y \ (z \ 1)) * y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,29726,a(flip),b,30390,a)].">
      <j1 rule="hyper" parents="63 29726 30390"/>
    </justification>
  </clause>

  <clause id="30409">
    <literal><![CDATA[
      a((x * (y \ z)) \ (K(x,u) * (y \ (T(z,w) * x))),v5,v6) = a(y,y * z,a(v6,v5,x * K(u,x)))
    ]]></literal>
    <justification jstring="[para(20703(a,1),30404(a,1,1))].">
      <j1 rule="para" parents="20703 30404"/>
    </justification>
  </clause>

  <clause id="30410">
    <literal><![CDATA[
      R(x,((y \ (y \ (z \ 1))) \ u) * a(y \ z,y,y),w) = R(x,((y \ (z \ 1)) * y) \ u,w)
    ]]></literal>
    <justification jstring="[para(29727(a,1),30408(a,1,2,2))].">
      <j1 rule="para" parents="29727 30408"/>
    </justification>
  </clause>

  <clause id="30411">
    <literal><![CDATA[
      R(x,((y \ (y \ (z \ 1))) \ u) * a(y * z,y,y),w) = R(x,((y \ (z \ 1)) * y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,29726,a(flip),b,30410,a)].">
      <j1 rule="hyper" parents="63 29726 30410"/>
    </justification>
  </clause>

  <clause id="30412">
    <literal><![CDATA[
      R(x,a(y,z,z) * ((z \ (z \ (y \ 1))) \ u),w) = R(x,((z \ (y \ 1)) * z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,29337,a(flip),b,30411,a)].">
      <j1 rule="hyper" parents="63 29337 30411"/>
    </justification>
  </clause>

  <clause id="30413">
    <literal><![CDATA[
      R(x,a(y,z,z) * (L(y \ 1,z,z) \ u),w) = R(x,((z \ (y \ 1)) * z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,29528,a(flip),b,30412,a)].">
      <j1 rule="hyper" parents="63 29528 30412"/>
    </justification>
  </clause>

  <clause id="30414">
    <literal><![CDATA[
      R(x,(L(y,z,z) \ u) * a(y,z,z),w) = R(x,((z \ (y \ 1)) * z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,22692,a(flip),b,30413,a)].">
      <j1 rule="hyper" parents="63 22692 30413"/>
    </justification>
  </clause>

  <clause id="30415">
    <literal><![CDATA[
      R(x,(L(y,z,z) \ u) * a(y,z,z),w) = R(x,(y \ 1) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,22414,a(flip),b,30414,a),flip(a)].">
      <j1 rule="hyper" parents="347 22414 30414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30417">
    <literal><![CDATA[
      R(x,(L(y,z,z) \ u) * a(y,z,z),w) = R(x,y \ u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,20655,a(flip),b,30415,a),flip(a)].">
      <j1 rule="hyper" parents="347 20655 30415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30418">
    <literal><![CDATA[
      a((x * (y \ z)) \ (T(y,K(z,x)) \ (z * x)),u,w) = a(y,y * z,a(w,u,x * K(z,x)))
    ]]></literal>
    <justification jstring="[para(21235(a,1),30409(a,1,1,2))].">
      <j1 rule="para" parents="21235 30409"/>
    </justification>
  </clause>

  <clause id="30419">
    <literal><![CDATA[
      a((x * (y \ z)) \ (T(y,K(x,z)) \ (z * x)),u,w) = a(y,y * z,a(w,u,x * K(z,x)))
    ]]></literal>
    <justification jstring="[para(7330(a,1),30418(a,1,1,2,1))].">
      <j1 rule="para" parents="7330 30418"/>
    </justification>
  </clause>

  <clause id="30420">
    <literal><![CDATA[
      a((x * (y \ z)) \ T(y \ (z * x),K(x,z)),u,w) = a(y,y * z,a(w,u,x * K(z,x)))
    ]]></literal>
    <justification jstring="[para(21402(a,2),30419(a,1,1,2))].">
      <j1 rule="para" parents="21402 30419"/>
    </justification>
  </clause>

  <clause id="30421">
    <literal><![CDATA[
      a((T(x,y) * (z \ y)) \ (z \ (x * y)),u,w) = a(z,z * y,a(w,u,x * K(y,x)))
    ]]></literal>
    <justification jstring="[para(21022(a,1),30420(a,1,1))].">
      <j1 rule="para" parents="21022 30420"/>
    </justification>
  </clause>

  <clause id="30422">
    <literal><![CDATA[
      a((x * (y \ z)) \ (y \ (x * z)),u,w) = a(y,y * z,a(w,u,x * K(z,x)))
    ]]></literal>
    <justification jstring="[hyper(23975,a,30421,a)].">
      <j1 rule="hyper" parents="23975 30421"/>
    </justification>
  </clause>

  <clause id="30424">
    <literal><![CDATA[
      a((x * (y \ z)) \ (y \ (x * z)),u,w) = a(y,y * z,a(w,u,x))
    ]]></literal>
    <justification jstring="[para(24080(a,1),30422(a,2,3))].">
      <j1 rule="para" parents="24080 30422"/>
    </justification>
  </clause>

  <clause id="30425">
    <literal><![CDATA[
      a(((x \ y) * T(z,u)) \ (x \ (T(z * K(x \ y,z),u) * y)),w,v5) = a(x,x * y,a(v5,w,T(z * K(x \ y,z),u)))
    ]]></literal>
    <justification jstring="[para(5063(a,1),30424(a,1,1,1))].">
      <j1 rule="para" parents="5063 30424"/>
    </justification>
  </clause>

  <clause id="30427">
    <literal><![CDATA[
      a(x,y,z) * (x * L(x \ u,x,a(x,y,z))) = x * (a(x,y,z) * (R(x,y,z) \ (a(x,y,z) * u)))
    ]]></literal>
    <justification jstring="[para(25493(a,1),29021(a,1,2,2))].">
      <j1 rule="para" parents="25493 29021"/>
    </justification>
  </clause>

  <clause id="30428">
    <literal><![CDATA[
      T(x * ((a(y,z,u) * x) \ w),a(y,z,L(u,x,x)) \ w) = (x \ 1) * ((a(y,z,u) * (x \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(16873,a,29134,a)].">
      <j1 rule="hyper" parents="16873 29134"/>
    </justification>
  </clause>

  <clause id="30429">
    <literal><![CDATA[
      ((x \ 1) * y) * (z * a(a(x,x,y),(x \ 1) * y,z)) = a(x,x,y) \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(14710(a,1),29234(a,2,1))].">
      <j1 rule="para" parents="14710 29234"/>
    </justification>
  </clause>

  <clause id="30430">
    <literal><![CDATA[
      ((x \ 1) * y) * (z * a(a(x,x,y),(x \ 1) * y,z)) = (x \ y) * (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,28541,a(flip),b,30429,a),flip(a)].">
      <j1 rule="hyper" parents="347 28541 30429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30431">
    <literal><![CDATA[
      ((x \ 1) * y) * (z * a(a(x,x,y),x * y,z)) = (x \ y) * (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(24151(a,1),30430(a,1,2,2))].">
      <j1 rule="para" parents="24151 30430"/>
    </justification>
  </clause>

  <clause id="30432">
    <literal><![CDATA[
      ((x \ 1) * y) * (z * a(x * y,a(x,x,y),z)) = (x \ y) * (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(26674(a,1),30431(a,1,2,2))].">
      <j1 rule="para" parents="26674 30431"/>
    </justification>
  </clause>

  <clause id="30433">
    <literal><![CDATA[
      ((x \ 1) * y) * L(z,a(x,x,y),x * y) = (x \ y) * (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(28768(a,1),30432(a,1,2))].">
      <j1 rule="para" parents="28768 30432"/>
    </justification>
  </clause>

  <clause id="30434">
    <literal><![CDATA[
      (x \ y) * (a(x,x,y) \ z) = ((x \ 1) * y) * z
    ]]></literal>
    <justification jstring="[para(29370(a,1),30433(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29370 30433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30435">
    <literal><![CDATA[
      a((x \ y) * (a(x,x,y) * z),u,w) = a(((x \ 1) * y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(30434(a,1),28399(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30434 28399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30436">
    <literal><![CDATA[
      L(L(x,y,a(z * u,z,w)) \ 1,y,a(z * u,z,w)) = L(x \ 1,y,a(w,v5,a(z,z,u)))
    ]]></literal>
    <justification jstring="[para(30224(a,1),29977(a,1,1,1))].">
      <j1 rule="para" parents="30224 29977"/>
    </justification>
  </clause>

  <clause id="30437">
    <literal><![CDATA[
      L(x \ 1,y,a(z,u,a(w,w,v5))) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(25956,a,30436,a),flip(a)].">
      <j1 rule="hyper" parents="25956 30436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30439">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(26382,a,30437,a)].">
      <j1 rule="hyper" parents="26382 30437"/>
    </justification>
  </clause>

  <clause id="30441">
    <literal><![CDATA[
      L(a(a(x,x,y),z,u) \ 1,w,v5) = L(u,z,a(x,x,y)) * (u \ 1)
    ]]></literal>
    <justification jstring="[para(30437(a,1),30019(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30437 30019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30442">
    <literal><![CDATA[
      L(x,y,a(a(z,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(29900,a,30439,a)].">
      <j1 rule="hyper" parents="29900 30439"/>
    </justification>
  </clause>

  <clause id="30443">
    <literal><![CDATA[
      (a(x,y,a(z,z,u)) * w) / v5 = a(x,y,a(z,z,u)) * (w / v5)
    ]]></literal>
    <justification jstring="[hyper(220,a,30439,a(flip),b,30206,a(flip))].">
      <j1 rule="hyper" parents="220 30439 30206"/>
    </justification>
  </clause>

  <clause id="30445">
    <literal><![CDATA[
      ((a(x,y,a(z,z,u)) * w) * (v5 * v6)) \ ((a(x,y,a(z,z,u)) * (w * v5)) * v6) = a(a(x,y,a(z,z,u)) * w,L(v5,w,a(x,y,a(z,z,u))),v6)
    ]]></literal>
    <justification jstring="[para(30439(a,1),540(a,1,1,2,1))].">
      <j1 rule="para" parents="30439 540"/>
    </justification>
  </clause>

  <clause id="30446">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * (w * v5) = w * (a(x,y,a(z,z,u)) * v5)
    ]]></literal>
    <justification jstring="[para(30439(a,1),23242(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30439 23242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30447">
    <literal><![CDATA[
      L(x,y,a(z,z,a(u,w,v5))) = x
    ]]></literal>
    <justification jstring="[para(29786(a,1),30439(a,1,3))].">
      <j1 rule="para" parents="29786 30439"/>
    </justification>
  </clause>

  <clause id="30448">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w),v5,v5)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(29961,a,30447,a)].">
      <j1 rule="hyper" parents="29961 30447"/>
    </justification>
  </clause>

  <clause id="30449">
    <literal><![CDATA[
      (a(x,x,a(y,z,u)) \ w) / v5 = w / (v5 * a(x,x,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(23265,a,30447,a)].">
      <j1 rule="hyper" parents="23265 30447"/>
    </justification>
  </clause>

  <clause id="30451">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,v5,v5))) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(29113(a,2),30448(a,1,3))].">
      <j1 rule="para" parents="29113 30448"/>
    </justification>
  </clause>

  <clause id="30452">
    <literal><![CDATA[
      L(x,y \ z,a(u,w,v5)) = L(x,y * z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(30100,a,30451,a),flip(a)].">
      <j1 rule="hyper" parents="30100 30451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30453">
    <literal><![CDATA[
      L(x,y,a(z,u \ w,v5)) = L(x,y,a(z,w * u,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,30105,a(flip),b,30451,a)].">
      <j1 rule="hyper" parents="63 30105 30451"/>
    </justification>
  </clause>

  <clause id="30454">
    <literal><![CDATA[
      L(x,y,a(z,u,w \ v5)) = L(x,y,a(z,u,w * v5))
    ]]></literal>
    <justification jstring="[para(14958(a,1),30451(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14958 30451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30456">
    <literal><![CDATA[
      L(x,y \ z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,a(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(30451(a,1),30100(a,1))].">
      <j1 rule="para" parents="30451 30100"/>
    </justification>
  </clause>

  <clause id="30457">
    <literal><![CDATA[
      L(x * a(y,z,a(u * w,x,v5)),u \ w,a(y,z,v5)) = L(x,a(y,z,v5),u * w)
    ]]></literal>
    <justification jstring="[hyper(347,a,29823,a(flip),b,30452,a),flip(a)].">
      <j1 rule="hyper" parents="347 29823 30452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30458">
    <literal><![CDATA[
      L(x,y \ a(z,u,w),a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(28650,a,30452,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="28650 30452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30460">
    <literal><![CDATA[
      L(x,y,a(z,u \ w,v5)) = L(x,y,a(z,u * w,v5))
    ]]></literal>
    <justification jstring="[para(24037(a,1),30453(a,2,3))].">
      <j1 rule="para" parents="24037 30453"/>
    </justification>
  </clause>

  <clause id="30461">
    <literal><![CDATA[
      L(x,y,a(z,u,w \ (x \ v5))) = L(x,y,a(z,u,(x * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,29757,a(flip),b,30454,a)].">
      <j1 rule="hyper" parents="63 29757 30454"/>
    </justification>
  </clause>

  <clause id="30462">
    <literal><![CDATA[
      L(x,y \ z,a(u,y * z,y \ z)) = x
    ]]></literal>
    <justification jstring="[hyper(27554,a,30460,a),flip(a)].">
      <j1 rule="hyper" parents="27554 30460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30463">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,x * y,z) \ u) = u * a(z,x * y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(29509,a,30462,a)].">
      <j1 rule="hyper" parents="29509 30462"/>
    </justification>
  </clause>

  <clause id="30464">
    <literal><![CDATA[
      L(x,y,a(z,y,u)) * R(y \ 1,a(z,y,u),a(z,y,u)) = (x * ((y \ 1) * a(z,y,u))) * (a(z,y,u) \ 1)
    ]]></literal>
    <justification jstring="[para(30458(a,1),27014(a,1,1))].">
      <j1 rule="para" parents="30458 27014"/>
    </justification>
  </clause>

  <clause id="30466">
    <literal><![CDATA[
      x \ (a(y,z,a(u,u,w)) * v5) = a(y,z,a(u,u,w)) * (x \ v5)
    ]]></literal>
    <justification jstring="[hyper(678,a,30446,a)].">
      <j1 rule="hyper" parents="678 30446"/>
    </justification>
  </clause>

  <clause id="30467">
    <literal><![CDATA[
      (x * (a(y,z,a(u,u,w)) * (v5 * v6))) \ ((x * v5) * (a(y,z,a(u,u,w)) * v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,v5,a(y,z,a(u,u,w)) * v6) = v7
    ]]></literal>
    <justification jstring="[para(30446(a,2),836(a,1,1,2))].">
      <j1 rule="para" parents="30446 836"/>
    </justification>
  </clause>

  <clause id="30468">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * (w * v5) = w * (a(z,z,a(x,y,u)) * v5)
    ]]></literal>
    <justification jstring="[para(29786(a,1),30446(a,2,2,1))].">
      <j1 rule="para" parents="29786 30446"/>
    </justification>
  </clause>

  <clause id="30469">
    <literal><![CDATA[
      (a(x,x,a(y,z,u)) * w) / v5 = w / (v5 * a(x,x,a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(28387(a,1),30449(a,1,1))].">
      <j1 rule="para" parents="28387 30449"/>
    </justification>
  </clause>

  <clause id="30470">
    <literal><![CDATA[
      L(x,y,a(z,u,(x * w) * v5)) = L(x,y,a(z,u,w * (x \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,30454,a(flip),b,30461,a),flip(a)].">
      <j1 rule="hyper" parents="63 30454 30461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30471">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * (w \ u) = w \ L(u,z,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(29836(a,1),30466(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29836 30466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30472">
    <literal><![CDATA[
      (x \ y) * a(z,z,a(u,w,y)) = x \ L(y,z,a(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(29794,a,30471,a)].">
      <j1 rule="hyper" parents="29794 30471"/>
    </justification>
  </clause>

  <clause id="30473">
    <literal><![CDATA[
      x \ ((y \ (a(z,u,a(w,w,v5)) * ((y * x) * v6))) / (a(w,w,a(z,u,v5)) * v6)) = a(y,x,a(w,w,a(z,u,v5)) * v6)
    ]]></literal>
    <justification jstring="[para(30468(a,2),23139(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="30468 23139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30474">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * (w * u) = w * L(u,y,a(x,z,z))
    ]]></literal>
    <justification jstring="[para(29836(a,1),30468(a,2,2))].">
      <j1 rule="para" parents="29836 30468"/>
    </justification>
  </clause>

  <clause id="30475">
    <literal><![CDATA[
      L(a(x,y,z) * u,w,a(z,z,v5)) = a(x,y,z) * L(u,w,a(v5,z,z))
    ]]></literal>
    <justification jstring="[hyper(29928,a,30474,a)].">
      <j1 rule="hyper" parents="29928 30474"/>
    </justification>
  </clause>

  <clause id="30476">
    <literal><![CDATA[
      L(a(a(x,x,y),z,u) \ 1,w,v5) = u \ L(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,1295,a(flip),b,30441,a),flip(a)].">
      <j1 rule="hyper" parents="347 1295 30441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30477">
    <literal><![CDATA[
      L(a(a(x,x,y),z,u) \ 1,w,v5) = a(x,x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(29880,a,30476,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="29880 30476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30478">
    <literal><![CDATA[
      L(a(x,x,a(y,z,u)) \ 1,w,v5) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(29790(a,1),30477(a,1,1,1))].">
      <j1 rule="para" parents="29790 30477"/>
    </justification>
  </clause>

  <clause id="30479">
    <literal><![CDATA[
      L(a(x,x,a(y,z,u)),w,v5) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(26334(a,1),30478(a,1,1))].">
      <j1 rule="para" parents="26334 30478"/>
    </justification>
  </clause>

  <clause id="30480">
    <literal><![CDATA[
      a(x,x,L(a(y,z,u),w,v5)) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(29297,a,30479,a)].">
      <j1 rule="hyper" parents="29297 30479"/>
    </justification>
  </clause>

  <clause id="30481">
    <literal><![CDATA[
      a(x,y,a(z,z,a(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,30479,a,b,28853,a),flip(a)].">
      <j1 rule="hyper" parents="129 30479 28853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30482">
    <literal><![CDATA[
      a(x,y,a(y,z,a(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(29875,a,30481,a)].">
      <j1 rule="hyper" parents="29875 30481"/>
    </justification>
  </clause>

  <clause id="30483">
    <literal><![CDATA[
      a(x,y,a(z,u,a(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[para(29803(a,1),30481(a,1,3))].">
      <j1 rule="para" parents="29803 30481"/>
    </justification>
  </clause>

  <clause id="30484">
    <literal><![CDATA[
      1 * a(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(a(x,y,z),w,a(v5,v5,v6)) = u
    ]]></literal>
    <justification jstring="[para(30481(a,1),29864(a,1,1))].">
      <j1 rule="para" parents="30481 29864"/>
    </justification>
  </clause>

  <clause id="30485">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),x,v5)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(189,a,29147,a,b,30482,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="189 29147 30482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30487">
    <literal><![CDATA[
      a(x,y,z) * 1 != u
    ]]></literal>
    <literal><![CDATA[
      L(a(x,y,z),x,a(w,v5,v6)) = u
    ]]></literal>
    <justification jstring="[para(30483(a,1),29921(a,1,2))].">
      <j1 rule="para" parents="30483 29921"/>
    </justification>
  </clause>

  <clause id="30488">
    <literal><![CDATA[
      L(x * 1,y,a(a(z,u,w),z,v5)) = L(x,a(a(z,u,w),z,v5),y)
    ]]></literal>
    <justification jstring="[para(30483(a,1),29987(a,1,1,2))].">
      <j1 rule="para" parents="30483 29987"/>
    </justification>
  </clause>

  <clause id="30489">
    <literal><![CDATA[
      a(x,x,a(y,z,L(u,w,v5))) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(29113(a,2),30480(a,1,3))].">
      <j1 rule="para" parents="29113 30480"/>
    </justification>
  </clause>

  <clause id="30490">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,w,v5))) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(29909,a,30485,a)].">
      <j1 rule="hyper" parents="29909 30485"/>
    </justification>
  </clause>

  <clause id="30491">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,x,v5))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(29113(a,2),30485(a,1,3))].">
      <j1 rule="para" parents="29113 30485"/>
    </justification>
  </clause>

  <clause id="30492">
    <literal><![CDATA[
      a(x,y,a(z,x,L(u,w,v5))) = a(x,x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(29932,a,30489,a)].">
      <j1 rule="hyper" parents="29932 30489"/>
    </justification>
  </clause>

  <clause id="30493">
    <literal><![CDATA[
      a(x,y,a(y,z,L(u,w,v5))) = a(y,y,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(29787,a,30492,a)].">
      <j1 rule="hyper" parents="29787 30492"/>
    </justification>
  </clause>

  <clause id="30494">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * u != w
    ]]></literal>
    <literal><![CDATA[
      R(u,x,a(x,z,L(y,v5,v6))) = w
    ]]></literal>
    <justification jstring="[para(30493(a,1),28910(a,1,1))].">
      <j1 rule="para" parents="30493 28910"/>
    </justification>
  </clause>

  <clause id="30495">
    <literal><![CDATA[
      L(x * a(y,y,a(z,x,u)),y,a(y,L(z,w,v5),u)) = L(x,a(y,y,u),L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(30493(a,1),29985(a,1,1,2))].">
      <j1 rule="para" parents="30493 29985"/>
    </justification>
  </clause>

  <clause id="30496">
    <literal><![CDATA[
      (a(x,x,a(y,z,u)) * w) / L(v5,v5 * w,a(a(x,z,L(y,v6,v7)),x,u)) = a(u,x,a(x,z,L(y,v6,v7))) * (w / v5)
    ]]></literal>
    <justification jstring="[para(30493(a,1),30196(a,1,1,1))].">
      <j1 rule="para" parents="30493 30196"/>
    </justification>
  </clause>

  <clause id="30497">
    <literal><![CDATA[
      L(a(x,y,z),u,a(w,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(30484,a,7,a)].">
      <j1 rule="hyper" parents="30484 7"/>
    </justification>
  </clause>

  <clause id="30498">
    <literal><![CDATA[
      L(a(x,y,z),u,a(w,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(30497(a,1),27579(a,1,1))].">
      <j1 rule="para" parents="30497 27579"/>
    </justification>
  </clause>

  <clause id="30499">
    <literal><![CDATA[
      L(a(x,y,z),u,a(w,v5,u)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(29895(a,1),30498(a,1))].">
      <j1 rule="para" parents="29895 30498"/>
    </justification>
  </clause>

  <clause id="30501">
    <literal><![CDATA[
      L(a(x,y,z),x,a(u,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(30487,a,8,a)].">
      <j1 rule="hyper" parents="30487 8"/>
    </justification>
  </clause>

  <clause id="30502">
    <literal><![CDATA[
      a(x,y,L(z,x,a(u,w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29297,a,30501,a)].">
      <j1 rule="hyper" parents="29297 30501"/>
    </justification>
  </clause>

  <clause id="30503">
    <literal><![CDATA[
      a(x,y,L(z,a(u,w,x),v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,30370,a,b,30502,a)].">
      <j1 rule="hyper" parents="63 30370 30502"/>
    </justification>
  </clause>

  <clause id="30504">
    <literal><![CDATA[
      a(x,y,z * a(x,z,a(u,w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,29163,a,b,30502,a)].">
      <j1 rule="hyper" parents="63 29163 30502"/>
    </justification>
  </clause>

  <clause id="30508">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),v5,y) \ (x * a(y,x,a(z,u,w))) = a(y,v5,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,28838,a(flip),b,30504,a)].">
      <j1 rule="hyper" parents="63 28838 30504"/>
    </justification>
  </clause>

  <clause id="30509">
    <literal><![CDATA[
      L(x,a(a(y,z,u),y,w),v5) = L(x,v5,a(a(y,z,u),y,w))
    ]]></literal>
    <justification jstring="[para(8(a,1),30488(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8 30488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30510">
    <literal><![CDATA[
      L(x,a(a(y,z,u),y,w),v5) = L(x,v5,a(y,z,a(w,y,u)))
    ]]></literal>
    <justification jstring="[para(29790(a,1),30509(a,2,3))].">
      <j1 rule="para" parents="29790 30509"/>
    </justification>
  </clause>

  <clause id="30511">
    <literal><![CDATA[
      L(x,a(a(y,z,L(u,w,v5)),y,v6),v7) = L(x,v7,a(y,y,a(u,z,v6)))
    ]]></literal>
    <justification jstring="[para(30492(a,1),30510(a,2,3))].">
      <j1 rule="para" parents="30492 30510"/>
    </justification>
  </clause>

  <clause id="30512">
    <literal><![CDATA[
      R(x,y,a(y,z,L(u,w,v5))) = L(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(30494,a,29884,a)].">
      <j1 rule="hyper" parents="30494 29884"/>
    </justification>
  </clause>

  <clause id="30513">
    <literal><![CDATA[
      L(x,y,a(y,z,L(u,w,v5))) = L(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(23284,a,30512,a)].">
      <j1 rule="hyper" parents="23284 30512"/>
    </justification>
  </clause>

  <clause id="30514">
    <literal><![CDATA[
      L(x,a(a(y,z,L(u,w,v5)),y,v6),v7) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,30447,a(flip),b,30511,a),flip(a)].">
      <j1 rule="hyper" parents="347 30447 30511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30517">
    <literal><![CDATA[
      L(x,a(y,z,a(u,y,L(w,v5,v6))),v7) = x
    ]]></literal>
    <justification jstring="[para(29790(a,1),30514(a,1,2))].">
      <j1 rule="para" parents="29790 30514"/>
    </justification>
  </clause>

  <clause id="30519">
    <literal><![CDATA[
      L(x,a(y,y,a(z,u,w)),v5) = x
    ]]></literal>
    <justification jstring="[para(30492(a,1),30517(a,1,2))].">
      <j1 rule="para" parents="30492 30517"/>
    </justification>
  </clause>

  <clause id="30521">
    <literal><![CDATA[
      (a(x,y,a(z,z,u)) \ w) * v5 = w * (a(a(x,y,u),z,z) \ v5)
    ]]></literal>
    <justification jstring="[para(30519(a,1),29826(a,1,1,2))].">
      <j1 rule="para" parents="30519 29826"/>
    </justification>
  </clause>

  <clause id="30522">
    <literal><![CDATA[
      (a(x,y,a(z,z,u)) * w) * v5 = w * (a(a(x,y,u),z,z) \ v5)
    ]]></literal>
    <justification jstring="[para(28387(a,1),30521(a,1,1))].">
      <j1 rule="para" parents="28387 30521"/>
    </justification>
  </clause>

  <clause id="30523">
    <literal><![CDATA[
      (a(x,y,a(z,z,u)) * w) * v5 = w * (a(x,y,a(z,z,u)) \ v5)
    ]]></literal>
    <justification jstring="[para(29790(a,1),30522(a,2,2,1))].">
      <j1 rule="para" parents="29790 30522"/>
    </justification>
  </clause>

  <clause id="30524">
    <literal><![CDATA[
      (a(x,y,a(z,z,u)) * w) * v5 = w * (a(x,y,a(z,z,u)) * v5)
    ]]></literal>
    <justification jstring="[para(28387(a,1),30523(a,2,2))].">
      <j1 rule="para" parents="28387 30523"/>
    </justification>
  </clause>

  <clause id="30525">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,x * y,z) \ u) = u * a(z,x * y,x * y)
    ]]></literal>
    <justification jstring="[para(29440(a,1),30463(a,2,2))].">
      <j1 rule="para" parents="29440 30463"/>
    </justification>
  </clause>

  <clause id="30526">
    <literal><![CDATA[
      x * L(a(y,z,z) * (x \ 1),u,a(z,z,y)) = L(a(y,z,z),u,x)
    ]]></literal>
    <justification jstring="[para(30475(a,2),29523(a,1,2))].">
      <j1 rule="para" parents="30475 29523"/>
    </justification>
  </clause>

  <clause id="30527">
    <literal><![CDATA[
      x * L(x \ a(y,z,z),u,a(z,z,y)) = L(a(y,z,z),u,x)
    ]]></literal>
    <justification jstring="[para(29442(a,1),30526(a,1,2,1))].">
      <j1 rule="para" parents="29442 30526"/>
    </justification>
  </clause>

  <clause id="30528">
    <literal><![CDATA[
      x * L(x \ a(y,z,z),u,a(z,z,y)) = a(y,z,L(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,29113,a,b,30527,a),flip(a)].">
      <j1 rule="hyper" parents="347 29113 30527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30529">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,y * x,z) \ u) = u * a(z,x * y,x * y)
    ]]></literal>
    <justification jstring="[para(21617(a,1),30525(a,1,2,1))].">
      <j1 rule="para" parents="21617 30525"/>
    </justification>
  </clause>

  <clause id="30530">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ (x * a(y,x,a(z,u,w))) = a(y,a(w,u,z),x)
    ]]></literal>
    <justification jstring="[para(26510(a,1),30508(a,1,1))].">
      <j1 rule="para" parents="26510 30508"/>
    </justification>
  </clause>

  <clause id="30531">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ a(y,x,a(z,u,w))) = a(y,a(w,u,z),x)
    ]]></literal>
    <justification jstring="[hyper(1429,a,30530,a)].">
      <j1 rule="hyper" parents="1429 30530"/>
    </justification>
  </clause>

  <clause id="30532">
    <literal><![CDATA[
      R(x \ L(x,y,a(z,u,w)),x,L(x,y,a(z,u,w)) \ a(y,x,a(z,u,w))) \ a(y,x,a(z,u,w)) = a(y,a(w,u,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,3164,a,b,30531,a)].">
      <j1 rule="hyper" parents="63 3164 30531"/>
    </justification>
  </clause>

  <clause id="30533">
    <literal><![CDATA[
      L(x * a(y,y,a(z,x,u)),y,a(y,z,L(u,w,v5))) = L(x,a(y,y,u),L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(30103,a,30495,a)].">
      <j1 rule="hyper" parents="30103 30495"/>
    </justification>
  </clause>

  <clause id="30534">
    <literal><![CDATA[
      L(x * a(y,y,a(z,x,u)),y,a(u,z,y)) = L(x,a(y,y,u),L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,30513,a(flip),b,30533,a)].">
      <j1 rule="hyper" parents="63 30513 30533"/>
    </justification>
  </clause>

  <clause id="30535">
    <literal><![CDATA[
      L(x,a(y,y,z),L(u,w,v5)) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(29957,a,30534,a),flip(a)].">
      <j1 rule="hyper" parents="29957 30534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30538">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,L(w,v5,v6))),z,a(y,u,L(w,v5,v6))) = L(x,a(y,u,w),L(z,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(30028,a,30099,a),flip(a)].">
      <j1 rule="hyper" parents="30028 30099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30539">
    <literal><![CDATA[
      L(x,a(L(y,z,u),w,v5),v6) = L(x,a(v5,w,y),L(v6,z,u))
    ]]></literal>
    <justification jstring="[hyper(29998,a,30538,a)].">
      <j1 rule="hyper" parents="29998 30538"/>
    </justification>
  </clause>

  <clause id="30540">
    <literal><![CDATA[
      L(x,a(y * (y * z),u,w),v5) = L(x,a(w,u,z),L(v5,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,24448,a,b,30539,a)].">
      <j1 rule="hyper" parents="63 24448 30539"/>
    </justification>
  </clause>

  <clause id="30541">
    <literal><![CDATA[
      L(x,a(y \ (z \ y),u,w),v5) = L(x,a(w,u,z),L(v5,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,25208,a(flip),b,30539,a)].">
      <j1 rule="hyper" parents="63 25208 30539"/>
    </justification>
  </clause>

  <clause id="30542">
    <literal><![CDATA[
      L(x,a(y,z,L(u,w,v5)),v6) = L(x,a(u,z,y),L(v6,w,v5))
    ]]></literal>
    <justification jstring="[para(29675(a,1),30539(a,1,2))].">
      <j1 rule="para" parents="29675 30539"/>
    </justification>
  </clause>

  <clause id="30543">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,L(w,v5,v6))),z,a(y,u,L(w,v5,v6))) = L(x,a(y,L(z,v5,v6),w),u)
    ]]></literal>
    <justification jstring="[hyper(30095,a,30099,a),flip(a)].">
      <j1 rule="hyper" parents="30095 30099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30544">
    <literal><![CDATA[
      L(x,a(y,L(z,u,w),v5),v6) = L(x,a(y,z,L(v5,u,w)),v6)
    ]]></literal>
    <justification jstring="[hyper(30024,a,30543,a),flip(a)].">
      <j1 rule="hyper" parents="30024 30543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30545">
    <literal><![CDATA[
      L(x,a(y,L(z,u,w),v5),v6) = L(x,a(v5,z,y),L(v6,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,30542,a(flip),b,30544,a),flip(a)].">
      <j1 rule="hyper" parents="347 30542 30544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30546">
    <literal><![CDATA[
      a(x,y,z) * L(x * (x \ u),x,a(z,y,x)) = x * (a(x,y,z) * (R(x,y,z) \ (a(x,y,z) * u)))
    ]]></literal>
    <justification jstring="[para(29348(a,2),30427(a,1,2))].">
      <j1 rule="para" parents="29348 30427"/>
    </justification>
  </clause>

  <clause id="30547">
    <literal><![CDATA[
      T(x * ((a(y,z,u) * x) \ w),w) = (x \ 1) * ((a(y,z,u) * (x \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(23080,a,30428,a)].">
      <j1 rule="hyper" parents="23080 30428"/>
    </justification>
  </clause>

  <clause id="30549">
    <literal><![CDATA[
      T(x * ((a(y,z,u) * x) \ w),w) = x * ((a(y,z,u) * x) \ w)
    ]]></literal>
    <justification jstring="[hyper(347,a,974,a(flip),b,30547,a),flip(a)].">
      <j1 rule="hyper" parents="347 974 30547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30550">
    <literal><![CDATA[
      x * (a(x,y,z) * (R(x,y,z) \ (a(x,y,z) * u))) = a(x,y,z) * L(u,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(10(a,1),30546(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 30546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30551">
    <literal><![CDATA[
      x * (a(x,y,z) * (R(x,y,z) \ (a(x,y,z) * u))) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,30177,a(flip),b,30550,a),flip(a)].">
      <j1 rule="hyper" parents="347 30177 30550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30553">
    <literal><![CDATA[
      x * (a(x,y,z) * ((R(x,y,z) \ u) * a(x,y,z))) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(25531(a,1),30551(a,1,2,2))].">
      <j1 rule="para" parents="25531 30551"/>
    </justification>
  </clause>

  <clause id="30554">
    <literal><![CDATA[
      x * (y * (L(L(y,z,x),z,x) \ (R(x,z,y) \ u))) = R(x,z,y) * (x \ u)
    ]]></literal>
    <justification jstring="[para(28395(a,1),30553(a,1,2))].">
      <j1 rule="para" parents="28395 30553"/>
    </justification>
  </clause>

  <clause id="30555">
    <literal><![CDATA[
      x * ((a(x,y,z) \ x) \ u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(29028(a,1),30554(a,1,2))].">
      <j1 rule="para" parents="29028 30554"/>
    </justification>
  </clause>

  <clause id="30556">
    <literal><![CDATA[
      ((x \ y) / x) * R(x,z,u) = (a(x,z,u) \ x) \ y
    ]]></literal>
    <justification jstring="[hyper(34,a,20930,a,b,30555,a)].">
      <j1 rule="hyper" parents="34 20930 30555"/>
    </justification>
  </clause>

  <clause id="30557">
    <literal><![CDATA[
      L(x,y,((z \ u) / z) * L(z,w,v5)) = L(x,y,(a(z,w,v5) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(30556(a,1),22863(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30556 22863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30558">
    <literal><![CDATA[
      a(a(x,y,z),u,a(x,y,z) * (u \ w)) * (u * (u \ (a(x,y,z) \ w))) = u * ((u * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(29574(a,1),29225(a,1,1))].">
      <j1 rule="para" parents="29574 29225"/>
    </justification>
  </clause>

  <clause id="30559">
    <literal><![CDATA[
      (L(R(x,y,z),x * L(x,y,z),u) \ (x * u)) \ (R(x,y,z) \ (x * u)) = a(z,y,a(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,26590,a(flip),b,29946,a),flip(a)].">
      <j1 rule="hyper" parents="347 26590 29946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30560">
    <literal><![CDATA[
      L(R(x,y,z),x * L(x,y,z),u) \ (x * u) = a(z,y,a(x,x,u)) \ (R(x,y,z) \ (x * u))
    ]]></literal>
    <justification jstring="[hyper(39,a,19984,a,b,30559,a),flip(a)].">
      <j1 rule="hyper" parents="39 19984 30559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30561">
    <literal><![CDATA[
      L(R(x,y,z),x * L(x,y,z),u) \ (x * u) = a(z,y,a(x,x,u)) \ (x * (R(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(1753(a,1),30560(a,2,2))].">
      <j1 rule="para" parents="1753 30560"/>
    </justification>
  </clause>

  <clause id="30562">
    <literal><![CDATA[
      L(R(x,y,z),x * L(x,y,z),u) \ (x * u) = (x * (R(x,y,z) \ u)) * a(z,y,a(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,28294,a(flip),b,30561,a),flip(a)].">
      <j1 rule="hyper" parents="347 28294 30561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30563">
    <literal><![CDATA[
      (x * (R(x,y,z) \ u)) * a(z,y,a(x,x,u)) = (R(x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,27764,a(flip),b,30562,a),flip(a)].">
      <j1 rule="hyper" parents="63 27764 30562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30564">
    <literal><![CDATA[
      x * ((R(x,y,z) \ u) * a(z,y,a(x,x,u))) = (R(x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,28514,a(flip),b,30563,a)].">
      <j1 rule="hyper" parents="63 28514 30563"/>
    </justification>
  </clause>

  <clause id="30565">
    <literal><![CDATA[
      x * ((R(x,y,z) \ u) * a(z,y,a(x,x,u))) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) \ u = w
    ]]></literal>
    <justification jstring="[para(30564(a,2),29065(a,1))].">
      <j1 rule="para" parents="30564 29065"/>
    </justification>
  </clause>

  <clause id="30566">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) * (R(x,z,y) \ u) = a(x,z,y) \ u
    ]]></literal>
    <justification jstring="[hyper(30565,a,29821,a),flip(a)].">
      <j1 rule="hyper" parents="30565 29821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30567">
    <literal><![CDATA[
      L(x,x,a(a(y * z,z,y),u,w)) * (R(x,u,a(y * z,z,y)) \ w) = a(x,u,a(z,z,y)) \ w
    ]]></literal>
    <justification jstring="[para(25274(a,1),30566(a,2,1))].">
      <j1 rule="para" parents="25274 30566"/>
    </justification>
  </clause>

  <clause id="30568">
    <literal><![CDATA[
      x * (R(x,y,y) \ z) = a(x,y,y) \ z
    ]]></literal>
    <justification jstring="[para(29436(a,1),30566(a,1,1))].">
      <j1 rule="para" parents="29436 30566"/>
    </justification>
  </clause>

  <clause id="30569">
    <literal><![CDATA[
      L(x,x,a(y * z,z,a(u,w,y))) * (R(x,w,a(y * z,z,y)) \ u) = a(x,w,a(z,z,y)) \ u
    ]]></literal>
    <justification jstring="[para(29790(a,1),30567(a,1,1,3))].">
      <j1 rule="para" parents="29790 30567"/>
    </justification>
  </clause>

  <clause id="30570">
    <literal><![CDATA[
      L(x,x,a(y,z,a(u,w,z * y))) * (R(x,w,a(y * z,z,y)) \ u) = a(x,w,a(z,z,y)) \ u
    ]]></literal>
    <justification jstring="[para(29842(a,1),30569(a,1,1,3))].">
      <j1 rule="para" parents="29842 30569"/>
    </justification>
  </clause>

  <clause id="30571">
    <literal><![CDATA[
      L(x,x,a(y,z,a(u,u,w))) * (R(x,z,a(w * u,u,w)) \ y) = a(x,z,a(u,u,w)) \ y
    ]]></literal>
    <justification jstring="[para(29791(a,1),30570(a,1,1,3))].">
      <j1 rule="para" parents="29791 30570"/>
    </justification>
  </clause>

  <clause id="30572">
    <literal><![CDATA[
      x * (R(x,y,a(z * u,u,z)) \ w) = a(x,y,a(u,u,z)) \ w
    ]]></literal>
    <justification jstring="[para(30439(a,1),30571(a,1,1))].">
      <j1 rule="para" parents="30439 30571"/>
    </justification>
  </clause>

  <clause id="30573">
    <literal><![CDATA[
      x * (L(x,y,a(z * u,u,z)) \ w) = a(x,y,a(u,u,z)) \ w
    ]]></literal>
    <justification jstring="[para(23247(a,1),30572(a,1,2,1))].">
      <j1 rule="para" parents="23247 30572"/>
    </justification>
  </clause>

  <clause id="30574">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,u)) \ w) = a(x,y,a(u,u,z)) \ w
    ]]></literal>
    <justification jstring="[para(23287(a,1),30573(a,1,2,1))].">
      <j1 rule="para" parents="23287 30573"/>
    </justification>
  </clause>

  <clause id="30575">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,u)) \ w) = a(x,y,a(u,u,z)) * w
    ]]></literal>
    <justification jstring="[hyper(347,a,28387,a(flip),b,30574,a),flip(a)].">
      <j1 rule="hyper" parents="347 28387 30574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30576">
    <literal><![CDATA[
      x * (L(x,y,a(z,z,u)) \ w) = a(x,y,a(z,z,u)) * w
    ]]></literal>
    <justification jstring="[para(27553(a,1),30575(a,1,2,1))].">
      <j1 rule="para" parents="27553 30575"/>
    </justification>
  </clause>

  <clause id="30577">
    <literal><![CDATA[
      L(x,y,a(z,u,u * x)) * w = x * (a(x,y,a(u,u,z)) * w)
    ]]></literal>
    <justification jstring="[para(30576(a,1),30021(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30576 30021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30578">
    <literal><![CDATA[
      x * (a(x,y,a(z,z,u)) * w) = L(x,y,a(z,z,u)) * w
    ]]></literal>
    <justification jstring="[para(29913(a,1),30577(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29913 30577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30579">
    <literal><![CDATA[
      L((x \ (y * (x \ y))) \ z,(1 / (y \ x)) \ (1 / (1 / (x \ y))),y \ x) = (x \ y) \ ((y \ x) * z)
    ]]></literal>
    <justification jstring="[para(25519(a,1),30143(a,1,1,1))].">
      <j1 rule="para" parents="25519 30143"/>
    </justification>
  </clause>

  <clause id="30580">
    <literal><![CDATA[
      L(a(x,x * y,x * y) * z,y \ x,(x / y) * (y / x)) = (y \ x) * (L(y \ x,x * y,x) \ z)
    ]]></literal>
    <justification jstring="[para(29161(a,1),30326(a,1,1,1))].">
      <j1 rule="para" parents="29161 30326"/>
    </justification>
  </clause>

  <clause id="30581">
    <literal><![CDATA[
      a(x,y,a(a(x,y,z) * (u \ w),u,z)) * (u * (u \ (a(x,y,z) \ w))) = u * ((u * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(29790(a,1),30558(a,1,1))].">
      <j1 rule="para" parents="29790 30558"/>
    </justification>
  </clause>

  <clause id="30582">
    <literal><![CDATA[
      L((x * (y \ x)) \ (y * z),(1 / (x \ y)) \ (1 / (1 / (y \ x))),x \ y) = (y \ x) \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(30164(a,1),30579(a,1,1))].">
      <j1 rule="para" parents="30164 30579"/>
    </justification>
  </clause>

  <clause id="30583">
    <literal><![CDATA[
      L(((x \ y) * (y \ x)) \ z,y \ x,(x / y) * (y / x)) = (y \ x) * (L(y \ x,x * y,x) \ z)
    ]]></literal>
    <justification jstring="[para(28106(a,1),30580(a,1,1))].">
      <j1 rule="para" parents="28106 30580"/>
    </justification>
  </clause>

  <clause id="30584">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,y * x,y) \ z) = ((y \ x) * (x \ y)) \ z
    ]]></literal>
    <justification jstring="[hyper(26322,a,30583,a),flip(a)].">
      <j1 rule="hyper" parents="26322 30583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30585">
    <literal><![CDATA[
      x * a(y,z * y,z * y) = ((y \ z) * (z \ y)) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,30529,a(flip),b,30584,a)].">
      <j1 rule="hyper" parents="63 30529 30584"/>
    </justification>
  </clause>

  <clause id="30586">
    <literal><![CDATA[
      a(x,y * x,y * x) * z = ((x \ y) * (y \ x)) \ z
    ]]></literal>
    <justification jstring="[hyper(20479,a,30585,a)].">
      <j1 rule="hyper" parents="20479 30585"/>
    </justification>
  </clause>

  <clause id="30587">
    <literal><![CDATA[
      a(x,(((y \ z) * (z \ y)) \ (z * y)) \ u,w) = a(x,L(z * y,z * y,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(30586(a,1),26530(a,1,2,1))].">
      <j1 rule="para" parents="30586 26530"/>
    </justification>
  </clause>

  <clause id="30588">
    <literal><![CDATA[
      a(x,y,a(a(x,y,z) * (u \ w),u,z)) * (a(x,y,z) \ w) = u * ((u * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(357,a,30581,a)].">
      <j1 rule="hyper" parents="357 30581"/>
    </justification>
  </clause>

  <clause id="30590">
    <literal><![CDATA[
      a(x,y,L(z,u,a(x,y,z) * (u \ w))) \ w = u * ((u * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,29938,a(flip),b,30588,a)].">
      <j1 rule="hyper" parents="63 29938 30588"/>
    </justification>
  </clause>

  <clause id="30591">
    <literal><![CDATA[
      L((x * (y \ x)) \ (y * z),(x \ y) * (y \ x),x \ y) = (y \ x) \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(3398(a,1),30582(a,1,2))].">
      <j1 rule="para" parents="3398 30582"/>
    </justification>
  </clause>

  <clause id="30592">
    <literal><![CDATA[
      ((1 / x) \ a(y,z,x)) \ (a(y,z,x) * u) = (x \ 1) * (u * a(((x \ 1) \ 1) * a(y,z,x),x \ 1,u))
    ]]></literal>
    <justification jstring="[para(23107(a,1),29235(a,1,1))].">
      <j1 rule="para" parents="23107 29235"/>
    </justification>
  </clause>

  <clause id="30593">
    <literal><![CDATA[
      x * L(x \ (a(y,x,z) * u),x,a(y,x,z)) = x \ ((x * a(y,x,z)) * u)
    ]]></literal>
    <justification jstring="[para(19988(a,1),29615(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19988 29615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30594">
    <literal><![CDATA[
      x \ ((x * a(y,x,z)) * u) = x * ((a(y,x,z) \ x) \ u)
    ]]></literal>
    <justification jstring="[para(28523(a,1),30593(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28523 30593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30595">
    <literal><![CDATA[
      x \ (y * ((a(z,y,u) \ y) \ x)) = a(z,y,u) * a(y,a(z,y,u),x)
    ]]></literal>
    <justification jstring="[hyper(128,a,30594,a(flip),b,20039,a(flip))].">
      <j1 rule="hyper" parents="128 30594 20039"/>
    </justification>
  </clause>

  <clause id="30596">
    <literal><![CDATA[
      a(x,y,z) \ (y * ((a(x,y,z) \ y) \ u)) = L(1 / u,a(x,y,z),y) \ 1
    ]]></literal>
    <justification jstring="[para(30594(a,1),25971(a,1,2))].">
      <j1 rule="para" parents="30594 25971"/>
    </justification>
  </clause>

  <clause id="30597">
    <literal><![CDATA[
      x \ (y * ((a(z,y,u) \ y) \ x)) = a(y,a(z,y,u),x) * a(z,y,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,19985,a,b,30595,a),flip(a)].">
      <j1 rule="hyper" parents="347 19985 30595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30598">
    <literal><![CDATA[
      a(x,y,z) \ (y * ((a(x,y,z) \ y) \ u)) = L(u,a(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,28754,a(flip),b,30596,a),flip(a)].">
      <j1 rule="hyper" parents="347 28754 30596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30599">
    <literal><![CDATA[
      a(x,y,z) * L(u,a(x,y,z),y) = y * ((a(x,y,z) \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(134,a,28752,a(flip),b,30596,a)].">
      <j1 rule="hyper" parents="134 28752 30596"/>
    </justification>
  </clause>

  <clause id="30600">
    <literal><![CDATA[
      L(1 / (a(x,y,z) \ u),a(x,y,z),y) \ 1 = a(x,y,z) \ (y * L(y \ u,y,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(28392(a,1),30596(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28392 30596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30601">
    <literal><![CDATA[
      x * ((a(y,x,z) \ x) \ a(u,w,x)) = a(y,x,z) * a(u,w,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,12360,a(flip),b,30598,a),flip(a)].">
      <j1 rule="hyper" parents="134 12360 30598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30602">
    <literal><![CDATA[
      L(1 / (a(x,y,z) \ u),a(x,y,z),y) \ 1 = (a(x,y,z) \ y) * (y \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,29902,a(flip),b,30600,a),flip(a)].">
      <j1 rule="hyper" parents="347 29902 30600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30603">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),y) = (a(x,y,z) \ y) * (y \ u)
    ]]></literal>
    <justification jstring="[hyper(28753,a,30602,a)].">
      <j1 rule="hyper" parents="28753 30602"/>
    </justification>
  </clause>

  <clause id="30604">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(z,y,x),y) = (a(x,y,z) \ y) * (y \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,28754,a(flip),b,30602,a)].">
      <j1 rule="hyper" parents="63 28754 30602"/>
    </justification>
  </clause>

  <clause id="30605">
    <literal><![CDATA[
      ((a(x,y,z) \ y) * (y \ u)) \ (a(x,y,z) \ u) = a(y,a(z,y,x),a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(30604(a,1),28838(a,2,1)),flip(a)].">
      <j1 rule="para" parents="30604 28838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30606">
    <literal><![CDATA[
      a(a(x,y,z),y,(a(z,y,x) \ y) * (y \ u)) = a(a(x,y,z),y,a(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(30604(a,1),29278(a,1,3))].">
      <j1 rule="para" parents="30604 29278"/>
    </justification>
  </clause>

  <clause id="30607">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,L(z,u,y))),z * a(u,z,y),a(u,z,y)) = z * L(z \ x,z,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(29163(a,1),30029(a,1,1,2,3))].">
      <j1 rule="para" parents="29163 30029"/>
    </justification>
  </clause>

  <clause id="30608">
    <literal><![CDATA[
      L(x,a(y,L(z,z,a(u,w,v5)),L(z,z,a(u,w,v5))),a(u,w,z) \ v5) = L(x,a(y,z,z),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,30043,a(flip),b,30044,a),flip(a)].">
      <j1 rule="hyper" parents="347 30043 30044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30610">
    <literal><![CDATA[
      L(x,a(y,z,z),a(u,w,z) \ v5) = L(x,a(y,z,z),v5)
    ]]></literal>
    <justification jstring="[para(26464(a,1),30608(a,1,2))].">
      <j1 rule="para" parents="26464 30608"/>
    </justification>
  </clause>

  <clause id="30611">
    <literal><![CDATA[
      L(T(a(x,y,y) \ z,u),a(x,y,y),u) = u \ (z * (a(x,y,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,23394,a(flip),b,30610,a),flip(a)].">
      <j1 rule="hyper" parents="63 23394 30610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30613">
    <literal><![CDATA[
      (a(x,y,y) * z) \ (u * z) = z \ (u * (a(x,y,y) \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,23179,a(flip),b,30611,a)].">
      <j1 rule="hyper" parents="63 23179 30611"/>
    </justification>
  </clause>

  <clause id="30614">
    <literal><![CDATA[
      (a(x,y,y) * z) \ (((z * u) / z) * z) = z \ ((a(x,y,y) \ z) * u)
    ]]></literal>
    <justification jstring="[para(23088(a,1),30613(a,2,2))].">
      <j1 rule="para" parents="23088 30613"/>
    </justification>
  </clause>

  <clause id="30615">
    <literal><![CDATA[
      (a(x,y,y) * z) \ (z * u) = z \ ((a(x,y,y) \ z) * u)
    ]]></literal>
    <justification jstring="[para(12(a,1),30614(a,1,2))].">
      <j1 rule="para" parents="12 30614"/>
    </justification>
  </clause>

  <clause id="30616">
    <literal><![CDATA[
      x \ ((a(y,z,z) \ x) * (u * a(y,z,z))) = R(u,a(y,z,z),x)
    ]]></literal>
    <justification jstring="[hyper(23201,a,30615,a),flip(a)].">
      <j1 rule="hyper" parents="23201 30615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30618">
    <literal><![CDATA[
      (x \ y) \ ((x \ L(y,y,z)) * (u * a(z,y,y))) = R(u,a(z,y,y),x \ y)
    ]]></literal>
    <justification jstring="[para(29457(a,1),30616(a,1,2,1))].">
      <j1 rule="para" parents="29457 30616"/>
    </justification>
  </clause>

  <clause id="30619">
    <literal><![CDATA[
      (x \ y) \ ((x \ L(y,y,z)) * (u * a(z,y,y))) = L(u,a(z,y,y),x \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,23225,a(flip),b,30618,a),flip(a)].">
      <j1 rule="hyper" parents="347 23225 30618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30620">
    <literal><![CDATA[
      L(x,T(y * z,z \ 1),(y * y) \ (y * z)) = L(x,y * ((y * z) \ y),(y * ((y * z) \ y)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(21572,a,30272,a)].">
      <j1 rule="hyper" parents="21572 30272"/>
    </justification>
  </clause>

  <clause id="30621">
    <literal><![CDATA[
      L(x,T(y * z,z \ 1),L(y \ z,y,y)) = L(x,y * ((y * z) \ y),(y * ((y * z) \ y)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2658,a,30620,a)].">
      <j1 rule="hyper" parents="2658 30620"/>
    </justification>
  </clause>

  <clause id="30622">
    <literal><![CDATA[
      L(x,T(y * z,z \ 1),z * (y \ 1)) = L(x,y * ((y * z) \ y),(y * ((y * z) \ y)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,23684,a(flip),b,30621,a)].">
      <j1 rule="hyper" parents="63 23684 30621"/>
    </justification>
  </clause>

  <clause id="30623">
    <literal><![CDATA[
      L(x,y * ((y * z) \ y),(y * ((y * z) \ y)) \ 1) = L(x,y * z,z * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(21722,a,30622,a),flip(a)].">
      <j1 rule="hyper" parents="21722 30622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30625">
    <literal><![CDATA[
      L(x,y * ((y * z) \ y),(z \ y) \ 1) = L(x,y * z,z * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,21563,a(flip),b,30623,a)].">
      <j1 rule="hyper" parents="63 21563 30623"/>
    </justification>
  </clause>

  <clause id="30626">
    <literal><![CDATA[
      L(x,y * (y \ (z \ y)),(z \ y) \ 1) = L(x,y * z,z * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,21880,a(flip),b,30625,a)].">
      <j1 rule="hyper" parents="63 21880 30625"/>
    </justification>
  </clause>

  <clause id="30627">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) \ 1) = L(x,z * y,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(10(a,1),30626(a,1,2))].">
      <j1 rule="para" parents="10 30626"/>
    </justification>
  </clause>

  <clause id="30628">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) \ 1) = L(x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(347,a,27086,a(flip),b,30627,a),flip(a)].">
      <j1 rule="hyper" parents="347 27086 30627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30630">
    <literal><![CDATA[
      L(x,y \ x,y \ x) = (1 / (y / x)) * y
    ]]></literal>
    <justification jstring="[hyper(63,a,9881,a(flip),b,30628,a),flip(a)].">
      <j1 rule="hyper" parents="63 9881 30628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30631">
    <literal><![CDATA[
      L(x,y,L(y,z \ y,z \ y)) = L(x,(1 / (z / y)) * z,y)
    ]]></literal>
    <justification jstring="[para(30630(a,1),1620(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30630 1620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30632">
    <literal><![CDATA[
      a((1 / (x / y)) * x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(((x \ y) \ 1) \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(30630(a,1),27961(a,1,1))].">
      <j1 rule="para" parents="30630 27961"/>
    </justification>
  </clause>

  <clause id="30633">
    <literal><![CDATA[
      L(x,y,L(y,z \ y,z \ y)) = L(x,((z / y) \ 1) * z,y)
    ]]></literal>
    <justification jstring="[hyper(347,a,21622,a(flip),b,30631,a),flip(a)].">
      <j1 rule="hyper" parents="347 21622 30631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30634">
    <literal><![CDATA[
      L(x,y,L(y,z \ y,z \ y)) = L(x,z * (z / y),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,21695,a(flip),b,30633,a),flip(a)].">
      <j1 rule="hyper" parents="347 21695 30633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30635">
    <literal><![CDATA[
      L(x,y,L(y,z \ y,z \ y)) = L(x,z * (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,21681,a(flip),b,30634,a),flip(a)].">
      <j1 rule="hyper" parents="347 21681 30634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30636">
    <literal><![CDATA[
      L(x,y * (z \ y),z) = L(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,29765,a(flip),b,30635,a),flip(a)].">
      <j1 rule="hyper" parents="63 29765 30635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30637">
    <literal><![CDATA[
      L(x,y \ z,y \ z) = L(x,z * y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(21758,a,30636,a),flip(a)].">
      <j1 rule="hyper" parents="21758 30636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30639">
    <literal><![CDATA[
      a(x,y * ((z \ y) \ L(y,u,L(w,y * z,z \ y))),v5) = a(x,z * L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(30637(a,1),29945(a,1,2,2,2,3))].">
      <j1 rule="para" parents="30637 29945"/>
    </justification>
  </clause>

  <clause id="30640">
    <literal><![CDATA[
      a(((x / y) \ 1) * x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(((x \ y) \ 1) \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(23899(a,1),30632(a,1))].">
      <j1 rule="para" parents="23899 30632"/>
    </justification>
  </clause>

  <clause id="30641">
    <literal><![CDATA[
      a(((x \ y) \ 1) \ x,z,u) = a(((y \ x) \ 1) * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(30640,a,23914,a)].">
      <j1 rule="hyper" parents="30640 23914"/>
    </justification>
  </clause>

  <clause id="30642">
    <literal><![CDATA[
      a(L(x,y * x,y * x),z,u) = a(((x \ y) \ 1) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,28026,a,b,30641,a)].">
      <j1 rule="hyper" parents="63 28026 30641"/>
    </justification>
  </clause>

  <clause id="30643">
    <literal><![CDATA[
      a(x,y,L(z,u * x,u * x)) = a(((x \ u) \ 1) * u,y,z)
    ]]></literal>
    <justification jstring="[hyper(29676,a,30642,a)].">
      <j1 rule="hyper" parents="29676 30642"/>
    </justification>
  </clause>

  <clause id="30644">
    <literal><![CDATA[
      a(x,y,z) * a(z,x * u,a(u * x,y,x)) = a(((x \ u) \ 1) * u,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,29926,a,b,30643,a)].">
      <j1 rule="hyper" parents="63 29926 30643"/>
    </justification>
  </clause>

  <clause id="30645">
    <literal><![CDATA[
      a(x,y,z) * a(z,y,a(x,u * x,u)) = a(((x \ u) \ 1) * u,y,z)
    ]]></literal>
    <justification jstring="[para(29939(a,1),30644(a,1,2))].">
      <j1 rule="para" parents="29939 30644"/>
    </justification>
  </clause>

  <clause id="30646">
    <literal><![CDATA[
      a(((x \ y) \ 1) * y,z,u) = a(x,z,L(u,y * x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,29805,a(flip),b,30645,a),flip(a)].">
      <j1 rule="hyper" parents="63 29805 30645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30647">
    <literal><![CDATA[
      a(x * ((y \ x) \ 1),z,u) = a(y,z,L(u,x * y,x))
    ]]></literal>
    <justification jstring="[hyper(23925,a,30646,a)].">
      <j1 rule="hyper" parents="23925 30646"/>
    </justification>
  </clause>

  <clause id="30648">
    <literal><![CDATA[
      a(x,y,L(z,(x * u) * x,x * u)) = a((x * u) * (u \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),30647(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 30647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30649">
    <literal><![CDATA[
      a(x * y,z,L(u,x * (T(x,w) * y),T(x,w))) = a(T(x,w) * (((x * y) \ T(x,w)) \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(1219(a,1),30647(a,2,3,2)),flip(a)].">
      <j1 rule="para" parents="1219 30647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30650">
    <literal><![CDATA[
      a(x,y,L(z,(x * u) * x,x * u)) = a(R(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[para(786(a,1),30648(a,2,1))].">
      <j1 rule="para" parents="786 30648"/>
    </justification>
  </clause>

  <clause id="30651">
    <literal><![CDATA[
      a(x,y,L(z,(x * u) * x,x * u)) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,29684,a(flip),b,30650,a),flip(a)].">
      <j1 rule="hyper" parents="347 29684 30650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30652">
    <literal><![CDATA[
      a(x,y,L(z,L(u,x,x),x * u)) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[para(21698(a,1),30651(a,1,3))].">
      <j1 rule="para" parents="21698 30651"/>
    </justification>
  </clause>

  <clause id="30653">
    <literal><![CDATA[
      a(x * y,z,L(u,x * (T(x,w) * y),T(x,w))) = a(x * (((x * y) \ x) \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(21052(a,1),30649(a,2,1))].">
      <j1 rule="para" parents="21052 30649"/>
    </justification>
  </clause>

  <clause id="30654">
    <literal><![CDATA[
      a(x * y,z,L(u,x * (T(x,w) * y),T(x,w))) = a(x * ((x \ (y \ x)) \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,24716,a(flip),b,30653,a),flip(a)].">
      <j1 rule="hyper" parents="347 24716 30653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30656">
    <literal><![CDATA[
      a(x * y,z,L(u,x * (T(x,w) * y),T(x,w))) = a((y \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,27963,a(flip),b,30654,a),flip(a)].">
      <j1 rule="hyper" parents="347 27963 30654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30657">
    <literal><![CDATA[
      a(x * y,z,L(u,x * (T(x,w) * y),x)) = a((y \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(20041(a,1),30656(a,1,3))].">
      <j1 rule="para" parents="20041 30656"/>
    </justification>
  </clause>

  <clause id="30658">
    <literal><![CDATA[
      a(x * y,z,L(u,x * (x * y),x)) = a((y \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(110(a,1),30657(a,1,3,2,2,1))].">
      <j1 rule="para" parents="110 30657"/>
    </justification>
  </clause>

  <clause id="30660">
    <literal><![CDATA[
      a(x * y,z,L(u,L(y,x,x),x)) = a((y \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(3609(a,1),30658(a,1,3))].">
      <j1 rule="para" parents="3609 30658"/>
    </justification>
  </clause>

  <clause id="30661">
    <literal><![CDATA[
      a(x * y,z,L(u,y,x)) = a((y \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(30133(a,1),30660(a,1,3))].">
      <j1 rule="para" parents="30133 30660"/>
    </justification>
  </clause>

  <clause id="30662">
    <literal><![CDATA[
      a((x \ 1) \ y,z,u) \ u != w
    ]]></literal>
    <literal><![CDATA[
      L(u,z,L(y * x,x,y)) = w
    ]]></literal>
    <justification jstring="[para(30661(a,1),29702(a,1,1))].">
      <j1 rule="para" parents="30661 29702"/>
    </justification>
  </clause>

  <clause id="30663">
    <literal><![CDATA[
      L(x,y,L(z * u,u,z)) = L(x,y,(u \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(30662,a,28841,a(flip))].">
      <j1 rule="hyper" parents="30662 28841"/>
    </justification>
  </clause>

  <clause id="30664">
    <literal><![CDATA[
      L(x,y,(z \ (u \ 1)) \ 1) = L(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(25986,a,30663,a)].">
      <j1 rule="hyper" parents="25986 30663"/>
    </justification>
  </clause>

  <clause id="30665">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ (u \ 1)) = L(x,y,(z \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(21596,a,30664,a),flip(a)].">
      <j1 rule="hyper" parents="21596 30664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30666">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ u) \ 1) = L(x,y,z \ (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(21514,a,30665,a),flip(a)].">
      <j1 rule="hyper" parents="21514 30665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30667">
    <literal><![CDATA[
      (x \ 1) * (y * a(((x \ 1) \ 1) * a(z,u,x),x \ 1,y)) = L(x \ y,x,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(21151,a,30592,a),flip(a)].">
      <j1 rule="hyper" parents="21151 30592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30668">
    <literal><![CDATA[
      (x \ 1) * (y * a((x \ 1) \ a(z,u,x),x \ 1,y)) = L(x \ y,x,a(z,u,x))
    ]]></literal>
    <justification jstring="[para(15052(a,1),30667(a,1,2,2,1))].">
      <j1 rule="para" parents="15052 30667"/>
    </justification>
  </clause>

  <clause id="30669">
    <literal><![CDATA[
      (x \ 1) * (y * a((x \ 1) \ a(z,u,x),x,y)) = L(x \ y,x,a(z,u,x))
    ]]></literal>
    <justification jstring="[para(14950(a,1),30668(a,1,2,2))].">
      <j1 rule="para" parents="14950 30668"/>
    </justification>
  </clause>

  <clause id="30670">
    <literal><![CDATA[
      (x \ 1) * (y * a(L(x,z,u),x,y)) = L(x \ y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[para(29220(a,1),30669(a,1,2,2))].">
      <j1 rule="para" parents="29220 30669"/>
    </justification>
  </clause>

  <clause id="30671">
    <literal><![CDATA[
      (x \ 1) * (y * a(x,x,L(y,z,u))) = L(x \ y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[para(29675(a,1),30670(a,1,2,2))].">
      <j1 rule="para" parents="29675 30670"/>
    </justification>
  </clause>

  <clause id="30672">
    <literal><![CDATA[
      (x \ a(x,x,L(y,z,u))) * y = L(x \ y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(26332,a,30671,a)].">
      <j1 rule="hyper" parents="26332 30671"/>
    </justification>
  </clause>

  <clause id="30673">
    <literal><![CDATA[
      L(x \ y,x,a(z,u,x)) / ((x \ 1) * y) = a(x,x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,30672,a(flip),b,26327,a)].">
      <j1 rule="hyper" parents="131 30672 26327"/>
    </justification>
  </clause>

  <clause id="30674">
    <literal><![CDATA[
      L(x \ y,z,a(u,x,x)) / ((x \ 1) * y) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(29890(a,1),30673(a,1,1))].">
      <j1 rule="para" parents="29890 30673"/>
    </justification>
  </clause>

  <clause id="30675">
    <literal><![CDATA[
      L(x \ y,z,a(u,x,x)) / ((x \ 1) * y) = a(x,x,L(y,x * z,u))
    ]]></literal>
    <justification jstring="[para(30036(a,1),30673(a,1,1))].">
      <j1 rule="para" parents="30036 30673"/>
    </justification>
  </clause>

  <clause id="30676">
    <literal><![CDATA[
      a(x,x,L(y,x * z,u)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,30674,a(flip),b,30675,a),flip(a)].">
      <j1 rule="hyper" parents="63 30674 30675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30677">
    <literal><![CDATA[
      a(x,x,L(y,z * x,u)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(21617(a,1),30676(a,1,3))].">
      <j1 rule="para" parents="21617 30676"/>
    </justification>
  </clause>

  <clause id="30678">
    <literal><![CDATA[
      (a(x,y,L(z,u,w)) * a(x,y,L(z,u,w))) * L(L(z,y,x),u,w) = L(z,u,w) * a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,21803,a(flip),b,29261,a),flip(a)].">
      <j1 rule="hyper" parents="347 21803 29261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30679">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,L(x,y,z)) = (a(u,w,x) * a(u,w,x)) * L(L(x,w,u),y,z)
    ]]></literal>
    <justification jstring="[para(27455(a,1),30678(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27455 30678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30680">
    <literal><![CDATA[
      L((a(x,y,z) * a(x,y,z)) * L(z,y,x),u,w) = L(z,u,w) * a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,3176,a,b,30679,a)].">
      <j1 rule="hyper" parents="347 3176 30679"/>
    </justification>
  </clause>

  <clause id="30682">
    <literal><![CDATA[
      L(L((a(x,y,z) * a(x,y,z)) * z,y,x),u,w) = L(z,u,w) * a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(3176(a,2),30680(a,1,1))].">
      <j1 rule="para" parents="3176 30680"/>
    </justification>
  </clause>

  <clause id="30683">
    <literal><![CDATA[
      L(L(x * (a(y,z,x) * a(y,z,x)),z,y),u,w) = L(x,u,w) * a(y,z,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(23221(a,1),30682(a,1,1,1))].">
      <j1 rule="para" parents="23221 30682"/>
    </justification>
  </clause>

  <clause id="30684">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,L(x,y,z)) = L(x * a(u,w,x),y,z)
    ]]></literal>
    <justification jstring="[para(28893(a,1),30683(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28893 30683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30685">
    <literal><![CDATA[
      R(x,(y * z) * L(u * a(w,v5,u),z,y),v6) = R(x,y * (z * L(u,v5,w)),v6)
    ]]></literal>
    <justification jstring="[para(30684(a,1),29279(a,1,2,2))].">
      <j1 rule="para" parents="30684 29279"/>
    </justification>
  </clause>

  <clause id="30686">
    <literal><![CDATA[
      R(x,y * (z * (u * a(w,v5,u))),v6) = R(x,y * (z * L(u,v5,w)),v6)
    ]]></literal>
    <justification jstring="[para(97(a,1),30685(a,1,2))].">
      <j1 rule="para" parents="97 30685"/>
    </justification>
  </clause>

  <clause id="30687">
    <literal><![CDATA[
      R(x,y * ((z * a(u,w,z)) * v5),v6) = R(x,y * (v5 * L(z,w,u)),v6)
    ]]></literal>
    <justification jstring="[hyper(22441,a,30686,a)].">
      <j1 rule="hyper" parents="22441 30686"/>
    </justification>
  </clause>

  <clause id="30688">
    <literal><![CDATA[
      R(x,(a(y,y,z) * (u * z)) * w,v5) = R(x,w * (u * L(z,y,y)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,29637,a,b,30687,a)].">
      <j1 rule="hyper" parents="63 29637 30687"/>
    </justification>
  </clause>

  <clause id="30689">
    <literal><![CDATA[
      R(x,y,(z \ a(z,z,u \ ((u \ w) \ R(u,v5,u)))) * (w \ u)) = R(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[hyper(347,a,30262,a(flip),b,29312,a),flip(a)].">
      <j1 rule="hyper" parents="347 30262 29312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30691">
    <literal><![CDATA[
      R(x,y,(z \ a(z,z,u * ((u \ w) \ R(u,v5,u)))) * (w \ u)) = R(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(29444(a,1),30689(a,1,3,1,2))].">
      <j1 rule="para" parents="29444 30689"/>
    </justification>
  </clause>

  <clause id="30692">
    <literal><![CDATA[
      R(x,y,(z \ a(z,z,u * ((u \ w) \ u))) * (w \ u)) = R(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(587(a,1),30691(a,1,3,1,2,3,2,2))].">
      <j1 rule="para" parents="587 30691"/>
    </justification>
  </clause>

  <clause id="30693">
    <literal><![CDATA[
      R(x,y,(z \ a(z,z,u \ w)) * (w \ u)) = R(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(29445(a,1),30692(a,1,3,1,2))].">
      <j1 rule="para" parents="29445 30692"/>
    </justification>
  </clause>

  <clause id="30694">
    <literal><![CDATA[
      R(x,y,(z \ a(z,z,u * w)) * (w \ u)) = R(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(29444(a,1),30693(a,1,3,1,2))].">
      <j1 rule="para" parents="29444 30693"/>
    </justification>
  </clause>

  <clause id="30696">
    <literal><![CDATA[
      R(x,y,z \ (u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,L(z,z,w * u) * (u \ w)) = v5
    ]]></literal>
    <justification jstring="[para(30694(a,1),29293(a,1))].">
      <j1 rule="para" parents="30694 29293"/>
    </justification>
  </clause>

  <clause id="30697">
    <literal><![CDATA[
      (a(x,y,z) \ T(u,T(w,v5))) * (T(u,T(w,v5)) \ w) = a(x,y,L(z,T(u,T(w,v5)),u * w)) \ w
    ]]></literal>
    <justification jstring="[para(16844(a,1),29324(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="16844 29324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30700">
    <literal><![CDATA[
      (a(x,y,z) \ T(u,T(w,v5))) * (T(u,T(w,v5)) \ w) = a(x,y,L(z,u,u * w)) \ w
    ]]></literal>
    <justification jstring="[para(21616(a,1),30697(a,2,1,3))].">
      <j1 rule="para" parents="21616 30697"/>
    </justification>
  </clause>

  <clause id="30702">
    <literal><![CDATA[
      T(a(x,y,z) \ u,T(w,v5)) * (T(u,T(w,v5)) \ w) = a(x,y,L(z,u,u * w)) \ w
    ]]></literal>
    <justification jstring="[para(23175(a,2),30700(a,1,1))].">
      <j1 rule="para" parents="23175 30700"/>
    </justification>
  </clause>

  <clause id="30703">
    <literal><![CDATA[
      a(x,y,L(z,u,u * w)) \ w = (w / u) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,25891,a(flip),b,30702,a),flip(a)].">
      <j1 rule="hyper" parents="63 25891 30702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30705">
    <literal><![CDATA[
      a(x,y,L(z,z,u)) \ u = (u / z) * (a(x,y,z) \ z)
    ]]></literal>
    <justification jstring="[para(12450(a,1),30703(a,1,1))].">
      <j1 rule="para" parents="12450 30703"/>
    </justification>
  </clause>

  <clause id="30706">
    <literal><![CDATA[
      a(x,y,L(z,u / w,(w \ u) * v5)) \ v5 = (v5 / (u / w)) * (a(x,y,z) \ (u / w))
    ]]></literal>
    <justification jstring="[para(21469(a,1),30703(a,1,1,3))].">
      <j1 rule="para" parents="21469 30703"/>
    </justification>
  </clause>

  <clause id="30707">
    <literal><![CDATA[
      a(x,y,L(z,z,u)) \ u = (u / z) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(28841(a,2),30705(a,2,2))].">
      <j1 rule="para" parents="28841 30705"/>
    </justification>
  </clause>

  <clause id="30708">
    <literal><![CDATA[
      x \ ((x / y) * L(y,z,u)) = a(u,z,L(y,y,x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(128,a,30707,a(flip),b,28348,a)].">
      <j1 rule="hyper" parents="128 30707 28348"/>
    </justification>
  </clause>

  <clause id="30709">
    <literal><![CDATA[
      (x * L(y,z,u)) / (x * y) = a(u,z,L(y,y,x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,21414,a,b,30708,a)].">
      <j1 rule="hyper" parents="63 21414 30708"/>
    </justification>
  </clause>

  <clause id="30710">
    <literal><![CDATA[
      (x * L(y,z,u)) / (x * y) = L(a(u,z,y) \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,29136,a,b,30709,a),flip(a)].">
      <j1 rule="hyper" parents="347 29136 30709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30711">
    <literal><![CDATA[
      (L(a(a(x,y,z),u,w) \ 1,w,v5) * v5) * w = v5 * (w * R(a(x,y,a(z,u,w)),v5,w))
    ]]></literal>
    <justification jstring="[para(30710(a,1),29881(a,1,1,1))].">
      <j1 rule="para" parents="30710 29881"/>
    </justification>
  </clause>

  <clause id="30712">
    <literal><![CDATA[
      a(x,y,L(z,u,(u \ 1) * w)) \ w = (w / (1 / u)) * (a(x,y,z) \ (1 / u))
    ]]></literal>
    <justification jstring="[para(3189(a,1),30706(a,1,1,3))].">
      <j1 rule="para" parents="3189 30706"/>
    </justification>
  </clause>

  <clause id="30713">
    <literal><![CDATA[
      a(x,y,L(z,u,w * u)) \ w = (w / (1 / u)) * (a(x,y,z) \ (1 / u))
    ]]></literal>
    <justification jstring="[para(24912(a,1),30712(a,1,1))].">
      <j1 rule="para" parents="24912 30712"/>
    </justification>
  </clause>

  <clause id="30714">
    <literal><![CDATA[
      (x / (1 / y)) * (a(z,u,w) \ (1 / y)) != v5
    ]]></literal>
    <literal><![CDATA[
      (a(z,u,w) \ y) * (y \ x) = v5
    ]]></literal>
    <justification jstring="[para(30713(a,1),29328(a,1))].">
      <j1 rule="para" parents="30713 29328"/>
    </justification>
  </clause>

  <clause id="30715">
    <literal><![CDATA[
      (L(a(x,y,a(z,u,w)) \ 1,z,v5) * v5) * z = v5 * (z * R(a(x,y,a(w,u,z)),v5,z))
    ]]></literal>
    <justification jstring="[para(29790(a,1),30711(a,1,1,1,1,1))].">
      <j1 rule="para" parents="29790 30711"/>
    </justification>
  </clause>

  <clause id="30716">
    <literal><![CDATA[
      (L(a(x,y,a(z,u,w)),z,v5) * v5) * z = v5 * (z * R(a(x,y,a(w,u,z)),v5,z))
    ]]></literal>
    <justification jstring="[para(26334(a,1),30715(a,1,1,1,1))].">
      <j1 rule="para" parents="26334 30715"/>
    </justification>
  </clause>

  <clause id="30717">
    <literal><![CDATA[
      (a(x,y,L(a(z,u,w),z,v5)) * v5) * z = v5 * (z * R(a(x,y,a(w,u,z)),v5,z))
    ]]></literal>
    <justification jstring="[para(29113(a,2),30716(a,1,1,1))].">
      <j1 rule="para" parents="29113 30716"/>
    </justification>
  </clause>

  <clause id="30718">
    <literal><![CDATA[
      (a(x,y,a(z,u,L(w,z,v5))) * v5) * z = v5 * (z * R(a(x,y,a(w,u,z)),v5,z))
    ]]></literal>
    <justification jstring="[para(29113(a,2),30717(a,1,1,1,3))].">
      <j1 rule="para" parents="29113 30717"/>
    </justification>
  </clause>

  <clause id="30719">
    <literal><![CDATA[
      (x * y) * a(z,u,a(y,w,L(v5,y,x))) = x * (y * R(a(z,u,a(v5,w,y)),x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,29428,a(flip),b,30718,a)].">
      <j1 rule="hyper" parents="63 29428 30718"/>
    </justification>
  </clause>

  <clause id="30720">
    <literal><![CDATA[
      (x * y) * a(z,u,a(y,w,L(v5,y,x))) = x * (y * a(z,u,L(a(v5,w,y),x,y)))
    ]]></literal>
    <justification jstring="[para(29117(a,2),30719(a,2,2,2))].">
      <j1 rule="para" parents="29117 30719"/>
    </justification>
  </clause>

  <clause id="30721">
    <literal><![CDATA[
      (x * y) * a(z,u,a(y,w,L(v5,y,x))) = x * (y * a(z,u,a(v5,w,y)))
    ]]></literal>
    <justification jstring="[para(12360(a,1),30720(a,2,2,2,3))].">
      <j1 rule="para" parents="12360 30720"/>
    </justification>
  </clause>

  <clause id="30723">
    <literal><![CDATA[
      (x * y) * a(z,u,a(y,w,L(v5,y,x))) = x * L(y,w,a(z,u,v5))
    ]]></literal>
    <justification jstring="[para(29807(a,1),30721(a,2,2))].">
      <j1 rule="para" parents="29807 30721"/>
    </justification>
  </clause>

  <clause id="30724">
    <literal><![CDATA[
      (x \ (a(y,z,u) * w)) * a(x,z,a(u,x \ (a(y,z,u) * w),y)) = a(y,z,u) * (x \ w)
    ]]></literal>
    <justification jstring="[hyper(347,a,28785,a(flip),b,29960,a),flip(a)].">
      <j1 rule="hyper" parents="347 28785 29960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30725">
    <literal><![CDATA[
      (x \ (a(y,z,u) * w)) * a(x,z,a(u,x \ (a(y,z,u) * w),y)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) * (x \ w) = v5
    ]]></literal>
    <justification jstring="[para(29960(a,2),28786(a,1))].">
      <j1 rule="para" parents="29960 28786"/>
    </justification>
  </clause>

  <clause id="30726">
    <literal><![CDATA[
      R(x,y,(((z * z) \ u) * (w * v5)) \ (w * (u * v5))) = L(x,y,a((z * z) \ u,v5 \ K(v6,v7),w))
    ]]></literal>
    <justification jstring="[hyper(63,a,22272,a(flip),b,30183,a)].">
      <j1 rule="hyper" parents="63 22272 30183"/>
    </justification>
  </clause>

  <clause id="30727">
    <literal><![CDATA[
      R(x,y,((z * u) * w) \ (z * (w * u))) = L(x,y,a((v5 * v5) \ w,u \ K(v6,v7),z))
    ]]></literal>
    <justification jstring="[hyper(22245,a,30726,a)].">
      <j1 rule="hyper" parents="22245 30726"/>
    </justification>
  </clause>

  <clause id="30729">
    <literal><![CDATA[
      R(x,y,((z * u) * w) \ (z * (w * u))) = L(x,y,a((v5 * v5) \ w,u,z))
    ]]></literal>
    <justification jstring="[para(24260(a,1),30727(a,2,3))].">
      <j1 rule="para" parents="24260 30727"/>
    </justification>
  </clause>

  <clause id="30730">
    <literal><![CDATA[
      R(x,y,((z * u) * w) \ (z * (w * u))) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,23945,a(flip),b,30729,a),flip(a)].">
      <j1 rule="hyper" parents="347 23945 30729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30731">
    <literal><![CDATA[
      R(x,y,((z * (K(u,w) * (v5 \ v6))) * T(v5,v7)) \ (z * (K(v5,v7) * (K(u,T(w,v5)) * v6)))) = L(x,y,a(T(v5,v7),K(u,w) * (v5 \ v6),z))
    ]]></literal>
    <justification jstring="[para(19548(a,2),30730(a,1,3,2,2))].">
      <j1 rule="para" parents="19548 30730"/>
    </justification>
  </clause>

  <clause id="30732">
    <literal><![CDATA[
      L(x,y,a(z,y,u)) * L(y \ 1,a(z,y,u),a(z,y,u)) = (x * ((y \ 1) * a(z,y,u))) * (a(z,y,u) \ 1)
    ]]></literal>
    <justification jstring="[para(15417(a,1),30464(a,1,2))].">
      <j1 rule="para" parents="15417 30464"/>
    </justification>
  </clause>

  <clause id="30733">
    <literal><![CDATA[
      (x * ((y \ 1) * a(z,y,u))) * (a(z,y,u) \ 1) = L(x,y,a(z,y,u)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(28339(a,1),30732(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28339 30732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30735">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,(w \ v5) * v6)),(w \ v5) * v6,a(u,z,y)) = L(x,a(u,z,y),(w \ (v5 \ 1)) * v6)
    ]]></literal>
    <justification jstring="[para(24334(a,1),30027(a,1,1,2,3))].">
      <j1 rule="para" parents="24334 30027"/>
    </justification>
  </clause>

  <clause id="30736">
    <literal><![CDATA[
      L(x,a(y,z,u),(w \ (v5 \ 1)) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,u),(w \ v5) * v6) = v7
    ]]></literal>
    <justification jstring="[para(30735(a,1),29948(a,1))].">
      <j1 rule="para" parents="30735 29948"/>
    </justification>
  </clause>

  <clause id="30737">
    <literal><![CDATA[
      L(x \ y,a(z,y,y),u) * u = (x \ y) * (((u / a(z,y,y)) * (x \ (a(z,y,y) * y))) / (x \ y))
    ]]></literal>
    <justification jstring="[para(30610(a,1),29421(a,1,1))].">
      <j1 rule="para" parents="30610 29421"/>
    </justification>
  </clause>

  <clause id="30738">
    <literal><![CDATA[
      L(x \ y,a(z,y,y),u) * u = (x \ y) * (((a(z,y,y) \ u) * (x \ (a(z,y,y) * y))) / (x \ y))
    ]]></literal>
    <justification jstring="[para(12666(a,1),30737(a,2,2,1,1))].">
      <j1 rule="para" parents="12666 30737"/>
    </justification>
  </clause>

  <clause id="30740">
    <literal><![CDATA[
      L(x \ y,a(z,y,y),u) * u = (x \ y) * (((a(z,y,y) \ u) * (a(z,y,y) * (x \ y))) / (x \ y))
    ]]></literal>
    <justification jstring="[para(29420(a,1),30738(a,2,2,1,2))].">
      <j1 rule="para" parents="29420 30738"/>
    </justification>
  </clause>

  <clause id="30741">
    <literal><![CDATA[
      L(x \ y,a(z,y,y),u) * u = (x \ y) * (((u * a(z,y,y)) * (a(z,y,y) \ (x \ y))) / (x \ y))
    ]]></literal>
    <justification jstring="[para(28640(a,1),30740(a,2,2,1))].">
      <j1 rule="para" parents="28640 30740"/>
    </justification>
  </clause>

  <clause id="30742">
    <literal><![CDATA[
      L(x \ y,a(z,y,y),u) * u = (x \ y) * (((u * a(z,y,y)) * (x \ L(y,y,z))) / (x \ y))
    ]]></literal>
    <justification jstring="[para(29457(a,1),30741(a,2,2,1,2))].">
      <j1 rule="para" parents="29457 30741"/>
    </justification>
  </clause>

  <clause id="30743">
    <literal><![CDATA[
      L(x \ y,a(z,y,y),u) * u = (x \ y) * ((x \ y) \ ((x \ L(y,y,z)) * (u * a(z,y,y))))
    ]]></literal>
    <justification jstring="[para(29638(a,1),30742(a,2,2))].">
      <j1 rule="para" parents="29638 30742"/>
    </justification>
  </clause>

  <clause id="30744">
    <literal><![CDATA[
      R(x,y,z) \ (R((x \ 1) \ 1,y,z) * (L(u,R(x,y,z) \ 1,R(x,y,z) \ 1) \ 1)) = x \ ((x \ 1) \ (u \ 1))
    ]]></literal>
    <justification jstring="[para(4725(a,2),29522(a,1,2,1))].">
      <j1 rule="para" parents="4725 29522"/>
    </justification>
  </clause>

  <clause id="30745">
    <literal><![CDATA[
      a(x,y,z * (a(u,u,(u * u) \ w) * (v5 \ (((u * u) \ w) \ 1)))) = a(x,y,z * (v5 \ ((u \ (u \ w)) \ 1)))
    ]]></literal>
    <justification jstring="[para(14922(a,1),29557(a,1,3,2,1))].">
      <j1 rule="para" parents="14922 29557"/>
    </justification>
  </clause>

  <clause id="30746">
    <literal><![CDATA[
      a(x,y,z * (a(u,u,w) * (v5 \ (((u * u) \ w) \ 1)))) = a(x,y,z * (v5 \ ((u \ (u \ w)) \ 1)))
    ]]></literal>
    <justification jstring="[para(14948(a,1),30745(a,1,3,2,1))].">
      <j1 rule="para" parents="14948 30745"/>
    </justification>
  </clause>

  <clause id="30747">
    <literal><![CDATA[
      a(x,y,z * (a(u,u,w) * (v5 \ ((u * u) \ w)))) = a(x,y,z * (v5 \ ((u \ (u \ w)) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(63,a,24986,a(flip),b,30746,a)].">
      <j1 rule="hyper" parents="63 24986 30746"/>
    </justification>
  </clause>

  <clause id="30749">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w \ (w \ v5)) \ 1))) = a(x,y,z * ((u \ v5) * a(w,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,25731,a(flip),b,30747,a),flip(a)].">
      <j1 rule="hyper" parents="63 25731 30747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30751">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w \ (w \ v5)) \ 1))) = a(x,y,z * (u \ L(v5,w,w)))
    ]]></literal>
    <justification jstring="[hyper(347,a,29556,a(flip),b,30749,a),flip(a)].">
      <j1 rule="hyper" parents="347 29556 30749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30752">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ (w \ v5)))) = a(x,y,z * (u \ L(v5,w,w)))
    ]]></literal>
    <justification jstring="[hyper(24581,a,30751,a)].">
      <j1 rule="hyper" parents="24581 30751"/>
    </justification>
  </clause>

  <clause id="30753">
    <literal><![CDATA[
      a(x,y,x * (L(z,x,x) \ u)) = a(x,y,x * (z \ L(u,x,x)))
    ]]></literal>
    <justification jstring="[hyper(29643,a,30752,a)].">
      <j1 rule="hyper" parents="29643 30752"/>
    </justification>
  </clause>

  <clause id="30754">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (a(x,y,z) * L(u,a(x,y,z),y * a(x,y,z))) = a(a(x,y,z),y,y \ u) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),29617(a,1,1,2))].">
      <j1 rule="para" parents="10 29617"/>
    </justification>
  </clause>

  <clause id="30756">
    <literal><![CDATA[
      L(x,y,a(z,(a(z,y,u) * (w * x)) * x,u)) = (a(z,y,a(x,w,u)) \ w) \ (a(z,y,u) \ (a(z,y,u) * (w * x)))
    ]]></literal>
    <justification jstring="[para(29790(a,1),30218(a,2,1,1))].">
      <j1 rule="para" parents="29790 30218"/>
    </justification>
  </clause>

  <clause id="30757">
    <literal><![CDATA[
      x \ ((a(y,z,a(u,u,w)) * (v5 \ ((v5 * x) * v6))) / (a(u,u,a(y,z,w)) * v6)) = a(v5,x,a(u,u,a(y,z,w)) * v6)
    ]]></literal>
    <justification jstring="[para(30466(a,1),30473(a,1,2,1))].">
      <j1 rule="para" parents="30466 30473"/>
    </justification>
  </clause>

  <clause id="30758">
    <literal><![CDATA[
      (a(x,x,a(y,z,u)) * w) / L(v5,v5 * w,a(x,z,a(u,x,L(y,v6,v7)))) = a(u,x,a(x,z,L(y,v6,v7))) * (w / v5)
    ]]></literal>
    <justification jstring="[para(29790(a,1),30496(a,1,2,3))].">
      <j1 rule="para" parents="29790 30496"/>
    </justification>
  </clause>

  <clause id="30759">
    <literal><![CDATA[
      L(x,y,a(z,(a(z,y,u) * (w * x)) * x,u)) = (a(z,y,a(x,w,u)) * w) \ (a(z,y,u) \ (a(z,y,u) * (w * x)))
    ]]></literal>
    <justification jstring="[para(28387(a,1),30756(a,2,1))].">
      <j1 rule="para" parents="28387 30756"/>
    </justification>
  </clause>

  <clause id="30760">
    <literal><![CDATA[
      (a(x,x,a(y,z,u)) * w) / L(v5,v5 * w,a(x,x,a(y,z,u))) = a(u,x,a(x,z,L(y,v6,v7))) * (w / v5)
    ]]></literal>
    <justification jstring="[para(30492(a,1),30758(a,1,2,3))].">
      <j1 rule="para" parents="30492 30758"/>
    </justification>
  </clause>

  <clause id="30761">
    <literal><![CDATA[
      a(x,y,a(y,z,L(u,w,v5))) * (v6 / v7) = (a(y,y,a(u,z,x)) * v6) / v7
    ]]></literal>
    <justification jstring="[para(30447(a,1),30760(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30447 30760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30763">
    <literal><![CDATA[
      a(x,y,a(y,z,L(u,w,v5))) * (v6 / v7) = v6 / (v7 * a(y,y,a(u,z,x)))
    ]]></literal>
    <justification jstring="[hyper(347,a,30469,a(flip),b,30761,a),flip(a)].">
      <j1 rule="hyper" parents="347 30469 30761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30764">
    <literal><![CDATA[
      x / (y * a(z,z,a(u,w,v5))) = a(z,z,a(u,w,v5)) * (x / y)
    ]]></literal>
    <justification jstring="[para(29841(a,1),30763(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29841 30763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30765">
    <literal><![CDATA[
      x / (a(y,y,a(z,u,w)) * v5) = a(y,y,a(z,u,w)) * (x / v5)
    ]]></literal>
    <justification jstring="[hyper(20220,a,30764,a)].">
      <j1 rule="hyper" parents="20220 30764"/>
    </justification>
  </clause>

  <clause id="30766">
    <literal><![CDATA[
      x \ (a(y,y,a(z,u,w)) * ((a(z,u,a(y,y,w)) * (v5 \ ((v5 * x) * v6))) / v6)) = a(v5,x,a(y,y,a(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[para(30765(a,1),30757(a,1,2))].">
      <j1 rule="para" parents="30765 30757"/>
    </justification>
  </clause>

  <clause id="30767">
    <literal><![CDATA[
      L(x,y,a(z,(a(z,y,u) * (w * x)) * x,u)) = (w * a(z,w,a(u,y,x))) \ (a(z,y,u) \ (a(z,y,u) * (w * x)))
    ]]></literal>
    <justification jstring="[hyper(347,a,29873,a(flip),b,30759,a),flip(a)].">
      <j1 rule="hyper" parents="347 29873 30759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30768">
    <literal><![CDATA[
      x \ (a(y,y,a(z,u,w)) * (a(z,u,a(y,y,w)) * ((v5 \ ((v5 * x) * v6)) / v6))) = a(v5,x,a(y,y,a(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[para(30443(a,1),30766(a,1,2,2))].">
      <j1 rule="para" parents="30443 30766"/>
    </justification>
  </clause>

  <clause id="30769">
    <literal><![CDATA[
      L(x,y,a(z,(a(z,y,u) * (w * x)) * x,u)) = (w * a(z,w,a(u,y,x))) \ (w * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),30767(a,2,2))].">
      <j1 rule="para" parents="9 30767"/>
    </justification>
  </clause>

  <clause id="30770">
    <literal><![CDATA[
      L(x,y,a(z,(a(z,y,u) * (w * x)) * x,u)) = L(x,w,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,29912,a(flip),b,30769,a),flip(a)].">
      <j1 rule="hyper" parents="347 29912 30769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30772">
    <literal><![CDATA[
      a(x,y,a(z,z,a(u,w,v5)) * v6) = y \ ((x \ ((x * y) * v6)) / v6)
    ]]></literal>
    <justification jstring="[para(29813(a,1),30768(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29813 30768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30773">
    <literal><![CDATA[
      a(x,y,a(z,z,a(u,w,v5)) * v6) = a(x,y,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,23139,a,b,30772,a),flip(a)].">
      <j1 rule="hyper" parents="347 23139 30772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30775">
    <literal><![CDATA[
      a(x,y,z * a(u,u,a(w,v5,v6))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(24180,a,30773,a)].">
      <j1 rule="hyper" parents="24180 30773"/>
    </justification>
  </clause>

  <clause id="30776">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v5))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(29125(a,1),30773(a,1,3))].">
      <j1 rule="para" parents="29125 30773"/>
    </justification>
  </clause>

  <clause id="30777">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,w,v5)) * v6) = a(x,y,v6)
    ]]></literal>
    <justification jstring="[para(29786(a,1),30773(a,1,3,1))].">
      <j1 rule="para" parents="29786 30773"/>
    </justification>
  </clause>

  <clause id="30778">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,z,v5))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(29847(a,1),30775(a,1,3))].">
      <j1 rule="para" parents="29847 30775"/>
    </justification>
  </clause>

  <clause id="30779">
    <literal><![CDATA[
      a(x,y \ z,a(u,w,v5)) = a(x,y * z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(30093,a,30776,a)].">
      <j1 rule="hyper" parents="30093 30776"/>
    </justification>
  </clause>

  <clause id="30780">
    <literal><![CDATA[
      a(x * (x * y),z,a(u,w,v5)) = a(y,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(29778,a,30776,a)].">
      <j1 rule="hyper" parents="29778 30776"/>
    </justification>
  </clause>

  <clause id="30782">
    <literal><![CDATA[
      a(x,y,a(z * (z * u),w,v5)) = a(x,y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,29697,a,b,30776,a)].">
      <j1 rule="hyper" parents="63 29697 30776"/>
    </justification>
  </clause>

  <clause id="30783">
    <literal><![CDATA[
      a(x,y,a(z,u \ w,v5)) = a(x,y,a(z,w * u,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,30084,a(flip),b,30776,a)].">
      <j1 rule="hyper" parents="63 30084 30776"/>
    </justification>
  </clause>

  <clause id="30784">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w \ v5,w,w \ (v6 \ 1)))) = a(x,y,a(z,u,v6 * (((v6 \ 1) / w) * v5)))
    ]]></literal>
    <justification jstring="[para(10194(a,1),30776(a,1,3,3)),flip(a)].">
      <j1 rule="para" parents="10194 30776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30785">
    <literal><![CDATA[
      a(x,y,a(z,u,w \ v5)) = a(x,y,a(z,u,w * v5))
    ]]></literal>
    <justification jstring="[para(14958(a,1),30776(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14958 30776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30786">
    <literal><![CDATA[
      a(x,y \ z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y * z,a(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(30776(a,1),30092(a,1))].">
      <j1 rule="para" parents="30776 30092"/>
    </justification>
  </clause>

  <clause id="30787">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,z,v5))) = a(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,29840,a,b,30778,a),flip(a)].">
      <j1 rule="hyper" parents="347 29840 30778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30789">
    <literal><![CDATA[
      (x * y) * a(z,u,a(y,w,v5)) = x * L(y,w,a(z,u,v5))
    ]]></literal>
    <justification jstring="[para(30778(a,1),30723(a,1,2))].">
      <j1 rule="para" parents="30778 30723"/>
    </justification>
  </clause>

  <clause id="30790">
    <literal><![CDATA[
      L(x * a(y,x,a(z,z,u)),z * a(u,z,y),a(u,z,y)) = z * L(z \ x,z,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(30787(a,1),30607(a,1,1,2))].">
      <j1 rule="para" parents="30787 30607"/>
    </justification>
  </clause>

  <clause id="30791">
    <literal><![CDATA[
      a(x \ y,a(x \ y,z,u),w) = a(w,x * y,a(u,z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(63,a,26601,a,b,30779,a)].">
      <j1 rule="hyper" parents="63 26601 30779"/>
    </justification>
  </clause>

  <clause id="30792">
    <literal><![CDATA[
      a(x,y * z,a(y \ z,u * (y \ z),u)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,29355,a(flip),b,30779,a),flip(a)].">
      <j1 rule="hyper" parents="63 29355 30779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30793">
    <literal><![CDATA[
      a(x,y \ (z \ y),a(u,w,v5)) = a(x,(z * y) * y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,24742,a(flip),b,30779,a)].">
      <j1 rule="hyper" parents="63 24742 30779"/>
    </justification>
  </clause>

  <clause id="30794">
    <literal><![CDATA[
      a(x,y * z,a(y,y,z)) * (y \ z) = L(y \ z,a(y,y,z),x)
    ]]></literal>
    <justification jstring="[para(30779(a,1),27293(a,1,1))].">
      <j1 rule="para" parents="30779 27293"/>
    </justification>
  </clause>

  <clause id="30795">
    <literal><![CDATA[
      a(x \ y,z,a(u,w,v5)) = a(x * y,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),30780(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 30780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30797">
    <literal><![CDATA[
      a(x,y,a(z \ u,w,v5)) = a(x,y,a(z * u,w,v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),30782(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="10 30782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30799">
    <literal><![CDATA[
      a(x,y,a(z,u \ w,v5)) = a(x,y,a(z,u * w,v5))
    ]]></literal>
    <justification jstring="[para(24037(a,1),30783(a,2,3))].">
      <j1 rule="para" parents="24037 30783"/>
    </justification>
  </clause>

  <clause id="30800">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u * w,v5)),v5,a(y,w \ u,z)) = L(x,a(y,w \ u,z),v5)
    ]]></literal>
    <justification jstring="[para(30783(a,1),29955(a,1,1,2))].">
      <j1 rule="para" parents="30783 29955"/>
    </justification>
  </clause>

  <clause id="30801">
    <literal><![CDATA[
      a(x,y,a(z,u,w \ (x \ v5))) = a(x,y,a(z,u,(w * x) * v5))
    ]]></literal>
    <justification jstring="[hyper(29603,a,30785,a)].">
      <j1 rule="hyper" parents="29603 30785"/>
    </justification>
  </clause>

  <clause id="30802">
    <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(30785(a,2),26564(a,1))].">
      <j1 rule="para" parents="30785 26564"/>
    </justification>
  </clause>

  <clause id="30803">
    <literal><![CDATA[
      a(x * (y \ x),z,a(u,w,v5)) = a(v5,w,a(u,z,L(y,y,x)))
    ]]></literal>
    <justification jstring="[hyper(29941,a,30795,a),flip(a)].">
      <j1 rule="hyper" parents="29941 30795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30804">
    <literal><![CDATA[
      a((x * y) * z,u,a(x,w,v5)) = a(x,w,a(v5,u,y \ (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(29816,a,30795,a),flip(a)].">
      <j1 rule="hyper" parents="29816 30795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30805">
    <literal><![CDATA[
      a(x \ y,z,a(u,w,v5)) = a(x * y,z,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(26560,a,30795,a)].">
      <j1 rule="hyper" parents="26560 30795"/>
    </justification>
  </clause>

  <clause id="30807">
    <literal><![CDATA[
      a(x,y,a(z \ u,w,v5)) = a(x,y,a(u * z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,26339,a,b,30797,a),flip(a)].">
      <j1 rule="hyper" parents="347 26339 30797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30808">
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) * x = R(x,y,a(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(133,a,30797,a(flip),b,28907,a(flip))].">
      <j1 rule="hyper" parents="133 30797 28907"/>
    </justification>
  </clause>

  <clause id="30809">
    <literal><![CDATA[
      a(x,y,z) * a(x,u,a(w * v5,y,z)) = a(x,y,L(z,u,w \ v5))
    ]]></literal>
    <justification jstring="[para(30797(a,1),29847(a,1,2))].">
      <j1 rule="para" parents="30797 29847"/>
    </justification>
  </clause>

  <clause id="30810">
    <literal><![CDATA[
      L(x * a(y,x,a(z * u,w,v5)),z \ u,a(v5,w,y)) = L(x,a(v5,w,y),z \ u)
    ]]></literal>
    <justification jstring="[para(30797(a,1),29987(a,1,1,2))].">
      <j1 rule="para" parents="30797 29987"/>
    </justification>
  </clause>

  <clause id="30811">
    <literal><![CDATA[
      L(x * a(y,z,a(u * w,x,v5)),z,a(u \ w,v5,y)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,a(u \ w,z,y),v5) = v6
    ]]></literal>
    <justification jstring="[para(30797(a,1),29949(a,1,1,2))].">
      <j1 rule="para" parents="30797 29949"/>
    </justification>
  </clause>

  <clause id="30812">
    <literal><![CDATA[
      a(x,y,(z \ u) * (u \ z)) = a(x,y,a(z,u * z,u))
    ]]></literal>
    <justification jstring="[hyper(29626,a,30799,a)].">
      <j1 rule="hyper" parents="29626 30799"/>
    </justification>
  </clause>

  <clause id="30813">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x \ y,z,a(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(30805(a,1),26560(a,1))].">
      <j1 rule="para" parents="30805 26560"/>
    </justification>
  </clause>

  <clause id="30814">
    <literal><![CDATA[
      a(x \ y,z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(30805(a,2),26560(a,1))].">
      <j1 rule="para" parents="30805 26560"/>
    </justification>
  </clause>

  <clause id="30815">
    <literal><![CDATA[
      a(x,y,a(z \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(30807(a,2),26340(a,1))].">
      <j1 rule="para" parents="30807 26340"/>
    </justification>
  </clause>

  <clause id="30816">
    <literal><![CDATA[
      a(x,y * z,y) * a(x,u,a(z,y * z,y)) = a(x,y * z,L(y,u,z \ y))
    ]]></literal>
    <justification jstring="[para(30812(a,1),30334(a,1,2))].">
      <j1 rule="para" parents="30812 30334"/>
    </justification>
  </clause>

  <clause id="30817">
    <literal><![CDATA[
      (x * y) * a(z,u,a(w,v5,y)) = x * L(y,u,a(w,v5,z))
    ]]></literal>
    <justification jstring="[hyper(29937,a,30789,a)].">
      <j1 rule="hyper" parents="29937 30789"/>
    </justification>
  </clause>

  <clause id="30820">
    <literal><![CDATA[
      R(x,y,a(z \ u,w,v5)) = L(x,y,a(z * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(29007,a,30808,a),flip(a)].">
      <j1 rule="hyper" parents="29007 30808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30821">
    <literal><![CDATA[
      L(x,y,a(z \ u,w,v5)) = L(x,y,a(z * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(23284,a,30820,a)].">
      <j1 rule="hyper" parents="23284 30820"/>
    </justification>
  </clause>

  <clause id="30824">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((w * u) * (w \ z))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(u,w,z * w)) = v5
    ]]></literal>
    <justification jstring="[para(25019(a,2),30802(a,1))].">
      <j1 rule="para" parents="25019 30802"/>
    </justification>
  </clause>

  <clause id="30825">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((z * w) \ (w * u))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(w,z,u * z)) = v5
    ]]></literal>
    <justification jstring="[para(29651(a,2),30802(a,1))].">
      <j1 rule="para" parents="29651 30802"/>
    </justification>
  </clause>

  <clause id="30826">
    <literal><![CDATA[
      a(x * (y \ x),z,a(u,w,v5)) = a(y,z,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,30490,a(flip),b,30803,a),flip(a)].">
      <j1 rule="hyper" parents="347 30490 30803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30827">
    <literal><![CDATA[
      a(x,y,a(z * (u \ z),w,v5)) = a(u,y,a(v5,w,x))
    ]]></literal>
    <justification jstring="[hyper(29857,a,30826,a)].">
      <j1 rule="hyper" parents="29857 30826"/>
    </justification>
  </clause>

  <clause id="30829">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      R(w,y,a(v6 * (x \ v6),u,z)) = v5
    ]]></literal>
    <justification jstring="[para(30827(a,1),28910(a,1,1))].">
      <j1 rule="para" parents="30827 28910"/>
    </justification>
  </clause>

  <clause id="30830">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),z,a(v5 * (y \ v5),u,w)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,a(v5 * (y \ v5),z,w),u) = v6
    ]]></literal>
    <justification jstring="[para(30827(a,1),29949(a,1,1,2))].">
      <j1 rule="para" parents="30827 29949"/>
    </justification>
  </clause>

  <clause id="30831">
    <literal><![CDATA[
      a(a(x,y,z),u,w \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(w * v5,u,a(x,y,z)) = v6
    ]]></literal>
    <justification jstring="[para(26591(a,2),30814(a,1))].">
      <j1 rule="para" parents="26591 30814"/>
    </justification>
  </clause>

  <clause id="30832">
    <literal><![CDATA[
      a(x * y,a(z,u,x * y),w) = a(w,y * x,a(z,u,y \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,29990,a(flip),b,30791,a)].">
      <j1 rule="hyper" parents="63 29990 30791"/>
    </justification>
  </clause>

  <clause id="30833">
    <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(347,a,24248,a(flip),b,30793,a),flip(a)].">
      <j1 rule="hyper" parents="347 24248 30793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30834">
    <literal><![CDATA[
      a(x,y \ (z \ y),a(u,w,v5)) = a(x,z,a(u,w,L(v5,y,y)))
    ]]></literal>
    <justification jstring="[hyper(347,a,30088,a(flip),b,30833,a),flip(a)].">
      <j1 rule="hyper" parents="347 30088 30833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30835">
    <literal><![CDATA[
      a(x,y \ (z \ y),a(u,w,v5)) = a(x,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,30776,a(flip),b,30834,a),flip(a)].">
      <j1 rule="hyper" parents="347 30776 30834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30836">
    <literal><![CDATA[
      a(x,y * (z \ y),a(u,w,v5)) = a(x,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(30786,a,30835,a)].">
      <j1 rule="hyper" parents="30786 30835"/>
    </justification>
  </clause>

  <clause id="30838">
    <literal><![CDATA[
      a(x,y,a(z,u * (w \ u),v5)) = a(z,w,a(v5,y,x))
    ]]></literal>
    <justification jstring="[hyper(29908,a,30836,a)].">
      <j1 rule="hyper" parents="29908 30836"/>
    </justification>
  </clause>

  <clause id="30839">
    <literal><![CDATA[
      L(x \ y,a(x,x,y),z) = 1 * (x \ y)
    ]]></literal>
    <justification jstring="[para(29357(a,1),30794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29357 30794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30840">
    <literal><![CDATA[
      L(x \ y,a(x,x,y),z) = x \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,7,a(flip),b,30839,a),flip(a)].">
      <j1 rule="hyper" parents="347 7 30839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30842">
    <literal><![CDATA[
      a(x,y,(z \ u) * (w * a(z,z,u))) = a(x,y,w * (a(z,z,u) * (z \ u)))
    ]]></literal>
    <justification jstring="[para(30840(a,1),24076(a,1,3,1))].">
      <j1 rule="para" parents="30840 24076"/>
    </justification>
  </clause>

  <clause id="30844">
    <literal><![CDATA[
      a(x,y,a(z,u,(w * x) * v5)) = a(x,y,a(z,u,w * (x \ v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,30785,a(flip),b,30801,a),flip(a)].">
      <j1 rule="hyper" parents="63 30785 30801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30845">
    <literal><![CDATA[
      a((x * y) * z,u,a(x,w,v5)) = a(x,w,a(v5,u,y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,30785,a(flip),b,30804,a),flip(a)].">
      <j1 rule="hyper" parents="347 30785 30804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30846">
    <literal><![CDATA[
      a(x,x * y,a(z,u,x \ y)) = a(z,u,a(x,y * x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,29832,a(flip),b,30832,a),flip(a)].">
      <j1 rule="hyper" parents="63 29832 30832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30847">
    <literal><![CDATA[
      a(x,x * y,a(x \ y,z,u)) = a(u,z,a(x,y * x,y))
    ]]></literal>
    <justification jstring="[hyper(26560,a,30846,a)].">
      <j1 rule="hyper" parents="26560 30846"/>
    </justification>
  </clause>

  <clause id="30848">
    <literal><![CDATA[
      a(x,x * (y \ z),a(y,z * y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,30792,a(flip),b,30847,a),flip(a)].">
      <j1 rule="hyper" parents="63 30792 30847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30849">
    <literal><![CDATA[
      a(x * (y * z),u,a(y,w,v5)) = a(y,u,a(v5,w,z * (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(29854,a,30844,a)].">
      <j1 rule="hyper" parents="29854 30844"/>
    </justification>
  </clause>

  <clause id="30850">
    <literal><![CDATA[
      a(x * (y * z),u,a(z,w,v5)) = a(z,u,a(v5,w,y * (z \ x)))
    ]]></literal>
    <justification jstring="[hyper(29850,a,30844,a)].">
      <j1 rule="hyper" parents="29850 30844"/>
    </justification>
  </clause>

  <clause id="30851">
    <literal><![CDATA[
      x * a(y,z,a(x,u,w * (y \ v5))) = L(x,u,a(v5 * (y * w),z,y))
    ]]></literal>
    <justification jstring="[para(30849(a,1),29807(a,1,2))].">
      <j1 rule="para" parents="30849 29807"/>
    </justification>
  </clause>

  <clause id="30852">
    <literal><![CDATA[
      a(x,y,L(z,u,w \ v5)) = a(x,y,L(z,u,w * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,29847,a(flip),b,30809,a),flip(a)].">
      <j1 rule="hyper" parents="63 29847 30809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30854">
    <literal><![CDATA[
      a(x,y,L(z,u,w * v5)) \ z = L(z,y,L(x,u,w \ v5))
    ]]></literal>
    <justification jstring="[para(30852(a,1),29701(a,1,1))].">
      <j1 rule="para" parents="30852 29701"/>
    </justification>
  </clause>

  <clause id="30855">
    <literal><![CDATA[
      L(x,y,L(z,u,w \ v5)) = L(x,y,L(z,u,w * v5))
    ]]></literal>
    <justification jstring="[hyper(29702,a,30854,a),flip(a)].">
      <j1 rule="hyper" parents="29702 30854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30856">
    <literal><![CDATA[
      a(x,y * ((z \ y) \ L(y,u,L(w,y * z,z * y))),v5) = a(x,z * L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(30855(a,1),30639(a,1,2,2,2))].">
      <j1 rule="para" parents="30855 30639"/>
    </justification>
  </clause>

  <clause id="30857">
    <literal><![CDATA[
      R(x,y,a(z * (u \ z),w,v5)) = L(x,y,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(30829,a,29884,a)].">
      <j1 rule="hyper" parents="30829 29884"/>
    </justification>
  </clause>

  <clause id="30858">
    <literal><![CDATA[
      L(x,y,a(z * (u \ z),w,v5)) = L(x,y,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(23284,a,30857,a)].">
      <j1 rule="hyper" parents="23284 30857"/>
    </justification>
  </clause>

  <clause id="30859">
    <literal><![CDATA[
      L(x,y,a(z * (u * w),v5,u)) = L(x,y,a(u,v5,w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(29920,a,30851,a),flip(a)].">
      <j1 rule="hyper" parents="29920 30851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30860">
    <literal><![CDATA[
      a(x,y,(z \ u) * (w * a(z,z,u))) = a(x,y,w * (z \ L(u,z,z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,29468,a(flip),b,30842,a),flip(a)].">
      <j1 rule="hyper" parents="347 29468 30842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30861">
    <literal><![CDATA[
      a(x,y,(z \ u) * (w * a(z,z,u))) = a(x,y,w * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(3202(a,1),30860(a,2,3,2))].">
      <j1 rule="para" parents="3202 30860"/>
    </justification>
  </clause>

  <clause id="30862">
    <literal><![CDATA[
      a(x,y,(z \ u) * (w * a(z,z,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * u) * w) = v5
    ]]></literal>
    <justification jstring="[para(30861(a,2),24557(a,1))].">
      <j1 rule="para" parents="30861 24557"/>
    </justification>
  </clause>

  <clause id="30863">
    <literal><![CDATA[
      a(x,y * z,L(y,u,z \ y)) = a(x,y * z,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,29847,a(flip),b,30816,a),flip(a)].">
      <j1 rule="hyper" parents="63 29847 30816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30864">
    <literal><![CDATA[
      a(x,y * z,L(y,u,z * y)) = a(x,y * z,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,30852,a(flip),b,30863,a)].">
      <j1 rule="hyper" parents="63 30852 30863"/>
    </justification>
  </clause>

  <clause id="30865">
    <literal><![CDATA[
      a(x,y * z,L(y,u,y * z)) = a(x,y * z,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(24588,a,30864,a)].">
      <j1 rule="hyper" parents="24588 30864"/>
    </justification>
  </clause>

  <clause id="30867">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u * w,v5)),v5,a(y,u * w,z)) = L(x,a(y,w \ u,z),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,30453,a(flip),b,30800,a)].">
      <j1 rule="hyper" parents="63 30453 30800"/>
    </justification>
  </clause>

  <clause id="30868">
    <literal><![CDATA[
      L(x * a(y,x,a(z * u,w,v5)),z * u,a(v5,w,y)) = L(x,a(v5,w,y),z \ u)
    ]]></literal>
    <justification jstring="[hyper(30456,a,30810,a)].">
      <j1 rule="hyper" parents="30456 30810"/>
    </justification>
  </clause>

  <clause id="30869">
    <literal><![CDATA[
      L(x,a(y,z \ u,w),v5) = L(x,a(y,u * z,w),v5)
    ]]></literal>
    <justification jstring="[hyper(30023,a,30867,a),flip(a)].">
      <j1 rule="hyper" parents="30023 30867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30870">
    <literal><![CDATA[
      L(x,a(y,z \ u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,u * z,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(30867(a,1),30023(a,1))].">
      <j1 rule="para" parents="30867 30023"/>
    </justification>
  </clause>

  <clause id="30871">
    <literal><![CDATA[
      L(x,a(y,z \ u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z * u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(30869(a,2),25022(a,1))].">
      <j1 rule="para" parents="30869 25022"/>
    </justification>
  </clause>

  <clause id="30872">
    <literal><![CDATA[
      L(x,y * (z * (y \ z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z * y,z),u) = w
    ]]></literal>
    <justification jstring="[para(21873(a,2),30870(a,1))].">
      <j1 rule="para" parents="21873 30870"/>
    </justification>
  </clause>

  <clause id="30873">
    <literal><![CDATA[
      L(x,(y \ z) * (z \ y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,a(z,y * z,y),u) = w
    ]]></literal>
    <justification jstring="[para(22780(a,2),30871(a,1))].">
      <j1 rule="para" parents="22780 30871"/>
    </justification>
  </clause>

  <clause id="30874">
    <literal><![CDATA[
      L(((x \ y) * (y \ x)) * z,a(x,y * x,y),x) = (y * ((x \ y) \ 1)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(30872,a,30307,a)].">
      <j1 rule="hyper" parents="30872 30307"/>
    </justification>
  </clause>

  <clause id="30875">
    <literal><![CDATA[
      L((x * (y \ x)) \ (y * z),a(y,x * y,x),x \ y) = (y \ x) \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(30873,a,30591,a)].">
      <j1 rule="hyper" parents="30873 30591"/>
    </justification>
  </clause>

  <clause id="30876">
    <literal><![CDATA[
      L(x,a(y,z,u),w \ v5) = L(x,a(y,z,u),w * v5)
    ]]></literal>
    <justification jstring="[hyper(30025,a,30868,a),flip(a)].">
      <j1 rule="hyper" parents="30025 30868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30877">
    <literal><![CDATA[
      L(x,a(y,z,u),w \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,u),w * v5) = v6
    ]]></literal>
    <justification jstring="[para(30868(a,1),30025(a,1))].">
      <j1 rule="para" parents="30868 30025"/>
    </justification>
  </clause>

  <clause id="30878">
    <literal><![CDATA[
      L(x,a(y,z,u),w \ v5) = L(x,a(y,z,u),v5 * w)
    ]]></literal>
    <justification jstring="[hyper(347,a,20042,a,b,30876,a),flip(a)].">
      <j1 rule="hyper" parents="347 20042 30876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30879">
    <literal><![CDATA[
      L((x \ (y \ (y / x))) * z,a(x,x,y),x * y) = (y * x) \ ((y / x) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,30249,a(flip),b,30876,a),flip(a)].">
      <j1 rule="hyper" parents="63 30249 30876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30880">
    <literal><![CDATA[
      L(x,a(y,z,u),w * (w \ v5)) = L(x,a(y,z,u),L(v5,w,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,27895,a(flip),b,30876,a),flip(a)].">
      <j1 rule="hyper" parents="63 27895 30876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30881">
    <literal><![CDATA[
      (x \ y) \ ((x \ L(y,y,z)) * (u * a(z,y,y))) = L(u,a(z,y,y),y * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,30619,a,b,30878,a)].">
      <j1 rule="hyper" parents="63 30619 30878"/>
    </justification>
  </clause>

  <clause id="30882">
    <literal><![CDATA[
      L(x,a(y,z,u),L(w,v5,v5)) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(10(a,1),30880(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 30880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30883">
    <literal><![CDATA[
      L(x,y,a(y,a(z,u,w),v5)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,29970,a(flip),b,30882,a),flip(a)].">
      <j1 rule="hyper" parents="41 29970 30882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30885">
    <literal><![CDATA[
      L(x,a(y,z,u),L(w,v5,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,u),w) = v6
    ]]></literal>
    <justification jstring="[para(30882(a,1),27631(a,1))].">
      <j1 rule="para" parents="30882 27631"/>
    </justification>
  </clause>

  <clause id="30887">
    <literal><![CDATA[
      x * (L(x,a(y,z,u),w) \ v5) = a(w,a(y,z,u),x) * v5
    ]]></literal>
    <justification jstring="[hyper(29510,a,30883,a)].">
      <j1 rule="hyper" parents="29510 30883"/>
    </justification>
  </clause>

  <clause id="30888">
    <literal><![CDATA[
      L(x,a(y * (y * z),u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,a(w,u,z),v5) = v6
    ]]></literal>
    <justification jstring="[para(30540(a,2),30885(a,1))].">
      <j1 rule="para" parents="30540 30885"/>
    </justification>
  </clause>

  <clause id="30889">
    <literal><![CDATA[
      L(a(x,a(y,z,u),w) \ 1,w,v5) = v5 \ (a(x,a(u,z,y),w) * v5)
    ]]></literal>
    <justification jstring="[para(30887(a,1),29432(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30887 29432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30891">
    <literal><![CDATA[
      (x * y) \ ((x / y) * z) = (y \ (x \ (x / y))) * z
    ]]></literal>
    <justification jstring="[hyper(29377,a,30879,a),flip(a)].">
      <j1 rule="hyper" parents="29377 30879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30893">
    <literal><![CDATA[
      R(x,y,(z \ (u \ (u / z))) * (w / (u / z))) = R(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[para(30891(a,1),22069(a,1,3))].">
      <j1 rule="para" parents="30891 22069"/>
    </justification>
  </clause>

  <clause id="30894">
    <literal><![CDATA[
      R(x,y,(z \ (u \ (u / z))) * ((u / z) \ w)) = R(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(22089,a,30893,a)].">
      <j1 rule="hyper" parents="22089 30893"/>
    </justification>
  </clause>

  <clause id="30895">
    <literal><![CDATA[
      R(x,y,(z \ (u \ (u / z))) * ((z \ u) \ w)) = R(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(22165,a,30894,a)].">
      <j1 rule="hyper" parents="22165 30894"/>
    </justification>
  </clause>

  <clause id="30896">
    <literal><![CDATA[
      R(x,y,(z \ (u \ (z \ u))) * ((z \ u) \ w)) = R(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,23842,a(flip),b,30895,a)].">
      <j1 rule="hyper" parents="63 23842 30895"/>
    </justification>
  </clause>

  <clause id="30897">
    <literal><![CDATA[
      R(x,y,a(z,u,u) * ((u \ z) \ w)) = R(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,30284,a(flip),b,30896,a)].">
      <j1 rule="hyper" parents="63 30284 30896"/>
    </justification>
  </clause>

  <clause id="30898">
    <literal><![CDATA[
      R(x,y,(z * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,((u \ z) \ w) * a(z,u,u)) = v5
    ]]></literal>
    <justification jstring="[para(30897(a,1),20517(a,1))].">
      <j1 rule="para" parents="30897 20517"/>
    </justification>
  </clause>

  <clause id="30899">
    <literal><![CDATA[
      R(x,y,((((z / u) * (u * u)) / u) \ z) * ((u \ (u \ z)) \ w)) = R(x,y,((u \ z) * u) \ w)
    ]]></literal>
    <justification jstring="[para(23152(a,2),30897(a,1,3,1))].">
      <j1 rule="para" parents="23152 30897"/>
    </justification>
  </clause>

  <clause id="30900">
    <literal><![CDATA[
      (x \ y) \ ((x \ L(y,y,z)) * (u * a(z,y,y))) = L(u,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,30040,a(flip),b,30881,a),flip(a)].">
      <j1 rule="hyper" parents="347 30040 30881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30901">
    <literal><![CDATA[
      L(x \ y,a(z,y,y),u) * u = (x \ y) * L(u,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[para(30900(a,1),30743(a,2,2))].">
      <j1 rule="para" parents="30900 30743"/>
    </justification>
  </clause>

  <clause id="30902">
    <literal><![CDATA[
      L(((x \ y) * (y \ x)) * z,x,a(x,y * x,y)) = (y * ((x \ y) \ 1)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(25494,a,30874,a)].">
      <j1 rule="hyper" parents="25494 30874"/>
    </justification>
  </clause>

  <clause id="30903">
    <literal><![CDATA[
      L((x * (y \ x)) \ (y * z),a(y,x * y,x),x * y) = (y \ x) \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(30877,a,30875,a)].">
      <j1 rule="hyper" parents="30877 30875"/>
    </justification>
  </clause>

  <clause id="30904">
    <literal><![CDATA[
      (x * ((y \ x) \ 1)) \ (y * z) = ((y \ x) * (x \ y)) * z
    ]]></literal>
    <justification jstring="[hyper(29378,a,30902,a),flip(a)].">
      <j1 rule="hyper" parents="29378 30902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30905">
    <literal><![CDATA[
      (x * ((y \ x) \ 1)) \ y = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(6762,a,30904,a)].">
      <j1 rule="hyper" parents="6762 30904"/>
    </justification>
  </clause>

  <clause id="30907">
    <literal><![CDATA[
      x * ((y * ((y \ z) * (y \ z))) \ (z * (y \ z))) = ((y \ z) * (z \ y)) \ x
    ]]></literal>
    <justification jstring="[para(30905(a,1),28162(a,2,1))].">
      <j1 rule="para" parents="30905 28162"/>
    </justification>
  </clause>

  <clause id="30908">
    <literal><![CDATA[
      x * ((y * (z \ y)) / (z * ((z \ y) * (z \ y)))) = ((z \ y) * (y \ z)) \ x
    ]]></literal>
    <justification jstring="[para(13424(a,2),30907(a,1,2))].">
      <j1 rule="para" parents="13424 30907"/>
    </justification>
  </clause>

  <clause id="30909">
    <literal><![CDATA[
      x * ((y * ((z \ y) \ 1)) / z) = ((z \ y) * (y \ z)) \ x
    ]]></literal>
    <justification jstring="[para(814(a,1),30908(a,1,2))].">
      <j1 rule="para" parents="814 30908"/>
    </justification>
  </clause>

  <clause id="30910">
    <literal><![CDATA[
      x * (y \ (z * ((y \ z) \ 1))) = ((y \ z) * (z \ y)) \ x
    ]]></literal>
    <justification jstring="[para(12693(a,1),30909(a,1,2))].">
      <j1 rule="para" parents="12693 30909"/>
    </justification>
  </clause>

  <clause id="30911">
    <literal><![CDATA[
      (x * T(x \ y,(x \ y) \ 1)) * ((x \ y) \ 1) = ((y \ x) * (x \ y)) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,28181,a,b,30910,a)].">
      <j1 rule="hyper" parents="63 28181 30910"/>
    </justification>
  </clause>

  <clause id="30912">
    <literal><![CDATA[
      (x * (x \ y)) * (1 / (x \ y)) = ((y \ x) * (x \ y)) \ x
    ]]></literal>
    <justification jstring="[hyper(63,a,6070,a(flip),b,30911,a)].">
      <j1 rule="hyper" parents="63 6070 30911"/>
    </justification>
  </clause>

  <clause id="30913">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ y = x * (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(628,a,30912,a),flip(a)].">
      <j1 rule="hyper" parents="628 30912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30915">
    <literal><![CDATA[
      T(((x \ y) * (y \ x)) \ y,T(z,(x \ y) * (y \ x))) = (x * (1 / (y \ x))) * K(y / ((x \ y) * (y \ x)),z)
    ]]></literal>
    <justification jstring="[para(30913(a,1),7426(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30913 7426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30916">
    <literal><![CDATA[
      (x * (((y \ z) * (z \ y)) \ z)) \ (((y \ z) * (z \ y)) \ (z * x)) = (((y \ z) * (z \ y)) * (x * (y * (1 / (z \ y))))) \ (z * x)
    ]]></literal>
    <justification jstring="[para(30913(a,1),21369(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="30913 21369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30917">
    <literal><![CDATA[
      a(x,1 / (y \ x),1 / (y \ x)) \ (z * (((x \ y) * (y \ x)) \ y)) = z * (x / ((1 / (y \ x)) \ 1))
    ]]></literal>
    <justification jstring="[para(30913(a,2),29294(a,1,2,2))].">
      <j1 rule="para" parents="30913 29294"/>
    </justification>
  </clause>

  <clause id="30918">
    <literal><![CDATA[
      a(x,y * ((z \ y) \ L(y,u,L(w,z * y,z))),v5) = a(x,z * L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(30018(a,1),30856(a,1,2,2,2))].">
      <j1 rule="para" parents="30018 30856"/>
    </justification>
  </clause>

  <clause id="30919">
    <literal><![CDATA[
      a(x,y * (z \ a(L(u,z * y,z),w,y)),v5) = a(x,z * L(y,w,u),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,30259,a(flip),b,30918,a)].">
      <j1 rule="hyper" parents="63 30259 30918"/>
    </justification>
  </clause>

  <clause id="30920">
    <literal><![CDATA[
      a(x,y * (z \ a(u,w,L(y,z * y,z))),v5) = a(x,z * L(y,w,u),v5)
    ]]></literal>
    <justification jstring="[para(29675(a,1),30919(a,1,2,2,2))].">
      <j1 rule="para" parents="29675 30919"/>
    </justification>
  </clause>

  <clause id="30921">
    <literal><![CDATA[
      a(x,y * (z \ a(u,w,z * (y \ z))),v5) = a(x,z * L(y,w,u),v5)
    ]]></literal>
    <justification jstring="[para(27730(a,1),30920(a,1,2,2,2))].">
      <j1 rule="para" parents="27730 30920"/>
    </justification>
  </clause>

  <clause id="30922">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w \ v5,w,w \ (v6 \ 1)))) = a(x,y,a(z,u,v6 * ((w \ (v6 \ 1)) * v5)))
    ]]></literal>
    <justification jstring="[para(24278(a,1),30784(a,2,3))].">
      <j1 rule="para" parents="24278 30784"/>
    </justification>
  </clause>

  <clause id="30923">
    <literal><![CDATA[
      L(x * a(y,x,a(z,z,u)),z,a(u,z,y)) = z * L(z \ x,z,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(28650,a,30790,a)].">
      <j1 rule="hyper" parents="28650 30790"/>
    </justification>
  </clause>

  <clause id="30925">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,x,u)) = L(y,a(z,x,u),x)
    ]]></literal>
    <justification jstring="[hyper(30025,a,30923,a),flip(a)].">
      <j1 rule="hyper" parents="30025 30923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30926">
    <literal><![CDATA[
      L(x,a(y,z,u),z * a(y,z,u)) = L(x,a(y,z,u),z)
    ]]></literal>
    <justification jstring="[hyper(29614,a,30925,a)].">
      <j1 rule="hyper" parents="29614 30925"/>
    </justification>
  </clause>

  <clause id="30927">
    <literal><![CDATA[
      L(x * (y \ 1),a(z,y,u),y) = L(x,y,a(z,y,u)) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3539,a,30925,a),flip(a)].">
      <j1 rule="hyper" parents="3539 30925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30928">
    <literal><![CDATA[
      L(x \ y,a(z,x,u),x) = x \ L(y,x,a(z,x,u))
    ]]></literal>
    <justification jstring="[hyper(3393,a,30925,a),flip(a)].">
      <j1 rule="hyper" parents="3393 30925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30929">
    <literal><![CDATA[
      a(x,y,z) * L(u,a(x,y,z),y) = (a(x,y,z) * y) * (y \ u)
    ]]></literal>
    <justification jstring="[hyper(134,a,30925,a(flip),b,26374,a)].">
      <j1 rule="hyper" parents="134 30925 26374"/>
    </justification>
  </clause>

  <clause id="30930">
    <literal><![CDATA[
      L(x * y,x,a(z,x,u)) = x * L(y,a(z,x,u),x)
    ]]></literal>
    <justification jstring="[hyper(134,a,30925,a(flip),b,3342,a),flip(a)].">
      <j1 rule="hyper" parents="134 30925 3342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30931">
    <literal><![CDATA[
      L(x * y,a(z,x,u),x) = x * L(y,x,a(z,x,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),30925(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 30925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30932">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),y) = y * ((a(x,y,z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(329(a,1),30925(a,1,2)),flip(a)].">
      <j1 rule="para" parents="329 30925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30933">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z),y) = y * ((a(x,y,z) \ y) \ u)
    ]]></literal>
    <justification jstring="[para(28523(a,1),30925(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28523 30925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30934">
    <literal><![CDATA[
      L(L(x,y,z) \ u,a(w,L(x,y,z),v5),L(x,y,z)) = L(x,y,z) \ L(u,L(x,y,z),a(w,x,L(v5,y,z)))
    ]]></literal>
    <justification jstring="[para(30102(a,1),30928(a,2,2))].">
      <j1 rule="para" parents="30102 30928"/>
    </justification>
  </clause>

  <clause id="30935">
    <literal><![CDATA[
      x \ L(y * (y \ x),y,a(z,y,u)) = a(y,a(z,y,u),x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(30930(a,2),29037(a,1,2))].">
      <j1 rule="para" parents="30930 29037"/>
    </justification>
  </clause>

  <clause id="30936">
    <literal><![CDATA[
      L(x * y,a(z,x,u),x) / y = L(y,x,a(z,x,u)) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(131,a,30931,a,b,20681,a)].">
      <j1 rule="hyper" parents="131 30931 20681"/>
    </justification>
  </clause>

  <clause id="30937">
    <literal><![CDATA[
      (x * a(y,x,z)) \ (a(x * a(y,x,z),a(y,x,z),u * (x * a(y,x,z))) \ u) = L((x * a(y,x,z)) \ u,a(y,x,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,29256,a,b,30926,a)].">
      <j1 rule="hyper" parents="63 29256 30926"/>
    </justification>
  </clause>

  <clause id="30938">
    <literal><![CDATA[
      x \ L(x,a(y,z,u),z) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,a(y,z,u),z * a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(30926(a,1),28631(a,1,2))].">
      <j1 rule="para" parents="30926 28631"/>
    </justification>
  </clause>

  <clause id="30939">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (a(x,y,z) * L(u,a(x,y,z),y)) = a(a(x,y,z),y,y \ u) \ 1
    ]]></literal>
    <justification jstring="[para(30926(a,1),30754(a,1,2,2))].">
      <j1 rule="para" parents="30926 30754"/>
    </justification>
  </clause>

  <clause id="30940">
    <literal><![CDATA[
      (x * ((y \ 1) * a(z,y,u))) * (a(z,y,u) \ 1) = L(x * (y \ 1),a(z,y,u),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,30733,a,b,30927,a)].">
      <j1 rule="hyper" parents="347 30733 30927"/>
    </justification>
  </clause>

  <clause id="30941">
    <literal><![CDATA[
      (a(x,y,z) * y) * (y \ u) = y * ((a(x,y,z) \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,30599,a(flip),b,30929,a),flip(a)].">
      <j1 rule="hyper" parents="63 30599 30929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30942">
    <literal><![CDATA[
      (a(x,y,z) * y) * (L(y,u,w) \ 1) = y * ((a(x,y,z) \ y) \ a(w,u,y))
    ]]></literal>
    <justification jstring="[para(28855(a,2),30941(a,1,2))].">
      <j1 rule="para" parents="28855 30941"/>
    </justification>
  </clause>

  <clause id="30943">
    <literal><![CDATA[
      (a(x,y,z) \ y) * (y \ u) = y * ((a(x,y,z) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,30603,a(flip),b,30932,a)].">
      <j1 rule="hyper" parents="63 30603 30932"/>
    </justification>
  </clause>

  <clause id="30944">
    <literal><![CDATA[
      (x * a(y,x,z)) \ (x * u) = x * ((a(y,x,z) * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,99,a(flip),b,30932,a)].">
      <j1 rule="hyper" parents="63 99 30932"/>
    </justification>
  </clause>

  <clause id="30945">
    <literal><![CDATA[
      a(a(x,y,z),y,y * ((a(z,y,x) * y) \ u)) = a(a(x,y,z),y,a(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(30943(a,1),30606(a,1,3))].">
      <j1 rule="para" parents="30943 30606"/>
    </justification>
  </clause>

  <clause id="30946">
    <literal><![CDATA[
      (x * ((a(y,x,z) * x) \ u)) \ (a(y,x,z) \ u) = a(x,a(z,x,y),a(y,x,z) \ u)
    ]]></literal>
    <justification jstring="[para(30943(a,1),30605(a,1,1))].">
      <j1 rule="para" parents="30943 30605"/>
    </justification>
  </clause>

  <clause id="30947">
    <literal><![CDATA[
      (a(x,y,z) \ y) \ (y * u) = y * ((a(x,y,z) \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(28634,a,30933,a)].">
      <j1 rule="hyper" parents="28634 30933"/>
    </justification>
  </clause>

  <clause id="30948">
    <literal><![CDATA[
      x * ((a(y,x,z) \ x) \ (x \ u)) = (a(y,x,z) \ x) \ u
    ]]></literal>
    <justification jstring="[para(10(a,1),30947(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 30947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30949">
    <literal><![CDATA[
      R(a(x,y,z),a(x,y,z) \ y,(y \ u) * (a(x,y,z) \ y)) = ((a(x,y,z) \ y) \ u) / (y \ u)
    ]]></literal>
    <justification jstring="[para(30948(a,1),27255(a,2,1))].">
      <j1 rule="para" parents="30948 27255"/>
    </justification>
  </clause>

  <clause id="30950">
    <literal><![CDATA[
      L(x,y,a(z,y,u)) * (x \ y) = x * L(x \ y,a(z,y,u),y)
    ]]></literal>
    <justification jstring="[hyper(3377,a,30936,a),flip(a)].">
      <j1 rule="hyper" parents="3377 30936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30951">
    <literal><![CDATA[
      x * L(x \ y,a(z,y,u),y) = a(a(z,y,u),y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(26562,a,30950,a),flip(a)].">
      <j1 rule="hyper" parents="26562 30950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30952">
    <literal><![CDATA[
      x * L(x \ y,a(z,y,u),y) = a(z,y,a(x,y,u)) \ y
    ]]></literal>
    <justification jstring="[para(29790(a,1),30951(a,2,1))].">
      <j1 rule="para" parents="29790 30951"/>
    </justification>
  </clause>

  <clause id="30953">
    <literal><![CDATA[
      x * L(x \ y,a(z,y,u),y) = a(z,y,a(x,y,u)) * y
    ]]></literal>
    <justification jstring="[hyper(347,a,28387,a(flip),b,30952,a),flip(a)].">
      <j1 rule="hyper" parents="347 28387 30952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30954">
    <literal><![CDATA[
      x * L(x \ y,a(z,y,u),y) = y * a(x,y,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,29845,a(flip),b,30953,a),flip(a)].">
      <j1 rule="hyper" parents="347 29845 30953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30955">
    <literal><![CDATA[
      L(x,a(y,x,z),x * u) = x * a(u,x,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(30241,a,30954,a)].">
      <j1 rule="hyper" parents="30241 30954"/>
    </justification>
  </clause>

  <clause id="30956">
    <literal><![CDATA[
      a(x,a(y,x,z),x * u) = a(u,x,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(34,a,28627,a,b,30955,a(flip))].">
      <j1 rule="hyper" parents="34 28627 30955"/>
    </justification>
  </clause>

  <clause id="30957">
    <literal><![CDATA[
      a(x,a(y,x,z),u * x) = a(u,x,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(24180,a,30956,a)].">
      <j1 rule="hyper" parents="24180 30956"/>
    </justification>
  </clause>

  <clause id="30958">
    <literal><![CDATA[
      a(x,a(y,x,z),x * (u * a(w,v5,v6))) = a(u * a(v6,v5,w),x,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,28014,a,b,30956,a),flip(a)].">
      <j1 rule="hyper" parents="347 28014 30956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30959">
    <literal><![CDATA[
      L(a(x,a(y,x,z),x * u) \ 1,x * u,w) = w \ (a(u,x,a(y,x,z)) * w)
    ]]></literal>
    <justification jstring="[para(30956(a,1),30889(a,2,2,1))].">
      <j1 rule="para" parents="30956 30889"/>
    </justification>
  </clause>

  <clause id="30960">
    <literal><![CDATA[
      a(x,a(y,x,z),u \ x) \ 1 = u \ L(u,x,a(y,x,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),30935(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 30935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30961">
    <literal><![CDATA[
      a(x,a(y,x,z),u \ x) \ 1 = a(y,x,a(u,x,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,29866,a(flip),b,30960,a),flip(a)].">
      <j1 rule="hyper" parents="347 29866 30960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30962">
    <literal><![CDATA[
      a(x,a(y,x,z),x * u) \ 1 = a(y,x,a(u,x,z))
    ]]></literal>
    <justification jstring="[para(29161(a,1),30961(a,1,1))].">
      <j1 rule="para" parents="29161 30961"/>
    </justification>
  </clause>

  <clause id="30963">
    <literal><![CDATA[
      a(x * y,a(z,y,u),y) = a(z,y,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(26557,a,30962,a)].">
      <j1 rule="hyper" parents="26557 30962"/>
    </justification>
  </clause>

  <clause id="30964">
    <literal><![CDATA[
      a(x * y,a(z,x,u),x) = a(z,x,a(y,x,u))
    ]]></literal>
    <justification jstring="[hyper(26556,a,30962,a)].">
      <j1 rule="hyper" parents="26556 30962"/>
    </justification>
  </clause>

  <clause id="30965">
    <literal><![CDATA[
      L(a(x,y,a(z,y,u)) * a(x,y,u),y,z * y) = a(x,y,L(u,z * y,y))
    ]]></literal>
    <justification jstring="[para(30963(a,1),29427(a,1,1,1))].">
      <j1 rule="para" parents="30963 29427"/>
    </justification>
  </clause>

  <clause id="30966">
    <literal><![CDATA[
      a(x * y,a(z,y,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,a(x,y,u)) = w
    ]]></literal>
    <justification jstring="[para(30963(a,2),29875(a,1))].">
      <j1 rule="para" parents="30963 29875"/>
    </justification>
  </clause>

  <clause id="30967">
    <literal><![CDATA[
      a(x,a(y,z,u),z * a(y,z,u)) = a(x,a(y,z,u),z)
    ]]></literal>
    <justification jstring="[hyper(30938,a,28625,a)].">
      <j1 rule="hyper" parents="30938 28625"/>
    </justification>
  </clause>

  <clause id="30968">
    <literal><![CDATA[
      T(a(x,a(y,z,u),z) * a(y,z,u),x) = a(y,z,L(u,z,x * z))
    ]]></literal>
    <justification jstring="[para(30967(a,1),30293(a,1,1,1))].">
      <j1 rule="para" parents="30967 30293"/>
    </justification>
  </clause>

  <clause id="30969">
    <literal><![CDATA[
      T(a(x,y,z) * a(y,a(x,y,z),u),u) = a(x,y,L(z,y,u * y))
    ]]></literal>
    <justification jstring="[para(28773(a,1),30968(a,1,1))].">
      <j1 rule="para" parents="28773 30968"/>
    </justification>
  </clause>

  <clause id="30970">
    <literal><![CDATA[
      a(x,a(y,x,z),u) * a(y,x,z) = a(y,x,L(z,x,u * x))
    ]]></literal>
    <justification jstring="[hyper(23149,a,30969,a)].">
      <j1 rule="hyper" parents="23149 30969"/>
    </justification>
  </clause>

  <clause id="30971">
    <literal><![CDATA[
      x \ (y * ((a(z,y,u) \ y) \ x)) = a(z,y,L(u,y,x * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,30597,a,b,30970,a)].">
      <j1 rule="hyper" parents="63 30597 30970"/>
    </justification>
  </clause>

  <clause id="30972">
    <literal><![CDATA[
      x * a(y,z,L(u,z,x * z)) = z * ((a(y,z,u) \ z) \ x)
    ]]></literal>
    <justification jstring="[hyper(134,a,30970,a(flip),b,30597,a)].">
      <j1 rule="hyper" parents="134 30970 30597"/>
    </justification>
  </clause>

  <clause id="30973">
    <literal><![CDATA[
      L(x \ ((a(y,z,u) \ z) \ (z * x)),x,z) = a(y,z,L(u,z,(z * x) * z))
    ]]></literal>
    <justification jstring="[hyper(686,a,30971,a)].">
      <j1 rule="hyper" parents="686 30971"/>
    </justification>
  </clause>

  <clause id="30974">
    <literal><![CDATA[
      R((a(x,y,z) \ y) \ y,a(x,y,z) \ y,u * (a(x,y,z) \ y)) = T(a(x,y,L(z,y,u * y)),a(x,y,z) \ y)
    ]]></literal>
    <justification jstring="[para(30971(a,1),27269(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30971 27269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30975">
    <literal><![CDATA[
      (x / y) * (y * a(z,y,u)) = y * ((a(z,y,u) \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,29145,a(flip),b,30972,a)].">
      <j1 rule="hyper" parents="63 29145 30972"/>
    </justification>
  </clause>

  <clause id="30976">
    <literal><![CDATA[
      (x / y) * (a(z,y,u) * y) = y * ((a(z,y,u) \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(20480,a,30975,a)].">
      <j1 rule="hyper" parents="20480 30975"/>
    </justification>
  </clause>

  <clause id="30977">
    <literal><![CDATA[
      x * ((a(y,x,z) \ x) \ a(u,w,x)) = x * (L(x,w,u) \ a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,27918,a(flip),b,30942,a),flip(a)].">
      <j1 rule="hyper" parents="63 27918 30942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30978">
    <literal><![CDATA[
      x * (L(x,y,z) \ a(u,x,w)) = a(u,x,w) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,30601,a(flip),b,30977,a),flip(a)].">
      <j1 rule="hyper" parents="63 30601 30977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30979">
    <literal><![CDATA[
      a(x * a(y,z,u),y,a(w,y,v5)) = a(y,a(v5,y,w),L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(29775,a,30958,a),flip(a)].">
      <j1 rule="hyper" parents="29775 30958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30980">
    <literal><![CDATA[
      a(x,a(y,x,z),L(x,u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(v5 * a(x,u,w),x,a(z,x,y)) = v6
    ]]></literal>
    <justification jstring="[para(30979(a,1),29875(a,1))].">
      <j1 rule="para" parents="30979 29875"/>
    </justification>
  </clause>

  <clause id="30981">
    <literal><![CDATA[
      L(a(x,y,L(z,y,u)),y,u * y) = a(x,y,L(z,u * y,y))
    ]]></literal>
    <justification jstring="[para(29800(a,1),30965(a,1,1))].">
      <j1 rule="para" parents="29800 30965"/>
    </justification>
  </clause>

  <clause id="30982">
    <literal><![CDATA[
      a(x,y,L(L(z,y,u),y,u * y)) = a(x,y,L(z,u * y,y))
    ]]></literal>
    <justification jstring="[hyper(29297,a,30981,a)].">
      <j1 rule="hyper" parents="29297 30981"/>
    </justification>
  </clause>

  <clause id="30983">
    <literal><![CDATA[
      L(x \ (y * ((a(z,y,u) \ y) \ x)),x,y) = a(z,y,L(u,y,(y * x) * y))
    ]]></literal>
    <justification jstring="[para(30947(a,1),30973(a,1,1,2))].">
      <j1 rule="para" parents="30947 30973"/>
    </justification>
  </clause>

  <clause id="30984">
    <literal><![CDATA[
      L(a(x,y,L(z,y,u * y)),u,y) = a(x,y,L(z,y,(y * u) * y))
    ]]></literal>
    <justification jstring="[para(30971(a,1),30983(a,1,1))].">
      <j1 rule="para" parents="30971 30983"/>
    </justification>
  </clause>

  <clause id="30985">
    <literal><![CDATA[
      a(x,y,L(z,y,(y * u) * y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(L(z,y,u * y),u,y)) = w
    ]]></literal>
    <justification jstring="[para(30984(a,1),29297(a,1))].">
      <j1 rule="para" parents="30984 29297"/>
    </justification>
  </clause>

  <clause id="30986">
    <literal><![CDATA[
      a(x,y,L(L(z,y,u * y),u,y)) = a(x,y,L(z,y,L(u,y,y)))
    ]]></literal>
    <justification jstring="[hyper(30985,a,24906,a)].">
      <j1 rule="hyper" parents="30985 24906"/>
    </justification>
  </clause>

  <clause id="30987">
    <literal><![CDATA[
      a(x,y,L(L(z,y,u * y),u,y)) = a(x,y,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(29747(a,1),30986(a,2,3))].">
      <j1 rule="para" parents="29747 30986"/>
    </justification>
  </clause>

  <clause id="30988">
    <literal><![CDATA[
      a(x,y,L(L(z,u,y),y,u)) = a(x,y,L(z,y,u * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,25585,a(flip),b,30987,a),flip(a)].">
      <j1 rule="hyper" parents="63 25585 30987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30989">
    <literal><![CDATA[
      a(x,y,L(L(z,y,u),y,u * y)) = a(x,y,L(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,25585,a(flip),b,30988,a),flip(a)].">
      <j1 rule="hyper" parents="63 25585 30988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30990">
    <literal><![CDATA[
      a(x,y,L(z,u * y,y)) = a(x,y,L(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,30982,a(flip),b,30989,a)].">
      <j1 rule="hyper" parents="63 30982 30989"/>
    </justification>
  </clause>

  <clause id="30991">
    <literal><![CDATA[
      a(x,y,L(z,x * y,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,29278,a(flip),b,30990,a),flip(a)].">
      <j1 rule="hyper" parents="347 29278 30990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30992">
    <literal><![CDATA[
      a(x,y,L((z * y) \ (y \ u),z,y)) = a(x,y,(y * (z * y)) \ u)
    ]]></literal>
    <justification jstring="[para(329(a,1),30990(a,1,3)),flip(a)].">
      <j1 rule="para" parents="329 30990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30993">
    <literal><![CDATA[
      a(x,y,L((y \ z) \ u,z,y)) = a(x,y,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(30141(a,1),30990(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30141 30990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30994">
    <literal><![CDATA[
      a(x,x \ y,L(z,x * (x * y),x * y)) = a(x,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(30124,a,30991,a)].">
      <j1 rule="hyper" parents="30124 30991"/>
    </justification>
  </clause>

  <clause id="30995">
    <literal><![CDATA[
      a(x,x \ y,L(z,L(y,x,x),x * y)) = a(x,x * y,z)
    ]]></literal>
    <justification jstring="[para(3609(a,1),30994(a,1,3))].">
      <j1 rule="para" parents="3609 30994"/>
    </justification>
  </clause>

  <clause id="30996">
    <literal><![CDATA[
      a(x,x \ y,L(z,y,y)) = a(x,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,30652,a(flip),b,30995,a)].">
      <j1 rule="hyper" parents="63 30652 30995"/>
    </justification>
  </clause>

  <clause id="30997">
    <literal><![CDATA[
      a(x,x * y,L(z,y,y)) = a(x,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(30122,a,30996,a)].">
      <j1 rule="hyper" parents="30122 30996"/>
    </justification>
  </clause>

  <clause id="30998">
    <literal><![CDATA[
      a(x,x * y,y \ z) = a(x,x * y,z * y)
    ]]></literal>
    <justification jstring="[hyper(25264,a,30997,a)].">
      <j1 rule="hyper" parents="25264 30997"/>
    </justification>
  </clause>

  <clause id="30999">
    <literal><![CDATA[
      a(x,x * (x * y),y \ (x \ z)) = a(x,x * (x * y),z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(29201,a,30998,a)].">
      <j1 rule="hyper" parents="29201 30998"/>
    </justification>
  </clause>

  <clause id="31000">
    <literal><![CDATA[
      a(x,x * (x \ y),z * (x \ y)) = a(x,y,(x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),30998(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 30998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31001">
    <literal><![CDATA[
      a(x,x * (x \ y),z * (x \ y)) = a(x,y,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,29173,a(flip),b,31000,a),flip(a)].">
      <j1 rule="hyper" parents="347 29173 31000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31002">
    <literal><![CDATA[
      a(x,x * (x \ y),z * (x \ y)) = a(x,y,(x * z) * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,27214,a(flip),b,31001,a),flip(a)].">
      <j1 rule="hyper" parents="347 27214 31001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31003">
    <literal><![CDATA[
      a(x,y,(x * z) * y) = a(x,y,z * (x \ y))
    ]]></literal>
    <justification jstring="[para(10(a,1),31002(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 31002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31004">
    <literal><![CDATA[
      a(x,y,x * (y \ L(z,x,x))) = a(x,y,z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(29592,a,31003,a)].">
      <j1 rule="hyper" parents="29592 31003"/>
    </justification>
  </clause>

  <clause id="31005">
    <literal><![CDATA[
      a(x,y,z * (x \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y * (x * z)) = u
    ]]></literal>
    <justification jstring="[para(31003(a,1),24180(a,1))].">
      <j1 rule="para" parents="31003 24180"/>
    </justification>
  </clause>

  <clause id="31006">
    <literal><![CDATA[
      a(x,y,L((z * y) \ (y \ u),z,y)) = a(x,y,L(z,y,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(347,a,24630,a(flip),b,30992,a),flip(a)].">
      <j1 rule="hyper" parents="347 24630 30992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31007">
    <literal><![CDATA[
      a(x,y,z \ (y \ (y \ u))) = a(x,y,L(z,y,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,25588,a(flip),b,31006,a)].">
      <j1 rule="hyper" parents="63 25588 31006"/>
    </justification>
  </clause>

  <clause id="31008">
    <literal><![CDATA[
      a(x,y,L(z,y,y) \ u) = a(x,y,z \ L(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,28608,a(flip),b,31007,a),flip(a)].">
      <j1 rule="hyper" parents="63 28608 31007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31009">
    <literal><![CDATA[
      a(x,y,(y \ z) \ L(u,y,y)) = a(x,y,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(24613,a,31008,a),flip(a)].">
      <j1 rule="hyper" parents="24613 31008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31010">
    <literal><![CDATA[
      a(x,x * (x * y),z * (x * y)) = a(x,L(y,x,x),y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(24173,a,30999,a),flip(a)].">
      <j1 rule="hyper" parents="24173 30999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31011">
    <literal><![CDATA[
      a(x,x * (x * y),z * (x * y)) = a(x,y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,30120,a(flip),b,31010,a),flip(a)].">
      <j1 rule="hyper" parents="347 30120 31010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31012">
    <literal><![CDATA[
      a(x,x * (x * y),z * (x * y)) = a(x,y,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(347,a,29574,a(flip),b,31011,a),flip(a)].">
      <j1 rule="hyper" parents="347 29574 31011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31013">
    <literal><![CDATA[
      a(x,L(y,x,x),z * (x * y)) = a(x,y,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(24173,a,31012,a)].">
      <j1 rule="hyper" parents="24173 31012"/>
    </justification>
  </clause>

  <clause id="31014">
    <literal><![CDATA[
      a(x,y,z * (x * y)) = a(x,y,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(30123,a,31013,a)].">
      <j1 rule="hyper" parents="30123 31013"/>
    </justification>
  </clause>

  <clause id="31015">
    <literal><![CDATA[
      a(x,y,z * (y * x)) = a(x,y,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(24190,a,31014,a)].">
      <j1 rule="hyper" parents="24190 31014"/>
    </justification>
  </clause>

  <clause id="31016">
    <literal><![CDATA[
      a(x,y,x * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (y * x)) = u
    ]]></literal>
    <justification jstring="[para(31014(a,1),24190(a,1))].">
      <j1 rule="para" parents="31014 24190"/>
    </justification>
  </clause>

  <clause id="31017">
    <literal><![CDATA[
      a(x,y,a(x,x,y) * (x * (y \ z))) = a(x,y,z * (y * x))
    ]]></literal>
    <justification jstring="[hyper(347,a,30068,a,b,31015,a)].">
      <j1 rule="hyper" parents="347 30068 31015"/>
    </justification>
  </clause>

  <clause id="31018">
    <literal><![CDATA[
      a(x,y,x * (a(x,x,y) * (y \ z))) = a(x,y,z * (y * x))
    ]]></literal>
    <justification jstring="[para(25377(a,1),31017(a,1,3))].">
      <j1 rule="para" parents="25377 31017"/>
    </justification>
  </clause>

  <clause id="31019">
    <literal><![CDATA[
      a(x,y,x * (L(y,x,x) \ z)) = a(x,y,z * (y * x))
    ]]></literal>
    <justification jstring="[para(29388(a,1),31018(a,1,3,2))].">
      <j1 rule="para" parents="29388 31018"/>
    </justification>
  </clause>

  <clause id="31020">
    <literal><![CDATA[
      a(x,y,x * (y \ L(z,x,x))) = a(x,y,z * (y * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,30753,a(flip),b,31019,a)].">
      <j1 rule="hyper" parents="63 30753 31019"/>
    </justification>
  </clause>

  <clause id="31021">
    <literal><![CDATA[
      a(x,y,z * (x \ y)) = a(x,y,z * (y * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,31004,a(flip),b,31020,a)].">
      <j1 rule="hyper" parents="63 31004 31020"/>
    </justification>
  </clause>

  <clause id="31022">
    <literal><![CDATA[
      a(x,y,z * (y * x)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y * (x * z)) = u
    ]]></literal>
    <justification jstring="[para(31021(a,1),31005(a,1))].">
      <j1 rule="para" parents="31021 31005"/>
    </justification>
  </clause>

  <clause id="31023">
    <literal><![CDATA[
      a(x,y,z * (x * y)) = a(x,y,y * (x * z))
    ]]></literal>
    <justification jstring="[hyper(31022,a,24082,a),flip(a)].">
      <j1 rule="hyper" parents="31022 24082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31024">
    <literal><![CDATA[
      a(x,y,z * (x * y)) = a(x,y,y * (z * x))
    ]]></literal>
    <justification jstring="[hyper(347,a,24082,a,b,31023,a),flip(a)].">
      <j1 rule="hyper" parents="347 24082 31023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31025">
    <literal><![CDATA[
      a(x,y,z * (x * y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y * (z * x)) = u
    ]]></literal>
    <justification jstring="[para(31023(a,2),24190(a,1))].">
      <j1 rule="para" parents="31023 24190"/>
    </justification>
  </clause>

  <clause id="31026">
    <literal><![CDATA[
      a(x,y,a(z,u,u * (w * z))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,a(z,y,w * (z * u))) = v5
    ]]></literal>
    <justification jstring="[para(31024(a,1),29875(a,1,3))].">
      <j1 rule="para" parents="31024 29875"/>
    </justification>
  </clause>

  <clause id="31027">
    <literal><![CDATA[
      L(a(x,a(y,x,z),x * u) \ 1,x * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(u,x,a(y,x,z)) = v5
    ]]></literal>
    <justification jstring="[para(30959(a,2),20017(a,1))].">
      <j1 rule="para" parents="30959 20017"/>
    </justification>
  </clause>

  <clause id="31028">
    <literal><![CDATA[
      (x * (y \ a(z,y,u))) * (a(z,y,u) \ 1) = L(x * (y \ 1),a(z,y,u),y)
    ]]></literal>
    <justification jstring="[para(26352(a,1),30940(a,1,1,2))].">
      <j1 rule="para" parents="26352 30940"/>
    </justification>
  </clause>

  <clause id="31029">
    <literal><![CDATA[
      a(x,y,z) \ (u * (y \ a(x,y,z))) = L(u * (y \ 1),a(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(28424,a,31028,a)].">
      <j1 rule="hyper" parents="28424 31028"/>
    </justification>
  </clause>

  <clause id="31030">
    <literal><![CDATA[
      L((x * T(y,z)) * (T(y,z) \ 1),a(u,T(y,z),w),T(y,z)) = a(u,T(y,z),w) \ ((x * y) * (y \ a(u,T(y,z),w)))
    ]]></literal>
    <justification jstring="[para(21035(a,1),31029(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21035 31029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31031">
    <literal><![CDATA[
      a(x,y,a(y * ((a(z,y,x) * y) \ u),y,z)) = a(a(x,y,z),y,a(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(29833,a,30945,a)].">
      <j1 rule="hyper" parents="29833 30945"/>
    </justification>
  </clause>

  <clause id="31032">
    <literal><![CDATA[
      a(a(x,y,z),y,a(x,y,z) * (y \ u)) = a(y,a(z,y,x),a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(29583,a,30946,a)].">
      <j1 rule="hyper" parents="29583 30946"/>
    </justification>
  </clause>

  <clause id="31033">
    <literal><![CDATA[
      a(x,y,a(a(x,y,z) * (y \ u),y,z)) = a(y,a(z,y,x),a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(29833,a,31032,a)].">
      <j1 rule="hyper" parents="29833 31032"/>
    </justification>
  </clause>

  <clause id="31034">
    <literal><![CDATA[
      L(a(x,a(y,x,z),u) \ 1,u,a(y,x,z)) = a(a(y,x,z),x,x \ u) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,29043,a(flip),b,30939,a)].">
      <j1 rule="hyper" parents="63 29043 30939"/>
    </justification>
  </clause>

  <clause id="31035">
    <literal><![CDATA[
      L(a(x,a(y,z,u),z),x,a(y,z,u)) = a(a(y,z,u),z,z \ x) \ 1
    ]]></literal>
    <justification jstring="[para(26491(a,1),31034(a,1,1))].">
      <j1 rule="para" parents="26491 31034"/>
    </justification>
  </clause>

  <clause id="31036">
    <literal><![CDATA[
      a(a(x,y,z),y,y \ u) \ 1 = a(u,a(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(25990,a,31035,a)].">
      <j1 rule="hyper" parents="25990 31035"/>
    </justification>
  </clause>

  <clause id="31037">
    <literal><![CDATA[
      a(a(x,y,z),y,u * y) \ 1 = a(u,a(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(29503,a,31036,a)].">
      <j1 rule="hyper" parents="29503 31036"/>
    </justification>
  </clause>

  <clause id="31040">
    <literal><![CDATA[
      a(x * y,y,a(z,y,u)) = a(x,a(z,y,u),y)
    ]]></literal>
    <justification jstring="[hyper(26599,a,31037,a)].">
      <j1 rule="hyper" parents="26599 31037"/>
    </justification>
  </clause>

  <clause id="31041">
    <literal><![CDATA[
      a(x,y,a(z * y,y,u)) = a(z,a(x,y,u),y)
    ]]></literal>
    <justification jstring="[hyper(29857,a,31040,a)].">
      <j1 rule="hyper" parents="29857 31040"/>
    </justification>
  </clause>

  <clause id="31042">
    <literal><![CDATA[
      a(x,a(y,x,z),u * a(y,x,z)) = a(u,a(y,x,z),x)
    ]]></literal>
    <justification jstring="[hyper(29830,a,31041,a)].">
      <j1 rule="hyper" parents="29830 31041"/>
    </justification>
  </clause>

  <clause id="31043">
    <literal><![CDATA[
      a(x,y,a(y * z,y,u)) = a(z,a(x,y,u),y) \ 1
    ]]></literal>
    <justification jstring="[para(31041(a,1),26336(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31041 26336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31044">
    <literal><![CDATA[
      a(x,y,a(y * z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,a(x,y,u),z) = w
    ]]></literal>
    <justification jstring="[para(31043(a,2),26556(a,1))].">
      <j1 rule="para" parents="31043 26556"/>
    </justification>
  </clause>

  <clause id="31045">
    <literal><![CDATA[
      a(x,a(y,x,z),(a(z,x,y) * x) \ u) = a(a(y,x,z),x,a(z,x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(31044,a,31031,a)].">
      <j1 rule="hyper" parents="31044 31031"/>
    </justification>
  </clause>

  <clause id="31046">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,y,v5 * y))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(y,a(x,y,a(w,u,z)),v5) = v6
    ]]></literal>
    <justification jstring="[para(29804(a,1),31044(a,1,3))].">
      <j1 rule="para" parents="29804 31044"/>
    </justification>
  </clause>

  <clause id="31047">
    <literal><![CDATA[
      a(x,a(y,x,z),a(z,x,y) \ (x \ u)) = a(a(y,x,z),x,a(z,x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(29275,a,31045,a)].">
      <j1 rule="hyper" parents="29275 31045"/>
    </justification>
  </clause>

  <clause id="31048">
    <literal><![CDATA[
      L(x * a(y,z,a(u * w,x,v5)),z,a(u * w,v5,y)) = L(x,a(u \ w,z,y),v5)
    ]]></literal>
    <justification jstring="[hyper(30811,a,30821,a),flip(a)].">
      <j1 rule="hyper" parents="30811 30821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31049">
    <literal><![CDATA[
      L(x,a(y \ z,u,w),v5) = L(x,a(y * z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(29949,a,31048,a),flip(a)].">
      <j1 rule="hyper" parents="29949 31048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31050">
    <literal><![CDATA[
      L(x,a(y * (z \ y),u,w),v5) = L(x,a(w,u,z),L(v5,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,30541,a(flip),b,31049,a),flip(a)].">
      <j1 rule="hyper" parents="63 30541 31049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31051">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w \ v5,w,w \ (v6 \ 1)))) = a(x,y,a(z,u,v6 * ((w \ v6) * v5)))
    ]]></literal>
    <justification jstring="[para(24960(a,1),30922(a,2,3))].">
      <j1 rule="para" parents="24960 30922"/>
    </justification>
  </clause>

  <clause id="31052">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w \ v5,w,w * (v6 \ 1)))) = a(x,y,a(z,u,v6 * ((w \ v6) * v5)))
    ]]></literal>
    <justification jstring="[para(30852(a,1),31051(a,1,3))].">
      <j1 rule="para" parents="30852 31051"/>
    </justification>
  </clause>

  <clause id="31053">
    <literal><![CDATA[
      R(x,y,(((z / u) / (u \ 1)) \ z) * ((u \ (u \ z)) \ w)) = R(x,y,((u \ z) * u) \ w)
    ]]></literal>
    <justification jstring="[para(798(a,1),30899(a,1,3,1,1))].">
      <j1 rule="para" parents="798 30899"/>
    </justification>
  </clause>

  <clause id="31054">
    <literal><![CDATA[
      R(x,y,(z \ ((z * (u \ 1)) * u)) * ((u \ (u \ z)) \ w)) = R(x,y,((u \ z) * u) \ w)
    ]]></literal>
    <justification jstring="[para(27933(a,1),31053(a,1,3,1))].">
      <j1 rule="para" parents="27933 31053"/>
    </justification>
  </clause>

  <clause id="31055">
    <literal><![CDATA[
      R(x,y,(z * (u \ (u / z))) \ ((z \ (z \ u)) \ w)) = R(x,y,((z \ u) * z) \ w)
    ]]></literal>
    <justification jstring="[para(28147(a,1),31054(a,1,3))].">
      <j1 rule="para" parents="28147 31054"/>
    </justification>
  </clause>

  <clause id="31056">
    <literal><![CDATA[
      R(x,y,(z * (u \ (u / z))) \ (L(u,z,z) \ w)) = R(x,y,((z \ u) * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,22390,a(flip),b,31055,a)].">
      <j1 rule="hyper" parents="63 22390 31055"/>
    </justification>
  </clause>

  <clause id="31057">
    <literal><![CDATA[
      R(x,y,(L(z,u,u) \ w) * a(z,u,u)) = R(x,y,((u \ z) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,28144,a(flip),b,31056,a)].">
      <j1 rule="hyper" parents="63 28144 31056"/>
    </justification>
  </clause>

  <clause id="31058">
    <literal><![CDATA[
      R(x,y,(L(z,u,u) \ w) * a(z,u,u)) = R(x,y,z \ w)
    ]]></literal>
    <justification jstring="[hyper(347,a,22065,a(flip),b,31057,a),flip(a)].">
      <j1 rule="hyper" parents="347 22065 31057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31060">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),z,a(w,u,y)) = L(x,a(v5 * (y \ v5),z,w),u)
    ]]></literal>
    <justification jstring="[hyper(30830,a,30858,a),flip(a)].">
      <j1 rule="hyper" parents="30830 30858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31061">
    <literal><![CDATA[
      L(x,a(y * (z \ y),u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,a(z,u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(31060(a,1),29957(a,1))].">
      <j1 rule="para" parents="31060 29957"/>
    </justification>
  </clause>

  <clause id="31062">
    <literal><![CDATA[
      L(x,a(y \ 1,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(7(a,1),31061(a,1,2,1))].">
      <j1 rule="para" parents="7 31061"/>
    </justification>
  </clause>

  <clause id="31063">
    <literal><![CDATA[
      L(x,a(y,z,u),L(w,u,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,a(u,z,y),w) = v6
    ]]></literal>
    <justification jstring="[para(31050(a,1),31061(a,1))].">
      <j1 rule="para" parents="31050 31061"/>
    </justification>
  </clause>

  <clause id="31064">
    <literal><![CDATA[
      a(x,1 / (y \ x),y \ x) \ (z * (((x \ y) * (y \ x)) \ y)) = z * (x / ((1 / (y \ x)) \ 1))
    ]]></literal>
    <justification jstring="[para(14923(a,1),30917(a,1,1))].">
      <j1 rule="para" parents="14923 30917"/>
    </justification>
  </clause>

  <clause id="31065">
    <literal><![CDATA[
      a(x,1 / (y \ x),x * y) \ (z * (((x \ y) * (y \ x)) \ y)) = z * (x / ((1 / (y \ x)) \ 1))
    ]]></literal>
    <justification jstring="[para(29161(a,1),31064(a,1,1))].">
      <j1 rule="para" parents="29161 31064"/>
    </justification>
  </clause>

  <clause id="31066">
    <literal><![CDATA[
      a(x,y \ x,x * y) \ (z * (((x \ y) * (y \ x)) \ y)) = z * (x / ((1 / (y \ x)) \ 1))
    ]]></literal>
    <justification jstring="[para(14964(a,1),31065(a,1,1))].">
      <j1 rule="para" parents="14964 31065"/>
    </justification>
  </clause>

  <clause id="31067">
    <literal><![CDATA[
      a(x,x * y,x * y) \ (z * (((x \ y) * (y \ x)) \ y)) = z * (x / ((1 / (y \ x)) \ 1))
    ]]></literal>
    <justification jstring="[para(30127(a,1),31066(a,1,1))].">
      <j1 rule="para" parents="30127 31066"/>
    </justification>
  </clause>

  <clause id="31068">
    <literal><![CDATA[
      a(x,x * y,x * y) \ (z * (x * (1 / (y \ x)))) = z * (x / ((1 / (y \ x)) \ 1))
    ]]></literal>
    <justification jstring="[para(30913(a,1),31067(a,1,2,2))].">
      <j1 rule="para" parents="30913 31067"/>
    </justification>
  </clause>

  <clause id="31069">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) * (z * (x * (1 / (y \ x)))) = z * (x / ((1 / (y \ x)) \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,28079,a(flip),b,31068,a)].">
      <j1 rule="hyper" parents="63 28079 31068"/>
    </justification>
  </clause>

  <clause id="31070">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) * (z * (x * (1 / (y \ x)))) = z * (x / (y \ x))
    ]]></literal>
    <justification jstring="[para(83(a,1),31069(a,2,2,2))].">
      <j1 rule="para" parents="83 31069"/>
    </justification>
  </clause>

  <clause id="31071">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) * (z * (x * (1 / (y \ x)))) = z * y
    ]]></literal>
    <justification jstring="[hyper(347,a,207,a(flip),b,31070,a),flip(a)].">
      <j1 rule="hyper" parents="347 207 31070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31074">
    <literal><![CDATA[
      L(L(x,y,z) \ u,a(w,L(x,y,z),v5),L(x,y,z)) = L(x,y,z) \ L(u,x,a(w,x,v5))
    ]]></literal>
    <justification jstring="[para(30101(a,1),30934(a,2,2))].">
      <j1 rule="para" parents="30101 30934"/>
    </justification>
  </clause>

  <clause id="31075">
    <literal><![CDATA[
      L(L(x,y,z) \ u,a(w,x,v5),L(L(x,y,z),y,z)) = L(x,y,z) \ L(u,x,a(v5,x,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,30545,a(flip),b,31074,a)].">
      <j1 rule="hyper" parents="63 30545 31074"/>
    </justification>
  </clause>

  <clause id="31077">
    <literal><![CDATA[
      L(L(x,y,z) \ u,a(w,x,v5),x) = L(x,y,z) \ L(u,x,a(v5,x,w))
    ]]></literal>
    <justification jstring="[hyper(27631,a,31075,a)].">
      <j1 rule="hyper" parents="27631 31075"/>
    </justification>
  </clause>

  <clause id="31079">
    <literal><![CDATA[
      (L(x,y,z) * (L(x,y,z) \ L(u,x,a(w,x,v5)))) \ u = a(x,a(v5,x,w),u \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(31077(a,1),29333(a,1,1,2))].">
      <j1 rule="para" parents="31077 29333"/>
    </justification>
  </clause>

  <clause id="31080">
    <literal><![CDATA[
      a(x,a(y,x,z),u \ L(x,w,v5)) = L(u,x,a(z,x,y)) \ u
    ]]></literal>
    <justification jstring="[hyper(374,a,31079,a),flip(a)].">
      <j1 rule="hyper" parents="374 31079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31082">
    <literal><![CDATA[
      a(x,a(y,x,z),u \ L(x,w,v5)) = a(z,x,a(u,x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,29820,a(flip),b,31080,a),flip(a)].">
      <j1 rule="hyper" parents="347 29820 31080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31083">
    <literal><![CDATA[
      T(((x \ y) * (y \ x)) \ y,T(z,(x \ y) * (y \ x))) = (x * (1 / (y \ x))) * K(((x \ y) * (y \ x)) \ y,z)
    ]]></literal>
    <justification jstring="[para(6620(a,1),30915(a,2,2,1))].">
      <j1 rule="para" parents="6620 30915"/>
    </justification>
  </clause>

  <clause id="31084">
    <literal><![CDATA[
      T(((x \ y) * (y \ x)) \ y,T(z,(x \ y) * (y \ x))) = (x * (1 / (y \ x))) * K(x * (1 / (y \ x)),z)
    ]]></literal>
    <justification jstring="[para(30913(a,1),31083(a,2,2,1))].">
      <j1 rule="para" parents="30913 31083"/>
    </justification>
  </clause>

  <clause id="31085">
    <literal><![CDATA[
      T(((x \ y) * (y \ x)) \ y,T(z,(x \ y) * (y \ x))) = (x * (1 / (y \ x))) * K(x * (1 * (x \ y)),z)
    ]]></literal>
    <justification jstring="[para(23448(a,1),31084(a,2,2))].">
      <j1 rule="para" parents="23448 31084"/>
    </justification>
  </clause>

  <clause id="31086">
    <literal><![CDATA[
      T(((x \ y) * (y \ x)) \ y,T(z,(x \ y) * (y \ x))) = (x * (1 / (y \ x))) * K(y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),31085(a,2,2,1))].">
      <j1 rule="para" parents="72 31085"/>
    </justification>
  </clause>

  <clause id="31087">
    <literal><![CDATA[
      T(((x \ y) * (y \ x)) \ y,T(z,(x \ y) * (y \ x))) = x * ((1 / (y \ x)) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,20033,a(flip),b,31086,a),flip(a)].">
      <j1 rule="hyper" parents="347 20033 31086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31088">
    <literal><![CDATA[
      T(((x \ y) * (y \ x)) \ y,T(z,(x \ y) * (y \ x))) = x * (1 / (T(y,z) \ x))
    ]]></literal>
    <justification jstring="[para(20822(a,1),31087(a,2,2))].">
      <j1 rule="para" parents="20822 31087"/>
    </justification>
  </clause>

  <clause id="31089">
    <literal><![CDATA[
      T(x * (1 / (y \ x)),T(z,(x \ y) * (y \ x))) = x * (1 / (T(y,z) \ x))
    ]]></literal>
    <justification jstring="[para(30913(a,1),31088(a,1,1))].">
      <j1 rule="para" parents="30913 31088"/>
    </justification>
  </clause>

  <clause id="31090">
    <literal><![CDATA[
      T(x * (1 / (y \ x)),z) = x * (1 / (T(y,z) \ x))
    ]]></literal>
    <justification jstring="[para(6619(a,1),31089(a,1,2))].">
      <j1 rule="para" parents="6619 31089"/>
    </justification>
  </clause>

  <clause id="31091">
    <literal><![CDATA[
      K(x,y) * (z * (1 / (x \ z))) = T(z * (1 / (x \ z)),y)
    ]]></literal>
    <justification jstring="[hyper(23659,a,31090,a(flip))].">
      <j1 rule="hyper" parents="23659 31090"/>
    </justification>
  </clause>

  <clause id="31092">
    <literal><![CDATA[
      R(a(x,y,z),a(x,y,z) \ y,u * (a(x,y,z) \ y)) = a(x,y,L(z,y,u * y))
    ]]></literal>
    <justification jstring="[hyper(933,a,30974,a(flip))].">
      <j1 rule="hyper" parents="933 30974"/>
    </justification>
  </clause>

  <clause id="31093">
    <literal><![CDATA[
      a(x,y,L(z,y,(y \ u) * y)) = ((a(x,y,z) \ y) \ u) / (y \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,30949,a(flip),b,31092,a),flip(a)].">
      <j1 rule="hyper" parents="63 30949 31092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31095">
    <literal><![CDATA[
      ((a(x,y,z) \ y) \ u) / (y \ u) = a(x,y,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(20043(a,1),31093(a,1,3)),flip(a)].">
      <j1 rule="para" parents="20043 31093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31096">
    <literal><![CDATA[
      (x \ y) \ ((a(z,x,u) \ x) \ y) = a(z,x,L(u,x,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,22806,a(flip),b,31095,a)].">
      <j1 rule="hyper" parents="63 22806 31095"/>
    </justification>
  </clause>

  <clause id="31098">
    <literal><![CDATA[
      (x \ y) \ ((a(z,x,x \ (y \ u)) \ x) \ y) = a(z,x,(y * x) \ u)
    ]]></literal>
    <justification jstring="[para(329(a,1),31096(a,2,3))].">
      <j1 rule="para" parents="329 31096"/>
    </justification>
  </clause>

  <clause id="31099">
    <literal><![CDATA[
      (x \ y) \ ((a(z,x,(y \ u) * x) \ x) \ y) = a(z,x,(y * x) \ u)
    ]]></literal>
    <justification jstring="[para(27214(a,1),31098(a,1,2,1,1))].">
      <j1 rule="para" parents="27214 31098"/>
    </justification>
  </clause>

  <clause id="31100">
    <literal><![CDATA[
      a(x,y,L((z \ u) * y,y,z)) = a(x,y,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,31096,a(flip),b,31099,a)].">
      <j1 rule="hyper" parents="63 31096 31099"/>
    </justification>
  </clause>

  <clause id="31101">
    <literal><![CDATA[
      a(x,y,L(T(z * u,u \ 1) * y,y,u \ 1)) = a(x,y,((u \ 1) * y) \ R(z,u,u))
    ]]></literal>
    <justification jstring="[para(787(a,1),31100(a,1,3,1,1))].">
      <j1 rule="para" parents="787 31100"/>
    </justification>
  </clause>

  <clause id="31102">
    <literal><![CDATA[
      a(x,y,L(T(z * u,u \ 1) * y,y,u)) = a(x,y,((u \ 1) * y) \ R(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(24896,a,31101,a)].">
      <j1 rule="hyper" parents="24896 31101"/>
    </justification>
  </clause>

  <clause id="31103">
    <literal><![CDATA[
      a(x,y,L((z * u) * y,y,u)) = a(x,y,((u \ 1) * y) \ R(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(24542,a,31102,a)].">
      <j1 rule="hyper" parents="24542 31102"/>
    </justification>
  </clause>

  <clause id="31104">
    <literal><![CDATA[
      a(x,y,L((z * u) * y,y,u)) = a(x,y,((u \ 1) * y) \ L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,25307,a(flip),b,31103,a),flip(a)].">
      <j1 rule="hyper" parents="347 25307 31103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31105">
    <literal><![CDATA[
      a(x,y,L((z * u) * y,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(y * u) \ L(z,u,u)) = w
    ]]></literal>
    <justification jstring="[para(31104(a,2),24295(a,1))].">
      <j1 rule="para" parents="31104 24295"/>
    </justification>
  </clause>

  <clause id="31106">
    <literal><![CDATA[
      a(L(x,a(y,z,u),w),a(u,z,a(w,x,y)),L(v5,w,a(y,z,u))) = a(x,a(w,x,a(u,z,y)),v5 * a(w,x,a(u,z,y)))
    ]]></literal>
    <justification jstring="[hyper(29676,a,29827,a)].">
      <j1 rule="hyper" parents="29676 29827"/>
    </justification>
  </clause>

  <clause id="31107">
    <literal><![CDATA[
      ((x * L(y,z,a(u,R(x,w,v5),L(x,w,v5)))) / x) * R(x,w,v5) = L(R(x,w,v5) * y,R(x,w,v5),a(u,z,R(x,w,v5)))
    ]]></literal>
    <justification jstring="[para(24889(a,1),29917(a,1,1,1,2,3))].">
      <j1 rule="para" parents="24889 29917"/>
    </justification>
  </clause>

  <clause id="31108">
    <literal><![CDATA[
      L((x * T(y,z)) * (T(y,z) \ 1),a(u,T(y,z),w),T(y,z)) = a(u,y,w) \ ((x * y) * (y \ a(u,T(y,z),w)))
    ]]></literal>
    <justification jstring="[para(23991(a,1),31030(a,2,1))].">
      <j1 rule="para" parents="23991 31030"/>
    </justification>
  </clause>

  <clause id="31109">
    <literal><![CDATA[
      L((x * T(y,z)) * (T(y,z) \ 1),a(u,T(y,z),w),T(y,z)) = a(u,y,w) \ ((x * y) * (y \ a(u,y,w)))
    ]]></literal>
    <justification jstring="[para(23991(a,1),31108(a,2,2,2,2))].">
      <j1 rule="para" parents="23991 31108"/>
    </justification>
  </clause>

  <clause id="31111">
    <literal><![CDATA[
      R(T(x,a(y,z,u)),z,a(y,z,u) * z) = L((x * T(z,w)) * (T(z,w) \ 1),a(y,T(z,w),u),T(z,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,27251,a(flip),b,31109,a)].">
      <j1 rule="hyper" parents="347 27251 31109"/>
    </justification>
  </clause>

  <clause id="31113">
    <literal><![CDATA[
      L((x * T(y,z)) * (T(y,z) \ 1),a(u,T(y,z),w),T(y,z)) = R(x,y,a(u,y,w) * y)
    ]]></literal>
    <justification jstring="[para(19939(a,1),31111(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19939 31111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31114">
    <literal><![CDATA[
      L((x * T(y,z)) * (T(y,z) \ 1),a(u,T(y,z),w),T(y,z)) = R(x,y,y * a(w,y,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,27782,a(flip),b,31113,a),flip(a)].">
      <j1 rule="hyper" parents="347 27782 31113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31115">
    <literal><![CDATA[
      L(R(x,T(y,z),T(y,z)),a(u,T(y,z),w),T(y,z)) = R(x,y,y * a(w,y,u))
    ]]></literal>
    <justification jstring="[para(786(a,1),31114(a,1,1))].">
      <j1 rule="para" parents="786 31114"/>
    </justification>
  </clause>

  <clause id="31116">
    <literal><![CDATA[
      L(R(x,T(y,z),y),a(u,T(y,z),w),T(y,z)) = R(x,y,y * a(w,y,u))
    ]]></literal>
    <justification jstring="[para(20040(a,1),31115(a,1,1))].">
      <j1 rule="para" parents="20040 31115"/>
    </justification>
  </clause>

  <clause id="31118">
    <literal><![CDATA[
      L(R(x,y,y),a(z,T(y,u),w),T(y,u)) = R(x,y,y * a(w,y,z))
    ]]></literal>
    <justification jstring="[para(20496(a,1),31116(a,1,1))].">
      <j1 rule="para" parents="20496 31116"/>
    </justification>
  </clause>

  <clause id="31120">
    <literal><![CDATA[
      L(R(x,y,y),a(z,y,u),T(y,w)) = R(x,y,y * a(u,y,z))
    ]]></literal>
    <justification jstring="[para(23991(a,1),31118(a,1,2))].">
      <j1 rule="para" parents="23991 31118"/>
    </justification>
  </clause>

  <clause id="31121">
    <literal><![CDATA[
      L(R(x,y,y),a(z,y,u),y) = R(x,y,y * a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(20103,a,31120,a)].">
      <j1 rule="hyper" parents="20103 31120"/>
    </justification>
  </clause>

  <clause id="31123">
    <literal><![CDATA[
      L(R(x,y,y) \ R(x,y,y * a(z,y,u)),w,v5) = a(R(x,y,y),a(u,y,z),L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(31121(a,1),29155(a,1,1,2))].">
      <j1 rule="para" parents="31121 29155"/>
    </justification>
  </clause>

  <clause id="31124">
    <literal><![CDATA[
      ((x * L(y,z,a(u,L(x,w,v5),L(x,w,v5)))) / x) * R(x,w,v5) = L(R(x,w,v5) * y,R(x,w,v5),a(u,z,R(x,w,v5)))
    ]]></literal>
    <justification jstring="[para(24805(a,1),31107(a,1,1,1,2,3))].">
      <j1 rule="para" parents="24805 31107"/>
    </justification>
  </clause>

  <clause id="31125">
    <literal><![CDATA[
      L(R(x,y,z) * u,R(x,y,z),a(w,v5,R(x,y,z))) = ((x * L(u,v5,a(w,x,x))) / x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(26464(a,1),31124(a,1,1,1,2,3)),flip(a)].">
      <j1 rule="para" parents="26464 31124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31127">
    <literal><![CDATA[
      L(R(x,y,z) * u,R(x,y,z),a(w,v5,R(x,y,z))) = (L(x * u,x,a(w,v5,x)) / x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(29905(a,2),31125(a,2,1,1))].">
      <j1 rule="para" parents="29905 31125"/>
    </justification>
  </clause>

  <clause id="31128">
    <literal><![CDATA[
      L(R(x,y,z) * u,R(x,y,z),a(w,v5,R(x,y,z))) = L((x * u) / x,x,a(w,v5,x)) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(29300(a,2),31127(a,2,1))].">
      <j1 rule="para" parents="29300 31127"/>
    </justification>
  </clause>

  <clause id="31129">
    <literal><![CDATA[
      L(R(x,y,z) * u,R(x,y,z),a(w,v5,R(x,y,z))) = R(x,y,z) * L(u,x,a(w,v5,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,21181,a(flip),b,31128,a),flip(a)].">
      <j1 rule="hyper" parents="347 21181 31128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31130">
    <literal><![CDATA[
      L(R(x,y,z) * u,R(x,y,z),a(w,v5,L(x,y,z))) = R(x,y,z) * L(u,x,a(w,v5,x))
    ]]></literal>
    <justification jstring="[para(24889(a,1),31129(a,1,3))].">
      <j1 rule="para" parents="24889 31129"/>
    </justification>
  </clause>

  <clause id="31131">
    <literal><![CDATA[
      L(R(x,y,z) * u,L(x,y,z),a(w,v5,L(x,y,z))) = R(x,y,z) * L(u,x,a(w,v5,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,21974,a(flip),b,31130,a)].">
      <j1 rule="hyper" parents="63 21974 31130"/>
    </justification>
  </clause>

  <clause id="31132">
    <literal><![CDATA[
      L(R(x,y,z) * u,x,a(w,v5,x)) = R(x,y,z) * L(u,x,a(w,v5,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,30101,a(flip),b,31131,a)].">
      <j1 rule="hyper" parents="63 30101 31131"/>
    </justification>
  </clause>

  <clause id="31134">
    <literal><![CDATA[
      L(x * R(y,z,u),y,a(w,v5,y)) = L(x,y,a(w,v5,y)) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(34,a,3374,a(flip),b,31132,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="34 3374 31132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31135">
    <literal><![CDATA[
      L(x * R(y,z,u),y,a(u,z,y)) = a(y,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,29429,a(flip),b,31134,a),flip(a)].">
      <j1 rule="hyper" parents="347 29429 31134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31136">
    <literal><![CDATA[
      L(x * R(y,z,u),y,a(y,z,u)) = a(y,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(27578,a,31135,a)].">
      <j1 rule="hyper" parents="27578 31135"/>
    </justification>
  </clause>

  <clause id="31137">
    <literal><![CDATA[
      L(x * R(T(y,x),z,u),T(y,x),a(T(y,x),z,u)) = a(T(y,x),z,u) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(347,a,251,a(flip),b,31136,a),flip(a)].">
      <j1 rule="hyper" parents="347 251 31136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31138">
    <literal><![CDATA[
      L(R(x,y,z) * u,T(x,u),a(T(x,u),y,z)) = a(T(x,u),y,z) * (x * u)
    ]]></literal>
    <justification jstring="[para(268(a,1),31137(a,1,1))].">
      <j1 rule="para" parents="268 31137"/>
    </justification>
  </clause>

  <clause id="31139">
    <literal><![CDATA[
      L(R(x,y,z) * u,T(x,u),a(x,y,z)) = a(T(x,u),y,z) * (x * u)
    ]]></literal>
    <justification jstring="[para(23894(a,1),31138(a,1,3))].">
      <j1 rule="para" parents="23894 31138"/>
    </justification>
  </clause>

  <clause id="31140">
    <literal><![CDATA[
      L(R(x,y,z) * u,x,a(x,y,z)) = a(T(x,u),y,z) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(21722,a,31139,a)].">
      <j1 rule="hyper" parents="21722 31139"/>
    </justification>
  </clause>

  <clause id="31143">
    <literal><![CDATA[
      L(R(x,y,z) * u,x,a(x,y,z)) = a(x,y,z) * (x * u)
    ]]></literal>
    <justification jstring="[para(23894(a,1),31140(a,2,1))].">
      <j1 rule="para" parents="23894 31140"/>
    </justification>
  </clause>

  <clause id="31144">
    <literal><![CDATA[
      L(R(x,y,z) * u,x,a(x,y,z)) = x * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(347,a,25377,a(flip),b,31143,a),flip(a)].">
      <j1 rule="hyper" parents="347 25377 31143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31146">
    <literal><![CDATA[
      ((x * (y / x)) / x) * R(y / (y / x),z,((y / x) \ y) * (z \ y)) = ((y / (y / x)) * z) * (z \ ((y / (y / x)) \ y))
    ]]></literal>
    <justification jstring="[para(22063(a,1),29587(a,1,2))].">
      <j1 rule="para" parents="22063 29587"/>
    </justification>
  </clause>

  <clause id="31147">
    <literal><![CDATA[
      a(((x \ y) * T(z,u)) \ (x \ ((z * K(x \ y,z)) * y)),w,v5) = a(x,x * y,a(v5,w,T(z * K(x \ y,z),u)))
    ]]></literal>
    <justification jstring="[hyper(24964,a,30425,a)].">
      <j1 rule="hyper" parents="24964 30425"/>
    </justification>
  </clause>

  <clause id="31149">
    <literal><![CDATA[
      a(((x \ y) * T(z,u)) \ (x \ (z * (K(x \ y,z) * y))),w,v5) = a(x,x * y,a(v5,w,T(z * K(x \ y,z),u)))
    ]]></literal>
    <justification jstring="[para(5331(a,1),31147(a,1,1,2,2))].">
      <j1 rule="para" parents="5331 31147"/>
    </justification>
  </clause>

  <clause id="31150">
    <literal><![CDATA[
      a(((x \ y) * T(z,u)) \ (x \ (z * (y * K(y / x,z)))),w,v5) = a(x,x * y,a(v5,w,T(z * K(x \ y,z),u)))
    ]]></literal>
    <justification jstring="[para(7440(a,1),31149(a,1,1,2,2,2))].">
      <j1 rule="para" parents="7440 31149"/>
    </justification>
  </clause>

  <clause id="31151">
    <literal><![CDATA[
      a(x,x * y,a(z,u,T(w * K(x \ y,w),v5))) = a(((x \ y) * T(w,v5)) \ (x \ (w * y)),u,z)
    ]]></literal>
    <justification jstring="[hyper(24963,a,31150,a),flip(a)].">
      <j1 rule="hyper" parents="24963 31150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31152">
    <literal><![CDATA[
      a(x,x * y,a(z,u,T(w * K(x \ y,w),v5))) = a(((x \ y) * w) \ (x \ (w * y)),u,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,23909,a(flip),b,31151,a),flip(a)].">
      <j1 rule="hyper" parents="347 23909 31151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31154">
    <literal><![CDATA[
      a(((x \ y) * z) \ (x \ (z * y)),u,w) = a(x,x * y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(5058(a,1),31152(a,1,3,3)),flip(a)].">
      <j1 rule="para" parents="5058 31152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31155">
    <literal><![CDATA[
      a(((x \ (x * y)) * z) \ (x \ (z * (x * y))),u,w) = a(x,L(y,x,x),a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,24114,a(flip),b,31154,a),flip(a)].">
      <j1 rule="hyper" parents="347 24114 31154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31156">
    <literal><![CDATA[
      a((x * y) \ (z \ (y * (z * x))),u,w) = a(z,L(x,z,z),a(w,u,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),31155(a,1,1,1,1))].">
      <j1 rule="para" parents="9 31155"/>
    </justification>
  </clause>

  <clause id="31157">
    <literal><![CDATA[
      a((x * y) \ (z \ (y * (z * x))),u,w) = a(z,x,a(w,u,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,30120,a(flip),b,31156,a),flip(a)].">
      <j1 rule="hyper" parents="347 30120 31156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31158">
    <literal><![CDATA[
      a(x,y,a(L(z,y,u),w,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y \ (u \ (x \ (u * (x * y)))),w,z) = v5
    ]]></literal>
    <justification jstring="[para(31157(a,1),29700(a,1))].">
      <j1 rule="para" parents="31157 29700"/>
    </justification>
  </clause>

  <clause id="31159">
    <literal><![CDATA[
      a(x \ (y \ (z \ (y * (z * x)))),u,w) = a(z,x,a(w,u,L(y,x,y)))
    ]]></literal>
    <justification jstring="[hyper(31158,a,29930,a)].">
      <j1 rule="hyper" parents="31158 29930"/>
    </justification>
  </clause>

  <clause id="31160">
    <literal><![CDATA[
      a(x \ (y \ (z \ (y * (z * x)))),u,w) = a(z,x,a(w,u,y))
    ]]></literal>
    <justification jstring="[para(12438(a,1),31159(a,2,3))].">
      <j1 rule="para" parents="12438 31159"/>
    </justification>
  </clause>

  <clause id="31162">
    <literal><![CDATA[
      a(x \ ((y / x) \ (a(z,x,u) \ (x * ((a(z,x,u) \ x) \ y)))),w,v5) = a(a(z,x,u),x,a(v5,w,y / x))
    ]]></literal>
    <justification jstring="[para(30976(a,1),31160(a,1,1,2,2,2))].">
      <j1 rule="para" parents="30976 31160"/>
    </justification>
  </clause>

  <clause id="31163">
    <literal><![CDATA[
      a(x \ ((y / x) \ L(y,a(z,x,u),x)),w,v5) = a(a(u,x,z),x,a(v5,w,y / x))
    ]]></literal>
    <justification jstring="[para(30598(a,1),31162(a,1,1,2,2))].">
      <j1 rule="para" parents="30598 31162"/>
    </justification>
  </clause>

  <clause id="31164">
    <literal><![CDATA[
      a(x \ (a(x,a(y,x,z),u) \ x),w,v5) = a(a(z,x,y),x,a(v5,w,u / x))
    ]]></literal>
    <justification jstring="[para(29092(a,1),31163(a,1,1,2))].">
      <j1 rule="para" parents="29092 31163"/>
    </justification>
  </clause>

  <clause id="31165">
    <literal><![CDATA[
      a(x \ L(x,a(y,x,z),u),w,v5) = a(a(y,x,z),x,a(v5,w,u / x))
    ]]></literal>
    <justification jstring="[para(28767(a,1),31164(a,1,1,2))].">
      <j1 rule="para" parents="28767 31164"/>
    </justification>
  </clause>

  <clause id="31166">
    <literal><![CDATA[
      a(a(x,y,z),y,a(u,w,v5 / y)) = a(a(y,a(x,y,z),v5),w,u)
    ]]></literal>
    <justification jstring="[para(28625(a,1),31165(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28625 31165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31167">
    <literal><![CDATA[
      a(a(x,y,z),y,a(u,w,v5 / y)) = a(y,a(x,y,z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,29790,a(flip),b,31166,a),flip(a)].">
      <j1 rule="hyper" parents="347 29790 31166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31168">
    <literal><![CDATA[
      a(a(x,y,z),y,a(u,w,y \ v5)) = a(y,a(x,y,z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(24071(a,1),31167(a,1,3))].">
      <j1 rule="para" parents="24071 31167"/>
    </justification>
  </clause>

  <clause id="31169">
    <literal><![CDATA[
      a(a(x,y,z),y,a(u,w,v5 * y)) = a(y,a(x,y,z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(30802,a,31168,a)].">
      <j1 rule="hyper" parents="30802 31168"/>
    </justification>
  </clause>

  <clause id="31170">
    <literal><![CDATA[
      a(x,y,a(a(z,u,w * y),y,v5)) = a(y,a(x,y,v5),a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(29833,a,31169,a)].">
      <j1 rule="hyper" parents="29833 31169"/>
    </justification>
  </clause>

  <clause id="31171">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,y,v5 * y))) = a(y,a(x,y,w),a(z,u,v5))
    ]]></literal>
    <justification jstring="[para(29790(a,1),31170(a,1,3))].">
      <j1 rule="para" parents="29790 31170"/>
    </justification>
  </clause>

  <clause id="31172">
    <literal><![CDATA[
      a(x,a(y,x,a(z,u,w)),v5) = a(x,a(y,x,z),a(w,u,v5))
    ]]></literal>
    <justification jstring="[hyper(31046,a,31171,a)].">
      <j1 rule="hyper" parents="31046 31171"/>
    </justification>
  </clause>

  <clause id="31173">
    <literal><![CDATA[
      a(x,a(y,z,a(u,x,w)),v5) = a(x,a(u,x,w),a(y,z,v5))
    ]]></literal>
    <justification jstring="[hyper(29834,a,31172,a)].">
      <j1 rule="hyper" parents="29834 31172"/>
    </justification>
  </clause>

  <clause id="31174">
    <literal><![CDATA[
      R(a(a(x,y,z),u,w),w,L(w,u,a(x,y,z)) \ a(u,w,a(x,y,z))) \ a(u,w,a(x,y,z)) = a(u,a(z,y,x),w)
    ]]></literal>
    <justification jstring="[para(28845(a,1),30532(a,1,1,1))].">
      <j1 rule="para" parents="28845 30532"/>
    </justification>
  </clause>

  <clause id="31175">
    <literal><![CDATA[
      R(a(a(x,y,z),u,w),w,a(u,w,a(x,y,z)) * L(w,u,a(x,y,z))) \ a(u,w,a(x,y,z)) = a(u,a(z,y,x),w)
    ]]></literal>
    <justification jstring="[para(27299(a,1),31174(a,1,1))].">
      <j1 rule="para" parents="27299 31174"/>
    </justification>
  </clause>

  <clause id="31176">
    <literal><![CDATA[
      a(a(x,y,z),u,L(w,w,a(u,w,a(x,y,z)) * L(w,u,a(x,y,z)))) \ a(u,w,a(x,y,z)) = a(u,a(z,y,x),w)
    ]]></literal>
    <justification jstring="[para(29117(a,2),31175(a,1,1))].">
      <j1 rule="para" parents="29117 31175"/>
    </justification>
  </clause>

  <clause id="31177">
    <literal><![CDATA[
      a(a(x,y,z),u,L(w,w,w * a(u,w,a(x,y,z)))) \ a(u,w,a(x,y,z)) = a(u,a(z,y,x),w)
    ]]></literal>
    <justification jstring="[para(26687(a,1),31176(a,1,1,3))].">
      <j1 rule="para" parents="26687 31176"/>
    </justification>
  </clause>

  <clause id="31178">
    <literal><![CDATA[
      a(a(x,y,z),u,1 / (1 / w)) \ a(u,w,a(x,y,z)) = a(u,a(z,y,x),w)
    ]]></literal>
    <justification jstring="[para(26359(a,1),31177(a,1,1,3))].">
      <j1 rule="para" parents="26359 31177"/>
    </justification>
  </clause>

  <clause id="31180">
    <literal><![CDATA[
      a(a(x,y,z),u,(1 / w) \ 1) \ a(u,w,a(x,y,z)) = a(u,a(z,y,x),w)
    ]]></literal>
    <justification jstring="[para(4122(a,1),31178(a,1,1))].">
      <j1 rule="para" parents="4122 31178"/>
    </justification>
  </clause>

  <clause id="31182">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ a(u,w,a(x,y,z)) = a(u,a(z,y,x),w)
    ]]></literal>
    <justification jstring="[para(83(a,1),31180(a,1,1,3))].">
      <j1 rule="para" parents="83 31180"/>
    </justification>
  </clause>

  <clause id="31183">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * a(u,w,a(x,y,z)) = a(u,a(z,y,x),w)
    ]]></literal>
    <justification jstring="[hyper(28438,a,31182,a)].">
      <j1 rule="hyper" parents="28438 31182"/>
    </justification>
  </clause>

  <clause id="31184">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(u,z,a(x,y,w)) = a(u,a(w,y,x),z)
    ]]></literal>
    <justification jstring="[para(29790(a,1),31183(a,1,1))].">
      <j1 rule="para" parents="29790 31183"/>
    </justification>
  </clause>

  <clause id="31185">
    <literal><![CDATA[
      (x * a(x,y,a(z,u,w))) * a(u,z,a(x,y,w)) = x * a(u,a(w,y,x),z)
    ]]></literal>
    <justification jstring="[para(31184(a,1),28514(a,2,2))].">
      <j1 rule="para" parents="31184 28514"/>
    </justification>
  </clause>

  <clause id="31186">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,y,a(w,z,u)) = a(u,a(w,y,x),z)
    ]]></literal>
    <justification jstring="[para(29788(a,2),31184(a,1,2))].">
      <j1 rule="para" parents="29788 31184"/>
    </justification>
  </clause>

  <clause id="31187">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(u,x,a(w,y,z)) = a(u,a(z,y,w),x)
    ]]></literal>
    <justification jstring="[para(29803(a,2),31184(a,1,1))].">
      <j1 rule="para" parents="29803 31184"/>
    </justification>
  </clause>

  <clause id="31188">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),v5,v6)) * a(v5,z,a(x,y,L(v6,u,w))) = a(v5,a(v6,y,x),L(z,u,w))
    ]]></literal>
    <justification jstring="[para(30088(a,1),31184(a,1,2))].">
      <j1 rule="para" parents="30088 31184"/>
    </justification>
  </clause>

  <clause id="31189">
    <literal><![CDATA[
      R(x,y,L(a(z,u,w),a(u,z,a(x,y,w)),a(u,z,a(x,y,w)))) = a(u,a(w,y,x),z) * (a(u,z,a(x,y,w)) \ x)
    ]]></literal>
    <justification jstring="[para(31184(a,1),30247(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31184 30247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31190">
    <literal><![CDATA[
      1 * a(x,y,a(z,y,a(u,w,v5))) = a(x,a(a(u,w,v5),y,z),y)
    ]]></literal>
    <justification jstring="[para(30482(a,1),31184(a,1,1))].">
      <j1 rule="para" parents="30482 31184"/>
    </justification>
  </clause>

  <clause id="31191">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(u,z,a(x,y,L(w,x,v5))) = a(u,a(L(w,x,v5),y,x),z)
    ]]></literal>
    <justification jstring="[para(30491(a,1),31184(a,1,1))].">
      <j1 rule="para" parents="30491 31184"/>
    </justification>
  </clause>

  <clause id="31192">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(u,v5 * (x \ v5),a(w,y,z)) = a(u,a(z,y,w),v5 * (x \ v5))
    ]]></literal>
    <justification jstring="[para(30827(a,1),31184(a,1,1))].">
      <j1 rule="para" parents="30827 31184"/>
    </justification>
  </clause>

  <clause id="31193">
    <literal><![CDATA[
      a(x,y * (z \ y),a(u,w,v5)) * a(x,z,a(v5,u,w)) = a(w,a(v5,y * (z \ y),x),u)
    ]]></literal>
    <justification jstring="[para(30838(a,1),31184(a,1,2))].">
      <j1 rule="para" parents="30838 31184"/>
    </justification>
  </clause>

  <clause id="31194">
    <literal><![CDATA[
      a(x,a(a(y,z,u),w,v5),w) = a(x,w,a(v5,w,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(135,a,31190,a),flip(a)].">
      <j1 rule="hyper" parents="135 31190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31195">
    <literal><![CDATA[
      a(x,a(y,z,a(u,w,v5)),z) = a(x,z,a(y,z,a(v5,w,u)))
    ]]></literal>
    <justification jstring="[hyper(26618,a,31194,a)].">
      <j1 rule="hyper" parents="26618 31194"/>
    </justification>
  </clause>

  <clause id="31196">
    <literal><![CDATA[
      a(x,a(y,z,a(u,w,v5)),z) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,z,a(y,z,a(v5,w,u))) = v6
    ]]></literal>
    <justification jstring="[para(31195(a,2),29875(a,1))].">
      <j1 rule="para" parents="31195 29875"/>
    </justification>
  </clause>

  <clause id="31197">
    <literal><![CDATA[
      R(x,y,a(z,u,w)) * a(u,z,a(x,y,w)) = x * a(u,a(w,y,x),z)
    ]]></literal>
    <justification jstring="[para(28958(a,2),31185(a,1,1))].">
      <j1 rule="para" parents="28958 31185"/>
    </justification>
  </clause>

  <clause id="31198">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * a(u,z,a(x,y,w)) = x * a(u,a(w,y,x),z)
    ]]></literal>
    <justification jstring="[para(23247(a,1),31197(a,1,1))].">
      <j1 rule="para" parents="23247 31197"/>
    </justification>
  </clause>

  <clause id="31199">
    <literal><![CDATA[
      a(x,a(L(y,z,u),w,z),v5) = a(z,w,a(v5,x,y)) * a(x,v5,a(z,w,y))
    ]]></literal>
    <justification jstring="[para(30778(a,1),31191(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30778 31191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31200">
    <literal><![CDATA[
      a(x,a(L(y,z,u),w,z),v5) = a(x,a(y,w,z),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,31184,a(flip),b,31199,a),flip(a)].">
      <j1 rule="hyper" parents="347 31184 31199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31202">
    <literal><![CDATA[
      a(x,a(y,z,u),w * (v5 \ w)) = a(v5,z,a(y,x,u)) * a(x,v5,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(30836(a,1),31192(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30836 31192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31203">
    <literal><![CDATA[
      a(x,a(y,z,u),w * (v5 \ w)) = a(x,a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,31187,a(flip),b,31202,a),flip(a)].">
      <j1 rule="hyper" parents="347 31187 31202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31205">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5,v5)) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(25590,a,31203,a)].">
      <j1 rule="hyper" parents="25590 31203"/>
    </justification>
  </clause>

  <clause id="31206">
    <literal><![CDATA[
      a(x,a(y,z,u),w \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,a(y,z,u),v5 * w) = v6
    ]]></literal>
    <justification jstring="[para(31203(a,1),24208(a,1))].">
      <j1 rule="para" parents="31203 24208"/>
    </justification>
  </clause>

  <clause id="31207">
    <literal><![CDATA[
      a(x,a(y,x,z),L(x,u,w) * v5) = a(z,x,a(v5,x,y))
    ]]></literal>
    <justification jstring="[hyper(31206,a,31082,a)].">
      <j1 rule="hyper" parents="31206 31082"/>
    </justification>
  </clause>

  <clause id="31208">
    <literal><![CDATA[
      a(x \ y,a(z,u,w),v5) = a(v5,a(z,u,w),y * x)
    ]]></literal>
    <justification jstring="[hyper(31206,a,28769,a),flip(a)].">
      <j1 rule="hyper" parents="31206 28769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31209">
    <literal><![CDATA[
      a(x \ y,a(z,u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(y * x,a(z,u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(31208(a,2),28775(a,1))].">
      <j1 rule="para" parents="31208 28775"/>
    </justification>
  </clause>

  <clause id="31210">
    <literal><![CDATA[
      a(x * a(y,z,u),y,a(w,y,v5)) = a(w,y,a(x,y,v5))
    ]]></literal>
    <justification jstring="[hyper(30980,a,31207,a)].">
      <j1 rule="hyper" parents="30980 31207"/>
    </justification>
  </clause>

  <clause id="31211">
    <literal><![CDATA[
      a(x,y,a(a(y,z,u) * w,y,v5)) = a(v5,y,a(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(29856,a,31210,a)].">
      <j1 rule="hyper" parents="29856 31210"/>
    </justification>
  </clause>

  <clause id="31213">
    <literal><![CDATA[
      a(x \ (y \ z),a(u,w,v5),L(y,y,x)) = a((x \ z) * y,a(u,w,v5),y)
    ]]></literal>
    <justification jstring="[hyper(31209,a,29785,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="31209 29785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31214">
    <literal><![CDATA[
      a(x \ (y \ z),a(u,y,w),L(y,y,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(u,y,a(x \ z,y,w)) = v5
    ]]></literal>
    <justification jstring="[para(31213(a,2),30966(a,1))].">
      <j1 rule="para" parents="31213 30966"/>
    </justification>
  </clause>

  <clause id="31215">
    <literal><![CDATA[
      a(x,a(y,z * (u \ z),w),v5) = a(w,u,a(v5,x,y)) * a(w,u,a(y,v5,x))
    ]]></literal>
    <justification jstring="[para(30836(a,1),31193(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30836 31193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31216">
    <literal><![CDATA[
      a(x,a(y,z * (u \ z),w),v5) = a(x,a(y,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,31186,a(flip),b,31215,a),flip(a)].">
      <j1 rule="hyper" parents="347 31186 31215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31218">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) * a(u,z,a(x,y,L(w,v5,v6))) = a(u,a(w,y,x),L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(29675(a,1),31188(a,1,1,3))].">
      <j1 rule="para" parents="29675 31188"/>
    </justification>
  </clause>

  <clause id="31219">
    <literal><![CDATA[
      a(x,a(L(y,z,u),w,v5),v6) = a(x,a(y,w,v5),L(v6,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,31184,a(flip),b,31218,a)].">
      <j1 rule="hyper" parents="63 31184 31218"/>
    </justification>
  </clause>

  <clause id="31220">
    <literal><![CDATA[
      a(x,a(y * (y * z),u,w),v5) = a(x,a(z,u,w),L(v5,y,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,26145,a,b,31219,a)].">
      <j1 rule="hyper" parents="63 26145 31219"/>
    </justification>
  </clause>

  <clause id="31221">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,u,v5)) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,31200,a(flip),b,31219,a),flip(a)].">
      <j1 rule="hyper" parents="63 31200 31219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31222">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5,a(v6,v7,y))) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(23120(a,1),31219(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23120 31219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31223">
    <literal><![CDATA[
      a(x,a(y,z,L(u,w,v5)),v6) = a(x,a(y,z,u),L(v6,w,v5))
    ]]></literal>
    <justification jstring="[para(29675(a,1),31219(a,1,2))].">
      <j1 rule="para" parents="29675 31219"/>
    </justification>
  </clause>

  <clause id="31224">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5,a(v6,v7,y))) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,28769,a,b,31222,a),flip(a)].">
      <j1 rule="hyper" parents="347 28769 31222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31225">
    <literal><![CDATA[
      a(x,a(y,x,a(z,u,w)),v5 * a(y,x,a(z,u,w))) = a(L(x,a(w,u,z),y),a(z,u,a(y,x,w)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,31106,a(flip),b,31222,a)].">
      <j1 rule="hyper" parents="63 31106 31222"/>
    </justification>
  </clause>

  <clause id="31226">
    <literal><![CDATA[
      a(x,a(y \ (z \ y),u,w),v5) = a(v5,a(w,u,z),L(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(28776,a,31223,a)].">
      <j1 rule="hyper" parents="28776 31223"/>
    </justification>
  </clause>

  <clause id="31227">
    <literal><![CDATA[
      a(x * y,a(z,x,u),L(x,w,v5)) = a(z,x,a(y,x,L(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,30964,a(flip),b,31223,a),flip(a)].">
      <j1 rule="hyper" parents="63 30964 31223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31228">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ a(z,x,a(u,y,w))) = a(u,a(w,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,30391,a,b,31224,a)].">
      <j1 rule="hyper" parents="63 30391 31224"/>
    </justification>
  </clause>

  <clause id="31229">
    <literal><![CDATA[
      a(x,a(y \ z,u,w),L(v5,y,y)) = a(x,a(y * z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),31220(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 31220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31230">
    <literal><![CDATA[
      a(x,a(y \ z,u,w),v5) = a(x,a(y * z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,31205,a(flip),b,31229,a)].">
      <j1 rule="hyper" parents="63 31205 31229"/>
    </justification>
  </clause>

  <clause id="31232">
    <literal><![CDATA[
      a(x,a(y * (z \ y),u,w),v5) = a(v5,a(w,u,z),L(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,31226,a(flip),b,31230,a),flip(a)].">
      <j1 rule="hyper" parents="63 31226 31230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31233">
    <literal><![CDATA[
      a(x,a(y * (z \ y),u,w),v5) = a(v5,a(w,u,z),x)
    ]]></literal>
    <justification jstring="[hyper(347,a,31221,a(flip),b,31232,a),flip(a)].">
      <j1 rule="hyper" parents="347 31221 31232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31235">
    <literal><![CDATA[
      L(a(x,a(y,x,z),x * u) \ 1,w,v5) = a(y,x,a(u,x,L(z,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,29143,a,b,31227,a)].">
      <j1 rule="hyper" parents="63 29143 31227"/>
    </justification>
  </clause>

  <clause id="31237">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(a(x,z,w),u,y) = a(z,a(w,u,x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,30978,a(flip),b,31228,a)].">
      <j1 rule="hyper" parents="63 30978 31228"/>
    </justification>
  </clause>

  <clause id="31238">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,z,a(y,u,w)) = a(z,a(w,u,x),y)
    ]]></literal>
    <justification jstring="[para(29790(a,1),31237(a,1,2))].">
      <j1 rule="para" parents="29790 31237"/>
    </justification>
  </clause>

  <clause id="31239">
    <literal><![CDATA[
      a(x,y,a(z,y,L(u,y * z,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,y,a(x,y,u)) = v5
    ]]></literal>
    <justification jstring="[para(31235(a,1),31027(a,1))].">
      <j1 rule="para" parents="31235 31027"/>
    </justification>
  </clause>

  <clause id="31241">
    <literal><![CDATA[
      a(x,a(y,x,a(z,u,w)),v5 * a(y,x,a(z,u,w))) = a(x,a(z,u,a(y,x,w)),L(v5,a(w,u,z),y))
    ]]></literal>
    <justification jstring="[hyper(347,a,29675,a(flip),b,31225,a),flip(a)].">
      <j1 rule="hyper" parents="347 29675 31225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31242">
    <literal><![CDATA[
      a(x,a(y,x,a(z,u,w)),v5 * a(y,x,a(z,u,w))) = a(x,a(y,x,w),a(z,u,L(v5,a(w,u,z),y)))
    ]]></literal>
    <justification jstring="[hyper(347,a,31173,a(flip),b,31241,a),flip(a)].">
      <j1 rule="hyper" parents="347 31173 31241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31243">
    <literal><![CDATA[
      a(x,a(y,x,a(z,u,w)),v5 * a(y,x,a(z,u,w))) = a(x,a(y,x,w),a(z,u,v5))
    ]]></literal>
    <justification jstring="[para(30503(a,1),31242(a,2,3))].">
      <j1 rule="para" parents="30503 31242"/>
    </justification>
  </clause>

  <clause id="31244">
    <literal><![CDATA[
      a(x,a(y,z,a(u,w,v5)),z) = a(z,a(y,z,v5),a(u,w,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,31042,a(flip),b,31243,a)].">
      <j1 rule="hyper" parents="63 31042 31243"/>
    </justification>
  </clause>

  <clause id="31246">
    <literal><![CDATA[
      a(x,a(y,x,z),a(u,w,v5)) = a(v5,x,a(y,x,a(z,w,u)))
    ]]></literal>
    <justification jstring="[hyper(31196,a,31244,a),flip(a)].">
      <j1 rule="hyper" parents="31196 31244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31247">
    <literal><![CDATA[
      R(x,y,L(a(z,u,w),a(u,z,a(x,y,w)),a(u,z,a(x,y,w)))) = a(u,a(w,y,x),z) * L(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[para(29828(a,1),31189(a,2,2))].">
      <j1 rule="para" parents="29828 31189"/>
    </justification>
  </clause>

  <clause id="31248">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * L(u,z,a(x,w,y)) = R(u,z,a(w,x,y))
    ]]></literal>
    <justification jstring="[para(28339(a,1),31247(a,1,3)),flip(a)].">
      <j1 rule="para" parents="28339 31247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31249">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * L(u,z,a(x,w,y)) = L(u,z,a(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,23247,a(flip),b,31248,a),flip(a)].">
      <j1 rule="hyper" parents="347 23247 31248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31250">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * L(u,z,a(x,w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(u,z,a(w,x,y)) = v5
    ]]></literal>
    <justification jstring="[para(31248(a,2),23284(a,1))].">
      <j1 rule="para" parents="31248 23284"/>
    </justification>
  </clause>

  <clause id="31252">
    <literal><![CDATA[
      ((x * (y / x)) / x) * R(y / (y / x),z,x * (z \ y)) = ((y / (y / x)) * z) * (z \ ((y / (y / x)) \ y))
    ]]></literal>
    <justification jstring="[para(83(a,1),31146(a,1,2,3,1))].">
      <j1 rule="para" parents="83 31146"/>
    </justification>
  </clause>

  <clause id="31253">
    <literal><![CDATA[
      (x / y) * R(y,z,y * (z \ x)) = ((x / (x / y)) * z) * (z \ ((x / (x / y)) \ x))
    ]]></literal>
    <justification jstring="[hyper(22625,a,31252,a)].">
      <j1 rule="hyper" parents="22625 31252"/>
    </justification>
  </clause>

  <clause id="31255">
    <literal><![CDATA[
      ((x / (x / y)) * z) * (z \ ((x / (x / y)) \ x)) = (y * z) * (z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,29582,a(flip),b,31253,a),flip(a)].">
      <j1 rule="hyper" parents="63 29582 31253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31256">
    <literal><![CDATA[
      ((x / (x / y)) * z) * (z \ (x / y)) = (y * z) * (z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(83(a,1),31255(a,1,2,2))].">
      <j1 rule="para" parents="83 31255"/>
    </justification>
  </clause>

  <clause id="31257">
    <literal><![CDATA[
      ((x / (x / a(y,z,u))) * w) * (w \ (x / a(y,z,u))) = (w * L(w \ (a(y,z,u) \ x),w,a(y,z,u))) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,26383,a,b,31256,a),flip(a)].">
      <j1 rule="hyper" parents="347 26383 31256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31259">
    <literal><![CDATA[
      ((x / (x / a(y,z,u))) * w) * (w \ (x / a(y,z,u))) = (w * ((a(y,z,u) * w) \ x)) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(329(a,1),31257(a,2,1,2))].">
      <j1 rule="para" parents="329 31257"/>
    </justification>
  </clause>

  <clause id="31260">
    <literal><![CDATA[
      a(x,L(L(y,a(z,u,w),v5),v5,a(z,u,w)),a(v5,y,a(w,u,z))) \ 1 = a(v5,y,a(w,u,z)) \ a(v5,y,a(w,u,L(z,y,x)))
    ]]></literal>
    <justification jstring="[para(29113(a,2),29158(a,2,2,3))].">
      <j1 rule="para" parents="29113 29158"/>
    </justification>
  </clause>

  <clause id="31261">
    <literal><![CDATA[
      L(x \ y,(y \ x) * x,a(z,u,w)) * ((x \ y) \ x) = x * a(z,u,a(x * ((x \ y) \ x),(x \ y) \ x,w))
    ]]></literal>
    <justification jstring="[hyper(931,a,29952,a)].">
      <j1 rule="hyper" parents="931 29952"/>
    </justification>
  </clause>

  <clause id="31262">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,(y \ x) * x,a(z,u,w)) \ x) = x * a(w,u,a(x * ((x \ y) \ x),(x \ y) \ x,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,27568,a(flip),b,31261,a)].">
      <j1 rule="hyper" parents="63 27568 31261"/>
    </justification>
  </clause>

  <clause id="31263">
    <literal><![CDATA[
      L(x / y,(x \ y) * y,a(z,u,w)) \ x = y * a(w,u,a(y * ((y \ x) \ y),(y \ x) \ y,z))
    ]]></literal>
    <justification jstring="[hyper(21412,a,31262,a)].">
      <j1 rule="hyper" parents="21412 31262"/>
    </justification>
  </clause>

  <clause id="31264">
    <literal><![CDATA[
      L(x / y,x,a(z,u,w)) \ x = y * a(w,u,a(y * ((y \ x) \ y),(y \ x) \ y,z))
    ]]></literal>
    <justification jstring="[para(30221(a,1),31263(a,1,1))].">
      <j1 rule="para" parents="30221 31263"/>
    </justification>
  </clause>

  <clause id="31265">
    <literal><![CDATA[
      L(x / y,x,a(z,u,w)) \ x = y * a(w,u,a(y * ((y \ x) \ y),(x \ y) * y,z))
    ]]></literal>
    <justification jstring="[para(24531(a,1),31264(a,2,2,3))].">
      <j1 rule="para" parents="24531 31264"/>
    </justification>
  </clause>

  <clause id="31266">
    <literal><![CDATA[
      L(x / y,x,a(z,u,w)) \ x = y * a(w,u,a(y * (y * (x \ y)),(x \ y) * y,z))
    ]]></literal>
    <justification jstring="[para(24405(a,1),31265(a,2,2,3))].">
      <j1 rule="para" parents="24405 31265"/>
    </justification>
  </clause>

  <clause id="31267">
    <literal><![CDATA[
      L(x / y,x,a(z,u,w)) \ x = y * a(w,u,a(x \ y,(x \ y) * y,z))
    ]]></literal>
    <justification jstring="[para(30782(a,1),31266(a,2,2))].">
      <j1 rule="para" parents="30782 31266"/>
    </justification>
  </clause>

  <clause id="31268">
    <literal><![CDATA[
      L(x / y,x,a(z,u,w)) \ x = y * a(w,u,a(x \ y,x,z))
    ]]></literal>
    <justification jstring="[para(30128(a,1),31267(a,2,2,3))].">
      <j1 rule="para" parents="30128 31267"/>
    </justification>
  </clause>

  <clause id="31270">
    <literal><![CDATA[
      L(x / y,x,a(z,u,w)) \ x = y * a(w,u,a(y * x,x,z))
    ]]></literal>
    <justification jstring="[para(29729(a,1),31268(a,2,2))].">
      <j1 rule="para" parents="29729 31268"/>
    </justification>
  </clause>

  <clause id="31271">
    <literal><![CDATA[
      a(L(x / y,x,a(z,u,w)),L(x / y,x,a(z,u,w)),x) / ((y * a(w,u,a(y * x,x,z))) / x) = L(x / y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(31270(a,1),18985(a,1,2,1))].">
      <j1 rule="para" parents="31270 18985"/>
    </justification>
  </clause>

  <clause id="31272">
    <literal><![CDATA[
      a(x \ y,z,L(u,x * ((w / (x * w)) \ 1),((x * w) \ w) \ 1)) = a(a(x \ 1,x,w) \ (((w / (x * w)) \ 1) \ y),z,u)
    ]]></literal>
    <justification jstring="[para(21471(a,1),30158(a,1,3))].">
      <j1 rule="para" parents="21471 30158"/>
    </justification>
  </clause>

  <clause id="31273">
    <literal><![CDATA[
      (x * (y \ z)) * ((y \ (z * x)) \ ((x * (y \ z)) \ (y \ (z * x)))) = a(y,y * z,a(x,x * (y \ z),y \ z)) \ 1
    ]]></literal>
    <justification jstring="[para(26994(a,1),30173(a,2,1))].">
      <j1 rule="para" parents="26994 30173"/>
    </justification>
  </clause>

  <clause id="31274">
    <literal><![CDATA[
      (x * (y \ z)) * ((y \ (z * x)) \ ((x * (y \ z)) \ (y \ (z * x)))) = a(x,x * (y \ z),a(y,z * y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(30846(a,1),31273(a,2,1))].">
      <j1 rule="para" parents="30846 31273"/>
    </justification>
  </clause>

  <clause id="31275">
    <literal><![CDATA[
      (x * (y \ z)) * ((y \ (z * x)) \ ((x * (y \ z)) \ (y \ (z * x)))) = 1 \ 1
    ]]></literal>
    <justification jstring="[para(30848(a,1),31274(a,2,1))].">
      <j1 rule="para" parents="30848 31274"/>
    </justification>
  </clause>

  <clause id="31276">
    <literal><![CDATA[
      (x * (y \ z)) * ((y \ (z * x)) \ ((x * (y \ z)) \ (y \ (z * x)))) = 1
    ]]></literal>
    <justification jstring="[hyper(347,a,68,a(flip),b,31275,a),flip(a)].">
      <j1 rule="hyper" parents="347 68 31275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31279">
    <literal><![CDATA[
      (x \ (y * z)) * ((z * (x \ y)) \ 1) = (z * (x \ y)) \ (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(189,a,19774,a,b,31276,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="189 19774 31276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31280">
    <literal><![CDATA[
      R(x,y,(z * (u \ w)) \ (u \ (w * z))) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,(z * (u \ w)) * (u \ (w * z))) = v5
    ]]></literal>
    <justification jstring="[para(31279(a,1),20896(a,1,3))].">
      <j1 rule="para" parents="31279 20896"/>
    </justification>
  </clause>

  <clause id="31281">
    <literal><![CDATA[
      (x * a(y,x,z)) \ (a(x,a(y,x,z),(u * (x * a(y,x,z))) * a(y,x,z)) \ u) = L((x * a(y,x,z)) \ u,a(y,x,z),x)
    ]]></literal>
    <justification jstring="[para(28770(a,1),30937(a,1,2,1))].">
      <j1 rule="para" parents="28770 30937"/>
    </justification>
  </clause>

  <clause id="31282">
    <literal><![CDATA[
      a(x \ y,z,L(u,x * ((w / (x * w)) \ 1),(w \ (x \ w)) \ 1)) = a(a(x \ 1,x,w) \ (((w / (x * w)) \ 1) \ y),z,u)
    ]]></literal>
    <justification jstring="[para(21900(a,1),31272(a,1,3))].">
      <j1 rule="para" parents="21900 31272"/>
    </justification>
  </clause>

  <clause id="31283">
    <literal><![CDATA[
      (x * a(y,x,z)) \ (a(u * (x * a(y,x,z)),a(y,x,z),x) \ u) = L((x * a(y,x,z)) \ u,a(y,x,z),x)
    ]]></literal>
    <justification jstring="[para(31042(a,1),31281(a,1,2,1))].">
      <j1 rule="para" parents="31042 31281"/>
    </justification>
  </clause>

  <clause id="31284">
    <literal><![CDATA[
      a(x \ y,z,L(u,x * ((w / (x * w)) \ 1),w \ ((x \ 1) \ w))) = a(a(x \ 1,x,w) \ (((w / (x * w)) \ 1) \ y),z,u)
    ]]></literal>
    <justification jstring="[para(27641(a,1),31282(a,1,3))].">
      <j1 rule="para" parents="27641 31282"/>
    </justification>
  </clause>

  <clause id="31285">
    <literal><![CDATA[
      a(x \ y,z,L(u,x * (w / (x * w)),w \ ((x \ 1) \ w))) = a(a(x \ 1,x,w) \ (((w / (x * w)) \ 1) \ y),z,u)
    ]]></literal>
    <justification jstring="[para(3229(a,1),31284(a,1,3))].">
      <j1 rule="para" parents="3229 31284"/>
    </justification>
  </clause>

  <clause id="31286">
    <literal><![CDATA[
      a(x \ y,z,L(u,x * ((x * w) \ w),w \ ((x \ 1) \ w))) = a(a(x \ 1,x,w) \ (((w / (x * w)) \ 1) \ y),z,u)
    ]]></literal>
    <justification jstring="[para(21681(a,1),31285(a,1,3))].">
      <j1 rule="para" parents="21681 31285"/>
    </justification>
  </clause>

  <clause id="31287">
    <literal><![CDATA[
      a(x \ y,z,L(u,x * (w \ (x \ w)),w \ ((x \ 1) \ w))) = a(a(x \ 1,x,w) \ (((w / (x * w)) \ 1) \ y),z,u)
    ]]></literal>
    <justification jstring="[para(21888(a,1),31286(a,1,3))].">
      <j1 rule="para" parents="21888 31286"/>
    </justification>
  </clause>

  <clause id="31288">
    <literal><![CDATA[
      a(a(x \ 1,x,y) \ (((y / (x * y)) \ 1) \ z),u,w) = a(x \ z,u,L(w,a(x,x,y),y \ ((x \ 1) \ y)))
    ]]></literal>
    <justification jstring="[para(21788(a,1),31287(a,1,3)),flip(a)].">
      <j1 rule="para" parents="21788 31287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31289">
    <literal><![CDATA[
      a(x,y,(z * (a(u,w,v5) \ a(v5,w,u))) \ v6) = a(x,y,z \ (a(u,w,v5) * (a(v5,w,u) \ v6)))
    ]]></literal>
    <justification jstring="[hyper(29199,a,28812,a)].">
      <j1 rule="hyper" parents="29199 28812"/>
    </justification>
  </clause>

  <clause id="31291">
    <literal><![CDATA[
      a(x,L(L(y \ 1,z * y,z * y),y,z),u) = a(x,L(z \ ((((z * y) \ 1) \ z) / z),z * (z \ (((z * y) \ 1) \ z)),z),u)
    ]]></literal>
    <justification jstring="[para(21681(a,1),30156(a,2,2))].">
      <j1 rule="para" parents="21681 30156"/>
    </justification>
  </clause>

  <clause id="31292">
    <literal><![CDATA[
      a(L(x / y,x,a(z,u,w)),L(y \ x,x,a(z,u,w)),x) / ((y * a(w,u,a(y * x,x,z))) / x) = L(x / y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(24024(a,1),31271(a,1,1))].">
      <j1 rule="para" parents="24024 31271"/>
    </justification>
  </clause>

  <clause id="31293">
    <literal><![CDATA[
      a(x,L(L(y \ 1,z * y,z * y),y,z),u) = a(x,L(z \ ((((z * y) \ 1) \ z) / z),((z * y) \ 1) \ z,z),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),31291(a,2,2,2))].">
      <j1 rule="para" parents="10 31291"/>
    </justification>
  </clause>

  <clause id="31295">
    <literal><![CDATA[
      a(x / y,L(y \ x,x,a(z,u,w)),L(x,x,a(z,u,w))) / ((y * a(w,u,a(y * x,x,z))) / x) = L(x / y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(29675(a,1),31292(a,1,1))].">
      <j1 rule="para" parents="29675 31292"/>
    </justification>
  </clause>

  <clause id="31296">
    <literal><![CDATA[
      a(x \ y,L(x \ y,y,a(z,u,w)),L(y,y,a(z,u,w))) / ((x * a(w,u,a(x * y,y,z))) / y) = L(y / x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(23893(a,1),31295(a,1,1))].">
      <j1 rule="para" parents="23893 31295"/>
    </justification>
  </clause>

  <clause id="31297">
    <literal><![CDATA[
      a(x \ y,x \ y,L(L(y,y,a(z,u,w)),y,a(z,u,w))) / ((x * a(w,u,a(x * y,y,z))) / y) = L(y / x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(29678(a,1),31296(a,1,1))].">
      <j1 rule="para" parents="29678 31296"/>
    </justification>
  </clause>

  <clause id="31298">
    <literal><![CDATA[
      a(x \ y,x \ y,y) / ((x * a(z,u,a(x * y,y,w))) / y) = L(y / x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(25583(a,1),31297(a,1,1))].">
      <j1 rule="para" parents="25583 31297"/>
    </justification>
  </clause>

  <clause id="31299">
    <literal><![CDATA[
      ((x / y) * (y / x)) / ((y * a(z,u,a(y * x,x,w))) / x) = L(x / y,x,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(19003(a,1),31298(a,1,1))].">
      <j1 rule="para" parents="19003 31298"/>
    </justification>
  </clause>

  <clause id="31301">
    <literal><![CDATA[
      ((x / y) * (y / x)) / L(y / x,x,a(z,u,w)) = L(x / y,x,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(29951(a,1),31299(a,1,2))].">
      <j1 rule="para" parents="29951 31299"/>
    </justification>
  </clause>

  <clause id="31302">
    <literal><![CDATA[
      (x / y) * (L(x / y,y,a(z,u,w)) \ (y / x)) = L(y / x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(21064,a,31301,a)].">
      <j1 rule="hyper" parents="21064 31301"/>
    </justification>
  </clause>

  <clause id="31303">
    <literal><![CDATA[
      (a(a(x,y,z),u,w * u) * u) / w = L(u / w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,30365,a(flip),b,31302,a)].">
      <j1 rule="hyper" parents="63 30365 31302"/>
    </justification>
  </clause>

  <clause id="31304">
    <literal><![CDATA[
      (L(x / y,y,a(z,u,w)) \ x) / x = L(y / x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(27228(a,2),31303(a,1,1))].">
      <j1 rule="para" parents="27228 31303"/>
    </justification>
  </clause>

  <clause id="31305">
    <literal><![CDATA[
      L(x / y,y,a(z,u,w)) \ x = x * L(x \ y,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(37,a,759,a,b,31304,a),flip(a)].">
      <j1 rule="hyper" parents="37 759 31304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31306">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,w)) = y * a(w,u,a(x * y,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,29797,a(flip),b,31305,a),flip(a)].">
      <j1 rule="hyper" parents="63 29797 31305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31307">
    <literal><![CDATA[
      (a(a(x,y,z) * u,a(x,y,z) * u,a(x,y,z)) \ w) * (a(x,y,z) \ 1) = w * L(a(x,y,z) \ 1,u,a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(14922(a,1),29400(a,1,1,1))].">
      <j1 rule="para" parents="14922 29400"/>
    </justification>
  </clause>

  <clause id="31308">
    <literal><![CDATA[
      (a(x,y,a(a(x,y,z) * u,u,z)) \ w) * (a(x,y,z) \ 1) = w * L(a(x,y,z) \ 1,u,a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(29818(a,1),31307(a,1,1,1))].">
      <j1 rule="para" parents="29818 31307"/>
    </justification>
  </clause>

  <clause id="31309">
    <literal><![CDATA[
      (x * (((y \ z) * (z \ y)) \ z)) \ (((y \ z) * (z \ y)) \ (z * x)) = (x * z) \ (z * x)
    ]]></literal>
    <justification jstring="[para(31071(a,1),30916(a,2,1))].">
      <j1 rule="para" parents="31071 30916"/>
    </justification>
  </clause>

  <clause id="31310">
    <literal><![CDATA[
      (x * (((y \ z) * (z \ y)) \ z)) \ (((y \ z) * (z \ y)) \ (z * x)) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,16,a,b,31309,a),flip(a)].">
      <j1 rule="hyper" parents="347 16 31309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31312">
    <literal><![CDATA[
      K(x,y) * (y * (((z \ x) * (x \ z)) \ x)) = ((z \ x) * (x \ z)) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,31310,a(flip),b,21377,a)].">
      <j1 rule="hyper" parents="133 31310 21377"/>
    </justification>
  </clause>

  <clause id="31313">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (y * z) = K(y,z) * (z * (x * (1 / (y \ x))))
    ]]></literal>
    <justification jstring="[para(30913(a,1),31312(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="30913 31312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31314">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (y * z) = z * (K(y,z) * (x * (1 / (y \ x))))
    ]]></literal>
    <justification jstring="[hyper(347,a,5353,a(flip),b,31313,a),flip(a)].">
      <j1 rule="hyper" parents="347 5353 31313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31315">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (y * z) = z * T(x * (1 / (y \ x)),z)
    ]]></literal>
    <justification jstring="[para(31091(a,1),31314(a,2,2))].">
      <j1 rule="para" parents="31091 31314"/>
    </justification>
  </clause>

  <clause id="31316">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (y * z) = (x * (1 / (y \ x))) * z
    ]]></literal>
    <justification jstring="[hyper(347,a,111,a(flip),b,31315,a),flip(a)].">
      <j1 rule="hyper" parents="347 111 31315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31317">
    <literal><![CDATA[
      a(x,L(y * z,y * z,z) \ u,w) = a(x,((z * (1 / (y \ z))) * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(31316(a,1),30587(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="31316 30587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31318">
    <literal><![CDATA[
      a(x,L(1 / (y \ z),z,z) \ u,w) = a(x,L(y * z,y * z,z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24836,a(flip),b,31317,a)].">
      <j1 rule="hyper" parents="347 24836 31317"/>
    </justification>
  </clause>

  <clause id="31319">
    <literal><![CDATA[
      a(x,L((y \ z) \ 1,z,z) \ u,w) = a(x,L(y * z,y * z,z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(24012,a,31318,a)].">
      <j1 rule="hyper" parents="24012 31318"/>
    </justification>
  </clause>

  <clause id="31320">
    <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(24175,a,31319,a),flip(a)].">
      <j1 rule="hyper" parents="24175 31319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31321">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ R(a(z,u,w) * (K(y,x) * v5),a(z,u,w) \ K(x,y),v6 * (a(z,u,w) \ K(x,y)))) = L(v5,a(w,u,z),v6)
    ]]></literal>
    <justification jstring="[para(28396(a,1),28761(a,1,2,2,1))].">
      <j1 rule="para" parents="28396 28761"/>
    </justification>
  </clause>

  <clause id="31322">
    <literal><![CDATA[
      L((x \ (x \ R(x,y,z))) \ u,(x \ R(x,y,z)) / x,((x \ R(x,y,z)) / x) \ 1) = 1 \ ((((x \ R(x,y,z)) / x) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(28589(a,1),29600(a,1,1,1))].">
      <j1 rule="para" parents="28589 29600"/>
    </justification>
  </clause>

  <clause id="31323">
    <literal><![CDATA[
      L((x * x) * (R(x,y,z) \ u),(x \ R(x,y,z)) / x,((x \ R(x,y,z)) / x) \ 1) = 1 \ ((((x \ R(x,y,z)) / x) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(1779(a,1),31322(a,1,1))].">
      <j1 rule="para" parents="1779 31322"/>
    </justification>
  </clause>

  <clause id="31324">
    <literal><![CDATA[
      L((x * x) * (R(x,y,z) \ u),(x \ R(x,y,z)) / x,x * (R(x,y,z) \ x)) = 1 \ ((((x \ R(x,y,z)) / x) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(29599(a,1),31323(a,1,3))].">
      <j1 rule="para" parents="29599 31323"/>
    </justification>
  </clause>

  <clause id="31325">
    <literal><![CDATA[
      L((x * x) * (R(x,y,z) \ u),x \ (x \ R(x,y,z)),x * (R(x,y,z) \ x)) = 1 \ ((((x \ R(x,y,z)) / x) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(21725,a,31324,a)].">
      <j1 rule="hyper" parents="21725 31324"/>
    </justification>
  </clause>

  <clause id="31326">
    <literal><![CDATA[
      L((x * x) * (R(x,y,z) \ u),x \ (x \ L(x,y,z)),x * (R(x,y,z) \ x)) = 1 \ ((((x \ R(x,y,z)) / x) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(23829,a,31325,a)].">
      <j1 rule="hyper" parents="23829 31325"/>
    </justification>
  </clause>

  <clause id="31327">
    <literal><![CDATA[
      L((x * x) * (R(x,y,z) \ u),L(x \ 1,y,z),x * (R(x,y,z) \ x)) = 1 \ ((((x \ R(x,y,z)) / x) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(3344(a,1),31326(a,1,2))].">
      <j1 rule="para" parents="3344 31326"/>
    </justification>
  </clause>

  <clause id="31328">
    <literal><![CDATA[
      L((x * x) * (R(x,y,z) \ u),L(x,y,z),x * (R(x,y,z) \ x)) = 1 \ ((((x \ R(x,y,z)) / x) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(3527,a,31327,a)].">
      <j1 rule="hyper" parents="3527 31327"/>
    </justification>
  </clause>

  <clause id="31329">
    <literal><![CDATA[
      L((x * x) * (R(x,y,z) \ u),L(x,y,z),x * (R(x,y,z) \ x)) = 1 \ ((x * (R(x,y,z) \ x)) * u)
    ]]></literal>
    <justification jstring="[para(29599(a,1),31328(a,2,2,1))].">
      <j1 rule="para" parents="29599 31328"/>
    </justification>
  </clause>

  <clause id="31330">
    <literal><![CDATA[
      L((x * x) * (R(x,y,z) \ u),L(x,y,z),x * (R(x,y,z) \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      (x * (R(x,y,z) \ x)) * u = w
    ]]></literal>
    <justification jstring="[para(31329(a,2),185(a,1))].">
      <j1 rule="para" parents="31329 185"/>
    </justification>
  </clause>

  <clause id="31331">
    <literal><![CDATA[
      L((x * x) * (R(x,y,z) \ u),L(x,y,z),x * (x \ L(x,y,z))) = (x * (R(x,y,z) \ x)) * u
    ]]></literal>
    <justification jstring="[hyper(31330,a,27637,a),flip(a)].">
      <j1 rule="hyper" parents="31330 27637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31332">
    <literal><![CDATA[
      L((x * x) * (R(x,y,z) \ u),L(x,y,z),L(x,y,z)) = (x * (R(x,y,z) \ x)) * u
    ]]></literal>
    <justification jstring="[para(10(a,1),31331(a,1,3))].">
      <j1 rule="para" parents="10 31331"/>
    </justification>
  </clause>

  <clause id="31333">
    <literal><![CDATA[
      L((x * x) * (R(x,y,z) \ u),x,x) = (x * (R(x,y,z) \ x)) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,27075,a(flip),b,31332,a)].">
      <j1 rule="hyper" parents="63 27075 31332"/>
    </justification>
  </clause>

  <clause id="31335">
    <literal><![CDATA[
      (x * (R(x,y,z) \ x)) * u = x * (x * (R(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(3249,a,31333,a),flip(a)].">
      <j1 rule="hyper" parents="3249 31333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31337">
    <literal><![CDATA[
      x * (x * (R(x,y,z) \ u)) = (a(x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[para(29058(a,1),31335(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29058 31335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31338">
    <literal><![CDATA[
      (a(x,y,y) \ x) * z = x * (a(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[para(30568(a,1),31337(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30568 31337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31339">
    <literal><![CDATA[
      (a(x,y,y) \ x) * R(y,z,u) = x / (R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(347,a,26469,a(flip),b,31338,a),flip(a)].">
      <j1 rule="hyper" parents="347 26469 31338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31340">
    <literal><![CDATA[
      (x / y) * L(z,y,L(x,y,y)) = x * (a(x,y,y) \ ((1 / y) * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,27901,a(flip),b,31338,a)].">
      <j1 rule="hyper" parents="63 27901 31338"/>
    </justification>
  </clause>

  <clause id="31342">
    <literal><![CDATA[
      R(x,y,z) * (x \ (u / (x \ 1))) = u / (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,27845,a,b,31339,a)].">
      <j1 rule="hyper" parents="63 27845 31339"/>
    </justification>
  </clause>

  <clause id="31343">
    <literal><![CDATA[
      a(x,L(((y \ (z / (y \ 1))) \ 1) * L(y,u,w),v5,v6),v7) = a(x,L(z / (R(y,u,w) \ 1),v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(31342(a,1),26836(a,2,2,1))].">
      <j1 rule="para" parents="31342 26836"/>
    </justification>
  </clause>

  <clause id="31344">
    <literal><![CDATA[
      (x / y) * L(z,y,L(x,y,y)) = x * (L(1 / y,y,x) * z)
    ]]></literal>
    <justification jstring="[para(27840(a,1),31340(a,2,2))].">
      <j1 rule="para" parents="27840 31340"/>
    </justification>
  </clause>

  <clause id="31345">
    <literal><![CDATA[
      x * (L(1 / y,y,x) * z) = (x / y) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(29747(a,1),31344(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29747 31344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31346">
    <literal><![CDATA[
      ((x / y) * L(z,y,x)) / T(x / y,z) = L(z,L(y,y,x),x)
    ]]></literal>
    <justification jstring="[para(31345(a,1),14590(a,1,1))].">
      <j1 rule="para" parents="31345 14590"/>
    </justification>
  </clause>

  <clause id="31347">
    <literal><![CDATA[
      (x / y) \ ((x / y) * L(z,y,x)) = L(z,x * (y \ x),x)
    ]]></literal>
    <justification jstring="[para(31345(a,1),30138(a,1,2))].">
      <j1 rule="para" parents="31345 30138"/>
    </justification>
  </clause>

  <clause id="31348">
    <literal><![CDATA[
      L(x,y * (z \ y),y) = L(x,z,y)
    ]]></literal>
    <justification jstring="[hyper(358,a,31347,a)].">
      <j1 rule="hyper" parents="358 31347"/>
    </justification>
  </clause>

  <clause id="31350">
    <literal><![CDATA[
      L(x,y \ z,z) = L(x,y * z,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,12401,a(flip),b,31348,a)].">
      <j1 rule="hyper" parents="63 12401 31348"/>
    </justification>
  </clause>

  <clause id="31351">
    <literal><![CDATA[
      a((x \ (y \ x)) \ (x \ z),u,w) = a((y \ x) \ z,u,L(w,y,x))
    ]]></literal>
    <justification jstring="[para(31348(a,1),30140(a,1,3)),flip(a)].">
      <j1 rule="para" parents="31348 30140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31352">
    <literal><![CDATA[
      a(x,L(L(y \ 1,z * y,z * y),y,z),u) = a(x,L(z \ ((((z * y) \ 1) \ z) / z),((z * y) \ 1) * z,z),u)
    ]]></literal>
    <justification jstring="[para(31350(a,1),31293(a,2,2))].">
      <j1 rule="para" parents="31350 31293"/>
    </justification>
  </clause>

  <clause id="31353">
    <literal><![CDATA[
      L(x,L(y,y,z),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(21354,a,31346,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="21354 31346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31354">
    <literal><![CDATA[
      L(x,y \ (y / (1 / z)),z * y) = L(x,z,z * y)
    ]]></literal>
    <justification jstring="[para(10249(a,1),31353(a,1,2))].">
      <j1 rule="para" parents="10249 31353"/>
    </justification>
  </clause>

  <clause id="31355">
    <literal><![CDATA[
      L(x,y \ ((1 / z) \ y),z * y) = L(x,z,z * y)
    ]]></literal>
    <justification jstring="[hyper(21763,a,31354,a)].">
      <j1 rule="hyper" parents="21763 31354"/>
    </justification>
  </clause>

  <clause id="31356">
    <literal><![CDATA[
      L(x,y \ ((z \ 1) \ y),z * y) = L(x,z,z * y)
    ]]></literal>
    <justification jstring="[hyper(21828,a,31355,a)].">
      <j1 rule="hyper" parents="21828 31355"/>
    </justification>
  </clause>

  <clause id="31357">
    <literal><![CDATA[
      L(x,y \ (z \ y),z * y) = L(x,z,z * y)
    ]]></literal>
    <justification jstring="[hyper(22672,a,31356,a)].">
      <j1 rule="hyper" parents="22672 31356"/>
    </justification>
  </clause>

  <clause id="31358">
    <literal><![CDATA[
      L(x,L(y,z,z),y * z) = L(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,30134,a(flip),b,31357,a)].">
      <j1 rule="hyper" parents="63 30134 31357"/>
    </justification>
  </clause>

  <clause id="31359">
    <literal><![CDATA[
      L(x,L(y,z,z),z * y) = L(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(20105,a,31358,a)].">
      <j1 rule="hyper" parents="20105 31358"/>
    </justification>
  </clause>

  <clause id="31360">
    <literal><![CDATA[
      a(x,y,L(z,u,u * x)) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[para(31359(a,1),30652(a,1,3))].">
      <j1 rule="para" parents="31359 30652"/>
    </justification>
  </clause>

  <clause id="31361">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,z)) = a(x,y,x * ((z \ x) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,30280,a(flip),b,31360,a),flip(a)].">
      <j1 rule="hyper" parents="63 30280 31360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31362">
    <literal><![CDATA[
      a(x,y,x * ((z \ x) * u)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(14994,a,31361,a),flip(a)].">
      <j1 rule="hyper" parents="14994 31361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31363">
    <literal><![CDATA[
      a(x,y,x * (z * (u \ x))) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(24190,a,31362,a)].">
      <j1 rule="hyper" parents="24190 31362"/>
    </justification>
  </clause>

  <clause id="31364">
    <literal><![CDATA[
      a(x,y,(R(x,z,z) * z) * u) = a(x,y,(u * z) * x)
    ]]></literal>
    <justification jstring="[hyper(30022,a,31363,a),flip(a)].">
      <j1 rule="hyper" parents="30022 31363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31365">
    <literal><![CDATA[
      a(x \ y,z,(x \ y) * (u * (y * a(x,x,y)))) = a(x \ y,z,(x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(15286(a,1),31363(a,1,3,2,2))].">
      <j1 rule="para" parents="15286 31363"/>
    </justification>
  </clause>

  <clause id="31366">
    <literal><![CDATA[
      a(x,y,(L(x,z,z) * z) * u) = a(x,y,(u * z) * x)
    ]]></literal>
    <justification jstring="[hyper(25282,a,31364,a)].">
      <j1 rule="hyper" parents="25282 31364"/>
    </justification>
  </clause>

  <clause id="31367">
    <literal><![CDATA[
      a(x,y,(z * u) * x) = a(x,y,z * (u \ x))
    ]]></literal>
    <justification jstring="[hyper(63,a,24930,a(flip),b,31366,a),flip(a)].">
      <j1 rule="hyper" parents="63 24930 31366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31368">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 \ z))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z * (w * v5),u,z)) = v6
    ]]></literal>
    <justification jstring="[para(31367(a,1),26528(a,1,3))].">
      <j1 rule="para" parents="31367 26528"/>
    </justification>
  </clause>

  <clause id="31369">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),v5 * (v6 \ v5),z)) = a(z,v6,a(u * (w \ z),y,x))
    ]]></literal>
    <justification jstring="[hyper(31368,a,30838,a)].">
      <j1 rule="hyper" parents="31368 30838"/>
    </justification>
  </clause>

  <clause id="31370">
    <literal><![CDATA[
      a(x * (y * z),u,a(x,w,v5)) = a(x,u,a(y * (z \ x),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,30838,a(flip),b,31369,a)].">
      <j1 rule="hyper" parents="63 30838 31369"/>
    </justification>
  </clause>

  <clause id="31371">
    <literal><![CDATA[
      a(x,y,a(z * (u \ x),w,v5)) = a(v5,y,a(x,w,x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(29858,a,31370,a),flip(a)].">
      <j1 rule="hyper" parents="29858 31370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31372">
    <literal><![CDATA[
      a(x,y,a(z * (u \ x),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a((z * u) * x,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(31371(a,2),29855(a,1))].">
      <j1 rule="para" parents="31371 29855"/>
    </justification>
  </clause>

  <clause id="31373">
    <literal><![CDATA[
      a(x \ y,z,(L(y,x,x) * u) * (x \ y)) = a(x \ y,z,(x \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,29620,a(flip),b,31365,a)].">
      <j1 rule="hyper" parents="63 29620 31365"/>
    </justification>
  </clause>

  <clause id="31374">
    <literal><![CDATA[
      a(x \ y,z,(L(y,x,x) * u) * (x \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x \ y,z,x * u) = w
    ]]></literal>
    <justification jstring="[para(31373(a,2),24449(a,1))].">
      <j1 rule="para" parents="31373 24449"/>
    </justification>
  </clause>

  <clause id="31375">
    <literal><![CDATA[
      a(x \ y,z,L(y,x,x) * (u \ (x \ y))) != w
    ]]></literal>
    <literal><![CDATA[
      a(x \ y,z,x * u) = w
    ]]></literal>
    <justification jstring="[para(31367(a,1),31374(a,1))].">
      <j1 rule="para" parents="31367 31374"/>
    </justification>
  </clause>

  <clause id="31376">
    <literal><![CDATA[
      a(x,L(L(y,z,u) * (y \ (w / (y \ 1))),v5,v6),v7) = a(x,L(w / (R(y,z,u) \ 1),v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,25029,a(flip),b,31343,a)].">
      <j1 rule="hyper" parents="63 25029 31343"/>
    </justification>
  </clause>

  <clause id="31377">
    <literal><![CDATA[
      a(x,L(y / (R(z,u,w) \ 1),v5,v6),v7) = a(x,L(y / (L(z,u,w) \ 1),v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(27852(a,1),31376(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="27852 31376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31378">
    <literal><![CDATA[
      a(x,L(y / (R(z,u,w) \ 1),v5,v6),v7) = a(x,L((L(z,u,w) \ 1) \ y,v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,24024,a(flip),b,31377,a),flip(a)].">
      <j1 rule="hyper" parents="347 24024 31377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31379">
    <literal><![CDATA[
      a(x,L(y / (R(z,u,w) \ 1),v5,v6),v7) = a(x,L(L(z,u,w) \ y,v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,24119,a(flip),b,31378,a),flip(a)].">
      <j1 rule="hyper" parents="347 24119 31378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31380">
    <literal><![CDATA[
      a(x,L((R(y,z,u) \ 1) \ w,v5,v6),v7) = a(x,L(L(y,z,u) \ w,v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(24585,a,31379,a)].">
      <j1 rule="hyper" parents="24585 31379"/>
    </justification>
  </clause>

  <clause id="31381">
    <literal><![CDATA[
      a(x,L(R(y,z,u) \ w,v5,v6),v7) = a(x,L(L(y,z,u) \ w,v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,24119,a(flip),b,31380,a)].">
      <j1 rule="hyper" parents="63 24119 31380"/>
    </justification>
  </clause>

  <clause id="31382">
    <literal><![CDATA[
      a(x,L(L(y,z,u) \ (w \ v5),R(y,z,u),w),v6) = a(x,(w * R(y,z,u)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(329(a,1),31381(a,1,2)),flip(a)].">
      <j1 rule="para" parents="329 31381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31383">
    <literal><![CDATA[
      a(x,L(L(y,z,u) \ (w \ v5),L(y,z,u),w),v6) = a(x,(w * R(y,z,u)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(21974(a,1),31382(a,1,2))].">
      <j1 rule="para" parents="21974 31382"/>
    </justification>
  </clause>

  <clause id="31384">
    <literal><![CDATA[
      a(x,(y * R(z,u,w)) \ v5,v6) = a(x,(y * L(z,u,w)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(329(a,1),31383(a,1,2)),flip(a)].">
      <j1 rule="para" parents="329 31383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31385">
    <literal><![CDATA[
      a(x,(y * L(y,z,u)) \ w,v5) = a(x,w * a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,29636,a(flip),b,31384,a),flip(a)].">
      <j1 rule="hyper" parents="63 29636 31384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31386">
    <literal><![CDATA[
      a(x,(y * L(z,u,w \ 1)) \ v5,v6) = a(x,(y * R(z,u,w)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(2190(a,1),31384(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2190 31384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31387">
    <literal><![CDATA[
      a(x,((y / z) * R(z,z,u)) \ w,v5) = a(x,(a(u,z,z) \ y) \ w,v5)
    ]]></literal>
    <justification jstring="[para(27836(a,1),31384(a,2,2,1))].">
      <j1 rule="para" parents="27836 31384"/>
    </justification>
  </clause>

  <clause id="31388">
    <literal><![CDATA[
      a(x,y * a(z,u,w),v5) = a(x,y * a(w,u,z),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,28900,a(flip),b,31385,a)].">
      <j1 rule="hyper" parents="63 28900 31385"/>
    </justification>
  </clause>

  <clause id="31389">
    <literal><![CDATA[
      a(x,a(y,z,u) * a(u,z,y),w) = 1
    ]]></literal>
    <justification jstring="[hyper(1352,a,31388,a),flip(a)].">
      <j1 rule="hyper" parents="1352 31388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31390">
    <literal><![CDATA[
      L(x,a(y,z,u) * a(u,z,y),w) = x
    ]]></literal>
    <justification jstring="[hyper(52,a,31389,a)].">
      <j1 rule="hyper" parents="52 31389"/>
    </justification>
  </clause>

  <clause id="31391">
    <literal><![CDATA[
      a(x,((a(y,z,u) * a(u,z,y)) * w) \ v5,v6) = a(x,(a(y,z,u) * a(u,z,y)) \ (w \ v5),v6)
    ]]></literal>
    <justification jstring="[para(31390(a,1),26032(a,1,2))].">
      <j1 rule="para" parents="31390 26032"/>
    </justification>
  </clause>

  <clause id="31392">
    <literal><![CDATA[
      a(x,y,(z * (a(u,w,v5) \ a(v5,w,u))) \ v6) = a(x,y,a(u,w,v5) * (a(v5,w,u) \ (z \ v6)))
    ]]></literal>
    <justification jstring="[para(31390(a,1),28811(a,1,3))].">
      <j1 rule="para" parents="31390 28811"/>
    </justification>
  </clause>

  <clause id="31393">
    <literal><![CDATA[
      a(x,(y * L(z,u,w \ 1)) \ v5,v6) = a(x,(y * L(z,u,w)) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,31384,a(flip),b,31386,a),flip(a)].">
      <j1 rule="hyper" parents="347 31384 31386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31394">
    <literal><![CDATA[
      a(x,(a(y,z,z) \ u) \ w,v5) = a(x,(u * a(z,z,y)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(26315(a,1),31387(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="26315 31387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31395">
    <literal><![CDATA[
      a(x,(y * a(z,u,u)) \ w,v5) = a(x,(y * a(u,u,z)) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(28383,a,31394,a)].">
      <j1 rule="hyper" parents="28383 31394"/>
    </justification>
  </clause>

  <clause id="31396">
    <literal><![CDATA[
      a(x,((L(y,z,u) \ w) * a(y,z,z)) \ v5,v6) = a(x,(L(L(y,z,u),z,z) \ w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(29389(a,1),31395(a,2,2,1))].">
      <j1 rule="para" parents="29389 31395"/>
    </justification>
  </clause>

  <clause id="31397">
    <literal><![CDATA[
      a(x,L((1 / T(y,z)) * u,y,y) \ w,v5) = a(x,(T(y,z) * L(u,y,y)) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,25721,a,b,31393,a)].">
      <j1 rule="hyper" parents="63 25721 31393"/>
    </justification>
  </clause>

  <clause id="31398">
    <literal><![CDATA[
      a(x,L((1 / T(y,z)) * u,y,y) \ w,v5) = a(x,(y * L(u,y,y)) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24270,a(flip),b,31397,a),flip(a)].">
      <j1 rule="hyper" parents="347 24270 31397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31400">
    <literal><![CDATA[
      a(x,L((1 / T(y,z)) * u,y,y) \ w,v5) = a(x,(y \ u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24619,a(flip),b,31398,a),flip(a)].">
      <j1 rule="hyper" parents="347 24619 31398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31401">
    <literal><![CDATA[
      a(x,((L(y,z,z) \ u) * a(y,z,z)) \ w,v5) = a(x,(y \ u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,27450,a(flip),b,31396,a),flip(a)].">
      <j1 rule="hyper" parents="347 27450 31396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31402">
    <literal><![CDATA[
      a(x,(y \ z) \ R(u,(L(y,w,w) \ z) * a(y,w,w),(L(y,w,w) \ z) * a(y,w,w)),v5) = a(x,T(u * (1 / ((L(y,w,w) \ z) * a(y,w,w))),(L(y,w,w) \ z) * a(y,w,w)),v5)
    ]]></literal>
    <justification jstring="[para(2263(a,2),31401(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2263 31401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31403">
    <literal><![CDATA[
      a(x,(a(y,z,u) * (a(u,z,y) * w)) \ v5,v6) = a(x,(a(y,z,u) * a(u,z,y)) \ (w \ v5),v6)
    ]]></literal>
    <justification jstring="[para(28365(a,1),31391(a,1,2,1))].">
      <j1 rule="para" parents="28365 31391"/>
    </justification>
  </clause>

  <clause id="31404">
    <literal><![CDATA[
      a(x,y,(z * (a(u,w,v5) \ a(v5,w,u))) \ v6) = a(x,y,z \ v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,26877,a(flip),b,31392,a),flip(a)].">
      <j1 rule="hyper" parents="347 26877 31392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31407">
    <literal><![CDATA[
      a(x,y,z \ (a(u,w,v5) * (a(v5,w,u) \ v6))) = a(x,y,z \ v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,31289,a(flip),b,31404,a)].">
      <j1 rule="hyper" parents="63 31289 31404"/>
    </justification>
  </clause>

  <clause id="31409">
    <literal><![CDATA[
      a(x,y,z \ (a(u,w,v5) * v6)) = a(x,y,z \ (a(v5,w,u) * v6))
    ]]></literal>
    <justification jstring="[para(9(a,1),31407(a,1,3,2,2))].">
      <j1 rule="para" parents="9 31407"/>
    </justification>
  </clause>

  <clause id="31410">
    <literal><![CDATA[
      a(x,(a(y,z,u) * (a(u,z,y) * w)) \ v5,v6) = a(x,(R(u,z,y) \ L(u,z,y)) * (w \ v5),v6)
    ]]></literal>
    <justification jstring="[para(29540(a,1),31403(a,2,2))].">
      <j1 rule="para" parents="29540 31403"/>
    </justification>
  </clause>

  <clause id="31411">
    <literal><![CDATA[
      a(x,(a(y,z,u) * (a(u,z,y) * w)) \ v5,v6) = a(x,(L(u,z,y) \ L(u,z,y)) * (w \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,29526,a(flip),b,31410,a),flip(a)].">
      <j1 rule="hyper" parents="347 29526 31410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31412">
    <literal><![CDATA[
      a(x,(a(y,z,u) * (a(u,z,y) * w)) \ v5,v6) = a(x,w \ v5,v6)
    ]]></literal>
    <justification jstring="[para(187(a,1),31411(a,2,2))].">
      <j1 rule="para" parents="187 31411"/>
    </justification>
  </clause>

  <clause id="31413">
    <literal><![CDATA[
      a(x,(a(y,z,u) \ w) \ v5,v6) = a(x,(a(u,z,y) * w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(10(a,1),31412(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 31412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31415">
    <literal><![CDATA[
      a(x,(a(y,z,u) * w) \ v5,v6) = a(x,(w * a(u,z,y)) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(28383,a,31413,a),flip(a)].">
      <j1 rule="hyper" parents="28383 31413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31418">
    <literal><![CDATA[
      a(x,(y * a(z \ 1,u,w)) \ v5,v6) = a(x,(a(w,u,z) * y) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(14922(a,1),31415(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14922 31415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31419">
    <literal><![CDATA[
      a(x,T(y * (z * a(u \ 1,w,v5)),z * a(u \ 1,w,v5)) / ((z * a(u \ 1,w,v5)) * (z * a(u \ 1,w,v5))),v6) = a(x,(a(v5,w,u) * z) \ R(y,z * a(u \ 1,w,v5),z * a(u \ 1,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(1312(a,2),31418(a,1,2))].">
      <j1 rule="para" parents="1312 31418"/>
    </justification>
  </clause>

  <clause id="31420">
    <literal><![CDATA[
      a(x,L(L(y \ 1,z * y,z * y),y,z),u) = a(x,L(z \ ((((z * y) \ 1) \ z) / z),z * (z * y),z),u)
    ]]></literal>
    <justification jstring="[para(21695(a,1),31352(a,2,2))].">
      <j1 rule="para" parents="21695 31352"/>
    </justification>
  </clause>

  <clause id="31421">
    <literal><![CDATA[
      a(x,L(L(y \ 1,z * y,z * y),y,z),u) = a(x,L(z \ ((((z * y) \ 1) \ z) / z),L(y,z,z),z),u)
    ]]></literal>
    <justification jstring="[para(3609(a,1),31420(a,2,2))].">
      <j1 rule="para" parents="3609 31420"/>
    </justification>
  </clause>

  <clause id="31422">
    <literal><![CDATA[
      a(x,L(L(y \ 1,z * y,z * y),y,z),u) = a(x,L(z \ ((((z * y) \ 1) \ z) / z),y,z),u)
    ]]></literal>
    <justification jstring="[para(30133(a,1),31421(a,2,2))].">
      <j1 rule="para" parents="30133 31421"/>
    </justification>
  </clause>

  <clause id="31423">
    <literal><![CDATA[
      a(x,L(L(y \ 1,z * y,z * y),y,z),u) = a(x,L(z \ (z \ (((z * y) \ 1) \ z)),y,z),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,24363,a(flip),b,31422,a),flip(a)].">
      <j1 rule="hyper" parents="347 24363 31422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31424">
    <literal><![CDATA[
      a(x,L(L(((y * z) \ 1) \ y,y,y),z,y),u) = a(x,L(L(z \ 1,y * z,y * z),z,y),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,24871,a(flip),b,31423,a)].">
      <j1 rule="hyper" parents="347 24871 31423"/>
    </justification>
  </clause>

  <clause id="31425">
    <literal><![CDATA[
      a(x,L(L(((y * z) \ 1) \ y,y,y),z,y),u) = a(x,R(y * z,y * z,z) \ y,u)
    ]]></literal>
    <justification jstring="[para(29494(a,1),31424(a,2,2))].">
      <j1 rule="para" parents="29494 31424"/>
    </justification>
  </clause>

  <clause id="31426">
    <literal><![CDATA[
      a(x,L(L(((y * z) \ 1) \ y,y,y),z,y),u) = a(x,L(y * z,y * z,z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,25130,a(flip),b,31425,a),flip(a)].">
      <j1 rule="hyper" parents="347 25130 31425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31427">
    <literal><![CDATA[
      a(x,L(L(((y * z) \ 1) \ y,y,y),z,y),u) = a(x,L(y \ z,z,z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,31320,a(flip),b,31426,a),flip(a)].">
      <j1 rule="hyper" parents="347 31320 31426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31428">
    <literal><![CDATA[
      a(x,L(L(((y * z) \ 1) \ y,y,y),z,y),u) = a(x,L(z \ y,z,z) * y,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,30267,a(flip),b,31427,a),flip(a)].">
      <j1 rule="hyper" parents="347 30267 31427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31429">
    <literal><![CDATA[
      a(x,L(L(((y * z) \ 1) \ y,y,y),z,y),u) = a(x,y * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,24594,a(flip),b,31428,a),flip(a)].">
      <j1 rule="hyper" parents="347 24594 31428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31430">
    <literal><![CDATA[
      a(x,L(L(((y * z) \ 1) \ y,y,y),z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,L(z,y,y),u) = w
    ]]></literal>
    <justification jstring="[para(31429(a,2),24392(a,1))].">
      <j1 rule="para" parents="31429 24392"/>
    </justification>
  </clause>

  <clause id="31431">
    <literal><![CDATA[
      a(x,L(((y * z) \ 1) \ y,y,y),a(u,w,L(v5,z,y))) = a(x,L(z,y,y),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(31430,a,30088,a),flip(a)].">
      <j1 rule="hyper" parents="31430 30088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31432">
    <literal><![CDATA[
      a(x,((y * z) \ 1) \ y,a(u,w,L(L(v5,z,y),y,y))) = a(x,L(z,y,y),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,30088,a(flip),b,31431,a)].">
      <j1 rule="hyper" parents="63 30088 31431"/>
    </justification>
  </clause>

  <clause id="31433">
    <literal><![CDATA[
      a(x,((y * z) \ 1) \ y,a(u,w,L(v5,z,y))) = a(x,L(z,y,y),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,30776,a(flip),b,31432,a)].">
      <j1 rule="hyper" parents="63 30776 31432"/>
    </justification>
  </clause>

  <clause id="31434">
    <literal><![CDATA[
      a(x,((y * z) \ 1) * y,a(u,w,L(v5,z,y))) = a(x,L(z,y,y),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(30786,a,31433,a)].">
      <j1 rule="hyper" parents="30786 31433"/>
    </justification>
  </clause>

  <clause id="31436">
    <literal><![CDATA[
      a(x,(y * z) * y,a(u,w,L(v5,z,y))) = a(x,L(z,y,y),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(24344,a,31434,a)].">
      <j1 rule="hyper" parents="24344 31434"/>
    </justification>
  </clause>

  <clause id="31437">
    <literal><![CDATA[
      a(x,L(y,z,z),a(u,w,L(v5,y,z))) = a(x,L(y,z,z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(24391,a,31436,a)].">
      <j1 rule="hyper" parents="24391 31436"/>
    </justification>
  </clause>

  <clause id="31438">
    <literal><![CDATA[
      a(x,y,a(z,u,L(L(w,y,v5),v5,v5))) = a(x,L(y,v5,v5),a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,30088,a(flip),b,31437,a)].">
      <j1 rule="hyper" parents="63 30088 31437"/>
    </justification>
  </clause>

  <clause id="31439">
    <literal><![CDATA[
      a(x,L(y,z,z),a(u,w,v5)) = a(x,y,a(u,w,L(v5,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,30776,a(flip),b,31438,a),flip(a)].">
      <j1 rule="hyper" parents="63 30776 31438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31441">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v5))) = a(x,y,a(z,u,L(w,y,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,30088,a(flip),b,31439,a)].">
      <j1 rule="hyper" parents="63 30088 31439"/>
    </justification>
  </clause>

  <clause id="31442">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,y,v5))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,30776,a(flip),b,31441,a),flip(a)].">
      <j1 rule="hyper" parents="63 30776 31441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31447">
    <literal><![CDATA[
      a(x,y * ((z * u) * (u \ z)),a(w,v5,L(v6,y * ((z * u) * (u \ z)),v7))) = a(x,a(u,u,z) * y,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,27275,a(flip),b,31442,a),flip(a)].">
      <j1 rule="hyper" parents="347 27275 31442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31450">
    <literal><![CDATA[
      a(x,L(L(y,a(z,u,w),v5),v5,a(z,u,w)),a(v5,y,a(w,u,z))) \ 1 = a(v5,y,a(w,u,z)) \ a(v5,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(31442(a,1),31260(a,2,2))].">
      <j1 rule="para" parents="31442 31260"/>
    </justification>
  </clause>

  <clause id="31459">
    <literal><![CDATA[
      a(x,y * ((y * z) * (z \ y)),a(u,w,L(v5,y * ((y * z) * (z \ y)),v6))) = a(x,L(y,z,z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,28932,a(flip),b,31447,a),flip(a)].">
      <j1 rule="hyper" parents="347 28932 31447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31460">
    <literal><![CDATA[
      a(x,y * ((y * z) * (z \ y)),a(u,w,L(v5,y * ((y * z) * (z \ y)),v6))) = a(x,y,a(u,w,L(v5,z,z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,30088,a(flip),b,31459,a),flip(a)].">
      <j1 rule="hyper" parents="347 30088 31459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31461">
    <literal><![CDATA[
      a(x,y * ((y * z) * (z \ y)),a(u,w,L(v5,v6,v6))) = a(x,y,a(u,w,L(v5,z,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,31441,a,b,31460,a)].">
      <j1 rule="hyper" parents="63 31441 31460"/>
    </justification>
  </clause>

  <clause id="31463">
    <literal><![CDATA[
      a(x,y \ ((y * z) * (z \ y)),a(u,w,v5)) = a(x,y,a(u,w,L(v5,z,z)))
    ]]></literal>
    <justification jstring="[hyper(30093,a,31461,a)].">
      <j1 rule="hyper" parents="30093 31461"/>
    </justification>
  </clause>

  <clause id="31465">
    <literal><![CDATA[
      a(x,R(T(y,y),z,y * z),a(u,w,v5)) = a(x,y,a(u,w,L(v5,z,z)))
    ]]></literal>
    <justification jstring="[para(27251(a,1),31463(a,1,2))].">
      <j1 rule="para" parents="27251 31463"/>
    </justification>
  </clause>

  <clause id="31466">
    <literal><![CDATA[
      a(x,R(y,z,y * z),a(u,w,v5)) = a(x,y,a(u,w,L(v5,z,z)))
    ]]></literal>
    <justification jstring="[para(110(a,1),31465(a,1,2,1))].">
      <j1 rule="para" parents="110 31465"/>
    </justification>
  </clause>

  <clause id="31467">
    <literal><![CDATA[
      a(x,L(y,z,y * z),a(u,w,v5)) = a(x,y,a(u,w,L(v5,z,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,24805,a(flip),b,31466,a)].">
      <j1 rule="hyper" parents="63 24805 31466"/>
    </justification>
  </clause>

  <clause id="31468">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,y * v5))) = a(x,y,a(z,u,L(w,v5,v5)))
    ]]></literal>
    <justification jstring="[hyper(63,a,30088,a(flip),b,31467,a)].">
      <j1 rule="hyper" parents="63 30088 31467"/>
    </justification>
  </clause>

  <clause id="31469">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,y * v5))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,30776,a(flip),b,31468,a),flip(a)].">
      <j1 rule="hyper" parents="347 30776 31468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31475">
    <literal><![CDATA[
      a(x,L(L(y,a(z,u,w),v5),v5,a(z,u,w)),a(v5,y,a(w,u,z))) \ 1 = 1
    ]]></literal>
    <justification jstring="[hyper(347,a,68,a(flip),b,31450,a),flip(a)].">
      <j1 rule="hyper" parents="347 68 31450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31479">
    <literal><![CDATA[
      a(x,L(y,a(z,u,w),v5),a(v5,y,L(a(w,u,z),v5,a(z,u,w)))) \ 1 = 1
    ]]></literal>
    <justification jstring="[para(30088(a,1),31475(a,1,1))].">
      <j1 rule="para" parents="30088 31475"/>
    </justification>
  </clause>

  <clause id="31481">
    <literal><![CDATA[
      a(x,L(y,a(z,u,w),v5),a(v5,y,a(w,u,z))) \ 1 = 1
    ]]></literal>
    <justification jstring="[para(27560(a,1),31479(a,1,1,3,3))].">
      <j1 rule="para" parents="27560 31479"/>
    </justification>
  </clause>

  <clause id="31484">
    <literal><![CDATA[
      a(x,y,a(z,y,L(a(u,w,v5),a(v5,w,u),z))) \ 1 = 1
    ]]></literal>
    <justification jstring="[para(30088(a,1),31481(a,1,1))].">
      <j1 rule="para" parents="30088 31481"/>
    </justification>
  </clause>

  <clause id="31487">
    <literal><![CDATA[
      a(x,y,a(z,y,a(u,w,v5))) \ 1 = 1
    ]]></literal>
    <justification jstring="[para(28455(a,1),31484(a,1,1,3,3))].">
      <j1 rule="para" parents="28455 31484"/>
    </justification>
  </clause>

  <clause id="31488">
    <literal><![CDATA[
      a(x,y,a(z,y,a(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(26335,a,31487,a)].">
      <j1 rule="hyper" parents="26335 31487"/>
    </justification>
  </clause>

  <clause id="31492">
    <literal><![CDATA[
      a(x,a(y,x,z),a(u,w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(63,a,31246,a,b,31488,a)].">
      <j1 rule="hyper" parents="63 31246 31488"/>
    </justification>
  </clause>

  <clause id="31494">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),w)) = 1
    ]]></literal>
    <justification jstring="[hyper(29811,a,31492,a)].">
      <j1 rule="hyper" parents="29811 31492"/>
    </justification>
  </clause>

  <clause id="31498">
    <literal><![CDATA[
      a(x,a(y,z,u),L(z,w,v5)) = a(x,a(y,z,u),z)
    ]]></literal>
    <justification jstring="[hyper(189,a,29147,a,b,31494,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="189 29147 31494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31499">
    <literal><![CDATA[
      a(x \ (y \ z),a(u,y,w),y) = a(u,y,a(x \ z,y,w))
    ]]></literal>
    <justification jstring="[hyper(31214,a,31498,a),flip(a)].">
      <j1 rule="hyper" parents="31214 31498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31500">
    <literal><![CDATA[
      L(R(x,y,y) \ R(x,y,y * a(z,y,u)),w,v5) = a(R(x,y,y),a(u,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,31123,a,b,31498,a)].">
      <j1 rule="hyper" parents="63 31123 31498"/>
    </justification>
  </clause>

  <clause id="31501">
    <literal><![CDATA[
      a((x * y) \ z,a(u,y,w),y) = a(u,y,a(x \ z,y,w))
    ]]></literal>
    <justification jstring="[hyper(29737,a,31499,a)].">
      <j1 rule="hyper" parents="29737 31499"/>
    </justification>
  </clause>

  <clause id="31502">
    <literal><![CDATA[
      a(x * (y * z),a(u,z,w),z) = a(u,z,a(y \ x,z,w))
    ]]></literal>
    <justification jstring="[hyper(31209,a,31501,a)].">
      <j1 rule="hyper" parents="31209 31501"/>
    </justification>
  </clause>

  <clause id="31503">
    <literal><![CDATA[
      a(x * (y * z),a(u,y,w),y) = a(u,y,a(z \ x,y,w))
    ]]></literal>
    <justification jstring="[hyper(23967,a,31502,a)].">
      <j1 rule="hyper" parents="23967 31502"/>
    </justification>
  </clause>

  <clause id="31504">
    <literal><![CDATA[
      (x * a(y,x,z)) \ (a(y,x,a(a(y,x,z) \ u,x,z)) \ u) = L((x * a(y,x,z)) \ u,a(y,x,z),x)
    ]]></literal>
    <justification jstring="[para(31503(a,1),31283(a,1,2,1))].">
      <j1 rule="para" parents="31503 31283"/>
    </justification>
  </clause>

  <clause id="31506">
    <literal><![CDATA[
      L(R(x,y,y) \ R(x,y,y * a(z,y,u)),w,v5) = a(x,a(u,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,29708,a(flip),b,31500,a),flip(a)].">
      <j1 rule="hyper" parents="347 29708 31500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31508">
    <literal><![CDATA[
      L(a(x,y,y) \ a(x,y,y * a(z,y,u)),w,v5) = a(x,a(u,y,z),y)
    ]]></literal>
    <justification jstring="[para(29345(a,2),31506(a,1,1))].">
      <j1 rule="para" parents="29345 31506"/>
    </justification>
  </clause>

  <clause id="31509">
    <literal><![CDATA[
      (x * a(y,x,z)) \ (a(y,x,a(a(y,x,z) * u,x,z)) \ u) = L((x * a(y,x,z)) \ u,a(y,x,z),x)
    ]]></literal>
    <justification jstring="[para(28398(a,1),31504(a,1,2,1,3))].">
      <j1 rule="para" parents="28398 31504"/>
    </justification>
  </clause>

  <clause id="31510">
    <literal><![CDATA[
      ((x \ R(R(x,y,z),y,z)) * (R(x,y,z) * R(x,y,z))) / R(R(x,y,z),y,z) = L(R(R(x,y,z),y,z),x,x \ R(R(x,y,z),y,z))
    ]]></literal>
    <justification jstring="[para(3692(a,1),30080(a,1,1,1))].">
      <j1 rule="para" parents="3692 30080"/>
    </justification>
  </clause>

  <clause id="31511">
    <literal><![CDATA[
      R(x,y,((z * (K(u,w) * (v5 \ v6))) * T(v5,v7)) \ ((K(v5,v7) * v6) * z)) = L(x,y,a(T(v5,v7),K(u,w) * (v5 \ v6),z))
    ]]></literal>
    <justification jstring="[hyper(63,a,22212,a(flip),b,30731,a)].">
      <j1 rule="hyper" parents="63 22212 30731"/>
    </justification>
  </clause>

  <clause id="31513">
    <literal><![CDATA[
      R(x,y,((z * (K(u,w) * (v5 \ v6))) * T(v5,v7)) \ (K(v5,v7) * (v6 * z))) = L(x,y,a(T(v5,v7),K(u,w) * (v5 \ v6),z))
    ]]></literal>
    <justification jstring="[para(20008(a,1),31511(a,1,3,2))].">
      <j1 rule="para" parents="20008 31511"/>
    </justification>
  </clause>

  <clause id="31514">
    <literal><![CDATA[
      R(x,y,T((z * (K(u,w) * (v5 \ v6))) * v5,K(v5,v7)) \ (v6 * z)) = L(x,y,a(T(v5,v7),K(u,w) * (v5 \ v6),z))
    ]]></literal>
    <justification jstring="[para(20705(a,1),31513(a,1,3))].">
      <j1 rule="para" parents="20705 31513"/>
    </justification>
  </clause>

  <clause id="31515">
    <literal><![CDATA[
      R(x,y,((z * (K(u,w) * (v5 \ v6))) * v5) \ (v6 * z)) = L(x,y,a(T(v5,v7),K(u,w) * (v5 \ v6),z))
    ]]></literal>
    <justification jstring="[hyper(22092,a,31514,a)].">
      <j1 rule="hyper" parents="22092 31514"/>
    </justification>
  </clause>

  <clause id="31516">
    <literal><![CDATA[
      R(x,y,(z * (u * (z \ w))) \ (w * u)) = L(x,y,a(T(z,v5),K(v6,v7) * (z \ w),u))
    ]]></literal>
    <justification jstring="[hyper(22815,a,31515,a)].">
      <j1 rule="hyper" parents="22815 31515"/>
    </justification>
  </clause>

  <clause id="31517">
    <literal><![CDATA[
      R(x,y,(z * (u \ w)) \ (u \ (w * z))) = L(x,y,a(T(u,v5),K(v6,v7) * (u \ w),z))
    ]]></literal>
    <justification jstring="[para(21369(a,1),31516(a,1,3))].">
      <j1 rule="para" parents="21369 31516"/>
    </justification>
  </clause>

  <clause id="31518">
    <literal><![CDATA[
      R(x,y,(z * (u \ w)) \ (u \ (w * z))) = L(x,y,a(T(u,v5),u \ w,z))
    ]]></literal>
    <justification jstring="[para(202(a,1),31517(a,2,3,2))].">
      <j1 rule="para" parents="202 31517"/>
    </justification>
  </clause>

  <clause id="31519">
    <literal><![CDATA[
      R(x,y,(z * (u \ w)) \ (u \ (w * z))) = L(x,y,a(u,u \ w,z))
    ]]></literal>
    <justification jstring="[para(110(a,1),31518(a,2,3,1))].">
      <j1 rule="para" parents="110 31518"/>
    </justification>
  </clause>

  <clause id="31520">
    <literal><![CDATA[
      R(x,y,(z * (u \ w)) \ (u \ (w * z))) = L(x,y,a(u,u * w,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,30460,a(flip),b,31519,a),flip(a)].">
      <j1 rule="hyper" parents="347 30460 31519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31521">
    <literal><![CDATA[
      R(x,y,(z * (u \ w)) * (u \ (w * z))) = L(x,y,a(u,u * w,z))
    ]]></literal>
    <justification jstring="[hyper(31280,a,31520,a)].">
      <j1 rule="hyper" parents="31280 31520"/>
    </justification>
  </clause>

  <clause id="31522">
    <literal><![CDATA[
      R(x,y,((z \ u) \ (u * w)) * (w * z)) = L(x,y,a(z \ u,(z \ u) * u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,22170,a(flip),b,31521,a)].">
      <j1 rule="hyper" parents="63 22170 31521"/>
    </justification>
  </clause>

  <clause id="31523">
    <literal><![CDATA[
      R(x,y,((z \ u) \ (u * w)) * (w * z)) = L(x,y,a(z \ u,z,w))
    ]]></literal>
    <justification jstring="[para(30128(a,1),31522(a,2,3))].">
      <j1 rule="para" parents="30128 31522"/>
    </justification>
  </clause>

  <clause id="31524">
    <literal><![CDATA[
      R(x,y,((z \ u) \ (u * w)) * (w * z)) = L(x,y,a(z * u,z,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,30821,a(flip),b,31523,a),flip(a)].">
      <j1 rule="hyper" parents="347 30821 31523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31525">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ R(a(z,u,w) * (K(y,x) * v5),a(z,u,w) \ K(x,y),v6 * a(z,u,w))) = L(v5,a(w,u,z),v6)
    ]]></literal>
    <justification jstring="[para(22134(a,1),31321(a,1,2,2))].">
      <j1 rule="para" parents="22134 31321"/>
    </justification>
  </clause>

  <clause id="31527">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ R(a(z,u,w) * (K(y,x) * v5),a(z,u,w),v6 * a(z,u,w))) = L(v5,a(w,u,z),v6)
    ]]></literal>
    <justification jstring="[para(22436(a,1),31525(a,1,2,2))].">
      <j1 rule="para" parents="22436 31525"/>
    </justification>
  </clause>

  <clause id="31529">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ L(a(z,u,w) * (K(y,x) * v5),a(z,u,w),v6 * a(z,u,w))) = L(v5,a(w,u,z),v6)
    ]]></literal>
    <justification jstring="[para(23225(a,1),31527(a,1,2,2))].">
      <j1 rule="para" parents="23225 31527"/>
    </justification>
  </clause>

  <clause id="31530">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) * L(a(z,u,w) \ (K(y,x) * v5),a(z,u,w),v6 * a(z,u,w))) = L(v5,a(w,u,z),v6)
    ]]></literal>
    <justification jstring="[para(3342(a,1),31529(a,1,2))].">
      <j1 rule="para" parents="3342 31529"/>
    </justification>
  </clause>

  <clause id="31531">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) * L(K(y,x) * (a(z,u,w) \ v5),a(z,u,w),v6 * a(z,u,w))) = L(v5,a(w,u,z),v6)
    ]]></literal>
    <justification jstring="[para(19547(a,1),31530(a,1,2,2,1))].">
      <j1 rule="para" parents="19547 31530"/>
    </justification>
  </clause>

  <clause id="31532">
    <literal><![CDATA[
      T(a(x,y,z),K(u,w)) * L(a(x,y,z) \ v5,a(x,y,z),v6 * a(x,y,z)) = L(v5,a(z,y,x),v6)
    ]]></literal>
    <justification jstring="[hyper(21326,a,31531,a)].">
      <j1 rule="hyper" parents="21326 31531"/>
    </justification>
  </clause>

  <clause id="31533">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ u,a(x,y,z),w * a(x,y,z)) = L(u,a(z,y,x),w)
    ]]></literal>
    <justification jstring="[para(2479(a,1),31532(a,1,1))].">
      <j1 rule="para" parents="2479 31532"/>
    </justification>
  </clause>

  <clause id="31534">
    <literal><![CDATA[
      (x \ ((a(y,z,u) \ x) * w)) * a(y,z,u) = L(w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,27325,a(flip),b,31533,a)].">
      <j1 rule="hyper" parents="63 27325 31533"/>
    </justification>
  </clause>

  <clause id="31536">
    <literal><![CDATA[
      T((x \ L(R(x,y,z),u,w)) \ a(v5,v6,x * L(L(x,y,z),u,w)),v7 \ L(R(v7,v8,v9),v10,v11)) = L(x \ L(R(x,y,z),u,w),v6,v5) \ 1
    ]]></literal>
    <justification jstring="[para(14986(a,1),29339(a,1,1,2))].">
      <j1 rule="para" parents="14986 29339"/>
    </justification>
  </clause>

  <clause id="31537">
    <literal><![CDATA[
      T((x \ L(R(x,y,z),y,z)) \ a(u,w,x * x),v5 \ L(R(v5,v6,v7),v8,v9)) = L(x \ L(R(x,y,z),y,z),w,u) \ 1
    ]]></literal>
    <justification jstring="[para(25566(a,1),31536(a,1,1,2))].">
      <j1 rule="para" parents="25566 31536"/>
    </justification>
  </clause>

  <clause id="31538">
    <literal><![CDATA[
      T((x \ L(R(x,y,z),y,z)) \ 1,u \ L(R(u,w,v5),v6,v7)) = L(x \ L(R(x,y,z),y,z),v8,v9) \ 1
    ]]></literal>
    <justification jstring="[para(553(a,1),31537(a,1,1,2))].">
      <j1 rule="para" parents="553 31537"/>
    </justification>
  </clause>

  <clause id="31539">
    <literal><![CDATA[
      L(x \ L(R(x,y,z),y,z),u,w) = x \ L(R(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(22957,a,31538,a),flip(a)].">
      <j1 rule="hyper" parents="22957 31538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31541">
    <literal><![CDATA[
      (L(R(x,y,z),y,z) \ x) \ 1 = x \ L(R(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(663,a,31539,a)].">
      <j1 rule="hyper" parents="663 31539"/>
    </justification>
  </clause>

  <clause id="31542">
    <literal><![CDATA[
      T((x / L(R(y,z,u),z,u)) * y,y \ L(R(y,z,u),z,u)) = (y \ L(R(y,z,u),z,u)) \ x
    ]]></literal>
    <justification jstring="[para(31539(a,1),13774(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31539 13774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31543">
    <literal><![CDATA[
      (a(x,y,z) \ a(z,y,x)) \ 1 = x \ L(R(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(29656(a,1),31541(a,1,1))].">
      <j1 rule="para" parents="29656 31541"/>
    </justification>
  </clause>

  <clause id="31544">
    <literal><![CDATA[
      a(x,y,z) * (a(z,y,x) \ 1) = x \ L(R(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,28788,a(flip),b,31543,a)].">
      <j1 rule="hyper" parents="63 28788 31543"/>
    </justification>
  </clause>

  <clause id="31545">
    <literal><![CDATA[
      a(x,y,z) \ a(z,y,x) = z \ L(R(z,y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(28424,a,31544,a)].">
      <j1 rule="hyper" parents="28424 31544"/>
    </justification>
  </clause>

  <clause id="31546">
    <literal><![CDATA[
      (x \ L(R(x,y,z),y,z)) \ u = a(z,y,x) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(31545(a,1),28788(a,1,1))].">
      <j1 rule="para" parents="31545 28788"/>
    </justification>
  </clause>

  <clause id="31547">
    <literal><![CDATA[
      T((x / L(R(y,z,u),z,u)) * y,y \ L(R(y,z,u),z,u)) = a(u,z,y) * (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,31546,a(flip),b,31542,a),flip(a)].">
      <j1 rule="hyper" parents="347 31546 31542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31548">
    <literal><![CDATA[
      T(x * (L(R(x,y,z),y,z) \ u),x \ L(R(x,y,z),y,z)) = a(z,y,x) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(22707(a,1),31547(a,1,1))].">
      <j1 rule="para" parents="22707 31547"/>
    </justification>
  </clause>

  <clause id="31549">
    <literal><![CDATA[
      a(x,y,z) * (a(z,y,x) \ u) = z * (L(R(z,y,x),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(22956,a,31548,a),flip(a)].">
      <j1 rule="hyper" parents="22956 31548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31551">
    <literal><![CDATA[
      (a(x,y,z) * T(a(z,y,x),u)) * L((a(x,y,z) * a(z,y,x)) \ a(x,y,z),w,v5) = z * (L(R(z,y,x),y,x) \ L(T(a(z,y,x),u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,21981,a,b,31549,a)].">
      <j1 rule="hyper" parents="63 21981 31549"/>
    </justification>
  </clause>

  <clause id="31552">
    <literal><![CDATA[
      a(T(L(x * (1 / y),y,y) \ (L(x * (1 / y),y,y) / z),u) * (y \ x),w,v5) = a(L(x * (1 / y),y,y) / z,w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,23891,a(flip),b,30346,a),flip(a)].">
      <j1 rule="hyper" parents="347 23891 30346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31554">
    <literal><![CDATA[
      a(T(L(x * (1 / y),y,y) \ (L(x * (1 / y),y,y) / z),u) * (y \ x),w,v5) = a(z \ L(x * (1 / y),y,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,23893,a(flip),b,31552,a),flip(a)].">
      <j1 rule="hyper" parents="347 23893 31552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31555">
    <literal><![CDATA[
      a(T(L(x * (1 / y),y,y) \ (L(x * (1 / y),y,y) / z),u) * (y \ x),w,v5) = a(z \ (y \ x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,30347,a(flip),b,31554,a),flip(a)].">
      <j1 rule="hyper" parents="347 30347 31554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31556">
    <literal><![CDATA[
      a(T((x * (1 / y)) \ ((x * (1 / y)) / z),u) * (y \ x),w,v5) = a(z \ (y \ x),w,v5)
    ]]></literal>
    <justification jstring="[para(30182(a,1),31555(a,1,1,1,1))].">
      <j1 rule="para" parents="30182 31555"/>
    </justification>
  </clause>

  <clause id="31557">
    <literal><![CDATA[
      a(((x * (1 / y)) \ ((x * (1 / y)) / z)) * (y \ x),u,w) = a(z \ (y \ x),u,w)
    ]]></literal>
    <justification jstring="[hyper(23955,a,31556,a)].">
      <j1 rule="hyper" parents="23955 31556"/>
    </justification>
  </clause>

  <clause id="31559">
    <literal><![CDATA[
      a(((x * (1 / y)) \ (z \ (x * (1 / y)))) * (y \ x),u,w) = a(z \ (y \ x),u,w)
    ]]></literal>
    <justification jstring="[hyper(24534,a,31557,a)].">
      <j1 rule="hyper" parents="24534 31557"/>
    </justification>
  </clause>

  <clause id="31560">
    <literal><![CDATA[
      a((x \ (y * (1 / z))) * a(y,z,z),u,w) = a(x \ (z \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,30407,a(flip),b,31559,a)].">
      <j1 rule="hyper" parents="63 30407 31559"/>
    </justification>
  </clause>

  <clause id="31561">
    <literal><![CDATA[
      a((x \ (y * (z \ 1))) * a(y,z,z),u,w) = a(x \ (z \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(25172,a,31560,a)].">
      <j1 rule="hyper" parents="25172 31560"/>
    </justification>
  </clause>

  <clause id="31584">
    <literal><![CDATA[
      T(a(x,a(y,z,z),L(u,x,a(y,z,z))) * a(y,z,z),L(u,x,a(y,z,z))) = (u * a(x,z,a(z,u,y))) \ L(a(y,z,z) * u,x,a(z,z,y))
    ]]></literal>
    <justification jstring="[para(30475(a,2),29959(a,2,2))].">
      <j1 rule="para" parents="30475 29959"/>
    </justification>
  </clause>

  <clause id="31585">
    <literal><![CDATA[
      (x * (a(y,z,a(u,u,w)) * (v5 * v6))) \ ((a(y,z,a(u,u,w)) * (x * v5)) * v6) = a(a(y,z,a(u,u,w)) * x,L(v5,x,a(y,z,a(u,u,w))),v6)
    ]]></literal>
    <justification jstring="[para(30524(a,1),30445(a,1,1))].">
      <j1 rule="para" parents="30524 30445"/>
    </justification>
  </clause>

  <clause id="31586">
    <literal><![CDATA[
      (a(x,y,z) * a(z,y,x)) * L((a(x,y,z) * a(z,y,x)) \ a(x,y,z),u,w) = z * (L(R(z,y,x),y,x) \ L(T(a(z,y,x),v5),u,w))
    ]]></literal>
    <justification jstring="[para(20005(a,1),31551(a,1,1,2))].">
      <j1 rule="para" parents="20005 31551"/>
    </justification>
  </clause>

  <clause id="31588">
    <literal><![CDATA[
      (a(x,y,z) * a(z,y,x)) * L(a(z,y,x) \ 1,u,w) = z * (L(R(z,y,x),y,x) \ L(T(a(z,y,x),v5),u,w))
    ]]></literal>
    <justification jstring="[para(28352(a,1),31586(a,1,2,1))].">
      <j1 rule="para" parents="28352 31586"/>
    </justification>
  </clause>

  <clause id="31589">
    <literal><![CDATA[
      x * (L(R(x,y,z),y,z) \ L(T(a(x,y,z),u),w,v5)) = a(x,y,L(z,w,v5)) \ (a(z,y,x) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(29250,a,31588,a),flip(a)].">
      <j1 rule="hyper" parents="29250 31588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31591">
    <literal><![CDATA[
      x * (L(R(x,y,z),y,z) \ L(T(a(x,y,z),u),w,v5)) = (a(x,y,L(z,w,v5)) \ a(z,y,x)) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,29716,a(flip),b,31589,a),flip(a)].">
      <j1 rule="hyper" parents="347 29716 31589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31592">
    <literal><![CDATA[
      x * (L(R(x,y,z),y,z) \ L(T(a(x,y,z),u),w,v5)) = (a(x,y,z) \ a(z,y,L(x,w,v5))) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(29532(a,1),31591(a,2,1))].">
      <j1 rule="para" parents="29532 31591"/>
    </justification>
  </clause>

  <clause id="31593">
    <literal><![CDATA[
      x * (L(R(x,y,z),y,z) \ L(T(a(x,y,z),u),w,v5)) = a(z,y,L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,19986,a(flip),b,31592,a),flip(a)].">
      <j1 rule="hyper" parents="347 19986 31592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31595">
    <literal><![CDATA[
      x * (L(R(x,y,z),y,z) \ L(a(x,y,z),u,w)) = a(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(110(a,1),31593(a,1,2,2,1))].">
      <j1 rule="para" parents="110 31593"/>
    </justification>
  </clause>

  <clause id="31596">
    <literal><![CDATA[
      x * (L(R(x,y,z),y,z) \ a(x,y,L(z,u,w))) = a(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(29113(a,2),31595(a,1,2,2))].">
      <j1 rule="para" parents="29113 31595"/>
    </justification>
  </clause>

  <clause id="31597">
    <literal><![CDATA[
      x * (L(R(x,x,y),x,y) \ a(x,x,L(y,z,u))) = a(y,x,L(x,z * x,u))
    ]]></literal>
    <justification jstring="[para(30677(a,1),31596(a,1,2,2))].">
      <j1 rule="para" parents="30677 31596"/>
    </justification>
  </clause>

  <clause id="31598">
    <literal><![CDATA[
      a(x,y,L(y,z * y,u)) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,31596,a(flip),b,31597,a),flip(a)].">
      <j1 rule="hyper" parents="63 31596 31597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31599">
    <literal><![CDATA[
      a(x,y,L(y,y * z,u)) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(21617(a,1),31598(a,1,3))].">
      <j1 rule="para" parents="21617 31598"/>
    </justification>
  </clause>

  <clause id="31600">
    <literal><![CDATA[
      x * a(y,z,a(L(z,z * u,w),v5,x)) = L(x,v5,a(y,z,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(31599(a,1),29807(a,2,3))].">
      <j1 rule="para" parents="31599 29807"/>
    </justification>
  </clause>

  <clause id="31601">
    <literal><![CDATA[
      x * a(y,z,a(z,u,L(x,z * w,v5))) = L(x,u,a(y,z,L(z,w,v5)))
    ]]></literal>
    <justification jstring="[para(29675(a,1),31600(a,1,2,3))].">
      <j1 rule="para" parents="29675 31600"/>
    </justification>
  </clause>

  <clause id="31602">
    <literal><![CDATA[
      L(x,y,a(y,z,L(u,y * w,v5))) = L(x,z,a(u,y,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(29933,a,31601,a)].">
      <j1 rule="hyper" parents="29933 31601"/>
    </justification>
  </clause>

  <clause id="31603">
    <literal><![CDATA[
      L(x,y,a(z,u,L(u,w,v5))) = L(x,u,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,30513,a(flip),b,31602,a),flip(a)].">
      <j1 rule="hyper" parents="63 30513 31602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31605">
    <literal><![CDATA[
      L(R(x,a(y,z,L(z,u,w)),v5) \ x,z,a(y,x,z)) = a(x,a(y,z,L(z,u,w)),v5) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,27496,a(flip),b,31603,a),flip(a)].">
      <j1 rule="hyper" parents="63 27496 31603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31606">
    <literal><![CDATA[
      L(R(x,a(y,z,L(z,u,w)),v5) \ x,z,a(y,x,z)) = a(x,a(y,z,z),L(v5,u,w)) \ 1
    ]]></literal>
    <justification jstring="[para(31223(a,1),31605(a,2,1))].">
      <j1 rule="para" parents="31223 31605"/>
    </justification>
  </clause>

  <clause id="31607">
    <literal><![CDATA[
      L(R(x,a(y,z,L(z,u,w)),v5) \ x,z,a(y,x,z)) = L(a(x,a(y,z,z),v5) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,29136,a,b,31606,a),flip(a)].">
      <j1 rule="hyper" parents="347 29136 31606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31608">
    <literal><![CDATA[
      L(R(x,a(y,z,L(z,u,w)),v5) \ x,z,a(y,x,z)) = a(v5,a(y,z,z),L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,29143,a(flip),b,31607,a),flip(a)].">
      <j1 rule="hyper" parents="347 29143 31607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31609">
    <literal><![CDATA[
      L(L(x,a(y,z,L(z,u,w)),v5) \ x,z,a(y,x,z)) = a(v5,a(y,z,z),L(x,u,w))
    ]]></literal>
    <justification jstring="[para(23225(a,1),31608(a,1,1,1))].">
      <j1 rule="para" parents="23225 31608"/>
    </justification>
  </clause>

  <clause id="31610">
    <literal><![CDATA[
      L(L(x,a(y,y,z),L(u,w,v5)) \ x,y,a(z,x,y)) = a(u,a(z,y,y),L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(30542(a,1),31609(a,1,1,1))].">
      <j1 rule="para" parents="30542 31609"/>
    </justification>
  </clause>

  <clause id="31611">
    <literal><![CDATA[
      L(L(x,a(y,y,z),u) \ x,y,a(z,x,y)) = a(u,a(z,y,y),L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(30535(a,1),31610(a,1,1,1))].">
      <j1 rule="para" parents="30535 31610"/>
    </justification>
  </clause>

  <clause id="31612">
    <literal><![CDATA[
      L(a(x,a(y,y,z),u),y,a(z,u,y)) = a(x,a(z,y,y),L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(28838(a,2),31611(a,1,1))].">
      <j1 rule="para" parents="28838 31611"/>
    </justification>
  </clause>

  <clause id="31614">
    <literal><![CDATA[
      a(x,a(y,z,z),L(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,a(z,z,y),u) = v6
    ]]></literal>
    <justification jstring="[para(31612(a,1),30499(a,1))].">
      <j1 rule="para" parents="31612 30499"/>
    </justification>
  </clause>

  <clause id="31615">
    <literal><![CDATA[
      (x * (a(y,z,a(u,u,w)) * (v5 * v6))) \ ((x * v5) * (a(y,z,a(u,u,w)) * v6)) = a(a(y,z,a(u,u,w)) * x,L(v5,x,a(y,z,a(u,u,w))),v6)
    ]]></literal>
    <justification jstring="[para(30524(a,1),31585(a,1,2))].">
      <j1 rule="para" parents="30524 31585"/>
    </justification>
  </clause>

  <clause id="31616">
    <literal><![CDATA[
      (x * (a(y,z,a(u,u,w)) * (v5 * v6))) \ ((x * v5) * (a(y,z,a(u,u,w)) * v6)) = a(a(y,z,a(u,u,w)) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(30439(a,1),31615(a,2,2))].">
      <j1 rule="para" parents="30439 31615"/>
    </justification>
  </clause>

  <clause id="31617">
    <literal><![CDATA[
      a(a(x,y,a(z,z,u)) * w,v5,v6) = a(w,v5,a(x,y,a(z,z,u)) * v6)
    ]]></literal>
    <justification jstring="[hyper(30467,a,31616,a),flip(a)].">
      <j1 rule="hyper" parents="30467 31616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31618">
    <literal><![CDATA[
      a(a(x,y,a(z,z,u)) * w,v5,v6) = a(w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,30777,a(flip),b,31617,a),flip(a)].">
      <j1 rule="hyper" parents="347 30777 31617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31620">
    <literal><![CDATA[
      a(x * (a(x,y,a(z,z,u)) * w),v5,v6) = a(x * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(25377(a,1),31618(a,1,1))].">
      <j1 rule="para" parents="25377 31618"/>
    </justification>
  </clause>

  <clause id="31622">
    <literal><![CDATA[
      a(L(x,y,a(z,z,u)) * w,v5,v6) = a(x * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(30578(a,1),31620(a,1,1))].">
      <j1 rule="para" parents="30578 31620"/>
    </justification>
  </clause>

  <clause id="31623">
    <literal><![CDATA[
      a(x * L(y,z,a(z,u,w)),v5,v6) = a(y * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,29916,a(flip),b,31622,a)].">
      <j1 rule="hyper" parents="63 29916 31622"/>
    </justification>
  </clause>

  <clause id="31624">
    <literal><![CDATA[
      ((x \ K(y,x \ 1)) * R(y,x \ K(y,x \ 1),x \ K(y,x \ 1))) * z = (y * (x \ 1)) * (z * a(y,x \ K(y,x \ 1),x))
    ]]></literal>
    <justification jstring="[para(24308(a,1),29607(a,2,2,2))].">
      <j1 rule="para" parents="24308 29607"/>
    </justification>
  </clause>

  <clause id="31625">
    <literal><![CDATA[
      ((x \ K(y,x \ 1)) * R(y,x \ K(y,x \ 1),x \ K(y,x \ 1))) * z = (y * (x \ 1)) * (z * a(y,x,x))
    ]]></literal>
    <justification jstring="[para(24260(a,1),31624(a,2,2,2))].">
      <j1 rule="para" parents="24260 31624"/>
    </justification>
  </clause>

  <clause id="31627">
    <literal><![CDATA[
      ((x \ K(y,x \ 1)) * R(y,x \ K(y,x \ 1),x)) * z = (y * (x \ 1)) * (z * a(y,x,x))
    ]]></literal>
    <justification jstring="[para(22086(a,1),31625(a,1,1,2))].">
      <j1 rule="para" parents="22086 31625"/>
    </justification>
  </clause>

  <clause id="31630">
    <literal><![CDATA[
      ((x \ K(y,x \ 1)) * R(y,x,x)) * z = (y * (x \ 1)) * (z * a(y,x,x))
    ]]></literal>
    <justification jstring="[para(22436(a,1),31627(a,1,1,2))].">
      <j1 rule="para" parents="22436 31627"/>
    </justification>
  </clause>

  <clause id="31631">
    <literal><![CDATA[
      (x * (y \ 1)) * (z * a(x,y,y)) = (R(x,y,y) * (y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(20406(a,1),31630(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20406 31630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31633">
    <literal><![CDATA[
      (x * (y \ 1)) * (z * a(x,y,y)) = R(x * (1 / y),y,y) * z
    ]]></literal>
    <justification jstring="[para(2273(a,2),31631(a,2,1))].">
      <j1 rule="para" parents="2273 31631"/>
    </justification>
  </clause>

  <clause id="31634">
    <literal><![CDATA[
      a(((L((x \ 1) * y,z,z) \ u) \ L((x \ 1) * y,x,x)) \ (x \ y),w,v5) = a(((((x \ 1) * y) \ u) \ ((x \ 1) * y)) \ L((x \ 1) * y,z,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,28008,a(flip),b,29486,a),flip(a)].">
      <j1 rule="hyper" parents="347 28008 29486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31636">
    <literal><![CDATA[
      a(((L((x \ 1) * y,x,x) \ z) \ L((x \ 1) * y,x,x)) \ (x \ y),u,w) = a(((((x \ 1) * y) \ z) \ ((x \ 1) * y)) \ (x \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,27994,a(flip),b,31634,a),flip(a)].">
      <j1 rule="hyper" parents="347 27994 31634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31637">
    <literal><![CDATA[
      a(((L((x \ 1) * y,x,x) \ z) \ L((x \ 1) * y,x,x)) \ (x \ y),u,w) = a((((x \ 1) * y) \ z) * a(x,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,29662,a(flip),b,31636,a),flip(a)].">
      <j1 rule="hyper" parents="347 29662 31636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31638">
    <literal><![CDATA[
      a((((x \ 1) * y) \ z) * a(x,x,y),u,w) = a(L((x \ 1) * y,x,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(27999,a,31637,a),flip(a)].">
      <j1 rule="hyper" parents="27999 31637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31639">
    <literal><![CDATA[
      a((((x \ 1) * y) \ z) * a(x,x,y),u,w) = a((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,28000,a(flip),b,31638,a),flip(a)].">
      <j1 rule="hyper" parents="347 28000 31638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31640">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ ((y * a(x,y,z)) \ (L(y * a(x,y,a(u,a(x,y,z),z)),y,a(x,y,z)) * u)) = a(y * a(x,y,z),L(a(x,y,z),a(x,y,z),u),u)
    ]]></literal>
    <justification jstring="[para(29790(a,1),28826(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="29790 28826"/>
    </justification>
  </clause>

  <clause id="31641">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ ((y * a(x,y,z)) \ (L(y * a(x,y,a(u,z,a(x,y,z))),y,a(x,y,z)) * u)) = a(y * a(x,y,z),L(a(x,y,z),a(x,y,z),u),u)
    ]]></literal>
    <justification jstring="[para(26624(a,1),31640(a,1,2,2,1,1,2,3))].">
      <j1 rule="para" parents="26624 31640"/>
    </justification>
  </clause>

  <clause id="31642">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ ((y * a(x,y,z)) \ (L(y * 1,y,a(x,y,z)) * u)) = a(y * a(x,y,z),L(a(x,y,z),a(x,y,z),u),u)
    ]]></literal>
    <justification jstring="[para(28516(a,1),31641(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="28516 31641"/>
    </justification>
  </clause>

  <clause id="31643">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ ((y * a(x,y,z)) \ (L(y,y,a(x,y,z)) * u)) = a(y * a(x,y,z),L(a(x,y,z),a(x,y,z),u),u)
    ]]></literal>
    <justification jstring="[para(8(a,1),31642(a,1,2,2,1,1))].">
      <j1 rule="para" parents="8 31642"/>
    </justification>
  </clause>

  <clause id="31645">
    <literal><![CDATA[
      a(x * a(y,x,z),L(a(y,x,z),a(y,x,z),u),u) = (a(y,x,z) \ u) \ ((x * a(y,x,z)) \ (x * u))
    ]]></literal>
    <justification jstring="[para(26355(a,1),31643(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="26355 31643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31646">
    <literal><![CDATA[
      a(x * a(y,x,z),L(a(y,x,z),a(y,x,z),u),u) = (a(y,x,z) \ u) \ (x * ((a(y,x,z) * x) \ u))
    ]]></literal>
    <justification jstring="[para(30944(a,1),31645(a,2,2))].">
      <j1 rule="para" parents="30944 31645"/>
    </justification>
  </clause>

  <clause id="31647">
    <literal><![CDATA[
      a(x * a(y,x,z),L(a(y,x,z),a(y,x,z),u),u) = a(a(y,x,z),x,a(y,x,z) * (x \ u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(347,a,29578,a(flip),b,31646,a),flip(a)].">
      <j1 rule="hyper" parents="347 29578 31646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31648">
    <literal><![CDATA[
      a(x * a(y,x,z),L(a(y,x,z),a(y,x,z),u),u) = a(y,x,a(a(y,x,z) * (x \ u),x,z)) \ 1
    ]]></literal>
    <justification jstring="[para(29790(a,1),31647(a,2,1))].">
      <j1 rule="para" parents="29790 31647"/>
    </justification>
  </clause>

  <clause id="31649">
    <literal><![CDATA[
      a(x * a(y,x,z),L(a(y,x,z),a(y,x,z),u),u) = a(y,x,a(a(y,x,z) * (x \ u),x,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,26334,a(flip),b,31648,a),flip(a)].">
      <j1 rule="hyper" parents="347 26334 31648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31650">
    <literal><![CDATA[
      a(x,y,a(a(x,y,z) * (y \ u),y,z)) = a(y * a(x,y,z),a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(28453(a,1),31649(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28453 31649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31651">
    <literal><![CDATA[
      a(x,y,a(a(x,y,z) * (y \ u),y,z)) = a(y,a(x,y,z),u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,28770,a(flip),b,31650,a),flip(a)].">
      <j1 rule="hyper" parents="347 28770 31650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31653">
    <literal><![CDATA[
      a(x,y,a(a(x,y,z) * (y \ u),y,z)) = a(u,a(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,31042,a(flip),b,31651,a),flip(a)].">
      <j1 rule="hyper" parents="347 31042 31651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31654">
    <literal><![CDATA[
      a(x,a(y,x,z),a(z,x,y) \ u) = a(u,a(z,x,y),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,31033,a(flip),b,31653,a)].">
      <j1 rule="hyper" parents="63 31033 31653"/>
    </justification>
  </clause>

  <clause id="31655">
    <literal><![CDATA[
      a(a(x,y,z),y,a(z,y,x) \ u) = a(y \ u,a(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,31047,a(flip),b,31654,a)].">
      <j1 rule="hyper" parents="63 31047 31654"/>
    </justification>
  </clause>

  <clause id="31656">
    <literal><![CDATA[
      a(a(x,y,z),y,a(z,y,x) \ u) = a(y,a(z,y,x),u * y)
    ]]></literal>
    <justification jstring="[hyper(347,a,31208,a(flip),b,31655,a),flip(a)].">
      <j1 rule="hyper" parents="347 31208 31655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31657">
    <literal><![CDATA[
      a(x,a(y,x,z),u * x) != w
    ]]></literal>
    <literal><![CDATA[
      a(a(y,x,z) * u,x,a(z,x,y)) = w
    ]]></literal>
    <justification jstring="[para(31656(a,1),30831(a,1))].">
      <j1 rule="para" parents="31656 30831"/>
    </justification>
  </clause>

  <clause id="31658">
    <literal><![CDATA[
      a(a(x,y,z) * u,y,a(z,y,x)) = a(u,y,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(31657,a,30957,a)].">
      <j1 rule="hyper" parents="31657 30957"/>
    </justification>
  </clause>

  <clause id="31659">
    <literal><![CDATA[
      a(x,y,a(a(x,y,z) * u,y,z)) = a(u,y,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(29908,a,31658,a)].">
      <j1 rule="hyper" parents="29908 31658"/>
    </justification>
  </clause>

  <clause id="31660">
    <literal><![CDATA[
      (x * a(y,x,z)) \ (a(u,x,a(z,x,y)) \ u) = L((x * a(y,x,z)) \ u,a(y,x,z),x)
    ]]></literal>
    <justification jstring="[para(31659(a,1),31509(a,1,2,1))].">
      <j1 rule="para" parents="31659 31509"/>
    </justification>
  </clause>

  <clause id="31661">
    <literal><![CDATA[
      (x * a(y,x,z)) \ (a(u,x,a(z,x,y)) * u) = L((x * a(y,x,z)) \ u,a(y,x,z),x)
    ]]></literal>
    <justification jstring="[para(28387(a,1),31660(a,1,2))].">
      <j1 rule="para" parents="28387 31660"/>
    </justification>
  </clause>

  <clause id="31662">
    <literal><![CDATA[
      L((x * a(y,x,z)) \ u,a(y,x,z),x) = (x * a(y,x,z)) \ R(u,x,a(z,x,y))
    ]]></literal>
    <justification jstring="[para(28908(a,2),31661(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28908 31661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31663">
    <literal><![CDATA[
      L((x * a(y,x,z)) \ u,a(y,x,z),x) = (x * a(y,x,z)) \ L(u,x,a(z,x,y))
    ]]></literal>
    <justification jstring="[para(23247(a,1),31662(a,2,2))].">
      <j1 rule="para" parents="23247 31662"/>
    </justification>
  </clause>

  <clause id="31664">
    <literal><![CDATA[
      (x * a(y,x,z)) \ L(u,x,a(z,x,y)) = a(y,x,z) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,28757,a(flip),b,31663,a),flip(a)].">
      <j1 rule="hyper" parents="63 28757 31663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31665">
    <literal><![CDATA[
      (x * a(y,z,a(u,x,w))) \ L(v5,x,a(a(u,z,y),x,w)) = a(w,x,a(u,z,y)) \ (x \ v5)
    ]]></literal>
    <justification jstring="[hyper(30026,a,31664,a)].">
      <j1 rule="hyper" parents="30026 31664"/>
    </justification>
  </clause>

  <clause id="31666">
    <literal><![CDATA[
      (x * a(y,z,a(z,x,u))) \ w = a(u,x,a(z,z,y)) \ (x \ w)
    ]]></literal>
    <justification jstring="[para(30442(a,1),31665(a,1,2))].">
      <j1 rule="para" parents="30442 31665"/>
    </justification>
  </clause>

  <clause id="31667">
    <literal><![CDATA[
      (x * a(y,z,a(z,x,u))) \ w = a(u,x,a(z,z,y)) * (x \ w)
    ]]></literal>
    <justification jstring="[hyper(347,a,28387,a(flip),b,31666,a),flip(a)].">
      <j1 rule="hyper" parents="347 28387 31666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31668">
    <literal><![CDATA[
      T(a(x,a(y,z,z),L(u,x,a(y,z,z))) * a(y,z,z),L(u,x,a(y,z,z))) = a(y,u,a(z,z,x)) * (u \ L(a(y,z,z) * u,x,a(z,z,y)))
    ]]></literal>
    <justification jstring="[hyper(63,a,31584,a,b,31667,a)].">
      <j1 rule="hyper" parents="63 31584 31667"/>
    </justification>
  </clause>

  <clause id="31669">
    <literal><![CDATA[
      T(a(x,a(y,z,z),L(u,x,a(y,z,z))) * a(y,z,z),L(u,x,a(y,z,z))) = a(y,u,a(z,z,x)) * (u * L(u \ a(y,z,z),x,a(z,z,y)))
    ]]></literal>
    <justification jstring="[para(20572(a,1),31668(a,2,2))].">
      <j1 rule="para" parents="20572 31668"/>
    </justification>
  </clause>

  <clause id="31670">
    <literal><![CDATA[
      T(a(x,a(y,z,z),L(u,x,a(y,z,z))) * a(y,z,z),L(u,x,a(y,z,z))) = a(y,u,a(z,z,x)) * a(y,z,L(z,x,u))
    ]]></literal>
    <justification jstring="[para(30528(a,1),31669(a,2,2))].">
      <j1 rule="para" parents="30528 31669"/>
    </justification>
  </clause>

  <clause id="31671">
    <literal><![CDATA[
      T(a(x,a(y,z,z),L(u,x,a(y,z,z))) * a(y,z,z),L(u,x,a(y,z,z))) = a(y,z,z * a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,30096,a(flip),b,31670,a),flip(a)].">
      <j1 rule="hyper" parents="347 30096 31670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31672">
    <literal><![CDATA[
      T(a(x,a(y,z,z),u) * a(y,z,z),L(u,x,a(y,z,z))) = a(y,z,z * a(u,z,x))
    ]]></literal>
    <justification jstring="[para(29278(a,1),31671(a,1,1,1))].">
      <j1 rule="para" parents="29278 31671"/>
    </justification>
  </clause>

  <clause id="31673">
    <literal><![CDATA[
      T(a(x,y,y) * a(z,a(x,y,y),u),L(z,u,a(x,y,y))) = a(x,y,y * a(z,y,u))
    ]]></literal>
    <justification jstring="[para(28773(a,1),31672(a,1,1))].">
      <j1 rule="para" parents="28773 31672"/>
    </justification>
  </clause>

  <clause id="31675">
    <literal><![CDATA[
      a(x,y,y) \ a(x,y,y * a(z,y,u)) = a(z,a(x,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(128,a,31673,a(flip),b,23077,a(flip))].">
      <j1 rule="hyper" parents="128 31673 23077"/>
    </justification>
  </clause>

  <clause id="31676">
    <literal><![CDATA[
      L(a(x,a(y,z,z),u),w,v5) = a(y,a(u,z,x),z)
    ]]></literal>
    <justification jstring="[para(31675(a,1),31508(a,1,1))].">
      <j1 rule="para" parents="31675 31508"/>
    </justification>
  </clause>

  <clause id="31677">
    <literal><![CDATA[
      a(x,a(y,z,z),L(u,w,v5)) = a(y,a(u,z,x),z)
    ]]></literal>
    <justification jstring="[hyper(29297,a,31676,a)].">
      <j1 rule="hyper" parents="29297 31676"/>
    </justification>
  </clause>

  <clause id="31678">
    <literal><![CDATA[
      a(x,a(y,z,u),z) = a(u,a(z,z,x),y)
    ]]></literal>
    <justification jstring="[hyper(31614,a,31677,a),flip(a)].">
      <j1 rule="hyper" parents="31614 31677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31679">
    <literal><![CDATA[
      a(x,a(y,z,u),L(z,w,v5)) = a(u,a(z,z,L(x,w,v5)),y)
    ]]></literal>
    <justification jstring="[hyper(29676,a,31678,a)].">
      <j1 rule="hyper" parents="29676 31678"/>
    </justification>
  </clause>

  <clause id="31680">
    <literal><![CDATA[
      a(x,a(y * (z \ y),y * (z \ y),z * y),u) = a(z * y,a(u,y * (z \ y),x),z)
    ]]></literal>
    <justification jstring="[hyper(29204,a,31678,a),flip(a)].">
      <j1 rule="hyper" parents="29204 31678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31682">
    <literal><![CDATA[
      a(x,a(y,z,a(z,z,x) \ u),z) \ u = ((u / a(z,z,x)) * (a(z,z,x) * y)) / y
    ]]></literal>
    <justification jstring="[para(31678(a,2),23150(a,1,1))].">
      <j1 rule="para" parents="31678 23150"/>
    </justification>
  </clause>

  <clause id="31683">
    <literal><![CDATA[
      a(x,a(y,y,L(z,u,w)),v5) = a(z,a(v5,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,31498,a(flip),b,31679,a),flip(a)].">
      <j1 rule="hyper" parents="63 31498 31679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31685">
    <literal><![CDATA[
      a(x,a(y,z,a(z,z,x) * u),z) \ u = ((u / a(z,z,x)) * (a(z,z,x) * y)) / y
    ]]></literal>
    <justification jstring="[para(28099(a,1),31682(a,1,1,2))].">
      <j1 rule="para" parents="28099 31682"/>
    </justification>
  </clause>

  <clause id="31686">
    <literal><![CDATA[
      a(x,a(y * (z \ y),y * (z \ y),z * y),u) = a(z * y,a(u,z,x),z)
    ]]></literal>
    <justification jstring="[hyper(347,a,31216,a(flip),b,31680,a),flip(a)].">
      <j1 rule="hyper" parents="347 31216 31680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31688">
    <literal><![CDATA[
      a(x,a(y * (z \ y),y * (z \ y),z * y),u) = a(u,z,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,30964,a(flip),b,31686,a),flip(a)].">
      <j1 rule="hyper" parents="347 30964 31686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31689">
    <literal><![CDATA[
      a(x,a(y * (z \ y),z,y * z),u) = a(u,z,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(30332(a,1),31688(a,1,2))].">
      <j1 rule="para" parents="30332 31688"/>
    </justification>
  </clause>

  <clause id="31690">
    <literal><![CDATA[
      a(x,a(y * z,z,z),u) = a(x,z,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,31233,a(flip),b,31689,a)].">
      <j1 rule="hyper" parents="63 31233 31689"/>
    </justification>
  </clause>

  <clause id="31692">
    <literal><![CDATA[
      a(x,a(y,y,z),u) = a(x,y,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,25124,a(flip),b,31690,a)].">
      <j1 rule="hyper" parents="63 25124 31690"/>
    </justification>
  </clause>

  <clause id="31694">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),y,v5)) = a(z,a(v5,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,31683,a(flip),b,31692,a),flip(a)].">
      <j1 rule="hyper" parents="63 31683 31692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31695">
    <literal><![CDATA[
      a(x,y,a(z,y,L(u,w,v5))) = a(z,a(u,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(30015,a,31694,a)].">
      <j1 rule="hyper" parents="30015 31694"/>
    </justification>
  </clause>

  <clause id="31696">
    <literal><![CDATA[
      a(x,a(y,z,u),z) = a(x,z,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(31239,a,31695,a),flip(a)].">
      <j1 rule="hyper" parents="31239 31695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31698">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,31696,a(flip),b,31191,a),flip(a)].">
      <j1 rule="hyper" parents="129 31696 31191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31701">
    <literal><![CDATA[
      a(x,y,a(a(y,y,x) * z,y,u)) \ z = ((z / a(y,y,x)) * (a(y,y,x) * u)) / u
    ]]></literal>
    <justification jstring="[para(31696(a,1),31685(a,1,1))].">
      <j1 rule="para" parents="31696 31685"/>
    </justification>
  </clause>

  <clause id="31705">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(29868,a,31698,a)].">
      <j1 rule="hyper" parents="29868 31698"/>
    </justification>
  </clause>

  <clause id="31708">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(26597,a,31698,a)].">
      <j1 rule="hyper" parents="26597 31698"/>
    </justification>
  </clause>

  <clause id="31709">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) = a(w,v5,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(347,a,31698,a,b,31698,a)].">
      <j1 rule="hyper" parents="347 31698 31698"/>
    </justification>
  </clause>

  <clause id="31718">
    <literal><![CDATA[
      a(x,y,L(z,x,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(189,a,29147,a,b,31698,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="189 29147 31698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31722">
    <literal><![CDATA[
      1 * a(x \ (y \ x),z,u) = a(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(31698(a,1),30053(a,1,1))].">
      <j1 rule="para" parents="31698 30053"/>
    </justification>
  </clause>

  <clause id="31723">
    <literal><![CDATA[
      a(x \ a(x,x,y),z,u) * 1 = a(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(31698(a,1),30360(a,1,2))].">
      <j1 rule="para" parents="31698 30360"/>
    </justification>
  </clause>

  <clause id="31729">
    <literal><![CDATA[
      a(x,y,z) / (u \ 1) = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(220,a,31705,a(flip),b,3196,a(flip))].">
      <j1 rule="hyper" parents="220 31705 3196"/>
    </justification>
  </clause>

  <clause id="31733">
    <literal><![CDATA[
      (1 / x) \ a(y,z,u) = x * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(31705(a,1),23183(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31705 23183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31736">
    <literal><![CDATA[
      (a(x,y,z) \ u) * z = u * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(31705(a,1),29935(a,1,2))].">
      <j1 rule="para" parents="31705 29935"/>
    </justification>
  </clause>

  <clause id="31739">
    <literal><![CDATA[
      L(x \ y,a(z,y,y),u) = L(x \ y,y,a(y,u,z))
    ]]></literal>
    <justification jstring="[para(31705(a,1),29995(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="31705 29995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31741">
    <literal><![CDATA[
      L(x,y,a(z,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(29915,a,31708,a)].">
      <j1 rule="hyper" parents="29915 31708"/>
    </justification>
  </clause>

  <clause id="31742">
    <literal><![CDATA[
      L(x,y,a(z,u,u)) = x
    ]]></literal>
    <justification jstring="[hyper(29900,a,31708,a)].">
      <j1 rule="hyper" parents="29900 31708"/>
    </justification>
  </clause>

  <clause id="31745">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(27578,a,31708,a)].">
      <j1 rule="hyper" parents="27578 31708"/>
    </justification>
  </clause>

  <clause id="31755">
    <literal><![CDATA[
      x * (a(x,y,z) * u) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,31144,a(flip),b,31708,a)].">
      <j1 rule="hyper" parents="63 31144 31708"/>
    </justification>
  </clause>

  <clause id="31756">
    <literal><![CDATA[
      a(x,y,z) * (x * u) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(63,a,31143,a(flip),b,31708,a)].">
      <j1 rule="hyper" parents="63 31143 31708"/>
    </justification>
  </clause>

  <clause id="31758">
    <literal><![CDATA[
      R(x,y,L(z,u,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,30236,a(flip),b,31708,a)].">
      <j1 rule="hyper" parents="63 30236 31708"/>
    </justification>
  </clause>

  <clause id="31760">
    <literal><![CDATA[
      L(x,y,z) * (z * (a(z,y,x) * u)) = x * (z * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,29542,a(flip),b,31708,a)].">
      <j1 rule="hyper" parents="63 29542 31708"/>
    </justification>
  </clause>

  <clause id="31764">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(31708(a,1),50(a,2))].">
      <j1 rule="para" parents="31708 50"/>
    </justification>
  </clause>

  <clause id="31774">
    <literal><![CDATA[
      a(x,y,y) \ (z * u) = z * (a(x,y,y) \ u)
    ]]></literal>
    <justification jstring="[para(31708(a,1),29907(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31708 29907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31775">
    <literal><![CDATA[
      (a(x,x,y) * z) \ u = z \ (a(x,x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(27584,a,31741,a),flip(a)].">
      <j1 rule="hyper" parents="27584 31741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31788">
    <literal><![CDATA[
      (x * a(y,y,z)) \ u = x \ (a(y,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,26388,a(flip),b,31741,a),flip(a)].">
      <j1 rule="hyper" parents="63 26388 31741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31792">
    <literal><![CDATA[
      L(x,y,a(z,u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(31741(a,1),27576(a,1,1))].">
      <j1 rule="para" parents="31741 27576"/>
    </justification>
  </clause>

  <clause id="31793">
    <literal><![CDATA[
      a(x,y,y) * (z * u) = z * (a(x,y,y) * u)
    ]]></literal>
    <justification jstring="[para(31741(a,1),27570(a,1,2,1))].">
      <j1 rule="para" parents="31741 27570"/>
    </justification>
  </clause>

  <clause id="31794">
    <literal><![CDATA[
      a(x,x,y) \ (z * u) = z * (a(x,x,y) \ u)
    ]]></literal>
    <justification jstring="[para(31741(a,1),28540(a,1,2,1))].">
      <j1 rule="para" parents="31741 28540"/>
    </justification>
  </clause>

  <clause id="31806">
    <literal><![CDATA[
      (x * y) * a(z,u,u) = x * (y * a(z,u,u))
    ]]></literal>
    <justification jstring="[para(31742(a,1),23241(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31742 23241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31808">
    <literal><![CDATA[
      a(x,a(y,z,z) * (u * w),v5) = a(x,w * (a(y,z,z) * u),v5)
    ]]></literal>
    <justification jstring="[para(31742(a,1),24040(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="31742 24040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31810">
    <literal><![CDATA[
      x * (L(x,y,z) \ u) = u * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(29509,a,31745,a)].">
      <j1 rule="hyper" parents="29509 31745"/>
    </justification>
  </clause>

  <clause id="31816">
    <literal><![CDATA[
      a(x,y,z) * (L(z,y,x) * u) = z * u
    ]]></literal>
    <justification jstring="[hyper(63,a,29346,a(flip),b,31745,a)].">
      <j1 rule="hyper" parents="63 29346 31745"/>
    </justification>
  </clause>

  <clause id="31822">
    <literal><![CDATA[
      x * ((a(y,x,x) \ z) * u) = L(x,x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(31745(a,1),29980(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="31745 29980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31835">
    <literal><![CDATA[
      a(x \ 1,y,L(z,x,u)) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(3188(a,1),31718(a,1,3))].">
      <j1 rule="para" parents="3188 31718"/>
    </justification>
  </clause>

  <clause id="31841">
    <literal><![CDATA[
      R(x,y,z \ u) = R(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(22241,a,31758,a)].">
      <j1 rule="hyper" parents="22241 31758"/>
    </justification>
  </clause>

  <clause id="31850">
    <literal><![CDATA[
      a(x,y,z) * (x * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) * u = w
    ]]></literal>
    <justification jstring="[para(31143(a,1),31764(a,1))].">
      <j1 rule="para" parents="31143 31764"/>
    </justification>
  </clause>

  <clause id="31851">
    <literal><![CDATA[
      R(x,y,((z \ u) \ w) * a(u,z,z)) = R(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(30898,a,31841,a)].">
      <j1 rule="hyper" parents="30898 31841"/>
    </justification>
  </clause>

  <clause id="31852">
    <literal><![CDATA[
      R(x,y,L(z,z,u * w) * (w \ u)) = R(x,y,(w \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(30696,a,31841,a)].">
      <j1 rule="hyper" parents="30696 31841"/>
    </justification>
  </clause>

  <clause id="31854">
    <literal><![CDATA[
      R(x,y,L(z,z,u) * u) = R(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(21221,a,31841,a)].">
      <j1 rule="hyper" parents="21221 31841"/>
    </justification>
  </clause>

  <clause id="31896">
    <literal><![CDATA[
      a(x * y,z,u) * a(w,v5,a(v5,v6,v7)) = a((y \ 1) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(31709(a,1),29924(a,1,2))].">
      <j1 rule="para" parents="31709 29924"/>
    </justification>
  </clause>

  <clause id="31919">
    <literal><![CDATA[
      L(a(x,y,z),u,u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,26346,a,b,31729,a(flip))].">
      <j1 rule="hyper" parents="35 26346 31729"/>
    </justification>
  </clause>

  <clause id="31920">
    <literal><![CDATA[
      a(x,y,L(z,u,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29297,a,31919,a)].">
      <j1 rule="hyper" parents="29297 31919"/>
    </justification>
  </clause>

  <clause id="31923">
    <literal><![CDATA[
      (1 / x) * a(y,z,u) = a(y,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,31919,a(flip),b,22044,a),flip(a)].">
      <j1 rule="hyper" parents="131 31919 22044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31925">
    <literal><![CDATA[
      T(a(x,y,z) * u,w) \ a(x,y,z) = T(u,w) \ 1
    ]]></literal>
    <justification jstring="[para(31919(a,1),23282(a,1,2))].">
      <j1 rule="para" parents="31919 23282"/>
    </justification>
  </clause>

  <clause id="31933">
    <literal><![CDATA[
      a(x,y,z \ u) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(25264,a,31920,a)].">
      <j1 rule="hyper" parents="25264 31920"/>
    </justification>
  </clause>

  <clause id="31934">
    <literal><![CDATA[
      a(x,y,z \ u) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(25257,a,31920,a)].">
      <j1 rule="hyper" parents="25257 31920"/>
    </justification>
  </clause>

  <clause id="31935">
    <literal><![CDATA[
      a(x,y,(z * u) * u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(24291,a,31920,a)].">
      <j1 rule="hyper" parents="24291 31920"/>
    </justification>
  </clause>

  <clause id="31937">
    <literal><![CDATA[
      a(x,y,z * (z * u)) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(14993,a,31920,a)].">
      <j1 rule="hyper" parents="14993 31920"/>
    </justification>
  </clause>

  <clause id="31939">
    <literal><![CDATA[
      a((x * x) * y,z,u) = a(x * (x * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,29695,a(flip),b,31920,a),flip(a)].">
      <j1 rule="hyper" parents="63 29695 31920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31940">
    <literal><![CDATA[
      a(x * (y \ 1),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,29691,a(flip),b,31920,a)].">
      <j1 rule="hyper" parents="63 29691 31920"/>
    </justification>
  </clause>

  <clause id="31942">
    <literal><![CDATA[
      a((x \ 1) * y,z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,29687,a(flip),b,31920,a),flip(a)].">
      <j1 rule="hyper" parents="63 29687 31920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31943">
    <literal><![CDATA[
      a((x \ 1) \ y,z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,29686,a(flip),b,31920,a)].">
      <j1 rule="hyper" parents="63 29686 31920"/>
    </justification>
  </clause>

  <clause id="31945">
    <literal><![CDATA[
      a(x,y,L(z * (u \ w),z,u)) = a(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24882,a(flip),b,31920,a)].">
      <j1 rule="hyper" parents="63 24882 31920"/>
    </justification>
  </clause>

  <clause id="31948">
    <literal><![CDATA[
      a(x,y,z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * u) = w
    ]]></literal>
    <justification jstring="[para(31920(a,1),14994(a,1))].">
      <j1 rule="para" parents="31920 14994"/>
    </justification>
  </clause>

  <clause id="31951">
    <literal><![CDATA[
      a(x,y,z) * (u \ 1) = u \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(31920(a,1),29322(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31920 29322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31958">
    <literal><![CDATA[
      a(x,y,(y \ z) * L(u,y,y)) = a(x,y,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,31009,a(flip),b,31934,a),flip(a)].">
      <j1 rule="hyper" parents="63 31009 31934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31959">
    <literal><![CDATA[
      a(x,y,(z * u) * ((z \ w) \ (u * w))) = a(x,y,a(w * z,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,30011,a(flip),b,31934,a),flip(a)].">
      <j1 rule="hyper" parents="63 30011 31934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31968">
    <literal><![CDATA[
      (a(x,y,z * u) \ u) * (u \ z) = u * L(u \ z,y,x)
    ]]></literal>
    <justification jstring="[para(31934(a,1),30375(a,1,1,1))].">
      <j1 rule="para" parents="31934 30375"/>
    </justification>
  </clause>

  <clause id="31969">
    <literal><![CDATA[
      a(x,y,(z * u) * ((w * u) * (w \ z))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(u,w,z * w)) = v5
    ]]></literal>
    <justification jstring="[para(31934(a,1),30824(a,1))].">
      <j1 rule="para" parents="31934 30824"/>
    </justification>
  </clause>

  <clause id="31995">
    <literal><![CDATA[
      x * (y * a(x,z,u)) = R(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(20023,a,31755,a)].">
      <j1 rule="hyper" parents="20023 31755"/>
    </justification>
  </clause>

  <clause id="31997">
    <literal><![CDATA[
      x \ R(R(x,y,z),u,z) = a(x,y,z) * a(x,u,z)
    ]]></literal>
    <justification jstring="[hyper(128,a,29709,a(flip),b,31755,a)].">
      <j1 rule="hyper" parents="128 29709 31755"/>
    </justification>
  </clause>

  <clause id="31999">
    <literal><![CDATA[
      (x / y) * R(y,z,u) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(34,a,20930,a,b,31755,a)].">
      <j1 rule="hyper" parents="34 20930 31755"/>
    </justification>
  </clause>

  <clause id="32030">
    <literal><![CDATA[
      a((L(x,y,z) \ u) * x,w,v5) = a(u * a(z,y,x),w,v5)
    ]]></literal>
    <justification jstring="[para(31810(a,1),23896(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31810 23896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32032">
    <literal><![CDATA[
      a((x \ y) * L(x,z,u),w,v5) = a(y * a(u,z,x),w,v5)
    ]]></literal>
    <justification jstring="[para(31810(a,1),28007(a,2,1))].">
      <j1 rule="para" parents="31810 28007"/>
    </justification>
  </clause>

  <clause id="32039">
    <literal><![CDATA[
      a(x,y,z) * R(a(x,y,z) \ u,a(x,y,z),L(z,y,x) * w) = ((u * (L(z,y,x) * w)) / (z * w)) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(31816(a,1),953(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="31816 953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32041">
    <literal><![CDATA[
      (a(x,y,z) * (L(z,y,x) * u)) \ ((L(z,y,x) * u) * w) = ((L(z,y,x) * u) * w) / T(z * u,w)
    ]]></literal>
    <justification jstring="[para(31816(a,1),23052(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="31816 23052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32044">
    <literal><![CDATA[
      a((x \ 1) \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y * x,z,u) = w
    ]]></literal>
    <justification jstring="[para(31940(a,1),23982(a,1))].">
      <j1 rule="para" parents="31940 23982"/>
    </justification>
  </clause>

  <clause id="32045">
    <literal><![CDATA[
      a((x \ 1) \ y,z,a(u,w,v5)) = a(x \ y,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(30813,a,31942,a)].">
      <j1 rule="hyper" parents="30813 31942"/>
    </justification>
  </clause>

  <clause id="32048">
    <literal><![CDATA[
      a(x,(a(y \ z,z,z) * u) * w,v5) = a(x,w * (u * a(y \ 1,z,z)),v5)
    ]]></literal>
    <justification jstring="[para(31942(a,1),28184(a,1,2,1,1))].">
      <j1 rule="para" parents="31942 28184"/>
    </justification>
  </clause>

  <clause id="32050">
    <literal><![CDATA[
      a(x,y,a((z \ 1) * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(31942(a,2),30815(a,1,3))].">
      <j1 rule="para" parents="31942 30815"/>
    </justification>
  </clause>

  <clause id="32055">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ u) = a(u * z,y,x) \ x
    ]]></literal>
    <justification jstring="[para(31943(a,1),28841(a,2,1))].">
      <j1 rule="para" parents="31943 28841"/>
    </justification>
  </clause>

  <clause id="32066">
    <literal><![CDATA[
      a((x * (y * z)) \ (x * y),u,w) = a(z \ 1,u,L(w,y * z,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,30030,a,b,31835,a)].">
      <j1 rule="hyper" parents="63 30030 31835"/>
    </justification>
  </clause>

  <clause id="32069">
    <literal><![CDATA[
      a(x \ (y \ x),z,u) = a(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(135,a,31722,a)].">
      <j1 rule="hyper" parents="135 31722"/>
    </justification>
  </clause>

  <clause id="32070">
    <literal><![CDATA[
      a((x * y) \ y,z,u) = a(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,25200,a,b,32069,a)].">
      <j1 rule="hyper" parents="63 25200 32069"/>
    </justification>
  </clause>

  <clause id="32071">
    <literal><![CDATA[
      a((x \ y) \ 1,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(32069(a,1),23984(a,1))].">
      <j1 rule="para" parents="32069 23984"/>
    </justification>
  </clause>

  <clause id="32073">
    <literal><![CDATA[
      x * (a(y,z,z) \ R(x \ a(y,z,z),u,w)) = a((a(y,z,z) \ x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(29069,a,31774,a),flip(a)].">
      <j1 rule="hyper" parents="29069 31774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32075">
    <literal><![CDATA[
      (x / (a(y,z,z) * (u * w))) * (a(y,z,z) * a(y,z,z)) = x / L(u * (a(y,z,z) \ w),a(y,z,z),a(y,z,z))
    ]]></literal>
    <justification jstring="[para(31774(a,1),897(a,2,2,1))].">
      <j1 rule="para" parents="31774 897"/>
    </justification>
  </clause>

  <clause id="32076">
    <literal><![CDATA[
      ((a(x,y,y) \ z) * u) \ (w \ ((a(x,y,y) \ (w * z)) * u)) = a(w,a(x,y,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(31774(a,2),14699(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="31774 14699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32077">
    <literal><![CDATA[
      L((x * y) / (z * a(u,w,w)),z,a(u,w,w)) = (x * (a(u,w,w) \ y)) / z
    ]]></literal>
    <justification jstring="[para(31774(a,1),26376(a,2,1))].">
      <j1 rule="para" parents="31774 26376"/>
    </justification>
  </clause>

  <clause id="32078">
    <literal><![CDATA[
      (a(x,x,y) * a(z,u,a(x,x,y) \ w)) \ w = L(a(x,x,y) \ w,u,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,28841,a,b,31775,a),flip(a)].">
      <j1 rule="hyper" parents="347 28841 31775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32079">
    <literal><![CDATA[
      x \ (a(y,y,z) \ (x * L(z * (L(L(z,y,y),y,y) \ u),w,v5))) = L(a(y,y,z) * L(u,w,v5),a(y,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(63,a,28498,a(flip),b,31788,a),flip(a)].">
      <j1 rule="hyper" parents="63 28498 31788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32084">
    <literal><![CDATA[
      a(x * (y * a(z,u,u)),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(a(z,u,u) * (y * x),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(31806(a,1),24409(a,1,1))].">
      <j1 rule="para" parents="31806 24409"/>
    </justification>
  </clause>

  <clause id="32086">
    <literal><![CDATA[
      a(x * (x * (y * (x \ z))),u,w) = a(y * ((x \ 1) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24593,a(flip),b,31939,a),flip(a)].">
      <j1 rule="hyper" parents="63 24593 31939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32087">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(32055(a,2),28866(a,1))].">
      <j1 rule="para" parents="32055 28866"/>
    </justification>
  </clause>

  <clause id="32088">
    <literal><![CDATA[
      a(x \ a(x,x,y),z,u) = a(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(142,a,31723,a)].">
      <j1 rule="hyper" parents="142 31723"/>
    </justification>
  </clause>

  <clause id="32089">
    <literal><![CDATA[
      a((x \ y) \ L(y,z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(a(u,z,y) * x,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(29633(a,1),32044(a,1))].">
      <j1 rule="para" parents="29633 32044"/>
    </justification>
  </clause>

  <clause id="32090">
    <literal><![CDATA[
      L(x,y,z * (u \ 1)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(32087,a,21470,a)].">
      <j1 rule="hyper" parents="32087 21470"/>
    </justification>
  </clause>

  <clause id="32092">
    <literal><![CDATA[
      a(x,y * L(z,u,w \ v5),v6) = a(x,y * L(z,u,v5 * w),v6)
    ]]></literal>
    <justification jstring="[para(32090(a,1),25128(a,1,2,2))].">
      <j1 rule="para" parents="32090 25128"/>
    </justification>
  </clause>

  <clause id="32094">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w \ v5,w,v6 \ w))) = a(x,y,a(z,u,v6 * ((w \ v6) * v5)))
    ]]></literal>
    <justification jstring="[para(32090(a,1),31052(a,1,3,3))].">
      <j1 rule="para" parents="32090 31052"/>
    </justification>
  </clause>

  <clause id="32095">
    <literal><![CDATA[
      L(x \ y,a(z,y,y),u) = x \ y
    ]]></literal>
    <justification jstring="[hyper(347,a,31708,a(flip),b,31739,a),flip(a)].">
      <j1 rule="hyper" parents="347 31708 31739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32097">
    <literal><![CDATA[
      (x \ y) * L(z,a(u,y,y),x) = (x \ y) * z
    ]]></literal>
    <justification jstring="[para(32095(a,1),30901(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32095 30901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32098">
    <literal><![CDATA[
      L(x,a(y,z,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(626,a,32097,a),flip(a)].">
      <j1 rule="hyper" parents="626 32097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32100">
    <literal><![CDATA[
      L(x,a(y,y,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(31063,a,32098,a)].">
      <j1 rule="hyper" parents="31063 32098"/>
    </justification>
  </clause>

  <clause id="32101">
    <literal><![CDATA[
      L(x,a(y,z,z),u) = L(x,a(w,v5,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,32098,a,b,32098,a)].">
      <j1 rule="hyper" parents="347 32098 32098"/>
    </justification>
  </clause>

  <clause id="32106">
    <literal><![CDATA[
      (a(x,y,y) \ z) * u = z * (a(x,y,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(134,a,32098,a(flip),b,28544,a)].">
      <j1 rule="hyper" parents="134 32098 28544"/>
    </justification>
  </clause>

  <clause id="32107">
    <literal><![CDATA[
      (a(x,y,y) * z) * u = z * (u * a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(134,a,32098,a(flip),b,21148,a)].">
      <j1 rule="hyper" parents="134 32098 21148"/>
    </justification>
  </clause>

  <clause id="32109">
    <literal><![CDATA[
      (x * a(y,y,z)) * u = x * (a(y,y,z) * u)
    ]]></literal>
    <justification jstring="[para(32098(a,1),26513(a,1,2))].">
      <j1 rule="para" parents="32098 26513"/>
    </justification>
  </clause>

  <clause id="32110">
    <literal><![CDATA[
      (a(x,x,y) * z) * u = z * (u * a(x,x,y))
    ]]></literal>
    <justification jstring="[para(32098(a,1),26515(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32098 26515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32128">
    <literal><![CDATA[
      a(a(x \ 1,x,y) \ (((y / (x * y)) \ 1) \ z),u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(32100(a,1),31288(a,2,3))].">
      <j1 rule="para" parents="32100 31288"/>
    </justification>
  </clause>

  <clause id="32129">
    <literal><![CDATA[
      (x * (a(y,z,z) \ (u * w))) \ (((a(y,z,z) \ x) * u) * w) = a(a(y,z,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(32106(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="32106 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32130">
    <literal><![CDATA[
      ((x * (a(y,z,z) \ u)) * w) / (u * w) = R(a(y,z,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(32106(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="32106 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32131">
    <literal><![CDATA[
      a((x * (y \ 1)) * (a(z,u,u) \ a(x,y,y)),w,v5) = a(a(z,u,u) \ (y \ x),w,v5)
    ]]></literal>
    <justification jstring="[para(32106(a,1),31561(a,1,1))].">
      <j1 rule="para" parents="32106 31561"/>
    </justification>
  </clause>

  <clause id="32132">
    <literal><![CDATA[
      (x * (a(y,z,z) \ u)) * w = (x * u) * (a(y,z,z) \ w)
    ]]></literal>
    <justification jstring="[para(31774(a,1),32106(a,1,1))].">
      <j1 rule="para" parents="31774 32106"/>
    </justification>
  </clause>

  <clause id="32133">
    <literal><![CDATA[
      a(x * (a(y,y,z) * u),w,v5) = a(u * (x * a(z,y,y)),w,v5)
    ]]></literal>
    <justification jstring="[para(32107(a,1),28050(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32107 28050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32137">
    <literal><![CDATA[
      R(x,y * (a(z,u,u) * w),v5) = R(x,w * (y * a(u,u,z)),v5)
    ]]></literal>
    <justification jstring="[para(32110(a,1),29658(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32110 29658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32138">
    <literal><![CDATA[
      R(x,(y * z) * (u * a(w,w,z)),v5) = R(x,u * (y * L(z,w,w)),v5)
    ]]></literal>
    <justification jstring="[para(32110(a,1),30688(a,1,2))].">
      <j1 rule="para" parents="32110 30688"/>
    </justification>
  </clause>

  <clause id="32144">
    <literal><![CDATA[
      L(x,y,z) * (R(z,y,x) * u) = x * (z * u)
    ]]></literal>
    <justification jstring="[para(31755(a,1),31760(a,1,2))].">
      <j1 rule="para" parents="31755 31760"/>
    </justification>
  </clause>

  <clause id="32145">
    <literal><![CDATA[
      a(x,L(y,z,x),L(u,z,y)) = (x * (y * u)) \ ((x * y) * u)
    ]]></literal>
    <justification jstring="[para(32144(a,1),30055(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32144 30055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32149">
    <literal><![CDATA[
      ((a(x,y,z) * a(x,y,z)) * (R(x,y,z) * R(x,y,z))) / R(R(x,y,z),y,z) = L(R(R(x,y,z),y,z),x,x \ R(R(x,y,z),y,z))
    ]]></literal>
    <justification jstring="[para(31997(a,1),31510(a,1,1,1))].">
      <j1 rule="para" parents="31997 31510"/>
    </justification>
  </clause>

  <clause id="32151">
    <literal><![CDATA[
      a(x,y,L(z * (u \ w),z,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * u) * w) = v5
    ]]></literal>
    <justification jstring="[para(31945(a,2),31948(a,1))].">
      <j1 rule="para" parents="31945 31948"/>
    </justification>
  </clause>

  <clause id="32152">
    <literal><![CDATA[
      a(x,y,(a(z,z,u) * w) \ v5) = a(x,y,a(z,z,u) * (w \ v5))
    ]]></literal>
    <justification jstring="[para(32100(a,1),31945(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32100 31945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32153">
    <literal><![CDATA[
      a(x,y,z * u) \ z = u * L(u \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,28502,a(flip),b,31968,a)].">
      <j1 rule="hyper" parents="63 28502 31968"/>
    </justification>
  </clause>

  <clause id="32154">
    <literal><![CDATA[
      a(a(x,y,z),u,w * (u * a(x,y,z))) \ w = (u * a(x,y,z)) * (u \ (a(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[para(26388(a,1),32153(a,2,2))].">
      <j1 rule="para" parents="26388 32153"/>
    </justification>
  </clause>

  <clause id="32155">
    <literal><![CDATA[
      ((x * y) \ (y * z)) * L(T(L(x \ z,x,y) \ z,y),u,w) = a(w,u,z * ((x * y) \ (y * z))) \ z
    ]]></literal>
    <justification jstring="[para(30384(a,2),32153(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="30384 32153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32156">
    <literal><![CDATA[
      a(x \ (L(y,(x \ 1) \ z,x \ 1) * z),u,a(w,v5,v6)) = a(((x \ 1) \ z) * T(y,z),u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(874(a,1),32045(a,1,1)),flip(a)].">
      <j1 rule="para" parents="874 32045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32157">
    <literal><![CDATA[
      (x * ((x * y) * (a(z,u,u) \ w))) / (x * ((a(z,u,u) \ y) * w)) = R(x,a(z,u,u) \ y,w)
    ]]></literal>
    <justification jstring="[para(32132(a,1),1768(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="32132 1768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32158">
    <literal><![CDATA[
      a(x,L(y,z,x),L(u,z,y)) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,14,a,b,32145,a),flip(a)].">
      <j1 rule="hyper" parents="347 14 32145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32161">
    <literal><![CDATA[
      (a(x,L(y,z,x),u) \ w) \ (a(u,L(y,z,x),a(y,z,x)) * w) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,30304,a,b,32158,a)].">
      <j1 rule="hyper" parents="63 30304 32158"/>
    </justification>
  </clause>

  <clause id="32162">
    <literal><![CDATA[
      a(x,(a(y,z,z) * u) * w,v5) = a(x,a(y,z,z) * (u * w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24037,a,b,31808,a)].">
      <j1 rule="hyper" parents="347 24037 31808"/>
    </justification>
  </clause>

  <clause id="32163">
    <literal><![CDATA[
      a(K(x,y) * ((z \ 1) \ u),w,v5) = a(u * z,w,v5) * a(v6,v7,a(v7,v8,v9))
    ]]></literal>
    <justification jstring="[hyper(347,a,23885,a,b,31896,a)].">
      <j1 rule="hyper" parents="347 23885 31896"/>
    </justification>
  </clause>

  <clause id="32164">
    <literal><![CDATA[
      a((x * y) * (z * a(u,x,x)),w,v5) = a(z * (R(x,x,u) * y),w,v5)
    ]]></literal>
    <justification jstring="[para(31756(a,1),32133(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="31756 32133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32165">
    <literal><![CDATA[
      a(x,y,(x * z) * u) = a(x,y,x * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(32151,a,31718,a)].">
      <j1 rule="hyper" parents="32151 31718"/>
    </justification>
  </clause>

  <clause id="32166">
    <literal><![CDATA[
      a(x,y,x * (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(x * z) * u) = w
    ]]></literal>
    <justification jstring="[para(31718(a,1),32151(a,1))].">
      <j1 rule="para" parents="31718 32151"/>
    </justification>
  </clause>

  <clause id="32169">
    <literal><![CDATA[
      a(x,y,x * (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(z * x) * u) = w
    ]]></literal>
    <justification jstring="[para(32165(a,1),24192(a,1))].">
      <j1 rule="para" parents="32165 24192"/>
    </justification>
  </clause>

  <clause id="32171">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (w \ v5)) * x = R(x,y,(a(z,z,u) * w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(133,a,32152,a(flip),b,28907,a(flip))].">
      <j1 rule="hyper" parents="133 32152 28907"/>
    </justification>
  </clause>

  <clause id="32172">
    <literal><![CDATA[
      a(x,y,(a(z,u,u) * (w * (a(u,u,z) * z))) \ v5) = a(x,y,a(u,u,z) * ((w * R(z,u,u)) \ v5))
    ]]></literal>
    <justification jstring="[para(30063(a,2),32152(a,1,3,1))].">
      <j1 rule="para" parents="30063 32152"/>
    </justification>
  </clause>

  <clause id="32173">
    <literal><![CDATA[
      a(x,a(y,z,z) * (u * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,w * (a(y,z,z) * u),v5) = v6
    ]]></literal>
    <justification jstring="[para(32162(a,1),23994(a,1))].">
      <j1 rule="para" parents="32162 23994"/>
    </justification>
  </clause>

  <clause id="32175">
    <literal><![CDATA[
      a(T(x,y * z) \ 1,u,L(w,z * T(x,y * z),y)) = a((L(x,z,y) * (y * z)) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(734(a,1),32066(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="734 32066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32176">
    <literal><![CDATA[
      a(a(x,y,z) * u,u,z) = a(u,u,z)
    ]]></literal>
    <justification jstring="[hyper(32089,a,29666,a)].">
      <j1 rule="hyper" parents="32089 29666"/>
    </justification>
  </clause>

  <clause id="32177">
    <literal><![CDATA[
      (a(x,y,a(z,z,u)) \ w) * (a(x,y,u) \ 1) = w * L(a(x,y,u) \ 1,z,a(x,y,u) * z)
    ]]></literal>
    <justification jstring="[para(32176(a,1),31308(a,1,1,1,3))].">
      <j1 rule="para" parents="32176 31308"/>
    </justification>
  </clause>

  <clause id="32178">
    <literal><![CDATA[
      ((x * y) * (a(z,u,u) \ w)) / (y * w) = R(a(z,u,u) \ x,y,w)
    ]]></literal>
    <justification jstring="[para(32132(a,1),32130(a,1,1))].">
      <j1 rule="para" parents="32132 32130"/>
    </justification>
  </clause>

  <clause id="32179">
    <literal><![CDATA[
      a((x * y) * (z * a(u,x,x)),w,v5) = a(z * (L(x,x,u) * y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,26963,a(flip),b,32164,a),flip(a)].">
      <j1 rule="hyper" parents="347 26963 32164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32180">
    <literal><![CDATA[
      R(x,y,(a(z,z,u) * w) \ v5) = R(x,y,a(z,z,u) * (w \ v5))
    ]]></literal>
    <justification jstring="[hyper(28910,a,32171,a),flip(a)].">
      <j1 rule="hyper" parents="28910 32171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32181">
    <literal><![CDATA[
      R(x,y,(z * a(u,w,w)) \ v5) = R(x,y,a(w,w,u) * (z \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,28493,a(flip),b,32180,a)].">
      <j1 rule="hyper" parents="63 28493 32180"/>
    </justification>
  </clause>

  <clause id="32182">
    <literal><![CDATA[
      R(x,y,(a(z,u,u) * w) \ v5) = R(x,y,a(u,u,z) * (w \ v5))
    ]]></literal>
    <justification jstring="[hyper(22098,a,32181,a)].">
      <j1 rule="hyper" parents="22098 32181"/>
    </justification>
  </clause>

  <clause id="32183">
    <literal><![CDATA[
      R(x,y,a(z,z,u) * ((R(u,z,z) \ w) \ v5)) = R(x,y,(u \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(29390(a,1),32182(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="29390 32182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32184">
    <literal><![CDATA[
      R(x,y,a(z,z,u) * ((R(u,z,z) \ w) \ v5)) = R(x,y,v5 * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(347,a,31841,a(flip),b,32183,a),flip(a)].">
      <j1 rule="hyper" parents="347 31841 32183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32185">
    <literal><![CDATA[
      (a(x,x,y) * a(z,u,a(x,x,y) * w)) \ w = L(a(x,x,y) \ w,u,z)
    ]]></literal>
    <justification jstring="[para(28099(a,1),32078(a,1,1,2))].">
      <j1 rule="para" parents="28099 32078"/>
    </justification>
  </clause>

  <clause id="32186">
    <literal><![CDATA[
      a(a(x,y,y) * (z * u),w,v5) = a(u * (a(y,y,x) * z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(32084,a,28049,a(flip))].">
      <j1 rule="hyper" parents="32084 28049"/>
    </justification>
  </clause>

  <clause id="32187">
    <literal><![CDATA[
      a(a(x \ 1,x,y) \ ((((x * y) \ y) \ 1) \ z),u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24622,a(flip),b,32128,a)].">
      <j1 rule="hyper" parents="63 24622 32128"/>
    </justification>
  </clause>

  <clause id="32188">
    <literal><![CDATA[
      a(a(x \ 1,x,y) * ((((x * y) \ y) \ 1) \ z),u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,28398,a(flip),b,32187,a)].">
      <j1 rule="hyper" parents="63 28398 32187"/>
    </justification>
  </clause>

  <clause id="32189">
    <literal><![CDATA[
      a(((((x * y) \ y) \ 1) \ z) * a(y,x,x),u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,28020,a(flip),b,32188,a)].">
      <j1 rule="hyper" parents="63 28020 32188"/>
    </justification>
  </clause>

  <clause id="32190">
    <literal><![CDATA[
      L(x,y,((((z * u) \ u) \ 1) \ w) * a(u,z,z)) = a(z \ w,y,x) \ x
    ]]></literal>
    <justification jstring="[para(32189(a,1),28841(a,2,1))].">
      <j1 rule="para" parents="32189 28841"/>
    </justification>
  </clause>

  <clause id="32191">
    <literal><![CDATA[
      L(x,y,((((z * u) \ u) \ 1) \ w) * a(u,z,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ w) = v5
    ]]></literal>
    <justification jstring="[para(32190(a,2),28866(a,1))].">
      <j1 rule="para" parents="32190 28866"/>
    </justification>
  </clause>

  <clause id="32192">
    <literal><![CDATA[
      (a(x,L(y,z,x),u) \ w) \ (a(u,y,a(y,z,L(x,z,x))) * w) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(30088(a,1),32161(a,1,2,1))].">
      <j1 rule="para" parents="30088 32161"/>
    </justification>
  </clause>

  <clause id="32193">
    <literal><![CDATA[
      a(K(x,y) * ((z \ 1) \ ((z \ 1) \ u)),w,v5) = a(u * (z * z),w,v5) * a(v6,v7,a(v7,v8,v9))
    ]]></literal>
    <justification jstring="[para(24219(a,1),32163(a,2,1))].">
      <j1 rule="para" parents="24219 32163"/>
    </justification>
  </clause>

  <clause id="32194">
    <literal><![CDATA[
      (a(x,L(y,z,x),u) \ w) \ (1 * w) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(31698(a,1),32192(a,1,2,1))].">
      <j1 rule="para" parents="31698 32192"/>
    </justification>
  </clause>

  <clause id="32196">
    <literal><![CDATA[
      a(x,L(y,z,x),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(235,a,32194,a)].">
      <j1 rule="hyper" parents="235 32194"/>
    </justification>
  </clause>

  <clause id="32197">
    <literal><![CDATA[
      a(x,(y * x) \ z,u) = a(x,y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(26033,a,32196,a),flip(a)].">
      <j1 rule="hyper" parents="26033 32196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32205">
    <literal><![CDATA[
      a(x,y,L(z,u,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,32158,a(flip),b,32196,a),flip(a)].">
      <j1 rule="hyper" parents="63 32158 32196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32211">
    <literal><![CDATA[
      a(x,y,z \ ((z / u) * (w * u))) = a(x,y,L(w,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(30075,a,32205,a),flip(a)].">
      <j1 rule="hyper" parents="30075 32205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32212">
    <literal><![CDATA[
      a((x * y) \ z,y,u) = a(x \ (y \ z),y,u)
    ]]></literal>
    <justification jstring="[hyper(29700,a,32205,a),flip(a)].">
      <j1 rule="hyper" parents="29700 32205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32218">
    <literal><![CDATA[
      a(x,y,(y \ z) \ u) = a(x,y,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,30993,a(flip),b,32205,a),flip(a)].">
      <j1 rule="hyper" parents="63 30993 32205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32219">
    <literal><![CDATA[
      a(x,y * z,L(y,u,z)) = a(x,y * z,y)
    ]]></literal>
    <justification jstring="[hyper(63,a,30865,a(flip),b,32205,a)].">
      <j1 rule="hyper" parents="63 30865 32205"/>
    </justification>
  </clause>

  <clause id="32236">
    <literal><![CDATA[
      a(x,y,z \ (y * u)) = a(x,y,(y \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(31948,a,32218,a),flip(a)].">
      <j1 rule="hyper" parents="31948 32218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32238">
    <literal><![CDATA[
      a(x,y,(y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * (y * u)) = w
    ]]></literal>
    <justification jstring="[para(32236(a,1),31948(a,1))].">
      <j1 rule="para" parents="32236 31948"/>
    </justification>
  </clause>

  <clause id="32239">
    <literal><![CDATA[
      a(x,y,z * (y * L(u,y,y))) = a(x,y,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(32238,a,31958,a)].">
      <j1 rule="hyper" parents="32238 31958"/>
    </justification>
  </clause>

  <clause id="32242">
    <literal><![CDATA[
      a(x,y,(y * z) \ u) = a(x,y,z * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,24931,a(flip),b,32239,a),flip(a)].">
      <j1 rule="hyper" parents="63 24931 32239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32243">
    <literal><![CDATA[
      a(x,y,z * ((z / u) * (w * u))) = a(x,y,L(w,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(31948,a,32211,a)].">
      <j1 rule="hyper" parents="31948 32211"/>
    </justification>
  </clause>

  <clause id="32244">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w \ v5,w,v6 * w))) = a(x,y,a(z,u,v6 * ((w \ v6) * v5)))
    ]]></literal>
    <justification jstring="[para(30852(a,1),32094(a,1,3))].">
      <j1 rule="para" parents="30852 32094"/>
    </justification>
  </clause>

  <clause id="32245">
    <literal><![CDATA[
      a(x,y,a(z,u,y * ((w \ y) * v5))) = a(x,y,a(z,u,w \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,31469,a(flip),b,32244,a),flip(a)].">
      <j1 rule="hyper" parents="63 31469 32244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32246">
    <literal><![CDATA[
      a(x,y,a(z,u,y * ((w \ y) * v5))) = a(x,y,a(z,u,w * v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,30785,a(flip),b,32245,a),flip(a)].">
      <j1 rule="hyper" parents="347 30785 32245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32247">
    <literal><![CDATA[
      a(x,y,a(z,y,u)) \ z = ((z / a(y,y,u)) * (a(y,y,u) * x)) / x
    ]]></literal>
    <justification jstring="[para(31211(a,1),31701(a,1,1))].">
      <j1 rule="para" parents="31211 31701"/>
    </justification>
  </clause>

  <clause id="32248">
    <literal><![CDATA[
      ((x / a(y,y,z)) * (a(y,y,z) * u)) / u = L(x,y,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(29829,a,32247,a),flip(a)].">
      <j1 rule="hyper" parents="29829 32247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32250">
    <literal><![CDATA[
      ((a(x,x,y) \ z) * (a(x,x,y) * u)) / u = L(z,x,a(u,x,y))
    ]]></literal>
    <justification jstring="[para(12966(a,1),32248(a,1,1,1))].">
      <j1 rule="para" parents="12966 32248"/>
    </justification>
  </clause>

  <clause id="32251">
    <literal><![CDATA[
      x \ ((x * a(y,y,z)) * (a(y,y,z) \ u)) = L(u,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,23293,a(flip),b,32250,a)].">
      <j1 rule="hyper" parents="63 23293 32250"/>
    </justification>
  </clause>

  <clause id="32252">
    <literal><![CDATA[
      L(x,a(y,y,z),u * a(y,y,z)) = L(x,y,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(28570,a,32251,a)].">
      <j1 rule="hyper" parents="28570 32251"/>
    </justification>
  </clause>

  <clause id="32253">
    <literal><![CDATA[
      L(x,y,a(z,y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,32100,a(flip),b,32252,a),flip(a)].">
      <j1 rule="hyper" parents="63 32100 32252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32275">
    <literal><![CDATA[
      a((x * (y \ 1)) * (a(z,u,u) * a(x,y,y)),w,v5) = a(a(z,u,u) \ (y \ x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,28399,a(flip),b,32131,a)].">
      <j1 rule="hyper" parents="63 28399 32131"/>
    </justification>
  </clause>

  <clause id="32276">
    <literal><![CDATA[
      a(R(x * (1 / y),y,y) * a(z,u,u),w,v5) = a(a(z,u,u) \ (y \ x),w,v5)
    ]]></literal>
    <justification jstring="[para(31633(a,1),32275(a,1,1))].">
      <j1 rule="para" parents="31633 32275"/>
    </justification>
  </clause>

  <clause id="32277">
    <literal><![CDATA[
      (x * (a(y,z,z) \ u)) \ (w \ ((a(y,z,z) \ (w * x)) * u)) = a(w,a(y,z,z) \ x,u)
    ]]></literal>
    <justification jstring="[para(32106(a,1),32076(a,1,1))].">
      <j1 rule="para" parents="32106 32076"/>
    </justification>
  </clause>

  <clause id="32278">
    <literal><![CDATA[
      (x * (y * (a(z,u,u) \ w))) \ (((a(z,u,u) \ x) * y) * w) = a(a(z,u,u) \ x,y,w)
    ]]></literal>
    <justification jstring="[para(31774(a,1),32129(a,1,1,2))].">
      <j1 rule="para" parents="31774 32129"/>
    </justification>
  </clause>

  <clause id="32279">
    <literal><![CDATA[
      (x * (a(y,z,z) \ u)) \ (w \ ((w * x) * (a(y,z,z) \ u))) = a(w,a(y,z,z) \ x,u)
    ]]></literal>
    <justification jstring="[para(32106(a,1),32277(a,1,2,2))].">
      <j1 rule="para" parents="32106 32277"/>
    </justification>
  </clause>

  <clause id="32280">
    <literal><![CDATA[
      (x * (y * (a(z,u,u) \ w))) \ ((x * (a(z,u,u) \ y)) * w) = a(a(z,u,u) \ x,y,w)
    ]]></literal>
    <justification jstring="[para(32106(a,1),32278(a,1,2,1))].">
      <j1 rule="para" parents="32106 32278"/>
    </justification>
  </clause>

  <clause id="32281">
    <literal><![CDATA[
      a(x,a(y,z,z) \ u,w) = a(x,u,a(y,z,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(14727,a,32279,a),flip(a)].">
      <j1 rule="hyper" parents="14727 32279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32282">
    <literal><![CDATA[
      a(x,a(y,z,z) \ u,w) = a(x,u,a(y,z,z) * w)
    ]]></literal>
    <justification jstring="[hyper(347,a,31934,a(flip),b,32281,a),flip(a)].">
      <j1 rule="hyper" parents="347 31934 32281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32283">
    <literal><![CDATA[
      a(x,a(y,z,z) * u,w) = a(x,u,a(y,z,z) * w)
    ]]></literal>
    <justification jstring="[hyper(28362,a,32282,a)].">
      <j1 rule="hyper" parents="28362 32282"/>
    </justification>
  </clause>

  <clause id="32284">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,a(z,u,u) * y,w) = v5
    ]]></literal>
    <justification jstring="[para(32282(a,1),28362(a,1))].">
      <j1 rule="para" parents="32282 28362"/>
    </justification>
  </clause>

  <clause id="32285">
    <literal><![CDATA[
      a(x,y * (a(z,u,u) * w),v5) = a(x,w * y,a(z,u,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(32173,a,32283,a)].">
      <j1 rule="hyper" parents="32173 32283"/>
    </justification>
  </clause>

  <clause id="32286">
    <literal><![CDATA[
      a(x,y * z,a(u \ (u \ z),w,w) * v5) = a(x,y * L(z,w,w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,30167,a(flip),b,32285,a),flip(a)].">
      <j1 rule="hyper" parents="63 30167 32285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32287">
    <literal><![CDATA[
      a(x,y * z,a(z,u,u) * w) = a(x,y * L(z,u,u),w)
    ]]></literal>
    <justification jstring="[para(5263(a,1),32286(a,1,3,1,1))].">
      <j1 rule="para" parents="5263 32286"/>
    </justification>
  </clause>

  <clause id="32288">
    <literal><![CDATA[
      (x * (y * (a(z,u,u) \ w))) \ ((x * y) * (a(z,u,u) \ w)) = a(a(z,u,u) \ x,y,w)
    ]]></literal>
    <justification jstring="[para(32132(a,1),32280(a,1,2))].">
      <j1 rule="para" parents="32132 32280"/>
    </justification>
  </clause>

  <clause id="32289">
    <literal><![CDATA[
      a(a(x,y,y) \ z,u,w) = a(z,u,a(x,y,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(836,a,32288,a),flip(a)].">
      <j1 rule="hyper" parents="836 32288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32290">
    <literal><![CDATA[
      a(a(x,y,y) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,a(x,y,y) * w) = v5
    ]]></literal>
    <justification jstring="[para(32289(a,2),28357(a,1))].">
      <j1 rule="para" parents="32289 28357"/>
    </justification>
  </clause>

  <clause id="32291">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,a(x,y,y) * w) = v5
    ]]></literal>
    <justification jstring="[para(28398(a,1),32290(a,1))].">
      <j1 rule="para" parents="28398 32290"/>
    </justification>
  </clause>

  <clause id="32292">
    <literal><![CDATA[
      a(L(x * y,y,y) * z,u,a(x,y,y) * w) = a((x * y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(32291,a,30403,a)].">
      <j1 rule="hyper" parents="32291 30403"/>
    </justification>
  </clause>

  <clause id="32293">
    <literal><![CDATA[
      a(x * (a(y,y,z) * u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u * x,w,a(z,y,y) * v5) = v6
    ]]></literal>
    <justification jstring="[para(32186(a,1),32291(a,1))].">
      <j1 rule="para" parents="32186 32291"/>
    </justification>
  </clause>

  <clause id="32294">
    <literal><![CDATA[
      a(((x \ 1) \ y) * z,u,a(y,x,x) * w) = a((y * x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,27997,a(flip),b,32292,a)].">
      <j1 rule="hyper" parents="63 27997 32292"/>
    </justification>
  </clause>

  <clause id="32295">
    <literal><![CDATA[
      a(x * (y \ z),u,a(z,y,y) * w) = a(((y \ 1) * z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(32293,a,30435,a)].">
      <j1 rule="hyper" parents="32293 30435"/>
    </justification>
  </clause>

  <clause id="32296">
    <literal><![CDATA[
      a(x * (y * a(z,u,u)),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x * y,w,a(z,u,u) * v5) = v6
    ]]></literal>
    <justification jstring="[para(32133(a,1),32293(a,1))].">
      <j1 rule="para" parents="32133 32293"/>
    </justification>
  </clause>

  <clause id="32297">
    <literal><![CDATA[
      a((x * y) * z,u,a(w,x,x) * v5) = a(z * (L(x,x,w) * y),u,v5)
    ]]></literal>
    <justification jstring="[hyper(32296,a,32179,a)].">
      <j1 rule="hyper" parents="32296 32179"/>
    </justification>
  </clause>

  <clause id="32298">
    <literal><![CDATA[
      a(x,y,a(z * (u * a(x,y,w)),u,w)) \ z = (u * a(x,y,w)) * (u \ (a(x,y,w) \ z))
    ]]></literal>
    <justification jstring="[para(29790(a,1),32154(a,1,1))].">
      <j1 rule="para" parents="29790 32154"/>
    </justification>
  </clause>

  <clause id="32299">
    <literal><![CDATA[
      (x * ((x * y) * (a(z,u,u) \ w))) / (x * (y * (a(z,u,u) \ w))) = R(x,a(z,u,u) \ y,w)
    ]]></literal>
    <justification jstring="[para(32106(a,1),32157(a,1,2,2))].">
      <j1 rule="para" parents="32106 32157"/>
    </justification>
  </clause>

  <clause id="32300">
    <literal><![CDATA[
      (a(x,y,a(z,z,u)) * w) * (a(x,y,u) \ 1) = w * L(a(x,y,u) \ 1,z,a(x,y,u) * z)
    ]]></literal>
    <justification jstring="[para(28387(a,1),32177(a,1,1))].">
      <j1 rule="para" parents="28387 32177"/>
    </justification>
  </clause>

  <clause id="32302">
    <literal><![CDATA[
      a(K(x,y) * ((z \ 1) \ ((z \ 1) \ u)),w,v5) = a(u * (z * z),w,v5) * a(v6,v7,a(v8,v8,v9))
    ]]></literal>
    <justification jstring="[hyper(29876,a,32193,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="29876 32193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32303">
    <literal><![CDATA[
      R(x,a(y,z,z) \ u,w) = R(x,u,a(y,z,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1768,a,b,32299,a),flip(a)].">
      <j1 rule="hyper" parents="63 1768 32299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32304">
    <literal><![CDATA[
      R(x,a(y,z,z) \ u,w) = R(x,u,w * a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,31841,a(flip),b,32303,a),flip(a)].">
      <j1 rule="hyper" parents="347 31841 32303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32305">
    <literal><![CDATA[
      ((x * y) * (a(z,u,u) \ w)) / (y * (a(z,u,u) \ w)) = R(x,a(z,u,u) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,20,a(flip),b,32303,a)].">
      <j1 rule="hyper" parents="347 20 32303"/>
    </justification>
  </clause>

  <clause id="32306">
    <literal><![CDATA[
      R(x,a(y,z,z) * u,w) = R(x,u,w * a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(28445,a,32304,a)].">
      <j1 rule="hyper" parents="28445 32304"/>
    </justification>
  </clause>

  <clause id="32307">
    <literal><![CDATA[
      R(x,y * (a(z,u,u) * w),v5) = R(x,y * w,v5 * a(z,u,u))
    ]]></literal>
    <justification jstring="[para(31793(a,1),32306(a,1,2))].">
      <j1 rule="para" parents="31793 32306"/>
    </justification>
  </clause>

  <clause id="32308">
    <literal><![CDATA[
      R(x,y * (z * a(u,u,w)),v5) = R(x,z * y,v5 * a(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,32137,a(flip),b,32307,a)].">
      <j1 rule="hyper" parents="63 32137 32307"/>
    </justification>
  </clause>

  <clause id="32309">
    <literal><![CDATA[
      R(x,y * (z * u),w * a(u,v5,v5)) = R(x,y * (z * L(u,v5,v5)),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,32138,a(flip),b,32308,a),flip(a)].">
      <j1 rule="hyper" parents="63 32138 32308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32310">
    <literal><![CDATA[
      x * L(a(y,z,u) \ 1,w,a(y,z,u) * w) = a(y,z,u) \ (a(y,z,a(w,w,u)) * x)
    ]]></literal>
    <justification jstring="[hyper(28424,a,32300,a),flip(a)].">
      <j1 rule="hyper" parents="28424 32300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32311">
    <literal><![CDATA[
      x * L(a(y,z,u) \ 1,w,a(y,z,u) * w) = a(y,z,a(w,w,u)) * (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(347,a,30466,a(flip),b,32310,a),flip(a)].">
      <j1 rule="hyper" parents="347 30466 32310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32312">
    <literal><![CDATA[
      x * L(a(y,z,u) \ 1,w,a(y,z,u) * w) = a(y,z,L(u,w,w)) \ x
    ]]></literal>
    <justification jstring="[hyper(347,a,29938,a(flip),b,32311,a),flip(a)].">
      <j1 rule="hyper" parents="347 29938 32311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32313">
    <literal><![CDATA[
      x * (y * ((a(z,u,w) * y) \ 1)) = a(z,u,L(w,y,y)) \ x
    ]]></literal>
    <justification jstring="[para(26305(a,1),32312(a,1,2))].">
      <j1 rule="para" parents="26305 32312"/>
    </justification>
  </clause>

  <clause id="32314">
    <literal><![CDATA[
      a(x,y,L(z,u,u)) \ (u \ 1) = ((1 / u) \ a(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(63,a,26041,a(flip),b,32313,a),flip(a)].">
      <j1 rule="hyper" parents="63 26041 32313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32315">
    <literal><![CDATA[
      ((1 / x) \ a(y,z,u)) \ 1 = x \ (a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(63,a,29146,a(flip),b,32314,a),flip(a)].">
      <j1 rule="hyper" parents="63 29146 32314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32316">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) / u) \ 1 = (1 / u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(39,a,22288,a,b,32315,a)].">
      <j1 rule="hyper" parents="39 22288 32315"/>
    </justification>
  </clause>

  <clause id="32317">
    <literal><![CDATA[
      ((x \ L(x,y,z)) / u) \ 1 = (1 / u) \ a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(63,a,29499,a(flip),b,32316,a)].">
      <j1 rule="hyper" parents="63 29499 32316"/>
    </justification>
  </clause>

  <clause id="32318">
    <literal><![CDATA[
      (a(x,y,z) / (1 / u)) \ 1 = (a(x,y,z) \ 1) / u
    ]]></literal>
    <justification jstring="[hyper(39,a,21966,a,b,32316,a)].">
      <j1 rule="hyper" parents="39 21966 32316"/>
    </justification>
  </clause>

  <clause id="32319">
    <literal><![CDATA[
      x / ((1 / y) \ a(z,u,x)) = L(x,u,z) / y
    ]]></literal>
    <justification jstring="[para(32317(a,1),23375(a,1,2))].">
      <j1 rule="para" parents="32317 23375"/>
    </justification>
  </clause>

  <clause id="32320">
    <literal><![CDATA[
      (L(x,y,z) / u) \ x = (1 / u) \ a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(214,a,32319,a)].">
      <j1 rule="hyper" parents="214 32319"/>
    </justification>
  </clause>

  <clause id="32321">
    <literal><![CDATA[
      ((1 / x) \ (a(y,z,u) * w)) / w = ((L(u,z,y) / x) \ u) * a(1 / x,(1 / x) * a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(32320(a,2),30131(a,2,1))].">
      <j1 rule="para" parents="32320 30131"/>
    </justification>
  </clause>

  <clause id="32322">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) / u,u,a(x,y,z)) = a(x,y,z) \ (1 / u)
    ]]></literal>
    <justification jstring="[para(32318(a,1),28479(a,1,1))].">
      <j1 rule="para" parents="32318 28479"/>
    </justification>
  </clause>

  <clause id="32323">
    <literal><![CDATA[
      1 / (x * a(y,z,u)) = a(y,z,u) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(23256,a,32322,a)].">
      <j1 rule="hyper" parents="23256 32322"/>
    </justification>
  </clause>

  <clause id="32324">
    <literal><![CDATA[
      1 / (a(x,y,z) * u) = a(x,y,z) \ (1 / u)
    ]]></literal>
    <justification jstring="[hyper(20220,a,32323,a)].">
      <j1 rule="hyper" parents="20220 32323"/>
    </justification>
  </clause>

  <clause id="32326">
    <literal><![CDATA[
      a(x * (y * y),z,u) * a(w,v5,a(v6,v6,v7)) = a((y \ 1) \ ((y \ 1) \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(23886,a,32302,a),flip(a)].">
      <j1 rule="hyper" parents="23886 32302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32328">
    <literal><![CDATA[
      a(x * (y * y),z,u) * a(w,v5,a(v6,v6,v7)) = a((y * x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,28003,a(flip),b,32326,a),flip(a)].">
      <j1 rule="hyper" parents="347 28003 32326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32329">
    <literal><![CDATA[
      a((x * y) * x,z,u) = a(y * (x * x),z,u)
    ]]></literal>
    <justification jstring="[hyper(26354,a,32328,a),flip(a)].">
      <j1 rule="hyper" parents="26354 32328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32330">
    <literal><![CDATA[
      ((L(x,y,z) * u) * w) / T(x * u,w) = (x * u) \ ((L(x,y,z) * u) * w)
    ]]></literal>
    <justification jstring="[para(31816(a,1),32041(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31816 32041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32332">
    <literal><![CDATA[
      a(x,y,(z * R(a(u,u,w) * w,u,u)) \ v5) = a(x,y,a(u,u,w) * ((z * R(w,u,u)) \ v5))
    ]]></literal>
    <justification jstring="[para(29401(a,1),32172(a,1,3,1))].">
      <j1 rule="para" parents="29401 32172"/>
    </justification>
  </clause>

  <clause id="32333">
    <literal><![CDATA[
      a(x,y,(z * L(a(u,u,w) * w,u,u)) \ v5) = a(x,y,a(u,u,w) * ((z * R(w,u,u)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(25715,a,32332,a)].">
      <j1 rule="hyper" parents="25715 32332"/>
    </justification>
  </clause>

  <clause id="32334">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * ((w * R(u,z,z)) \ v5)) = a(x,y,(w * u) \ v5)
    ]]></literal>
    <justification jstring="[para(15301(a,1),32333(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="15301 32333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32335">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * ((w * R(u,z,z)) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(w * u) * v5) = v6
    ]]></literal>
    <justification jstring="[para(32334(a,2),31948(a,1))].">
      <j1 rule="para" parents="32334 31948"/>
    </justification>
  </clause>

  <clause id="32336">
    <literal><![CDATA[
      a(T(x,y * z) \ 1,u,L(w,z * T(x,y * z),y)) = a(L(x,z,y) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,32070,a(flip),b,32175,a),flip(a)].">
      <j1 rule="hyper" parents="347 32070 32175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32338">
    <literal><![CDATA[
      a(T(x,y * z) \ 1,u,L(w,z * T(x,y * z),y)) = a(x \ 1,u,L(w,z,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,29673,a(flip),b,32336,a),flip(a)].">
      <j1 rule="hyper" parents="347 29673 32336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32339">
    <literal><![CDATA[
      a(T(x,y * z) \ 1,u,L(w,z * x,y)) = a(x \ 1,u,L(w,z,y))
    ]]></literal>
    <justification jstring="[para(21614(a,1),32338(a,1,3))].">
      <j1 rule="para" parents="21614 32338"/>
    </justification>
  </clause>

  <clause id="32340">
    <literal><![CDATA[
      a(x \ 1,y,L(z,u * x,w)) = a(x \ 1,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(23959,a,32339,a)].">
      <j1 rule="hyper" parents="23959 32339"/>
    </justification>
  </clause>

  <clause id="32343">
    <literal><![CDATA[
      a(x \ 1,y,L(z,u,w)) \ a(x \ 1,y,z) = a(w,u * x,a(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(32340(a,1),29147(a,1,1))].">
      <j1 rule="para" parents="32340 29147"/>
    </justification>
  </clause>

  <clause id="32344">
    <literal><![CDATA[
      a(x,y * z,a(z \ 1,u,w)) = a(x,y,a(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(29151,a,32343,a),flip(a)].">
      <j1 rule="hyper" parents="29151 32343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32345">
    <literal><![CDATA[
      a(x,y * z,a(z \ 1,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,25006,a(flip),b,32344,a),flip(a)].">
      <j1 rule="hyper" parents="347 25006 32344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32346">
    <literal><![CDATA[
      a(x,y * z,a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(25010,a,32345,a)].">
      <j1 rule="hyper" parents="25010 32345"/>
    </justification>
  </clause>

  <clause id="32347">
    <literal><![CDATA[
      a(x,y * x,a(z,u,w)) = a(w,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(29867,a,32346,a)].">
      <j1 rule="hyper" parents="29867 32346"/>
    </justification>
  </clause>

  <clause id="32348">
    <literal><![CDATA[
      a(x,y * z,a(u,w,y)) = a(u,z,a(y,w,x))
    ]]></literal>
    <justification jstring="[hyper(29853,a,32346,a)].">
      <j1 rule="hyper" parents="29853 32346"/>
    </justification>
  </clause>

  <clause id="32349">
    <literal><![CDATA[
      a(x,x * y,a(z,u,w)) = a(w,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(29852,a,32346,a)].">
      <j1 rule="hyper" parents="29852 32346"/>
    </justification>
  </clause>

  <clause id="32350">
    <literal><![CDATA[
      a(x,y,a(z,u * x,w)) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(29796,a,32346,a)].">
      <j1 rule="hyper" parents="29796 32346"/>
    </justification>
  </clause>

  <clause id="32351">
    <literal><![CDATA[
      a(x,(y * (K(z,u) * w)) * v5,a(K(z,u) * (w * v5),v6,v7)) = a(x,R(y,w,v5),a(K(z,u) * (w * v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(22431(a,1),32346(a,1,2))].">
      <j1 rule="para" parents="22431 32346"/>
    </justification>
  </clause>

  <clause id="32352">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * x != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y * z,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(32346(a,1),28910(a,1,1))].">
      <j1 rule="para" parents="32346 28910"/>
    </justification>
  </clause>

  <clause id="32353">
    <literal><![CDATA[
      L(x,y,a(z,u * w,w)) = x * a(z,u,a(w,y,x))
    ]]></literal>
    <justification jstring="[para(32346(a,1),29807(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32346 29807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32354">
    <literal><![CDATA[
      L(x,y,a(z,u * x,w)) = a(z,u,a(x,y,w)) * x
    ]]></literal>
    <justification jstring="[para(32346(a,1),29877(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32346 29877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32355">
    <literal><![CDATA[
      a(x,y,L(z,u * w,w)) = a(x,y,z) * a(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[para(32346(a,1),29847(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32346 29847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32356">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),z * u,a(u,w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(u,z * u,y),w) = v5
    ]]></literal>
    <justification jstring="[para(32346(a,1),29949(a,1,1,2))].">
      <j1 rule="para" parents="32346 29949"/>
    </justification>
  </clause>

  <clause id="32357">
    <literal><![CDATA[
      a(x,y,a(z,u * x,w)) = a(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,29803,a,b,32350,a),flip(a)].">
      <j1 rule="hyper" parents="347 29803 32350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32358">
    <literal><![CDATA[
      a(x,y,a(z,x \ u,w)) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,30783,a,b,32350,a)].">
      <j1 rule="hyper" parents="63 30783 32350"/>
    </justification>
  </clause>

  <clause id="32359">
    <literal><![CDATA[
      a(x,y,a(z,u * x,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(32357(a,2),29863(a,1))].">
      <j1 rule="para" parents="32357 29863"/>
    </justification>
  </clause>

  <clause id="32360">
    <literal><![CDATA[
      (x \ (a(y,z,u) * w)) * a(y,a(y,z,u) * w,a(x,z,u)) = a(y,z,u) * (x \ w)
    ]]></literal>
    <justification jstring="[para(32358(a,1),30724(a,1,2))].">
      <j1 rule="para" parents="32358 30724"/>
    </justification>
  </clause>

  <clause id="32361">
    <literal><![CDATA[
      L(x,y,a(z,u * w,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(32353(a,2),29921(a,1))].">
      <j1 rule="para" parents="32353 29921"/>
    </justification>
  </clause>

  <clause id="32362">
    <literal><![CDATA[
      L(x,y,a(z,u * x,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,29877,a(flip),b,32354,a),flip(a)].">
      <j1 rule="hyper" parents="347 29877 32354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32363">
    <literal><![CDATA[
      L(x,x * y,a(z,u,w)) = L(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(29899,a,32362,a)].">
      <j1 rule="hyper" parents="29899 32362"/>
    </justification>
  </clause>

  <clause id="32364">
    <literal><![CDATA[
      L(x,y,a(z,x * u,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(27581,a,32362,a)].">
      <j1 rule="hyper" parents="27581 32362"/>
    </justification>
  </clause>

  <clause id="32365">
    <literal><![CDATA[
      L(x,y,a(z,a(z,y,u) * (w * x),u)) = L(x,w,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,30770,a(flip),b,32362,a),flip(a)].">
      <j1 rule="hyper" parents="63 30770 32362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32366">
    <literal><![CDATA[
      (a(x,y,z) * (u / w)) \ (a(x,y,z) * u) = L(w,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,30205,a(flip),b,32362,a)].">
      <j1 rule="hyper" parents="63 30205 32362"/>
    </justification>
  </clause>

  <clause id="32367">
    <literal><![CDATA[
      (a(x,y,z) * u) / ((w \ u) * a(x,y,z)) = L(w,y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,30161,a(flip),b,32362,a)].">
      <j1 rule="hyper" parents="63 30161 32362"/>
    </justification>
  </clause>

  <clause id="32368">
    <literal><![CDATA[
      L(L(x,y,z),x * u,a(w,v5,v6)) = L(L(x,v5,a(w,u,v6)),y,z)
    ]]></literal>
    <justification jstring="[para(32363(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32363 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32369">
    <literal><![CDATA[
      L(x \ 1,y,a(z,x * u,w)) = L(x \ 1,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(24151(a,1),32364(a,1,3))].">
      <j1 rule="para" parents="24151 32364"/>
    </justification>
  </clause>

  <clause id="32370">
    <literal><![CDATA[
      L(L(L(x,y,z) \ 1,u,a(w,v5,v6)),y,z) = L(x \ 1,u,a(v6,(L(x,y,z) \ 1) * v5,w))
    ]]></literal>
    <justification jstring="[para(32364(a,1),25960(a,1,1))].">
      <j1 rule="para" parents="32364 25960"/>
    </justification>
  </clause>

  <clause id="32371">
    <literal><![CDATA[
      a(x,y * x,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,y,a(x,u,z)) = v5
    ]]></literal>
    <justification jstring="[para(29839(a,1),32359(a,1))].">
      <j1 rule="para" parents="29839 32359"/>
    </justification>
  </clause>

  <clause id="32373">
    <literal><![CDATA[
      L(x,y * z,a(y,u,w)) = L(x,u,a(w,z,y))
    ]]></literal>
    <justification jstring="[hyper(32361,a,29894,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="32361 29894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32374">
    <literal><![CDATA[
      L(x,y * z,a(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u,a(w,z,y)) = v5
    ]]></literal>
    <justification jstring="[para(29894(a,2),32361(a,1))].">
      <j1 rule="para" parents="29894 32361"/>
    </justification>
  </clause>

  <clause id="32377">
    <literal><![CDATA[
      R(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y * z,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(28908(a,2),32352(a,1))].">
      <j1 rule="para" parents="28908 32352"/>
    </justification>
  </clause>

  <clause id="32378">
    <literal><![CDATA[
      R(x,y * z,a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(32377,a,23247,a)].">
      <j1 rule="hyper" parents="32377 23247"/>
    </justification>
  </clause>

  <clause id="32379">
    <literal><![CDATA[
      L(x,y * z,a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(23284,a,32378,a)].">
      <j1 rule="hyper" parents="23284 32378"/>
    </justification>
  </clause>

  <clause id="32380">
    <literal><![CDATA[
      L(x,y,a(z,u,w * a(y,z,z))) = L(x,u,a(z,y * z,w))
    ]]></literal>
    <justification jstring="[hyper(30169,a,32379,a),flip(a)].">
      <j1 rule="hyper" parents="30169 32379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32381">
    <literal><![CDATA[
      L(x,y,a(z,z * u,w)) = L(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(29904,a,32379,a)].">
      <j1 rule="hyper" parents="29904 32379"/>
    </justification>
  </clause>

  <clause id="32383">
    <literal><![CDATA[
      L(x,y,a(z,z * u,w)) = a(z,y,a(x,u,w)) * x
    ]]></literal>
    <justification jstring="[hyper(347,a,29877,a,b,32381,a),flip(a)].">
      <j1 rule="hyper" parents="347 29877 32381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32384">
    <literal><![CDATA[
      a(x,y,a(z,z * u,w)) = a(z,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(29891,a,32383,a)].">
      <j1 rule="hyper" parents="29891 32383"/>
    </justification>
  </clause>

  <clause id="32385">
    <literal><![CDATA[
      L(x,y,a(z,z * u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u,a(z,y,w)) = v5
    ]]></literal>
    <justification jstring="[para(32383(a,2),29799(a,1))].">
      <j1 rule="para" parents="32383 29799"/>
    </justification>
  </clause>

  <clause id="32386">
    <literal><![CDATA[
      a(x,y,a(z,z * u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(32384(a,2),29863(a,1))].">
      <j1 rule="para" parents="32384 29863"/>
    </justification>
  </clause>

  <clause id="32387">
    <literal><![CDATA[
      L(x,y * z,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(29897(a,2),32385(a,1))].">
      <j1 rule="para" parents="29897 32385"/>
    </justification>
  </clause>

  <clause id="32388">
    <literal><![CDATA[
      a(x,y,a(z,u * w,w)) = a(z,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(32386,a,29851,a),flip(a)].">
      <j1 rule="hyper" parents="32386 29851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32389">
    <literal><![CDATA[
      a(x,y,a(z,u * w,u)) = a(z,y,a(u,w,x))
    ]]></literal>
    <justification jstring="[hyper(32386,a,29803,a),flip(a)].">
      <j1 rule="hyper" parents="32386 29803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32390">
    <literal><![CDATA[
      a(x,y,a(z,x * u,w)) = a(w,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(32386,a,29803,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="32386 29803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32391">
    <literal><![CDATA[
      a(x,y,a(z,x * u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,y,a(x,u,z)) = v5
    ]]></literal>
    <justification jstring="[para(29803(a,2),32386(a,1))].">
      <j1 rule="para" parents="29803 32386"/>
    </justification>
  </clause>

  <clause id="32392">
    <literal><![CDATA[
      x * a(y,z,a(u,x * (w * x),w * x)) = w * L(w \ x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(32388(a,2),31306(a,2,2)),flip(a)].">
      <j1 rule="para" parents="32388 31306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32393">
    <literal><![CDATA[
      a((x * y) \ z,u,a(L(w,y,x),((x * y) \ z) * v5,v6)) = a(v6,u,a(y \ (x \ z),v5,w))
    ]]></literal>
    <justification jstring="[para(29688(a,1),32390(a,2,3))].">
      <j1 rule="para" parents="29688 32390"/>
    </justification>
  </clause>

  <clause id="32394">
    <literal><![CDATA[
      a(x,y,L(z,u * w,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,29847,a(flip),b,32355,a),flip(a)].">
      <j1 rule="hyper" parents="347 29847 32355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32397">
    <literal><![CDATA[
      a(x,y,L(z,u * w,u)) = a(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[para(12390(a,1),32394(a,1,3))].">
      <j1 rule="para" parents="12390 32394"/>
    </justification>
  </clause>

  <clause id="32399">
    <literal><![CDATA[
      L(x,y * x,a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(29915,a,32365,a)].">
      <j1 rule="hyper" parents="29915 32365"/>
    </justification>
  </clause>

  <clause id="32401">
    <literal><![CDATA[
      L(L(x,y,z),u * x,a(w,v5,v6)) = L(L(x,u,a(w,v5,v6)),y,z)
    ]]></literal>
    <justification jstring="[para(32399(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32399 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32402">
    <literal><![CDATA[
      x * a(y,z,a(u,L(w,x,x),w * x)) = w * L(w \ x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(24244(a,1),32392(a,1,2,3))].">
      <j1 rule="para" parents="24244 32392"/>
    </justification>
  </clause>

  <clause id="32403">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,w)) = y * a(z,u,a(w,x,y * x))
    ]]></literal>
    <justification jstring="[para(30319(a,1),32402(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="30319 32402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32404">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,w)) = y * a(w,u,a(y * x,x,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,29846,a,b,32403,a),flip(a)].">
      <j1 rule="hyper" parents="347 29846 32403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32405">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),z,a(u,w,y)) = L(x,a(u,z * u,y),w)
    ]]></literal>
    <justification jstring="[hyper(32356,a,32379,a),flip(a)].">
      <j1 rule="hyper" parents="32356 32379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32406">
    <literal><![CDATA[
      L(x,a(y,z * y,u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(29949,a,32405,a),flip(a)].">
      <j1 rule="hyper" parents="29949 32405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32407">
    <literal><![CDATA[
      L(x,a(y,y * z,u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(25022,a,32406,a)].">
      <j1 rule="hyper" parents="25022 32406"/>
    </justification>
  </clause>

  <clause id="32408">
    <literal><![CDATA[
      L(x,a((y * y) * z,z * u,w),v5) = L(x,a((y * y) * z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(24460(a,1),32406(a,1,2))].">
      <j1 rule="para" parents="24460 32406"/>
    </justification>
  </clause>

  <clause id="32409">
    <literal><![CDATA[
      L(x,a(y \ (z \ y),z * ((y * z) \ u),w),v5) = L(x,a(y \ (z \ y),(z \ y) \ u,w),v5)
    ]]></literal>
    <justification jstring="[para(29417(a,1),32407(a,1,2,2))].">
      <j1 rule="para" parents="29417 32407"/>
    </justification>
  </clause>

  <clause id="32410">
    <literal><![CDATA[
      L(x,a(y \ a(y,y,z),(y \ z) * L(u,z,y \ 1),w),v5) = L(x,a(y \ a(y,y,z),z * u,w),v5)
    ]]></literal>
    <justification jstring="[para(29975(a,1),32407(a,1,2,2))].">
      <j1 rule="para" parents="29975 32407"/>
    </justification>
  </clause>

  <clause id="32411">
    <literal><![CDATA[
      L(x,a(y * (y * z),z * u,w),v5) = L(x,a((y * y) * z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(31939(a,1),32408(a,1,2))].">
      <j1 rule="para" parents="31939 32408"/>
    </justification>
  </clause>

  <clause id="32412">
    <literal><![CDATA[
      L(x,a((y * y) * z,u,w),v5) = L(x,a(w,z * u,z),v5)
    ]]></literal>
    <justification jstring="[hyper(30888,a,32411,a),flip(a)].">
      <j1 rule="hyper" parents="30888 32411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32413">
    <literal><![CDATA[
      L(x,a(y * (y * z),u,w),v5) = L(x,a(w,z * u,z),v5)
    ]]></literal>
    <justification jstring="[para(31939(a,1),32412(a,1,2))].">
      <j1 rule="para" parents="31939 32412"/>
    </justification>
  </clause>

  <clause id="32414">
    <literal><![CDATA[
      L(x,a(y,z * u,z),w) = L(x,a(y,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(30888,a,32413,a),flip(a)].">
      <j1 rule="hyper" parents="30888 32413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32415">
    <literal><![CDATA[
      x \ L(x,a(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,a(y,u * z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(32414(a,1),28631(a,1,2))].">
      <j1 rule="para" parents="32414 28631"/>
    </justification>
  </clause>

  <clause id="32416">
    <literal><![CDATA[
      L(x,a(y,z * y,z),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(32414(a,2),29384(a,1))].">
      <j1 rule="para" parents="32414 29384"/>
    </justification>
  </clause>

  <clause id="32417">
    <literal><![CDATA[
      (x \ y) \ ((y \ x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * (x \ y)) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(30903(a,1),32416(a,1))].">
      <j1 rule="para" parents="30903 32416"/>
    </justification>
  </clause>

  <clause id="32418">
    <literal><![CDATA[
      a(x,a(y,z * u,z),w) = a(x,a(y,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(32415,a,28625,a)].">
      <j1 rule="hyper" parents="32415 28625"/>
    </justification>
  </clause>

  <clause id="32419">
    <literal><![CDATA[
      (x * (y \ x)) \ (y * z) = (x \ (y * (x \ y))) * z
    ]]></literal>
    <justification jstring="[hyper(32417,a,27004,a)].">
      <j1 rule="hyper" parents="32417 27004"/>
    </justification>
  </clause>

  <clause id="32420">
    <literal><![CDATA[
      R(x,(y * ((z \ y) \ 1)) \ (z * u),w) = R(x,(y \ (z * (y \ z))) * u,w)
    ]]></literal>
    <justification jstring="[para(32419(a,1),20656(a,2,2))].">
      <j1 rule="para" parents="32419 20656"/>
    </justification>
  </clause>

  <clause id="32421">
    <literal><![CDATA[
      R(x,(y \ (z * (y \ z))) * u,w) = R(x,((z \ y) * (y \ z)) * u,w)
    ]]></literal>
    <justification jstring="[para(30904(a,1),32420(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30904 32420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32422">
    <literal><![CDATA[
      R(x,(y \ ((y \ z) * z)) * u,w) = R(x,((z \ y) * (y \ z)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,27121,a,b,32421,a)].">
      <j1 rule="hyper" parents="63 27121 32421"/>
    </justification>
  </clause>

  <clause id="32423">
    <literal><![CDATA[
      R(x,y * (a(z,u \ z,u) \ 1),w) = R(x,((u \ z) * (z \ u)) * y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,30265,a,b,32422,a)].">
      <j1 rule="hyper" parents="63 30265 32422"/>
    </justification>
  </clause>

  <clause id="32424">
    <literal><![CDATA[
      R(x,y * (a(z,z * u,u) \ 1),w) = R(x,((u \ z) * (z \ u)) * y,w)
    ]]></literal>
    <justification jstring="[para(30127(a,1),32423(a,1,2,2,1))].">
      <j1 rule="para" parents="30127 32423"/>
    </justification>
  </clause>

  <clause id="32425">
    <literal><![CDATA[
      R(x,((y \ z) * (z \ y)) * u,w) = R(x,u * a(z,z * y,y),w)
    ]]></literal>
    <justification jstring="[hyper(2365,a,32424,a),flip(a)].">
      <j1 rule="hyper" parents="2365 32424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32426">
    <literal><![CDATA[
      R(x,y * ((z \ u) * (u \ z)),w) = R(x,y * a(u,u * z,z),w)
    ]]></literal>
    <justification jstring="[hyper(22117,a,32425,a)].">
      <j1 rule="hyper" parents="22117 32425"/>
    </justification>
  </clause>

  <clause id="32427">
    <literal><![CDATA[
      R(x,y * ((T(z,u) \ T(z * u,z)) * (T(z * u,z) \ T(z,u))),w) = R(x,y * a(T(z * u,z),(z * u) * R(z,u,z),T(z,u)),w)
    ]]></literal>
    <justification jstring="[para(4386(a,1),32426(a,2,2,2,2))].">
      <j1 rule="para" parents="4386 32426"/>
    </justification>
  </clause>

  <clause id="32428">
    <literal><![CDATA[
      (x \ (a(y,z,u) * w)) * a(y,z,a(x,w,u)) = a(y,z,u) * (x \ w)
    ]]></literal>
    <justification jstring="[para(29923(a,1),32360(a,1,2))].">
      <j1 rule="para" parents="29923 32360"/>
    </justification>
  </clause>

  <clause id="32429">
    <literal><![CDATA[
      a(x,y,z \ (a(u,u,w) * v5)) = a(x,y,a(u,u,w) * (z \ v5))
    ]]></literal>
    <justification jstring="[para(32428(a,1),30775(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32428 30775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32430">
    <literal><![CDATA[
      a(x,y,z \ (a(u,w,w) * v5)) = a(x,y,a(w,w,u) * (z \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,31409,a,b,32429,a)].">
      <j1 rule="hyper" parents="63 31409 32429"/>
    </justification>
  </clause>

  <clause id="32431">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (w \ v5)) * x = R(x,y,w \ (a(u,z,z) * v5))
    ]]></literal>
    <justification jstring="[hyper(133,a,32430,a(flip),b,28907,a(flip))].">
      <j1 rule="hyper" parents="133 32430 28907"/>
    </justification>
  </clause>

  <clause id="32432">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (w \ (u * v5))) = a(x,y,w \ (R(u,z,z) * v5))
    ]]></literal>
    <justification jstring="[para(31756(a,1),32430(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="31756 32430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32433">
    <literal><![CDATA[
      R(x,y,z \ (a(u,w,w) * v5)) = R(x,y,a(w,w,u) * (z \ v5))
    ]]></literal>
    <justification jstring="[hyper(28910,a,32431,a),flip(a)].">
      <j1 rule="hyper" parents="28910 32431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32434">
    <literal><![CDATA[
      R(x,y,a(z,z,u) * (w \ (L(u,z,z) \ v5))) = R(x,y,w \ (u \ v5))
    ]]></literal>
    <justification jstring="[hyper(29639,a,32433,a),flip(a)].">
      <j1 rule="hyper" parents="29639 32433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32435">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (w \ (u * v5))) = a(x,y,w \ (L(u,z,z) * v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,25782,a(flip),b,32432,a),flip(a)].">
      <j1 rule="hyper" parents="347 25782 32432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32436">
    <literal><![CDATA[
      R(x,y,a(z,z,u) * (w \ (L(u,z,z) \ v5))) = R(x,y,(u \ v5) * w)
    ]]></literal>
    <justification jstring="[hyper(347,a,31841,a(flip),b,32434,a),flip(a)].">
      <j1 rule="hyper" parents="347 31841 32434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32437">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (w \ (u * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w * (L(u,z,z) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(32435(a,2),31948(a,1))].">
      <j1 rule="para" parents="32435 31948"/>
    </justification>
  </clause>

  <clause id="32438">
    <literal><![CDATA[
      L(x \ 1,y,a(z,(L(x,u,w) \ 1) * v5,v6)) = L(x \ 1,y,a(v6,v5,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,25960,a(flip),b,32370,a),flip(a)].">
      <j1 rule="hyper" parents="63 25960 32370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32440">
    <literal><![CDATA[
      L(x \ 1,y,a(z,L(x,u,w) * v5,v6)) = L(x \ 1,y,a(v6,v5,z))
    ]]></literal>
    <justification jstring="[para(24151(a,1),32438(a,1,3))].">
      <j1 rule="para" parents="24151 32438"/>
    </justification>
  </clause>

  <clause id="32441">
    <literal><![CDATA[
      L(x \ 1,y,a(z,x * (L(x,u,w) * v5),v6)) = L(x \ 1,y,a(z,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,32369,a,b,32440,a)].">
      <j1 rule="hyper" parents="63 32369 32440"/>
    </justification>
  </clause>

  <clause id="32442">
    <literal><![CDATA[
      L(x,a(y \ (z \ y),(z \ y) \ u,w),v5) = L(x,a(z \ 1,z * ((y * z) \ u),w),v5)
    ]]></literal>
    <justification jstring="[para(32069(a,1),32409(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32069 32409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32443">
    <literal><![CDATA[
      L(x,a(y \ (z \ y),(z \ y) \ u,w),v5) = L(x,a(z,z * ((y * z) \ u),w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,22769,a(flip),b,32442,a),flip(a)].">
      <j1 rule="hyper" parents="347 22769 32442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32445">
    <literal><![CDATA[
      L(x,a(y \ (z \ y),(z \ y) \ u,w),v5) = L(x,a(z,(y * z) \ u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,32407,a(flip),b,32443,a),flip(a)].">
      <j1 rule="hyper" parents="347 32407 32443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32446">
    <literal><![CDATA[
      L(x,a(y \ (z \ y),(z \ y) \ u,w),v5) = L(x,a(z,y \ (z \ u),w),v5)
    ]]></literal>
    <justification jstring="[para(32197(a,1),32445(a,2,2))].">
      <j1 rule="para" parents="32197 32445"/>
    </justification>
  </clause>

  <clause id="32447">
    <literal><![CDATA[
      L(x,a(y \ (z \ y),(z \ y) \ u,w),v5) = L(x,a(z,(z \ u) * y,w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,30869,a(flip),b,32446,a),flip(a)].">
      <j1 rule="hyper" parents="347 30869 32446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32448">
    <literal><![CDATA[
      L(x,a(y \ 1,(y \ z) \ u,w),v5) = L(x,a(y,(y \ u) * z,w),v5)
    ]]></literal>
    <justification jstring="[para(32069(a,1),32447(a,1,2))].">
      <j1 rule="para" parents="32069 32447"/>
    </justification>
  </clause>

  <clause id="32449">
    <literal><![CDATA[
      L(x,a(y \ 1,z * (y \ u),w),v5) = L(x,a(y,(y \ z) * u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(30870,a,32448,a)].">
      <j1 rule="hyper" parents="30870 32448"/>
    </justification>
  </clause>

  <clause id="32451">
    <literal><![CDATA[
      L(x,a(y,(y \ z) * u,w),v5) = L(x,a(y,z * (y \ u),w),v5)
    ]]></literal>
    <justification jstring="[hyper(31062,a,32449,a),flip(a)].">
      <j1 rule="hyper" parents="31062 32449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32452">
    <literal><![CDATA[
      ((1 / x) \ (a(y,z,u) * a(y,z,u))) / a(y,z,u) = ((L(u,z,y) / x) \ u) * a(1 / x,1 / x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(28667(a,1),32321(a,2,2))].">
      <j1 rule="para" parents="28667 32321"/>
    </justification>
  </clause>

  <clause id="32453">
    <literal><![CDATA[
      a(x \ (L(y,(x \ 1) \ z,x \ 1) * z),u,a(w,v5,v6)) = a(((x \ 1) \ z) * y,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,23901,a(flip),b,32156,a),flip(a)].">
      <j1 rule="hyper" parents="347 23901 32156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32455">
    <literal><![CDATA[
      a(x \ (L(y,x \ z,x \ 1) * z),u,a(w,v5,v6)) = a(((x \ 1) \ z) * y,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(3608(a,1),32453(a,1,1,2,1))].">
      <j1 rule="para" parents="3608 32453"/>
    </justification>
  </clause>

  <clause id="32456">
    <literal><![CDATA[
      a(x \ (L(y,x \ z,x) * z),u,a(w,v5,v6)) = a(((x \ 1) \ z) * y,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(26781,a,32455,a)].">
      <j1 rule="hyper" parents="26781 32455"/>
    </justification>
  </clause>

  <clause id="32457">
    <literal><![CDATA[
      a(((x \ 1) \ y) * z,u,a(w,v5,v6)) = a((x \ y) * T(z,y),u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(874(a,1),32456(a,1,1)),flip(a)].">
      <j1 rule="para" parents="874 32456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32458">
    <literal><![CDATA[
      a(((x \ 1) \ y) * z,u,a(w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a((x \ y) * z,u,a(w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(32457(a,2),23964(a,1))].">
      <j1 rule="para" parents="32457 23964"/>
    </justification>
  </clause>

  <clause id="32460">
    <literal><![CDATA[
      L(x,a(y \ a(y,y,z),(y \ z) * L(u,z,1 * y),w),v5) = L(x,a(y \ a(y,y,z),z * u,w),v5)
    ]]></literal>
    <justification jstring="[para(32092(a,1),32410(a,1,2))].">
      <j1 rule="para" parents="32092 32410"/>
    </justification>
  </clause>

  <clause id="32461">
    <literal><![CDATA[
      L(x,a(y \ a(y,y,z),(y \ z) * L(u,z,y),w),v5) = L(x,a(y \ a(y,y,z),z * u,w),v5)
    ]]></literal>
    <justification jstring="[para(7(a,1),32460(a,1,2,2,2,3))].">
      <j1 rule="para" parents="7 32460"/>
    </justification>
  </clause>

  <clause id="32462">
    <literal><![CDATA[
      L(x,a(y \ 1,(y \ z) * L(u,z,y),w),v5) = L(x,a(y \ a(y,y,z),z * u,w),v5)
    ]]></literal>
    <justification jstring="[para(32088(a,1),32461(a,1,2))].">
      <j1 rule="para" parents="32088 32461"/>
    </justification>
  </clause>

  <clause id="32463">
    <literal><![CDATA[
      L(x,a(y \ a(y,y,z),z * u,w),v5) = L(x,a(y,(y \ z) * L(u,z,y),w),v5)
    ]]></literal>
    <justification jstring="[hyper(31062,a,32462,a),flip(a)].">
      <j1 rule="hyper" parents="31062 32462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32465">
    <literal><![CDATA[
      L(x,a(y \ a(y,y,z),z * u,w),v5) = L(x,a(y,z * (y \ L(u,z,y)),w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,32451,a(flip),b,32463,a),flip(a)].">
      <j1 rule="hyper" parents="347 32451 32463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32466">
    <literal><![CDATA[
      L(x,a(y,z * (y \ L(u,z,y)),w),v5) = L(x,a(y \ 1,z * u,w),v5)
    ]]></literal>
    <justification jstring="[para(32088(a,1),32465(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32088 32465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32467">
    <literal><![CDATA[
      L(x,a(y,z * (y \ L(u,z,y)),w),v5) = L(x,a(y,z * u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,22769,a(flip),b,32466,a),flip(a)].">
      <j1 rule="hyper" parents="347 22769 32466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32469">
    <literal><![CDATA[
      a(x,(y * (K(z,u) * w)) * v5,a(w * v5,v6,v7)) = a(x,R(y,w,v5),a(K(z,u) * (w * v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(23885(a,1),32351(a,1,3))].">
      <j1 rule="para" parents="23885 32351"/>
    </justification>
  </clause>

  <clause id="32470">
    <literal><![CDATA[
      a(x,R(y,z,u),a(K(w,v5) * (z * u),v6,v7)) = a(x,u * (y * z),a(z * u,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(24478,a,32469,a),flip(a)].">
      <j1 rule="hyper" parents="24478 32469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32472">
    <literal><![CDATA[
      a(x,y * (z * u),a(u * y,w,v5)) = a(x,R(z,u,y),a(u * y,w,v5))
    ]]></literal>
    <justification jstring="[para(202(a,1),32470(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="202 32470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32473">
    <literal><![CDATA[
      a(x,y * (z * u),a(u * y,w,v5)) = a(x,L(z,u,y),a(u * y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,24805,a(flip),b,32472,a),flip(a)].">
      <j1 rule="hyper" parents="347 24805 32472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32474">
    <literal><![CDATA[
      a(x,y * (z * u),a(u * y,w,v5)) = a(x,z,a(u * y,w,L(v5,u,y)))
    ]]></literal>
    <justification jstring="[hyper(347,a,30088,a(flip),b,32473,a),flip(a)].">
      <j1 rule="hyper" parents="347 30088 32473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32475">
    <literal><![CDATA[
      x \ (x * (a(y,y,z) \ L(z * (L(L(z,y,y),y,y) \ u),w,v5))) = L(a(y,y,z) * L(u,w,v5),a(y,y,z),x)
    ]]></literal>
    <justification jstring="[para(31794(a,1),32079(a,1,2))].">
      <j1 rule="para" parents="31794 32079"/>
    </justification>
  </clause>

  <clause id="32476">
    <literal><![CDATA[
      ((1 / x) \ (a(y,z,u) * a(y,z,u))) / a(y,z,u) = ((L(u,z,y) / x) \ u) * a(1 / x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(14964(a,1),32452(a,2,2))].">
      <j1 rule="para" parents="14964 32452"/>
    </justification>
  </clause>

  <clause id="32477">
    <literal><![CDATA[
      ((1 / x) \ (a(y,z,u) * a(y,z,u))) / a(y,z,u) = ((L(u,z,y) / x) \ u) * a(x \ 1,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(4024(a,1),32476(a,2,2))].">
      <j1 rule="para" parents="4024 32476"/>
    </justification>
  </clause>

  <clause id="32478">
    <literal><![CDATA[
      ((1 / x) \ (a(y,z,u) * a(y,z,u))) / a(y,z,u) = ((L(u,z,y) / x) \ u) * a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(29259(a,1),32477(a,2,2))].">
      <j1 rule="para" parents="29259 32477"/>
    </justification>
  </clause>

  <clause id="32479">
    <literal><![CDATA[
      (L(x,y,z) / u) \ L(x,u,a(u,y,z)) = ((1 / u) \ (a(z,y,x) * a(z,y,x))) / a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,30472,a(flip),b,32478,a)].">
      <j1 rule="hyper" parents="347 30472 32478"/>
    </justification>
  </clause>

  <clause id="32480">
    <literal><![CDATA[
      (L(x,y,z) / u) \ L(x,u,a(u,y,z)) = (u * (a(z,y,x) * a(z,y,x))) / a(z,y,x)
    ]]></literal>
    <justification jstring="[para(458(a,1),32479(a,2,1))].">
      <j1 rule="para" parents="458 32479"/>
    </justification>
  </clause>

  <clause id="32481">
    <literal><![CDATA[
      a(x,y,z) \ (u * (a(x,y,z) * a(x,y,z))) = (L(z,y,x) / u) \ L(z,u,a(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,19977,a(flip),b,32480,a)].">
      <j1 rule="hyper" parents="347 19977 32480"/>
    </justification>
  </clause>

  <clause id="32482">
    <literal><![CDATA[
      (L(x,y,z) / u) \ L(x,u,a(u,y,z)) = u * (a(z,y,x) \ (a(z,y,x) * a(z,y,x)))
    ]]></literal>
    <justification jstring="[hyper(28382,a,32481,a),flip(a)].">
      <j1 rule="hyper" parents="28382 32481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32483">
    <literal><![CDATA[
      (L(x,y,z) / u) \ L(x,u,a(u,y,z)) = u * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(347,a,20019,a(flip),b,32482,a),flip(a)].">
      <j1 rule="hyper" parents="347 20019 32482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32487">
    <literal><![CDATA[
      (L(x,y,z) / u) \ x = u * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(31708(a,1),32483(a,1,2))].">
      <j1 rule="para" parents="31708 32483"/>
    </justification>
  </clause>

  <clause id="32489">
    <literal><![CDATA[
      (x * a(y,z,u)) \ u = x \ L(u,z,y)
    ]]></literal>
    <justification jstring="[para(32487(a,1),22973(a,1,1))].">
      <j1 rule="para" parents="32487 22973"/>
    </justification>
  </clause>

  <clause id="32490">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * ((z \ 1) * a(z,u,w)) = (z * a(x,y,a(z,u,w))) \ a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,28576,a,b,32489,a)].">
      <j1 rule="hyper" parents="347 28576 32489"/>
    </justification>
  </clause>

  <clause id="32494">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * ((z \ 1) * a(z,u,w)) = L(z,u,a(x,y,w)) \ a(z,u,w)
    ]]></literal>
    <justification jstring="[para(29793(a,1),32490(a,2,1))].">
      <j1 rule="para" parents="29793 32490"/>
    </justification>
  </clause>

  <clause id="32495">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (z \ a(z,u,w)) = L(z,u,a(x,y,w)) \ a(z,u,w)
    ]]></literal>
    <justification jstring="[para(15264(a,1),32494(a,1,2))].">
      <j1 rule="para" parents="15264 32494"/>
    </justification>
  </clause>

  <clause id="32496">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ a(x,y,w) = x \ a(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,29153,a(flip),b,32495,a),flip(a)].">
      <j1 rule="hyper" parents="63 29153 32495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32497">
    <literal><![CDATA[
      ((a(x,y,z) * a(x,y,z)) * (x * R(R(x,y,z),y,z))) / R(R(x,y,z),y,z) = L(R(R(x,y,z),y,z),x,x \ R(R(x,y,z),y,z))
    ]]></literal>
    <justification jstring="[para(30079(a,1),32149(a,1,1,2))].">
      <j1 rule="para" parents="30079 32149"/>
    </justification>
  </clause>

  <clause id="32498">
    <literal><![CDATA[
      (x * (L(L(x,y,z),y,z) \ (z * R(R(z,y,x),y,x)))) / R(R(z,y,x),y,x) = L(R(R(z,y,x),y,x),z,z \ R(R(z,y,x),y,x))
    ]]></literal>
    <justification jstring="[para(27419(a,1),32497(a,1,1))].">
      <j1 rule="para" parents="27419 32497"/>
    </justification>
  </clause>

  <clause id="32499">
    <literal><![CDATA[
      L(R(R(x,y,z),y,z),x,x \ R(R(x,y,z),y,z)) = (R(R(x,y,z),y,z) * R(R(x,y,z),y,z)) / R(R(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(30396(a,1),32498(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30396 32498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32500">
    <literal><![CDATA[
      L(R(R(x,y,z),y,z),x,x \ R(R(x,y,z),y,z)) = (R(x,y,z) * R(R(R(x,y,z),y,z),y,z)) / R(R(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(30079(a,1),32499(a,2,1))].">
      <j1 rule="para" parents="30079 32499"/>
    </justification>
  </clause>

  <clause id="32501">
    <literal><![CDATA[
      L(R(R(x,y,z),y,z),x,x \ R(R(x,y,z),y,z)) = R(R(R(x,y,z),y,z),y,z) * (R(R(x,y,z),y,z) \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,20692,a(flip),b,32500,a),flip(a)].">
      <j1 rule="hyper" parents="347 20692 32500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32502">
    <literal><![CDATA[
      L(R(R(x,y,z),y,z),x,x \ R(R(x,y,z),y,z)) = R(R(R(x,y,z),y,z),y,z) * L(a(x,y,z) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(29779(a,1),32501(a,2,2))].">
      <j1 rule="para" parents="29779 32501"/>
    </justification>
  </clause>

  <clause id="32503">
    <literal><![CDATA[
      L(R(R(x,y,z),y,z),x,x \ R(R(x,y,z),y,z)) = R(R(R(x,y,z),y,z),y,z) * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(15045(a,1),32502(a,2,2))].">
      <j1 rule="para" parents="15045 32502"/>
    </justification>
  </clause>

  <clause id="32504">
    <literal><![CDATA[
      L(R(R(x,y,z),y,z),x,x \ R(R(x,y,z),y,z)) = a(x,y,z) \ R(R(R(x,y,z),y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,28348,a(flip),b,32503,a),flip(a)].">
      <j1 rule="hyper" parents="347 28348 32503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32506">
    <literal><![CDATA[
      L(R(R(x,y,z),y,z),x,a(x,y,z) * a(x,y,z)) = a(x,y,z) \ R(R(R(x,y,z),y,z),y,z)
    ]]></literal>
    <justification jstring="[para(31997(a,1),32504(a,1,3))].">
      <j1 rule="para" parents="31997 32504"/>
    </justification>
  </clause>

  <clause id="32507">
    <literal><![CDATA[
      a(x,y,z) \ R(R(R(x,y,z),y,z),y,z) = R(R(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(27886,a,32506,a),flip(a)].">
      <j1 rule="hyper" parents="27886 32506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32509">
    <literal><![CDATA[
      a(R(R(R(x,y,z),y,z),y,z) * L(u,a(x,y,z),a(x,y,z) * R(R(R(x,y,z),y,z),y,z)),w,v5) = a((u * a(x,y,z)) * R(R(x,y,z),y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(32507(a,1),27280(a,2,1,2))].">
      <j1 rule="para" parents="32507 27280"/>
    </justification>
  </clause>

  <clause id="32510">
    <literal><![CDATA[
      R(x,y * (T(z * K(z * u,u),u) * (T(u * z,u) \ T(u,z))),w) = R(x,y * a(T(u * z,u),(u * z) * R(u,z,u),T(u,z)),w)
    ]]></literal>
    <justification jstring="[para(15470(a,2),32427(a,1,2,2,1))].">
      <j1 rule="para" parents="15470 32427"/>
    </justification>
  </clause>

  <clause id="32511">
    <literal><![CDATA[
      R(x,y * a(T(z * u,z),(z * u) * R(z,u,z),T(z,u)),w) = R(x,y * ((z \ T(u * z,z)) * (T(z * u,z) \ T(z,u))),w)
    ]]></literal>
    <justification jstring="[para(6171(a,1),32510(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6171 32510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32512">
    <literal><![CDATA[
      R(x,y * a(T(z * u,z),(z * u) * R(z,u,z),T(z,u)),w) = R(x,y * ((z \ T(u * z,z)) * (T(z * u,z) \ z)),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,22494,a(flip),b,32511,a),flip(a)].">
      <j1 rule="hyper" parents="347 22494 32511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32514">
    <literal><![CDATA[
      R(x,y * a(T(z * u,z),(z * u) * R(z,u,z),T(z,u)),w) = R(x,((z \ T(u * z,z)) * ((z * u) \ z)) * y,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,22505,a(flip),b,32512,a),flip(a)].">
      <j1 rule="hyper" parents="347 22505 32512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32516">
    <literal><![CDATA[
      R(x,y * a(T(z * u,z),(z * u) * R(z,u,z),T(z,u)),w) = R(x,((z \ T(u * z,z)) * (z \ (z / u))) * y,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,22554,a(flip),b,32514,a),flip(a)].">
      <j1 rule="hyper" parents="347 22554 32514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32517">
    <literal><![CDATA[
      R(x,y * a(T(z * u,z),(z * u) * R(z,u,z),T(z,u)),w) = R(x,((z \ (u * z)) * (z \ (z / u))) * y,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,22499,a(flip),b,32516,a),flip(a)].">
      <j1 rule="hyper" parents="347 22499 32516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32519">
    <literal><![CDATA[
      R(x,y * a(T(z * u,z),(z * u) * R(z,u,z),T(z,u)),w) = R(x,(T(u,z) * (z \ (z / u))) * y,w)
    ]]></literal>
    <justification jstring="[para(22(a,2),32517(a,2,2,1,1))].">
      <j1 rule="para" parents="22 32517"/>
    </justification>
  </clause>

  <clause id="32520">
    <literal><![CDATA[
      R(x,y * a(T(z * u,z),(z * u) * R(z,u,z),T(z,u)),w) = R(x,(u * (z \ (z / u))) * y,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,22423,a(flip),b,32519,a),flip(a)].">
      <j1 rule="hyper" parents="347 22423 32519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32522">
    <literal><![CDATA[
      R(x,y * a(T(z * u,z),(z * u) * R(z,u,z),z),w) = R(x,(u * (z \ (z / u))) * y,w)
    ]]></literal>
    <justification jstring="[para(24067(a,1),32520(a,1,2,2))].">
      <j1 rule="para" parents="24067 32520"/>
    </justification>
  </clause>

  <clause id="32524">
    <literal><![CDATA[
      R(x,y * a(T(z * u,z),(z * u) * L(z,u,z),z),w) = R(x,(u * (z \ (z / u))) * y,w)
    ]]></literal>
    <justification jstring="[para(25119(a,1),32522(a,1,2,2))].">
      <j1 rule="para" parents="25119 32522"/>
    </justification>
  </clause>

  <clause id="32525">
    <literal><![CDATA[
      R(x,y * a(T(z * u,z),z * (u * z),z),w) = R(x,(u * (z \ (z / u))) * y,w)
    ]]></literal>
    <justification jstring="[para(97(a,1),32524(a,1,2,2,2))].">
      <j1 rule="para" parents="97 32524"/>
    </justification>
  </clause>

  <clause id="32526">
    <literal><![CDATA[
      R(x,y * a(T(z * u,z),L(u,z,z),z),w) = R(x,(u * (z \ (z / u))) * y,w)
    ]]></literal>
    <justification jstring="[para(24244(a,1),32525(a,1,2,2))].">
      <j1 rule="para" parents="24244 32525"/>
    </justification>
  </clause>

  <clause id="32527">
    <literal><![CDATA[
      R(x,y * a(z * u,L(u,z,z),z),w) = R(x,(u * (z \ (z / u))) * y,w)
    ]]></literal>
    <justification jstring="[para(23894(a,1),32526(a,1,2,2))].">
      <j1 rule="para" parents="23894 32526"/>
    </justification>
  </clause>

  <clause id="32529">
    <literal><![CDATA[
      R(x,(y * (z \ (z / y))) * u,w) = R(x,u * a(z * y,y,z),w)
    ]]></literal>
    <justification jstring="[para(30198(a,1),32527(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="30198 32527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32530">
    <literal><![CDATA[
      R(x,(y * (z \ (z / y))) * u,w) = R(x,u * a(z,y,y),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,28511,a(flip),b,32529,a),flip(a)].">
      <j1 rule="hyper" parents="347 28511 32529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32531">
    <literal><![CDATA[
      R(x,(y \ z) * a(y * z,u,u),w) = R(x,L(y \ z,u,u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,29667,a(flip),b,32530,a),flip(a)].">
      <j1 rule="hyper" parents="63 29667 32530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32532">
    <literal><![CDATA[
      R(x,T(y * (z * z),u) * a(u * (y * ((z * z) * u)),w,w),v5) = R(x,L(u \ (y * ((z * z) * u)),w,w),v5)
    ]]></literal>
    <justification jstring="[para(123(a,1),32531(a,1,2,1))].">
      <j1 rule="para" parents="123 32531"/>
    </justification>
  </clause>

  <clause id="32533">
    <literal><![CDATA[
      R(x,T(a(y * (z * ((u * u) * y)),w,w) * (z * (u * u)),y),v5) = R(x,L(y \ (z * ((u * u) * y)),w,w),v5)
    ]]></literal>
    <justification jstring="[para(18943(a,2),32532(a,1,2))].">
      <j1 rule="para" parents="18943 32532"/>
    </justification>
  </clause>

  <clause id="32534">
    <literal><![CDATA[
      R(x,a(y * (z * ((u * u) * y)),w,w) * (z * (u * u)),v5) = R(x,L(y \ (z * ((u * u) * y)),w,w),v5)
    ]]></literal>
    <justification jstring="[hyper(22439,a,32533,a)].">
      <j1 rule="hyper" parents="22439 32533"/>
    </justification>
  </clause>

  <clause id="32535">
    <literal><![CDATA[
      R(x,a(y * (z * ((u * u) * y)),w,w) * z,v5) = R(x,L(y \ (z * ((u * u) * y)),w,w),v5)
    ]]></literal>
    <justification jstring="[hyper(20903,a,32534,a)].">
      <j1 rule="hyper" parents="20903 32534"/>
    </justification>
  </clause>

  <clause id="32538">
    <literal><![CDATA[
      R(x,a(y * (z * ((u * u) * y)),w,w) * z,v5) = R(x,L(T(z * (u * u),y),w,w),v5)
    ]]></literal>
    <justification jstring="[para(123(a,1),32535(a,2,2,1))].">
      <j1 rule="para" parents="123 32535"/>
    </justification>
  </clause>

  <clause id="32539">
    <literal><![CDATA[
      R(x,a(y * (z * ((u * u) * y)),w,w) * z,v5) = R(x,L(z * (u * u),w,w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,20554,a(flip),b,32538,a),flip(a)].">
      <j1 rule="hyper" parents="347 20554 32538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32541">
    <literal><![CDATA[
      R(x,a(y * (z * ((u * u) * y)),w,w) * z,v5) = R(x,L(z,w,w),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,2251,a(flip),b,32539,a),flip(a)].">
      <j1 rule="hyper" parents="347 2251 32539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32543">
    <literal><![CDATA[
      R(x,y,z * a(u * (y * ((w * w) * u)),v5,v5)) = R(x,L(y,v5,v5),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,32306,a(flip),b,32541,a)].">
      <j1 rule="hyper" parents="63 32306 32541"/>
    </justification>
  </clause>

  <clause id="32544">
    <literal><![CDATA[
      a(R(R(R(x,y,z),y,z),y,z) * L(u,a(x,y,z),a(x,y,z) * L(R(R(x,y,z),y,z),y,z)),w,v5) = a((u * a(x,y,z)) * R(R(x,y,z),y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(22863(a,1),32509(a,1,1,2))].">
      <j1 rule="para" parents="22863 32509"/>
    </justification>
  </clause>

  <clause id="32545">
    <literal><![CDATA[
      a(R(R(R(x,y,z),y,z),y,z) * L(u,a(x,y,z),a(x,y,z) * L(L(R(x,y,z),y,z),y,z)),w,v5) = a((u * a(x,y,z)) * R(R(x,y,z),y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(22868(a,1),32544(a,1,1,2))].">
      <j1 rule="para" parents="22868 32544"/>
    </justification>
  </clause>

  <clause id="32546">
    <literal><![CDATA[
      a(R(R(R(x,y,z),y,z),y,z) * L(u,a(x,y,z),a(x,y,z) * R(x,y,z)),w,v5) = a((u * a(x,y,z)) * R(R(x,y,z),y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(27538(a,1),32545(a,1,1,2))].">
      <j1 rule="para" parents="27538 32545"/>
    </justification>
  </clause>

  <clause id="32548">
    <literal><![CDATA[
      a(R(R(R(x,y,z),y,z),y,z) * L(u,a(x,y,z),R(R(x,y,z),y,z)),w,v5) = a((u * a(x,y,z)) * R(R(x,y,z),y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(29710(a,1),32546(a,1,1,2,3))].">
      <j1 rule="para" parents="29710 32546"/>
    </justification>
  </clause>

  <clause id="32549">
    <literal><![CDATA[
      a(R(R(R(x,y,z),y,z),y,z) * L(u,a(x,y,z),L(R(x,y,z),y,z)),w,v5) = a((u * a(x,y,z)) * R(R(x,y,z),y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(23670(a,1),32548(a,1,1,2))].">
      <j1 rule="para" parents="23670 32548"/>
    </justification>
  </clause>

  <clause id="32550">
    <literal><![CDATA[
      a(R(R(R(x,y,z),y,z),y,z) * L(u,a(x,y,z),L(L(x,y,z),y,z)),w,v5) = a((u * a(x,y,z)) * R(R(x,y,z),y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(23686(a,1),32549(a,1,1,2))].">
      <j1 rule="para" parents="23686 32549"/>
    </justification>
  </clause>

  <clause id="32551">
    <literal><![CDATA[
      a(R(R(R(x,y,z),y,z),y,z) * L(u,a(x,y,z),x),w,v5) = a((u * a(x,y,z)) * R(R(x,y,z),y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(27537(a,1),32550(a,1,1,2))].">
      <j1 rule="para" parents="27537 32550"/>
    </justification>
  </clause>

  <clause id="32552">
    <literal><![CDATA[
      a(R(R(R(x,y,z),y,z),y,z) * L(u,x,a(x,y,z)),w,v5) = a((u * a(x,y,z)) * R(R(x,y,z),y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(25493(a,1),32551(a,1,1,2))].">
      <j1 rule="para" parents="25493 32551"/>
    </justification>
  </clause>

  <clause id="32554">
    <literal><![CDATA[
      a((x * a(y,z,u)) * R(R(y,z,u),z,u),w,v5) = a(x * R(R(R(y,z,u),z,u),z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,31623,a(flip),b,32552,a),flip(a)].">
      <j1 rule="hyper" parents="63 31623 32552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32556">
    <literal><![CDATA[
      a((x * a(y,z,u)) * R(R(y,z,u),z,u),w,v5) = a(x * L(R(R(y,z,u),z,u),z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,26216,a(flip),b,32554,a),flip(a)].">
      <j1 rule="hyper" parents="347 26216 32554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32557">
    <literal><![CDATA[
      a((x * a(y,z,u)) * R(R(y,z,u),z,u),w,v5) = a(x * L(L(R(y,z,u),z,u),z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,26812,a(flip),b,32556,a),flip(a)].">
      <j1 rule="hyper" parents="347 26812 32556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32558">
    <literal><![CDATA[
      a((x * a(y,z,u)) * R(R(y,z,u),z,u),w,v5) = a(x * R(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,27973,a(flip),b,32557,a),flip(a)].">
      <j1 rule="hyper" parents="347 27973 32557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32560">
    <literal><![CDATA[
      a((x * a(y,z,u)) * R(R(y,z,u),z,u),w,v5) = a(x * L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,26216,a(flip),b,32558,a),flip(a)].">
      <j1 rule="hyper" parents="347 26216 32558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32561">
    <literal><![CDATA[
      a((x * a(y,z,u)) * L(R(y,z,u),z,u),w,v5) = a(x * L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26217,a,32560,a)].">
      <j1 rule="hyper" parents="26217 32560"/>
    </justification>
  </clause>

  <clause id="32562">
    <literal><![CDATA[
      a((x * a(y,z,u)) * L(L(y,z,u),z,u),w,v5) = a(x * L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,26812,a(flip),b,32561,a)].">
      <j1 rule="hyper" parents="63 26812 32561"/>
    </justification>
  </clause>

  <clause id="32563">
    <literal><![CDATA[
      a((x * a(y,z,u)) * y,w,v5) = a(x * L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,27973,a(flip),b,32562,a)].">
      <j1 rule="hyper" parents="63 27973 32562"/>
    </justification>
  </clause>

  <clause id="32564">
    <literal><![CDATA[
      a(x * (a(x,y,z) * u),w,v5) = a(u * L(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(24409,a,32563,a)].">
      <j1 rule="hyper" parents="24409 32563"/>
    </justification>
  </clause>

  <clause id="32566">
    <literal><![CDATA[
      a(T(x \ (y \ 1),z) \ u,T(x \ (y \ 1),z) * x,L(w,T(x \ (y \ 1),z),x)) = a((y \ K(x \ (y \ 1),z)) \ (x * u),(x \ (y \ 1)) * x,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24147,a(flip),b,30000,a),flip(a)].">
      <j1 rule="hyper" parents="347 24147 30000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32568">
    <literal><![CDATA[
      a(T(x \ (y \ 1),z) \ u,T(x \ (y \ 1),z) * x,L(w,T(x \ (y \ 1),z),x)) = a((y \ K(x \ (y \ 1),z)) \ (x * u),y \ 1,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24038,a(flip),b,32566,a),flip(a)].">
      <j1 rule="hyper" parents="347 24038 32566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32570">
    <literal><![CDATA[
      a(T(x \ (y \ 1),z) \ u,T(x \ (y \ 1),z) * x,L(w,T(x \ (y \ 1),z),x)) = a((y \ K(x \ (y \ 1),z)) \ (x * u),y,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,14950,a(flip),b,32568,a),flip(a)].">
      <j1 rule="hyper" parents="347 14950 32568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32571">
    <literal><![CDATA[
      a(T(x \ (y \ 1),z) \ u,T(x \ (y \ 1),z) * x,L(w,T(x \ (y \ 1),z),x)) = a((y \ 1) \ (x * u),y,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,23910,a(flip),b,32570,a),flip(a)].">
      <j1 rule="hyper" parents="347 23910 32570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32573">
    <literal><![CDATA[
      a(T(x \ (y \ 1),z) \ u,T(x \ (y \ 1),z) * x,L(w,T(x \ (y \ 1),z),x)) = a(y * (x * u),y,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,29723,a(flip),b,32571,a),flip(a)].">
      <j1 rule="hyper" parents="347 29723 32571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32574">
    <literal><![CDATA[
      a(T(x \ (y \ 1),z) \ u,T(x \ (y \ 1),z) * x,L(w,x \ (y \ 1),x)) = a(y * (x * u),y,w)
    ]]></literal>
    <justification jstring="[para(21616(a,1),32573(a,1,3))].">
      <j1 rule="para" parents="21616 32573"/>
    </justification>
  </clause>

  <clause id="32576">
    <literal><![CDATA[
      a(T(x \ (y \ 1),z) \ u,T(x \ (y \ 1),z) * x,L(w,x * (y \ 1),x)) = a(y * (x * u),y,w)
    ]]></literal>
    <justification jstring="[para(30135(a,1),32574(a,1,3))].">
      <j1 rule="para" parents="30135 32574"/>
    </justification>
  </clause>

  <clause id="32577">
    <literal><![CDATA[
      a(T(x \ (y \ 1),z) \ u,T(x \ (y \ 1),z) * x,L(w,x * y,x)) = a(y * (x * u),y,w)
    ]]></literal>
    <justification jstring="[para(3229(a,1),32576(a,1,3))].">
      <j1 rule="para" parents="3229 32576"/>
    </justification>
  </clause>

  <clause id="32578">
    <literal><![CDATA[
      a(T(x \ (y \ 1),z) \ u,(x \ (y \ 1)) * x,L(w,x * y,x)) = a(y * (x * u),y,w)
    ]]></literal>
    <justification jstring="[hyper(23995,a,32577,a)].">
      <j1 rule="hyper" parents="23995 32577"/>
    </justification>
  </clause>

  <clause id="32579">
    <literal><![CDATA[
      a(T(x \ (y \ 1),z) \ u,y \ 1,L(w,x * y,x)) = a(y * (x * u),y,w)
    ]]></literal>
    <justification jstring="[hyper(23993,a,32578,a)].">
      <j1 rule="hyper" parents="23993 32578"/>
    </justification>
  </clause>

  <clause id="32581">
    <literal><![CDATA[
      a(T(x \ (y \ 1),z) \ u,y,L(w,x * y,x)) = a(y * (x * u),y,w)
    ]]></literal>
    <justification jstring="[hyper(14965,a,32579,a)].">
      <j1 rule="hyper" parents="14965 32579"/>
    </justification>
  </clause>

  <clause id="32583">
    <literal><![CDATA[
      a((x \ (y \ 1)) \ z,y,L(u,x * y,x)) = a(y * (x * z),y,u)
    ]]></literal>
    <justification jstring="[hyper(23959,a,32581,a)].">
      <j1 rule="hyper" parents="23959 32581"/>
    </justification>
  </clause>

  <clause id="32584">
    <literal><![CDATA[
      a((x \ (y \ 1)) \ z,y,L(u,y,x)) = a(y * (x * z),y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,32397,a(flip),b,32583,a)].">
      <j1 rule="hyper" parents="63 32397 32583"/>
    </justification>
  </clause>

  <clause id="32599">
    <literal><![CDATA[
      T(L(R(x,y,z),u,a(w,v5,z)),x) / (L(x,u,a(w,v5,z)) * L(x,u,a(w,v5,z))) = L(x,u,a(w,v5,z)) \ R(a(x,y,z),L(x,u,a(w,v5,z)),L(x,u,a(w,v5,z)))
    ]]></literal>
    <justification jstring="[para(19937(a,1),29942(a,1,1))].">
      <j1 rule="para" parents="19937 29942"/>
    </justification>
  </clause>

  <clause id="32600">
    <literal><![CDATA[
      L(T(R(x,y,z),x),u,a(w,v5,z)) / (L(x,u,a(w,v5,z)) * L(x,u,a(w,v5,z))) = L(x,u,a(w,v5,z)) \ R(a(x,y,z),L(x,u,a(w,v5,z)),L(x,u,a(w,v5,z)))
    ]]></literal>
    <justification jstring="[para(25(a,2),32599(a,1,1))].">
      <j1 rule="para" parents="25 32599"/>
    </justification>
  </clause>

  <clause id="32602">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ R(a(x,v5,w),L(x,y,a(z,u,w)),L(x,y,a(z,u,w))) = L(R(x,v5,w),y,a(z,u,w)) / (L(x,y,a(z,u,w)) * L(x,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(200(a,1),32600(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="200 32600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32603">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ R(a(x,v5,w),L(x,y,a(z,u,w)),L(x,y,a(z,u,w))) = L(R(x,v5,w),y,a(z,u,w)) / (x * L(L(x,y,a(z,u,w)),y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(25561(a,1),32602(a,2,2))].">
      <j1 rule="para" parents="25561 32602"/>
    </justification>
  </clause>

  <clause id="32604">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ R(a(x,v5,w),L(x,y,a(z,u,w)),L(x,y,a(z,u,w))) = L(R(x,v5,w),y,a(z,u,w)) / (x * x)
    ]]></literal>
    <justification jstring="[para(26375(a,1),32603(a,2,2,2))].">
      <j1 rule="para" parents="26375 32603"/>
    </justification>
  </clause>

  <clause id="32605">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ R(a(x,v5,w),L(x,y,a(z,u,w)),L(x,y,a(z,u,w))) = L(R(x,v5,w) / (x * x),y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,3177,a,b,32604,a),flip(a)].">
      <j1 rule="hyper" parents="347 3177 32604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32606">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ R(a(x,v5,w),L(x,y,a(z,u,w)),L(x,y,a(z,u,w))) = L(x \ a(x,v5,w),y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(28972(a,1),32605(a,2,1))].">
      <j1 rule="para" parents="28972 32605"/>
    </justification>
  </clause>

  <clause id="32607">
    <literal><![CDATA[
      L(x \ a(x,y,z),u,a(w,v5,z)) = L(x,u,a(w,v5,z)) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(25488(a,1),32606(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25488 32606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32608">
    <literal><![CDATA[
      L(x \ a(x,y,z),y,a(u,w,z)) = x \ a(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,32496,a(flip),b,32607,a),flip(a)].">
      <j1 rule="hyper" parents="347 32496 32607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32612">
    <literal><![CDATA[
      a(x,y,L(z,y,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(38,a,32253,a(flip),b,32608,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="38 32253 32608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32615">
    <literal><![CDATA[
      L(x \ a(x,y,z),y,a(u,w,z)) != x \ v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,L(z,w,u)) = v5
    ]]></literal>
    <justification jstring="[para(32608(a,2),47(a,1))].">
      <j1 rule="para" parents="32608 47"/>
    </justification>
  </clause>

  <clause id="32616">
    <literal><![CDATA[
      a(x,y,(y * z) \ L(u,z,z)) = a(x,y,(u * z) * y)
    ]]></literal>
    <justification jstring="[hyper(31105,a,32612,a)].">
      <j1 rule="hyper" parents="31105 32612"/>
    </justification>
  </clause>

  <clause id="32622">
    <literal><![CDATA[
      a((x \ (y \ 1)) \ z,y,u) = a(y * (x * z),y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,32584,a(flip),b,32612,a),flip(a)].">
      <j1 rule="hyper" parents="63 32584 32612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32623">
    <literal><![CDATA[
      L(a(x,y,z),y,u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,29113,a(flip),b,32612,a)].">
      <j1 rule="hyper" parents="63 29113 32612"/>
    </justification>
  </clause>

  <clause id="32649">
    <literal><![CDATA[
      a(x,y,z * (y \ L(u,z,z))) = a(x,y,(u * z) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,32242,a(flip),b,32616,a)].">
      <j1 rule="hyper" parents="63 32242 32616"/>
    </justification>
  </clause>

  <clause id="32650">
    <literal><![CDATA[
      a(x,(y \ z) \ R(u,(L(y,w,w) \ z) * a(y,w,w),(L(y,w,w) \ z) * a(y,w,w)),v5) = a(x,T(u * (a(y,w,w) \ (1 / (L(y,w,w) \ z))),(L(y,w,w) \ z) * a(y,w,w)),v5)
    ]]></literal>
    <justification jstring="[para(32323(a,1),31402(a,2,2,1,2))].">
      <j1 rule="para" parents="32323 31402"/>
    </justification>
  </clause>

  <clause id="32651">
    <literal><![CDATA[
      a(x,(y \ z) \ R(u,(L(y,w,w) \ z) * a(y,w,w),(L(y,w,w) \ z) * a(y,w,w)),v5) = a(x,u * (a(y,w,w) \ (1 / (L(y,w,w) \ z))),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,23991,a(flip),b,32650,a),flip(a)].">
      <j1 rule="hyper" parents="347 23991 32650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32653">
    <literal><![CDATA[
      a(x,(y \ z) \ R(u,(L(y,w,w) \ z) * a(y,w,w),(L(y,w,w) \ z) * a(y,w,w)),v5) = a(x,u * (a(y,w,w) \ ((L(y,w,w) \ z) \ 1)),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24255,a(flip),b,32651,a),flip(a)].">
      <j1 rule="hyper" parents="347 24255 32651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32654">
    <literal><![CDATA[
      a(x,(y \ z) \ R(u,(L(y,w,w) \ z) * a(y,w,w),(L(y,w,w) \ z) * a(y,w,w)),v5) = a(x,(a(y,w,w) \ (L(y,w,w) \ z)) * u,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24574,a(flip),b,32653,a),flip(a)].">
      <j1 rule="hyper" parents="347 24574 32653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32655">
    <literal><![CDATA[
      a(x,(y \ z) \ R(u,(L(y,w,w) \ z) * a(y,w,w),(L(y,w,w) \ z) * a(y,w,w)),v5) = a(x,(a(y,w,w) * (L(y,w,w) \ z)) * u,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,28075,a(flip),b,32654,a),flip(a)].">
      <j1 rule="hyper" parents="347 28075 32654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32656">
    <literal><![CDATA[
      a(x,(y \ z) \ R(u,(L(y,w,w) \ z) * a(y,w,w),y \ z),v5) = a(x,(a(y,w,w) * (L(y,w,w) \ z)) * u,v5)
    ]]></literal>
    <justification jstring="[para(31058(a,1),32655(a,1,2,2))].">
      <j1 rule="para" parents="31058 32655"/>
    </justification>
  </clause>

  <clause id="32657">
    <literal><![CDATA[
      a(x,(y \ z) \ R(u,y \ z,y \ z),w) = a(x,(a(y,v5,v5) * (L(y,v5,v5) \ z)) * u,w)
    ]]></literal>
    <justification jstring="[para(30417(a,1),32656(a,1,2,2))].">
      <j1 rule="para" parents="30417 32656"/>
    </justification>
  </clause>

  <clause id="32659">
    <literal><![CDATA[
      a(x,T(y * (1 / (z \ u)),z \ u),w) = a(x,(a(z,v5,v5) * (L(z,v5,v5) \ u)) * y,w)
    ]]></literal>
    <justification jstring="[para(2263(a,2),32657(a,1,2))].">
      <j1 rule="para" parents="2263 32657"/>
    </justification>
  </clause>

  <clause id="32661">
    <literal><![CDATA[
      a(x,(a(y,z,z) * (L(y,z,z) \ u)) * w,v5) = a(x,w * (1 / (y \ u)),v5)
    ]]></literal>
    <justification jstring="[hyper(23992,a,32659,a),flip(a)].">
      <j1 rule="hyper" parents="23992 32659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32663">
    <literal><![CDATA[
      a(x,(a(y,z,z) * (L(y,z,z) \ u)) * w,v5) = a(x,w * ((y \ u) \ 1),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24043,a(flip),b,32661,a),flip(a)].">
      <j1 rule="hyper" parents="347 24043 32661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32664">
    <literal><![CDATA[
      a(x,(a(y,z,z) * (L(y,z,z) \ u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,(y \ u) * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(32663(a,2),24161(a,1))].">
      <j1 rule="para" parents="32663 24161"/>
    </justification>
  </clause>

  <clause id="32665">
    <literal><![CDATA[
      a(x,a(y,z,z) * ((L(y,z,z) \ u) * w),v5) = a(x,(y \ u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(32664,a,32162,a),flip(a)].">
      <j1 rule="hyper" parents="32664 32162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32666">
    <literal><![CDATA[
      a(x,(y \ T(L(y,z,z) * (u * (L(y,z,z) \ 1)),w)) * v5,v6) = a(x,a(y,z,z) * ((T(u,w) * (L(y,z,z) \ 1)) * v5),v6)
    ]]></literal>
    <justification jstring="[para(1136(a,1),32665(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1136 32665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32667">
    <literal><![CDATA[
      a(x,(y \ T(L(y,z,z) * (u * (L(y,z,z) \ 1)),w)) * v5,v6) = a(x,a(y,z,z) * ((T(u,w) * L(y,z,z)) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,24688,a(flip),b,32666,a),flip(a)].">
      <j1 rule="hyper" parents="347 24688 32666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32668">
    <literal><![CDATA[
      a(x,(y \ T(L(y,z,z) * (u * (L(y,z,z) \ 1)),w)) * v5,v6) = a(x,a(y,z,z) * ((u * L(y,z,z)) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,24595,a(flip),b,32667,a),flip(a)].">
      <j1 rule="hyper" parents="347 24595 32667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32670">
    <literal><![CDATA[
      a(x,a(y,z,z) * ((u * L(y,z,z)) * w),v5) = a(x,(y \ T(y * (u * (y \ 1)),v6)) * w,v5)
    ]]></literal>
    <justification jstring="[para(27199(a,1),32668(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="27199 32668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32671">
    <literal><![CDATA[
      a(x,a(y,z,z) * ((u * L(y,z,z)) * w),v5) = a(x,(T(u,v6) * (y \ 1)) * w,v5)
    ]]></literal>
    <justification jstring="[para(1136(a,1),32670(a,2,2,1))].">
      <j1 rule="para" parents="1136 32670"/>
    </justification>
  </clause>

  <clause id="32673">
    <literal><![CDATA[
      a(x,a(y,z,z) * ((u * L(y,z,z)) * w),v5) = a(x,w * (y * T(u,v6)),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24683,a(flip),b,32671,a),flip(a)].">
      <j1 rule="hyper" parents="347 24683 32671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32674">
    <literal><![CDATA[
      a(x,a(y,z,z) * ((u * L(y,z,z)) * w),v5) = a(x,w * (y * u),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,24045,a(flip),b,32673,a),flip(a)].">
      <j1 rule="hyper" parents="347 24045 32673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32675">
    <literal><![CDATA[
      a(x,T(y * (z * a(u \ 1,w,v5)),z) / ((z * a(u \ 1,w,v5)) * (z * a(u \ 1,w,v5))),v6) = a(x,(a(v5,w,u) * z) \ R(y,z * a(u \ 1,w,v5),z * a(u \ 1,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(23047(a,1),31419(a,1,2,1))].">
      <j1 rule="para" parents="23047 31419"/>
    </justification>
  </clause>

  <clause id="32676">
    <literal><![CDATA[
      a(x,((y * a(z \ 1,u,w)) * (y * a(z \ 1,u,w))) \ T(v5 * (y * a(z \ 1,u,w)),y),v6) = a(x,(a(w,u,z) * y) \ R(v5,y * a(z \ 1,u,w),y * a(z \ 1,u,w)),v6)
    ]]></literal>
    <justification jstring="[hyper(24412,a,32675,a)].">
      <j1 rule="hyper" parents="24412 32675"/>
    </justification>
  </clause>

  <clause id="32678">
    <literal><![CDATA[
      a(x,((y * a(z \ 1,u,w)) * (y * a(z \ 1,u,w))) \ (v5 * (y * a(z \ 1,u,w))),v6) = a(x,(a(w,u,z) * y) \ R(v5,y * a(z \ 1,u,w),y * a(z \ 1,u,w)),v6)
    ]]></literal>
    <justification jstring="[hyper(24002,a,32676,a)].">
      <j1 rule="hyper" parents="24002 32676"/>
    </justification>
  </clause>

  <clause id="32679">
    <literal><![CDATA[
      a(x,(a(y,z,u) * w) \ R(v5,w * a(u \ 1,z,y),w * a(u \ 1,z,y)),v6) = a(x,v5 * (w * a(u \ 1,z,y)),v6)
    ]]></literal>
    <justification jstring="[hyper(24159,a,32678,a),flip(a)].">
      <j1 rule="hyper" parents="24159 32678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32682">
    <literal><![CDATA[
      a(x,(a(y,z,u) * w) \ R(v5,w * a(u \ 1,z,y),a(y,z,u) * w),v6) = a(x,v5 * (w * a(u \ 1,z,y)),v6)
    ]]></literal>
    <justification jstring="[para(27783(a,1),32679(a,1,2,2))].">
      <j1 rule="para" parents="27783 32679"/>
    </justification>
  </clause>

  <clause id="32683">
    <literal><![CDATA[
      a(x,(a(y,z,u) * w) \ R(v5,a(y,z,u) * w,a(y,z,u) * w),v6) = a(x,v5 * (w * a(u \ 1,z,y)),v6)
    ]]></literal>
    <justification jstring="[para(29335(a,1),32682(a,1,2,2))].">
      <j1 rule="para" parents="29335 32682"/>
    </justification>
  </clause>

  <clause id="32684">
    <literal><![CDATA[
      a(x,T(y * (1 / (a(z,u,w) * v5)),a(z,u,w) * v5),v6) = a(x,y * (v5 * a(w \ 1,u,z)),v6)
    ]]></literal>
    <justification jstring="[para(2263(a,2),32683(a,1,2))].">
      <j1 rule="para" parents="2263 32683"/>
    </justification>
  </clause>

  <clause id="32685">
    <literal><![CDATA[
      a(x,T(y * (a(z,u,w) \ (1 / v5)),a(z,u,w) * v5),v6) = a(x,y * (v5 * a(w \ 1,u,z)),v6)
    ]]></literal>
    <justification jstring="[para(32324(a,1),32684(a,1,2,1,2))].">
      <j1 rule="para" parents="32324 32684"/>
    </justification>
  </clause>

  <clause id="32686">
    <literal><![CDATA[
      a(x,y * (a(z,u,w) \ (1 / v5)),v6) = a(x,y * (v5 * a(w \ 1,u,z)),v6)
    ]]></literal>
    <justification jstring="[hyper(23992,a,32685,a)].">
      <j1 rule="hyper" parents="23992 32685"/>
    </justification>
  </clause>

  <clause id="32687">
    <literal><![CDATA[
      a(x,y * (a(z,u,w) \ (v5 \ 1)),v6) = a(x,y * (v5 * a(w \ 1,u,z)),v6)
    ]]></literal>
    <justification jstring="[hyper(24418,a,32686,a)].">
      <j1 rule="hyper" parents="24418 32686"/>
    </justification>
  </clause>

  <clause id="32689">
    <literal><![CDATA[
      a(x,y * (z * a(u \ 1,w,v5)),v6) = a(x,(a(v5,w,u) \ z) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(24577,a,32687,a),flip(a)].">
      <j1 rule="hyper" parents="24577 32687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32691">
    <literal><![CDATA[
      ((K(x,K(y,z)) * u) * (K(x,K(y,z)) * (L(u,w,v5) \ (K(K(y,z),x) * u)))) * ((K(x,K(y,z)) * u) * v6) = (K(x,K(y,z)) * u) * (((K(x,K(y,z)) * u) * (L(K(x,K(y,z)) * u,w,v5) \ (K(x,K(y,z)) * u))) * v6)
    ]]></literal>
    <justification jstring="[para(21270(a,1),26074(a,1,1,2,2))].">
      <j1 rule="para" parents="21270 26074"/>
    </justification>
  </clause>

  <clause id="32692">
    <literal><![CDATA[
      ((K(x,K(y,z)) * u) * (K(x,K(y,z)) * (K(x,K(y,z)) * (L(u,w,v5) \ u)))) * ((K(x,K(y,z)) * u) * v6) = (K(x,K(y,z)) * u) * (((K(x,K(y,z)) * u) * (L(K(x,K(y,z)) * u,w,v5) \ (K(x,K(y,z)) * u))) * v6)
    ]]></literal>
    <justification jstring="[para(17030(a,1),32691(a,1,1,2,2))].">
      <j1 rule="para" parents="17030 32691"/>
    </justification>
  </clause>

  <clause id="32693">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (((K(x,K(y,z)) * u) * (L(K(x,K(y,z)) * u,w,v5) \ (K(x,K(y,z)) * u))) * v6) = ((K(x,K(y,z)) * u) * (L(u,w,v5) \ u)) * ((K(x,K(y,z)) * u) * v6)
    ]]></literal>
    <justification jstring="[para(7319(a,1),32692(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7319 32692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32695">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (((K(x,K(y,z)) * u) * (L(K(x,K(y,z)) * u,w,v5) \ (K(x,K(y,z)) * u))) * v6) = (K(x,K(y,z)) * (u * (L(u,w,v5) \ u))) * ((K(x,K(y,z)) * u) * v6)
    ]]></literal>
    <justification jstring="[para(16846(a,1),32693(a,2,1))].">
      <j1 rule="para" parents="16846 32693"/>
    </justification>
  </clause>

  <clause id="32696">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (((K(x,K(y,z)) * u) * (L(K(x,K(y,z)) * u,w,v5) \ (K(x,K(y,z)) * u))) * v6) = (1 / L(u \ K(K(y,z),x),w,v5)) * ((K(x,K(y,z)) * u) * v6)
    ]]></literal>
    <justification jstring="[para(21954(a,1),32695(a,2,1))].">
      <j1 rule="para" parents="21954 32695"/>
    </justification>
  </clause>

  <clause id="32697">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (((K(x,K(y,z)) * u) * (L(K(x,K(y,z)) * u,w,v5) \ (K(x,K(y,z)) * u))) * v6) = (1 / L(u \ K(y,K(x,z)),w,v5)) * ((K(x,K(y,z)) * u) * v6)
    ]]></literal>
    <justification jstring="[para(7291(a,1),32696(a,2,1,2,1,2))].">
      <j1 rule="para" parents="7291 32696"/>
    </justification>
  </clause>

  <clause id="32698">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (((K(x,K(y,z)) * u) * (L(K(x,K(y,z)) * u,w,v5) \ (K(x,K(y,z)) * u))) * v6) = (L(1 / u,w,v5) \ K(x,K(y,z))) * ((K(x,K(y,z)) * u) * v6)
    ]]></literal>
    <justification jstring="[para(21958(a,1),32697(a,2,1))].">
      <j1 rule="para" parents="21958 32697"/>
    </justification>
  </clause>

  <clause id="32699">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (((K(x,K(y,z)) * u) * (L(K(x,K(y,z)) * u,w,v5) \ (K(x,K(y,z)) * u))) * v6) = (L(1 / u,w,v5) \ K(x,K(y,z))) * (K(x,K(y,z)) * (u * v6))
    ]]></literal>
    <justification jstring="[para(16846(a,1),32698(a,2,2))].">
      <j1 rule="para" parents="16846 32698"/>
    </justification>
  </clause>

  <clause id="32700">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (((K(x,K(y,z)) * u) * (L(K(x,K(y,z)) * u,w,v5) \ (K(x,K(y,z)) * u))) * v6) = (L(1 / u,w,v5) \ 1) * (u * v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,17081,a(flip),b,32699,a),flip(a)].">
      <j1 rule="hyper" parents="347 17081 32699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32702">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (((K(x,K(y,z)) * u) * (K(x,K(y,z)) * (L(K(x,K(y,z)) * u,w,v5) \ u))) * v6) = (L(1 / u,w,v5) \ 1) * (u * v6)
    ]]></literal>
    <justification jstring="[para(17000(a,1),32700(a,1,2,1,2))].">
      <j1 rule="para" parents="17000 32700"/>
    </justification>
  </clause>

  <clause id="32703">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (((K(x,K(y,z)) * u) * (K(x,K(y,z)) * (L(u,w,v5) \ (K(K(y,z),x) * u)))) * v6) = (L(1 / u,w,v5) \ 1) * (u * v6)
    ]]></literal>
    <justification jstring="[para(21270(a,1),32702(a,1,2,1,2,2))].">
      <j1 rule="para" parents="21270 32702"/>
    </justification>
  </clause>

  <clause id="32704">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (((K(x,K(y,z)) * u) * (K(x,K(y,z)) * (K(x,K(y,z)) * (L(u,w,v5) \ u)))) * v6) = (L(1 / u,w,v5) \ 1) * (u * v6)
    ]]></literal>
    <justification jstring="[para(17030(a,1),32703(a,1,2,1,2,2))].">
      <j1 rule="para" parents="17030 32703"/>
    </justification>
  </clause>

  <clause id="32705">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (((K(x,K(y,z)) * u) * (L(u,w,v5) \ u)) * v6) = (L(1 / u,w,v5) \ 1) * (u * v6)
    ]]></literal>
    <justification jstring="[para(7319(a,1),32704(a,1,2,1,2))].">
      <j1 rule="para" parents="7319 32704"/>
    </justification>
  </clause>

  <clause id="32707">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * ((K(x,K(y,z)) * (u * (L(u,w,v5) \ u))) * v6) = (L(1 / u,w,v5) \ 1) * (u * v6)
    ]]></literal>
    <justification jstring="[para(16846(a,1),32705(a,1,2,1))].">
      <j1 rule="para" parents="16846 32705"/>
    </justification>
  </clause>

  <clause id="32708">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * ((1 / L(u \ K(K(y,z),x),w,v5)) * v6) = (L(1 / u,w,v5) \ 1) * (u * v6)
    ]]></literal>
    <justification jstring="[para(21954(a,1),32707(a,1,2,1))].">
      <j1 rule="para" parents="21954 32707"/>
    </justification>
  </clause>

  <clause id="32709">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * ((1 / L(u \ K(y,K(x,z)),w,v5)) * v6) = (L(1 / u,w,v5) \ 1) * (u * v6)
    ]]></literal>
    <justification jstring="[para(7291(a,1),32708(a,1,2,1,2,1,2))].">
      <j1 rule="para" parents="7291 32708"/>
    </justification>
  </clause>

  <clause id="32710">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * ((L(1 / u,w,v5) \ K(x,K(y,z))) * v6) = (L(1 / u,w,v5) \ 1) * (u * v6)
    ]]></literal>
    <justification jstring="[para(21958(a,1),32709(a,1,2,1))].">
      <j1 rule="para" parents="21958 32709"/>
    </justification>
  </clause>

  <clause id="32711">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * ((L(1 / u,w,v5) \ K(x,K(y,z))) * v6)) = (L(1 / u,w,v5) \ 1) * (u * v6)
    ]]></literal>
    <justification jstring="[hyper(20093,a,32710,a)].">
      <j1 rule="hyper" parents="20093 32710"/>
    </justification>
  </clause>

  <clause id="32712">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * (x * u) = x * ((L(1 / x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(19224,a,32711,a),flip(a)].">
      <j1 rule="hyper" parents="19224 32711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32713">
    <literal><![CDATA[
      R((L(x,y,z) \ x) \ u,L(x,y,z) \ x,x * ((L(1 / x,y,z) \ 1) * L(x,y,z))) = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(32712(a,1),27352(a,1,3))].">
      <j1 rule="para" parents="32712 27352"/>
    </justification>
  </clause>

  <clause id="32714">
    <literal><![CDATA[
      R((L(x,y,z) \ x) \ u,L(x,y,z) \ x,x * (((1 / x) \ 1) * x)) = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(21389(a,1),32713(a,1,3,2))].">
      <j1 rule="para" parents="21389 32713"/>
    </justification>
  </clause>

  <clause id="32715">
    <literal><![CDATA[
      R((L(x,y,z) \ x) \ u,L(x,y,z) \ x,x * (x * x)) = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(83(a,1),32714(a,1,3,2,1))].">
      <j1 rule="para" parents="83 32714"/>
    </justification>
  </clause>

  <clause id="32717">
    <literal><![CDATA[
      R((L(x,y,z) \ x) \ u,L(x,y,z) \ x,x) = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(2186,a,32715,a)].">
      <j1 rule="hyper" parents="2186 32715"/>
    </justification>
  </clause>

  <clause id="32719">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,x * L(x,y,z),x) = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(26251,a,32717,a)].">
      <j1 rule="hyper" parents="26251 32717"/>
    </justification>
  </clause>

  <clause id="32721">
    <literal><![CDATA[
      L((L(x,y,z) \ x) \ u,x,x \ L(x,y,z)) = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3653,a(flip),b,32719,a)].">
      <j1 rule="hyper" parents="63 3653 32719"/>
    </justification>
  </clause>

  <clause id="32722">
    <literal><![CDATA[
      x * ((L(1 / x,y,z) \ 1) \ u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,28715,a(flip),b,32721,a),flip(a)].">
      <j1 rule="hyper" parents="63 28715 32721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32723">
    <literal><![CDATA[
      x * ((x * (L(x,y,z) \ x)) \ u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(63,a,3737,a(flip),b,32722,a)].">
      <j1 rule="hyper" parents="63 3737 32722"/>
    </justification>
  </clause>

  <clause id="32724">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) \ u = ((x \ u) / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(34,a,21007,a,b,32723,a),flip(a)].">
      <j1 rule="hyper" parents="34 21007 32723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32725">
    <literal><![CDATA[
      ((x \ y) / x) * L(x,z,u) = (x * a(u,z,x)) \ y
    ]]></literal>
    <justification jstring="[para(28838(a,2),32724(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="28838 32724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32727">
    <literal><![CDATA[
      L(x,y,(a(z,u,w) \ z) \ v5) = L(x,y,(z * a(w,u,z)) \ v5)
    ]]></literal>
    <justification jstring="[para(32725(a,1),30557(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32725 30557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32728">
    <literal><![CDATA[
      L(x,y,(a(z,u,w) \ z) \ v5) = L(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,28945,a(flip),b,32727,a),flip(a)].">
      <j1 rule="hyper" parents="347 28945 32727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32729">
    <literal><![CDATA[
      L(x,y,(a(z,u,w) * z) \ v5) = L(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,28662,a(flip),b,32728,a)].">
      <j1 rule="hyper" parents="63 28662 32728"/>
    </justification>
  </clause>

  <clause id="32730">
    <literal><![CDATA[
      L(x,y,R(z,u,w) \ v5) = L(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(28908(a,2),32729(a,1,3,1))].">
      <j1 rule="para" parents="28908 32729"/>
    </justification>
  </clause>

  <clause id="32731">
    <literal><![CDATA[
      R(x,y,z) \ (R((x \ 1) \ 1,y,z) * (L(u,R(x,y,z) \ 1,L(x,y,z) \ 1) \ 1)) = x \ ((x \ 1) \ (u \ 1))
    ]]></literal>
    <justification jstring="[para(32730(a,1),30744(a,1,2,2,1))].">
      <j1 rule="para" parents="32730 30744"/>
    </justification>
  </clause>

  <clause id="32732">
    <literal><![CDATA[
      R(x,y,z) \ (R((x \ 1) \ 1,y,z) * (L(u,R(x,y,z) \ 1,L(x \ 1,y,z)) \ 1)) = x \ ((x \ 1) \ (u \ 1))
    ]]></literal>
    <justification jstring="[para(27543(a,2),32731(a,1,2,2,1))].">
      <j1 rule="para" parents="27543 32731"/>
    </justification>
  </clause>

  <clause id="32733">
    <literal><![CDATA[
      R(x,y,z) \ (R((x \ 1) \ 1,y,z) * (L(u,R(x,y,z),L(x \ 1,y,z)) \ 1)) = x \ ((x \ 1) \ (u \ 1))
    ]]></literal>
    <justification jstring="[para(3188(a,1),32732(a,1,2,2,1))].">
      <j1 rule="para" parents="3188 32732"/>
    </justification>
  </clause>

  <clause id="32734">
    <literal><![CDATA[
      R(x,y,z) \ (R((x \ 1) \ 1,y,z) * (L(u,L(x,y,z),L(x \ 1,y,z)) \ 1)) = x \ ((x \ 1) \ (u \ 1))
    ]]></literal>
    <justification jstring="[para(21974(a,1),32733(a,1,2,2,1))].">
      <j1 rule="para" parents="21974 32733"/>
    </justification>
  </clause>

  <clause id="32735">
    <literal><![CDATA[
      R(x,y,z) \ (R((x \ 1) \ 1,y,z) * (L(u,x,x \ 1) \ 1)) = x \ ((x \ 1) \ (u \ 1))
    ]]></literal>
    <justification jstring="[para(27145(a,1),32734(a,1,2,2,1))].">
      <j1 rule="para" parents="27145 32734"/>
    </justification>
  </clause>

  <clause id="32736">
    <literal><![CDATA[
      K(x,x \ 1) * (L(y,x,x \ 1) \ 1) = x \ ((x \ 1) \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,21920,a(flip),b,32735,a)].">
      <j1 rule="hyper" parents="63 21920 32735"/>
    </justification>
  </clause>

  <clause id="32738">
    <literal><![CDATA[
      L(x,y,y \ 1) \ K(y,y \ 1) = y \ ((y \ 1) \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(2856,a,32736,a)].">
      <j1 rule="hyper" parents="2856 32736"/>
    </justification>
  </clause>

  <clause id="32739">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) \ 1 = x \ ((x \ 1) \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(63,a,3499,a(flip),b,32738,a)].">
      <j1 rule="hyper" parents="63 3499 32738"/>
    </justification>
  </clause>

  <clause id="32740">
    <literal><![CDATA[
      R(x,y * (((z \ ((z \ 1) \ (u \ 1))) * z) * w),v5) = R(x,(L(u * z,z,z) * w) * y,v5)
    ]]></literal>
    <justification jstring="[para(32739(a,1),22560(a,1,2,2,1,1))].">
      <j1 rule="para" parents="32739 22560"/>
    </justification>
  </clause>

  <clause id="32741">
    <literal><![CDATA[
      R(x,(L(y * z,z,z) * u) * w,v5) = R(x,w * (((z \ 1) \ T(y \ 1,z)) * u),v5)
    ]]></literal>
    <justification jstring="[para(1844(a,1),32740(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1844 32740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32742">
    <literal><![CDATA[
      R(x,(L(y * z,z,z) * u) * w,v5) = R(x,w * (u * ((z \ 1) \ (y \ 1))),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,22519,a(flip),b,32741,a),flip(a)].">
      <j1 rule="hyper" parents="347 22519 32741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32744">
    <literal><![CDATA[
      R(x,(L(y * z,z,z) * u) * w,v5) = R(x,w * (u * ((z \ 1) \ y)),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,22547,a(flip),b,32742,a),flip(a)].">
      <j1 rule="hyper" parents="347 22547 32742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32745">
    <literal><![CDATA[
      R(x,(L(y * z,z,z) * u) * w,v5) = R(x,w * (u * (z \ y)),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,25905,a(flip),b,32744,a),flip(a)].">
      <j1 rule="hyper" parents="347 25905 32744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32746">
    <literal><![CDATA[
      R(x,y * (z * L(u * w,w,w)),v5) = R(x,y * (z * (w \ u)),v5)
    ]]></literal>
    <justification jstring="[hyper(22477,a,32745,a)].">
      <j1 rule="hyper" parents="22477 32745"/>
    </justification>
  </clause>

  <clause id="35032">
    <literal><![CDATA[
      a(x,y,a(z,u,w \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w * v5)) = v6
    ]]></literal>
    <justification jstring="[para(31933(a,2),26564(a,1,3))].">
      <j1 rule="para" parents="31933 26564"/>
    </justification>
  </clause>

  <clause id="36384">
    <literal><![CDATA[
      T((x / (a(y,z,z) * u)) * a(y,z,z),u) = L(u,a(w,v5,v5),v6) \ x
    ]]></literal>
    <justification jstring="[para(32101(a,1),29741(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32101 29741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36394">
    <literal><![CDATA[
      T((x / (y * (L(L(y,y,z),y,z) \ u))) * a(z,y,y),a(z,y,y) * u) = L(a(z,y,y) * u,a(w,v5,v5),v6) \ x
    ]]></literal>
    <justification jstring="[para(28142(a,1),36384(a,1,1,1,2))].">
      <j1 rule="para" parents="28142 36384"/>
    </justification>
  </clause>

  <clause id="36398">
    <literal><![CDATA[
      T(((x / y) * (z \ L(L(z,z,u),z,u))) * a(u,z,z),a(u,z,z) * y) = L(a(u,z,z) * y,a(w,v5,v5),v6) \ x
    ]]></literal>
    <justification jstring="[para(27462(a,1),36394(a,1,1,1))].">
      <j1 rule="para" parents="27462 36394"/>
    </justification>
  </clause>

  <clause id="36401">
    <literal><![CDATA[
      T(a(x,y,y) \ (z / u),a(x,y,y) * u) = L(a(x,y,y) * u,a(w,v5,v5),v6) \ z
    ]]></literal>
    <attribute><![CDATA[
      label(flip_matches_hint)
    ]]></attribute>
    <justification jstring="[para(28086(a,1),36398(a,1,1))].">
      <j1 rule="para" parents="28086 36398"/>
    </justification>
  </clause>

  <clause id="36402">
    <literal><![CDATA[
      x / L(a(y,z,z) * u,a(w,v5,v5),v6) = a(y,z,z) \ (x / u)
    ]]></literal>
    <justification jstring="[hyper(19955,a,36401,a)].">
      <j1 rule="hyper" parents="19955 36401"/>
    </justification>
  </clause>

  <clause id="36403">
    <literal><![CDATA[
      x / (a(y,z,z) * u) = a(y,z,z) \ (x / u)
    ]]></literal>
    <justification jstring="[para(398(a,1),36402(a,1,2))].">
      <j1 rule="para" parents="398 36402"/>
    </justification>
  </clause>

  <clause id="36404">
    <literal><![CDATA[
      x / (y * a(z,u,u)) = a(z,u,u) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(20221,a,36403,a)].">
      <j1 rule="hyper" parents="20221 36403"/>
    </justification>
  </clause>

  <clause id="36405">
    <literal><![CDATA[
      (a(x,y,y) \ (z / (u * w))) * (a(x,y,y) * a(x,y,y)) = z / L(u * (a(x,y,y) \ w),a(x,y,y),a(x,y,y))
    ]]></literal>
    <justification jstring="[para(36403(a,1),32075(a,1,1))].">
      <j1 rule="para" parents="36403 32075"/>
    </justification>
  </clause>

  <clause id="36406">
    <literal><![CDATA[
      L(a(x,y,y) \ ((z * u) / w),w,a(x,y,y)) = (z * (a(x,y,y) \ u)) / w
    ]]></literal>
    <justification jstring="[para(36404(a,1),32077(a,1,1))].">
      <j1 rule="para" parents="36404 32077"/>
    </justification>
  </clause>

  <clause id="36407">
    <literal><![CDATA[
      (x * (a(y,z,z) \ u)) / w != v5
    ]]></literal>
    <literal><![CDATA[
      a(y,z,z) \ ((x * u) / w) = v5
    ]]></literal>
    <justification jstring="[para(36406(a,1),31792(a,1))].">
      <j1 rule="para" parents="36406 31792"/>
    </justification>
  </clause>

  <clause id="36408">
    <literal><![CDATA[
      a(x,y,y) \ (((z * u) * w) / (u * w)) = R(a(x,y,y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(36407,a,32178,a)].">
      <j1 rule="hyper" parents="36407 32178"/>
    </justification>
  </clause>

  <clause id="36409">
    <literal><![CDATA[
      R(a(x,y,y) \ z,u,w) = a(x,y,y) \ R(z,u,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),36408(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 36408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36410">
    <literal><![CDATA[
      R(a(x,y,y) \ z,u,w) * v5 = R(z,u,w) * (a(x,y,y) \ v5)
    ]]></literal>
    <justification jstring="[para(36409(a,2),32106(a,1,1))].">
      <j1 rule="para" parents="36409 32106"/>
    </justification>
  </clause>

  <clause id="36411">
    <literal><![CDATA[
      x * R(a(y,z,z) \ (x \ a(y,z,z)),u,w) = a((a(y,z,z) \ x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(36409(a,2),32073(a,1,2))].">
      <j1 rule="para" parents="36409 32073"/>
    </justification>
  </clause>

  <clause id="36412">
    <literal><![CDATA[
      a((a(x,y,y) \ z) \ 1,u,w) = z * R(z \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(29459(a,1),36411(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="29459 36411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36413">
    <literal><![CDATA[
      a((a(x,y,y) \ z) \ 1,u,w) = a(z \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,28909,a(flip),b,36412,a),flip(a)].">
      <j1 rule="hyper" parents="347 28909 36412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36416">
    <literal><![CDATA[
      a(x \ a(y,z,z),u,w) = a(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(32071,a,36413,a)].">
      <j1 rule="hyper" parents="32071 36413"/>
    </justification>
  </clause>

  <clause id="36417">
    <literal><![CDATA[
      a((x \ (y \ ((z \ (y \ z)) \ 1))) \ 1,u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(30352,a,36416,a),flip(a)].">
      <j1 rule="hyper" parents="30352 36416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36418">
    <literal><![CDATA[
      a((x \ ((y \ (x \ y)) \ 1)) \ z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(32071,a,36417,a)].">
      <j1 rule="hyper" parents="32071 36417"/>
    </justification>
  </clause>

  <clause id="36419">
    <literal><![CDATA[
      a(((x \ (y \ x)) * y) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[para(28202(a,1),36418(a,1,1))].">
      <j1 rule="para" parents="28202 36418"/>
    </justification>
  </clause>

  <clause id="36420">
    <literal><![CDATA[
      a(x * a(y,y,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24652,a(flip),b,36419,a)].">
      <j1 rule="hyper" parents="63 24652 36419"/>
    </justification>
  </clause>

  <clause id="36421">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(28017,a,36420,a)].">
      <j1 rule="hyper" parents="28017 36420"/>
    </justification>
  </clause>

  <clause id="36422">
    <literal><![CDATA[
      a(x * a(y,z,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(28015,a,36420,a)].">
      <j1 rule="hyper" parents="28015 36420"/>
    </justification>
  </clause>

  <clause id="36423">
    <literal><![CDATA[
      a(a(x,x,y) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(23925,a,36420,a)].">
      <j1 rule="hyper" parents="23925 36420"/>
    </justification>
  </clause>

  <clause id="36426">
    <literal><![CDATA[
      a(((x \ 1) * y) \ z,u,w) = a((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,31639,a(flip),b,36420,a),flip(a)].">
      <j1 rule="hyper" parents="63 31639 36420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36427">
    <literal><![CDATA[
      a(x * (y * R(z,z,y)),u,w) = a(x * (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(29547(a,1),36420(a,1,1))].">
      <j1 rule="para" parents="29547 36420"/>
    </justification>
  </clause>

  <clause id="36429">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(32291,a,36421,a)].">
      <j1 rule="hyper" parents="32291 36421"/>
    </justification>
  </clause>

  <clause id="36431">
    <literal><![CDATA[
      a(x,y,z) * (x * a(u,w,w)) = R(x * a(u,w,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,36422,a(flip),b,28907,a(flip))].">
      <j1 rule="hyper" parents="133 36422 28907"/>
    </justification>
  </clause>

  <clause id="36432">
    <literal><![CDATA[
      a(x,y,z) \ z != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x * a(w,v5,v5)) = u
    ]]></literal>
    <justification jstring="[para(36422(a,1),28866(a,1,1))].">
      <j1 rule="para" parents="36422 28866"/>
    </justification>
  </clause>

  <clause id="36438">
    <literal><![CDATA[
      a(x,a(y,z,z) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(32284,a,36429,a)].">
      <j1 rule="hyper" parents="32284 36429"/>
    </justification>
  </clause>

  <clause id="36440">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(26874,a,36429,a)].">
      <j1 rule="hyper" parents="26874 36429"/>
    </justification>
  </clause>

  <clause id="36441">
    <literal><![CDATA[
      a(x,y,z * a(u,w,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(24180,a,36429,a)].">
      <j1 rule="hyper" parents="24180 36429"/>
    </justification>
  </clause>

  <clause id="36442">
    <literal><![CDATA[
      a(x * (L(y,y,z) * u),w,v5) = a((y * u) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,32297,a(flip),b,36429,a)].">
      <j1 rule="hyper" parents="63 32297 36429"/>
    </justification>
  </clause>

  <clause id="36443">
    <literal><![CDATA[
      a(((x \ 1) \ y) * z,u,w) = a((y * x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,32294,a(flip),b,36429,a),flip(a)].">
      <j1 rule="hyper" parents="63 32294 36429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36444">
    <literal><![CDATA[
      a(x,y * L(z,u,u),w) = a(x,y * z,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,32287,a(flip),b,36429,a)].">
      <j1 rule="hyper" parents="63 32287 36429"/>
    </justification>
  </clause>

  <clause id="36447">
    <literal><![CDATA[
      a(x,(y * L(z,u,u)) * w,v5) = a(x,w * (z * y),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,32674,a(flip),b,36438,a),flip(a)].">
      <j1 rule="hyper" parents="63 32674 36438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36449">
    <literal><![CDATA[
      a(x,L(y,y,z) * u,w) = a(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(31816(a,1),36438(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31816 36438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36454">
    <literal><![CDATA[
      a(x,y,z * (u * a(w,w,v5))) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(29120(a,1),36440(a,1,3))].">
      <j1 rule="para" parents="29120 36440"/>
    </justification>
  </clause>

  <clause id="36455">
    <literal><![CDATA[
      a(x,y,L(z,u,u) * w) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(29362(a,1),36440(a,1,3)),flip(a)].">
      <j1 rule="para" parents="29362 36440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36456">
    <literal><![CDATA[
      a(x,y,z * L(u,w,w)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(29394(a,1),36440(a,1,3)),flip(a)].">
      <j1 rule="para" parents="29394 36440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36457">
    <literal><![CDATA[
      (a(x,x,y) * a(z,u,w)) \ w = L(a(x,x,y) \ w,u,z)
    ]]></literal>
    <justification jstring="[para(36440(a,1),32185(a,1,1,2))].">
      <j1 rule="para" parents="36440 32185"/>
    </justification>
  </clause>

  <clause id="36459">
    <literal><![CDATA[
      L(x,y,a(z,u,w * a(v5,v6,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,u,a(z,y,w)) = v7
    ]]></literal>
    <justification jstring="[para(36441(a,2),29903(a,1,3))].">
      <j1 rule="para" parents="36441 29903"/>
    </justification>
  </clause>

  <clause id="36460">
    <literal><![CDATA[
      a(x,y * (z \ u),w) = a(x,y * (z * u),w)
    ]]></literal>
    <justification jstring="[hyper(24488,a,36444,a),flip(a)].">
      <j1 rule="hyper" parents="24488 36444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36461">
    <literal><![CDATA[
      a(x,L(y,z,z) * u,w) = a(x,u * y,w)
    ]]></literal>
    <justification jstring="[hyper(23994,a,36444,a)].">
      <j1 rule="hyper" parents="23994 36444"/>
    </justification>
  </clause>

  <clause id="36463">
    <literal><![CDATA[
      a(x,y \ z,u) = a(x,y * z,u)
    ]]></literal>
    <justification jstring="[hyper(24348,a,36449,a)].">
      <j1 rule="hyper" parents="24348 36449"/>
    </justification>
  </clause>

  <clause id="36464">
    <literal><![CDATA[
      a(x,y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ z,u) = w
    ]]></literal>
    <justification jstring="[para(36449(a,1),24348(a,1))].">
      <j1 rule="para" parents="36449 24348"/>
    </justification>
  </clause>

  <clause id="36465">
    <literal><![CDATA[
      a(x,y * (y * z),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(26007,a,36463,a),flip(a)].">
      <j1 rule="hyper" parents="26007 36463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36475">
    <literal><![CDATA[
      a(x,y \ (x \ z),u) = a(x,(y * x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,32197,a(flip),b,36463,a)].">
      <j1 rule="hyper" parents="63 32197 36463"/>
    </justification>
  </clause>

  <clause id="36476">
    <literal><![CDATA[
      a(x,L((1 / T(y,z)) * u,y,y) * w,v5) = a(x,(y \ u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,31400,a(flip),b,36463,a),flip(a)].">
      <j1 rule="hyper" parents="63 31400 36463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36477">
    <literal><![CDATA[
      a(x,y * (L(z * u,u,u) * w),v5) = a(x,y \ (w * (u \ z)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,27698,a(flip),b,36463,a),flip(a)].">
      <j1 rule="hyper" parents="63 27698 36463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36480">
    <literal><![CDATA[
      a(x,y * z,u) \ u = L(u,y \ z,x)
    ]]></literal>
    <justification jstring="[para(36463(a,1),28841(a,2,1)),flip(a)].">
      <j1 rule="para" parents="36463 28841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36488">
    <literal><![CDATA[
      L(x,y \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,u) = w
    ]]></literal>
    <justification jstring="[para(36480(a,1),28866(a,1))].">
      <j1 rule="para" parents="36480 28866"/>
    </justification>
  </clause>

  <clause id="36490">
    <literal><![CDATA[
      a(x \ y,z,y * (u \ (x \ y))) = a(x \ y,z,x * u)
    ]]></literal>
    <justification jstring="[hyper(31375,a,36455,a),flip(a)].">
      <j1 rule="hyper" parents="31375 36455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36491">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * u)) = a(x,y,w * z)
    ]]></literal>
    <justification jstring="[hyper(25254,a,36455,a)].">
      <j1 rule="hyper" parents="25254 36455"/>
    </justification>
  </clause>

  <clause id="36492">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * w)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(25253,a,36455,a)].">
      <j1 rule="hyper" parents="25253 36455"/>
    </justification>
  </clause>

  <clause id="36494">
    <literal><![CDATA[
      a(x,y,z * (u \ w)) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,25321,a(flip),b,36456,a)].">
      <j1 rule="hyper" parents="63 25321 36456"/>
    </justification>
  </clause>

  <clause id="36495">
    <literal><![CDATA[
      a(x,y,z * (u \ w)) = a(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,25318,a(flip),b,36456,a)].">
      <j1 rule="hyper" parents="63 25318 36456"/>
    </justification>
  </clause>

  <clause id="36497">
    <literal><![CDATA[
      a(x,L(y,z,z) * u,w) = a(x,y * u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24037,a,b,36461,a),flip(a)].">
      <j1 rule="hyper" parents="347 24037 36461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36498">
    <literal><![CDATA[
      a(x,L(y,z,z) * (((u * (w * y)) / (u * y)) * u),v5) = a(x,u * (R(w,u,y) * y),v5)
    ]]></literal>
    <justification jstring="[para(1743(a,1),36461(a,2,2))].">
      <j1 rule="para" parents="1743 36461"/>
    </justification>
  </clause>

  <clause id="36506">
    <literal><![CDATA[
      a(x,L(y,z,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u * y,w) = v5
    ]]></literal>
    <justification jstring="[para(36497(a,2),23994(a,1))].">
      <j1 rule="para" parents="36497 23994"/>
    </justification>
  </clause>

  <clause id="36507">
    <literal><![CDATA[
      a(x,y * (z \ u),w) = a(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24046,a,b,36460,a),flip(a)].">
      <j1 rule="hyper" parents="347 24046 36460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36509">
    <literal><![CDATA[
      a(x,y * (z * a(u,w,z * (y \ z))),v5) = a(x,z * L(y,w,u),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,30921,a(flip),b,36460,a),flip(a)].">
      <j1 rule="hyper" parents="63 30921 36460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36510">
    <literal><![CDATA[
      a(x,y * (z \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y * (u * z),w) = v5
    ]]></literal>
    <justification jstring="[para(36460(a,2),24006(a,1))].">
      <j1 rule="para" parents="36460 24006"/>
    </justification>
  </clause>

  <clause id="36511">
    <literal><![CDATA[
      a(x,y * (L(y,z,u) * w),v5) = a(x,w * a(u,z,y),v5)
    ]]></literal>
    <justification jstring="[para(31810(a,1),36460(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31810 36460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36512">
    <literal><![CDATA[
      a(x,y \ (x \ z),u) = a(x,(x * y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(347,a,24318,a,b,36475,a),flip(a)].">
      <j1 rule="hyper" parents="347 24318 36475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36515">
    <literal><![CDATA[
      a(x,y,z * (y * x)) = a(x,y,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(31016,a,36494,a)].">
      <j1 rule="hyper" parents="31016 36494"/>
    </justification>
  </clause>

  <clause id="36519">
    <literal><![CDATA[
      L(x,y,a(z * (u * w),v5,u)) = L(x,y,a(u,v5,w * (u * z)))
    ]]></literal>
    <justification jstring="[para(36494(a,1),30859(a,2,3))].">
      <j1 rule="para" parents="36494 30859"/>
    </justification>
  </clause>

  <clause id="36520">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * ((w * R(u,z,z)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(w * u) * v5) = v6
    ]]></literal>
    <justification jstring="[para(36494(a,1),32335(a,1))].">
      <j1 rule="para" parents="36494 32335"/>
    </justification>
  </clause>

  <clause id="36521">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (w * (u * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w * (L(u,z,z) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(36494(a,1),32437(a,1))].">
      <j1 rule="para" parents="36494 32437"/>
    </justification>
  </clause>

  <clause id="36522">
    <literal><![CDATA[
      a(x,y,(z * x) * u) = a(x,y,x * (u * z))
    ]]></literal>
    <justification jstring="[hyper(32169,a,36495,a)].">
      <j1 rule="hyper" parents="32169 36495"/>
    </justification>
  </clause>

  <clause id="36523">
    <literal><![CDATA[
      a(x,y,(x * z) * u) = a(x,y,x * (u * z))
    ]]></literal>
    <justification jstring="[hyper(32166,a,36495,a)].">
      <j1 rule="hyper" parents="32166 36495"/>
    </justification>
  </clause>

  <clause id="36524">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((w * u) * (z * w))) = a(x,y,a(w,z,u * z))
    ]]></literal>
    <justification jstring="[hyper(30825,a,36495,a),flip(a)].">
      <j1 rule="hyper" parents="30825 36495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36525">
    <literal><![CDATA[
      a(x \ (y \ (z * (x * y))),u,w * (v5 * v6)) = a(z,u,L(w * (v6 \ v5),x,y))
    ]]></literal>
    <justification jstring="[hyper(30012,a,36495,a),flip(a)].">
      <j1 rule="hyper" parents="30012 36495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36526">
    <literal><![CDATA[
      a(x,y,z * (u / w)) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(24207,a,36495,a)].">
      <j1 rule="hyper" parents="24207 36495"/>
    </justification>
  </clause>

  <clause id="36529">
    <literal><![CDATA[
      a(x,y,z * (L(u,z,z) * y)) = a(x,y,(u * z) * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,32649,a(flip),b,36495,a),flip(a)].">
      <j1 rule="hyper" parents="63 32649 36495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36530">
    <literal><![CDATA[
      a(x,y,(z * u) * ((u * w) * (z \ w))) = a(x,y,a(w * z,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,31959,a(flip),b,36495,a),flip(a)].">
      <j1 rule="hyper" parents="63 31959 36495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36531">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((u * w) * (w * z))) = a(x,y,a(w,z,u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,29648,a(flip),b,36495,a),flip(a)].">
      <j1 rule="hyper" parents="63 29648 36495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36533">
    <literal><![CDATA[
      L(x,y,a(z,u,(x * w) * v5)) = L(x,y,a(z,u,w * (v5 * x)))
    ]]></literal>
    <justification jstring="[para(36495(a,1),30470(a,2,3))].">
      <j1 rule="para" parents="36495 30470"/>
    </justification>
  </clause>

  <clause id="36534">
    <literal><![CDATA[
      a((x * y) * z,u,a(x,w,v5)) = a(x,w,a(v5,u,y * (z * x)))
    ]]></literal>
    <justification jstring="[para(36495(a,1),30845(a,2,3))].">
      <j1 rule="para" parents="36495 30845"/>
    </justification>
  </clause>

  <clause id="36535">
    <literal><![CDATA[
      a(x * (y * z),u,a(z,w,v5)) = a(z,u,a(v5,w,y * (x * z)))
    ]]></literal>
    <justification jstring="[para(36495(a,1),30850(a,2,3))].">
      <j1 rule="para" parents="36495 30850"/>
    </justification>
  </clause>

  <clause id="36536">
    <literal><![CDATA[
      ((x * y) \ (y * z)) * L(T(L(x \ z,x,y) \ z,y),u,w) = a(w,u,z * ((y * z) * (x * y))) \ z
    ]]></literal>
    <justification jstring="[para(36495(a,1),32155(a,2,1))].">
      <j1 rule="para" parents="36495 32155"/>
    </justification>
  </clause>

  <clause id="36538">
    <literal><![CDATA[
      a(x,x * ((a(y,x,x) \ z) * u),u) = a(x,(L(x,x,y) \ z) * u,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,30208,a(flip),b,36507,a),flip(a)].">
      <j1 rule="hyper" parents="63 30208 36507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36540">
    <literal><![CDATA[
      a(x,a(y,z,u),w * (v5 \ v6)) * L(u,z,a(x,w * (v6 * v5),y)) = L(u,z,a(w * (v5 \ v6),x,y))
    ]]></literal>
    <justification jstring="[para(36507(a,1),31249(a,1,2,3))].">
      <j1 rule="para" parents="36507 31249"/>
    </justification>
  </clause>

  <clause id="36541">
    <literal><![CDATA[
      L(x,a(y,z * (L(u,z,y) * y),w),v5) = L(x,a(y,z * u,w),v5)
    ]]></literal>
    <justification jstring="[para(36507(a,1),32467(a,1,2))].">
      <j1 rule="para" parents="36507 32467"/>
    </justification>
  </clause>

  <clause id="36542">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (y * z))) = a(x,u,a(z,y,z * (y * w)))
    ]]></literal>
    <justification jstring="[para(36515(a,1),29839(a,1,3)),flip(a)].">
      <j1 rule="para" parents="36515 29839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36543">
    <literal><![CDATA[
      a(x,y,z * (x * u)) = a(x,y,x * (z * u))
    ]]></literal>
    <justification jstring="[hyper(24297,a,36522,a)].">
      <j1 rule="hyper" parents="24297 36522"/>
    </justification>
  </clause>

  <clause id="36544">
    <literal><![CDATA[
      a(x,y,y * (z * x)) = a(x,y,x * (z * y))
    ]]></literal>
    <justification jstring="[hyper(31025,a,36543,a)].">
      <j1 rule="hyper" parents="31025 36543"/>
    </justification>
  </clause>

  <clause id="36545">
    <literal><![CDATA[
      L(x,y,a(z,u,w * (z * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,u,a(z,y,z * (w * v5))) = v6
    ]]></literal>
    <justification jstring="[para(36543(a,2),29903(a,1,3))].">
      <j1 rule="para" parents="36543 29903"/>
    </justification>
  </clause>

  <clause id="36546">
    <literal><![CDATA[
      a(x,y,(z \ u) * w) = a(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(30862,a,36454,a),flip(a)].">
      <j1 rule="hyper" parents="30862 36454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36547">
    <literal><![CDATA[
      a(x,y,z * a(u,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(36454(a,1),14920(a,1))].">
      <j1 rule="para" parents="36454 14920"/>
    </justification>
  </clause>

  <clause id="36548">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(26876(a,2),36547(a,1))].">
      <j1 rule="para" parents="26876 36547"/>
    </justification>
  </clause>

  <clause id="36550">
    <literal><![CDATA[
      a(((x \ 1) * y) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z * (x \ y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(32295(a,1),36548(a,1))].">
      <j1 rule="para" parents="32295 36548"/>
    </justification>
  </clause>

  <clause id="36553">
    <literal><![CDATA[
      a((((x * y) \ y) \ y) \ z,u,w) = a(((x \ 1) \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,27991,a(flip),b,36426,a),flip(a)].">
      <j1 rule="hyper" parents="63 27991 36426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36554">
    <literal><![CDATA[
      L(x,y,z * a(u,w,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36432,a,28841,a(flip))].">
      <j1 rule="hyper" parents="36432 28841"/>
    </justification>
  </clause>

  <clause id="36555">
    <literal><![CDATA[
      L(x,y,(((z * u) \ u) \ 1) \ w) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[hyper(32191,a,36554,a),flip(a)].">
      <j1 rule="hyper" parents="32191 36554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36556">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z * u) \ w) = v5
    ]]></literal>
    <justification jstring="[para(36554(a,1),29611(a,1))].">
      <j1 rule="para" parents="36554 29611"/>
    </justification>
  </clause>

  <clause id="36558">
    <literal><![CDATA[
      a((x \ y) * z,u,a(w,v5,v6)) = a((y * x) * z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(32458,a,36443,a)].">
      <j1 rule="hyper" parents="32458 36443"/>
    </justification>
  </clause>

  <clause id="36560">
    <literal><![CDATA[
      a((x * (y \ 1)) * z,u,w) = a((y \ x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24457,a(flip),b,36443,a),flip(a)].">
      <j1 rule="hyper" parents="63 24457 36443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36561">
    <literal><![CDATA[
      a(x,y,a((z \ u) * w,v5,v6)) = a(x,y,a((u * z) * w,v5,v6))
    ]]></literal>
    <justification jstring="[para(36443(a,1),25016(a,1,3)),flip(a)].">
      <j1 rule="para" parents="36443 25016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36562">
    <literal><![CDATA[
      a((x * y) * z,u,a(w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a((y \ x) * z,u,a(w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(36443(a,1),32458(a,1))].">
      <j1 rule="para" parents="36443 32458"/>
    </justification>
  </clause>

  <clause id="36563">
    <literal><![CDATA[
      a(x,y \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y * z,u) = w
    ]]></literal>
    <justification jstring="[para(26009(a,1),36506(a,1))].">
      <j1 rule="para" parents="26009 36506"/>
    </justification>
  </clause>

  <clause id="36565">
    <literal><![CDATA[
      L(x,y,z * ((u * w) \ w)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(32087,a,36555,a)].">
      <j1 rule="hyper" parents="32087 36555"/>
    </justification>
  </clause>

  <clause id="36567">
    <literal><![CDATA[
      L(x,y,z * (u \ (w \ u))) = L(x,y,w \ z)
    ]]></literal>
    <justification jstring="[hyper(22881,a,36565,a)].">
      <j1 rule="hyper" parents="22881 36565"/>
    </justification>
  </clause>

  <clause id="36569">
    <literal><![CDATA[
      L(x,y,(z * ((z * u) \ z)) \ w) = L(x,y,w * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,22386,a(flip),b,36567,a),flip(a)].">
      <j1 rule="hyper" parents="63 22386 36567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36571">
    <literal><![CDATA[
      a(x,y,a((z * (u \ 1)) * w,v5,v6)) * a(x,(z * (u \ 1)) * w,a(y,v5,v6)) = a((u \ z) * w,a(v6,v5,x),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,31238,a,b,36560,a)].">
      <j1 rule="hyper" parents="63 31238 36560"/>
    </justification>
  </clause>

  <clause id="36572">
    <literal><![CDATA[
      a(x * (y * L(z,z,y)),u,w) = a(x * (y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(26409,a,36427,a)].">
      <j1 rule="hyper" parents="26409 36427"/>
    </justification>
  </clause>

  <clause id="36574">
    <literal><![CDATA[
      a((L(x,x,y) * z) * u,w,v5) = a((x * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(23925,a,36442,a)].">
      <j1 rule="hyper" parents="23925 36442"/>
    </justification>
  </clause>

  <clause id="36576">
    <literal><![CDATA[
      a(x,y * ((z \ u) * w),v5) = a(x,y * ((u * z) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,27686,a(flip),b,36447,a)].">
      <j1 rule="hyper" parents="63 27686 36447"/>
    </justification>
  </clause>

  <clause id="36577">
    <literal><![CDATA[
      a(x,y \ (z \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y * (u * z),w) = v5
    ]]></literal>
    <justification jstring="[para(36463(a,2),36510(a,1))].">
      <j1 rule="para" parents="36463 36510"/>
    </justification>
  </clause>

  <clause id="36579">
    <literal><![CDATA[
      a(x * (y / (z \ 1)),u,w) = a(x * (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(2008(a,1),36572(a,1,1,2))].">
      <j1 rule="para" parents="2008 36572"/>
    </justification>
  </clause>

  <clause id="36580">
    <literal><![CDATA[
      a(x * ((y \ 1) \ z),u,w) = a(x * (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(23983,a,36579,a)].">
      <j1 rule="hyper" parents="23983 36579"/>
    </justification>
  </clause>

  <clause id="36581">
    <literal><![CDATA[
      a(x * (x * (y * (x \ z))),u,w) = a(y * (z * x),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,32086,a,b,36580,a)].">
      <j1 rule="hyper" parents="63 32086 36580"/>
    </justification>
  </clause>

  <clause id="36582">
    <literal><![CDATA[
      a((L(x \ 1,x \ 1,y) * (x * (z * (x \ 1)))) * u,w,v5) = a((L(z,x,x) * (x \ 1)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(3212(a,1),36574(a,2,1,1))].">
      <j1 rule="para" parents="3212 36574"/>
    </justification>
  </clause>

  <clause id="36583">
    <literal><![CDATA[
      a(x,(x * y) * z,u) = a(x,y * (z * x),u)
    ]]></literal>
    <justification jstring="[hyper(36577,a,36512,a),flip(a)].">
      <j1 rule="hyper" parents="36577 36512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36584">
    <literal><![CDATA[
      a(x,(y * x) * z,u) = a(x,y * (z * x),u)
    ]]></literal>
    <justification jstring="[hyper(36577,a,36475,a),flip(a)].">
      <j1 rule="hyper" parents="36577 36475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36585">
    <literal><![CDATA[
      a(x,y * ((z * (u * (a(w,v5,w) \ y))) * u),v6) = a(x,L(z,y,u),v6)
    ]]></literal>
    <justification jstring="[hyper(36577,a,28601,a)].">
      <j1 rule="hyper" parents="36577 28601"/>
    </justification>
  </clause>

  <clause id="36586">
    <literal><![CDATA[
      a(x,(x * y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y * (z * x),u) = w
    ]]></literal>
    <justification jstring="[para(36512(a,1),36577(a,1))].">
      <j1 rule="para" parents="36512 36577"/>
    </justification>
  </clause>

  <clause id="36587">
    <literal><![CDATA[
      R(x * a(y,z,z),u,w) = R(x,u,w) * a(y,z,z)
    ]]></literal>
    <justification jstring="[hyper(31850,a,36431,a),flip(a)].">
      <j1 rule="hyper" parents="31850 36431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36588">
    <literal><![CDATA[
      a(R((x * (1 / y)) * a(z,u,u),y,y),w,v5) = a(a(z,u,u) \ (y \ x),w,v5)
    ]]></literal>
    <justification jstring="[para(36587(a,2),32276(a,1,1))].">
      <j1 rule="para" parents="36587 32276"/>
    </justification>
  </clause>

  <clause id="36589">
    <literal><![CDATA[
      L(a(x,x,y) \ z,u,w) = a(x,x,y) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,32489,a(flip),b,36457,a),flip(a)].">
      <j1 rule="hyper" parents="63 32489 36457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36591">
    <literal><![CDATA[
      x \ (x * L(a(y,y,z) \ (z * (L(L(z,y,y),y,y) \ u)),w,v5)) = L(a(y,y,z) * L(u,w,v5),a(y,y,z),x)
    ]]></literal>
    <justification jstring="[para(36589(a,2),32475(a,1,2,2))].">
      <j1 rule="para" parents="36589 32475"/>
    </justification>
  </clause>

  <clause id="36592">
    <literal><![CDATA[
      a(x \ y,z,y * ((x \ y) * u)) = a(x \ y,z,x * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,36495,a(flip),b,36490,a)].">
      <j1 rule="hyper" parents="63 36495 36490"/>
    </justification>
  </clause>

  <clause id="36593">
    <literal><![CDATA[
      a(x,y * (L(y,z,u) * w),v5) = a(x,w * a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,31388,a,b,36511,a),flip(a)].">
      <j1 rule="hyper" parents="347 31388 36511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36594">
    <literal><![CDATA[
      L(x \ 1,y,a(z,u * a(w,v5,x),v6)) = L(x \ 1,y,a(z,u,v6))
    ]]></literal>
    <justification jstring="[para(36511(a,1),32441(a,1,3))].">
      <j1 rule="para" parents="36511 32441"/>
    </justification>
  </clause>

  <clause id="36597">
    <literal><![CDATA[
      L(x,y,(z \ u) \ w) = L(x,y,w * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(63,a,21563,a(flip),b,36569,a)].">
      <j1 rule="hyper" parents="63 21563 36569"/>
    </justification>
  </clause>

  <clause id="36600">
    <literal><![CDATA[
      a(x,y * ((z / u) * w),v5) = a(x,y * ((z * u) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24252,a,b,36576,a)].">
      <j1 rule="hyper" parents="63 24252 36576"/>
    </justification>
  </clause>

  <clause id="36601">
    <literal><![CDATA[
      a(x * (y \ z),u,a(w,v5,v6)) = a(x * (z * y),u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,30780,a(flip),b,36581,a)].">
      <j1 rule="hyper" parents="63 30780 36581"/>
    </justification>
  </clause>

  <clause id="36602">
    <literal><![CDATA[
      a(x,y,a(z * (u \ w),v5,v6)) = a(x,y,a(z * (w * u),v5,v6))
    ]]></literal>
    <justification jstring="[para(36581(a,1),30782(a,1,3)),flip(a)].">
      <j1 rule="para" parents="36581 30782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36603">
    <literal><![CDATA[
      a(x,y,a(z,L(x,u,w) * v5,v6)) = a(v6,y,a(x,v5 * a(x,u,w),z))
    ]]></literal>
    <justification jstring="[para(36593(a,1),32384(a,1,3)),flip(a)].">
      <j1 rule="para" parents="36593 32384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36604">
    <literal><![CDATA[
      a(x,y * ((z * u) * u),w) = a(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),36600(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 36600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36605">
    <literal><![CDATA[
      a(x,(y * (z * y)) * u,w) = a(x,u * z,w)
    ]]></literal>
    <justification jstring="[hyper(24247,a,36604,a)].">
      <j1 rule="hyper" parents="24247 36604"/>
    </justification>
  </clause>

  <clause id="36607">
    <literal><![CDATA[
      L(x,y,(z * u) \ 1) = L(x,y,z \ (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(36556,a,30666,a)].">
      <j1 rule="hyper" parents="36556 30666"/>
    </justification>
  </clause>

  <clause id="36608">
    <literal><![CDATA[
      L(x,y,(z * (u \ (z \ 1))) \ w) = L(x,y,(z \ (u \ z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(36556,a,21905,a)].">
      <j1 rule="hyper" parents="36556 21905"/>
    </justification>
  </clause>

  <clause id="36609">
    <literal><![CDATA[
      L(x,y,((z \ a(u,w,u)) \ v5) \ v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z * v5) \ v6) = v7
    ]]></literal>
    <justification jstring="[para(27314(a,2),36556(a,1))].">
      <j1 rule="para" parents="27314 36556"/>
    </justification>
  </clause>

  <clause id="36612">
    <literal><![CDATA[
      L(x,y,a(z,u * z,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(32380(a,1),36459(a,1))].">
      <j1 rule="para" parents="32380 36459"/>
    </justification>
  </clause>

  <clause id="36613">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (y * z))) = a(x,u,a(z,y,z * (w * y)))
    ]]></literal>
    <justification jstring="[para(24082(a,1),36542(a,2,3))].">
      <j1 rule="para" parents="24082 36542"/>
    </justification>
  </clause>

  <clause id="36614">
    <literal><![CDATA[
      a(((x \ 1) \ y) \ z,u,w) = a((x * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(23960,a,36553,a),flip(a)].">
      <j1 rule="hyper" parents="23960 36553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36615">
    <literal><![CDATA[
      a(x * (y * y),z,a(u,w,v5)) = a(x,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(188(a,1),36601(a,1,1)),flip(a)].">
      <j1 rule="para" parents="188 36601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36616">
    <literal><![CDATA[
      a(x,y,a((z * u) * x,w,v5)) = a(x,y,a(z * (x * u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(31372,a,36602,a)].">
      <j1 rule="hyper" parents="31372 36602"/>
    </justification>
  </clause>

  <clause id="36617">
    <literal><![CDATA[
      L(x,y,(z \ ((z * u) \ z)) \ w) = L(x,y,(u \ (z \ 1)) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,26063,a(flip),b,36608,a),flip(a)].">
      <j1 rule="hyper" parents="63 26063 36608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36618">
    <literal><![CDATA[
      a(x,y,a(z,u,z * (w * u))) * z = L(z,y,a(x,u,w * (u * z)))
    ]]></literal>
    <justification jstring="[para(36613(a,1),29877(a,1,1))].">
      <j1 rule="para" parents="36613 29877"/>
    </justification>
  </clause>

  <clause id="36619">
    <literal><![CDATA[
      L(x,y,z * (((u * w) \ u) \ u)) = L(x,y,(w \ (u \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,36597,a(flip),b,36617,a)].">
      <j1 rule="hyper" parents="63 36597 36617"/>
    </justification>
  </clause>

  <clause id="36620">
    <literal><![CDATA[
      L(x,y,(z \ (u \ 1)) \ w) = L(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(21530,a,36619,a),flip(a)].">
      <j1 rule="hyper" parents="21530 36619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36621">
    <literal><![CDATA[
      L(x,y,z * ((u \ 1) \ w)) = L(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36597,a(flip),b,36620,a)].">
      <j1 rule="hyper" parents="63 36597 36620"/>
    </justification>
  </clause>

  <clause id="36622">
    <literal><![CDATA[
      a(x,y,L(z,u,w * (v5 \ v6))) = a(x,y,L(z,u,w * (v5 * v6)))
    ]]></literal>
    <justification jstring="[para(36621(a,1),24918(a,1,3)),flip(a)].">
      <j1 rule="para" parents="36621 24918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36623">
    <literal><![CDATA[
      a(x,y,L(z,u,a(x,y,z) * (u * w))) \ w = u * ((u * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(36622(a,1),30590(a,1,1))].">
      <j1 rule="para" parents="36622 30590"/>
    </justification>
  </clause>

  <clause id="36624">
    <literal><![CDATA[
      a(x,y * ((1 / T(z,u)) * w),v5) = a(x,(z \ w) \ y,v5)
    ]]></literal>
    <justification jstring="[hyper(36506,a,36476,a)].">
      <j1 rule="hyper" parents="36506 36476"/>
    </justification>
  </clause>

  <clause id="36625">
    <literal><![CDATA[
      a(x,y * ((T(z,u) \ 1) * w),v5) = a(x,(z \ w) \ y,v5)
    ]]></literal>
    <justification jstring="[hyper(24417,a,36624,a)].">
      <j1 rule="hyper" parents="24417 36624"/>
    </justification>
  </clause>

  <clause id="36627">
    <literal><![CDATA[
      a(x,y * (T(z,u) * w),v5) = a(x,(z \ w) \ y,v5)
    ]]></literal>
    <justification jstring="[hyper(24724,a,36625,a)].">
      <j1 rule="hyper" parents="24724 36625"/>
    </justification>
  </clause>

  <clause id="36628">
    <literal><![CDATA[
      a(x,(y \ z) \ u,w) = a(x,(y * z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(24475,a,36627,a),flip(a)].">
      <j1 rule="hyper" parents="24475 36627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36629">
    <literal><![CDATA[
      a(x,(y \ z) * u,w) = a(x,(y * z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(36563,a,36628,a)].">
      <j1 rule="hyper" parents="36563 36628"/>
    </justification>
  </clause>

  <clause id="36630">
    <literal><![CDATA[
      a(x,(y \ z) * u,w) = a(x,(z * y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,24318,a,b,36629,a),flip(a)].">
      <j1 rule="hyper" parents="347 24318 36629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36631">
    <literal><![CDATA[
      a(x,y * (z * a(u \ 1,w,v5)),v6) = a(x,(a(v5,w,u) * z) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,32689,a,b,36629,a)].">
      <j1 rule="hyper" parents="63 32689 36629"/>
    </justification>
  </clause>

  <clause id="36632">
    <literal><![CDATA[
      a((x * y) \ z,u,a(L(w,y,x),((x * y) * z) * v5,v6)) = a(v6,u,a(y \ (x \ z),v5,w))
    ]]></literal>
    <justification jstring="[para(36629(a,1),32393(a,1,3))].">
      <j1 rule="para" parents="36629 32393"/>
    </justification>
  </clause>

  <clause id="36635">
    <literal><![CDATA[
      a(x,(y \ z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,(y * z) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(36630(a,2),24008(a,1))].">
      <j1 rule="para" parents="36630 24008"/>
    </justification>
  </clause>

  <clause id="36636">
    <literal><![CDATA[
      a(x,y,(z * u) * ((w * u) * (z * w))) = a(x,y,a(w,z,u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,36546,a(flip),b,36524,a)].">
      <j1 rule="hyper" parents="63 36546 36524"/>
    </justification>
  </clause>

  <clause id="36637">
    <literal><![CDATA[
      a(x,y,(z * u) * ((u * w) * (w * z))) = a(x,y,a(w,z,u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,36546,a(flip),b,36531,a)].">
      <j1 rule="hyper" parents="63 36546 36531"/>
    </justification>
  </clause>

  <clause id="36638">
    <literal><![CDATA[
      a(x,y,a(z,u * a(w,v5,x),v6)) = x * L(x \ 1,y,a(z,u,v6))
    ]]></literal>
    <justification jstring="[para(36594(a,1),29222(a,1,2)),flip(a)].">
      <j1 rule="para" parents="36594 29222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36639">
    <literal><![CDATA[
      a(x,y,a(z,u * a(w,v5,x),v6)) = x \ L(x,y,a(z,u,v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,3343,a(flip),b,36638,a),flip(a)].">
      <j1 rule="hyper" parents="347 3343 36638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36640">
    <literal><![CDATA[
      a(x,y,a(z,u * a(w,v5,x),v6)) = a(z,u,a(x,y,v6))
    ]]></literal>
    <justification jstring="[hyper(29880,a,36639,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="29880 36639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36641">
    <literal><![CDATA[
      a(x,y,a(z,u * a(w,v5,z),v6)) = a(x,u,a(z,y,v6))
    ]]></literal>
    <justification jstring="[hyper(29857,a,36640,a)].">
      <j1 rule="hyper" parents="29857 36640"/>
    </justification>
  </clause>

  <clause id="36642">
    <literal><![CDATA[
      a(x,a(y,z,u) * w,a(u,v5,v6)) = a(v6,w,a(u,v5,x))
    ]]></literal>
    <justification jstring="[hyper(29810,a,36640,a)].">
      <j1 rule="hyper" parents="29810 36640"/>
    </justification>
  </clause>

  <clause id="36643">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),z * a(v5,v6,u),a(y,w,u)) = L(x,a(u,z * a(v5,v6,u),y),w)
    ]]></literal>
    <justification jstring="[para(36640(a,1),29988(a,1,1,2))].">
      <j1 rule="para" parents="36640 29988"/>
    </justification>
  </clause>

  <clause id="36644">
    <literal><![CDATA[
      a(x,(1 / (y * z)) \ a(u,w,y),v5) = a(x,z * L(y,w,u),v5)
    ]]></literal>
    <justification jstring="[para(29430(a,1),36509(a,1,2))].">
      <j1 rule="para" parents="29430 36509"/>
    </justification>
  </clause>

  <clause id="36646">
    <literal><![CDATA[
      a(x,(y * z) * a(u,w,y),v5) = a(x,z * L(y,w,u),v5)
    ]]></literal>
    <justification jstring="[para(31733(a,1),36644(a,1,2))].">
      <j1 rule="para" parents="31733 36644"/>
    </justification>
  </clause>

  <clause id="36648">
    <literal><![CDATA[
      a(x,y * (z * a(u,w,y)),v5) = a(x,z * L(y,w,u),v5)
    ]]></literal>
    <justification jstring="[para(12362(a,1),36646(a,1,2))].">
      <j1 rule="para" parents="12362 36646"/>
    </justification>
  </clause>

  <clause id="36649">
    <literal><![CDATA[
      a(x,y,a(z,u * L(x,w,v5),v6)) = a(v6,y,a(x,u * a(v5,w,x),z))
    ]]></literal>
    <justification jstring="[para(36648(a,1),32390(a,1,3))].">
      <j1 rule="para" parents="36648 32390"/>
    </justification>
  </clause>

  <clause id="36650">
    <literal><![CDATA[
      a(x,(L(x,x,y) \ z) * u,u) = a(x,L(x,x,y) * (z * u),u)
    ]]></literal>
    <justification jstring="[para(31822(a,1),36538(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31822 36538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36651">
    <literal><![CDATA[
      a(x,(L(x,x,y) \ z) * u,u) = a(x,x * (z * u),u)
    ]]></literal>
    <justification jstring="[hyper(347,a,36449,a(flip),b,36650,a),flip(a)].">
      <j1 rule="hyper" parents="347 36449 36650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36652">
    <literal><![CDATA[
      a(x,(L(x,x,y) * z) * u,u) = a(x,x * (z * u),u)
    ]]></literal>
    <justification jstring="[hyper(36635,a,36651,a)].">
      <j1 rule="hyper" parents="36635 36651"/>
    </justification>
  </clause>

  <clause id="36654">
    <literal><![CDATA[
      a(x,(x * y) * z,z) = a(x,x * (y * z),z)
    ]]></literal>
    <justification jstring="[hyper(24649,a,36652,a)].">
      <j1 rule="hyper" parents="24649 36652"/>
    </justification>
  </clause>

  <clause id="36655">
    <literal><![CDATA[
      a(x,y * (z * x),z) = a(x,x * (y * z),z)
    ]]></literal>
    <justification jstring="[hyper(36586,a,36654,a)].">
      <j1 rule="hyper" parents="36586 36654"/>
    </justification>
  </clause>

  <clause id="36656">
    <literal><![CDATA[
      a(x,y * T(((x \ 1) * z) * x,u),(x \ 1) * T(z,u)) = a(x,x * (y * ((x \ 1) * T(z,u))),(x \ 1) * T(z,u))
    ]]></literal>
    <justification jstring="[para(4872(a,2),36655(a,1,2,2))].">
      <j1 rule="para" parents="4872 36655"/>
    </justification>
  </clause>

  <clause id="36657">
    <literal><![CDATA[
      a(x,y * ((z * (u * y)) * (a(w,v5,w) \ u)),v6) = a(x,L(z,y,u),v6)
    ]]></literal>
    <justification jstring="[para(12144(a,1),36585(a,1,2,2))].">
      <j1 rule="para" parents="12144 36585"/>
    </justification>
  </clause>

  <clause id="36658">
    <literal><![CDATA[
      L(x,y,z * (u \ (w \ a(v5,v6,v5)))) = L(x,y,(w * u) \ z)
    ]]></literal>
    <justification jstring="[hyper(36609,a,36597,a),flip(a)].">
      <j1 rule="hyper" parents="36609 36597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36659">
    <literal><![CDATA[
      L(x,y,(z \ (u \ 1)) * w) = L(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(20621,a,36658,a)].">
      <j1 rule="hyper" parents="20621 36658"/>
    </justification>
  </clause>

  <clause id="36660">
    <literal><![CDATA[
      L(x,a(y,z,u),(w * v5) \ v6) = L(x,a(y,z,u),(v5 \ w) * v6)
    ]]></literal>
    <justification jstring="[hyper(30736,a,36659,a),flip(a)].">
      <j1 rule="hyper" parents="30736 36659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36661">
    <literal><![CDATA[
      L(x,a(y,z,u),(w \ v5) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,u),(v5 * w) * v6) = v7
    ]]></literal>
    <justification jstring="[para(36660(a,1),30877(a,1))].">
      <j1 rule="para" parents="36660 30877"/>
    </justification>
  </clause>

  <clause id="36662">
    <literal><![CDATA[
      L(x,y,a(z,u,w * (u * x))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u,a(z,y,x * (w * u))) = v5
    ]]></literal>
    <justification jstring="[para(36618(a,1),29799(a,1))].">
      <j1 rule="para" parents="36618 29799"/>
    </justification>
  </clause>

  <clause id="36663">
    <literal><![CDATA[
      a(x,(a(y \ z,z,z) * u) * w,v5) = a(x,(a(z,z,y) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,32048,a,b,36631,a)].">
      <j1 rule="hyper" parents="63 32048 36631"/>
    </justification>
  </clause>

  <clause id="36664">
    <literal><![CDATA[
      a(x,y,a(z,u * a(w,v5,x),v6)) = a(x,y,a(z,u * L(x,v5,w),v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,29803,a,b,36649,a)].">
      <j1 rule="hyper" parents="347 29803 36649"/>
    </justification>
  </clause>

  <clause id="36665">
    <literal><![CDATA[
      x * a(y,z,a(u,w * a(v5,v6,u),x)) = L(x,w * L(u,v6,v5),a(u,z,y))
    ]]></literal>
    <justification jstring="[para(36649(a,1),29793(a,1,2))].">
      <j1 rule="para" parents="36649 29793"/>
    </justification>
  </clause>

  <clause id="36666">
    <literal><![CDATA[
      a(x,(y * (z * (y * u))) * u,w) = a(x,L(z,u,y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,24983,a(flip),b,36657,a)].">
      <j1 rule="hyper" parents="63 24983 36657"/>
    </justification>
  </clause>

  <clause id="36667">
    <literal><![CDATA[
      a(x,((y * (z * u)) * z) * u,w) = a(x,L(y,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(24008,a,36666,a)].">
      <j1 rule="hyper" parents="24008 36666"/>
    </justification>
  </clause>

  <clause id="36668">
    <literal><![CDATA[
      a(x,a(y \ z,z,z) * (u * w),v5) = a(x,(a(z,z,y) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,32162,a(flip),b,36663,a)].">
      <j1 rule="hyper" parents="63 32162 36663"/>
    </justification>
  </clause>

  <clause id="36669">
    <literal><![CDATA[
      a(a(x,x,y) * z,u,a(w,v5 * L(a(x,x,y) * z,v6,v7),v8)) = a(z,u,a(w,v5 * a(v7,v6,a(x,x,y) * z),v8))
    ]]></literal>
    <justification jstring="[hyper(63,a,36423,a(flip),b,36664,a),flip(a)].">
      <j1 rule="hyper" parents="63 36423 36664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36670">
    <literal><![CDATA[
      a(x,a(y * z,z,z) * (u * w),v5) = a(x,(a(z,z,y) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,29530,a(flip),b,36668,a)].">
      <j1 rule="hyper" parents="63 29530 36668"/>
    </justification>
  </clause>

  <clause id="36671">
    <literal><![CDATA[
      a(x,(a(y,y,z) * u) * w,v5) = a(x,a(z,y,y) * (u * w),v5)
    ]]></literal>
    <justification jstring="[hyper(28482,a,36670,a),flip(a)].">
      <j1 rule="hyper" parents="28482 36670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36672">
    <literal><![CDATA[
      a(x,(y * a(z,z,u)) * w,v5) = a(x,a(u,z,z) * (y * w),v5)
    ]]></literal>
    <justification jstring="[hyper(24008,a,36671,a)].">
      <j1 rule="hyper" parents="24008 36671"/>
    </justification>
  </clause>

  <clause id="36673">
    <literal><![CDATA[
      a(x,a(y,z,z) * (u * w),v5) = a(x,u * (a(z,z,y) * w),v5)
    ]]></literal>
    <justification jstring="[para(32109(a,1),36672(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32109 36672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36674">
    <literal><![CDATA[
      a(x,y * (a(z,z,u) * w),v5) = a(x,y * w,a(u,z,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,32283,a(flip),b,36673,a),flip(a)].">
      <j1 rule="hyper" parents="63 32283 36673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36675">
    <literal><![CDATA[
      a(x,y * (a(z,z,u) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y * w,v5) = v6
    ]]></literal>
    <justification jstring="[para(36674(a,2),36548(a,1))].">
      <j1 rule="para" parents="36674 36548"/>
    </justification>
  </clause>

  <clause id="36677">
    <literal><![CDATA[
      a(x,y * (L(z,u,u) * w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y * (w * z),v5) = v6
    ]]></literal>
    <justification jstring="[para(29563(a,1),36675(a,1))].">
      <j1 rule="para" parents="29563 36675"/>
    </justification>
  </clause>

  <clause id="36678">
    <literal><![CDATA[
      a(x,y \ (z * (u \ w)),v5) = a(x,y * (z * (w * u)),v5)
    ]]></literal>
    <justification jstring="[hyper(36677,a,36477,a),flip(a)].">
      <j1 rule="hyper" parents="36677 36477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36679">
    <literal><![CDATA[
      a(x,y * (z * (u \ w)),v5) = a(x,y * (z * (w * u)),v5)
    ]]></literal>
    <justification jstring="[hyper(36563,a,36678,a)].">
      <j1 rule="hyper" parents="36563 36678"/>
    </justification>
  </clause>

  <clause id="36680">
    <literal><![CDATA[
      a(x,L(y,z,z) * (u * (w * v5)),v6) = a(x,(u * (v5 \ w)) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(36506,a,36679,a),flip(a)].">
      <j1 rule="hyper" parents="36506 36679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36682">
    <literal><![CDATA[
      a(x,(y * (z \ u)) * w,v5) = a(x,(y * (u * z)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(36506,a,36680,a),flip(a)].">
      <j1 rule="hyper" parents="36506 36680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36683">
    <literal><![CDATA[
      a(x,(y * (z / u)) * w,v5) = a(x,(y * (z * u)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,24936,a,b,36682,a)].">
      <j1 rule="hyper" parents="63 24936 36682"/>
    </justification>
  </clause>

  <clause id="36684">
    <literal><![CDATA[
      L(x,y * L(z,u,w),a(z,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,y * a(w,u,z),a(v6,v5,z)) = v7
    ]]></literal>
    <justification jstring="[para(36665(a,1),29921(a,1))].">
      <j1 rule="para" parents="36665 29921"/>
    </justification>
  </clause>

  <clause id="36685">
    <literal><![CDATA[
      L(x,y * L(z,u,w),a(z,v5,v6)) = x * a(v6,y,a(z,v5,x))
    ]]></literal>
    <justification jstring="[para(36641(a,1),36665(a,1,2)),flip(a)].">
      <j1 rule="para" parents="36641 36665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36686">
    <literal><![CDATA[
      L(x,y * L(z,u,w),a(z,v5,v6)) = L(x,v5,a(v6,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,29807,a(flip),b,36685,a),flip(a)].">
      <j1 rule="hyper" parents="347 29807 36685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36688">
    <literal><![CDATA[
      L(x,L(y,z,u) * w,a(y,v5,v6)) = L(x,v5,a(v6,w,y))
    ]]></literal>
    <justification jstring="[hyper(21666,a,36686,a)].">
      <j1 rule="hyper" parents="21666 36686"/>
    </justification>
  </clause>

  <clause id="36689">
    <literal><![CDATA[
      L(x,L(y,z,u) * w,a(y,v5,v6)) = L(x,y * w,a(y,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,32373,a,b,36688,a),flip(a)].">
      <j1 rule="hyper" parents="347 32373 36688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36690">
    <literal><![CDATA[
      L(x,L(y,z,u) * w,a(y,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,v5,a(v6,w,y)) = v7
    ]]></literal>
    <justification jstring="[para(36689(a,2),32374(a,1))].">
      <j1 rule="para" parents="36689 32374"/>
    </justification>
  </clause>

  <clause id="36691">
    <literal><![CDATA[
      a(x,y,(z * R(u,w,w)) * v5) = a(x,y,(z * u) * v5)
    ]]></literal>
    <justification jstring="[hyper(36520,a,36440,a),flip(a)].">
      <j1 rule="hyper" parents="36520 36440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36692">
    <literal><![CDATA[
      a(x,y,(z * L(u,w,w)) * v5) = a(x,y,(z * u) * v5)
    ]]></literal>
    <justification jstring="[hyper(25285,a,36691,a)].">
      <j1 rule="hyper" parents="25285 36691"/>
    </justification>
  </clause>

  <clause id="36693">
    <literal><![CDATA[
      a(x,y,(z * (u \ w)) * v5) = a(x,y,(z * (w * u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(25711,a,36692,a)].">
      <j1 rule="hyper" parents="25711 36692"/>
    </justification>
  </clause>

  <clause id="36694">
    <literal><![CDATA[
      a(x,y,(z * (u / w)) * v5) = a(x,y,(z * (u * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(24530,a,36693,a)].">
      <j1 rule="hyper" parents="24530 36693"/>
    </justification>
  </clause>

  <clause id="36695">
    <literal><![CDATA[
      a(x,y,z * (L(u,w,w) * v5)) = a(x,y,z * (u * v5))
    ]]></literal>
    <justification jstring="[hyper(36521,a,36440,a)].">
      <j1 rule="hyper" parents="36521 36440"/>
    </justification>
  </clause>

  <clause id="36697">
    <literal><![CDATA[
      a(x,y,(z * u) * y) = a(x,y,u * (z * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,36529,a(flip),b,36695,a)].">
      <j1 rule="hyper" parents="63 36529 36695"/>
    </justification>
  </clause>

  <clause id="36698">
    <literal><![CDATA[
      a(x,y,z * ((u / w) * v5)) = a(x,y,z * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,25333,a(flip),b,36695,a),flip(a)].">
      <j1 rule="hyper" parents="63 25333 36695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36703">
    <literal><![CDATA[
      a(x \ (y \ (z \ (y * (z * x)))),u,w * (v5 * u)) = a(z,x,a((v5 * w) * u,u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,31160,a(flip),b,36697,a),flip(a)].">
      <j1 rule="hyper" parents="63 31160 36697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36705">
    <literal><![CDATA[
      (a(x,y,z * (u * y)) * w) / ((v5 \ w) * a(x,y,(u * z) * y)) = L(v5,y,a((u * z) * y,w,x))
    ]]></literal>
    <justification jstring="[para(36697(a,1),32367(a,1,1,1))].">
      <j1 rule="para" parents="36697 32367"/>
    </justification>
  </clause>

  <clause id="36706">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) * v5)) = a(x,y,z * ((w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(24421,a,36698,a)].">
      <j1 rule="hyper" parents="24421 36698"/>
    </justification>
  </clause>

  <clause id="36708">
    <literal><![CDATA[
      a(x,y,z * ((z * u) * (w * u))) = a(x,y,L(w,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,32243,a(flip),b,36698,a),flip(a)].">
      <j1 rule="hyper" parents="63 32243 36698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36709">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * R(w,v5,v6))) = a(x,y,z * (a(w,v5,v6) * u))
    ]]></literal>
    <justification jstring="[para(31999(a,1),36698(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="31999 36698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36710">
    <literal><![CDATA[
      a(x,y,z * ((u * (w \ (v5 * v5))) * v6)) = a(x,y,z * (v6 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,24949,a(flip),b,36706,a),flip(a)].">
      <j1 rule="hyper" parents="63 24949 36706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36711">
    <literal><![CDATA[
      a(x,y,a(z,u,y * ((y * w) * v5))) = a(x,y,a(z,u,w * v5))
    ]]></literal>
    <justification jstring="[para(36706(a,1),32246(a,1,3))].">
      <j1 rule="para" parents="36706 32246"/>
    </justification>
  </clause>

  <clause id="36712">
    <literal><![CDATA[
      a(x,y,z * ((u * z) * (w * u))) = a(x,y,L(w,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(24427,a,36708,a)].">
      <j1 rule="hyper" parents="24427 36708"/>
    </justification>
  </clause>

  <clause id="36713">
    <literal><![CDATA[
      a(x,y,z * ((u * w) * L(w,v5,v6))) = a(x,y,z * (a(w,v5,v6) * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,25313,a(flip),b,36709,a)].">
      <j1 rule="hyper" parents="63 25313 36709"/>
    </justification>
  </clause>

  <clause id="36715">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ v5))) = a(x,y,z * (u * (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,25084,a(flip),b,36710,a),flip(a)].">
      <j1 rule="hyper" parents="63 25084 36710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36716">
    <literal><![CDATA[
      a(x,y,(z * u) * ((w * u) * (z * w))) = a(x,y,a(u,w,z * w))
    ]]></literal>
    <justification jstring="[hyper(31969,a,36715,a),flip(a)].">
      <j1 rule="hyper" parents="31969 36715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36717">
    <literal><![CDATA[
      a(x,y,(z * u) * ((u * w) * (w * z))) = a(x,y,a(w * z,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,36530,a(flip),b,36715,a),flip(a)].">
      <j1 rule="hyper" parents="63 36530 36715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36718">
    <literal><![CDATA[
      a(x,y,a(z,u,w * u)) = a(x,y,a(w,z,u * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,36636,a(flip),b,36716,a)].">
      <j1 rule="hyper" parents="63 36636 36716"/>
    </justification>
  </clause>

  <clause id="36719">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w * x),w * x,a(y,z,u)) = x * a(u,z,a(w,y,x * y))
    ]]></literal>
    <justification jstring="[para(36718(a,1),29814(a,2,2))].">
      <j1 rule="para" parents="36718 29814"/>
    </justification>
  </clause>

  <clause id="36720">
    <literal><![CDATA[
      a(x,y,a(a(z,u,w) \ v5,v6,w * v6)) = a(x,y,a(v6,w,v5 * L(w,u,z)))
    ]]></literal>
    <justification jstring="[para(31736(a,1),36718(a,1,3,3)),flip(a)].">
      <j1 rule="para" parents="31736 36718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36721">
    <literal><![CDATA[
      a(x,y,a(z * u,u,w)) = a(x,y,a(z,u,w * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,36637,a(flip),b,36717,a),flip(a)].">
      <j1 rule="hyper" parents="63 36637 36717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36722">
    <literal><![CDATA[
      a(x,y,a(z * u,z,w)) = a(x,y,a(u,z,w * z))
    ]]></literal>
    <justification jstring="[hyper(26340,a,36721,a)].">
      <j1 rule="hyper" parents="26340 36721"/>
    </justification>
  </clause>

  <clause id="36723">
    <literal><![CDATA[
      a(x,y,z) * ((u / w) * (a(x,y,z) \ w)) = u * a(x,y,a(u,w,z * w))
    ]]></literal>
    <justification jstring="[para(36721(a,1),29936(a,2,2))].">
      <j1 rule="para" parents="36721 29936"/>
    </justification>
  </clause>

  <clause id="36724">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,w)) = y * a(w,u,a(y,x,z * x))
    ]]></literal>
    <justification jstring="[para(36721(a,1),32404(a,2,2))].">
      <j1 rule="para" parents="36721 32404"/>
    </justification>
  </clause>

  <clause id="36725">
    <literal><![CDATA[
      a(x,y,a(y * z,u,w)) = a(x,u,a(z,y,w * y))
    ]]></literal>
    <justification jstring="[hyper(29875,a,36722,a)].">
      <j1 rule="hyper" parents="29875 36722"/>
    </justification>
  </clause>

  <clause id="36726">
    <literal><![CDATA[
      a(x,y,a(z * u,z,w)) = a(w,y,a(u,z,x * z))
    ]]></literal>
    <justification jstring="[hyper(29858,a,36722,a)].">
      <j1 rule="hyper" parents="29858 36722"/>
    </justification>
  </clause>

  <clause id="36727">
    <literal><![CDATA[
      a(x,y,a(z,u,w * u)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,a(u * z,y,w)) = v5
    ]]></literal>
    <justification jstring="[para(36722(a,1),29875(a,1))].">
      <j1 rule="para" parents="36722 29875"/>
    </justification>
  </clause>

  <clause id="36728">
    <literal><![CDATA[
      a(x,y,a(z * u,z,w * ((z * u) * y))) = a(x,y,a(u,z,(y * (w * (z * u))) * z))
    ]]></literal>
    <justification jstring="[hyper(31026,a,36725,a)].">
      <j1 rule="hyper" parents="31026 36725"/>
    </justification>
  </clause>

  <clause id="36729">
    <literal><![CDATA[
      x * R(x \ 1,y,a(y * z,u,w)) = a(x \ 1,u,a(z,y,w * y))
    ]]></literal>
    <justification jstring="[hyper(28974,a,36725,a)].">
      <j1 rule="hyper" parents="28974 36725"/>
    </justification>
  </clause>

  <clause id="36730">
    <literal><![CDATA[
      a(x,y,a(y * z,u,w)) = a(x,y,a(z,u,w * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,29839,a,b,36725,a),flip(a)].">
      <j1 rule="hyper" parents="347 29839 36725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36731">
    <literal><![CDATA[
      a(x,y,a(z,z * ((1 / z) * u),w * (z * ((1 / z) * u)))) = a(x,z * ((1 / z) * u),a(L(u * z,z,z \ 1),y,w))
    ]]></literal>
    <justification jstring="[para(3378(a,1),36725(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="3378 36725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36732">
    <literal><![CDATA[
      a(x,y,a(z,(u \ w) * u,v5 * ((u \ w) * u))) = a(x,(u \ w) * u,a(w * z,y,v5))
    ]]></literal>
    <justification jstring="[para(23904(a,1),36725(a,1,3)),flip(a)].">
      <j1 rule="para" parents="23904 36725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36733">
    <literal><![CDATA[
      a(x,y,a(z,u,w * u)) = a(w,y,a(z,u,x * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,36722,a(flip),b,36726,a)].">
      <j1 rule="hyper" parents="63 36722 36726"/>
    </justification>
  </clause>

  <clause id="36734">
    <literal><![CDATA[
      a(x,y,a(z * y,u,w)) = a(x,y,a(z,u,w * y))
    ]]></literal>
    <justification jstring="[hyper(26340,a,36730,a)].">
      <j1 rule="hyper" parents="26340 36730"/>
    </justification>
  </clause>

  <clause id="36735">
    <literal><![CDATA[
      a(x * y,z,a(u,y,w)) = a(x,z,a(u,y,w * y))
    ]]></literal>
    <justification jstring="[hyper(29858,a,36733,a)].">
      <j1 rule="hyper" parents="29858 36733"/>
    </justification>
  </clause>

  <clause id="36736">
    <literal><![CDATA[
      a(x * y,z,a((u * y) \ (w \ 1),y,u)) = a(x,z,a(w \ ((u * y) \ 1),y,u * y))
    ]]></literal>
    <justification jstring="[para(29784(a,2),36735(a,2,3))].">
      <j1 rule="para" parents="29784 36735"/>
    </justification>
  </clause>

  <clause id="36737">
    <literal><![CDATA[
      a(x,y,a(z,u,w * u)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,y,a(z,u,x * u)) = v5
    ]]></literal>
    <justification jstring="[para(36735(a,1),29858(a,1))].">
      <j1 rule="para" parents="36735 29858"/>
    </justification>
  </clause>

  <clause id="36738">
    <literal><![CDATA[
      a(x * y,z,a(u,y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,z,a(u,y,w * y)) = v5
    ]]></literal>
    <justification jstring="[para(29808(a,1),36737(a,1))].">
      <j1 rule="para" parents="29808 36737"/>
    </justification>
  </clause>

  <clause id="36739">
    <literal><![CDATA[
      a(x,y,a(z * u,z,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(u,z,w * z)) = v5
    ]]></literal>
    <justification jstring="[para(36726(a,2),36737(a,1))].">
      <j1 rule="para" parents="36726 36737"/>
    </justification>
  </clause>

  <clause id="36740">
    <literal><![CDATA[
      a(x,y,a(z * u,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w * u)) = v5
    ]]></literal>
    <justification jstring="[para(18294(a,2),36739(a,1,3))].">
      <j1 rule="para" parents="18294 36739"/>
    </justification>
  </clause>

  <clause id="36741">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,w)) = L(y,x,a(w,u,z * x))
    ]]></literal>
    <justification jstring="[hyper(347,a,29793,a(flip),b,36724,a),flip(a)].">
      <j1 rule="hyper" parents="347 29793 36724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36742">
    <literal><![CDATA[
      x * a(y,z,a(u,w,x * w)) = L(x,w,a(u,z,y * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,32403,a(flip),b,36741,a)].">
      <j1 rule="hyper" parents="63 32403 36741"/>
    </justification>
  </clause>

  <clause id="36743">
    <literal><![CDATA[
      a(x \ 1,y,a((z \ 1) * u,w,v5 * w)) = x * R(x \ 1,w,a(w * (z \ u),y,v5))
    ]]></literal>
    <justification jstring="[para(31942(a,2),36729(a,2,3)),flip(a)].">
      <j1 rule="para" parents="31942 36729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36744">
    <literal><![CDATA[
      a(x,y,z) * ((u / w) * (a(x,y,z) \ w)) = L(u,w,a(x,y,z * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,29793,a(flip),b,36723,a),flip(a)].">
      <j1 rule="hyper" parents="347 29793 36723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36745">
    <literal><![CDATA[
      a(x * y,x,a(z,u,w)) * y = L(y,x,a(z,u,w * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,28599,a,b,36744,a)].">
      <j1 rule="hyper" parents="63 28599 36744"/>
    </justification>
  </clause>

  <clause id="36746">
    <literal><![CDATA[
      (a(x,y,z * (u * w)) * (u / w)) \ (a(x,y,z * (u * w)) * u) = a((u * w) * w,u * w,a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(347,a,30206,a(flip),b,36745,a)].">
      <j1 rule="hyper" parents="347 30206 36745"/>
    </justification>
  </clause>

  <clause id="36747">
    <literal><![CDATA[
      a(x * (y \ 1),x,a(z,u,w)) * (y \ 1) = y \ a(y,x,a(w * x,u,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,29252,a(flip),b,36745,a),flip(a)].">
      <j1 rule="hyper" parents="347 29252 36745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36748">
    <literal><![CDATA[
      a((x \ y) * T(y,z),x \ T(y,z),a(u,w,v5)) * y = L(y,x \ T(y,z),a(u,w,v5 * (x \ T(y,z))))
    ]]></literal>
    <justification jstring="[para(13108(a,1),36745(a,1,1,1))].">
      <j1 rule="para" parents="13108 36745"/>
    </justification>
  </clause>

  <clause id="36749">
    <literal><![CDATA[
      a(x * y,x,a(z,u,(w * (v5 / x)) * x)) * y = L(y,x,a(z,u,R(w * (v5 / (1 / x)),x,x)))
    ]]></literal>
    <justification jstring="[para(22518(a,2),36745(a,2,3,3))].">
      <j1 rule="para" parents="22518 36745"/>
    </justification>
  </clause>

  <clause id="36750">
    <literal><![CDATA[
      a(x * y,x,a(z,u,w)) * y = L(y,x,a(w,u,z * x))
    ]]></literal>
    <justification jstring="[para(26501(a,1),36745(a,1,1))].">
      <j1 rule="para" parents="26501 36745"/>
    </justification>
  </clause>

  <clause id="36751">
    <literal><![CDATA[
      a(x * y,x,a(z,u,a(w,v5,v6))) * y = L(y,x,a(a(z,u,v6),v5,w * x))
    ]]></literal>
    <justification jstring="[para(29790(a,1),36745(a,1,1,3))].">
      <j1 rule="para" parents="29790 36745"/>
    </justification>
  </clause>

  <clause id="36752">
    <literal><![CDATA[
      a(x * (1 * y),x,a(z,u,w)) * (y \ 1) = y \ a(y,x,a(w * x,u,z))
    ]]></literal>
    <justification jstring="[para(36601(a,1),36747(a,1,1))].">
      <j1 rule="para" parents="36601 36747"/>
    </justification>
  </clause>

  <clause id="36753">
    <literal><![CDATA[
      L(x,y,a(a(z,u,w),v5,v6 * y)) = L(x,y,a(z,u,a(v6,v5,w) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,36745,a(flip),b,36751,a),flip(a)].">
      <j1 rule="hyper" parents="63 36745 36751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36754">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w * y,v5,v6))) = L(x,y,a(z,u,a(w,v5,v6) * y))
    ]]></literal>
    <justification jstring="[para(29790(a,1),36753(a,1,3))].">
      <j1 rule="para" parents="29790 36753"/>
    </justification>
  </clause>

  <clause id="36755">
    <literal><![CDATA[
      a(x * y,x,a(z,u,w)) * (y \ 1) = y \ a(y,x,a(w * x,u,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),36752(a,1,1,1,2))].">
      <j1 rule="para" parents="7 36752"/>
    </justification>
  </clause>

  <clause id="36756">
    <literal><![CDATA[
      a(x * y,x,a(z,u,w)) = a(y,x,a(w * x,u,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,31951,a,b,36755,a),flip(a)].">
      <j1 rule="hyper" parents="35 31951 36755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36758">
    <literal><![CDATA[
      a(x,y,a(z * y,u,w)) * x = L(x,y,a(z,u,w * y))
    ]]></literal>
    <justification jstring="[para(36756(a,1),36750(a,1,1))].">
      <j1 rule="para" parents="36756 36750"/>
    </justification>
  </clause>

  <clause id="36759">
    <literal><![CDATA[
      L(x,y,a(z * y,u,w)) = L(x,y,a(z,u,w * y))
    ]]></literal>
    <justification jstring="[hyper(29007,a,36758,a)].">
      <j1 rule="hyper" parents="29007 36758"/>
    </justification>
  </clause>

  <clause id="36760">
    <literal><![CDATA[
      L(x,y,a(y * z,u,w)) = L(x,y,a(z,u,w * y))
    ]]></literal>
    <justification jstring="[hyper(27583,a,36759,a)].">
      <j1 rule="hyper" parents="27583 36759"/>
    </justification>
  </clause>

  <clause id="36761">
    <literal><![CDATA[
      L(x,y,a(z,u * w,a(v5,v6,u) * y)) = L(x,y,a(v5,w,a(u,v6,y * z)))
    ]]></literal>
    <justification jstring="[para(32348(a,1),36760(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32348 36760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36762">
    <literal><![CDATA[
      L(x,y,a(z,u * w,a(v5 * y,v6,u))) = L(x,y,a(v5,w,a(u,v6,y * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,36754,a,b,36761,a)].">
      <j1 rule="hyper" parents="63 36754 36761"/>
    </justification>
  </clause>

  <clause id="36763">
    <literal><![CDATA[
      L(x,y,a(z * y,u,a(w,v5,v6))) = L(x,y,a(z,u,a(w,v5,y * v6)))
    ]]></literal>
    <justification jstring="[para(32348(a,1),36762(a,1,3))].">
      <j1 rule="para" parents="32348 36762"/>
    </justification>
  </clause>

  <clause id="36764">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,y * v6))) = L(x,y,a(z,u,a(w,v5,v6) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,36759,a(flip),b,36763,a),flip(a)].">
      <j1 rule="hyper" parents="63 36759 36763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36765">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w * y,v5,v6))) = L(x,y,a(z,u,a(w,v5,y * v6)))
    ]]></literal>
    <justification jstring="[hyper(347,a,36754,a,b,36764,a)].">
      <j1 rule="hyper" parents="347 36754 36764"/>
    </justification>
  </clause>

  <clause id="36766">
    <literal><![CDATA[
      L(x,y,a(z,u,a(y * w,v5,v6))) = L(x,y,a(z,u,a(w,v5,y * v6)))
    ]]></literal>
    <justification jstring="[para(23896(a,1),36765(a,1,3,3))].">
      <j1 rule="para" parents="23896 36765"/>
    </justification>
  </clause>

  <clause id="36767">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,y * v6))) = L(x,y,a(z,u,a(v6,v5,y * w)))
    ]]></literal>
    <justification jstring="[para(26516(a,1),36765(a,1,3))].">
      <j1 rule="para" parents="26516 36765"/>
    </justification>
  </clause>

  <clause id="36768">
    <literal><![CDATA[
      a(x,y,L(z * (u \ w),v5,v6)) = a(x,y,L(z * (w * u),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(30012,a,36525,a),flip(a)].">
      <j1 rule="hyper" parents="30012 36525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36769">
    <literal><![CDATA[
      a(x,y,L(z * (u * w),z,w)) = a(x,y,(z * w) * u)
    ]]></literal>
    <justification jstring="[hyper(32151,a,36768,a),flip(a)].">
      <j1 rule="hyper" parents="32151 36768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36770">
    <literal><![CDATA[
      a(x,y,(z * y) * u) = a(x,y,z * (u * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,32205,a(flip),b,36769,a),flip(a)].">
      <j1 rule="hyper" parents="63 32205 36769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36771">
    <literal><![CDATA[
      L(x,y,a(z,u,w * (v5 * u))) = L(x,y,a(z,u,v5 * (w * u)))
    ]]></literal>
    <justification jstring="[para(36770(a,1),27575(a,1,3))].">
      <j1 rule="para" parents="36770 27575"/>
    </justification>
  </clause>

  <clause id="36772">
    <literal><![CDATA[
      a(R(x * ((1 / y) * a(z,u,u)),y,y),w,v5) = a(a(z,u,u) \ (y \ x),w,v5)
    ]]></literal>
    <justification jstring="[para(31806(a,1),36588(a,1,1,1))].">
      <j1 rule="para" parents="31806 36588"/>
    </justification>
  </clause>

  <clause id="36773">
    <literal><![CDATA[
      L(x,y * a(z,u,w),a(v5,v6,w)) = L(x,v6,a(v5,y,w))
    ]]></literal>
    <justification jstring="[hyper(36684,a,36686,a)].">
      <j1 rule="hyper" parents="36684 36686"/>
    </justification>
  </clause>

  <clause id="36776">
    <literal><![CDATA[
      a(R(x * (a(y,z,z) / u),u,u),w,v5) = a(a(y,z,z) \ (u \ x),w,v5)
    ]]></literal>
    <justification jstring="[para(31923(a,1),36772(a,1,1,1,2))].">
      <j1 rule="para" parents="31923 36772"/>
    </justification>
  </clause>

  <clause id="36777">
    <literal><![CDATA[
      a(x * (a(y,z,z) / u),w,L(v5,u,u)) = a(a(y,z,z) \ (u \ x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(29721,a,36776,a)].">
      <j1 rule="hyper" parents="29721 36776"/>
    </justification>
  </clause>

  <clause id="36778">
    <literal><![CDATA[
      a(a(x,y,y) \ (z \ u),w,v5) = a(u * (a(x,y,y) / z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,31920,a(flip),b,36777,a),flip(a)].">
      <j1 rule="hyper" parents="63 31920 36777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36780">
    <literal><![CDATA[
      a(a(x,y,y) \ (z \ u),w,v5) = a(u * (z \ a(x,y,y)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,23934,a(flip),b,36778,a),flip(a)].">
      <j1 rule="hyper" parents="347 23934 36778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36781">
    <literal><![CDATA[
      a(x * (y \ a(z,u,u)),w,v5) = a(y \ x,w,a(z,u,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(32290,a,36780,a),flip(a)].">
      <j1 rule="hyper" parents="32290 36780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36782">
    <literal><![CDATA[
      a((x \ (y \ x)) \ z,u,a(x,y,y) * w) = a(y * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,28256,a(flip),b,36781,a),flip(a)].">
      <j1 rule="hyper" parents="63 28256 36781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36783">
    <literal><![CDATA[
      a((x \ (y \ x)) \ z,u,w) = a(y * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(36548,a,36782,a)].">
      <j1 rule="hyper" parents="36548 36782"/>
    </justification>
  </clause>

  <clause id="36784">
    <literal><![CDATA[
      a((x \ y) \ z,u,w) = a((y \ x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(24537,a,36783,a)].">
      <j1 rule="hyper" parents="24537 36783"/>
    </justification>
  </clause>

  <clause id="36786">
    <literal><![CDATA[
      a((x \ y) \ z,u,L(w,x,y)) = a(x * (y \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,31351,a(flip),b,36783,a)].">
      <j1 rule="hyper" parents="63 31351 36783"/>
    </justification>
  </clause>

  <clause id="36788">
    <literal><![CDATA[
      a(((x \ 1) \ y) * z,x,u) = a(x * (y * z),x,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,32622,a(flip),b,36784,a),flip(a)].">
      <j1 rule="hyper" parents="63 32622 36784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36790">
    <literal><![CDATA[
      a((x \ y) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z * (y \ x),u,w) = v5
    ]]></literal>
    <justification jstring="[para(36784(a,2),23925(a,1))].">
      <j1 rule="para" parents="36784 23925"/>
    </justification>
  </clause>

  <clause id="36791">
    <literal><![CDATA[
      a((x * y) * z,y,u) = a(y * (x * z),y,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,36443,a(flip),b,36788,a)].">
      <j1 rule="hyper" parents="63 36443 36788"/>
    </justification>
  </clause>

  <clause id="36793">
    <literal><![CDATA[
      a((x \ y) * z,u,L(w,y,x)) = a(y * (x \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,36784,a(flip),b,36786,a)].">
      <j1 rule="hyper" parents="63 36784 36786"/>
    </justification>
  </clause>

  <clause id="36794">
    <literal><![CDATA[
      a(x * (y \ (z \ 1)),u,w) = a((z * y) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(36790,a,36614,a)].">
      <j1 rule="hyper" parents="36790 36614"/>
    </justification>
  </clause>

  <clause id="36795">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),a(z,u,w),y * x) = x * a(w,u,a(y,z,x * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,32401,a(flip),b,36719,a)].">
      <j1 rule="hyper" parents="63 32401 36719"/>
    </justification>
  </clause>

  <clause id="36796">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),a(z,u,w),y * x) = L(x,z,a(y,u,w * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,36742,a(flip),b,36795,a),flip(a)].">
      <j1 rule="hyper" parents="347 36742 36795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36797">
    <literal><![CDATA[
      a(x \ (y \ (z \ (y * (z * x)))),u,w * (v5 * u)) = a(z,x,a(v5 * w,u,y * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,36721,a(flip),b,36703,a),flip(a)].">
      <j1 rule="hyper" parents="347 36721 36703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36798">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),w,v5)) = a(x,y,a(u * z,w,v5 * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,31160,a(flip),b,36797,a)].">
      <j1 rule="hyper" parents="63 31160 36797"/>
    </justification>
  </clause>

  <clause id="36799">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),u,v5)) = a(x,y,a(w * z,u,v5 * u))
    ]]></literal>
    <justification jstring="[hyper(26341,a,36798,a)].">
      <j1 rule="hyper" parents="26341 36798"/>
    </justification>
  </clause>

  <clause id="36800">
    <literal><![CDATA[
      a(x,y,a(a(x,y,z) * u,w,z * w)) \ u = (w * a(x,y,z)) * (w \ (a(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(36799(a,1),32298(a,1,1))].">
      <j1 rule="para" parents="36799 32298"/>
    </justification>
  </clause>

  <clause id="36801">
    <literal><![CDATA[
      a(x,L(y,z,z) * (((u * (w * y)) * (u * y)) * u),v5) = a(x,u * (R(w,u,y) * y),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,36600,a(flip),b,36498,a)].">
      <j1 rule="hyper" parents="63 36600 36498"/>
    </justification>
  </clause>

  <clause id="36802">
    <literal><![CDATA[
      a(x \ y,z,a(u,(x \ y) * x,w * ((x \ y) * x))) = a(w,x,a(x \ y,z,y * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,32349,a(flip),b,36732,a),flip(a)].">
      <j1 rule="hyper" parents="347 32349 36732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36803">
    <literal><![CDATA[
      a(x * y,z,a(u \ (y \ (w \ 1)),y,u)) = a(x,z,a(w \ ((u * y) \ 1),y,u * y))
    ]]></literal>
    <justification jstring="[para(32212(a,1),36736(a,1,3))].">
      <j1 rule="para" parents="32212 36736"/>
    </justification>
  </clause>

  <clause id="36804">
    <literal><![CDATA[
      a(x \ 1,y,a((z \ 1) * u,w,v5 * w)) = x * L(x \ 1,w,a(w * (z \ u),y,v5))
    ]]></literal>
    <justification jstring="[para(23247(a,1),36743(a,2,2))].">
      <j1 rule="para" parents="23247 36743"/>
    </justification>
  </clause>

  <clause id="36805">
    <literal><![CDATA[
      a(x,(((y * (z * u)) * (y * u)) * y) * u,w) = a(x,y * (R(z,y,u) * u),w)
    ]]></literal>
    <justification jstring="[hyper(36506,a,36801,a)].">
      <j1 rule="hyper" parents="36506 36801"/>
    </justification>
  </clause>

  <clause id="36806">
    <literal><![CDATA[
      a(x,L(y * (z * u),u,y),w) = a(x,y * (R(z,y,u) * u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,36667,a(flip),b,36805,a)].">
      <j1 rule="hyper" parents="63 36667 36805"/>
    </justification>
  </clause>

  <clause id="36807">
    <literal><![CDATA[
      a(x,L(y * (z * u),u,y),w) = a(x,y * (L(z,y,u) * u),w)
    ]]></literal>
    <justification jstring="[hyper(25137,a,36806,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="25137 36806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36808">
    <literal><![CDATA[
      L(x,a(y,L(z * (u * y),y,z),w),v5) = L(x,a(y,z * u,w),v5)
    ]]></literal>
    <justification jstring="[para(36807(a,2),36541(a,1,2))].">
      <j1 rule="para" parents="36807 36541"/>
    </justification>
  </clause>

  <clause id="36809">
    <literal><![CDATA[
      L(x,a(y,z * (u * w),w),L(v5,w,z)) = L(x,a(w,z * u,y),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,30545,a(flip),b,36808,a)].">
      <j1 rule="hyper" parents="63 30545 36808"/>
    </justification>
  </clause>

  <clause id="36810">
    <literal><![CDATA[
      L(x,a(y,z * (u * y),w),v5) = L(x,a(y,z * u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(31063,a,36809,a)].">
      <j1 rule="hyper" parents="31063 36809"/>
    </justification>
  </clause>

  <clause id="36811">
    <literal><![CDATA[
      a(x \ y,z,a((x \ y) * u,(x \ y) * x,w * ((x \ y) * x))) = a(w,x,a(x \ y,z,x * u))
    ]]></literal>
    <justification jstring="[para(36592(a,1),36802(a,2,3))].">
      <j1 rule="para" parents="36592 36802"/>
    </justification>
  </clause>

  <clause id="36812">
    <literal><![CDATA[
      a(x * y,z,a(u * (y \ (w \ 1)),y,u)) = a(x,z,a(w \ ((u * y) \ 1),y,u * y))
    ]]></literal>
    <justification jstring="[hyper(30815,a,36803,a)].">
      <j1 rule="hyper" parents="30815 36803"/>
    </justification>
  </clause>

  <clause id="36813">
    <literal><![CDATA[
      a(x,y,a(z \ ((u * w) \ 1),w,u * w)) = a(x * w,y,a((z * w) \ u,w,u))
    ]]></literal>
    <justification jstring="[para(36794(a,1),36812(a,1,3)),flip(a)].">
      <j1 rule="para" parents="36794 36812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36814">
    <literal><![CDATA[
      a(x,y,a(z \ ((u * w) \ 1),w,u * w)) = a(x * w,y,a(z \ (w \ u),w,u))
    ]]></literal>
    <justification jstring="[para(32212(a,1),36813(a,2,3))].">
      <j1 rule="para" parents="32212 36813"/>
    </justification>
  </clause>

  <clause id="36815">
    <literal><![CDATA[
      a(x,y,a(z \ ((u * w) \ 1),w,u * w)) = a(x * w,y,a(z * (w \ u),w,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,30797,a(flip),b,36814,a),flip(a)].">
      <j1 rule="hyper" parents="347 30797 36814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36816">
    <literal><![CDATA[
      a(x,y,a(z \ ((u * w) \ 1),w,u * w)) = a(x * w,y,a(z * (u * w),w,u))
    ]]></literal>
    <justification jstring="[hyper(347,a,36602,a(flip),b,36815,a),flip(a)].">
      <j1 rule="hyper" parents="347 36602 36815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36817">
    <literal><![CDATA[
      a(x,y,a(z \ ((u * w) \ 1),w,u * w)) = a(x * w,y,a(u * z,w,u * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,36798,a(flip),b,36816,a),flip(a)].">
      <j1 rule="hyper" parents="347 36798 36816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36818">
    <literal><![CDATA[
      a((x * y) \ z,u,a(w,((x * y) * z) * v5,L(v6,y,x))) = a(v6,u,a(y \ (x \ z),v5,w))
    ]]></literal>
    <justification jstring="[hyper(30015,a,36632,a)].">
      <j1 rule="hyper" parents="30015 36632"/>
    </justification>
  </clause>

  <clause id="36819">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),w,a(y,z,u)) = L(x,a(u,z * a(v5,v6,u),y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,36773,a(flip),b,36643,a)].">
      <j1 rule="hyper" parents="63 36773 36643"/>
    </justification>
  </clause>

  <clause id="36820">
    <literal><![CDATA[
      L(x,a(y,z * a(u,w,y),v5),v6) = L(x,a(v5,z,y),v6)
    ]]></literal>
    <justification jstring="[hyper(29835,a,36819,a),flip(a)].">
      <j1 rule="hyper" parents="29835 36819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36822">
    <literal><![CDATA[
      L(x,a(y,z * a(y,u,w),v5),v6) = L(x,a(v5,z,y),v6)
    ]]></literal>
    <justification jstring="[para(31388(a,1),36820(a,1,2))].">
      <j1 rule="para" parents="31388 36820"/>
    </justification>
  </clause>

  <clause id="36823">
    <literal><![CDATA[
      a(x * y,x,a(z,u,(w * (v5 * x)) * x)) * y = L(y,x,a(z,u,R(w * (v5 / (1 / x)),x,x)))
    ]]></literal>
    <justification jstring="[para(36694(a,1),36749(a,1,1,3))].">
      <j1 rule="para" parents="36694 36749"/>
    </justification>
  </clause>

  <clause id="36824">
    <literal><![CDATA[
      a(x * y,x,a(z,u,x * ((x * w) * v5))) * y = L(y,x,a(z,u,R(v5 * (w / (1 / x)),x,x)))
    ]]></literal>
    <justification jstring="[para(24506(a,1),36823(a,1,1,3))].">
      <j1 rule="para" parents="24506 36823"/>
    </justification>
  </clause>

  <clause id="36825">
    <literal><![CDATA[
      L(x,y,a(z,u,R(w * (v5 / (1 / y)),y,y))) = a(y * x,y,a(z,u,v5 * w)) * x
    ]]></literal>
    <justification jstring="[para(36711(a,1),36824(a,1,1)),flip(a)].">
      <j1 rule="para" parents="36711 36824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36826">
    <literal><![CDATA[
      L(x,y,a(z,u,R(w * (v5 / (1 / y)),y,y))) = L(x,y,a(z,u,(v5 * w) * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,36745,a(flip),b,36825,a),flip(a)].">
      <j1 rule="hyper" parents="347 36745 36825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36827">
    <literal><![CDATA[
      L(x,y,a(z,u,((w * (v5 / y)) * y) * y)) = L(x,y,a(z,u,(v5 * w) * y))
    ]]></literal>
    <justification jstring="[para(22518(a,1),36826(a,1,3,3))].">
      <j1 rule="para" parents="22518 36826"/>
    </justification>
  </clause>

  <clause id="36828">
    <literal><![CDATA[
      L(x,y,a(z,u,(w * v5) * y)) = L(x,y,a(z,u,v5 * (w / y)))
    ]]></literal>
    <justification jstring="[para(31935(a,1),36827(a,1,3)),flip(a)].">
      <j1 rule="para" parents="31935 36827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36830">
    <literal><![CDATA[
      L(x,y,a(z,u,(w * v5) * y)) = L(x,y,a(z,u,v5 * (w * y)))
    ]]></literal>
    <justification jstring="[para(36526(a,1),36828(a,2,3))].">
      <j1 rule="para" parents="36526 36828"/>
    </justification>
  </clause>

  <clause id="36831">
    <literal><![CDATA[
      a(x,a(y,z,u),w * (v5 * v6)) * L(u,z,a(x,w * (v5 * v6),y)) = L(u,z,a(w * (v6 \ v5),x,y))
    ]]></literal>
    <justification jstring="[para(36495(a,1),36540(a,1,1))].">
      <j1 rule="para" parents="36495 36540"/>
    </justification>
  </clause>

  <clause id="36832">
    <literal><![CDATA[
      a((L(x \ 1,x,y) * (x * (z * (x \ 1)))) * u,w,v5) = a((L(z,x,x) * (x \ 1)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(3188(a,1),36582(a,1,1,1,1))].">
      <j1 rule="para" parents="3188 36582"/>
    </justification>
  </clause>

  <clause id="36833">
    <literal><![CDATA[
      a(((x \ 1) * (L(x,x,y) * (z * (x \ 1)))) * u,w,v5) = a((L(z,x,x) * (x \ 1)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(3556(a,1),36832(a,1,1,1))].">
      <j1 rule="para" parents="3556 36832"/>
    </justification>
  </clause>

  <clause id="36834">
    <literal><![CDATA[
      a(((x \ 1) * (x * (y * L(x \ 1,x,z)))) * u,w,v5) = a((L(y,x,x) * (x \ 1)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(21204(a,1),36833(a,1,1,1,2))].">
      <j1 rule="para" parents="21204 36833"/>
    </justification>
  </clause>

  <clause id="36835">
    <literal><![CDATA[
      a(x * (y \ (y * (z * L(y \ 1,y,u)))),w,v5) = a((L(z,y,y) * (y \ 1)) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(36550,a,36834,a)].">
      <j1 rule="hyper" parents="36550 36834"/>
    </justification>
  </clause>

  <clause id="36836">
    <literal><![CDATA[
      a((L(x,y,y) * (y \ 1)) * z,u,w) = a(z * (x * L(y \ 1,y,v5)),u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),36835(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 36835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36837">
    <literal><![CDATA[
      a((x \ L(y,x,x)) * z,u,w) = a(z * (y * L(x \ 1,x,v5)),u,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,36560,a(flip),b,36836,a)].">
      <j1 rule="hyper" parents="63 36560 36836"/>
    </justification>
  </clause>

  <clause id="36839">
    <literal><![CDATA[
      a(x * (y * L(z \ 1,z,u)),w,v5) = a(((z \ 1) * y) * x,w,v5)
    ]]></literal>
    <justification jstring="[para(3202(a,1),36837(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3202 36837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36840">
    <literal><![CDATA[
      a(x * (y * L(z \ 1,z,u)),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x * (z \ y),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(36839(a,2),36550(a,1))].">
      <j1 rule="para" parents="36839 36550"/>
    </justification>
  </clause>

  <clause id="36841">
    <literal><![CDATA[
      a(x * (y * (z \ (u \ z))),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x * (u \ y),w,v5) = v6
    ]]></literal>
    <justification jstring="[para(24719(a,1),36840(a,1))].">
      <j1 rule="para" parents="24719 36840"/>
    </justification>
  </clause>

  <clause id="36842">
    <literal><![CDATA[
      (a(x,y,z * (u * y)) * w) / ((v5 \ w) * a(x,y,z * (u * y))) = L(v5,y,a((u * z) * y,w,x))
    ]]></literal>
    <justification jstring="[para(36697(a,1),36705(a,1,2,2))].">
      <j1 rule="para" parents="36697 36705"/>
    </justification>
  </clause>

  <clause id="36843">
    <literal><![CDATA[
      a(x \ y,z,a((x \ y) * u,(x \ y) * x,w * ((x \ y) * x))) = a(w,x,a(x * y,z,x * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,30797,a(flip),b,36811,a),flip(a)].">
      <j1 rule="hyper" parents="347 30797 36811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36844">
    <literal><![CDATA[
      L(x,y,a(z * (u \ w),v5,v6)) = L(x,y,a(z * (w * u),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(31250,a,36831,a),flip(a)].">
      <j1 rule="hyper" parents="31250 36831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36845">
    <literal><![CDATA[
      a(x \ 1,y,a((z \ 1) * u,w,v5 * w)) = x * L(x \ 1,w,a(w * (u * z),y,v5))
    ]]></literal>
    <justification jstring="[para(36844(a,1),36804(a,2,2))].">
      <j1 rule="para" parents="36844 36804"/>
    </justification>
  </clause>

  <clause id="36846">
    <literal><![CDATA[
      a(x \ 1,y,a((z \ 1) * u,w,v5 * w)) = x \ L(x,w,a(w * (u * z),y,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,3343,a(flip),b,36845,a),flip(a)].">
      <j1 rule="hyper" parents="347 3343 36845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36847">
    <literal><![CDATA[
      L(x,y,a((z * u) * y,w,v5)) = L(x,y,a(u * (z * y),w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,32367,a(flip),b,36842,a),flip(a)].">
      <j1 rule="hyper" parents="63 32367 36842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36848">
    <literal><![CDATA[
      L(x,y,a(z * (u * y),w,v5)) = L(x,y,a(u * z,w,v5 * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,36759,a(flip),b,36847,a),flip(a)].">
      <j1 rule="hyper" parents="63 36759 36847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36849">
    <literal><![CDATA[
      a(x \ y,z,a((x \ y) * u,(x \ y) * x,w * ((y * x) * x))) = a(w,x,a(x * y,z,x * u))
    ]]></literal>
    <justification jstring="[para(36706(a,1),36843(a,1,3))].">
      <j1 rule="para" parents="36706 36843"/>
    </justification>
  </clause>

  <clause id="36850">
    <literal><![CDATA[
      a(x \ y,z,a((x \ y) * u,(x \ y) * x,y * w)) = a(w,x,a(x * y,z,x * u))
    ]]></literal>
    <justification jstring="[para(36492(a,1),36849(a,1,3))].">
      <j1 rule="para" parents="36492 36849"/>
    </justification>
  </clause>

  <clause id="36851">
    <literal><![CDATA[
      a(x \ y,z,a((x \ y) * u,y,y * w)) = a(w,x,a(x * y,z,x * u))
    ]]></literal>
    <justification jstring="[para(24038(a,1),36850(a,1,3))].">
      <j1 rule="para" parents="24038 36850"/>
    </justification>
  </clause>

  <clause id="36854">
    <literal><![CDATA[
      ((x * y) \ (y * z)) * L(T(L(x \ z,x,y) \ z,y),u,w) = a(w,u,L(x,y,z * y)) \ z
    ]]></literal>
    <justification jstring="[para(36712(a,1),36536(a,2,1))].">
      <j1 rule="para" parents="36712 36536"/>
    </justification>
  </clause>

  <clause id="36855">
    <literal><![CDATA[
      ((x * y) \ (y * z)) * L(T(L(x \ z,x,y) \ z,y),u,w) = (a(w,u,x) \ y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(347,a,29152,a(flip),b,36854,a),flip(a)].">
      <j1 rule="hyper" parents="347 29152 36854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36856">
    <literal><![CDATA[
      ((x * y) \ (y * z)) * L(((x * y) \ (y * z)) \ z,u,w) = (a(w,u,x) \ y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(30384(a,1),36855(a,1,2,1))].">
      <j1 rule="para" parents="30384 36855"/>
    </justification>
  </clause>

  <clause id="36857">
    <literal><![CDATA[
      (x * y) \ ((y * L(y \ (x * y),z,u)) * w) = (a(u,z,x) \ y) * (y \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,1989,a(flip),b,36856,a)].">
      <j1 rule="hyper" parents="63 1989 36856"/>
    </justification>
  </clause>

  <clause id="36858">
    <literal><![CDATA[
      (x * y) \ ((L(x,z,u) * y) * w) = (a(u,z,x) \ y) * (y \ w)
    ]]></literal>
    <justification jstring="[para(737(a,1),36857(a,1,2,1))].">
      <j1 rule="para" parents="737 36857"/>
    </justification>
  </clause>

  <clause id="36859">
    <literal><![CDATA[
      a((x \ y) * T(y,z),x * T(y,z),a(u,w,v5)) * y = L(y,x \ T(y,z),a(u,w,v5 * (x \ T(y,z))))
    ]]></literal>
    <justification jstring="[para(30779(a,1),36748(a,1,1))].">
      <j1 rule="para" parents="30779 36748"/>
    </justification>
  </clause>

  <clause id="36860">
    <literal><![CDATA[
      L(x,y \ T(x,z),a(u,w,v5 * (y \ T(x,z)))) = a((y \ x) * T(x,z),x * y,a(u,w,v5)) * x
    ]]></literal>
    <justification jstring="[para(24147(a,1),36859(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24147 36859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36861">
    <literal><![CDATA[
      L(x,y \ T(x,z),a(u,w,v5 * (y \ T(x,z)))) = a((y \ x) * x,x * y,a(u,w,v5)) * x
    ]]></literal>
    <justification jstring="[para(23901(a,1),36860(a,2,1))].">
      <j1 rule="para" parents="23901 36860"/>
    </justification>
  </clause>

  <clause id="36864">
    <literal><![CDATA[
      L(x,y \ T(x,z),a(u,w,v5 * (y \ T(x,z)))) = a((x * y) * x,x * y,a(u,w,v5)) * x
    ]]></literal>
    <justification jstring="[para(36558(a,1),36861(a,2,1))].">
      <j1 rule="para" parents="36558 36861"/>
    </justification>
  </clause>

  <clause id="36865">
    <literal><![CDATA[
      L(x,y \ T(x,z),a(u,w,v5 * (y \ T(x,z)))) = a(y * (x * x),x * y,a(u,w,v5)) * x
    ]]></literal>
    <justification jstring="[para(32329(a,1),36864(a,2,1))].">
      <j1 rule="para" parents="32329 36864"/>
    </justification>
  </clause>

  <clause id="36866">
    <literal><![CDATA[
      L(x,y \ T(x,z),a(u,w,v5 * (y \ T(x,z)))) = a(y,x * y,a(u,w,v5)) * x
    ]]></literal>
    <justification jstring="[para(36615(a,1),36865(a,2,1))].">
      <j1 rule="para" parents="36615 36865"/>
    </justification>
  </clause>

  <clause id="36867">
    <literal><![CDATA[
      L(x,y \ T(x,z),a(u,w,v5 * (y \ T(x,z)))) = a(v5,x,a(y,w,u)) * x
    ]]></literal>
    <justification jstring="[para(32347(a,1),36866(a,2,1))].">
      <j1 rule="para" parents="32347 36866"/>
    </justification>
  </clause>

  <clause id="36869">
    <literal><![CDATA[
      L(x,y \ T(x,z),a(u,w,v5 * (y \ T(x,z)))) = x * a(y,x,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,29845,a(flip),b,36867,a),flip(a)].">
      <j1 rule="hyper" parents="347 29845 36867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36870">
    <literal><![CDATA[
      L(x,y \ T(x,z),a(u,w,v5 * (T(x,z) * y))) = x * a(y,x,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(36495(a,1),36869(a,1,3))].">
      <j1 rule="para" parents="36495 36869"/>
    </justification>
  </clause>

  <clause id="36871">
    <literal><![CDATA[
      L(x,y \ T(x,z),a(u,w,(x * y) * v5)) = x * a(y,x,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(24365(a,1),36870(a,1,3))].">
      <j1 rule="para" parents="24365 36870"/>
    </justification>
  </clause>

  <clause id="36872">
    <literal><![CDATA[
      L(x,y \ T(x,z),a(u,w,y * (v5 * x))) = x * a(y,x,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,36533,a(flip),b,36871,a)].">
      <j1 rule="hyper" parents="63 36533 36871"/>
    </justification>
  </clause>

  <clause id="36874">
    <literal><![CDATA[
      L(x,y * T(x,z),a(u,w,y * (v5 * x))) = x * a(y,x,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(36488,a,36872,a)].">
      <j1 rule="hyper" parents="36488 36872"/>
    </justification>
  </clause>

  <clause id="36875">
    <literal><![CDATA[
      L(x,y * x,a(z,u,y * (w * x))) = x * a(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(21729,a,36874,a)].">
      <j1 rule="hyper" parents="21729 36874"/>
    </justification>
  </clause>

  <clause id="36876">
    <literal><![CDATA[
      L(x,y,a(z,u,y * (w * x))) = x * a(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,32399,a(flip),b,36875,a)].">
      <j1 rule="hyper" parents="63 32399 36875"/>
    </justification>
  </clause>

  <clause id="36877">
    <literal><![CDATA[
      L(x,y,a(y * (z * x),u,w)) = x * a(y,x,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(27578,a,36876,a)].">
      <j1 rule="hyper" parents="27578 36876"/>
    </justification>
  </clause>

  <clause id="36878">
    <literal><![CDATA[
      a(x \ 1,y,a((x \ 1) * z,u,w * u)) = x \ (x * a(u,x,a(w,y,z)))
    ]]></literal>
    <justification jstring="[para(36877(a,1),36846(a,2,2))].">
      <j1 rule="para" parents="36877 36846"/>
    </justification>
  </clause>

  <clause id="36879">
    <literal><![CDATA[
      a(x \ 1,y,a((x \ 1) * z,u,w * u)) = a(u,x,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,9,a(flip),b,36878,a),flip(a)].">
      <j1 rule="hyper" parents="347 9 36878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36880">
    <literal><![CDATA[
      a(x \ 1,y,a(x * z,u,w * u)) = a(u,x,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(32050,a,36879,a)].">
      <j1 rule="hyper" parents="32050 36879"/>
    </justification>
  </clause>

  <clause id="36882">
    <literal><![CDATA[
      a(x,y,a(x * z,u,w * u)) = a(u,x,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(29260,a,36880,a)].">
      <j1 rule="hyper" parents="29260 36880"/>
    </justification>
  </clause>

  <clause id="36883">
    <literal><![CDATA[
      a(x,y,a(z * u,w,z * w)) = a(w,z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(36737,a,36882,a)].">
      <j1 rule="hyper" parents="36737 36882"/>
    </justification>
  </clause>

  <clause id="36884">
    <literal><![CDATA[
      a(x,y,a(y * (x * z),u,w)) = a(y,x,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(36727,a,36882,a)].">
      <j1 rule="hyper" parents="36727 36882"/>
    </justification>
  </clause>

  <clause id="36885">
    <literal><![CDATA[
      a(x * (y * z),y,a(z,u,z * w)) = a(y * z,z,a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(32359,a,36882,a)].">
      <j1 rule="hyper" parents="32359 36882"/>
    </justification>
  </clause>

  <clause id="36886">
    <literal><![CDATA[
      a(x,y,a(x * z,u,u * w)) = a(u,x,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(26564,a,36882,a)].">
      <j1 rule="hyper" parents="26564 36882"/>
    </justification>
  </clause>

  <clause id="36887">
    <literal><![CDATA[
      (((x / y) * (y * a((y \ x) * z,u,w * u))) / a((y \ x) * z,u,w * u)) \ x = a(u,y \ x,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,23152,a,b,36882,a)].">
      <j1 rule="hyper" parents="63 23152 36882"/>
    </justification>
  </clause>

  <clause id="36888">
    <literal><![CDATA[
      a(x,y,a(x * z,u,(w * v5) * u)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u,x,a(v5 * w,y,z)) = v6
    ]]></literal>
    <justification jstring="[para(36882(a,2),26340(a,1))].">
      <j1 rule="para" parents="36882 26340"/>
    </justification>
  </clause>

  <clause id="36890">
    <literal><![CDATA[
      a(x,y,a(z \ ((u * w) \ 1),w,u * w)) = a(w,u,a(x * w,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,36817,a,b,36883,a)].">
      <j1 rule="hyper" parents="63 36817 36883"/>
    </justification>
  </clause>

  <clause id="36891">
    <literal><![CDATA[
      a(x,y,a(z,u,y * (w * x))) = a(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(26563,a,36884,a)].">
      <j1 rule="hyper" parents="26563 36884"/>
    </justification>
  </clause>

  <clause id="36892">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * z != v5
    ]]></literal>
    <literal><![CDATA[
      L(z,x,a(x * (y * w),u,y)) = v5
    ]]></literal>
    <justification jstring="[para(36884(a,1),29864(a,1,1))].">
      <j1 rule="para" parents="36884 29864"/>
    </justification>
  </clause>

  <clause id="36893">
    <literal><![CDATA[
      a(x,y,a(y * (x * z),u,(y * (x * z)) * (w * u))) = a(y,x,a(u * (w * (y * (x * z))),u,z))
    ]]></literal>
    <justification jstring="[para(36544(a,1),36884(a,1,3))].">
      <j1 rule="para" parents="36544 36884"/>
    </justification>
  </clause>

  <clause id="36894">
    <literal><![CDATA[
      a(x,y \ x,a(z,u,w)) = a(z,y,a(y * x,u,y * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36851,a(flip),b,36886,a),flip(a)].">
      <j1 rule="hyper" parents="63 36851 36886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36895">
    <literal><![CDATA[
      a(x,y \ (z \ u),a(w,v5,(y \ (z \ u)) * (v6 * x))) = a((z * y) \ u,x,L(a(w,v5,v6),y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,29688,a,b,36891,a),flip(a)].">
      <j1 rule="hyper" parents="347 29688 36891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36896">
    <literal><![CDATA[
      a(x,y,a(z,u,y * ((w * x) * L(T(x,v5),v6,v7)))) = a(y,x,a(z,u,w * L(T(x,v5),v6,v7)))
    ]]></literal>
    <justification jstring="[para(23523(a,1),36891(a,1,3,3,2))].">
      <j1 rule="para" parents="23523 36891"/>
    </justification>
  </clause>

  <clause id="36897">
    <literal><![CDATA[
      L(x * a(a(y,z,u * (w * v5)),x,a(v6,u,v5)),v6,a(u,v5,a(y,z,w))) = L(x,a(v5,u,a(y,z,u * (w * v5))),v6)
    ]]></literal>
    <justification jstring="[para(36891(a,1),29987(a,1,3))].">
      <j1 rule="para" parents="36891 29987"/>
    </justification>
  </clause>

  <clause id="36898">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) * L(v6,a(z,x,a(x * (w * y),u,y)),v5) = v5 * (a(z,x,a(x * (w * y),u,y)) * v6)
    ]]></literal>
    <justification jstring="[para(36891(a,1),29911(a,1,1,1))].">
      <j1 rule="para" parents="36891 29911"/>
    </justification>
  </clause>

  <clause id="36899">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,u * (a(x,y,z) * v6))) = a(u,L(x,y,z),a(w,v5,v6 * x))
    ]]></literal>
    <justification jstring="[para(36713(a,1),36891(a,1,3))].">
      <j1 rule="para" parents="36713 36891"/>
    </justification>
  </clause>

  <clause id="36900">
    <literal><![CDATA[
      a(x,y * x,a(z,u,w)) = a(z,y,a(y * x,u,y * w))
    ]]></literal>
    <justification jstring="[hyper(36563,a,36894,a)].">
      <j1 rule="hyper" parents="36563 36894"/>
    </justification>
  </clause>

  <clause id="36901">
    <literal><![CDATA[
      a(x,y,a(y * z,u,y * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,y,a(z,u,x)) = v5
    ]]></literal>
    <justification jstring="[para(36900(a,1),32371(a,1))].">
      <j1 rule="para" parents="36900 32371"/>
    </justification>
  </clause>

  <clause id="36902">
    <literal><![CDATA[
      a(x,y,a(x * z,u,y * (w * x))) = a(y * x,x,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,36535,a(flip),b,36885,a)].">
      <j1 rule="hyper" parents="63 36535 36885"/>
    </justification>
  </clause>

  <clause id="36903">
    <literal><![CDATA[
      a(x * y,y,a(z,u,w)) = a(x,y,a(y * w,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,36891,a(flip),b,36902,a),flip(a)].">
      <j1 rule="hyper" parents="63 36891 36902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36904">
    <literal><![CDATA[
      a(x * y,y,a(z,u,w)) = a(x,y,a(w,u,z * y))
    ]]></literal>
    <justification jstring="[hyper(347,a,36730,a(flip),b,36903,a),flip(a)].">
      <j1 rule="hyper" parents="347 36730 36903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36905">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6 * u))) = a(x,y,a(z,u,a(v6,v5,w) * u))
    ]]></literal>
    <justification jstring="[para(36904(a,1),36721(a,1,3))].">
      <j1 rule="para" parents="36904 36721"/>
    </justification>
  </clause>

  <clause id="36906">
    <literal><![CDATA[
      L(x,y,a(y * (z * u),w,z)) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(36892,a,29877,a)].">
      <j1 rule="hyper" parents="36892 29877"/>
    </justification>
  </clause>

  <clause id="36907">
    <literal><![CDATA[
      L(x,y,a(z,u,u * (z * w))) = L(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(29900,a,36906,a)].">
      <j1 rule="hyper" parents="29900 36906"/>
    </justification>
  </clause>

  <clause id="36908">
    <literal><![CDATA[
      L(x,y,a(z,u,w * (z * y))) = L(x,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36519,a(flip),b,36906,a)].">
      <j1 rule="hyper" parents="63 36519 36906"/>
    </justification>
  </clause>

  <clause id="36911">
    <literal><![CDATA[
      L(x,y,a(z,u,z * (y * w))) = L(x,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(36545,a,36907,a)].">
      <j1 rule="hyper" parents="36545 36907"/>
    </justification>
  </clause>

  <clause id="36913">
    <literal><![CDATA[
      L(x,y,a(z,u,w * (z * u))) = L(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[para(31023(a,2),36907(a,1,3))].">
      <j1 rule="para" parents="31023 36907"/>
    </justification>
  </clause>

  <clause id="36914">
    <literal><![CDATA[
      L(x,y,(z * (u * y)) \ L(z * (u * y),w,u)) = L(x,w,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(28896,a,36908,a)].">
      <j1 rule="hyper" parents="28896 36908"/>
    </justification>
  </clause>

  <clause id="36915">
    <literal><![CDATA[
      L(x,y,a(z,u,(w * ((y * z) * u)) * y)) = L(x,y,a(u,y * z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36760,a(flip),b,36913,a)].">
      <j1 rule="hyper" parents="63 36760 36913"/>
    </justification>
  </clause>

  <clause id="36916">
    <literal><![CDATA[
      a(x,y,a(z * ((u * w) \ 1),w,u * w)) = a(w,u,a(x * w,y,z))
    ]]></literal>
    <justification jstring="[hyper(30815,a,36890,a)].">
      <j1 rule="hyper" parents="30815 36890"/>
    </justification>
  </clause>

  <clause id="36917">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6 * u))) * x = R(x,y,a(z,u,a(v6,v5,w) * u))
    ]]></literal>
    <justification jstring="[hyper(133,a,36905,a,b,28907,a(flip))].">
      <j1 rule="hyper" parents="133 36905 28907"/>
    </justification>
  </clause>

  <clause id="36918">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5) \ v6,a(v5,w,u * (a(u,w,v5) \ v6)))) = a(x,y,a(z,a(u,w,v5) \ v6,v6))
    ]]></literal>
    <justification jstring="[para(10(a,1),36905(a,2,3,3))].">
      <j1 rule="para" parents="10 36905"/>
    </justification>
  </clause>

  <clause id="36919">
    <literal><![CDATA[
      L(L(x,a(y,z,u),a(w,v5,v6) * x),a(w,v5,v6) * x,a(y,z,u)) = x * a(u,z,a(y,x,a(v6,v5,w * x)))
    ]]></literal>
    <justification jstring="[para(36905(a,2),29814(a,2,2))].">
      <j1 rule="para" parents="36905 29814"/>
    </justification>
  </clause>

  <clause id="36920">
    <literal><![CDATA[
      L(x,y,a(z,u,(z * y) * w) \ 1) = L(x,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[para(28922(a,1),36914(a,1,3))].">
      <j1 rule="para" parents="28922 36914"/>
    </justification>
  </clause>

  <clause id="36921">
    <literal><![CDATA[
      L(x,y,a(z,u,z * (w * y)) \ 1) = L(x,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[para(36523(a,1),36920(a,1,3,1))].">
      <j1 rule="para" parents="36523 36920"/>
    </justification>
  </clause>

  <clause id="36922">
    <literal><![CDATA[
      L(x,y,a(z * (u * y),w,z)) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(27582,a,36921,a)].">
      <j1 rule="hyper" parents="27582 36921"/>
    </justification>
  </clause>

  <clause id="36923">
    <literal><![CDATA[
      L(x,y,a(z * u,w,u * y)) = L(x,w,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,36848,a(flip),b,36922,a)].">
      <j1 rule="hyper" parents="63 36848 36922"/>
    </justification>
  </clause>

  <clause id="36924">
    <literal><![CDATA[
      L(x,y,a(z * (u * w),z,w * y)) = L(x,z,a(y,w,u * z))
    ]]></literal>
    <justification jstring="[para(36791(a,1),36923(a,1,3))].">
      <j1 rule="para" parents="36791 36923"/>
    </justification>
  </clause>

  <clause id="36925">
    <literal><![CDATA[
      L(x,y,a(z,u,((y * z) * u) * (w * y))) = L(x,y,a(u,y * z,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36830,a(flip),b,36915,a)].">
      <j1 rule="hyper" parents="63 36830 36915"/>
    </justification>
  </clause>

  <clause id="36926">
    <literal><![CDATA[
      a(x,y,a((z * u) \ w,u,z * u)) = a(u,z,a(x * u,y,w))
    ]]></literal>
    <justification jstring="[para(29728(a,1),36916(a,1,3))].">
      <j1 rule="para" parents="29728 36916"/>
    </justification>
  </clause>

  <clause id="36927">
    <literal><![CDATA[
      a(x,y,a(z \ (u \ w),u,z * u)) = a(u,z,a(x * u,y,w))
    ]]></literal>
    <justification jstring="[para(32212(a,1),36926(a,1,3))].">
      <j1 rule="para" parents="32212 36926"/>
    </justification>
  </clause>

  <clause id="36928">
    <literal><![CDATA[
      a(x,y,a(z * (u \ w),u,z * u)) = a(u,z,a(x * u,y,w))
    ]]></literal>
    <justification jstring="[hyper(30815,a,36927,a)].">
      <j1 rule="hyper" parents="30815 36927"/>
    </justification>
  </clause>

  <clause id="36929">
    <literal><![CDATA[
      a(x,y,a(z * x,u,w)) = a(x,y,a(z,u,x \ w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36883,a(flip),b,36928,a),flip(a)].">
      <j1 rule="hyper" parents="63 36883 36928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36930">
    <literal><![CDATA[
      a(x,y,a(z * x,u,w)) = a(x,y,a(z,u,x * w))
    ]]></literal>
    <justification jstring="[hyper(347,a,30785,a(flip),b,36929,a),flip(a)].">
      <j1 rule="hyper" parents="347 30785 36929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36931">
    <literal><![CDATA[
      a(x,y,a(z * x,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,x * w)) = v5
    ]]></literal>
    <justification jstring="[para(36929(a,2),35032(a,1))].">
      <j1 rule="para" parents="36929 35032"/>
    </justification>
  </clause>

  <clause id="36932">
    <literal><![CDATA[
      a(x,y,a(x * z,u,w)) = a(x,y,a(z,u,x * w))
    ]]></literal>
    <justification jstring="[hyper(26340,a,36930,a)].">
      <j1 rule="hyper" parents="26340 36930"/>
    </justification>
  </clause>

  <clause id="36933">
    <literal><![CDATA[
      a(x,y,a(z,u,x * w)) * x = R(x,y,a(z * x,u,w))
    ]]></literal>
    <justification jstring="[hyper(133,a,36930,a(flip),b,28907,a(flip))].">
      <j1 rule="hyper" parents="133 36930 28907"/>
    </justification>
  </clause>

  <clause id="36934">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,y * w)),u,a(y,z * y,w)) = L(x,a(w,u,y),z * y)
    ]]></literal>
    <justification jstring="[para(36930(a,1),29993(a,1,1,2))].">
      <j1 rule="para" parents="36930 29993"/>
    </justification>
  </clause>

  <clause id="36935">
    <literal><![CDATA[
      a(x,L(y,z,u),a(x * w,v5,v6)) = a(x,y,a(w,v5,x * L(v6,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,30088,a,b,36932,a)].">
      <j1 rule="hyper" parents="63 30088 36932"/>
    </justification>
  </clause>

  <clause id="36936">
    <literal><![CDATA[
      a((x \ y) * T(x,y),z,a(((x \ y) * T(x,y)) * u,w,T(x,v5))) = a((x \ y) * T(x,y),z,a(u,w,x * ((x \ y) * T(x,v5))))
    ]]></literal>
    <justification jstring="[para(22019(a,1),36932(a,2,3,3))].">
      <j1 rule="para" parents="22019 36932"/>
    </justification>
  </clause>

  <clause id="36937">
    <literal><![CDATA[
      a(R(x,y,z),u,a(R(x,y,z) * w,v5,L(z,y,x))) = a(R(x,y,z),u,a(w,v5,x * z))
    ]]></literal>
    <justification jstring="[para(29303(a,1),36932(a,2,3,3))].">
      <j1 rule="para" parents="29303 36932"/>
    </justification>
  </clause>

  <clause id="36938">
    <literal><![CDATA[
      x * a(y,z,a(u,w,y * v5)) = x * a(y,w,a(v5,z,y * u))
    ]]></literal>
    <justification jstring="[para(36932(a,1),29870(a,1,2))].">
      <j1 rule="para" parents="36932 29870"/>
    </justification>
  </clause>

  <clause id="36939">
    <literal><![CDATA[
      R(x,y,a(z * x,u,w)) = L(x,y,a(z,u,x * w))
    ]]></literal>
    <justification jstring="[hyper(29007,a,36933,a),flip(a)].">
      <j1 rule="hyper" parents="29007 36933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36940">
    <literal><![CDATA[
      L(x,y,a(z * x,u,w)) = L(x,y,a(z,u,x * w))
    ]]></literal>
    <justification jstring="[hyper(23284,a,36939,a)].">
      <j1 rule="hyper" parents="23284 36939"/>
    </justification>
  </clause>

  <clause id="36941">
    <literal><![CDATA[
      a(x * y,z,a(u,w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y,z,a(x,w,y * u)) = v5
    ]]></literal>
    <justification jstring="[para(29803(a,2),36931(a,1))].">
      <j1 rule="para" parents="29803 36931"/>
    </justification>
  </clause>

  <clause id="36942">
    <literal><![CDATA[
      a(x,y,a(z * (x * u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z * u,w,x * v5)) = v6
    ]]></literal>
    <justification jstring="[para(36616(a,1),36931(a,1))].">
      <j1 rule="para" parents="36616 36931"/>
    </justification>
  </clause>

  <clause id="36943">
    <literal><![CDATA[
      L(x,y,a(z,u,(y * z) * ((w * y) * u))) = L(x,y,a(u,y * z,w))
    ]]></literal>
    <justification jstring="[para(36770(a,1),36925(a,1,3))].">
      <j1 rule="para" parents="36770 36925"/>
    </justification>
  </clause>

  <clause id="36944">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,v5,x * v6)) = a(x,y,a(w,v5,x * L(v6,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,36932,a(flip),b,36935,a)].">
      <j1 rule="hyper" parents="63 36932 36935"/>
    </justification>
  </clause>

  <clause id="36945">
    <literal><![CDATA[
      L(x,y,a(z,u,z * (((w * y) * u) * y))) = L(x,y,a(u,y * z,w))
    ]]></literal>
    <justification jstring="[para(36522(a,1),36943(a,1,3))].">
      <j1 rule="para" parents="36522 36943"/>
    </justification>
  </clause>

  <clause id="36946">
    <literal><![CDATA[
      a(x,y,a(z,u,L(x * w,v5,v6))) = a(x,y,a(z,u,x * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(63,a,30088,a(flip),b,36944,a)].">
      <j1 rule="hyper" parents="63 30088 36944"/>
    </justification>
  </clause>

  <clause id="36947">
    <literal><![CDATA[
      L(x,y,a(z,u,z * (y * ((y * w) * u)))) = L(x,y,a(u,y * z,w))
    ]]></literal>
    <justification jstring="[para(24407(a,1),36945(a,1,3))].">
      <j1 rule="para" parents="24407 36945"/>
    </justification>
  </clause>

  <clause id="36948">
    <literal><![CDATA[
      a(x,y,a(z,u,L(x * w,v5,w))) = a(x,y,a(z,u,x * w))
    ]]></literal>
    <justification jstring="[para(12439(a,1),36946(a,2,3))].">
      <j1 rule="para" parents="12439 36946"/>
    </justification>
  </clause>

  <clause id="36949">
    <literal><![CDATA[
      L(x,y,a(z,u,(z * w) * y)) = L(x,z,a(y,z * u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36911,a(flip),b,36947,a)].">
      <j1 rule="hyper" parents="63 36911 36947"/>
    </justification>
  </clause>

  <clause id="36950">
    <literal><![CDATA[
      L(x,y,a(z,u,z * (y * w))) = L(x,z,a(y,z * u,w))
    ]]></literal>
    <justification jstring="[para(36523(a,1),36949(a,1,3))].">
      <j1 rule="para" parents="36523 36949"/>
    </justification>
  </clause>

  <clause id="36951">
    <literal><![CDATA[
      L(x,y,a(z,y * u,w)) = L(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36911,a(flip),b,36950,a),flip(a)].">
      <j1 rule="hyper" parents="63 36911 36950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36952">
    <literal><![CDATA[
      L(x,y * z,a(u,z,w)) = L(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(29899,a,36951,a)].">
      <j1 rule="hyper" parents="29899 36951"/>
    </justification>
  </clause>

  <clause id="36954">
    <literal><![CDATA[
      a(x,y,L(a(z,u,y * (a(x,w,v5) * v6)),w,v5)) = a(y,L(x,w,v5),a(z,u,v6 * x))
    ]]></literal>
    <justification jstring="[hyper(29676,a,36899,a)].">
      <j1 rule="hyper" parents="29676 36899"/>
    </justification>
  </clause>

  <clause id="36955">
    <literal><![CDATA[
      a(x,y,a(z,u,L(y * (a(x,w,v5) * v6),w,v5))) = a(y,L(x,w,v5),a(z,u,v6 * x))
    ]]></literal>
    <justification jstring="[para(29113(a,2),36954(a,1,3))].">
      <j1 rule="para" parents="29113 36954"/>
    </justification>
  </clause>

  <clause id="36956">
    <literal><![CDATA[
      a(R(x,y,z),u,a(L(x,y,z) * w,v5,L(z,y,x))) = a(R(x,y,z),u,a(w,v5,x * z))
    ]]></literal>
    <justification jstring="[para(26806(a,1),36937(a,1,3))].">
      <j1 rule="para" parents="26806 36937"/>
    </justification>
  </clause>

  <clause id="36957">
    <literal><![CDATA[
      a(x,y,L(a(L(x,z,u) * w,v5,L(u,z,x)),z,u)) = a(R(x,z,u),y,a(w,v5,x * u))
    ]]></literal>
    <justification jstring="[hyper(29721,a,36956,a)].">
      <j1 rule="hyper" parents="29721 36956"/>
    </justification>
  </clause>

  <clause id="36958">
    <literal><![CDATA[
      a(x,y,a(L(x,z,u) * w,v5,L(u,z,x))) = a(R(x,z,u),y,a(w,v5,x * u))
    ]]></literal>
    <justification jstring="[para(27542(a,1),36957(a,1,3))].">
      <j1 rule="para" parents="27542 36957"/>
    </justification>
  </clause>

  <clause id="36959">
    <literal><![CDATA[
      a(R(x,y,z),u,a(w,v5,x * z)) = a(x,u,a(L(x,y,z) * w,v5,z))
    ]]></literal>
    <justification jstring="[hyper(29205,a,36958,a),flip(a)].">
      <j1 rule="hyper" parents="29205 36958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36961">
    <literal><![CDATA[
      a(x,y,a(L(x,z,u) * w,v5,u)) = a(x,y,L(a(w,v5,x * u),z,u))
    ]]></literal>
    <justification jstring="[hyper(29721,a,36959,a),flip(a)].">
      <j1 rule="hyper" parents="29721 36959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36963">
    <literal><![CDATA[
      a(x,y,a(L(x,z,u) * w,v5,u)) = a(x,y,a(w,v5,L(x * u,z,u)))
    ]]></literal>
    <justification jstring="[para(29113(a,2),36961(a,2,3))].">
      <j1 rule="para" parents="29113 36961"/>
    </justification>
  </clause>

  <clause id="36964">
    <literal><![CDATA[
      a(x,y,a(L(x,z,u) * w,v5,u)) = a(x,y,a(w,v5,x * u))
    ]]></literal>
    <justification jstring="[hyper(347,a,36948,a(flip),b,36963,a),flip(a)].">
      <j1 rule="hyper" parents="347 36948 36963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36966">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,y * w)),L(y,v5,w) \ u,a(y,z,w)) = L(x,a(y,z,w),L(y,v5,w) * u)
    ]]></literal>
    <justification jstring="[para(36964(a,1),30457(a,1,1,2))].">
      <j1 rule="para" parents="36964 30457"/>
    </justification>
  </clause>

  <clause id="36967">
    <literal><![CDATA[
      a(x,y,a(z,u,w * L(T(y,v5),v6,v7))) = a(y,x,a(z,u,x * ((w * y) * L(y,v6,v7))))
    ]]></literal>
    <justification jstring="[para(24302(a,1),36896(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24302 36896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36969">
    <literal><![CDATA[
      a(x,y,a(z,u,w * L(T(y,v5),v6,v7))) = a(y,x,a(z,u,x * (a(y,v6,v7) * w)))
    ]]></literal>
    <justification jstring="[para(36713(a,1),36967(a,2,3))].">
      <j1 rule="para" parents="36713 36967"/>
    </justification>
  </clause>

  <clause id="36970">
    <literal><![CDATA[
      a(x,y \ (z \ u),a(w,v5,(y * (z \ u)) * (v6 * x))) = a((z * y) \ u,x,L(a(w,v5,v6),y,z))
    ]]></literal>
    <justification jstring="[para(36546(a,1),36895(a,1,3))].">
      <j1 rule="para" parents="36546 36895"/>
    </justification>
  </clause>

  <clause id="36971">
    <literal><![CDATA[
      a(x,y \ (z \ u),a(w,v5,(y * (u * z)) * (v6 * x))) = a((z * y) \ u,x,L(a(w,v5,v6),y,z))
    ]]></literal>
    <justification jstring="[para(36693(a,1),36970(a,1,3))].">
      <j1 rule="para" parents="36693 36970"/>
    </justification>
  </clause>

  <clause id="36972">
    <literal><![CDATA[
      a(x,y * (z * u),a(w,v5,(y * (z * u)) * (v6 * x))) = a((u * y) \ z,x,L(a(w,v5,v6),y,u))
    ]]></literal>
    <justification jstring="[hyper(36577,a,36971,a)].">
      <j1 rule="hyper" parents="36577 36971"/>
    </justification>
  </clause>

  <clause id="36973">
    <literal><![CDATA[
      a((x * y) \ z,u,L(a(w,v5,v6),y,x)) = a(y * (z * x),u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,36891,a(flip),b,36972,a),flip(a)].">
      <j1 rule="hyper" parents="63 36891 36972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36974">
    <literal><![CDATA[
      a((x * y) \ z,u,a(w,v5,L(v6,y,x))) = a(y * (z * x),u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(29113(a,2),36973(a,1,3))].">
      <j1 rule="para" parents="29113 36973"/>
    </justification>
  </clause>

  <clause id="36975">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5) \ v6,a(v5,w,u * (a(u,w,v5) \ v6)))) = a(x,y,a(z,a(u,w,v5) * v6,v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,30799,a(flip),b,36918,a),flip(a)].">
      <j1 rule="hyper" parents="347 30799 36918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36976">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5) \ v6,a(v5,w,u * (a(u,w,v5) \ v6)))) = a(z,y,a(v6,a(u,w,v5),x))
    ]]></literal>
    <justification jstring="[hyper(347,a,32388,a(flip),b,36975,a),flip(a)].">
      <j1 rule="hyper" parents="347 32388 36975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36977">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5) \ v6,a(v5,w,u * (v6 * a(u,w,v5))))) = a(z,y,a(v6,a(u,w,v5),x))
    ]]></literal>
    <justification jstring="[para(36495(a,1),36976(a,1,3,3))].">
      <j1 rule="para" parents="36495 36976"/>
    </justification>
  </clause>

  <clause id="36978">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5) \ v6,a(v5,w,R(u,w,v5) * v6))) = a(z,y,a(v6,a(u,w,v5),x))
    ]]></literal>
    <justification jstring="[para(31995(a,1),36977(a,1,3,3,3))].">
      <j1 rule="para" parents="31995 36977"/>
    </justification>
  </clause>

  <clause id="36979">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5) \ v6,a(v5,w,L(u,w,v5) * v6))) = a(z,y,a(v6,a(u,w,v5),x))
    ]]></literal>
    <justification jstring="[para(25242(a,1),36978(a,1,3,3))].">
      <j1 rule="para" parents="25242 36978"/>
    </justification>
  </clause>

  <clause id="36980">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5) * v6,a(v5,w,L(u,w,v5) * v6))) = a(z,y,a(v6,a(u,w,v5),x))
    ]]></literal>
    <justification jstring="[hyper(63,a,30799,a(flip),b,36979,a)].">
      <j1 rule="hyper" parents="63 30799 36979"/>
    </justification>
  </clause>

  <clause id="36981">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w) * v5,v5,a(w,u,v6))) = a(v6,y,a(v5,a(z,u,w),x))
    ]]></literal>
    <justification jstring="[para(36642(a,1),36980(a,1,3))].">
      <j1 rule="para" parents="36642 36980"/>
    </justification>
  </clause>

  <clause id="36983">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),v5,a(v6,u,w * v5))) = a(v6,y,a(v5,a(z,u,w),x))
    ]]></literal>
    <justification jstring="[para(36904(a,1),36981(a,1,3))].">
      <j1 rule="para" parents="36904 36981"/>
    </justification>
  </clause>

  <clause id="36984">
    <literal><![CDATA[
      a(x,y,a(z,u,L(a(w,v5,v6 * u),v5,v6))) = a(w,y,a(u,a(z,v5,v6),x))
    ]]></literal>
    <justification jstring="[hyper(30015,a,36983,a)].">
      <j1 rule="hyper" parents="30015 36983"/>
    </justification>
  </clause>

  <clause id="36986">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6 * u))) = a(w,y,a(u,a(z,v5,v6),x))
    ]]></literal>
    <justification jstring="[para(32623(a,1),36984(a,1,3,3))].">
      <j1 rule="para" parents="32623 36984"/>
    </justification>
  </clause>

  <clause id="36989">
    <literal><![CDATA[
      R(x,y,a(z,u,a(w,v5,v6) * u)) = a(v6,y,a(u,a(z,v5,w),x)) * x
    ]]></literal>
    <justification jstring="[para(36986(a,1),36917(a,1,1)),flip(a)].">
      <j1 rule="para" parents="36986 36917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36990">
    <literal><![CDATA[
      R(x,y,a(z,u,a(w,v5,v6) * u)) = L(x,y,a(u,a(z,v5,w),v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,29884,a(flip),b,36989,a),flip(a)].">
      <j1 rule="hyper" parents="347 29884 36989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36991">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6) * u)) = L(x,y,a(u,a(z,v5,w),v6))
    ]]></literal>
    <justification jstring="[hyper(23284,a,36990,a)].">
      <j1 rule="hyper" parents="23284 36990"/>
    </justification>
  </clause>

  <clause id="36992">
    <literal><![CDATA[
      L(L(x,a(y,z,u),a(w,v5,v6)),a(w,v5,v6),a(y,z,u) * x) = x * a(v6,v5,a(w,x,a(u,z,y * x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,32401,a(flip),b,36919,a)].">
      <j1 rule="hyper" parents="63 32401 36919"/>
    </justification>
  </clause>

  <clause id="36993">
    <literal><![CDATA[
      L(x,y,a(a(z,u,w),v5,v6 * y)) = x * a(v6,v5,a(y,x,a(w,u,z * x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,36796,a(flip),b,36992,a)].">
      <j1 rule="hyper" parents="63 36796 36992"/>
    </justification>
  </clause>

  <clause id="36994">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w * y,v5,v6))) = x * a(w,v5,a(y,x,a(v6,u,z * x)))
    ]]></literal>
    <justification jstring="[para(29790(a,1),36993(a,1,3))].">
      <j1 rule="para" parents="29790 36993"/>
    </justification>
  </clause>

  <clause id="36995">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,y * v6))) = x * a(w,v5,a(y,x,a(v6,u,z * x)))
    ]]></literal>
    <justification jstring="[hyper(63,a,36765,a(flip),b,36994,a)].">
      <j1 rule="hyper" parents="63 36765 36994"/>
    </justification>
  </clause>

  <clause id="36996">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,y * v6))) = x * a(v6,v5,a(x,a(y,u,z),w))
    ]]></literal>
    <justification jstring="[para(36986(a,1),36995(a,2,2))].">
      <j1 rule="para" parents="36986 36995"/>
    </justification>
  </clause>

  <clause id="36997">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,y * v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,u,z),a(v6,v5,w)) = v7
    ]]></literal>
    <justification jstring="[para(36996(a,2),29920(a,1))].">
      <j1 rule="para" parents="36996 29920"/>
    </justification>
  </clause>

  <clause id="36998">
    <literal><![CDATA[
      a(x,y,a((z \ u) * w,v5,v6)) * a(x,(u * (z \ 1)) * w,a(y,v5,v6)) = a((z \ u) * w,a(v6,v5,x),y)
    ]]></literal>
    <justification jstring="[para(36560(a,1),36571(a,1,1,3))].">
      <j1 rule="para" parents="36560 36571"/>
    </justification>
  </clause>

  <clause id="36999">
    <literal><![CDATA[
      x \ (x * L(y * (L(L(y,z,z),z,z) \ (a(z,z,y) \ u)),w,v5)) = L(a(z,z,y) * L(u,w,v5),a(z,z,y),x)
    ]]></literal>
    <justification jstring="[para(27903(a,1),36591(a,1,2,2,1))].">
      <j1 rule="para" parents="27903 36591"/>
    </justification>
  </clause>

  <clause id="37000">
    <literal><![CDATA[
      (a(x,y,z * (u * w)) * (u / w)) \ (a(x,y,z * (u * w)) * u) = a(w * (w * u),u * w,a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[para(24228(a,1),36746(a,2,1))].">
      <j1 rule="para" parents="24228 36746"/>
    </justification>
  </clause>

  <clause id="37001">
    <literal><![CDATA[
      (((x / y) * (y * a((y \ x) * z,u,w * u))) / a((y \ x) * z,u,w * u)) \ x = a(u,y * x,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,36463,a(flip),b,36887,a),flip(a)].">
      <j1 rule="hyper" parents="347 36463 36887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37002">
    <literal><![CDATA[
      L(a(x,x,y) * L(z,u,w),a(x,x,y),v5) = v5 \ (v5 * L(y * (L(y,x,x) \ z),u,w))
    ]]></literal>
    <justification jstring="[para(29488(a,1),36999(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="29488 36999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37004">
    <literal><![CDATA[
      L(a(x,x,y) * L(z,u,w),a(x,x,y),v5) = v5 \ (v5 * L(z * a(x,x,y),u,w))
    ]]></literal>
    <justification jstring="[para(31810(a,1),37002(a,2,2,2,1))].">
      <j1 rule="para" parents="31810 37002"/>
    </justification>
  </clause>

  <clause id="37005">
    <literal><![CDATA[
      L(x * a(y,y,z),u,w) = a(y,y,z) * L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(28913,a,37004,a)].">
      <j1 rule="hyper" parents="28913 37004"/>
    </justification>
  </clause>

  <clause id="37006">
    <literal><![CDATA[
      a(x,L(y,a(z,z,u),L(w,v5,v6)) * L(w * a(z,z,u),v5,v6),v7) = a(x,L(w,v5,v6) * (a(z,z,u) * y),v7)
    ]]></literal>
    <justification jstring="[para(37005(a,2),24319(a,1,2,2))].">
      <j1 rule="para" parents="37005 24319"/>
    </justification>
  </clause>

  <clause id="37007">
    <literal><![CDATA[
      a(x,L(y,z,u) * (a(w,w,v5) * v6),v7) = a(x,v6 * L(y * a(w,w,v5),z,u),v7)
    ]]></literal>
    <justification jstring="[para(32100(a,1),37006(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="32100 37006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37008">
    <literal><![CDATA[
      a(x,y * L(z * a(u,u,w),v5,v6),v7) = a(x,L(z,v5,v6) * y,v7)
    ]]></literal>
    <justification jstring="[hyper(36675,a,37007,a),flip(a)].">
      <j1 rule="hyper" parents="36675 37007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37009">
    <literal><![CDATA[
      a(x,y * L(a(z,z,u) * w,v5,v6),v7) = a(x,L(w,v5,v6) * y,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,24602,a,b,37008,a)].">
      <j1 rule="hyper" parents="63 24602 37008"/>
    </justification>
  </clause>

  <clause id="37011">
    <literal><![CDATA[
      (a(x,y,z * (u * w)) * (u / w)) \ (a(x,y,z * (u * w)) * u) = a(u,u * w,a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[para(30780(a,1),37000(a,2,1))].">
      <j1 rule="para" parents="30780 37000"/>
    </justification>
  </clause>

  <clause id="37013">
    <literal><![CDATA[
      (a(x,y,z * (u * w)) * (u / w)) \ (a(x,y,z * (u * w)) * u) = a(z,w,a(u,y,x)) * w
    ]]></literal>
    <justification jstring="[para(32349(a,1),37011(a,2,1))].">
      <j1 rule="para" parents="32349 37011"/>
    </justification>
  </clause>

  <clause id="37014">
    <literal><![CDATA[
      (a(x,y,z * (u * w)) * (u / w)) \ (a(x,y,z * (u * w)) * u) = w * a(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,29845,a(flip),b,37013,a),flip(a)].">
      <j1 rule="hyper" parents="347 29845 37013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37015">
    <literal><![CDATA[
      L(x,y,a(z,u,w * (u * x))) = x * a(u,x,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,32366,a(flip),b,37014,a)].">
      <j1 rule="hyper" parents="63 32366 37014"/>
    </justification>
  </clause>

  <clause id="37016">
    <literal><![CDATA[
      L(x,y,a(z,u,x * (w * y))) = x * a(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(36662,a,37015,a)].">
      <j1 rule="hyper" parents="36662 37015"/>
    </justification>
  </clause>

  <clause id="37017">
    <literal><![CDATA[
      L(x,y,a(z,u,w * (x * u))) = x * a(u,x,a(z,y,w))
    ]]></literal>
    <justification jstring="[para(24082(a,1),37015(a,1,3))].">
      <j1 rule="para" parents="24082 37015"/>
    </justification>
  </clause>

  <clause id="37018">
    <literal><![CDATA[
      L(x,y,a(z,u,x * (w * u))) = x * a(u,x,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(29903,a,37016,a)].">
      <j1 rule="hyper" parents="29903 37016"/>
    </justification>
  </clause>

  <clause id="37019">
    <literal><![CDATA[
      a(x,y,a(z,u,z * (w * u))) = a(u,z,a(x,y,w))
    ]]></literal>
    <justification jstring="[hyper(29879,a,37016,a)].">
      <j1 rule="hyper" parents="29879 37016"/>
    </justification>
  </clause>

  <clause id="37020">
    <literal><![CDATA[
      L(x,y,a(z * x,u,w * y)) = x * a(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36940,a,b,37016,a)].">
      <j1 rule="hyper" parents="63 36940 37016"/>
    </justification>
  </clause>

  <clause id="37021">
    <literal><![CDATA[
      x * a(y,x,a(z,u,y * w)) = L(x,y,a(z,u,w * x))
    ]]></literal>
    <justification jstring="[para(36491(a,1),37016(a,1,3)),flip(a)].">
      <j1 rule="para" parents="36491 37016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37022">
    <literal><![CDATA[
      x * a(y,x,a(z,u,w * y)) = L(x,y,a(z,u,w * x))
    ]]></literal>
    <justification jstring="[para(36492(a,1),37016(a,1,3)),flip(a)].">
      <j1 rule="para" parents="36492 37016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37026">
    <literal><![CDATA[
      a(x,y,a(z,(u * (w / u)) \ v5,z * (K(u \ w,u) * v5))) = a((u * (w / u)) \ v5,z,a(x,y,w))
    ]]></literal>
    <justification jstring="[para(10316(a,1),37019(a,1,3,3,2))].">
      <j1 rule="para" parents="10316 37019"/>
    </justification>
  </clause>

  <clause id="37027">
    <literal><![CDATA[
      x * a(y,z,a(u,x,y * w)) = L(x,y,a(w,z,u * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,36938,a,b,37021,a)].">
      <j1 rule="hyper" parents="63 36938 37021"/>
    </justification>
  </clause>

  <clause id="37028">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w * x)),u,a(y,z * y,w)) = L(x,a(w,u,y),z * y)
    ]]></literal>
    <justification jstring="[para(37021(a,1),36934(a,1,1))].">
      <j1 rule="para" parents="37021 36934"/>
    </justification>
  </clause>

  <clause id="37029">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w * x)),L(y,v5,z) \ w,a(y,u,z)) = L(x,a(y,u,z),L(y,v5,z) * w)
    ]]></literal>
    <justification jstring="[para(37027(a,1),36966(a,1,1))].">
      <j1 rule="para" parents="37027 36966"/>
    </justification>
  </clause>

  <clause id="37030">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w * x)),u,a(y,z,w)) = L(x,a(w,u,y),z * y)
    ]]></literal>
    <justification jstring="[hyper(36612,a,37028,a)].">
      <j1 rule="hyper" parents="36612 37028"/>
    </justification>
  </clause>

  <clause id="37031">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w * x)),L(y,v5,z) * w,a(y,u,z)) = L(x,a(y,u,z),L(y,v5,z) * w)
    ]]></literal>
    <justification jstring="[hyper(36488,a,37029,a)].">
      <j1 rule="hyper" parents="36488 37029"/>
    </justification>
  </clause>

  <clause id="37032">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w * x)),u,a(z,w,y)) = L(x,a(y,u,z),L(y,v5,z) * w)
    ]]></literal>
    <justification jstring="[hyper(36690,a,37031,a)].">
      <j1 rule="hyper" parents="36690 37031"/>
    </justification>
  </clause>

  <clause id="37034">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w * x)),u,a(z,w,y)) = L(x,a(y,u,z),y * w)
    ]]></literal>
    <justification jstring="[para(534(a,1),37032(a,2,3,1))].">
      <j1 rule="para" parents="534 37032"/>
    </justification>
  </clause>

  <clause id="37035">
    <literal><![CDATA[
      L(x,a(y,z,u),L(y,w,u) * v5) = L(x,a(y,z,u),y * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,37032,a(flip),b,37034,a)].">
      <j1 rule="hyper" parents="63 37032 37034"/>
    </justification>
  </clause>

  <clause id="37036">
    <literal><![CDATA[
      L(x,a(y,z,u),L(u,w,y) * v5) = L(1 / x,a(u,z,y),u * v5) \ 1
    ]]></literal>
    <justification jstring="[para(37035(a,1),28754(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37035 28754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37037">
    <literal><![CDATA[
      L(x,a(y,z,u),L(u,w,y) * v5) = L(x,a(y,z,u),u * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,28754,a(flip),b,37036,a),flip(a)].">
      <j1 rule="hyper" parents="347 28754 37036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37038">
    <literal><![CDATA[
      a((x * (y / x)) \ z,u,a(w,v5,y)) = a(w,v5,a(u,(x * (y / x)) \ z,u * z))
    ]]></literal>
    <justification jstring="[para(24078(a,1),37026(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24078 37026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37039">
    <literal><![CDATA[
      a((x * (y / x)) \ z,u,a(w,v5,y)) = a(w,v5,a(u,(x * (y / x)) * z,u * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,30799,a(flip),b,37038,a),flip(a)].">
      <j1 rule="hyper" parents="347 30799 37038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37041">
    <literal><![CDATA[
      a((x * (y / x)) \ z,u,a(w,v5,y)) = a(w,v5,a(u,(x * (y * x)) * z,u * z))
    ]]></literal>
    <justification jstring="[para(36683(a,1),37039(a,2,3))].">
      <j1 rule="para" parents="36683 37039"/>
    </justification>
  </clause>

  <clause id="37042">
    <literal><![CDATA[
      a((x * (y / x)) \ z,u,a(w,v5,y)) = a(w,v5,a(u,z * y,u * z))
    ]]></literal>
    <justification jstring="[para(36605(a,1),37041(a,2,3))].">
      <j1 rule="para" parents="36605 37041"/>
    </justification>
  </clause>

  <clause id="37044">
    <literal><![CDATA[
      (a((x \ y) * z,u,w * u) \ ((y / x) * (x * a((x \ y) * z,u,w * u)))) \ y = a(u,x * y,a(w,x,z))
    ]]></literal>
    <justification jstring="[para(19977(a,1),37001(a,1,1))].">
      <j1 rule="para" parents="19977 37001"/>
    </justification>
  </clause>

  <clause id="37045">
    <literal><![CDATA[
      (a((x \ y) * z,u,w * u) * ((y / x) * (a((x \ y) * z,u,w * u) \ x))) \ y = a(u,x * y,a(w,x,z))
    ]]></literal>
    <justification jstring="[para(28534(a,1),37044(a,1,1))].">
      <j1 rule="para" parents="28534 37044"/>
    </justification>
  </clause>

  <clause id="37046">
    <literal><![CDATA[
      L(x,y,a((y \ x) * z,u,(w * u) * y)) \ x = a(u,y * x,a(w,y,z))
    ]]></literal>
    <justification jstring="[para(36744(a,1),37045(a,1,1))].">
      <j1 rule="para" parents="36744 37045"/>
    </justification>
  </clause>

  <clause id="37047">
    <literal><![CDATA[
      L(x,y,a((y \ x) * z,u,w * (y * u))) \ x = a(u,y * x,a(w,y,z))
    ]]></literal>
    <justification jstring="[para(36770(a,1),37046(a,1,1,3))].">
      <j1 rule="para" parents="36770 37046"/>
    </justification>
  </clause>

  <clause id="37048">
    <literal><![CDATA[
      a((x \ y) * z,u,a(y,x,w * (x * u))) = a(u,x * y,a(w,x,z))
    ]]></literal>
    <justification jstring="[hyper(29883,a,37047,a)].">
      <j1 rule="hyper" parents="29883 37047"/>
    </justification>
  </clause>

  <clause id="37049">
    <literal><![CDATA[
      a((x * y) * z,u,a(x,y,w * (y * u))) = a(u,y * x,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,36558,a(flip),b,37048,a)].">
      <j1 rule="hyper" parents="63 36558 37048"/>
    </justification>
  </clause>

  <clause id="37050">
    <literal><![CDATA[
      a(x,y,a(z * (y * u),u,y * (w * x))) = a(u,y * x,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36534,a(flip),b,37049,a)].">
      <j1 rule="hyper" parents="63 36534 37049"/>
    </justification>
  </clause>

  <clause id="37051">
    <literal><![CDATA[
      a(x,y,a(z * (x * u),u,w)) = a(u,x * y,a(z,x,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36891,a(flip),b,37050,a)].">
      <j1 rule="hyper" parents="63 36891 37050"/>
    </justification>
  </clause>

  <clause id="37052">
    <literal><![CDATA[
      a(x,y,a(x * z,u,w * u)) = a(u,x * y,a(z,x,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36798,a(flip),b,37051,a)].">
      <j1 rule="hyper" parents="63 36798 37051"/>
    </justification>
  </clause>

  <clause id="37053">
    <literal><![CDATA[
      a(x,y * z,a(u,y,w)) = a(x,y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,36882,a(flip),b,37052,a),flip(a)].">
      <j1 rule="hyper" parents="63 36882 37052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37054">
    <literal><![CDATA[
      (x / (y * z)) * (a(u,w,w) \ (a(u,w,w) * a(u,w,w))) = x / L(y * (a(u,w,w) \ z),a(u,w,w),a(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,32106,a(flip),b,36405,a)].">
      <j1 rule="hyper" parents="63 32106 36405"/>
    </justification>
  </clause>

  <clause id="37056">
    <literal><![CDATA[
      a(a(x,x,y) * z,u,a(w,v5 * L(a(x,x,y) * z,v6,v7),v8)) = a(z,u,a(w,v5 * a(v7,v6,z),v8))
    ]]></literal>
    <justification jstring="[para(36440(a,1),36669(a,2,3,2,2))].">
      <j1 rule="para" parents="36440 36669"/>
    </justification>
  </clause>

  <clause id="37057">
    <literal><![CDATA[
      a(a(x,x,y) * z,u,a(w,v5 * L(a(x,x,y) * z,v6,v7),v8)) = a(w,v5,a(z,u,v8))
    ]]></literal>
    <justification jstring="[hyper(347,a,36640,a(flip),b,37056,a),flip(a)].">
      <j1 rule="hyper" parents="347 36640 37056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37060">
    <literal><![CDATA[
      a(a(x,x,y) * z,u,a(w,L(z,v5,v6) * v7,v8)) = a(w,v7,a(z,u,v8))
    ]]></literal>
    <justification jstring="[para(37009(a,1),37057(a,1,3))].">
      <j1 rule="para" parents="37009 37057"/>
    </justification>
  </clause>

  <clause id="37061">
    <literal><![CDATA[
      a(x,y,a(z,L(x,u,w) * v5,v6)) = a(z,v5,a(x,y,v6))
    ]]></literal>
    <justification jstring="[hyper(11564,a,37060,a)].">
      <j1 rule="hyper" parents="11564 37060"/>
    </justification>
  </clause>

  <clause id="37063">
    <literal><![CDATA[
      a(x,y,a(z,u * a(z,w,v5),v6)) = a(v6,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(63,a,36603,a(flip),b,37061,a)].">
      <j1 rule="hyper" parents="63 36603 37061"/>
    </justification>
  </clause>

  <clause id="37066">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),a(u,z * a(u,v5,v6),y),w) = L(x,w,a(u,z * a(u,v5,v6),y))
    ]]></literal>
    <justification jstring="[para(37063(a,1),23358(a,1,1,2))].">
      <j1 rule="para" parents="37063 23358"/>
    </justification>
  </clause>

  <clause id="37067">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),a(y,z,u),w) = L(x,w,a(u,z * a(u,v5,v6),y))
    ]]></literal>
    <justification jstring="[hyper(63,a,36822,a(flip),b,37066,a)].">
      <j1 rule="hyper" parents="63 36822 37066"/>
    </justification>
  </clause>

  <clause id="37069">
    <literal><![CDATA[
      L(x,y,a(z,u * a(z,w,v5),v6)) = L(x,y,a(v6,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,29809,a(flip),b,37067,a),flip(a)].">
      <j1 rule="hyper" parents="63 29809 37067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37070">
    <literal><![CDATA[
      L(x * a(y,z,a(a(u,w,v5),x,w * (v6 * v5))),u,a(w,v5,a(y,z,v6))) = L(x,a(v5,w,a(y,z,w * (v6 * v5))),u)
    ]]></literal>
    <justification jstring="[para(29790(a,1),36897(a,1,1,2))].">
      <j1 rule="para" parents="29790 36897"/>
    </justification>
  </clause>

  <clause id="37071">
    <literal><![CDATA[
      x / L(y * (a(z,u,u) \ w),a(z,u,u),a(z,u,u)) = (x / (y * w)) * a(z,u,u)
    ]]></literal>
    <justification jstring="[hyper(20586,a,37054,a),flip(a)].">
      <j1 rule="hyper" parents="20586 37054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37076">
    <literal><![CDATA[
      x / (y * (a(z,u,u) \ w)) = (x / (y * w)) * a(z,u,u)
    ]]></literal>
    <justification jstring="[para(28061(a,1),37071(a,1,2))].">
      <j1 rule="para" parents="28061 37071"/>
    </justification>
  </clause>

  <clause id="37078">
    <literal><![CDATA[
      (((x * y) * (a(z,u,u) \ w)) / (y * w)) * a(z,u,u) = R(x,a(z,u,u) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(63,a,32305,a(flip),b,37076,a),flip(a)].">
      <j1 rule="hyper" parents="63 32305 37076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37081">
    <literal><![CDATA[
      R(a(x,y,y) \ z,u,w) * a(x,y,y) = R(z,a(x,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(32178(a,1),37078(a,1,1))].">
      <j1 rule="para" parents="32178 37078"/>
    </justification>
  </clause>

  <clause id="37082">
    <literal><![CDATA[
      R(a(x,y,y) \ z,u,w) * a(x,y,y) = R(z,u,w * a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(347,a,32304,a(flip),b,37081,a),flip(a)].">
      <j1 rule="hyper" parents="347 32304 37081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37083">
    <literal><![CDATA[
      R(x,y,z) * (a(u,w,w) \ a(u,w,w)) = R(x,y,z * a(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36410,a(flip),b,37082,a)].">
      <j1 rule="hyper" parents="63 36410 37082"/>
    </justification>
  </clause>

  <clause id="37084">
    <literal><![CDATA[
      R(x,y,z * a(u,w,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(37083(a,1),230(a,1))].">
      <j1 rule="para" parents="37083 230"/>
    </justification>
  </clause>

  <clause id="37085">
    <literal><![CDATA[
      R(x,L(y,z,z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(37084,a,32543,a),flip(a)].">
      <j1 rule="hyper" parents="37084 32543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37086">
    <literal><![CDATA[
      R(x,y * (z * L(u,w,w)),v5) = R(x,y * (z * u),v5)
    ]]></literal>
    <justification jstring="[hyper(37084,a,32309,a),flip(a)].">
      <j1 rule="hyper" parents="37084 32309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37087">
    <literal><![CDATA[
      R(x,y,(z \ u) \ w) = R(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(37084,a,31851,a)].">
      <j1 rule="hyper" parents="37084 31851"/>
    </justification>
  </clause>

  <clause id="37088">
    <literal><![CDATA[
      R(x,y,a(z,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(27782(a,2),37084(a,1))].">
      <j1 rule="para" parents="27782 37084"/>
    </justification>
  </clause>

  <clause id="37090">
    <literal><![CDATA[
      R(x,y \ z,u) = R(x,y * z,u)
    ]]></literal>
    <justification jstring="[hyper(21090,a,37085,a)].">
      <j1 rule="hyper" parents="21090 37085"/>
    </justification>
  </clause>

  <clause id="37097">
    <literal><![CDATA[
      R(x,((y * z) \ (z * u)) * (y \ u),w) = L(x,a(z,y,u * y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,29669,a(flip),b,37090,a),flip(a)].">
      <j1 rule="hyper" parents="63 29669 37090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37101">
    <literal><![CDATA[
      R(x,y,z * (u \ w)) = R(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,31841,a(flip),b,37087,a)].">
      <j1 rule="hyper" parents="63 31841 37087"/>
    </justification>
  </clause>

  <clause id="37102">
    <literal><![CDATA[
      R(x,y,a(z,z,u) * ((L(u,z,z) \ w) * v5)) = R(x,y,(u \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,32436,a(flip),b,37101,a),flip(a)].">
      <j1 rule="hyper" parents="63 32436 37101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37103">
    <literal><![CDATA[
      R(x,y,a(z,z,u) * (w * (R(u,z,z) \ v5))) = R(x,y,w * (u \ v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,32184,a(flip),b,37101,a),flip(a)].">
      <j1 rule="hyper" parents="63 32184 37101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37104">
    <literal><![CDATA[
      R(x,y,L(z,z,u * w) * (u * w)) = R(x,y,(w \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,31852,a(flip),b,37101,a),flip(a)].">
      <j1 rule="hyper" parents="63 31852 37101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37105">
    <literal><![CDATA[
      R(x,y,((z * u) \ (u * w)) * (w * z)) = L(x,y,a(u,z,w * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,29033,a(flip),b,37101,a),flip(a)].">
      <j1 rule="hyper" parents="63 29033 37101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37106">
    <literal><![CDATA[
      R(x,y,z * (u * L(w * v5,w,w))) = R(x,y,z * ((w \ v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,27444,a(flip),b,37101,a),flip(a)].">
      <j1 rule="hyper" parents="63 27444 37101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37107">
    <literal><![CDATA[
      R(x,y,z * (u * (w * ((v5 * w) \ w)))) = R(x,y,((v5 \ w) \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,22281,a(flip),b,37101,a),flip(a)].">
      <j1 rule="hyper" parents="63 22281 37101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37109">
    <literal><![CDATA[
      R(x,y * (z * (u \ w)),v5) = R(x,y * (z * (w * u)),v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,32746,a(flip),b,37086,a)].">
      <j1 rule="hyper" parents="63 32746 37086"/>
    </justification>
  </clause>

  <clause id="37110">
    <literal><![CDATA[
      R(x,y * (z \ u),w) = R(x,y * (z * u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,27804,a(flip),b,37086,a)].">
      <j1 rule="hyper" parents="63 27804 37086"/>
    </justification>
  </clause>

  <clause id="37112">
    <literal><![CDATA[
      R(x,(y * z) * u,w) = R(x,u * (z \ y),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,22473,a,b,37110,a)].">
      <j1 rule="hyper" parents="347 22473 37110"/>
    </justification>
  </clause>

  <clause id="37114">
    <literal><![CDATA[
      R(x,(y \ z) * u,w) = R(x,(z * y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,20553,a,b,37112,a)].">
      <j1 rule="hyper" parents="347 20553 37112"/>
    </justification>
  </clause>

  <clause id="37115">
    <literal><![CDATA[
      R(x,y * (z \ u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y * (z * u),w) = v5
    ]]></literal>
    <justification jstring="[para(37112(a,1),22477(a,1))].">
      <j1 rule="para" parents="37112 22477"/>
    </justification>
  </clause>

  <clause id="37117">
    <literal><![CDATA[
      R(x,((y * z) * (u \ y)) * (u * z),w) = L(x,a(u * y,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,30254,a(flip),b,37114,a),flip(a)].">
      <j1 rule="hyper" parents="63 30254 37114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37119">
    <literal><![CDATA[
      R(x,y * (z * (((u * u) \ w) * v5)),v6) = R(x,(z * (v5 \ w)) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,22569,a(flip),b,37109,a),flip(a)].">
      <j1 rule="hyper" parents="63 22569 37109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37120">
    <literal><![CDATA[
      R(x,y,(z \ u) * w) = R(x,y,(u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,31854,a(flip),b,37104,a),flip(a)].">
      <j1 rule="hyper" parents="63 31854 37104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37124">
    <literal><![CDATA[
      R(x,((y * z) \ (z * u)) * (y * u),w) = L(x,a(z,y,u * y),w)
    ]]></literal>
    <justification jstring="[hyper(37115,a,37097,a)].">
      <j1 rule="hyper" parents="37115 37097"/>
    </justification>
  </clause>

  <clause id="37125">
    <literal><![CDATA[
      R(x,y,((z * u) * (w * z)) * (u * w)) = L(x,y,a(z,w,u * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,37120,a(flip),b,37105,a)].">
      <j1 rule="hyper" parents="63 37120 37105"/>
    </justification>
  </clause>

  <clause id="37126">
    <literal><![CDATA[
      R(x,((y * z) * (u * y)) * (u * z),w) = L(x,a(y,u,z * u),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,37114,a(flip),b,37124,a)].">
      <j1 rule="hyper" parents="63 37114 37124"/>
    </justification>
  </clause>

  <clause id="37127">
    <literal><![CDATA[
      R(x,y,(L(z,u,u) \ w) * v5) = R(x,y,(z \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(37088,a,37102,a)].">
      <j1 rule="hyper" parents="37088 37102"/>
    </justification>
  </clause>

  <clause id="37128">
    <literal><![CDATA[
      R(x,y,(z * L(u,w,w)) * v5) = R(x,y,(u \ z) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,37120,a(flip),b,37127,a)].">
      <j1 rule="hyper" parents="63 37120 37127"/>
    </justification>
  </clause>

  <clause id="37130">
    <literal><![CDATA[
      R(x,y,(z * L(u,w,w)) * v5) = R(x,y,(z * u) * v5)
    ]]></literal>
    <justification jstring="[hyper(347,a,37120,a(flip),b,37128,a),flip(a)].">
      <j1 rule="hyper" parents="347 37120 37128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37131">
    <literal><![CDATA[
      R(x,y,z * (R(u,w,w) \ v5)) = R(x,y,z * (u \ v5))
    ]]></literal>
    <justification jstring="[hyper(37088,a,37103,a)].">
      <j1 rule="hyper" parents="37088 37103"/>
    </justification>
  </clause>

  <clause id="37132">
    <literal><![CDATA[
      R(x,y,z * (u * R(w,v5,v5))) = R(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[hyper(63,a,37101,a(flip),b,37131,a)].">
      <j1 rule="hyper" parents="63 37101 37131"/>
    </justification>
  </clause>

  <clause id="37133">
    <literal><![CDATA[
      R(x,y,z * (u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z * (w * L(u,v6,v6))) = v5
    ]]></literal>
    <justification jstring="[para(37132(a,1),27774(a,1))].">
      <j1 rule="para" parents="37132 27774"/>
    </justification>
  </clause>

  <clause id="37134">
    <literal><![CDATA[
      R(x,y,z * (u * L(w,v5,v5))) = R(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(37133,a,37101,a)].">
      <j1 rule="hyper" parents="37133 37101"/>
    </justification>
  </clause>

  <clause id="37135">
    <literal><![CDATA[
      R(x,y,z * ((u \ w) \ v5)) = R(x,y,z * (v5 * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(63,a,37106,a(flip),b,37134,a)].">
      <j1 rule="hyper" parents="63 37106 37134"/>
    </justification>
  </clause>

  <clause id="37137">
    <literal><![CDATA[
      R(x,y,z * ((u \ (w \ u)) \ v5)) = R(x,y,z * (v5 * ((u * w) * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,22231,a(flip),b,37135,a)].">
      <j1 rule="hyper" parents="63 22231 37135"/>
    </justification>
  </clause>

  <clause id="37138">
    <literal><![CDATA[
      R(x,(y * (z \ u)) * w,v5) = R(x,(y * (z * u)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,22899,a(flip),b,37119,a),flip(a)].">
      <j1 rule="hyper" parents="63 22899 37119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37139">
    <literal><![CDATA[
      R(x,((y * z) * (u * y)) * (u * z),w) = L(x,a(u * y,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,37117,a(flip),b,37138,a),flip(a)].">
      <j1 rule="hyper" parents="63 37117 37138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37140">
    <literal><![CDATA[
      L(x,a(y * z,y,u),w) = L(x,a(z,y,u * y),w)
    ]]></literal>
    <justification jstring="[hyper(63,a,37126,a(flip),b,37139,a),flip(a)].">
      <j1 rule="hyper" parents="63 37126 37139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37141">
    <literal><![CDATA[
      L(x,a(y,z,u * z),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(u,z,y * z),w) = v5
    ]]></literal>
    <justification jstring="[para(37140(a,1),28765(a,1))].">
      <j1 rule="para" parents="37140 28765"/>
    </justification>
  </clause>

  <clause id="37142">
    <literal><![CDATA[
      R(x,y,z * ((u \ (w \ u)) \ v5)) = R(x,y,(v5 * L(w,u,u)) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,27779,a(flip),b,37137,a),flip(a)].">
      <j1 rule="hyper" parents="347 27779 37137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37143">
    <literal><![CDATA[
      R(x,y,z * ((u \ (w \ u)) \ v5)) = R(x,y,(v5 * w) * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,37130,a(flip),b,37142,a),flip(a)].">
      <j1 rule="hyper" parents="347 37130 37142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37145">
    <literal><![CDATA[
      R(x,y,z * (u * (w * (v5 \ w)))) = R(x,y,(u * v5) * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,37135,a(flip),b,37143,a)].">
      <j1 rule="hyper" parents="63 37135 37143"/>
    </justification>
  </clause>

  <clause id="37146">
    <literal><![CDATA[
      R(x,y,((z \ u) \ w) * v5) = R(x,y,(w * (z * u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(63,a,37107,a(flip),b,37145,a)].">
      <j1 rule="hyper" parents="63 37107 37145"/>
    </justification>
  </clause>

  <clause id="37148">
    <literal><![CDATA[
      R(x,y,((z * u) * (w * z)) * (u * w)) = L(x,y,a(w * z,w,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,31524,a(flip),b,37146,a),flip(a)].">
      <j1 rule="hyper" parents="63 31524 37146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37150">
    <literal><![CDATA[
      L(x,y,a(z * u,z,w)) = L(x,y,a(u,z,w * z))
    ]]></literal>
    <justification jstring="[hyper(63,a,37125,a(flip),b,37148,a),flip(a)].">
      <j1 rule="hyper" parents="63 37125 37148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37151">
    <literal><![CDATA[
      L(x,y,a(z,u,a(y * w,v5,v6))) = L(x,u,a(w,y,a(z,v5,v6) * y))
    ]]></literal>
    <justification jstring="[hyper(29910,a,37150,a)].">
      <j1 rule="hyper" parents="29910 37150"/>
    </justification>
  </clause>

  <clause id="37152">
    <literal><![CDATA[
      L(x,y,a(z * u,w,(u * y) * w)) = L(x,w,a(y,u,z * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36924,a(flip),b,37150,a),flip(a)].">
      <j1 rule="hyper" parents="63 36924 37150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37153">
    <literal><![CDATA[
      L(x,y,a(z * u,w,y * (u * w))) = L(x,w,a(y,u,z * w))
    ]]></literal>
    <justification jstring="[para(36697(a,1),37152(a,1,3))].">
      <j1 rule="para" parents="36697 37152"/>
    </justification>
  </clause>

  <clause id="37154">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,y * v6))) = L(x,u,a(w,y,a(z,v5,v6) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,36766,a(flip),b,37151,a)].">
      <j1 rule="hyper" parents="63 36766 37151"/>
    </justification>
  </clause>

  <clause id="37155">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,y * v6))) = L(x,u,a(y,a(w,v5,z),v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,36991,a(flip),b,37154,a),flip(a)].">
      <j1 rule="hyper" parents="347 36991 37154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37156">
    <literal><![CDATA[
      L(x,a(y,z,u),a(w,v5,v6)) = L(x,z,a(y,a(v6,v5,u),w))
    ]]></literal>
    <justification jstring="[hyper(36997,a,37155,a)].">
      <j1 rule="hyper" parents="36997 37155"/>
    </justification>
  </clause>

  <clause id="37157">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,y * v6))) = L(x,u,a(y,a(v6,v5,z),w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36767,a,b,37155,a)].">
      <j1 rule="hyper" parents="63 36767 37155"/>
    </justification>
  </clause>

  <clause id="37159">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,v5),v6)) = L(x,y,a(z,a(v6,w,v5),u))
    ]]></literal>
    <justification jstring="[hyper(63,a,37155,a(flip),b,37157,a)].">
      <j1 rule="hyper" parents="63 37155 37157"/>
    </justification>
  </clause>

  <clause id="37160">
    <literal><![CDATA[
      L(L(x,y,a(z,a(u,w,v5),v6)),a(z,y,u),a(v6,w,v5)) = x * a(z,y,a(a(v6,w,v5),x,u))
    ]]></literal>
    <justification jstring="[para(37159(a,1),29989(a,1,1))].">
      <j1 rule="para" parents="37159 29989"/>
    </justification>
  </clause>

  <clause id="37161">
    <literal><![CDATA[
      L(L(x,y,a(z,a(u,w,v5),v6)),y,a(z,a(v5,w,u),v6)) = x * a(z,y,a(a(v6,w,v5),x,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,37156,a(flip),b,37160,a)].">
      <j1 rule="hyper" parents="63 37156 37160"/>
    </justification>
  </clause>

  <clause id="37162">
    <literal><![CDATA[
      x * a(y,z,a(a(u,w,v5),x,v6)) = x
    ]]></literal>
    <justification jstring="[hyper(27588,a,37161,a),flip(a)].">
      <j1 rule="hyper" parents="27588 37161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37164">
    <literal><![CDATA[
      a(x,y,a(a(z,u,w),v5,v6)) = 1
    ]]></literal>
    <justification jstring="[hyper(137,a,37162,a),flip(a)].">
      <j1 rule="hyper" parents="137 37162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37165">
    <literal><![CDATA[
      a(a(x,y,z),u,a(w,v5,v6)) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,37162,a,b,29798,a),flip(a)].">
      <j1 rule="hyper" parents="129 37162 29798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37167">
    <literal><![CDATA[
      x \ (a(y,z,a(u,w,v5)) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(y,z,a(u,w,v5)) * (x \ v6) = v7
    ]]></literal>
    <justification jstring="[para(37162(a,1),30725(a,1))].">
      <j1 rule="para" parents="37162 30725"/>
    </justification>
  </clause>

  <clause id="37179">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) * 1 = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(37164(a,1),29922(a,1,2))].">
      <j1 rule="para" parents="37164 29922"/>
    </justification>
  </clause>

  <clause id="37187">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      L(x,z,a(u,w,a(v5,v6,v7))) = y
    ]]></literal>
    <justification jstring="[para(37165(a,1),29864(a,1,1))].">
      <j1 rule="para" parents="37165 29864"/>
    </justification>
  </clause>

  <clause id="37188">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6))) = x
    ]]></literal>
    <justification jstring="[hyper(37187,a,7,a)].">
      <j1 rule="hyper" parents="37187 7"/>
    </justification>
  </clause>

  <clause id="37190">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) \ v6 = v5 \ (a(x,y,a(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(27584,a,37188,a),flip(a)].">
      <j1 rule="hyper" parents="27584 37188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37195">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,v5),v6)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,37157,a(flip),b,37188,a)].">
      <j1 rule="hyper" parents="63 37157 37188"/>
    </justification>
  </clause>

  <clause id="37199">
    <literal><![CDATA[
      (x * y) * a(z,u,a(w,v5,v6)) = x * (a(z,u,a(w,v5,v6)) * y)
    ]]></literal>
    <justification jstring="[para(37188(a,1),23239(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37188 23239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37206">
    <literal><![CDATA[
      a(x,y,L(z,a(u,w,v5),v6)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(32615,a,37195,a)].">
      <j1 rule="hyper" parents="32615 37195"/>
    </justification>
  </clause>

  <clause id="37209">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,v5),v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(37195(a,1),50(a,2))].">
      <j1 rule="para" parents="37195 50"/>
    </justification>
  </clause>

  <clause id="37219">
    <literal><![CDATA[
      a((x \ a(y,z,u)) * w,v5,v6) = a(a(y,z,u) * (x \ w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,36793,a(flip),b,37206,a),flip(a)].">
      <j1 rule="hyper" parents="63 36793 37206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37227">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(142,a,37179,a)].">
      <j1 rule="hyper" parents="142 37179"/>
    </justification>
  </clause>

  <clause id="37249">
    <literal><![CDATA[
      a(x,y * (z * u),a(u * y,w,v5)) = a(x,z,a(u * y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,32474,a,b,37227,a)].">
      <j1 rule="hyper" parents="63 32474 37227"/>
    </justification>
  </clause>

  <clause id="37250">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,v5),v6)) = a(x,y,a(z,u,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,30083,a,b,37227,a)].">
      <j1 rule="hyper" parents="63 30083 37227"/>
    </justification>
  </clause>

  <clause id="37251">
    <literal><![CDATA[
      a((x * y) \ z,u,a(w,v5,v6)) = a(y * (z * x),u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,36974,a(flip),b,37227,a),flip(a)].">
      <j1 rule="hyper" parents="63 36974 37227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37252">
    <literal><![CDATA[
      a(x,y,a(z,u,y * (a(x,w,v5) * v6))) = a(y,L(x,w,v5),a(z,u,v6 * x))
    ]]></literal>
    <justification jstring="[hyper(63,a,36955,a(flip),b,37227,a),flip(a)].">
      <j1 rule="hyper" parents="63 36955 37227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37253">
    <literal><![CDATA[
      a((x * y) \ z,u,a(w,((x * y) * z) * v5,v6)) = a(v6,u,a(y \ (x \ z),v5,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36818,a(flip),b,37227,a),flip(a)].">
      <j1 rule="hyper" parents="63 36818 37227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37261">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(x,y,z)) = v7
    ]]></literal>
    <justification jstring="[para(37227(a,2),29908(a,1))].">
      <j1 rule="para" parents="37227 29908"/>
    </justification>
  </clause>

  <clause id="37262">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,v5,v6))) = a(w,y,a(z,u,x)) * x
    ]]></literal>
    <justification jstring="[para(37227(a,1),29931(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37227 29931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37273">
    <literal><![CDATA[
      a(x,y,a(z,u,(w * v5) * v6)) = a(x,y,a(z,u,w * (v6 * v5)))
    ]]></literal>
    <justification jstring="[para(36769(a,1),37227(a,1,3))].">
      <j1 rule="para" parents="36769 37227"/>
    </justification>
  </clause>

  <clause id="37275">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,v5),v6 * L(u,w,v5))) = a(x * L(u,w,v5),y,a(z,u,v6))
    ]]></literal>
    <justification jstring="[hyper(36738,a,37250,a)].">
      <j1 rule="hyper" parents="36738 37250"/>
    </justification>
  </clause>

  <clause id="37279">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,v5,v6))) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,29884,a(flip),b,37262,a),flip(a)].">
      <j1 rule="hyper" parents="347 29884 37262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37289">
    <literal><![CDATA[
      L(x,y,a(z,u,(w * v5) * v6)) = L(x,y,a(z,u,w * (v6 * v5)))
    ]]></literal>
    <justification jstring="[para(36769(a,1),37279(a,1,3))].">
      <j1 rule="para" parents="36769 37279"/>
    </justification>
  </clause>

  <clause id="37290">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = v7
    ]]></literal>
    <justification jstring="[para(29817(a,1),37261(a,1))].">
      <j1 rule="para" parents="29817 37261"/>
    </justification>
  </clause>

  <clause id="37293">
    <literal><![CDATA[
      a(x,y,a(z,u,(w * v5) * v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v6 * v5))) = v7
    ]]></literal>
    <justification jstring="[para(36769(a,1),37290(a,1,3))].">
      <j1 rule="para" parents="36769 37290"/>
    </justification>
  </clause>

  <clause id="37294">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) \ v6 = v5 \ (a(x,y,a(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[para(28387(a,1),37190(a,2,2))].">
      <j1 rule="para" parents="28387 37190"/>
    </justification>
  </clause>

  <clause id="37295">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * v6) = v5 * (a(w,y,a(x,u,z)) * v6)
    ]]></literal>
    <justification jstring="[hyper(29849,a,37199,a)].">
      <j1 rule="hyper" parents="29849 37199"/>
    </justification>
  </clause>

  <clause id="37299">
    <literal><![CDATA[
      a((x * y) * z,u,a(w,v5,v6)) = a(y * (z * x),u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(30814,a,37251,a)].">
      <j1 rule="hyper" parents="30814 37251"/>
    </justification>
  </clause>

  <clause id="37301">
    <literal><![CDATA[
      a((x * y) \ z,u,a(w,v5,L(v6,v7,v8))) != v9
    ]]></literal>
    <literal><![CDATA[
      a(y * (z * x),u,a(w,v5,v6)) = v9
    ]]></literal>
    <justification jstring="[para(37251(a,2),37290(a,1))].">
      <j1 rule="para" parents="37251 37290"/>
    </justification>
  </clause>

  <clause id="37303">
    <literal><![CDATA[
      a(x,y,a(y * (x * z),u,y * ((w * u) * (x * z)))) = a(y,x,a(u * (w * (y * (x * z))),u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,36893,a(flip),b,37273,a),flip(a)].">
      <j1 rule="hyper" parents="63 36893 37273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37307">
    <literal><![CDATA[
      (x * y) \ (x * (a(z,u,a(w,v5,v6)) * (y * v7))) = L(a(v6,u,a(z,v5,w)) * v7,y,x)
    ]]></literal>
    <justification jstring="[para(37295(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="37295 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37308">
    <literal><![CDATA[
      ((a(x,y,a(z,u,w)) * v5) * (L(v6,v5,a(x,y,a(z,u,w))) * v7)) \ ((v5 * (a(w,y,a(x,u,z)) * v6)) * v7) = a(a(x,y,a(z,u,w)) * v5,L(v6,v5,a(x,y,a(z,u,w))),v7)
    ]]></literal>
    <justification jstring="[para(37295(a,1),540(a,1,2,1))].">
      <j1 rule="para" parents="37295 540"/>
    </justification>
  </clause>

  <clause id="37309">
    <literal><![CDATA[
      a((x \ y) * z,u,a(w,v5,v6)) = a(x * (z * y),u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(36562,a,37299,a)].">
      <j1 rule="hyper" parents="36562 37299"/>
    </justification>
  </clause>

  <clause id="37311">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) \ v6 = a(x,y,a(z,u,w)) * (v5 \ v6)
    ]]></literal>
    <justification jstring="[hyper(37167,a,37294,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="37167 37294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37312">
    <literal><![CDATA[
      x \ (y * (a(z,u,a(w,v5,v6)) * v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(v6,v5,z)) * (x \ (y * v7)) = v8
    ]]></literal>
    <justification jstring="[para(37295(a,1),37167(a,1,2))].">
      <j1 rule="para" parents="37295 37167"/>
    </justification>
  </clause>

  <clause id="37316">
    <literal><![CDATA[
      (x * (a(y,z,a(u,w,v5)) * v6)) \ v7 = a(u,z,a(v5,w,y)) * ((x * v6) \ v7)
    ]]></literal>
    <justification jstring="[para(37295(a,1),37311(a,1,1))].">
      <j1 rule="para" parents="37295 37311"/>
    </justification>
  </clause>

  <clause id="37317">
    <literal><![CDATA[
      a(x * (y * z),u,a(w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(v6,v5,a(w,u,y * (x * z))) = v7
    ]]></literal>
    <justification jstring="[para(29804(a,2),37293(a,1))].">
      <j1 rule="para" parents="29804 37293"/>
    </justification>
  </clause>

  <clause id="37318">
    <literal><![CDATA[
      a(x,y,a(z,u,y * (a(x,w,v5) * v6))) = a(y,x,a(z,u,L(v6 * x,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(347,a,30088,a(flip),b,37252,a),flip(a)].">
      <j1 rule="hyper" parents="347 30088 37252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37320">
    <literal><![CDATA[
      a(x,y,a(z,u,y * (a(x,w,v5) * v6))) = a(y,x,a(z,u,v6 * x))
    ]]></literal>
    <justification jstring="[hyper(347,a,37227,a(flip),b,37318,a),flip(a)].">
      <j1 rule="hyper" parents="347 37227 37318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37322">
    <literal><![CDATA[
      a(x,y,a(z,u,w * L(T(y,v5),v6,v7))) = a(x,y,a(z,u,w * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,36969,a,b,37320,a)].">
      <j1 rule="hyper" parents="63 36969 37320"/>
    </justification>
  </clause>

  <clause id="37324">
    <literal><![CDATA[
      a(x,y,a(z,u,w * L(y,v5,v6))) = a(x,y,a(z,u,w * y))
    ]]></literal>
    <justification jstring="[para(110(a,1),37322(a,1,3,3,2,1))].">
      <j1 rule="para" parents="110 37322"/>
    </justification>
  </clause>

  <clause id="37325">
    <literal><![CDATA[
      a(x * L(y,z,u),w,a(v5,y,v6)) = a(v6,y,a(v5,w,x * y))
    ]]></literal>
    <justification jstring="[hyper(29811,a,37324,a)].">
      <j1 rule="hyper" parents="29811 37324"/>
    </justification>
  </clause>

  <clause id="37326">
    <literal><![CDATA[
      a(x * L(y,z,u),w,a(v5,y,v6)) = a(x,w,a(v5,y,v6 * L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,37250,a(flip),b,37275,a),flip(a)].">
      <j1 rule="hyper" parents="63 37250 37275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37328">
    <literal><![CDATA[
      a(x,y,a(z,u,w * L(u,v5,v6))) = a(w,u,a(z,y,x * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,37325,a(flip),b,37326,a),flip(a)].">
      <j1 rule="hyper" parents="63 37325 37326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37330">
    <literal><![CDATA[
      a(x,y,a(a(z,u,w) \ v5,v6,w * v6)) = a(v5,w,a(v6,y,x * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36720,a,b,37328,a)].">
      <j1 rule="hyper" parents="63 36720 37328"/>
    </justification>
  </clause>

  <clause id="37331">
    <literal><![CDATA[
      a(x,y,a(a(z,u,w) * v5,v6,w * v6)) = a(v5,w,a(v6,y,x * w))
    ]]></literal>
    <justification jstring="[hyper(30815,a,37330,a)].">
      <j1 rule="hyper" parents="30815 37330"/>
    </justification>
  </clause>

  <clause id="37333">
    <literal><![CDATA[
      a(x,y,a(z,u,w * y)) \ x = (z * a(w,u,y)) * (z \ (a(w,u,y) \ x))
    ]]></literal>
    <justification jstring="[para(37331(a,1),36800(a,1,1))].">
      <j1 rule="para" parents="37331 36800"/>
    </justification>
  </clause>

  <clause id="37334">
    <literal><![CDATA[
      a(x,y,a(z,u,w * y)) * x = (z * a(w,u,y)) * (z \ (a(w,u,y) \ x))
    ]]></literal>
    <justification jstring="[hyper(28437,a,37333,a)].">
      <j1 rule="hyper" parents="28437 37333"/>
    </justification>
  </clause>

  <clause id="37336">
    <literal><![CDATA[
      (x * a(y,z,u)) * (x \ (a(y,z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(w,u,a(x,z,y * u)) = v5
    ]]></literal>
    <justification jstring="[para(37334(a,1),29007(a,1))].">
      <j1 rule="para" parents="37334 29007"/>
    </justification>
  </clause>

  <clause id="37337">
    <literal><![CDATA[
      a((x * y) * z,u,a(w,((x * y) * z) * v5,v6)) = a(v6,u,a(y \ (x \ z),v5,w))
    ]]></literal>
    <justification jstring="[hyper(30814,a,37253,a)].">
      <j1 rule="hyper" parents="30814 37253"/>
    </justification>
  </clause>

  <clause id="37340">
    <literal><![CDATA[
      a((x * y) \ z,u,a(w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(y * (z * x),u,a(w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(398(a,1),37301(a,1,3,3))].">
      <j1 rule="para" parents="398 37301"/>
    </justification>
  </clause>

  <clause id="37341">
    <literal><![CDATA[
      a(x,y,a(z \ (u \ w),v5,v6)) = a(x,y,a((u * z) * w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(32391,a,37337,a),flip(a)].">
      <j1 rule="hyper" parents="32391 37337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37342">
    <literal><![CDATA[
      a(x,y,a((z * u) * w,v5,v6)) = a(x,y,a(u * (z \ w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(30815,a,37341,a),flip(a)].">
      <j1 rule="hyper" parents="30815 37341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37343">
    <literal><![CDATA[
      a(x,y,a((z * u) * w,v5,v6)) = a(x,y,a(u * (w * z),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(347,a,36602,a(flip),b,37342,a),flip(a)].">
      <j1 rule="hyper" parents="347 36602 37342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37344">
    <literal><![CDATA[
      a(x,y,a((z \ u) * w,v5,v6)) = a(x,y,a(z * (w * u),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(63,a,36561,a,b,37343,a)].">
      <j1 rule="hyper" parents="63 36561 37343"/>
    </justification>
  </clause>

  <clause id="37345">
    <literal><![CDATA[
      a(x,y,a((z * u) * w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(u * (z * w),v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(37343(a,2),26341(a,1))].">
      <j1 rule="para" parents="37343 26341"/>
    </justification>
  </clause>

  <clause id="37347">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),v5,v6)) * a(x,(w * (z \ 1)) * u,a(y,v5,v6)) = a((z \ w) * u,a(v6,v5,x),y)
    ]]></literal>
    <justification jstring="[para(37344(a,1),36998(a,1,1))].">
      <j1 rule="para" parents="37344 36998"/>
    </justification>
  </clause>

  <clause id="37348">
    <literal><![CDATA[
      a(x,y,a(z * (u * y),w,v5)) = a(x,y,a(u * z,w,v5 * y))
    ]]></literal>
    <justification jstring="[hyper(37345,a,36734,a)].">
      <j1 rule="hyper" parents="37345 36734"/>
    </justification>
  </clause>

  <clause id="37349">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),v5,v6)) = a(x,y,a(v6,v5,w * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(37345,a,26516,a)].">
      <j1 rule="hyper" parents="37345 26516"/>
    </justification>
  </clause>

  <clause id="37351">
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5 * w)) = a(x,y,a(v5,w,z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(63,a,36799,a(flip),b,37349,a)].">
      <j1 rule="hyper" parents="63 36799 37349"/>
    </justification>
  </clause>

  <clause id="37352">
    <literal><![CDATA[
      a(x * (y * z),u,a(w,v5,v6)) = a(v6,v5,a(z * (y * x),u,w))
    ]]></literal>
    <justification jstring="[hyper(29811,a,37349,a(flip))].">
      <j1 rule="hyper" parents="29811 37349"/>
    </justification>
  </clause>

  <clause id="37353">
    <literal><![CDATA[
      a(x,y,a(z,u,x * (u * w))) = a(u,x,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36882,a(flip),b,37351,a),flip(a)].">
      <j1 rule="hyper" parents="63 36882 37351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37354">
    <literal><![CDATA[
      a(x * y,z,a(u,w,x * ((w * v5) * y))) = a(w,x * y,a(u,z,v5))
    ]]></literal>
    <justification jstring="[hyper(37293,a,37353,a)].">
      <j1 rule="hyper" parents="37293 37353"/>
    </justification>
  </clause>

  <clause id="37355">
    <literal><![CDATA[
      a(x * y,z,a(u,w,x * ((w * v5) * y))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(w,x \ y,a(u,z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(37354(a,2),36464(a,1))].">
      <j1 rule="para" parents="37354 36464"/>
    </justification>
  </clause>

  <clause id="37356">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * ((v5 * v6) \ (v5 * (v6 * v7))) = L(a(z,y,a(w,u,x)) * v7,v6,v5)
    ]]></literal>
    <justification jstring="[hyper(37312,a,37307,a)].">
      <j1 rule="hyper" parents="37312 37307"/>
    </justification>
  </clause>

  <clause id="37357">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) * v5,v6,v7) = a(w,y,a(x,u,z)) * L(v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(18(a,2),37356(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 37356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37358">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) * v5,v6,v7) = L(v5,v6,v7) * a(z,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(29848,a,37357,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="29848 37357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37359">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) * w,u,a(y,z,x)) = w * a(z,a(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,31198,a(flip),b,37358,a),flip(a)].">
      <j1 rule="hyper" parents="347 31198 37358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37360">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),u,a(y,z,w)) = x * a(z,a(w,u,x),y)
    ]]></literal>
    <justification jstring="[para(29884(a,1),37359(a,1,1))].">
      <j1 rule="para" parents="29884 37359"/>
    </justification>
  </clause>

  <clause id="37361">
    <literal><![CDATA[
      L((a(x,a(y,z,u),w) \ u) \ v5,L(L(u,w,a(x,z,y)),z,a(w,x,y)),a(x,a(y,z,u),w)) = u \ (a(x,a(y,z,u),w) * v5)
    ]]></literal>
    <justification jstring="[para(37360(a,2),30141(a,1,2))].">
      <j1 rule="para" parents="37360 30141"/>
    </justification>
  </clause>

  <clause id="37362">
    <literal><![CDATA[
      L(L(x,y,a(z,x * u,w)),x * u,a(y,z,w)) = x * a(z,a(w,x * u,L(x,v5,u)),y)
    ]]></literal>
    <justification jstring="[para(32219(a,2),37360(a,2,2,2))].">
      <j1 rule="para" parents="32219 37360"/>
    </justification>
  </clause>

  <clause id="37363">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),x * u,a(y,w,z)) = x * a(w,a(z,x * u,L(x,v5,u)),y)
    ]]></literal>
    <justification jstring="[para(32364(a,1),37362(a,1,1))].">
      <j1 rule="para" parents="32364 37362"/>
    </justification>
  </clause>

  <clause id="37364">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),z,a(w,u,y)) = x * a(y,a(w,x * u,L(x,v5,u)),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,32368,a(flip),b,37363,a)].">
      <j1 rule="hyper" parents="63 32368 37363"/>
    </justification>
  </clause>

  <clause id="37365">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),z,a(w,u,y)) = x * a(y,a(w,x * u,x),z)
    ]]></literal>
    <justification jstring="[para(534(a,1),37364(a,2,2,2,3))].">
      <j1 rule="para" parents="534 37364"/>
    </justification>
  </clause>

  <clause id="37366">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),z,a(w,u,y)) = x * a(y,a(w,u,x),z)
    ]]></literal>
    <justification jstring="[para(32418(a,1),37365(a,2,2))].">
      <j1 rule="para" parents="32418 37365"/>
    </justification>
  </clause>

  <clause id="37367">
    <literal><![CDATA[
      a(((x * a(y,a(z,u,x),w)) \ v5) * L(x,y,a(w,u,z)),v6,v7) = a(v5 * a(a(z,u,y),w,L(x,y,a(w,u,z))),v6,v7)
    ]]></literal>
    <justification jstring="[para(37366(a,1),32030(a,1,1,1,1))].">
      <j1 rule="para" parents="37366 32030"/>
    </justification>
  </clause>

  <clause id="37368">
    <literal><![CDATA[
      a((x * y) * (z * u),w,a(z * u,y,z)) = a(w,z,a(y * (x * (w * (z * u))),y,u))
    ]]></literal>
    <justification jstring="[hyper(36901,a,37303,a)].">
      <j1 rule="hyper" parents="36901 37303"/>
    </justification>
  </clause>

  <clause id="37369">
    <literal><![CDATA[
      a(x,y,a(z * (u * (x * (y * w))),z,w)) = a(y,z,a(w * (y * (u * z)),x,y * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,37352,a(flip),b,37368,a),flip(a)].">
      <j1 rule="hyper" parents="63 37352 37368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37370">
    <literal><![CDATA[
      a(x,y,a(z * (x * (u * y)),w,x * z)) = a(w,x,a(u * (w * (x * z)),y,z * y))
    ]]></literal>
    <justification jstring="[hyper(36739,a,37369,a),flip(a)].">
      <j1 rule="hyper" parents="36739 37369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37371">
    <literal><![CDATA[
      L(x,a(y,z,a(u,w,z * (v5 * y))),v6) = L(x,v6,a(z,y,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(37162(a,1),37070(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37162 37070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37372">
    <literal><![CDATA[
      L(x,a(y,z,a(u,w,z * (v5 * y))),v6) = x
    ]]></literal>
    <justification jstring="[hyper(347,a,37188,a(flip),b,37371,a),flip(a)].">
      <j1 rule="hyper" parents="347 37188 37371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37375">
    <literal><![CDATA[
      L(x,a(y,z,a(u,w,v5)),v6) = x
    ]]></literal>
    <justification jstring="[para(36891(a,1),37372(a,1,2))].">
      <j1 rule="para" parents="36891 37372"/>
    </justification>
  </clause>

  <clause id="37386">
    <literal><![CDATA[
      x * (a(y,z,a(z * (u * w),v5,w)) * v6) = (a(z,w,a(y,v5,u)) * x) * v6
    ]]></literal>
    <justification jstring="[para(37375(a,1),36898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37375 36898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37387">
    <literal><![CDATA[
      x * (a(y,z,a(u * w,v5,w * z)) * v6) = (a(z,w,a(y,v5,u)) * x) * v6
    ]]></literal>
    <justification jstring="[para(36730(a,1),37386(a,1,2,1))].">
      <j1 rule="para" parents="36730 37386"/>
    </justification>
  </clause>

  <clause id="37388">
    <literal><![CDATA[
      a(x,x * (y * ((x \ 1) * T(z,u))),(x \ 1) * T(z,u)) = a(x,y * T(((x \ 1) * z) * x,u),(x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(24185,a,36656,a),flip(a)].">
      <j1 rule="hyper" parents="24185 36656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37389">
    <literal><![CDATA[
      a(x,x * (y * ((x \ 1) * T(z,u))),(x \ 1) * T(z,u)) = a(x,y * T(((x \ 1) * z) * x,u),x * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,24327,a(flip),b,37388,a),flip(a)].">
      <j1 rule="hyper" parents="347 24327 37388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37390">
    <literal><![CDATA[
      a(x,x * (y * ((x \ 1) * T(z,u))),(x \ 1) * T(z,u)) = a(x,(((x \ 1) * z) * x) * y,x * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,24147,a(flip),b,37389,a),flip(a)].">
      <j1 rule="hyper" parents="347 24147 37389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37392">
    <literal><![CDATA[
      a(x,x * (y * ((x \ 1) * T(z,u))),(x \ 1) * T(z,u)) = a(x,((x \ 1) * z) * (y * x),x * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,36584,a(flip),b,37390,a),flip(a)].">
      <j1 rule="hyper" parents="347 36584 37390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37393">
    <literal><![CDATA[
      a(x,x * (y * ((x \ 1) * T(z,u))),(x \ 1) * T(z,u)) = a(x,(x * z) * (y * x),x * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,24784,a(flip),b,37392,a),flip(a)].">
      <j1 rule="hyper" parents="347 24784 37392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37394">
    <literal><![CDATA[
      a(x,x * (y * ((x \ 1) * T(z,u))),(x \ 1) * T(z,u)) = a(x,z * ((y * x) * x),x * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,36583,a(flip),b,37393,a),flip(a)].">
      <j1 rule="hyper" parents="347 36583 37393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37395">
    <literal><![CDATA[
      a(x,x * (y * ((x \ 1) * T(z,u))),(x \ 1) * T(z,u)) = a(x,z * y,x * z)
    ]]></literal>
    <justification jstring="[hyper(347,a,36604,a(flip),b,37394,a),flip(a)].">
      <j1 rule="hyper" parents="347 36604 37394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37396">
    <literal><![CDATA[
      a(x,x * (y * ((x \ 1) * T(z,u))),(x \ 1) * z) = a(x,z * y,x * z)
    ]]></literal>
    <justification jstring="[hyper(24185,a,37395,a)].">
      <j1 rule="hyper" parents="24185 37395"/>
    </justification>
  </clause>

  <clause id="37398">
    <literal><![CDATA[
      a(x,x * (y * ((x \ 1) * T(z,u))),x * z) = a(x,z * y,x * z)
    ]]></literal>
    <justification jstring="[hyper(24449,a,37396,a)].">
      <j1 rule="hyper" parents="24449 37396"/>
    </justification>
  </clause>

  <clause id="37399">
    <literal><![CDATA[
      a(x,x * (y * ((x \ 1) * z)),x * z) = a(x,z * y,x * z)
    ]]></literal>
    <justification jstring="[hyper(24416,a,37398,a)].">
      <j1 rule="hyper" parents="24416 37398"/>
    </justification>
  </clause>

  <clause id="37400">
    <literal><![CDATA[
      a(x,x * ((x * y) * z),x * y) = a(x,y * z,x * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,25741,a(flip),b,37399,a)].">
      <j1 rule="hyper" parents="63 25741 37399"/>
    </justification>
  </clause>

  <clause id="37401">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u * w,z * u)),z * u,a(z,z * ((z * u) * w),y)) = L(x,a(z,z * ((z * u) * w),y),z * u)
    ]]></literal>
    <justification jstring="[para(37400(a,1),29954(a,1,1,2,3))].">
      <j1 rule="para" parents="37400 29954"/>
    </justification>
  </clause>

  <clause id="37402">
    <literal><![CDATA[
      a(x,y,a(z * u,(z * u) * ((1 / (z * u)) * w),v5 * ((z * u) * ((1 / (z * u)) * w)))) = a(x,(z * u) * ((1 / (z * u)) * w),a(L(w * (z * u),z * u,z \ (u \ 1)),y,v5))
    ]]></literal>
    <justification jstring="[para(36607(a,1),36731(a,2,3,1))].">
      <j1 rule="para" parents="36607 36731"/>
    </justification>
  </clause>

  <clause id="37403">
    <literal><![CDATA[
      L((a(x,a(y,z,u),w) * u) \ v5,L(L(u,x,a(w,z,y)),z,a(x,w,y)),a(w,a(y,z,u),x)) = u \ (a(w,a(y,z,u),x) * v5)
    ]]></literal>
    <justification jstring="[para(28388(a,1),37361(a,1,1,1))].">
      <j1 rule="para" parents="28388 37361"/>
    </justification>
  </clause>

  <clause id="37404">
    <literal><![CDATA[
      (a(x,a(y,z,u),w) * u) \ v5 = u \ (a(w,a(y,z,u),x) * v5)
    ]]></literal>
    <justification jstring="[hyper(37209,a,37403,a)].">
      <j1 rule="hyper" parents="37209 37403"/>
    </justification>
  </clause>

  <clause id="37405">
    <literal><![CDATA[
      (x * a(y,a(z,u,x),w)) \ v5 = x \ (a(w,a(z,u,x),y) * v5)
    ]]></literal>
    <justification jstring="[hyper(20024,a,37404,a)].">
      <j1 rule="hyper" parents="20024 37404"/>
    </justification>
  </clause>

  <clause id="37407">
    <literal><![CDATA[
      a((x \ (a(y,a(z,u,x),w) * v5)) * L(x,w,a(y,u,z)),v6,v7) = a(v5 * a(a(z,u,w),y,L(x,w,a(y,u,z))),v6,v7)
    ]]></literal>
    <justification jstring="[para(37405(a,1),37367(a,1,1,1))].">
      <j1 rule="para" parents="37405 37367"/>
    </justification>
  </clause>

  <clause id="37408">
    <literal><![CDATA[
      a((a(x,a(y,z,u),w) * v5) * a(a(x,z,y),w,u),v6,v7) = a(v5 * a(a(y,z,w),x,L(u,w,a(x,z,y))),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,32032,a(flip),b,37407,a)].">
      <j1 rule="hyper" parents="63 32032 37407"/>
    </justification>
  </clause>

  <clause id="37409">
    <literal><![CDATA[
      a((a(x,a(y,z,u),w) * v5) * a(x,z,a(u,w,y)),v6,v7) = a(v5 * a(a(y,z,w),x,L(u,w,a(x,z,y))),v6,v7)
    ]]></literal>
    <justification jstring="[para(29790(a,1),37408(a,1,1,2))].">
      <j1 rule="para" parents="29790 37408"/>
    </justification>
  </clause>

  <clause id="37410">
    <literal><![CDATA[
      a((x \ y) * T(x,y),z,a(((x \ y) * T(x,y)) * u,w,x)) = a((x \ y) * T(x,y),z,a(u,w,x * ((x \ y) * T(x,v5))))
    ]]></literal>
    <justification jstring="[para(24067(a,1),36936(a,1,3))].">
      <j1 rule="para" parents="24067 36936"/>
    </justification>
  </clause>

  <clause id="37412">
    <literal><![CDATA[
      a((x \ y) * T(x,y),z,a(u,w,x * ((x \ y) * T(x,v5)))) = a((x \ y) * T(x,y),z,a(((x \ y) * x) * u,w,x))
    ]]></literal>
    <justification jstring="[para(24224(a,1),37410(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24224 37410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37413">
    <literal><![CDATA[
      a((x \ y) * T(x,y),z,a(u,w,x * ((x \ y) * T(x,v5)))) = a((x \ y) * T(x,y),z,a(y * u,w,x))
    ]]></literal>
    <justification jstring="[para(23904(a,1),37412(a,2,3))].">
      <j1 rule="para" parents="23904 37412"/>
    </justification>
  </clause>

  <clause id="37415">
    <literal><![CDATA[
      a((x \ y) * T(x,y),z,a(u,w,x * ((x \ y) * T(x,v5)))) = a((x \ y) * x,z,a(y * u,w,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,23901,a(flip),b,37413,a),flip(a)].">
      <j1 rule="hyper" parents="347 23901 37413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37418">
    <literal><![CDATA[
      a((x \ y) * T(x,y),z,a(u,w,x * ((x \ y) * T(x,v5)))) = a(x,z,a(x \ y,w,x * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(36941,a,37415,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36941 37415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37419">
    <literal><![CDATA[
      a((x \ y) * T(x,y),z,a(u,w,x * ((x \ y) * T(x,v5)))) = a(x,z,a(x * y,w,x * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(347,a,30797,a(flip),b,37418,a),flip(a)].">
      <j1 rule="hyper" parents="347 30797 37418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37420">
    <literal><![CDATA[
      a((x \ y) * T(x,y),z,a(u,w,x * ((x \ y) * T(x,v5)))) = a(x,z,a(y,w,x * (x * (y * u))))
    ]]></literal>
    <justification jstring="[hyper(347,a,36932,a(flip),b,37419,a),flip(a)].">
      <j1 rule="hyper" parents="347 36932 37419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37421">
    <literal><![CDATA[
      a((x \ y) * T(x,y),z,a(u,w,x * ((x \ y) * T(x,v5)))) = a(x,z,a(y,w,y * u))
    ]]></literal>
    <justification jstring="[para(31937(a,1),37420(a,2,3))].">
      <j1 rule="para" parents="31937 37420"/>
    </justification>
  </clause>

  <clause id="37422">
    <literal><![CDATA[
      a((x \ y) * T(x,y),z,a(u,w,x * y)) = a(x,z,a(y,w,y * u))
    ]]></literal>
    <justification jstring="[para(249(a,1),37421(a,1,3,3,2))].">
      <j1 rule="para" parents="249 37421"/>
    </justification>
  </clause>

  <clause id="37424">
    <literal><![CDATA[
      a((x \ y) * x,z,a(u,w,x * y)) = a(x,z,a(y,w,y * u))
    ]]></literal>
    <justification jstring="[hyper(23964,a,37422,a)].">
      <j1 rule="hyper" parents="23964 37422"/>
    </justification>
  </clause>

  <clause id="37425">
    <literal><![CDATA[
      a(x,y,a(z,u,w * x)) = a(w,y,a(x,u,x * z))
    ]]></literal>
    <justification jstring="[hyper(23954,a,37424,a)].">
      <j1 rule="hyper" parents="23954 37424"/>
    </justification>
  </clause>

  <clause id="37427">
    <literal><![CDATA[
      a(x,y,a(z,u * w,z * u)) = a(z,y,a(u,w,x * z))
    ]]></literal>
    <justification jstring="[hyper(32386,a,37425,a),flip(a)].">
      <j1 rule="hyper" parents="32386 37425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37429">
    <literal><![CDATA[
      a((x * (y / x)) \ z,u,a(w,v5,y)) = a(u,v5,a(z,y,w * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,37042,a,b,37427,a)].">
      <j1 rule="hyper" parents="63 37042 37427"/>
    </justification>
  </clause>

  <clause id="37430">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w * y)),y * z,a(y,y * ((y * z) * u),w)) = L(x,a(y,y * ((y * z) * u),w),y * z)
    ]]></literal>
    <justification jstring="[para(37427(a,1),37401(a,1,1,2))].">
      <j1 rule="para" parents="37427 37401"/>
    </justification>
  </clause>

  <clause id="37431">
    <literal><![CDATA[
      a((x / y) * (z * y),u,a(w,v5,x)) = a(u,v5,a(z,x,w * u))
    ]]></literal>
    <justification jstring="[hyper(37340,a,37429,a)].">
      <j1 rule="hyper" parents="37340 37429"/>
    </justification>
  </clause>

  <clause id="37432">
    <literal><![CDATA[
      a((x \ y) * (z * x),u,a(w,v5,y)) = a(u,v5,a(z,y,w * u))
    ]]></literal>
    <justification jstring="[hyper(23962,a,37431,a)].">
      <j1 rule="hyper" parents="23962 37431"/>
    </justification>
  </clause>

  <clause id="37433">
    <literal><![CDATA[
      a(x * ((y * x) * z),u,a(w,v5,z)) = a(u,v5,a(y,z,w * u))
    ]]></literal>
    <justification jstring="[hyper(63,a,37309,a(flip),b,37432,a)].">
      <j1 rule="hyper" parents="63 37309 37432"/>
    </justification>
  </clause>

  <clause id="37434">
    <literal><![CDATA[
      a(x,y,a(z,u,(w * v5) * (v5 * x))) = a(u,y,a(w,x,z * u))
    ]]></literal>
    <justification jstring="[hyper(37317,a,37433,a)].">
      <j1 rule="hyper" parents="37317 37433"/>
    </justification>
  </clause>

  <clause id="37435">
    <literal><![CDATA[
      a(x,y,a(z,u,w * ((v5 * x) * v5))) = a(u,y,a(w,x,z * u))
    ]]></literal>
    <justification jstring="[hyper(37293,a,37434,a)].">
      <j1 rule="hyper" parents="37293 37434"/>
    </justification>
  </clause>

  <clause id="37436">
    <literal><![CDATA[
      a(x,y,a(z,u,w * x)) = a(u,y,a(w,x,u * z))
    ]]></literal>
    <justification jstring="[para(24325(a,1),37435(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24325 37435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37437">
    <literal><![CDATA[
      L(x * a(x,y,a(z,u,x * w)),y,a(w,z * u,u)) = L(x,a(w,y,u),z * u)
    ]]></literal>
    <justification jstring="[para(37436(a,1),29985(a,1,1,2))].">
      <j1 rule="para" parents="37436 29985"/>
    </justification>
  </clause>

  <clause id="37438">
    <literal><![CDATA[
      L(R(x,y,a(z,u,x * w)),y,a(w,z * u,u)) = L(x,a(w,y,u),z * u)
    ]]></literal>
    <justification jstring="[para(28958(a,2),37437(a,1,1))].">
      <j1 rule="para" parents="28958 37437"/>
    </justification>
  </clause>

  <clause id="37439">
    <literal><![CDATA[
      L(L(x,y,a(z,u,x * w)),y,a(w,z * u,u)) = L(x,a(w,y,u),z * u)
    ]]></literal>
    <justification jstring="[para(23247(a,1),37438(a,1,1))].">
      <j1 rule="para" parents="23247 37438"/>
    </justification>
  </clause>

  <clause id="37440">
    <literal><![CDATA[
      L(x,a(y,z,u),w * u) != v5
    ]]></literal>
    <literal><![CDATA[
      L(L(x,z,a(w,u,x * y)),z,a(y,w,u)) = v5
    ]]></literal>
    <justification jstring="[para(37439(a,1),32361(a,1))].">
      <j1 rule="para" parents="37439 32361"/>
    </justification>
  </clause>

  <clause id="37441">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w * x)),y * z,a(y,y * ((y * z) * u),w)) = L(x,a(y,y * ((y * z) * u),w),y * z)
    ]]></literal>
    <justification jstring="[para(37022(a,1),37430(a,1,1))].">
      <j1 rule="para" parents="37022 37430"/>
    </justification>
  </clause>

  <clause id="37442">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w * x)),(y * z) * u,a(y,y * z,w)) = L(x,a(y,y * ((y * z) * u),w),y * z)
    ]]></literal>
    <justification jstring="[hyper(32385,a,37441,a)].">
      <j1 rule="hyper" parents="32385 37441"/>
    </justification>
  </clause>

  <clause id="37443">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w * x)),z,a(y,(y * z) * u,w)) = L(x,a(y,y * ((y * z) * u),w),y * z)
    ]]></literal>
    <justification jstring="[hyper(32385,a,37442,a)].">
      <j1 rule="hyper" parents="32385 37442"/>
    </justification>
  </clause>

  <clause id="37444">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w * x)),z,a(y,z * (u * y),w)) = L(x,a(y,y * ((y * z) * u),w),y * z)
    ]]></literal>
    <justification jstring="[para(36583(a,1),37443(a,1,3))].">
      <j1 rule="para" parents="36583 37443"/>
    </justification>
  </clause>

  <clause id="37445">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w * x)),u * y,a(y,z,w)) = L(x,a(y,y * ((y * z) * u),w),y * z)
    ]]></literal>
    <justification jstring="[hyper(63,a,36951,a(flip),b,37444,a)].">
      <j1 rule="hyper" parents="63 36951 37444"/>
    </justification>
  </clause>

  <clause id="37446">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w * x)),u,a(y,z,w)) = L(x,a(y,y * ((y * z) * u),w),y * z)
    ]]></literal>
    <justification jstring="[hyper(32387,a,37445,a)].">
      <j1 rule="hyper" parents="32387 37445"/>
    </justification>
  </clause>

  <clause id="37447">
    <literal><![CDATA[
      L(x,a(y,y * ((y * z) * u),w),y * z) = L(x,a(w,u,y),z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,37030,a(flip),b,37446,a),flip(a)].">
      <j1 rule="hyper" parents="63 37030 37446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37448">
    <literal><![CDATA[
      L(x,a(y,(y * z) * u,w),y * z) = L(x,a(w,u,y),z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,32407,a(flip),b,37447,a)].">
      <j1 rule="hyper" parents="63 32407 37447"/>
    </justification>
  </clause>

  <clause id="37449">
    <literal><![CDATA[
      L(x,a(y,z * (u * y),w),y * z) = L(x,a(w,u,y),z * y)
    ]]></literal>
    <justification jstring="[para(36583(a,1),37448(a,1,2))].">
      <j1 rule="para" parents="36583 37448"/>
    </justification>
  </clause>

  <clause id="37450">
    <literal><![CDATA[
      L(x,a(y,z * u,w),y * z) = L(x,a(w,u,y),z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,36810,a(flip),b,37449,a)].">
      <j1 rule="hyper" parents="63 36810 37449"/>
    </justification>
  </clause>

  <clause id="37451">
    <literal><![CDATA[
      ((a(x,y,a(z,u,w)) * v5) * (v6 * v7)) \ ((v5 * (a(w,y,a(x,u,z)) * v6)) * v7) = a(a(x,y,a(z,u,w)) * v5,L(v6,v5,a(x,y,a(z,u,w))),v7)
    ]]></literal>
    <justification jstring="[para(37188(a,1),37308(a,1,1,2,1))].">
      <j1 rule="para" parents="37188 37308"/>
    </justification>
  </clause>

  <clause id="37452">
    <literal><![CDATA[
      a(x,y,a(z * u,(z * u) * ((1 / (z * u)) * w),v5 * ((z * u) * ((1 / (z * u)) * w)))) = a(x,(z * u) * ((1 / (z * u)) * w),a(w * (z * u),y,L(v5,z * u,z \ (u \ 1))))
    ]]></literal>
    <justification jstring="[hyper(347,a,29930,a(flip),b,37402,a),flip(a)].">
      <j1 rule="hyper" parents="347 29930 37402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37453">
    <literal><![CDATA[
      a(x,y,a(z * u,(z * u) * ((1 / (z * u)) * w),v5 * ((z * u) * ((1 / (z * u)) * w)))) = a(x,(z * u) * ((1 / (z * u)) * w),a(w * (z * u),y,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,37227,a(flip),b,37452,a),flip(a)].">
      <j1 rule="hyper" parents="347 37227 37452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37455">
    <literal><![CDATA[
      a(x,y,a(z * u,(z * u) * ((1 / (z * u)) * w),v5 * ((z * u) * ((1 / (z * u)) * w)))) = a(x,1 / (z * u),a(w * (z * u),y,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,37249,a(flip),b,37453,a),flip(a)].">
      <j1 rule="hyper" parents="347 37249 37453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37456">
    <literal><![CDATA[
      a(x,y,a(z * u,(z * u) * ((1 / (z * u)) * w),v5 * ((z * u) * ((1 / (z * u)) * w)))) = a(x,z * u,a(w * (z * u),y,v5))
    ]]></literal>
    <justification jstring="[hyper(347,a,14964,a(flip),b,37455,a),flip(a)].">
      <j1 rule="hyper" parents="347 14964 37455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37457">
    <literal><![CDATA[
      a(x,y,a(x * z,(x * z) * ((1 / (x * z)) * u),w * ((x * z) * ((1 / (x * z)) * u)))) = a(w,z,a(x,y,u * (x * z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,32349,a(flip),b,37456,a),flip(a)].">
      <j1 rule="hyper" parents="347 32349 37456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37458">
    <literal><![CDATA[
      a(x,y,a(x * z,(x * z) * ((1 / (x * z)) * u),w * ((x * z) * (((x * z) \ 1) * u)))) = a(w,z,a(x,y,u * (x * z)))
    ]]></literal>
    <justification jstring="[para(24504(a,1),37457(a,1,3))].">
      <j1 rule="para" parents="24504 37457"/>
    </justification>
  </clause>

  <clause id="37459">
    <literal><![CDATA[
      a(x,y,a(x * z,(x * z) * ((1 / (x * z)) * u),w * L(u,x * z,x * z))) = a(w,z,a(x,y,u * (x * z)))
    ]]></literal>
    <justification jstring="[para(3197(a,1),37458(a,1,3,3,2))].">
      <j1 rule="para" parents="3197 37458"/>
    </justification>
  </clause>

  <clause id="37460">
    <literal><![CDATA[
      a(x,y,a(x * z,(x * z) * ((1 / (x * z)) * u),w * u)) = a(w,z,a(x,y,u * (x * z)))
    ]]></literal>
    <justification jstring="[para(36456(a,1),37459(a,1,3))].">
      <j1 rule="para" parents="36456 37459"/>
    </justification>
  </clause>

  <clause id="37462">
    <literal><![CDATA[
      a(x,y,a(x * z,(x * z) * ((1 * (x * z)) * u),w * u)) = a(w,z,a(x,y,u * (x * z)))
    ]]></literal>
    <justification jstring="[para(36600(a,1),37460(a,1,3))].">
      <j1 rule="para" parents="36600 37460"/>
    </justification>
  </clause>

  <clause id="37463">
    <literal><![CDATA[
      a(x,y,a(x * z,(x * z) * ((x * z) * u),w * u)) = a(w,z,a(x,y,u * (x * z)))
    ]]></literal>
    <justification jstring="[para(7(a,1),37462(a,1,3,2,2,1))].">
      <j1 rule="para" parents="7 37462"/>
    </justification>
  </clause>

  <clause id="37464">
    <literal><![CDATA[
      a(x,y,a(x * z,u,w * u)) = a(w,z,a(x,y,u * (x * z)))
    ]]></literal>
    <justification jstring="[para(36465(a,1),37463(a,1,3))].">
      <j1 rule="para" parents="36465 37463"/>
    </justification>
  </clause>

  <clause id="37465">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (z * y))) = a(w,z,a(x,u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,36882,a(flip),b,37464,a),flip(a)].">
      <j1 rule="hyper" parents="63 36882 37464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37467">
    <literal><![CDATA[
      a(x,y,a(z,u,(y * (w * (u * z))) * u)) = a(w,u * z,a(x,u,y))
    ]]></literal>
    <justification jstring="[hyper(63,a,36728,a(flip),b,37465,a)].">
      <j1 rule="hyper" parents="63 36728 37465"/>
    </justification>
  </clause>

  <clause id="37468">
    <literal><![CDATA[
      a(x,y,a(z,u,(y * (w * (u * z))) * u)) = a(w,u,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(347,a,37053,a(flip),b,37467,a),flip(a)].">
      <j1 rule="hyper" parents="347 37053 37467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37469">
    <literal><![CDATA[
      a(x,y,a(x * z,u,(y * (w * (u * (x * z)))) * u)) = a(y,u,a(x,z,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,32389,a(flip),b,37468,a),flip(a)].">
      <j1 rule="hyper" parents="347 32389 37468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37470">
    <literal><![CDATA[
      a(x,y,a((z * (x * (y * u))) * w,w,u)) = a(w,x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(36888,a,37469,a)].">
      <j1 rule="hyper" parents="36888 37469"/>
    </justification>
  </clause>

  <clause id="37471">
    <literal><![CDATA[
      a(x,y,a(z * (x * (y * u)),w,u * w)) = a(w,x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(36740,a,37470,a)].">
      <j1 rule="hyper" parents="36740 37470"/>
    </justification>
  </clause>

  <clause id="37472">
    <literal><![CDATA[
      a(x,y,a(z * (x * (u * y)),w,x * z)) = a(y,w,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(63,a,37370,a,b,37471,a)].">
      <j1 rule="hyper" parents="63 37370 37471"/>
    </justification>
  </clause>

  <clause id="37473">
    <literal><![CDATA[
      a(x,y,a(z * (u * y),w,x * (x * z))) = a(y,w,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(36942,a,37472,a)].">
      <j1 rule="hyper" parents="36942 37472"/>
    </justification>
  </clause>

  <clause id="37474">
    <literal><![CDATA[
      a(x,y,a(z * (u * y),w,z)) = a(y,w,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(31937(a,1),37473(a,1,3))].">
      <j1 rule="para" parents="31937 37473"/>
    </justification>
  </clause>

  <clause id="37475">
    <literal><![CDATA[
      a(x,y,a(z * u,w,u * y)) = a(y,w,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(63,a,37348,a(flip),b,37474,a)].">
      <j1 rule="hyper" parents="63 37348 37474"/>
    </justification>
  </clause>

  <clause id="37478">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) * v6 = v5 * (a(x,u,a(z,y,w)) * v6)
    ]]></literal>
    <justification jstring="[para(37475(a,1),37387(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="37475 37387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37479">
    <literal><![CDATA[
      (x * (a(y,z,a(u,w,v5)) * v6)) * v7 = (x * v6) * (a(u,w,a(v5,z,y)) * v7)
    ]]></literal>
    <justification jstring="[para(37295(a,1),37478(a,1,1))].">
      <j1 rule="para" parents="37295 37478"/>
    </justification>
  </clause>

  <clause id="37480">
    <literal><![CDATA[
      (x * (a(y,z,a(u,w,v5)) * (v6 * v7))) \ ((x * (a(v5,w,a(y,z,u)) * v6)) * v7) = a(a(y,w,a(u,z,v5)) * x,L(v6,x,a(y,w,a(u,z,v5))),v7)
    ]]></literal>
    <justification jstring="[para(37478(a,1),37451(a,1,1))].">
      <j1 rule="para" parents="37478 37451"/>
    </justification>
  </clause>

  <clause id="37481">
    <literal><![CDATA[
      (x * (a(y,z,a(u,w,v5)) * (v6 * v7))) \ ((x * v6) * (a(y,z,a(u,w,v5)) * v7)) = a(a(y,w,a(u,z,v5)) * x,L(v6,x,a(y,w,a(u,z,v5))),v7)
    ]]></literal>
    <justification jstring="[para(37479(a,1),37480(a,1,2))].">
      <j1 rule="para" parents="37479 37480"/>
    </justification>
  </clause>

  <clause id="37482">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * ((v5 * (a(w,y,a(x,u,z)) * (v6 * v7))) \ ((v5 * v6) * v7)) = a(a(w,u,a(x,y,z)) * v5,L(v6,v5,a(w,u,a(x,y,z))),v7)
    ]]></literal>
    <justification jstring="[hyper(37312,a,37481,a)].">
      <j1 rule="hyper" parents="37312 37481"/>
    </justification>
  </clause>

  <clause id="37483">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(x,y,a(z,u,w)) * ((v5 * (v6 * v7)) \ ((v5 * v6) * v7))) = a(a(w,u,a(x,y,z)) * v5,L(v6,v5,a(w,u,a(x,y,z))),v7)
    ]]></literal>
    <justification jstring="[para(37316(a,1),37482(a,1,2))].">
      <j1 rule="para" parents="37316 37482"/>
    </justification>
  </clause>

  <clause id="37484">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)) * v5,L(v6,v5,a(x,y,a(z,u,w))),v7) = a(z,u,a(w,y,x)) * (a(z,u,a(w,y,x)) * a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(14(a,2),37483(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14 37483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37485">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)) * v5,L(v6,v5,a(x,y,a(z,u,w))),v7) = a(w,y,x) * (L(L(a(w,y,x),u,z),u,z) \ a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(347,a,28496,a(flip),b,37484,a),flip(a)].">
      <j1 rule="hyper" parents="347 28496 37484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37486">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)) * v5,L(v6,v5,a(x,y,a(z,u,w))),v7) = a(w,y,x) * (a(w,y,x) \ a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(26291(a,1),37485(a,2,2,1))].">
      <j1 rule="para" parents="26291 37485"/>
    </justification>
  </clause>

  <clause id="37487">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)) * v5,L(v6,v5,a(x,y,a(z,u,w))),v7) = a(v5,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,10,a(flip),b,37486,a),flip(a)].">
      <j1 rule="hyper" parents="347 10 37486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37490">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)) * v5,v6,v7) = a(v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(37188(a,1),37487(a,1,2))].">
      <j1 rule="para" parents="37188 37487"/>
    </justification>
  </clause>

  <clause id="37491">
    <literal><![CDATA[
      a(x * a(y,z,a(u,w,v5)),v6,v7) = a(x,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(23925,a,37490,a)].">
      <j1 rule="hyper" parents="23925 37490"/>
    </justification>
  </clause>

  <clause id="37493">
    <literal><![CDATA[
      a((a(x,y,a(z,u,w)) * v5) * a(z,u,w),v6,v7) = a(v5 * a(z,u,w),v6,v7)
    ]]></literal>
    <justification jstring="[para(23111(a,2),37490(a,1,1))].">
      <j1 rule="para" parents="23111 37490"/>
    </justification>
  </clause>

  <clause id="37495">
    <literal><![CDATA[
      a(a(x,y,L(z,u,w)) * v5,v6,v7) = a(v5 * a(x,y,z),v6,v7)
    ]]></literal>
    <justification jstring="[para(29154(a,1),37490(a,1,1))].">
      <j1 rule="para" parents="29154 37490"/>
    </justification>
  </clause>

  <clause id="37497">
    <literal><![CDATA[
      a(x * a(a(y,z,u),w,L(v5,u,a(w,z,y))),v6,v7) = a(a(w,a(y,z,v5),u) * x,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,37409,a(flip),b,37491,a)].">
      <j1 rule="hyper" parents="63 37409 37491"/>
    </justification>
  </clause>

  <clause id="37499">
    <literal><![CDATA[
      a(x * a(y,z,L(u,w,v5)),v6,v7) = a(x * a(y,z,u),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(23925,a,37495,a)].">
      <j1 rule="hyper" parents="23925 37495"/>
    </justification>
  </clause>

  <clause id="37500">
    <literal><![CDATA[
      a((R(x,y,a(z,u,w)) * v5) * a(z,u,w),v6,v7) = a((x * v5) * a(z,u,w),v6,v7)
    ]]></literal>
    <justification jstring="[para(31756(a,1),37493(a,1,1,1))].">
      <j1 rule="para" parents="31756 37493"/>
    </justification>
  </clause>

  <clause id="37501">
    <literal><![CDATA[
      a((L(x,y,a(z,u,w)) * v5) * a(z,u,w),v6,v7) = a((x * v5) * a(z,u,w),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,26397,a(flip),b,37500,a)].">
      <j1 rule="hyper" parents="63 26397 37500"/>
    </justification>
  </clause>

  <clause id="37502">
    <literal><![CDATA[
      a((x * y) * a(z,u,w),v5,v6) = a(x * (a(z,u,w) * y),v5,v6)
    ]]></literal>
    <justification jstring="[para(26381(a,1),37501(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26381 37501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37503">
    <literal><![CDATA[
      a(a(x,y,z) * (u * w),v5,v6) = a(w * (a(x,y,z) * u),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(24409,a,37502,a)].">
      <j1 rule="hyper" parents="24409 37502"/>
    </justification>
  </clause>

  <clause id="37504">
    <literal><![CDATA[
      a(x * (a(y,z,u) * (w \ 1)),v5,v6) = a((w \ x) * a(y,z,u),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,36560,a(flip),b,37502,a),flip(a)].">
      <j1 rule="hyper" parents="63 36560 37502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37505">
    <literal><![CDATA[
      a(a(x,y,L(z,u,w)) * ((w * u) * v5),v6,v7) = a(v5 * (w * (u * a(x,y,z))),v6,v7)
    ]]></literal>
    <justification jstring="[para(29120(a,1),37503(a,2,1,2))].">
      <j1 rule="para" parents="29120 37503"/>
    </justification>
  </clause>

  <clause id="37506">
    <literal><![CDATA[
      a((x \ y) * a(z,u,w),v5,v6) = a(y * (x \ a(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(31951(a,1),37504(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="31951 37504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37508">
    <literal><![CDATA[
      a(x * (T(a(y,z,u) * w,v5) \ a(y,z,u)),v6,v7) = a(a(y,z,u) * ((w * a(y,z,u)) \ x),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,24564,a(flip),b,37506,a),flip(a)].">
      <j1 rule="hyper" parents="63 24564 37506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37509">
    <literal><![CDATA[
      a(((x * y) * z) * a(u,w,v5),v6,v7) = a(z * (x * (y * a(u,w,v5))),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,37495,a(flip),b,37505,a)].">
      <j1 rule="hyper" parents="63 37495 37505"/>
    </justification>
  </clause>

  <clause id="37511">
    <literal><![CDATA[
      a((x * y) * (a(z,u,w) * v5),v6,v7) = a(v5 * (x * (y * a(z,u,w))),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,37502,a(flip),b,37509,a)].">
      <j1 rule="hyper" parents="63 37502 37509"/>
    </justification>
  </clause>

  <clause id="37512">
    <literal><![CDATA[
      a((x \ (y \ x)) * (z * (u * a(w,v5,v6))),v7,v8) = a((z * u) * (y \ a(w,v5,v6)),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(36841,a,37511,a),flip(a)].">
      <j1 rule="hyper" parents="36841 37511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37514">
    <literal><![CDATA[
      a(a(x,a(y,z,u),w) * v5,v6,v7) = a(v5 * a(a(y,z,w),x,u),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,37499,a(flip),b,37497,a),flip(a)].">
      <j1 rule="hyper" parents="63 37499 37497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37516">
    <literal><![CDATA[
      a(a(x,a(y,z,u),w) * v5,v6,v7) = a(v5 * a(y,z,a(u,x,w)),v6,v7)
    ]]></literal>
    <justification jstring="[para(29790(a,1),37514(a,2,1,2))].">
      <j1 rule="para" parents="29790 37514"/>
    </justification>
  </clause>

  <clause id="37517">
    <literal><![CDATA[
      a(a(x,a(y,z,u),w) * v5,v6,v7) = a(v5,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,37491,a(flip),b,37516,a),flip(a)].">
      <j1 rule="hyper" parents="347 37491 37516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37519">
    <literal><![CDATA[
      a(x * (a(y,a(z,u,w),v5) * v6),v7,v8) = a(v6 * x,v7,v8)
    ]]></literal>
    <justification jstring="[hyper(63,a,37503,a(flip),b,37517,a)].">
      <j1 rule="hyper" parents="63 37503 37517"/>
    </justification>
  </clause>

  <clause id="37520">
    <literal><![CDATA[
      a((L(x,a(y,z,u),w) * v5) * v6,v7,v8) = a(v6 * (x * v5),v7,v8)
    ]]></literal>
    <justification jstring="[para(31816(a,1),37519(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="31816 37519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37521">
    <literal><![CDATA[
      a(x \ (y * (z * a(u,w,v5))),v6,v7) = a((y * z) * (x \ a(u,w,v5)),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(23954,a,37512,a)].">
      <j1 rule="hyper" parents="23954 37512"/>
    </justification>
  </clause>

  <clause id="37522">
    <literal><![CDATA[
      a((R(x,a(y,z,u),w) * w) * (v5 \ a(y,z,u)),v6,v7) = a(v5 \ ((x * a(y,z,u)) * T(w,a(y,z,u))),v6,v7)
    ]]></literal>
    <justification jstring="[para(9598(a,1),37521(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9598 37521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37523">
    <literal><![CDATA[
      a(a(x,y,z) * ((u * a(x,y,z)) \ w),v5,v6) = a(w * (T(u,v7) \ 1),v5,v6)
    ]]></literal>
    <justification jstring="[para(31925(a,1),37508(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="31925 37508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37524">
    <literal><![CDATA[
      a(T(x,y) \ z,u,w) = a(a(v5,v6,v7) * ((x * a(v5,v6,v7)) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(347,a,31940,a(flip),b,37523,a)].">
      <j1 rule="hyper" parents="347 31940 37523"/>
    </justification>
  </clause>

  <clause id="37526">
    <literal><![CDATA[
      a(a(x,y,z) * ((u * a(x,y,z)) \ w),v5,v6) = a(u \ w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(23959,a,37524,a),flip(a)].">
      <j1 rule="hyper" parents="23959 37524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37527">
    <literal><![CDATA[
      a((x * L(y,x,a(z,u,w))) \ v5,v6,v7) = a(a(z,u,w) * (((a(z,u,w) * x) * y) \ v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(26383(a,1),37526(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="26383 37526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37528">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)) * ((v5 * L(w,y,a(z,u,x))) \ v6),v7,v8) = a((v5 * w) \ v6,v7,v8)
    ]]></literal>
    <justification jstring="[para(30817(a,1),37526(a,1,1,2,1))].">
      <j1 rule="para" parents="30817 37526"/>
    </justification>
  </clause>

  <clause id="37529">
    <literal><![CDATA[
      a((x * L(y,z,a(u,w,v5))) \ v6,v7,v8) = a((x * y) \ v6,v7,v8)
    ]]></literal>
    <justification jstring="[hyper(63,a,37490,a(flip),b,37528,a)].">
      <j1 rule="hyper" parents="63 37490 37528"/>
    </justification>
  </clause>

  <clause id="37531">
    <literal><![CDATA[
      a(a(x,y,z) * (((a(x,y,z) * u) * w) \ v5),v6,v7) = a((u * w) \ v5,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,37529,a(flip),b,37527,a),flip(a)].">
      <j1 rule="hyper" parents="63 37529 37527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37533">
    <literal><![CDATA[
      a((R(x,a(y,z,u),w) * w) * (v5 \ a(y,z,u)),v6,v7) = a(v5 \ ((x * a(y,z,u)) * w),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,23937,a(flip),b,37522,a),flip(a)].">
      <j1 rule="hyper" parents="347 23937 37522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37536">
    <literal><![CDATA[
      a((L(x,a(y,z,u),w) * w) * (v5 \ a(y,z,u)),v6,v7) = a(v5 \ ((x * a(y,z,u)) * w),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,26397,a(flip),b,37533,a)].">
      <j1 rule="hyper" parents="63 26397 37533"/>
    </justification>
  </clause>

  <clause id="37537">
    <literal><![CDATA[
      a(x \ ((y * a(z,u,w)) * v5),v6,v7) = a((x \ a(z,u,w)) * (y * v5),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(63,a,37520,a(flip),b,37536,a),flip(a)].">
      <j1 rule="hyper" parents="63 37520 37536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37539">
    <literal><![CDATA[
      a(x \ ((y * a(z,u,w)) * v5),v6,v7) = a(a(z,u,w) * (x \ (y * v5)),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(347,a,37219,a(flip),b,37537,a),flip(a)].">
      <j1 rule="hyper" parents="347 37219 37537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37540">
    <literal><![CDATA[
      a(a(x,y,z) * (((u * a(x,y,z)) * w) \ (u * (w * v5))),v6,v7) = a(L(v5,w,u * a(x,y,z)),v6,v7)
    ]]></literal>
    <justification jstring="[para(18(a,2),37539(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 37539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37541">
    <literal><![CDATA[
      a(a(x,y,z) * (((u * a(x,y,z)) * w) \ (u * (w * v5))),v6,v7) = a(v5,v6,L(v7,w,u * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,29675,a(flip),b,37540,a),flip(a)].">
      <j1 rule="hyper" parents="347 29675 37540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37542">
    <literal><![CDATA[
      a(a(x,y,z) * (((T(u,w) * a(x,y,z)) * v5) \ (u * (v5 * v6))),v7,v8) = a(v6,v7,L(v8,v5,T(u,w) * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,24489,a(flip),b,37541,a)].">
      <j1 rule="hyper" parents="63 24489 37541"/>
    </justification>
  </clause>

  <clause id="37543">
    <literal><![CDATA[
      a(a(x,y,z) * ((T(a(x,y,z) * u,w) * v5) \ (u * (v5 * v6))),v7,v8) = a(v6,v7,L(v8,v5,T(u,w) * a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(23109(a,2),37542(a,1,1,2,1,1))].">
      <j1 rule="para" parents="23109 37542"/>
    </justification>
  </clause>

  <clause id="37544">
    <literal><![CDATA[
      a(a(x,y,z) * (((a(x,y,z) * u) * w) \ (u * (w * v5))),v6,v7) = a(v5,v6,L(v7,w,T(u,v8) * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,24225,a(flip),b,37543,a)].">
      <j1 rule="hyper" parents="63 24225 37543"/>
    </justification>
  </clause>

  <clause id="37546">
    <literal><![CDATA[
      a((x * y) \ (x * (y * z)),u,w) = a(z,u,L(w,y,T(x,v5) * a(v6,v7,v8)))
    ]]></literal>
    <justification jstring="[hyper(63,a,37531,a(flip),b,37544,a)].">
      <j1 rule="hyper" parents="63 37531 37544"/>
    </justification>
  </clause>

  <clause id="37548">
    <literal><![CDATA[
      a(x,y,L(z,u,T(w,v5) * a(v6,v7,v8))) = a(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(18(a,2),37546(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 37546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37549">
    <literal><![CDATA[
      a(x,y,L(z,u,T(w,v5) * a(v6,v7,v8))) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(347,a,29675,a(flip),b,37548,a),flip(a)].">
      <j1 rule="hyper" parents="347 29675 37548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37550">
    <literal><![CDATA[
      a(x,y,L(z,u,w * a(v5,v6,v7))) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(110(a,1),37549(a,1,3,3,1))].">
      <j1 rule="para" parents="110 37549"/>
    </justification>
  </clause>

  <clause id="37551">
    <literal><![CDATA[
      a(x,y,L(z,u,a(w,v5,v6) * v7)) = a(x,y,L(z,u,v7))
    ]]></literal>
    <justification jstring="[para(14036(a,1),37549(a,1,3,3))].">
      <j1 rule="para" parents="14036 37549"/>
    </justification>
  </clause>

  <clause id="37552">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(x,y,z) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w * a(v6,v7,v8),u,a(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(37550(a,1),29151(a,1,1))].">
      <j1 rule="para" parents="37550 29151"/>
    </justification>
  </clause>

  <clause id="37554">
    <literal><![CDATA[
      a(x,y,L(z,u,u * w)) \ w = u * ((u * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(37551(a,1),36623(a,1,1))].">
      <j1 rule="para" parents="37551 36623"/>
    </justification>
  </clause>

  <clause id="37555">
    <literal><![CDATA[
      (x / y) * (a(z,u,w) \ y) = y * ((y * a(z,u,w)) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,30703,a(flip),b,37554,a)].">
      <j1 rule="hyper" parents="63 30703 37554"/>
    </justification>
  </clause>

  <clause id="37557">
    <literal><![CDATA[
      (1 / x) * (((1 / x) * a(y,z,u)) \ w) = (a(y,z,u) \ x) * (x \ w)
    ]]></literal>
    <justification jstring="[hyper(30714,a,37555,a),flip(a)].">
      <j1 rule="hyper" parents="30714 37555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37558">
    <literal><![CDATA[
      (1 / x) * ((a(y,z,u) / x) \ w) = (a(y,z,u) \ x) * (x \ w)
    ]]></literal>
    <justification jstring="[para(31923(a,1),37557(a,1,2,1))].">
      <j1 rule="para" parents="31923 37557"/>
    </justification>
  </clause>

  <clause id="37559">
    <literal><![CDATA[
      x * ((a(y,z,u) / (x \ 1)) \ w) = (a(y,z,u) \ x) * (x \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,6489,a(flip),b,37558,a)].">
      <j1 rule="hyper" parents="63 6489 37558"/>
    </justification>
  </clause>

  <clause id="37560">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (u \ w) = u * ((a(x,y,z) * u) \ w)
    ]]></literal>
    <justification jstring="[para(31729(a,1),37559(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="31729 37559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37562">
    <literal><![CDATA[
      (x * y) \ ((L(x,z,u) * y) * w) = y * ((a(u,z,x) * y) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,36858,a,b,37560,a)].">
      <j1 rule="hyper" parents="63 36858 37560"/>
    </justification>
  </clause>

  <clause id="37563">
    <literal><![CDATA[
      x / (y * ((a(z,u,w) * y) \ x)) = a(z,u,L(w,y,x * y))
    ]]></literal>
    <justification jstring="[hyper(220,a,37560,a(flip),b,29152,a)].">
      <j1 rule="hyper" parents="220 37560 29152"/>
    </justification>
  </clause>

  <clause id="37564">
    <literal><![CDATA[
      (x * ((a(y,z,u) * x) \ w)) \ w = a(y,z,L(u,x,w * x))
    ]]></literal>
    <justification jstring="[para(37560(a,1),29325(a,1,1))].">
      <j1 rule="para" parents="37560 29325"/>
    </justification>
  </clause>

  <clause id="37565">
    <literal><![CDATA[
      T((x * ((a(y,z,u) * x) \ w)) * (a(y,z,L(u,x,w * x)) * (w / (x * ((a(y,z,u) * x) \ w)))),T(x * ((a(y,z,u) * x) \ w),w)) = (((x * ((a(y,z,u) * x) \ w)) \ w) \ 1) \ w
    ]]></literal>
    <justification jstring="[para(37564(a,1),9302(a,1,1,2,1))].">
      <j1 rule="para" parents="37564 9302"/>
    </justification>
  </clause>

  <clause id="37566">
    <literal><![CDATA[
      ((L(x,y,z) * u) * w) / T(x * u,w) = u * ((a(z,y,x) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,32330,a,b,37562,a)].">
      <j1 rule="hyper" parents="63 32330 37562"/>
    </justification>
  </clause>

  <clause id="37567">
    <literal><![CDATA[
      (x * (L(y,z,u) * w)) / (y * w) = w * ((a(u,z,y) * w) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,22986,a(flip),b,37566,a)].">
      <j1 rule="hyper" parents="63 22986 37566"/>
    </justification>
  </clause>

  <clause id="37568">
    <literal><![CDATA[
      a(x,y,z) * R(a(x,y,z) \ u,a(x,y,z),L(z,y,x) * w) = (w * ((a(x,y,z) * w) \ u)) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(37567(a,1),32039(a,2,1))].">
      <j1 rule="para" parents="37567 32039"/>
    </justification>
  </clause>

  <clause id="37569">
    <literal><![CDATA[
      a(x * a(y,z,u),w,a(v5,v6,v7)) = a(x,w,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(37552,a,29147,a)].">
      <j1 rule="hyper" parents="37552 29147"/>
    </justification>
  </clause>

  <clause id="37571">
    <literal><![CDATA[
      a(x,y,a(z * a(u,w,v5),v6,v7)) = a(z,v6,a(x,y,v7))
    ]]></literal>
    <justification jstring="[hyper(29787,a,37569,a)].">
      <j1 rule="hyper" parents="29787 37569"/>
    </justification>
  </clause>

  <clause id="37575">
    <literal><![CDATA[
      a(x,y,a(z * a(u,w,v5),v6,v7)) = a(x,y,a(v7,v6,z))
    ]]></literal>
    <justification jstring="[hyper(347,a,29788,a,b,37571,a),flip(a)].">
      <j1 rule="hyper" parents="347 29788 37571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37577">
    <literal><![CDATA[
      a(x,y,a(z * (a(u,w,v5) * v6),v7,v8)) = a(z * v6,v7,a(x,y,v8))
    ]]></literal>
    <justification jstring="[para(37502(a,1),37571(a,1,3))].">
      <j1 rule="para" parents="37502 37571"/>
    </justification>
  </clause>

  <clause id="37578">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),z,a(y,w * a(v5,v6,v7),u)) != v8
    ]]></literal>
    <literal><![CDATA[
      L(x,a(y,z,u),w * a(v5,v6,v7)) = v8
    ]]></literal>
    <justification jstring="[para(37575(a,1),30024(a,1,1,2))].">
      <j1 rule="para" parents="37575 30024"/>
    </justification>
  </clause>

  <clause id="37579">
    <literal><![CDATA[
      a(x,y,a(z * L(u,w,v5),v6,v7)) = a(u * z,v6,a(x,y,v7))
    ]]></literal>
    <justification jstring="[para(32564(a,1),37577(a,1,3))].">
      <j1 rule="para" parents="32564 37577"/>
    </justification>
  </clause>

  <clause id="37580">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6) * v7)) = a(w * v7,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(29859,a,37579,a)].">
      <j1 rule="hyper" parents="29859 37579"/>
    </justification>
  </clause>

  <clause id="37581">
    <literal><![CDATA[
      a(x * ((y * z) * u),y,a(w,v5,L(x,v6,v7) * u)) = a(y,L(x,v6,v7) \ u,a(w,v5,z))
    ]]></literal>
    <justification jstring="[hyper(37355,a,37580,a),flip(a)].">
      <j1 rule="hyper" parents="37355 37580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37582">
    <literal><![CDATA[
      a(x * y,z,a(u,w,x * ((w * v5) * y))) = a(w,L(x,v6,v7) \ y,a(u,z,v5))
    ]]></literal>
    <justification jstring="[hyper(63,a,37580,a(flip),b,37581,a)].">
      <j1 rule="hyper" parents="63 37580 37581"/>
    </justification>
  </clause>

  <clause id="37584">
    <literal><![CDATA[
      a(x,L(y,z,u) \ w,a(v5,v6,v7)) = a(x,y * w,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(63,a,37354,a(flip),b,37582,a),flip(a)].">
      <j1 rule="hyper" parents="63 37354 37582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37585">
    <literal><![CDATA[
      a(x,L(y,z,u) * w,a(v5,v6,v7)) = a(x,y * w,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(36563,a,37584,a)].">
      <j1 rule="hyper" parents="36563 37584"/>
    </justification>
  </clause>

  <clause id="37586">
    <literal><![CDATA[
      a(x,y * L(z,u,w),a(v5,v6,v7)) = a(x,z * y,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(23994,a,37585,a)].">
      <j1 rule="hyper" parents="23994 37585"/>
    </justification>
  </clause>

  <clause id="37587">
    <literal><![CDATA[
      a(x,(y * z) * u,a(w,v5,v6)) = a(x,z * (u * y),a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(24160,a,37586,a)].">
      <j1 rule="hyper" parents="24160 37586"/>
    </justification>
  </clause>

  <clause id="37588">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),v5,v6)) * a(x,(z \ 1) * (u * w),a(y,v5,v6)) = a((z \ w) * u,a(v6,v5,x),y)
    ]]></literal>
    <justification jstring="[para(37587(a,1),37347(a,1,2))].">
      <j1 rule="para" parents="37587 37347"/>
    </justification>
  </clause>

  <clause id="37589">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),z,a(u,w,y)) = L(x,a(y,z,u),w * a(y,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(37578,a,37069,a),flip(a)].">
      <j1 rule="hyper" parents="37578 37069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37590">
    <literal><![CDATA[
      L(x,a(y,z,u),w * a(y,v5,v6)) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(29949,a,37589,a),flip(a)].">
      <j1 rule="hyper" parents="29949 37589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37593">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(z,y,x),w) = w \ ((a(x,y,z) \ w) * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,27324,a(flip),b,37590,a),flip(a)].">
      <j1 rule="hyper" parents="63 27324 37590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37596">
    <literal><![CDATA[
      ((x \ ((a(y,z,u) \ x) * w)) * a(y,z,u)) * ((a(y,z,u) \ w) \ w) = L(w * a(y,z,u),a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(37593(a,1),25922(a,1,1,1))].">
      <j1 rule="para" parents="37593 25922"/>
    </justification>
  </clause>

  <clause id="37597">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),v5,v6)) * a(x,z * (u * w),a(y,v5,v6)) = a((z \ w) * u,a(v6,v5,x),y)
    ]]></literal>
    <justification jstring="[para(24151(a,1),37588(a,1,2))].">
      <j1 rule="para" parents="24151 37588"/>
    </justification>
  </clause>

  <clause id="37598">
    <literal><![CDATA[
      a((x \ y) * z,a(u,w,v5),v6) = a(x * (z * y),a(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(63,a,31238,a(flip),b,37597,a),flip(a)].">
      <j1 rule="hyper" parents="63 31238 37597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37599">
    <literal><![CDATA[
      x * a(y * (z * u),a(w,v5,v6),x) = L(x,a(w,v5,v6),(y \ u) * z)
    ]]></literal>
    <justification jstring="[para(37598(a,1),28768(a,1,2))].">
      <j1 rule="para" parents="37598 28768"/>
    </justification>
  </clause>

  <clause id="37600">
    <literal><![CDATA[
      L(x,a(y,z,u),(w \ v5) * v6) = L(x,a(y,z,u),w * (v6 * v5))
    ]]></literal>
    <justification jstring="[hyper(29072,a,37599,a),flip(a)].">
      <j1 rule="hyper" parents="29072 37599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37601">
    <literal><![CDATA[
      L(x,a(y,z,u),(w * v5) * v6) = L(x,a(y,z,u),v5 * (v6 * w))
    ]]></literal>
    <justification jstring="[hyper(36661,a,37600,a)].">
      <j1 rule="hyper" parents="36661 37600"/>
    </justification>
  </clause>

  <clause id="37602">
    <literal><![CDATA[
      L(x,a(y,z,u),w * (v5 * v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      L(x,a(u,z,y),v5 * (v6 * w)) = v7
    ]]></literal>
    <justification jstring="[para(37601(a,1),26514(a,1))].">
      <j1 rule="para" parents="37601 26514"/>
    </justification>
  </clause>

  <clause id="37603">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * ((a(u,z,y) \ x) \ x) = L(x * a(u,z,y),a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(31534(a,1),37596(a,1,1))].">
      <j1 rule="para" parents="31534 37596"/>
    </justification>
  </clause>

  <clause id="37604">
    <literal><![CDATA[
      L(x * a(y,z,u),a(u,z,y),w) = L(x,a(u,z,y),w) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(19984(a,1),37603(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19984 37603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37605">
    <literal><![CDATA[
      L(x * a(y,z,u),a(u,z,y),w) = a(y,z,u) * L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(347,a,26512,a(flip),b,37604,a),flip(a)].">
      <j1 rule="hyper" parents="347 26512 37604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37607">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ u,a(x,y,z),L(z,y,x) * w) = (w * ((a(x,y,z) * w) \ u)) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(23225(a,1),37568(a,1,2))].">
      <j1 rule="para" parents="23225 37568"/>
    </justification>
  </clause>

  <clause id="37608">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ u,a(x,y,z),z * w) = (w * ((a(x,y,z) * w) \ u)) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(37037(a,1),37607(a,1,2))].">
      <j1 rule="para" parents="37037 37607"/>
    </justification>
  </clause>

  <clause id="37609">
    <literal><![CDATA[
      L((a(x,y,z) \ u) * a(x,y,z),a(z,y,x),z * w) = (w * ((a(x,y,z) * w) \ u)) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(63,a,37605,a,b,37608,a)].">
      <j1 rule="hyper" parents="63 37605 37608"/>
    </justification>
  </clause>

  <clause id="37611">
    <literal><![CDATA[
      (x * ((a(y,z,u) * x) \ w)) * a(y,z,u) = L(w,a(u,z,y),u * x)
    ]]></literal>
    <justification jstring="[para(19986(a,1),37609(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19986 37609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37612">
    <literal><![CDATA[
      ((x / (x / a(y,z,u))) * w) * (w \ (x / a(y,z,u))) = L(x,a(u,z,y),u * w)
    ]]></literal>
    <justification jstring="[hyper(63,a,31259,a,b,37611,a)].">
      <j1 rule="hyper" parents="63 31259 37611"/>
    </justification>
  </clause>

  <clause id="37613">
    <literal><![CDATA[
      (a(x,y,z) * u) * (u \ (a(x,y,z) \ w)) = L(w,a(z,y,x),z * u)
    ]]></literal>
    <justification jstring="[hyper(63,a,31256,a(flip),b,37612,a)].">
      <j1 rule="hyper" parents="63 31256 37612"/>
    </justification>
  </clause>

  <clause id="37614">
    <literal><![CDATA[
      T((x * ((a(y,z,u) * x) \ w)) * (a(y,z,L(u,x,w * x)) * a(y,z,L(u,x,w * x))),T(x * ((a(y,z,u) * x) \ w),w)) = (((x * ((a(y,z,u) * x) \ w)) \ w) \ 1) \ w
    ]]></literal>
    <justification jstring="[para(37563(a,1),37565(a,1,1,2,2))].">
      <j1 rule="para" parents="37563 37565"/>
    </justification>
  </clause>

  <clause id="37615">
    <literal><![CDATA[
      T((x * ((a(y,z,u) * x) \ w)) * (a(y,z,u) * a(y,z,u)),T(x * ((a(y,z,u) * x) \ w),w)) = (((x * ((a(y,z,u) * x) \ w)) \ w) \ 1) \ w
    ]]></literal>
    <justification jstring="[para(27455(a,1),37614(a,1,1,2))].">
      <j1 rule="para" parents="27455 37614"/>
    </justification>
  </clause>

  <clause id="37616">
    <literal><![CDATA[
      T(x * (((a(y,z,u) * x) \ w) * (a(y,z,u) * a(y,z,u))),T(x * ((a(y,z,u) * x) \ w),w)) = (((x * ((a(y,z,u) * x) \ w)) \ w) \ 1) \ w
    ]]></literal>
    <justification jstring="[para(33(a,1),37615(a,1,1))].">
      <j1 rule="para" parents="33 37615"/>
    </justification>
  </clause>

  <clause id="37618">
    <literal><![CDATA[
      T(x * ((a(y,z,u) \ x) \ w),T(x * ((a(y,z,u) * x) \ w),w)) = (((x * ((a(y,z,u) * x) \ w)) \ w) \ 1) \ w
    ]]></literal>
    <justification jstring="[para(28661(a,1),37616(a,1,1,2))].">
      <j1 rule="para" parents="28661 37616"/>
    </justification>
  </clause>

  <clause id="37619">
    <literal><![CDATA[
      T(x * ((a(y,z,u) \ x) \ w),x * ((a(y,z,u) * x) \ w)) = (((x * ((a(y,z,u) * x) \ w)) \ w) \ 1) \ w
    ]]></literal>
    <justification jstring="[para(30549(a,1),37618(a,1,2))].">
      <j1 rule="para" parents="30549 37618"/>
    </justification>
  </clause>

  <clause id="37620">
    <literal><![CDATA[
      T(x * ((a(y,z,u) \ x) \ w),x * (x \ (a(y,z,u) \ w))) = (((x * ((a(y,z,u) * x) \ w)) \ w) \ 1) \ w
    ]]></literal>
    <justification jstring="[hyper(63,a,22937,a(flip),b,37619,a)].">
      <j1 rule="hyper" parents="63 22937 37619"/>
    </justification>
  </clause>

  <clause id="37621">
    <literal><![CDATA[
      T(x * ((a(y,z,u) \ x) \ w),a(y,z,u) \ w) = (((x * ((a(y,z,u) * x) \ w)) \ w) \ 1) \ w
    ]]></literal>
    <justification jstring="[para(10(a,1),37620(a,1,2))].">
      <j1 rule="para" parents="10 37620"/>
    </justification>
  </clause>

  <clause id="37622">
    <literal><![CDATA[
      (((x * ((a(y,z,u) * x) \ w)) \ w) \ 1) \ w = T(x * ((a(y,z,u) \ x) \ w),w)
    ]]></literal>
    <justification jstring="[hyper(23080,a,37621,a),flip(a)].">
      <j1 rule="hyper" parents="23080 37621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37625">
    <literal><![CDATA[
      (((x * ((a(y,z,u) * x) \ w)) \ w) \ 1) \ w = x * ((a(y,z,u) \ x) \ w)
    ]]></literal>
    <justification jstring="[hyper(347,a,20881,a(flip),b,37622,a),flip(a)].">
      <j1 rule="hyper" parents="347 20881 37622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37626">
    <literal><![CDATA[
      (a(x,y,L(z,u,w * u)) \ 1) \ w = u * ((a(x,y,z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(37564(a,1),37625(a,1,1,1))].">
      <j1 rule="para" parents="37564 37625"/>
    </justification>
  </clause>

  <clause id="37627">
    <literal><![CDATA[
      x * a(y,z,L(u,w,x * w)) = w * ((a(y,z,u) \ w) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,28351,a(flip),b,37626,a)].">
      <j1 rule="hyper" parents="63 28351 37626"/>
    </justification>
  </clause>

  <clause id="37630">
    <literal><![CDATA[
      (x / y) * (y * a(z,u,w)) = y * ((a(z,u,w) \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(63,a,29145,a(flip),b,37627,a)].">
      <j1 rule="hyper" parents="63 29145 37627"/>
    </justification>
  </clause>

  <clause id="37632">
    <literal><![CDATA[
      (x * a(y,z,u)) * (x \ w) = x * ((a(y,z,u) \ x) \ w)
    ]]></literal>
    <justification jstring="[hyper(63,a,23094,a(flip),b,37630,a)].">
      <j1 rule="hyper" parents="63 23094 37630"/>
    </justification>
  </clause>

  <clause id="37633">
    <literal><![CDATA[
      (a(x,y,z) * u) * (u \ w) = u * ((a(x,y,z) \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(20248,a,37632,a)].">
      <j1 rule="hyper" parents="20248 37632"/>
    </justification>
  </clause>

  <clause id="37634">
    <literal><![CDATA[
      x * ((a(y,z,u) \ x) \ (a(y,z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(w,u,a(x,z,y * u)) = v5
    ]]></literal>
    <justification jstring="[para(37632(a,1),37336(a,1))].">
      <j1 rule="para" parents="37632 37336"/>
    </justification>
  </clause>

  <clause id="37635">
    <literal><![CDATA[
      x * ((a(y,z,u) \ x) \ (a(y,z,u) \ w)) = L(w,a(u,z,y),u * x)
    ]]></literal>
    <justification jstring="[hyper(63,a,37613,a(flip),b,37633,a),flip(a)].">
      <j1 rule="hyper" parents="63 37613 37633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37637">
    <literal><![CDATA[
      L(x,a(y,z,u),y * w) = L(x,y,a(w,z,u * y))
    ]]></literal>
    <justification jstring="[hyper(37634,a,37635,a),flip(a)].">
      <j1 rule="hyper" parents="37634 37635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37638">
    <literal><![CDATA[
      L(x,a(y,z,u),y * w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(w,z,u * y)) = v5
    ]]></literal>
    <justification jstring="[para(37635(a,1),37634(a,1))].">
      <j1 rule="para" parents="37635 37634"/>
    </justification>
  </clause>

  <clause id="37639">
    <literal><![CDATA[
      L(x,a(y,z,u),u * w) = L(x,u,a(w,z,y * u))
    ]]></literal>
    <justification jstring="[hyper(28764,a,37637,a)].">
      <j1 rule="hyper" parents="28764 37637"/>
    </justification>
  </clause>

  <clause id="37640">
    <literal><![CDATA[
      L(x,y,a(z,z * u,w * y)) = L(x,a(w,u,y),z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,37450,a(flip),b,37637,a),flip(a)].">
      <j1 rule="hyper" parents="63 37450 37637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37641">
    <literal><![CDATA[
      L(x,y,a(z,u,w * y)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,a(w,u,y),y * z) = v5
    ]]></literal>
    <justification jstring="[para(37637(a,1),28764(a,1))].">
      <j1 rule="para" parents="37637 28764"/>
    </justification>
  </clause>

  <clause id="37642">
    <literal><![CDATA[
      L(x,a(y,z,u),w * (v5 * y)) = L(x,y,a(w * v5,z,u * y))
    ]]></literal>
    <justification jstring="[hyper(37602,a,37639,a)].">
      <j1 rule="hyper" parents="37602 37639"/>
    </justification>
  </clause>

  <clause id="37643">
    <literal><![CDATA[
      L(x,a(y,z,u * z),(y * z) * w) = L(x,y * z,a(w,z,u * (y * z)))
    ]]></literal>
    <justification jstring="[hyper(37141,a,37639,a)].">
      <j1 rule="hyper" parents="37141 37639"/>
    </justification>
  </clause>

  <clause id="37644">
    <literal><![CDATA[
      L(L(x,y,z),a(u,w,x * v5),(x * v5) * v6) = L(L(x,w,a(v6,v5,u * (x * v5))),y,z)
    ]]></literal>
    <justification jstring="[hyper(347,a,32368,a(flip),b,37639,a),flip(a)].">
      <j1 rule="hyper" parents="347 32368 37639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37645">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w * u)),a(w,y,u),u * z) = L(x,a(z,u,w * u),y)
    ]]></literal>
    <justification jstring="[hyper(347,a,29984,a(flip),b,37639,a),flip(a)].">
      <j1 rule="hyper" parents="347 29984 37639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37647">
    <literal><![CDATA[
      L(x,a(y,z,u),w * u) = L(x,z,a(w,u,y * u))
    ]]></literal>
    <justification jstring="[hyper(32385,a,37640,a),flip(a)].">
      <j1 rule="hyper" parents="32385 37640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37648">
    <literal><![CDATA[
      L(L(x,y,a(z,u,x * w)),y,a(w,z,u)) = L(x,y,a(z,u,w * u))
    ]]></literal>
    <justification jstring="[hyper(37440,a,37647,a)].">
      <j1 rule="hyper" parents="37440 37647"/>
    </justification>
  </clause>

  <clause id="37651">
    <literal><![CDATA[
      L(x,a(y,z,u),u * w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u,a(w,z,y * u)) = v5
    ]]></literal>
    <justification jstring="[para(26497(a,1),37638(a,1))].">
      <j1 rule="para" parents="26497 37638"/>
    </justification>
  </clause>

  <clause id="37652">
    <literal><![CDATA[
      L(x,a(y,z,u * z),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x * a(u * z,x,a(w,z,y)),a(u,w,z),z * y) = v5
    ]]></literal>
    <justification jstring="[para(29991(a,1),37641(a,1))].">
      <j1 rule="para" parents="29991 37641"/>
    </justification>
  </clause>

  <clause id="37653">
    <literal><![CDATA[
      L(x,a(y,z,u * z),z * (w * y)) = L(x,y * z,a(w,z,u * (y * z)))
    ]]></literal>
    <justification jstring="[hyper(63,a,37601,a(flip),b,37643,a)].">
      <j1 rule="hyper" parents="63 37601 37643"/>
    </justification>
  </clause>

  <clause id="37654">
    <literal><![CDATA[
      L(x,y * z,a(u,z,w * (y * z))) = L(x,y,a(z * u,z,(w * z) * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,37642,a(flip),b,37653,a),flip(a)].">
      <j1 rule="hyper" parents="63 37642 37653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37655">
    <literal><![CDATA[
      L(x,y * z,a(u,z,w * (y * z))) = L(x,y,a(z * u,z,w * (y * z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,37289,a(flip),b,37654,a),flip(a)].">
      <j1 rule="hyper" parents="347 37289 37654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37656">
    <literal><![CDATA[
      L(x,y * z,a(u,z,w * (y * z))) = L(x,y,a(u,z,(w * (y * z)) * z))
    ]]></literal>
    <justification jstring="[hyper(347,a,37150,a(flip),b,37655,a),flip(a)].">
      <j1 rule="hyper" parents="347 37150 37655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37657">
    <literal><![CDATA[
      L(x,y * z,a(u,z,w * (y * z))) = L(x,y,a(u,z,(y * z) * (w * z)))
    ]]></literal>
    <justification jstring="[para(36697(a,1),37656(a,2,3))].">
      <j1 rule="para" parents="36697 37656"/>
    </justification>
  </clause>

  <clause id="37658">
    <literal><![CDATA[
      L(x,y * z,a(u,z,w * (y * z))) = L(x,y,a(u,z,y * ((w * z) * z)))
    ]]></literal>
    <justification jstring="[hyper(347,a,37289,a(flip),b,37657,a),flip(a)].">
      <j1 rule="hyper" parents="347 37289 37657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37659">
    <literal><![CDATA[
      L(x,y * z,a(u,z,w * (y * z))) = L(x,y,a(u,z,w * y))
    ]]></literal>
    <justification jstring="[para(36492(a,1),37658(a,2,3))].">
      <j1 rule="para" parents="36492 37658"/>
    </justification>
  </clause>

  <clause id="37660">
    <literal><![CDATA[
      L(x,y,a(z,u,w * (y * u))) = L(x,y,a(z,u,w * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,36952,a(flip),b,37659,a)].">
      <j1 rule="hyper" parents="63 36952 37659"/>
    </justification>
  </clause>

  <clause id="37662">
    <literal><![CDATA[
      L(x,y,a(z,u,y * (w * u))) = L(x,y,a(z,u,w * y))
    ]]></literal>
    <justification jstring="[hyper(63,a,36771,a,b,37660,a)].">
      <j1 rule="hyper" parents="63 36771 37660"/>
    </justification>
  </clause>

  <clause id="37663">
    <literal><![CDATA[
      L(x,y,a(z * u,w,u * y)) = L(x,w,a(y,u,z * w))
    ]]></literal>
    <justification jstring="[hyper(63,a,37153,a(flip),b,37662,a),flip(a)].">
      <j1 rule="hyper" parents="63 37153 37662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37664">
    <literal><![CDATA[
      L(x,y,a(z,u,w * y)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36923,a(flip),b,37663,a),flip(a)].">
      <j1 rule="hyper" parents="63 36923 37663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37665">
    <literal><![CDATA[
      L(x,y,a(z * x,u,w)) = x * a(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,37020,a(flip),b,37664,a),flip(a)].">
      <j1 rule="hyper" parents="63 37020 37664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37666">
    <literal><![CDATA[
      L(x,y,a(z,u,x * w)) = x * a(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,36940,a(flip),b,37665,a)].">
      <j1 rule="hyper" parents="63 36940 37665"/>
    </justification>
  </clause>

  <clause id="37667">
    <literal><![CDATA[
      L(L(x,y,a(z,u,x * (w * u))),a(w,y,u),u * z) = L(x,a(z,u,w * u),y)
    ]]></literal>
    <justification jstring="[para(37666(a,2),37645(a,1,1))].">
      <j1 rule="para" parents="37666 37645"/>
    </justification>
  </clause>

  <clause id="37668">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),a(w,u,y),y * z) = L(x,a(z,y,w * y),u)
    ]]></literal>
    <justification jstring="[para(37018(a,1),37667(a,1,1))].">
      <j1 rule="para" parents="37018 37667"/>
    </justification>
  </clause>

  <clause id="37669">
    <literal><![CDATA[
      L(L(x,y,a(z,u,x * w)),a(w,u,y),y * z) = L(x,a(z,y,w * y),u)
    ]]></literal>
    <justification jstring="[para(37666(a,2),37668(a,1,1))].">
      <j1 rule="para" parents="37666 37668"/>
    </justification>
  </clause>

  <clause id="37670">
    <literal><![CDATA[
      L(L(x,y,a(z,u,x * w)),y,a(z,u,w * y)) = L(x,a(z,y,w * y),u)
    ]]></literal>
    <justification jstring="[hyper(37651,a,37669,a)].">
      <j1 rule="hyper" parents="37651 37669"/>
    </justification>
  </clause>

  <clause id="37671">
    <literal><![CDATA[
      L(L(x,y,a(z,u,x * w)),y,a(z,u,w)) = L(x,a(z,y,w * y),u)
    ]]></literal>
    <justification jstring="[hyper(63,a,37664,a(flip),b,37670,a)].">
      <j1 rule="hyper" parents="63 37664 37670"/>
    </justification>
  </clause>

  <clause id="37672">
    <literal><![CDATA[
      L(L(x,y,z),a(u,w,x * v5),(x * v5) * v6) = L(x * a(v5,x,a(v6,w,u)),y,z)
    ]]></literal>
    <justification jstring="[para(37017(a,1),37644(a,2,1))].">
      <j1 rule="para" parents="37017 37644"/>
    </justification>
  </clause>

  <clause id="37673">
    <literal><![CDATA[
      L(L(x,y,z),a(u,w,x * v5),(x * v5) * v6) = L(L(x,v5,a(v6,w,x * u)),y,z)
    ]]></literal>
    <justification jstring="[para(37666(a,2),37672(a,2,1))].">
      <j1 rule="para" parents="37666 37672"/>
    </justification>
  </clause>

  <clause id="37674">
    <literal><![CDATA[
      L(L(x,y,z),x * u,a(w,v5,v6 * (x * u))) = L(L(x,u,a(w,v5,x * v6)),y,z)
    ]]></literal>
    <justification jstring="[hyper(37651,a,37673,a)].">
      <j1 rule="hyper" parents="37651 37673"/>
    </justification>
  </clause>

  <clause id="37675">
    <literal><![CDATA[
      L(L(x,y,a(z,u,x * w)),v5,v6) = L(L(x,v5,v6),x * y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(63,a,37664,a(flip),b,37674,a),flip(a)].">
      <j1 rule="hyper" parents="63 37664 37674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37676">
    <literal><![CDATA[
      L(L(x,y,a(z,u,x * w)),v5,v6) = L(L(x,u,a(z,y,w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(347,a,32368,a(flip),b,37675,a),flip(a)].">
      <j1 rule="hyper" parents="347 32368 37675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37677">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),u,a(z,y,w)) = L(x,a(z,u,w * u),y)
    ]]></literal>
    <justification jstring="[hyper(63,a,37671,a(flip),b,37676,a),flip(a)].">
      <j1 rule="hyper" parents="63 37671 37676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37678">
    <literal><![CDATA[
      L(x,a(y,z,u * z),w) = x
    ]]></literal>
    <justification jstring="[hyper(29901,a,37677,a),flip(a)].">
      <j1 rule="hyper" parents="29901 37677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37680">
    <literal><![CDATA[
      L(x * a(y * z,x,a(u,z,w)),a(y,u,z),z * w) = x
    ]]></literal>
    <justification jstring="[hyper(37652,a,37678,a)].">
      <j1 rule="hyper" parents="37652 37678"/>
    </justification>
  </clause>

  <clause id="37681">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w * u)),a(y,z,u),u * w) = x
    ]]></literal>
    <justification jstring="[para(36735(a,1),37680(a,1,1,2))].">
      <j1 rule="para" parents="36735 37680"/>
    </justification>
  </clause>

  <clause id="37682">
    <literal><![CDATA[
      L(L(x,y,a(z,u,x * (w * u))),a(y,z,u),u * w) = x
    ]]></literal>
    <justification jstring="[para(37666(a,2),37681(a,1,1))].">
      <j1 rule="para" parents="37666 37681"/>
    </justification>
  </clause>

  <clause id="37683">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),a(u,z,y),y * w) = x
    ]]></literal>
    <justification jstring="[para(37018(a,1),37682(a,1,1))].">
      <j1 rule="para" parents="37018 37682"/>
    </justification>
  </clause>

  <clause id="37685">
    <literal><![CDATA[
      L(L(x,y,a(z,u,x * w)),a(u,z,y),y * w) = x
    ]]></literal>
    <justification jstring="[para(37666(a,2),37683(a,1,1))].">
      <j1 rule="para" parents="37666 37683"/>
    </justification>
  </clause>

  <clause id="37686">
    <literal><![CDATA[
      L(L(x,y,a(z,u,x * w)),y,a(w,z,u * y)) = x
    ]]></literal>
    <justification jstring="[hyper(37651,a,37685,a)].">
      <j1 rule="hyper" parents="37651 37685"/>
    </justification>
  </clause>

  <clause id="37687">
    <literal><![CDATA[
      L(L(x,y,a(z,u,x * w)),y,a(w,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,37664,a(flip),b,37686,a)].">
      <j1 rule="hyper" parents="63 37664 37686"/>
    </justification>
  </clause>

  <clause id="37688">
    <literal><![CDATA[
      L(x,y,a(z,u,w * u)) = x
    ]]></literal>
    <justification jstring="[hyper(63,a,37648,a(flip),b,37687,a)].">
      <j1 rule="hyper" parents="63 37648 37687"/>
    </justification>
  </clause>

  <clause id="37695">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[para(12(a,1),37688(a,1,3,3))].">
      <j1 rule="para" parents="12 37688"/>
    </justification>
  </clause>

  <clause id="37765">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = 1
    ]]></literal>
    <justification jstring="[hyper(129,a,37695,a,b,28853,a),flip(a)].">
      <j1 rule="hyper" parents="129 37695 28853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37766">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("aa1")
    ]]></attribute>
    <justification jstring="[resolve(37765,a,64,a)].">
      <j1 rule="resolve" parents="37765 64"/>
    </justification>
  </clause>

</proof>

</proofs>
